International Nuclear Information System (INIS)
Moawad, S. M.; Ibrahim, D. A.
2016-01-01
The equilibrium properties of three-dimensional ideal magnetohydrodynamics (MHD) are investigated. Incompressible and compressible flows are considered. The governing equations are taken in a steady state such that the magnetic field is parallel to the plasma flow. Equations of stationary equilibrium for both of incompressible and compressible MHD flows are derived and described in a mathematical mode. For incompressible MHD flows, Alfvénic and non-Alfvénic flows with constant and variable magnetofluid density are investigated. For Alfvénic incompressible flows, the general three-dimensional solutions are determined with the aid of two potential functions of the velocity field. For non-Alfvénic incompressible flows, the stationary equilibrium equations are reduced to two differential constraints on the potential functions, flow velocity, magnetofluid density, and the static pressure. Some examples which may be of some relevance to axisymmetric confinement systems are presented. For compressible MHD flows, equations of the stationary equilibrium are derived with the aid of a single potential function of the velocity field. The existence of three-dimensional solutions for these MHD flows is investigated. Several classes of three-dimensional exact solutions for several cases of nonlinear equilibrium equations are presented.
The Statistical Mechanics of Ideal MHD Turbulence
Shebalin, John V.
2003-01-01
Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.
Linear ideal MHD stability calculations for ITER
International Nuclear Information System (INIS)
Hogan, J.T.
1988-01-01
A survey of MHD stability limits has been made to address issues arising from the MHD--poloidal field design task of the US ITER project. This is a summary report on the results obtained to date. The study evaluates the dependence of ballooning, Mercier and low-n ideal linear MHD stability on key system parameters to estimate overall MHD constraints for ITER. 17 refs., 27 figs
Regular shock refraction in planar ideal MHD
International Nuclear Information System (INIS)
Delmont, P; Keppens, R
2010-01-01
We study the classical problem of planar shock refraction at an oblique density discontinuity, separating two gases at rest, in planar ideal (magneto)hydrodynamics. In the hydrodynamical case, 3 signals arise and the interface becomes Richtmyer-Meshkov unstable due to vorticity deposition on the shocked contact. In the magnetohydrodynamical case, on the other hand, when the normal component of the magnetic field does not vanish, 5 signals will arise. The interface then typically remains stable, since the Rankine-Hugoniot jump conditions in ideal MHD do not allow for vorticity deposition on a contact discontinuity. We present an exact Riemann solver based solution strategy to describe the initial self similar refraction phase. Using grid-adaptive MHD simulations, we show that after reflection from the top wall, the interface remains stable.
Statistical Theory of the Ideal MHD Geodynamo
Shebalin, J. V.
2012-01-01
A statistical theory of geodynamo action is developed, using a mathematical model of the geodynamo as a rotating outer core containing an ideal (i.e., no dissipation), incompressible, turbulent, convecting magnetofluid. On the concentric inner and outer spherical bounding surfaces the normal components of the velocity, magnetic field, vorticity and electric current are zero, as is the temperature fluctuation. This allows the use of a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity, current and the temperature fluctuation. The resulting dynamical system, based on the Boussinesq form of the magnetohydrodynamic (MHD) equations, represents MHD turbulence in a spherical domain. These basic equations (minus the temperature equation) and boundary conditions have been used previously in numerical simulations of forced, decaying MHD turbulence inside a sphere [1,2]. Here, the ideal case is studied through statistical analysis and leads to a prediction that an ideal coherent structure will be found in the form of a large-scale quasistationary magnetic field that results from broken ergodicity, an effect that has been previously studied both analytically and numerically for homogeneous MHD turbulence [3,4]. The axial dipole component becomes prominent when there is a relatively large magnetic helicity (proportional to the global correlation of magnetic vector potential and magnetic field) and a stationary, nonzero cross helicity (proportional to the global correlation of velocity and magnetic field). The expected angle of the dipole moment vector with respect to the rotation axis is found to decrease to a minimum as the average cross helicity increases for a fixed value of magnetic helicity and then to increase again when average cross helicity approaches its maximum possible value. Only a relatively small value of cross helicity is needed to produce a dipole moment vector that is aligned at approx.10deg with the
A civil engineering approach to ideal MHD
International Nuclear Information System (INIS)
Jensen, V.O.
1992-01-01
It is well known that a magnetic field can be conceived as a medium where an isotropic compressive stress, B 2 /2μ 0 , is superimposed on a tensile stress, B 2 /μ 0 , parallel to the lines of force. When a stationary ideal MHD plasma is present in the magnetic field, the particle pressure adds to the magnetic stresses to form a combined stress tensor. Calculations of plasma equilibria based on this concept are very similar to calculations in civil engineering of static structures based on compressive, tensile, and shear stresses. Therefore the very simple physical pictures known from civil engineering when used in plasma physics provide simple physical understanding and facilitate the physical interpretation of the results. In an earlier paper the concept was used to derive and discuss the equilibrium equations for θ-, Z-, and screw pinches and the Grad-Shafranov shift in a tokamak plasma with circular cross sections of the flux surfaces. Here the concept is used to discuss the virial theorem and to obtain a simple physical interpretation of this theorem. We also reconsider the Grad-Shafranov shift in a tokamak plasma and show that a situation where all flux surfaces have circular cross sections cannot be an exact solution to the ideal MHD equations. (author) 3 refs., 3 figs
Ideal MHD properties for proposed noncircular tokamaks
International Nuclear Information System (INIS)
Helton, F.J.; Greene, J.M.
1986-01-01
We obtain Double Dee, TFXC-C, Big Dee, and JET equlibria which are optimized with respect to both shape and current profile for stability to ideal MHD modes. With a wall reasonably far from the plasma surface we find that the external kink constrains q 1 to be above two, where q 1 is the plasma surface value of the safety factor, and the ballooning mode limits the value of β. Then a relevant stable β value for the Double Dee reactor design is over 7%. Such a Double Dee equilibrium is not in a separated second stability region and thus does not have a problem with accessibility. A relevant stable β value for the TFCX-C reactor design is over 6%. Equivalent relevant stable β values for the Big Dee (17%) and JET (7%) are included for calibration purposes. We compare these relevant stable β values with the β's determined by two recent scaling laws
Magnetic stresses in ideal MHD plasmas
DEFF Research Database (Denmark)
Jensen, V.O.
1995-01-01
The concept of magnetic stresses in ideal MHD plasma theory is reviewed and revisited with the aim of demonstrating its advantages as a basis for calculating and understanding plasma equilibria. Expressions are derived for the various stresses that transmit forces in a magnetized plasma...... and it is shown that the resulting magnetic forces on a finite volume element can be obtained by integrating the magnetic stresses over the surface of the element. The concept is used to rederive and discuss the equilibrium conditions for axisymmetric toroidal plasmas, including the virial theorem...... and the Shafranov shift. The method had pedagogical merits as it simplifies the calculations, improves the physical understanding and facilitates an assessment of the approximations made in the calculations....
The structure of ideal MHD Alfven modes
International Nuclear Information System (INIS)
Turnbull, A.D.; Chu, M.S.; Lao, L.L.; Greene, J.M.; Strait, E.J.; Chance, M.S.
1991-01-01
Continuum Alfven modes have undergone a resurgence in interest with the recent realization that so-called Toroidicity-Induced Alfven Eigenmodes (TAE modes) can be destabilized either by energetic beam ions in a strongly heated plasma or by alpha particles in a burning plasma. The GATO Ideal MHD Stability code, which minimizes the potential energy according to a variational formulation, has now been modified to isolate and calculate stable continuum eigenmodes. The existence of the TAE mode and its associated gap has been verified, using this code, for a circular cross-section, finite aspect ratio equilibrium. Moreover, the eigenfrequencies and eigenmodes obtained from this variational calculation are found to be in extremely good quantitative agreement with those obtained from the non-variational NOVA code. A systematic survey of the stable continuum has further revealed a surprising diversity in the structure of the continuum Alfven modes; the logarithmic singularity can be so broad, in some cases, as to occupy the whole cross-section. This has important implications for heating experiments which aim to locally excite the plasma by rf waves in the Alfven frequency range. The structure of several representative examples is discussed. The Alfven continuum, in general, and the TAE mode and its associated gap, in particular, are also found to be strongly modified by cross-sectional shaping. The dependence of the spectrum on various shaping factors is explored
Numerical study of the axisymmetric ideal MHD stability of Extrap
International Nuclear Information System (INIS)
Benda, M.
1993-04-01
A numerical study of the free-boundary axisymmetric (n=0) ideal magnetohydrodynamical (MHD) motions of the Extrap device is presented. The dependence of stability on current profiles in the plasma and currents in the external conductors is investigated. Results are shown for linear growth-rates and nonlinear saturation amplitudes and their dependence on plasma radius as well as on the conducting shell radius. A method combined of two different algorithms has been developed and tested. The interior region of the plasma is simulated by means of a Lagrangian Finite Element Method (FEM) for ideal magnetohydrodynamics, The method is based on a nonlinear radiation principle for the Lagrangian description of ideal MHD. The Boundary Element Method (BEM) is used together with the Lagrangian FEM to simulate nonlinear motion of an ideal MHD plasma behaviour in a vacuum region under the influence of external magnetic fields. 31 refs
Construction of a Roe linearization for the ideal MHD equations
International Nuclear Information System (INIS)
Cargo, P.; Gallice, G.; Raviart, P.A.
1996-01-01
In [3], Munz has constructed a Roe linearization for the equations of gas dynamics in Lagrangian coordinates. We extend this construction to the case of the ideal magnetohydrodynamics equations again in Lagrangian coordinates. As a consequence we obtain a Roe linearization for the MHD equations in Eulerian coordinates. (author)
Ideal MHD stability analysis of KSTAR target AT mode
International Nuclear Information System (INIS)
Yi, S.M.; Kim, J.H.; You, K.I.; Kim, J.Y.
2009-01-01
Full text: A main research objective of KSTAR (Korea Superconducting Tokamak Advanced Research) device is to demonstrate the steady-state operation capability of high-performance AT (Advanced Tokamak) mode. To meet this goal, it is critical for KSTAR to have a good MHD stability boundary, particularly against the high-beta ideal instabilities such as the external kink and the ballooning modes. To support this MHD stability KSTAR has been designed to have a strong plasma shape and a close interval between plasma and passive- plate wall. During the conceptual design phase of KSTAR, a preliminary study was performed to estimate the high beta MHD stability limit of KSTAR target AT mode using PEST and VACUUM codes and it was shown that the target AT mode can be stable up to β N ∼ 5 with a well-defined plasma pressure and current profiles. Recently, a new calculation has been performed to estimate the ideal stability limit in various KSTAR operating conditions using DCON code, and it has been observed that there is some difference between the new and old calculation results, particularly in the dependence of the maximum β N value on the toroidal mode number. Here, we thus present a more detailed analysis of the ideal MHD stability limit of KSTAR target AT mode using various codes, which include GATO as well as PEST and DCON, in the comparison of calculation results among the three codes. (author)
An innovative method for ideal and resistive MHD stability analysis of tokamaks
International Nuclear Information System (INIS)
Tokuda, S.
2001-01-01
An advanced asymptotic matching method of ideal and resistive MHD stability analysis in tokamaks is reported. A solution method for the two dimensional Newcomb equation, a dispersion relation for an unstable ideal MHD mode in tokamaks and a new scheme for solving resistive MHD inner layer equations as an initial value problem are reported. (author)
An innovative method for ideal and resistive MHD stability analysis of tokamaks
International Nuclear Information System (INIS)
Tokuda, S.
2001-01-01
An advanced asymptotic matching method of ideal and resistive MHD stability analysis in tokamak is reported. The report explains a solution method of two-dimensional Newcomb equation, dispersion relation for an unstable ideal MHD mode in tokamak, and a new scheme for solving resistive MHD inner layer equations as an initial-value problem. (author)
Ideal MHD B limits in the BIG DEE tokamak
International Nuclear Information System (INIS)
Helton, F.J.; Bernard, L.C.; Greene, J.M.
1983-01-01
Using D-D reactions, tokamak reactors become economically attractive when B (the ratio of volume averaged pressure to magnetic pressure) exceeds 5 percent. Ideal MID instabilities are of great concern because they have the potential to limit B below this range and so extensive studies have been done to determine ideal MHD B limits. As B increases with inverse aspect ratio, elongation and triangularity, the Doublet III upgrade machine -- BIG DEE -- is particularly suited to study the possibility of very high B. The authors have done computations to determine ideal MHD B limits for various plasma shapes and elongations in BIG DEE. They have determined that for q at the plasma surface greater than 2, B is limited by the ballooning mode if the wall is reasonably close to the plasma surface (d/a < 1.5 where d and a are the wall and plasma radii respectively). On the other hand, for q at the plasma surface less than 2, the n=1 external kink is unstable even with a wall close by. Thus, relevant values of limiting B can be obtained by assuming that the external kink limits the value of q at the limiter to a value greater than 2 and that the ballooning modes limit B. Under this assumption, a relevant B limit for the BIG DEE would be over 18%. For such an equilibrium, the wall position necessary to stabilize the n=1 and n=2 modes is 2a and the equilibrium is stable for n=3
Ideal MHD beta-limits of poloidally asymmetric equilibria
Energy Technology Data Exchange (ETDEWEB)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in ..beta../sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is ..beta../sub critical/ approx. = 6.5%.
Ideal MHD beta-limits of poloidally asymmetric equilibria
International Nuclear Information System (INIS)
Todd, A.M.M.; Miller, A.E.; Grimm, R.C.; Okabayashi, M.; Dalhed, H.E. Jr.
1981-05-01
The ideal MHD stability of poloidally asymmetric equilibria, which are typical of a tokamak reactor design with a single-null poloidal divertor is examined. As with symmetric equilibria, stability to non-axisymmetric modes improves with increasing triangularity and ellipticity, and with lower edge safety factor. Pressure profiles optimized with respect to ballooning stability are obtained for an asymmetric shape, resulting in β/sub critical/ approx. = 5.7%. The corresponding value for an equivalent symmetric shape is β/sub critical/ approx. = 6.5%
Eigenvalues of the simplified ideal MHD ballooning equation
International Nuclear Information System (INIS)
Paris, R.B.; Auby, N.; Dagazian, R.Y.
1986-01-01
The investigation of the spectrum of the simplified differential equation describing the variation of the amplitude of the ideal MHD ballooning instability along magnetic field lines constitutes a multiparameter Schroedinger eigenvalue problem. An exact eigenvalue relation for the discrete part of the spectrum is obtained in terms of the oblate spheroidal functions. The dependence of the eigenvalues lambda on the two free parameters γ 2 and μ 2 of the equation is discussed, together with certain analytical approximations in the limits of small and large γ 2 . A brief review of the principal properties of the spheroidal functions is given in an appendix
Investigations on high speed MHD liquid flow
International Nuclear Information System (INIS)
Yamasaki, Takasuke; Kamiyama, Shin-ichi.
1982-01-01
Lately, the pressure drop problem of MHD two-phase flow in a duct has been investigated theoretically and experimentally in conjunction with the problems of liquid metal MHD two-phase flow power-generating cycle or of liquid metal boiling two-phase flow in the blanket of a nuclear fusion reactor. Though many research results have been reported so far for MHD single-phase flow, the hydrodynamic studies on high speed two-phase flow are reported only rarely, specifically the study dealing with the generation of cavitation is not found. In the present investigation, the basic equation was derived, analyzing the high speed MHD liquid flow in a diverging duct as the one-dimensional flow of homogeneous two-phase fluid of small void ratio. Furthermore, the theoretical solution for the effect of magnetic field on cavitation-generating conditions was tried. The pressure distribution in MHD flow in a duct largely varies with load factor, and even if the void ratio is small, the pressure distribution in two-phase flow is considerably different from that in single-phase flow. Even if the MHD two-phase flow in a duct is subsonic flow at the throat, the critical conditions may be achieved sometimes in a diverging duct. It was shown that cavitation is more likely to occur as magnetic field becomes more intense if it is generated downstream of the throat. This explains the experimental results qualitatively. (Wakatsuki, Y.)
Some rigorous results concerning spectral theory for ideal MHD
International Nuclear Information System (INIS)
Laurence, P.
1986-01-01
Spectral theory for linear ideal MHD is laid on a firm foundation by defining appropriate function spaces for the operators associated with both the first- and second-order (in time and space) partial differential operators. Thus, it is rigorously established that a self-adjoint extension of F(xi) exists. It is shown that the operator L associated with the first-order formulation satisfies the conditions of the Hille--Yosida theorem. A foundation is laid thereby within which the domains associated with the first- and second-order formulations can be compared. This allows future work in a rigorous setting that will clarify the differences (in the two formulations) between the structure of the generalized eigenspaces corresponding to the marginal point of the spectrum ω = 0
Some rigorous results concerning spectral theory for ideal MHD
International Nuclear Information System (INIS)
Laurence, P.
1985-05-01
Spectral theory for linear ideal MHD is laid on a firm foundation by defining appropriate function spaces for the operators associated with both the first and second order (in time and space) partial differential operators. Thus, it is rigorously established that a self-adjoint extension of F(xi) exists. It is shown that the operator L associated with the first order formulation satisfies the conditions of the Hille-Yosida theorem. A foundation is laid thereby within which the domains associated with the first and second order formulations can be compared. This allows future work in a rigorous setting that will clarify the differences (in the two formulations) between the structure of the generalized eigenspaces corresponding to the marginal point of the spectrum ω = 0
Stability of ideal MHD configurations. I. Realizing the generality of the G operator
Keppens, R.; Demaerel, T.
2016-12-01
A field theoretical approach, applied to the time-reversible system described by the ideal magnetohydrodynamic (MHD) equations, exposes the full generality of MHD spectral theory. MHD spectral theory, which classified waves and instabilities of static or stationary, usually axisymmetric or translationally symmetric configurations, actually governs the stability of flowing, (self-)gravitating, single fluid descriptions of nonlinear, time-dependent idealized plasmas, and this at any time during their nonlinear evolution. At the core of this theory is a self-adjoint operator G , discovered by Frieman and Rotenberg [Rev. Mod. Phys. 32, 898 (1960)] in its application to stationary (i.e., time-independent) plasma states. This Frieman-Rotenberg operator dictates the acceleration identified by a Lagrangian displacement field ξ , which connects two ideal MHD states in four-dimensional space-time that share initial conditions for density, entropy, and magnetic field. The governing equation reads /d 2 ξ d t 2 = G [ ξ ] , as first noted by Cotsaftis and Newcomb [Nucl. Fusion, Suppl. Part 2, 447 and 451 (1962)]. The time derivatives at left are to be taken in the Lagrangian way, i.e., moving with the flow v. Physically realizable displacements must have finite energy, corresponding to being square integrable in the Hilbert space of displacements equipped with an inner product rule, for which the G operator is self-adjoint. The acceleration in the left-hand side features the Doppler-Coriolis operator v . ∇ , which is known to become an antisymmetric operator when restricting attention to stationary equilibria. Here, we present all derivations needed to get to these insights and connect results throughout the literature. A first illustration elucidates what can happen when self-gravity is incorporated and presents aspects that have been overlooked even in simple uniform media. Ideal MHD flows, as well as Euler flows, have essentially 6 + 1 wave types, where the 6 wave modes
Numerical study of MHD supersonic flow control
Ryakhovskiy, A. I.; Schmidt, A. A.
2017-11-01
Supersonic MHD flow around a blunted body with a constant external magnetic field has been simulated for a number of geometries as well as a range of the flow parameters. Solvers based on Balbas-Tadmor MHD schemes and HLLC-Roe Godunov-type method have been developed within the OpenFOAM framework. The stability of the solution varies depending on the intensity of magnetic interaction The obtained solutions show the potential of MHD flow control and provide insights into for the development of the flow control system. The analysis of the results proves the applicability of numerical schemes, that are being used in the solvers. A number of ways to improve both the mathematical model of the process and the developed solvers are proposed.
Studies on the crossed flow type MHD turbines
International Nuclear Information System (INIS)
Hori, Toshihiro; Katsurai, Makoto
1981-01-01
The studies on crossed flow type MHD turbines were performed to improve its characteristics. Two-dimensional models were considered for the analytical studies. To compensate the edge effect of magnetic field, the magnetic field gradient by tapering was considered. An iron-core structure and an air-core structure were investigated. It was found that the ideal characteristics can be obtained when there is the tapered length more than one wave length. Various methods for the improvement of magnetic field were studied in the case of practical crossed flow type MHD turbines. The methods were the adjustment with an iron-core, and the adoption of a curved channel. It can be expected to obtain the internal efficiency of more than 70 percent, when the number of pole-pairs is more than 10 and the radius of curvature of a few times of rotor radius is given to a curved channel. (Kato, T.)
Ideal MHD stability of high poloidal beta equilibria in TFTR
International Nuclear Information System (INIS)
Sabbagh, S.A.; Mauel, M.E.; Navratil, G.A.; Bell, M.G.; Budny, R.V.; Chance, M.S.; Fredrickson, E.D.; Jardin, S.C.; Manickam, J.; McCune, D.C.; McGuire, K.M.; Wieland, R.M.; Zarnstorff, M.C.; Phillips, M.W.; Hughes, M.H.; Kesner, J.
1991-01-01
Recent experiments in TFTR have expanded the operating space of the device to include plasmas with values of var-epsilon β p dia ≡ 2μ 0 var-epsilon perpendicular >/ p >> 2 as large as 1.6, and Troyon normalized diamagnetic beta β N dia ≡ β t perpendicular aB t /10 -8 I p as large as 4.7. At values of var-epsilon β p dia ≥ 1.3, a separatrix was observed to enter the vacuum vessel, producing a naturally diverted discharge. Plasmas with large values of var-epsilon β p dia were created with both the plasma current, I p , held constant and with I p decreased, or ramped down, before the start of neutral beam injection. A convenient characterization of the change in I p using experimental parameters can be defined by the ratio of I p before the ramp down, to I p during the neutral beam heating phase, F I p . The ideal MHD stability of these equilibria is investigated to determine their location in stability space, and to study the role of plasma current and pressure profile modification in the creation of these high var-epsilon β p and β N plasmas. The evolution of these plasmas is modelled from experimental data using the TRANSP code. Two-dimensional equilibria are computed from the TRANSP results and used as input to both high and low-n stability codes including PEST. The high var-epsilon β p equilibria, which generally have an oblate cross-sectional shape, are in the first stability region to high-n ballooning modes. At constant I p , these equilibria generally have maximum pressure gradients near the magnetic axis and are stable to n=1 modes without a stabilizing conducting wall. The effect of the current profile shape on the stability of low-n kink/ballooning modes and the requirements for these plasmas to access the second stability region are examined. 6 refs
Energy Technology Data Exchange (ETDEWEB)
Galkowski, A. [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad`s ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs.
Variational Integration for Ideal MHD with Built-in Advection Equations
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yao [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Qin, Hong [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Burby, J. W. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States); Bhattacharjee, A. [Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2014-08-05
Newcomb's Lagrangian for ideal MHD in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and momentum preserving, the schemes inherit built-in advection equations from Newcomb's formulation, and therefore avoid solving them and the accompanying error and dissipation. We implement the method in 2D and show that numerical reconnection does not take place when singular current sheets are present. We then apply it to studying the dynamics of the ideal coalescence instability with multiple islands. The relaxed equilibrium state with embedded current sheets is obtained numerically.
Ideal MHD Stability Prediction and Required Power for EAST Advanced Scenario
Chen, Junjie; Li, Guoqiang; Qian, Jinping; Liu, Zixi
2012-11-01
The Experimental Advanced Superconducting Tokamak (EAST) is the first fully superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. The ideal magnetohydrodynamic (MHD) stability and required power for the EAST advanced tokamak (AT) scenario with negative central shear and double transport barrier (DTB) are investigated. With the equilibrium code TOQ and stability code GATO, the ideal MHD stability is analyzed. It is shown that a moderate ratio of edge transport barriers' (ETB) height to internal transport barriers' (ITBs) height is beneficial to ideal MHD stability. The normalized beta βN limit is about 2.20 (without wall) and 3.70 (with ideal wall). With the scaling law of energy confinement time, the required heating power for EAST AT scenario is calculated. The total heating power Pt increases as the toroidal magnetic field BT or the normalized beta βN is increased.
Ideal MHD Stability Prediction and Required Power for EAST Advanced Scenario
International Nuclear Information System (INIS)
Chen Junjie; Li Guoqiang; Qian Jinping; Liu Zixi
2012-01-01
The Experimental Advanced Superconducting Tokamak (EAST) is the first fully superconducting tokamak with a D-shaped cross-sectional plasma presently in operation. The ideal magnetohydrodynamic (MHD) stability and required power for the EAST advanced tokamak (AT) scenario with negative central shear and double transport barrier (DTB) are investigated. With the equilibrium code TOQ and stability code GATO, the ideal MHD stability is analyzed. It is shown that a moderate ratio of edge transport barriers' (ETB) height to internal transport barriers' (ITBs) height is beneficial to ideal MHD stability. The normalized beta β N limit is about 2.20 (without wall) and 3.70 (with ideal wall). With the scaling law of energy confinement time, the required heating power for EAST AT scenario is calculated. The total heating power P t increases as the toroidal magnetic field B T or the normalized beta β N is increased. (magnetically confined plasma)
Axisymmetric ideal magnetohydrodynamic equilibria with incompressible flows
International Nuclear Information System (INIS)
Tasso, H.; Throumoulopoulos, G.N.
1997-12-01
It is shown that the ideal MHD equilibrium states of an axisymmetric plasma with incompressible flows are governed by an elliptic partial differential equation for the poloidal magnetic flux function ψ containing five surface quantities along with a relation for the pressure. Exact equilibria are constructed including those with non vanishing poloidal and toroidal flows and differentially varying radial electric fields. Unlike the case in cylindrical incompressible equilibria with isothermal magnetic surfaces which should have necessarily circular cross sections [G. N. Throumoulopoulos and H. Tasso, Phys. Plasmas 4, 1492 (1997)], no restriction appears on the shapes of the magnetic surfaces in the corresponding axisymmetric equilibria. The latter equilibria satisfy a set of six ordinary differential equations which for flows parallel to the magnetic field B can be solved semianalytically. In addition, it is proved the non existence of incompressible axisymmetric equilibria with (a) purely poloidal flows and (b) non-parallel flows with isothermal magnetic surfaces and vertical stroke B vertical stroke = vertical stroke B vertical stroke (ψ) (omnigenous equilibria). (orig.)
International Nuclear Information System (INIS)
Garcia, M.
1995-01-01
An electric vortex is the circulation of electron space charge about a magnetic field line that is transported by ion momentum. In cold, or low β flow the vortex diameter is the minimum length scale of charge neutrality. The distinctive feature of the vortex is its radial electric field which manifests the interplay of electrostatics, magnetism, and motion
MHD equilibrium of toroidal fusion plasma with stationary flows
International Nuclear Information System (INIS)
Galkowski, A.
1994-01-01
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad's ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs
Numerical study of shock waves in non-ideal magnetogasdynamics (MHD
Directory of Open Access Journals (Sweden)
Addepalli Ramu
2016-01-01
Full Text Available One-dimensional unsteady adiabatic flow of strong converging shock waves in cylindrical or spherical symmetry in MHD, which is propagating into plasma, is analyzed. The plasma is assumed to be non-ideal gas whose equation of state is of Mie–Gruneisen type. Suitable transformations reduce the governing equations into ordinary differential equations of Poincare type. In the present work, McQueen and Royce equations of state (EOS have been considered with suitable material constants and the spherical and cylindrical cases are worked out in detail to investigate the behavior and the influence on the shock wave propagation by energy input and β(ρ/ρ0, the measure of shock strength. The similarity solution is valid for adiabatic flow as long as the counter pressure is neglected. The numerical technique applied in this paper provides a global solution to the implosion problem for the flow variables, the similarity exponent α for different Gruneisen parameters. It is shown that increasing β(ρ/ρ0 does not automatically decelerate the shock front but the velocity and pressure behind the shock front increases quickly in the presence of the magnetic field and decreases slowly and become constant. This becomes true whether the piston is accelerated, is moving at constant speed or is decelerated. These results are presented through the illustrative graphs and tables. The magnetic field effects on the flow variables through a medium and total energy under the influence of strong magnetic field are also presented.
Combined effects of radiation and chemical reaction on MHD flow ...
African Journals Online (AJOL)
(2016) have studied unsteady MHD flow in porous media over exponentially accelerated plate ... boundary layer flow of heat and mass transfer over a moving vertical plate with suction. ... flow considering free convection over a porous plate.
Ideal and resistive MHD stability of internal kink modes in circular and shaped tokamaks
International Nuclear Information System (INIS)
Bondeson, A.; Luetjens, H.; Vlad, G.
1992-01-01
Recent results for the MHD stability of internal kink modes in tokamaks are reviewed. In general, ideal stability is more restrictive than the conventionally cited limit β p p is the poloidal beta at the q = 1 surface). This holds, in particular, for shaped equilibria, where low shear in combination with elliptic shaping can drastically reduce the pressure limit. Also in resistive MHD, interchange effects are frequently destabilizing, and resistive stability at β p ≥0.05 is achieved, for circular section, only with a very restricted class of current profiles, and not at all for JET-shaped cross section. (author) 9 figs., 24 refs
Numerical Simulation of 3D Viscous MHD Flows
National Research Council Canada - National Science Library
Golovachov, Yurii P; Kurakin, Yurii A; Schmidt, Alexander A; Van Wie, David M
2003-01-01
.... Flows in hypersonic intakes are considered. Preliminary results showed that local MHD interaction in the inlet part of the intake model was the most effective for control over plasma flow field...
Two dimensional MHD flows between porous boundaries
International Nuclear Information System (INIS)
Gratton, F.T.
1994-01-01
Similarity solutions of dissipative MHD equations representing conducting fluids injected through porous walls and flowing out in both directions from the center of the channel, are studied as a function of four non dimensional parameters, Reynolds number R e , magnetic Reynolds number R m , Alfvenic Mach number, M A , and pressure gradient coefficient, C. The effluence is restrained by an external magnetic field normal to the walls. When R m m >>1, the solution may model a collision of plasmas of astrophysical interest. In this case the magnetic field lines help to drive the outflow acting jointly with the pressure gradient. The law for C as a function of the other parameters is given for several asymptotic limits. (author). 3 refs, 6 figs
The instability criterion for ideal and resistive MHD modes
International Nuclear Information System (INIS)
Li Ding
2002-01-01
The instability criterions for ideal helical perturbation and resistive kink/tearing modes are derived for arbitrary q profile. It is found that the q=1 mode can be unstable only within the q=1 surface in positive shear plasma. The instability region is enlarged as q 0 decreases and/or the current density is flatted. The instability can be completely suppressed in the reverse shear plasma for peaked, and flatted current profile. The q>1 modes are stable in the plasma core and marginal stable within the rational surface in the positive shear plasma. They become more stable in the plasma core and still marginal stable around the rational surface in the reversed shear plasma. It is shown that in the positive shear plasma, the q=1, 5/4, 4/3, 3/2 and 2/1 modes are in turn destabilized and becomes dominant unstable mode as q 0 increases for fixed q a . In the reversed shear plasma, all the q=1 and q>1 modes can be stable when q0 1 modes in turn becomes unstable as q 0 (>1) increases. At first, the inner branch is stable while the outer branch weakly unstable. Then, the both branches can become strongly unstable as q0 increases. (author)
Ideal MHD stability and performance of ITER steady-state scenarios with ITBs
Poli, F. M.; Kessel, C. E.; Chance, M. S.; Jardin, S. C.; Manickam, J.
2012-06-01
Non-inductive steady-state scenarios on ITER will need to operate with internal transport barriers (ITBs) in order to reach adequate fusion gain at typical currents of 9 MA. The large pressure gradients at the location of the internal barrier are conducive to the development of ideal MHD instabilities that may limit the plasma performance and may lead to plasma disruptions. Fully non-inductive scenario simulations with five combinations of heating and current drive sources are presented in this work, with plasma currents in the range 7-10 MA. For each configuration the linear, ideal MHD stability is analysed for variations of the Greenwald fraction and of the pressure peaking factor around the operating point, aiming at defining an operational space for stable, steady-state operations at optimized performance. It is shown that plasmas with lower hybrid heating and current drive maintain the minimum safety factor above 1.5, which is desirable in steady-state operations to avoid neoclassical tearing modes. Operating with moderate ITBs at 2/3 of the minor radius, these plasmas have a minimum safety factor above 2, are ideal MHD stable and reach Q ≳ 5 operating above the ideal no-wall limit.
NON-IDEAL MHD EFFECTS AND MAGNETIC BRAKING CATASTROPHE IN PROTOSTELLAR DISK FORMATION
International Nuclear Information System (INIS)
Li Zhiyun; Krasnopolsky, Ruben; Shang Hsien
2011-01-01
Dense, star-forming cores of molecular clouds are observed to be significantly magnetized. A realistic magnetic field of moderate strength has been shown to suppress, through catastrophic magnetic braking, the formation of a rotationally supported disk (RSD) during the protostellar accretion phase of low-mass star formation in the ideal MHD limit. We address, through two-dimensional (axisymmetric) simulations, the question of whether realistic levels of non-ideal effects, computed with a simplified chemical network including dust grains, can weaken the magnetic braking enough to enable an RSD to form. We find that ambipolar diffusion (AD), the dominant non-ideal MHD effect over most of the density range relevant to disk formation, does not enable disk formation, at least in two dimensions. The reason is that AD allows the magnetic flux that would be dragged into the central stellar object in the ideal MHD limit to pile up instead in a small circumstellar region, where the magnetic field strength (and thus the braking efficiency) is greatly enhanced. We also find that, on the scale of tens of AU or more, a realistic level of Ohmic dissipation does not weaken the magnetic braking enough for an RSD to form, either by itself or in combination with AD. The Hall effect, the least explored of these three non-ideal MHD effects, can spin up the material close to the central object to a significant, supersonic rotation speed, even when the core is initially non-rotating, although the spun-up material remains too sub-Keplerian to form an RSD. The problem of catastrophic magnetic braking that prevents disk formation in dense cores magnetized to realistic levels remains unresolved. Possible resolutions of this problem are discussed.
Glasser, Alexander; Kolemen, Egemen; Glasser, A. H.
2018-03-01
Active feedback control of ideal MHD stability in a tokamak requires rapid plasma stability analysis. Toward this end, we reformulate the δW stability method with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the generic tokamak ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD matrix Riccati differential equation. Since Riccati equations are prevalent in the control theory literature, such a shift in perspective brings to bear a range of numerical methods that are well-suited to the robust, fast solution of control problems. We discuss the usefulness of Riccati techniques in solving the stiff ordinary differential equations often encountered in ideal MHD stability analyses—for example, in tokamak edge and stellarator physics. We demonstrate the applicability of such methods to an existing 2D ideal MHD stability code—DCON [A. H. Glasser, Phys. Plasmas 23, 072505 (2016)]—enabling its parallel operation in near real-time, with wall-clock time ≪1 s . Such speed may help enable active feedback ideal MHD stability control, especially in tokamak plasmas whose ideal MHD equilibria evolve with inductive timescale τ≳ 1s—as in ITER.
Ideal MHD stability and characteristics of edge localized modes on CFETR
Li, Ze-Yu; Chan, V. S.; Zhu, Yi-Ren; Jian, Xiang; Chen, Jia-Le; Cheng, Shi-Kui; Zhu, Ping; Xu, Xue-Qiao; Xia, Tian-Yang; Li, Guo-Qiang; Lao, L. L.; Snyder, P. B.; Wang, Xiao-Gang; the CFETR Physics Team
2018-01-01
Investigation on the equilibrium operation regime, its ideal magnetohydrodynamics (MHD) stability and edge localized modes (ELM) characteristics is performed for the China Fusion Engineering Test Reactor (CFETR). The CFETR operation regime study starts with a baseline scenario (R = 5.7 m, B T = 5 T) derived from multi-code integrated modeling, with key parameters {{β }N},{{β }T},{{β }p} varied to build a systematic database. These parameters, under profile and pedestal constraints, provide the foundation for the engineering design. The long wavelength low-n global ideal MHD stability of the CFETR baseline scenario, including the wall stabilization effect, is evaluated by GATO. It is found that the low-n core modes are stable with a wall at r/a = 1.2. An investigation of intermediate wavelength ideal MHD modes (peeling ballooning modes) is also carried out by multi-code benchmarking, including GATO, ELITE, BOUT++ and NIMROD. A good agreement is achieved in predicting edge-localized instabilities. Nonlinear behavior of ELMs for the baseline scenario is simulated using BOUT++. A mix of grassy and type I ELMs is identified. When the size and magnetic field of CFETR are increased (R = 6.6 m, B T = 6 T), collisionality correspondingly increases and the instability is expected to shift to grassy ELMs.
Quantum chaos theory and the spectrum of ideal-MHD instabilities in toroidal plasmas
International Nuclear Information System (INIS)
Dewar, Robert L.; Carolin, Nuehrenberg; Tatsuno, Tomoya
2004-01-01
In a fully 3-D system such as a stellarator, the toroidal mode number n ceases to be a good quantum number - all ns within a given mode family being coupled. It is found that the discrete spectrum of unstable ideal MHD (magnetohydrodynamic) instabilities ceases to exist unless MHD is modified (regularized) by introducing a short-perpendicular-wavelength cutoff. Attempts to use ray tracing to estimate the regularized MHD spectrum fail due to the occurrence of chaotic ray trajectories. In quantum chaos theory, strong chaos in the semiclassical limit leads to eigenvalue statistics the same as those of a suitable ensemble of random matrices. For instance, the probability distribution function for the separation between neighboring eigenvalues is as derived from random matrix theory and goes to zero at zero separation. This contrasts with the Poissonian distribution found in separable systems, showing that a signature of quantum chaos is level repulsion. In order to determine whether eigenvalues of the regularized MHD problem obey the same statistics as those of the Schroedinger equation in both the separable 1-D case and the chaotic 3-D cases, we have assembled data sets of ideal MHD eigenvalues for a Suydam-unstable cylindrical (1-D) equilibrium using Mathematica and a Mercier-unstable (3-D) equilibrium using the CAS3D code. In the 1-D case, we find that the unregularized Suydam-approximation spectrum has an anomalous peak at zero eigenvalue separation. On the other hand, regularization by restricting the domain of κsub(perpendicular) recovers the expected Poissonian distribution. In the 3-D case we find strong evidence of level repulsion within mode families, but mixing mode families produces Poissonian statistics. (author)
Unsteady MHD free convective flow past a vertical porous plate ...
African Journals Online (AJOL)
user
International Journal of Engineering, Science and Technology .... dimensional MHD boundary layer on the body with time varying temperature. ... flow of an electrically conducting fluid past an infinite vertical porous flat plate coinciding with.
Newtonian CAFE: a new ideal MHD code to study the solar atmosphere
González-Avilés, J. J.; Cruz-Osorio, A.; Lora-Clavijo, F. D.; Guzmán, F. S.
2015-12-01
We present a new code designed to solve the equations of classical ideal magnetohydrodynamics (MHD) in three dimensions, submitted to a constant gravitational field. The purpose of the code centres on the analysis of solar phenomena within the photosphere-corona region. We present 1D and 2D standard tests to demonstrate the quality of the numerical results obtained with our code. As solar tests we present the transverse oscillations of Alfvénic pulses in coronal loops using a 2.5D model, and as 3D tests we present the propagation of impulsively generated MHD-gravity waves and vortices in the solar atmosphere. The code is based on high-resolution shock-capturing methods, uses the Harten-Lax-van Leer-Einfeldt (HLLE) flux formula combined with Minmod, MC, and WENO5 reconstructors. The divergence free magnetic field constraint is controlled using the Flux Constrained Transport method.
Ideal, steady-state, axisymmetric magnetohydrodynamic equations with flow
International Nuclear Information System (INIS)
Baransky, Y.A.
1987-01-01
The motivation of this study is to gain additional understanding of the effect of rotation on the equilibrium of a plasma. The axisymmetric equilibria of ideal magnetohydrodynamics (MHD) with flow have been studied numerically and analytically. A general discussion is provided of previous work on plasmas with flow and comparisons are made to the static model. A variational principle has been derived for the two dimensional problem with comments as to appropriate boundary conditions. An inverse aspect ratio expansion has been used for a study of the toroidal flow equation for both low- and high-β. The inverse aspect ratio expansion has also been used for a study of equations with both poloidal and toroidal flow. An overview is provided of the adaptive finite-difference code which was developed to solve the full equations. (FI)
Maximum β limited by ideal MHD ballooning instabilites in JT-60
International Nuclear Information System (INIS)
Seki, Shogo; Azumi, Masashi
1986-03-01
Maximum β limited by ideal MHD ballooning instabilities is investigated on divertor configurations in JT-60. Maximum β against ballooning modes in JT-60 has strong dependecy on the distribution of the safety factor over the magnetic surfaces. Maximum β is ∼ 2 % for q 0 = 1.0, while more than 3 % for q 0 = 1.5. These results suggest that the profile control of the safety factor, especially on the magnetic axis, is attractive to the higher β operation in JT-60. (author)
New method for computing ideal MHD normal modes in axisymmetric toroidal geometry
International Nuclear Information System (INIS)
Wysocki, F.; Grimm, R.C.
1984-11-01
Analytic elimination of the two magnetic surface components of the displacement vector permits the normal mode ideal MHD equations to be reduced to a scalar form. A Galerkin procedure, similar to that used in the PEST codes, is implemented to determine the normal modes computationally. The method retains the efficient stability capabilities of the PEST 2 energy principle code, while allowing computation of the normal mode frequencies and eigenfunctions, if desired. The procedure is illustrated by comparison with earlier various of PEST and by application to tilting modes in spheromaks, and to stable discrete Alfven waves in tokamak geometry
Liu, Yong; Shu, Chi-Wang; Zhang, Mengping
2018-02-01
We present a discontinuous Galerkin (DG) scheme with suitable quadrature rules [15] for ideal compressible magnetohydrodynamic (MHD) equations on structural meshes. The semi-discrete scheme is analyzed to be entropy stable by using the symmetrizable version of the equations as introduced by Godunov [32], the entropy stable DG framework with suitable quadrature rules [15], the entropy conservative flux in [14] inside each cell and the entropy dissipative approximate Godunov type numerical flux at cell interfaces to make the scheme entropy stable. The main difficulty in the generalization of the results in [15] is the appearance of the non-conservative "source terms" added in the modified MHD model introduced by Godunov [32], which do not exist in the general hyperbolic system studied in [15]. Special care must be taken to discretize these "source terms" adequately so that the resulting DG scheme satisfies entropy stability. Total variation diminishing / bounded (TVD/TVB) limiters and bound-preserving limiters are applied to control spurious oscillations. We demonstrate the accuracy and robustness of this new scheme on standard MHD examples.
MHD Flows in Compact Astrophysical Objects Accretion, Winds and Jets
Beskin, Vasily S
2010-01-01
Accretion flows, winds and jets of compact astrophysical objects and stars are generally described within the framework of hydrodynamical and magnetohydrodynamical (MHD) flows. Analytical analysis of the problem provides profound physical insights, which are essential for interpreting and understanding the results of numerical simulations. Providing such a physical understanding of MHD Flows in Compact Astrophysical Objects is the main goal of this book, which is an updated translation of a successful Russian graduate textbook. The book provides the first detailed introduction into the method of the Grad-Shafranov equation, describing analytically the very broad class of hydrodynamical and MHD flows. It starts with the classical examples of hydrodynamical accretion onto relativistic and nonrelativistic objects. The force-free limit of the Grad-Shafranov equation allows us to analyze in detail the physics of the magnetospheres of radio pulsars and black holes, including the Blandford-Znajek process of energy e...
Reminimization of energy integral and stability limit for non-ideal MHD (magnetohydrodynamic) plasma
International Nuclear Information System (INIS)
Kondoh, Y.
1988-03-01
The stability condition of relaxed states is derived from the energy principle for the non-ideal MHD plasma. An Euler equation for the reminimization of energy integral is derived and shown to give the marginal stable, non-singular perturbations for the stability condition. An extended stability limit for the β = 0 relaxed states is derived from the stability condition, with use of the eigenvalue analysis for the Euler equation. By using the perturbation method, the extended stability limit is solved in the 1st order approximation to explain the deviation of the experimental stability limit from the idealized stability limit by Taylor. A procedure to get overall stability limit against both the non-singular and the singular perturbations is discussed. 25 refs
Modelling of diamagnetic stabilization of ideal MHD eigenmodes associated with the transport barrier
International Nuclear Information System (INIS)
Huysmans, G.; Sharapov, S.; Mikhailovskii, A.; Kerner, W.
2001-01-01
A new code, MISHKA-D (Drift MHD), has been developed as an extension of the ideal MHD code MISHKA-1 in order to investigate the finite gyroradius stabilizing effect of ion diamagnetic drift frequency, ω *i , on linear ideal MHD eigenmodes in tokamaks with shaped plasma cross-section. The MISHKA-D code gives a self-consistent computation of both stable and unstable eigenmodes with eigenvalues [γ] ≅ ω *i in plasmas with strong radial variation in the ion diamagnetic frequency. Test results of the MISHKA-D code show good agreement with the analytically obtained ω *i -spectrum and stability limits of the internal kink mode, n/m=1/1, used as a benchmark case. Finite-n ballooning and low-n kink (peeling) modes in the edge transport barrier just inside the separatrix are studied for H-mode plasma with the ω *i -effect included. The ion diamagnetic stabilization of the ballooning modes is found to be most effective for narrow edge pedestals. For low enough plasma density the ω *i - stabilization can lead to a second zone of ballooning stability, in which all the ballooning modes are stable for any value of the pressure gradient. For internal transport barriers typical of JET optimised shear discharges, the stabilizing influence of ion diamagnetic frequency on the n=1 global pressure driven disruptive mode is studied. A strong radial variation of ω *i is found to significantly decrease the stabilizing ω *i - effect on the n=1 mode, in comparison with the case of constant ω *i estimated at the foot of the internal transport barrier. (author)
Dependence of ideal MHD kink and ballooning modes on plasma shape and profiles in tokamaks
International Nuclear Information System (INIS)
Todd, A.M.M.; Manickam, J.; Okabayashi, M.; Chance, M.S.; Grimm, R.C.; Greene, J.M.; Johnson, J.L.
1978-08-01
Extensive numerical studies of ideal MHD instabilities have been carried out to gain insight into the parametric dependence of critical β's in tokamaks. The large number of interrelated equilibrium quantities involved in establishing a critical β has demanded a careful, systematic survey in order to isolate this dependence. The results of this survey establish the scaling with geometrical quantities including aspect ratio, elongation, and triangularity in the parameter regimes appropriate for both current and reactor-sized plasmas. A moderate dependence on the pressure profile and a strong variation with the current profile is found. The principal result is that for aspect ratio R/a approximately equal to 3, critical β's are of the order of 2% for circular cross sections and 5% for plasmas with elongation K approximately equal to 2; somewhat higher values could be achieved with more optimal shaping. Finally, sequences of equilibria have been analyzed to compare critical β as a function of toroidal mode number n. We conclude that the infinite-n analytic ballooning theory provides a sufficient condition for ideal MHD internal mode stability. Low-n free boundary modes appear to set a lower limit
Ideal-MHD beta limits: scaling laws and comparison with Doublet III high-beta plasmas
International Nuclear Information System (INIS)
Bernard, L.C.; Bhadra, D.K.; Helton, F.J.; Lao, L.L.; Todd, T.N.
1983-06-01
Doublet III (DIII) recently has achieved a value for #betta#, the ratio of volume averaged plasma to magnetic pressure, of 4.5%. This #betta# value is in the range required for an economically attractive tokamak reactor, and also close to the relevant limit predicted by ideal-MHD theory. It is therefore of great interest to assess the validity of the theory by comparison with experiment and thus to have a basis for the prediction of future reactor performance. A large variety of plasma shapes have been obtained in DIII. These shapes can be divided into two classes: (1) limiter discharges, and (2) diverted discharges, which are of great interest because of their good confinement in the H-mode operation. We derive simple scaling laws from the variation of optimized ideal-MHD beta limits (#betta#/sub c/) with plasma shape parameters. The current profile is optimized for fixed plasma shapes, separately for the high-n (ballooning) and the low-n (kink) modes. Results are presented in the form of suitability normalized curves of #betta# versus poloidal beta, #betta#/sub p/, for both ballooning and kink modes in order to simultaneously compare all the DIII experimental data
Performance and flow characteristics of MHD seawater thruster
Energy Technology Data Exchange (ETDEWEB)
Doss, E.D.
1990-01-01
The main goal of the research is to investigate the effects of strong magnetic fields on the electrical and flow fields inside MHD thrusters. The results of this study is important in the assessment of the feasibility of MHD seawater propulsion for the Navy. To accomplish this goal a three-dimensional fluid flow computer model has been developed and applied to study the concept of MHD seawater propulsion. The effects of strong magnetic fields on the current and electric fields inside the MHD thruster and their interaction with the flow fields, particularly those in the boundary layers, have been investigated. The results of the three-dimensional computations indicate that the velocity profiles are flatter over the sidewalls of the thruster walls in comparison to the velocity profiles over the electrode walls. These nonuniformities in the flow fields give rise to nonuniform distribution of the skin friction along the walls of the thrusters, where higher values are predicted over the sidewalls relative to those over the electrode walls. Also, a parametric study has been performed using the three-dimensional MHD flow model to analyze the performance of continuous electrode seawater thrusters under different operating parameters. The effects of these parameters on the fluid flow characteristics, and on the thruster efficiency have been investigated. Those parameters include the magnetic field (10--20 T), thruster diameter, surface roughness, flow velocity, and the electric load factor. The results show also that the thruster performance improves with the strength of the magnetic field and thruster diameter, and the efficiency decreases with the flow velocity and surface roughness.
Evolution of solar magnetic arcades. I. Ideal MHD evolution under footpoint shearing
International Nuclear Information System (INIS)
Choe, G.S.; Lee, L.C.
1996-01-01
The ideal MHD evolution of a single magnetic arcade undergoing footpoint motions in a two-dimensional Cartesian geometry is investigated using numerical simulation. Also, force-free states of the same arcade are constructed with the use of a magnetofrictional method, which is formulated differently from those used in previous studies. In MHD simulations, no instability or nonequilibrium is found to the value of shear 100 times as large as the footprint separation in the potential field. The evolutionary sequence is composed of three distinct phases. The first phase is characterized by the increase of the toroidal field strength and the second phase by a sort of self-similar expansion. In the third phase, the formation and growth of a central current layer are conspicuous. With increasing shear, the maximum current density increases, the width of the current layer decreases, and the feet of the current layer, which bifurcates above the bottom boundary, get closer to each other. The field lines in the current layer tend to thread the bottom boundary nearly horizontally for a large shear. From our results, it is inductively inferred that the magnetic arcade in a two-dimensional Cartesian geometry approaches an open field as the shear increases indefinitely. copyright 1996 The American Astronomical Society
International Nuclear Information System (INIS)
Redi, M.H.; Diallo, A.; Cooper, W.A.; Fu, G.Y.
2000-01-01
Concerns about the flexibility and robustness of a compact quasiaxial stellarator design are addressed by studying the effects of varied pressure and rotational transform profiles on expected performance. For thirty, related, fully three-dimensional configurations the global, ideal magnetohydrodynamic stability is evaluated as well as energetic particle transport. It is found that tokamak intuition is relevant to understanding the magnetohydrodynamic stability, with pressure gradient driving terms and shear stabilization controlling both the periodicity preserving, N=0, and the non-periodicity preserving, N=1, unstable kink modes. Global kink modes are generated by steeply peaked pressure profiles near the half radius and edge localized kink modes are found for plasmas with steep pressure profiles at the edge as well as with edge rotational transform above 0.5. Energetic particle transport is not strongly dependent on these changes of pressure and current (or rotational transform) profiles, although a weak inverse dependence on pressure peaking through the corresponding Shafranov shift is found. While good transport and MHD stability are not anticorrelated in these equilibria, stability only results from a delicate balance of the pressure and shear stabilization forces. A range of interesting MHD behaviors is found for this large set of equilibria, exhibiting similar particle transport properties
MHD Hele-Shaw flow of Rivlin-Ericksen fluid
International Nuclear Information System (INIS)
Ghosh, B.C.; Sengupta, P.R.
1995-01-01
In this paper, an attempt has been made to study the MHD Hele-Shaw flow of Rivlin-Ericksen visco-elastic fluid assuming the pressure gradient to be proportional to exp (-nt). The velocity components are obtained and the effect of visco-elasticity is discussed on velocity components. (author). 8 refs
Thermosolutal MHD flow and radiative heat transfer with viscous ...
African Journals Online (AJOL)
This paper investigates double diffusive convection MHD flow past a vertical porous plate in a chemically active fluid with radiative heat transfer in the presence of viscous work and heat source. The resulting nonlinear dimensionless equations are solved by asymptotic analysis technique giving approximate analytic ...
Hall effects on MHD flow past an accelerated plate
International Nuclear Information System (INIS)
Soundalgekar, V.M.; Ravi, S.; Hiremath, S.B.
1980-01-01
An exact solution of the MHD flow of an incompressible, electrically conducting, viscous fluid past a uniformly accelerated plate is presented. The velocity profiles are shown graphically and the numerical values of axial and transverse components of skin friction are tabulated. At high values of the Hall parameter, ωtau, the velocity is found to be oscillatory near the plate. (author)
Modeling of flow-dominated MHD instabilities at WiPPAL using NIMROD
Flanagan, K.; McCollam, K. J.; Milhone, J.; Mirnov, V. V.; Nornberg, M. D.; Peterson, E. E.; Siller, R.; Forest, C. B.
2017-10-01
Using the NIMROD (non-ideal MHD with rotation - open discussion) code developed at UW-Madison, we model two different flow scenarios to study the onset of MHD instabilities in flow-dominated plasmas in the Big Red Ball (BRB) and the Plasma Couette Experiment (PCX). Both flows rely on volumetric current drive, where a large current is drawn through the plasma across a weak magnetic field, injecting J × B torque across the whole volume. The first scenario uses a vertical applied magnetic field and a mostly radial injected current to create Couette-like flows which may excite the magnetorotational instability (MRI). In the other scenario, a quadrupolar field is applied to create counter-rotating von Karman-like flow that demonstrates a dynamo-like instability. For both scenarios, the differences between Hall and MHD Ohm's laws are explored. The implementation of BRB geometry in NIMROD, details of the observed flows, and instability results are shown. This work was funded by DoE and NSF.
Ideal MHD stability of internal kinks in circular and shaped tokamaks
International Nuclear Information System (INIS)
Luetjens, H.; Bondeson, A.; Vlad, G.
