Directory of Open Access Journals (Sweden)
Taha Aziz
2013-01-01
Full Text Available The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.
Group classification of steady two-dimensional boundary-layer stagnation-point flow equations
Nadjafikhah, Mehdi; Hejazi, Seyed Reza
2010-01-01
Lie symmetry group method is applied to study the boundary-layer equations for two-dimensional steady flow of an incompressible, viscous fluid near a stagnation point at a heated stretching sheet placed in a porous medium equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.
Directory of Open Access Journals (Sweden)
Boričić Zoran
2009-01-01
Full Text Available This paper concerns with unsteady two-dimensional temperature laminar magnetohydrodynamic (MHD boundary layer of incompressible fluid. It is assumed that induction of outer magnetic field is function of longitudinal coordinate with force lines perpendicular to the body surface on which boundary layer forms. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in inductionless approximation. Characteristic properties of fluid are constant because velocity of flow is much lower than speed of light and temperature difference is small enough (under 50ºC . Introduced assumptions simplify considered problem in sake of mathematical solving, but adopted physical model is interesting from practical point of view, because its relation with large number of technically significant MHD flows. Obtained partial differential equations can be solved with modern numerical methods for every particular problem. Conclusions based on these solutions are related only with specific temperature MHD boundary layer problem. In this paper, quite different approach is used. First new variables are introduced and then sets of similarity parameters which transform equations on the form which don't contain inside and in corresponding boundary conditions characteristics of particular problems and in that sense equations are considered as universal. Obtained universal equations in appropriate approximation can be solved numerically once for all. So-called universal solutions of equations can be used to carry out general conclusions about temperature MHD boundary layer and for calculation of arbitrary particular problems. To calculate any particular problem it is necessary also to solve corresponding momentum integral equation.
Froessling, Nils
1958-01-01
The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
Two-Dimensional Thermal Boundary Layer Corrections for Convective Heat Flux Gauges
Kandula, Max; Haddad, George
2007-01-01
This work presents a CFD (Computational Fluid Dynamics) study of two-dimensional thermal boundary layer correction factors for convective heat flux gauges mounted in flat plate subjected to a surface temperature discontinuity with variable properties taken into account. A two-equation k - omega turbulence model is considered. Results are obtained for a wide range of Mach numbers (1 to 5), gauge radius ratio, and wall temperature discontinuity. Comparisons are made for correction factors with constant properties and variable properties. It is shown that the variable-property effects on the heat flux correction factors become significant
A Coordinate Transformation for Unsteady Boundary Layer Equations
Directory of Open Access Journals (Sweden)
Paul G. A. CIZMAS
2011-12-01
Full Text Available This paper presents a new coordinate transformation for unsteady, incompressible boundary layer equations that applies to both laminar and turbulent flows. A generalization of this coordinate transformation is also proposed. The unsteady boundary layer equations are subsequently derived. In addition, the boundary layer equations are derived using a time linearization approach and assuming harmonically varying small disturbances.
Symmetries of boundary layer equations of power-law fluids of second grade
Institute of Scientific and Technical Information of China (English)
Mehmet Pakdemirli; Yi(g)it Aksoy; Muhammet Y(u)r(u)soy; Chaudry Masood Khalique
2008-01-01
A modified power-law fluid of second grade is considered. The model is a combination of power-law and second grade fluid in which the fluid may exhibit normal stresses, shear thinning or shear thickening behaviors. The equations of motion are derived for two dimensional incom-pressible flows, and from which the boundary layer equations are derived. Symmetries of the boundary layer equations are found by using Lie group theory, and then group classifica-tion with respect to power-law index is performed. By using one of the symmetries, namely the scaling symmetry, the partial differential system is transformed into an ordinary differential system, which is numerically integrated under the classical boundary layer conditions. Effects of power-law index and second grade coefficient on the boundary layers are shown and solutions are contrasted with the usual second grade fluid solutions.
Two-dimensional energy spectra in a high Reynolds number turbulent boundary layer
Chandran, Dileep; Baidya, Rio; Monty, Jason; Marusic, Ivan
2016-11-01
The current study measures the two-dimensional (2D) spectra of streamwise velocity component (u) in a high Reynolds number turbulent boundary layer for the first time. A 2D spectra shows the contribution of streamwise (λx) and spanwise (λy) length scales to the streamwise variance at a given wall height (z). 2D spectra could be a better tool to analyse spectral scaling laws as it is devoid of energy aliasing errors that could be present in one-dimensional spectra. A novel method is used to calculate the 2D spectra from the 2D correlation of u which is obtained by measuring velocity time series at various spanwise locations using hot-wire anemometry. At low Reynolds number, the shape of the 2D spectra at a constant energy level shows λy √{ zλx } behaviour at larger scales which is in agreement with the literature. However, at high Reynolds number, it is observed that the square-root relationship gradually transforms into a linear relationship (λy λx) which could be caused by the large packets of eddies whose length grows proportionately to the growth of its width. Additionally, we will show that this linear relationship observed at high Reynolds number is consistent with attached eddy predictions. The authors gratefully acknowledge the support from the Australian Research Council.
Institute of Scientific and Technical Information of China (English)
2008-01-01
A coupled boundary element method (BEM) and finite difference method (FDM) are applied to solve conjugate heat transfer problem of a two-dimensional air-cooled turbine blade boundary layer. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. The Navier-Stokes equations are solved by HIT-NS code. In this code, the FDM is adopted and is used to resolve the convective heat transfer in the fluid region. The BEM code is used to resolve the conduction heat transfer in the solid region. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The numerical results from the BEM adopted in this paper are in good agreement with the results of analyrical solution and the results of commercial code, such as Fluent 6.2. The BEM avoids the complicated mesh needed in other computation method and saves the computation time. The results prove that the BEM adopted in this paper can give the same precision in numerical results with less boundary points. Comparing the conjugate results with the numerical results of an adiabatic wall flow solution, it reveals a significant difference in the distribution of metal temperatures. The results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines.
BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS
Institute of Scientific and Technical Information of China (English)
彭艳
2014-01-01
In this paper, we consider an initial-boundary value problem for some nonlinear evolution equations with damping and diffusion. The main purpose is to investigate the boundary layer effect and the convergence rates as the diffusion parameterαgoes to zero.
Fundamental interactions of vortical structures with boundary layers in two-dimensional flows
DEFF Research Database (Denmark)
Coutsias, E.A.; Lynov, Jens-Peter
1991-01-01
in the vorticity-stream function representation for bounded geometries. Fundamental processes connected to vorticity detachment from the boundary layers caused by the proximity of vortical structures are described. These processes include enstrophy enhancement of the main flow during bursting events, and pinning...
DESIGN OF TWO-DIMENSIONAL SUPERSONIC TURBINE ROTOR BLADES WITH BOUNDARY-LAYER CORRECTION
Goldman, L. J.
1994-01-01
A computer program has been developed for the design of supersonic rotor blades where losses are accounted for by correcting the ideal blade geometry for boundary layer displacement thickness. The ideal blade passage is designed by the method of characteristics and is based on establishing vortex flow within the passage. Boundary-layer parameters (displacement and momentum thicknesses) are calculated for the ideal passage, and the final blade geometry is obtained by adding the displacement thicknesses to the ideal nozzle coordinates. The boundary-layer parameters are also used to calculate the aftermixing conditions downstream of the rotor blades assuming the flow mixes to a uniform state. The computer program input consists essentially of the rotor inlet and outlet Mach numbers, upper- and lower-surface Mach numbers, inlet flow angle, specific heat ratio, and total flow conditions. The program gas properties are set up for air. Additional gases require changes to be made to the program. The computer output consists of the corrected rotor blade coordinates, the principal boundary-layer parameters, and the aftermixing conditions. This program is written in FORTRAN IV for batch execution and has been implemented on an IBM 7094. This program was developed in 1971.
Nonparallel stability of two-dimensional nonuniformly heated boundary-layer flows
Nayfeh, A. H.; El-Hady, N. M.
1979-01-01
An analysis is presented for the linear stability of water boundary-layer flows over nonuniformly flat plates. Included in the analysis are disturbances due to velocity, pressure, temperatures, density, and transport properties as well as variations of the liquid properties with temperature. The method of multiple scales is used to account for the nonparallelism of the mean flow. In contrast with previous analyses, the nonsimilarity of the mean flow is taken into account. No analysis agrees, even qualitatively, with the experimental data when similar profiles are used. However, both the parallel and nonparallel results qualitatively agree with the experimental results of Strazisar and Reshotko when nonsimilar profiles are used.
Symmetry Analysis and Exact Solutions of the 2D Unsteady Incompressible Boundary-Layer Equations
Han, Zhong; Chen, Yong
2017-01-01
To find intrinsically different symmetry reductions and inequivalent group invariant solutions of the 2D unsteady incompressible boundary-layer equations, a two-dimensional optimal system is constructed which attributed to the classification of the corresponding Lie subalgebras. The comprehensiveness and inequivalence of the optimal system are shown clearly under different values of invariants. Then by virtue of the optimal system obtained, the boundary-layer equations are directly reduced to a system of ordinary differential equations (ODEs) by only one step. It has been shown that not only do we recover many of the known results but also find some new reductions and explicit solutions, which may be previously unknown. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11275072, 11435005, 11675054, and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213
Barnwell, Richard W.
1993-01-01
The derivation of the accurate, second-order, almost linear, approximate equation governing the defect stream function for nonequilibrium compressible turbulent boundary layers is reviewed. The similarity of this equation to the heat conduction equation is exploited in the development of an unconditionally stable, tridiagonal computational method which is second-order accurate in the marching direction and fourth-order accurate in the surface-normal direction. Results compare well with experimental data. Nonlinear effects are shown to be small. This two-dimensional method is simple and has been implemented on a programmable calculator.
Numerical Investigation on Two-dimensional Boundary Layer Flow with Transition
Institute of Scientific and Technical Information of China (English)
Yong Zhao; Tianlin Wang; Zhi Zong
2014-01-01
As a basic problem in many engineering applications, transition from laminar to turbulence still remains a difficult problem in computational fluid dynamics (CFD). A numerical study of one transitional flow in two-dimensional is conducted by Reynolds averaged numerical simulation (RANS) in this paper. Turbulence model plays a significant role in the complex flows’ simulation, and four advanced turbulence models are evaluated. Numerical solution of frictional resistance coefficient is compared with the measured one in the transitional zone, which indicates that Wilcox (2006) k-ω model with correction is the best candidate. Comparisons of numerical and analytical solutions for dimensionless velocity show that averaged streamwise dimensionless velocity profiles correct the shape rapidly in transitional region. Furthermore, turbulence quantities such as turbulence kinetic energy, eddy viscosity, and Reynolds stress are also studied, which are helpful to learn the transition’s behavior.
George, Jacob
The present study deals with the effects of sparsely distributed three-dimensional elements on two-dimensional (2-D) and three-dimensional (3-D) turbulent boundary layers (TBL) such as those that occur on submarines, ship hulls, etc. This study was achieved in three parts: Part 1 dealt with the cylinders when placed individually in the turbulent boundary layers, thereby considering the effect of a single perturbation on the TBL; Part 2 considered the effects when the same individual elements were placed in a sparse and regular distribution, thus studying the response of the flow to a sequence of perturbations; and in Part 3, the distributions were subjected to 3-D turbulent boundary layers, thus examining the effects of streamwise and spanwise pressure gradients on the same perturbed flows as considered in Part 2. The 3-D turbulent boundary layers were generated by an idealized wing-body junction flow. Detailed 3-velocity-component Laser-Doppler Velocimetry (LDV) and other measurements were carried out to understand and describe the rough-wall flow structure. The measurements include mean velocities, turbulence quantities (Reynolds stresses and triple products), skin friction, surface pressure and oil flow visualizations in 2-D and 3-D rough-wall flows for Reynolds numbers, based on momentum thickness, greater than 7000. Very uniform circular cylindrical roughness elements of 0.38mm, 0.76mm and 1.52mm height (k) were used in square and diagonal patterns, yielding six different roughness geometries of rough-wall surface. For the 2-D rough-wall flows, the roughness Reynolds numbers, k +, based on the element height (k) and the friction velocity (Utau), range from 26 to 131. Results for the 2-D rough-wall flows reveal that the velocity-defect law is similar for both smooth and rough surfaces, and the semi-logarithmic velocity-distribution curve is shifted by an amount DeltaU/U, depending on the height of the roughness element, showing that Delta U/Utau is a function
Frankl, F.; Voishel, V.
1943-01-01
In the present report an investigation is made on a flat plate in a two-dimensional compressible flow of the effect of compressibility and heating on the turbulent frictional drag coefficient in the boundary layer of an airfoil or wing radiator. The analysis is based on the Prandtl-Karman theory of the turbulent boundary later and the Stodola-Crocco, theorem on the linear relation between the total energy of the flow and its velocity. Formulas are obtained for the velocity distribution and the frictional drag law in a turbulent boundary later with the compressibility effect and heat transfer taken into account. It is found that with increase of compressibility and temperature at full retardation of the flow (the temperature when the velocity of the flow at a given point is reduced to zero in case of an adiabatic process in the gas) at a constant R (sub x), the frictional drag coefficient C (sub f) decreased, both of these factors acting in the same sense.
Langevin equation model of dispersion in the convective boundary layer
Energy Technology Data Exchange (ETDEWEB)
Nasstrom, J S
1998-08-01
This dissertation presents the development and evaluation of a Lagrangian stochastic model of vertical dispersion of trace material in the convective boundary layer (CBL). This model is based on a Langevin equation of motion for a fluid particle, and assumes the fluid vertical velocity probability distribution is skewed and spatially homogeneous. This approach can account for the effect of large-scale, long-lived turbulent structures and skewed vertical velocity distributions found in the CBL. The form of the Langevin equation used has a linear (in velocity) deterministic acceleration and a skewed randomacceleration. For the case of homogeneous fluid velocity statistics, this ""linear-skewed" Langevin equation can be integrated explicitly, resulting in a relatively efficient numerical simulation method. It is shown that this approach is more efficient than an alternative using a "nonlinear-Gaussian" Langevin equation (with a nonlinear deterministic acceleration and a Gaussian random acceleration) assuming homogeneous turbulence, and much more efficient than alternative approaches using Langevin equation models assuming inhomogeneous turbulence. "Reflection" boundary conditions for selecting a new velocity for a particle that encounters a boundary at the top or bottom of the CBL were investigated. These include one method using the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated, and two alternatives in which the magnitudes of these velocities are negatively correlated and uncorrelated. The constraint that spatial and velocity distributions of a well-mixed tracer must be the same as those of the fluid, was used to develop the Langevin equation models and the reflection boundary conditions. The two Langevin equation models and three reflection methods were successfully tested using cases for which exact, analytic statistical properties of particle velocity and position are known, including well
Characteristics of the boundary-layer equations of the minimum time-to-climb problem
Ardema, M. D.
1976-01-01
In many singular perturbation solutions of optimal control problems, the most difficult numerical task is to solve the boundary-layer equations. However, these equations have a special structure that may often be used to expedite their solution. This paper begins by noting the general nature of the boundary-layer equations for optimal control problems. These results are then applied to the aircraft minimum time-to-climb problem. A specific numerical example is considered to illustrate the characteristics of the solution of the boundary-layer equations for this problem.
Equations for a laminar boundary layer of a dilated liquid in a transverse magnetic field
Energy Technology Data Exchange (ETDEWEB)
Samokhin, V.N.
1984-01-01
A system of equations is examined which describes the magnetohydrodynamic boundary layer of a dilated liquid in a transverse magnetic field. The self modeling problem with an exponential law of change in the speed of the external stream and magnetic induction is studied. Localization of the perturbation in the liquid speed in the boundary layer is established and the change in the properties of the solution associated with this is shown.
Boundary Layer Equations and Lie Group Analysis of a Sisko Fluid
Directory of Open Access Journals (Sweden)
Gözde Sarı
2012-01-01
Full Text Available Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non-Newtonian parameters on the solutions are discussed.
Parker, E. N.
1985-01-01
The dynamics of magnetic fibrils in the convective zone of a star is investigated analytically, deriving mean-field equations for the two-dimensional transverse motion of an incompressible fluid containing numerous small widely spaced circular cylinders. The equations of Parker (1982) are extended to account for the inertial effects of local flow around the cylinders. The linear field equation for the stream function at the onset of convection is then rewritten, neglecting large-scale heat transport, and used to construct a model of convective counterflow. The Kelvin impulse and fluid momentum, convective motion initiated by a horizontal impulse, and the effects of a viscous boundary layer are considered in appendices.
On singular solutions of a magnetohydrodynamic nonlinear boundary layer equation
Directory of Open Access Journals (Sweden)
Mohammed Guedda
2007-05-01
Full Text Available This paper concerns the singular solutions of the equation $$ f''' +kappa ff''-eta {f'}^2 = 0, $$ where $eta < 0$ and $kappa = 0$ or 1. This equation arises when modelling heat transfer past a vertical flat plate embedded in a saturated porous medium with an applied magnetic field. After suitable normalization, $f'$ represents the velocity parallel to the surface or the non-dimensional fluid temperature. Our interest is in solutions which develop a singularity at some point (the blow-up point. In particular, we shall examine in detail the behavior of $f$ near the blow-up point.
A two-dimensional iterative panel method and boundary layer model for bio-inspired multi-body wings
Blower, Christopher J.; Dhruv, Akash; Wickenheiser, Adam M.
2014-03-01
The increased use of Unmanned Aerial Vehicles (UAVs) has created a continuous demand for improved flight capabilities and range of use. During the last decade, engineers have turned to bio-inspiration for new and innovative flow control methods for gust alleviation, maneuverability, and stability improvement using morphing aircraft wings. The bio-inspired wing design considered in this study mimics the flow manipulation techniques performed by birds to extend the operating envelope of UAVs through the installation of an array of feather-like panels across the airfoil's upper and lower surfaces while replacing the trailing edge flap. Each flap has the ability to deflect into both the airfoil and the inbound airflow using hinge points with a single degree-of-freedom, situated at 20%, 40%, 60% and 80% of the chord. The installation of the surface flaps offers configurations that enable advantageous maneuvers while alleviating gust disturbances. Due to the number of possible permutations available for the flap configurations, an iterative constant-strength doublet/source panel method has been developed with an integrated boundary layer model to calculate the pressure distribution and viscous drag over the wing's surface. As a result, the lift, drag and moment coefficients for each airfoil configuration can be calculated. The flight coefficients of this numerical method are validated using experimental data from a low speed suction wind tunnel operating at a Reynolds Number 300,000. This method enables the aerodynamic assessment of a morphing wing profile to be performed accurately and efficiently in comparison to Computational Fluid Dynamics methods and experiments as discussed herein.
Linearization of the boundary-layer equations of the minimum time-to-climb problem
Ardema, M. D.
1979-01-01
Ardema (1974) has formally linearized the two-point boundary value problem arising from a general optimal control problem, and has reviewed the known stability properties of such a linear system. In the present paper, Ardema's results are applied to the minimum time-to-climb problem. The linearized zeroth-order boundary layer equations of the problem are derived and solved.
A Generic Length-scale Equation For Second-order Turbulence Models of Oceanic Boundary Layers
Umlauf, L.; Burchard, H.
A generic transport equation for a generalized length-scale in second-order turbulence closure models for geophysical boundary layers is suggested. This variable consists of the products of powers of the turbulent kinetic energy, k, and the integral length-scale, l. The new approach generalizes traditional second-order models used in geophysical boundary layer modelling, e.g. the Mellor-Yamada model and the k- model, which, however, can be recovered as special cases. It is demonstrated how this new model can be calibrated with measurements in some typical geophysical boundary layer flows. As an example, the generic model is applied to the uppermost oceanic boundary layer directly influenced by the effects of breaking surface waves. Recent measurements show that in this layer the classical law of the wall is invalid, since there turbulence is dominated by turbulent transport of TKE from above, and not by shear-production. A widely accepted approach to describe the wave-affected layer with a one-equation turbulence model was suggested by Craig and Banner (1994). Here, some deficien- cies of their solutions are pointed out and a generalization of their ideas for the case of two-equation models is suggested. Direct comparison with very recently obtained measurements of the dissipation rate, , in the wave-affected boundary layer with com- puted results clearly demonstrate that only the generic two-equation model yields cor- rect predictions for the profiles of and the turbulent length scale, l. Also, the pre- dicted velocity profiles in the wave-affected layer, important e.g. for the interpretation of surface drifter experiments, are reproduced correctly only by the generic model. Implementation and computational costs of the generic model are comparable with traditonal two-equation models.
An extension of the transpired skin-friction equation to compressible turbulent boundary layers
Silva-Freire, Atila P.
1988-11-01
A skin-friction equation for transpired incompressible turbulent boundary layer, proposed in a previous paper (Silva-Freire, 1988), is extended to compressible flow. The expression derived here is simple and gives more consistent results than the momentum-integral equation. The difficulty with the present formulation, however, is that the wake profile parameter due to injection has to be carefully determined in order to obtain good results.
Stability analysis of Boundary Layer in Poiseuille Flow Through A Modified Orr-Sommerfeld Equation
Monwanou, A V; Orou, J B Chabi; 10.5539/apr.v4n4p138
2013-01-01
For applications regarding transition prediction, wing design and control of boundary layers, the fundamental understanding of disturbance growth in the flat-plate boundary layer is an important issue. In the present work we investigate the stability of boundary layer in Poiseuille flow. We normalize pressure and time by inertial and viscous effects. The disturbances are taken to be periodic in the spanwise direction and time. We present a set of linear governing equations for the parabolic evolution of wavelike disturbances. Then, we derive modified Orr-Sommerfeld equations that can be applied in the layer. Contrary to what one might think, we find that Squire's theorem is not applicable for the boundary layer. We find also that normalization by inertial or viscous effects leads to the same order of stability or instability. For the 2D disturbances flow ($\\theta=0$), we found the same critical Reynolds number for our two normalizations. This value coincides with the one we know for neutral stability of the k...
A general polynomial solution to convection–dispersion equation using boundary layer theory
Indian Academy of Sciences (India)
Jiao Wang; Ming’an Shao; Laiming Huang; Xiaoxu Jia
2017-04-01
A number of models have been established to simulate the behaviour of solute transport due to chemical pollution, both in croplands and groundwater systems. An approximate polynomial solution to convection–dispersion equation (CDE) based on boundary layer theory has been verified for the use to describe solute transport in semi-infinite systems such as soil column. However, previous studies have only proposed low order polynomial solutions such as parabolic and cubic polynomials. This paper presents a general polynomial boundary layer solution to CDE. Comparison with exact solution suggests the prediction accuracy of the boundary layer solution varies with the order of polynomial expression and soil transport parameters. The results show that prediction accuracy increases with increasing order up to parabolic or cubic polynomial function and with no distinct relationship between accuracy and order for higher order polynomials ($n\\geqslant 3$). Comparison of two critical solute transport parameters (i.e., dispersion coefficient and retardation factor), estimated by the boundary layer solution and obtained by CXTFIT curve-fitting, shows a good agreement. The study shows that the general solution can determine the appropriate orders of polynomials for approximate CDE solutions that best describe solute concentration profiles and optimal solute transport parameters. Furthermore, the general polynomial solution to CDE provides a simple approach to solute transport problems, a criterion for choosing the right orders of polynomials for soils with different transport parameters. It is also a potential approach for estimating solute transport parameters of soils in the field.
UPWIND DISCONTINUOUS GALERKIN METHODS FOR TWO DIMENSIONAL NEUTRON TRANSPORT EQUATIONS
Institute of Scientific and Technical Information of China (English)
袁光伟; 沈智军; 闫伟
2003-01-01
In this paper the upwind discontinuous Galerkin methods with triangle meshes for two dimensional neutron transport equations will be studied.The stability for both of the semi-discrete and full-discrete method will be proved.
Operator splitting for two-dimensional incompressible fluid equations
Holden, Helge; Karper, Trygve K
2011-01-01
We analyze splitting algorithms for a class of two-dimensional fluid equations, which includes the incompressible Navier-Stokes equations and the surface quasi-geostrophic equation. Our main result is that the Godunov and Strang splitting methods converge with the expected rates provided the initial data are sufficiently regular.
A near-wall four-equation turbulence model for compressible boundary layers
Sommer, T. P.; So, R. M. C.; Zhang, H. S.
1992-01-01
A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon(sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, the numerical predictions are in very good agreement with measurements and there are significant improvements in the predictions of mean flow properties at high Mach numbers.
Hamiltonian formalism of two-dimensional Vlasov kinetic equation.
Pavlov, Maxim V
2014-12-08
In this paper, the two-dimensional Benney system describing long wave propagation of a finite depth fluid motion and the multi-dimensional Russo-Smereka kinetic equation describing a bubbly flow are considered. The Hamiltonian approach established by J. Gibbons for the one-dimensional Vlasov kinetic equation is extended to a multi-dimensional case. A local Hamiltonian structure associated with the hydrodynamic lattice of moments derived by D. J. Benney is constructed. A relationship between this hydrodynamic lattice of moments and the two-dimensional Vlasov kinetic equation is found. In the two-dimensional case, a Hamiltonian hydrodynamic lattice for the Russo-Smereka kinetic model is constructed. Simple hydrodynamic reductions are presented.
Institute of Scientific and Technical Information of China (English)
Liancun Zheng; Chen Liang; Xinxin Zhang
2007-01-01
An improved shooting method was presented for solving the natural convention boundary layer equations,with a coupling of the velocity field to the temperature field.The numerical results are consistent with the approximate solution obtained by former researchers.
Control Operator for the Two-Dimensional Energized Wave Equation
Directory of Open Access Journals (Sweden)
Sunday Augustus REJU
2006-07-01
Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.
Numerical blowup in two-dimensional Boussinesq equations
Yin, Zhaohua
2009-01-01
In this paper, we perform a three-stage numerical relay to investigate the finite time singularity in the two-dimensional Boussinesq approximation equations. The initial asymmetric condition is the middle-stage output of a $2048^2$ run, the highest resolution in our study is $40960^2$, and some signals of numerical blowup are observed.
Application of higher-order numerical methods to the boundary-layer equations
Wornom, S. F.
1978-01-01
A fourth-order method is presented for calculating numerical solutions to parabolic, partial differential equations in two variables or ordinary differential equations. The method is the natural extension of the second-order Keller Box Scheme to fourth order and is demonstrated with application to the incompressible, laminar and turbulent boundary-layer equations for both attached and separated flows. The efficiency of the present method is compared with other higher-order methods; namely, the Keller Box Scheme with Richardson extrapolation, the method of deferred corrections, the three-point spline methods, and a modified finite-element method. For equivalent accuracy, numerical results show the present method to be more efficient than the other higher-order methods for both laminar and turbulent flows.
On energy boundary layer equations in power law non-Newtonian fluids
Institute of Scientific and Technical Information of China (English)
郑连存; 张欣欣
2008-01-01
The hear transfer mechanism and the constitutive models for energy boundary layer in power law fluids were investigated.Two energy transfer constitutive equations models were proposed based on the assumption of similarity of velocity field momentum diffusion and temperature field heat transfer.The governing systems of partial different equations were transformed into ordinary differential equations respectively by using the similarity transformation group.One model was assumed that Prandtl number is a constant,and the other model was assumed that viscosity diffusion is analogous to thermal diffusion.The solutions were presented analytically and numerically by using the Runge-Kutta formulas and shooting technique and the associated transfer characteristics were discussed.
Institute of Scientific and Technical Information of China (English)
LU Chang-gen; CAO Wei-dong; QIAN Jian-hua
2006-01-01
A new method for direct numerical simulation of incompressible Navier-Stokes equations is studied in the paper. The compact finite difference and the non-linear terms upwind compact finite difference schemes on non-uniform meshes in x and y directions are developed respectively. With the Fourier spectral expansion in the spanwise direction, three-dimensional N-S equation are converted to a system of two-dimensional equations. The third-order mixed explicit-implicit scheme is employed for time integration. The treatment of the three-dimensional non-reflecting outflow boundary conditions is presented, which is important for the numerical simulations of the problem of transition in boundary layers, jets, and mixing layer. The numerical results indicate that high accuracy, stabilization and efficiency are achieved by the proposed numerical method. In addition, a theory model for the coherent structure in a laminar boundary layer is also proposed, based on which the numerical method is implemented to the non-linear evolution of coherent structure. It is found that the numerical results of the distribution of Reynolds stress, the formation of high shear layer, and the event of ejection and sweeping, match well with the observed characteristics of the coherent structures in a turbulence boundary layer.
Lyapunov Computational Method for Two-Dimensional Boussinesq Equation
Mabrouk, Anouar Ben
2010-01-01
A numerical method is developed leading to Lyapunov operators to approximate the solution of two-dimensional Boussinesq equation. It consists of an order reduction method and a finite difference discretization. It is proved to be uniquely solvable and analyzed for local truncation error for consistency. The stability is checked by using Lyapunov criterion and the convergence is studied. Some numerical implementations are provided at the end of the paper to validate the theoretical results.
Hall, P.
1985-01-01
The Taylor-Gortler vortex instability equations are formulated for steady and unsteady interacting boundary layer flows of the type which arise in triple-deck theory. The effective Gortler number is shown to be a function of the all shape in the boundary layer and the possibility of both steady and unsteady Taylor-Gortler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Gortler vortices exist before the boundary layers at the wall develop the Goldstein singularity. As an example of an unsteady spatially varying basic state the instability of high frequency large amplitude Tollmien-Schlichting waves in a curved channel were considered. It is shown that they are unstable in the first Stokes layer stage of the hierarchy of nonlinear states. The Tollmien-Schlichting waves are shown to be unstable in the presence of both convex and concave curvature.
Equation of State of the Two-Dimensional Hubbard Model
Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael
2016-04-01
The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.
Ene, Remus-Daniel; Marinca, Vasile; Marinca, Bogdan
2016-01-01
Analytic approximate solutions using Optimal Homotopy Perturbation Method (OHPM) are given for steady boundary layer flow over a nonlinearly stretching wall in presence of partial slip at the boundary. The governing equations are reduced to nonlinear ordinary differential equation by means of similarity transformations. Some examples are considered and the effects of different parameters are shown. OHPM is a very efficient procedure, ensuring a very rapid convergence of the solutions after only two iterations.
Institute of Scientific and Technical Information of China (English)
XIONG Lei; LI haijiao; ZHANG Lewen
2008-01-01
The fourth-order B spline wavelet scaling functions are used to solve the two-dimensional unsteady diffusion equation. The calculations from a case history indicate that the method provides high accuracy and the computational efficiency is enhanced due to the small matrix derived from this method.The respective features of 3-spline wavelet scaling functions, 4-spline wavelet scaling functions and quasi-wavelet used to solve the two-dimensional unsteady diffusion equation are compared. The proposed method has potential applications in many fields including marine science.
The Chandrasekhar's Equation for Two-Dimensional Hypothetical White Dwarfs
De, Sanchari
2014-01-01
In this article we have extended the original work of Chandrasekhar on the structure of white dwarfs to the two-dimensional case. Although such two-dimensional stellar objects are hypothetical in nature, we strongly believe that the work presented in this article may be prescribed as Master of Science level class problem for the students in physics.
Invariant Subspaces of the Two-Dimensional Nonlinear Evolution Equations
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Chunrong Zhu
2016-11-01
Full Text Available In this paper, we develop the symmetry-related methods to study invariant subspaces of the two-dimensional nonlinear differential operators. The conditional Lie–Bäcklund symmetry and Lie point symmetry methods are used to construct invariant subspaces of two-dimensional differential operators. We first apply the multiple conditional Lie–Bäcklund symmetries to derive invariant subspaces of the two-dimensional operators. As an application, the invariant subspaces for a class of two-dimensional nonlinear quadratic operators are provided. Furthermore, the invariant subspace method in one-dimensional space combined with the Lie symmetry reduction method and the change of variables is used to obtain invariant subspaces of the two-dimensional nonlinear operators.
Barnwell, R. W.; Dejarnette, F. R.; Wahls, R. A.
1987-01-01
A new turbulent boundary-layer method is developed which models the inner region with the law of the wall while the outer region uses Clauser's eddy viscosity in Matsuno's finite-difference method. The match point between the inner and outer regions as well as the wall shear stress are determined at each marching step during the computation. Results obtained for incompressible, two-dimensional flow over flat plates and ellipses are compared with solutions from a baseline method which uses a finite-difference method for the entire boundary layer. Since the present method used the finite-difference method in the outer region only, the number of grid points required was about half that needed for the baseline method. Accurate displacement and momentum thicknesses were predicted for all cases. Skin friction was predicted well for the flat plate, but the accuracy decreased significantly for the ellipses. Adding a wake functions to the law of the wall allows some of the pressure gradient effect to be taken into account thereby increasing the accuracy of the method.
Shalaev, V. I.
2016-10-01
Singularities appearing in solutions of 3D laminar boundary layer (BL) equations, when two streamline families are collided, are discussed. For conical bodies, equations are investigated using asymptotic methods. Analytical solutions are obtained for the outer BL region; their singularities in the runoff plane are studied. The asymptotic flow structure near the singularity is constructed on the base of Navier-Stokes equations at large Reynolds numbers. For different flow regions analytical solutions are found and are matched with BL equation solutions. Properties of BL equations for the near-wall region in the runoff plane are investigated and a criterion of the solution disappearing is found. It is shown that this criterion separates two different topological flow structures and corresponds to the singularity appearance in this plane in solutions of full equations. Calculations confirmed obtained results are presented.
Hall, Philip; Bennett, James
1986-01-01
The Taylor-Goertler vortex instability equations are formulated for steady and unsteady interacting boundary-layer flows. The effective Goertler number is shown to be a function of the wall shape in the boundary layer and the possibility of both steady and unsteady Taylor-Goertler modes exists. As an example the steady flow in a symmetrically constricted channel is considered and it is shown that unstable Goertler vortices exist before the boundary layers at the wall develop the Goldstein singularity discussed by Smith and Daniels (1981). As an example of an unsteady spatially varying basic state, it is considered the instability of high-frequency large-amplitude two- and three-dimensional Tollmien-Schlichting waves in a curved channel. It is shown that they are unstable in the first 'Stokes-layer stage' of the hierarchy of nonlinear states discussed by Smith and Burggraf (1985). This instability of Tollmien-Schlichting waves in an internal flow can occur in the presence of either convex or concave curvature. Some discussion of this instability in external flows is given.
Analysis of turbulent boundary layers
Cebeci, Tuncer
1974-01-01
Analysis of Turbulent Boundary Layers focuses on turbulent flows meeting the requirements for the boundary-layer or thin-shear-layer approximations. Its approach is devising relatively fundamental, and often subtle, empirical engineering correlations, which are then introduced into various forms of describing equations for final solution. After introducing the topic on turbulence, the book examines the conservation equations for compressible turbulent flows, boundary-layer equations, and general behavior of turbulent boundary layers. The latter chapters describe the CS method for calculati
A method for calculating turbulent boundary layers and losses in the flow channels of turbomachines
Schumann, Lawrence F.
1987-01-01
An interactive inviscid core flow-boundary layer method is presented for the calculation of turbomachine channel flows. For this method, a one-dimensional inviscid core flow is assumed. The end-wall and blade surface boundary layers are calculated using an integral entrainment method. The boundary layers are assumed to be collateral and thus are two-dimensional. The boundary layer equations are written in a streamline coordinate system. The streamwise velocity profiles are approximated by power law profiles. Compressibility is accounted for in the streamwise direction but not in the normal direction. Equations are derived for the special cases of conical and two-dimensional rectangular diffusers. For these cases, the assumptions of a one-dimensional core flow and collateral boundary layers are valid. Results using the method are compared with experiment and good quantitative agreement is obtained.
NONLINEAR GALERKIN METHODS FOR SOLVING TWO DIMENSIONAL NEWTON-BOUSSINESQ EQUATIONS
Institute of Scientific and Technical Information of China (English)
GUOBOLING
1995-01-01
The nonlinear Galerkin methods for solving two-dimensional Newton-Boussinesq equations are proposed. The existence and uniqueness of global generalized solution of these equations,and the convergence of approximate solutions are also obtained.
Costa, C. P.; Vilhena, M. T.; Moreira, D. M.; Tirabassi, T.
We present a three-dimensional solution of the steady-state advection-diffusion equation considering a vertically inhomogeneous planetary boundary layer (PBL). We reach this goal applying the generalized integral transform technique (GITT), a hybrid method that had solved a wide class of direct and inverse problems mainly in the area of heat transfer and fluid mechanics. The transformed problem is solved by the advection-diffusion multilayer model (ADMM) method, a semi-analytical solution based on a discretization of the PBL in sub-layers where the advection-diffusion equation is solved by the Laplace transform technique. Numerical simulations are presented and the performances of the solution are compared against field experiments data.
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A. Aghili
2011-12-01
Full Text Available In this work,we present new theorems on two-dimensional Laplace transformation. We also develop some applications based on these results. The two-dimensional Laplace transformation is useful in the solution of non-homogeneous partial differential equations. In the last section a boundary value problem is solved by using the double Laplace-Carson transform.
Bertolotti, F. P.; Herbert, TH.
1991-01-01
The application of linearized parabolic stability equations (PSE) to compressible flow is considered. The effect of mean-flow nonparallelism is found to be weak on 2D waves and strong on 3D waves. Results for a single choice of free-stream parameters that corresponds to the atmospheric conditions at 15,000 m above sea level are presented.
Kuehl, Joseph
2016-11-01
The parabolized stability equations (PSE) have been developed as an efficient and powerful tool for studying the stability of advection-dominated laminar flows. In this work, a new "wavepacket" formulation of the PSE is presented. This method accounts for the influence of finite-bandwidth-frequency distributions on nonlinear stability calculations. The methodology is motivated by convolution integrals and is found to appropriately represent nonlinear energy transfer between primary modes and harmonics, in particular nonlinear feedback, via a "nonlinear coupling coefficient." It is found that traditional discrete mode formulations overestimate nonlinear feedback by approximately 70%. This results in smaller maximum disturbance amplitudes than those observed experimentally. The new formulation corrects this overestimation, accounts for the generation of side lobes responsible for spectral broadening and results in disturbance saturation amplitudes consistent with experiment. A Mach 6 flared-cone example is presented. Support from the AFOSR Young Investigator Program via Grant FA9550-15-1-0129 is gratefully acknowledges.
On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers
Guedda, Mohamed
2008-01-01
The present work deals with the two-dimensional incompressible,laminar, steady-state boundary layer equations. First, we determinea family of velocity distributions outside the boundary layer suchthat these problems may have similarity solutions. Then, we examenin detail new exact solutions, called Pseudo--similarity, where the external velocity varies inversely-linear with the distance along the surface $ (U_e(x) = U_\\infty x^{-1}). The present work deals with the two-dimensional incompressible, laminar, steady-state boundary layer equations. First, we determine a family of velocity distributions outside the boundary layer such that these problems may have similarity solutions. Then, we examenin detail new exact solutions. The analysis shows that solutions exist only for a lateral suction. For specified conditions, we establish the existence of an infinite number of solutions, including monotonic solutions and solutions which oscillate an infinite number of times and tend to a certain limit. The properties o...
Solution of two-dimensional Fredholm integral equation via RBF-triangular method
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Amir Fallahzadeh
2012-04-01
Full Text Available In this paper, a new method is introduced to solve a two-dimensional Fredholm integral equation. The method is based on the approximation by Gaussian radial basis functions and triangular nodes and weights. Also, a new quadrature is introduced to approximate the two dimensional integrals which is called the triangular method. The results of the example illustrate the accuracy of the proposed method increases.
Yehorchenko, Irina
2010-01-01
We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional and hidden symmetries of the original equations.
Asymptotic Behavior of the Newton-Boussinesq Equation in a Two-Dimensional Channel
Fucci, Guglielmo; Singh, Preeti
2007-01-01
We prove the existence of a global attractor for the Newton-Boussinesq equation defined in a two-dimensional channel. The asymptotic compactness of the equation is derived by the uniform estimates on the tails of solutions. We also establish the regularity of the global attractor.
TWO-DIMENSIONAL RIEMANN PROBLEMS:FROM SCALAR CONSERVATION LAWS TO COMPRESSIBLE EULER EQUATIONS
Institute of Scientific and Technical Information of China (English)
Li Jiequan; Sheng Wancheng; Zhang Tong; Zheng Yuxi
2009-01-01
In this paper we survey the authors' and related work on two-dimensional Rie-mann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections: 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
赵才地
2004-01-01
This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.
Integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time
Institute of Scientific and Technical Information of China (English)
YAN Jun
2005-01-01
The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equations of motion are also found.
Boundary layers in stochastic thermodynamics.
Aurell, Erik; Mejía-Monasterio, Carlos; Muratore-Ginanneschi, Paolo
2012-02-01
We study the problem of optimizing released heat or dissipated work in stochastic thermodynamics. In the overdamped limit these functionals have singular solutions, previously interpreted as protocol jumps. We show that a regularization, penalizing a properly defined acceleration, changes the jumps into boundary layers of finite width. We show that in the limit of vanishing boundary layer width no heat is dissipated in the boundary layer, while work can be done. We further give an alternative interpretation of the fact that the optimal protocols in the overdamped limit are given by optimal deterministic transport (Burgers equation).
Loop equations and Virasoro constraints in non-perturbative two-dimensional quantum gravity
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Dijkgraaf, R.; Verlinde, H. (Princeton Univ., NJ (USA). Joseph Henry Labs.); Verlinde, E. (Institute for Advanced Study, Princeton, NJ (USA). School of Natural Sciences)
1991-01-21
We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one-matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro algebra. We give an interpretation of these equations in topological gravity and discuss their extension to multi-matrix models. For the multi-critical models the loop equation naturally singles out the operators corresponding to the primary fields of the minimal models. (orig.).
Loop Equations and Virasoro Constraints in Non-Perturbative Two-Dimensional Quantum Gravity
Dijkgraaf, Robbert; Verlinde, Herman; Verlinde, Erik
We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one-matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro algebra. We give an interpretation of these equations in topological gravity and discuss their extension to multi-matrix models. For the multi-critical models the loop equation naturally singles out the operators corresponding to the primary fields of the minimal models.
Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations
Abdulwahhab, Muhammad Alim
2016-10-01
Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.
Solution of the two- dimensional heat equation for a rectangular plate
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Nurcan BAYKUŞ SAVAŞANERİL
2015-11-01
Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.
Analytic Solution for Two-Dimensional Heat Equation for an Ellipse Region
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Nurcan Baykus Savasaneril
2016-01-01
Full Text Available In this study, an altenative method is presented for the solution of two-dimensional heat equation in an ellipse region. In this method, the solution function of the problem is based on the Green, and therefore on elliptic functions. To do this, it is made use of the basic consepts associated with elliptic integrals, conformal mappings and Green functions.
de Snoo, H; Winkler, Henrik
2005-01-01
The class of two-dimensional trace-normed canonical systems of differential equations on R is considered with selfadjoint interface conditions at 0. If one or both of the intervals around 0 are H-indivisible the interface conditions which give rise to selfadjoint relations (multi-valued operators) a
The transfer function analysis of various schemes for the two-dimensional shallow-water equations
Neta, B.; DeVito, C.L.
1988-01-01
In this paper various finite difference and finite element approximations to the linearized two-dimensional shallow-water equations are analyzed. This analysis complements previous results for the one-dimensional case. The first author would like to thank the NPS Foundation Research program for its support of this research.
T, M P Ramirez
2012-01-01
Using a conjecture that allows to approach separable-variables conductivity functions, the elements of the Modern Pseudoanalytic Function Theory are used, for the first time, to numerically solve the Dirichlet boundary value problem of the two-dimensional Electrical Impedance Equation, when the conductivity function arises from geometrical figures, located within bounded domains.
Bound states of two-dimensional Schr\\"{o}dinger-Newton equations
Stubbe, Joachim
2008-01-01
We prove an existence and uniqueness result for ground states and for purely angular excitations of two-dimensional Schr\\"{o}dinger-Newton equations. From the minimization problem for ground states we obtain a sharp version of a logarithmic Hardy-Littlewood-Sobolev type inequality.
Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM
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Reza Abazari
2013-01-01
Full Text Available The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM, and compared with the differential transform method (DTM. The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.
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Musa Danjuma SHEHU
2008-06-01
Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.
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Sohrab Bazm
2016-02-01
Full Text Available In this study, the Bernoulli polynomials are used to obtain an approximate solution of a class of nonlinear two-dimensional integral equations. To this aim, the operational matrices of integration and the product for Bernoulli polynomials are derived and utilized to reduce the considered problem to a system of nonlinear algebraic equations. Some examples are presented to illustrate the efficiency and accuracy of the method.
Soliton solutions of the two-dimensional KdV-Burgers equation by homotopy perturbation method
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Molabahrami, A. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of)], E-mail: a_m_bahrami@yahoo.com; Khani, F. [Department of Mathematics, Ilam University, PO Box 69315516, Ilam (Iran, Islamic Republic of); Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)], E-mail: farzad_khani59@yahoo.com; Hamedi-Nezhad, S. [Bakhtar Institute of Higher Education, PO Box 696, Ilam (Iran, Islamic Republic of)
2007-10-29
In this Letter, the He's homotopy perturbation method (HPM) to finding the soliton solutions of the two-dimensional Korteweg-de Vries Burgers' equation (tdKdVB) for the initial conditions was applied. Numerical solutions of the equation were obtained. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. The results reveal that the HPM is very effective and simple.
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S. M. Sadatrasoul
2014-01-01
Full Text Available We introduce some generalized quadrature rules to approximate two-dimensional, Henstock integral of fuzzy-number-valued functions. We also give error bounds for mappings of bounded variation in terms of uniform modulus of continuity. Moreover, we propose an iterative procedure based on quadrature formula to solve two-dimensional linear fuzzy Fredholm integral equations of the second kind (2DFFLIE2, and we present the error estimation of the proposed method. Finally, some numerical experiments confirm the theoretical results and illustrate the accuracy of the method.
Introduction to computational techniques for boundary layers
Energy Technology Data Exchange (ETDEWEB)
Blottner, F.G.
1979-09-01
Finite-difference procedures to solve boundary layer flows in fluid mechanics are explained. The governing equations and the transformations utilized are described. Basic solution techniques are illustrated with the similar boundary layer equations. Nonsimilar solutions are developed for the incompressible equations. Various example problems are solved, and the numerical results in the Fortran listing of the computer codes are presented.
The Analysis of the Two-dimensional Diffusion Equation With a Source
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Sunday Augustus REJU
2006-07-01
Full Text Available This study presents a new variant analysis and simulations of the two-dimensional energized wave equation remarkably different from the diffusion equations studied earlier studied. The objective functional and the dynamical energized wave are penalized to form a function called the Hamiltonian function. From this function, we obtained the necessary conditions for the optimal solutions using the maximum principle. By applying the Fourier solution to the first order differential equation, the analytical solutions for the state and control are obtained. The solutions are simulated to give visual physical interpretation of the waves and the numerical values.
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Vineet K., E-mail: vineetsriiitm@gmail.com [ISRO Telemetry, Tracking and Command Network (ISTRAC), Bangalore-560058 (India); Awasthi, Mukesh K. [Department of Mathematics, University of Petroleum and Energy Studies, Dehradun-248007 (India); Singh, Sarita [Department of Mathematics, WIT- Uttarakhand Technical University, Dehradun-248007 (India)
2013-12-15
This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
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Vineet K. Srivastava
2013-12-01
Full Text Available This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM, for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
Ye, Xia; Zhang, Jianwen
2016-08-01
This paper concerns the asymptotic behavior of the solution to an initial-boundary value problem of the cylindrically symmetric Navier-Stokes equations with large data for compressible heat-conducting ideal fluids, as the shear viscosity μ goes to zero. A suitable corrector function (the so-called boundary-layer type function) is constructed to eliminate the disparity of boundary values. As by-products, the convergence rates of the derivatives in L 2 are obtained and the boundary-layer thickness (BL-thickness) of the value O≤ft({μα}\\right) with α \\in ≤ft(0,1/2\\right) is shown by an alternative method, compared with the results proved in Jiang and Zhang (2009 SIAM J. Math. Anal. 41 237-68) and Qin et al (2015 Arch. Ration. Mech. Anal. 216 1049-86).
Multi-Symplectic Splitting Method for Two-Dimensional Nonlinear Schriidinger Equation
Institute of Scientific and Technical Information of China (English)
陈亚铭; 朱华君; 宋松和
2011-01-01
Using the idea of splitting numerical methods and the multi-symplectic methods, we propose a multisymplectic splitting （MSS） method to solve the two-dimensional nonlinear Schrodinger equation （2D-NLSE） in this paper. It is further shown that the method constructed in this way preserve the global symplectieity exactly. Numerical experiments for the plane wave solution and singular solution of the 2D-NLSE show the accuracy and effectiveness of the proposed method.
Regularity of Stagnation Point-form Solutions of the Two-dimensional Euler Equations
Sarria, Alejandro
2013-01-01
A class of semi-bounded solutions of the two-dimensional incompressible Euler equations, satisfying either periodic or Dirichlet boundary conditions, is examined. For smooth initial data, new blowup criteria in terms of the initial concavity profile is presented and the effects that the boundary conditions have on the global regularity of solutions is discussed. In particular, by deriving a formula for a general solution along Lagrangian trajectories, we describe how p...
Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2003-01-01
The subject of the paper is the derivation and analysis of third order finite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the first order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation from the piecewise constants, to feed into the calculation of the fluxes. We estimate the truncation error and give numerical examples to demonstrate the higher order...
Measurement of the Equation of State of the Two-Dimensional Hubbard Model
Miller, Luke; Cocchi, Eugenio; Drewes, Jan; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Koehl, Michael
2016-05-01
The subtle interplay between kinetic energy, interactions and dimensionality challenges our comprehension of strongly-correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, 0 constitute benchmarks for state-of-the-art theoretical approaches.
Quadrature-free spline method for two-dimensional Navier-Stokes equation
Institute of Scientific and Technical Information of China (English)
HU Xian-liang; HAN Dan-fu
2008-01-01
In this paper,a quadrature-free scheme of spline method for two-dimensional Navier-Stokes equation is derived,which can dramatically improve the efficiency of spline method for fluid problems proposed by Lai and Wenston(2004). Additionally,the explicit formulation for boundary condition with up to second order derivatives is presented. The numerical simulations on several benchmark problems show that the scheme is very efficient.
Eventual Regularity of the Two-Dimensional Boussinesq Equations with Supercritical Dissipation
Jiu, Quansen; Wu, Jiahong; Yang, Wanrong
2015-02-01
This paper studies solutions of the two-dimensional incompressible Boussinesq equations with fractional dissipation. The spatial domain is a periodic box. The Boussinesq equations concerned here govern the coupled evolution of the fluid velocity and the temperature and have applications in fluid mechanics and geophysics. When the dissipation is in the supercritical regime (the sum of the fractional powers of the Laplacians in the velocity and the temperature equations is less than 1), the classical solutions of the Boussinesq equations are not known to be global in time. Leray-Hopf type weak solutions do exist. This paper proves that such weak solutions become eventually regular (smooth after some time ) when the fractional Laplacian powers are in a suitable supercritical range. This eventual regularity is established by exploiting the regularity of a combined quantity of the vorticity and the temperature as well as the eventual regularity of a generalized supercritical surface quasi-geostrophic equation.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
Stagg, G. W.; Parker, N. G.; Barenghi, C. F.
2017-03-01
We model the superfluid flow of liquid helium over the rough surface of a wire (used to experimentally generate turbulence) profiled by atomic force microscopy. Numerical simulations of the Gross-Pitaevskii equation reveal that the sharpest features in the surface induce vortex nucleation both intrinsically (due to the raised local fluid velocity) and extrinsically (providing pinning sites to vortex lines aligned with the flow). Vortex interactions and reconnections contribute to form a dense turbulent layer of vortices with a nonclassical average velocity profile which continually sheds small vortex rings into the bulk. We characterize this layer for various imposed flows. As boundary layers conventionally arise from viscous forces, this result opens up new insight into the nature of superflows.
Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
Ablowitz, Mark J.; Demirci, Ali; Ma, Yi-Ping
2016-10-01
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using step like initial data along a parabolic front. Employing a parabolic similarity reduction exactly reduces the study of such DSWs in two space one time (2 + 1) dimensions to finding DSW solutions of (1 + 1) dimensional equations. With this ansatz, the KP and 2DBO equations can be exactly reduced to the cylindrical Korteweg-de Vries (cKdV) and cylindrical Benjamin-Ono (cBO) equations, respectively. Whitham modulation equations which describe DSW evolution in the cKdV and cBO equations are derived and Riemann type variables are introduced. DSWs obtained from the numerical solutions of the corresponding Whitham systems and direct numerical simulations of the cKdV and cBO equations are compared with very good agreement obtained. In turn, DSWs obtained from direct numerical simulations of the KP and 2DBO equations are compared with the cKdV and cBO equations, again with good agreement. It is concluded that the (2 + 1) DSW behavior along self similar parabolic fronts can be effectively described by the DSW solutions of the reduced (1 + 1) dimensional equations.
Anti-periodic traveling wave solution to a forced two-dimensional generalized KdV-Burgers equation
Institute of Scientific and Technical Information of China (English)
TAN Junyu
2003-01-01
The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied.Some theorems concerning the boundness, existence and uniqueness of the solution to this equation are proved.
Analytical solutions of the two-dimensional Dirac equation for a topological channel intersection
Anglin, J. R.; Schulz, A.
2017-01-01
Numerical simulations in a tight-binding model have shown that an intersection of topologically protected one-dimensional chiral channels can function as a beam splitter for noninteracting fermions on a two-dimensional lattice [Qiao, Jung, and MacDonald, Nano Lett. 11, 3453 (2011), 10.1021/nl201941f; Qiao et al., Phys. Rev. Lett. 112, 206601 (2014), 10.1103/PhysRevLett.112.206601]. Here we confirm this result analytically in the corresponding continuum k .p model, by solving the associated two-dimensional Dirac equation, in the presence of a "checkerboard" potential that provides a right-angled intersection between two zero-line modes. The method by which we obtain our analytical solutions is systematic and potentially generalizable to similar problems involving intersections of one-dimensional systems.
Protein Conformational Change Based on a Two-dimensional Generalized Langevin Equation
Institute of Scientific and Technical Information of China (English)
Ying-xi Wang; Shuang-mu Linguang; Nan-rong Zhao; Yi-jing Yan
2011-01-01
A two-dimensional generalized Langevin equation is proposed to describe the protein conformational change,compatible to the electron transfer process governed by atomic packing density model.We assume a fractional Gaussian noise and a white noise through bond and through space coordinates respectively,and introduce the coupling effect coming from both fluctuations and equilibrium variances.The general expressions for autocorrelation functions of distance fluctuation and fluorescence lifetime variation are derived,based on which the exact conformational change dynamics can be evaluated with the aid of numerical Laplace inversion technique.We explicitly elaborate the short time and long time approximations.The relationship between the two-dimensional description and the one-dimensional theory is also discussed.
Chavanis, Pierre-Henri
2013-01-01
We complete the literature on the statistical mechanics of point vortices in two-dimensional hydrodynamics. Using a maximum entropy principle, we determine the multi-species Boltzmann-Poisson equation and establish a form of virial theorem. Using a maximum entropy production principle (MEPP), we derive a set of relaxation equations towards statistical equilibrium. These relaxation equations can be used as a numerical algorithm to compute the maximum entropy state. We mention the analogies with the Fokker-Planck equations derived by Debye and H\\"uckel for electrolytes. We then consider the limit of strong mixing (or low energy). To leading order, the relationship between the vorticity and the stream function at equilibrium is linear and the maximization of the entropy becomes equivalent to the minimization of the enstrophy. This expansion is similar to the Debye-H\\"uckel approximation for electrolytes, except that the temperature is negative instead of positive so that the effective interaction between like-si...
Unsteady separated boundary layer in a transonic diffuser flow with self-excited oscillations
Hsieh, T.; Coakley, T. J.
1986-01-01
A numerical investigation of two-dimensional unsteady boundary layer in a transonic diffuser flow with self-excited oscillations and strong flow separation by solving the compressible, Reynolds-averaged, thin-layer Navier-Stokes equations with two-equations turbulence model is described. Three different meshes with constant streamwise mesh distribution and varying vertical mesh distribution were used. Results obtained indicate that a refinement of mesh studied here has minimal effect on the mean boundary layer flow but significantly increases the amplitude of oscillation of all flow variables. Comparisons of unsteady wall pressure, velocity profile, terminal shock, and separation pocket among computations and with experiment are presented.
Small global solutions to the damped two-dimensional Boussinesq equations
Adhikari, Dhanapati; Cao, Chongsheng; Wu, Jiahong; Xu, Xiaojing
The two-dimensional (2D) incompressible Euler equations have been thoroughly investigated and the resolution of the global (in time) existence and uniqueness issue is currently in a satisfactory status. In contrast, the global regularity problem concerning the 2D inviscid Boussinesq equations remains widely open. In an attempt to understand this problem, we examine the damped 2D Boussinesq equations and study how damping affects the regularity of solutions. Since the damping effect is insufficient in overcoming the difficulty due to the “vortex stretching”, we seek unique global small solutions and the efforts have been mainly devoted to minimizing the smallness assumption. By positioning the solutions in a suitable functional setting (more precisely, the homogeneous Besov space B˚∞,11), we are able to obtain a unique global solution under a minimal smallness assumption.
Kuiper, Logan K
2016-01-01
An approximate solution to the two dimensional Navier Stokes equation with periodic boundary conditions is obtained by representing the x any y components of fluid velocity with complex Fourier basis vectors. The chosen space of basis vectors is finite to allow for numerical calculations, but of variable size. Comparisons of the resulting approximate solutions as they vary with the size of the chosen vector space allow for extrapolation to an infinite basis vector space. Results suggest that such a solution, with the full basis vector space and which would give the exact solution, would fail for certain initial velocity configurations when initial velocity and time t exceed certain limits.
On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅰ)
Institute of Scientific and Technical Information of China (English)
HUANG Dai-wen; GUO Bo-ling
2007-01-01
The initial boundary value problem for the two-dimensional primitive equations of large scale oceanic motion in geophysics is considered.It is assumed that the depth of the ocean is a positive constant.Firstly,if the initial data are square integrable,then by Fadeo-Galerkin method,the existence of the global weak solutions for the problem is obtained.Secondly, if the initial data and their vertical derivatives axe all square integrable,then by Faedo-Galerkin method and anisotropic inequalities,the existerce and uniqueness of the giobal weakly strong solution for the above initial boundary problem axe obtained.
On two-dimensional large-scale primitive equations in oceanic dynamics(Ⅱ)
Institute of Scientific and Technical Information of China (English)
HUANG Dai-wen; GUO Bo-ling
2007-01-01
The initial boundary value problem for the two-dimensional primitive equations of largescale oceanic motion in geophysics is considered sequetially.Here the depth of the ocean is positive but not always a constant.By Faedo-Galerkin method and anisotropic inequalities,the existence and uniqueness of the global weakly strong solution and global strong solution for the problem are obtained.Moreover,by studying the asymptotic behavior of solutions for the above problem,the energy is exponential decay with time is proved.
Cellular neural network analysis for two-dimensional bioheat transfer equation.
Niu, J H; Wang, H Z; Zhang, H X; Yan, J Y; Zhu, Y S
2001-09-01
The cellular neural network (CNN) method is applied to solve the Pennes bioheat transfer equation, and its feasibility is demonstrated. Numerical solutions were obtained for a cellular neural network for a two-dimensional steady-state temperature field obtained from focused and unfocused ultrasound heat sources. Transient-state temperature fields were also studied and compared with experimental results obtained elsewhere. The cellular neural networks' key features of asynchronous parallel processing, continuous-time dynamics and local interaction enable real-time temperature field estimation for clinical hyperthermia.
Blow-up conditions for two dimensional modified Euler-Poisson equations
Lee, Yongki
2016-09-01
The multi-dimensional Euler-Poisson system describes the dynamic behavior of many important physical flows, yet as a hyperbolic system its solution can blow-up for some initial configurations. This article strives to advance our understanding on the critical threshold phenomena through the study of a two-dimensional modified Euler-Poisson system with a modified Riesz transform where the singularity at the origin is removed. We identify upper-thresholds for finite time blow-up of solutions for the modified Euler-Poisson equations with attractive/repulsive forcing.
Ultrashort light bullets described by the two-dimensional sine-Gordon equation
Leblond, Hervé; 10.1103/PHYSREVA.81.063815
2011-01-01
By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal wave forms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time and are therefore not steady-state lumps.
Magnetohydrodynamic cross-field boundary layer flow
Directory of Open Access Journals (Sweden)
D. B. Ingham
1982-01-01
Full Text Available The Blasius boundary layer on a flat plate in the presence of a constant ambient magnetic field is examined. A numerical integration of the MHD boundary layer equations from the leading edge is presented showing how the asymptotic solution described by Sears is approached.
Numerical study of the laminar shock boundary layer interaction
Katzer, E.
1985-02-01
The interaction of an oblique shock wave with a laminar boundary layer on an adiabatic flat plate was analyzed numerically with solutions of the two dimensional Navier-Stokes equations using McCormack's explicit finite volume method. The agreement between numerical calculations and experimental results is good. Local and global properties of the interaction region are discussed regarding shock strength, separation bubble length using a similarity law, and separation environment. The asymetrical structure inside the separation bubble produces an asymetrical shape of the wall shear stress distribution. The calculation speed was increased by algorithm vectorization on a CRAY 1S supercomputer. Further investigations for determination of a similarity law in interaction with turbulent boundary layer, of the physical mechanisms of the laminar interaction, and for study of the wall temperature transfer are recommended.
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
The dynamics of two-dimensional discrete structures is studied in the framework of the generalized two-dimensional discrete nonlinear Schrodinger equation. The nonlinear coupling in the form of the Ablowitz-Ladik nonlinearity and point impurities is taken into account. The stability properties...
Exact Solutions of Two-dimensional and Tri-dimensional Consolidation Equations
Di Francesco, Romolo
2011-01-01
The exact solution of Terzaghi's consolidation equation has further highlighted the limits of this theory in the one-dimensional field as, like Taylor's approximate solution, it overestimates the decay times of the phenomenon; on the other hand, one only needs to think about the accumulation pattern of sedimentary-basin soils to understand how their internal structure fits in more with the model of transversely isotropic medium, so as to result in the development of two- and three-dimensional consolidation models. This is the reason why, using Terzaghi's theory and his exact solution as starting point, two-dimensional and three-dimensional consolidation equations have been proposed, in an attempt to find their corresponding exact solutions which constitute more reliable forecasting models. Lastly, results show how this phenomenon is predominantly influenced by the dimensions of the horizontal plane affected by soil consolidation and permeabilities that behave according to three coordinate axes.
Generalized scale-invariant solutions to the two-dimensional stationary Navier-Stokes equations
Guillod, Julien
2014-01-01
New explicit solutions to the incompressible Navier-Stokes equations in $\\mathbb{R}^{2}\\setminus\\left\\{ \\boldsymbol{0}\\right\\}$ are determined, which generalize the scale-invariant solutions found by Hamel. These new solutions are invariant under a particular combination of the scaling and rotational symmetries. They are the only solutions invariant under this new symmetry in the same way as the Hamel solutions are the only scale-invariant solutions. While the Hamel solutions are parameterized by a discrete parameter $n$, the flux $\\Phi$ and an angle $\\theta_{0}$, the new solutions generalize the Hamel solutions by introducing an additional parameter $a$ which produces a rotation. The new solutions decay like $\\left|\\boldsymbol{x}\\right|^{-1}$ as the Hamel solutions, and exhibit spiral behavior. The new variety of asymptotes induced by the existence of these solutions further emphasizes the difficulties faced when trying to establish the asymptotic behavior of the Navier-Stokes equations in a two-dimensional ...
A numerical method for computing unsteady 2-D boundary layer flows
Krainer, Andreas
1988-01-01
A numerical method for computing unsteady two-dimensional boundary layers in incompressible laminar and turbulent flows is described and applied to a single airfoil changing its incidence angle in time. The solution procedure adopts a first order panel method with a simple wake model to solve for the inviscid part of the flow, and an implicit finite difference method for the viscous part of the flow. Both procedures integrate in time in a step-by-step fashion, in the course of which each step involves the solution of the elliptic Laplace equation and the solution of the parabolic boundary layer equations. The Reynolds shear stress term of the boundary layer equations is modeled by an algebraic eddy viscosity closure. The location of transition is predicted by an empirical data correlation originating from Michel. Since transition and turbulence modeling are key factors in the prediction of viscous flows, their accuracy will be of dominant influence to the overall results.
Stability of separating subsonic boundary layers
Masad, Jamal A.; Nayfeh, Ali H.
1994-01-01
The primary and subharmonic instabilities of separating compressible subsonic two-dimensional boundary layers in the presence of a two-dimensional roughness element on a flat plate are investigated. The roughness elements considered are humps and forward- and backward-facing steps. The use of cooling and suction to control these instabilities is studied. The similarities and differences between the instability characteristics of separating boundary layers and those of the boundary layer over a flat plate with a zero pressure gradient are pointed out and discussed. The theoretical results agree qualitatively and quantitatively with the experimental data of Dovgal and Kozlov. Cooling and suction decrease the growth rates of primary and subharmonic waves in the attached-flow regions but increase them in the separated-flow regions.
National Research Council Canada - National Science Library
S Pamuk; N Pamuk
2014-01-01
In this paper, we obtain the particular exact solutions of the two-dimensional heat and mass transfer equation with power-law temperature-dependent thermal con- ductivity using the Adomian's decomposition method...
Non-Lie Symmetry Group and New Exact Solutions for the Two-Dimensional KdV-Burgers Equation
Institute of Scientific and Technical Information of China (English)
WANG Hong; TIAN Ying-Hui; CHEN Han-Lin
2011-01-01
@@ By using the modified Clarkson-Kruskal (CK) direct method, we obtain the non-Lie symmetry group of the two-dimensional KdV-Burgers equation.Under some constraint conditions, Lie point symmetry is also obtained.Through the symmetry group, some new exact solutions of the two-dimensional KdV-Burgers equation are found.%By using the modified Clarkson-Kruskal (CK) direct method, we obtain the non-Lie symmetry group of the two-dimensional KdV-Burgers equation. Under some constraint conditions, Lie point symmetry is also obtained.Through the symmetry group, some new exact solutions of the two-dimensional KdV-Burgers equation are found.
Study of effect of a smooth hump on hypersonic boundary layer instability
Park, Donghun; Park, Seung O.
2016-12-01
Effect of a two-dimensional smooth hump on linear instability of hypersonic boundary layer is studied by using parabolized stability equations. Linear evolution of mode S over a hump is analyzed for Mach 4.5 and 5.92 flat plate and Mach 7.1 sharp cone boundary layers. Mean flow for stability analysis is obtained by solving the parabolized Navier-Stokes equations. Hump with height smaller than local boundary layer thickness is considered. The case of flat plate and sharp cone without the hump are also studied to provide comparable data. For flat plate boundary layers, destabilization and stabilization effect is confirmed for hump located at upstream and downstream of synchronization point, respectively. Results of parametric studies to examine the effect of hump height, location, etc., are also given. For sharp cone boundary layer, stabilization influence of hump is also identified for a specific range of frequency. Stabilization influence of hump on convective instability of mode S is found to be a possible cause of previous experimental observations of delaying transition in hypersonic boundary layers.
Arikan, Orhan
1994-05-01
Well bore measurements of conductivity, gravity, and surface measurements of magnetotelluric fields can be modeled as a two-dimensional integral equation with additive measurement noise. The governing integral equation has the form of convolution in the first dimension and projection in the second dimension. However, these two operations are not in separable form. In these applications, given a set of measurements, efficient and robust estimation of the underlying physical property is required. For this purpose, a regularized inversion algorithm for the governing integral equation is presented in this paper. Singular value decomposition of the measurement kernels is used to exploit convolution-projection structure of the integral equation, leading to a form where measurements are related to the physical property by a two-stage operation: projection followed by convolution. On the other hand, estimation of the physical property can be carried out by a two-stage inversion algorithm: deconvolution followed by back projection. A regularization method for the required multichannel deconvolution is given. Some important details of the algorithm are addressed in an application to wellbore induction measurements of conductivity.