1992-04-01
Stability limits for the internal kink mode in tokamaks are calculated for different current profiles and plasma cross sections using ideal magnetohydrodynamics (MHD). The maximum stable poloidal beta at the q = 1 surface (β p ) is sensitive to the current profile, but for circular cross sections, it is typically between 0.1 and 0.2. Large aspect ratio theory gives similar predictions when the appropriate boundary conditions are applied at the plasma-vacuum surface. The pressure driven internal kink is significantly destabilized by ellipticity. For JET geometry, the β p -limit is typically between 0.05 and 0.1, but arbitrarily low limits can result if the shear is reduced at the q=1 surface. A large aspect ratio expansion of the Mercier criterion retaining the effects of ellipticity and triangularity is given to illustrate the destabilizing influence of ellipticity. (author) 17 figs., 16 refs
Ideal MHD equilibrium of a weakly toroidal plasma column with elongated cross-section
International Nuclear Information System (INIS)
Heesch, E.J.M. van; Schuurman, W.
1980-07-01
Solutions are obtained of the ideal MHD equations describing the equilibrium of a weakly toroidal plasma with an elliptic cross-section surrounded by a force-free magnetic field with constant ratio between current density and magnetic field strength. The force-free field parameter causes the stagnation points to recede along the major axis of the ellipse. Above a certain value of the force-free field parameter, stagnation points do not exist, so that the compression ratio of the plasma column is no longer limited. The analysis was carried out to first order in the force-free field parameter as well as to second order for an estimate of the error
Ideal MHD stability properties of pressure-driven modes in low shear tokamaks
International Nuclear Information System (INIS)
Manickam, J.; Pomphrey, N.; Todd, A.M.M.
1987-03-01
The role of shear in determining the ideal MHD stability properties of tokamaks is discussed. In particular, we assess the effects of low shear within the plasma upon pressure-driven modes. The standard ballooning theory is shown to break down, as the shear is reduced and the growth rate is shown to be an oscillatory function of n, the toroidal mode number, treated as a continuous parameter. The oscillations are shown to depend on both the pressure and safety-factor profiles. When the shear is sufficiently weak, the oscillations can result in bands of unstable n values which are present even when the standard ballooning theory predicts complete stability. These instabilities are named ''infernal modes.'' The occurrence of these instabilities at integer n is shown to be a sensitive function of q-axis, raising the possibility of a sharp onset as plasma parameters evolve. 20 refs., 31 figs
Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field
Moawad, S. M.; Moawad
2013-10-01
The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.
Direct numerical simulation of MHD flow with electrically conducting wall
International Nuclear Information System (INIS)
Satake, S.; Kunugi, T.; Naito, N.; Sagara, A.
2006-01-01
The 2D vortex problem and 3D turbulent channel flow are treated numerically to assess the effect of electrically conducting walls on turbulent MHD flow. As a first approximation, the twin vortex pair is considered as a model of a turbulent eddy near the wall. As the eddy approaches and collides with the wall, a high value electrical potential is induced inside the wall. The Lorentz force, associated with the potential distribution, reduces the velocity gradient in the near-wall region. When considering a fully developed turbulent channel flow, a high electrical conductivity wall was chosen to emphasize the effect of electromagnetic coupling between the wall and the flow. The analysis was performed using DNS. The results are compared with a non-MHD flow and MHD flow in the insulated channel. The mean velocity within the logarithmic region in the case of the electrically conducting wall is slightly higher than that in the non-conducting wall case. Thus, the drag is smaller compared to that in the non-conducting wall case due to a reduction of the Reynolds stress in the near wall region through the Lorentz force. This mechanism is explained via reduction of the production term in the Reynolds shear stress budget
Magnus: A New Resistive MHD Code with Heat Flow Terms
Navarro, Anamaría; Lora-Clavijo, F. D.; González, Guillermo A.
2017-07-01
We present a new magnetohydrodynamic (MHD) code for the simulation of wave propagation in the solar atmosphere, under the effects of electrical resistivity—but not dominant—and heat transference in a uniform 3D grid. The code is based on the finite-volume method combined with the HLLE and HLLC approximate Riemann solvers, which use different slope limiters like MINMOD, MC, and WENO5. In order to control the growth of the divergence of the magnetic field, due to numerical errors, we apply the Flux Constrained Transport method, which is described in detail to understand how the resistive terms are included in the algorithm. In our results, it is verified that this method preserves the divergence of the magnetic fields within the machine round-off error (˜ 1× {10}-12). For the validation of the accuracy and efficiency of the schemes implemented in the code, we present some numerical tests in 1D and 2D for the ideal MHD. Later, we show one test for the resistivity in a magnetic reconnection process and one for the thermal conduction, where the temperature is advected by the magnetic field lines. Moreover, we display two numerical problems associated with the MHD wave propagation. The first one corresponds to a 3D evolution of a vertical velocity pulse at the photosphere-transition-corona region, while the second one consists of a 2D simulation of a transverse velocity pulse in a coronal loop.
MHD-flow in slotted channels with conducting walls
International Nuclear Information System (INIS)
Evtushenko, I.A.; Kirillov, I.R.; Reed, C.B.
1994-07-01
A review of experimental results is presented for magnetohydrodynamic (MHD) flow in rectangular channels with conducting walls and high aspect ratios (longer side parallel to the applied magnetic field), which are called slotted channels. The slotted channel concept was conceived at Efremov Institute as a method for reducing MHD pressure drop in liquid metal cooled blanket design. The experiments conducted by the authors were aimed at studying both fully developed MHD-flow, and the effect of a magnetic field on the hydrodynamics of 3-D flows in slotted channels. Tests were carried out on five models of the slotted geometry. A good agreement between test and theoretical results for the pressure drop in slotted channels was demonstrated. Application of a open-quotes one-electrode movable probeclose quotes for velocity measurement permitted measurement of the M-shape velocity profiles in the slotted channels. Suppression of 3-D inertial effects in slotted channels of complex geometry was demonstrated based on potential distribution data
Effect of Grain Size on Differential Desorption of Volatile Species and on Non-ideal MHD Diffusivity
Zhao, Bo; Caselli, Paola; Li, Zhi-Yun
2018-05-01
We developed a chemical network for modeling the chemistry and non-ideal MHD effects from the collapsing dense molecular clouds to protostellar disks. First, we re-formulated the cosmic-ray desorption rate by considering the variations of desorption rate over the grain size distribution. We find that the differential desorption of volatile species is amplified by the grains larger than 0.1 μm, because larger grains are heated to a lower temperature by cosmic-rays and hence more sensitive to the variations in binding energies. As a result, atomic nitrogen N is ˜2 orders of magnitude more abundant than CO; N2H+ also becomes a few times more abundant than HCO+ due to the increased gas-phase N2. However, the changes in ionization fraction due to freeze-out and desorption only have minor effects on the non-ideal MHD diffusivities. Our chemical network confirms that the very small grains (VSGs: below a few 100 Å) weakens the efficiency of both ambipolar diffusion and Hall effect. In collapsing dense cores, a maximum ambipolar diffusion is achieved when truncating the MRN size distribution at 0.1 μm, and for a maximum Hall effect, the truncation occurs at 0.04 μm. We conclude that the grain size distribution is crucial to the differential depletion between CO and N2 related molecules, as well as to the non-ideal MHD diffusivities in dense cores.
Identification of, and transition to, the second region of ideal MHD stability in tokamaks
International Nuclear Information System (INIS)
Sabbagh, S.A.
1990-01-01
The second region of ideal MHD stability in tokamaks is studied by considering the behavior of the second region boundary for self- consistently calculated, marginally stable, second region equilibria and the characteristics of numerically computed transport sequences that achieve second stability. Equilibria with pressure profiles, p(ψ), that are marginally stable to the second region on each flux surface are generated numerically. This constraint eliminates p(ψ) as an independent variable, and reduces the predictor variables to the tokamak parameters and the q profile. The primary response functions considered are the plasma figures of merit, β and var-epsilon β p , and the normalized pressure gradient, α. Variations of the radial wavenumber in the ballooning equation negligibly affect the second region boundary for these equilibria. The second region boundary is sensitive to variations in the q profile at small aspect ratio, A, and will stabilize or destabilize depending on the balance of higher order var-epsilon = A -1 modifications of the normal field line curvature, κ n . These effects are a competition between the stabilizing geometric magnetic well of the toroidal field component of κ n and the destabilizing poloidal field component of κ n . The latter term becomes competitive in high var-epsilon β p plasmas with large Shafranov shifts. Simple analytic models are presented that reproduce the scaling of the marginally stable second region values of α and var-epsilon β p , and stability diagrams illustrating the behavior of the high-n unstable region for various parameters are shown
Ideal stability of cylindrical plasma in the presence of mass flow
International Nuclear Information System (INIS)
Bondeson, A.; Iacono, R.
1988-11-01
The ideal stability of cylindrical plasma with mass flows is investigated using the guiding centre plasma (GCP) model of Grad. For rotating plasmas, the kinetic treatment of the parallel motion in GCP gives significantly different results than fluid models, where the pressures are obtained from equations of state. In particular, GCP removes the resonance with slow magnetoacoustic waves and the loss of stability that results in magnetohydrodynamics (MHD) for near-soni flows. Because of the strong kinetic damping of the sound waves in an isothermal plasma, the slow waves have little influence on plasma stability in GCP at low β. In the large aspect ratio, low-β tokamak ordering, Alfvenic flows are needed to change the ideal GCP stability significantly. At lowest order in the inverse aspect ratio, flow can be favorable or unfavorable for stability of local modes depending on the profiles, but external kinks are always destilized by flow if the velocity vanishes at the edge. For high-β, reversed field pinch equilibria, numerical computations show that flow can be stabilizing for local modes, but external modes are destabilized by flow. It is shown that in three dimensions, the MHD equilibrium problem becomes hyperbolic for arbitrarily small flows across the magnetic field, whereas in GCP the equilibrium remains elliptic for sub-Alfvenic flows. (author) 7 figs., 1 tab, 32 refs
Effects of couple stresses in MHD channel flow
International Nuclear Information System (INIS)
Soundalgekar, V.M.; Aranake, R.N.
1977-01-01
An analysis of fully developed MHD channel flow of an electrically conducting incompressible fluid, taking into account the couple stresses, is carried out. Exact solutions are derived for velocity profiles, current density, skin-friction and coefficient of mass flux. They are influenced by the magnetic field, the loading parameter k, and the non-dimensional parameter (a=b 1 /lambda). Their variations with respect to M, k and a are represented graphically, this is followed by a physical discussion. It is observed that the couple stresses are more effective in the presence of a very weak magnetic field. (Auth.)
Heat transfer to MHD oscillatory dusty fluid flow in a channel filled ...
Indian Academy of Sciences (India)
The flow of fluids through porous media has become ... convection-radiation interaction with heat transfer in boundary layer flow over a flat plate sub- ... Unsteady MHD free convection flow of a compressible fluid past a moving vertical plate in.
Numerical simulation of magnetohydrodynamic (MHD) flow with internal heat generation
International Nuclear Information System (INIS)
Bokade, Vipin; Bhandarkar, U.V.; Bodi, Kowsik
2016-01-01
A strong magnetic field is used to confine the plasma in a fusion reactor. This magnetic field also affects the flow of Lead-Lithium (breeder/coolant) in the breeding blanket. So it is important to study MHD flow of Lead-Lithium (Pb-Li). Open-source toolbox, OpenFOAM, is used to study single phase behaviour of Pb-Li. As the induced magnetic field is very small, Ni et al. electric potential algorithm is employed in OpenFOAM and validated with analytical results. This solver can also solve the temperature field with heat source term. Simulations are carried out in 2D straight channel for various values of Hartmann Number ranging from 100 to 5000 and velocity profile, temperature, current density and pressure drop are studied. (author)
The stability of ideal and resistive ballooning modes in the presence of equilibrium flows
International Nuclear Information System (INIS)
Sundaram, A.K.; Sen, A.
1989-01-01
Ideal and resistive ballooning modes have been the topic of extensive study in view of their important role in constraining plasma β or in causing degradation in electron energy confinement time. Much of these works in the literature have been done for static equilibrium. Recently several experiments on ISX, PDX and currently on TFTR and JET have demonstrated the presence of toroidal and poloidal flows due to asymmetry in the neutral beam injection (NBI). Also equilibrium flows can arise through diffusive processes in tokamak plasmas. Such flows induced by external sources or dissipative processes affect the form and location of the magnetic surfaces and also modify the density and pressure profiles in the equilibrium. In this paper, we therefore examine the effect of mass flows on the evolution of high (m,n) ideal and resistive ballooning modes using the simplified MHD equations. (author) 2 refs
Effects of couple stresses on MHD Couette flow
International Nuclear Information System (INIS)
Soundalgekar, V.M.; Aranake, R.N.
1978-01-01
An exact analysis of the effects of the couple stresses on the MHD Couette flow of an electrically conducting, viscous incompressible fluid is carried out. Closed form solutions are derived for the velocity, the current density, the skin-friction at the lower plate, the force to move the upper plate, and the coefficient of mass flux for (i) A→infinity, and (ii) 2M/A 1, where a is the couple stress parameter and M is the Hartmann number. These are shown graphically followed by a discussion. During the course of discussion the effects of A are quantitatively compared with those in the ordinary case. It is observed that in the presence of a magnetic field the skin friction is affected by the couple stresses. (Auth.)
On MHD nonlinear stretching flow of Powell–Eyring nanomaterial
Directory of Open Access Journals (Sweden)
Tasawar Hayat
Full Text Available This communication addresses the magnetohydrodynamic (MHD flow of Powell–Eyring nanomaterial bounded by a nonlinear stretching sheet. Novel features regarding thermophoresis and Brownian motion are taken into consideration. Powell–Eyring fluid is electrically conducted subject to non-uniform applied magnetic field. Assumptions of small magnetic Reynolds number and boundary layer approximation are employed in the mathematical development. Zero nanoparticles mass flux condition at the sheet is selected. Adequate transformation yield nonlinear ordinary differential systems. The developed nonlinear systems have been computed through the homotopic approach. Effects of different pertinent parameters on velocity, temperature and concentration fields are studied and analyzed. Further numerical data of skin friction and heat transfer rate is also tabulated and interpreted. Keywords: Powell–Eyring fluid, Magnetohydrodynamics, Nanomaterial, Nonlinear stretching surface
On axisymmetric resistive MHD equilibria with flow free of Pfirsch-Schlüter diffusion
Throumoulopoulos, George N.; Tasso, Henri
2002-11-01
The equilibrium of an axisymmetric magnetically confined plasma with anisotropic electrical conductivity and flows parallel to the magnetic field is investigated within the framework of the MHD theory by keeping the convective flow term in the momentum equation. It turns out that the stationary states are determined by a second-order partial differential equation for the poloidal magnetic flux function along with a Bernoulli equation for the density identical in form with the respective ideal MHD equations; equilibrium consistent expressions for the conductivities σ_allel and σ_⊥ parallel and perpendicular to the magnetic field are also derived from Ohm's and Faraday's laws. Unlike in the case of stationary states with isotropic conductivity and parallel flows (see [1]) the equilibrium is compatible with non-vanishing poloidal currents. For incompressible flows exact solutions of the above mentioned set of equations can be constructed with σ_allel and σ_⊥ profiles compatible with collisional conductivity profiles, i.e. profiles peaked close to the magnetic axis, vanishing on the boundary and such that σ_allel> σ_⊥. In particular, an exact equilibrium describing a toroidal plasma of arbitrary aspect ratio being contained within a perfectly conducting boundary of rectangular cross-section and peaked toroidal current density profile vanishing on the boundary is further considered. For this equilibrium in the case of vanishing flows the difference σ_allel-σ_⊥ for the reversed field pinch scaling Bp Bt (where Bp and Bt are the poloidal and toroidal magnetic field components) is nearly two times larger than that for the tokamak scaling B_p 0.1 B_t. [1] G. N. Throumoulopoulos, H. Tasso, J. Plasma Physics 64, 601 (2000).
Exact solutions for MHD flow of couple stress fluid with heat transfer
Directory of Open Access Journals (Sweden)
Najeeb Alam Khan
2016-01-01
Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.
Poli, Francesca
2012-10-01
Steady state scenarios envisaged for ITER aim at optimizing the bootstrap current, while maintaining sufficient confinement and stability to provide the necessary fusion yield. Non-inductive scenarios will need to operate with Internal Transport Barriers (ITBs) in order to reach adequate fusion gain at typical currents of 9 MA. However, the large pressure gradients associated with ITBs in regions of weak or negative magnetic shear can be conducive to ideal MHD instabilities in a wide range of βN, reducing the no-wall limit. Scenarios are established as relaxed flattop states with time-dependent transport simulations with TSC [1]. Fully non-inductive configurations with current in the range of 7-10 MA and various heating mixes (NB, EC, IC and LH) have been studied against variations of the pressure profile peaking and of the Greenwald fraction. It is found that stable equilibria have qmin> 2 and moderate ITBs at 2/3 of the minor radius [2]. The ExB flow shear from toroidal plasma rotation is expected to be low in ITER, with a major role in the ITB dynamics being played by magnetic geometry. Combinations of H&CD sources that maintain reverse or weak magnetic shear profiles throughout the discharge and ρ(qmin)>=0.5 are the focus of this work. The ITER EC upper launcher, designed for NTM control, can provide enough current drive off-axis to sustain moderate ITBs at mid-radius and maintain a non-inductive current of 8-9MA and H98>=1.5 with the day one heating mix. LH heating and current drive is effective in modifying the current profile off-axis, facilitating the formation of stronger ITBs in the rampup phase, their sustainment at larger radii and larger bootstrap fraction. The implications for steady state operation and fusion performance are discussed.[4pt] [1] Jardin S.C. et al, J. Comput. Phys. 66 (1986) 481[0pt] [2] Poli F.M. et al, Nucl. Fusion 52 (2012) 063027.
International Nuclear Information System (INIS)
Zhang, Xiujie; Pan, Chuanjie; Xu, Zengyu
2013-01-01
Highlights: ► 2D MHD code based on a fully developed modeling is developed and validated by Samad analytical results. ► The results of MHD effect of liquid metal through circular pipes at high Hartmann numbers are given. ► M type velocity profile is observed for MHD circular pipe flow at high wall conductance ratio condition. ► Non-uniform wall electrical conductivity leads to high jet velocity in Robert layers. -- Abstract: Magnetohydrodynamics (MHD) laminar flows through circular pipes are studied in this paper by numerical simulation under the conditions of Hartmann numbers from 18 to 10000. The code is developed based on a fully developed modeling and validated by Samad's analytical solution and Chang's asymptotic results. After the code validation, numerical simulation is extended to high Hartmann number for MHD circular pipe flows with conducting walls, and numerical results such as velocity distribution and MHD pressure gradient are obtained. Typical M-type velocity is observed but there is not such a big velocity jet as that of MHD rectangular duct flows even under the conditions of high Hartmann numbers and big wall conductance ratio. The over speed region in Robert layers becomes smaller when Hartmann numbers increase. When Hartmann number is fixed and wall conductance ratios change, the dimensionless velocity is through one point which is in agreement with Samad's results, the locus of maximum value of velocity jet is same and effects of wall conductance ratio only on the maximum value of velocity jet. In case of Robert walls are treated as insulating and Hartmann walls as conducting for circular pipe MHD flows, there is big velocity jet like as MHD rectangular duct flows of Hunt's case 2
Particle orbits and non-ideal MHD stability of Z-pinches
International Nuclear Information System (INIS)
Faghihi, M.
1987-01-01
Particle orbits in a linear EXTRAP vacuum magnetic field configuration are computed. The results indicate that, with an applied electric field along the axis, the particles starting near the magnetic stagnation line would gain substantial energy in the 'free fall', and are the most efficient ones to participate in the ionization process. The acquired energy depends on the electric field strength; the required value of the field is determined. The influence of the pressure anisotropy on the small wavelength internal kink (m=1) mode instability in a Z-pinch, using a generalization of Freidbergs perpendicular MHD model, is investigated. It is found that the stability criterion can not be fulfilled without violation of the fire hose stability condition. This investigation is also performed using the double-adiabatic theory. A finite Larmor radius treatment of the small wavelength kink instabilities for a Z-pinch geometry is presented. It is shown that, when the gyroviscosity is included in the perpendicular MHD model, exponentially growing Alfven waves are predicted even in a homogeneous static equilibrium with isotropic plasma pressure. The Hall effect in the incompressible Hall fluid model is considered. It is found that the Hall parameter reduces the growth rates of the kink modes, but it does not yield complete stabilization (author)
Particle orbits and non-ideal MHD stability of Z-pinches
Energy Technology Data Exchange (ETDEWEB)
Faghihi, M.
1987-01-01
Particle orbits in a linear EXTRAP vacuum magnetic field configuration are computed. The results indicate that, with an applied electric field along the axis, the particles starting near the magnetic stagnation line would gain substantial energy in the 'free fall', and are the most efficient ones to participate in the ionization process. The acquired energy depends on the electric field strength; the required value of the field is determined. The influence of the pressure anisotropy on the small wavelength internal kink (m=1) mode instability in a Z-pinch, using a generalization of Freidbergs perpendicular MHD model, is investigated. It is found that the stability criterion can not be fulfilled without violation of the fire hose stability condition. This investigation is also performed using the double-adiabatic theory. A finite Larmor radius treatment of the small wavelength kink instabilities for a Z-pinch geometry is presented. It is shown that, when the gyroviscosity is included in the perpendicular MHD model, exponentially growing Alfven waves are predicted even in a homogeneous static equilibrium with isotropic plasma pressure. The Hall effect in the incompressible Hall fluid model is considered. It is found that the Hall parameter reduces the growth rates of the kink modes, but it does not yield complete stabilization
Soret and Hall effects on unsteady MHD free convection flow of ...
African Journals Online (AJOL)
International Journal of Engineering, Science and Technology ... effects on unsteady MHD free convection flow of radiating and chemically reactive fluid ... Expressions for shear stress, rate of heat transfer and rate of mass transfer at the plate ...
Hall-magnetohydrodynamic waves in flowing ideal incompressible solar-wind plasmas
International Nuclear Information System (INIS)
Zhelyazkov, I
2010-01-01
It is well established now that the solar atmosphere, from the photosphere to the corona and the solar wind, is a highly structured medium. Satellite observations have confirmed the presence of steady flows there. Here, we investigate the propagation of magnetohydrodynamic (MHD) eigenmodes (kink and sausage surface waves) travelling along an ideal incompressible flowing plasma cylinder (flux tube) surrounded by a flowing plasma environment in the framework of the Hall magnetohydrodynamics. The propagation characteristics of the waves are studied in a reference frame moving with the mass flow outside the tube. In general, the flows change the waves' phase velocities compared with their magnitudes in a static MHD flux tube and the Hall effect extends the number of the possible wave dispersion curves. It turns out that while the kink waves, considered in the context of the standard magnetohydrodynamics, are unstable against the Kelvin-Helmholtz instability, they become stable when the Hall term in the generalized Ohm's law is taken into account. The sausage waves are stable in both considerations. All results concerning the waves' propagation and their stability/instability status are obtained on the basis of the linearized Hall-magnetohydrodynamic equations and are applicable mainly to the solar wind plasmas.
Performance of MHD coatings in flowing Li at 700 deg
International Nuclear Information System (INIS)
Pint, B.; Pawel, S.J.; Howell, M.; Moser, J.L.; Garner, G.W.; Santella, M.L.; Tortorelli, P.F.; Di Stefano, J.R.
2007-01-01
Full text of publication follows: A thermal convection loop was constructed from V-4Cr-4Ti tubing and operated in vacuum at a maximum Li temperature of 700 deg. C for ∼1000 h.. Due to slow Li flow (∼1 cm/s) in the loop, the temperature gradient was ∼340 deg. C. Specimens in the hot and cold legs of the loop included V-4Cr-4Ti spacers, tensile specimens (SS-3 type) and coupons coated by physical vapor deposition with yttria and over coated with unalloyed vanadium. Based on prior work, the multi-layer electrically-insulating coatings were developed to reduce the magneto hydrodynamic (MHD) force expected in the first wall of a lithium cooled blanket in a magnetic confinement fusion reactor. Characterization of the specimens after exposure will include: (1) mass change and chemistry change as a function of location in the temperature gradient, (2) the effect of Li exposure on the tensile properties of V-4Cr-4Ti and (3) characterization of the properties and microstructure of the coatings after exposure. Of particular interest will be the coating resistivity after exposure and any degradation of the thin (∼10 μm) vanadium overlayer. Chemistry of the Li before and after the experiment will be compared in order to assess any mass transfer effects. (authors)
MHD biconvective flow of Powell Eyring nanofluid over stretched surface
Naseem, Faiza; Shafiq, Anum; Zhao, Lifeng; Naseem, Anum
2017-06-01
The present work is focused on behavioral characteristics of gyrotactic microorganisms to describe their role in heat and mass transfer in the presence of magnetohydrodynamic (MHD) forces in Powell-Eyring nanofluids. Implications concerning stretching sheet with respect to velocity, temperature, nanoparticle concentration and motile microorganism density were explored to highlight influential parameters. Aim of utilizing microorganisms was primarily to stabilize the nanoparticle suspension due to bioconvection generated by the combined effects of buoyancy forces and magnetic field. Influence of Newtonian heating was also analyzed by taking into account thermophoretic mechanism and Brownian motion effects to insinuate series solutions mediated by homotopy analysis method (HAM). Mathematical model captured the boundary layer regime that explicitly involved contemporary non linear partial differential equations converted into the ordinary differential equations. To depict nanofluid flow characteristics, pertinent parameters namely bioconvection Lewis number Lb, traditional Lewis number Le, bioconvection Péclet number Pe, buoyancy ratio parameter Nr, bioconvection Rayleigh number Rb, thermophoresis parameter Nt, Hartmann number M, Grashof number Gr, and Eckert number Ec were computed and analyzed. Results revealed evidence of hydromagnetic bioconvection for microorganism which was represented by graphs and tables. Our findings further show a significant effect of Newtonian heating over a stretching plate by examining the coefficient values of skin friction, local Nusselt number and the local density number. Comparison was made between Newtonian fluid and Powell-Eyring fluid on velocity field and temperature field. Results are compared of with contemporary studies and our findings are found in excellent agreement with these studies.
Preliminary Study of Ideal Operational MHD Beta Limit in HL-2A Tokamak Plasmas
International Nuclear Information System (INIS)
Shen Yong; Dong Jiaqi; He Hongda; Turnbull, A. D.
2009-01-01
Magnetohydrodynamic (MHD) n = 1 kink mode with n the toroidal mode number is studied and the operational beta limit, constrained by the mode, is calculated for the equilibrium of HL-2A by using the GATO code. Approximately the same beta limit is obtained for configurations with a value of the axial safety factor q 0 both larger and less than 1. Without the stabilization of the conducting wall, the beta limit is found to be 0.821% corresponding to a normalized beta value of β c N = 2.56 for a typical HL-2A discharge with a plasma current I p = 0.245 MA, and the scaling of β c N ∼constant is confirmed. (magnetically confined plasma)
Directory of Open Access Journals (Sweden)
S.M. Moawad
Full Text Available In this paper, the equilibrium properties of some ideal and resistive magnetohydrodynamics (MHD are investigated. The governing equations are taken in the steady state for parallel and non-parallel flow to magnetic filed. The governing equations are reduced to Bernoulli-Grad-Shafranov system. The problem of finding exact equilibria to the governing equations in the presence of incompressible mass flows is studied. Several nonlinear equilibria of the governing equations are obtained with aid of constructed constraints. The obtained results cover several previously configurations and include new considerations about the nonlinearity of magnetic flux stream variables. The possibility of applying the obtained results to magnetic confinement devices are discussed. Keywords: Magnetohydrodynamics, Axisymmetric plasma, Resistivity, Incompressible flows, Exact equilibria, Magnetic confinement devices
Limits of possible operation of the R-tokamak due to ideal MHD instabilities
International Nuclear Information System (INIS)
Naitou, H.; Yamazaki, K.; Takemoto, Y.; Abe, Y.; Gruber, R.; Saurenmann, H.; Troyon, F.
1984-09-01
A series of MHD stability calculations has been made with the ERATO code to know the maximum β which can be expected for the R-Tokamak using the parameters of the second phase design (an aspect ratio of 2.75, ellipticity of 1.8 and triangularity of 0.3). The highest β obtained under the condition that both the n=1 free boundary mode (with no wall stabilization) and the n=infinity ballooning modes are stable is about 6% at qsub(s)--2.0 and qsub(o) at the Mercier limit on axis. This result has been found by performing some optimization of the current and pressure profiles. If only the ballooning modes are concerned, the limiting β becomes 8.6%. The sensitivity of the result to elongation has been studied. It has been found that the maximum β increases and then decreases with elongation. The optimum β is obtained for an elongation of 1.8 if both the n=1 kink and n=infinity ballooning limits are considered and of 2.0 if only ballooning modes are considered. These results are compared with proposed scaling laws. (author)
Flow aerodynamics modeling of an MHD swirl combustor - calculations and experimental verification
International Nuclear Information System (INIS)
Gupta, A.K.; Beer, J.M.; Louis, J.F.; Busnaina, A.A.; Lilley, D.G.
1981-01-01
This paper describes a computer code for calculating the flow dynamics of constant density flow in the second stage trumpet shaped nozzle section of a two stage MHD swirl combustor for application to a disk generator. The primitive pressure-velocity variable, finite difference computer code has been developed to allow the computation of inert nonreacting turbulent swirling flows in an axisymmetric MHD model swirl combustor. The method and program involve a staggered grid system for axial and radial velocities, and a line relaxation technique for efficient solution of the equations. Tue produces as output the flow field map of the non-dimensional stream function, axial and swirl velocity. 19 refs
The application of finite element method for mhd viscous flow over a porous stretching sheet
International Nuclear Information System (INIS)
Mahmood, R.; Sajid, M.
2007-01-01
This work is concerned with the magnetohydrodynamic (MHD) viscous flow due to a porous stretching sheet. The similarity solution of the problem is obtained using finite element method. The physical quantities of interest like the fluid velocity and skin friction coefficient is obtained and discussed under the influence of suction parameter and Hartman number. It is evident from the results that MHD can be used to control the boundary layer thickness. (author)
Multi-scale-nonlinear interactions among macro-MHD mode, micro-turbulence, and zonal flow
International Nuclear Information System (INIS)
Ishizawa, Akihiro; Nakajima, Noriyoshi
2007-01-01
This is the first numerical simulation demonstrating that macro-magnetohydrodynamic (macro-MHD) mode is exited as a result of multi-scale interaction in a quasi-steady equilibrium formed by a balance between zonal flow and micro-turbulence via reduced-two-fluid simulation. Only after obtaining the equilibrium which includes zonal flow and the turbulence caused by kinetic ballooning mode is this simulation of macro-MHD mode, double tearing mode, accomplished. In the quasi-steady equilibrium a macro-fluctuation which has the same helicity as that of double tearing mode is a part of the turbulence until it grows as a macro-MHD mode finally. When the macro-MHD grows it effectively utilize free energy of equilibrium current density gradient because of positive feedback loop between suppression of zonal flow and growth of the macro-fluctuation causing magnetic reconnection. Thus once the macro-MHD grows from the quasi-equilibrium, it does not go back. This simulation is more comparable with experimental observation of growing macro-fluctuation than traditional MHD simulation of linear instabilities in a static equilibrium. (author)
Luo, Ercang
2012-06-01
This paper analyzes the thermodynamic cycle of oscillating-flow regenerative machines. Unlike the classical analysis of thermodynamic textbooks, the assumptions for pistons' movement limitations are not needed and only ideal flowing and heat transfer should be maintained in our present analysis. Under such simple assumptions, the meso-scale thermodynamic cycles of each gas parcel in typical locations of a regenerator are analyzed. It is observed that the gas parcels in the regenerator undergo Lorentz cycle in different temperature levels, whereas the locus of all gas parcels inside the regenerator is the Ericson-like thermodynamic cycle. Based on this new finding, the author argued that ideal oscillating-flow machines without heat transfer and flowing losses is not the Stirling cycle. However, this new thermodynamic cycle can still achieve the same efficiency of the Carnot heat engine and can be considered a new reversible thermodynamic cycle under two constant-temperature heat sinks.
Impact of Heat and Mass Transfer on MHD Oscillatory Flow of Jeffery ...
African Journals Online (AJOL)
The objective of this paper is to study Dufour, Soret and thermal conductivity on unsteady heat and mass transfer of magneto hydrodynamic (MHD) oscillatory flow of Jeffery fluid through a porous medium in a channel. The partial differential equations governing the flow have been solved numerically using semi-implicit ...
Effect of electromagnetic coupling on MHD flow in the manifold of fusion liquid metal blanket
Energy Technology Data Exchange (ETDEWEB)
Chen, Hongli, E-mail: hlchen1@ustc.edu.cn; Meng, Zi; Feng, Jingchao; He, Qingyun
2014-10-15
In fusion liquid metal (LM) blanket, magnetohydrodynamics (MHD) effects will dominate the flow patterns and the heat transfer characteristics of the liquid metal flow. Manifold is a key component in LM blanket in charge of distributing or collecting the liquid metal coolant. In this region, the complex three dimensional MHD phenomena will be occurred, and the velocity, pressure and flow rate distributions may be dramatically influenced. One important aspect is the electromagnetic coupling effect resulting from an exchange of electric currents between two neighboring fluid domains that can lead to modifications of flow distribution and pressure drop compared to that in electrical separated channels. Understanding the electromagnetic coupling effect in manifold is necessary to optimize the liquid metal blanket design. In this work, a numerical study was carried out to investigate the effect of electromagnetic coupling on MHD flow in a manifold region. The typical manifold geometry in LM blanket was considered, a rectangular supply duct entering a rectangular expansion area, finally feeding into 3 rectangular parallel channels. This paper investigated the effect of electromagnetic coupling on MHD flow in a manifold region. Different electromagnetic coupling modes with different combinations of electrical conductivity of walls were studied numerically. The flow distribution and pressure drop of these modes have been evaluated.
MHD pressure drop of imperfect insulation of liquid metal flow
International Nuclear Information System (INIS)
Horiike, H.; Nishiura, R.; Inoue, S.; Miyazaki, K.
2000-01-01
An experiment was performed to study magnetohydrodynamic (MHD) pressure gradient in the case of an imperfect electric insulation coating when using NaK loop. Test channels with uniform defects in their coating were made by painting inner surface with acrylic lacquer insulation. It was found that the exponent to B -- which is 1 for insulated walls, and 2 for conducting ones, was very sensitive to crack fractions lower than 25%. The pressure gradient was found to increase almost linearly with the fraction
Computations of ideal and real gas high altitude plume flows
Feiereisen, William J.; Venkatapathy, Ethiraj
1988-01-01
In the present work, complete flow fields around generic space vehicles in supersonic and hypersonic flight regimes are studied numerically. Numerical simulation is performed with a flux-split, time asymptotic viscous flow solver that incorporates a generalized equilibrium chemistry model. Solutions to generic problems at various altitude and flight conditions show the complexity of the flow, the equilibrium chemical dissociation and its effect on the overall flow field. Viscous ideal gas solutions are compared against equilibrium gas solutions to illustrate the effect of equilibrium chemistry. Improved solution accuracy is achieved through adaptive grid refinement.
Conical flow near singular rays. [shock generation in ideal gas
Zahalak, G. I.; Myers, M. K.
1974-01-01
The steady flow of an ideal gas past a conical body is investigated by the method of matched asymptotic expansions, with particular emphasis on the flow near the singular ray occurring in linearized theory. The first-order problem governing the flow in this region is formulated, leading to the equation of Kuo, and an approximate solution is obtained in the case of compressive flow behind the main front. This solution is compared with the results of previous investigations with a view to assessing the applicability of the Lighthill-Whitham theories.
MHD flow of Kuvshinski fluid through porous medium with temperature gradient heat source
International Nuclear Information System (INIS)
Goyal, Mamta; Banshiwal, Anna
2014-01-01
MHD free convection time dependent flow of a viscous, dissipative, incompressible, electrically conducting, non Newtonian fluid name as Kuvshinski fluid past an infinite vertical plate is considered The plate is moving with uniform velocity in the direction of flow. Analytical solutions have been obtained for velocity, temperature and concentration using perturbation technique. The effects of governing parameter on flow quantities are discussed with the help of graphs. (author)
Flow Reversal of Fully-Developed Mixed MHD Convection in Vertical Channels
International Nuclear Information System (INIS)
Saleh, H.; Hashim, I.
2010-01-01
The present analysis is concerned with flow reversal phenomena of the fully-developed laminar combined free and forced MHD convection in a vertical parallel-plate channel. The effect of viscous dissipation is taken into account. Flow reversal adjacent to the cold (or hot) wall is found to exist within the channel as Gr/Re is above (or below) a threshold value. Parameter zones for the occurrence of reversed flow are presented. (fundamental areas of phenomenology(including applications))
Experimental study of MHD effects on turbulent flow of flibe simulant fluid in a circular pipe
International Nuclear Information System (INIS)
Takeuchi, Junichi; Morley, N.B.; Abdou, M.A.; Satake, Shin-ichi; Yokomine, Takehiko
2007-01-01
Experimental studies of MHD turbulent pipe flow of Flibe simulant fluid have been conducted as a part of US-Japan JUPITER-II collaboration. Flibe is considered as a promising candidate for coolant and tritium breeder in some fusion reactor design concepts because of its low electrical conductivity compared to liquid metals. This reduces the MHD pressure drop to a negligible level; however, turbulence can be significantly suppressed by MHD effects in fusion reactor magnetic field conditions. Heat transfer in the Flibe coolant is characterized by its high Prandtl number. In order to achieve sufficient heat transfer and to prevent localized heat concentration in a high Prandtl number coolant, high turbulence is essential. Even though accurate prediction of the MHD effects on heat transfer for high Prandtl number fluids in the fusion environment is very important, reliable data is not available. In these experiments, an aqueous solution of potassium hydroxide is used as a simulant fluid for Flibe. This paper presents the experimental results obtained by flow field measurement using particle image velocimetry (PIV) technique. The PIV measurements provide 2-dimensional 2-velocity component information on the MHD flow field. The test section is a circular pipe with 89 mm inner diameter and 7.0 m in length, which is 79 times pipe diameter. This relatively large diameter pipe is selected in order to maximize the MHD effects measured by Hartmann number (Ha=BL(sigma/mu)1/2), and to allow better resolution of the flow in the near-wall region. The test section is placed under maximum 2 Tesla magnetic fields for 1.4m of the axial length. The hydrodynamic developing length under the magnetic field is expected to be 1.2 m. In order to apply PIV technique in the magnetic field condition, special optical devices and visualization sections were created. PIV measurements are performed for Re = 11600 with variable Hartmann numbers. The turbulence statistics of the MHD turbulent flow
Effect of slip velocity on oscillatory MHD flow of stretched surface ...
African Journals Online (AJOL)
The study of unsteady magnetohydrodynamic heat and mass transfer in MHD flow of an incompressible, electrically conducting, viscous fluid past an infinite vertical porous plate along with porous medium of time dependent permeability with radiative heat transfer and variable suction has been made. Analytical solution of ...
International Nuclear Information System (INIS)
Kobayashi, Junichi
1979-01-01
The study on the transient flow characteristics in MHD ducts under orthogonal magnetic field is divided into handling two problems: the problem of changing pressure gradient in a uniform orthogonal magnetic field and the problem in which the orthogonal magnetic field itself changes with time. The former has been investigated by many persons, but the latter has not been investigated so often as the former because of its difficulty of handling. In addition, if it is intended to grasp properly the transient flow characteristics in actual MHD ducts, it will be also important that the effects of the electric conductivity of side walls and aspect ratio are clarified. In other words, this paper deals with the problem in which a uniform orthogonal magnetic field is suddenly applied in such manner as Heaviside's step function to or removed from the conductive fluids flowing in sufficiently long rectangular MHD ducts. First, the MHD fundamental equations are described, then they are normalized to give boundary conditions and initial conditions. Next, the transient flow and the derived magnetic field characteristics are numerically analyzed by the difference calculus, and thus the effects of conductor, insulated wall, aspect ratio, Hartmann number, magnetic Prandtl number and others on the above characteristics are clarified. (Wakatsuki, Y.)
Effect of Hartmann layer resolution for MHD flow in a straight ...
Indian Academy of Sciences (India)
851–861. c Indian Academy of Sciences. Effect of Hartmann layer resolution for MHD flow in a straight, conducting duct at high Hartmann numbers. SHARANYA SUBRAMANIAN1,∗, P K SWAIN2,. A V DESHPANDE1 and P SATYAMURTHY2. 1Mechanical Engineering Department, Veermata Jijabai Technological Institute,.
The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet
International Nuclear Information System (INIS)
Sajid, M.; Hayat, T.
2009-01-01
This work is concerned with the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet. The cases of two dimensional and axisymmetric shrinking have been discussed. Exact series solution is obtained using the homotopy analysis method (HAM). The convergence of the obtained series solution is discussed explicitly. The obtained HAM solution is valid for all values of the suction parameter and Hartman number.
MHD free convection flow past an oscillating plate in the presence of ...
African Journals Online (AJOL)
The study of unsteady magnetohydrodynamic heat and mass transfer in MHD flow past an infinite vertical oscillating plate through porous medium, taking account of the presence of free convection and mass transfer. The energy and chemical species equations are solved in closed form by Laplace-transform technique and ...
Electromagnetic interactions between the U-25 superconducting magnet and the U-25 B MHD flow train
International Nuclear Information System (INIS)
Smith, R.P.; Niemann, R.C.; Kraimer, M.R.; Zinneman, T.E.
1978-01-01
Fluctuating voltage signals on the potential taps of the Argonne National Laboratory (ANL) 5.0 Tesla MHD Superconducting Dipole Magnet have been observed during MHD power generation at the U-25 B Facility at the High Temperature Institute (IVAN), Moscow, U.S.S.R. The voltage fluctuations are analyzed with special emphasis on magnet stability. Various other thermodynamic and electrical parameters of the U-25 B flow train have been recorded and statistical correlations between these signals and the signals observed at the magnet terminals are described
Biot-Savart helicity versus physical helicity: A topological description of ideal flows
Sahihi, Taliya; Eshraghi, Homayoon
2014-08-01
For an isentropic (thus compressible) flow, fluid trajectories are considered as orbits of a family of one parameter, smooth, orientation-preserving, and nonsingular diffeomorphisms on a compact and smooth-boundary domain in the Euclidian 3-space which necessarily preserve a finite measure, later interpreted as the fluid mass. Under such diffeomorphisms the Biot-Savart helicity of the pushforward of a divergence-free and tangent to the boundary vector field is proved to be conserved and since these circumstances present an isentropic flow, the conservation of the "Biot-Savart helicity" is established for such flows. On the other hand, the well known helicity conservation in ideal flows which here we call it "physical helicity" is found to be an independent constant with respect to the Biot-Savart helicity. The difference between these two helicities reflects some topological features of the domain as well as the velocity and vorticity fields which is discussed and is shown for simply connected domains the two helicities coincide. The energy variation of the vorticity field is shown to be formally the same as for the incompressible flow obtained before. For fluid domains consisting of several disjoint solid tori, at each time, the harmonic knot subspace of smooth vector fields on the fluid domain is found to have two independent base sets with a special type of orthogonality between these two bases by which a topological description of the vortex and velocity fields depending on the helicity difference is achieved since this difference is shown to depend only on the harmonic knot parts of velocity, vorticity, and its Biot-Savart vector field. For an ideal magnetohydrodynamics (MHD) flow three independent constant helicities are reviewed while the helicity of magnetic potential is generalized for non-simply connected domains by inserting a special harmonic knot field in the dynamics of the magnetic potential. It is proved that the harmonic knot part of the vorticity
On accelerated flow of MHD powell-eyring fluid via homotopy analysis method
Salah, Faisal; Viswanathan, K. K.; Aziz, Zainal Abdul
2017-09-01
The aim of this article is to obtain the approximate analytical solution for incompressible magnetohydrodynamic (MHD) flow for Powell-Eyring fluid induced by an accelerated plate. Both constant and variable accelerated cases are investigated. Approximate analytical solution in each case is obtained by using the Homotopy Analysis Method (HAM). The resulting nonlinear analysis is carried out to generate the series solution. Finally, Graphical outcomes of different values of the material constants parameters on the velocity flow field are discussed and analyzed.
MHD flow layer formation at boundaries of magnetic islands in tokamak plasmas
International Nuclear Information System (INIS)
Jiaqi Dong; Yongxing Long; Zongze Mou; Jinhua Zhang
2005-01-01
Non-linear development of double tearing modes induced by electron viscosity is numerically simulated. MHD flow layers are demonstrated to merge in the development of the modes. The sheared flows are shown to lie just at the boundaries of the magnetic islands, and to have sufficient levels required for internal transport barrier (ITB) formation. Possible correlation between the layer formation and triggering of experimentally observed ITBs, preferentially formed in proximities of rational flux surfaces of low safety factors, is discussed. (author)
Directory of Open Access Journals (Sweden)
M. Jayachandra Babu
2017-12-01
Full Text Available The knowledge of heat and mass transfer of MHD flows over different geometries is very important for heat exchangers design, transpiration, fiber coating, etc. With this initiation, a mathematical model is proposed to investigate the two-dimensional flow, heat and mass transfer of magnetohydrodynamic flow over three different geometries (vertical cone, vertical wedge, and a vertical plate. Cattaneo-Christov heat flux with external magnetic field, thermophoresis and Brownian movement effect are introduced in the model. Runge-Kutta and Newtonâs methods are employed to solve the altered governing nonlinear equations. The influences of the parameters of concern on the common profiles (velocity, temperature, and concentration are conversed (in three cases. By viewing the same parameters, skin friction coefficient, heat and mass transfer rates are discussed with the assistance of tables. It is discovered that the momentum and thermal boundary layers are non-uniform for the MHD flow over three geometries (vertical cone, wedge, and a plate. Thermal and solutal Grashof numbers regulate the temperature and concentration fields. The heat and mass transfer rates of the flow over a cone are highly influenced by the thermal relaxation parameter. Keywords: MHD, Cattaneo-Christov heat flux, Thermal relaxation, Thermophoresis, Brownian motion
Heat transfer enhancement of free surface MHD-flow by a protrusion wall
International Nuclear Information System (INIS)
Hulin Huang; Bo Li
2010-01-01
Due to the magnetohydrodynamic (MHD) effect on the flow, which degrades heat transfer coefficients by pulsation suppression of external magnetic field on the flow, a hemispherical protrusion wall is applied to free surface MHD-flow system as a heat transfer enhancement, because the hemispherical protrusion wall has some excellent characteristics including high heat transfer coefficients, low friction factors and high overall thermal performances. So, the characteristics of the fluid flow and heat transfer of the free surface MHD-flow with hemispherical protrusion wall are simulated numerically and the influence of some parameters, such as protrusion height δ/D, and Hartmann number, are also discussed in this paper. It is found that, in the range of Hartmann number 30 ≤ Ha ≤ 70, the protrusion wall assemblies can achieve heat transfer enhancements (Nu/Nu 0 ) of about 1.3-2.3 relative to the smooth channel, while the friction loss (f/f 0 ) increases by about 1.34-1.45. Thus, the high Nusselt number can be obtained when the protrusion wall with a radically lower friction loss increase, which may help get much higher overall thermal performances.
MHD Flow Towards a Permeable Surface with Prescribed Wall Heat Flux
International Nuclear Information System (INIS)
Ishak, Anuar; Nazar, Roslinda; Pop, Ioan
2009-01-01
The steady magnetohydrodynamic (MHD) mixed convection flow towards a vertical permeable surface with prescribed heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides the solutions usually reported in the literature for the opposing fow
Physical Model Development and Benchmarking for MHD Flows in Blanket Design
Energy Technology Data Exchange (ETDEWEB)
Ramakanth Munipalli; P.-Y.Huang; C.Chandler; C.Rowell; M.-J.Ni; N.Morley; S.Smolentsev; M.Abdou
2008-06-05
An advanced simulation environment to model incompressible MHD flows relevant to blanket conditions in fusion reactors has been developed at HyPerComp in research collaboration with TEXCEL. The goals of this phase-II project are two-fold: The first is the incorporation of crucial physical phenomena such as induced magnetic field modeling, and extending the capabilities beyond fluid flow prediction to model heat transfer with natural convection and mass transfer including tritium transport and permeation. The second is the design of a sequence of benchmark tests to establish code competence for several classes of physical phenomena in isolation as well as in select (termed here as “canonical”,) combinations. No previous attempts to develop such a comprehensive MHD modeling capability exist in the literature, and this study represents essentially uncharted territory. During the course of this Phase-II project, a significant breakthrough was achieved in modeling liquid metal flows at high Hartmann numbers. We developed a unique mathematical technique to accurately compute the fluid flow in complex geometries at extremely high Hartmann numbers (10,000 and greater), thus extending the state of the art of liquid metal MHD modeling relevant to fusion reactors at the present time. These developments have been published in noted international journals. A sequence of theoretical and experimental results was used to verify and validate the results obtained. The code was applied to a complete DCLL module simulation study with promising results.
Physical Model Development and Benchmarking for MHD Flows in Blanket Design
International Nuclear Information System (INIS)
Munipalli, Ramakanth; Huang, P.-Y.; Chandler, C.; Rowell, C.; Ni, M.-J.; Morley, N.; Smolentsev, S.; Abdou, M.
2008-01-01
An advanced simulation environment to model incompressible MHD flows relevant to blanket conditions in fusion reactors has been developed at HyPerComp in research collaboration with TEXCEL. The goals of this phase-II project are two-fold: The first is the incorporation of crucial physical phenomena such as induced magnetic field modeling, and extending the capabilities beyond fluid flow prediction to model heat transfer with natural convection and mass transfer including tritium transport and permeation. The second is the design of a sequence of benchmark tests to establish code competence for several classes of physical phenomena in isolation as well as in select (termed here as 'canonical',) combinations. No previous attempts to develop such a comprehensive MHD modeling capability exist in the literature, and this study represents essentially uncharted territory. During the course of this Phase-II project, a significant breakthrough was achieved in modeling liquid metal flows at high Hartmann numbers. We developed a unique mathematical technique to accurately compute the fluid flow in complex geometries at extremely high Hartmann numbers (10,000 and greater), thus extending the state of the art of liquid metal MHD modeling relevant to fusion reactors at the present time. These developments have been published in noted international journals. A sequence of theoretical and experimental results was used to verify and validate the results obtained. The code was applied to a complete DCLL module simulation study with promising results.
Compressible gas flow through idealized cracks of large aspect ratio
International Nuclear Information System (INIS)
Chivers, T.C.; Skinner, J.; Williams, M.E.
1975-07-01
Gas flow through large aspect ratio idealized cracks is considered, where isothermal conditions with choking at exit are assumed in the theoretical analysis. For smooth wall cracks, comparisons are made between experimentally determined flowrates and those predicted, and good agreement is shown. This is followed by consideration of flow through a notional crack to examine the influence of width and surface roughness. By considering flow as simply proportional to Wsup(n), the treatment shows 'n' to reduce with W increasing, but surface roughness increases 'n' over the value appropriate to smooth conditions. From these observations it is concluded that further work is required to determine:- (i) real crack geometry and its influence on any leak-before-break philosophy, and (ii) the influence of real surface roughness on flowrate. (author)
Energy Technology Data Exchange (ETDEWEB)
Xu Zengyu [Southwestern Institute of Physics, P.O. Box 432, Chengdu, Sichuan 610041 (China)]. E-mail: xuzy@swip.ac.cn; Pan Chuanjie [Southwestern Institute of Physics, P.O. Box 432, Chengdu, Sichuan 610041 (China); Wei Wenhao [Southwestern Institute of Physics, P.O. Box 432, Chengdu, Sichuan 610041 (China); Kang Weishan [Southwestern Institute of Physics, P.O. Box 432, Chengdu, Sichuan 610041 (China)
2006-02-15
MHD phenomena in a duct flow were studied experimentally by using copper electrodes inserted into the wall of a perfectly insulated duct. The electrodes were connected using a copper wire to imitate different insulator coating imperfection conditions. The experimental results show instabilities of electric potential at the wall (surface instabilities) as well as instabilities in the pressure and velocity (bulk instabilities). The instabilities are strongly dependent on the scale of the copper wire. Three different cases were studied (at the same flow regimes, but with different electrode connections), where the potential at the duct wall is smaller, equal to or higher than the product of duct diameter 2a and transverse magnetic field B and average velocity V . MHD pressure drop {delta}P also exhibits significant changes.
International Nuclear Information System (INIS)
Kim, Hee Reyoung; Park, Jon Ho; Kim, Jong Man; Nam, Ho Yoon; Choi, Jong Hyun
2001-01-01
Magnetic field has many effects on the hydraulic pressure drop of fluids with high electrical conductivity. The theoretical solution about MHD pressure drop is sought for the uniform current density model with simplified physical geometry. Using the MHD equation in the rectangular duct of the sodium liquid flow under a transverse magnetic field, the electrical potential is sought in terms of the duct geometry and the electrical parameters of the liquid metal and duct material. By the product of the induced current inside the liquid metal and transverse magnetic field, the pressure gradients is found as a function of the duct size and the electrical conductivity of the liquid metal. The theoretically predicted pressure drop is compared with experimental results on the change of flow velocity and magnetic flux density
Exact solution for MHD flow of a generalized Oldroyd-B fluid with modified Darcy's law
International Nuclear Information System (INIS)
Khan, M.; Hayat, T.; Asghar, S.
2005-12-01
This paper deals with an exact solution for the magnetohydrodynamic (MHD) flow of a generalized Oldroyd-B fluid in a circular pipe. For the description of such a fluid, the fractional calculus approach has been used throughout the analysis. Based on modified Darcy's law for generalized Oldroyd-B fluid, the velocity field is calculated analytically. Several known solutions can be recovered as the limiting cases of our solution. (author)
Contribution to the study of rotating disc induced MHD flows
International Nuclear Information System (INIS)
Herve, P.
1983-01-01
Influence of a magnetic field on electroconductor viscous fluid flow generated by disks in rotation is studied here. Flow in rectilinear conduct is first studied, together with velocity, force and current line repartition. Then a case more general is dealt with a toroidal conduct with disk drive. The influence of electric conductivity and of the thickness of the mobile disk are detailed. Couple study leads to think to a transmission by fluid variable by magnetic field variations. At last, a radial flow with a source in the middle of it is studied with a disk rotation. Analysis of velocity and pressure evolution shows a pump effect [fr
Flow predictions for MHD channels with an approximation for three-dimensional effects
International Nuclear Information System (INIS)
Blottner, F.G.