Extrapolation of Nystrom solution for two dimensional nonlinear Fredholm integral equations
Guoqiang, Han; Jiong, Wang
2001-09-01
In this paper, we analyze the existence of asymptotic error expansion of the Nystrom solution for two-dimensional nonlinear Fredholm integral equations of the second kind. We show that the Nystrom solution admits an error expansion in powers of the step-size h and the step-size k. For a special choice of the numerical quadrature, the leading terms in the error expansion for the Nystrom solution contain only even powers of h and k, beginning with terms h2p and k2q. These expansions are useful for the application of Richardson extrapolation and for obtaining sharper error bounds. Numerical examples show that how Richardson extrapolation gives a remarkable increase of precision, in addition to faster convergence.
The solution of the two-dimensional sine-Gordon equation using the method of lines
Bratsos, A. G.
2007-09-01
The method of lines is used to transform the initial/boundary-value problem associated with the two-dimensional sine-Gordon equation in two space variables into a second-order initial-value problem. The finite-difference methods are developed by replacing the matrix-exponential term in a recurrence relation with rational approximants. The resulting finite-difference methods are analyzed for local truncation error, stability and convergence. To avoid solving the nonlinear system a predictor-corrector scheme using the explicit method as predictor and the implicit as corrector is applied. Numerical solutions for cases involving the most known from the bibliography line and ring solitons are given.
Malkov, Ewgenij A.; Poleshkin, Sergey O.; Kudryavtsev, Alexey N.; Shershnev, Anton A.
2016-10-01
The paper presents the software implementation of the Boltzmann equation solver based on the deterministic finite-difference method. The solver allows one to carry out parallel computations of rarefied flows on a hybrid computational cluster with arbitrary number of central processor units (CPU) and graphical processor units (GPU). Employment of GPUs leads to a significant acceleration of the computations, which enables us to simulate two-dimensional flows with high resolution in a reasonable time. The developed numerical code was validated by comparing the obtained solutions with the Direct Simulation Monte Carlo (DSMC) data. For this purpose the supersonic flow past a flat plate at zero angle of attack is used as a test case.
Derivation of asymptotic two-dimensional time-dependent equations for ocean wave propagation
Lannes, David
2007-01-01
A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic models can be recovered by a simple asymptotic expansion of this operator, in function of the shallowness parameter (shallow water limit) or the steepness parameter (deep water limit). Based on this method, a new two-dimensional fully dispersive model for small wave steepness is also derived, which extends to uneven bottom the approach developed by Matsuno \\cite{matsuno3} and Choi \\cite{choi}. This model is still valid in shallow water but with less precision than what can be achieved with Green-Naghdi model, when fully nonlinear waves are considered. The combination, or the coupling, of the new fully dispersive equati...
Institute of Scientific and Technical Information of China (English)
GONG Lun-Xun; CAO Jian-Li; PAN Jun-Ting; ZHANG Hua; JIAO Wan-Tang
2008-01-01
Based on the second integrable case of known two-dimensional Hamiltonian system with a quartic potential, we propose a 4×4 matrix spectral problem and derive a hierarchy of coupled KdV equations and their Hamiltonian structures. It is shown that solutions of the coupled KdV equations in the hierarchy are reduced to solving two compatible systems of ordinary differential equations. As an application, quite a few explicit solutions of the coupled KdV equations are obtained via using separability for the second integrable case of the two-dimensional Hamiltonian system.
Indian Academy of Sciences (India)
ALY R SEADAWY
2017-09-01
Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the twodimensional nonlinear KP equation by implementing sech–tanh, sinh–cosh, extended direct algebraic and fraction direct algebraicmethods. We found the electrostatic field potential and electric field in the form travellingwave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of $\\it{Mathematica}$ program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.
Directory of Open Access Journals (Sweden)
Chunye Gong
2014-01-01
Full Text Available It is very time consuming to solve fractional differential equations. The computational complexity of two-dimensional fractional differential equation (2D-TFDE with iterative implicit finite difference method is O(MxMyN2. In this paper, we present a parallel algorithm for 2D-TFDE and give an in-depth discussion about this algorithm. A task distribution model and data layout with virtual boundary are designed for this parallel algorithm. The experimental results show that the parallel algorithm compares well with the exact solution. The parallel algorithm on single Intel Xeon X5540 CPU runs 3.16–4.17 times faster than the serial algorithm on single CPU core. The parallel efficiency of 81 processes is up to 88.24% compared with 9 processes on a distributed memory cluster system. We do think that the parallel computing technology will become a very basic method for the computational intensive fractional applications in the near future.
Wang, Zhiheng
2014-12-10
A meshless local radial basis function method is developed for two-dimensional incompressible Navier-Stokes equations. The distributed nodes used to store the variables are obtained by the philosophy of an unstructured mesh, which results in two main advantages of the method. One is that the unstructured nodes generation in the computational domain is quite simple, without much concern about the mesh quality; the other is that the localization of the obtained collocations for the discretization of equations is performed conveniently with the supporting nodes. The algebraic system is solved by a semi-implicit pseudo-time method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly solved. The proposed method is validated by several benchmark problems, including natural convection in a square cavity, the lid-driven cavity flow, and the natural convection in a square cavity containing a circular cylinder, and very good agreement with the existing results are obtained.
Directory of Open Access Journals (Sweden)
Otstavnov Evgeniy Igorevich
2013-05-01
Full Text Available In the article, the two-dimensional boundary layer is considered on the basis of the Lagrangian approach to the continuous medium description using coordinates of particles. Classical L. Prandtl’s method of Navier-Stokes equation simplification through expansion of dependent variables in a series is applied to develop the model. Direct transformation of widely used Euler equations derived by L. Prandtl generates the same result. Boundary conditions are regarded as one-sided or non-holonomic restrictions from the viewpoint of analytical mechanics.The mass conservation equation can be detached from the main equation of motion. At the same time, one can conclude that a particle starting its motion from an internal part of the layer will remain there without reaching any boundary in a finite time. The perpendicular coordinate evolution can be calculated when one has a law of motion along the boundary employed using the standard approach to the certain PDE solution. The model presentation is based on the Hamiltonian apparatus of classical mechanics. Derivatives of spatial variables take the form of the Poisson brackets. Hence, the full equation for the Newton’s second law has acceleration and doubled application of Poisson brackets. The pressure gradient is a function of a single coordinate; therefore, it can be eliminated by another Poisson bracket application due to the symmetric property of the skew.Приведен вывод уравнений плоского пограничного слоя с использованием подхода Лагранжа. Граничные условия рассмотрены с позиций теоретической механики в качестве связей, наложенных на систему. Уравнение движения вдоль границы отделяется, что дает еще одну форму скалярного описания плоского погранслоя.
Tone, Florentina
2011-01-01
Pursuing our work in [18], [17], [20], [5], we consider in this article the two-dimensional thermohydraulics equations. We discretize these equations in time using the implicit Euler scheme and we prove that the global attractors generated by the numerical scheme converge to the global attractor of the continuous system as the time-step approaches zero.
Quenched dynamics of two-dimensional solitons and vortices in the Gross-Pitaevskii equation
Chen, Qian-Yong; Malomed, Boris A
2012-01-01
We consider a two-dimensional (2D) counterpart of the experiment that led to the creation of quasi-1D bright solitons in Bose-Einstein condensates (BECs) [Nature 417, 150--153 (2002)]. We start by identifying the ground state of the 2D Gross-Pitaevskii equation for repulsive interactions, with a harmonic-oscillator (HO) trap, and with or without an optical lattice (OL). Subsequently, we switch the sign of the interaction to induce interatomic attraction and monitor the ensuing dynamics. Regions of the stable self-trapping and catastrophic collapse of 2D fundamental solitons are identified in the parameter plane of the OL strength and BEC norm. The increase of the OL strength expands the persistence domain for the solitons to larger norms. For single-charged solitary vortices, in addition to the survival and collapse regimes, an intermediate one is identified, where the vortex resists the collapse but loses its structure, transforming into a fundamental soliton. The same setting may also be implemented in the ...
Numerical investigations on the finite time singularity in two-dimensional Boussinesq equations
Yin, Z
2006-01-01
To investigate the finite time singularity in three-dimensional (3D) Euler flows, the simplified model of 3D axisymmetric incompressible fluids (i.e., two-dimensional Boussinesq approximation equations) is studied numerically. The system describes a cap-like hot zone of fluid rising from the bottom, while the edges of the cap lag behind, forming eye-like vortices. The hot liquid is driven by the buoyancy and meanwhile attracted by the vortices, which leads to the singularity-forming mechanism in our simulation. In the previous 2D Boussinesq simulations, the symmetricial initial data is used. However, it is observed that the adoption of symmetry leads to coordinate singularity. Moreover, as demonstrated in this work that the locations of peak values for the vorticity and the temperature gradient becomes far apart as $t$ approaches the predicted blow-up time. This suggests that the symmetry assumption may be unreasonable for searching solution blow-ups. One of the main contributions of this work is to propose a...
General solution of the Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Str., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2016-06-15
The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.
Hamiltonian structure for two-dimensional extended Green-Naghdi equations
Matsuno, Yoshimasa
2016-06-01
The two-dimensional Green-Naghdi (GN) shallow-water model for surface gravity waves is extended to incorporate the arbitrary higher-order dispersive effects. This can be achieved by developing a novel asymptotic analysis applied to the basic nonlinear water wave problem. The linear dispersion relation for the extended GN system is then explored in detail. In particular, we use its characteristics to discuss the well-posedness of the linearized problem. As illustrative examples of approximate model equations, we derive a higher-order model that is accurate to the fourth power of the dispersion parameter in the case of a flat bottom topography, and address the related issues such as the linear dispersion relation, conservation laws and the pressure distribution at the fluid bottom on the basis of this model. The original Green-Naghdi (GN) model is then briefly described in the case of an uneven bottom topography. Subsequently, the extended GN system presented here is shown to have the same Hamiltonian structure as that of the original GN system. Last, we demonstrate that Zakharov's Hamiltonian formulation of surface gravity waves is equivalent to that of the extended GN system by rewriting the former system in terms of the momentum density instead of the velocity potential at the free surface.
Time integration algorithms for the two-dimensional Euler equations on unstructured meshes
Slack, David C.; Whitaker, D. L.; Walters, Robert W.
1994-06-01
Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.
Positioning in a flat two-dimensional space-time: the delay master equation
Coll, Bartolomé; Morales-Lladosa, Juan Antonio
2010-01-01
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [Phys. Rev. D {\\bf 73}, 084017 (2006); {\\bf 74}, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here we study generic relativistic positioning systems in the Minkowski plane. We analyze the information that can be obtained from the data received by a user of the positioning system. We show that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. We illustrate these result...
Theoretical Analysis of Stationary Potential Flows and Boundary Layers at High Speed
Oswaititsch, K.; Wieghardt, K.
1948-01-01
The present report consists of two parts. The first part deals with the two-dimensional stationary flow in the presence of local supersonic zones. A numerical method of integration of the equation of gas dynamics is developed. Proceeding from solutions at great distance from the body the flow pattern is calculated step by step. Accordingly the related body form is obtained at the end of the calculation. The second part treats the relationship between the displacement thickness of laminar and turbulent boundary layers and the pressure distribution at high speeds. The stability of the boundary layer is investigated, resulting in basic differences in the behavior of subsonic and supersonic flows. Lastly, the decisive importance of the boundary layer for the pressure distribution, particularly for thin profiles, is demonstrated.
Directory of Open Access Journals (Sweden)
Farshid Mirzaee
2014-06-01
Full Text Available In this paper, we present a numerical method for solving two-dimensional Fredholm–Volterra integral equations (F-VIE. The method reduces the solution of these integral equations to the solution of a linear system of algebraic equations. The existence and uniqueness of the solution and error analysis of proposed method are discussed. The method is computationally very simple and attractive. Finally, numerical examples illustrate the efficiency and accuracy of the method.
On the coupling between a supersonic boundary layer and a flexible surface
Frendi, Abdelkader; Maestrello, Lucio; Bayliss, Alvin
1992-01-01
The coupling between a two-dimensional, supersonic, laminar boundary layer and a flexible surface is studied using direct numerical computations of the Navier-Stokes equations coupled with the plate equation. The flexible surface is forced to vibrate by plane acoustic waves at normal incidence emanated by a sound source located on the side of the flexible surface opposite to the boundary layer. The effect of the source excitation frequency on the surface vibration and boundary layer stability is analyzed. We find that, for frequencies near the fifth natural frequency of the surface or lower, large disturbances are introduced in the boundary layer which may alter its stability characteristics. The interaction between a stable two-dimensional disturbance of Tollmien-Schlichting (TS) type with the vibrating surface is also studied. We find that the disturbance level is higher over the vibrating flexible surface than that obtained when the surface is rigid, which indicates a strong coupling between flow and structure. However, in the absence of the sound source the disturbance level over the rigid and flexible surfaces are identical. This result is due to the high frequency of the TS disturbance which does not couple with the flexible surface.
Maccormack, R. W.; Baldwin, B. S.
1975-01-01
A numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described. This method was originally presented in 1970 and has since been modified during the development of computer programs at Ames for implementing models that account for the effects of turbulence in shock-induced separated flows. Although this paper does not describe the turbulence models themselves, a complete description of the basic numerical method is given with emphasis on the choice of a computational mesh for high Reynolds number flows, finite-difference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.
Directory of Open Access Journals (Sweden)
H. S. Shukla
2014-11-01
Full Text Available In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.
Schlichting (Deceased), Hermann
2017-01-01
This new edition of the near-legendary textbook by Schlichting and revised by Gersten presents a comprehensive overview of boundary-layer theory and its application to all areas of fluid mechanics, with particular emphasis on the flow past bodies (e.g. aircraft aerodynamics). The new edition features an updated reference list and over 100 additional changes throughout the book, reflecting the latest advances on the subject.
Alpha models and boundary-layer turbulence
Cheskidov, Alexey
We study boundary-layer turbulence using the Navier-Stokes-alpha model obtaining an extension of the Prandtl equations for the averaged flow in a turbulent boundary layer. In the case of a zero pressure gradient flow along a flat plate, we derive a nonlinear fifth-order ordinary differential equation, an extension of the Blasius equation. We study it analytically and prove the existence of a two-parameter family of solutions satisfying physical boundary conditions. From this equation we obtain a theoretical prediction of the skin-friction coefficient in a wide range of Reynolds numbers based on momentum thickness, and deduce the maximal value of the skin-friction coefficient in the turbulent boundary layer. The two-parameter family of solutions to the equation matches experimental data in the transitional boundary layers with different free stream turbulence intensity. A one-parameter sub-family of solutions, obtained using our skin-friction coefficient law, matches experimental data in the turbulent boundary layer for moderately large Reynolds numbers.
Institute of Scientific and Technical Information of China (English)
XING Yong-Zhong
2009-01-01
The analytical solution of a multidimensional Langevin equation at the overdamping limit is obtained and the probability of particles passing over a two-dimensional saddle point is discussed. These results may break a path for studying further the fusion in superheavy elements synthesis.
Coupling Navier-stokes and Cahn-hilliard Equations in a Two-dimensional Annular flow Configuration
Vignal, Philippe
2015-06-01
In this work, we present a novel isogeometric analysis discretization for the Navier-Stokes- Cahn-Hilliard equation, which uses divergence-conforming spaces. Basis functions generated with this method can have higher-order continuity, and allow to directly discretize the higher- order operators present in the equation. The discretization is implemented in PetIGA-MF, a high-performance framework for discrete differential forms. We present solutions in a two- dimensional annulus, and model spinodal decomposition under shear flow.
DEFF Research Database (Denmark)
Khare, A.; Rasmussen, K. O.; Samuelsen, Mogens Rugholm
2010-01-01
We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the e......We show that the two-dimensional, nonlinear Schrodinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show...
The compressible Gortler problem in two-dimensional boundary layers
Dando, Andrew H.; Seddougui, Sharon O.
1993-01-01
In this paper the authors investigate the growth rates of Gortler vortices in a compressible flow in the inviscid limit of large Gortler number. Numerical solutions are obtained for O(1) wavenumbers. The further limits of (i) large Mach number and (ii) large wavenumber with O(1) Mach number are considered. It is shown that two different types of disturbance mode can appear in this problem. The first is a wall layer mode, so named as it has its eigenfunctions trapped in a thin layer near the wall. The other mode investigated is confined to a thin layer away from the wall and termed a trapped-layer mode for large wavenumbers and an adjustment-layer mode for large Mach numbers, since then this mode has its eigenfunctions concentrated in the temperature adjustment layer. It is possible to investigate the near crossing of the modes which occurs in each of the limits mentioned. The inviscid limit does not predict a fastest growing mode, but does enable a most dangerous mode to be identified for O(1) Mach number. For hypersonic flow the most dangerous mode depends on the size of the Gortler number.
ON NONLINEAR STABILITY IN NONPARALLEL BOUNDARY LAYER FLOW
Institute of Scientific and Technical Information of China (English)
TANG Deng-bin; WANG Wei-zhi
2004-01-01
The nonlinear stability problem in nonparallel boundary layer flow for two-dimensional disturbances was studied by using a newly presented method called Parabolic Stability Equations (PSE). A series of new modes generated by the nonlinear interaction of disturbance waves were tabulately analyzed, and the Mean Flow Distortion (MFD) was numerically given. The computational techniques developed, including the higher-order spectral method and the more effective algebraic mapping, increased greatly the numerical accuracy and the rate of convergence. With the predictor-corrector approach in the marching procedure, the normalization condition was satisfied, and the stability of numerical calculation could be ensured. With different initial amplitudes, the nonlinear stability of disturbance wave was studied. The results of examples show good agreement with the data given by the DNS using the full Navier-Stokes equations.
Laminar boundary-layer flow of non-Newtonian fluid
Lin, F. N.; Chern, S. Y.
1979-01-01
A solution for the two-dimensional and axisymmetric laminar boundary-layer momentum equation of power-law non-Newtonian fluid is presented. The analysis makes use of the Merk-Chao series solution method originally devised for the flow of Newtonian fluid. The universal functions for the leading term in the series are tabulated for n from 0.2 to 2. Equations governing the universal functions associated with the second and the third terms are provided. The solution together with either Lighthill's formula or Chao's formula constitutes a simple yet general procedure for the calculation of wall shear and surface heat transfer rate. The theory was applied to flows over a circular cylinder and a sphere and the results compared with published data.
Khare, Avinash; Samuelsen, Mogens R; Saxena, Avadh; 10.1088/1751-8113/43/37/375209
2010-01-01
We show that the two-dimensional, nonlinear Schr\\"odinger lattice with a saturable nonlinearity admits periodic and pulse-like exact solutions. We establish the general formalism for the stability considerations of these solutions and give examples of stability diagrams. Finally, we show that the effective Peierls-Nabarro barrier for the pulse-like soliton solution is zero.
Irshad, Ranah; Bowles, N. E.; Calcutt, S. B.; Hurley, J.
2010-10-01
The Boundary Layer Radiometer is a small, low mass (<1kg) radiometer with only a single moving part - a scan/calibration mirror. The instrument consists of a three mirror telescope system incorporating an intermediate focus for use with miniature infrared and visible filters. It also has an integrated low power blackbody calibration target to provide long-term calibration stability The instrument may be used as an upward looking boundary layer radiometer for both the terrestrial and Martian atmospheres with appropriate filters for the mid-infrared carbon dioxide band, as well as a visible channel for the detection of aerosol components such as dust. The scan mirror may be used to step through different positions from the local horizon to the zenith, allowing the vertical temperature profile of the atmosphere to be retrieved. The radiometer uses miniature infrared filter assemblies developed for previous space-based instruments by Oxford, Cardiff and Reading Universities. The intermediate focus allows for the use of upstream blocking filters and baffles, which not only simplifies the design of the filters and focal plane assembly, but also reduces the risk of problems due to stray light. Combined with the calibration target this means it has significant advantages over previous generations of small radiometers.
Institute of Scientific and Technical Information of China (English)
Bai Jing-Song; Zhang Zhan-Ji; Li Ping; Zhong Min
2006-01-01
Based on the classical Roe method, we develop an interface capture method according to the general equation of state, and extend the single-fluid Roe method to the two-dimensional (2D) multi-fluid flows, as well as construct the continuous Roe matrix for the whole flow field. The interface capture equations and fluid dynamic conservative equations are coupled together and solved by using any high-resolution schemes that usually suit for the single-fluid flows. Some numerical examples are given to illustrate the solution of 1D and 2D multi-fluid Riemann problems.
Fang, Li; Guo, Zhenhua
2016-04-01
The aim of this paper is to establish the global well-posedness and large-time asymptotic behavior of the strong solution to the Cauchy problem of the two-dimensional compressible Navier-Stokes equations with vacuum. It is proved that if the shear viscosity {μ} is a positive constant and the bulk viscosity {λ} is the power function of the density, that is, {λ=ρ^{β}} with {β in [0,1],} then the Cauchy problem of the two-dimensional compressible Navier-Stokes equations admits a unique global strong solution provided that the initial data are of small total energy. This result can be regarded as the extension of the well-posedness theory of classical compressible Navier-Stokes equations [such as Huang et al. (Commun Pure Appl Math 65:549-585, 2012) and Li and Xin (http://arxiv.org/abs/1310.1673) respectively]. Furthermore, the large-time behavior of the strong solution to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations had been also obtained.
Marco Pedro Ramirez-Tachiquin; Cesar Marco Antonio Robles Gonzalez; Rogelio Adrian Hernandez-Becerril; Ariana Guadalupe Bucio Ramirez
2013-01-01
Based upon the elements of the modern pseudoanalytic function theory, we analyze a new method for numerically solving the forward Dirichlet boundary value problem corresponding to the two-dimensional electrical impedance equation. The analysis is performed by introducing interpolating piecewise separable-variables conductivity functions in the unit circle. To warrant the effectiveness of the posed method, we consider several examples of conductivity functions, whose boundary condi...
Directory of Open Access Journals (Sweden)
shadan sadigh behzadi
2012-03-01
Full Text Available In this present paper, we solve a two-dimensional nonlinear Volterra-Fredholm integro-differential equation by using the following powerful, efficient but simple methods: (i Modified Adomian decomposition method (MADM, (ii Variational iteration method (VIM, (iii Homotopy analysis method (HAM and (iv Modified homotopy perturbation method (MHPM. The uniqueness of the solution and the convergence of the proposed methods are proved in detail. Numerical examples are studied to demonstrate the accuracy of the presented methods.
Boundary layer transition studies
Watmuff, Jonathan H.
1995-02-01
A small-scale wind tunnel previously used for turbulent boundary layer experiments was modified for two sets of boundary layer transition studies. The first study concerns a laminar separation/turbulent reattachment. The pressure gradient and unit Reynolds number are the same as the fully turbulent flow of Spalart and Watmuff. Without the trip wire, a laminar layer asymptotes to a Falkner & Skan similarity solution in the FPG. Application of the APG causes the layer to separate and a highly turbulent and approximately 2D mean flow reattachment occurs downstream. In an effort to gain some physical insight into the flow processes a small impulsive disturbance was introduced at the C(sub p) minimum. The facility is totally automated and phase-averaged data are measured on a point-by-point basis using unprecedently large grids. The evolution of the disturbance has been tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. At first, the amplitude decays exponentially with streamwise distance in the APG region, where the layer remains attached, i.e. the layer is viscously stable. After separation, the rate of decay slows, and a point of minimum amplitude is reached where the contours of the wave packet exhibit dispersive characteristics. From this point, exponential growth of the amplitude of the disturbance is observed in the detached shear layer, i.e. the dominant instability mechanism is inviscid. A group of large-scale 3D vortex loops emerges in the vicinity of the reattachment. Remarkably, the second loop retains its identify far downstream in the turbulent boundary layer. The results provide a level of detail usually associated with CFD. Substantial modifications were made to the facility for the second study concerning disturbances generated by Suction Holes for laminar flow Control (LFC). The test section incorporates suction through interchangeable porous test surfaces. Detailed studies have been made using isolated
Boundary layer transition studies
Watmuff, Jonathan H.
1995-01-01
A small-scale wind tunnel previously used for turbulent boundary layer experiments was modified for two sets of boundary layer transition studies. The first study concerns a laminar separation/turbulent reattachment. The pressure gradient and unit Reynolds number are the same as the fully turbulent flow of Spalart and Watmuff. Without the trip wire, a laminar layer asymptotes to a Falkner & Skan similarity solution in the FPG. Application of the APG causes the layer to separate and a highly turbulent and approximately 2D mean flow reattachment occurs downstream. In an effort to gain some physical insight into the flow processes a small impulsive disturbance was introduced at the C(sub p) minimum. The facility is totally automated and phase-averaged data are measured on a point-by-point basis using unprecedently large grids. The evolution of the disturbance has been tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. At first, the amplitude decays exponentially with streamwise distance in the APG region, where the layer remains attached, i.e. the layer is viscously stable. After separation, the rate of decay slows, and a point of minimum amplitude is reached where the contours of the wave packet exhibit dispersive characteristics. From this point, exponential growth of the amplitude of the disturbance is observed in the detached shear layer, i.e. the dominant instability mechanism is inviscid. A group of large-scale 3D vortex loops emerges in the vicinity of the reattachment. Remarkably, the second loop retains its identify far downstream in the turbulent boundary layer. The results provide a level of detail usually associated with CFD. Substantial modifications were made to the facility for the second study concerning disturbances generated by Suction Holes for laminar flow Control (LFC). The test section incorporates suction through interchangeable porous test surfaces. Detailed studies have been made using isolated
Sun, HongGuang; Liu, Xiaoting; Zhang, Yong; Pang, Guofei; Garrard, Rhiannon
2017-09-01
Fractional-order diffusion equations (FDEs) extend classical diffusion equations by quantifying anomalous diffusion frequently observed in heterogeneous media. Real-world diffusion can be multi-dimensional, requiring efficient numerical solvers that can handle long-term memory embedded in mass transport. To address this challenge, a semi-discrete Kansa method is developed to approximate the two-dimensional spatiotemporal FDE, where the Kansa approach first discretizes the FDE, then the Gauss-Jacobi quadrature rule solves the corresponding matrix, and finally the Mittag-Leffler function provides an analytical solution for the resultant time-fractional ordinary differential equation. Numerical experiments are then conducted to check how the accuracy and convergence rate of the numerical solution are affected by the distribution mode and number of spatial discretization nodes. Applications further show that the numerical method can efficiently solve two-dimensional spatiotemporal FDE models with either a continuous or discrete mixing measure. Hence this study provides an efficient and fast computational method for modeling super-diffusive, sub-diffusive, and mixed diffusive processes in large, two-dimensional domains with irregular shapes.
The Plasmasphere Boundary Layer
Directory of Open Access Journals (Sweden)
D. L. Carpenter
2004-12-01
Full Text Available As an inner magnetospheric phenomenon the plasmapause region is of interest for a number of reasons, one being the occurrence there of geophysically important interactions between the plasmas of the hot plasma sheet and of the cool plasmasphere. There is a need for a conceptual framework within which to examine and discuss these interactions and their consequences, and we therefore suggest that the plasmapause region be called the Plasmasphere Boundary Layer, or PBL. Such a term has been slow to emerge because of the complexity and variability of the plasma populations that can exist near the plasmapause and because of the variety of criteria used to identify the plasmapause in experimental data. Furthermore, and quite importantly in our view, a substantial obstacle to the consideration of the plasmapause region as a boundary layer has been the longstanding tendency of textbooks on space physics to limit introductory material on the plasmapause phenomenon to zeroth order descriptions in terms of ideal MHD theory, thus implying that the plasmasphere is relatively well understood. A textbook may introduce the concept of shielding of the inner magnetosphere from perturbing convection electric fields, but attention is not usually paid to the variety of physical processes reported to occur in the PBL, such as heating, instabilities, and fast longitudinal flows, processes which must play roles in plasmasphere dynamics in concert with the flow regimes associated with the major dynamo sources of electric fields. We believe that through the use of the PBL concept in future textbook discussions of the plasmasphere and in scientific communications, much progress can be made on longstanding questions about the physics involved in the formation of the plasmapause and in the cycles of erosion and recovery of the plasmasphere.
Key words. Magnetospheric physics (plasmasphere; plasma convection; MHD waves and instabilities
Structure of turbulence in three-dimensional boundary layers
Subramanian, Chelakara S.
1993-01-01
This report provides an overview of the three dimensional turbulent boundary layer concepts and of the currently available experimental information for their turbulence modeling. It is found that more reliable turbulence data, especially of the Reynolds stress transport terms, is needed to improve the existing modeling capabilities. An experiment is proposed to study the three dimensional boundary layer formed by a 'sink flow' in a fully developed two dimensional turbulent boundary layer. Also, the mean and turbulence field measurement procedure using a three component laser Doppler velocimeter is described.
Directory of Open Access Journals (Sweden)
Mohammad Siddique
2010-08-01
Full Text Available Parabolic partial differential equations with nonlocal boundary conditions arise in modeling of a wide range of important application areas such as chemical diffusion, thermoelasticity, heat conduction process, control theory and medicine science. In this paper, we present the implementation of positivity- preserving Padé numerical schemes to the two-dimensional diffusion equation with nonlocal time dependent boundary condition. We successfully implemented these numerical schemes for both Homogeneous and Inhomogeneous cases. The numerical results show that these Padé approximation based numerical schemes are quite accurate and easily implemented.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
A Finite-Element Solution of the Navier-Stokes Equations for Two-Dimensional and Axis-Symmetric Flow
Directory of Open Access Journals (Sweden)
Sven Ø. Wille
1980-04-01
Full Text Available The finite element formulation of the Navier-Stokes equations is derived for two-dimensional and axis-symmetric flow. The simple triangular, T6, isoparametric element is used. The velocities are interpolated by quadratic polynomials and the pressure is interpolated by linear polynomials. The non-linear simultaneous equations are solved iteratively by the Newton-Raphson method and the element matrix is given in the Newton-Raphson form. The finite element domain is organized in substructures and an equation solver which works on each substructure is specially designed. This equation solver needs less storage in the computer and is faster than the traditional banded equation solver. To reduce the amount of input data an automatic mesh generator is designed. The input consists of the coordinates of eight points defining each substructure with the corresponding boundary conditions. In order to interpret the results they are plotted on a calcomp plotter. Examples of plots of the velocities, the streamlines and the pressure inside a two-dimensional flow divider and an axis-symmetric expansion of a tube are shown for various Reynolds numbers.
Costigliola, V.
2010-09-01
It has long been known that specific atmospheric processes, such as weather and longer-term climatic fluctuations, affect human health. The biometeorological literature refers to this relationship as meteorotropism, defined as a change in an organism that is correlated with a change in atmospheric conditions. Plenty of (patho)physiological functions are affected by those conditions - like the respiratory diseases - and currently it is difficult to put any limits for pathologies developed in reply. Nowadays the importance of atmospheric boundary layer and health is increasingly recognised. A number of epidemiologic studies have reported associations between ambient concentrations of air pollution, specifically particulate pollution, and adverse health effects, even at the relatively low concentrations of pollution found. Since 1995 there have been over twenty-one studies from four continents that have explicitly examined the association between ambient air pollutant mixes and daily mortality. Statistically significant and positive associations have been reported in data from various locations around the world, all with varying air pollutant concentrations, weather conditions, population characteristics and public health policies. Particular role has been given to atmospheric boundary layer processes, the impact of which for specific patient-cohort is, however, not well understood till now. Assessing and monitoring air quality are thus fundamental to improve Europe's welfare. One of current projects run by the "European Medical Association" - PASODOBLE will develop and demonstrate user-driven downstream information services for the regional and local air quality sectors by combining space-based and in-situ data with models in 4 thematic service lines: - Health community support for hospitals, pharmacies, doctors and people at risk - Public information for regions, cities, tourist industry and sporting event organizers - Compliance monitoring support on particulate
A correction on two dimensional KdV equation with topography
Institute of Scientific and Technical Information of China (English)
XU Zhaoting; Efim PELINOVSKY; SHEN Guojin; Tapiana TALIPOVA
2004-01-01
The correction on the 2D KdV equation derived by Djordjevic and Redekopp is presented. A lapsus calami in the 2D KdV equation is removed by means of the conservation principle of the energy flux in a wave ray tube. The results show that the coefficient of the third term in the inhomogeneous term of 2D KdV equation in the paper of Djordjevic and Redekopp is 2, instead of 3.
Initial and Boundary Value Problems for Two-Dimensional Non-hydrostatic Boussinesq Equations
Institute of Scientific and Technical Information of China (English)
沈春; 孙梅娜
2005-01-01
Based on the theory of stratification, the weU-posedness of the initial and boundary value problems for the system of twodimensional non-hydrostatic Boussinesq equations was discussed. The sufficient and necessary conditions of the existence and uniqueness for the solution of the equations were given for some representative initial and boundary value problems. Several special cases were discussed.
Construction of Green's Functions for the Two-Dimensional Static Klein-Gordon Equation
Institute of Scientific and Technical Information of China (English)
MELNIKOV Yu. A.
2011-01-01
In contrast to the cognate Laplace equation, for which a vast number of Green's functions is available, the field is not that developed for the static Klein-Gordon equation. The latter represents, nonetheless, a natural area for application of some of the methods that are proven productive for the Laplace equation. The perspective looks especially attractive for the methods of images and eigenfunction expansion.This study is based on our experience recently gained on the construction of Green's functions for elliptic partial differential equations. An extensive list of boundary-value problems formulated for the static Klein-Gordon equation is considered. Computerfriendly representations of their Green's functions are obtained, most of which have never been published before.
Szmelter, J.; Marchant, M. J.; Evans, A.; Weatherill, N. P.