1978-01-01
A finite-difference procedure has been formulated for predicting the flow properties across channels. A quasi-two-dimensional approach has been developed which allows the three-dimensional channel effects to be taken into account. Comparison of the numerical solutions with experimental results show that this approach is a reasonable approximation for MHD flow conditions if there is not significant merging of the wall boundary layers. The resulting code provides a technique to obtain the flow details in the symmetry plane of the channel and requires only a small amount of computer time
Numerical investigation of MHD flow with Soret and Dufour effect
Hayat, Tasawar; Nasir, Tehreem; Khan, Muhammad Ijaz; Alsaedi, Ahmed
2018-03-01
This paper describes the flow due to an exponentially curved surface subject to Soret and Dufour effects. Nonlinear velocity is considered. Exponentially curved stretchable sheet induced the flow. Fluid is electrical conducting through constant applied magnetic field. The governing flow expressions are reduced to ordinary ones and then tackled by numerical technique (Built-in-Shooting). Impacts of various flow variables on the dimensionless velocity, concentration and temperature fields are graphically presented and discussed in detail. Skin friction coefficient and Sherwood and Nusselt numbers are studied through graphs. Furthermore it is observed that Soret and Dufour variables regulate heat and mass transfer rates. It is also noteworthy that velocity decays for higher magnetic variable. Skin friction magnitude decays via curvature and magnetic variables. Also mass transfer gradient or rate of mass transport enhances for higher estimations of curvature parameter and Schmidt number.
Heat Transfer In Magnetohydrodynamic (Mhd) Couette Flow Of A ...
African Journals Online (AJOL)
component plasma. The flow is induced by two horizontal walls moving relative to each other along their common axis in the presence of a uniformly applied transverse magnetic field and the analysis made under the following assumptions: (i) ...
Unsteady MHD flow in porous media past over exponentially ...
African Journals Online (AJOL)
International Journal of Engineering, Science and Technology ... rotation and magnetic field on the flow past an exponentially accelerated vertical plate with ... Let (u, v, w) be the components of the velocity vector V. Then using the equation.
MHD shear flows with non-constant transverse magnetic field
International Nuclear Information System (INIS)
Núñez, Manuel
2012-01-01
Viscous conducting flows parallel to a fixed plate are studied. In contrast with the Hartmann setting, the problem is not linearized near a fixed transverse magnetic field, although the field tends to be transversal far from the wall. While general solutions may be formally obtained for all cases, their behavior is far more clear when the magnetic Prandtl number equals one. We consider two different instances: a fixed magnetic field at the wall, or an insulating sheet. The evolution of the flow and the magnetic field both near the plate and far from it are detailed, analyzing the possibility of reverse flow and instability of the solutions. -- Highlights: ► A conducting shear flow does not leave a transverse magnetic field invariant. ► Solutions are found for all cases, but these are more useful when kinetic and magnetic diffusivities coincide. ► Dirichlet and Neumann conditions on the magnetic field are studied. ► Reverse flow, and eventual instability, are possible.
Unsteady MHD stagnation flow over a moving wall
International Nuclear Information System (INIS)
Kumari, M.; Nath, G.
2006-01-01
The unsteady viscous stagnation flow of an electrically conducting fluid over a continuously moving wall with an applied magnetic field has been investigated when the free stream and wall velocities increase arbitrarily with time. The flow is initially (t = 0) steady and at time t > 0, it becomes unsteady. The semi-similar solution of the unsteady Navier-Stokes equations along with the energy equation governing the flow and heat transfer has been obtained numerically. Also the self-similar solution is obtained when the surface and free stream velocities vary inversely as a linear function of time. The shear stress and the heat transfer increase with time and magnetic field. The surface shear stress vanishes for certain value of the ratio of the wall velocity to the free stream velocity. (author)
Hall effects on MHD flow past an accelerated plate
Directory of Open Access Journals (Sweden)
Deka R.K.
2008-01-01
Full Text Available The simultaneous effects of rotation and Hall current on the hydromagnetic flow past an accelerated horizontal plate relative to a rotating fluid is presented. It is found that for given values of m (Hall parameter, M (Hartmann number and an imposed rotation parameter Ω satisfying Ω = M 2m/(1 + m2, the transverse motion (transverse to the main flow disappears and the fluid moves in the direction of the plate only. The effects of the parameters m, M and Ω on the axial and transverse velocity profiles are shown graphically, whereas the effects of the parameters on the skin-friction components are shown by tabular values.
On soft stability loss in rotating turbulent MHD flows
International Nuclear Information System (INIS)
Kapusta, Arkady; Mikhailovich, Boris
2014-01-01
The problem of the stability of turbulent flows of liquid metal in a cylindrical cavity against small velocity disturbances under the action of a rotating magnetic field (RMF) has been studied. The flow is considered in the induction-free approximation using the ‘external’ friction model. A system of dimensionless equations is examined in cylindrical coordinates. The results of computations performed on the basis of this mathematical model using the exchange of stabilities principle have shown a good consistency between the critical values of computed and experimental Reynolds numbers. (paper)
Unsteady MHD free convection flow and heat transfer along an ...
African Journals Online (AJOL)
Steady free convection flow of an electrically conducting fluid along an infinite vertical porous plate under Arrhenius kinetics are investigated in the presence of strong transverse magnetic field imposed perpendicularly to the plate .A similarity parameter length scale (h) as a function of time and the suction velocity are ...
Magnetic and velocity fields MHD flow of a stretched vertical ...
African Journals Online (AJOL)
Analytical solutions for heat and mass transfer by laminar flow of Newtonian, viscous, electrically conducting and heat generation/absorbing fluid on a continuously moving vertical permeable surface with buoyancy in the presence of a magnetic field and a first order chemical reaction are reported. The solutions for magnetic ...
MHD flow of a uniformly stretched vertical permeable membrane in ...
African Journals Online (AJOL)
We present a magneto - hydrodynamic flow of a uniformly stretched vertical permeable surface undergoing Arrhenius heat reaction. The analytical solutions are obtained for concentration, temperature and velocity fields using an asymptotic approximation, similar to that of Ayeni et al 2004. It is shown that the temperature ...
Influence of viscous dissipation and radiation on MHD Couette flow ...
African Journals Online (AJOL)
The overall analysis of the study of these parameters in various degrees show an increase in the velocity profile of the fluid, while radiation parameter decreases the temperature profile; viscous dissipation and Reynolds number increase the temperature profile of the fluid. Key word: Couette flow, viscous dissipation, ...
International Nuclear Information System (INIS)
Kessel, C.E.; Manickam, J.; Menard, J.E.; Jardin, S.C.; Kaye, S.M.
1999-01-01
The ARIES reactor study group has found an economically attractive ST-based reactor configuration with: A = 1.6, κ = 3.4, delta = 0.65, β = 50%, β N = 7.3, f BS = 0.95, R 0 = 3.2 meters, B t0 = 2.08 Tesla, and I P = 28.5 MA which yields a cost of electricity of approximately 80mils/kWh. MHD stability analysis finds that a broad pressure profile is optimal for wall-stabilizing the pressure driven kink modes typical of such configurations, and that wall stabilization is crucial to achieving the high β needed for an economical power plant. The 6MW high-harmonic fast wave system presently being installed on NSTX should allow real-time control of the plasma β, and in combination with NBI may permit experimental investigations of the effect of pressure profile peaking on MHD stability in the near-term. In the longer term, ejection of ions through resonant interaction with HHFW might be used to induce a controllable edge radial electric field with potentially interesting effects on edge MHD and confinement
Application of Fourier transform to MHD flow over an accelerated plate with partial-slippage
Directory of Open Access Journals (Sweden)
Salman Ahmad
2014-06-01
Full Text Available Magneto-Hydrodynamic (MHD flow over an accelerated plate is investigated with partial slip conditions. Generalized Fourier Transform is used to get the exact solution not only for uniform acceleration but also for variable acceleration. The numerical solution is obtained by using linear finite element method in space and One-Step-θ-scheme in time. The resulting discretized algebraic systems are solved by applying geometric-multigrid approach. Numerical solutions are compared with the obtained Fourier transform results. Many interesting results related with slippage and MHD effects are discussed in detail through graphical sketches and tables. Application of Dirac-Delta function is one of the main features of present work.
MHD and heat transfer benchmark problems for liquid metal flow in rectangular ducts
International Nuclear Information System (INIS)
Sidorenkov, S.I.; Hua, T.Q.; Araseki, H.
1994-01-01
Liquid metal cooling systems of a self-cooled blanket in a tokamak reactor will likely include channels of rectangular cross section where liquid metal is circulated in the presence of strong magnetic fields. MHD pressure drop, velocity distribution and heat transfer characteristics are important issues in the engineering design considerations. Computer codes for the reliable solution of three-dimensional MHD flow problems are needed for fusion relevant conditions. Argonne National Laboratory and The Efremov Institute have jointly defined several benchmark problems for code validation. The problems, described in this paper, are based on two series of rectangular duct experiments conducted at ANL; one of the series is a joint ANL/Efremov experiment. The geometries consist of variation of aspect ratio and wall thickness (thus wall conductance ratio). The transverse magnetic fields are uniform and nonuniform in the axial direction
Inclusion of pressure and flow in the KITES MHD equilibrium code
International Nuclear Information System (INIS)
Raburn, Daniel; Fukuyama, Atsushi
2013-01-01
One of the simplest self-consistent models of a plasma is single-fluid magnetohydrodynamic (MHD) equilibrium with no bulk fluid flow under axisymmetry. However, both fluid flow and non-axisymmetric effects can significantly impact plasma equilibrium and confinement properties: in particular, fluid flow can produce profile pedestals, and non-axisymmetric effects can produce islands and stochastic regions. There exist a number of computational codes which are capable of calculating equilibria with arbitrary flow or with non-axisymmetric effects. Previously, a concept for a code to calculate MHD equilibria with flow in non-axisymmetric systems was presented, called the KITES (Kyoto ITerative Equilibrium Solver) code. Since then, many of the computational modules for the KITES code have been completed, and the work-in-progress KITES code has been used to calculate non-axisymmetric force-free equilibria. Additional computational modules are required to allow the KITES code to calculate equilibria with pressure and flow. Here, the authors report on the approaches used in developing these modules and provide a sample calculation with pressure. (author)
Hall effects on unsteady MHD flow between two rotating disks with non-coincident parallel axes
Energy Technology Data Exchange (ETDEWEB)
Barik, R.N., E-mail: barik.rabinarayan@rediffmail.com [Department of Mathematics, Trident Academy of Technology, Bhubaneswar (India); Dash, G.C., E-mail: gcdash@indiatimes.com [Department of Mathematics, S.O.A. University, Bhubaneswar (India); Rath, P.K., E-mail: pkrath_1967@yahoo.in [Department of Mathematics, B.R.M. International Institute of Technology, Bhubaneswar (India)
2013-01-15
Hall effects on the unsteady MHD rotating flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes have been studied. There exists an axisymmetric solution to this problem. The governing equations are solved by applying Laplace transform method. It is found that the torque experienced by the disks decreases with an increase in either the Hall parameter, m or the rotation parameter, S{sup 2}. Further, the axis of rotation has no effect on the fluid flow. (author)
Hall effects on unsteady MHD flow between two rotating disks with non-coincident parallel axes
International Nuclear Information System (INIS)
Barik, R.N.; Dash, G.C.; Rath, P.K.
2013-01-01
Hall effects on the unsteady MHD rotating flow of a viscous incompressible electrically conducting fluid between two rotating disks with non-coincident parallel axes have been studied. There exists an axisymmetric solution to this problem. The governing equations are solved by applying Laplace transform method. It is found that the torque experienced by the disks decreases with an increase in either the Hall parameter, m or the rotation parameter, S 2 . Further, the axis of rotation has no effect on the fluid flow. (author)
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Construction program for a large superconducting MHD magnet system at the coal-fired flow facility
International Nuclear Information System (INIS)
Wang, S.T.; Genens, L.; Gonczy, J.; Ludwig, H.; Lieberg, M.; Kraft, E.; Gacek, D.; Huang, Y.C.; Chen, C.J.
1980-01-01
The Argonne National Laboratory has designed and is constructing a 6 T large aperture superconducting MHD magnet for use in the Coal-Fired Flow Facility (CFFF) at the University of Tennessee Space Institute (UTSI) at Tullahoma, Tennessee. The magnet system consists of the superconducting magnet, a magnet power supply, an integrated instrumentation for operation, control and protection, and a complete cryogenic facility including a CTI Model 2800 helium refrigerator/liquefier with two compressors, helium gas handling system and a 7500 liter liquid helium dewar. The complete system will be tested at Argonne, IL in 1981. The magnet design is reviewed, and the coil fabrication programs are described in detail
MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate
International Nuclear Information System (INIS)
Bhattacharyya, Krishnendu; Mukhopadhyay, Swati; Layek, G. C.
2011-01-01
An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate. (fundamental areas of phenomenology(including applications))
Khan, Imad; Ullah, Shafquat; Malik, M. Y.; Hussain, Arif
2018-06-01
The current analysis concentrates on the numerical solution of MHD Carreau fluid flow over a stretching cylinder under the influences of homogeneous-heterogeneous reactions. Modelled non-linear partial differential equations are converted into ordinary differential equations by using suitable transformations. The resulting system of equations is solved with the aid of shooting algorithm supported by fifth order Runge-Kutta integration scheme. The impact of non-dimensional governing parameters on the velocity, temperature, skin friction coefficient and local Nusselt number are comprehensively delineated with the help of graphs and tables.
An Optimal Homotopy Asymptotic Approach Applied to Nonlinear MHD Jeffery-Hamel Flow
Directory of Open Access Journals (Sweden)
Vasile Marinca
2011-01-01
Full Text Available A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow. This technique called the Optimal Homotopy Asymptotic Method (OHAM does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper lead to the conclusion that the accuracy of the obtained results is growing along with increasing the number of constants in the auxiliary function, which are determined using a computer technique. The results obtained through the proposed method are in very good agreement with the numerical results.
The Ekman-Hartmann layer in MHD Taylor-Couette flow
Szklarski, Jacek; Rüdiger, Günther
2007-01-01
We study magnetic effects induced by rigidly rotating plates enclosing a cylindrical MHD Taylor-Couette flow at the finite aspect ratio $H/D=10$. The fluid confined between the cylinders is assumed to be liquid metal characterized by small magnetic Prandtl number, the cylinders are perfectly conducting, an axial magnetic field is imposed $\\Ha \\approx 10$, the rotation rates correspond to $\\Rey$ of order $10^2-10^3$. We show that the end-plates introduce, besides the well known Ekman circulati...
Effect of external circuit on heat transfer in MHD Couette flow
International Nuclear Information System (INIS)
Soundalgekar, V.M.
1982-01-01
An exact solution of energy equation in fully-developed MHD Coutte flow has been derived. Temperature profiles are shown in open- and short-circuit cases. It has been observed that in short circuit case, temperature and Nusselt number (Nu) increase with increasing M, whereas in open-circuit case, with increasing M, the temperature decreases. Also in open-circuit case, Nu increases with increasing M when M is small, but at large values of M, Nu decreases with increasing M. (author)
Effects of induced magnetic field on large scale pulsed MHD generator with two phase flow
International Nuclear Information System (INIS)
Ishikawa, M.; Koshiba, Y.; Matsushita, T.
2004-01-01
A large pulsed MHD generator 'SAKHALIN' was constructed in Russia (the former Soviet-Union) and operated with solid fuels. The 'SAKHALIN' with the channel length of 4.5 m could demonstrate the electric power output of 510 MW. The effects of induced magnetic field and two phase flow on the shock wave within the 'SAKHALIN' generator have been studied by time dependent, one dimensional analyses. It has been shown that the magnetic Reynolds number is about 0.58 for Run No. 1, and the induced magnetic flux density is about 20% at the entrance and exit of the MHD channel. The shock wave becomes stronger when the induced magnetic field is taken into account, when the operation voltage becomes low. The working gas plasma contains about 40% of liquid particles (Al 2 O 3 ) in weight, and the present analysis treats the liquid particles as another gas. In the case of mono-phase flow, the sharp shock wave is induced when the load voltage becomes small such as 500 V with larger Lorentz force, whereas in the case of two phase flow, the shock wave becomes less sharp because of the interaction with liquid particles
Molokov, S. Y.; Allen, J. E.
A magnetohydrodynamic (MHD) flow of conducting fluid between two concentric insulating cylinders in strong radial magnetic field which is parallel to a free surface of a fluid is investigated by means of matched asymptotic expansions method. The flow region is divided into various subregions and leading terms of asymptotic expansions as M tends towards infinity (M is the Hartmann number) of solutions of problems governing flow in these subregions are obtained.
The Influence of Uniform Suction/Injection on Heat Transfer of MHD Hiemenz Flow in Porous Media
DEFF Research Database (Denmark)
Ghsemi, E; Soleimani, S; Barari, Amin
2012-01-01
The steady two-dimensional laminar forced magneto-hydrodynamic (MHD) Hiemenz flow against a flat plate with variable wall temperature in a porous medium is analyzed. The transformed nonlinear boundary-layer equations are solved analytically by homotopy analysis method (HAM). Results for the veloc...
MHD convective flow of magnetite-Fe3O4 nanoparticles by curved stretching sheet
Directory of Open Access Journals (Sweden)
Tasawar Hayat
Full Text Available Present work is devoted to convective flow of ferrofluid due to non linear stretching curved sheet. Electrically conducting fluid is considered in the presence of uniform magnetic field. Nanofluid comprises water and magnetite-Fe3O4 as nanoparticles. Thermal radiation and heat generation/absorption are explained. Homotopy concept is utilized for the development of solutions. Highly nonlinear partial differential systems are reduced into the nonlinear ordinary differential system. Impact of non-dimensional radius of curvature and power law index on the physical quantities like fluid pressure, velocity and temperature field are examined. Computations for surface shear stress and heat transfer rate also analyzed. Keywords: MHD nanofluid, Thermal radiation, Porous medium, Convective boundary conditions, Non-linear curved stretching sheet
Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate
Ramli, Norshafira; Ahmad, Syakila; Pop, Ioan
2017-08-01
In this study, the problem of MHD flow and heat transfer of ferrofluids over a moving flat plate with slip effect and uniform heat flux is considered. The governing ordinary differential equations are solved via shooting method. The effect of slip parameter on the dimensionless velocity, temperature, skin friction and Nusselt numbers are numerically studied for the three selected ferroparticles; magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Mn-Zn ferrite (Mn-ZnFe2O4) with water-based fluid. The results indicate that dual solutions exist for a plate moving towards the origin. It is found that the slip process delays the boundary layer separation. Moreover, the velocity and thermal boundary-layer thicknesses decrease in the first solution while increase with the increase of the value of slip parameters in second solution.
MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects
Institute of Scientific and Technical Information of China (English)
M Ramzan; M Farooq; T Hayat; A Alsaedi; J Cao
2015-01-01
Combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained. Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.
MHD from a Microscopic Concept and Onset of Turbulence in Hartmann Flow
International Nuclear Information System (INIS)
Jirkovsky, L.; Bo-ot, L. Ma.; Chiang, C. M.
2010-01-01
We derive higher order magneto-hydrodynamic (MHD) equations from a microscopic picture using projection and perturbation formalism. In an application to Hartmann flow we find velocity profiles flattening towards the center at the onset of turbulence in hydrodynamic limit. Comparison with the system under the effect of a uniform magnetic field yields difference in the onset of turbulence consistent with observations, showing that the presence of magnetic field inhibits onset of instability or turbulence. The laminar-turbulent transition is demonstrated in a phase transition plot of the development in time of the relative average velocities vs. Reynolds number showing a sharp increase of the relative average velocity at the transition point as determined by the critical Reynolds number. (physics of gases, plasmas, and electric discharges)
MHD Boundary Layer Flow of Dilatant Fluid in a Divergent Channel with Suction or Blowing
International Nuclear Information System (INIS)
Bhattacharyya, Krishnendu; Layek, G. C.
2011-01-01
An analysis is carried out to study a steady magnetohydrodynamic (MHD) boundary layer flow of an electrically conducting incompressible power-law non-Newtonian fluid through a divergent channel. The channel walls are porous and subjected to either suction or blowing of equal magnitude of the same kind of fluid on both walls. The fluid is permeated by a magnetic field produced by electric current along the line of intersection of the channel walls. The governing partial differential equation is transformed into a self-similar nonlinear ordinary differential equation using similarity transformations. The possibility of boundary layer flow in a divergent channel is analyzed with the power-law fluid model. The analysis reveals that the boundary layer flow (without separation) is possible for the case of the dilatant fluid model subjected to suitable suction velocity applied through its porous walls, even in the absence of a magnetic field. Further, it is found that the boundary layer flow is possible even in the presence of blowing for a suitable value of the magnetic parameter. It is found that the velocity increases with increasing values of the power-law index for the case of dilatant fluid. The effects of suction/blowing and magnetic field on the velocity are shown graphically and discussed physically. (fundamental areas of phenomenology(including applications))
Entropy generation minimization of a MHD (magnetohydrodynamic) flow in a microchannel
Energy Technology Data Exchange (ETDEWEB)
Ibanez, Guillermo [Universidad de Ciencias y Artes de Chiapas, Tuxtla Gutierrez, Chiapas 29000 (Mexico); Cuevas, Sergio [Centro de Investigacion en Energia, Universidad Nacional Autonoma de Mexico A.P. 34, Temixco, Mor. 62580 (Mexico)
2010-10-15
The dissipative processes that arise in a microchannel flow subjected to electromagnetic interactions, as occurs in a MHD (magnetohydrodynamic) micropump, are analyzed. The entropy generation rate is used as a tool for the assessment of the intrinsic irreversibilities present in the microchannel owing to viscous friction, heat flow and electric conduction. The flow in a parallel plate microchannel produced by a Lorentz force created by a transverse magnetic field and an injected electric current is considered assuming a thermally fully developed flow and conducting walls of finite thickness. The conjugate heat transfer problem in the fluid and solid walls is solved analytically using thermal boundary conditions of the third kind at the outer surfaces of the walls and continuity of temperature and heat flux across the fluid-wall interfaces. Velocity, temperature and current density fields in the fluid and walls are used to calculate the global entropy generation rate. Conditions under which this quantity is minimized are determined for specific values of the geometrical and physical parameters of the system. The Nusselt number is also calculated and explored for different conditions. Results can be used to determine optimized conditions that lead to a minimum dissipation consistent with the physical constraints demanded by the microdevice. (author)
International Nuclear Information System (INIS)
Samtaney, Ravi
2009-01-01
We present a numerical method to solve the linear stability of impulsively accelerated density interfaces in two dimensions such as those arising in the Richtmyer-Meshkov instability. The method uses an Eulerian approach, and is based on an unwind method to compute the temporally evolving base state and a flux vector splitting method for the perturbations. The method is applicable to either gas dynamics or magnetohydrodynamics. Numerical examples are presented for cases in which a hydrodynamic shock interacts with a single or double density interface, and a doubly shocked single density interface. Convergence tests show that the method is spatially second order accurate for smooth flows, and between first and second order accurate for flows with shocks
Numerical investigation of MHD flow of blood and heat transfer in a stenosed arterial segment
Energy Technology Data Exchange (ETDEWEB)
Majee, Sreeparna; Shit, G.C., E-mail: gcs@math.jdvu.ac.in
2017-02-15
A numerical investigation of unsteady flow of blood and heat transfer has been performed with an aim to provide better understanding of blood flow through arteries under stenotic condition. The blood is treated as Newtonian fluid and the arterial wall is considered to be rigid having deposition of plaque in its lumen. The heat transfer characteristic has been analyzed by taking into consideration of the dissipation of energy due to applied magnetic field and the viscosity of blood. The vorticity-stream function formulation has been adopted to solve the problem using implicit finite difference method by developing well known Peaceman–Rachford Alternating Direction Implicit (ADI) scheme. The quantitative profile analysis of velocity, temperature and wall shear stress as well as Nusselt number is carried out over the entire arterial segment. The streamline and temperature contours have been plotted to understand the flow pattern in the diseased artery, which alters significantly in the downstream of the stenosis in the presence of magnetic field. Both the wall shear stress and Nusselt number increases with increasing magnetic field strength. However, wall shear stress decreases and Nusselt number enhances with Reynolds number. The results show that with an increase in the magnetic field strength upto 8 T, does not causes any damage to the arterial wall, but the study is significant for assessing temperature rise during hyperthermic treatment. - Highlights: • Fully numerical simulation is carried out for MHD blood flow in stenosed artery. • Dissipation of energy due to both magnetic field and blood viscosity is considered. • Strong Vortices are observed at the downstream of the stenosis in the arterial wall. • Flow reversal of blood is reduced by applying sufficient magnetic field strength. • Isothermal lines are strongly distorted in the presence of magnetic field strength.
International Nuclear Information System (INIS)
Ahmad, Rida; Mustafa, M.; Hayat, T.; Alsaedi, A.
2016-01-01
Recent advancements in nanotechnology have led to the discovery of new generation coolants known as nanofluids. Nanofluids possess novel and unique characteristics which are fruitful in numerous cooling applications. Current work is undertaken to address the heat transfer in MHD three-dimensional flow of magnetic nanofluid (ferrofluid) over a bidirectional exponentially stretching sheet. The base fluid is considered as water which consists of magnetite–Fe 3 O 4 nanoparticles. Exponentially varying surface temperature distribution is accounted. Problem formulation is presented through the Maxwell models for effective electrical conductivity and effective thermal conductivity of nanofluid. Similarity transformations give rise to a coupled non-linear differential system which is solved numerically. Appreciable growth in the convective heat transfer coefficient is observed when nanoparticle volume fraction is augmented. Temperature exponent parameter serves to enhance the heat transfer from the surface. Moreover the skin friction coefficient is directly proportional to both magnetic field strength and nanoparticle volume fraction. - Highlights: • Nanofluid flow due to exponentially stretching sheet. • Exponentially varying surface temperature distribution is accounted. • Sparrow–Gregg type Hills (SGH) for temperature distribution exist. • Numerical values of local Nusselt number are presented. • Cooling performance of ferrofluid is superior to pure water.
Numerical analysis of MHD Casson Navier's slip nanofluid flow yield by rigid rotating disk
Rehman, Khalil Ur; Malik, M. Y.; Zahri, Mostafa; Tahir, M.
2018-03-01
An exertion is perform to report analysis on Casson liquid equipped above the rigid disk for z bar > 0 as a semi-infinite region. The flow of Casson liquid is achieve through rotation of rigid disk with constant angular frequency Ω bar . Magnetic interaction is consider by applying uniform magnetic field normal to the axial direction. The nanosized particles are suspended in the Casson liquid and rotation of disk is manifested with Navier's slip condition, heat generation/absorption and chemical reaction effects. The obtain flow narrating differential equations subject to MHD Casson nanofluid are transformed into ordinary differential system. For this purpose the Von Karman way of scheme is executed. To achieve accurate trends a computational algorithm is develop rather than to go on with usual build-in scheme. The effects logs of involved parameters, namely magnetic field parameter, Casson fluid parameter, slip parameter, thermophoresis and Brownian motion parameters on radial, tangential velocities, temperature, nanoparticles concentration, Nusselt and Sherwood numbers are provided by means of graphical and tabular structures. It is observed that both tangential and radial velocities are decreasing function of Casson fluid parameter.
MHD model of magnetosheath flow: comparison with AMPTE/IRM observations on 24 October, 1985
Directory of Open Access Journals (Sweden)
C. J. Farrugia
1998-05-01
Full Text Available We compare numerical results obtained from a steady-state MHD model of solar wind flow past the terrestrial magnetosphere with documented observations made by the AMPTE/IRM spacecraft on 24 October, 1985, during an inbound crossing of the magnetosheath. Observations indicate that steady conditions prevailed during this about 4 hour-long crossing. The magnetic shear at spacecraft entry into the magnetosphere was 15°. A steady density decrease and a concomitant magnetic field pile-up were observed during the 40 min interval just preceding the magnetopause crossing. In this plasma depletion layer (1 the plasma beta dropped to values below unity; (2 the flow speed tangential to the magnetopause was enhanced; and (3 the local magnetic field and velocity vectors became increasingly more orthogonal to each other as the magnetopause was approached (Phan et al., 1994. We model parameter variations along a spacecraft orbit approximating that of AMPTE/IRM, which was at slightly southern GSE latitudes and about 1.5 h post-noon Local Time. We model the magnetopause as a tangential discontinuity, as suggested by the observations, and take as input solar wind parameters those measured by AMPTE/IRM just prior to its bow shock crossing. We find that computed field and plasma profiles across the magnetosheath and plasma depletion layer match all observations closely. Theoretical predictions on stagnation line flow near this low-shear magnetopause are confirmed by the experimental findings. Our theory does not give, and the data on this pass do not show, any localized density enhancements in the inner magnetosheath region just outside the plasma depletion layer.Key words. Steady-state magnetosheath · Plasma depletion layer · Stagnation line flow
CFD Investigation of Flow Past Idealized Engine Nacelle Clutter
National Research Council Canada - National Science Library
Casper, Matthew S
2007-01-01
...), to resolve the flow-field dynamics inside the clutter element and determine mechanisms accounting for the failure of suppressant spray droplets from traversing the array under low-speed, free-stream conditions (ReD = 1, 575...
International Nuclear Information System (INIS)
Hayat, Tasawar; Imtiaz, Maria; Alsaedi, Ahmed; Almezal, Saleh
2016-01-01
This paper investigates the steady two-dimensional magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid over a stretching surface with homogeneous–heterogeneous reactions. Characteristics of relaxation time for heat flux are captured by employing new heat flux model proposed by Christov. A system of ordinary differential equations is obtained by using suitable transformations. Convergent series solutions are derived. Impacts of various pertinent parameters on the velocity, temperature and concentration are discussed. Analysis of the obtained results shows that fluid relaxation and retardation time constants have reverse behavior on the velocity and concentration fields. Also temperature distribution decreases for larger values of thermal relaxation time. - Highlights: • Cattaneo–Christov heat flux model is used to study the MHD flow of an Oldroyd-B fluid. • Velocity is decreasing function of Hartman number. • Increasing values of the strengths of homogeneous and heterogeneous reaction parameters decrease the wall concentration.
Directory of Open Access Journals (Sweden)
S. Mamatha Upadhya
2018-06-01
Full Text Available A Comprehensive study on laminar, magnetohydrodynamic (MHD boundary layer flow of nanofluid (water + Silver, water + Graphene embedded with conducting micrometer sized dust particles over a stretching cylinder with the incorporation of Cattaneo-Christov heat flux model is conducted. Appropriate similarity variables are employed to the flow governing equations and the resulting ordinary differential equations are solved by employing Runge-Kutta-Fehlberg method. The results for varied controlling parameters for both dusty nano fluid and dust phase are shown through graphs, table and discussed in detail. Authentication of the obtained results is provided by comparing with published results. Results indicate that Graphene + water dusty nanofluid shows better heat transfer performance compared with Silver + water dusty nanofluid. Improvement in thermal relaxation boosts temperature distribution in both fluid and dust phase. Keywords: Graphene nano particles, Silver nano particles, Stretching cylinder, Dusty fluid, Cattaneo-Christov heat flux, MHD
Ahamad, N. Ameer; Ravikumar, S.; Govindaraju, Kalimuthu
2017-07-01
The aim of the present attempt was to investigate an effect of slip and joule heating on MHD peristaltic Newtonian fluid through an asymmetric vertical tapered channel under influence of radiation. The Mathematical modeling is investigated by utilizing long wavelength and low Reynolds number assumptions. The effects of Hartmann number, porosity parameter, volumetric flow rate, radiation parameter, non uniform parameter, shift angle, Prandtl number, Brinkman number, heat source/sink parameter on temperature characteristics are presented graphically and discussed in detail.
International Nuclear Information System (INIS)
Witalis, E.A.
1965-12-01
Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given
Energy Technology Data Exchange (ETDEWEB)
Witalis, E A
1965-12-15
Rigorous derivations are given of the basic equations and methods available for the analysis of transverse MHD flow when Hall currents are not suppressed. The gas flow is taken to be incompressible and viscous with uniform tensor conductivity and arbitrary magnetic Reynold's number. The magnetic field is perpendicular to the flow and has variable strength. Analytical solutions can be obtained either in terms of the induced magnetic field or from two types of electric potential. The relevant set of suitable simplifications, restrictive conditions and boundary value considerations for each method is given.
Swarnalathamma, B. V.; Krishna, M. Veera
2017-07-01
We studied heat transfer on MHD convective flow of viscous electrically conducting heat generating/absorbing fluid through porous medium in a rotating channel under uniform transverse magnetic field normal to the channel and taking Hall current. The flow is governed by the Brinkman's model. The diagnostic solutions for the velocity and temperature are obtained by perturbation technique and computationally discussed with respect to flow parameters through the graphs. The skin friction and Nusselt number are also evaluated and computationally discussed with reference to pertinent parameters in detail.
Directory of Open Access Journals (Sweden)
Yahaya Shagaiya Daniel
2018-04-01
Full Text Available The combined effects of thermal stratification, applied electric and magnetic fields, thermal radiation, viscous dissipation and Joules heating are numerically studied on a boundary layer flow of electrical conducting nanofluid over a nonlinearly stretching sheet with variable thickness. The governing equations which are partial differential equations are converted to a couple of ordinary differential equations with suitable similarity transformation techniques and are solved using implicit finite difference scheme. The electrical conducting nanofluid particle fraction on the boundary is passively rather than actively controlled. The effects of the emerging parameters on the electrical conducting nanofluid velocity, temperature, and nanoparticles concentration volume fraction with skin friction, heat transfer characteristics are examined with the aids of graphs and tabular form. It is observed that the variable thickness enhances the fluid velocity, temperature, and nanoparticle concentration volume fraction. The heat and mass transfer rate at the surface increases with thermal stratification resulting to a reduction in the fluid temperature. Electric field enhances the nanofluid velocity which resolved the sticking effects caused by a magnetic field which suppressed the profiles. Radiative heat transfer and viscous dissipation are sensitive to an increase in the fluid temperature and thicker thermal boundary layer thickness. Comparison with published results is examined and presented. Keywords: MHD nanofluid, Variable thickness, Thermal radiation, Similarity solution, Thermal stratification
Particle simulation algorithms with short-range forces in MHD and fluid flow
International Nuclear Information System (INIS)
Cable, S.; Tajima, T.; Umegaki, K.
1992-07-01
Attempts are made to develop numerical algorithms for handling fluid flows involving liquids and liquid-gas mixtures. In these types of systems, the short-range intermolecular interactions are important enough to significantly alter behavior predicted on the basis of standard fluid mechanics and magnetohydrodynamics alone. We have constructed a particle-in-cell (PIC) code for the purpose of studying the effects of these interactions. Of the algorithms considered, the one which has been successfully implemented is based on a MHD particle code developed by Brunel et al. In the version presented here, short range forces are included in particle motion by, first, calculating the forces between individual particles and then, to prevent aliasing, interpolating these forces to the computational grid points, then interpolating the forces back to the particles. The code has been used to model a simple two-fluid Rayleigh-Taylor instability. Limitations to the accuracy of the code exist at short wavelengths, where the effects of the short-range forces would be expected to be most pronounced
Effect of Induced Magnetic Field on MHD Mixed Convection Flow in Vertical Microchannel
Jha, B. K.; Aina, B.
2017-08-01
The present work presents a theoretical investigation of an MHD mixed convection flow in a vertical microchannel formed by two electrically non-conducting infinite vertical parallel plates. The influence of an induced magnetic field arising due to motion of an electrically conducting fluid is taken into consideration. The governing equations of the motion are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field. The expressions for the induced current density and skin friction have also been obtained. The effects of various non-dimensional parameters such as rarefaction, fluid wall interaction, the Hartmann number and the magnetic Prandtl number on the velocity, the induced magnetic field, the temperature, the induced current density, and skin friction have been presented in a graphical form. It is found that the effect of the Hartmann number and magnetic Prandtl number on the induced current density is found to have a decreasing nature at the central region of the microchannel.
Shiraishi, Junya; Miyato, Naoaki; Matsunaga, Go
2016-05-10
It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle's Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas.
MHD equilibrium with toroidal rotation
International Nuclear Information System (INIS)
Li, J.
1987-03-01
The present work attempts to formulate the equilibrium of axisymmetric plasma with purely toroidal flow within ideal MHD theory. In general, the inertial term Rho(v.Del)v caused by plasma flow is so complicated that the equilibrium equation is completely different from the Grad-Shafranov equation. However, in the case of purely toroidal flow the equilibrium equation can be simplified so that it resembles the Grad-Shafranov equation. Generally one arbitrary two-variable functions and two arbitrary single variable functions, instead of only four single-variable functions, are allowed in the new equilibrium equations. Also, the boundary conditions of the rotating (with purely toroidal fluid flow, static - without any fluid flow) equilibrium are the same as those of the static equilibrium. So numerically one can calculate the rotating equilibrium as a static equilibrium. (author)
Energy Technology Data Exchange (ETDEWEB)
Smolentsev, S., E-mail: sergey@fusion.ucla.edu [University of California, Los Angeles (United States); Courtessole, C.; Abdou, M.; Sharafat, S. [University of California, Los Angeles (United States); Sahu, S. [Institute of Plasma Research (India); Sketchley, T. [University of California, Los Angeles (United States)
2016-10-15
Highlights: • Numerical studies were performed as a pre-experimental analysis to the experiment on MHD PbLi flows in a rectangular duct with a flow channel insert (FCI). • Dynamic testing of foam-based SiC foam-based CVD coated FCI has been performed using MaPLE facility at UCLA. • Two physical models were proposed to explain the experimental results and 3D and 2D computations performed using COMSOL, HIMAG and UCLA codes. • The obtained results suggest that more work on FCI development, fabrication and testing has to be done to assure good hermetic properties before the implementation in a fusion device. - Abstract: A flow channel insert (FCI) is the key element of the DCLL blanket concept. The FCI serves as electrical and thermal insulator to reduce the MHD pressure drop and to decouple the temperature-limited ferritic structure from the flowing hot lead-lithium (PbLi) alloy. The main focus of the paper is on numerical computations to simulate MHD flows in the first experiments on PbLi flows in a stainless steel rectangular duct with a foam-based silicon carbide (SiC) FCI. A single uninterrupted long-term (∼6500 h) test has recently been performed on a CVD coated FCI sample in the flowing PbLi in a magnetic field up to 1.5 T at the PbLi temperature of 300 °C using the MaPLE loop at UCLA. An unexpectedly high MHD pressure drop measured in this experiment suggests that a PbLi ingress into the FCI occurred in the course of the experiment, resulting in degradation of electroinsulating FCI properties. The ingress through the protective CVD layer was further confirmed by the post-experimental microscopic analysis of the FCI. The numerical modeling included 2D and 3D computations using HIMAG, COMSOL and a UCLA research code to address important flow features associated with the FCI finite length, fringing magnetic field, rounded FCI corners and also to predict changes in the MHD pressure drop in the unwanted event of a PbLi ingress. Two physical
Surface wave propagation in an ideal Hall-magnetohydrodynamic plasma jet in flowing environment
International Nuclear Information System (INIS)
Sikka, Himanshu; Kumar, Nagendra; Zhelyazkov, Ivan
2004-01-01
The behavior of the Hall-magnetohydrodynamic (Hall-MHD) sausage and kink waves is studied in the presence of steady flow. The influence of the flow both inside and outside the plasma slab is taken into account. The plasma in the environment is considered to be cold and moves with the different flow velocity outside the slab. In the limit of parallel propagation, dispersion relation is derived to discuss the propagation of both the modes. Numerical results for the propagation characteristics are obtained for different Alfvenic Mach number ratios inside and outside the slab. It is found that the dispersion curves for both surface modes, namely, the sausage and kink ones in cold plasma show complexities in their behavior in terms of multivalued portions of the curves. These multivalued portions correspond to the different normalized phase velocities for the same value of Alfvenic Mach number. In contrast to the conventional MHD surface waves which are assumed to be pure surface waves or pseudosurface waves, surface waves are obtained which are bulk waves for very small dimensionless wave numbers, then turn to leaky waves and finally transform to pure surface waves for values of dimensionless wave number greater than one
Effect of toroidal plasma flow and flow shear on global MHD modes
International Nuclear Information System (INIS)
Chu, M.S.; Greene, J.M.; Jensen, T.H.; Miller, R.L.; Bondeson, A.; Johnson, R.W.; Mauel, M.E.
1995-01-01
The effect of a subsonic toroidal flow on the linear magnetohydrodynamic stability of a tokamak plasma surrounded by an external resistive wall is studied. A complex non-self-adjoint eigenvalue problem for the stability of general kink and tearing modes is formulated, solved numerically, and applied to high β tokamaks. Results indicate that toroidal plasma flow, in conjunction with dissipation in the plasma, can open a window of stability for the position of the external wall. In this window, stable plasma beta values can significantly exceed those predicted by the Troyon scaling law with no wall. Computations utilizing experimental data indicate good agreement with observations
Relaxation with high-speed plasma flows and singularity analysis in MHD equilibrium
International Nuclear Information System (INIS)
Shiraishi, Junya; Ohsaki, Shuichi; Yoshida, Zensho
2004-01-01
Relaxation model that leads to plasma confinement with rigid-rotation is presented. This model applies to Jupiter's magnetosphere. It is shown that the invariance of canonical angular momentum of electron fluid, which is realized by axisymmetry through self-organization process, yields plasma confinement. including poloidal flows in equilibrium equation makes the problem rather complicated. Singularity due to the poloidal flow is focused on. It is shown that the singular equation for equilibrium has the same structure as the equation for linear Alfven wave. Since the singular solution for equilibrium equation is physically inadequate, the singularity may be removed by another physical effect. The Hall-effect is taken into account as a singular perturbation that removes the singularity of equilibrium equation for ideal magnetohydrodynamics. (author)
International Nuclear Information System (INIS)
McCarthy, K.A.; Abdou, M.A.
1991-01-01
A computationally fast and efficient method for analyzing MHD flow at high Hartmann number and interaction parameter is presented and used to analyze a multiple duct geometry. This type of geometry is of practical interest in fusion applications. Because the Hartmann number and interaction parameter are generally large in fusion applications, the inertial and viscous terms in the Navier-Stokes equation can often be neglected in the core flow region, making this equation linear. In addition, because the magnetic fields in a fusion reactor vary slowly and the magnetic Reynolds number is small, the induced magnetic field can be neglected. The resulting equations representing core flow have certain characteristics which make it possible to reduce them to two dimensional without losing the three dimensional characteristics. The method which has been developed is an 'iterative' method. A velocity profile is assumed, then Ohm's law and the current conservation equation are combined and used to solve for the potential distribution in a plane in the fluid, and in a surface in the duct wall. The potential variation along magnetic field lines is checked, and if necessary, the velocities are adjusted. This procedure is repeated until the potentials along field lines vary to within a specified error. The analysis of the multiple duct geometry shows the importance of global effects. The results of two basic cases are presented. In the first, the average velocity in each duct is the same, but the wall conductance ratios of the walls perpendicular to the magnetic field vary from duct to duct. The total pressure drop in the electrically connected ducts was greater than or equal to the total pressure drop in the same ducts electrically isolated. In addition, the velocity profile in the ducts can be significantly affected by the presence of neighboring ducts. (orig./AH)
Shoaib Anwar, Muhammad; Rasheed, Amer
2017-07-01
Heat transfer through a Forchheimer medium in an unsteady magnetohydrodynamic (MHD) developed differential-type fluid flow is analyzed numerically in this study. The boundary layer flow is modeled with the help of the fractional calculus approach. The fluid is confined between infinite parallel plates and flows by motion of the plates in their own plane. Both the plates have variable surface temperature. Governing partial differential equations with appropriate initial and boundary conditions are solved by employing a finite-difference scheme to discretize the fractional time derivative and finite-element discretization for spatial variables. Coefficients of skin friction and local Nusselt numbers are computed for the fractional model. The flow behavior is presented for various values of the involved parameters. The influence of different dimensionless numbers on skin friction and Nusselt number is discussed by tabular results. Forchheimer medium flows that involve catalytic converters and gas turbines can be modeled in a similar manner.
Directory of Open Access Journals (Sweden)
M.M. Bhatti
2016-06-01
Full Text Available In this article, the simultaneous effects of slip and Magnetohydrodynamics (MHD on peristaltic blood flow of Jeffrey fluid model have been investigated in a non-uniform porous channel. The governing equation of blood flow for Jeffrey fluid model is solved with the help of long wavelength and creeping flow regime. The solution of the resulting differential equation is solved analytically and a closed form solution is presented. The impact of all the physical parameters is plotted for velocity profile and pressure rise. Nowadays, Magnetohydrodynamics is applicable in various magnetic drug targeting for cancer diseases and also very helpful to control the flow. The present analysis is also described for Newtonian fluid (λ1→0 as a special case of our study. It is observed that magnitude of the velocity is opposite near the walls due to slip effects whereas similar behavior has been observed for magnetic field.
Krishna, M. Veera; Swarnalathamma, B. V.
2017-07-01
We considered the transient MHD flow of a reactive second grade fluid through porous medium between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The governing equations are solved by Laplace transform technique. The effects of the pertinent parameters on the velocity, temperature are discussed in detail. The shear stress and Nusselt number at the plates are also obtained analytically and computationally discussed with reference to governing parameters.
Raju, R. Srinivasa; Ramesh, K.
2018-05-01
The purpose of this work is to study the grid independence of finite element method on MHD Casson fluid flow past a vertically inclined plate filled in a porous medium in presence of chemical reaction, heat absorption, an external magnetic field and slip effect has been investigated. For this study of grid independence, a mathematical model is developed and analyzed by using appropriate mathematical technique, called finite element method. Grid study discussed with the help of numerical values of velocity, temperature and concentration profiles in tabular form. avourable comparisons with previously published work on various special cases of the problem are obtained.
International Nuclear Information System (INIS)
Inoue, Akira; Aritomi, Masanori; Takahashi, Minoru; Matsuzaki, Mitsuo; Narita, Yoshihito; Yano, Toshikazu.
1987-01-01
Pressure drop and heat transfer coefficient of helium-lithium annular-mist flow in a rectangular duct were investigated experimentally under a transverse magnetic field at system pressure of 0.2 MPa. A ratio of MHD pressure drop to that of non-magnetic field increases with magnetic flux density and a mass flow rate ratio of lithium to helium in low helium velocity region. However, as increasing the helium velocity, the increment of MHD pressure drop with the magnetic flux density is much reduced and then becomes almost zero. At this condition, the MHD pressure drop of the annular-mist flow becomes much smaller than that of lithium single phase flow with the same lithium mass flow at the high magnetic flux density. Heat transfer coefficient ratio of the helium-lithium annular-mist flow to helium single phase in the non-magnetic field is well correlated by a ratio of the mass flow rate of lithium to helium. The heat transfer coefficient in the magnetic field increases with the magnetic flux density and then terminates at a certain value depending on the mass flow rate ratio and the helium velocity. These characteristics of the MHD pressure drop and the heat transfer in the magnetic field suggest that the helium-lithium annular-mist flow is effectively applicable to cooling of the high heat flux wall in a strong magnetic field like a first wall of a magnetic confinement fusion reactors. (author)
MHD flow of Powell-Eyring nanofluid over a non-linear stretching sheet with variable thickness
Directory of Open Access Journals (Sweden)
T. Hayat
Full Text Available This research explores the magnetohydrodynamic (MHD boundary layer flow of Powell-Eyring nanofluid past a non-linear stretching sheet of variable thickness. An electrically conducting fluid is considered under the characteristics of magnetic field applied transverse to the sheet. The mathematical expressions are accomplished via boundary layer access, Brownian motion and thermophoresis phenomena. The flow analysis is subjected to a recently established conditions requiring zero nanoparticles mass flux. Adequate transformations are implemented for the reduction of partial differential systems to the ordinary differential systems. Series solutions for the governing nonlinear flow of momentum, temperature and nanoparticles concentration have been executed. Physical interpretation of numerous parameters is assigned by graphical illustrations and tabular values. Moreover the numerical data of drag coefficient and local heat transfer rate are executed and discussed. It is investigated that higher wall thickness parameter results in the reduction of velocity distribution. Effects of thermophoresis parameter on temperature and concentration profiles are qualitatively similar. Both the temperature and concentration profiles are enhanced for higher values of thermophoresis parameter. Keywords: MHD, Variable thicked surface, Powell-Eyring nanofluid, Zero mass flux conditions
Directory of Open Access Journals (Sweden)
Nor Athirah Mohd Zin
Full Text Available In this article, the influence of thermal radiation on unsteady magnetohydrodynamics (MHD free convection flow of rotating Jeffrey nanofluid passing through a porous medium is studied. The silver nanoparticles (AgNPs are dispersed in the Kerosene Oil (KO which is chosen as conventional base fluid. Appropriate dimensionless variables are used and the system of equations is transformed into dimensionless form. The resulting problem is solved using the Laplace transform technique. The impact of pertinent parameters including volume fraction Ï, material parameters of Jeffrey fluid Î»1, Î», rotation parameter r, Hartmann number Ha, permeability parameter K, Grashof number Gr, Prandtl number Pr, radiation parameter Rd and dimensionless time t on velocity and temperature profiles are presented graphically with comprehensive discussions. It is observed that, the rotation parameter, due to the Coriolis force, tends to decrease the primary velocity but reverse effect is observed in the secondary velocity. It is also observed that, the Lorentz force retards the fluid flow for both primary and secondary velocities. The expressions for skin friction and Nusselt number are also evaluated for different values of emerging parameters. A comparative study with the existing published work is provided in order to verify the present results. An excellent agreement is found. Keywords: Jeffrey nanofluid, AgNPs, MHD and Porosity, Rotating flow, Laplace transform technique
Proceedings of the workshop on nonlinear MHD and extended MHD
International Nuclear Information System (INIS)
1998-01-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database
Proceedings of the workshop on nonlinear MHD and extended MHD
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-12-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.
Directory of Open Access Journals (Sweden)
Farhad Ali
2013-01-01
on free convection unsteady magnetohydrodynamic (MHD flow of viscous fluid embedded in a porous medium is presented. The flow in the fluid is induced due to uniform motion of the plate. The dimensionless coupled linear partial differential equations are solved by using Laplace transform method. The solutions that have been obtained are expressed in simple forms in terms of elementary function exp(· and complementary error function erfc(·. They satisfy the governing equations; all imposed initial and boundary conditions and can immediately be reduced to their limiting solutions. The influence of various embedded flow parameters such as the Hartmann number, permeability parameter, Grashof number, dimensionless time, Prandtl number, chemical reaction parameter, Schmidt number, and Soret number is analyzed graphically. Numerical solutions for skin friction, Nusselt number, and Sherwood number are also obtained in tabular forms.
Directory of Open Access Journals (Sweden)
Uday Singh Rajput
2017-11-01
Full Text Available Effects of rotation and radiation on unsteady MHD flow past a vertical plate with variable wall temperature and mass diffusion in the presence of Hall current is studied here. Earlier we studied chemical reaction effect on unsteady MHD flow past an exponentially accelerated inclined plate with variable temperature and mass diffusion in the presence of Hall current. We had obtained the results which were in agreement with the desired flow phenomenon. To study further, we are changing the model by considering radiation effect on fluid, and changing the geometry of the model. Here in this paper we are taking the plate positioned vertically upward and rotating with velocity Ω . Further, medium of the flow is taken as porous. The plate temperature and the concentration level near the plate increase linearly with time. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations under consideration have been solved by Laplace transform technique. The model contains equations of motion, diffusion equation and equation of energy. To analyze the solution of the model, desirable sets of the values of the parameters have been considered. The governing equations involved in the flow model are solved by the Laplace-transform technique. The results obtained have been analyzed with the help of graphs drawn for different parameters. The numerical values obtained for the drag at boundary and Nusselt number have been tabulated. We found that the values obtained for velocity, concentration and temperature are in concurrence with the actual flow of the fluid
Elms: MHD Instabilities at the transport barrier
Energy Technology Data Exchange (ETDEWEB)
Huysmans, G.T.A
2005-07-01
Significant progress has been made in recent years both on the experimental characterisation of ELMs (edge localized modes) and the theory and modelling of ELMs. The observed maximum pressure gradient is in good agreement with the calculated ideal MHD stability limits due to peeling-ballooning modes. The dependence on plasma current and plasma shape are also reproduced by the ideal MHD model. It will be a challenge to verify experimentally the influence of the extensions to the ideal MHD theory such as the possibly incomplete diamagnetic stabilisation, the influence of shear flow, finite resistivity or the stabilizing influence of the separatrix on peeling modes. The observations of the filamentary structures find their explanation in the theory and simulations of the early non-linear phase of the evolution of ballooning modes. One of the remaining open questions is what determines the size of the ELM and its duration. This is related to the loss mechanism of energy and density. Some heuristic descriptions of possible mechanisms have been proposed in literature but none of the models so far makes quantitative predictions on the ELM size. Also the numerical simulations are not yet advanced to the point where the full ELM crash can be modelled. The theory and simulations of the ELMs are necessary to decide between the possible parameters, such as the collisionality or the parallel transport time, that are proposed for the extrapolation of ELM sizes to ITER.
Elms: MHD Instabilities at the transport barrier
International Nuclear Information System (INIS)
Huysmans, G.T.A.
2005-01-01
Significant progress has been made in recent years both on the experimental characterisation of ELMs (edge localized modes) and the theory and modelling of ELMs. The observed maximum pressure gradient is in good agreement with the calculated ideal MHD stability limits due to peeling-ballooning modes. The dependence on plasma current and plasma shape are also reproduced by the ideal MHD model. It will be a challenge to verify experimentally the influence of the extensions to the ideal MHD theory such as the possibly incomplete diamagnetic stabilisation, the influence of shear flow, finite resistivity or the stabilizing influence of the separatrix on peeling modes. The observations of the filamentary structures find their explanation in the theory and simulations of the early non-linear phase of the evolution of ballooning modes. One of the remaining open questions is what determines the size of the ELM and its duration. This is related to the loss mechanism of energy and density. Some heuristic descriptions of possible mechanisms have been proposed in literature but none of the models so far makes quantitative predictions on the ELM size. Also the numerical simulations are not yet advanced to the point where the full ELM crash can be modelled. The theory and simulations of the ELMs are necessary to decide between the possible parameters, such as the collisionality or the parallel transport time, that are proposed for the extrapolation of ELM sizes to ITER
International Nuclear Information System (INIS)
Yamamoto, Yoshinobu; Kunugi, Tomoaki
2015-01-01
Graphical abstract: - Highlights: • For the first time, the MHD heat transfer DNS database corresponding to the typical nondimensional parameters of the fusion blanket design using molten salt, were established. • MHD heat transfer correlation was proposed and about 20% of the heat transfer degradation was evaluated under the design conditions. • The contribution of the turbulent diffusion to heat transfer is increased drastically with increasing Hartmann number. - Abstract: The high-Prandtl number passive scalar transport of the turbulent channel flow imposed a wall-normal magnetic field is investigated through the large-scale direct numerical simulation (DNS). All essential turbulence scales of velocities and temperature are resolved by using 2048 × 870 × 1024 computational grid points in stream, vertical, and spanwise directions. The heat transfer phenomena for a Prandtl number of 25 were observed under the following flow conditions: the bulk Reynolds number of 14,000 and Hartman number of up to 28. These values were equivalent to the typical nondimensional parameters of the fusion blanket design proposed by Wong et al. As a result, a high-accuracy DNS database for the verification of magnetohydrodynamic turbulent heat transfer models was established for the first time, and it was confirmed that the heat transfer correlation for a Prandtl number of 5.25 proposed by Yamamoto and Kunugi was applicable to the Prandtl number of 25 used in this study
Energy Technology Data Exchange (ETDEWEB)
Yamamoto, Yoshinobu, E-mail: yamamotoy@yamanashi.ac.jp [Department of Mechanical Systems Engineering, University of Yamanashi, 4-3-11 Takeda, Kofu 400-8511 (Japan); Kunugi, Tomoaki [Department of Nuclear Engineering, Kyoto University Yoshida, Sakyo, Kyoto 606-8501 (Japan)
2015-01-15
Graphical abstract: - Highlights: • For the first time, the MHD heat transfer DNS database corresponding to the typical nondimensional parameters of the fusion blanket design using molten salt, were established. • MHD heat transfer correlation was proposed and about 20% of the heat transfer degradation was evaluated under the design conditions. • The contribution of the turbulent diffusion to heat transfer is increased drastically with increasing Hartmann number. - Abstract: The high-Prandtl number passive scalar transport of the turbulent channel flow imposed a wall-normal magnetic field is investigated through the large-scale direct numerical simulation (DNS). All essential turbulence scales of velocities and temperature are resolved by using 2048 × 870 × 1024 computational grid points in stream, vertical, and spanwise directions. The heat transfer phenomena for a Prandtl number of 25 were observed under the following flow conditions: the bulk Reynolds number of 14,000 and Hartman number of up to 28. These values were equivalent to the typical nondimensional parameters of the fusion blanket design proposed by Wong et al. As a result, a high-accuracy DNS database for the verification of magnetohydrodynamic turbulent heat transfer models was established for the first time, and it was confirmed that the heat transfer correlation for a Prandtl number of 5.25 proposed by Yamamoto and Kunugi was applicable to the Prandtl number of 25 used in this study.
A stationary bulk planar ideal flow solution for the double shearing model
Lyamina, E. A.; Kalenova, N. V.; Date, P. P.
2018-04-01
This paper provides a general ideal flow solution for the double shearing model of pressure-dependent plasticity. This new solution is restricted to a special class of stationary planar flows. A distinguished feature of this class of solutions is that one family of characteristic lines is straight. The solution is analytic. The mapping between Cartesian and principal lines based coordinate systems is given in parametric form with characteristic coordinates being the parameters. A simple relation that connects the scale factor for one family of coordinate curves of the principal lines based coordinate system and the magnitude of velocity is derived. The original ideal flow theory is widely used as the basis for inverse methods for the preliminary design of metal forming processes driven by minimum plastic work. The new theory extends this area of application to granular materials.
Directory of Open Access Journals (Sweden)
A.M. Rashad
2017-04-01
Full Text Available The present study explores the impact of anistropic slip on transient three dimensional MHD flow of Cobalt-kerosene ferrofluid over an inclined radiate stretching surface. The governing partial differential equations for this study are solved by the Thomas algorithm with finite-difference type. The impacts of several significant parameters on flow and heat transfer characteristics are exhibited graphically. The conclusion is revealed that the local Nusselt number is significantly promoted due to influence of thermal radiation whereas diminished with elevating the solid volume fraction, magnet parameter and slip factors. Further, the skin friction coefficients visualizes a considerable enhancement with boosting the magnet and radiation parameters, but a prominent reduction is recorded by elevating the solid volume fraction and slip factors.
Directory of Open Access Journals (Sweden)
A. Sami Bataineh
2016-09-01
Full Text Available In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein polynomials with their operational matrices and collocation method. Under some regularity conditions, upper bounds of the absolute errors are given. We apply the residual correction procedure which may estimate the absolute error to the problem. We may estimate the absolute error by using a procedure depends on the sequence of the approximate solutions. For some certain cases, we apply the method to the problem in the numerical examples. Moreover, we test the impact of changing the flow parameters numerically. The results are consistent with the results of Runge-Kutta fourth order method and homotopy analysis method.
Ferdows, M.; Khan, M.S.; Alam, M.M.; Sun, S.
2012-01-01
Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed. 2012 M. Ferdows et al.
Mamatha Upadhya, S.; Raju, C. S. K.; Saleem, S.; Alderremy, A. A.; Mahesha
2018-06-01
A Comprehensive study on laminar, magnetohydrodynamic (MHD) boundary layer flow of nanofluid (water + Silver, water + Graphene) embedded with conducting micrometer sized dust particles over a stretching cylinder with the incorporation of Cattaneo-Christov heat flux model is conducted. Appropriate similarity variables are employed to the flow governing equations and the resulting ordinary differential equations are solved by employing Runge-Kutta-Fehlberg method. The results for varied controlling parameters for both dusty nano fluid and dust phase are shown through graphs, table and discussed in detail. Authentication of the obtained results is provided by comparing with published results. Results indicate that Graphene + water dusty nanofluid shows better heat transfer performance compared with Silver + water dusty nanofluid. Improvement in thermal relaxation boosts temperature distribution in both fluid and dust phase.
Rubab, Khansa; Mustafa, M
2016-01-01
This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.
Ideal flow theory for the double - shearing model as a basis for metal forming design
Alexandrov, S.; Trung, N. T.
2018-02-01
In the case of Tresca’ solids (i.e. solids obeying the Tresca yield criterion and its associated flow rule) ideal flows have been defined elsewhere as solenoidal smooth deformations in which an eigenvector field associated everywhere with the greatest principal stress (and strain rate) is fixed in the material. Under such conditions all material elements undergo paths of minimum plastic work, a condition which is often advantageous for metal forming processes. Therefore, the ideal flow theory is used as the basis of a procedure for the preliminary design of such processes. The present paper extends the theory of stationary planar ideal flow to pressure dependent materials obeying the double shearing model and the double slip and rotation model. It is shown that the original problem of plasticity reduces to a purely geometric problem. The corresponding system of equations is hyperbolic. The characteristic relations are integrated in elementary functions. In regions where one family of characteristics is straight, mapping between the principal lines and Cartesian coordinates is determined by linear ordinary differential equations. An illustrative example is provided.
Multi-region relaxed magnetohydrodynamics with flow
Energy Technology Data Exchange (ETDEWEB)
Dennis, G. R., E-mail: graham.dennis@anu.edu.au; Dewar, R. L.; Hole, M. J. [Research School of Physics and Engineering, Australian National University, ACT 0200 (Australia); Hudson, S. R. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States)
2014-04-15
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes plasma flow. This new model is a generalization of Woltjer's model of relaxed magnetohydrodynamics equilibria with flow. We prove that as the number of plasma regions becomes infinite, our extension of MRxMHD reduces to ideal MHD with flow. We also prove that some solutions to MRxMHD with flow are not time-independent in the laboratory frame, and instead have 3D structure which rotates in the toroidal direction with fixed angular velocity. This capability gives MRxMHD potential application to describing rotating 3D MHD structures such as 'snakes' and long-lived modes.
Numerical investigation of the LM MHD flows in a curved duct with an FCI with varying slot locations
International Nuclear Information System (INIS)
Yang, Jong Hoon; Yan, Yue; Kim, Chang Nyung
2016-01-01
Highlights: • This study numerically investigates the liquid-metal magnetohydrodynamic flows in a curved duct with an FCI. • The effects of the location of FCI slot and of the curvature radius on the flow behavior are reviewed. • The influence of the FCI slot position on the equalization of the pressure in the inner fluid region (inside the FCI) and the gap fluid region (outer the FCI) is examined. - Abstract: This study numerically investigates the liquid-metal (LM) magnetohydrodynamic (MHD) flows in a curved duct with an FCI having three different slot locations and having no slot under a uniform magnetic field perpendicular to the duct. The flow velocity, current density, electric potential, Lorentz force, and pressure in different flow situations are presented in detail. The effects of the location of FCI slot and of the curvature radius on the flow behavior are reviewed. The flow field is examined with an introduction of the electric-field component and electro-motive component of the current, allowing us to analyze the interdependency of the flow variables. The effect of the FCI slot position on the equalization of the pressure in the inner fluid region (inside the FCI) and the gap fluid region (outer the FCI) is examined. The result shows that and the case with an FCI slot located in the neutral position yields the smallest pressure gradient in the main flow direction among the cases with an FCI slot, resulting in the smallest pressure drop. Also, in a flow situation with smaller radius of curvature with the FCI slot in the neutral position, the axial velocity near the inner (in terms of the curvature) part of a cross-section is higher than that near the outer part.
International Nuclear Information System (INIS)
D'Arcy, D.
1977-08-01
Trays with multiple box downcomers are often used in chemical process plants nowadays. In order to make a theoretical assessment of the mass transfer efficiency of such trays, knowledge is needed of the time spent by the liquid at various parts of the tray. An idealized but reasonable flow pattern has been assumed and the local velocities and transit times along ten equally-spaced stream lines have been computed. Numerical and graphical results are presented. (author)
Wind energy: an application of Bernoulli's theorem generalized to isentropic flow of ideal gases
International Nuclear Information System (INIS)
De Luca, R; Desideri, P
2013-01-01
By considering the extension of Bernoulli's theorem to the case of the isentropic flow of ideal gases we conceive a small-scale wind–energy system able to work in the presence of low wind velocities in any direction. The flow of air inside a hyperbolically shaped pipe is studied using elementary physics concepts. The results obtained show that wind velocity in the system increases for decreasing cross-sectional areas, allowing a lower cut-in wind speed and an increase in the annual energy production of the device. (paper)
On the accuracy of Whitham's method. [for steady ideal gas flow past cones
Zahalak, G. I.; Myers, M. K.
1974-01-01
The steady flow of an ideal gas past a conical body is studied by the method of matched asymptotic expansions and by Whitham's method in order to assess the accuracy of the latter. It is found that while Whitham's method does not yield a correct asymptotic representation of the perturbation field to second order in regions where the flow ahead of the Mach cone of the apex is disturbed, it does correctly predict the changes of the second-order perturbation quantities across a shock (the first-order shock strength). The results of the analysis are illustrated by a special case of a flat, rectangular plate at incidence.
Complex blood flow patterns in an idealized left ventricle: A numerical study
Tagliabue, Anna; Dedè, Luca; Quarteroni, Alfio
2017-09-01
In this paper, we study the blood flow dynamics in a three-dimensional (3D) idealized left ventricle of the human heart whose deformation is driven by muscle contraction and relaxation in coordination with the action of the mitral and aortic valves. We propose a simplified but realistic mathematical treatment of the valves function based on mixed time-varying boundary conditions (BCs) for the Navier-Stokes equations modeling the flow. These switchings in time BCs, from natural to essential and vice versa, model either the open or the closed configurations of the valves. At the numerical level, these BCs are enforced by means of the extended Nitsche's method (Tagliabue et al., Int. J. Numer. Methods Fluids, 2017). Numerical results for the 3D idealized left ventricle obtained by means of Isogeometric Analysis are presented, discussed in terms of both instantaneous and phase-averaged quantities of interest and validated against those available in the literature, both experimental and computational. The complex blood flow patterns are analysed to describe the characteristic fluid properties, to show the transitional nature of the flow, and to highlight its main features inside the left ventricle. The sensitivity of the intraventricular flow patterns to the mitral valve properties is also investigated.
Directory of Open Access Journals (Sweden)
Mohammad Mehdi Rashidi
2010-01-01
Full Text Available The purpose of this study is to approximate the stream function and temperature distribution of the MHD flow in a laminar liquid film from a horizontal stretching surface. In this paper DTM-Padé method was used which is a combination of differential transform method (DTM and Padé approximant. The DTM solutions are only valid for small values of independent variables. Comparison between the solutions obtained by the DTM and the DTM-Padé with numerical solution (fourth-order Runge–Kutta revealed that the DTM-Padé method is an excellent method for solving MHD boundary-layer equations.
Directory of Open Access Journals (Sweden)
R. N. Barik
2013-09-01
Full Text Available An analysis is made to study the effects of diffusion-thermo and chemical reaction on fully developed laminar MHD flow of electrically conducting viscous incompressible fluid in a vertical channel formed by two vertical parallel plates was taken into consideration with uniform temperature and concentration. The analytical solution by Laplace transform technique of partial differential equations is used to obtain the expressions for the velocity, temperature and concentration. It is interesting to note that during the course of computation, the transient solution at large time coincides with steady state solution derived separately and the diffusion-thermo effect creates an anomalous situation in temperature and velocity profiles for small Prandtl numbers. The study is restricted to only destructive reaction and non-conducting case cannot be derived as a particular case still it is quite interesting and more realistic than the earlier one.
Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.
2017-06-01
Unsteady MHD free convection flow past a vertical porous plate in porous medium with radiation, diffusion thermo, thermal diffusion and heat source are analyzed. The governing non-linear, partial differential equations are transformed into dimensionless by using non-dimensional quantities. Then the resultant dimensionless equations are solved numerically by applying an efficient, accurate and conditionally stable finite difference scheme of explicit type with the help of a computer programming language Compaq Visual Fortran. The stability and convergence analysis has been carried out to establish the effect of velocity, temperature, concentration, skin friction, Nusselt number, Sherwood number, stream lines and isotherms line. Finally, the effects of various parameters are presented graphically and discussed qualitatively.
Numerical modelling of flow structures over idealized transverse aeolian dunes of varying geometry
Parsons, Daniel R.; Walker, Ian J.; Wiggs, Giles F. S.
2004-04-01
A Computational Fluid Dynamics (CFD) model (PHOENICS™ 3.5) previously validated for wind tunnel measurements is used to simulate the streamwise and vertical velocity flow fields over idealized transverse dunes of varying height ( h) and stoss slope basal length ( L). The model accurately reproduced patterns of: flow deceleration at the dune toe; stoss flow acceleration; vertical lift in the crest region; lee-side flow separation, re-attachment and reversal; and flow recovery distance. Results indicate that the flow field over transverse dunes is particularly sensitive to changes in dune height, with an increase in height resulting in flow deceleration at the toe, streamwise acceleration and vertical lift at the crest, and an increase in the extent of, and strength of reversed flows within, the lee-side separation cell. In general, the length of the separation zone varied from 3 to 15 h from the crest and increased over taller, steeper dunes. Similarly, the flow recovery distance ranged from 45 to >75 h and was more sensitive to changes in dune height. For the range of dune shapes investigated in this study, the differing effects of height and stoss slope length raise questions regarding the applicability of dune aspect ratio as a parameter for explaining airflow over transverse dunes. Evidence is also provided to support existing research on: streamline curvature and the maintenance of sand transport in the toe region; vertical lift in the crest region and its effect on grainfall delivery; relations between the turbulent shear layer and downward forcing of flow re-attachment; and extended flow recovery distances beyond the separation cell. Field validation is required to test these findings in natural settings. Future applications of the model will characterize turbulence and shear stress fields, examine the effects of more complex isolated dune forms and investigate flow over multiple dunes.
Doubly stratified MHD tangent hyperbolic nanofluid flow due to permeable stretched cylinder
Nagendramma, V.; Leelarathnam, A.; Raju, C. S. K.; Shehzad, S. A.; Hussain, T.
2018-06-01
An investigation is exhibited to analyze the presence of heat source and sink in doubly stratified MHD incompressible tangent hyperbolic fluid due to stretching of cylinder embedded in porous space under nanoparticles. To develop the mathematical model of tangent hyperbolic nanofluid, movement of Brownian and thermophoretic are accounted. The established equations of continuity, momentum, thermal and solutal boundary layers are reassembled into sets of non-linear expressions. These assembled expressions are executed with the help of Runge-Kutta scheme with MATLAB. The impacts of sundry parameters are illustrated graphically and the engineering interest physical quantities like skin friction, Nusselt and Sherwood number are examined by computing numerical values. It is clear that the power-law index parameter and curvature parameter shows favorable effect on momentum boundary layer thickness whereas Weissennberg number reveals inimical influence.
Chemical reaction in MHD flow past a vertical plate with mass ...
African Journals Online (AJOL)
flow in a vertical double passage channel using Robin boundary conditions. ... the diffusion of a chemically reactive species in a laminar boundary layer flow. ...... hydrodynamic flow past a flat plate will Hall effects, Journal of the Physical.
Experimental investigations of the steady flow through an idealized model of a femoral artery bypass
Directory of Open Access Journals (Sweden)
Giurgea Corina
2014-03-01
Full Text Available The present paper presents the steps taken by the authors in the first stage of an experimental program within a larger national research project whose objective is to characterize the flow through a femoral artery bypass with a view to finding solutions for its optimization. The objective of the stage is to investigate by means of the PIV method the stationary flow through a bypass model with an idealized geometry. A bypass assembly which reunites the idealized geometry models of the proximal and distal anastomoses, and which respects the lengths of a femoral artery bypass was constructed on the basis of data for a real patient provided by medical investigations. With the aim of testing the model and the established experimental set-up with regard to their suitability for the assessment of the velocity field associated to the steady flow through the bypass, three zones that can restore the whole distal anastomosis were PIV investigated. The measurements were taken in the conditions of maintained inflow at the bypass entry of 0.9 l / min (Re = 600. The article presents comparatively the flow spectra and the velocity fields for each zone obtained in two situations: with the femoral artery completely occluded and completely open.
Hyhlík, Tomáš
2018-06-01
The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.
Directory of Open Access Journals (Sweden)
Hyhlík Tomáš
2018-01-01
Full Text Available The article deals with the development of incompressible ideal gas like model, which can be used as a part of mathematical model describing natural draft wet-cooling tower flow, heat and mass transfer. It is shown, based on the results of a complex mathematical model of natural draft wet-cooling tower flow, that behaviour of pressure, temperature and density is very similar to the case of hydrostatics of moist air, where heat and mass transfer in the fill zone must be taken into account. The behaviour inside the cooling tower is documented using density, pressure and temperature distributions. The proposed equation for the density is based on the same idea like the incompressible ideal gas model, which is only dependent on temperature, specific humidity and in this case on elevation. It is shown that normalized density difference of the density based on proposed model and density based on the nonsimplified model is in the order of 10-4. The classical incompressible ideal gas model, Boussinesq model and generalised Boussinesq model are also tested. These models show deviation in percentages.
Multi-region relaxed magnetohydrodynamics with anisotropy and flow
Energy Technology Data Exchange (ETDEWEB)
Dennis, G. R., E-mail: graham.dennis@anu.edu.au; Dewar, R. L.; Hole, M. J. [Research School of Physics and Engineering, Australian National University, Canberra, Australian Capital Territory 0200 (Australia); Hudson, S. R. [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States)
2014-07-15
We present an extension of the multi-region relaxed magnetohydrodynamics (MRxMHD) equilibrium model that includes pressure anisotropy and general plasma flows. This anisotropic extension to our previous isotropic model is motivated by Sun and Finn's model of relaxed anisotropic magnetohydrodynamic equilibria. We prove that as the number of plasma regions becomes infinite, our anisotropic extension of MRxMHD reduces to anisotropic ideal MHD with flow. The continuously nested flux surface limit of our MRxMHD model is the first variational principle for anisotropic plasma equilibria with general flow fields.
International Nuclear Information System (INIS)
Smolentsev, Sergey; Morley, Neil; Abdou, Mohamed
2005-01-01
The paper presents details of a new numerical code for analysis of a fully developed MHD flow in a channel of a liquid metal blanket using various insulation techniques. The code has specially been designed for channels with a 'sandwich' structure of several materials with different physical properties. The code includes a finite-volume formulation, automatically generated Hartmann number sensitive meshes, and effective convergence acceleration technique. Tests performed at Ha ∼ 10 4 have showed very good accuracy. As an illustration, two blanket flows have been considered: Pb-17Li flow in a channel with a silicon carbide flow channel insert, and Li flow in a channel with insulating coating
E.Hemalatha; N. Bhaskar Reddy
2015-01-01
This paper analyzes the radiation and chemical reaction effects on MHD steady two-dimensional laminar viscous incompressible radiating boundary layer flow over a flat plate in the presence of internal heat generation and convective boundary condition. It is assumed that lower surface of the plate is in contact with a hot fluid while a stream of cold fluid flows steadily over the upper surface with a heat source that decays exponentially. The Rosseland approximation is used to desc...
MHD free convection flow of a non-Newtonian power-law fluid over ...
African Journals Online (AJOL)
... flow have been presented for various parameters such as Prandtl number, flow behavior index (n), porous plate parameter and magnetic parameter. The local Nusselt number and skin friction coefficient is also presented graphically. Keywords: Magnetohydrodynamic flow; free convection flow; Non-Newtonian power-law
Spiral blood flows in an idealized 180-degree curved artery model
Bulusu, Kartik V.; Kulkarni, Varun; Plesniak, Michael W.
2017-11-01
Understanding of cardiovascular flows has been greatly advanced by the Magnetic Resonance Velocimetry (MRV) technique and its potential for three-dimensional velocity encoding in regions of anatomic interest. The MRV experiments were performed on a 180-degree curved artery model using a Newtonian blood analog fluid at the Richard M. Lucas Center at Stanford University employing a 3 Tesla General Electric (Discovery 750 MRI system) whole body scanner with an eight-channel cardiac coil. Analysis in two regions of the model-artery was performed for flow with Womersley number=4.2. In the entrance region (or straight-inlet pipe) the unsteady pressure drop per unit length, in-plane vorticity and wall shear stress for the pulsatile, carotid artery-based flow rate waveform were calculated. Along the 180-degree curved pipe (curvature ratio =1/7) the near-wall vorticity and the stretching of the particle paths in the vorticity field are visualized. The resultant flow behavior in the idealized curved artery model is associated with parameters such as Dean number and Womersley number. Additionally, using length scales corresponding to the axial and secondary flow we attempt to understand the mechanisms leading to the formation of various structures observed during the pulsatile flow cycle. Supported by GW Center for Biomimetics and Bioinspired Engineering (COBRE), MRV measurements in collaboration with Prof. John K. Eaton and, Dr. Chris Elkins at Stanford University.
A coupled systems code-CFD MHD solver for fusion blanket design
Energy Technology Data Exchange (ETDEWEB)
Wolfendale, Michael J., E-mail: m.wolfendale11@imperial.ac.uk; Bluck, Michael J.
2015-10-15
Highlights: • A coupled systems code-CFD MHD solver for fusion blanket applications is proposed. • Development of a thermal hydraulic systems code with MHD capabilities is detailed. • A code coupling methodology based on the use of TCP socket communications is detailed. • Validation cases are briefly discussed for the systems code and coupled solver. - Abstract: The network of flow channels in a fusion blanket can be modelled using a 1D thermal hydraulic systems code. For more complex components such as junctions and manifolds, the simplifications employed in such codes can become invalid, requiring more detailed analyses. For magnetic confinement reactor blanket designs using a conducting fluid as coolant/breeder, the difficulties in flow modelling are particularly severe due to MHD effects. Blanket analysis is an ideal candidate for the application of a code coupling methodology, with a thermal hydraulic systems code modelling portions of the blanket amenable to 1D analysis, and CFD providing detail where necessary. A systems code, MHD-SYS, has been developed and validated against existing analyses. The code shows good agreement in the prediction of MHD pressure loss and the temperature profile in the fluid and wall regions of the blanket breeding zone. MHD-SYS has been coupled to an MHD solver developed in OpenFOAM and the coupled solver validated for test geometries in preparation for modelling blanket systems.
Ideal shocks in 2-layer flow Part I: Under a rigid lid
Jiang, Qingfang; Smith, Ronald B.
2011-01-01
Previous work on the classical problem of shocks in a 2-layer density-stratified fluid used eithera parameterized momentum exchange or an assumed Bernoulli loss. We propose a new theorybased on a set of viscous model equations. We define an idealized shock in two-layer densitystratified flow under a rigid lid as a jump or drop of the interface in which (1) the force balanceremains nearly hydrostatic in the shock, (2) there is no exchange of momentum between thetwo layers except by pressure fo...
Flow of ideal fluid through a central region of a nuclear reactor wire-spaced fuel subassembly
International Nuclear Information System (INIS)
Schmid, J.
1991-04-01
The results are given of calculations of the flow of an ideal fluid through the central region of a nuclear reactor wire-spaced fuel subassembly. The computer code used is briefly described. (author). 10 figs., 4 refs
A fast numerical method for ideal fluid flow in domains with multiple stirrers
Nasser, Mohamed M. S.; Green, Christopher C.
2018-03-01
A collection of arbitrarily-shaped solid objects, each moving at a constant speed, can be used to mix or stir ideal fluid, and can give rise to interesting flow patterns. Assuming these systems of fluid stirrers are two-dimensional, the mathematical problem of resolving the flow field—given a particular distribution of any finite number of stirrers of specified shape and speed—can be formulated as a Riemann-Hilbert (R-H) problem. We show that this R-H problem can be solved numerically using a fast and accurate algorithm for any finite number of stirrers based around a boundary integral equation with the generalized Neumann kernel. Various systems of fluid stirrers are considered, and our numerical scheme is shown to handle highly multiply connected domains (i.e. systems of many fluid stirrers) with minimal computational expense.
Heat-flow equation motivated by the ideal-gas shock wave.
Holian, Brad Lee; Mareschal, Michel
2010-08-01
We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.
International Nuclear Information System (INIS)
Kambe, Tsutomu
2013-01-01
A new representation of the solution to Euler's equation of motion is presented by using a system of expressions for compressible rotational flows of an ideal fluid. This is regarded as a generalization of Bernoulli's theorem to compressible rotational flows. The present expressions are derived from the variational principle. The action functional for the principle consists of the main terms of the total kinetic, potential and internal energies, together with three additional terms yielding the equations of continuity, entropy and a third term that provides the rotational component of velocity field. The last term has the form of scalar product satisfying gauge symmetry with respect to both translation and rotation. This is a generalization of the Clebsch transformation from a physical point of view. It is verified that the system of new expressions, in fact, satisfies Euler's equation of motion. (paper)
MHD channel performance for potential early commercial MHD power plants
International Nuclear Information System (INIS)
Swallom, D.W.
1981-01-01
The commercial viability of full and part load early commercial MHD power plants is examined. The load conditions comprise a mass flow of 472 kg/sec in the channel, Rosebud coal, 34% by volume oxygen in the oxidizer preheated to 922 K, and a one percent by mass seeding with K. The full load condition is discussed in terms of a combined cycle plant with optimized electrical output by the MHD channel. Various electrical load parameters, pressure ratios, and magnetic field profiles are considered for a baseload MHD generator, with a finding that a decelerating flow rate yields slightly higher electrical output than a constant flow rate. Nominal and part load conditions are explored, with a reduced gas mass flow rate and an enriched oxygen content. An enthalpy extraction of 24.6% and an isentropic efficiency of 74.2% is predicted for nominal operation of a 526 MWe MHD generator, with higher efficiencies for part load operation
Armaghani, T.; Esmaeili, H.; Mohammadpoor, Y. A.; Pop, I.
2018-01-01
In this paper, the steady mixed convection flow and heat transfer of water-copper oxide nanofluid in an open C-shaped enclosure is investigated numerically. The enclosure is under constant magnetic field. Effects of Richardson number, magnetic and nanofluid volume fraction parameters are studied and discussed. The nanofluid with a cold temperature of T C and a velocity of u c enters the enclosure from the top right corner and exits from the bottom right corner. The vertical wall of the left side is subjected to a hot and constant temperature T h . Also, other walls are insulated. It is found that the heat transfer is increased via increasing the Hartmann and Reynolds numbers. For low Reynolds numbers, the enhances of the Hartman number leads to a slightly increases of the average Nusselt number, but for high Reynolds numbers, the average Nusselt number gets an ascending trend and the increase in the Hartmann number shows its effect more pronounced. Also, with increase in Ri, the effect of nanofluid on the heat transfer increases. Due to practical impotence, the study of mixed convection heat transfer in enclosures and various shaped of cavities has attracted remarkable attentions in the past few decades. Significant applications of the mixed convection flow can be found in atmospheric flows, solar energy storage, heat exchangers, lubrication technology, drying technologies, cooling of the electronic devices, etc. The present results are original and new for the problem of MHD mixed convection flow and heat transfer in an open C-shaped enclosure using water-copper oxide nanofluid. Comparison of the obtained results with those from the open literature (Mahmoodi et al. [24]) is acceptable.
MHD stability properties of a system of reduced toroidal MHD equations
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1993-01-01
A system of reduced toroidal magneto-hydrodynamic (MHD) equations is derived from a general scalar representation of the complete MHD system, using an ordering in terms of the inverse aspect ratio ε of a toroidal plasma. It is shown that the energy principle for the reduced equations is identical with the usual energy principle of the complete MHD system, to the appropriate order in ε. Thus, the reduced equations have the same ideal MHD stability limits as the full MHD equations. (authors). 6 refs
MHD flow of a dusty viscoelastic liquid through a porous medium between two inclined parallel plates
International Nuclear Information System (INIS)
Singh, A.K.; Singh, N.P.
1996-01-01
Magnetohydrodynamic flow of a dusty viscoelastic liquid (Oldroyd B-liquid) through a porous medium between two parallel plates inclined to the horizon has been studied. The liquid velocity, dust particle velocity and flux of flow have been obtained. Earlier results have been deduced as particular cases of the present investigation. The physical situation of the motion has been discussed graphically. (author)
Numerical simulation of MHD flows in inhomogeneous and instationary magnetic fields
International Nuclear Information System (INIS)
Ehrhard, Sebastian
2016-01-01
In this work, I develop a numerical model for magnetohydrodynamic flows in unsteady an inhomogeneous flow. The model is implemented in the finite-volume based CFD-code OpenFOAM. Some verification and validation tests are made on several standard problems of magnetohydrodynamics. Finally I successful modelled an electromagnetic flowmeter with the code.
Chemical reaction on MHD flow and heat transfer of a nanofluid ...
African Journals Online (AJOL)
DR OKE
International Journal of Engineering, Science and Technology ... problem of laminar fluid flow which results from the stretching of a flat surface in a nanofluid ... boundary-layer flow past a vertical plate, using a model in which Brownian motion ...
GAUGE PRINCIPLE AND VARIATIONAL FORMULATION FOR FLOWS OF AN IDEAL FLUID
Institute of Scientific and Technical Information of China (English)
KAMBE Tsutomu
2003-01-01
A gauge principle is applied to mass flows of an ideal compressible fluid subject to Galilei transformation. A free-field Lagrangian defined at the outset is invariant with respect to global SO(3) gauge transformations as well as Galilei transformations. The action principle leads to the equation of potential flows under constraint of a continuity equation. However, the irrotational flow is not invariant with respect to local SO(3) gauge transformations. According to the gauge principle,a gauge-covariant derivative is defined by introducing a new gauge field. Galilei invariance of the derivative requires the gauge field to coincide with the vorticity, i.e. the curl of the velocity field. A full gauge-covariant variational formulation is proposed on the basis of the Hamilton's principle and an assoicated Lagrangian. By means of an isentropic material variation taking into account individual particle motion, the Euler's equation of motion is derived for isentropic flows by using the covariant derivative. Noether's law associated with global SO(3) gauge invariance leads to the conservation of total angular momentum. In addition, the Lagrangian has a local symmetry of particle permutation which results in local conservation law equivalent to the vorticity equation.
A comparison of hyperbolic solvers for ideal and real gas flows
Directory of Open Access Journals (Sweden)
R. M. L. Coelho
2006-09-01
Full Text Available Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to second-order by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. These methods require the so-called Roe's average state, which is frequently difficult and sometimes impossible to obtain. Other methods that do not require the average state are best suited for complex equations of state. Of these, the VFRoe, AUSM+ and Hybrid Lax-Friedrich-Lax-Wendroff methods were compared for one-dimensional compressible flows of a Van der Waals gas. All methods were evaluated regarding their accuracy for given mesh sizes and their computational cost for a given solution accuracy. It was shown that, even though they require more floating points and indirect addressing operations per time step, for a given time interval for integration the second-order methods are less-time consuming than the first-order methods for a required accuracy. It was also shown that AUSM+ and VFRoe are the most accurate methods and that AUSM+ is much faster than the others, and is thus recommended for nonideal one-phase gas flows.
Directory of Open Access Journals (Sweden)
Mohammed Almakki
2017-07-01
Full Text Available The entropy generation in unsteady three-dimensional axisymmetric magnetohydrodynamics (MHD nanofluid flow over a non-linearly stretching sheet is investigated. The flow is subject to thermal radiation and a chemical reaction. The conservation equations are solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasi-linearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account. The nanofluid particle volume fraction on the boundary is passively controlled. The results show that as the Hartmann number increases, both the Nusselt number and the Sherwood number decrease, whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with respect to some physical parameters.
International Nuclear Information System (INIS)
Takase, K.; Hasan, M.Z.
1995-01-01
Convective heat transfer in MHD laminar flow through rectangular channels in the plasma-facing components of a fusion reactor has been analyzed numerically to investigate the effects of channel aspect ratio, defined as the ratio of the lengths of the plasma-facing side to the other side. The adverse effect of the nonuniformity of surface heat flus on Nusselt number (Nu) at the plasma-facing side can be alleviated by increasing the aspect ratio of a rectangular duct. At the center and corner of the plasma-facing side of a square duct, the Nu of non-MHD flow are 6.8 and 2.2, respectively, for uniform surface heat flux. In the presence of a strong magnetic field, Nu at the center and corner increases to 22 and 3.6, respectively. However, when the heat flux is highly nonuniform, as in the plasma-facing components, Nu decreases from 22 to 3.1 at the center and from 3.6 to 3.1 at the corner. When the aspect ratio is increased to 4, Nu at the center and corner increase to 5 and 4.7. Along the circumference of a rectangular channel, there are locations where the wall temperature is equal to or less than the bulk coolant temperature, thus making the Nu with conventional definition infinity or negative. The ratio between Nu of MHD flow and Nu of non-MHD flow for various aspect ratios is constant in the region of Hartmann number of more than 200 at least. On the other hand, its ratio increases monotonously with increasing the aspect ratio
Effects of mass transfer on MHD flow of casson fluid with chemical reaction and suction
Directory of Open Access Journals (Sweden)
S. A. Shehzad
2013-03-01
Full Text Available Effect of mass transfer in the magnetohydrodynamic flow of a Casson fluid over a porous stretching sheet is addressed in the presence of a chemical reaction. A series solution for the resulting nonlinear flow is computed. The skin friction coefficient and local Sherwood number are analyzed through numerical values for various parameters of interest. The velocity and concentration fields are illustrated for several pertinent flow parameters. We observed that the Casson parameter and Hartman number have similar effects on the velocity in a qualitative sense. We further analyzed that the concentration profile decreases rapidly in comparison to the fluid velocity when we increased the values of the suction parameter.
Computation of tokamak equilibria with steady flow
International Nuclear Information System (INIS)
Kerner, W.; Tokuda, Shinji
1987-08-01
The equations for ideal MHD equilibria with stationary flow are reexamined and addressed as numerically applied to tokamak configurations with a free plasma boundary. Both the isothermal (purely toroidal flow) and the poloidal flow cases are treated. Experiment-relevant states with steady flow (so far only in the toroidal direction) are computed by the modified SELENE40 code. (author)
Directory of Open Access Journals (Sweden)
Wubshet Ibrahim
2015-12-01
Full Text Available Two-dimensional boundary layer flow of nanofluid fluid past a stretching sheet is examined. The paper reveals the effect of non-linear radiative heat transfer on magnetohydrodynamic (MHD stagnation point flow past a stretching sheet with convective heating. Condition of zero normal flux of nanoparticles at the wall for the stretched flow is considered. The nanoparticle fractions on the boundary are considered to be passively controlled. The solution for the velocity, temperature and nanoparticle concentration depends on parameters viz. Prandtl number Pr, velocity ratio parameter A, magnetic parameter M, Lewis number Le, Brownian motion Nb, and the thermophoresis parameter Nt. Moreover, the problem is governed by temperature ratio parameter (Nr=TfT∞ and radiation parameter Rd. Similarity transformation is used to reduce the governing non-linear boundary-value problems into coupled higher order non-linear ordinary differential equation. These equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters. Numerical results are obtained for velocity, temperature and concentration, as well as the skin friction coefficient and local Nusselt number. The results indicate that the skin friction coefficient Cf increases as the values of magnetic parameter M increase and decreases as the values of velocity ratio parameter A increase. The local Nusselt number −θ′(0 decreases as the values of thermophoresis parameter Nt and radiation parameter Nr increase and it increases as the values of both Biot number Bi and Prandtl number Pr increase. Furthermore, radiation has a positive effect on temperature and concentration profiles.
Molokov, S. Y.; Allen, J. E.
Magnetohydrodynamic (MHD) flows of viscous incompressible fluid in strong magnetic fields parallel to a free surface of fluid are investigated. The problem of flow in an open channel due to a moving side wall in uniform magnetic field is considered, and treated by means of matched asymptotic expansions method. The flow region is divided into various subregions and leading terms of asymptotic expansions as M tends towards infinity (M is the Hartmann number) of solutions of correspondent problems in each subregion are obtained. An exact analytic solution of equations governing the free-surface layer of thickness of order M to the minus 1/2 power is obtained.
Directory of Open Access Journals (Sweden)
S. Srinivas
2016-01-01
Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.
Heat transfer in MHD flow of dusty viscoelastic (Walters' liquid model ...
Indian Academy of Sciences (India)
fluid in porous medium on a parallel plate channel inclined at an angle θ. ... temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The ... Walters [2] proposed a theoretical model for elastoviscous fluids.
International Nuclear Information System (INIS)
Vasil'ev, S.A.; Dovganchuk, I.I.; Sozinov, Y.A.
1988-01-01
The laminar flow of a liquid metal in the clearance between rotating disks is examined in an axial magnetic field. A comparison is made between the experimental and calculated values of the potential difference
International Nuclear Information System (INIS)
Hua, T.Q.; Walker, J.S.; Picologlou, B.F.; Reed, C.B.
1988-07-01
Magnetohydrodynamic flows of liquid metals in rectangular ducts with thin conducting walls in the presence of strong nonuniform transverse magnetic fields are examined. The interaction parameter and Hartmann number are assumed to be large, whereas the magnetic Reynolds number is assumed to be small. Under these assumptions, viscous and inertial effects are confined in very thin boundary layers adjacent to the walls. A significant fraction of the fluid flow is concentrated in the boundary layers adjacent to the side walls which are parallel to the magnetic field. This paper describes the analysis and numerical methods for obtaining 3-D solutions for flow parameters outside these layers, without solving explicitly for the layers themselves. Numerical solutions are presented for cases which are relevant to the flows of liquid metals in fusion reactor blankets. Experimental results obtained from the ALEX experiments at Argonne National Laboratory are used to validate the numerical code. In general, the agreement is excellent. 5 refs., 14 figs
International Nuclear Information System (INIS)
Chakraborty, S.; Borkakati, A.K.
1999-01-01
An unsteady viscous incompressible free convection flow of an electrically conducting fluid between two heated vertical parallel plates is considered in presence of a uniform magnetic field applied transversely to the flow. The approximate analytical solutions for velocity, induced field and temperature distributions are obtained for small and large magnetic Reynolds number. The skin-friction on the two plates are obtained and plotted graphically. The problem is extended for thermometric case. (author)
Qasim, Muhammad; Khan, Zafar Hayat; Khan, Waqar Ahmad; Ali Shah, Inayat
2014-01-01
This study investigates the magnetohydrodynamic (MHD) flow of ferrofluid along a stretching cylinder. The velocity slip and prescribed surface heat flux boundary conditions are employed on the cylinder surface. Water as conventional base fluid containing nanoparticles of magnetite (Fe3O4) is used. Comparison between magnetic (Fe3O4) and non-magnetic (Al2O3) nanoparticles is also made. The governing non-linear partial differential equations are reduced to non-linear ordinary differential equations and then solved numerically using shooting method. Present results are compared with the available data in the limiting cases. The present results are found to be in an excellent agreement. It is observed that with an increase in the magnetic field strength, the percent difference in the heat transfer rate of magnetic nanoparticles with Al2O3 decreases. Surface shear stress and the heat transfer rate at the surface increase as the curvature parameter increases, i.e curvature helps to enhance the heat transfer.
Alias Suba, Subbu; Muthucumaraswamy, R.
2018-04-01
A numerical analysis of transient radiative MHD(MagnetoHydroDynamic) natural convective flow of a viscous, incompressible, electrically conducting and rotating fluid along a semi-infinite isothermal vertical plate is carried out taking into consideration Hall current, rotation and first order chemical reaction.The coupled non-linear partial differential equations are expressed in difference form using implicit finite difference scheme. The difference equations are then reduced to a system of linear algebraic equations with a tri-diagonal structure which is solved by Thomas Algorithm. The primary and secondary velocity profiles, temperature profile, concentration profile, skin friction, Nusselt number and Sherwood Number are depicted graphically for a range of values of rotation parameter, Hall parameter,magnetic parameter, chemical reaction parameter, radiation parameter, Prandtl number and Schmidt number.It is recognized that rate of heat transfer and rate of mass transfer decrease with increase in time but they increase with increasing values of radiation parameter and Schmidt number respectively.
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C. Sulochana
2016-02-01
Full Text Available We analyzed the momentum and heat transfer characteristics of unsteady MHD flow of a dusty nanofluid over a vertical stretching surface in presence of volume fraction of dust and nano particles with non uniform heat source/sink. We considered two types of nanofluids namely Ag-water and Cu-water embedded with conducting dust particles. The governing equations are transformed in to nonlinear ordinary differential equations by using similarity transformation and solved numerically using Shooting technique. The effects of non-dimensional governing parameters on velocity and temperature profiles for fluid and dust phases are discussed and presented through graphs. Also, the skin friction coefficient and Nusselt number are discussed and presented for two dusty nanofluids separately in tabular form. Results indicate that an increase in the volume fraction of dust particles enhances the heat transfer in Cu-water nanofluid compared with Ag-water nanofluid and a raise in the volume fraction of nano particles shows uniform heat transfer in both Cu-water and Ag-water nanofluids.
Nasir, Saleem; Islam, Saeed; Gul, Taza; Shah, Zahir; Khan, Muhammad Altaf; Khan, Waris; Khan, Aurang Zeb; Khan, Saima
2018-05-01
In this article the modeling and computations are exposed to introduce the new idea of MHD three-dimensional rotating flow of nanofluid through a stretching sheet. Single wall carbon nanotubes (SWCNTs) are utilized as a nano-sized materials while water is used as a base liquid. Single-wall carbon nanotubes (SWNTs) parade sole assets due to their rare structure. Such structure has significant optical and electronics features, wonderful strength and elasticity, and high thermal and chemical permanence. The heat exchange phenomena are deliberated subject to thermal radiation and moreover the impact of nanoparticles Brownian motion and thermophoresis are involved in the present investigation. For the nanofluid transport mechanism, we implemented the Xue model (Xue, Phys B Condens Matter 368:302-307, 2005). The governing nonlinear formulation based upon the law of conservation of mass, quantity of motion, thermal field and nanoparticles concentrations is first modeled and then solved by homotopy analysis method (HAM). Moreover, the graphical result has been exposed to investigate that in what manner the velocities, heat and nanomaterial concentration distributions effected through influential parameters. The mathematical facts of skin friction, Nusselt number and Sherwood number are presented through numerical data for SWCNTs.
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Yahaya Shagaiya Daniel
2015-09-01
Full Text Available This paper investigates the theoretical influence of buoyancy and thermal radiation on MHD flow over a stretching porous sheet. The model which constituted highly nonlinear governing equations is transformed using similarity solution and then solved using homotopy analysis method (HAM. The analysis is carried out up to the 5th order of approximation and the influences of different physical parameters such as Prandtl number, Grashof number, suction/injection parameter, thermal radiation parameter and heat generation/absorption coefficient and also Hartman number on dimensionless velocity, temperature and the rate of heat transfer are investigated and discussed quantitatively with the aid of graphs. Numerical results obtained are compared with the previous results published in the literature and are found to be in good agreement. It was found that when the buoyancy parameter and the fluid velocity increase, the thermal boundary layer decreases. In case of the thermal radiation, increasing the thermal radiation parameter produces significant increases in the thermal conditions of the fluid temperature which cause more fluid in the boundary layer due to buoyancy effect, causing the velocity in the fluid to increase. The hydrodynamic boundary layer and thermal boundary layer thickness increase as a result of increase in radiation.
Mishra, A.; Sharma, B. K.
2017-11-01
A numerical study of an oscillatory unsteady MHD flow and heat and mass transfer in a vertical rotating channel with an inclined uniform magnetic field and the Hall effect is carried out. The conservation equations of momentum, energy, and species are formulated in a rotating frame of reference with inclusion of the buoyancy effects and Lorentz forces. The Lorentz forces are determined by using the generalized Ohm law with the Hall parameter taken into account. The obtained coupled partial differential equations are nondimensionalized and solved numerically by using the explicit finite difference method. The effects of various model parameters, like the Hall parameter, Hartmann number, wall suction/injection parameter, rotation parameter, angle of magnetic field inclination, Prandtl number, Schmidt number, etc., on the channel velocities, skin friction coefficients, Nusselt number, and the Sherwood number are examined. It is found that the influence of the Hartmann number and Hall parameter on the channel velocities and skin friction coefficients is dependent on the value of the wall suction/injection parameter.
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Arun Gupta
2016-07-01
Full Text Available The flow-shop scheduling problem (FSP has been widely studied in the literature and having a very active research area. Over the last few decades, a number of heuristic/meta-heuristic solution techniques have been developed. Some of these techniques offer excellent effectiveness and efficiency at the expense of substantial implementation efforts and being extremely complicated. This paper brings out the application of a Multi-Criteria Decision Making (MCDM method known as techniques for order preference by similarity to an ideal solution (TOPSIS using different weighting schemes in flow-shop environment. The objective function is identification of a job sequence which in turn would have minimum makespan (total job completion time. The application of the proposed method to flow shop scheduling is presented and explained with a numerical example. The results of the proposed TOPSIS based technique of FSP are also compared on the basis of some benchmark problems and found compatible with the results obtained from other standard procedures.
Local invariants in non-ideal flows of neutral fluids and two-fluid plasmas
Zhu, Jian-Zhou
2018-03-01
The main objective is the locally invariant geometric object of any (magneto-)fluid dynamics with forcing and damping (nonideal), while more attention is paid to the untouched dynamical properties of two-fluid fashion. Specifically, local structures, beyond the well-known "frozen-in" to the barotropic flows of the generalized vorticities, of the two-fluid model of plasma flows are presented. More general non-barotropic situations are also considered. A modified Euler equation [T. Tao, "Finite time blowup for Lagrangian modifications of the three-dimensional Euler equation," Ann. PDE 2, 9 (2016)] is also accordingly analyzed and remarked from the angle of view of the two-fluid model, with emphasis on the local structures. The local constraints of high-order differential forms such as helicity, among others, find simple formulation for possible practices in modeling the dynamics. Thus, the Cauchy invariants equation [N. Besse and U. Frisch, "Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces," J. Fluid Mech. 825, 412 (2017)] may be enabled to find applications in non-ideal flows. Some formal examples are offered to demonstrate the calculations, and particularly interestingly the two-dimensional-three-component (2D3C) or the 2D passive scalar problem presents that a locally invariant Θ = 2θζ, with θ and ζ being, respectively, the scalar value of the "vertical velocity" (or the passive scalar) and the "vertical vorticity," may be used as if it were the spatial density of the globally invariant helicity, providing a Lagrangian prescription to control the latter in some situations of studying its physical effects in rapidly rotating flows (ubiquitous in atmosphere of astrophysical objects) with marked 2D3C vortical modes or in purely 2D passive scalars.
Numerical simulation of MHD pulsatile flow of a biofluid in a channel
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Kashif Ali
2015-08-01
Full Text Available The purpose of this paper is to numerically study the interaction of an external magnetic field with the flow of a biofluid through a Darcy-Forchhmeir porous channel, due to an oscillatory pressure gradient, in the presence of wall transpiration as well as chemical reaction considerations. We have noticed that if the Reynolds number of the wall transpiration flow is increased, the average (or maximum velocity of the main flow direction is raised. Similar effect has also been observed for the rheological parameter and the Darcy parameter, whereas an opposite trend has been noted for both the Forchheimer quadratic drag parameter and the magnetic parameter. Further, an increase in the Reynolds number results in straightening the concentration profile, thus making it an almost linear function of the dimensionless spatial variable.
Unsteady MHD blood flow through porous medium in a parallel plate channel
Latha, R.; Rushi Kumar, B.
2017-11-01
In this study, we have analyzed heat and mass transfer effects on unsteady blood flow through parallel plate channel in a saturated porous medium in the presence of a transverse magnetic field with thermal radiation. The governing higher order nonlinear PDE’S are converted to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using boundary conditions by choosing the axial flow transport and the fields of concentration and temperature apart from the normal velocity as a function of y and t. The effects of different pertinent parameters appeared in this model viz thermal radiation, Prandtl number, Heat source parameter, Hartmann number, Permeability parameter, Decay parameter on axial flow transport and the normal velocity are analyzed in detail.
Prasad, D. V. V. Krishna; Chaitanya, G. S. Krishna; Raju, R. Srinivasa
2018-05-01
The aim of this research work is to find the EFGM solutions of the unsteady magnetohydromagnetic natural convection heat transfer flow of a rotating, incompressible, viscous, Boussinesq fluid is presented in this study in the presence of radiative heat transfer. The Rosseland approximation for an optically thick fluid is invoked to describe the radiative flux. Numerical results obtained show that a decrease in the temperature boundary layer occurs when the Prandtl number and the radiation parameter are increased and the flow velocity approaches steady state as the time parameter t is increased. These findings are in quantitative agreement with earlier reported studies.
MHD flow in multichannel U-bends: Screening experiments and theoretical analysis
International Nuclear Information System (INIS)
Reimann, J.; Molokov, S.; Platnieks, I.; Platacis, E.
1993-02-01
In electrically coupled multichannel ducts with a U-bend geometry magnetohydrodynamic effects are expected to cause strongly ununiform distributions of flow rates Q i and pressure drops Δp i in the individual channels. A multichannel U-bend geometry is part of the KfK self-cooled Pb-17 Li blanket design (radial-toroidal-radial channels). However, inserts are proposed which isolate electrically the radial channels (not the toroidal ones). To investigate the multichannel effect (MCE), screening experiments were performed at LAS, Riga, with different flow channel geometries and channel numbers between 1 and 5 and using InGaSn as liquid metal. These experiments were carried out with either Δp i ∼const or Q i ∼const. Hartmann Numbers were varied between 0 and ∼1600 (maximum magnetic field strength: 4.1 T) and Interaction Parameters between 0 and 10000. For experiments with electrically conducting walls between the channels, the volume flow rates in the outer channels are significantly larger than those in the inner channels in the experiments with Δp i ∼const. For Q i ∼const., this tendency is reversed, with the highest pressure drop in the middle channel and the lowest in the outer channels. The flow geometry with electrically separated radial channels, similar to the KfK-design result in a fairly even flow rate and pressure drop distribution. The single channels behave approximately like electrically separated channels; no marked MCE occurrs. A theoretical analysis was carried out to describe the MCE for the multichannel U-bend with thin electrically conducting outside walls. This analysis is based on the Core Flow Approximation (CFA), valid for infinitely large Interaction Parameters and Hartmann Numbers. The theory predicts correctly all tendencies observed for the pressure measurements. Moreover, the method is able to describe in detail the flow structure in the toroidal channel. The most essential result is that the flow rate in the layer close to the
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Govindarajan Arunachalam
2014-01-01
Full Text Available An investigation of unsteady MHD free convective flow and mass transfer during the motion of a viscous incompressible fluid through a porous medium, bounded by an infinite vertical porous surface, in a rotating system is presented. The porous plane surface and the porous medium are assumed to rotate in a solid body rotation. The vertical surface is subjected to uniform constant suction perpendicular to it and the temperature at this surface fluctuates in time about a non-zero constant mean. Analytical expressions for the velocity, temperature and concentration fields are obtained using the perturbation technique. The effects of R (rotation parameter, k0 (permeability parameter, M (Hartmann number and w (frequency parameter on the flow characteristics are discussed. It is observed that the primary velocity component decreases with the increase in either of the rotation parameter R, the permeability parameter k0, or the Hartmann number M. It is also noted that the primary skin friction increases whenever there is an increase in the Grashof number Gr or the modified Grashof number Gm. It is clear that the heat transfer coefficient in terms of the Nusselt number decreases in the case of both air and water when there is an increase in the Hartmann number M. It is observed that the magnitude of the secondary velocity profiles increases whenever there is an increase in either of the Grashof number or the modified Grashof number for mass transfer or the permeability of the porous media. Concentration profiles decreases with an increase in the Schmidt number.
Heat transfer to MHD oscillatory dusty fluid flow in a channel filled ...
Indian Academy of Sciences (India)
In this paper, we examine the combined effects of thermal radiation, buoyancy force and magnetic field on oscillatory flow of a conducting optically thin dusty fluid through a vertical channel filled with a saturated porous medium. The governing partial differential equations are obtained and solved analytically by variable ...
Numerical solution of heat and mass transfer in MHD flow in the ...
African Journals Online (AJOL)
We present a magnetohydrodynamic flow of a uniformly stretched vertical permeable surface undergoing Arrhenius heat reaction. It is shown that the temperature, concentration and the velocity fields depend on the chemical reaction parameter. The values of temperature field increase as the order of the reaction increases, ...
MHD flow and heat transfer of a viscous reacting fluid over a ...
African Journals Online (AJOL)
This paper presents a boundary layer flow analysis for a viscous, incompressible, electrically conducting reacting fluid over a stretching sheet in the presence of a magnetic field. It is shown that the Hartmann, Prandtl and the Eckert numbers have effect on the velocity and temperature fields. Journal of the Nigerian ...
Second law analysis of slip velocity on oscillatory MHD flow of ...
African Journals Online (AJOL)
This paper reports the analytical calculation of entropy generation due to unsteady heat and mass transfer flow of an incompressible, electrically conducting, and viscous fluid past an infinite vertical porous plate along with porous medium of time dependent permeability with radiative heat transfer and variable suction.
Hall effect on MHD flow of visco-elastic micro-polar fluid layer ...
African Journals Online (AJOL)
Department of Mathematics, Meerut College, Meerut, Uttar Pradesh, INDIA ... the micro-polar heat conduction parameter has stabilizing effect when. 1. 2. ∈> ...... 1964, Elastico-viscous boundary layer flow, Proceedings of the Cambridge Philosophical Society, ... fluid”, Indian Journal of Pure and Applied Mathematics, Vol.
Unsteady free convection MHD flow between two heated vertical parallel conducting plates
International Nuclear Information System (INIS)
Sanyal, D.C.; Adhikari, A.
2006-01-01
Unsteady free convection flow of a viscous incompressible electrically conducting fluid between two heated conducting vertical parallel plates subjected to a uniform transverse magnetic field is considered. The approximate analytical solutions for velocity, induced field and temperature distribution are obtained for small and large values of magnetic Reynolds number. The problem is also extended to thermometric case. (author)
International Nuclear Information System (INIS)
Aiba, N.; Tokuda, S.; Oyama, N.; Ozeki, T.; Furukawa, M.