A cell vertex finite volume Jameson scheme is used to solve the 2D compressible, laminar, viscous fluid flow equations on locally embedded multiblock meshes. The proposed algorithm is applicable to both the Euler and Navier-Stokes equations. It is concluded that the adaptivity method is very successful in efficiently improving the accuracy of the solution. Both the mesh generator and the flow equation solver which are based on a quadtree data structure offer good flexibility in the treatment of interfaces. It is concluded that methods under consideration lead to accurate flow solutions.
Ibrahim, A. H.; Tiwari, S. N.; Smith, R. E.
1997-01-01
Variational methods (VM) sensitivity analysis employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.
CHEBYSHEV SPECTRAL-FINITE ELEMENT METHOD FOR TWO-DIMENSIONAL UNSTEADY NAVIER-STOKES EQUATION
Institute of Scientific and Technical Information of China (English)
Benyu Guo; Songnian He; Heping Ma
2002-01-01
A mixed Chebyshev spectral-finite element method is proposed for solving two-dimensionalunsteady Navier-Stokes equation. The generalized stability and convergence are proved.The numerical results show the advantages of this method.
Two-Dimensional Saddle Point Equation of Ginzburg-Landau Hamiltonian for the Diluted Ising Model
Institute of Scientific and Technical Information of China (English)
WU Xin-Tian
2006-01-01
@@ The saddle point equation of Ginzburg-Landau Hamiltonian for the diluted Ising model is developed. The ground state is solved numerically in two dimensions. The result is partly explained by the coarse-grained approximation.
From Discreteness to Continuity: Dislocation Equation for Two-Dimensional Triangular Lattice
Institute of Scientific and Technical Information of China (English)
WANG Shao-Feng
2007-01-01
@@ A systematic method from the discreteness to the continuity is presented for the dislocation equation of the triangular lattice. A modification of the Peierls equation has been derived strictly. The modified equation includes the higher order corrections of the discrete effect which are important for the core structure of dislocation. It is observed that the modified equation possesses a universal form which is model-independent except the factors.The factors, which depend on the detail of the model, are related to the derivatives of the kernel at its zero point in the wave-vector space. The results open a way to deal with the complicated models because what one needs to do is to investigate the behaviour near the zero point of the kernel in the wave-vector space instead of calculating the kernel completely.
Institute of Scientific and Technical Information of China (English)
HUANG RUI; YIN JING-XUE; WANG LIANG-WEI
2011-01-01
In this paper we consider the initial boundary value problem of CahnHilliard equation with concentration dependent mobility and gradient dependent potential. By the Lp type estimates and the theory of Morrey spaces, we prove the H(o)der continuity of the solutions. Then we obtain the existence of global classical solutions. The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.
An equation for pressure of a two-dimensional Yukawa liquid
Feng, Yan; Li, Wei; Wang, Qiaoling; Lin, Wei; Goree, John; Liu, Bin
2016-10-01
Thermodynamic behavior of two-dimensional (2D) dusty plasmas has been studied experimentally and theoretically recently. As a crucial parameter in thermodynamics, the pressure of dusty plasmas arises from frequent collisions of individual dust particles. Here, equilibrium molecular dynamical simulations were performed to study the pressure of 2D Yukawa liquids. A simple analytical expression for the pressure of a 2D Yukawa liquid is found by fitting the obtained pressure data over a wide range of temperatures, from the coldest close to the melting point, to the hottest about 70 times higher than the melting points. The obtained expression verifies that the pressure can be written as the sum of a potential term which is a simple multiple of the Coulomb potential energy at a distance of Wigner-Seitz radius, and a kinetic term which is a multiple of the one for an ideal gas. Dimensionless coefficients for each of these terms are found empirically, by fitting. The resulting analytical expression, with its empirically determined coefficients, is plotted as isochors, or curves of constant area. These results should be applicable to 2D dusty plasmas. Work in China supported by by the National Natural Science Foundation of China under Grant No. 11505124, the 1000 Youth Talents Plan, and startup funds from Soochow University. Work in the US supported by DOE & NSF.
Two-Dimensional Riemann Solver for Euler Equations of Gas Dynamics
Brio, M.; Zakharian, A. R.; Webb, G. M.
2001-02-01
We construct a Riemann solver based on two-dimensional linear wave contributions to the numerical flux that generalizes the one-dimensional method due to Roe (1981, J. Comput. Phys.43, 157). The solver is based on a multistate Riemann problem and is suitable for arbitrary triangular grids or any other finite volume tessellations of the plane. We present numerical examples illustrating the performance of the method using both first- and second-order-accurate numerical solutions. The numerical flux contributions are due to one-dimensional waves and multidimensional waves originating from the corners of the computational cell. Under appropriate CFL restrictions, the contributions of one-dimensional waves dominate the flux, which explains good performance of dimensionally split solvers in practice. The multidimensional flux corrections increase the accuracy and stability, allowing a larger time step. The improvements are more pronounced on a coarse mesh and for large CFL numbers. For the second-order method, the improvements can be comparable to the improvements resulting from a less diffusive limiter.
Zhang, Jiwei; Xu, Zhenli; Wu, Xiaonan
2009-04-01
This paper aims to design local absorbing boundary conditions (LABCs) for the two-dimensional nonlinear Schrödinger equations on a rectangle by extending the unified approach. Based on the time-splitting idea, the main process of the unified approach is to approximate the kinetic energy part by a one-way equation, unite it with the potential energy equation, and then obtain the well-posed and accurate LABCs on the artificial boundaries. In the corners, we use the (1,1)-Padé approximation to the kinetic term and also unite it with the nonlinear term to give some local corner boundary conditions. Numerical tests are given to verify the stable and tractable advantages of the method.
Analytical solution for the convectively-mixed atmospheric boundary layer
Ouwersloot, H.G.; Vilà-Guerau de Arellano, J.
2013-01-01
Based on the prognostic equations of mixed-layer theory assuming a zeroth order jump at the entrainment zone, analytical solutions for the boundary-layer height evolution are derived with different degrees of accuracy. First, an exact implicit expression for the boundary-layer height for a situation
Note on a differentiation formula, with application to the two-dimensional Schrödinger equation
2017-01-01
A method for obtaining discretization formulas for the derivatives of a function is presented, which relies on a generalization of divided differences. These modified divided differences essentially correspond to a change of the dependent variable. This method is applied to the numerical solution of the eigenvalue problem for the two-dimensional Schrödinger equation, where standard methods converge very slowly while the approach proposed here gives accurate results. The presented approach has the merit of being conceptually simple and might prove useful in other instances. PMID:28178300
Zabihi, F.; Saffarian, M.
2016-07-01
The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.
Effect of the acoustic boundary layer on the wave propagation in ducts
Nayfeh, A. H.
1973-01-01
An analysis is presented for the wave propagation in two-dimensional and circular lined ducts taking into account the effects of viscosity in both the mean and the acoustic problems. The method of composite expansions is used to express each acoustic flow quantity as the sum of an inviscid part and a boundary layer part insignificant outside a thin layer next to the wall. The problem is reduced to solving a second-order ordinary differential equation for the pressure perturbation as in the inviscid acoustic case but with a modified specific wall admittance. An analytic expression is presented for the variation of the modified admittance with the wall and flow parameters, such as the acoustic boundary layer thickness, the mean velocity and temperature gradients at the wall, the frequency of oscillation, and the wavelength.
Spin eigen-states of Dirac equation for quasi-two-dimensional electrons
Energy Technology Data Exchange (ETDEWEB)
Eremko, Alexander, E-mail: eremko@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Brizhik, Larissa, E-mail: brizhik@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); Loktev, Vadim, E-mail: vloktev@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine); National Technical University of Ukraine “KPI”, Peremohy av., 37, Kyiv, 03056 (Ukraine)
2015-10-15
Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.
A Genuinely Two-Dimensional Scheme for the Compressible Euler Equations
Sidilkover, David
1996-01-01
We present a new genuinely multidimensional discretization for the compressible Euler equations. It is the only high-resolution scheme known to us where Gauss-Seidel relaxation is stable when applied as a smoother directly to the resulting high-resolution scheme. This allows us to construct a very simple and highly efficient multigrid steady-state solver. The scheme is formulated on triangular (possibly unstructured) meshes.
Numerical computation of the critical energy constant for two-dimensional Boussinesq equations
Kolkovska, N.; Angelow, K.
2015-10-01
The critical energy constant is of significant interest for the theoretical and numerical analysis of Boussinesq type equations. In the one-dimensional case this constant is evaluated exactly. In this paper we propose a method for numerical evaluation of this constant in the multi-dimensional cases by computing the ground state. Aspects of the numerical implementation are discussed and many numerical results are demonstrated.
The Difference Format of Landau-Lifshitz Equation in Two-dimensional Case
Directory of Open Access Journals (Sweden)
Zhong Taiyong
2015-01-01
Full Text Available In this paper, the author considers a difference scheme of Laudau-Lifshitz equation (LL for short and modulus of unj which are constantly remaining equal to 1. Using this iteration format error which is ordered to t/2h2 , the author comes to a conclusion based on several initial simulations. According to some conditions, the author gives the numerical solution, the examples of exact solution and the error comparisons of the solutions.
MARG2D code. 1. Eigenvalue problem for two dimensional Newcomb equation
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1997-10-01
A new method and a code MARG2D have been developed to solve the 2-dimensional Newcomb equation which plays an important role in the magnetohydrodynamic (MHD) stability analysis in an axisymmetric toroidal plasma such as a tokamak. In the present formulation, an eigenvalue problem is posed for the 2-D Newcomb equation, where the weight function (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen so that an eigenfunction correctly behaves as the linear combination of the small solution and the analytical solutions around each of the rational surfaces. Thus, the difficulty on solving the 2-D Newcomb equation has been resolved. By using the MARG2D code, the ideal MHD marginally stable state can be identified for a 2-D toroidal plasma. The code is indispensable on computing the outer-region matching data necessary for the resistive MHD stability analysis. Benchmark with ERATOJ, an ideal MHD stability code, has been carried out and the MARG2D code demonstrates that it indeed identifies both stable and marginally stable states against ideal MHD motion. (author)
An adaptive, high-order phase-space remapping for the two-dimensional Vlasov-Poisson equations
Wang, Bei; Colella, Phil
2012-01-01
The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poisson solver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.
Energy Technology Data Exchange (ETDEWEB)
Chen, Yong [Ningbo Univ., Ningbo (China). Department of Mathematics; Shanghai Jiao-Tong Univ., Shangai (China). Department of Physics; Chinese Academy of sciences, Beijing (China). Key Laboratory of Mathematics Mechanization
2005-03-01
A general method to uniformly construct exact solutions in terms of special function of nonlinear partial differential equations is presented by means of a more general ansatz and symbolic computation. Making use of the general method, we can successfully obtain the solutions found by the method proposed by Fan (J. Phys. A., 36 (2003) 7009) and find other new and more general solutions, which include polynomial solutions, exponential solutions, rational solutions, triangular periodic wave solution, soliton solutions, soliton-like solutions and Jacobi, Weierstrass doubly periodic wave solutions. A general variable-coefficient two-dimensional KdV equation is chosen to illustrate the method. As a result, some new exact soliton-like solutions are obtained. planets. The numerical results are given in tables. The results are discussed in the conclusion.
T., M P Ramirez; Hernandez-Becerril, R A
2012-01-01
Based upon elements of the modern Pseudoanalytic Function Theory, we analyse a new method for numerically approaching the solution of the Dirichlet boundary value problem, corresponding to the two-dimensional Electrical Impedance Equation. The analysis is performed by interpolating piecewise separable-variables conductivity functions, that are eventually used in the numerical calculations in order to obtain finite sets of orthonormal functions, whose linear combinations succeed to approach the imposed boundary conditions. To warrant the effectiveness of the numerical method, we study six different examples of conductivity. The boundary condition for every case is selected considering one exact solution of the Electrical Impedance Equation. The work intends to discuss the contributions of these results into the field of the Electrical Impedance Tomography.
Two Hybrid Methods for Solving Two-Dimensional Linear Time-Fractional Partial Differential Equations
Directory of Open Access Journals (Sweden)
B. A. Jacobs
2014-01-01
Full Text Available A computationally efficient hybridization of the Laplace transform with two spatial discretization techniques is investigated for numerical solutions of time-fractional linear partial differential equations in two space variables. The Chebyshev collocation method is compared with the standard finite difference spatial discretization and the absolute error is obtained for several test problems. Accurate numerical solutions are achieved in the Chebyshev collocation method subject to both Dirichlet and Neumann boundary conditions. The solution obtained by these hybrid methods allows for the evaluation at any point in time without the need for time-marching to a particular point in time.
Ying, Michael; Yung, Dennis M C; Ho, Karen K L
2008-01-01
This study aimed to develop a new two-dimensional (2-D) ultrasound thyroid volume estimation equation using three-dimensional (3-D) ultrasound as the standard of reference, and to compare the thyroid volume estimation accuracy of the new equation with three previously reported equations. 2-D and 3-D ultrasound examinations of the thyroid gland were performed in 150 subjects with normal serum thyrotropin (TSH, thyroid-stimulating hormone) and free thyroxine (fT4) levels (63 men and 87 women, age range: 17 to 71 y). In each subject, the volume of both thyroid lobes was measured by 3-D ultrasound. On 2-D ultrasound, the craniocaudal (CC), lateromedial (LM) and anteroposterior (AP) dimensions of the thyroid lobes were measured. The equation was derived by correlating the volume of the thyroid lobes measured with 3-D ultrasound and the product of the three dimensions measured with 2-D ultrasound using linear regression analysis, in 75 subjects without thyroid nodule. The accuracy of thyroid volume estimation of the new equation and the three previously reported equations was evaluated and compared in another 75 subjects (without thyroid nodule, n = 30; with thyroid nodule, n = 45). It is suggested that volume of thyroid lobe may be estimated as: volume of thyroid lobe = 0.38.(CC.LM.AP) + 1.76. Result showed that the new equation (16.9% to 36.1%) had a significantly smaller thyroid volume estimation error than the previously reported equations (20.8% to 54.9%) (p thyroid volume estimation error when thyroid glands with nodules were examined (p thyroid volume equation, 2-D ultrasound can be a useful alternative in thyroid volume measurement when 3-D ultrasound is not available.
Astrophysical Boundary Layers: A New Picture
Belyaev, Mikhail; Rafikov, Roman R.; Mclellan Stone, James
2016-04-01
Accretion is a ubiquitous process in astrophysics. In cases when the magnetic field is not too strong and a disk is formed, accretion can proceed through the mid plane all the way to the surface of the central compact object. Unless that compact object is a black hole, a boundary layer will be formed where the accretion disk touches its surfaces. The boundary layer is both dynamically and observationally significant as up to half of the accretion energy is dissipated there.Using a combination of analytical theory and computer simulations we show that angular momentum transport and accretion in the boundary layer is mediated by waves. This breaks with the standard astrophysical paradigm of an anomalous turbulent viscosity that drives accretion. However, wave-mediated angular momentum transport is a natural consequence of "sonic instability." The sonic instability, which we describe analytically and observe in our simulations, is a close cousin of the Papaloizou-Pringle instability. However, it is very vigorous in the boundary layer due to the immense radial velocity shear present at the equator.Our results are applicable to accreting neutron stars, white dwarfs, protostars, and protoplanets.
Multiple paths to subharmonic laminar breakdown in a boundary layer
Zang, Thomas A.; Hussaini, M. Yousuff
1990-01-01
Numerical simulations demonstrate that laminar breakdown in a boundary layer induced by the secondary instability of two-dimensional Tollmien-Schlichting waves to three-dimensional subharmonic disturbancews need not take the conventional lambda vortex/high-shear layer path.
Global stability analysis of axisymmetric boundary layers
Vinod, N
2016-01-01
This paper presents the linear global stability analysis of the incompressible axisymmetric boundary layer on a circular cylinder. The base flow is parallel to the axis of the cylinder at inlet. The pressure gradient is zero in the streamwise direction. The base flow velocity profile is fully non-parallel and non-similar in nature. The boundary layer grows continuously in the spatial directions. Linearized Navier-Stokes(LNS) equations are derived for the disturbance flow quantities in the cylindrical polar coordinates. The LNS equations along with homogeneous boundary conditions forms a generalized eigenvalues problem. Since the base flow is axisymmetric, the disturbances are periodic in azimuthal direction. Chebyshev spectral collocation method and Arnoldi's iterative algorithm is used for the solution of the general eigenvalues problem. The global temporal modes are computed for the range of Reynolds numbers and different azimuthal wave numbers. The largest imaginary part of the computed eigenmodes are nega...
Hurricane Boundary-Layer Theory
2010-01-01
2501. Kundu PK. 1990. Fluid Mechanics . Academic Press: San Diego, USA. Kuo HL. 1982. Vortex boundary layer under quadratic surface stress. Boundary...identification of two mechanisms for the spin-up of the mean tangential circulation of a hurricane. The first involves convergence of absolute angular...momentum above the boundary layer, where this quantity is approximately conserved. This mechanism acts to spin up the outer circulation at radii
Dynamics of a two-dimensional system of rational difference equations of Leslie--Gower type
Directory of Open Access Journals (Sweden)
Kulenović MRS
2011-01-01
Full Text Available Abstract We investigate global dynamics of the following systems of difference equations x n + 1 = α 1 + β 1 x n A 1 + y n y n + 1 = γ 2 y n A 2 + B 2 x n + y n , n = 0 , 1 , 2 , … where the parameters α 1, β 1, A 1, γ 2, A 2, B 2 are positive numbers, and the initial conditions x 0 and y 0 are arbitrary nonnegative numbers. We show that this system has rich dynamics which depends on the region of parametric space. We show that the basins of attractions of different locally asymptotically stable equilibrium points or non-hyperbolic equilibrium points are separated by the global stable manifolds of either saddle points or non-hyperbolic equilibrium points. We give examples of a globally attractive non-hyperbolic equilibrium point and a semi-stable non-hyperbolic equilibrium point. We also give an example of two local attractors with precisely determined basins of attraction. Finally, in some regions of parameters, we give an explicit formula for the global stable manifold. Mathematics Subject Classification (2000 Primary: 39A10, 39A11 Secondary: 37E99, 37D10
Aizawa, N.; Kuznetsova, Z.; Toppan, F.
2016-04-01
Conformal Galilei algebras (CGAs) labeled by d, ℓ (where d is the number of space dimensions and ℓ denotes a spin-ℓ representation w.r.t. the 𝔰𝔩(2) subalgebra) admit two types of central extensions, the ordinary one (for any d and half-integer ℓ) and the exotic central extension which only exists for d = 2 and ℓ ∈ ℕ. For both types of central extensions, invariant second-order partial differential equations (PDEs) with continuous spectrum were constructed by Aizawa et al. [J. Phys. A 46, 405204 (2013)]. It was later proved by Aizawa et al. [J. Math. Phys. 3, 031701 (2015)] that the ordinary central extensions also lead to oscillator-like PDEs with discrete spectrum. We close in this paper the existing gap, constructing a new class of second-order invariant PDEs for the exotic centrally extended CGAs; they admit a discrete and bounded spectrum when applied to a lowest weight representation. These PDEs are markedly different with respect to their ordinary counterparts. The ℓ = 1 case (which is the prototype of this class of extensions, just like the ℓ = /1 2 Schrödinger algebra is the prototype of the ordinary centrally extended CGAs) is analyzed in detail.
Impermeability Through a Perforated Domain for the Incompressible two dimensional Euler Equations
Lacave, Christophe; Masmoudi, Nader
2016-09-01
We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size {\\varepsilon} separated by distances {d_{\\varepsilon}} and the fluid fills the exterior. If the inclusions are distributed on the unit square, the asymptotic behavior depends on the limit of {d_{\\varepsilon}}\\varepsilon} when {\\varepsilon} goes to zero. If {frac{d_{\\varepsilon}}\\varepsilon to infty}, then the limit motion is not perturbed by the porous medium, namely, we recover the Euler solution in the whole space. If, on the contrary, {frac{d_{\\varepsilon}}\\varepsilon to 0}, then the fluid cannot penetrate the porous region, namely, the limit velocity verifies the Euler equations in the exterior of an impermeable square. If the inclusions are distributed on the unit segment then the behavior depends on the geometry of the inclusion: it is determined by the limit of {frac{d_{\\varepsilon}/\\varepsilon^{2+frac1γ}} where {γ in (0,infty]} is related to the geometry of the lateral boundaries of the obstacles. If {d_{\\varepsilon}/\\varepsilon^{2+frac1γ} to infty}, then the presence of holes is not felt at the limit, whereas an impermeable wall appears if this limit is zero. Therefore, for a distribution in one direction, the critical distance depends on the shape of the inclusions; in particular, it is equal to {\\varepsilon3} for balls.
Institute of Scientific and Technical Information of China (English)
SONG; Yuquan(宋玉泉); LIU; Shumei(刘术梅)
2002-01-01
Superplastic forming has been extensively applied to manufacture parts and components with complex shapes or high-precisions. However, superplastic formation is in multi-stress state. In a long time, uniaxial tensile constitutive equation has been directly generalized to deal with multi-stress state. Whether so doing is feasible or not needs to be proved in theory. This paper first summarizes the establishing processes of superplastic tensile and bulging constitutive equation with variable m, and, using the analytical expressions of equivalent stress ? and equivalent strain rateof free bulge based on the fundamentals of continuum medium plastic mechanics, derives the analytical expressions of optimum loading rules for superplastic free bulge. By comparing the quantitative results on typical superplastic alloy ZnAl22, it is shown that one-dimensional tensile constitutive equations cannot be directly generalized to deal with two-dimensional bulging quantitative mechanical problems; only superplastic bulging constitutive equation based on bulging stress state can be used to treat the quantitative mechanical problems of bulge.
Nonclassical Symmetry Analysis of Heated Two-Dimensional Flow Problems
Naeem, Imran; Naz, Rehana; Khan, Muhammad Danish
2015-12-01
This article analyses the nonclassical symmetries and group invariant solution of boundary layer equations for two-dimensional heated flows. First, we derive the nonclassical symmetry determining equations with the aid of the computer package SADE. We solve these equations directly to obtain nonclassical symmetries. We follow standard procedure of computing nonclassical symmetries and consider two different scenarios, ξ1≠0 and ξ1=0, ξ2≠0. Several nonclassical symmetries are reported for both scenarios. Furthermore, numerous group invariant solutions for nonclassical symmetries are derived. The similarity variables associated with each nonclassical symmetry are computed. The similarity variables reduce the system of partial differential equations (PDEs) to a system of ordinary differential equations (ODEs) in terms of similarity variables. The reduced system of ODEs are solved to obtain group invariant solution for governing boundary layer equations for two-dimensional heated flow problems. We successfully formulate a physical problem of heat transfer analysis for fluid flow over a linearly stretching porous plat and, with suitable boundary conditions, we solve this problem.
Energy Technology Data Exchange (ETDEWEB)
Hoang-Do, Ngoc-Tram; Hoang, Van-Hung; Le, Van-Hoang [Department of Physics, Ho Chi Minh City University of Pedagogy, 280 An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-05-15
The Feranchuk-Komarov operator method is developed by combining with the Levi-Civita transformation in order to construct analytical solutions of the Schroedinger equation for a two-dimensional exciton in a uniform magnetic field of arbitrary strength. As a result, analytical expressions for the energy of the ground and excited states are obtained with a very high precision of up to four decimal places. Especially, the precision is uniformly stable for the whole range of the magnetic field. This advantage appears due to the consideration of the asymptotic behaviour of the wave-functions in strong magnetic field. The results could be used for various physical analyses and the method used here could also be applied to other atomic systems.
Directory of Open Access Journals (Sweden)
M. G. Hafez
2016-01-01
Full Text Available Two-dimensional three-component plasma system consisting of nonextensive electrons, positrons, and relativistic thermal ions is considered. The well-known Kadomtsev-Petviashvili-Burgers and Kadomtsev-Petviashvili equations are derived to study the basic characteristics of small but finite amplitude ion acoustic waves of the plasmas by using the reductive perturbation method. The influences of positron concentration, electron-positron and ion-electron temperature ratios, strength of electron and positrons nonextensivity, and relativistic streaming factor on the propagation of ion acoustic waves in the plasmas are investigated. It is revealed that the electrostatic compressive and rarefactive ion acoustic waves are obtained for superthermal electrons and positrons, but only compressive ion acoustic waves are found and the potential profiles become steeper in case of subthermal positrons and electrons.
Coherent structures in wave boundary layers. Part 1. Oscillatory motion
DEFF Research Database (Denmark)
Carstensen, Stefan; Sumer, B. Mutlu; Fredsøe, Jørgen
2010-01-01
This work concerns oscillatory boundary layers over smooth beds. It comprises combined visual and quantitative techniques including bed shear stress measurements. The experiments were carried out in an oscillating water tunnel. The experiments reveal two significant coherent flow structures: (i......) Vortex tubes, essentially two-dimensional vortices close to the bed extending across the width of the boundary-layer flow, caused by an inflectional-point shear layer instability. The imprint of these vortices in the bed shear stress is a series of small, insignificant kinks and dips. (ii) Turbulent...
Calculation of a boundary layer with phase transformations
Dorosh, N. D.; Kharitonov, A. A.
A method for the analysis of a laminar boundary layer with phase transformations is developed. It is noted that volume gas condensation can occur in the case of flow past a cooled surface, drops becoming aggregated in groups in the process of condensation. The concept of group density and concentration is proposed, and this approach is used to investigate a boundary layer near the stagnation point of a two-dimensional blunt body in a flow of molecular oxygen. Profiles of temperature, stream function, and concentration of liquid-oxygen droplet groups are determined for various values of the condensation rate.
Boundary layer control for airships
Pake, F. A.; Pipitone, S. J.
1975-01-01
An investigation is summarized of the aerodynamic principle of boundary layer control for nonrigid LTA craft. The project included a wind tunnel test on a BLC body of revolution at zero angle of attack. Theoretical analysis is shown to be in excellent agreement with the test data. Methods are evolved for predicting the boundary layer development on a body of revolution and the suction pumping and propulsive power requirements. These methods are used to predict the performance characteristics of a full-scale airship. The analysis indicates that propulsive power reductions of 15 to 25 percent and endurance improvements of 20 to 40 percent may be realized in employing boundary-layer control to nonrigid airships.
The aqueous thermal boundary layer
Katsaros, Kristina B.
1980-02-01
This article reviews the available data, measurement techniques, and present understanding of the millimeter thick aqueous thermal boundary layer. A temperature difference between the surface and lower strata, δT, of the order of a few tenths to -1 °C have been observed. Techniques ranging from miniature mercury thermometers and electrical point sensors to optical interferometry and infrared radiometry have been employed. Many processes influence the temperature structure in this thin boundary layer. Among them are: the net upward heat flux due to evaporation and sensible heat transfer; infrared and solar radiation; and the turbulence near the interface due to wind mixing, wave breaking and current shear. Presence of solute and surface-active materials stimulate or dampen these mixing processes thereby influencing boundary-layer thickness and temperature structure.
Asymptotic analysis and boundary layers
Cousteix, Jean
2007-01-01
This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The first part is devoted to a general comprehensive presentation of the tools of asymptotic analysis. It gives the keys to understand a boundary-layer problem and explains the methods to construct an approximation. The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows. The advantages of SCEM are discussed in comparison with the standard Method of Matched Asymptotic Expansions. In particular, for the first time, the theory of Interactive Boundary Layer is fully justified. With its chapter summaries, detailed derivations of results, discussed examples and fully worked out problems and solutions, the book is self-contained. It is written on a mathematical level accessible to graduate and post-graduate students of engineering and physics with a good knowledge in fluid mechanics. Researchers and practitioners will estee...
Nonparallel stability of boundary layers
Nayfeh, Ali H.
1987-01-01
The asymptotic formulations of the nonparallel linear stability of incompressible growing boundary layers are critically reviewed. These formulations can be divided into two approaches. The first approach combines a numerical method with either the method of multiple scales, or the method of averaging, of the Wentzel-Kramers-Brillouin (WKB) approximation; all these methods yield the same result. The second approach combined a multi-structure theory with the method of multiple scales. The first approach yields results that are in excellent agreement with all available experimental data, including the growth rates as well as the neutral stability curve. The derivation of the linear stability of the incompressible growing boundary layers is explained.
Stability of three-dimensional boundary layers
Nayfeh, A. H.
1979-01-01
A theory is presented for the three-dimensional stability of boundary layers. Equations are derived for the evolution of a disturbance having a given frequency and originating at a given curve. These equations are used to determine the rays along which the disturbance energy propagates. It is shown that the results can be obtained by using the saddle-point method, or kinematic wave theory, or the method of multiple scales. Extension of the theory to the case of a wave packet is also presented.
Bursting frequency prediction in turbulent boundary layers
Energy Technology Data Exchange (ETDEWEB)
LIOU,WILLIAM W.; FANG,YICHUNG
2000-02-01
The frequencies of the bursting events associated with the streamwise coherent structures of spatially developing incompressible turbulent boundary layers were predicted using global numerical solution of the Orr-Sommerfeld and the vertical vorticity equations of hydrodynamic stability problems. The structures were modeled as wavelike disturbances associated with the turbulent mean flow. The global method developed here involves the use of second and fourth order accurate finite difference formula for the differential equations as well as the boundary conditions. An automated prediction tool, BURFIT, was developed. The predicted resonance frequencies were found to agree very well with previous results using a local shooting technique and measured data.
Directory of Open Access Journals (Sweden)
A. Malvandi
2014-01-01
Full Text Available Steady two-dimensional boundary layer flow of a nanofluid past a nonlinear stretching sheet is investigated analytically using the Homotopy Analysis Method (HAM. The employed model for nanofluid includes twocomponent four-equation non-homogeneous equilibrium model that incorporates the effects of Brownian motion ( Nb , thermophoresis ( Nt and Lewis number ( Le simultaneously. The basic partial boundary layer equations have been reduced to a two-point boundary value problem via the similarity variables. Analytical results are in best agreements with those existing in the literatures. The outcomes signify the decreasing trend of heat transfer rate with thermophoresis, Brownian motion and Lewis number. However, concentration rate has a sensitive behavior with parameters, especially the Brownian motion and thermophoresis parameters. Also, the weak points of numerical methods in such problems have been mentioned and the efficiency of HAM, as an alternative approach, in solving these kinds of nonlinear coupled problems has been shown.
Institute of Scientific and Technical Information of China (English)
XIE Xiaoqiang
2012-01-01
The goal of this article is to study the boundary layer of Navier-Stokes/Allen-Cahn system in a channel at small viscosity.We prove that there exists a boundary layer at the outlet(down-wind)of thickness v,where v,is the kinematic viscosity.The convergence in L2 of the solutions of the Navier-Stokes/Allen-Cahn equations to that of the Euler/Allen-Cahn equations at the vanishing viscosity was established.In two dimensional case we are able to derive the physically relevant uniform in space and time estimates,which is derived by the idea of better control on the tangential derivative and the use of an anisotropic Sobolve imbedding.
On the global existence and uniqueness of solutions to the nonstationary boundary layer system
Institute of Scientific and Technical Information of China (English)
ZHANG; Jianwen; ZHAO; Junning
2006-01-01
In this paper, we study the problem of boundary layer for nonstationary flows of viscous incompressible fluids. There are some open problems in the field of boundary layer. The method used here is mainly based on a transformation which reduces the boundary layer system to an initial-boundary value problem for a single quasilinear parabolic equation. We prove the existence of weak solutions to the modified nonstationary boundary layer system. Moreover, the stability and uniqueness of weak solutions are discussed.
Numerical simulation of tsunami-scale wave boundary layers
DEFF Research Database (Denmark)
Williams, Isaac A.; Fuhrman, David R.
2016-01-01
demonstrating the ability to reproduce accurate velocity profiles, turbulence, and bed shear stresses on both smooth and rough beds.The validated model is then employed for the study of transient wave boundary layers at full tsunami scales,covering a wide and realistic geophysical range in terms of the flow......, is newly extended to incorporate a transitional variant of the standard two-equation k–ω turbulence closure. The developed numerical model is successfully validated against recent experimental measurements involving transient solitary wave boundary layers as well as for oscillatory flows, collectively......This paper presents a numerical study of the boundary layer flow and properties induced by tsunami-scalewaves. For this purpose, an existing one-dimensional vertical (1DV) boundary layer model, based on the horizontal component of the incompressible Reynolds-averaged Navier–Stokes (RANS) equations...
Shockwave-boundary layer interactions
Glepman, R.
2014-01-01
Shock wave-boundary layer interactions are a very common feature in both transonic and supersonic flows. They can be encountered on compressor and turbine blades, in supersonic jet inlets, on transonic wings, on the stabilization fins of missiles and in many more situations. Because of their major i
the Martian atmospheric boundary layer
DEFF Research Database (Denmark)
Petrosyan, A.; Galperin, B.; Larsen, Søren Ejling
2011-01-01
The planetary boundary layer (PBL) represents the part of the atmosphere that is strongly influenced by the presence of the underlying surface and mediates the key interactions between the atmosphere and the surface. On Mars, this represents the lowest 10 km of the atmosphere during the daytime...
Stability of Boundary Layer Flow.