2009-01-01
Effects of a sheared toroidal rotation are investigated numerically on the stability of the MHD modes in the tokamak edge pedestal, which relate to the type-I edge-localized mode. A linear MHD stability code MINERVA is newly developed for solving the Frieman-Rotenberg equation that is the linear ideal MHD equation with flow. Numerical stability analyses with this code reveal that the sheared toroidal rotation destabilizes edge localized MHD modes for rotation frequencies which are experimentally achievable, though the ballooning mode stability changes little by rotation. This rotation effect on the edge MHD stability becomes stronger as the toroidal mode number of the unstable MHD mode increases when the stability analysis was performed for MHD modes with toroidal mode numbers smaller than 40. The toroidal mode number of the unstable MHD mode depends on the stabilization of the current-driven mode and the ballooning mode by increasing the safety factor. This dependence of the toroidal mode number of the unstable mode on the safety factor is considered to be the reason that the destabilization by toroidal rotation is stronger for smaller edge safety factors.
Thermo-diffusion effects on MHD stagnation point flow towards a stretching sheet in a nanofluid
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Umar Khan
2014-09-01
Full Text Available Thermodiffusion effects on stagnation point flow of a nanofluid towards a stretching surface with applied magnetic field is presented. Similarity transforms are applied to reduce the equations that govern the flow to a system of nonlinear ordinary differential equations. Runge-Kutta-Fehlberg method is applied to solve the system. Results are compared with existing solutions that are special cases to our problem. Concrete graphical analysis is carried out to study the effects of different emerging parameters such as stretching ratio A, magnetic influence parameter M, Prandtl number Pr, Lewis number Le, Brownian motion parameter Nb, thermophoresis parameter Nt, nanofluid Lewis number Ln, modified Dufour parameter Nd and Dufour solutal number Ld coupled with comprehensive discussions. Numerical effects of local Nusselt number, local Sherwood number and nanofluid Sherwood number are also discussed.
Scrutiny of underdeveloped nanofluid MHD flow and heat conduction in a channel with porous walls
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M. Fakour
2014-11-01
Full Text Available In this paper, laminar fluid flow and heat transfer in channel with permeable walls in the presence of a transverse magnetic field is investigated. Least square method (LSM for computing approximate solutions of nonlinear differential equations governing the problem. We have tried to show reliability and performance of the present method compared with the numerical method (Runge–Kutta fourth-rate to solve this problem. The influence of the four dimensionless numbers: the Hartmann number, Reynolds number, Prandtl number and Eckert number on non-dimensional velocity and temperature profiles are considered. The results show analytical present method is very close to numerically method. In general, increasing the Reynolds and Hartman number is reduces the nanofluid flow velocity in the channel and the maximum amount of temperature increase and increasing the Prandtl and Eckert number will increase the maximum amount of theta.
Heat transfer analysis for unsteady MHD flow past a non-isothermal stretching surface
International Nuclear Information System (INIS)
Mukhopadhyay, Swati
2011-01-01
Highlights: ► Unsteady boundary layer flow and heat transfer over a non-isothermal stretching sheet in a magnetic field are studied. ► Fluid velocity and temperature decrease for increasing unsteadiness parameter. ► Fluid velocity decreases but temperature increases with the increasing values of the Hartman number. ► The sheet temperature in respect of distance and time has analogous effects on the heat transfer. - Abstract: An analysis is made for the unsteady two-dimensional magneto-hydrodynamic flow of an incompressible viscous and electrically conducting fluid over a stretching surface having a variable and general form of surface temperature which removes the restrictions of the particular forms of prescribed surface temperature. Similarity solutions for the transformed governing equations are obtained. The transformed boundary layer equations are solved numerically for some values of the involved parameters, namely the unsteadiness parameter, magnetic parameter, the temperature exponent parameters. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. It is found that the fluid velocity and temperature decrease for increasing unsteadiness parameter. Fluid velocity decreases with the increasing values of the Hartman number resulting an increase in the temperature field in steady as well in unsteady case. It is observed that the variation of the sheet temperature in respect of distance and time has analogous effects both on the free surface temperature and on the heat transfer rate (Nusselt number) at the sheet.
Numerical investigation of MHD flow of blood and heat transfer in a stenosed arterial segment
Majee, Sreeparna; Shit, G. C.
2017-02-01
A numerical investigation of unsteady flow of blood and heat transfer has been performed with an aim to provide better understanding of blood flow through arteries under stenotic condition. The blood is treated as Newtonian fluid and the arterial wall is considered to be rigid having deposition of plaque in its lumen. The heat transfer characteristic has been analyzed by taking into consideration of the dissipation of energy due to applied magnetic field and the viscosity of blood. The vorticity-stream function formulation has been adopted to solve the problem using implicit finite difference method by developing well known Peaceman-Rachford Alternating Direction Implicit (ADI) scheme. The quantitative profile analysis of velocity, temperature and wall shear stress as well as Nusselt number is carried out over the entire arterial segment. The streamline and temperature contours have been plotted to understand the flow pattern in the diseased artery, which alters significantly in the downstream of the stenosis in the presence of magnetic field. Both the wall shear stress and Nusselt number increases with increasing magnetic field strength. However, wall shear stress decreases and Nusselt number enhances with Reynolds number. The results show that with an increase in the magnetic field strength upto 8 T, does not causes any damage to the arterial wall, but the study is significant for assessing temperature rise during hyperthermic treatment.
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Asma Khalid
2018-06-01
Full Text Available The intention here is to investigate the effects of wall couple stress with energy and concentration transfer in magnetohydrodynamic (MHD flow of a micropolar fluid embedded in a porous medium. The mathematical model contains the set of linear conservation forms of partial differential equations. Laplace transforms and convolution technique are used for computation of exact solutions of velocity, microrotations, temperature and concentration equations. Numerical values of skin friction, couple wall stress, Nusselt and Sherwood numbers are also computed. Characteristics for the significant variables on the physical quantities are graphically discussed. Comparison with previously published work in limiting sense shows an excellent agreement. Keywords: Micropolor fluid, Microrotation, MHD, Porosity, Wall couple stress, Exact solutions
MHD rotating flow and heat transfer through a channel with Hall effects
International Nuclear Information System (INIS)
Ghosh, Sushil Kumar
2016-01-01
The present investigation is the flow and heat transfer of a viscous fluid through a rotating channel about the vertical axis under the influence of transverse magnetic field. The linear temperature dependent density has been introduced along with the induced magnetic field in horizontal directions. To study the temperature distribution, the energy equation consisting of viscous dissipation and joule heating term is solved analytically. The velocity distribution in axial and vertical directions is found to be interesting such as the magnetic Reynolds number and the parameter appears due to buoyancy forces have a substantial contribution to influence the flow pattern. Also the results obtained in the study for magnetic induction variables as well as temperature distribution put forward some significant insight in the fluid flow and heat transfer. The important observation of the present study is that the temperature distribution takes the higher values in the vicinity of the upper wall and this happens due to the fact of buoyancy force and channel rotation. This is a key parameter to worm up or cool down the fluid in a useful purposes. - Highlights: • The important observation of the present study is that the temperature distribution takes the higher values in the vicinity of the upper wall and this happens due to the fact of buoyancy force and channel rotation. • Buoyancy is a key parameter to worm up or cool down the fluid in useful purposes. • It may be predicted that the effect of buoyancy force and magnetic induction force suppress the flow at the lower wall and the effect of the forces lost its potential at the layers near to the upper walls. • It may suggest that the bouncy effect has more prominent role in the fluid flow phenomena as well as heat transfer than magnetic induction and Lorentz force. • The rotation enhances the advantage of circulation of fluid in up and down and tries to make the heat balance within the layers. Our result is true
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M. Farooq
Full Text Available This article studies MHD double stratified stagnation point flow of Carreau fluid towards a non linear stretchable surface with radiation. Features of heat and mass transfer are evaluated by using convective boundary conditions. Resulting nonlinear problems are solved and studied for the velocity, temperature and concentration fields. Heat and mass transfer rates in addition to skin friction are discussed. Besides this for the verification of the present findings, the results of presented analysis have been compared with the available works in particular situations and reasonable agreement is noted. Keywords: Convective boundary condition, Thermal radiation, Double stratification, Stagnation point flow
Viscous dissipation and Joule heating effects in MHD 3D flow with heat and mass fluxes
Muhammad, Taseer; Hayat, Tasawar; Shehzad, Sabir Ali; Alsaedi, Ahmed
2018-03-01
The present research explores the three-dimensional stretched flow of viscous fluid in the presence of prescribed heat (PHF) and concentration (PCF) fluxes. Mathematical formulation is developed in the presence of chemical reaction, viscous dissipation and Joule heating effects. Fluid is electrically conducting in the presence of an applied magnetic field. Appropriate transformations yield the nonlinear ordinary differential systems. The resulting nonlinear system has been solved. Graphs are plotted to examine the impacts of physical parameters on the temperature and concentration distributions. Skin friction coefficients and local Nusselt and Sherwood numbers are computed and analyzed.
Viscous and Joule heating effects on MHD free convection flow with variable plate temperature
International Nuclear Information System (INIS)
Hossain, M.A.
1990-09-01
A steady two-dimensional laminar boundary layer flow of a viscous incompressible and electrically conducting fluid past a vertical heated plate with variable temperature in the presence of a transverse uniform magnetic field has been investigated by bringing the effect of viscous and Joules heating. The non-dimensional boundary layer equations are solved using the implicit finite difference method along with Newton's approximation for small Prandtl number chosen as typical of coolant liquid metals at operating temperature. (author). 10 refs, 2 figs, 1 tab
Shah, Zahir; Islam, Saeed; Gul, Taza; Bonyah, Ebenezer; Altaf Khan, Muhammad
2018-06-01
The current research aims to examine the combined effect of magnetic and electric field on micropolar nanofluid between two parallel plates in a rotating system. The nanofluid flow between two parallel plates is taken under the influence of Hall current. The flow of micropolar nanofluid has been assumed in steady state. The rudimentary governing equations have been changed to a set of differential nonlinear and coupled equations using suitable similarity variables. An optimal approach has been used to acquire the solution of the modelled problems. The convergence of the method has been shown numerically. The impact of the Skin friction on velocity profile, Nusslet number on temperature profile and Sherwood number on concentration profile have been studied. The influences of the Hall currents, rotation, Brownian motion and thermophoresis analysis of micropolar nanofluid have been mainly focused in this work. Moreover, for comprehension the physical presentation of the embedded parameters that is, coupling parameter N1 , viscosity parameter Re , spin gradient viscosity parameter N2 , rotating parameter Kr , Micropolar fluid constant N3 , magnetic parameter M , Prandtl number Pr , Thermophoretic parameter Nt , Brownian motion parameter Nb , and Schmidt number Sc have been plotted and deliberated graphically.
Sambath, P.; Pullepu, Bapuji; Hussain, T.; Ali Shehzad, Sabir
2018-03-01
The consequence of thermal radiation in laminar natural convective hydromagnetic flow of viscous incompressible fluid past a vertical cone with mass transfer under the influence of chemical reaction with heat source/sink is presented here. The surface of the cone is focused to a variable wall temperature (VWT) and wall concentration (VWC). The fluid considered here is a gray absorbing and emitting, but non-scattering medium. The boundary layer dimensionless equations governing the flow are solved by an implicit finite-difference scheme of Crank-Nicolson which has speedy convergence and stable. This method converts the dimensionless equations into a system of tri-diagonal equations and which are then solved by using well known Thomas algorithm. Numerical solutions are obtained for momentum, temperature, concentration, local and average shear stress, heat and mass transfer rates for various values of parameters Pr, Sc, λ, Δ, Rd are established with graphical representations. We observed that the liquid velocity decreased for higher values of Prandtl and Schmidt numbers. The temperature is boost up for decreasing values of Schimdt and Prandtl numbers. The enhancement in radiative parameter gives more heat to liquid due to which temperature is enhanced significantly.
Modeling of fully coupled MHD flows in annular linear induction pumps
International Nuclear Information System (INIS)
Roman, C.; Dumont, M.; Letout, S.; Courtessole, C.; Fautrelle, Y.; Vitry, S.; Rey, F.
2014-01-01
The paper studies specific pumping characteristics of the Annular Linear Induction Pumps (ALIP) with travelling field for liquid sodium. The present work is focused on the analysis of very large electromagnetic pumps able to provide high flow rates. The magnetic Reynolds number is quite large, therefore, it is necessary to take into account the full magnetohydrodynamic interaction between the electromagnetic field and the liquid metal flow inside pump channel. We couple the electromagnetic aspects with the hydrodynamic ones by means of two commercial softwares. The geometry considered here is 2D axisymmetric. It is found that in such induction pumps the effect of convection is very important. Two main effects have been put forth. Firstly, due to the magnetic entrainment significant end effects are observed for large velocities. This leads to the existence of regions where the axial force is negative. Secondly, a Hartmann effect occurs near the walls. The electric current and the corresponding forces are confined near the wall in Hartmann layers. Global stability of e.m. pump is also analysed. (authors)
Simulation of MHD CuO–water nanofluid flow and convective heat transfer considering Lorentz forces
Energy Technology Data Exchange (ETDEWEB)
Sheikholeslami, Mohsen; Bandpy, Mofid Gorji [Department of Mechanical Engineering, Babol University of Technology, Babol (Iran, Islamic Republic of); Ellahi, R., E-mail: rellahi@engr.ucr.edu [Department of Mechanical Engineering, University of California Riverside (United States); Department of Mathematics and Statistics, FBAS, IIUI, H-10 Sector, Islamabad (Pakistan); Zeeshan, A. [Department of Mathematics and Statistics, FBAS, IIUI, H-10 Sector, Islamabad (Pakistan)
2014-11-15
Magnetic field effect on CuO–water nanofluid flow and heat transfer in an enclosure which is heated from below is investigated. Lattice Boltzmann method is applied to solve the governing equations. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. In this model effect of Brownian motion on the effective thermal conductivity is considered. Effect of active parameter such as: Hartmann number, heat source length, nanoparticle volume fraction and Rayleigh numbers on the flow and heat transfer characteristics have been examined. The results reveal that the enhancement in heat transfer increases as Hartmann number and heat source length increase but it decreases with increase of Rayleigh number. Also it can be found that effect of Hartmann number and heat source length is more pronounced at high Rayleigh number. - Highlights: • This paper analyses the magnetic effect on CuO–water nanofluid. • Koo–Kleinstreuer–Li correlation and Lattice Boltzmann method are used. • Effects of pertinent parameters are presented through tables and graphs.
MHD flow over a permeable stretching/shrinking sheet of a nanofluid with suction/injection
Directory of Open Access Journals (Sweden)
Sandeep Naramgari
2016-06-01
Full Text Available In this study we analyzed the influence of thermal radiation and chemical reaction on two dimensional steady magnetohydrodynamic flow of a nanofluid past a permeable stretching/shrinking sheet in the presence of suction/injection. We considered nanofluid volume fraction on the boundary is submissive controlled, which makes the present study entirely different from earlier studies and physically more realistic. The equations governing the flow are solved numerically. Effects of non-dimensional governing parameters on velocity, temperature and concentration profiles are discussed and presented through graphs. Also, coefficient of skin friction and local Nusselt number is investigated for stretching/shrinking and suction/injection cases separately and presented through tables. Comparisons with existed results are presented. Present results have an excellent agreement with the existed studies under some special assumptions. Results indicate that the enhancement in Brownian motion and thermophoresis parameters depreciates the nanoparticle concentration and increases the mass transfer rate. Dual solutions exist only for certain range of stretching/shrinking and suction/injection parameters.
A study of heat and mass transfer on magnetohydrodynamic (MHD flow of nanoparticles
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Syed Tauseef Mohyud-Din
2018-03-01
Full Text Available Investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate is presented using Buongiorno's model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticles volume fraction are passively controlled on the boundary rather than actively. The partial differential equations governing the flow are reduced to a system of nonlinear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters is provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers. The passive control model can be used to control the boundary layer thickness as well as the rate of mass transfer at the wall. Keywords: Nanofluid, Brownian motion, Thermophoresis, Nusselt number, Sherwood number
Energy Technology Data Exchange (ETDEWEB)
Ehrhard, Sebastian
2016-07-01
In this work, I develop a numerical model for magnetohydrodynamic flows in unsteady an inhomogeneous flow. The model is implemented in the finite-volume based CFD-code OpenFOAM. Some verification and validation tests are made on several standard problems of magnetohydrodynamics. Finally I successful modelled an electromagnetic flowmeter with the code.
Directory of Open Access Journals (Sweden)
Poonia Hemant
2010-01-01
Full Text Available An unsteady, two-dimensional, hydromagnetic, laminar mixed convective boundary layer flow of an incompressible and electrically-conducting fluid along an infinite vertical plate embedded in the porous medium with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and graphical results for velocity, temperature and concentration profiles within the boundary layer are discussed. The results show that increased cooling (Gr > 0 of the plate and the Eckert number leads to a rise in the velocity profile. Also, an increase in Eckert number leads to an increase in the temperature. Effects of Sc on velocity and concentration are discussed and shown graphically.
MHD forced and free convection boundary layer flow near the leading edge
International Nuclear Information System (INIS)
Hossain, M.A.; Ahmed, M.
1988-07-01
Magnetohydrodynamic forced and free convection flow of an electrically conducting viscous incompressible fluid past a vertical flat plate with uniform heat flux in the presence of a magnetic field acting normal to the plate that moves with the fluid has been studied near the leading edge of the plate. The coupled non-linear equations are solved by the method of superposition for the values of the Prandtl number ranges from 0.01 to 10.0. The velocity and the temperature profiles are presented graphically and the values of the wall shear-stress as well as the heat transfer rate are presented in tabular form showing the effect of the buoyancy force and the applied magnetic field. To show the accuracy of the present method some typical values are compared with the available one. (author). 17 refs, 3 figs, 2 tabs
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N. Sandeep
2016-03-01
Full Text Available We analyzed the unsteady magnetohydrodynamic radiative flow and heat transfer characteristics of a dusty nanofluid over an exponentially permeable stretching surface in presence of volume fraction of dust and nano particles. We considered two types of nanofluids namely Cu-water and CuO-water embedded with conducting dust particles. The governing equations are transformed into nonlinear ordinary differential equations by using similarity transformation and solved numerically using Runge–Kutta based shooting technique. The effects of non-dimensional governing parameters namely magneticfield parameter, mass concentration of dust particles, fluid particle interaction parameter, volume fraction of dust particles, volume fraction of nano particles, unsteadiness parameter, exponential parameter, radiation parameter and suction/injection parameter on velocity profiles for fluid phase, dust phase and temperature profiles are discussed and presented through graphs. Also, friction factor and Nusselt numbers are discussed and presented for two dusty nanofluids separately. Comparisons of the present study were made with existing studies under some special assumptions. The present results have an excellent agreement with existing studies. Results indicated that the enhancement in fluid particle interaction increases the heat transfer rate and depreciates the wall friction. Also, radiation parameter has the tendency to increase the temperature profiles of the dusty nanofluid.
Directory of Open Access Journals (Sweden)
Zeeshan Khan
Full Text Available Modern optical fibers require a double-layer coating on the glass fiber in order to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride (PVC and low and high density polyethylene (LDPE/HDPE, nylon and Polysulfone. One of the most important things which affect the final product after processing is the design of the coating die. In the present study, double-layer optical fiber coating is performed using melt polymer satisfying Oldroyd 8-constant fluid model in a pressure type die with the effect of magneto-hydrodynamic (MHD. Wet-on-wet coating process is applied for double-layer optical fiber coating. The coating process in the coating die is modeled as a simple two-layer Couette flow of two immiscible fluids in an annulus with an assigned pressure gradient. Based on the assumptions of fully developed laminar and MHD flow, the Oldroyd 8-constant model of non-Newtonian fluid of two immiscible resin layers is modeled. The governing nonlinear equations are solved analytically by the new technique of Optimal Homotopy Asymptotic Method (OHAM. The convergence of the series solution is established. The results are also verified by the Adomian Decomposition Method (ADM. The effect of important parameters such as magnetic parameter Mi, the dilatant constant α, the Pseodoplastic constant β, the radii ratio δ, the pressure gradient Ω, the speed of fiber optics V, and the viscosity ratio κ on the velocity profiles, thickness of coated fiber optics, volume flow rate, and shear stress on the fiber optics are investigated. At the end the result of the present work is also compared with the experimental results already available in the literature by taking non-Newtonian parameters tends to zero. Keywords: Non-Newtonian fluid, Oldroyd 8-constant fluid, MHD flow, Double-layer fiber coating, OHAM, ADM, Wet-on-wet coating process
O'Connell, R.; Forest, C. B.; Plard, F.; Kendrick, R.; Lovell, T.; Thomas, M.; Bonazza, R.; Jensen, T.; Politzer, P.; Gerritsen, W.; McDowell, M.
1997-11-01
A MHD experiment is being constructed which will have the possibility of showing dynamo action: the self--generation of currents from fluid motion. The design allows sufficient experimental flexibility and diagnostic access to study a variety of issues central to dynamo theory, including mean--field electrodynamics and saturation (backreaction physics). Initially, helical flows required for dynamo action will be driven by propellers embedded in liquid sodium. The flow fields will first be measured using laser doppler velocimetry in a water experiment with an identical fluid Reynolds number. The magnetic field evolution will then be predicted using a MHD code, replacing the water with sodium; if growing magnetic fields are found, the experiment will be repeated with sodium.
Energy Technology Data Exchange (ETDEWEB)
Kittell, David E.; Cummock, Nick R.; Son, Steven F. [School of Mechanical Engineering, Purdue University, West Lafayette, Indiana 47907 (United States)
2016-08-14
Small scale characterization experiments using only 1–5 g of a baseline ammonium nitrate plus fuel oil (ANFO) explosive are discussed and simulated using an ignition and growth reactive flow model. There exists a strong need for the small scale characterization of non-ideal explosives in order to adequately survey the wide parameter space in sample composition, density, and microstructure of these materials. However, it is largely unknown in the scientific community whether any useful or meaningful result may be obtained from detonation failure, and whether a minimum sample size or level of confinement exists for the experiments. In this work, it is shown that the parameters of an ignition and growth rate law may be calibrated using the small scale data, which is obtained from a 35 GHz microwave interferometer. Calibration is feasible when the samples are heavily confined and overdriven; this conclusion is supported with detailed simulation output, including pressure and reaction contours inside the ANFO samples. The resulting shock wave velocity is most likely a combined chemical-mechanical response, and simulations of these experiments require an accurate unreacted equation of state (EOS) in addition to the calibrated reaction rate. Other experiments are proposed to gain further insight into the detonation failure data, as well as to help discriminate between the role of the EOS and reaction rate in predicting the measured outcome.
Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin
2014-01-08
The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al . 2012 Proc. R. Soc. A 468 , 1799-1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi-Dirac or Bose-Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.
Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin
2014-01-01
The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al. 2012 Proc. R. Soc. A 468, 1799–1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas. PMID:24399919
Nonequilibrium fluctuations in micro-MHD effects on electrodeposition
International Nuclear Information System (INIS)
Aogaki, Ryoichi; Morimoto, Ryoichi; Asanuma, Miki
2010-01-01
In copper electrodeposition under a magnetic field parallel to electrode surface, different roles of two kinds of nonequilibrium fluctuations for micro-magnetohydrodynamic (MHD) effects are discussed; symmetrical fluctuations are accompanied by the suppression of three dimensional (3D) nucleation by micro-MHD flows (the 1st micro-MHD effect), whereas asymmetrical fluctuations controlling 2D nucleation yield secondary nodules by larger micro-MHD flows (the 2nd micro-MHD effect). Though the 3D nucleation with symmetrical fluctuations is always suppressed by the micro-MHD flows, due to the change in the rate-determining step from electron transfer to mass transfer, the 2D nucleation with asymmetrical fluctuations newly turns unstable, generating larger micro-MHD flows. As a result, round semi-spherical deposits, i.e., secondary nodules are yielded. Using computer simulation, the mechanism of the 2nd micro-MHD effect is validated.
Khalid, Asma; Khan, Ilyas; Khan, Arshad; Shafie, Sharidan
2018-06-01
The intention here is to investigate the effects of wall couple stress with energy and concentration transfer in magnetohydrodynamic (MHD) flow of a micropolar fluid embedded in a porous medium. The mathematical model contains the set of linear conservation forms of partial differential equations. Laplace transforms and convolution technique are used for computation of exact solutions of velocity, microrotations, temperature and concentration equations. Numerical values of skin friction, couple wall stress, Nusselt and Sherwood numbers are also computed. Characteristics for the significant variables on the physical quantities are graphically discussed. Comparison with previously published work in limiting sense shows an excellent agreement.
International Nuclear Information System (INIS)
Falgarone, Edith; Rieutord, Michel; Richard, Denis; Zahn, Jean-Paul; Dauchot, Olivier; Daviaud, Francois; Dubrulle, Berengere; Laval, Jean-Philippe; Noullez, Alain; Bourgoin, Mickael; Odier, Philippe; Pinton, Jean-Francois; Leveque, Emmanuel; Chainais, Pierre; Abry, Patrice; Mordant, Nicolas; Michel, Olivier; Marie, Louis; Chiffaudel, Arnaud; Daviaud, Francois; Petrelis, Francois; Fauve, Stephan; Nore, C.; Brachet, M.-E.; Politano, H.; Pouquet, A.; Leorat, Jacques; Grapin, Roland; Brun, Sacha; Delour, Jean; Arneodo, Alain; Muzy, Jean-Francois; Magnaudet, Jacques; Braza, Marianna; Boree, Jacques; Maurel, S.; Ben, L.; Moreau, J.; Bazile, R.; Charnay, G.; Lewandowski, Roger; Laveder, Dimitri; Bouchet, Freddy; Sommeria, Joel; Le Gal, P.; Eloy, C.; Le Dizes, S.; Schneider, Kai; Farge, Marie; Bottausci, Frederic; Petitjeans, Philippe; Maurel, Agnes; Carlier, Johan; Anselmet, Fabien
2001-05-01
This publication gathers extended summaries of presentations proposed during two days on astrophysics and magnetohydrodynamics (MHD). The first session addressed astrophysics and MHD: The cold interstellar medium, a low ionized turbulent plasma; Turbulent convection in stars; Turbulence in differential rotation; Protoplanetary disks and washing machines; gravitational instability and large structures; MHD turbulence in the sodium von Karman flow; Numerical study of the dynamo effect in the Taylor-Green eddy geometry; Solar turbulent convection under the influence of rotation and of the magnetic field. The second session addressed the description of turbulence: Should we give up cascade models to describe the spatial complexity of the velocity field in a developed turbulence?; What do we learn with RDT about the turbulence at the vicinity of a plane surface?; Qualitative explanation of intermittency; Reduced model of Navier-Stokes equations: quickly extinguished energy cascade; Some mathematical properties of turbulent closure models. The third session addressed turbulence and coherent structures: Alfven wave filamentation and formation of coherent structures in dispersive MHD; Statistical mechanics for quasi-geo-strophic turbulence: applications to Jupiter's coherent structures; Elliptic instabilities; Physics and modelling of turbulent detached unsteady flows in aerodynamics and fluid-structure interaction; Intermittency and coherent structures in a washing machine: a wavelet analysis of joint pressure/velocity measurements; CVS filtering of 3D turbulent mixing layer using orthogonal wavelets. The last session addressed experimental methods: Lagrangian velocity measurements; Energy dissipation and instabilities within a locally stretched vortex; Study by laser imagery of the generation and breakage of a compressed eddy flow; Study of coherent structures of turbulent boundary layer at high Reynolds number
The influence of molecular complexity on expanding flows of ideal and dense gases
Harinck, J.; Guardone, A.; Colonna, P.
2009-01-01
This paper presents an investigation about the effect of the complexity of a fluid molecule on the fluid dynamic quantities sound speed, velocity, and Mach number in isentropic expansions. Ideal-gas and dense-gas expansions are analyzed, using the polytropic ideal gas and Van der Waals thermodynamic
Multi-region relaxed Hall magnetohydrodynamics with flow
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Lingam, Manasvi, E-mail: mlingam@princeton.edu [Department of Astrophysical Sciences, Princeton University, Princeton, New Jersey 08544 (United States); Abdelhamid, Hamdi M., E-mail: hamdi@ppl.k.u-tokyo.ac.jp [Graduate School of Frontier Sciences, The University of Tokyo, Kashiwanoha, Kashiwa, Chiba 277-8561 (Japan); Physics Department, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Hudson, Stuart R., E-mail: shudson@pppl.gov [Princeton Plasma Physics Laboratory, PO Box 451, Princeton, New Jersey 08543 (United States)
2016-08-15
The recent formulations of multi-region relaxed magnetohydrodynamics (MRxMHD) have generalized the famous Woltjer-Taylor states by incorporating a collection of “ideal barriers” that prevent global relaxation and flow. In this paper, we generalize MRxMHD with flow to include Hall effects, and thereby obtain the partially relaxed counterparts of the famous double Beltrami states as a special subset. The physical and mathematical consequences arising from the introduction of the Hall term are also presented. We demonstrate that our results (in the ideal MHD limit) constitute an important subset of ideal MHD equilibria, and we compare our approach against other variational principles proposed for deriving the partially relaxed states.
Real-gas effects 1: Simulation of ideal gas flow by cryogenic nitrogen and other selected gases
Hall, R. M.
1980-01-01
The thermodynamic properties of nitrogen gas do not thermodynamically approximate an ideal, diatomic gas at cryogenic temperatures. Choice of a suitable equation of state to model its behavior is discussed and the equation of Beattie and Bridgeman is selected as best meeting the needs for cryogenic wind tunnel use. The real gas behavior of nitrogen gas is compared to an ideal, diatomic gas for the following flow processes: isentropic expansion; normal shocks; boundary layers; and shock wave boundary layer interactions. The only differences in predicted pressure ratio between nitrogen and an ideal gas that may limit the minimum operating temperatures of transonic cryogenic wind tunnels seem to occur at total pressures approaching 9atmospheres and total temperatures 10 K below the corresponding saturation temperature, where the differences approach 1 percent for both isentropic expansions and normal shocks. Several alternative cryogenic test gases - air, helium, and hydrogen - are also analyzed. Differences in air from an ideal, diatomic gas are similar in magnitude to those of nitrogen. Differences for helium and hydrogen are over an order of magnitude greater than those for nitrogen or air. Helium and hydrogen do not approximate the compressible flow of an ideal, diatomic gas.
Characteristics of laminar MHD fluid hammer in pipe
International Nuclear Information System (INIS)
Huang, Z.Y.; Liu, Y.J.
2016-01-01
As gradually wide applications of MHD fluid, transportation as well as control with pumps and valves is unavoidable, which induces MHD fluid hammer. The paper attempts to combine MHD effect and fluid hammer effect and to investigate the characteristics of laminar MHD fluid hammer. A non-dimensional fluid hammer model, based on Navier–Stocks equations, coupling with Lorentz force is numerically solved in a reservoir–pipe–valve system with uniform external magnetic field. The MHD effect is represented by the interaction number which associates with the conductivity of the MHD fluid as well as the external magnetic field and can be interpreted as the ratio of Lorentz force to Joukowsky force. The transient numerical results of pressure head, average velocity, wall shear stress, velocity profiles and shear stress profiles are provided. The additional MHD effect hinders fluid motion, weakens wave front and homogenizes velocity profiles, contributing to obvious attenuation of oscillation, strengthened line packing and weakened Richardson annular effect. Studying the characteristics of MHD laminar fluid hammer theoretically supplements the gap of knowledge of rapid-transient MHD flow and technically provides beneficial information for MHD pipeline system designers to better devise MHD systems. - Highlights: • Characteristics of laminar MHD fluid hammer are discussed by simulation. • MHD effect has significant influence on attenuation of wave. • MHD effect strengthens line packing. • MHD effect inhibits Richardson annular effect.
Directory of Open Access Journals (Sweden)
K.V.S. Raju
2014-06-01
Full Text Available This paper deals with a steady MHD forced convective flow of a viscous fluid of finite depth in a saturated porous medium over a fixed horizontal channel with thermally insulated and impermeable bottom wall in the presence of viscous dissipation and joule heating. The governing equations are solved in the closed form and the exact solutions are obtained for velocity and temperature distributions when the temperatures on the fixed bottom and on the free surface are prescribed. The expressions for flow rate, mean velocity, temperature, mean temperature, mean mixed temperature in the flow region and the Nusselt number on the free surface have been obtained. The cases of large and small values of porosity coefficients have been obtained as limiting cases. Further, the cases of small depth (shallow fluid and large depth (deep fluid are also discussed. The results are presented and discussed with the help of graphs.
Wind Tunnel Study on Flows over Various Two-dimensional Idealized Urban-liked Surfaces
Ho, Yat-Kiu; Liu, Chun-Ho
2013-04-01
Extensive human activities (e.g. increased traffic emissions) emit a wide range of pollutants resulting in poor urban area air quality. Unlike open, flat and homogenous rural terrain, urban surface is complicated by the presence of buildings, obstacles and narrow streets. The irregular urban surfaces thus form a random roughness that further modifies the near-surface flows and pollutant dispersion. In this study, a physical modelling approach is employed to commence a series of wind tunnel experiments to study the urban-area air pollution problems. The flow characteristics over different hypothetical urban roughness surfaces were studied in a wind tunnel in isothermal conditions. Preliminary experiments were conducted based on six types of idealized two-dimensional (2D) street canyon models with various building-height-to-street-width (aspect) ratios (ARs) 1, 1/2, 1/4, 1/8, 1/10 and 1/12. The main instrumentation is an in-house 90o X-hotwire anemometry. In each set of configuration, a sampling street canyon was selected near the end of the streamwise domain. Its roof level, i.e. the transverse between the mid points of the upstream and downstream buildings, was divided into eight segments. The measurements were then recorded on the mid-plane of the spannwise domain along the vertical profile (from building roof level to the ceiling of wind tunnel) of the eight segments. All the data acquisition processes were handled by the NI data acquisition modules, NI 9239 and CompactDAQ-9188 hardware. Velocity calculation was carried out in the post-processing stage on a digital computer. The two-component flow velocities and velocity fluctuations were calculated at each sampling points, therefore, for each model, a streamwise average of eight vertical profiles of mean velocity and velocity fluctuations was presented. A plot of air-exchange rate (ACH) against ARs was also presented in order to examine the ventilation performance of different tested models. Preliminary results
Anisotropic plasma with flows in tokamak: Steady state and stability
International Nuclear Information System (INIS)
Ilgisonis, V.I.
1996-01-01
An adequate description of equilibrium and stability of anisotropic plasma with macroscopic flows in tokamaks is presented. The Chew-Goldberger-Low (CGL) approximation is consistently used to analyze anisotropic plasma dynamics. The admissible structure of a stationary flow is found to be the same as in the ideal magnetohydrodynamics with isotropic pressure (MHD), which means an allowance for the same relabeling symmetry as in ideal MHD systems with toroidally nested magnetic surfaces. A generalization of the Grad-Shafranov equation for the case of anisotropic plasma with flows confined in the axisymmetric magnetic field is derived. A variational principle was obtained, which allows for a stability analysis of anisotropic pressure plasma with flows, and takes into account the conservation laws resulting from the relabeling symmetry. This principle covers the previous stability criteria for static CGL plasma and for ideal MHD flows in isotropic plasma as well. copyright 1996 American Institute of Physics
Advanced energy utilization MHD power generation
International Nuclear Information System (INIS)
2008-01-01
The 'Technical Committee on Advanced Energy Utilization MHD Power Generation' was started to establish advanced energy utilization technologies in Japan, and has been working for three years from June 2004 to May 2007. This committee investigated closed cycle MHD, open cycle MHD, and liquid metal MHD power generation as high-efficiency power generation systems on the earth. Then, aero-space application and deep space exploration technologies were investigated as applications of MHD technology. The spin-off from research and development on MHD power generation such as acceleration and deceleration of supersonic flows was expected to solve unstart phenomena in scramjet engine and also to solve abnormal heating of aircrafts by shock wave. In addition, this committee investigated researches on fuel cells, on secondary batteries, on connection of wind power system to power grid, and on direct energy conversion system from nuclear fusion reactor for future. The present technical report described results of investigations by the committee. (author)
MHD instabilities in heliotron/torsatron
International Nuclear Information System (INIS)
Wakatani, Masahiro; Nakamura, Yuji; Ichiguchi, Katsuji
1992-01-01
Recent theoretical results on MHD instabilities in heliotron/torsatron are reviewed. By comparing the results with experimental data in Heliotron E, Heliotron DR and ATF, it is pointed out that resistive interchange modes are the most crucial instabilities, since the magnetic hill occupies a substantial region of the plasma column. Development of three-dimensional MHD equilibrium codes has made significant progress. By applying the local stability criteria shown by D 1 (ideal MHD mode) and D R (resistive MHD mode) to the equilibria given by the three-dimensional codes such as BETA and VMEC, stability thresholds for the low n ideal modes or the low n resistive modes may be estimated with resonable accuracy, where n is a toroidal mode number. (orig.)
International Nuclear Information System (INIS)
Reed, C.B.; Mattas, R.F.; Smith, D.L.; Chung, H.; Tsai, H.-C.; Morgan, G.D.; Wille, G.W.; Young, C.
1996-01-01
To test the magnetohydrodynamic (MHD) pressure drop reduction performance of candidate insulator coatings for the ITER Vanadium/Lithium Breeding Blanket, a test section comprised of a V- 4Cr-4Ti liner inside a stainless steel pipe was designed and fabricated. Theoretically, the MHD pressure drop reduction benefit resulting, from an electrically insulating coating on a vanadium- lined pipe is identical to the benefit derived from an insulated pipe fabricated of vanadium alone. A duplex test section design consisting of a V alloy liner encased in a SS pressure boundary provided protection for vanadium from atmospheric contamination during operation at high temperature and obviated any potential problems with vanadium welding while also minimizing the amount of V alloy material required. From the MHD and insulator coating- point of view, the test section outer SS wall and inner V alloy liner can be modeled simply as a wall having a sandwich construction. Two 52.3 mm OD x 2.9 m long V-alloy tubes were fabricated by Century Tubes from 64 mm x 200 mm x 1245 mm extrusions produced by Teledyne Wah Chang. The test section's duplex structure was subsequently fabricated at Century Tubes by drawing down a SS pipe (2 inch schedule 10) over one of the 53.2 mm diameter V tubes
Equations of state for self-excited MHD generator studies
Energy Technology Data Exchange (ETDEWEB)
Rogers, F.J.; Ross, M.; Haggin, G.L.; Wong, L.K.
1980-02-26
We have constructed a state-of-the-art equation of state (EOS) for argon covering the temperature density range attainable by currently proposed self-excited MHD generators. The EOS for conditions in the flow channel was obtained primarily by a non-ideal plasma code (ACTEX) that is based on a many body activity expansion. For conditions in the driver chamber the EOS was primarily obtained from a fluid code (HDFP) that calculates the fluid properties from perturbation theory based on the insulator interatomic pair potential but including electronic excitations. The results are in agreement with several sets of experimental data in the 0.6 - 91 GPa pressure range.
Hall, R. M.; Adcock, J. B.
1981-01-01
The real gas behavior of nitrogen, the gas normally used in transonic cryogenic tunnels, is reported for the following flow processes: isentropic expansion, normal shocks, boundary layers, and interactions between shock waves and boundary layers. The only difference in predicted pressure ratio between nitrogen and an ideal gas which may limit the minimum operating temperature of transonic cryogenic wind tunnels occur at total pressures approaching 9 atm and total temperatures 10 K below the corresponding saturation temperature. These pressure differences approach 1 percent for both isentropic expansions and normal shocks. Alternative cryogenic test gases were also analyzed. Differences between air and an ideal diatomic gas are similar in magnitude to those for nitrogen and should present no difficulty. However, differences for helium and hydrogen are over an order of magnitude greater than those for nitrogen or air. It is concluded that helium and cryogenic hydrogen would not approximate the compressible flow of an ideal diatomic gas.
MHD stability analysis of helical system plasmas
International Nuclear Information System (INIS)
Nakamura, Yuji
2000-01-01
Several topics of the MHD stability studies in helical system plasmas are reviewed with respect to the linear and ideal modes mainly. Difference of the method of the MHD stability analysis in helical system plasmas from that in tokamak plasmas is emphasized. Lack of the cyclic (symmetric) coordinate makes an analysis more difficult. Recent topic about TAE modes in a helical system is also described briefly. (author)
International Nuclear Information System (INIS)
Trommer, G.
1979-08-01
This report deals with theoretical calculations of MHD pressure losses of liquid-lithium flows in tubes of circular cross-section exposed to strong magnetic fields. Some simplifying assumptions were introduced, yielding an analytical solution which allows the pressure drop and losses in double tubes of coaxial geometry to be compared with those in normal flow pipes. The investigations show that coaxial ducts require much more pumping power than normal ones under similar conditions. This great difference of the properties of the two duct types will decrease if the pipes are embedded in materials of good electrical conductivity. In this case the normal duct will afford a drastic increase in the pressure drop, while the coaxial one will be nearly unaffected. But even under these conditions the losses of the latter will dominate. (orig.)
Magnetohydrodynamic (MHD) power generation
International Nuclear Information System (INIS)
Chandra, Avinash
1980-01-01
The concept of MHD power generation, principles of operation of the MHD generator, its design, types, MHD generator cycles, technological problems to be overcome, the current state of the art in USA and USSR are described. Progress of India's experimental 5 Mw water-gas fired open cycle MHD power generator project is reported in brief. (M.G.B.)
Neoclassical MHD equations for tokamaks
International Nuclear Information System (INIS)
Callen, J.D.; Shaing, K.C.
1986-03-01
The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion
International Nuclear Information System (INIS)
Likhachev, A P; Medin, S A
2010-01-01
The simultaneous development of the MHD instabilities of Raylegh-Taylor and Kelvin-Helmholtz types at the interface between high-conducting plasmoid and surrounding non- or low-conducting gas is considered. The linear stage of the RTI development is studied analytically for incompressible and compressible fluids. The nonlinear stage of the individual development of the RTI and the coupled development of both instabilities has been investigated numerically. The time-dependent two-dimensional numerical model based on the solution of the Euler gasdynamic equations with body momentum and energy sources of MHD origin has been developed and used in calculations. A disturbance introducing in the background flow has been periodic with varied assignment type and wave length. Fundamental difference between the results of linear and nonlinear analysis has been revealed. In particular, the increment of the RTI development at nonlinear stage is one-two order of magnitude less than that predicted by linear theory and rather weakly depends on initial disturbance mode. In linear analysis the coupled development of the RTI and the KHI is determined by simple summing of the two effects in the expression of wave increment, whereas in nonlinear case the mutual influence of the instabilities leads to essential alterations in their development, main of which is the intensive 'layer-by-layer' destruction of the plasmoid surface.
Directory of Open Access Journals (Sweden)
S.M. Arifuzzaman
2018-04-01
Full Text Available This paper concerns with the modelling of an unsteady natural convective and higher order chemically reactive magnetohydrodynamics (MHD fluid flow with the effect of heat and radiation absorption. The flow is generated through a vertical oscillating porous plate. Boundary layer approximations is carried out to establish a flow model which represents the time dependent momentum, energy and diffusion balance equations. Before being solved numerically, the governing partial differential equations (PDEs were transformed into a set of nonlinear ordinary differential equation (ODEs by using non-similar technique. A very efficient numerical approach solves the obtained nonlinear coupled ODEs so called Explicit Finite Difference Method (EFDM. An algorithm is implemented in Compaq Visual Fortran 6.6a as a solving tool. In addition, the stability and convergence analysis (SCA is examined and shown explicitly. The advantages of SCA is its optimizes the accuracy of system parameters such as Prandtl number (Pr and Schmidt number (Sc.The velocity, temperature and concentration fields in the boundary layer region are studied in detail and the outcomes are shown in graphically with the influence of various pertinent parameters such as Grashof number (Gr, modified Grashof number (Gr, magnetic parameter (M, Darcy number (Da,Prandtl number (Pr, Schmidt number (Sc, radiation (R, heat sink (Q,radiation absorption (Q1, Eckert number (Ec, Dufour number (Du,Soret number (Sr, Schmidt number (Sc, reaction index (P and chemical reaction (Kr. Furthermore, the effect of skin friction coefficient (Cf, Nusselt number (Nu and Sherwood number (Sh are also examined graphically. Keywords: MHD, Oscillating porous plate, Radiation absorption, High order chemical reaction, EFDM
Directory of Open Access Journals (Sweden)
G. Nath
2012-12-01
Full Text Available Self-similar solutions are obtained for unsteady, one-dimensional isothermal flow behind a shock wave in a rotational axisymmetric non-ideal gas in the presence of an azimuthal magnetic field. The shock wave is driven out by a piston moving with time according to power law. The fluid velocities and the azimuthal magnetic field in the ambient medium are assumed to be varying and obeying a power law. The density of the ambient medium is assumed to be constant. The gas is assumed to be non-ideal having infinite electrical conductivity and the angular velocity of the ambient medium is assumed to be decreasing as the distance from the axis increases. It is expected that such an angular velocity may occur in the atmospheres of rotating planets and stars. The effects of the non-idealness of the gas and the Alfven-Mach number on the flow-field are obtained. It is shown that the presence of azimuthal magnetic field and the rotation of the medium has decaying effect on the shock wave. Also, a comparison is made between rotating and non-rotating cases.
Free-boundary perturbed MHD equilibria
International Nuclear Information System (INIS)
Nührenberg, C
2012-01-01
The concept of perturbed ideal MHD equilibria [Boozer A H and Nuhrenberg C 2006 Phys. Plasmas 13 102501] is employed to study the influence of external error-fields and of small plasma-pressure changes on toroidal plasma equilibria. In tokamak and stellarator free-boundary calculations, benchmarks were successful of the perturbed-equilibrium version of the CAS3D stability code [Nührenberg C et al. 2009 Phys. Rev. Lett. 102 235001] with the ideal MHD equilibrium code NEMEC [Hirshman S P et al. 1986 Comput. Phys. Commun. 43 143].
Jusoh, Rahimah; Nazar, Roslinda
2018-04-01
The magnetohydrodynamic (MHD) stagnation point flow and heat transfer of an electrically conducting nanofluid over a nonlinear stretching/shrinking sheet is studied numerically. Mathematical modelling and analysis are attended in the presence of viscous dissipation. Appropriate similarity transformations are used to reduce the boundary layer equations for momentum, energy and concentration into a set of ordinary differential equations. The reduced equations are solved numerically using the built in bvp4c function in Matlab. The numerical and graphical results on the effects of various parameters on the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number are analyzed and discussed in this paper. The study discovers the existence of dual solutions for a certain range of the suction parameter. The conducted stability analysis reveals that the first solution is stable and feasible, while the second solution is unstable.
Shateyi, Stanford; Marewo, Gerald T.
2018-05-01
We numerically investigate a mixed convection model for a magnetohydrodynamic (MHD) Jeffery fluid flowing over an exponentially stretching sheet. The influence of thermal radiation and chemical reaction is also considered in this study. The governing non-linear coupled partial differential equations are reduced to a set of coupled non-linear ordinary differential equations by using similarity functions. This new set of ordinary differential equations are solved numerically using the Spectral Quasi-Linearization Method. A parametric study of physical parameters involved in this study is carried out and displayed in tabular and graphical forms. It is observed that the velocity is enhanced with increasing values of the Deborah number, buoyancy and thermal radiation parameters. Furthermore, the temperature and species concentration are decreasing functions of the Deborah number. The skin friction coefficient increases with increasing values of the magnetic parameter and relaxation time. Heat and mass transfer rates increase with increasing values of the Deborah number and buoyancy parameters.
International Nuclear Information System (INIS)
Zniber, K.; Oubarra, A.; Lahjomri, J.
2005-01-01
An MHD laminar flow through a two dimensional channel subjected to a uniform magnetic field and heated at the walls of the conduit over the whole length with a sinusoidal heat flux of vanishing mean value or not, is studied analytically. General expressions of the temperature distribution and of the local and mean Nusselt numbers are obtained by using the technique of linear operators in the case of negligible Joule and viscous dissipation and by taking into account the axial conduction effect. The principal results show that an increase of the local Nusselt number with Hartmann number is observed, and, far from the inlet section, the average heat transfer between the fluid and the walls shows a significant improvement at all values of Hartmann number used when the frequency of the prescribed sinusoidal wall heat flux is increasing in the case of vanishing mean value of the heat flux and this is true especially at low Peclet numbers
Adem, Abdullahi Rashid; Moawad, Salah M.
2018-05-01
In this paper, the steady-state equations of ideal magnetohydrodynamic incompressible flows in axisymmetric domains are investigated. These flows are governed by a second-order elliptic partial differential equation as a type of generalized Grad-Shafranov equation. The problem of finding exact equilibria to the full governing equations in the presence of incompressible mass flows is considered. Two different types of constraints on position variables are presented to construct exact solution classes for several nonlinear cases of the governing equations. Some of the obtained results are checked for their applications to magnetic confinement plasma. Besides, they cover many previous configurations and include new considerations about the nonlinearity of magnetic flux stream variables.
On nonlinear MHD-stability of toroidal magnetized plasma
International Nuclear Information System (INIS)
Ilgisonis, V.I.; Pastukhov, V.P.
1994-01-01
The variational approach to analyze the nonlinear MHD stability of ideal plasma in toroidal magnetic field is proposed. The potential energy functional to be used is expressed in terms of complete set of independent Lagrangian invariants, that allows to take strictly into account all the restrictions inherent in the varied functions due to MHD dynamic equations. (author). 3 refs
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Muhammad Ramzan
Full Text Available The aim of present paper is to study the series solution of time dependent MHD second grade incompressible nanofluid towards a stretching sheet. The effects of mixed convection and thermal radiation are also taken into account. Because of nanofluid model, effects Brownian motion and thermophoresis are encountered. The resulting nonlinear momentum, heat and concentration equations are simplified using appropriate transformations. Series solutions have been obtained for velocity, temperature and nanoparticle fraction profiles using Homotopy Analysis Method (HAM. Convergence of the acquired solution is discussed critically. Behavior of velocity, temperature and concentration profiles on the prominent parameters is depicted and argued graphically. It is observed that temperature and concentration profiles show similar behavior for thermophoresis parameter Νt but opposite tendency is noted in case of Brownian motion parameter Νb. It is further analyzed that suction parameter S and Hartman number Μ depict decreasing behavior on velocity profile.
Sucharitha, G.; Sreenadh, S.; Lakshminarayana, P.; Sushma, K.
2017-11-01
The slip and heat transfer effects on MHD peristaltic transport of a nanofluid in a non-uniform symmetric/asymmetric channel have studied under the assumptions of elongated wave length and negligible Reynolds number. From the simplified governing equations, the closed form solutions for velocity, stream function, temperature and concentrations are obtained. Also dual solutions are discussed for symmetric and asymmetric channel cases. The effects of important physical parameters are explained graphically. The slip parameter decreases the fluid velocity in middle of the channel whereas it increases the velocity at the channel walls. Temperature and concentration are decreasing and increasing functions of radiation parameter respectively. Moreover, velocity, temperature and concentrations are high in symmetric channel when compared with asymmetric channel.
Ideal point error for model assessment in data-driven river flow forecasting
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C. W. Dawson
2012-08-01
Full Text Available When analysing the performance of hydrological models in river forecasting, researchers use a number of diverse statistics. Although some statistics appear to be used more regularly in such analyses than others, there is a distinct lack of consistency in evaluation, making studies undertaken by different authors or performed at different locations difficult to compare in a meaningful manner. Moreover, even within individual reported case studies, substantial contradictions are found to occur between one measure of performance and another. In this paper we examine the ideal point error (IPE metric – a recently introduced measure of model performance that integrates a number of recognised metrics in a logical way. Having a single, integrated measure of performance is appealing as it should permit more straightforward model inter-comparisons. However, this is reliant on a transferrable standardisation of the individual metrics that are combined to form the IPE. This paper examines one potential option for standardisation: the use of naive model benchmarking.
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B. R. Rout
2013-01-01
Full Text Available This paper aims to investigate the influence of chemical reaction and the combined effects of internal heat generation and a convective boundary condition on the laminar boundary layer MHD heat and mass transfer flow over a moving vertical flat plate. The lower surface of the plate is in contact with a hot fluid while the stream of cold fluid flows over the upper surface with heat source and chemical reaction. The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. The effects of physical parameters on the velocity, temperature, and concentration profiles are illustrated graphically. A table recording the values of skin friction, heat transfer, and mass transfer at the plate is also presented. The discussion focuses on the physical interpretation of the results as well as their comparison with previous studies which shows good agreement as a special case of the problem.
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Fiaz Ur Rehman
2018-03-01
Full Text Available In the present paper a theoretical investigation is performed to analyze heat and mass transport enhancement of water-based nanofluid for three dimensional (3D MHD stagnation-point flow caused by an exponentially stretched surface. Water is considered as a base fluid. There are three (3 types of nanoparticles considered in this study namely, CuO (Copper oxide, Fe3O4 (Magnetite, and Al2O3 (Alumina are considered along with water. In this problem we invoked the boundary layer phenomena and suitable similarity transformation, as a result our three dimensional non-linear equations of describing current problem are transmuted into nonlinear and non-homogeneous differential equations involving ordinary derivatives. We solved the final equations by applying homotopy analysis technique. Influential outcomes of aggressing parameters involved in this study, effecting profiles of temperature field and velocity are explained in detail. Graphical results of involved parameters appearing in considered nanofluid are presented separately. It is worth mentioning that Skin-friction along x and y-direction is maximum for Copper oxide-water nanofluid and minimum for Alumina-water nanofluid. Result for local Nusselt number is maximum for Copper oxide-water nanofluid and is minimum for magnetite-water nanofluid. Keywords: Heat transfer, Nanofluids, Stagnation-point flow, Three-dimensional flow, Nano particles, Boundary layer
Idealized debris flow in flume with bed driven by a conveyor belt
Ling, Chi-Hai; Chen, Cheng-lung
1989-01-01
The generalized viscoplastic fluid (GVF) model is used to derive the theoretical expressions of two-dimensional velocities and surface profile for debris flow established in a flume with bed driven by a conveyor belt. The rheological parameters of the GVF model are evaluated through the comparison of theoretical results with measured data. A slip velocity of the established (steady) nonuniform flow on the moving bed (i.e., the conveyor belt) is observed, and a relation between the slip velocity and the velocity gradient at the bed is derived. Two belts, one rough and the other smooth, were tested. The flow profile in the flume is found to be linear and dependent on the roughness of the belt, but not much on its speed.
The ideal oxygen/nitrous oxide fresh gas flow sequence with the Anesthesia Delivery Unit machine.