1980-03-01
and Teske (1975). We can conclude (as in the case of ducting) that theoretical models of boundary layer structure and associated radar structure...FI33 (Secret). Hitney, (1978) "Surface Duct Effects," Naval Ocean Systems Center, San Diego, Calif., Report No. TD144. Lewellen, W. S., and M. E. Teske
Cyclone with boundary layer displacement
Energy Technology Data Exchange (ETDEWEB)
Gorton-Huelgerth, A.; Hoffmann, D.; Staudinger, G. [Technische Universitaet Graz, Graz (Austria). Inst. fuer Verfahrenstechnik, Abt. fuer Apparatebau und Mechanische Verfahrenstechnik
1998-12-31
In a cyclone the boundary layers at the cover plate and outside of the vortex finder are considered to affect the separation efficiency of a cyclone. To improve separation efficiency, the boundary layers at and the space between vortex finder and cover plate were investigated. Two identical cyclones, 400 mm diameter and 990 mm long were manufactured with high precision from stainless steel. One was equipped with openings for insertion of velocity probes; the opening could be closed with glass windows to allow Laser Doppler Anemometry. The other cyclone was used for testing separation efficiency. Velocity measurements by both conventional pressure probes and Laser Doppler Anemometry revealed that only a minor part of the boundary layer at the outside of the vortex finder reaches the lower end of it, because the axial velocity is slowed down drastically. Light sheet visualization showed that there exists a heavily particle loaded boundary layer at the cover plate. There are no particles at the lower part of the vortex finder. This can be explained by the radial mass exchange. The effect of vortex finder length on separation efficiency was investigated by varying the length of the vortex finder and measuring the separation efficiency using a limestone powder as test material. It was found that the separation efficiency is not sensitive to the length of the vortex finder. Particle slip increases only where the vortex finder is definitely shorter than its diameter. It was tried to improve the separation efficiency by introducing an air curtain along the vortex finder. The positive effect on separation efficiency and particle cut size is minimal. Results from velocity measurements with cylinder pressure probes in the boundary layer do not fit the results from other measurement techniques. Many older measurements were made with these probes. The conclusions drawn and the design rules deduced are to be questioned. 17 refs., 21 figs., 2 tabs.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Because of the strong structural sensitivity of superplasticity, the deformation rule must be affected by stress-state. It is necessary to prove whether one-dimensional tensile constitutive equation can be directly generalized to deal with the two-dimensional mechanical problems or not. In this paper, theoretical results of fill-forming bulge have been derived from both one-dimensional tensile and two-dimensional bulging constitutive equation with variable m value. By comparing theoretical analysis and experimental results made on typical superplastic alloy Zn-wt22%Al, it is shown that one-dimensional tensile constitutive equation cannot be directly generalized to deal with two-dimensional mechanical questions. A method to correct deviation between theoretical and experimental results is also proposed.
Stability of the laminar boundary layer for an imperfect gas
Gasperas, G.
The linear perturbation equations are derived for the general case of a compressible imperfect gas characterized by an equation of state utilizing a compressibility factor. The specific case of the Beattie-Bridgeman gas is chosen for calculation. Amplification curves calculated using the Beattie-Bridgeman equation of state for two representative flat plate boundary layers are presented.
Numerical methods for hypersonic boundary layer stability
Malik, M. R.
1990-01-01
Four different schemes for solving compressible boundary layer stability equations are developed and compared, considering both the temporal and spatial stability for a global eigenvalue spectrum and a local eigenvalue search. The discretizations considered encompass: (1) a second-order-staggered finite-difference scheme; (2) a fourth-order accurate, two-point compact scheme; (3) a single-domain Chebychev spectral collocation scheme; and (4) a multidomain spectral collocation scheme. As Mach number increases, the performance of the single-domain collocation scheme deteriorates due to the outward movement of the critical layer; a multidomain spectral method is accordingly designed to furnish superior resolution of the critical layer.
Boundary layer flow and heat transfer of Cross fluid over a stretching sheet
Khan, Masood; Rahman, Masood ur
2016-01-01
The current study is a pioneering work in presenting the boundary layer equations for the two-dimensional flow and heat transfer of the Cross fluid over a linearly stretching sheet. The system of partial differential equations is turned down into highly non-linear ordinary differential equations by applying suitable similarity transformations. The stretching sheet solutions are presented via. a numerical technique namely the shooting method and graphs are constructed for the shear-thinning as well as shear-thickening regime. The impact of the emerging parameters namely the power-law index , the local Weissenberg number and the Prandtl number on the velocity and temperature fields are investigated through graphs. Numerical values of the local skin friction coefficient and the local Nusselt number are also presented in tabular form. For some limiting cases, comparisons with previously available results in the literature are made and an excellent agreement is achieved.
Stability of compressible boundary layers
Nayfeh, Ali H.
1989-01-01
The stability of compressible 2-D and 3-D boundary layers is reviewed. The stability of 2-D compressible flows differs from that of incompressible flows in two important features: There is more than one mode of instability contributing to the growth of disturbances in supersonic laminar boundary layers and the most unstable first mode wave is 3-D. Whereas viscosity has a destabilizing effect on incompressible flows, it is stabilizing for high supersonic Mach numbers. Whereas cooling stabilizes first mode waves, it destabilizes second mode waves. However, second order waves can be stabilized by suction and favorable pressure gradients. The influence of the nonparallelism on the spatial growth rate of disturbances is evaluated. The growth rate depends on the flow variable as well as the distance from the body. Floquet theory is used to investigate the subharmonic secondary instability.
Transition in hypersonic boundary layers
Zhang, Chuanhong; Zhu, Yiding; Chen, Xi; Yuan, Huijing; Wu, Jiezhi; Chen, Shiyi; Lee, Cunbiao; Gad-el-Hak, Mohamed
2015-10-01
Transition and turbulence production in a hypersonic boundary layer is investigated in a Mach 6 wind tunnel using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. It is found that the second-mode instability is a key modulator of the transition process. Although the second-mode is primarily an acoustic wave, it causes the formation of high-frequency vortical waves, which triggers a fast transition to turbulence.
Transition in hypersonic boundary layers
Directory of Open Access Journals (Sweden)
Chuanhong Zhang
2015-10-01
Full Text Available Transition and turbulence production in a hypersonic boundary layer is investigated in a Mach 6 wind tunnel using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. It is found that the second-mode instability is a key modulator of the transition process. Although the second-mode is primarily an acoustic wave, it causes the formation of high-frequency vortical waves, which triggers a fast transition to turbulence.
Directory of Open Access Journals (Sweden)
N. N. Nefedov
2016-01-01
Full Text Available Parabolic singularly perturbed problems have been actively studied in recent years in connection with a large number of practical applications: chemical kinetics, synergetics, astrophysics, biology, and so on. In this work a singularly perturbed periodic problem for a parabolic reaction-diﬀusion equation is studied in the two-dimensional case. The case when there is an internal transition layer under unbalanced nonlinearity is considered. The internal layer is localised near the so called transitional curve. An asymptotic expansion of the solution is constructed and an asymptotics for the transitional curve is determined. The asymptotical expansion consists of a regular part, an interior layer part and a boundary part. In this work we focus on the interior layer part. In order to describe it in the neighborhood of the transition curve the local coordinate system is introduced and the stretched variables are used. To substantiate the asymptotics thus constructed, the asymptotic method of diﬀerential inequalities is used. The upper and lower solutions are constructed by suﬃciently complicated modiﬁcation of the asymptotic expansion of the solution. The Lyapunov asymptotical stability of the solution was proved by using the method of contracting barriers. This method is based on the asymptotic comparison principle and uses the upper and lower solutions which are exponentially tending to the solution to the problem. As a result, the solution is locally unique.The article is published in the authors’ wording.
Shock Wave-Boundary Layer Interaction in Forced Shock Oscillations
Institute of Scientific and Technical Information of China (English)
Piotr Doerffer; Oskar Szulc; Franco Magagnato
2003-01-01
The flow in transonic diffusers as well as in supersonic air intakes becomes often unsteady due to shock wave boundary layer interaction. The oscillations may be induced by natural separation unsteadiness or may be forced by boundary conditions. Significant improvement of CFD tools, increase of computer resources as well as development of experimental methods have again.drawn the attention of researchers to this topic.To investigate the problem forced oscillations of transonic turbulent flow in asymmetric two-dimensional Laval nozzle were considered. A viscous, perfect gas flow, was numerically simulated using the Reynolds-averaged compressible Navier-Stokes solver SPARC, employing a two-equation, eddy viscosity, turbulence closure in the URANS approach.For time-dependent and stationary flow simulations, Mach numbers upstream of the shock between 1.2 and 1.4 were considered. Comparison of computed and experimental data for steady states generally gave acceptable agreement. In the case of forced oscillations, a harmonic pressure variation was prescribed at the exit plane resulting in shock wave motion. Excitation frequencies between 0 Hz and 1024 Hz were investigated at the same pressure amplitude.The main result of the work carried out is the relation between the amplitude of the shock wave motion and the excitation frequency in the investigated range. Increasing excitation frequency resulted in decreasing amplitude of the shock movement. At high frequencies a natural mode of shock oscillation (of small amplitude) was observed which is not sensitive to forced excitement.
Bruning, J.; Dobrokhotov, S.Y.; Katsnelson, M.I.; Minenkov, D.S.
2016-01-01
We consider the two-dimensional stationary Schrodinger and Dirac equations in the case of radial symmetry. A radially symmetric potential simulates the tip of a scanning tunneling microscope. We construct semiclassical asymptotic forms for generalized eigenfunctions and study the local density of st
Institute of Scientific and Technical Information of China (English)
宋丽娜; 王维国
2012-01-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Song, Li-Na; Wang, Wei-Guo
2012-08-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Cannata, F; Nishnianidze, D N
2002-01-01
Two new methods for investigation of two-dimensional quantum systems, whose Hamiltonians are not amenable to separation of variables, are proposed. 1)The first one - $SUSY-$ separation of variables - is based on the intertwining relations of Higher order SUSY Quantum Mechanics (HSUSY QM) with supercharges allowing for separation of variables. 2)The second one is a generalization of shape invariance. While in one dimension shape invariance allows to solve algebraically a class of (exactly solvable) quantum problems, its generalization to higher dimensions has not been yet explored. Here we provide a formal framework in HSUSY QM for two-dimensional quantum mechanical systems for which shape invariance holds. Given the knowledge of one eigenvalue and eigenfunction, shape invariance allows to construct a chain of new eigenfunctions and eigenvalues. These methods are applied to a two-dimensional quantum system, and partial explicit solvability is achieved in the sense that only part of the spectrum is found analyt...
Directory of Open Access Journals (Sweden)
Bhupesh Kumar Mahatha
2016-01-01
Full Text Available Two dimensional steady hydromagnetic boundary layer flow of a viscous, incompressible, and electrically conducting nanofluid past a stretching sheet with Newtonian heating, in the presence of viscous and Joule dissipations is studied. The transport equations include the combined effects of Brownian motion and thermophoresis. The governing nonlinear partial differential equations are transformed to a set of nonlinear ordinary differential equations which are then solved using Spectral Relaxation Method (SRM and the results are validated by comparison with numerical approximations obtained using the Matlab in-built boundary value problem solver bvp4c, and with existing results available in literature. Numerical values of fluid velocity, fluid temperature and species concentration are displayed graphically versus boundary layer coordinate for various values of pertinent flow parameters whereas those of skin friction, rate of heat transfer and rate of mass transfer at the plate are presented in tabular form for various values of pertinent flow parameters. Such nanofluid flows are useful in many applications in heat transfer, including microelectronics, fuel cells, pharmaceutical processes, and hybrid-powered engines, engine cooling/vehicle thermal management, domestic refrigerator, chiller, heat exchanger, in grinding, machining and in boiler flue gas temperature reduction.
Energy Technology Data Exchange (ETDEWEB)
Hoang-Do, Ngoc-Tram [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam); Pham, Dang-Lan [Institute for Computational Science and Technology, Quang Trung Software Town, District 12, Ho Chi Minh City (Viet Nam); Le, Van-Hoang, E-mail: hoanglv@hcmup.edu.vn [Department of Physics, Ho Chi Minh City University of Pedagogy 280, An Duong Vuong Street, District 5, Ho Chi Minh City (Viet Nam)
2013-08-15
Exact numerical solutions of the Schrödinger equation for a two-dimensional exciton in a constant magnetic field of arbitrary strength are obtained for not only the ground state but also high excited states. Toward this goal, the operator method is developed by combining with the Levi-Civita transformation which transforms the problem under investigation into that of a two-dimensional anharmonic oscillator. This development of the non-perturbation method is significant because it can be applied to other problems of two-dimensional atomic systems. The obtained energies and wave functions set a new record for their precision of up to 20 decimal places. Analyzing the obtained data we also find an interesting result that exact analytical solutions exist at some values of magnetic field intensity.
Energy Technology Data Exchange (ETDEWEB)
Zhang Guangjun [School of Aerospace, Xi' an Jiao Tong University, Xi' an (China) and School of Life and Science and Technology, Xi' an Jiao Tong University, Xi' an (China) and School of Science, Air Force Engineering University, Xi' an (China)], E-mail: Zhanggj3@126.com; Xu Jianxue [School of Aerospace, Xi' an Jiao Tong University, Xi' an (China)], E-mail: jxxu@mail.xjtu.edu.cn; Wang Jue [School of Life and Science and Technology, Xi' an Jiao Tong University, Xi' an (China); Yue Zhifeng; Zou Hailin [School of Aerospace, Xi' an Jiao Tong University, Xi' an (China)
2009-11-30
In this paper stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator is analyzed by moment method. This kind of novel transition refers to the one among three potential well on two sides of bifurcation point of original system at the presence of internal noise. Several conclusions are drawn. First, the semi-analytical result of stochastic resonance induced by the novel random transitions of two-dimensional weak damping bistable Duffing oscillator can be obtained, and the semi-analytical result is qualitatively compatible with the one of Monte Carlo simulation. Second, a bifurcation of double-branch fixed point curves occurs in the moment equations with noise intensity as their bifurcation parameter. Third, the bifurcation of moment equations corresponds to stochastic resonance of original system. Finally, the mechanism of stochastic resonance is presented from another viewpoint through analyzing the energy transfer induced by the bifurcation of moment equation.
Exact solutions of a two-dimensional cubic–quintic discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Khare, Avinash; Rasmussen, Kim Ø; Samuelsen, Mogens Rugholm
2011-01-01
We show that a two-dimensional generalized cubic–quintic Ablowitz–Ladik lattice admits periodic solutions that can be expressed in analytical form. The framework for the stability analysis of these solutions is developed and applied to reveal the intricate stability behavior of this nonlinear sys...
Linear Controllers for Turbulent Boundary Layers
Lim, Junwoo; Kim, John; Kang, Sung-Moon; Speyer, Jason
2000-11-01
Several recent studies have shown that controllers based on a linear system theory work surprisingly well in turbulent flows, suggesting that a linear mechanism may play an important role even in turbulent flows. It has been also shown that non-normality of the linearized Navier-Stokes equations is an essential characteristic in the regeneration of near-wall turbulence structures in turbulent boundary layers. A few controllers designed to reduce the role of different linear mechanisms, including that to minimize the non-normality of the linearized Navier-Stokes equations, have been developed and applied to a low Reynolds nubmer turbulent channel flow. A reduced-order model containing the most controllable and observables modes is derived for each system. Other existing control schemes, such as Choi et al's opposition control, have been examined from the point of a linear system control. Further discussion on controller design, such as choice of cost function and other control parameters, will be presented.
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)
M. M. Rashidi
2012-01-01
Full Text Available In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid. It is clear that by the use of second auxiliary parameter, the straight line region in ℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a prescribed surface temperature (PST and (b prescribed heat flux (PHF. The effect of involved parameters on velocity and temperature is investigated.
Leaky waves in boundary layer flow
Pralits, Jan
2005-11-01
Linear stability analysis of boundary layer flow is traditionally performed by solving the Orr-Sommerfeld equation (OSE), either in a temporal or a spatial framework. The mode structure of the OSE is in both cases composed of a finite number of discrete modes which decay at infinity in the wall- normal direction y, and a continuous spectrum of propagating modes behaving as (±ik y) when y->∞, with real k. A peculiarity of this structure is that the number of discrete modes changes with the Reynolds number, Re. They indeed seem to disappear behind the continuous spectrum at certain Re. This phenomenon is here investigated by studying the response of the Blasius boundary layer forced instantaneously in space and time. Since the solution of the forced and homogeneous Laplace-transformed problem both depend on the free-stream boundary conditions, it is shown here that a suitable change of variables can remove the branch cut in the Laplace plane. As a result, integration of the inverse Laplace transform along the two sides of the branch cut, which gives rise to the continuous spectrum, can be replaced by a sum of residues corresponding to an additional set of discrete eigenvalues. These new modes grow at infinity in the y direction, and are analogous to the leaky waves found in the theory of optical waveguides, i.e. optical fibers, which are attenuated in the direction of the waveguide but grow unbounded in the direction perpendicular to it.
Boundary layer structure in turbulent Rayleigh-Benard convection
Shi, Nan; Schumacher, Joerg
2012-01-01
The structure of the boundary layers in turbulent Rayleigh-Benard convection is studied by means of three-dimensional direct numerical simulations. We consider convection in a cylindrical cell at an aspect ratio one for Rayleigh numbers of Ra=3e+9 and 3e+10 at fixed Prandtl number Pr=0.7. Similar to the experimental results in the same setup and for the same Prandtl number, the structure of the laminar boundary layers of the velocity and temperature fields is found to deviate from the prediction of the Prandtl-Blasius-Pohlhausen theory. Deviations decrease when a dynamical rescaling of the data with an instantaneously defined boundary layer thickness is performed and the analysis plane is aligned with the instantaneous direction of the large-scale circulation in the closed cell. Our numerical results demonstrate that important assumptions which enter existing classical laminar boundary layer theories for forced and natural convection are violated, such as the strict two-dimensionality of the dynamics or the s...
Energy Technology Data Exchange (ETDEWEB)
Shizawa, T. [Science Univ. of Tokyo (Japan); Eaton, J.K. [Stanford Univ., CA (United States). Dept. of Mechanical Engineering
1990-12-31
The interaction of a longitudinal vortex with a pressure-driven, three dimensional turbulent boundary layer was investigated experimentally. The vortex was attenuated much more rapidly in the three dimensional layer than in a two-dimensional boundary layer. The persistence for the vortex-induced perturbation was strongly dependent on the sign of the vortex.
Magnetohydrodynamic boundary layer nanofluid flow and heat transfer over a stretching surface
Ali, M.; Alim, M. A.; Nasrin, R.; Alam, M. S.; Chowdhury, M. Z. U.
2017-06-01
The present study is performed to investigate the effect of unsteadiness, stretching ratio, Brownian motion, thermophoresis and magnetic parameter on boundary layer such as momentum, thermal and nanoparticle concentration. In this respect we have considered the magnetohydrodynamic (MHD) unsteady boundary layer nanofluid flow and heat - mass transfer over a stretching surface. The dimensionless governing equations are unsteady, two-dimensional coupled and non-linear ordinary differential equations. The numerical solution is taken by applying the Nachtsgeim-Swigert shooting iteration technique along with Runge-Kutta integration scheme. The effects of various dimensionless parameters on velocity, temperature and nanoparticle concentration are discussed numerically and shown graphically. Therefore, from the figures it is observed that the results of velocity profile increases for increasing values of magnetic parameter and unsteadiness parameter but decreases for stretching ratio parameter, the temperature profile decreases in presence of Brownian motion, unsteadiness parameter, stretching ratio parameter and thermophoresis parameter but increases for magnetic parameter and, the nanoparticle concentration decreases for increasing values of thermophoresis parameter, unsteadiness parameter and stretching ratio parameter whereas the reverse trend arises for Brownian motion & magnetic parameter. For validity and accuracy the present results are compared with previously published work and found good agreement.
Thermophoretically augmented mass transfer rates to solid walls across laminar boundary layers
Gokoglu, S. A.; Rosner, D. E.
1986-01-01
Predictions of mass transfer (heavy vapor and small particle deposition) rates to solid walls, including the effects of thermal (Soret) diffusion ('thermophoresis' for small particles), are made by numerically solving the two-dimensional self-similar forced convection laminar boundary-layer equations with variable properties, covering the particle size range from vapor molecules up to the size threshold for inertial (dynamical nonequilibrium) effects. The effect of thermophoresis is predicted to be particularly important for submicron particle deposition on highly cooled solid surfaces, with corresponding enhancement factors at atmospheric conditions being over a thousand-fold at T(w)/T(e) equal to about 0.6. As a consequence of this mass transfer mechanism, the particle size dependence of the mass transfer coefficient to a cooled wall will be much weaker than for the corresponding case of isothermal capture by Brownian-convective diffusion.
Institute of Scientific and Technical Information of China (English)
Muhaimin; R. Kandasamy; Azme B. Khamis
2008-01-01
This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.
Energy Technology Data Exchange (ETDEWEB)
Lok, Yian Yian [Academic Service Center, Kolej Universiti Teknikal Kebangsaan Malaysia, 75450 Ayer Keroh, Melaka (Malaysia); Amin, Norsarahaida [Department of Mathematics, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia); Pop, Ioan [Faculty of Mathematics, University of Cluj, R-3400, CP 253, Cluj (Romania)
2003-11-01
The growth of the boundary layer flow of a viscous and incompressible micro-polar fluid started impulsively from rest near the rear stagnation point of a two-dimensional plane surface is studied theoretically. The transformed non-similar boundary-layer equations are solved numerically using a very efficient finite-difference method known as Keller-box method. This method may present well-behaved solutions for the transient (small time) solution up to the separation boundary layer flow. Numerical results are given for the reduced velocity and micro-rotation profiles, as well as for the skin friction coefficient when the material parameter K takes the values K=0 (Newtonian fluid), 0.5, 1, 1.1, 1.5, 2, 2.5 and 3 with the boundary condition for micro-rotation n=0 (strong concentration of microelements) and n=1/2 (weak concentration of microelements), respectively. Important features of these flow characteristics are shown on graphs and in tables. (authors)
The vertical structure of the boundary layer around compact objects
Hertfelder, Marius; Kley, Wilhelm
2017-09-01
Context. Mass transfer due to Roche lobe overflow leads to the formation of an accretion disk around a weakly magnetized white dwarf (WD) in cataclysmic variables. At the inner edge of the disk, the gas comes upon the surface of the WD and has to get rid of its excess kinetic energy in order to settle down on the more slowly rotating outer stellar layers. This region is known as the boundary layer (BL). Aims: In this work we investigate the vertical structure of the BL, which is still poorly understood. We shall provide details of the basic structure of the two-dimensional (2D) BL and how it depends on parameters such as stellar mass and rotation rate, as well as the mass-accretion rate. We further investigate the destination of the disk material and compare our results with previous one-dimensional (1D) simulations. Methods: We solve the 2D equations of radiation hydrodynamics in a spherical (r-ϑ) geometry using a parallel grid-based code that employs a Riemann solver. The radiation energy is considered in the two-temperature approach with a radiative flux given by the flux-limited diffusion approximation. Results: The BL around a non-rotating WD is characterized by a steep drop in angular velocity over a width of only 1% of the stellar radius, a heavy depletion of mass, and a high temperature ( 500 000 K) as a consequence of the strong shear. Variations in Ω∗,M∗, and Ṁ influence the extent of the changes of the variables in the BL but not the general structure. Depending on Ω∗, the disk material travels up to the poles or is halted at a certain latitude. The extent of mixing with the stellar material also depends on Ω∗. We find that the 1D approximation matches the 2D data well, apart from an underestimated temperature.
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...
Effect of roughness on the stability of boundary layers
Nayfeh, Ali H.; Ragab, Saad A.; Al-Maaitah, Ayman
1987-01-01
An analysis is conducted on the effect of imperfections consisting of humps and dips on the stability of incompressible flows over flat plates. The mean flow is calculated using interacting boundary layers. Linear quasiparallel spatial stability is used to calculate the growth rates and mode shapes of two-dimensional disturbances. Then, the amplification factor is computed. A search for the most dangerous frequency is conducted based on an amplification factor of 9 in the shortest distance. Correlations are made with the transition experiment of Walker and Greening using the e sup 9 method.
Modelling stable atmospheric boundary layers over snow
Sterk, H.A.M.
2015-01-01
Thesis entitled: Modelling Stable Atmospheric Boundary Layers over Snow H.A.M. Sterk Wageningen, 29th of April, 2015 Summary The emphasis of this thesis is on the understanding and forecasting of the Stable Boundary Layer (SBL) over snow-covered surfaces. SBLs typically form at night and in polar re
Modelling stable atmospheric boundary layers over snow
Sterk, H.A.M.
2015-01-01
Thesis entitled: Modelling Stable Atmospheric Boundary Layers over Snow H.A.M. Sterk Wageningen, 29th of April, 2015 Summary The emphasis of this thesis is on the understanding and forecasting of the Stable Boundary Layer (SBL) over snow-covered surfaces. SBLs typically form at night and in polar re
Modelling stable atmospheric boundary layers over snow
Sterk, H.A.M.
2015-01-01
Thesis entitled: Modelling Stable Atmospheric Boundary Layers over Snow H.A.M. Sterk Wageningen, 29th of April, 2015 Summary The emphasis of this thesis is on the understanding and forecasting of the Stable Boundary Layer (SBL) over snow-covered surfaces. SBLs typically form at night and in polar
Directory of Open Access Journals (Sweden)
Qingxue Huang
2017-01-01
Full Text Available In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent.
Experimental investigation of wave boundary layer
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2003-01-01
A review is presented of experimental investigation of wave boundary layer. The review is organized in six main sections. The first section describes the wave boundary layer in a real-life environment and its simulation in the laboratory in an oscillating water tunnel and in a water tank...... with an oscillating seabed. A brief account is given of measured quantities, measurement techniques (LDA, PIV, flow visualization) and limitations/constraints in the experimental investigation of the wave boundary layer in the laboratory. The second section concentrates on uniform oscillating boundary layers...... with a smooth bed. The boundary layer process is described over the entire range of the Reynolds number (Re from practically nil to Re = O(107)), from the laminar regime to the transitional regime and to the fully developed turbulent regime. The third section focuses on the effect of the boundary roughness...
Structure of relaminarizing turbulent boundary layers
Ramesh, O.; Patwardhan, Saurabh
2014-11-01
Relaminarization of a turbulent boundary layer in a strongly accelerated flow has received a great attention in recent times. It has been found that such relaminarization is a general and regularly occurring phenomenon in the leading-edge region of a swept wing of an airplane (van Dam et al., 1993). In this work, we investigate the effect of initial Reynolds number on the process of relaminarization in turbulent boundary layers. The experimental and numerical investigation of relaminarizing turbulent boundary layers undergoing same history reveals that the boundary layer with higher initial Reynolds number relaminarizes at a lower pressure gradient value compared to the one with lower Reynolds number. This effect can be explained on the inviscid theory proposed earlier in the literature. Further, various parameter criteria proposed to predict relaminarization, are assessed and the structure of relaminarizing boundary layers is investigated. A mechanism for stabilization of near-wall low speed streaks is proposed.
Surface modes in sheared boundary layers over impedance linings
Brambley, E. J.
2013-08-01
Surface modes, being duct modes localized close to the duct wall, are analysed within a lined cylindrical duct with uniform flow apart from a thin boundary layer. As well as full numerical solutions of the Pridmore-Brown equation, simplified mathematical models are given where the duct lining and boundary layer are lumped together and modelled using a single boundary condition (a modification of the Myers boundary condition previously proposed by the author), from which a surface mode dispersion relation is derived. For a given frequency, up to six surface modes are shown to exist, rather than the maximum of four for uniform slipping flow. Not only is the different number and behaviour of surface modes important for frequency-domain mode-matching techniques, which depend on having found all relevant modes during matching, but the thin boundary layer is also shown to lead to different convective and absolute stability than for uniform slipping flow. Numerical examples are given comparing the predictions of the surface mode dispersion relation to full solutions of the Pridmore-Brown equation, and the accuracy with which surface modes are predicted is shown to be significantly increased compared with the uniform slipping flow assumption. The importance of not only the boundary layer thickness but also its profile (tanh or linear) is demonstrated. A Briggs-Bers stability analysis is also performed under the assumption of a mass-spring-damper or Helmholtz resonator impedance model.
Particulate plumes in boundary layers with obstacles
Petrosyan, Arakel; Karelsky, Kirill
2013-04-01
This presentation is aimed at creating and realization of new physical model of impurity transfer (solid particles and heavy gases) in areas with non-flat and/or nonstationary boundaries. The main idea of suggested method is to use non-viscous equations for solid particles transport modeling in the vicinity of complex boundary. In viscous atmosphere with as small as one likes coefficient of molecular viscosity, the non-slip boundary condition on solid surface must be observed. This postulates the reduction of velocity to zero at a solid surface. It is unconditionally in this case Prandtle hypothesis must be observed: for rather wide range of conditions in the surface neighboring layers energy dissipation of atmosphere flows is comparable by magnitude with manifestation of inertia forces. That is why according to Prandtle hypothesis in atmosphere movement characterizing by a high Reynolds number the boundary layer is forming near a planet surface, within which the required transition from zero velocities at the surface to magnitudes at the external boundary of the layer that are quite close to ones in ideal atmosphere flow. In that layer fast velocity gradients cause viscous effects to be comparable in magnitude with inertia forces influence. For conditions considered essential changes of hydrodynamic fields near solid boundary caused not only by non-slip condition but also by a various relief of surface: mountains, street canyons, individual buildings. Transport of solid particles, their ascent and precipitation also result in dramatic changes of meteorological fields. As dynamic processes of solid particles transfer accompanying the flow past of complex relief surface by wind flows is of our main interest we are to use equations of non-viscous hydrodynamic. We should put up with on the one hand idea of big wind gradients in the boundary layer and on the other hand disregard of molecular viscosity in two-phase atmosphere equations.We deal with describing big field
Institute of Scientific and Technical Information of China (English)
莫则尧; 符尚武
2003-01-01
Two dimensional three temperatures energy equation is a kind of very impor-tant partial differential equation. In general, we discrete such equation with full implicit nine points stencil on Lagrange structured grid and generate a non-linear sparse algebraic equation including nine diagonal lines. This paper will discuss the iterative solver for such non-linear equations. We linearize the equations by fixing the coefficient matrix, and iteratively solve the linearized algebraic equation with Krylov subspace iterative method. We have applied the iterative method presented in this paper to the code Lared-Ⅰ for numerical simulation of two dimensional threetemperatures radial fluid dynamics, and have obtained efficient results.
Energy Technology Data Exchange (ETDEWEB)
Kravchenko, Vladislav V [Seccion de Posgrado e Investigacion, Escuela Superior de IngenierIa Mecanica y Electrica, Instituto Politecnico Nacional, C.P.07738 Mexico DF (Mexico)
2005-05-06
We consider the real stationary two-dimensional Schroedinger equation. With the aid of any of its particular solutions, we construct a Vekua equation possessing the following special property. The real parts of its solutions are solutions of the original Schroedinger equation and the imaginary parts are solutions of an associated Schroedinger equation with a potential having the form of a potential obtained after the Darboux transformation. Using Bers' theory of Taylor series for pseudoanalytic functions, we obtain a locally complete system of solutions of the original Schroedinger equation which can be constructed explicitly for an ample class of Schroedinger equations. For example it is possible when the potential is a function of one Cartesian, spherical, parabolic or elliptic variable. We give some examples of application of the proposed procedure for obtaining a locally complete system of solutions of the Schroedinger equation. The procedure is algorithmically simple and can be implemented with the aid of a computer system of symbolic or numerical calculation.
DEFF Research Database (Denmark)
Gaididei, Yu. B.; Christiansen, Peter Leth
2008-01-01
We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered...... and unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under...
Footprints of funnel vortices in a turbulent boundary layer
Gurka, Roi; Liberzon, Alex; Hetsroni, Gad
2003-11-01
The topology of large scale funnel structures in a turbulent boundary layer in a flume is investigated experimentally. The large scale structure is reconstructed from the proper orthogonal decomposition (POD) eigenmodes, calculated from the two-dimensional projections of the fluctuated vorticity field realizations. The instantaneous two-dimensional velocity field realizations are obtained using Particle Image Velocimetry (PIV) technique. The dominant funnel structure appears to have a longitudinal streamwise orientation, an inclination angle of 8 degrees, streamwise length of 1000 wall units, and a distance between the neighboring structures of about 100 wall units in the spanwise direction. The spatial characteristics of the funnel structure, measured in the streamwise - wall normal plane of the flume, has been found to be independent of the Reynolds number. The identification technique is based on all the data set and provide a statistical descrition of the structure footprint.
New Algebraic Approaches to Classical Boundary Layer Problems
Institute of Scientific and Technical Information of China (English)
Xiao Ping XU
2011-01-01
Classical non-steady boundary layer equations are fundamental nonlinear partial differential equations in the boundary layer theory of fluid dynamics. In this paper, we introduce various schemes with multiple parameter functions to solve these equations and obtain many families of new explicit exact solutions with multiple parameter functions. Moreover, symmetry transformations are used to simplify our arguments. The technique of moving frame is applied in the three-dimensional case in order to capture the rotational properties of the fluid. In particular, we obtain a family of solutions singular on any moving surface, which may be used to study turbulence. Many other solutions are analytic related to trigonometric and hyperbolic functions, which reflect various wave characteristics of the fluid. Our solutions may also help engineers to develop more effective algorithms to find physical numeric solutions to practical models.
Jansen, TL; Hayashi, T; Zhuang, W; Mukamel, S
2005-01-01
The effects of hydrogen-bond forming and breaking kinetics on the linear and coherent third-order infrared spectra of the OH stretch of HOD in D2O are described by Markovian, not necessarily Gaussian, fluctuations and simulated using the stochastic Liouville equations. Slow (0.5 ps) fluctuations are
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of pressure gradient and the historical variation of eddy viscosity, so the model is with memory. Numerical calculation by solving boundary layer equations was carried out for the five pressure driven three dimensional turbulent boundary layers developed on flat plates, swept-wing, and prolate spheroid in symmetrical plane. Comparing the computational results with the experimental data, it is obvious that the prediction will be more accurate if the proposed closure equations are used, especially for the turbulent shear stresses.
A new numerical method for solving two-dimensional variable-order anomalous sub-diffusion equation
Directory of Open Access Journals (Sweden)
Jiang Wei
2016-01-01
Full Text Available The novelty and innovativeness of this paper are the combination of reproducing kernel theory and spline, this leads to a new simple but effective numerical method for solving variable-order anomalous sub-diffusion equation successfully. This combination overcomes the weaknesses of piecewise polynomials that can not be used to solve differential equations directly because of lack of the smoothness. Moreover, new bases of reproducing kernel spaces are constructed. On the other hand, the existence of any ε-approximate solution is proved and an effective method for obtaining the ε-approximate solution is established. A numerical example is given to show the accuracy and effectiveness of theoretical results.
Effect of a bulge on the secondary instability of boundary layers
Nayfeh, Ali H.; Ragab, Saad A.
1987-01-01
The influence of a two-dimensional hump on the three-dimensional (3-D) subharmonic secondary instability on a flat plate is investigated. The mean flow is calculated using interacting boundary layers, thereby accounting for the inviscid/viscous interaction. The primary wave is taken in the form of a two-dimensional (2-D) Tollmien-Schlichting (T-S) wave. The secondary wave is taken in the form of a 3-D subharmonic T-S wave.
Directory of Open Access Journals (Sweden)
Puskar Raj SHARMA
2012-01-01
Full Text Available Aim of the paper is to investigate solution of twodimensional linear parabolic partial differential equation with non-local boundary conditions using Homotopy Perturbation Method (HPM. This method is not only reliable in obtaining solution of such problems in series form with high accuracy but it also guarantees considerable saving of the calculation volume and time as compared to other methods. The application of the method has been illustrated through an example
DNS of compressible turbulent boundary layer around a sharp cone
Institute of Scientific and Technical Information of China (English)
LI XinLiang; FU DeXun; MA YanWen
2008-01-01
Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh-order up-wind biased finite difference scheme and sixth-order central difference scheme.The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch.The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer,Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow.The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations,The turbulent energy equation in the cylindrical coordinate is given and turbulent en-ergy budget is studied.The computed results show that the effect of circumferen-tial curvature on turbulence characteristics is not obvious.
Institute of Scientific and Technical Information of China (English)
Ying-hui ZHANG; Zhong TAN
2011-01-01
In this paper,we are concerned with the asymptotic behaviour of a weak solution to the NavierStokes equations for compressible barotropic flow in two space dimensions with the pressure function satisfying p(ρ) =a(ρ)logd(ρ) for large (ρ).Here d ＞ 2,a ＞ 0.We introduce useful tools from the theory of Orlicz spaces and construct a suitable function which approximates the density for time going to infinity.Using properties of this function,we can prove the strong convergence of the density to its limit state.The behaviour of the velocity field and kinetic energy is also briefly discussed.
Prediction of mean flow data for adiabatic 2-D compressible turbulent boundary layers
Motallebi, F.
1997-01-01
This book presents a method for the prediction of mean flow data (i.e. skin friction, velocity profile and shape parameter) for adiabatic two-dimensional compressible turbulent boundary layers at zero pressure gradient. The transformed law of the wall, law of the lake, the van Driest model for the
Prediction of mean flow data for adiabatic 2-D compressible turbulent boundary layers
Motallebi, F.
1997-01-01
This book presents a method for the prediction of mean flow data (i.e. skin friction, velocity profile and shape parameter) for adiabatic two-dimensional compressible turbulent boundary layers at zero pressure gradient. The transformed law of the wall, law of the lake, the van Driest model for the c
Oyegbesan, A. O.; Algermissen, J.
1986-01-01
A numerical investigation of heat and mass transfer in a dissociated laminar boundary layer of air on an isothermal flat plate is carried out for different degrees of cooling of the wall. A finite-difference chemical model is used to study elementary reactions involving NO2 and N2O. The analysis is based on equations of continuity, momentum, energy, conservation and state for the two-dimensional viscous flow of a reacting multicomponent mixtures. Attention is given to the effects of both catalyticity and noncatalyticity of the wall.
Energy Technology Data Exchange (ETDEWEB)
Djouder, M., E-mail: djouder-madjid@ummto.dz; Kermoun, F.; Mitiche, M. D.; Lamrous, O. [Laboratoire de Physique et Chimie Quantique, Université Mouloud Mammeri Tizi-Ouzou, BP 17 RP, 15000 Tizi-Ouzou (Algeria)
2016-01-15
Dust particles observed in universe as well as in laboratory and technological plasma devices are still under investigation. At low temperature, these particles are strongly negatively charged and are able to form a 2D or 3D coulomb crystal. In this work, our aim was to check the ideal gas law validity for a 2D single-layer dust crystal recently reported in the literature. For this purpose, we have simulated, using the molecular dynamics method, its thermodynamic properties for different values of dust particles number and confinement parameters. The obtained results have allowed us to invalidate the ideal gas behaviour and to propose an effective equation of state which assumes a near zero dust temperature. Furthermore, the value of the calculated sound velocity was found to be in a good agreement with experimental data published elsewhere.
Hsieh, Y. H.; Yu, Y. T.; Tuan, P. H.; Tung, J. C.; Huang, K. F.; Chen, Y. F.
2017-02-01
The trajectory equations for classical periodic orbits in the equilateral-triangular and circular billiards are systematically extracted from quantum stationary coherent states. The relationship between the phase factors of quantum stationary coherent states and the initial positions of classical periodic orbits is analytically derived. In addition, the stationary coherent states with noncoprime parametric numbers are shown to correspond to the multiple periodic orbits, which cannot be explicable in the one-particle picture. The stationary coherent states are further verified to be linked to the resonant modes that are generally observed in the experimental wave system excited by a localized and unidirectional source. The excellent agreement between the resonant modes and the stationary coherent states not only manifests the importance of classical features in experimental systems but also paves the way to manipulate the mesoscopic wave functions localized on the periodic orbits for applications.
Three-dimensional stability of growing boundary layers
Nayfeh, A. H.
1980-01-01
A theory is developed for the linear stability of three-dimensional growing boundary layers. The method of multiple scales is used to derive partial-differential equations describing the temporal and spatial evolution of the complex amplitudes and wavenumbers of the disturbances. In general, these equations are elliptic unless certain conditions are satisfied. For a monochromatic disturbance, these conditions demand that the ratio of the components of the complex group velocity be real and thereby relate the direction of growth of the disturbance to the disturbance wave angle. For a nongrowing boundary layer, this condition reduces to d-alpha/d-beta being real, in agreement with the result obtained by using the saddle-point method. For a wavepacket, these conditions demand that the components of the group velocity be real.
Goertler instability. [for boundary layer flow over curved walls
Ragab, S. A.; Nayfeh, A. H.
1981-01-01
Goertler instability for boundary-layer flows over generally curved walls is considered. The full-linearized disturbance equations are obtained in an orthogonal curvilinear coordinate system. A perturbation procedure to account for second-order effects is used to determine the effects of the displacement thickness and the variation of the streamline curvature on the neutral stability of the Blasius flow. The streamwise pressure gradient in the mean flow is accounted for by solving the nonsimilar boundary-layer equations. Growth rates are obtained for the actual mean flow and compared with those for the Blasius flow and the Falkner-Skan flows. The results demonstrate the strong influence of the streamwise pressure gradient and the nonsimilarity of the basic flow on the stability characteristics.
Transient thermal response of turbulent compressible boundary layers
DEFF Research Database (Denmark)
Li, Hongwei; Nalim, M. Razi; Merkle, Charles L.
2011-01-01
and Smith, and the turbulent Prandtl number formulation originally developed by Kays and Crawford. The governing differential equations are discretized with the Keller-box method. The numerical accuracy is validated through grid-independence studies and comparison with the steady state solution......-dimensional semi-infinite flat plate. The compressible Reynolds-averaged boundary layer equations are transformed into incompressible form through the Dorodnitsyn-Howarth transformation and then solved with similarity transformations. Turbulence is modeled using a two-layer eddy viscosity model developed by Cebeci....... In turbulent flow as in laminar, the transient heat transfer rates are very different from that obtained from quasi-steady analysis. It is found that the time scale for response of the turbulent boundary layer to far-field temperature changes is 40% less than for laminar flow, and the turbulent local Nusselt...
BUBBLE - an urban boundary layer meteorology project
DEFF Research Database (Denmark)
Rotach, M.W.; Vogt, R.; Bernhofer, C.
2005-01-01
The Basel urban Boundary Layer Experiment (BUBBLE) was a year-long experimental effort to investigate in detail the boundary layer structure in the City of Basel, Switzerland. At several sites over different surface types (urban, sub-urban and rural reference) towers up to at least twice the main...... a very detailed physical scale-model in a wind tunnel. In the present paper details of all these activities are presented together with first results....
Bakar, Nor Ashikin Abu; Bachok, Norfifah; Arifin, Norihan Md.
2016-06-01
The study of the steady two dimensional boundary layer flow of a copper (Cu)-water nanofluid on a moving plate is investigated. The assumption is the plate moves in the same or opposite direction to the free stream. The nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using a similarity variables,then a shooting technique is used to solved it numerically. The numerical results for skin friction coefficient, the local Nusselt number, the local Sherwood number as well as the velocity, temperature and concentration profiles are obtained. The effect of nanoparticle volume fraction, Brownian motion and thermophoresis parameters on heat transfer are examined. The results show that the local Nusselt number and the local Sherwood number increase with increasing in the Brownian motion parameter Nb and thermophoresis parameter Nt.
Boundary Layers in Laminar Vortex Flows.
Baker, Glenn Leslie
A detailed experimental study of the flow in an intense, laminar, axisymmetric vortex has been conducted in the Purdue Tornado Vortex Simulator. The complicated nature of the flow in the boundary layer of laboratory vortices and presumably on that encountered in full-scale tornadoes has been examined. After completing a number of modifications to the existing facility to improve the quality of the flow in the simulator, hot-film anemometry was employed for making velocity-component and turbulence-intensity measurements of both the free-stream and boundary layer portions of the flow. The measurements represent the first experimental boundary layer investigation of a well-defined vortex flow to appear in the literature. These results were compared with recent theoretical work by Burggraf, Stewartson and Belcher (1971) and with an exact similarity solution for line-sink boundary layers developed by the author. A comparison is also made with the numerical simulation of Wilson (1981) in which the boundary conditions were matched to those of the present experimental investigation. Expressions for the vortex core radius, the maximum tangential velocity and the maximum pressure drop are given in terms of dimensionless modeling parameters. References. Burggraf, O. R., K. Stewartson and R. Belcher, Boundary layer. induced by a potential vortex. Phys. Fluids 14, 1821-1833 (1971). Wilson, T., M. S. thesis, Vortex Boundary Layer Dynamics, Univ. Calif. Davis (1981).
Neutral stability calculations for boundary-layer flows
Nayfeh, A. H.; Padhye, A.
1980-01-01
An analysis is presented of the parallel neutral stability of three-dimensional incompressible, isothermal boundary-layer flows. A Taylor-series expansion of the dispersion relation is used to derive the general eigenvalues. These equations are functions of the complex group velocity. These relations are verified by numerical results obtained for two- and three-dimensional disturbances in two- and three-dimensional flows.
Simulation of hypersonic shock wave - laminar boundary layer interactions
Kianvashrad, N.; Knight, D.
2017-06-01
The capability of the Navier-Stokes equations with a perfect gas model for simulation of hypersonic shock wave - laminar boundary layer interactions is assessed. The configuration is a hollow cylinder flare. The experimental data were obtained by Calspan-University of Buffalo (CUBRC) for total enthalpies ranging from 5.07 to 21.85 MJ/kg. Comparison of the computed and experimental surface pressure and heat transfer is performed and the computed §ow¦eld structure is analyzed.
Halliday, I; Lishchuk, S V; Spencer, T J; Pontrelli, G; Evans, P C
2016-08-01
We present a method for applying a class of velocity-dependent forces within a multicomponent lattice Boltzmann equation simulation that is designed to recover continuum regime incompressible hydrodynamics. This method is applied to the problem, in two dimensions, of constraining to uniformity the tangential velocity of a vesicle membrane implemented within a recent multicomponent lattice Boltzmann simulation method, which avoids the use of Lagrangian boundary tracers. The constraint of uniform tangential velocity is carried by an additional contribution to an immersed boundary force, which we derive here from physical arguments. The result of this enhanced immersed boundary force is to apply a physically appropriate boundary condition at the interface between separated lattice fluids, defined as that region over which the phase-field varies most rapidly. Data from this enhanced vesicle boundary method are in agreement with other data obtained using related methods [e.g., T. Krüger, S. Frijters, F. Günther, B. Kaoui, and J. Harting, Eur. Phys. J. 222, 177 (2013)10.1140/epjst/e2013-01834-y] and underscore the importance of a correct vesicle membrane condition.
Settle, Sean O.
2013-01-01
The primary aim of this paper is to answer the question, What are the highest-order five- or nine-point compact finite difference schemes? To answer this question, we present several simple derivations of finite difference schemes for the one- and two-dimensional Poisson equation on uniform, quasi-uniform, and nonuniform face-to-face hyperrectangular grids and directly prove the existence or nonexistence of their highest-order local accuracies. Our derivations are unique in that we do not make any initial assumptions on stencil symmetries or weights. For the one-dimensional problem, the derivation using the three-point stencil on both uniform and nonuniform grids yields a scheme with arbitrarily high-order local accuracy. However, for the two-dimensional problem, the derivation using the corresponding five-point stencil on uniform and quasi-uniform grids yields a scheme with at most second-order local accuracy, and on nonuniform grids yields at most first-order local accuracy. When expanding the five-point stencil to the nine-point stencil, the derivation using the nine-point stencil on uniform grids yields at most sixth-order local accuracy, but on quasi- and nonuniform grids yields at most fourth- and third-order local accuracy, respectively. © 2013 Society for Industrial and Applied Mathematics.
Mclean, J. D.; Randall, J. L.
1979-01-01
A system of computer programs for calculating three dimensional transonic flow over wings, including details of the three dimensional viscous boundary layer flow, was developed. The flow is calculated in two overlapping regions: an outer potential flow region, and a boundary layer region in which the first order, three dimensional boundary layer equations are numerically solved. A consistent matching of the two solutions is achieved iteratively, thus taking into account viscous-inviscid interaction. For the inviscid outer flow calculations, the Jameson-Caughey transonic wing program FLO 27 is used, and the boundary layer calculations are performed by a finite difference boundary layer prediction program. Interface programs provide communication between the two basic flow analysis programs. Computed results are presented for the NASA F8 research wing, both with and without distributed surface suction.
Calculation of Turbulent Boundary Layers Using the Dissipation Integral Method
Institute of Scientific and Technical Information of China (English)
MatthiasBuschmann
1999-01-01
This paper gives an introduction into the dissipation integral method.The general integral equations for the three-dimensional case are derved.It is found that for a practical calculation algorithm the integral monentum equation and the integral energy equation are msot useful.Using Two different sets of mean velocity profiles the hyperbolical character of a dissipation integral method is shown.Test cases for two-and three-dimensional boundary layers are analysed and discussed.The paper concludes with a discussion of the advantages and limits of dissipation integral methods.
JavanNezhad, R.; Meshkatee, A. H.; Ghader, S.; Ahmadi-Givi, F.
2016-09-01
This study is devoted to application of the fourth-order compact MacCormack scheme to spatial differencing of the conservative form of two-dimensional and non-hydrostatic equation of a dry atmosphere. To advance the solution in time a four-stage Runge-Kutta method is used. To perform the simulations, two test cases including evolution of a warm bubble and a cold bubble in a neutral atmosphere with open and rigid boundaries are employed. In addition, the second-order MacCormack and the standard fourth-order compact MacCormack schemes are used to perform the simulations. Qualitative and quantitative assessment of the numerical results for different test cases exhibit the superiority of the fourth-order compact MacCormack scheme on the second-order method.
Golbabai, Ahmad; Nikpour, Ahmad
2016-10-01
In this paper, two-dimensional Schrödinger equations are solved by differential quadrature method. Key point in this method is the determination of the weight coefficients for approximation of spatial derivatives. Multiquadric (MQ) radial basis function is applied as test functions to compute these weight coefficients. Unlike traditional DQ methods, which were originally defined on meshes of node points, the RBFDQ method requires no mesh-connectivity information and allows straightforward implementation in an unstructured nodes. Moreover, the calculation of coefficients using MQ function includes a shape parameter c. A new variable shape parameter is introduced and its effect on the accuracy and stability of the method is studied. We perform an analysis for the dispersion error and different internal parameters of the algorithm are studied in order to examine the behavior of this error. Numerical examples show that MQDQ method can efficiently approximate problems in complexly shaped domains.
Desbuquois, Rémi; Yefsah, Tarik; Chomaz, Lauriane; Weitenberg, Christof; Corman, Laura; Nascimbène, Sylvain; Dalibard, Jean
2014-07-11
We present a general "fit-free" method for measuring the equation of state (EoS) of a scale-invariant gas. This method, which is inspired from the procedure introduced by Ku et al. [Science 335, 563 (2012)] for the unitary three-dimensional Fermi gas, provides a general formalism which can be readily applied to any quantum gas in a known trapping potential, in the frame of the local density approximation. We implement this method on a weakly interacting two-dimensional Bose gas across the Berezinskii-Kosterlitz-Thouless transition and determine its EoS with unprecedented accuracy in the critical region. Our measurements provide an important experimental benchmark for classical-field approaches which are believed to accurately describe quantum systems in the weakly interacting but nonperturbative regime.
Institute of Scientific and Technical Information of China (English)
Reza; Taghavi; Z.; Mahmood; Salary; Amir; Kolaei
2009-01-01
This article presents a linear eddy-viscosity turbulence model for predicting bypass and natural transition in boundary layers by using Reynolds-averaged Navier-Stokes (RANS) equations. The model includes three transport equations, separately, to compute laminar kinetic energy, turbulent kinetic energy, and dissipation rate in a flow field. It needs neither correlations of intermittency factors nor knowledge of the transition onset. Two transition tests are carried out: flat plate boundary layer under zero ...
Directory of Open Access Journals (Sweden)
S.K. Parida
2015-12-01
Full Text Available This work considers the two-dimensional steady MHD boundary layer flow of heat and mass transfer over a flat plate with partial slip at the surface subjected to the convective heat flux. The particular attraction lies in searching the effects of variable viscosity and variable thermal diffusivity on the behavior of the flow. In addition, non-linear thermal radiation effects and thermophoresis are taken into account. The governing nonlinear partial differential equations for the flow, heat and mass transfer are transformed into a set of coupled nonlinear ordinary differential equations by using similarity variable, which are solved numerically by applying Runge–Kutta fourth–fifth order integration scheme in association with quasilinear shooting technique. The novel results for the dimensionless velocity, temperature, concentration and ambient Prandtl number within the boundary layer are displayed graphically for various parameters that characterize the flow. The local skin friction, Nusselt number and Sherwood number are shown graphically. The numerical results obtained for the particular case are fairly in good agreement with the result of Rahman [6].
Directory of Open Access Journals (Sweden)
A. Malvandi
2015-01-01
Full Text Available The objective of this paper is to consider both effects of slip and convective heat boundary conditions on steady two-dimensional boundary layer flow of a nanofluid over a stretching sheet in the presence of blowing/suction simultaneously. Flow meets the Navier's slip condition at the surface and Biot number is also used to consider the effects of convective heat transfer. The employed model for nanofluid includes two-component four-equation nonhomogeneous equilibrium model that incorporates the effects of nanoparticle migration owing to Brownian motion and thermophoresis. The basic partial boundary layer equations have been transformed into a two-point boundary value problem via similarity variables. Results for impermeable isothermal surface and also no-slip boundary condition were in best agreements with those existing in literatures. Effects of governing parameters such as Biot number (Bi, slip parameter (λ, thermophoresis (Nt, Prandtl number (Pr, Lewis number (Le, Brownian motion (Nb and blowing/suction (S on reduced Nusselt and Sherwood numbers are analyzed and discussed in details. The obtained results indicate that unlike heat transfer rate, concentration rate is very sensitive to all parameters among which Le, S and Pr are the most effective ones.
Tomé, M. F.; Bertoco, J.; Oishi, C. M.; Araujo, M. S. B.; Cruz, D.; Pinho, F. T.; Vynnycky, M.
2016-04-01
This work is concerned with the numerical solution of the K-BKZ integral constitutive equation for two-dimensional time-dependent free surface flows. The numerical method proposed herein is a finite difference technique for simulating flows possessing moving surfaces that can interact with solid walls. The main characteristics of the methodology employed are: the momentum and mass conservation equations are solved by an implicit method; the pressure boundary condition on the free surface is implicitly coupled with the Poisson equation for obtaining the pressure field from mass conservation; a novel scheme for defining the past times t‧ is employed; the Finger tensor is calculated by the deformation fields method and is advanced in time by a second-order Runge-Kutta method. This new technique is verified by solving shear and uniaxial elongational flows. Furthermore, an analytic solution for fully developed channel flow is obtained that is employed in the verification and assessment of convergence with mesh refinement of the numerical solution. For free surface flows, the assessment of convergence with mesh refinement relies on a jet impinging on a rigid surface and a comparison of the simulation of a extrudate swell problem studied by Mitsoulis (2010) [44] was performed. Finally, the new code is used to investigate in detail the jet buckling phenomenon of K-BKZ fluids.
RANS Modeling of Benchmark Shockwave / Boundary Layer Interaction Experiments
Georgiadis, Nick; Vyas, Manan; Yoder, Dennis
2010-01-01
This presentation summarizes the computations of a set of shock wave / turbulent boundary layer interaction (SWTBLI) test cases using the Wind-US code, as part of the 2010 American Institute of Aeronautics and Astronautics (AIAA) shock / boundary layer interaction workshop. The experiments involve supersonic flows in wind tunnels with a shock generator that directs an oblique shock wave toward the boundary layer along one of the walls of the wind tunnel. The Wind-US calculations utilized structured grid computations performed in Reynolds-averaged Navier-Stokes mode. Three turbulence models were investigated: the Spalart-Allmaras one-equation model, the Menter Shear Stress Transport wavenumber-angular frequency two-equation model, and an explicit algebraic stress wavenumber-angular frequency formulation. Effects of grid resolution and upwinding scheme were also considered. The results from the CFD calculations are compared to particle image velocimetry (PIV) data from the experiments. As expected, turbulence model effects dominated the accuracy of the solutions with upwinding scheme selection indicating minimal effects.!
Boundary Layer for the Navier-Stokes-alpha Model of Fluid Turbulence
Cheskidov, A.
We study boundary-layer turbulence using the Navier-Stokes-alpha model obtaining an extension of the Prandtl equations for the averaged flow in a turbulent boundary layer. In the case of a zero pressure gradient flow along a flat plate, we derive a nonlinear fifth-order ordinary differential equation, which is an extension of the Blasius equation. We study it analytically and prove the existence of a two-parameter family of solutions satisfying physical boundary conditions. Matching these parameters with the skin-friction coefficient and the Reynolds number based on momentum thickness, we get an agreement of the solutions with experimental data in the laminar and transitional boundary layers, as well as in the turbulent boundary layer for moderately large Reynolds numbers.
Boundary layer physics over snow and ice
Directory of Open Access Journals (Sweden)
P. S. Anderson
2007-06-01
Full Text Available A general understanding of the physics of advection and turbulent mixing within the near surface atmosphere assists the interpretation and predictive power of air chemistry theory. The theory of the physical processes involved in diffusion of trace gas reactants in the near surface atmosphere is still incomplete. Such boundary layer theory is least understood over snow and ice covered surfaces, due in part to the thermo-optical properties of the surface. Polar boundary layers have additional aspects to consider, due to the possibility of long periods without diurnal forcing and enhanced Coriolis effects.
This paper provides a review of present concepts in polar boundary layer meteorology, which will generally apply to atmospheric flow over snow and ice surfaces. It forms a companion paper to the chemistry review papers in this special issue of ACP.
THERMAL BOUNDARY LAYER IN CFB BOILER RISER
Institute of Scientific and Technical Information of China (English)
Jinwei; Wang; Xinmu; Zhao; Yu; Wang; Xing; Xing; Jiansheng; Zhang; Guangxi; Yue
2006-01-01
Measurement of temperature profiles of gas-solid two-phase flow at different heights in commercial-scale circulating fluidized bed (CFB) boilers was carried out. Experimental results showed that the thickness of thermal boundary layer was generally independent of the distance from the air distributor, except when close to the riser outlet. Through analysis of flow and combustion characteristics in the riser, it was found that the main reasons for the phenomena were: 1) the hydrodynamic boundary layer was thinner than the thermal layer and hardly changed along the CFB boiler height, and 2) both radial and axial mass and heat exchanges were strong in the CFB boiler. Numerical simulation of gas flow in the outlet zone confirmed that the distribution of the thermal boundary layer was dominated by the flow field characteristics.
Identification of Lagrangian coherent structures in the turbulent boundary layer
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vor- tices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is im- plemented to get the ensemble-averaged inclination angle θ R of typical LCS. θ R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y+=100. The ensem- ble-averaged convection velocity Uc of typical LCS is finally calculated from temporal-spatial correla- tion analysis of FTLE field. It is found that the wall-normal profile of the convection velocity Uc(y) ac- cords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the down- stream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond.
Identification of Lagrangian coherent structures in the turbulent boundary layer
Institute of Scientific and Technical Information of China (English)
PAN Chong; WANG JinJun; ZHANG Cao
2009-01-01
Using Finite-Time Lyapunov Exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vor-tices extending deep into the near wall region with an inclination angle θto the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of # accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is im-plemented to get the ensemble-averaged inclination angle θR of typical LCS. θR first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of 8 saturates at Y+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around Y+=100. The ensem-ble-averaged convection velocity Uc of typical LCS is finally calculated from temporal-spatial correla-tion analysis of FTLE field. It is found that the wall-normal profile of the convection velocity Uc(Y) ac-cords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the down-stream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond.
Shock Train/Boundary-Layer Interaction in Rectangular Scramjet Isolators
Geerts, Jonathan Simon
Numerous studies of the dual-mode scramjet isolator, a critical component in preventing inlet unstart and/or vehicle loss by containing a collection of flow disturbances called a shock train, have been performed since the dual-mode propulsion cycle was introduced in the 1960s. Low momentum corner flow and other three-dimensional effects inherent to rectangular isolators have, however, been largely ignored in experimental studies of the boundary layer separation driven isolator shock train dynamics. Furthermore, the use of two dimensional diagnostic techniques in past works, be it single-perspective line-of-sight schlieren/shadowgraphy or single axis wall pressure measurements, have been unable to resolve the three-dimensional flow features inside the rectangular isolator. These flow characteristics need to be thoroughly understood if robust dual-mode scramjet designs are to be fielded. The work presented in this thesis is focused on experimentally analyzing shock train/boundary layer interactions from multiple perspectives in aspect ratio 1.0, 3.0, and 6.0 rectangular isolators with inflow Mach numbers ranging from 2.4 to 2.7. Secondary steady-state Computational Fluid Dynamics studies are performed to compare to the experimental results and to provide additional perspectives of the flow field. Specific issues that remain unresolved after decades of isolator shock train studies that are addressed in this work include the three-dimensional formation of the isolator shock train front, the spatial and temporal low momentum corner flow separation scales, the transient behavior of shock train/boundary layer interaction at specific coordinates along the isolator's lateral axis, and effects of the rectangular geometry on semi-empirical relations for shock train length prediction. (Abstract shortened by ProQuest.).
The Ocean Boundary Layer beneath Hurricane Frances
Dasaro, E. A.; Sanford, T. B.; Terrill, E.; Price, J.
2006-12-01
The upper ocean beneath the peak winds of Hurricane Frances (57 m/s) was measured using several varieties of air-deployed floats as part of CBLAST. A multilayer structure was observed as the boundary layer deepened from 20m to 120m in about 12 hours. Bubbles generated by breaking waves create a 10m thick surface layer with a density anomaly, due to the bubbles, of about 1 kg/m3. This acts to lubricate the near surface layer. A turbulent boundary layer extends beneath this to about 40 m depth. This is characterized by large turbulent eddies spanning the boundary layer. A stratified boundary layer grows beneath this reaching 120m depth. This is characterized by a gradient Richardson number of 1/4, which is maintained by strong inertial currents generated by the hurricane, and smaller turbulent eddies driven by the shear instead of the wind and waves. There is little evidence of mixing beneath this layer. Heat budgets reveal the boundary layer to be nearly one dimensional through much of the deepening, with horizontal and vertical heat advection becoming important only after the storm had passed. Turbulent kinetic energy measurements support the idea of reduced surface drag at high wind speeds. The PWP model correctly predicts the degree of mixed layer deepening if the surface drag is reduced at high wind speed. Overall, the greatest uncertainty in understanding the ocean boundary layer at these extreme wind speeds is a characterization of the near- surface processes which govern the air-sea fluxes and surface wave properties.
Messaris, G. T.; Papastavrou, C. A.; Loukopoulos, V. C.; Karahalios, G. T.
2009-08-01
A new finite-difference method is presented for the numerical solution of the Navier-Stokes equations of motion of a viscous incompressible fluid in two (or three) dimensions and in the primitive-variable formulation. Introducing two auxiliary functions of the coordinate system and considering the form of the initial equation on lines passing through the nodal point (x0, y0) and parallel to the coordinate axes, we can separate it into two parts that are finally reduced to ordinary differential equations, one for each dimension. The final system of linear equations in n-unknowns is solved by an iterative technique and the method converges rapidly giving satisfactory results. For the pressure variable we consider a pressure Poisson equation with suitable Neumann boundary conditions. Numerical results, confirming the accuracy of the proposed method, are presented for configurations of interest, like Poiseuille flow and the flow between two parallel plates with step under the presence of a pressure gradient.
DEFF Research Database (Denmark)
Chivaee, Hamid Sarlak; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
2012-01-01
Large eddy simulation (LES) of flow in a wind farm is studied in neutral as well as thermally stratified atmospheric boundary layer (ABL). An approach has been practiced to simulate the flow in a fully developed wind farm boundary layer. The approach is based on the Immersed Boundary Method (IBM......) and involves implementation of an arbitrary prescribed initial boundary layer (See [1]). A prescribed initial boundary layer profile is enforced through the computational domain using body forces to maintain a desired flow field. The body forces are then stored and applied on the domain through the simulation...... and the boundary layer shape will be modified due to the interaction of the turbine wakes and buoyancy contributions. The implemented method is capable of capturing the most important features of wakes of wind farms [1] while having the advantage of resolving the wall layer with a coarser grid than typically...
Nature, theory and modelling of geophysical convective planetary boundary layers
Zilitinkevich, Sergej
2015-04-01
Geophysical convective planetary boundary layers (CPBLs) are still poorly reproduced in oceanographic, hydrological and meteorological models. Besides the mean flow and usual shear-generated turbulence, CPBLs involve two types of motion disregarded in conventional theories: 'anarchy turbulence' comprised of the buoyancy-driven plumes, merging to form larger plumes instead of breaking down, as postulated in conventional theory (Zilitinkevich, 1973), large-scale organised structures fed by the potential energy of unstable stratification through inverse energy transfer in convective turbulence (and performing non-local transports irrespective of mean gradients of transporting properties). C-PBLs are strongly mixed and go on growing as long as the boundary layer remains unstable. Penetration of the mixed layer into the weakly turbulent, stably stratified free flow causes turbulent transports through the CPBL outer boundary. The proposed theory, taking into account the above listed features of CPBL, is based on the following recent developments: prognostic CPBL-depth equation in combination with diagnostic algorithm for turbulence fluxes at the CPBL inner and outer boundaries (Zilitinkevich, 1991, 2012, 2013; Zilitinkevich et al., 2006, 2012), deterministic model of self-organised convective structures combined with statistical turbulence-closure model of turbulence in the CPBL core (Zilitinkevich, 2013). It is demonstrated that the overall vertical transports are performed mostly by turbulence in the surface layer and entrainment layer (at the CPBL inner and outer boundaries) and mostly by organised structures in the CPBL core (Hellsten and Zilitinkevich, 2013). Principal difference between structural and turbulent mixing plays an important role in a number of practical problems: transport and dispersion of admixtures, microphysics of fogs and clouds, etc. The surface-layer turbulence in atmospheric and marine CPBLs is strongly enhanced by the velocity shears in
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
[Objective] The aim was to study the characteristics of the changes of the urban boundary layer thermodynamic stability induced by heat island effect and their influences on precipitation.[Method] Proceeding from the thermodynamic equation,the changes of urban boundary layer thermodynamic stability caused by the urban heat disturbance and the mean state of heat island effect were discussed.The influence of the changes of urban boundary layer thermodynamic stability on the precipitation was expounded.Combini...
Earth's magnetosphere formed by the low-latitude boundary layer
Heikkila, W J
2011-01-01
The author argues that, after five decades of debate about the interactive of solar wind with the magnetosphere, it is time to get back to basics. Starting with Newton's law, this book also examines Maxwell's equations and subsidiary equations such as continuity, constitutive relations and the Lorentz transformation; Helmholtz' theorem, and Poynting's theorem, among other methods for understanding this interaction. Includes chapters on prompt particle acceleration to high energies, plasma transfer event, and the low latitude boundary layer More than 200 figures illustrate the text Includes a color insert.
Studies of stability of blade cascade suction surface boundary layer
Institute of Scientific and Technical Information of China (English)
DONG Xue-zhi; YAN Pei-gang; HAN Wan-jin
2007-01-01
Compressible boundary layers stability on blade cascade suction surface was discussed by wind tunnel experiment and numerical solution. Three dimensional disturbance wave Parabolized Stability Equations(PSE) of orthogonal Curvilinear Coordinates in compressible flow was deducted. The surface pressure of blade in wind tunnel experiment was measured. The Falkner-Skan equation was solved under the boundary conditions of experiment result, and velocity, pressure and temperature of average flow were obtained. Substituted this result for discretization of the PSE Eigenvalue Problem, the stability problem can be solved.
Directory of Open Access Journals (Sweden)
Khairy Zaimi
2012-01-01
Full Text Available The steady two-dimensional boundary layer flow of a nanofluid over a shrinking sheet with thermal radiation and suction effects is studied. The resulting system of ordinary differential equations is solved numerically using a shooting method for three different types of nanoparticles, namely, copper (Cu, alumina (Al2O3, and titania (TiO2. The results obtained for the velocity and temperature profiles as well as the skin friction coefficient and the local Nusselt number for some values of the governing parameters, namely, the nanoparticle volume fraction, shrinking, suction, and viscous dissipation parameters, are discussed. The numerical results show that dual solutions exist in a certain range of suction parameter.