Hendrickx, Jan F A; Cardinael, Sara; Carette, Rik; Lemmens, Hendrikus J M; De Wolf, Andre M
2007-06-01
To determine whether early reduction of oxygen and nitrous oxide fresh gas flow from 6 L/min to 0.7 L/min could be accomplished while maintaining end-expired nitrous oxide concentration > or =50% with an Anesthesia Delivery Unit anesthesia machine. Prospective, randomized clinical study. Large teaching hospital in Belgium. 53 ASA physical status I and II patients requiring general endotracheal anesthesia and controlled mechanical ventilation. Patients were randomly assigned to one of 4 groups depending on the duration of high oxygen/nitrous oxide fresh gas flow (two and 4 L/min, respectively) before lowering total fresh gas flow to 0.7 L/min (0.3 and 0.4 L/min oxygen and nitrous oxide, respectively): one, two, three, or 5 minutes (1-minute group, 2-minute group, 3-minute group, and 5-minute group), with n = 10, 12, 13, and 8, respectively. The course of the end-expired nitrous oxide concentration and bellows volume deficit at end-expiration was compared among the 4 groups during the first 30 minutes. At the end of the high-flow period the end-expired nitrous oxide concentration was 35.6 +/- 6.2%, 48.4 +/- 4.8%, 53.7 +/- 8.7%, and 57.3 +/- 1.6% in the 4 groups, respectively. Thereafter, the end-expired nitrous oxide concentration decreased to a nadir of 36.1 +/- 4.5%, 45.4 +/- 3.8%, 50.9 +/- 6.1%, and 55.4 +/- 2.8% after three, 4, 6, and 8 minutes after flows were lowered in the 1- to 5-minute groups, respectively. A decrease in bellows volume was observed in most patients, but was most pronounced in the 2-minute group. The bellows volume deficit gradually faded within 15 to 20 minutes in all 4 groups. A 3-minute high-flow period (oxygen and nitrous oxide fresh gas flow of 2 and 4 L/min, respectively) suffices to attain and maintain end-expired nitrous oxide concentration > or =50% and ensures an adequate bellows volume during the ensuing low-flow period.
Guizzo, Francesca; Cadinu, Mara
2017-06-01
Although previous research has demonstrated that objectification impairs female cognitive performance, no research to date has investigated the mechanisms underlying such decrement. Therefore, we tested the role of flow experience as one mechanism leading to performance decrement under sexual objectification. Gaze gender was manipulated by having male versus female experimenters take body pictures of female participants (N = 107) who then performed a Sustained Attention to Response Task. As predicted, a moderated mediation model showed that under male versus female gaze, higher internalization of beauty ideals was associated with lower flow, which in turn decreased performance. The implications of these results are discussed in relation to objectification theory and strategies to prevent sexually objectifying experiences. © 2016 The British Psychological Society.
Energy Technology Data Exchange (ETDEWEB)
None
1979-01-01
Progress is reported on the following tasks: characterization of coal for open-cycle MHD power generation systems; compressive creep and strength studies of MHD preheater materials; preparation of coals for utilization in direct coal-fired MHD generation; characterization of volatile matter in coal; MHD materials evaluation; operability of the Moderate Temperature Slag Flow Facility; slag-seed equilibria and separations related to the MHD system; thermionic emission of coal and electrode materials; MHD instrumentation, consolidated inversion simulator, and data acquisition; combined MHD-steam plant cycle analysis and control; and slag physical properties - electrical and thermal conductivity. (WHK)
Energy Technology Data Exchange (ETDEWEB)
Krasnov, D.; Boeck, T. [Technische Univ. Ilmenau (Germany). Inst. of Thermodynamics and Fluid Mechanics; Braiden, L.; Molokov, S. [Conventry Univ. (United Kingdom). Dept. of Mathematics and Physics; Buehler, L. [Karlsruher Institut fuer Technologie (Germany). Inst. fuer Kern- und Energietechnik, Programm Kernfusion
2016-07-01
Pressure-driven magnetohydrodynamic duct flows in a transverse, wall-parallel and uniform field have been studied by direct numerical. The conducting Hartmann walls give rise to a laminar velocity distribution with strong jets at the side walls, which are susceptible to flow instability. The onset of time-dependent flow as well as fully developed turbulent flow have been explored in a wide range of parameters.
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S. Baag
2017-01-01
Full Text Available In this paper, the steady magnetohydrodynamic (MHD mixed convection stagnation point flow of an incompressible and electrically conducting micropolar fluid past a vertical flat plate is investigated. The effects of induced magnetic field, heat generation/absorption and chemical reaction have been taken into account during the present study. Numerical solutions are obtained by using the Runge–Kutta fourth order scheme with shooting technique. The skin friction and rate of heat and mass transfer at the bounding surface are also calculated. The generality of the present study is assured of by discussing the works of Ramachandran et al. (1988, Lok et al. (2005 and Ishak et al. (2008 as particular cases. It is interesting to note that the results of the previous authors are in good agreement with the results of the present study tabulated which is evident from the tabular values. Further, the novelty of the present analysis is to account for the effects of first order chemical reaction in a flow of reactive diffusing species in the presence of heat source/sink. The discussion of the present study takes care of both assisting and opposing flows. From the computational aspect, it is remarked that results of finite difference (Ishak et al. (2008 and Runge–Kutta associated with shooting technique (present method yield same numerical results with a certain degree of accuracy. It is important to note that the thermal buoyancy parameter in opposing flow acts as a controlling parameter to prevent back flow. Diffusion of lighter foreign species, suitable for initiating a destructive reaction, is a suggestive measure for reducing skin friction.
Chung, Joon Ho; Shin, Yong Sam; Lim, Yong Cheol; Park, Minjung
2009-01-01
Internal carotid artery (ICA) trapping can be used for treating intracranial giant aneurysm, blood blister-like aneurysms and ICA rupture during the surgery. We present a novel ICA trapping technique which can be used with insufficient collaterals flow via anterior communicating artery (AcoA) and posterior communicating artery (PcoA). A patient was admitted with severe headache and the cerebral angiography demonstrated a typical blood blister-like aneurysm at the contralateral side of PcoA. F...
An Experimental Investigation of the Flow Past an Idealized Wing-Body Junction
1990-07-01
kilooras per meter cubed) x 1.120746 viscosity ( oeters squired per second) a !.63427SE-35 Atmospheric pressure (Pascals) ’: 95575 Velocity of...per oeter cubed) =1.106 viscosity (Neters squared per second) =1.65237E-05 Ataospheric pressure (Pascals) = 94000 Velocity of undisturbed free streac...system of the laser anemometer Flow tetoerature (degrees centigrade) =24.6 density (kilograms per Peter cubed) =1.105086 visa-sity ( oeters scuarec ner
MHD stability, operational limits and disruptions
International Nuclear Information System (INIS)
1999-01-01
The present physics understandings of magnetohydrodynamic (MHD) stability of tokamak plasmas, the threshold conditions for onset of MHD instability, and the resulting operational limits on attainable plasma pressure (beta limit) and density (density limit), and the consequences of plasma disruption and disruption related effects are reviewed and assessed in the context of their application to a future DT burning reactor prototype tokamak experiment such as ITER. The principal considerations covered within the MHD stability and beta limit assessments are (i) magnetostatic equilibrium, ideal MHD stability and the resulting ideal MHD beta limit; (ii) sawtooth oscillations and the coupling of sawtooth activity to other types of MHD instability; (iii) neoclassical island resistive tearing modes and the corresponding limits on beta and energy confinement; (iv) wall stabilization of ideal MHD instabilities and resistive wall instabilities; (v) mode locking effects of non-axisymmetric error fields; (vi) edge localized MHD instabilities (ELMs, etc.); and (vii) MHD instabilities and beta/pressure gradient limits in plasmas with actively modified current and magnetic shear profiles. The principal considerations covered within the density limit assessments are (i) empirical density limits; (ii) edge power balance/radiative density limits in ohmic and L-mode plasmas; and (iii) edge parameter related density limits in H-mode plasmas. The principal considerations covered in the disruption assessments are (i) disruption causes, frequency and MHD instability onset; (ii) disruption thermal and current quench characteristics; (iii) vertical instabilities (VDEs), both before and after disruption, and plasma and in-vessel halo currents; (iv) after disruption runaway electron formation, confinement and loss; (v) fast plasma shutdown (rapid externally initiated dissipation of plasma thermal and magnetic energies); (vi) means for disruption avoidance and disruption effect mitigation; and
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M. Schüssler
Full Text Available Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere ('convective collapse' are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 10^{5} G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.
Key words. Solar physics · astrophysics and astronomy (photosphere and chromosphere; stellar interiors and dynamo theory; numerical simulation studies.
Linear Simulations of the Cylindrical Richtmyer-Meshkov Instability in Hydrodynamics and MHD
Gao, Song
2013-05-01
The Richtmyer-Meshkov instability occurs when density-stratified interfaces are impulsively accelerated, typically by a shock wave. We present a numerical method to simulate the Richtmyer-Meshkov instability in cylindrical geometry. The ideal MHD equations are linearized about a time-dependent base state to yield linear partial differential equations governing the perturbed quantities. Convergence tests demonstrate that second order accuracy is achieved for smooth flows, and the order of accuracy is between first and second order for flows with discontinuities. Numerical results are presented for cases of interfaces with positive Atwood number and purely azimuthal perturbations. In hydrodynamics, the Richtmyer-Meshkov instability growth of perturbations is followed by a Rayleigh-Taylor growth phase. In MHD, numerical results indicate that the perturbations can be suppressed for sufficiently large perturbation wavenumbers and magnetic fields.
MHD stability of vertically asymmetric tokamak equilibria
International Nuclear Information System (INIS)
Dalhed, H.E.; Grimm, R.C.; Johnson, J.L.
1981-03-01
The ideal MHD stability properties of a special class of vertically asymmetric tokamak equilibria are examined. The calculations confirm that no major new physical effects are introduced and the modifications can be understood by conventional arguments. The results indicate that significant departures from up-down symmetry can be tolerated before the reduction in β becomes important for reactor operation
Lee, Jeffrey M.
1999-01-01
This study establishes a consistent set of differential equations for use in describing the steady secondary flows generated by periodic compression and expansion of an ideal gas in pulse tubes. Also considered is heat transfer between the gas and the tube wall of finite thickness. A small-amplitude series expansion solution in the inverse Strouhal number is proposed for the two-dimensional axisymmetric mass, momentum and energy equations. The anelastic approach applies when shock and acoustic energies are small compared with the energy needed to compress and expand the gas. An analytic solution to the ordered series is obtained in the strong temperature limit where the zeroth-order temperature is constant. The solution shows steady velocities increase linearly for small Valensi number and can be of order I for large Valensi number. A conversion of steady work flow to heat flow occurs whenever temperature, velocity or phase angle gradients are present. Steady enthalpy flow is reduced by heat transfer and is scaled by the Prandtl times Valensi numbers. Particle velocities from a smoke-wire experiment were compared with predictions for the basic and orifice pulse tube configurations. The theory accurately predicted the observed steady streaming.
The Impact of Dry Midlevel Air on Hurricane Intensity in Idealized Simulations with No Mean Flow
Braun, Scott A.; Sippel, Jason A.; Nolan, David S.
2012-01-01
This study examines the potential negative influences of dry midlevel air on the development of tropical cyclones (specifically, its role in enhancing cold downdraft activity and suppressing storm development). The Weather Research and Forecasting model is used to construct two sets of idealized simulations of hurricane development in environments with different configurations of dry air. The first set of simulations begins with dry air located north of the vortex center by distances ranging from 0 to 270 km, whereas the second set of simulations begins with dry air completely surrounding the vortex, but with moist envelopes in the vortex core ranging in size from 0 to 150 km in radius. No impact of the dry air is seen for dry layers located more than 270 km north of the initial vortex center (approximately 3 times the initial radius of maximum wind). When the dry air is initially closer to the vortex center, it suppresses convective development where it entrains into the storm circulation, leading to increasingly asymmetric convection and slower storm development. The presence of dry air throughout the domain, including the vortex center, substantially slows storm development. However, the presence of a moist envelope around the vortex center eliminates the deleterious impact on storm intensity. Instead, storm size is significantly reduced. The simulations suggest that dry air slows intensification only when it is located very close to the vortex core at early times. When it does slow storm development, it does so primarily by inducing outward- moving convective asymmetries that temporarily shift latent heating radially outward away from the high-vorticity inner core.
Lyapunov stability analysis of magnetohydrodynamic plasma equilibria with axisymmetric toroidal flow
International Nuclear Information System (INIS)
Almaguer, J.A.; Hameiri, E.; Herrera, J.; Holm, D.D.
1988-01-01
Lyapunov stability conditions for ideal magnetohydrodynamic (MHD) plasmas with mass flow in axisymmetric toroidal geometry are determined in the Eulerian representation. Axisymmetric equilibrium solutions of ideal MHD are associated to critical points of a nonlinearly conserved Lyapunov functional consisting of the sum of the total energy and the following flux-weighted quantities: the circulation along field lines, the angular momentum, the toroidal flux, and the mass content within each flux tube. Conditions sufficient for Lyapunov stability of these equilibria against axisymmetric perturbations are found by taking advantage of the Hamiltonian formalism for ideal MHD. In particular [see Eq. (60)], it is sufficient for Lyapunov stability under linearized dynamics that an axisymmetric equilibrium be subsonic in the appropriate rotating frame, lie in the first elliptic regime of the Bernoulli--Grad--Shafranov (BGS) system of equations, and satisfy one additional, more complicated, condition. Effects of boundary conditions, nonlinearity, and three-dimensionality on MHD stability are also discussed
Directory of Open Access Journals (Sweden)
Farhad Ali
2013-01-01
Full Text Available The focus of this paper is to analyze the influence of thermal radiation on some unsteady magnetohydrodynamic (MHD free convection flows of an incompressible Brinkman type fluid past a vertical flat plate embedded in a porous medium with the Newtonian heating boundary condition. The fluid is considered as a gray absorbing-emitting but nonscattering medium and the Rosseland approximation in the energy equations is used to describe the radiative heat flux for optically thick fluid. For a detailed analysis of the problem, four important situations of flow due to (i impulsive motion of the plate (ii uniform acceleration of the plate (iii nonuniform acceleration of the plate, and (iv highly nonuniform acceleration of the plate are considered. The governing equations are first transformed into a system of dimensionless equations and then solved analytically using the Laplace transform technique. Numerical results for temperature and velocity are shown graphically, while skin friction and Nusselt number are computed in tables. The results show that temperature and velocity increase on increasing radiation and Newtonian heating parameters. However, the results of magnetic and porosity parameters on velocity are found quite opposite.
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Mohammad Ishaq
2018-05-01
Full Text Available This research paper investigates entropy generation analysis on two-dimensional nanofluid film flow of Eyring–Powell fluid with heat amd mass transmission over an unsteady porous stretching sheet in the existence of uniform magnetic field (MHD. The flow of liquid films are taken under the impact of thermal radiation. The basic time dependent equations of heat transfer, momentum and mass transfer are modeled and converted to a system of differential equations by employing appropriate similarity transformation with unsteady dimensionless parameters. Entropy analysis is the main focus in this work and the impact of physical parameters on the entropy profile are discussed in detail. The influence of thermophoresis and Brownian motion has been taken in the nanofluids model. An optima approach has been applied to acquire the solution of modeled problem. The convergence of the HAM (Homotopy Analysis Method has been presented numerically. The disparity of the Nusslet number, Skin friction, Sherwood number and their influence on the velocity, heat and concentration fields has been scrutinized. Moreover, for comprehension, the physical presentation of the embedded parameters are explored analytically for entropy generation and discussed.
Qayyum, Sajid; Hayat, Tasawar; Shehzad, Sabir Ali; Alsaedi, Ahmed
2018-03-01
This article concentrates on the magnetohydrodynamic (MHD) stagnation point flow of tangent hyperbolic nanofluid in the presence of buoyancy forces. Flow analysis caused due to stretching surface. Characteristics of heat transfer are examined under the influence of thermal radiation and heat generation/absorption. Newtonian conditions for heat and mass transfer are employed. Nanofluid model includes Brownian motion and thermophoresis. The governing nonlinear partial differential systems of the problem are transformed into a systems of nonlinear ordinary differential equations through appropriate variables. Impact of embedded parameters on the velocity, temperature and nanoparticle concentration fields are presented graphically. Numerical computations are made to obtain the values of skin friction coefficient, local Nusselt and Sherwood numbers. It is concluded that velocity field enhances in the frame of mixed convection parameter while reverse situation is observed due to power law index. Effect of Brownian motion parameter on the temperature and heat transfer rate is quite reverse. Moreover impact of solutal conjugate parameter on the concentration and local Sherwood number is quite similar.
Saeidi, Sheida
Two important components of a liquid breeder blanket of a fusion power reactor are the liquid breeder/coolant and the steel structure that the liquid is enclosed in. One candidate combination for such components is Lead-Lithium (PbLi) eutectic alloy and advanced Reduced Activation Ferritic/Martensitic (RAFM) steel. The research performed here is aimed at: (1) better understanding of corrosion processes in the system including RAFM steel and flowing PbLi in the presence of a strong magnetic field and (2) prediction of corrosion losses in conditions of a Dual Coolant Lead Lithium (DCLL) blanket, which is at present the key liquid metal blanket concept in the US. To do this, numerical and analytical tools have been developed and then applied to the analysis of corrosion processes. First, efforts were taken to develop a computational suite called TRANSMAG (Transport phenomena in Magnetohydrodynamic Flows) as an analysis tool for corrosion processes in the PbLi/RAFM system, including transport of corrosion products in MHD laminar and turbulent flows. The computational approach in TRANSMAG is based on simultaneous solution of flow, energy and mass transfer equations with or without a magnetic field, assuming mass transfer controlled corrosion and uniform dissolution of iron in the flowing PbLi. Then, the new computational tool was used to solve an inverse mass transfer problem where the saturation concentration of iron in PbLi was reconstructed from the experimental data resulting in the following correlation: CS = e 13.604--12975/T, where T is the temperature of PbLi in K and CS is in wppm. The new correlation for saturation concentration was then used in the analysis of corrosion processes in laminar flows in a rectangular duct in the presence of a strong transverse magnetic field. As shown in this study, the mass loss increases with the magnetic field such that the corrosion rate in the presence of a magnetic field can be a few times higher compared to purely
Numerical Solutions for Supersonic Flow of an Ideal Gas Around Blunt Two-Dimensional Bodies
Fuller, Franklyn B.
1961-01-01
The method described is an inverse one; the shock shape is chosen and the solution proceeds downstream to a body. Bodies blunter than circular cylinders are readily accessible, and any adiabatic index can be chosen. The lower limit to the free-stream Mach number available in any case is determined by the extent of the subsonic field, which in turn depends upon the body shape. Some discussion of the stability of the numerical processes is given. A set of solutions for flows about circular cylinders at several Mach numbers and several values of the adiabatic index is included.
Chung, Joon Ho; Shin, Yong Sam; Lim, Yong Cheol; Park, Minjung
2009-04-01
Internal carotid artery (ICA) trapping can be used for treating intracranial giant aneurysm, blood blister-like aneurysms and ICA rupture during the surgery. We present a novel ICA trapping technique which can be used with insufficient collaterals flow via anterior communicating artery (AcoA) and posterior communicating artery (PcoA). A patient was admitted with severe headache and the cerebral angiography demonstrated a typical blood blister-like aneurysm at the contralateral side of PcoA. For trapping the aneurysm, the first clip was placed at the ICA just proximal to the aneurysm whereas the distal clip was placed obliquely proximal to the origin of the PcoA to preserve blood flow from the PcoA to the distal ICA. The patient was completely recovered with good collaterals filling to the right ICA territories via AcoA and PcoA. This technique may be an effective treatment option for trapping the aneurysm, especially when the PcoA preservation is mandatory.
International Nuclear Information System (INIS)
Walker, J.S.
1986-04-01
This paper treats the liquid-metal MHD flow in a semi-infinite rectangular duct and a semi-infinite trapezoidal duct, which are connected by a finite-length transition duct. There is a strong, transverse, uniform magnetic field. The walls parallel to the magnetic field (sides) remain parallel, while the walls intersecting the magnetic field are twisted in the transition duct to provide the change in cross sectional shape. The left side has a constant height, while the height of the right side increases or decreases in the transition duct. This geometry gives a skewed velocity profile with a high velocity near the left side, provided the right side is relatively thick. All walls are thin and electrically conducting, but the sides are considerably thicker than the other walls. The application is to fusion-reactor blankets in which a high velocity near the first wall (separating the plasma chamber from the coolant) improves the thermal performance. Junctions of different ducts with walls parallel to the magnetic field are treated for the first time. In expansions, contractions and other geometric transition ducts, as well as in straight ducts with axially varying magnetic fields, the fluid flow and electric currents are concentrated in boundary layers adjacent to the sides and in the side. At a junction with a straight duct with a uniform magnetic field, the flow and current must transfer from the boundary layers adn sides to the core regions. These transfers at junctions play a key role in any three-dimensional flow
International Nuclear Information System (INIS)
Baoku, I.G.; Olajuwon, B.I.; Mustapha, A.O.
2013-01-01
Highlights: ► We model the flow of a MHD third grade fluid, heat and mass transfer in a porous medium with partial slip flow regime. ► We examine the effects of pertinent parameters on the velocity, temperature and species concentration distributions. ► The values momentum and thermal boundary layers increase with increasing third grade parameter β. ► The consequences of increasing the permeability parameter m and partial slip parameter λ give rise to fluid velocity. ► The magnetic field parameter H decreases the momentum boundary layer and increases the concentration boundary layer. -- Abstract: The influence of third grade, partial slip and other thermophysical parameters on the steady flow, heat and mass transfer of viscoelastic third grade fluid past an infinite vertical insulated plate subject to suction across the boundary layer has been investigated. The space occupying the fluid is porous. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. An efficient numerical scheme of midpoint technique with Richardson’s extrapolation is employed to solve the governing system of coupled nonlinear equations of momentum, energy and concentration. Numerical calculations were carried out for different values of various interesting non-dimensional quantities in the slip flow regime with heat and mass transfer and were shown with the aid of figures. The values of the wall shear stress, the local rate of heat and mass transfers were obtained and tabulated. The analysis shows that as the fluid becomes more shear thickening, the momentum boundary layer decreases but the thermal boundary layer increases; the magnetic field strength is found to decrease with an increasing temperature distribution when the porous plate is insulated. The consequences of increasing the permeability parameter and Schmidt number decrease both the momentum
Energy Technology Data Exchange (ETDEWEB)
Walker, J.S.
1986-04-01
This paper treats the liquid-metal MHD flow in a semi-infinite rectangular duct and a semi-infinite trapezoidal duct, which are connected by a finite-length transition duct. There is a strong, transverse, uniform magnetic field. The walls parallel to the magnetic field (sides) remain parallel, while the walls intersecting the magnetic field are twisted in the transition duct to provide the change in cross sectional shape. The left side has a constant height, while the height of the right side increases or decreases in the transition duct. This geometry gives a skewed velocity profile with a high velocity near the left side, provided the right side is relatively thick. All walls are thin and electrically conducting, but the sides are considerably thicker than the other walls. The application is to fusion-reactor blankets in which a high velocity near the first wall (separating the plasma chamber from the coolant) improves the thermal performance. Junctions of different ducts with walls parallel to the magnetic field are treated for the first time. In expansions, contractions and other geometric transition ducts, as well as in straight ducts with axially varying magnetic fields, the fluid flow and electric currents are concentrated in boundary layers adjacent to the sides and in the side. At a junction with a straight duct with a uniform magnetic field, the flow and current must transfer from the boundary layers adn sides to the core regions. These transfers at junctions play a key role in any three-dimensional flow.
Reddy, B. Siva Kumar; Rao, K. V. Surya Narayana; Vijaya, R. Bhuvana
2017-07-01
In this paper, we have considered the unsteady magnetohydrodynamic squeezing axi-symmetric flow of water-nanofluid through saturated porous medium between two parallel disks. The equations for the governing flow are solved by Galerkin optimal Homotopy asymptotic method. The effects of non-dimensional parameters on velocity, temperature and concentration have been discussed with the help of graphs. Also we obtained local Nusselt number and computationally discussed with reference to flow parameters.
Route analysis for MHD equilibria
International Nuclear Information System (INIS)
Kikuchi, Fumio; Aizawa, Tatsuhiko
1982-01-01
In Tokamak facilities which are promising in nuclear fusion reactor development, the plasma in the core is often described by MHD approximation. Specifically, since an axisymmetric torus is approximately assumed as the first wall (shell) shape in actual Tokamak facilities, the Grad-Shafranov equation to be satisfied by an axisymmetric equilibrium solution for ideal MHD fluid must be solved, and the characteristics of its solution must be clarified. This paper shows the outline of the numerical calculation which employs both the incremental method taking the particular incremental nodal point values as the control parameters and the interaction method in accordance with Newton method at the same time, the analysis objective being a non-linear eigenvalue problem dealing the boundary of plasma region with surrounding vacuum region as the free boundary. Next, the detailed route analysis of the equilibrium solution is performed, utilizing the above numerical calculation technique, to clarify the effect of shell shape on the behaviour of the equilibrium solution. As the shape of the shell, a rectangular section torus, which have a notch depression at a part of the shell inner boundary, is considered. In the paper, the fundamental MHD equation and its approximate solution by the finite element method, the behaviour of plasma equilibrium solution in a shell having a notch, and the effect of notch shapes on plasma behaviour are described. This analysis verifies the effectiveness of the calculation method. (Wakatsuki, Y.)
Bifurcation theory for toroidal MHD instabilities
International Nuclear Information System (INIS)
Maschke, E.K.; Morros Tosas, J.; Urquijo, G.
1992-01-01
Using a general representation of magneto-hydrodynamics in terms of stream functions and potentials, proposed earlier, a set of reduced MHD equations for the case of toroidal geometry had been derived by an appropriate ordering with respect to the inverse aspect ratio. When all dissipative terms are neglected in this reduced system, it has the same linear stability limits as the full ideal MHD equations, to the order considered. When including resistivity, thermal conductivity and viscosity, we can apply bifurcation theory to investigate nonlinear stationary solution branches related to various instabilities. In particular, we show that a stationary solution of the internal kink type can be found
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M.A. Imran
2018-03-01
Full Text Available The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest’s and Tzou’s algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary we found that viscous (fractional and ordinary fluids are swiftest than Maxwell (fractional and ordinary fluids. Keywords: Free convection, Slip, Maxwell fluid, Newtonian heating, Exponentially accelerated plate, Caputo-Fabrizio fractional derivatives, Stehfest’s and Tzou’s algorithms
Imran, M. A.; Riaz, M. B.; Shah, N. A.; Zafar, A. A.
2018-03-01
The aim of this article is to investigate the unsteady natural convection flow of Maxwell fluid with fractional derivative over an exponentially accelerated infinite vertical plate. Moreover, slip condition, radiation, MHD and Newtonian heating effects are also considered. A modern definition of fractional derivative operator recently introduced by Caputo and Fabrizio has been used to formulate the fractional model. Semi analytical solutions of the dimensionless problem are obtained by employing Stehfest's and Tzou's algorithms in order to find the inverse Laplace transforms for temperature and velocity fields. Temperature and rate of heat transfer for non-integer and integer order derivatives are computed and reduced to some known solutions from the literature. Finally, in order to get insight of the physical significance of the considered problem regarding velocity and Nusselt number, some graphical illustrations are made using Mathcad software. As a result, in comparison between Maxwell and viscous fluid (fractional and ordinary) we found that viscous (fractional and ordinary) fluids are swiftest than Maxwell (fractional and ordinary) fluids.
Kumaresan, E.; Vijaya Kumar, A. G.; Rushi Kumar, B.
2017-11-01
This article studies, an exact solution of unsteady MHD free convection boundary-layer flow of a silver nanofluid past an exponentially accelerated moving vertical plate through aporous medium in the presence of thermal radiation, transverse applied amagnetic field, radiation absorption and Heat generation or absorption with chemical reaction are investigated theoretically. We consider nanofluids contain spherical shaped nanoparticle of silverwith a nanoparticle volume concentration range smaller than or equal to 0.04. This phenomenon is modeled in the form of partial differential equations with initial boundary conditions. Some suitable dimensional variables are introduced. The corresponding dimensionless equations with boundary conditions are solved by using Laplace transform technique. The exact solutions for velocity, energy, and species are obtained, also the corresponding numerical values of nanofluid velocity, temperature and concentration profiles are represented graphically. The expressions for skin friction coefficient, the rate of heat transfer and mass transfer are derived. The present study finds applications involving heat transfer, enhancement of thermal conductivity and other applications like transportation, industrial cooling applications, heating buildings and reducing pollution, energy applications and solar absorption. The effect of heat transfer is found to be more pronounced in a silver-water nanofluid than in the other nanofluids.
Ur Rehman, Fiaz; Nadeem, Sohail; Ur Rehman, Hafeez; Ul Haq, Rizwan
2018-03-01
In the present paper a theoretical investigation is performed to analyze heat and mass transport enhancement of water-based nanofluid for three dimensional (3D) MHD stagnation-point flow caused by an exponentially stretched surface. Water is considered as a base fluid. There are three (3) types of nanoparticles considered in this study namely, CuO (Copper oxide), Fe3O4 (Magnetite), and Al2O3 (Alumina) are considered along with water. In this problem we invoked the boundary layer phenomena and suitable similarity transformation, as a result our three dimensional non-linear equations of describing current problem are transmuted into nonlinear and non-homogeneous differential equations involving ordinary derivatives. We solved the final equations by applying homotopy analysis technique. Influential outcomes of aggressing parameters involved in this study, effecting profiles of temperature field and velocity are explained in detail. Graphical results of involved parameters appearing in considered nanofluid are presented separately. It is worth mentioning that Skin-friction along x and y-direction is maximum for Copper oxide-water nanofluid and minimum for Alumina-water nanofluid. Result for local Nusselt number is maximum for Copper oxide-water nanofluid and is minimum for magnetite-water nanofluid.
Experimental and theoretical studies of the effects of nonuniformities in equilibrium MHD generators
International Nuclear Information System (INIS)
Rosenbaum, M.; Shamma, S.E.; Louis, J.F.
1980-01-01
An experimental study of the effects of thermal and velocity nonuniformities is performed in an equilibrium plasma for a range of Hall parameters. An electrodeless MHD disk generator with radial flow is chosen as the ideal geometry for these experiments. By introducing equally spaced cold blades in the flow, it is possible to create well defined two-dimensional wake nonuniformities with strong variations of the plasma properties in the direction normal to the magnetic field and the flow. This type of nonuniformity is predicted to provide the strongest reduction of Hall coefficient and effective conductivity for high values of Hall parameter. This degradation is controlled by both the level of nonuniformities and the value of the ideal Hall parameter. The former is dependent upon the number of blades (root mean square deviation of the conductivity), and the latter is dependent upon the values of the magnetic field intensities. The results provide basic quantitative information about the effects of conductivity and velocity nonuniformities on the performance of equilibrium MHD generators over a wide range of Hall coefficients, between 2 and 7. Reduction formulae are established between the effective and ideal Hall parameters for different levels of nonuniformities intensities. Theoretical predictions are derived from a detailed two-dimensional electrodynamic analysis and a simplified engineering model based on a generalization of Rosa's layer model. These experiments validate the analytical studies and support the use of the theoretical layer models in describing the effect of boundary layers on the performance of linear generators
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Jawad Ahmed
Full Text Available This paper examines the boundary layer flow and heat transfer characteristic in power law fluid model over unsteady radially stretching sheet under the influence of convective boundary conditions. A uniform magnetic field is applied transversely to the direction of the flow. The governing time dependent nonlinear boundary layer equations are reduced into nonlinear ordinary differential equations with the help of similarity transformations. The transformed coupled ordinary differential equations are then solved analytically by homotopy analysis method (HAM and numerically by shooting procedure. Effects of various governing parameters like, power law index n, magnetic parameter M, unsteadiness A, suction/injection S, Biot number γ and generalized Prandtl number Pr on velocity, temperature, local skin friction and the local Nusselt number are studied and discussed. It is found from the analysis that the magnetic parameter diminishes the velocity profile and the corresponding thermal boundary layer thickness. Keywords: Axisymmetric flow, Power law fluid, Unsteady stretching, Convective boundary conditions
International Nuclear Information System (INIS)
Singh, K.; Rawat, S. K.; Kumar, M.
2016-01-01
Heat and mass transfer behavior of unsteady flow of squeezing between two parallel plates in the sight of uniform magnetic field with slip velocity effect is investigated. The governing equations representing fluid flow have been transformed into nonlinear ordinary differential equations using similarity transformation. The equations thus obtained have been solved numerically using Runge-Kutta-Fehlberg method with shooting technique. Effects on the behavior of velocity, temperature, and concentration for various values of relevant parameters are illustrated graphically. The skin-friction coefficient and heat and mass transfer rate are also tabulated for various governing parameters. The results indicate that, for nano fluid flow, the rates of heat and mass transfer are inversely proportional to nanoparticle volume fraction and magnetic parameter. The rate of mass transfer increases with increasing values of Schmidt number and squeeze number.
Neoclassical MHD descriptions of tokamak plasmas
International Nuclear Information System (INIS)
Callen, J.D.; Kim, Y.B.; Sundaram, A.K.
1988-01-01
Considerable progress has been made in extending neoclassical MHD theory and in exploring the linear instabilities, nonlinear behavior and turbulence models it implies for tokamak plasmas. The areas highlighted in this paper include: extension of the neoclassical MHD equations to include temperature-gradient and heat flow effects; the free energy and entropy evolution implied by this more complete description; a proper ballooning mode formalism analysis of the linear instabilities; a new rippling mode type instability; numerical simulation of the linear instabilities which exhibit a smooth transition from resistive ballooning modes at high collisionality to neoclassical MHD modes at low collisionality; numerical simulation of the nonlinear growth of a single helicity tearing mode; and a Direct-Interaction-Approximation model of neoclassical MHD turbulence and the anomalous transport it induces which substantially improves upon previous mixing length model estimates. 34 refs., 2 figs
Cheng, Wai-Chi; Porté-Agel, Fernando
2015-05-01
Large-eddy simulations (LES) are performed to simulate the atmospheric boundary-layer (ABL) flow through idealized urban canopies represented by uniform arrays of cubes in order to better understand atmospheric flow over rural-to-urban surface transitions. The LES framework is first validated with wind-tunnel experimental data. Good agreement between the simulation results and the experimental data are found for the vertical and spanwise profiles of the mean velocities and velocity standard deviations at different streamwise locations. Next, the model is used to simulate ABL flows over surface transitions from a flat homogeneous terrain to aligned and staggered arrays of cubes with height . For both configurations, five different frontal area densities , equal to 0.028, 0.063, 0.111, 0.174 and 0.250, are considered. Within the arrays, the flow is found to adjust quickly and shows similar structure to the wake of the cubes after the second row of cubes. An internal boundary layer is identified above the cube arrays and found to have a similar depth in all different cases. At a downstream location where the flow immediately above the cube array is already adjusted to the surface, the spatially-averaged velocity is found to have a logarithmic profile in the vertical. The values of the displacement height are found to be quite insensitive to the canopy layout (aligned vs. staggered) and increase roughly from to as increases from 0.028 to 0.25. Relatively larger values of the aerodynamic roughness length are obtained for the staggered arrays, compared with the aligned cases, and a maximum value of is found at for both configurations. By explicitly calculating the drag exerted by the cubes on the flow and the drag coefficients of the cubes using our LES results, and comparing the results with existing theoretical expressions, we show that the larger values of for the staggered arrays are related to the relatively larger drag coefficients of the cubes for that
An entropic solver for ideal Lagrangian magnetohydrodynamics
International Nuclear Information System (INIS)
Bezard, F.; Despres, B.
1999-01-01
In this paper, the authors adapt to the ideal 1D lagrangian MHD equations a class of numerical schemes of order one in time and space presented in an earlier paper and applied to the gas dynamics system. They use some properties of systems of conservation laws with zero entropy flux which describe fluid models invariant by galilean transformation and reversible for regular solutions. These numerical schemes satisfy an entropy inequality under CFL conditions. In the last section, they describe a particular scheme for the MHD equations and show with some numerical applications its robustness and accuracy. The generalization to full Eulerian multidimensional MHD will be the subject of a forthcoming paper
Ideal Magnetohydrodynamic Stability of the NCSX
International Nuclear Information System (INIS)
Fu, Guo Yong; Isaev, Maxim Yu; Ku, Long-Poe; Mikhailov, M.; Redi, M.H; Sanchez, Raul; Subbotin, A; Hirshman, Steven Paul; Cooper, W. Anthony; Monticello, D.; Reiman, A.H.; Zarnstorff, M.C.
2007-01-01
The ideal magnetohydrodynamic (MHD) stability of the National Compact Stellarator Experiment (NCSX) is extensively analyzed using the most advanced three-dimensional MHD codes. It is shown that the NCSX is stable to finite-n MHD modes, including the vertical mode, external kink modes and ballooning modes. However, high-n external kink modes that peak near the plasma edge are found to be weakly unstable. A global calculation shows that finite-n ballooning modes are significantly more stable than the local infinite-n modes
The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid
Directory of Open Access Journals (Sweden)
D. R. V. S. R. K. Sastry
2013-01-01
Full Text Available The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.
MHD heat and mass diffusion flow by natural convection past a surface embedded in a porous medium
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Chaudhary R.C.
2009-01-01
Full Text Available This paper presents an analytical study of the transient hydromagnetic natural convection flow past a vertical plate embedded in a porous medium, taking account of the presence of mass diffusion and fluctuating temperature about time at the plate. The governing equations are solved in closed form by the Laplace-transform technique. The results are obtained for temperature, velocity, penetration distance, Nusselt number and skin-friction. The effects of various parameters are discussed on the flow variables and presented by graphs.
MHD pilot industrial applications
International Nuclear Information System (INIS)
Freeman, M.; Riviere-Wekstein, G.
1994-01-01
MHD industrial applications (and their historical developments) are sketched in the fields of nuclear fission, nuclear fusion and marine vehicles propelling. Nuclear fission projects resulted in promising prototypes between 1972 and 1980, especially for liquid-metal MHD generators. All of them have been stopped by the scientific policies of the governments. Nuclear fusion projects used mainly the equilibrium plasma of tokamak type reactors; some military projects used pulsed plasma to perform pulsed MHD generators. Marine vehicle propelling is the most advanced field. By june 1992, the japanese sea-going boat 'Yamato 1' was sailing with two MHD propellers. A few months later, the building of 'Yamato 2' has begun
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Wubshet Ibrahim
Full Text Available This article presents the effect of thermal radiation on magnetohydrodynamic flow of tangent hyperbolic fluid with nanoparticle past an enlarging sheet with second order slip and convective boundary condition. Condition of zero normal flux of nanoparticles at the wall is used for the concentration boundary condition, which is the current topic that have yet to be studied extensively. The solution for the velocity, temperature and nanoparticle concentration is governed by parameters viz. power-law index (n, Weissenberg number We, Biot number Bi, Prandtl number Pr, velocity slip parameters δ and γ, Lewis number Le, Brownian motion parameter Nb and the thermophoresis parameter Nt. Similarity transformation is used to metamorphosed the governing non-linear boundary-value problem into coupled higher order non-linear ordinary differential equation. The succeeding equations were numerically solved using the function bvp4c from the matlab for different values of emerging parameters. Numerical results are deliberated through graphs and tables for velocity, temperature, concentration, the skin friction coefficient and local Nusselt number. The results designate that the skin friction coefficient Cf deplete as the values of Weissenberg number We, slip parameters γ and δ upturn and it rises as the values of power-law index n increase. The local Nusselt number -θ′(0 decreases as slip parameters γ and δ, radiation parameter Nr, Weissenberg number We, thermophoresis parameter Nt and power-law index n increase. However, the local Nusselt number increases as the Biot number Bi increase. Keywords: Tangent hyperbolic fluid, Second order slip flow, MHD, Convective boundary condition, Radiation effect, Passive control of nanoparticles
M. Salem, A.; Rania, Fathy
2012-05-01
The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic (MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented, taking into account thermal radiation and internal heat genberation/absorbtion. The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung—Kutta method with the shooting technique. A comparison with previously published work has been carried out and the results are found to be in good agreement. The results are analyzed for the effect of different physical parameters, such as the variable viscosity and thermal conductivity, the ratio of free stream velocity to stretching velocity, the magnetic field, the porosity, the radiation and suction/injection on the flow, and the heat and mass transfer characteristics. The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1. In addition, the imposition of fluid suction increases both the rate of heat and mass transfer, whereas fluid injection shows the opposite effect.
International Nuclear Information System (INIS)
Salem, A. M.; Fathy, Rania
2012-01-01
The effect of variable viscosity and thermal conductivity on steady magnetohydrodynamic (MHD) heat and mass transfer flow of viscous and incompressible fluid near a stagnation point towards a permeable stretching sheet embedded in a porous medium are presented, taking into account thermal radiation and internal heat genberation/absorbtion. The stretching velocity and the ambient fluid velocity are assumed to vary linearly with the distance from the stagnation point. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing fundamental equations are first transformed into a system of ordinary differential equations using a scaling group of transformations and are solved numerically by using the fourth-order Rung—Kutta method with the shooting technique. A comparison with previously published work has been carried out and the results are found to be in good agreement. The results are analyzed for the effect of different physical parameters, such as the variable viscosity and thermal conductivity, the ratio of free stream velocity to stretching velocity, the magnetic field, the porosity, the radiation and suction/injection on the flow, and the heat and mass transfer characteristics. The results indicate that the inclusion of variable viscosity and thermal conductivity into the fluids of light and medium molecular weight is able to change the boundary-layer behavior for all values of the velocity ratio parameter λ except for λ = 1. In addition, the imposition of fluid suction increases both the rate of heat and mass transfer, whereas fluid injection shows the opposite effect. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Relativistic MHD simulations of stellar core collapse and magnetars
Energy Technology Data Exchange (ETDEWEB)
Font, Jose A; Gabler, Michael [Departamento de AstronomIa y Astrofisica, Universitat de Valencia, 46100 Burjassot (Valencia) (Spain); Cerda-Duran, Pablo; Mueller, Ewald [Max-Planck-Institut fuer Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany); Stergioulas, Nikolaos, E-mail: j.antonio.font@uv.es [Department of Physics, Aristotle University of Thessaloniki, Thessaloniki 54124 (Greece)
2011-02-01
We present results from simulations of magneto-rotational stellar core collapse along with Alfven oscillations in magnetars. These simulations are performed with the CoCoA/CoCoNuT code, which is able to handle ideal MHD flows in dynamical spacetimes in general relativity. Our core collapse simulations highlight the importance of genuine magnetic effects, like the magneto-rotational instability, for the dynamics of the flow. For the modelling of magnetars we use the anelastic approximation to general relativistic MHD, which allows for an effective suppression of fluid modes and an accurate description of Alfven waves. We further compute Alfven oscillation frequencies along individual magnetic field lines with a semi-analytic approach. Our work confirms previous results based on perturbative approaches regarding the existence of two families of quasi-periodic oscillations (QPOs), with harmonics at integer multiples of the fundamental frequency. Additional material is presented in the accompanying contribution by Gabler et al (2010b) in these proceedings.
Javed, T.; Ghaffari, A.; Ahmad, H.
2016-05-01
The unsteady stagnation point flow impinging obliquely on a flat plate in presence of a uniform applied magnetic field due to an oscillating stream has been studied. The governing partial differential equations are transformed into dimensionless form and the stream function is expressed in terms of Hiemenz and tangential components. The dimensionless partial differential equations are solved numerically by using well-known implicit finite difference scheme named as Keller-box method. The obtained results are compared with those available in the literature. It is observed that the results are in excellent agreement with the previous studies. The effects of pertinent parameters involved in the problem namely magnetic parameter, Prandtl number and impinging angle on flow and heat transfer characteristics are illustrated through graphs. It is observed that the influence of magnetic field strength increases the fluid velocity and by the increase of obliqueness parameter, the skin friction increases.
Flow and heat transfer of MHD graphene oxide-water nanofluid between two non-parallel walls
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Azimi Mohammadreza
2017-01-01
Full Text Available The steady 2-D heat transfer and flow between two non-parallel walls of a graphene oxide nanofluid in presence of uniform magnetic field are investigated in this paper. The analytical solution of the non-linear problem is obtained by Galerkin optimal homotopy asymptotic method. At first a similarity transformation is used to reduce the partial differential equations modeling the flow and heat transfer to ordinary non-linear differential equation systems containing the semi angle between the plate’s parameter, Reynolds number, the magnetic field strength, nanoparticle volume fraction, Eckert and Prandtl numbers. Finally, the obtained analytical results have been compared with results achieved from previous works in some cases.
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M.M. Bhatti
2016-09-01
Full Text Available In this article, combine effects of Magnetohydrodynamics and partial slip on Blood flow of Ree–Eyring fluid through a porous medium have been investigated. The walls of the non-uniform porous channel are considered as compliant. The governing equation of Ree–Eyring fluid for blood flow are simplified using long wavelength and low Reynolds number approximation. The obtained resulting equation are solved analytically and exact solution has been obtained. The impact of different physical parameters such as Hartmann number, slip parameter, porous parameter, wall rigidity parameter, wall tension and mass characterization parameter are taken into account. It is found that velocity distribution increases due to slip effects while its behavior is opposite for Hartmann number. Trapping mechanism has also taken under consideration by drawing contour streamlines.
Ramesh, K.
2017-07-01
In the current article, we have discussed the Poiseuille flow of an incompressible magnetohydrodynamic Jeffrey fluid between parallel plates through homogeneous porous medium using slip boundary conditions under the effect of heat transfer. The equations governing the fluid flow are modeled in Cartesian coordinate system. The energy equation is considered under the effects viscous dissipation and heat generation. Analytical solutions for the velocity and temperature profiles are obtained. The effects of the various involved parameters on the velocity and temperature profiles are studied and the results are presented through the graphs. It is observed from our analysis that, with increase of slip parameter and pressure gradient increase the velocity. The temperature is an increasing function of heat generation parameter, Brinkman number, thermal slip parameter and non-Newtonian fluid parameter.
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Taza Gul
Full Text Available This article aims to study the thin film layer flowing on a vertical oscillating belt. The flow is considered to satisfy the constitutive equation of unsteady second grade fluid. The governing equation for velocity and temperature fields with subjected initial and boundary conditions are solved by two analytical techniques namely Adomian Decomposition Method (ADM and Optimal Homotopy Asymptotic Method (OHAM. The comparisons of ADM and OHAM solutions for velocity and temperature fields are shown numerically and graphically for both the lift and drainage problems. It is found that both these solutions are identical. In order to understand the physical behavior of the embedded parameters such as Stock number, frequency parameter, magnetic parameter, Brinkman number and Prandtl number, the analytical results are plotted graphically and discussed.
Gul, Taza; Islam, Saeed; Shah, Rehan Ali; Khan, Ilyas; Khalid, Asma; Shafie, Sharidan
2014-01-01
This article aims to study the thin film layer flowing on a vertical oscillating belt. The flow is considered to satisfy the constitutive equation of unsteady second grade fluid. The governing equation for velocity and temperature fields with subjected initial and boundary conditions are solved by two analytical techniques namely Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The comparisons of ADM and OHAM solutions for velocity and temperature fields are shown numerically and graphically for both the lift and drainage problems. It is found that both these solutions are identical. In order to understand the physical behavior of the embedded parameters such as Stock number, frequency parameter, magnetic parameter, Brinkman number and Prandtl number, the analytical results are plotted graphically and discussed. PMID:25383797
HEAT AND MASS TRANSFER FOR VISCO-ELASTIC MHD BOUNDARY LAYER FLOW PAST A VERTICAL FLAT PLATE
Rita Choudhury; Hridi Ranjan Deb
2012-01-01
The two-dimensional free convection flow of visco-elastic and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to ordinary differential equation by introducing appropriate co-ordinate transformation. The analytical expressions for the velocity, temperature and species concentration fields have been obtained. The corresponding expressions for the non-dimensional rates of he...
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R. Kandasamy
2016-03-01
Full Text Available The objective of the present work was to investigate theoretically the effect of single walled carbon nanotubes (SWCNTs in the presence of water and seawater with variable stream condition due to solar radiation energy. The conclusion is drawn that the flow motion and the temperature field for SWCNTs in the presence of base fluid are significantly influenced by magnetic field, convective radiation and thermal stratification. Thermal boundary layer of SWCNTs-water is compared to that of Cu-water, absorbs the incident solar radiation and transits it to the working fluid by convection.
International Nuclear Information System (INIS)
Salem, Ahmed M.
2007-01-01
The problem of flow and heat transfer of an electrically conducting viscoelastic fluid over a continuously stretching sheet in the presence of a uniform magnetic field is analyzed for the case of power-law variation in the sheet temperature. The fluid viscosity and thermal conductivity are assumed to vary as a function of temperature. The basic equations comprising the balance laws of mass, linear momentum, and energy modified to include the electromagnetic force effect, the viscous dissipation, internal heat generation or absorption and work due to deformation are solved numerically
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Çilingir Süngü İnci
2017-01-01
Full Text Available This study is to examine the steady two dimensional laminar flow of a viscous incompressible electrically conducting fluid over a continuous surface. In this study DTM-Padé method is used to solve which is a combination of differential transform method (DTM and Padé approximant. Comparisons between the solutions obtained by DTM and DTM-Padé and are shown that DTM-Padé is the completely powerful method then DTM for solving the problems in which boundary conditions at infinity. Also in this study the effect of Magnetic and Radiation parameters, Prandtl number and Eckert number for velocity and temperature distributions are investigated.
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Boričić Zoran
2005-01-01
Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.
Wavelets solution of MHD 3-D fluid flow in the presence of slip and thermal radiation effects
Usman, M.; Zubair, T.; Hamid, M.; Haq, Rizwan Ul; Wang, Wei
2018-02-01
This article is devoted to analyze the magnetic field, slip, and thermal radiations effects on generalized three-dimensional flow, heat, and mass transfer in a channel of lower stretching wall. We supposed two various lateral direction rates for the lower stretching surface of the wall while the upper wall of the channel is subjected to constant injection. Moreover, influence of thermal slip on the temperature profile beside the viscous dissipation and Joule heating is also taken into account. The governing set of partial differential equations of the heat transfer and flow are transformed to nonlinear set of ordinary differential equations (ODEs) by using the compatible similarity transformations. The obtained nonlinear ODE set tackled by means of a new wavelet algorithm. The outcomes obtained via modified Chebyshev wavelet method are compared with Runge-Kutta (order-4). The worthy comparison, error, and convergence analysis shows an excellent agreement. Additionally, the graphical representation for various physical parameters including the skin friction coefficient, velocity, the temperature gradient, and the temperature profiles are plotted and discussed. It is observed that for a fixed value of velocity slip parameter a suitable selection of stretching ratio parameter can be helpful in hastening the heat transfer rate and in reducing the viscous drag over the stretching sheet. Finally, the convergence analysis is performed which endorsing that this proposed method is well efficient.
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N. Akmal
2018-05-01
Full Text Available The present study gives an account of the heat transfer characteristics of the squeezing flow of a nanofluid between two flat plates with upper plate moving vertically and the lower in the horizontal direction. Tiwari and Das nanofluid model has been utilized to give a comparative analysis of the heat transfer in the Cu-water and Al2O3–water nanofluids with entropy generation. The modeling is carried out with the consideration of Lorentz forces to observe the effect of magnetic field on the flow. The Joule heating effect is included to discuss the heat dissipation in the fluid and its effect on the entropy of the system. The nondimensional ordinary differential equations are solved using the Keller box method to assess the numerical results which are presented by the graphs and tables. An interesting observation is that the entropy is generated more near the lower plate as compared with that at the upper plate. Also, the heat transfer rate is found to be higher for the Cu nanoparticles in comparison with the Al2O3 nanoparticles.
Towards Integrated Pulse Detonation Propulsion and MHD Power
Litchford, Ron J.; Thompson, Bryan R.; Lineberry, John T.
1999-01-01
The interest in pulse detonation engines (PDE) arises primarily from the advantages that accrue from the significant combustion pressure rise that is developed in the detonation process. Conventional rocket engines, for example, must obtain all of their compression from the turbopumps, while the PDE provides additional compression in the combustor. Thus PDE's are expected to achieve higher I(sub sp) than conventional rocket engines and to require smaller turbopumps. The increase in I(sub sp) and the decrease in turbopump capacity must be traded off against each other. Additional advantages include the ability to vary thrust level by adjusting the firing rate rather than throttling the flow through injector elements. The common conclusion derived from these aggregated performance attributes is that PDEs should result in engines which are smaller, lower in cost, and lighter in weight than conventional engines. Unfortunately, the analysis of PDEs is highly complex due to their unsteady operation and non-ideal processes. Although the feasibility of the basic PDE concept has been proven in several experimental and theoretical efforts, the implied performance improvements have yet to be convincingly demonstrated. Also, there are certain developmental issues affecting the practical application of pulse detonation propulsion systems which are yet to be fully resolved. Practical detonation combustion engines, for example, require a repetitive cycle of charge induction, mixing, initiation/propagation of the detonation wave, and expulsion/scavenging of the combustion product gases. Clearly, the performance and power density of such a device depends upon the maximum rate at which this cycle can be successfully implemented. In addition, the electrical energy required for direct detonation initiation can be significant, and a means for direct electrical power production is needed to achieve self-sustained engine operation. This work addresses the technological issues associated
Energy Technology Data Exchange (ETDEWEB)
Emec, Ju. P.; Panasevich, L. L. [Institut Elektrodinamiki AN USSR, Kiev, USSR (Ukraine)
1968-11-15
The authors provide a solution to the problem of current distribution in a magnetohydrodynamic duct with permeable electrodes in which the conductivity of the moving medium is assumed to have a tensorial character. Permeable electrodes strongly influence the current distribution in the neighbourhood of the conducting walls of the duct. By appropriate blowing or sucking of the electrically conducting medium, we can suppress the end effects on the electrodes (due to the Hall effect in the flow and to the geometry of the duct); in this way the current distribution can be evened out. The authors find in their paper the necessary and sufficient conditions for which the current density takes on limited values near both ends of a permeable electrode. The velocity distribution on the conducting wall will be variable in sign as in some places there will be a blowing effect, mothers a sucking one. Another effect associated with the use of permeable electrodes is related to the integral characteristics of MHD converters. Thus, given anisotropic conductivity (due to the Hall effect) in a linear MHD duct with two permeable electrodes, the properties of Hall and Faraday energy converters will be combined if the conducting medium is blown through one electrode and sucked through the second. A flow scheme of this kind is studied in the paper. Mathematically, when the electric field is found a solution is obtained to the Riemann-Gilbert heterogeneous boundary value problem with discontinuous coefficients. This problem reduces to the Riemann boundary value problem (in the case of a zone belonging to a class of automorphic functions) and its solution, based on the properties of Cauchy integrals, is obtained in closed form. (author) [Russian] Daetsja reshenie zadachi o raspredelenii toka v magnitogidrodinamicheskom kanale s pronicaemymi jelektrodami pri tenzornom haraktere provodimosti dvizhushhejsja sredy. Nalichie pronicaemyh jelektrodov okazyvaet sushhestvennoe vlijanie na
MHD power generation for the synthetic-fuels industry
International Nuclear Information System (INIS)
Jones, M.S. Jr.