An analytical model for the amplitude of lee waves forming on the boundary layer inversion
Sachsperger, Johannes; Serafin, Stefano; Stiperski, Ivana; Grubišić, Vanda
2016-04-01
Lee waves are horizontally propagating gravity waves with a typical wavelength of 5-15 km that may be generated when stratified flow is lifted over a mountain. A frequently observed type of such waves is that of interfacial lee waves. Those develop, similar to surface waves on a free water surface, when the upstream flow features a density discontinuity. Such conditions are often present for example at the capping inversion in boundary layer flow. The dynamics of interfacial lee waves can be described concisely with linear interfacial gravity wave theory. However, while this theoretical framework accurately describes the wavelength, it fails to properly predict the amplitude of lee waves. It is well known that large amplitude lee waves may lead to low-level turbulence, which poses a potential hazard for aviation. Therefore, this property of interfacial lee waves deserves further attention. In this study, we develop a simple analytical model for the amplitude of lee waves forming on the boundary layer inversion. This model is based on the energetics of two-layer flow. We obtain an expression for the wave amplitude by equating the energy loss across an internal jump with the energy radiation through lee waves. The verification of the result with water tank experiments of density-stratified two-layer flow over two-dimensional topography from the HYDRALAB campaign shows good agreement between theory and observations. This new analytical model may be useful in determining potential hazards of interfacial lee waves with negligible computational cost as compared to numerical weather prediction models.
Effect of bulges on the stability of boundary layers
Nayfeh, Ali H.; Ragab, Saad A.; Al-Maaitah, Ayman A.
1988-01-01
The instability of flows around hump and dip imperfections is investigated. The mean flow is calculated using interacting boundary layers, thereby accounting for viscous/inviscid interaction and separation bubbles. Then, the two-dimensional linear stability of this flow is analyzed, and the amplification factors are computed. Results are obtained for several height/width ratios and locations. The theoretical results have been used to correlate the experimental results of Walker and Greening (1942). The observed transition locations are found to correspond to amplification factors varying between 7.4 and 10.0, consistent with previous results for flat plates. The method accounts for both viscous and shear-layer instabilities. Separation is found to increase significantly the amplification factor.
MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate
Institute of Scientific and Technical Information of China (English)
Krishnendu Bhattacharyya; Swati Mukhopadhyay; G.C.Layek
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.%@@ 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.
Magnetic Domination of Recollimation Boundary Layers in Relativistic Jets
Kohler, Susanna
2012-01-01
We study the collimation of relativistic magnetohydrodynamic jets by the pressure of an ambient medium, in the limit where the jet interior loses causal contact with its surroundings. This follows up a hydrodynamic study in a previous paper, adding the effects of a toroidal magnetic field threading the jet. As the ultrarelativistic jet encounters an ambient medium with a pressure profile with a radial scaling of p ~ r^-eta where 2
Institute of Scientific and Technical Information of China (English)
沈春; 孙梅娜
2005-01-01
Based on the theory of stratification, the well-posedness of the initial and boundary value problems for the system of two-dimensional non-hydrostatic Boussinesq equations was discussed. The sufficient and necessary conditions of the existence and uniqueness for the solution of the equations were given for some representative initial and boundary value problems. Several special cases were discussed.
Turbulent Boundary Layers - Experiments, Theory and Modelling
1980-01-01
DEVELOPMENT (ORGANISATION DU TRAITE DE L’ATLANTIQUE NORD ) AGARD Conference Proceedings No.271 TURBULENT BOUNDARY LAYERS - EXPERIMENTS, THEORY AND...photographs of Figures 21 and 22. In this case, the photographs are taken with a single flash strobe and thus yield the instantaneous positions of the
Comments on Hypersonic Boundary-Layer Transition
1990-09-01
laver transition results from instabilities as described by linear stability theory, then the disturbance growth historias follow a prescribed...mechanism by which boundary-layer disturbance growth is generally initiated and establishes the initial distur- banca amplitude at the onset of disturbance
Boundary layer control device for duct silencers
Schmitz, Fredric H. (Inventor); Soderman, Paul T. (Inventor)
1993-01-01
A boundary layer control device includes a porous cover plate, an acoustic absorber disposed under the porous cover plate, and a porous flow resistive membrane interposed between the porous cover plate and the acoustic absorber. The porous flow resistive membrane has a flow resistance low enough to permit sound to enter the acoustic absorber and high enough to damp unsteady flow oscillations.
Atmospheric Boundary Layers: Modeling and Parameterization
Holtslag, A.A.M.
2015-01-01
In this contribution we deal with the representation of the atmospheric boundary layer (ABL) for modeling studies of weather, climate, and air quality. As such we review the major characteristics of the ABL, and summarize the basic parameterizations for the description of atmospheric turbulence and
2004-08-28
the tunnel floor. Each piece of wood is routered on their respective ends to provide the necessary support and a smooth continuation of the test...0 . Ci (P q 0No U)ý2- N0’ t - - - 000099997799CýC 7N CCD C Aý 0.6 CD) -A- C. 4(oC1 r -M C 00 CC C4- III A >. 0. o) CN t N- m-L w N-C~ t o9 E CNC ...C, -: E+ +0 - IL IL0 CN 0 7 C\\Ic? 4? CA U) N 0C0000000 C N’ C> ’ý CN(? *U C) ot C -- (L 0 D00 0o 0) * Uý (’JD CNC >1L oC (L 7 N U’) + u Co 0>00000000
Boundary-Value Problem for Two-Dimensional Fluctuations in Boundary Layers
1985-07-01
inviscid analysis by P. Durbin "Distortion of turbulence by a constant-shear layer adjacent to a wall," private communication (1977). (l.2e) 2-D...vortices near a boundary," ~ of the Americ~ p ~ ~ , Volume 20, Number 9 (November 1975). 21. Hultgren, Lennart S. and Gustavsson, L. Hakan, " Algebraic
Controls on boundary layer ventilation: Boundary layer processes and large-scale dynamics
Sinclair, V. A.; Gray, S. L.; Belcher, S. E.
2010-06-01
Midlatitude cyclones are important contributors to boundary layer ventilation. However, it is uncertain how efficient such systems are at transporting pollutants out of the boundary layer, and variations between cyclones are unexplained. In this study 15 idealized baroclinic life cycles, with a passive tracer included, are simulated to identify the relative importance of two transport processes: horizontal divergence and convergence within the boundary layer and large-scale advection by the warm conveyor belt. Results show that the amount of ventilation is insensitive to surface drag over a realistic range of values. This indicates that although boundary layer processes are necessary for ventilation they do not control the magnitude of ventilation. A diagnostic for the mass flux out of the boundary layer has been developed to identify the synoptic-scale variables controlling the strength of ascent in the warm conveyor belt. A very high level of correlation (R2 values exceeding 0.98) is found between the diagnostic and the actual mass flux computed from the simulations. This demonstrates that the large-scale dynamics control the amount of ventilation, and the efficiency of midlatitude cyclones to ventilate the boundary layer can be estimated using the new mass flux diagnostic. We conclude that meteorological analyses, such as ERA-40, are sufficient to quantify boundary layer ventilation by the large-scale dynamics.
Stability of boundary layers with porous suction strips: Experiment and theory
Reynolds, G. A.; Saric, W. S.; Reed, H. L.; Nayfeh, A. H.
1982-01-01
Low turbulence tunnel experiments on the stability and transition of 2 D boundary layers on flat plates with and without suction are described. A number of general suction cases are discussed. Test results showed that the maximum stabilization occurred when the suction was moved toward the Branch I neutral point. An analytical study of the stability of two dimensional, incompressible boundary layer flows over plates with suction through porous strips was performed. The mean flow was calculated using linearized triple deck, closed form solutions. The stability results of the triple deck theory are shown to be in good agreement with those of the interacting boundary layers. An analytical optimization scheme for the suction configuration was developd. Numerical calculations were performed corresponding to the experimental configurations. In each case, the theory correctly predicts the experimental results.
Design and construction of a low-velocity boundary-layer temperature probe
Blackwell, B. F.; Moffat, R. J.
1974-01-01
This paper presents the results of a study performed to determine the probe geometry and thermal characteristics for a low-velocity boundary-layer temperature probe capable of eliminating conduction errors. Design curves for four common thermoelectric pairs are presented, and an experimental turbulent boundary-layer temperature profile is compared with the theoretical laminar sublayer equation to verify that the probe eliminates conduction errors.
Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet
Masood Khan; Hashim
2015-01-01
This article studies the Carreau viscosity model (which is a generalized Newtonian model) and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical ...
PIV-based pressure fluctuations in the turbulent boundary layer
Ghaemi, Sina; Ragni, Daniele; Scarano, Fulvio
2012-12-01
The unsteady pressure field is obtained from time-resolved tomographic particle image velocimetry (Tomo-PIV) measurement within a fully developed turbulent boundary layer at free stream velocity of U ∞ = 9.3 m/s and Reθ = 2,400. The pressure field is evaluated from the velocity fields measured by Tomo-PIV at 10 kHz invoking the momentum equation for unsteady incompressible flows. The spatial integration of the pressure gradient is conducted by solving the Poisson pressure equation with fixed boundary conditions at the outer edge of the boundary layer. The PIV-based evaluation of the pressure field is validated against simultaneous surface pressure measurement using calibrated condenser microphones mounted behind a pinhole orifice. The comparison shows agreement between the two pressure signals obtained from the Tomo-PIV and the microphones with a cross-correlation coefficient of 0.6 while their power spectral densities (PSD) overlap up to 3 kHz. The impact of several parameters governing the pressure evaluation from the PIV data is evaluated. The use of the Tomo-PIV system with the application of three-dimensional momentum equation shows higher accuracy compared to the planar version of the technique. The results show that the evaluation of the wall pressure can be conducted using a domain as small as half the boundary layer thickness (0.5δ99) in both the streamwise and the wall normal directions. The combination of a correlation sliding-average technique, the Lagrangian approach to the evaluation of the material derivative and the planar integration of the Poisson pressure equation results in the best agreement with the pressure measurement of the surface microphones.
Modeling the summertime Arctic cloudy boundary layer
Energy Technology Data Exchange (ETDEWEB)
Curry, J.A.; Pinto, J.O. [Univ. of Colorado, Boulder, CO (United States); McInnes, K.L. [CSIRO Division of Atmospheric Research, Mordialloc (Australia)
1996-04-01
Global climate models have particular difficulty in simulating the low-level clouds during the Arctic summer. Model problems are exacerbated in the polar regions by the complicated vertical structure of the Arctic boundary layer. The presence of multiple cloud layers, a humidity inversion above cloud top, and vertical fluxes in the cloud that are decoupled from the surface fluxes, identified in Curry et al. (1988), suggest that models containing sophisticated physical parameterizations would be required to accurately model this region. Accurate modeling of the vertical structure of multiple cloud layers in climate models is important for determination of the surface radiative fluxes. This study focuses on the problem of modeling the layered structure of the Arctic summertime boundary-layer clouds and in particular, the representation of the more complex boundary layer type consisting of a stable foggy surface layer surmounted by a cloud-topped mixed layer. A hierarchical modeling/diagnosis approach is used. A case study from the summertime Arctic Stratus Experiment is examined. A high-resolution, one-dimensional model of turbulence and radiation is tested against the observations and is then used in sensitivity studies to infer the optimal conditions for maintaining two separate layers in the Arctic summertime boundary layer. A three-dimensional mesoscale atmospheric model is then used to simulate the interaction of this cloud deck with the large-scale atmospheric dynamics. An assessment of the improvements needed to the parameterizations of the boundary layer, cloud microphysics, and radiation in the 3-D model is made.
Directory of Open Access Journals (Sweden)
Kazutaka Yanase
2016-12-01
Full Text Available The boundary layers of rainbow trout, Oncorhynchus mykiss [0.231±0.016 m total body length (L (mean±s.d.; N=6], swimming at 1.6±0.09 L s−1 (N=6 in an experimental flow channel (Reynolds number, Re=4×105 with medium turbulence (5.6% intensity were examined using the particle image velocimetry technique. The tangential flow velocity distributions in the pectoral and pelvic surface regions (arc length from the rostrum, lx=71±8 mm, N=3, and lx=110±13 mm, N=4, respectively were approximated by a laminar boundary layer model, the Falkner−Skan equation. The flow regime over the pectoral and pelvic surfaces was regarded as a laminar flow, which could create less skin-friction drag than would be the case with turbulent flow. Flow separation was postponed until vortex shedding occurred over the posterior surface (lx=163±22 mm, N=3. The ratio of the body-wave velocity to the swimming speed was in the order of 1.2. This was consistent with the condition of the boundary layer laminarization that had been confirmed earlier using a mechanical model. These findings suggest an energy-efficient swimming strategy for rainbow trout in a turbulent environment.
An experimental investigation of the three-dimensional boundary layer on a rotating disk
Littell, Howard Steven
The velocity field above a large spinning disk has been studied using pressure probes and hotwire anemometers. The flowfield consists of a three-dimensional boundary layer due to a crossflow caused by centrifugal forces. The disk was 1 m in diameter and was spun at speeds up to 1500 rpm, giving momentum thickness Reynolds numbers in excess of 6000. The mean flow in both the laminar and turbulent regimes compares well with previous studies of 'infinite' smooth rotating disks. All six Reynolds stresses and the ten triple products have been measured using established crosswire anemometry techniques. These results are compared to previous three-dimensional boundary layer measurements and several key differences are noted. The ratio of the shear stress vector magnitude to the turbulent kinetic energy is a common descriptor of boundary layer flow and is used in many modeling efforts because it is usually a constant over most of a two-dimensional boundary layer. Three-dimensionality has been observed to depress this parameter near the wall in many pressure-driven boundary layers. In the disk flow, this parameter was at a maximum near the wall at close to the 2-D value, but dropped off almost linearly away from the wall. Two-point velocity correlations were also measured using a pair of crosswire anemometers to gain insight into the structure of the turbulence. These measurements were obtained at two different heights at momentum thickness Reynolds numbers of 2650 and 5000 to test for possible scaling effects. These measurements showed that the turbulence exhibits asymmetry in the crossflow direction, which cannot occur in two-dimensional boundary layers. A mechanism by which the crossflow may be modifying the turbulence structure is proposed which exhibits several features of the asymmetric two-point correlations.
Juknevičius, Vaidas; Ruseckas, Julius; Armaitis, Jogundas
2017-09-01
This paper presents new findings concerning the dynamics of the slow height variations in surfaces produced by the two-dimensional isotropic Kuramoto-Sivashinsky equation with an additional nonlinear term. In addition to the disordered cellular patterns of specific size evident at small scales, slow height variations of scale-free character become increasingly evident when the system size is increased. This paper focuses on the parameter range in which the kinetic roughening with eventual saturation in surface roughness and coarseness is obtained, and the statistical and dynamical properties of surfaces in the long-time stationary regime are investigated. The resulting long-range scaling properties of the saturated surface roughness consistent with the power-law shape of the surface spectrum at small wave numbers are obtained in a wider parameter range than previously reported. The temporal properties of these long-range height variations are investigated by analysing the time series of surface roughness fluctuations. The resulting power-spectral densities can be expressed as a generalized Lorentzian whose cut-off frequency varies with system size. The dependence of this lower cut-off frequency on the smallest wave number connects spatial and temporal properties and gives new insight into the surface evolution on large scales.
Asllanaj, Fatmir; Fumeron, Sebastien
2012-07-01
Optical tomography is a medical imaging technique based on light propagation in the near infrared (NIR) part of the spectrum. We present a new way of predicting the short-pulsed NIR light propagation using a time-dependent two-dimensional-global radiative transfer equation in an absorbing and strongly anisotropically scattering medium. A cell-vertex finite-volume method is proposed for the discretization of the spatial domain. The closure relation based on the exponential scheme and linear interpolations was applied for the first time in the context of time-dependent radiative heat transfer problems. Details are given about the application of the original method on unstructured triangular meshes. The angular space (4πSr) is uniformly subdivided into discrete directions and a finite-differences discretization of the time domain is used. Numerical simulations for media with physical properties analogous to healthy and metastatic human liver subjected to a collimated short-pulsed NIR light are presented and discussed. As expected, discrepancies between the two kinds of tissues were found. In particular, the level of light flux was found to be weaker (inside the medium and at boundaries) in the healthy medium than in the metastatic one.
Boundary layer flow on a moving surface in otherwise quiescent pseudo-plastic non-Newtonian fluids
Institute of Scientific and Technical Information of China (English)
Liancun Zheng; Liu Ting; Xinxin Zhang
2008-01-01
A theoretical analysis for the boundary layer flow over a continuous moving surface in an otherwise quiescent pseudo-plastic non-Newtonian fluid medium was presented. The types of potential flows necessary for similar solutions to the boundary layer equations were determined and the solutions were numerically presented for different values of power law exponent.
Study of laminar boundary layer instability noise study on a controlled diffusion airfoil
Jaiswal, Prateek; Sanjose, Marlene; Moreau, Stephane
2016-11-01
Detailed experimental study has been carried out on a Controlled Diffusion (CD) airfoil at 5° angle of attack and at chord based Reynolds number of 1 . 5 ×105 . All the measurements were done in an open-jet anechoic wind tunnel. The airfoil mock-up is held between two side plates, to keep the flow two-dimensional. PIV measurements have been performed in the wake and on the boundary layer of the airfoil. Pressure sensor probes on the airfoil were used to detect mean airfoil loading and remote microphone probes were used to measure unsteady pressure fluctuations on the surface of the airfoil. Furthermore the far field acoustic pressure was measured using an 1/2 inch ICP microphone. The results confirm very later transition of a laminar boundary layer to a turbulent boundary layer on the suction side of the airfoil. The process of transition of laminar to turbulent boundary layer comprises of turbulent reattachment of a separated shear layer. The pressure side of the boundary layer is found to be laminar and stable. Therefore tonal noise generated is attributed to events on suction side of the airfoil. The flow transition and emission of tones are further investigated in detail thanks to the complementary DNS study.
Lin, Wenxian; Armfield, S W; Patterson, J C; Lei, Chengwang
2009-06-01
In this paper, the scalings incorporating the Prandtl number (Pr) dependence have been obtained by a scaling analysis for the unsteady natural convection boundary layer of an initially quiescent isothermal Newtonian fluid of Pr>1 produced by the sudden imposition of a higher temperature on a vertical plate. It is shown that the transient flow behavior of the resulting boundary layer can be described by a three-region structure and at the start-up stage the boundary layer development is one dimensional and independent of height due to the dominance of pure conduction; however, at steady state it becomes two dimensional and height dependent as the flow becomes dominated by convection. Numerical results demonstrate that the scalings representing the thermal boundary layer development accurately represent their Pr dependence over the whole stage of flow development. The scalings representing the viscous boundary layer development are generally in good agreement with the numerical results with the Pr variation over the whole stage of flow development, although there are small deviations from the numerical results with the Pr variation that are within acceptable limits for scaling.
An interactive boundary layer modelling methodology for aerodynamic flows
CSIR Research Space (South Africa)
Smith, L
2013-01-01
Full Text Available between the two flow regions, whereby a fictitious velocity is induced into the boundary layer to simulate its effect. The drawback of this scheme, however, is that it does not strictly conserve mass. The objective of this study is to develop a method... and turbulent flows, which eliminate the direct link between the profile shape and the pressure gradient, making them suitable for flow with strong interaction. The resulting two equations read: ( ) 2 2 2 fe e e C d dU U MH d d =−++ ξ θ ξ θ...
Directory of Open Access Journals (Sweden)
K. GANGADHAR
2013-01-01
Full Text Available A mathematical model is presented for a two-dimensional, steady, incompressible electrically conducting, laminar free convection boundary layer flow of a continuously moving vertical porous plate in a chemically reactive and porous medium in the presence of a transverse magnetic field. The basic equations governing the flow are in the form of partial differential equations and have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The problem is tackled numerically using shooting techniques with the forth order Runga-Kutta method. Pertinent results with respect to embedded parameters are displayed graphically for the velocity,temperature and concentration profiles and were discussed quantitatively.
Institute of Scientific and Technical Information of China (English)
A A AFIFY; M J UDDIN; M FERDOWS
2014-01-01
Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic (MHD) flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transfor-mation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The ob-tained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta-Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
Budget of Turbulent Kinetic Energy in a Shock Wave Boundary-Layer Interaction
Vyas, Manan A.; Waindim, Mbu; Gaitonde, Datta V.
2016-01-01
Implicit large-eddy simulation (ILES) of a shock wave/boundary-layer interaction (SBLI) was performed. Quantities present in the exact equation of the turbulent kinetic energy transport were accumulated and used to calculate terms like production, dissipation, molecular diffusion, and turbulent transport. The present results for a turbulent boundary layer were validated by comparison with direct numerical simulation data. It was found that a longer development domain was necessary for the boundary layer to reach an equilibrium state and a finer mesh resolution would improve the predictions. In spite of these findings, trends of the present budget match closely with that of the direct numerical simulation. Budgets for the SBLI region are presented at key axial stations. These budgets showed interesting dynamics as the incoming boundary layer transforms and the terms of the turbulent kinetic energy budget change behavior within the interaction region.
Boundary layer control of rotating convection systems.
King, Eric M; Stellmach, Stephan; Noir, Jerome; Hansen, Ulrich; Aurnou, Jonathan M
2009-01-15
Turbulent rotating convection controls many observed features of stars and planets, such as magnetic fields, atmospheric jets and emitted heat flux patterns. It has long been argued that the influence of rotation on turbulent convection dynamics is governed by the ratio of the relevant global-scale forces: the Coriolis force and the buoyancy force. Here, however, we present results from laboratory and numerical experiments which exhibit transitions between rotationally dominated and non-rotating behaviour that are not determined by this global force balance. Instead, the transition is controlled by the relative thicknesses of the thermal (non-rotating) and Ekman (rotating) boundary layers. We formulate a predictive description of the transition between the two regimes on the basis of the competition between these two boundary layers. This transition scaling theory unifies the disparate results of an extensive array of previous experiments, and is broadly applicable to natural convection systems.
Active control of ionized boundary layers
Mendes, R V
1997-01-01
The challenging problems, in the field of control of chaos or of transition to chaos, lie in the domain of infinite-dimensional systems. Access to all variables being impossible in this case and the controlling action being limited to a few collective variables, it will not in general be possible to drive the whole system to the desired behaviour. A paradigmatic problem of this type is the control of the transition to turbulence in the boundary layer of fluid motion. By analysing a boundary layer flow for an ionized fluid near an airfoil, one concludes that active control of the transition amounts to the resolution of an generalized integro-differential eigenvalue problem. To cope with the required response times and phase accuracy, electromagnetic control, whenever possible, seems more appropriate than mechanical control by microactuators.
MHD Turbulence in Accretion Disk Boundary Layers
Chan, Chi-kwan
2012-01-01
The physical modeling of the accretion disk boundary layer, the region where the disk meets the surface of the accreting star, usually relies on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. The standard model for turbulent shear viscosity, widely adopted in astrophysics, satisfies this assumption by construction. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability is inefficient in this inner disk region. I will discuss the results of a recent study on the generation of hydromagnetic stresses and energy density in the boundary layer around a weakly magnetized star. Our findings suggest that although magnetic energy density can be significantly amplified in this region, angular momentum transport is rather inefficient. This seems consistent with the results obtained in numerical simulations...
Supersonic Turbulent Boundary Layer: DNS and RANS
Institute of Scientific and Technical Information of China (English)
XU Jing-Lei; MA Hui-Yang
2007-01-01
We assess the performance of a few turbulence models for Reynolds averaged Navier-Stokes (RANS) simulation of supersonic boundary layers, compared to the direct numerical simulations (DNS) of supersonic flat-plate turbulent boundary layers, carried out by Gao et al. [Chin. Phys. Lett. 22 (2005) 1709] and Huang et al. [Sci.Chin. 48 (2005) 614], as well as some available experimental data. The assessment is made for two test cases, with incoming Mach numbers and Reynolds numbers M = 2.25, Re = 365, 000/in, and M = 4.5, Re - 1.7 × 107/m,respectively. It is found that in the first case the prediction of RANS models agrees well with the DNS and the experimental data, while for the second case the agreement of the DNS models with experiment is less satisfactory.The compressibility effect on the RANS models is discussed.
Turbulent boundary layer over flexible plates
Rostami, Parand; Ioppolo, Tindaro
2016-11-01
This research describes the structure of a turbulent boundary layer flow with a zero pressure gradient over elastic plates. The elastic plates made of a thin aluminum sheets with thickness between 50 and 500 microns were placed on the floor of a subsonic wind tunnel and exposed to a turbulent boundary layer flow with a free stream velocity between 20m/s and 100m/s. The ceiling of the test section of the wind tunnel is adjustable so that a nearly zero pressure gradient is obtained in the test section. Hot-wire anemometry was used to measure the velocity components. Mean, fluctuating velocities and Reynolds stresses will be presented and compared with the values of a rigid plate.
BOREAS AFM-6 Boundary Layer Height Data
Wilczak, James; Hall, Forrest G. (Editor); Newcomer, Jeffrey A. (Editor); Smith, David E. (Technical Monitor)
2000-01-01
The Boreal Ecosystem-Atmosphere Study (BOREAS) Airborne Fluxes and Meteorology (AFM)-6 team from National Oceanic and Atmospheric Adminsitration/Environment Technology Laboratory (NOAA/ETL) operated a 915-MHz wind/Radio Acoustic Sounding System (RASS) profiler system in the Southern Study Area (SSA) near the Old Jack Pine (OJP) site. This data set provides boundary layer height information over the site. The data were collected from 21 May 1994 to 20 Sep 1994 and are stored in tabular ASCII files. The boundary layer height data are available from the Earth Observing System Data and Information System (EOSDIS) Oak Ridge National Laboratory (ORNL) Distributed Active Archive Center (DAAC). The data files are available on a CD-ROM (see document number 20010000884).
Analytic prediction for planar turbulent boundary layers
Chen, Xi
2016-01-01
Analytic predictions of mean velocity profile (MVP) and streamwise ($x$) development of related integral quantities are presented for flows in channel and turbulent boundary layer (TBL), based on a symmetry analysis of eddy length and total stress. Specific predictions are the friction velocity $u_\\tau$: ${ U_e/u_\\tau }\\approx 2.22\\ln Re_x+2.86-3.83\\ln(\\ln Re_x)$; the boundary layer thickness $\\delta_e$: $x/\\delta_e \\approx 7.27\\ln Re_x-5.18-12.52\\ln(\\ln Re_x)$; the momentum thickness Reynolds number: $Re_x/Re_\\theta=4.94[{(\\ln {{\\mathop{\\rm Re}\
Instabilities and transition in boundary layers
Indian Academy of Sciences (India)
N Vinod; Rama Govindarajan
2005-03-01
Some recent developments in boundary layer instabilities and transition are reviewed. Background disturbance levels determine the instability mechanism that ultimately leads to turbulence. At low noise levels, the traditional Tollmien–Schlichting route is followed, while at high levels, a `by-pass' route is more likely. Our recent work shows that spot birth is related to the pattern of secondary instability in either route.
2007 Program of Study: Boundary Layers
2008-06-01
PM Coalescence of charged water droplets Andrew Belmonte, Pennsylvania State University August 9 - 10:30 AM Multiscale analysis of strongly...Properties of Helium Near the Liquid-Vapor Critical Point. J. low Temp. Phys. 46, 115-135. [15] Polezhaev, V. I. and Soboleva, E. B. 2004 Rayleigh...through which potassium permanganate was added in most of the experiments in order to detect a possible appearance of boundary layer separation and
Experimental studies on transitional separated boundary layers
Serna Serrano, José
2013-01-01
Separated transitional boundary layers appear on key aeronautical processes such as the flow around wings or turbomachinery blades. The aim of this thesis is the study of these flows in representative scenarios of technological applications, gaining knowledge about phenomenology and physical processes that occur there and, developing a simple model for scaling them. To achieve this goal, experimental measurements have been carried out in a low speed facility, ensuring the flow homogeneity and...
Three dimensional boundary layers in internal flows
Bodonyi, R. J.
1987-01-01
A numerical study of the effects of viscous-inviscid interactions in three-dimensional duct flows is presented. In particular interacting flows for which the oncoming flow is not fully-developed were considered. In this case there is a thin boundary layer still present upstream of the surface distortion, as opposed to the fully-developed pipe flow situation wherein the flow is viscous across the cross section.
Turbulent oceanic western-boundary layers at low latitude
Quam Cyrille Akuetevi, Cataria; Wirth, Achim
2013-04-01
Low latitude oceanic western-boundary layers range within the most turbulent regions in the worlds ocean. The Somali current system with the Great Whirl and the Brazilian current system with its eddy shedding are the most prominent examples. Results from analytical calculations and integration of a one layer reduced-gravity fine resolution shallow water model is used to entangle this turbulent dynamics. Two types of wind-forcing are applied: a remote Trade wind forcing with maximum shear along the equator and a local Monsoon wind forcing with maximum shear in the vicinity of the boundary. For high values of the viscosity (> 1000m2s-1) the stationary solutions compare well to analytical predictions using Munk and inertial layer theory. When lowering the friction parameter time dependence results. The onset of instability is strongly influenced by inertial effects. The unstable boundary current proceeds as a succession of anti-cyclonic coherent eddies performing a chaotic dynamics in a turbulent flow. The dynamics is governed by the turbulent fluxes of mass and momentum. We determine these fluxes by analyzing the (potential) vorticity dynamics. We demonstrate that the boundary-layer can be separated in four sub-layers, which are (starting from the boundary): (1) the viscous sub-layer (2) the turbulent buffer-layer (3) the layer containing the coherent structures and (4) the extended boundary layer. The characteristics of each sub-layer and the corresponding turbulent fluxes are determined, as are the dependence on latitude and the type of forcing. A new pragmatic method of determining the eddy viscosity, based on Munk-layer theory, is proposed. Results are compared to observations and solutions of the multi-level primitive equation model (DRAKKAR).
Hadamard States and Two-dimensional Gravity
Salehi, H
2001-01-01
We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.
Energy Technology Data Exchange (ETDEWEB)
Huerst, C.; Schulz, A.; Wittig, S. [Univ. Karlsruhe (Germany). Lehrstuhl und Inst. fuer Thermische Stroemungsmaschinen
1995-04-01
The present study compares measured and computed heat transfer coefficients for high-speed boundary layer nozzle flows under engine Reynolds number conditions (U{sub {infinity}} = 230 {divided_by} 880 m/s, Re* = 0.37 {divided_by} 1.07 {times} 10{sup 6}). Experimental data have been obtained by heat transfer measurements in a two-dimensional, nonsymmetric, convergent-divergent nozzle. The nozzle wall is convectively cooled using water passages. The coolant heat transfer data and nozzle surface temperatures are used as boundary conditions for a three-dimensional finite-element code, which is employed to calculate the temperature distribution inside the nozzle wall. Heat transfer coefficients along the hot gas nozzle wall are derived from the temperature gradients normal to the surface. The results are compared with numerical heat transfer predictions using the low-Reynolds-number {kappa}-{epsilon} turbulence model by Lam and Bremhorst. Influence of compressibility in the transport equations for the turbulence properties is taken into account by using the local averaged density. The results confirm that this simplification leads to good results for transonic and low supersonic flows.
Katra, Itzhak; Elperin, Tov; Fominykh, Andrew; Krasovitov, Boris; Yizhaq, Hezi
2016-03-01
A two-dimensional model for particulate matter (PM) dispersion due to dust emission from soils is presented. Field experiments were performed at a dust source site (Negev loess soil) with a portable boundary layer wind tunnel to determine the emitted PM fluxes for different wind speeds and varying soil conditions. The numerical model is formulated using parameterizations based on the aeolian experiments. The wind velocity profiles used in the simulations were fitted from data obtained in field measurements. Size distribution of the emitted dust particles in the numerical simulations was taken into account using a Monte Carlo method. The PM concentration distributions at a distance of several kilometers from the dust source under specific shear velocities and PM fluxes from the soil were determined numerically by solving advection-diffusion equation. The obtained PM10 concentrations under typical wind and soil conditions are supported by PM data recorded over time in a standard environmental monitoring station. The model enhances our capacity of quantification of dust processes to support climate models as well as health risk assessment.
On the boundary layer structure near a highly permeable porous interface
Dalwadi, Mohit P; Waters, Sarah L; Oliver, James M
2015-01-01
The method of matched asymptotic expansions is used to study the canonical problem of steady laminar flow through a narrow two-dimensional channel blocked by a tight-fitting finite-length highly permeable porous obstacle. We investigate the behaviour of the local flow close to the interface between the single-phase and porous regions (governed by the incompressible Navier--Stokes and Darcy flow equations, respectively). We solve for the local flow in the limits of low and high Reynolds number, facilitating an understanding of the nature of the transition from Poiseuille to plug to Poiseuille flow in each of these limits. Significant analytic progress is made in the high-Reynolds-number limit, as we are able to explore in detail the rich boundary layer structure that occurs. We derive general results for the interfacial stress and for the conditions that couple the flow in the regions away from the interface. We consider the three-dimensional generalization to unsteady laminar flow through and around a tight-f...
Many-body microhydrodynamics of colloidal particles with active boundary layers
Singh, Rajesh; Ghose, Somdeb; Adhikari, R.
2015-06-01
Colloidal particles with active boundary layers—regions surrounding the particles where non-equilibrium processes produce large velocity gradients—are common in many physical, chemical and biological contexts. The velocity or stress at the edge of the boundary layer determines the exterior fluid flow and, hence, the many-body interparticle hydrodynamic interaction. Here, we present a method to compute the many-body hydrodynamic interaction between N spherical active particles induced by their exterior microhydrodynamic flow. First, we use a boundary integral representation of the Stokes equation to eliminate bulk fluid degrees of freedom. Then, we expand the boundary velocities and tractions of the integral representation in an infinite-dimensional basis of tensorial spherical harmonics and, on enforcing boundary conditions in a weak sense on the surface of each particle, obtain a system of linear algebraic equations for the unknown expansion coefficients. The truncation of the infinite series, fixed by the degree of accuracy required, yields a finite linear system that can be solved accurately and efficiently by iterative methods. The solution linearly relates the unknown rigid body motion to the known values of the expansion coefficients, motivating the introduction of propulsion matrices. These matrices completely characterize hydrodynamic interactions in active suspensions just as mobility matrices completely characterize hydrodynamic interactions in passive suspensions. The reduction in the dimensionality of the problem, from a three-dimensional partial differential equation to a two-dimensional integral equation, allows for dynamic simulations of hundreds of thousands of active particles on multi-core computational architectures. In our simulation of 104 active colloidal particle in a harmonic trap, we find that the necessary and sufficient ingredients to obtain steady-state convective currents, the so-called ‘self-assembled pump’, are (a) one
Meng, J. C. S.