1982-01-01
The integration of open cycle MHD with various processes for the recovery of hydrocarbons for heavy oil deposits, oil sands, and oil shales are examined along with its use in producing medium Btu gas, synthetic natural gas and solvent refined coal. The major features of the MHD cycle which are of interest are: (a) the ability to produce hydrogen through the shift reaction by introducing H 2 O into the substoichiometric combustion product flow exiting the MHD diffuser, (b) the use of high temperature waste heat in the MHD exhaust, and (c) the ability of the seed in the MHD flow to remove sulfur from the combustion products. Therefore the use of the MHD cycle allows coal to be used in an environmentally acceptable manner in place of hydrocarbons which are now used to produce process heat and hydrogen. The appropriate plant sizes are in the range of 25 to 50 MWe and the required MHD generator enthalpy extraction efficiencies are low. Sale of electricity produced, over and above that used in the process, can provide a revenue stream which can improve the economics of the hydrocarbon processing. This, coupled with the replacement of coal for hydrocarbons in certain phases of the process, should improve the overall economics, while not requiring a high level of performance by the MHD components. Therefore, this area should be an early target of opportunity for the commercialization of MHD
An approach to verification and validation of MHD codes for fusion applications
Energy Technology Data Exchange (ETDEWEB)
Smolentsev, S., E-mail: sergey@fusion.ucla.edu [University of California, Los Angeles (United States); Badia, S. [Centre Internacional de Mètodes Numèrics en Enginyeria, Barcelona (Spain); Universitat Politècnica de Catalunya – Barcelona Tech (Spain); Bhattacharyay, R. [Institute for Plasma Research, Gandhinagar, Gujarat (India); Bühler, L. [Karlsruhe Institute of Technology (Germany); Chen, L. [University of Chinese Academy of Sciences, Beijing (China); Huang, Q. [Institute of Nuclear Energy Safety Technology, Chinese Academy of Sciences, Hefei, Anhui (China); Jin, H.-G. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Krasnov, D. [Technische Universität Ilmenau (Germany); Lee, D.-W. [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of); Mas de les Valls, E. [Centre Internacional de Mètodes Numèrics en Enginyeria, Barcelona (Spain); Universitat Politècnica de Catalunya – Barcelona Tech (Spain); Mistrangelo, C. [Karlsruhe Institute of Technology (Germany); Munipalli, R. [HyPerComp, Westlake Village (United States); Ni, M.-J. [University of Chinese Academy of Sciences, Beijing (China); Pashkevich, D. [St. Petersburg State Polytechnical University (Russian Federation); Patel, A. [Universitat Politècnica de Catalunya – Barcelona Tech (Spain); Pulugundla, G. [University of California, Los Angeles (United States); Satyamurthy, P. [Bhabha Atomic Research Center (India); Snegirev, A. [St. Petersburg State Polytechnical University (Russian Federation); Sviridov, V. [Moscow Power Engineering Institute (Russian Federation); Swain, P. [Bhabha Atomic Research Center (India); and others
2015-11-15
Highlights: • Review of status of MHD codes for fusion applications. • Selection of five benchmark problems. • Guidance for verification and validation of MHD codes for fusion applications. - Abstract: We propose a new activity on verification and validation (V&V) of MHD codes presently employed by the fusion community as a predictive capability tool for liquid metal cooling applications, such as liquid metal blankets. The important steps in the development of MHD codes starting from the 1970s are outlined first and then basic MHD codes, which are currently in use by designers of liquid breeder blankets, are reviewed. A benchmark database of five problems has been proposed to cover a wide range of MHD flows from laminar fully developed to turbulent flows, which are of interest for fusion applications: (A) 2D fully developed laminar steady MHD flow, (B) 3D laminar, steady developing MHD flow in a non-uniform magnetic field, (C) quasi-two-dimensional MHD turbulent flow, (D) 3D turbulent MHD flow, and (E) MHD flow with heat transfer (buoyant convection). Finally, we introduce important details of the proposed activities, such as basic V&V rules and schedule. The main goal of the present paper is to help in establishing an efficient V&V framework and to initiate benchmarking among interested parties. The comparison results computed by the codes against analytical solutions and trusted experimental and numerical data as well as code-to-code comparisons will be presented and analyzed in companion paper/papers.
Directory of Open Access Journals (Sweden)
Mohammad Aghamajidi
2018-03-01
Nusselt number and an increasing effect on entropy generation number. In addition, our computation shows that all three quantities of skin friction coefficient, local Nusselt number and entropy generation number are the increasing functions of spin parameter. Finally, this simulation represents the feasibility of using magnetic rotating body drives in novel nuclear space propulsion engines and this model has important applications in heat transfer enhancement in renewable energy systems and industrial thermal management. Keywords: Natural-convective flow, Spinning vertical cone, Nanofluids, Entropy generation, Tiwari-Das nanofluid model, Magnetohydrodynamics (MHD
Manideep, P.; Raju, R. Srinivasa; Rao, T. Siva Nageswar; Reddy, G. Jithender
2018-05-01
This paper deals, an unsteady magnetohydrodynamic heat transfer natural convection flow of non-Newtonian Casson fluid over an inclined vertical plate embedded in a porous media with the presence of boundary conditions such as oscillating velocity, constant wall temperature. The governing dimensionless boundary layer partial differential equations are reduced to simultaneous algebraic linear equation for velocity, temperature of Casson fluid through finite element method. Those equations are solved by Thomas algorithm after imposing the boundary conditions through MATLAB for analyzing the behavior of Casson fluid velocity and temperature with various physical parameters. Also analyzed the local skin-friction and rate of heat transfer. Compared the present results with earlier reported studies, the results are comprehensively authenticated and robust FEM.
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Swati Mukhopadhyay
2013-09-01
Full Text Available The boundary layer flow and heat transfer towards a porous exponential stretching sheet in presence of a magnetic field is presented in this analysis. Velocity slip and thermal slip are considered instead of no-slip conditions at the boundary. Thermal radiation term is incorporated in the temperature equation. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and energy equations into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter as well as with the increasing magnetic parameter. Temperature increases with the increasing values of magnetic parameter. Temperature is found to decrease with an increase of thermal slip parameter. Thermal radiation enhances the effective thermal diffusivity and the temperature rises.
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Muthucumaraswamy R.
2010-01-01
Full Text Available An exact analysis of rotation effects on unsteady flow of an incompressible and electrically conducting fluid past a uniformly accelerated infinite isothermal vertical plate, under the action of transversely applied magnetic field has been presented. The plate temperature is raised to Tw and the concentration level near the plate is also raised to C′w . The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles, temperature and concentration are studied for different physical parameters like thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number and time. It is observed that the velocity increases with increasing values of thermal Grashof number or mass Grashof number. It is also observed that the velocity increases with decreasing magnetic field parameter.
Mahanthesh, B.; Gireesha, B. J.; Shehzad, S. A.; Rauf, A.; Kumar, P. B. Sampath
2018-05-01
This research is made to visualize the nonlinear radiated flow of hydromagnetic nano-fluid induced due to rotation of the disk. The considered nano-fluid is a mixture of water and Ti6Al4V or AA7072 nano-particles. The various shapes of nanoparticles like lamina, column, sphere, tetrahedron and hexahedron are chosen in the analysis. The irregular heat source and nonlinear radiative terms are accounted in the law of energy. We used the heat flux condition instead of constant surface temperature condition. Heat flux condition is more relativistic and according to physical nature of the problem. The problem is made dimensionless with the help of suitable similarity constraints. The Runge-Kutta-Fehlberg scheme is adopted to find the numerical solutions of governing nonlinear ordinary differential systems. The solutions are plotted by considering the various values of emerging physical constraints. The effects of various shapes of nanoparticles are drawn and discussed.
Directory of Open Access Journals (Sweden)
Maria Imtiaz
Full Text Available This paper looks at the flow of Jeffrey fluid due to a curved stretching sheet. Effect of homogeneous-heterogeneous reactions is considered. An electrically conducting fluid in the presence of applied magnetic field is considered. Convective boundary conditions model the heat transfer analysis. Transformation method reduces the governing nonlinear partial differential equations into the ordinary differential equations. Convergence of the obtained series solutions is explicitly discussed. Characteristics of sundry parameters on the velocity, temperature and concentration profiles are analyzed by plotting graphs. Computations for pressure, skin friction coefficient and surface heat transfer rate are presented and examined. It is noted that fluid velocity and temperature through curvature parameter are enhanced. Increasing values of Biot number correspond to the enhancement in temperature and Nusselt number.
Khan, Junaid Ahmad; Mustafa, M.
2018-03-01
Boundary layer flow around a stretchable rough cylinder is modeled by taking into account boundary slip and transverse magnetic field effects. The main concern is to resolve heat/mass transfer problem considering non-linear radiative heat transfer and temperature/concentration jump aspects. Using conventional similarity approach, the equations of motion and heat transfer are converted into a boundary value problem whose solution is computed by shooting method for broad range of slip coefficients. The proposed numerical scheme appears to improve as the strengths of magnetic field and slip coefficients are enhanced. Axial velocity and temperature are considerably influenced by a parameter M which is inversely proportional to the radius of cylinder. A significant change in temperature profile is depicted for growing wall to ambient temperature ratio. Relevant physical quantities such as wall shear stress, local Nusselt number and local Sherwood number are elucidated in detail.
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M. Idrees
2018-03-01
Full Text Available An analysis is performed for the fluid dynamics incorporating the variation of viscosity and thermal conductivity on an unsteady two-dimensional free surface flow of a viscous incompressible conducting fluid taking into account the effect of a magnetic field. Surface tension quadratically vary with temperature while fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The boundary layer partial differential equations in cartesian coordinates are transformed into a system of nonlinear ordinary differential equations (ODEs by similarity transformation. The developed nonlinear equations are solved analytically by Homotopy Analysis Method (HAM while numerically by using the shooting method. The Effects of natural parameters such as the variable viscosity parameter A, variable thermal conductivity parameter N, Hartmann number Ma, film Thickness, unsteadiness parameter S, Thermocapillary number M and Prandtl number Pr on the velocity and temperature profiles are investigated. The results for the surface skin friction coefficient f″(0, Nusselt number (heat flux -θ′(0 and free surface temperature θ(1 are presented graphically and in tabular form. Keywords: Variable viscosity and thermal conductivity, Thermocapillary number, Magnetic field, Thin film, Unsteady stretching surface
Abd Elazem, Nader Y.; Ebaid, Abdelhalim
2017-12-01
In this paper, the effect of partial slip boundary condition on the heat and mass transfer of the Cu-water and Ag-water nanofluids over a stretching sheet in the presence of magnetic field and radiation. Such partial slip boundary condition has attracted much attention due to its wide applications in industry and chemical engineering. The flow is basically governing by a system of partial differential equations which are reduced to a system of ordinary differential equations. This system has been exactly solved, where exact analytical expression has been obtained for the fluid velocity in terms of exponential function, while the temperature distribution, and the nanoparticles concentration are expressed in terms of the generalized incomplete gamma function. In addition, explicit formulae are also derived from the rates of heat transfer and mass transfer. The effects of the permanent parameters on the skin friction, heat transfer coefficient, rate of mass transfer, velocity, the temperature profile, and concentration profile have been discussed through tables and graphs.
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Junaid Ahmad Khan
2018-03-01
Full Text Available Boundary layer flow around a stretchable rough cylinder is modeled by taking into account boundary slip and transverse magnetic field effects. The main concern is to resolve heat/mass transfer problem considering non-linear radiative heat transfer and temperature/concentration jump aspects. Using conventional similarity approach, the equations of motion and heat transfer are converted into a boundary value problem whose solution is computed by shooting method for broad range of slip coefficients. The proposed numerical scheme appears to improve as the strengths of magnetic field and slip coefficients are enhanced. Axial velocity and temperature are considerably influenced by a parameter M which is inversely proportional to the radius of cylinder. A significant change in temperature profile is depicted for growing wall to ambient temperature ratio. Relevant physical quantities such as wall shear stress, local Nusselt number and local Sherwood number are elucidated in detail. Keywords: Stretchable boundary, Thermal radiation, Chemical reaction, Mathematical modeling, Non-linear differential system, Mass transfer
Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet
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M.M. Rashidi
2017-03-01
Full Text Available The purpose of this article is to study and analyze the convective flow of a third grade non-Newtonian fluid due to a linearly stretching sheet subject to a magnetic field. The dimensionless entropy generation equation is obtained by solving the reduced momentum and energy equations. The momentum and energy equations are reduced to a system of ordinary differential equations by a similarity method. The optimal homotopy analysis method (OHAM is used to solve the resulting system of ordinary differential equations. The effects of the magnetic field, Biot number and Prandtl number on the velocity component and temperature are studied. The results show that the thermal boundary-layer thickness gets decreased with increasing the Prandtl number. In addition, Brownian motion plays an important role to improve thermal conductivity of the fluid. The main purpose of the paper is to study the effects of Reynolds number, dimensionless temperature difference, Brinkman number, Hartmann number and other physical parameters on the entropy generation. These results are analyzed and discussed.
Idrees, M.; Rehman, Sajid; Shah, Rehan Ali; Ullah, M.; Abbas, Tariq
2018-03-01
An analysis is performed for the fluid dynamics incorporating the variation of viscosity and thermal conductivity on an unsteady two-dimensional free surface flow of a viscous incompressible conducting fluid taking into account the effect of a magnetic field. Surface tension quadratically vary with temperature while fluid viscosity and thermal conductivity are assumed to vary as a linear function of temperature. The boundary layer partial differential equations in cartesian coordinates are transformed into a system of nonlinear ordinary differential equations (ODEs) by similarity transformation. The developed nonlinear equations are solved analytically by Homotopy Analysis Method (HAM) while numerically by using the shooting method. The Effects of natural parameters such as the variable viscosity parameter A, variable thermal conductivity parameter N, Hartmann number Ma, film Thickness, unsteadiness parameter S, Thermocapillary number M and Prandtl number Pr on the velocity and temperature profiles are investigated. The results for the surface skin friction coefficient f″ (0) , Nusselt number (heat flux) -θ‧ (0) and free surface temperature θ (1) are presented graphically and in tabular form.
Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows
Matsuoka, C.; Nishihara, K.; Sano, T.
2017-04-01
A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in two-dimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However, it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.
Dynamics of nonlinear resonant slow MHD waves in twisted flux tubes
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R. Erdélyi
2002-01-01
Full Text Available Nonlinear resonant magnetohydrodynamic (MHD waves are studied in weakly dissipative isotropic plasmas in cylindrical geometry. This geometry is suitable and is needed when one intends to study resonant MHD waves in magnetic flux tubes (e.g. for sunspots, coronal loops, solar plumes, solar wind, the magnetosphere, etc. The resonant behaviour of slow MHD waves is confined in a narrow dissipative layer. Using the method of simplified matched asymptotic expansions inside and outside of the narrow dissipative layer, we generalise the so-called connection formulae obtained in linear MHD for the Eulerian perturbation of the total pressure and for the normal component of the velocity. These connection formulae for resonant MHD waves across the dissipative layer play a similar role as the well-known Rankine-Hugoniot relations connecting solutions at both sides of MHD shock waves. The key results are the nonlinear connection formulae found in dissipative cylindrical MHD which are an important extension of their counterparts obtained in linear ideal MHD (Sakurai et al., 1991, linear dissipative MHD (Goossens et al., 1995; Erdélyi, 1997 and in nonlinear dissipative MHD derived in slab geometry (Ruderman et al., 1997. These generalised connection formulae enable us to connect solutions obtained at both sides of the dissipative layer without solving the MHD equations in the dissipative layer possibly saving a considerable amount of CPU-time when solving the full nonlinear resonant MHD problem.
Nath, G.; Pathak, R. P.; Dutta, Mrityunjoy
2018-01-01
Similarity solutions for the flow of a non-ideal gas behind a strong exponential shock driven out by a piston (cylindrical or spherical) moving with time according to an exponential law is obtained. Solutions are obtained, in both the cases, when the flow between the shock and the piston is isothermal or adiabatic. The shock wave is driven by a piston moving with time according to an exponential law. Similarity solutions exist only when the surrounding medium is of constant density. The effects of variation of ambient magnetic field, non-idealness of the gas, adiabatic exponent and gravitational parameter are worked out in detail. It is shown that the increase in the non-idealness of the gas or the adiabatic exponent of the gas or presence of magnetic field have decaying effect on the shock wave. Consideration of the isothermal flow and the self-gravitational field increase the shock strength. Also, the consideration of isothermal flow or the presence of magnetic field removes the singularity in the density distribution, which arises in the case of adiabatic flow. The result of our study may be used to interpret measurements carried out by space craft in the solar wind and in neighborhood of the Earth's magnetosphere.
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Om Prakash
2011-06-01
Full Text Available The present paper is concerned with the study of MHD free convective flow of a visco-elastic (Kuvshinski type dusty gas through a porous medium induced by the motion of a semi-infinite flat plate under the influence of radiative heat transfer moving with velocity decreasing exponentially with time. The expressions for velocity distribution of a dusty gas and dust particles, concentration profile and temperature field are obtained. The effect of Schmidt number (Sc, Magnetic field parameter (M and Radiation parameter (N on velocity distribution of dusty gas and dust particles, concentration and temperature distribution are discussed graphically.
On the stability of dissipative MHD equilibria
International Nuclear Information System (INIS)
Teichmann, J.
1979-04-01
The global stability of stationary equilibria of dissipative MHD is studied uisng the direct Liapunov method. Sufficient and necessary conditions for stability of the linearized Euler-Lagrangian system with the full dissipative operators are given. The case of the two-fluid isentropic flow is discussed. (orig.)
International Nuclear Information System (INIS)
Takeda, Tatsuoki
1985-01-01
In this article analyses of the MHD stabilities which govern the global behavior of a fusion plasma are described from the viewpoint of the numerical computation. First, we describe the high accuracy calculation of the MHD equilibrium and then the analysis of the linear MHD instability. The former is the basis of the stability analysis and the latter is closely related to the limiting beta value which is a very important theoretical issue of the tokamak research. To attain a stable tokamak plasma with good confinement property it is necessary to control or suppress disruptive instabilities. We, next, describe the nonlinear MHD instabilities which relate with the disruption phenomena. Lastly, we describe vectorization of the MHD codes. The above MHD codes for fusion plasma analyses are relatively simple though very time-consuming and parts of the codes which need a lot of CPU time concentrate on a small portion of the codes, moreover, the codes are usually used by the developers of the codes themselves, which make it comparatively easy to attain a high performance ratio on the vector processor. (author)
MHD deceleration of fusion reaction products
International Nuclear Information System (INIS)
Chow, S.; Bohachevsky, I.O.
1979-04-01
The feasibility of magnetohydrodynamic (MHD) deceleration of fuel pellet debris ions exiting from an inertial confinement fusion (ICF) reactor cavity is investigated using one-dimensional flow equations. For engineering reasons, induction-type devices are emphasized; their performance characteristics are similar to those of electrode-type decelerators. Results of the analysis presented in this report indicate that MHD decelerators can be designed within conventional magnet technology to not only decelerate the high-energy fusion pellet debris ions but also to produce some net electric power in the process
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Pandit K. K.
2017-12-01
Full Text Available An investigation of the effects of a chemical reaction and thermal radiation on unsteady MHD free convection heat and mass transfer flow of an electrically conducting, viscous, incompressible fluid past a vertical infinite flat plate embedded in a porous medium is carried out. The flow is induced by a general time-dependent movement of the vertical plate, and the cases of ramped temperature and isothermal plates are studied. An exact solution of the governing equations is obtained in closed form by the Laplace Transform technique. Some applications of practical interest for different types of plate motions are discussed. The numerical values of fluid velocity, temperature and species concentration are displayed graphically whereas the numerical values of skin friction, Nusselt number and Sherwood number are presented in a tabular form for various values of pertinent flow parameters for both ramped temperature and isothermal plates.
Pandit, K. K.; Sarma, D.; Singh, S. I.
2017-12-01
An investigation of the effects of a chemical reaction and thermal radiation on unsteady MHD free convection heat and mass transfer flow of an electrically conducting, viscous, incompressible fluid past a vertical infinite flat plate embedded in a porous medium is carried out. The flow is induced by a general time-dependent movement of the vertical plate, and the cases of ramped temperature and isothermal plates are studied. An exact solution of the governing equations is obtained in closed form by the Laplace Transform technique. Some applications of practical interest for different types of plate motions are discussed. The numerical values of fluid velocity, temperature and species concentration are displayed graphically whereas the numerical values of skin friction, Nusselt number and Sherwood number are presented in a tabular form for various values of pertinent flow parameters for both ramped temperature and isothermal plates.
MHD Ballooning Instability in the Plasma Sheet
International Nuclear Information System (INIS)
Cheng, C.Z.; Zaharia, S.
2003-01-01
Based on the ideal-MHD model the stability of ballooning modes is investigated by employing realistic 3D magnetospheric equilibria, in particular for the substorm growth phase. Previous MHD ballooning stability calculations making use of approximations on the plasma compressibility can give rise to erroneous conclusions. Our results show that without making approximations on the plasma compressibility the MHD ballooning modes are unstable for the entire plasma sheet where beta (sub)eq is greater than or equal to 1, and the most unstable modes are located in the strong cross-tail current sheet region in the near-Earth plasma sheet, which maps to the initial brightening location of the breakup arc in the ionosphere. However, the MHD beq threshold is too low in comparison with observations by AMPTE/CCE at X = -(8 - 9)R(sub)E, which show that a low-frequency instability is excited only when beq increases over 50. The difficulty is mitigated by considering the kinetic effects of ion gyrorad ii and trapped electron dynamics, which can greatly increase the stabilizing effects of field line tension and thus enhance the beta(sub)eq threshold [Cheng and Lui, 1998]. The consequence is to reduce the equatorial region of the unstable ballooning modes to the strong cross-tail current sheet region where the free energy associated with the plasma pressure gradient and magnetic field curvature is maximum
Energy Technology Data Exchange (ETDEWEB)
Aaagard Madsen, H.
1983-01-01
The ideal and the real energy conversion in a straight bladed vertical axis wind turbine (VAWT) with variable pitch has been studied on basis of the actuator cylinder flow model and experimental data from free wind tests on a 9 m/sup 2/ turbine. Particularly, the theoretical upper power limit of VAWT's has been focused upon in the light of the already existing theories for horizontal axis wind turbines (HAWT's). A remarkable result, differing from prior theories, has turned out through the computations with the actuator cylinder flow model and that is: The maximum ideal power coefficient for VAWT's seams neither to be bounded by the Lanchester-Betz power coefficient limit of 16/27 (actuator disc concept), nor by Glauert's ideal power coefficient curve (taking into account the tip speed ratio), both limits derived with particular reference to HAWT's. Concerning the agreement between analysis and the measurements of the power coefficient, the rotor drag coefficient and the flow velocity vector adjacent to the swept area, it was in general found to be good. However, there seems still to be need for future research on the influence of turbulence in the free wind and dynamic stall on the real energy conversion in VAWT's.
Priority pollutant analysis of MHD-derived combustion products
Parks, Katherine D.
An important factor in developing Magnetohydrodynamics (MHD) for commercial applications is environmental impact. Consequently, an effort was initiated to identify and quantify any possible undesirable minute chemical constituents in MHD waste streams, with special emphasis on the priority pollutant species. This paper discusses how priority pollutant analyses were used to accomplish the following goals at the University of Tennessee Space Institute (UTSI): comparison of the composition of solid combustion products collected from various locations along a prototypical MHD flow train during the firing of Illinois No. 6 and Montana Rosebud coals; comparison of solid waste products generated from MHD and conventional power plant technologies; and identification of a suitable disposal option for various MHD derived combustion products. Results from our ongoing research plans for gas phase sampling and analysis of priority pollutant volatiles, semi-volatiles, and metals are discussed.
Analysis of Design Variables of Annular Linear Induction Electromagnetic Pump using an MHD Model
Energy Technology Data Exchange (ETDEWEB)
Kwak, Jae Sik; Kim, Hee Reyoung [Ulsan National Institute of Science and Technology, Ulsan (Korea, Republic of)
2015-05-15
The generated force is affected by lots of factors including electrical input, hydrodynamic flow, geometrical shape, and so on. These factors, which are the design variables of an ALIP, should be suitably analyzed to optimally design an ALIP. Analysis on the developed pressure and efficiency of the ALIP according to the change of design variables is required for the ALIP satisfying requirements. In this study, the design variables of the ALIP are analyzed by using ideal MHD analysis model. Electromagnetic force and efficiency are derived by analyzing the main design variables such as pump core length, inner core diameter, flow gap and turns of coils. The developed pressure and efficiency of the ALIP were derived and analyzed on the change of the main variables such as pump core length, inner core diameter, flow gap, and turns of coils of the ALIP.
Criteria for Scaled Laboratory Simulations of Astrophysical MHD Phenomena
International Nuclear Information System (INIS)
Ryutov, D. D.; Drake, R. P.; Remington, B. A.
2000-01-01
We demonstrate that two systems described by the equations of the ideal magnetohydrodynamics (MHD) evolve similarly, if the initial conditions are geometrically similar and certain scaling relations hold. The thermodynamic properties of the gas must be such that the internal energy density is proportional to the pressure. The presence of the shocks is allowed. We discuss the applicability conditions of the ideal MHD and demonstrate that they are satisfied with a large margin both in a number of astrophysical objects, and in properly designed simulation experiments with high-power lasers. This allows one to perform laboratory experiments whose results can be used for quantitative interpretation of various effects of astrophysical MHD. (c) 2000 The American Astronomical Society
Stationary shear flows in CGL anisotropic toroidal plasmas
International Nuclear Information System (INIS)
Pastukhov, V.P.; Ilgisonis, V.I.
1996-01-01
Recently a general structure of stationary shear flows in toroidal plasmas was obtained in the frame of ideal isotropic-pressure MHD model. The structure of the stationary plasma flows was shown to be determined by a hidden symmetry of MHD equations inherent in the toroidal systems with nested magnetic surfaces. However, the characteristic frequencies of the stationary plasma motion can considerably exceed the collisional frequencies in real plasma experiments. In this case the CGL collisionless MHD model seems to be more adequate than the simplified isotropic-pressure MHD model to describe the stationary plasma flows. In this paper we have generalized our approach to analyze the stationary plasma flows in the frame of the collisionless CGL model. We have found again that the hidden symmetry inherent in the toroidal topology results in two integral invariants which depend on two independent surface functions. The structure of stationary flows for CGL model is still the same as for isotropic MHD, however, the pressure tensor components satisfy a appreciably modifies the steady state force-balance equation. These results are applied to analyze the generalized equilibrium in axisymmetric (tokamak-like) magnetic confinement systems
MHD stability analyses of a tokamak plasma by time-dependent codes
International Nuclear Information System (INIS)
Kurita, Gen-ichi
1982-07-01
The MHD properties of a tokamak plasma are investigated by using time evolutional codes. As for the ideal MHD modes we have analyzed the external modes including the positional instability. Linear and nonlinear ideal MHD codes have been developed. Effects of the toroidicity and conducting shell on the external kink mode are studied minutely by the linear code. A new rezoning algorithm is devised and it is successfully applied to express numerically the axisymmetric plasma perturbation in a cylindrical geometry. As for the resistive MHD modes we have developed nonlinear codes on the basis of the reduced set of the resistive MHD equations. By using the codes we have studied the major disruption processes and properties of the low n resistive modes. We have found that the effects of toroidicity and finite poloidal beta are very important. Considering the above conclusion we propose a new scenario of the initiation of the major disruption. (author)
Study of MHD stability beta limit in LHD by hierarchy integrated simulation code
International Nuclear Information System (INIS)
Sato, M.; Watanabe, K.Y.; Nakamura, Y.
2008-10-01
The beta limit by the ideal MHD instabilities (so-called 'MHD stability beta limit') for helical plasmas is studied by a hierarchy integrated simulation code. A numerical model for the effect of the MHD instabilities is introduced such that the pressure profile is flattened around the rational surface due to the MHD instabilities. The width of the flattening of the pressure gradient is determined from the width of the eigenmode structure of the MHD instabilities. It is assumed that there is the upper limit of the mode number of the MHD instabilities which directly affect the pressure gradient. The upper limit of the mode number is determined using a recent high beta experiment in the Large Helical Device (LHD). The flattening of the pressure gradient is calculated by the transport module in a hierarchy integrated code. The achievable volume averaged beta value in the LHD is expected to be beyond 6%. (author)
2-D skin-current toroidal-MHD-equilibrium code
International Nuclear Information System (INIS)
Feinberg, B.; Niland, R.A.; Coonrod, J.; Levine, M.A.
1982-09-01
A two-dimensional, toroidal, ideal MHD skin-current equilibrium computer code is described. The code is suitable for interactive implementation on a minicomptuer. Some examples of the use of the code for design and interpretation of toroidal cusp experiments are presented
A nonlinear resistive MHD-code in cylindrical geometry
International Nuclear Information System (INIS)
Jakoby, A.
1987-11-01
A computer code has been developed which solves the full compressible resistive magnetohydrodynamic (MHD) equations in cylindrical geometry. The variables are expanded in Fourier series in the poloidal and axial directions while finite differences are used in the radial direction. The time advance is accomplished by using a semi-implicit predictor-corrector-scheme. Applications to the ideal m=1 ideal kink saturation in the nonlinear regime and the subsequent decay of the singular current layer due to resistivity are presented. (orig.)
Petrick, Michael; Pierson, Edward S.; Schreiner, Felix
1980-01-01
According to the present invention, coal combustion gas is the primary working fluid and copper or a copper alloy is the electrodynamic fluid in the MHD generator, thereby eliminating the heat exchangers between the combustor and the liquid-metal MHD working fluids, allowing the use of a conventional coalfired steam bottoming plant, and making the plant simpler, more efficient and cheaper. In operation, the gas and liquid are combined in a mixer and the resulting two-phase mixture enters the MHD generator. The MHD generator acts as a turbine and electric generator in one unit wherein the gas expands, drives the liquid across the magnetic field and thus generates electrical power. The gas and liquid are separated, and the available energy in the gas is recovered before the gas is exhausted to the atmosphere. Where the combustion gas contains sulfur, oxygen is bubbled through a side loop to remove sulfur therefrom as a concentrated stream of sulfur dioxide. The combustor is operated substoichiometrically to control the oxide level in the copper.
Institute of Scientific and Technical Information of China (English)
李俊峰; 倪明玖
2011-01-01
在低磁场雷诺数条件下,基于电势泊松方程,发展了交错网格下可以精确计算电流和洛伦兹力(电磁力)的相容守恒格式.采用压力为变量的原始变量法求解不可压缩Navier-Stokes方程,所计算的电流满足电荷守恒定律,所计算的电磁力满足动量守恒定律.对金属流体在Hartmann数50～5000范围内验证了格式的精确性.交错网格下相容守恒格式的发展为后续MHD稳定性分析、湍流的大涡模拟及直接数值模拟提供很好的选择.%A consistent and conservative scheme has been extended and developed on a staggered grid system for liquid metal MHD flow at a low magnetic Reynolds number by solving electrical potential Poisson equation based on the Ohm's law and the charge conservation law. The consistent scheme is used to ensure the calculated current density conserves the charge, and the divergence formula of the Lorentz force is used to ensure the momentum conservation. Simulation of liquid metal flows in a three-dimensional straight channel is conducted and compared with the analytical solutions from Shercliff's and Hunt's. The numerical results are in good agreement with analytical solutions for the Hartmann numbers from 50 to 5000. A fully conservative scheme on a staggered grid, which can conserve mass, momentum and kinetic energy and charge, is then developed with the central-symmetrical scheme for the convective term and the pressure term and with the consistent and conservative scheme for the calculation of the current density and the Lorentz force. A fully conservative scheme can be a good tool for numerical analysis of MHD flow instability, large eddy simulation (LES) and direct-numerical simulation (DNS) of MHD turbulence.
A Study on the Evaluation of Real Gas vs. Ideal Gas for its Application to the CO2 Leak Flow Model
International Nuclear Information System (INIS)
Jung, Hwa-Young; Lee, Jeong Ik
2015-01-01
The leak can cause various mechanical and thermal problems. Moreover, CO 2 also reacts with sodium by producing some solid reaction products (i.e. Na 2 CO 3 , Na 2 O, etc.), toxic gas (i.e. CO) and heat. Prior to applying the S-CO 2 Brayton cycle to the SFRs, the important safety issues that can occur in the Na-CO 2 heat exchanger should be evaluated. For this, it is essential to predict a CO 2 leak mechanism when the pressure boundary fails. The degree of sodium-CO 2 reaction is determined by several factors; a crack or rupture size, the interfacial area between sodium and CO 2 , the amount of released CO 2 , and so on. In order to simulate more reasonable and realistic CO 2 leak flow, one needs to evaluate and improve some limitations found from the previous studies. The dynamic response in the CO 2 side should be considered for varying mass flux at the nozzle exit over time. Thus, it is necessary to investigate more practical flow model to evaluate the system condition change and its consequences during the CO 2 leak. For the flow modeling, it is obvious that a real gas effect and friction force should be considered. However, due to its complexity and difficulty, it is generally assumed that CO 2 behaves as an ideal gas, and an isentropic critical flow without considering the friction force was applied for the analysis so far. In this paper, before incorporating the real gas effect and friction force to the model, gas properties are evaluated as the first step. The fluid properties of CO 2 is studied to observe how strong the real gas effect can be under SFR operating conditions. From this result, it is determined that which gas model is applicable to the CO 2 leak flow model for simulating the accident scenario in the given conditions of Na-CO 2 heat exchanger. The ideal gas law and the isentropic critical flow model are generally applied to predict the state and the flow rate of CO 2 leak in the Na-CO 2 heat exchanger previously. However, to simulate a
International Nuclear Information System (INIS)
Zhang, Xiaoshun; Yu, Tao; Yang, Bo; Zheng, Limin; Huang, Linni
2015-01-01
Highlights: • A novel optimal carbon-energy combined-flow (OCECF) model is firstly established. • A novel approximate ideal multi-objective solution Q(λ) learning is designed. • The proposed algorithm has a high convergence stability and reliability. • The proposed algorithm can be applied for OCECF in a large-scale power grid. - Abstract: This paper proposes a novel approximate ideal multi-objective solution Q(λ) learning for optimal carbon-energy combined-flow in multi-energy power systems. The carbon emissions, fuel cost, active power loss, voltage deviation and carbon emission loss are chosen as the optimization objectives, which are simultaneously optimized by five different Q-value matrices. The dynamic optimal weight of each objective is calculated online from the entire Q-value matrices such that the greedy action policy can be obtained. Case studies are carried out to evaluate the optimization performance for carbon-energy combined-flow in an IEEE 118-bus system and the regional power grid of southern China.
Gabersek, Sasa.; Durran, Dale R.
2004-12-01
Gap winds produced by a uniform airstream flowing over an isolated flat-top ridge cut by a straight narrow gap are investigated by numerical simulation. On the scale of the entire barrier, the proportion of the oncoming flow that passes through the gap is relatively independent of the nondimensional mountain height , even over that range of for which there is the previously documented transition from a “flow over the ridge” regime to a “flow around” regime.The kinematics and dynamics of the gap flow itself were investigated by examining mass and momentum budgets for control volumes at the entrance, central, and exit regions of the gap. These analyses suggest three basic behaviors: the linear regime (small ) in which there is essentially no enhancement of the gap flow; the mountain wave regime ( 1.5) in which vertical mass and momentum fluxes play a crucial role in creating very strong winds near the exit of the gap; and the upstream-blocking regime ( 5) in which lateral convergence generates the strongest winds near the entrance of the gap.Trajectory analysis of the flow in the strongest events, the mountain wave events, confirms the importance of net subsidence in creating high wind speeds. Neglect of vertical motion in applications of Bernoulli's equation to gap flows is shown to lead to unreasonable wind speed predictions whenever the temperature at the gap exit exceeds that at the gap entrance. The distribution of the Bernoulli function on an isentropic surface shows a correspondence between regions of high Bernoulli function and high wind speeds in the gap-exit jet similar to that previously documented for shallow-water flow.
MHD diffuser model test program
Energy Technology Data Exchange (ETDEWEB)
Idzorek, J J
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment.
MHD diffuser model test program
International Nuclear Information System (INIS)
Idzorek, J.J.
1976-07-01
Experimental results of the aerodynamic performance of seven candidate diffusers are presented to assist in determining their suitability for joining an MHD channel to a steam generator at minimum spacing. The three dimensional diffusers varied in area ratio from 2 to 3.8 and wall half angle from 2 to 5 degrees. The program consisted of five phases: (1) tailoring a diffuser inlet nozzle to a 15 percent blockage; (2) comparison of isolated diffusers at enthalpy ratios 0.5 to 1.0 with respect to separation characteristics and pressure recovery coefficients; (3) recording the optimum diffuser exit flow distribution; (4) recording the internal flow distribution within the steam generator when attached to the diffuser; and (5) observing isolated diffuser exhaust dynamic characteristics. The 2 and 2-1/3 degree half angle rectangular diffusers showed recovery coefficients equal to 0.48 with no evidence of flow separation or instability. Diffusion at angles greater than these produced flow instabilities and with angles greater than 3 degrees random flow separation and reattachment
Combined ideal and kinetic effects on reversed shear Alfven eigenmodes
International Nuclear Information System (INIS)
Gorelenkov, N. N.; Kramer, G. J.; Nazikian, R.
2011-01-01
A reversed shear Alfven eigenmodes (RSAEs) theory has been developed for reversed magnetic field shear plasmas when the safety factor minimum, q min , is at or above a rational value. The modes we study are known sometimes as either the bottom of the frequency sweep or the down sweeping RSAEs. We show that, strictly speaking, the ideal MHD theory is not compatible with the eigenmode solution in the reversed shear plasma with q min above integer values. Corrected by a special analytic finite Larmor radius (FLR) condition, MHD dispersion of these modes nevertheless can be developed. Numerically, MHD structure can serve as a good approximation for the RSAEs.The large radial scale part of the analytic RSAE solution can be obtained from ideal MHD and expressed in terms of the Legendre functions. The kinetic equation with FLR effects for the eigenmode is solved numerically and agrees with the analytic solutions. Properties of RSAEs and their potential implications for plasma diagnostics are discussed.
Resistive MHD Stability Analysis in Near Real-time
Glasser, Alexander; Kolemen, Egemen
2017-10-01
We discuss the feasibility of a near real-time calculation of the tokamak Δ' matrix, which summarizes MHD stability to resistive modes, such as tearing and interchange modes. As the operational phase of ITER approaches, solutions for active feedback tokamak stability control are needed. It has been previously demonstrated that an ideal MHD stability analysis is achievable on a sub- O (1 s) timescale, as is required to control phenomena comparable with the MHD-evolution timescale of ITER. In the present work, we broaden this result to incorporate the effects of resistive MHD modes. Such modes satisfy ideal MHD equations in regions outside narrow resistive layers that form at singular surfaces. We demonstrate that the use of asymptotic expansions at the singular surfaces, as well as the application of state transition matrices, enable a fast, parallelized solution to the singular outer layer boundary value problem, and thereby rapidly compute Δ'. Sponsored by US DOE under DE-SC0015878 and DE-FC02-04ER54698.
Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.
1992-01-01
A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.
Hamilton, H. H., II; Spall, J. R.
1986-01-01
A time-asymptotic method has been used to obtain steady-flow solutions for axisymmetric inviscid flow over several blunt bodies including spheres, paraboloids, ellipsoids, and spherically blunted cones. Comparisons with experimental data and results of other computational methods have demonstrated that accurate solutions can be obtained using this approach. The method should prove useful as an analysis tool for comparing with experimental data and for making engineering calculations for blunt reentry vehicles.
Nonlinear MHD dynamo operating at equipartition
DEFF Research Database (Denmark)
Archontis, V.; Dorch, Bertil; Nordlund, Åke
2007-01-01
Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......, and that it can saturate at a level significantly higher than intermittent turbulent dynamos, namely at energy equipartition, for high values of the magnetic and fluid Reynolds numbers. The equipartition solution however does not remain time-independent during the simulation but exhibits a much more intricate...
Noncanonical Hamiltonian density formulation of hydrodynamics and ideal MHD
International Nuclear Information System (INIS)
Morrison, P.J.; Greene, J.M.
1980-04-01
A new Hamiltonian density formulation of a perfect fluid with or without a magnetic field is presented. Contrary to previous work the dynamical variables are the physical variables, rho, v, B, and s, which form a noncanonical set. A Poisson bracket which satisfies the Jacobi identity is defined. This formulation is transformed to a Hamiltonian system where the dynamical variables are the spatial Fourier coefficients of the fluid variables
Energetic particle effects on global MHD modes
International Nuclear Information System (INIS)
Cheng, C.Z.
1990-01-01
The effects of energetic particles on MHD type modes are studied by analytical theories and the nonvariational kinetic-MHD stability code (NOVA-K). In particular we address the problems of (1) the stabilization of ideal MHD internal kink modes and the excitation of resonant ''fishbone'' internal modes and (2) the alpha particle destabilization of toroidicity-induced Alfven eigenmodes (TAE) via transit resonances. Analytical theories are presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral-beam injection (NBI) or ion cyclotron resonant heating (ICRH), a stability window for the n=1 internal kink mode in the hot particle beat space exists even in the absence of core ion finite Larmor radius effect (finite ω *i ). On the other hand, the trapped alpha particles are found to resonantly excite instability of the n=1 internal mode and can lower the critical beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha particle pressure. 23 refs., 5 figs
MHD thrust vectoring of a rocket engine
Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic
2016-09-01
In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.
Spectrum of resistive MHD modes in cylindrical plasmas
International Nuclear Information System (INIS)
Ryu, C.M.; Grimm, R.C.
1983-07-01
A numerical study of the normal modes of a compressible resistive MHD fluid in cylindrical geometry is presented. Resistivity resolves the shear Alfven and slow magnetosonic continua of ideal MHD into discrete spectra and gives rise to heavily damped modes whose frequencies lie on specific lines in the complex plane. Fast magnetosonic waves are less affected but are also damped. Overstable modes arise from the shear Alfven spectrum. The stabilizing effect of favorable average curvature is shown. Eigenfunctions illustrating the nature of typical normal modes are displayed
International Nuclear Information System (INIS)
Huysmans, G.
1998-03-01
One of the aims of the JET, the Joint European Torus, project is to optimise the maximum fusion performance as measured by the neutron rate. At present, two different scenarios are developed at JET to achieve the high performance the so-called Hot-Ion H-mode scenario and the more recent development of the Optimised Shear scenario. Both scenarios have reached similar values of the neutron rate in Deuterium plasmas, up to 5 10 17 neutrons/second. Both scenarios are characterised by a transport barrier, i.e., a region in the plasma where the confinement is improved. The Hot-Ion H-mode has a transport barrier at the plasma boundary just inside the separatrix, an Optimised Shear plasma exhibits a transport barrier at about mid radius. Associated with the improved confinement of the transport barriers are locally large pressure gradients. It is these pressure gradients which, either directly or indirectly, can drive MHD instabilities. The instabilities limit the maximum performance. In the optimised shear scenario a global MHD instability leads to a disruptive end of the discharge. In the Hot-Ion H-mode plasmas, so-called Outer Modes can occur which are localised at the plasma boundary and lead to a saturation of the plasma performance. In this paper, two examples of the MHD instabilities are discussed and identified by comparing the experimentally observed modes with theoretical calculations from the ideal MHD code MISHKA-1. Also, the MHD stability boundaries of the two scenarios are presented. Section 3 contains a discussion of the mode observed just before the disruption
Experiments and models of MHD jets and their relevance to astrophysics and solar physics
Bellan, Paul
2017-10-01
MHD-driven flows exist in both space and lab plasmas because the MHD force-balance equation J × B - ∇ P = 0 can only be satisfied in situations having an unusual degree of symmetry. In the normal situation where such symmetry does not exist, an arbitrary magnetic field B and its associated current J =μ0- 1 ∇ × B provide a magnetic force F = J × B having the character of a torque, i.e., ∇ × F ≠ 0 . Because ∇ × ∇ P = 0 is a mathematical identity, no pressure gradient can balance this torque so a flow is driven. Additionally, since ideal MHD has magnetic flux frozen into the frame of the moving plasma, the flow convects frozen-in magnetic flux. If the flow slows and piles up, both the plasma and the frozen-in magnetic flux will be compressed. This magnetic flux compression amplifies both the frozen-in B and its associated J . Slowing down thus increases certain components of F , in particular the pinch force associated with the electric current in the flow direction. This increased pinching causes the flow to self-collimate if the leading edge of the flow moves slower than the trailing part so there is compression in the flow frame. The result is that the flow self-collimates and forms a narrow jet. Self-collimating jets with embedded electric current and helical magnetic field are analogous to the straight cylindrical approximation of a tokamak, but now with the length of the cylinder continuously increasing and the radius depending on axial position. The flows are directed from axial regions having small radius to axial regions having large radius. The flow velocity is proportional to the axial electric current and is a significant fraction of the Alfvén velocity. Examples of these MHD-driven flows are astrophysical jets, certain solar coronal situations, and the initial plasma produced by the coaxial magnetized plasma guns used for making spheromaks. The above picture has been developed from laboratory measurements, analytic models, and numerical
Energy Technology Data Exchange (ETDEWEB)
Vlaykov, Dimitar G., E-mail: Dimitar.Vlaykov@ds.mpg.de [Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany); Max-Planck-Institut für Dynamik und Selbstorganisation, Am Faßberg 17, D-37077 Göttingen (Germany); Grete, Philipp [Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen (Germany); Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, D-37077 Göttingen (Germany); Schmidt, Wolfram [Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, D-21029 Hamburg (Germany); Schleicher, Dominik R. G. [Departamento de Astronomía, Facultad Ciencias Físicas y Matemáticas, Universidad de Concepción, Av. Esteban Iturra s/n Barrio Universitario, Casilla 160-C (Chile)
2016-06-15
Compressible magnetohydrodynamic (MHD) turbulence is ubiquitous in astrophysical phenomena ranging from the intergalactic to the stellar scales. In studying them, numerical simulations are nearly inescapable, due to the large degree of nonlinearity involved. However, the dynamical ranges of these phenomena are much larger than what is computationally accessible. In large eddy simulations (LESs), the resulting limited resolution effects are addressed explicitly by introducing to the equations of motion additional terms associated with the unresolved, subgrid-scale dynamics. This renders the system unclosed. We derive a set of nonlinear structural closures for the ideal MHD LES equations with particular emphasis on the effects of compressibility. The closures are based on a gradient expansion of the finite-resolution operator [W. K. Yeo (CUP, 1993)] and require no assumptions about the nature of the flow or magnetic field. Thus, the scope of their applicability ranges from the sub- to the hyper-sonic and -Alfvénic regimes. The closures support spectral energy cascades both up and down-scale, as well as direct transfer between kinetic and magnetic resolved and unresolved energy budgets. They implicitly take into account the local geometry, and in particular, the anisotropy of the flow. Their properties are a priori validated in Paper II [P. Grete et al., Phys. Plasmas 23, 062317 (2016)] against alternative closures available in the literature with respect to a wide range of simulation data of homogeneous and isotropic turbulence.
Pal, Abhro; Anupindi, Kameswararao; Delorme, Yann; Ghaisas, Niranjan; Shetty, Dinesh A; Frankel, Steven H
2014-07-01
In the present study, we performed large eddy simulation (LES) of axisymmetric, and 75% stenosed, eccentric arterial models with steady inflow conditions at a Reynolds number of 1000. The results obtained are compared with the direct numerical simulation (DNS) data (Varghese et al., 2007, "Direct Numerical Simulation of Stenotic Flows. Part 1. Steady Flow," J. Fluid Mech., 582, pp. 253-280). An inhouse code (WenoHemo) employing high-order numerical methods for spatial and temporal terms, along with a 2nd order accurate ghost point immersed boundary method (IBM) (Mark, and Vanwachem, 2008, "Derivation and Validation of a Novel Implicit Second-Order Accurate Immersed Boundary Method," J. Comput. Phys., 227(13), pp. 6660-6680) for enforcing boundary conditions on curved geometries is used for simulations. Three subgrid scale (SGS) models, namely, the classical Smagorinsky model (Smagorinsky, 1963, "General Circulation Experiments With the Primitive Equations," Mon. Weather Rev., 91(10), pp. 99-164), recently developed Vreman model (Vreman, 2004, "An Eddy-Viscosity Subgrid-Scale Model for Turbulent Shear Flow: Algebraic Theory and Applications," Phys. Fluids, 16(10), pp. 3670-3681), and the Sigma model (Nicoud et al., 2011, "Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations," Phys. Fluids, 23(8), 085106) are evaluated in the present study. Evaluation of SGS models suggests that the classical constant coefficient Smagorinsky model gives best agreement with the DNS data, whereas the Vreman and Sigma models predict an early transition to turbulence in the poststenotic region. Supplementary simulations are performed using Open source field operation and manipulation (OpenFOAM) ("OpenFOAM," http://www.openfoam.org/) solver and the results are inline with those obtained with WenoHemo.
International Nuclear Information System (INIS)
Fedorczak, N; Manz, P; Chakraborty Thakur, S; Xu, M; Tynan, G R
2013-01-01
The consequences of vorticity conservation on the spatio-temporal interaction of a E × B zonal shear with a generic pattern of plasma potential modes are investigated in a magnetized plasma environment. Eddies organized on a chain along the zonal direction are locally depleted, resulting in what appears to be a radial decorrelation by the shear flow in the absence of dissipation. The eddy depletion occurs due to a transfer of enstrophy from the chain to the shear flow during the progressive growth in the chain anisotropy. The rate of zonal shear acceleration is derived analytically and its expression is validated by numerical simulations. The rate is proportional to the chain amplitude in the weak shear regime and to the shearing rate in the strong shear regime. Basic properties of the model are validated with fast visible imaging data collected on a magnetized plasma column experiment. A characteristic vorticity flux across the edge shear layer of tokamak plasmas is associated with the model predictions. The dependence of the interaction rate with turbulence amplitude and shearing rate could be an important ingredient of the low to high confinement mode transition. (paper)
Pseudo-MHD ballooning modes in tokamak plasmas
International Nuclear Information System (INIS)
Callen, J.D.; Hegna, C.C.
1996-08-01
The MHD description of a plasma is extended to allow electrons to have both fluid-like and adiabatic-regime responses within an instability eigenmode. In the resultant open-quotes pseudo-MHDclose quotes model, magnetic field line bending is reduced in the adiabatic electron regime. This makes possible a new class of ballooning-type, long parallel extent, MHD-like instabilities in tokamak plasmas for α > s 2 (2 7/3 /9) (r p /R 0 ) or-d√Β/dr > (2 1/6 /3)(s/ R 0q ), which is well below the ideal-MHD stability boundary. The marginally stable pressure profile is similar in both magnitude and shape to that observed in ohmically heated tokamak plasmas
Neoclassical MHD equilibria with ohmic current
International Nuclear Information System (INIS)
Tokuda, Shinji; Takeda, Tatsuoki; Okamoto, Masao.
1989-01-01
MHD equilibria of tokamak plasmas with neoclassical current effects (neoclassical conductivity and bootstrap current) were calculated self-consistently. Neoclassical effects on JFT-2M tokamak plasmas, sustained by ohmic currents, were studied. Bootstrap currents flow little for L-mode type equilibria because of low attainable values of poloidal beta, β J . H-mode type equilibria give bootstrap currents of 30% ohmic currents for β J attained by JFT-2M and 100% for β J ≥ 1.5, both of which are sufficient to change the current profiles and the resultant MHD equilibria. Neoclassical conductivity which has roughly half value of the classical Spitzer conductivity brings peaked ohmic current profiles to yield low safety factor at the magnetic axis. Neoclassical conductivity reduces the value of effective Z(Z eff ) which is necessary to give the observed one-turn voltage but it needs impurities accumulating at the center when such peaked current profiles are not observed. (author)
Engineering design and development of lead lithium loop for thermo-fluid MHD studies
International Nuclear Information System (INIS)
Kumar, M.; Patel, Anita; Jaiswal, A.; Ranjan, A.; Mohanta, D.; Sahu, S.; Saraswat, A.; Rao, T.S.; Mehta, V.; Bhattacharyay, R.; Rajendra Kumar, E.
2017-01-01
In the frame of the design and development of LLCB TBM, number of R and D activities is in progress in the area of Pb-Li technology development. Molten Pb-Li is used as a tritium breeder and also as a coolant for the internals of the TBM structure. In presence of strong plasma confining toroidal magnetic field, motion of electrically conducting Pb-Li leads to Magneto Hydro Dynamic (MHD) phenomena, as a consequence of which the flow profile of Pb-Li is significantly modified inside the Pb-Li channels of TBM. This causes additional pressure drop inside TBM and affects the heat transfer from internal structure. The detail studies of these MHD effects are of prime importance for successful design of LLCB TBM and its performance evaluation. Although, various numerical MHD codes have been developed, validated in simple flow configuration and are being used to study MHD phenomena in LLCB TBM, experimental validation of these codes in TBM relevant complex flow geometry is yet to be performed. A Pb-Li MHD experimental loop is, therefore, being developed at IPR to perform thermo-fluid MHD experiments in various LLCB TBM relevant flow configuration. MHD experiments are planned with different test sections instrumented with potential pins, thermo couples, etc. under a uniform magnetic field of ∼1.4 T. The obtained experimental data will be analyzed to understand the MHD phenomena in TBM like flow configuration and also for validation of MHD codes. This paper describes the detailed process as well as engineering design of the Pb-Li MHD loop and its major components along with the plan of MHD experiments in various test mock ups. (author)
MHD power conversion employing liquid metals
International Nuclear Information System (INIS)
Houben, J.W.M.A.; Massee, P.
1969-02-01
The work performed in the field of MHD generation of electricity by means of liquid metals is described. It is shown that the study of two-phase flows is essential in this topic of research; two-phase flows are therefore described. Two types of generators which can be utilized with liquid metals have been studied. The results of this study are described. A short survey of the prospects of other liquid metal systems which emerge from a study of the literature is given. Finally, conclusions are drawn concerning possibilities for further investigation
Directory of Open Access Journals (Sweden)
M.M. Bhatti
2017-09-01
Full Text Available In this article, heat and mass transfer with Joule heating on magnetohydrodynamic (MHD peristaltic blood under the influence of Hall effect is examined. Mathematical modelling is based on momentum, energy and concentration which are taken into account using ohms law. The governing partial differential equations are further simplified by neglecting the inertial forces and long wavelength approximations. Exact solutions have been presented for velocity, temperature and concentration profile. The influence of all the physical pertinent parameters is taken into account with the help graphs. It is found that Hartmann number and Hall parameter shows opposite behaviour on velocity, temperature and concentration profile. It is worth mentioning that pressure rise also depicts opposite behaviour for Hartmann number and Hall parameter. The present analysis is also presented for Newtonian fluid (α→0 as a special case for our study. It is observed that Hall Effect and magnetic field shows opposite behaviour on velocity and temperature profile. Temperature profile increases due to the increment in Prandtl number and Eckert number. Numerical comparison is also presented between the existing published results by taking α=0,M=0 as a special case of our study.
International Nuclear Information System (INIS)
Kotschenreuther, M.
1985-07-01
The dynamics of ideal and kinetic ballooning modes are considered analytically including parallel ion dynamics, but without electron dissipation. For ideal modes, parallel dynamics predominantly determine the growth rate when β is within approx.30% of the ideal threshold, resulting in a substantial reduction in growth rate. Compressibility also eliminates the stabilization effects of finite Larmor radius (FLR); FLR effects (when temperature gradients are neglected) can even increase the growth rate above the MHD value. Temperature gradients accentuate this by adding a new source of free energy independent of the MHD drive, in this region of ballooning coordinate corresponding in MHD to the continuum. Analytic dispersion relations are derived demonstrating the effects above; the formalism emphasizes the similarities between the ideal MHD and kinetic cases
Ida, Masato; Taniguchi, Nobuyuki
2003-09-01
This paper introduces a candidate for the origin of the numerical instabilities in large eddy simulation repeatedly observed in academic and practical industrial flow computations. Without resorting to any subgrid-scale modeling, but based on a simple assumption regarding the streamwise component of flow velocity, it is shown theoretically that in a channel-flow computation, the application of the Gaussian filtering to the incompressible Navier-Stokes equations yields a numerically unstable term, a cross-derivative term, which is similar to one appearing in the Gaussian filtered Vlasov equation derived by Klimas [J. Comput. Phys. 68, 202 (1987)] and also to one derived recently by Kobayashi and Shimomura [Phys. Fluids 15, L29 (2003)] from the tensor-diffusivity subgrid-scale term in a dynamic mixed model. The present result predicts that not only the numerical methods and the subgrid-scale models employed but also only the applied filtering process can be a seed of this numerical instability. An investigation concerning the relationship between the turbulent energy scattering and the unstable term shows that the instability of the term does not necessarily represent the backscatter of kinetic energy which has been considered a possible origin of numerical instabilities in large eddy simulation. The present findings raise the question whether a numerically stable subgrid-scale model can be ideally accurate.
Grundland, A. M.; Lalague, L.
1996-04-01
This paper presents a new method of constructing, certain classes of solutions of a system of partial differential equations (PDEs) describing the non-stationary and isentropic flow for an ideal compressible fluid. A generalization of the symmetry reduction method to the case of partially-invariant solutions (PISs) has been formulated. We present a new algorithm for constructing PISs and discuss in detail the necessary conditions for the existence of non-reducible PISs. All these solutions have the defect structure 0305-4470/29/8/019/img1 and are computed from four-dimensional symmetric subalgebras. These theoretical considerations are illustrated by several examples. Finally, some new classes of invariant solutions obtained by the symmetry reduction method are included. These solutions represent central, conical, rational, spherical, cylindrical and non-scattering double waves.
Experimental investigation of MHD effects in a manifold of a downstream circular pipe
International Nuclear Information System (INIS)
Xu Zengyu; Pan Chuanjie; Wei Wenhao; Chen Xiaoqiong; Zhang Yanxu
2001-01-01
The velocity distribution in the mid-plane of the cross section of a main pipe in the region of a junction is investigated. The result confirms that the MHD-flow near the junction is strongly affected by the junction itself. This holds even if the bypass pipe is closed. The MHD pressure drops are also measured, and a three-dimensional (3D) factor of MHD pressure drop due to manifold effects is obtained with theoretical analysis and comparing with experimental data. The factor is directly proportional to Hartmann number Ha. Two dimensional MHD pressure drop is also discussed
International Nuclear Information System (INIS)
1991-10-01
The current MHD program being implemented is a result of a consensus established in public meetings held by the Department of Energy in 1984. Essential elements of the current program include: (1) develop technical and environmental data for the integrated MHD topping cycle system through POC testing (1,000 hours); (2) develop technical and environmental data for the integrated MHD bottoming cycle sub system through POC testing (4,000 hours); (3) design, construct, and operate a seed regeneration POC facility (SRPF) capable of processing spent seed materials from the MHD bottoming cycle; (4) prepare conceptual designs for a site specific MHD retrofit plant; and (5) continue system studies and supporting research necessary for system testing. The current MHD program continues to be directed toward coal fired power plant applications, both stand-alone and retrofit. Development of a plant should enhance the attractiveness of MHD for applications other than electrical power. MHD may find application in electrical energy intensive industries and in the defense sector
International Nuclear Information System (INIS)
Petit, J.P.
1995-01-01
Jean-Pierre PETIT, one of the best MHD specialists, is telling this technology story and he is insisting on its military consequences. Civil MHD is only one iceberg emerged part, including a lot of leader technologies, interesting he defense. 3 notes
Directory of Open Access Journals (Sweden)
Muthuraj R.
2012-01-01
Full Text Available A mathematical model is developed to examine the effect of chemical reaction on MHD mixed convective heat and mass transfer flow of a couple-stress fluid in vertical porous space in the presence of temperature dependent heat source with travelling thermal waves. The dimensionless governing equations are assumed to be made up of two parts: a mean part corresponding to the fully developed mean flow, and a small perturbed part, using amplitude as a small parameter. The analytical solution of perturbed part have been carried out by using the long-wave approximation. The expressions for the zeroth-order and the first order solutions are obtained and the results of the heat and mass transfer characteristics are presented graphically for various values of parameters entering into the problem. It is noted that velocity of the fluid increases with the increase of the couple stress parameter and increasing the chemical reaction parameter leads suppress the velocity of the fluid. Cross velocity decreases with an increase of the phase angle. The increase of the chemical reaction parameter and Schmidt number lead to decrease the fluid concentration. The hydrodynamic case for a non-porous space in the absence of the temperature dependent heat source for Newtonian fluid can be captured as a limiting case of our analysis by taking, and α1→0, Da→∞, a→∞.
Present state of research and development of MHD power generation
International Nuclear Information System (INIS)
Ikeda, Shigeru
1978-01-01
MHD power generation can obtain electric energy directly from the heat energy of high speed plasma flow, and the power generating plant of 1 million kW can be realized by this method. When the MHD power generation method is combined before conventional thermal power generation method, the thermal efficiency can be raised to about 60% as compared with 38% in thermal power generation plants. The research and development of MHD power generation are in progress in USA and USSR. The research and development in Japan are in the second stage now after the first stage project for 10 years, and the Mark 7 generator with 100 kW electric output for 200 hr continuous operation is under construction. The MHD power generation is divided into three types according to the conductive fluids used, namely combustion type for thermal power generation, unequilibrated type and liquid metal type for nuclear power generation. The principle of MHD power generation and the constitution of the plant are explained. In Japan, the Mark 2 generator generated 1,180 kW for 1 min in 1971, and the Mark 3 generator generated 1.9 kW continuously for 110 hr in 1967. The MHD generator with superconducting magnet succeeded in 1969 to generate 25 kW for 6 min. The second stage project aimes at collecting design data and obtaining operational experience for the construction of 10 MW class pilot plant, and the Mark 7 and 8 generators are planned. (Kako, I.)
Dijkstra, Y.M.; Brouwer, R.L.; Schuttelaars, H.M.; Schramkowski, G.P.
2017-01-01
The iFlow modelling framework is a width-averaged model for the systematic analysis of the water motion and sediment transport processes in estuaries and tidal rivers. The distinctive solution method, a mathematical perturbation method, used in the model allows for identification of the effect of
Directory of Open Access Journals (Sweden)
Y. M. Dijkstra
2017-07-01
Full Text Available The iFlow modelling framework is a width-averaged model for the systematic analysis of the water motion and sediment transport processes in estuaries and tidal rivers. The distinctive solution method, a mathematical perturbation method, used in the model allows for identification of the effect of individual physical processes on the water motion and sediment transport and study of the sensitivity of these processes to model parameters. This distinction between processes provides a unique tool for interpreting and explaining hydrodynamic interactions and sediment trapping. iFlow also includes a large number of options to configure the model geometry and multiple choices of turbulence and salinity models. Additionally, the model contains auxiliary components, including one that facilitates easy and fast sensitivity studies. iFlow has a modular structure, which makes it easy to include, exclude or change individual model components, called modules. Depending on the required functionality for the application at hand, modules can be selected to construct anything from very simple quasi-linear models to rather complex models involving multiple non-linear interactions. This way, the model complexity can be adjusted to the application. Once the modules containing the required functionality are selected, the underlying model structure automatically ensures modules are called in the correct order. The model inserts iteration loops over groups of modules that are mutually dependent. iFlow also ensures a smooth coupling of modules using analytical and numerical solution methods. This way the model combines the speed and accuracy of analytical solutions with the versatility of numerical solution methods. In this paper we present the modular structure, solution method and two examples of the use of iFlow. In the examples we present two case studies, of the Yangtze and Scheldt rivers, demonstrating how iFlow facilitates the analysis of model results, the
Dijkstra, Yoeri M.; Brouwer, Ronald L.; Schuttelaars, Henk M.; Schramkowski, George P.
2017-07-01
The iFlow modelling framework is a width-averaged model for the systematic analysis of the water motion and sediment transport processes in estuaries and tidal rivers. The distinctive solution method, a mathematical perturbation method, used in the model allows for identification of the effect of individual physical processes on the water motion and sediment transport and study of the sensitivity of these processes to model parameters. This distinction between processes provides a unique tool for interpreting and explaining hydrodynamic interactions and sediment trapping. iFlow also includes a large number of options to configure the model geometry and multiple choices of turbulence and salinity models. Additionally, the model contains auxiliary components, including one that facilitates easy and fast sensitivity studies. iFlow has a modular structure, which makes it easy to include, exclude or change individual model components, called modules. Depending on the required functionality for the application at hand, modules can be selected to construct anything from very simple quasi-linear models to rather complex models involving multiple non-linear interactions. This way, the model complexity can be adjusted to the application. Once the modules containing the required functionality are selected, the underlying model structure automatically ensures modules are called in the correct order. The model inserts iteration loops over groups of modules that are mutually dependent. iFlow also ensures a smooth coupling of modules using analytical and numerical solution methods. This way the model combines the speed and accuracy of analytical solutions with the versatility of numerical solution methods. In this paper we present the modular structure, solution method and two examples of the use of iFlow. In the examples we present two case studies, of the Yangtze and Scheldt rivers, demonstrating how iFlow facilitates the analysis of model results, the understanding of the
Effect of Trapped Energetic Ions on MHD Activity in Spherical Tori
International Nuclear Information System (INIS)
White, R.B.; Kolesnichenko, Ya.I.; Lutsenko, V.V.; Marchenko, V.S.
2002-01-01
It is shown that the increase of beta (the ratio of plasma pressure to the magnetic field pressure) may change the character of the influence of trapped energetic ions on MHD stability in spherical tori. Namely, the energetic ions, which stabilize MHD modes (such as the ideal-kink mode, collisionless tearing mode, and semi-collisional tearing mode) at low beta, have a destabilizing influence at high beta unless the radial distribution of the energetic ions is very peaked
de Ruyter, D.J.; Spiecker, B.
2008-01-01
This article argues that sex education should include sexual ideals. Sexual ideals are divided into sexual ideals in the strict sense and sexual ideals in the broad sense. It is argued that ideals that refer to the context that is deemed to be most ideal for the gratification of sexual ideals in the
Nonlinear MHD dynamics of tokamak plasmas on multiple time scales
International Nuclear Information System (INIS)
Kruger, S.E.; Schnack, D.D.; Brennan, D.P.; Gianakon, T.A.; Sovinec, C.R.
2003-01-01
Two types of numerical, nonlinear simulations using the NIMROD code are presented. In the first simulation, we model the disruption occurring in DIII-D discharge 87009 as an ideal MHD instability driven unstable by neutral-beam heating. The mode grows faster than exponential, but on a time scale that is a hybrid of the heating rate and the ideal MHD growth rate as predicted by analytic theory. The second type of simulations, which occur on a much longer time scale, focus on the seeding of tearing modes by sawteeth. Pressure effects play a role both in the exterior region solutions and in the neoclassical drive terms. The results of both simulations are reviewed and their implications for experimental analysis is discussed. (author)
Goya - an MHD equilibrium code for toroidal plasmas
International Nuclear Information System (INIS)
Scheffel, J.
1984-09-01
A description of the GOYA free-boundary equilibrium code is given. The non-linear Grad-Shafranov equation of ideal MHD is solved in a toroidal geometry for plasmas with purely poloidal magnetic fields. The code is based on a field line-tracing procedure, making storage of a large amount of information on a grid unnecessary. Usage of the code is demonstrated by computations of equi/libria for the EXTRAP-T1 device. (Author)
A. Sinha; J.C. Misra; G.C. Shit
2016-01-01
This paper presents a theoretical analysis of blood flow and heat transfer in a permeable vessel in the presence of an external magnetic field. The unsteadiness in the coupled flow and temperature fields is considered to be caused due to the time-dependent stretching velocity and the surface temperature of the vessel. The non-uniform heat source/sink effect on blood flow and heat transfer is taken into account. This study is of potential value in the clinical treatment of cardiovascular disor...
Combined Ideal and Kinetic Effects on Reversed Shear Alfven Eigenmodes
International Nuclear Information System (INIS)
Gorelenkov, N.N.; Kramer, G.J.; Nazikian, R.
2011-01-01
A theory of Reversed Shear Alfven Eigenmodes (RSAEs) is developed for reversed magnetic field shear plasmas when the safety factor minimum, qmin, is at or above a rational value. The modes we study are known sometimes as either the bottom of the frequency sweep or the down sweeping RSAEs. We show that the ideal MHD theory is not compatible with the eigenmode solution in the reversed shear plasma with qmin above integer values. Corrected by special analytic FLR condition MHD dispersion of these modes nevertheless can be developed. Large radial scale part of the analytic RSAE solution can be obtained from ideal MHD and expressed in terms of the Legendre functions. The kinetic equation with FLR effects for the eigenmode is solved numerically and agrees with the analytic solutions. Properties of RSAEs and their potential implications for plasma diagnostics are discussed.
International Nuclear Information System (INIS)
Goyal, Mamta; Bansal, J.L.
1993-01-01
The growth of the boundary layer in an accelerated flow of an electricity conducting fluid past a symmetrical placed body in the presence of uniform transverse magnetic field fixed relative to the body has been studied. The boundary layer equation has been solved by using a method previously developed by Pozzi, based on expressing the unknown velocity in term of an error function and on using differential and integral relations obtained from the balance equation. As examples, the impulsive flow past a circular cylinder and uniformly accelerated flow over a flat plate are considered. It is found that the effect of the magnetic field is to decelerate the fluid motion which results in an earlier boundary layer separation in the impulsive flow past a circular cylinder. The results show a good agreement with the numerical data available in the literature. (author). 30 refs., 4 figs., 2 tabs
Ferdows, M.; Khalequ, T. S.; Tzirtzilakis, E. E.; Sun, Shuyu
2017-01-01
differential equations, governing the flow field under consideration, have been transformed by a similarity transformation into a systemof nonlinear ordinary differential equations and then solved numerically. Resulting non-dimensional velocity and temperature
International Nuclear Information System (INIS)
Rahimi Eosboee, M.; Pourmahmoud, N.; Mirzaie, I.; Mohajeri Khameneh, P.; Majidyfar, S.
2012-01-01
Control of a fluid flow velocity profile by injection and suction of a non-ionized fluid in presence of a uniform steady magnetic field has important technical applications. In this paper, the unsteady incompressible and viscous conducting fluid flow has been investigated in a circular channel. The channel walls are assumed to be non-conducting and porous. They are subjected to a uniform steady magnetic field which is perpendicular to the axis of channel, then and suction and injection are applied at the walls. The well known equations of Magnetohydrodynamics are governed to the motion of an electrically conducting fluid flow that is subjected to magnetic field. The numerical solution is carried out by finite difference approach. The results of present numerical simulation shown that the flow injection and suction through the wall can be controlled effectively, the main flow in channel especially in industrial purposes. The results are obtained for different values of the injected and sucked non-ionized flow rate and the effect of Hartman number on the velocity profile is investigated. Finally, a good agreement is seen between the presented results and the corresponding data of finite element method.
Radiation heat transfer within an open-cycle MHD generator channel
Delil, A. A. M.
1983-05-01
Radiation heat transfer in an MHD generator was modeled using the Sparrow and Cess model for radiation in an emitting, absorbing and scattering medium. The resulting general equations can be considerably reduced by introducing simplifying approximations for the channel and MHD gas properties. The simplifications lead to an engineering model, which is very useful for one-dimensional channel flow approximation. The model can estimate thermo-optical MHD gas properties, which can be substituted in the energy equation. The model considers the contribution of solid particles in the MHD gas to radiation heat transfer, considerable in coal-fired closed cycle MHD generators. The modeling is applicable also for other types of flow at elevated temperatures, where radiation heat transfer is an important quantity.
Dogonchi, A. S.; Ganji, D. D.
2018-06-01
In this study, buoyancy MHD nanofluid flow and heat transfer over a stretching sheet in the presence of Joule heating and thermal radiation impacts, are studied. Cattaneo-Christov heat flux model instead of conventional Fourier's law of heat conduction is applied to investigate the heat transfer characteristics. A similarity transformation is used to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The obtained non-linear ordinary differential equations are solved numerically. The impacts of diverse active parameters such as the magnetic parameter, the radiation parameter, the buoyancy parameter, the heat source parameter, the volume fraction of nanofluid and the thermal relaxation parameter are examined on the velocity and temperature profiles. In addition, the value of the Nusselt number is calculated and presented through figures. The results demonstrate that the temperature profile is lower in the case of Cattaneo-Christov heat flux model as compared to Fourier's law. Moreover, the Nusselt number raises with the raising volume fraction of nanofluid and it abates with the ascending the radiation parameter.
Directory of Open Access Journals (Sweden)
A. M. Salem
2013-01-01
Full Text Available A numerical model is developed to study the effects of temperature-dependent viscosity on heat and mass transfer flow of magnetohydrodynamic(MHD micropolar fluids with medium molecular weight along a permeable stretching surface embedded in a non-Darcian porous medium in the presence of viscous dissipation and chemical reaction. The governing boundary equations for momentum, angular momentum (microrotation, and energy and mass transfer are transformed to a set of nonlinear ordinary differential equations by using similarity solutions which are then solved numerically by shooting technique. A comparison between the analytical and the numerical solutions has been included. The effects of the various physical parameters entering into the problem on velocity, microrotation, temperature and concentration profiles are presented graphically. Finally, the effects of pertinent parameters on local skin-friction coefficient, local Nusselt number and local Sherwood number are also presented graphically. One important observation is that for some kinds of mixtures (e.g., H2, air with light and medium molecular weight, the magnetic field and temperature-dependent viscosity effects play a significant role and should be taken into consideration as well.
Annular MHD Physics for Turbojet Energy Bypass
Schneider, Steven J.
2011-01-01
The use of annular Hall type MHD generator/accelerator ducts for turbojet energy bypass is evaluated assuming weakly ionized flows obtained from pulsed nanosecond discharges. The equations for a 1-D, axisymmetric MHD generator/accelerator are derived and numerically integrated to determine the generator/accelerator performance characteristics. The concept offers a shockless means of interacting with high speed inlet flows and potentially offers variable inlet geometry performance without the complexity of moving parts simply by varying the generator loading parameter. The cycle analysis conducted iteratively with a spike inlet and turbojet flying at M = 7 at 30 km altitude is estimated to have a positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at an aggressive 2200 deg K. The annular MHD Hall generator/accelerator is L = 3 m in length with a B(sub r) = 5 Tesla magnetic field and a conductivity of sigma = 5 mho/m for the generator and sigma= 1.0 mho/m for the accelerator. The calculated isentropic efficiency for the generator is eta(sub sg) = 84 percent at an enthalpy extraction ratio, eta(sub Ng) = 0.63. The calculated isentropic efficiency for the accelerator is eta(sub sa) = 81 percent at an enthalpy addition ratio, eta(sub Na) = 0.62. An assessment of the ionization fraction necessary to achieve a conductivity of sigma = 1.0 mho/m is n(sub e)/n = 1.90 X 10(exp -6), and for sigma = 5.0 mho/m is n(sub e)/n = 9.52 X 10(exp -6).
Non-ideal magnetohydrodynamics on a moving mesh
Marinacci, Federico; Vogelsberger, Mark; Kannan, Rahul; Mocz, Philip; Pakmor, Rüdiger; Springel, Volker
2018-05-01
In certain astrophysical systems, the commonly employed ideal magnetohydrodynamics (MHD) approximation breaks down. Here, we introduce novel explicit and implicit numerical schemes of ohmic resistivity terms in the moving-mesh code AREPO. We include these non-ideal terms for two MHD techniques: the Powell 8-wave formalism and a constrained transport scheme, which evolves the cell-centred magnetic vector potential. We test our implementation against problems of increasing complexity, such as one- and two-dimensional diffusion problems, and the evolution of progressive and stationary Alfvén waves. On these test problems, our implementation recovers the analytic solutions to second-order accuracy. As first applications, we investigate the tearing instability in magnetized plasmas and the gravitational collapse of a rotating magnetized gas cloud. In both systems, resistivity plays a key role. In the former case, it allows for the development of the tearing instability through reconnection of the magnetic field lines. In the latter, the adopted (constant) value of ohmic resistivity has an impact on both the gas distribution around the emerging protostar and the mass loading of magnetically driven outflows. Our new non-ideal MHD implementation opens up the possibility to study magneto-hydrodynamical systems on a moving mesh beyond the ideal MHD approximation.
MHD oxidant intermediate temperature ceramic heater study
Carlson, A. W.; Chait, I. L.; Saari, D. P.; Marksberry, C. L.
1981-09-01
The use of three types of directly fired ceramic heaters for preheating oxygen enriched air to an intermediate temperature of 1144K was investigated. The three types of ceramic heaters are: (1) a fixed bed, periodic flow ceramic brick regenerative heater; (2) a ceramic pebble regenerative heater. The heater design, performance and operating characteristics under conditions in which the particulate matter is not solidified are evaluated. A comparison and overall evaluation of the three types of ceramic heaters and temperature range determination at which the particulate matter in the MHD exhaust gas is estimated to be a dry powder are presented.
Khalil-Ur-Rehman; Malik, M. Y.; Bilal, S.; Bibi, M.
The current analysis reports the untapped characteristics of magneto-hydrodynamic dual convection boundary layer stagnation point flow of Powell-Eyring fluid by way of cylindrical surface. Flow exploration is carried out with the combined effects of thermal and solutal stratification. The strength of temperature and concentration adjacent to the cylindrical surface is assumed to be greater than the ambient fluid. Flow conducting mathematically modelled equations are fairly transformed into system of coupled non-linear ordinary differential equations with the aid of suitable transformations. The computations are made against these resultant coupled equations through shooting technique by the support of fifth order Runge-Kutta algorithm. A parametric study is performed to examine the effect logs of various pertinent flow controlling parameters on the velocity, temperature and concentration flow regime. The achieved outcomes are validated by developing comparison with existing published literature. In addition, numerical values of skin friction coefficient and Nusselt number are presented graphically for two different geometries namely, plate and cylinder.
INCORPORATING AMBIPOLAR AND OHMIC DIFFUSION IN THE AMR MHD CODE RAMSES
International Nuclear Information System (INIS)
Masson, J.; Mulet-Marquis, C.; Chabrier, G.; Teyssier, R.; Hennebelle, P.
2012-01-01
We have implemented non-ideal magnetohydrodynamics (MHD) effects in the adaptive mesh refinement code RAMSES, namely, ambipolar diffusion and Ohmic dissipation, as additional source terms in the ideal MHD equations. We describe in details how we have discretized these terms using the adaptive Cartesian mesh, and how the time step is diminished with respect to the ideal case, in order to perform a stable time integration. We have performed a large suite of test runs, featuring the Barenblatt diffusion test, the Ohmic diffusion test, the C-shock test, and the Alfvén wave test. For the latter, we have performed a careful truncation error analysis to estimate the magnitude of the numerical diffusion induced by our Godunov scheme, allowing us to estimate the spatial resolution that is required to address non-ideal MHD effects reliably. We show that our scheme is second-order accurate, and is therefore ideally suited to study non-ideal MHD effects in the context of star formation and molecular cloud dynamics.
Magnetic levitation and MHD propulsion
Energy Technology Data Exchange (ETDEWEB)
Tixador, P [CNRS/CRTBT-LEG, 38 - Grenoble (France)
1994-04-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried our in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ..) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. (orig.).
Magnetic levitation and MHD propulsion
International Nuclear Information System (INIS)
Tixador, P.
1994-01-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried our in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ..) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. (orig.)
Directory of Open Access Journals (Sweden)
Shivaiah S.
2012-01-01
Full Text Available The objective of this paper is to analyze the effect of chemical reaction on unsteady magneto hydrodynamic free convective fluid flow past a vertical porous plate in the presence of suction or injection. The governing equations of the flow field are solved numerically by a finite element method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-friction coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.
Ferdows, M.
2017-03-10
A steady two-dimensional free convective flow of a viscous incompressible fluid along a vertical stretching sheet with the effect of magnetic field, radiation and variable thermal conductivity in porous media is analyzed. The nonlinear partial differential equations, governing the flow field under consideration, have been transformed by a similarity transformation into a systemof nonlinear ordinary differential equations and then solved numerically. Resulting non-dimensional velocity and temperature profiles are then presented graphically for different values of the parameters. Finally, the effects of the pertinent parameters, which are of physical and engineering interest, are examined both in graphical and tabular form.
Experimental rigs for MHD studies
International Nuclear Information System (INIS)
Venkataramani, N.; Jayakumar, R.; Iyer, D.R.; Dixit, N.S.
1976-01-01
An MHD experimental rig is a miniature MHD installation consisting of basic equipments necessary for specific investigations. Some of the experimental rigs used in the investigations being carried out at the Bhabha Atomic Research Centre, Bombay (India) are dealt with. The experiments included diagnostics and evaluation of materials in seeded combustion plasmas and argon plasmas. The design specifications, schematics and some of the results of the investigations are also mentioned. (author)
1990-10-01
The current magnetohydrodynamic MHD program being implemented is a result of a consensus established in public meetings held by the Department of Energy in 1984. The public meetings were followed by the formulation of a June 1984 Coal-Fired MHD Preliminary Transition and Program Plan. This plan focused on demonstrating the proof-of-concept (POC) of coal-fired MHD electric power plants by the early 1990s. MHD test data indicate that while there are no fundamental technical barriers impeding the development of MHD power plants, technical risk remains. To reduce the technical risk three key subsystems (topping cycle, bottoming cycle, and seed regeneration) are being assembled and tested separately. The program does not require fabrication of a complete superconducting magnet, but rather the development and testing of superconductor cables. The topping cycle system test objectives can be achieved using a conventional iron core magnet system already in place at a DOE facility. Systems engineering-derived requirements and analytical modeling to support scale-up and component design guide the program. In response to environmental, economic, engineering, and utility acceptance requirements, design choices and operating modes are tested and refined to provide technical specifications for meeting commercial criteria. These engineering activities are supported by comprehensive and continuing systems analyses to establish realistic technical requirements and cost data. Essential elements of the current program are to: develop technical and environmental data for the integrated MHD topping cycle and bottoming cycle systems through POC testing (1000 and 4000 hours, respectively); design, construct, and operate a POC seed regeneration system capable of processing spent seed materials from the MHD bottoming cycle; prepare conceptual designs for a site specific MHD retrofit plant; and continue supporting research necessary for system testing.
Effect of chemical reaction on unsteady MHD free convective two ...
African Journals Online (AJOL)
The effect of flow parameters on the coefficient of skin friction, Nusselt number and Sherwood number are also tabulated and discussed appropriately. It was observed that the increase in chemical reaction coefficient/parameter suppresses both velocity and concentration profiles. Keywords: Chemical Reaction, MHD, ...
Superconducting dipole magnet for the UTSI MHD facility
International Nuclear Information System (INIS)
Wang, S.T.; Niemann, R.C.; Turner, L.R.
1978-01-01
The Argonne National Laboratory is designing and will build a large superconducting dipole magnet system for use in the Coal Fired Flow MHD Research Facility at the University of Tennessee Space Institute (UTSI). Presented in detail are the conceptual design of the magnet geometry, conductor design, cryostability evaluation, magnetic pressure computation, structural design, cryostat design, the cryogenics system design, and magnet instrumentations and control
MHD stability limits in the TCV Tokamak
International Nuclear Information System (INIS)
Reimerdes, H.
2001-07-01
Magnetohydrodynamic (MHD) instabilities can limit the performance and degrade the confinement of tokamak plasmas. The Tokamak a Configuration Variable (TCV), unique for its capability to produce a variety of poloidal plasma shapes, has been used to analyse various instabilities and compare their behaviour with theoretical predictions. These instabilities are perturbations of the magnetic field, which usually extend to the plasma edge where they can be detected with magnetic pick-up coils as magnetic fluctuations. A spatially dense set of magnetic probes, installed inside the TCV vacuum vessel, allows for a fast observation of these fluctuations. The structure and temporal evolution of coherent modes is extracted using several numerical methods. In addition to the setup of the magnetic diagnostic and the implementation of analysis methods, the subject matter of this thesis focuses on four instabilities, which impose local and global stability limits. All of these instabilities are relevant for the operation of a fusion reactor and a profound understanding of their behaviour is required in order to optimise the performance of such a reactor. Sawteeth, which are central relaxation oscillations common to most standard tokamak scenarios, have a significant effect on central plasma parameters. In TCV, systematic scans of the plasma shape have revealed a strong dependence of their behaviour on elongation κ and triangularity δ, with high κ, and low δ leading to shorter sawteeth with smaller crashes. This shape dependence is increased by applying central electron cyclotron heating. The response to additional heating power is determined by the role of ideal or resistive MHD in triggering the sawtooth crash. For plasma shapes where additional heating and consequently, a faster increase of the central pressure shortens the sawteeth, the low experimental limit of the pressure gradient within the q = 1 surface is consistent with ideal MHD predictions. The observed decrease
3-D nonlinear evolution of MHD instabilities
International Nuclear Information System (INIS)
Bateman, G.; Hicks, H.R.; Wooten, J.W.
1977-03-01
The nonlinear evolution of ideal MHD internal instabilities is investigated in straight cylindrical geometry by means of a 3-D initial-value computer code. These instabilities are characterized by pairs of velocity vortex cells rolling off each other and helically twisted down the plasma column. The cells persist until the poloidal velocity saturates at a few tenths of the Alfven velocity. The nonlinear phase is characterized by convection around these essentially fixed vortex cells. For example, the initially centrally peaked temperature profile is convected out and around to form an annulus of high temperature surrounding a small region of lower temperature. Weak, centrally localized instabilities do not alter the edge of the plasma. Strong, large-scale instabilities, resulting from a stronger longitudinal equilibrium current, drive the plasma against the wall. After three examples of instability are analyzed in detail, the numerical methods and their verification are discussed
Stability analysis of resistive MHD modes via a new numerical matching technique
International Nuclear Information System (INIS)
Furukawa, M.; Tokuda, S.; Zheng, L.-J.
2009-01-01
Full text: Asymptotic matching technique is one of the principal methods for calculating linear stability of resistive magnetohydrodynamics (MHD) modes such as tearing modes. In applying the asymptotic method, the plasma region is divided into two regions: a thin inner layer around the mode-resonant surface and ideal MHD regions except for the layer. If we try to solve this asymptotic matching problem numerically, we meet practical difficulties. Firstly, the inertia-less ideal MHD equation or the Newcomb equation has a regular singular point at the mode-resonant surface, leading to the so-called big and small solutions. Since the big solution is not square-integrable, it needs sophisticated treatment. Even if such a treatment is applied, the matching data or the ratio of small solution to the big one, has been revealed to be sensitive to local MHD equilibrium accuracy and grid structure at the mode-resonant surface by numerical experiments. Secondly, one of the independent solutions in the inner layer, which should be matched onto the ideal MHD solution, is not square-integrable. The response formalism has been adopted to resolve this problem. In the present paper, we propose a new method for computing the linear stability of resistive MHD modes via matching technique, where the plasma region is divided into ideal MHD regions and an inner region with finite width. The matching technique using an inner region with finite width was recently developed for ideal MHD modes in cylindrical geometry, and good performance was shown. Our method extends this idea to resistive MHD modes. In the inner region, the low-beta reduced MHD equations are solved, and the solution is matched onto the solution of the Newcomb equation by using boundary conditions such that the parallel electric field vanishes properly as approaching the computational boundaries. If we use the inner region with finite width, the practical difficulties raised above can be avoided from the beginning. Figure
Energy Technology Data Exchange (ETDEWEB)
Karimipour, Arash; Taghipour, Abdolmajid [Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad (Iran, Islamic Republic of); Malvandi, Amir, E-mail: amirmalvandi@aut.ac.ir [Department of Mechanical Engineering, Neyshabur Branch, Islamic Azad University, Neyshabur (Iran, Islamic Republic of)
2016-12-01
This paper aims to investigate magnetic field and slip effects on developing laminar forced convection of nanofluids in the microchannels. A novel mixture of water and FMWNT carbon nanotubes is used as the working fluid. To do this, fluid flow and heat transfer through a microchannel is simulated by a computer code in FORTRAN language. The mixture of FMWNT carbon nanotubes suspended in water is considered as the nanofluid. Slip velocity is supposed as the hydrodynamic boundary condition while the microchannel's lower wall is insulated and the top wall is under the effect of a constant heat flux. Moreover, the flow field is subjected to a magnetic field with a constant strength. The results are presented as the velocity, temperature and Nusselt number profiles. It is observed that nanofluid composed of water and carbon nanotubes (FMWNT) can work well to increase the heat transfer rate along the microchannel walls. Furthermore, it is indicated that imposing the magnetic field is very effective at the thermally developing region. In contrast, the magnetic field effect at fully developed region is insignificant, especially at low values of Reynolds number. - Highlights: • Simulation of water/FMWNT carbon nanotubes flow in a microchannel. • The effects of magnetic field strength on nanofluid's slip velocity. • The effects of Ha, Re, ϕ and slip coefficient on averaged Nusselt number. • Magnetic field effect at developing flow region is significant.
Resonant MHD modes with toroidal coupling
International Nuclear Information System (INIS)
Connor, J.W.; Hastie, R.J.; Taylor, J.B.
1990-07-01
This is part 2 of a study of resonant perturbations, such as resistive tearing and ballooning modes, in a torus. These are described by marginal ideal mhd equations in the regions between resonant surfaces; matching across these surfaces provides the dispersion relation. In part 1 we described how all the necessary information from the ideal mhd calculations could be represented by a so-called E-matrix. We also described the calculation of this E-matrix for tearing modes (even parity in perturbed magnetic field) in a large aspect ratio torus. There the toroidal modes comprise coupled cylinder tearing modes and the E-matrix is a generalization of the familiar Δ' quantity in a cylinder. In the present paper we discuss resistive ballooning, or twisting-modes, which have odd-parity in perturbed magnetic field. We show that, unlike the tearing modes, these odd-parity modes are instrinsically toroidal and are not directly related to the odd-parity modes in a cylinder. This is evident from the analysis of the high-n limit in ballooning-space, where a transition from a stable Δ' to an unstable Δ' occurs for the twisting mode when the ballooning effect exceeds the interchange effect, which can occur even at large aspect ratio (as in a tokamak). Analysis of the high-n limit in coordinate space, rather than ballooning space, clarifies this singular behaviour and indicates how one may define twisting-mode Δ'. It also yields a prescription for treating low-n twisting modes and a method for calculating an E-matrix for resistive ballooning modes in a large aspect ratio tokamak. The elements of this matrix are given in terms of cylindrical tearing mode solutions
Qualification of MHD effects in dual-coolant DEMO blanket and approaches to their modelling
International Nuclear Information System (INIS)
Mas de les Valls, E.; Batet, L.; Medina, V. de; Fradera, J.; Sedano, L.A.
2011-01-01
Design refinements of vertical insulated banana-shaped liquid metal channels are being considered as a progress of conceptual design of dual-coolant liquid metal blankets (DEMO specifications). Among them: (a) optimised channel geometry and (b) improvements on flow channel inserts. Progress of channel conceptual design is conducted in parallel with underlying physics of MHD models in diverse aspects: (1) MHD models, (2) MHD turbulence, (3) LM buoyancy effects, (4) three-dimensional flows, and (5) LM/FCI/wall electrical and thermal coupling; in order to progress on common liquid metal flow characterisation, pressure drop and three-dimensional flows. The analyses are assumed as extension of those previous carried out for the DCLL blankets for new design refinements. At the present stage of the conceptual design progress, a preliminary thermofluid MHD study is of crucial interest for further design improvements and future detailed modelling. The paper overviews the ongoing modelling studies, making model refinements explicit, and anticipates some modelling results.
MHD PbLi experiments in MaPLE loop at UCLA
International Nuclear Information System (INIS)
Courtessole, C.; Smolentsev, S.; Sketchley, T.; Abdou, M.
2016-01-01
Highlights: • The paper overviews the MaPLE facility at UCLA: one-of-a-few PbLi MHD loop in the world. • We present the progress achieved in development and testing of high-temperature PbLi flow diagnostics. • The most important MHD experiments carried out since the first loop operation in 2011 are summarized. - Abstract: Experiments on magnetohydrodynamic (MHD) flows are critical to understanding complex flow phenomena in ducts of liquid metal blankets, in particular those that utilize eutectic alloy lead–lithium as breeder/coolant, such as self-cooled, dual-coolant and helium-cooled lead–lithium blanket concepts. The primary goal of MHD experiments at UCLA using the liquid metal flow facility called MaPLE (Magnetohydrodynamic PbLi Experiment) is to address important MHD effects, heat transfer and flow materials interactions in blanket-relevant conditions. The paper overviews the one-of-a-kind MaPLE loop at UCLA and presents recent experimental activities, including the development and testing of high-temperature PbLi flow diagnostics and experiments that have been performed since the first loop operation in 2011. We also discuss MaPLE upgrades, which need to be done to substantially expand the experimental capabilities towards a new class of MHD flow phenomena that includes buoyancy effects.
MHD PbLi experiments in MaPLE loop at UCLA
Energy Technology Data Exchange (ETDEWEB)
Courtessole, C., E-mail: cyril@fusion.ucla.edu; Smolentsev, S.; Sketchley, T.; Abdou, M.
2016-11-01
Highlights: • The paper overviews the MaPLE facility at UCLA: one-of-a-few PbLi MHD loop in the world. • We present the progress achieved in development and testing of high-temperature PbLi flow diagnostics. • The most important MHD experiments carried out since the first loop operation in 2011 are summarized. - Abstract: Experiments on magnetohydrodynamic (MHD) flows are critical to understanding complex flow phenomena in ducts of liquid metal blankets, in particular those that utilize eutectic alloy lead–lithium as breeder/coolant, such as self-cooled, dual-coolant and helium-cooled lead–lithium blanket concepts. The primary goal of MHD experiments at UCLA using the liquid metal flow facility called MaPLE (Magnetohydrodynamic PbLi Experiment) is to address important MHD effects, heat transfer and flow materials interactions in blanket-relevant conditions. The paper overviews the one-of-a-kind MaPLE loop at UCLA and presents recent experimental activities, including the development and testing of high-temperature PbLi flow diagnostics and experiments that have been performed since the first loop operation in 2011. We also discuss MaPLE upgrades, which need to be done to substantially expand the experimental capabilities towards a new class of MHD flow phenomena that includes buoyancy effects.
Energy Technology Data Exchange (ETDEWEB)
Melnikov, I.A., E-mail: corpuskula@gmail.com; Sviridov, E.V.; Sviridov, V.G.; Razuvanov, N.G.
2016-11-15
Highlights: • Local and averaged heat transfer coefficient are measured. • Free convection influence on MHD-flow is investigated. • The region with the free convection effect of MHD-heat transfer is found. • Temperature low-frequency fluctuations of abnormally high amplitude are detected. • Analysis of the MHD-heat transfer experimental data is performed. - Abstract: The article is devoted to the results of experimental investigation of heat transfer for a downward mercury flow in a vertical round tube in the presence of a transverse magnetic with non-uniform heat flux along the tube circumference.
Directory of Open Access Journals (Sweden)
N. Bhaskar Reddy
2014-01-01
Full Text Available An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement.
Directory of Open Access Journals (Sweden)
N. Sandeep
2015-12-01
Full Text Available The aim of the present study is to investigate the influence of non-uniform heat source/sink, mass transfer and chemical reaction on an unsteady mixed convection boundary layer flow of a magneto-micropolar fluid past a stretching/shrinking sheet in the presence of viscous dissipation and suction/injection. The governing equations of the flow, heat and mass transfer are transformed into system of nonlinear ordinary differential equations by using similarity transformation and then solved numerically using Shooting technique with Matlab Package. The influence of non-dimensional governing parameters on velocity, microrotation, temperature and concentration profiles are discussed and presented with the help of their graphical representations. Also, friction factor, heat and mass transfer rates have been computed and presented through tables. Under some special conditions, present results are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.
Directory of Open Access Journals (Sweden)
G. Sreedevi
2016-03-01
Full Text Available An analysis has been carried out on the influence of radiation absorption, variable viscosity, Hall current of a magnetohydrodynamic free-convective flow and heat and mass transfer over a stretching sheet in the presence of heat generation/absorption. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The boundary-layer equations governing the fluid flow, heat and mass transfer under consideration have been reduced to a system of nonlinear ordinary differential equations by employing a similarity transformation. Using the finite difference scheme, numerical solutions to the transform ordinary differential equations have been obtained and the results are presented graphically. The numerical results obtained are in good agreement with the existing scientific literature.
Directory of Open Access Journals (Sweden)
Motsa Sandile Sydney
2015-01-01
Full Text Available The behaviour of unsteady non-Darcian magnetohydrodynamic fluid flow past an impulsively started vertical porous surface is investigated. The effect of thermophoresis due to migration of colloidal particles in response to a macroscopic temperature gradient is taken into account. It is assumed that both dynamic viscosity and thermal conductivity are linear functions of temperature. The governing equations are non-dimensionalized by using suitable similarity transformation which can unravel the behaviour of the flow at short time and long time periods. A novel iteration scheme, called bivariate spectral local linearization method is developed for solving the corresponding systems of highly non-linear partial differential equations. The results of the numerical solutions obtained are presented graphically and analyzed for the effects of the various important parameters entering into the problem on velocity, temperature, and concentration field within the boundary layer.
Numerical and adaptive grid methods for ideal magnetohydrodynamics
Loring, Burlen
2008-02-01
In this thesis numerical finite difference methods for ideal magnetohydrodynamics(MHD) are investigated. A review of the relevant physics, essential for interpreting the results of numerical solutions and constructing validation cases, is presented. This review includes a discusion of the propagation of small amplitude waves in the MHD system as well as a thorough discussion of MHD shocks, contacts and rarefactions and how they can be piece together to obtain a solutions to the MHD Riemann problem. Numerical issues relevant to the MHD system such as: the loss of nonlinear numerical stability in the presence of discontinuous solutions, the introduction of spurious forces due to the growth of the divergence of the magnetic flux density, the loss of pressure positivity, and the effects of non-conservative numerical methods are discussed, along with the practical approaches which can be used to remedy or minimize the negative consequences of each. The use of block structured adaptive mesh refinement is investigated in the context of a divergence free MHD code. A new method for conserving magnetic flux across AMR grid interfaces is developed and a detailed discussion of our implementation of this method using the CHOMBO AMR framework is given. A preliminary validation of the new method for conserving magnetic flux density across AMR grid interfaces illustrates that the method works. Finally a number of code validation cases are examined spurring a discussion of the strengths and weaknesses of the numerics employed.
Adeniyan, A.,
2013-01-01
The numerical investigation of a stagnation point boundary layer flow , mass and heat transfer of a steady two dimensional , incompressible , viscous electrically conducting, chemically reacting laminar fluid over a vertical convectively heated , electrically neutral flat plate exposed to a transverse uniform magnetic field has been carried out to examine the influence of the simultaneous presence of the effects of a convective boundary condition, chemical reaction, heat transfer and suctio...
International Nuclear Information System (INIS)
1968-01-01
Proceedings of a Symposium on Magnetohydrodynamic Electrical Power Generation held by the IAEA at Warsaw, 24-30 July 1968. The meeting was attended by some 300 participants from 21 countries and three international organizations. In contrast to the Symposium held two years ago, much more emphasis was placed on the economic aspects of using MHD generators in large-scale power generation. Among closed- cycle systems, the prospects of linking an ultra-high-temperature reactor with an MHD generator were explored, and the advantages gained by having a liquid-metal generator as a 'topper' in a conventional steam generating plant were presented. Comments were made about the disproportionate effect of end and boundary conditions in experimental MHD generators on the main plasma parameters, and estimates were made of the interrelationship to be expected in real generators. The estimates will have to await confirmation until results are obtained on large-scale prototype MHD systems. Progress in materials research, in design and construction of auxiliary equipment such as heat exchangers, supercooled magnets (which are- now commercially available), etc., is accompanied by sophisticated ideas of plant design. The Proceedings are complemented by three Round Table Discussions in which chosen experts from various countries discuss the outlook for closed-cycle gas, closed-cycle liquid-metal and open-cycle MHD, and give their views as to the most fruitful course to follow to achieve economic full-scale power generation. Contents: (Vol. I) 1. Closed-Cycle MHD with Gaseous Working Fluids: (a) Diagnostics (3 papers); (b) Steady-state non-equilibrium ionization (8 papers); (c) Transient non-equilibrium ionization (7 papers); (d) Pre-ionization and gas discharge (4 papers); (e) Fields and flow in MHD channels (10 papers); (0 Instabilities (8 papers); (g) Generator design and performance studies (6 papers); (Vol. II) (h) Shock waves (6 papers); (i) Power generation experiments (13 papers
Directory of Open Access Journals (Sweden)
A. Sinha
2016-09-01
Full Text Available This paper presents a theoretical analysis of blood flow and heat transfer in a permeable vessel in the presence of an external magnetic field. The unsteadiness in the coupled flow and temperature fields is considered to be caused due to the time-dependent stretching velocity and the surface temperature of the vessel. The non-uniform heat source/sink effect on blood flow and heat transfer is taken into account. This study is of potential value in the clinical treatment of cardiovascular disorders accompanied by accelerated circulation. The problem is treated mathematically by reducing it to a system of coupled nonlinear differential equations, which have been solved by using similarity transformation and boundary layer approximation. The resulting nonlinear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. Computational results are obtained for the velocity, temperature, the skin-friction coefficient and the rate of heat transfer in the vessel. The estimated results are compared with another analytical study reported earlier in scientific literatures. The present study reveals that the heat transfer rate is enhanced as the value of the unsteadiness parameter increases, but it reduces as the space-dependence parameter for heat source/sink increases.
Further analysis of MHD acceleration for a hypersonic wind tunnel
International Nuclear Information System (INIS)
Christiansen, M.J.; Schmidt, H.J.; Chapman, J.N.
1995-01-01
A previously completed MHD study of the use of an MHD accelerator with seeded air from a state-of-the-art arc heater, was generally hailed as showing that the system studied has some promise of meeting the most critical hypersonic testing requirements. However, some concerns existed about certain aspects of the results. This paper discusses some of these problems and presents analysis of potential solutions. Specifically the problems addressed are; reducing the amount of seed in the flow, reducing test chamber temperatures, and reducing the oxygen dissociation. Modeling techniques are used to study three design variables of the MHD accelerator. The accelerator channel inlet Mach number, the accelerator channel divergence angle, and the magnetic field strength are all studied. These variables are all optimized to meet the goals for seed, temperature, and dissociated oxygen reduction. The results of this paper are encouraging, showing that all three goals can be met. General relationships are observed as to how the design variables affect the performance of the MHD accelerator facility. This paper expands on the results presented in the UTSI report and further supports the feasibility of MHD acceleration as a means to provide hypersonic flight simulation
International Nuclear Information System (INIS)
Soler, Roberto; Terradas, Jaume; Oliver, Ramón; Goossens, Marcel
2013-01-01
Magnetohydrodynamic (MHD) waves are ubiquitously observed in the solar atmosphere. Kink waves are a type of transverse MHD waves in magnetic flux tubes that are damped due to resonant absorption. The theoretical study of kink MHD waves in solar flux tubes is usually based on the simplification that the transverse variation of density is confined to a nonuniform layer much thinner than the radius of the tube, i.e., the so-called thin boundary approximation. Here, we develop a general analytic method to compute the dispersion relation and the eigenfunctions of ideal MHD waves in pressureless flux tubes with transversely nonuniform layers of arbitrary thickness. Results for kink waves are produced and compared with fully numerical resistive MHD eigenvalue computations in the limit of small resistivity. We find that the frequency and resonant damping rate are the same in both ideal and resistive cases. The actual results for thick nonuniform layers deviate from the behavior predicted in the thin boundary approximation and strongly depend on the shape of the nonuniform layer. The eigenfunctions in ideal MHD are very different from those in resistive MHD. The ideal eigenfunctions display a global character regardless of the thickness of the nonuniform layer, while the resistive eigenfunctions are localized around the resonance and are indistinguishable from those of ordinary resistive Alfvén modes. Consequently, the spatial distribution of wave energy in the ideal and resistive cases is dramatically different. This poses a fundamental theoretical problem with clear observational consequences
Mahmoud, Mostafa A. A.; Megahed, Ahmed M.
2017-10-01
Theoretical and numerical outcomes of the non-Newtonian Casson liquid thin film fluid flow owing to an unsteady stretching sheet which exposed to a magnetic field, Ohmic heating and slip velocity phenomena is reported here. The non-Newtonian thermal conductivity is imposed and treated as it vary with temperature. The nonlinear partial differential equations governing the non-Newtonian Casson thin film fluid are simplified into a group of highly nonlinear ordinary differential equations by using an adequate dimensionless transformations. With this in mind, the numerical solutions for the ordinary conservation equations are found using an accurate shooting iteration technique together with the Runge-Kutta algorithm. The lineaments of the thin film flow and the heat transfer characteristics for the pertinent parameters are discussed through graphs. The results obtained here detect many concern for the local Nusselt number and the local skin-friction coefficient in which they may be beneficial for the material processing industries. Furthermore, in some special conditions, the present problem has an excellent agreement with previously published work.
Directory of Open Access Journals (Sweden)
P.BalaAnki Reddy
2017-12-01
Full Text Available This paper focuses on a theoretical analysis of a steady two-dimensional magnetohydrodynamic boundary layer flow of a Maxwell fluid over an exponentially stretching surface in the presence of velocity slip and convective boundary condition. This model is used for a nanofluid, which incorporates the effects of Brownian motion and thermophoresis. The resulting non-linear partial differential equations of the governing flow field are converted into a system of coupled non-linear ordinary differential equations by using suitable similarity transformations, and the resultant equations are then solved numerically by using Runge-Kutta fourth order method along with shooting technique. A parametric study is conducted to illustrate the behavior of the velocity, temperature and concentration. The influence of significant parameters on velocity, temperature, concentration, skin friction coefficient and Nusselt number has been studied and numerical results are presented graphically and in tabular form. The reported numerical results are compared with previously published works on various special cases and are found to be an in excellent agreement. It is found that momentum boundary layer thickness decreases with the increase of magnetic parameter. It can also be found that the thermal boundary layer thickness increases with Brownian motion and thermophoresis parameters.
International Nuclear Information System (INIS)
Azimi, Mohammadreza
2017-01-01
Investigation for unsteady squeezing viscous flow is one of the most important research topics due to its wide range of engineering applications such as polymer processing and lubrication systems. The aim of the present paper is to study the unsteady squeezing viscous graphene oxide-water nanofluid flow with heat transfer between two infinite parallel plates. The governing equations, continuity, momentum and energy for this problem are reduced to coupled nonlinear ordinary differential equations using a similarity transformation. The transmuted model is shown to be controlled by a number of thermo-physical parameters, viz., moving parameter, graphene oxide nanoparticles solid volume fraction, Eckert and Prandtl numbers. Nusselt number and skin friction parameter are obtained for various values of GO solid volume fraction and Eckert number. Comparison between analytical results and numerical ones achieved by fourth order Runge-Kutta method revealed that our analytical method can be a simple, powerful and efficient technique for finding analytical solutions in science and engineering nonlinear differential equations. (author)
International Nuclear Information System (INIS)
Mukhopadhyay, Swati; Arif, M. Golam; Pk M Wazed Ali
2013-01-01
The aim of this article is to present the effects of transpiration on the unsteady two-dimensional boundary layer flow of non-Newtonian fluid passing through a stretching sheet in the presence of a first order constructive/destructive chemical reaction. The upper-convected Maxwell (UCM) model is used here to characterize the non-Newtonian behavior of the fluid. Using similarity solutions, the governing nonlinear partial differential equations are transformed into ordinary ones and are then solved numerically by the shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. The fluid velocity initially decreases as the unsteadiness parameter increases and the concentration decreases significantly due to the increase in the unsteadiness. The effect of increasing values of transpiration (suction) and the Maxwell parameter is to suppress the velocity field; however, the concentration is enhanced as transpiration (suction) and the Maxwell parameter increase. Also, it is found that the fluid velocity decreases as the magnetic parameter increases; however, the concentration increases in this case. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
MHD stability limits in the TCV Tokamak
Energy Technology Data Exchange (ETDEWEB)
Reimerdes, H. [Ecole Polytechnique Federale de Lausanne, Centre de Recherches en Physique des Plasmas (CRPP), CH-1015 Lausanne (Switzerland)
2001-07-01
Magnetohydrodynamic (MHD) instabilities can limit the performance and degrade the confinement of tokamak plasmas. The Tokamak a Configuration Variable (TCV), unique for its capability to produce a variety of poloidal plasma shapes, has been used to analyse various instabilities and compare their behaviour with theoretical predictions. These instabilities are perturbations of the magnetic field, which usually extend to the plasma edge where they can be detected with magnetic pick-up coils as magnetic fluctuations. A spatially dense set of magnetic probes, installed inside the TCV vacuum vessel, allows for a fast observation of these fluctuations. The structure and temporal evolution of coherent modes is extracted using several numerical methods. In addition to the setup of the magnetic diagnostic and the implementation of analysis methods, the subject matter of this thesis focuses on four instabilities, which impose local and global stability limits. All of these instabilities are relevant for the operation of a fusion reactor and a profound understanding of their behaviour is required in order to optimise the performance of such a reactor. Sawteeth, which are central relaxation oscillations common to most standard tokamak scenarios, have a significant effect on central plasma parameters. In TCV, systematic scans of the plasma shape have revealed a strong dependence of their behaviour on elongation {kappa} and triangularity {delta}, with high {kappa}, and low {delta} leading to shorter sawteeth with smaller crashes. This shape dependence is increased by applying central electron cyclotron heating. The response to additional heating power is determined by the role of ideal or resistive MHD in triggering the sawtooth crash. For plasma shapes where additional heating and consequently, a faster increase of the central pressure shortens the sawteeth, the low experimental limit of the pressure gradient within the q = 1 surface is consistent with ideal MHD predictions. The