1973-01-01
The laminar base flow field of a two-dimensional reentry body has been studied by Telenin's method. The flow domain was divided into strips along the x-axis, and the flow variations were represented by Lagrange interpolation polynomials in the transformed vertical coordinate. The complete Navier-Stokes equations were used in the near wake region, and the boundary layer equations were applied elsewhere. The boundary conditions consisted of the flat plate thermal boundary layer in the forebody region and the near wake profile in the downstream region. The resulting two-point boundary value problem of 33 ordinary differential equations was then solved by the multiple shooting method. The detailed flow field and thermal environment in the base region are presented in the form of temperature contours, Mach number contours, velocity vectors, pressure distributions, and heat transfer coefficients on the base surface. The maximum heating rate was found on the centerline, and the two-dimensional stagnation point flow solution was adquate to estimate the maximum heating rate so long as the local Reynolds number could be obtained.
Sonic eddy model of the turbulent boundary layer
Breidenthal, Robert; Dintilhac, Paul; Williams, Owen
2016-11-01
A model of the compressible turbulent boundary layer is proposed. It is based on the notion that turbulent transport by an eddy requires that information of nonsteady events propagates across the diameter of that eddy during one rotation period. The finite acoustic signaling speed then controls the turbulent fluxes. As a consequence, the fluxes are limited by the largest eddies that satisfies this requirement. Therefore "sonic eddies" with a rotational Mach number of about unity would determine the skin friction, which is predicted to vary inversely with Mach number. This sonic eddy model contrasts with conventional models that are based on the energy equation and variations in the density. The effect of density variations is known to be weak in free shear flows, and the sonic eddy model assumes the same for the boundary layer. In general, Mach number plays two simultaneous roles in compressible flow, one related to signaling and the other related to the energy equation. The predictions of the model are compared with experimental data and DNS results from the literature.
Outer layer effects in wind-farm boundary layers: Coriolis forces and boundary layer height
Allaerts, Dries; Meyers, Johan
2015-11-01
In LES studies of wind-farm boundary layers, scale separation between the inner and outer region of the atmospheric boundary layer (ABL) is frequently assumed, i.e., wind turbines are presumed to fall within the inner layer and are not affected by outer layer effects. However, modern wind turbine and wind farm design tends towards larger rotor diameters and farm sizes, which means that outer layer effects will become more important. In a prior study, it was already shown for fully-developed wind farms that the ABL height influences the power performance. In this study, we use the in-house LES code SP-Wind to investigate the importance of outer layer effects on wind-farm boundary layers. In a suite of LES cases, the ABL height is varied by imposing a capping inversion with varying inversion strengths. Results indicate the growth of an internal boundary layer (IBL), which is limited in cases with low inversion layers. We further find that flow deceleration combined with Coriolis effects causes a change in wind direction throughout the farm. This effect increases with decreasing boundary layer height, and can result in considerable turbine wake deflection near the end of the farm. The authors are supported by the ERC (ActiveWindFarms, grant no: 306471). Computations were performed on VSC infrastructiure (Flemish Supercomputer Center), funded by the Hercules Foundation and the Flemish Government-department EWI.
Full-Scale Spectrum of Boundary-Layer Winds
Larsén, Xiaoli G.; Larsen, Søren E.; Petersen, Erik L.
2016-05-01
Extensive mean meteorological data and high frequency sonic anemometer data from two sites in Denmark, one coastal onshore and one offshore, have been used to study the full-scale spectrum of boundary-layer winds, over frequencies f from about 1 yr^{-1} to 10 Hz. 10-min cup anemometer data are used to estimate the spectrum from about 1 yr^{-1} to 0.05 min^{-1}; in addition, using 20-Hz sonic anemometer data, an ensemble of 1-day spectra covering the range 1 day^{-1} to 10 Hz has been calculated. The overlapping region in these two measured spectra is in good agreement. Classical topics regarding the various spectral ranges, including the spectral gap, are revisited. Following the seasonal peak at 1 yr^{-1}, the frequency spectrum fS( f) increases with f^{+1} and gradually reaches a peak at about 0.2 day^{-1}. From this peak to about 1 hr^{-1}, the spectrum fS( f) decreases with frequency with a -2 slope, followed by a -2/3 slope, which can be described by fS(f)=a_1f^{-2/3}+a_2f^{-2}, ending in the frequency range for which the debate on the spectral gap is ongoing. It is shown here that the spectral gap exists and can be modelled. The linear composition of the horizontal wind variation from the mesoscale and microscale gives the observed spectrum in the gap range, leading to a suggestion that mesoscale and microscale processes are uncorrelated. Depending on the relative strength of the two processes, the gap may be deep or shallow, visible or invisible. Generally, the depth of the gap decreases with height. In the low frequency region of the gap, the mesoscale spectrum shows a two-dimensional isotropic nature; in the high frequency region, the classical three-dimensional boundary-layer turbulence is evident. We also provide the cospectrum of the horizontal and vertical components, and the power spectra of the three velocity components over a wide range from 1 day^{-1} to 10 Hz, which is useful in determining the necessary sample duration when measuring turbulence
A New Spectral Local Linearization Method for Nonlinear Boundary Layer Flow Problems
Directory of Open Access Journals (Sweden)
S. S. Motsa
2013-01-01
Full Text Available We propose a simple and efficient method for solving highly nonlinear systems of boundary layer flow problems with exponentially decaying profiles. The algorithm of the proposed method is based on an innovative idea of linearizing and decoupling the governing systems of equations and reducing them into a sequence of subsystems of differential equations which are solved using spectral collocation methods. The applicability of the proposed method, hereinafter referred to as the spectral local linearization method (SLLM, is tested on some well-known boundary layer flow equations. The numerical results presented in this investigation indicate that the proposed method, despite being easy to develop and numerically implement, is very robust in that it converges rapidly to yield accurate results and is more efficient in solving very large systems of nonlinear boundary value problems of the similarity variable boundary layer type. The accuracy and numerical stability of the SLLM can further be improved by using successive overrelaxation techniques.
Turbulent dispersion in cloud-topped boundary layers
Verzijlbergh, R.A.; Jonker, H.J.J.; Heus, T.; Vilà-Guerau de Arellano, J.
2009-01-01
Compared to dry boundary layers, dispersion in cloud-topped boundary layers has received less attention. In this LES based numerical study we investigate the dispersion of a passive tracer in the form of Lagrangian particles for four kinds of atmospheric boundary layers: 1) a dry convective boundary
Benchmarking high order finite element approximations for one-dimensional boundary layer problems
Malagu, M.; Benvenuti, E.; Simone, A.
2013-01-01
In this article we investigate the application of high order approximation techniques to one-dimensional boundary layer problems. In particular, we use second order differential equations and coupled second order differential equations as case studies. The accuracy and convergence rate of numerical
Boundary layer heights derived from velocity spectra
Energy Technology Data Exchange (ETDEWEB)
Hoejstrup, J.; Barthelmie, R.J. [Risoe National Lab., Roskilde (Denmark); Kaellstrand, B. [Univ. of Uppsala, Uppsala (Sweden)
1997-10-01
It is a well-known fact that the height of the mixed layer determines the size of the largest and most energetic eddies that can be observed in the unstable boundary layer, and consequently a peak can be observed in the power spectra of the along-wind velocity component at scales comparable to the mixed layer depth. We will now show how the mixed layer depth can be derived from the u-specta and the results will be compared with direct measurements using pibal and tethersonde measurements. (au)
Turbulent Boundary Layer Flow over Superhydrophobic Surfaces
2013-05-10
Figure 1 were a highly viscous fluid, such as honey , the boundary layer would be thick while if the fluid were water, a low-viscosity fluid, the boundary...drag has become even more important. In response to this need, and with the benefit of modern technology, the drag-reduction field is replete with...manufactured with “riblets,” small ridges on the order of fractions of millimeters, built-into the hull or skin that seek to reduce frictional drag. The
Self-similar magnetohydrodynamic boundary layers
Energy Technology Data Exchange (ETDEWEB)
Nunez, Manuel; Lastra, Alberto, E-mail: mnjmhd@am.uva.e [Departamento de Analisis Matematico, Universidad de Valladolid, 47005 Valladolid (Spain)
2010-10-15
The boundary layer created by parallel flow in a magnetized fluid of high conductivity is considered in this paper. Under appropriate boundary conditions, self-similar solutions analogous to the ones studied by Blasius for the hydrodynamic problem may be found. It is proved that for these to be stable, the size of the Alfven velocity at the outer flow must be smaller than the flow velocity, a fact that has a ready physical explanation. The process by which the transverse velocity and the thickness of the layer grow with the size of the Alfven velocity is detailed.
Modeling of particulate plumes transportation in boundary layers with obstacles
Karelsky, K. V.; Petrosyan, A. S.
2012-04-01
This presentation is aimed at creating and realization of new physical model of impurity transfer (solid particles and heavy gases) in areas with non-flat and/or nonstationary boundaries. The main idea of suggested method is to use non-viscous equations for solid particles transport modeling in the vicinity of complex boundary. In viscous atmosphere with as small as one likes coefficient of molecular viscosity, the non-slip boundary condition on solid surface must be observed. This postulates the reduction of velocity to zero at a solid surface. It is unconditionally in this case Prandtle hypothesis must be observed: for rather wide range of conditions in the surface neighboring layers energy dissipation of atmosphere flows is comparable by magnitude with manifestation of inertia forces. That is why according to Prandtle hypothesis in atmosphere movement characterizing by a high Reynolds number the boundary layer is forming near a planet surface, within which the required transition from zero velocities at the surface to magnitudes at the external boundary of the layer that are quite close to ones in ideal atmosphere flow. In that layer fast velocity gradients cause viscous effects to be comparable in magnitude with inertia forces influence. For conditions considered essential changes of hydrodynamic fields near solid boundary caused not only by nonslip condition but also by a various relief of surface: mountains, street canyons, individual buildings. Transport of solid particles, their ascent and precipitation also result in dramatic changes of meteorological fields. As dynamic processes of solid particles transfer accompanying the flow past of complex relief surface by wind flows is of our main interest we are to use equations of non-viscous hydrodynamic. We should put up with on the one hand idea of high wind gradients in the boundary layer and on the other hand disregard of molecular viscosity in two-phase atmosphere equations. We deal with describing high
Transportation of particulate plumes in boundary layer with obstacles
Petrosyan, A.; Karelsky, K.; Smirnov, I.
2010-05-01
This presentation is aimed at creating and realization of new physical model of impurity transfer (solid particles and heavy gases) in areas with non-flat and/or nonstationary boundaries. The main idea of suggested method is to use non-viscous equations for solid particles transport modeling in the vicinity of complex boundary. In viscous atmosphere with as small as one likes coefficient of molecular viscosity, the non-slip boundary condition on solid surface must be observed. This postulates the reduction of velocity to zero at a solid surface. It is unconditionally in this case Prandtle hypothesis must be observed: for rather wide range of conditions in the surface neighboring layers energy dissipation of atmosphere flows is comparable by magnitude with manifestation of inertia forces. That is why according to Prandtle hypothesis in atmosphere movement characterizing by a high Reynolds number the boundary layer is forming near a planet surface, within which the required transition from zero velocities at the surface to magnitudes at the external boundary of the layer that are quite close to ones in ideal atmosphere flow. In that layer fast velocity gradients cause viscous effects to be comparable in magnitude with inertia forces influence. For conditions considered essential changes of hydrodynamic fields near solid boundary caused not only by nonslip condition but also by a various relief of surface: mountains, street canyons, individual buildings. Transport of solid particles, their ascent and precipitation also result in dramatic changes of meteorological fields. As dynamic processes of solid particles transfer accompanying the flow past of complex relief surface by wind flows is of our main interest we are to use equations of non-viscous hydrodynamic. We should put up with on the one hand idea of high wind gradients in the boundary layer and on the other hand disregard of molecular viscosity in two-phase atmosphere equations. We deal with describing high
Transport of Particulates in Boundary Layer with Obstacles
Karelsky, Kirill; Petrosyan, Arakel
2014-05-01
This presentation is aimed at creating and realization of new physical model of impurity transfer (solid particles and heavy gases) in areas with non-flat and/or nonstationary boundaries. The main idea of suggested method is to use non-viscous equations for solid particles transport modeling in the vicinity of complex boundary. In viscous atmosphere with as small as one likes coefficient of molecular viscosity, the non-slip boundary condition on solid surface must be observed. This postulates the reduction of velocity to zero at a solid surface. It is unconditionally in this case Prandtle hypothesis must be observed: for rather wide range of conditions in the surface neighboring layers energy dissipation of atmosphere flows is comparable by magnitude with manifestation of inertia forces. That is why according to Prandtle hypothesis in atmosphere movement characterizing by a high Reynolds number the boundary layer is forming near a planet surface, within which the required transition from zero velocities at the surface to magnitudes at the external boundary of the layer that are quite close to ones in ideal atmosphere flow. In that layer fast velocity gradients cause viscous effects to be comparable in magnitude with inertia forces influence. For conditions considered essential changes of hydrodynamic fields near solid boundary caused not only by nonslip condition but also by a various relief of surface: mountains, street canyons, individual buildings. Transport of solid particles, their ascent and precipitation also result in dramatic changes of meteorological fields. As dynamic processes of solid particles transfer accompanying the flow past of complex relief surface by wind flows is of our main interest we are to use equations of non-viscous hydrodynamic. We should put up with on the one hand idea of high wind gradients in the boundary layer and on the other hand disregard of molecular viscosity in two-phase atmosphere equations. We deal with describing high
Boundary Layer Flow of Second Grade Fluid in a Cylinder with Heat Transfer
Directory of Open Access Journals (Sweden)
S. Nadeem
2012-01-01
Full Text Available An analysis is carried out to obtain the similarity solution of the steady boundary layer flow and heat transfer of a second grade through a horizontal cylinder. The governing partial differential equations along with the boundary conditions are reduced to dimensionless form by using the boundary layer approximation and applying suitable similarity transformation. The resulting nonlinear coupled system of ordinary differential equations subject to the appropriate boundary conditions is solved by homotopy analysis method (HAM. The effects of the physical parameters on the flow and heat transfer characteristics of the model are presented. The behavior of skin friction coefficient and Nusselt numbers is studied for different parameters.
Aerosol fluxes in the marine boundary layer
Petelski, Tomasz; Zieliński, Tymon; Makuch, Przemysław; Kowalczyk, Jakub; Ponczkowska, Agnieszka; Drozdowska, Violetta; Piskozub, Jacek
2010-05-01
We present aerosol emission fluxes and concentrations calculated from in-situ measurement in the Nordic Sea from R/V Oceania. We compare vertical fluxes calculated with the eddy correlation and gradient methods. We use the results to test the hypothesis that marine aerosol emitted from the sea surface helps to clear the boundary layer from other aerosol particles. As the emitted droplets do not dry out in the highly humid surface layer air and because of their sizes most of them are deposited quickly at the sea surface. Therefore marine aerosol has many features of rain meaning that the deposition in the marine boundary layer in high wind events is controlled not only by the "dry" processes but also by the "wet" scavenging. We have estimated the effectiveness of the process using our own measurements of vertical aerosol fluxes in the Nordic Seas. This process could explain observed phenomenon of lower Arctic aerosol optical thickness (AOT) when the air masses moved over open sea than over sea-ice. We show a negative correlation between the sea-ice coverage in the seas adjacent to Svalbard and monthly AOT values in Ny Alesund.
A global boundary-layer height climatology
Energy Technology Data Exchange (ETDEWEB)
Dop, H. van; Krol, M.; Holtslag, B. [Inst. for Marine and Atmospheric Research Utrecht, IMAU, Utrecht (Netherlands)
1997-10-01
In principle the ABL (atmospheric boundary layer) height can be retrieved from atmospheric global circulation models since they contain algorithms which determine the intensity of the turbulence as a function of height. However, these data are not routinely available, or on a (vertical) resolution which is too crude in view of the application. This justifies the development of a separate algorithm in order to define the ABL. The algorithm should include the generation of turbulence by both shear and buoyancy and should be based on readily available atmospheric parameters. There is obviously a wide application for boundary heights in off-line global and regional chemistry and transport modelling. It is also a much used parameter in air pollution meteorology. In this article we shall present a theory which is based on current insights in ABL dynamics. The theory is applicable over land and sea surfaces in all seasons. The theory is (for various reasons) not valid in mountainous areas. In areas where boundary-layer clouds or deep cumulus convection are present the theory does not apply. However, the same global atmospheric circulation models contain parameterizations for shallow and deep convection from which separate estimates can be obtained for the extent of vertical mixing. (au)
Turbulent boundary layer over a chine.
Panchapakesan, N. R.; Joubert, P. N.
1999-11-01
The flow over an edge aligned with the streamwise direction is studied as a representative of the turbulent boundary layers developing over hard chines found on the hulls of ships and catamarans. We present results of a traditional experimental investigation of this geometry in a wind tunnel with pitot tubes and hot-wires. The chine model consisted of two surfaces made of varnished fibre boards with leading edges of airfoil sections and a 90 degree corner. The boundary layer was tripped with wires close to the leading edge. The model was housed in a test section of length 6.5 m in a closed circuit wind tunnel. The experiments were conducted at a unit Reynolds number of 680,000 /m corresponding to a nominal free stream velocity of 10 m/s. The mean velocity field and the associated integral parameters obtained with pitot tube measurements are presented for different streamwise locations from 0.2 to 4.7 m from the trip wire. The flow at the two farthest locations were also studied with single and 'x' hot-wires. The secondary mean flow and the turbulence field in the corner region are described with these measurements.
Directory of Open Access Journals (Sweden)
Savić Slobodan
2006-01-01
Full Text Available This paper investigates ionized gas flow in the boundary layer when its electroconductivity is varied. The flow is planar and the contour is porous. At first, it is assumed that the ionized gas electroconductivity σ depends only on the longitudinal variable. Then we adopt that it is a function of the ratio of the longitudinal velocity and the velocity at the outer edge of the boundary layer. For both electroconductivity variation laws, by application of the general similarity method, the governing boundary layer equations are brought to a generalized form and numerically solved in a four-parametric three times localized approximation. Based on many tabular solutions, we have shown diagrams of the most important nondimensional values and characteristic boundary layer functions for both of the assumed laws. Finally, some conclusions about influence of certain physical values on ionized gas flow in the boundary layer have been drawn. .
Large Eddy Simulation and Study of the Urban Boundary Layer
Institute of Scientific and Technical Information of China (English)
苗世光; 蒋维楣
2004-01-01
Based on a pseudo-spectral large eddy simulation (LES) model, an LES model with an anisotropy turbulent kinetic energy (TKE) closure model and an explicit multi-stage third-order Runge-Kutta scheme is established. The modeling and analysis show that the LES model can simulate the planetary boundary layer (PBL) with a uniform underlying surface under various stratifications very well. Then, similar to the description of a forest canopy, the drag term on momentum and the production term of TKE by subgrid city buildings are introduced into the LES equations to account for the area-averaged effect of the subgrid urban canopy elements and to simulate the meteorological fields of the urban boundary layer (UBL). Numerical experiments and comparison analysis show that: (1) the result from the LES of the UBL with a proposed formula for the drag coefficient is consistent and comparable with that from wind tunnel experiments and an urban subdomain scale model; (2) due to the effect of urban buildings, the wind velocity near the canopy is decreased, turbulence is intensified, TKE, variance, and momentum flux are increased, the momentum and heat flux at the top of the PBL are increased, and the development of the PBL is quickened; (3) the height of the roughness sublayer (RS) of the actual city buildings is the maximum building height (1.5-3 times the mean building height), and a constant flux layer (CFL) exists in the lower part of the UBL.
Analysis of boundary layer flow over a porous nonlinearly stretching sheet with partial slip at
Directory of Open Access Journals (Sweden)
Swati Mukhopadhyay
2013-12-01
Full Text Available The boundary layer flow of a viscous incompressible fluid toward a porous nonlinearly stretching sheet is considered in this analysis. Velocity slip is considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equation corresponding to the momentum equation into nonlinear ordinary differential equation. Numerical solution of this equation is obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter.
Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet
Institute of Scientific and Technical Information of China (English)
Krishnendu Bhattacharyya
2011-01-01
An analysis is made to study boundary layer flow and heat transfer over an exponentially shrinking sheet.Using similarity transformations in exponential form,the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations,which are then solved numerically using a very effcient shooting method. The analysis reveals the conditions for the existence of steady boundary layer flow due to exponential shrinking of the sheet and it is found that when the mass suction parameter exceeds a certain critical value,steady flow is possible.The dual solutions for velocity and temperature distributions are obtained.With increasing values of the mass suction parameter,the skin friction coefficient increases for the first solution and decreases for the second solution.
Characterization of an incipiently separated shock wave/turbulent boundary layer interaction
Schreyer, A.-M.; Dussauge, J.-P.; Krämer, E.
2017-03-01
The turbulence structure in a shock wave/turbulent boundary layer interaction at incipient separation was investigated in order to get insight into turbulence generation and amplification mechanisms in such flow fields. The flow along a two-dimensional 11.5° compression corner was studied experimentally at a Mach number of M=2.53 and with a momentum-thickness Reynolds number of Re_{θ }=5370. From hot-wire boundary layer traverses and surface heat-flux density fluctuation measurements with the fast-response atomic layer thermopile, the turbulence structure and amplification was described. Space-time correlations of the mass-flux fluctuations across the boundary layer and the surface heat-flux density fluctuations were measured to further characterize the development of the turbulence structure across the interaction. The large-scale boundary layer structures are concealed by shock-related effects in the strongly disturbed shock-foot region. Shortly downstream, however, large-scale structures dominate the signal again, just as in the incoming flow. A mechanism explaining this behavior is suggested.
Flowfield measurements in a separated and reattached flat plate turbulent boundary layer
Patrick, William P.
1987-03-01
The separation and reattachment of a large-scale, two-dimensional turbulent boundary layer at low subsonic speed on a flat plate has been studied experimentally. The separation bubble was 55 cm long and had a maximum bubble thickness, measured to the height of the mean dividing streamline, of 17 cm, which was twice the thickness of the inlet boundary layer. A combination of laser velocimetry, hot-wire anemometry, pneumatic probing techniques, and flow visualization were used as diagnostics. Principal findings were that an outer inviscid rotational flow was defined which essentially convected over the blockage associated with the inner, viscously dominated bubble recirculation region. A strong backflow region in which the flow moved upstream 100 percent of the time was measured near the test surface over the central 35 percent of the bubble. A laminar backflow boundary layer having pseudo-turbulent characteristics including a log-linear velocity profile was generated under the highly turbulent backflow. Velocity profile shapes in the reversed flow region matched a previously developed universal backflow profile at the upstream edge of the separation region but not in the steady backflow region downstream. A smoke flow visualization movie and hot-film measurements revealed low frequency nonperiodic flapping at reattachment. However, forward flow fraction data at reattachment and mean velocity profiles in the redeveloping boundary layer downstream of reattachment correlated with backward-facing step data when the axial dimension was scaled by the distance from the maximum bubble thickness to reattachment.
Breaking the boundary layer symmetry in turbulent convection using wall geometry
Toppaladoddi, Srikanth; Wettlaufer, John S
2014-01-01
We systematically probe the interaction of the boundary layer with the core flow during two-dimensional turbulent Rayleigh-B\\'{e}nard convection using numerical simulations and scaling theory. The boundary layer/core flow interaction is manipulated by configuring the top plate with a sinusoidal geometry and breaking the symmetry between the top and bottom thermal boundary layers. At long wavelength the planar results are recovered. However, at intermediate wavelengths, and for Rayleigh numbers ($Ra$) such that the amplitude of the roughness elements is larger than the boundary layer thickness, there is enhanced cold plume production at the tips of the elements. It is found that, while the interior of the flow is well mixed as in the classical theory of Malkus, the mean temperature is lower than that in the planar case. For a Prandtl number of unity and $Ra = 10^6$ to $2.5 \\times 10^9$ we find a Nusselt number ($Nu$) scaling law of $Nu = 0.052 \\times Ra^{0.34}$, in good agreement with recent experiments. The c...
Omori, S.; Gross, K. W.
1973-01-01
The turbulent kinetic energy equation is coupled with boundary layer equations to solve the characteristics of compressible turbulent boundary layers with mass injection and combustion. The Reynolds stress is related to the turbulent kinetic energy using the Prandtl-Wieghardt formulation. When a lean mixture of hydrogen and nitrogen is injected through a porous plate into the subsonic turbulent boundary layer of air flow and ignited by external means, the turbulent kinetic energy increases twice as much as that of noncombusting flow with the same mass injection rate of nitrogen. The magnitudes of eddy viscosity between combusting and noncombusting flows with injection, however, are almost the same due to temperature effects, while the distributions are different. The velocity profiles are significantly affected by combustion. If pure hydrogen as a transpiration coolant is injected into a rocket nozzle boundary layer flow of combustion products, the temperature drops significantly across the boundary layer due to the high heat capacity of hydrogen. At a certain distance from the wall hydrogen reacts with the combustion products, liberating an extensive amount of heat.
Receptivity of Hypersonic Boundary Layers to Acoustic and Vortical Disturbances (Invited)
Balakumar, P.
2015-01-01
Boundary-layer receptivity to two-dimensional acoustic and vortical disturbances for hypersonic flows over two-dimensional and axi-symmetric geometries were numerically investigated. The role of bluntness, wall cooling, and pressure gradients on the receptivity and stability were analyzed and compared with the sharp nose cases. It was found that for flows over sharp nose geometries in adiabatic wall conditions the instability waves are generated in the leading-edge region and that the boundary layer is much more receptive to slow acoustic waves as compared to the fast waves. The computations confirmed the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary layer transition. The receptivity coefficients in flows over blunt bodies are orders of magnitude smaller than that for the sharp cone cases. Wall cooling stabilizes the first mode strongly and destabilizes the second mode. However, the receptivity coefficients are also much smaller compared to the adiabatic case. The adverse pressure gradients increased the unstable second mode regions.
Cooper, B. P., Jr.
1979-01-01
A model for the boundary layer at the exit plane of a rocket nozzle was developed which, unlike most previous models, includes the subsonic sublayer. The equations for the flow near the nozzle exit plane are presented and the method by which the subsonic sublayer transitions to supersonic flow in the plume is described. The resulting model describes the entire boundary layer and can be used to provide a startline for method-of-characteristics calculations of plume flowfields. The model was incorporated into a method of characteristics computer program and comparisons of computed results to experimental data show good agreement. The data used in the comparisons were obtained in tests in which mass fluxes from a 22.2-N (5 lbf) thrust engine were measured at angles off the nozzle centerline of up to 150 deg. Additional comparisons were made with data obtained during tests of a 0.89-N (0.2 lbr) monopropellant thruster and from the OH-64 space shuttle heating tests. The agreement with the data indicates that the model can be used for calculating plume backflow properties.
Directory of Open Access Journals (Sweden)
Mohammed J Uddin
Full Text Available Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Some measurements in synthetic turbulent boundary layers
Savas, O.
1980-01-01
Synthetic turbulent boundary layers are examined which were constructed on a flat plate by generating systematic moving patterns of turbulent spots in a laminar flow. The experiments were carried out in a wind tunnel at a Reynolds number based on plate length of 1,700,000. Spots were generated periodically in space and time near the leading edge to form a regular hexagonal pattern. The disturbance mechanism was a camshaft which displaced small pins momentarily into the laminar flow at frequencies up to 80 Hz. The main instrumentation was a rake of 24 hot wires placed across the flow in a line parallel to the surface. The main measured variable was local intermittency; i.e., the probability of observing turbulent flow at a particular point in space and time. The results are reported in x-t diagrams showing the evolution of various synthetic flows along the plate. The dimensionless celerity or phase velocity of the large eddies is found to be 0.88, independent of eddy scale. All patterns with sufficiently small scales eventually showed loss of coherence as they moved downstream. A novel phenomenon called eddy transposition was observed in several flows which contained appreciable laminar regions. The large eddies shifted in formation to new positions, intermediate to their original ones, while preserving their hexagonal pattern. The present results, together with some empirical properties of a turbulent spot, are used to estimate the best choice of scales for constructing a synthetic boundary layer suitable for detailed study. The values recommended are: spanwise scale/thickness = 2.5, streamwise scale/thickness = 8.
Institute of Scientific and Technical Information of China (English)
黄健; 戴正德
2004-01-01
在本文中,我们在Banach空间考虑二维广义Ginzburg-Landau方程的指数吸引子,且得到其分形维度估计.%In this paper, we consider the exponential attractor for the derivative two - dimensional Ginzburg - Landau equation in Banach space Xαp and also obtain the estimation of the fractal dimension.
Aerodynamic Heating in Hypersonic Boundary Layers:\\ Role of Dilatational Waves
Zhu, Yiding; Wu, Jiezhi; Chen, Shiyi; Lee, Cunbiao; Gad-el-Hak, Mohamed
2016-01-01
The evolution of multi-mode instabilities in a hypersonic boundary layer and their effects on aerodynamic heating are investigated. Experiments are conducted in a Mach 6 wind tunnel using Rayleigh-scattering flow visualization, fast-response pressure sensors, fluorescent temperature-sensitive paint (TSP), and particle image velocimetry (PIV). Calculations are also performed based on both parabolized stability equations (PSE) and direct numerical simulations (DNS). It is found that second-mode dilatational waves, accompanied by high-frequency alternating fluid compression and expansion, produce intense aerodynamic heating in a small region that rapidly heats the fluid passing through it. As a result, the surface temperature rapidly increases and results in an overshoot over the nominal transitional value. When the dilatation waves decay downstream, the surface temperature decreases gradually until transition is completed. A theoretical analysis is provided to interpret the temperature distribution affected by ...
Direct force wall shear measurements in pressure-driven three-dimensional turbulent boundary layers
Mcallister, J. E.; Tennant, M. H.; Pierce, F. J.
1982-01-01
Unique, simultaneous direct measurements of the magnitude and direction of the local wall shear stress in a pressure-driven three-dimensional turbulent boundary layer are presented. The flow is also described with an oil streak wall flow pattern, a map of the wall shear stress-wall pressure gradient orientations, a comparison of the wall shear stress directions relative to the directions of the nearest wall velocity as measured with a typical, small boundary layer directionally sensitive claw probe, as well as limiting wall streamline directions from the oil streak patterns, and a comparison of the freestream streamlines and the wall flow streamlines. A review of corrections for direct force sensing shear meters for two-dimensional flows is presented with a brief discussion of their applicability to three-dimensional devices.
DNS of laminar-turbulent boundary layer transition induced by solid obstacles
Orlandi, Paolo; Bernardini, Matteo
2015-01-01
Results of numerical simulations obtained by a staggered finite difference scheme together with an efficient immersed boundary method are presented to understand the effects of the shape of three-dimensional obstacles on the transition of a boundary layer from a laminar to a turbulent regime. Fully resolved Direct Numerical Simulations (DNS), highlight that the closer to the obstacle the symmetry is disrupted the smaller is the transitional Reynolds number. It has been also found that the transition can not be related to the critical roughness Reynolds number used in the past. The simulations highlight the differences between wake and inflectional instabilities, proving that two-dimensional tripping devices are more efficient in promoting the transition. Simulations at high Reynolds number demonstrate that the reproduction of a real experiment with a solid obstacle at the inlet is an efficient tool to generate numerical data bases for understanding the physics of boundary layers. The quality of the numerical ...
Wang, T.; Simon, T. W.
1987-01-01
The test section of the present experiment to ascertain the effects of convex curvature and freestream turbulence on boundary layer momentum and heat transfer during natural transition provided a two-dimensional boundary layer flow on a uniformly heated curved surface, with bending to various curvature radii, R. Attention is given to results for the cases of R = infinity, 180 cm, and 90 cm, each with two freestream turbulence intensity levels. While the mild convex curvature of R = 180 cm delays transition, further bending to R = 90 cm leads to no signifucant further delay of transition. Cases with both curvature and higher freestream disturbance effects exhibit the latter's pronounced dominance. These data are pertinent to the development of transition prediction models for gas turbine blade design.
Study of interaction between shock wave and unsteady boundary layer
Institute of Scientific and Technical Information of China (English)
董志勇; 韩肇元
2003-01-01
This paper reports theoretical and experimental study of a new type of interaction of a moving shock wave with an unsteady boundary layer. This type of shock wave-boundary layer interaction describes a moving shock wave interaction with an unsteady boundary layer induced by another shock wave and a rarefaction wave. So it is different from the interaction of a stationary shock wave with steady boundary layer, also different from the interaction of a reflected moving shock wave at the end of a shock tube with unsteady boundary layer induced by an incident shock. Geometrical shock dynamics is used for the theoretical analysis of the shock wave-unsteady boundary layer interaction, and a double-driver shock tube with a rarefaction wave bursting diaphragm is used for the experimental investigation in this work.
Kim, S.W.; Park, S.U.; Pino, D.; Vilà-Guerau de Arellano, J.
2006-01-01
Basic entrainment equations applicable to the sheared convective boundary layer (CBL) are derived by assuming an inversion layer with a finite depth, i.e., the first-order jump model. Large-eddy simulation data are used to determine the constants involved in the parameterizations of the entrainment
Similarity solutions to a laminar boundary layer problem in power law fluids
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A suitable similarity transformation is introduced to reduce the laminar boundary layer equations of power law fluids to a class of singular nonlinear two-point boundary value problems. The skin friction and shear stress distributions for boundary layer flow over a moving flat plate are investigated by utilizing the shooting technique. Results indicate that for each fixed value of the power law exponent n or the velocity ratio parameter (, the skin friction and shear stress decrease with the increasing of n or ( respectively.
Comparison two different LES closure models of the transitional boundary layer flow
Ivanov, Dimitry; Chorny, Andrei
2016-11-01
The goal of the present research is to measure the velocity profile in the thin boundary layer of a flat plate at zero angle of attack. We consider a flow over a flat plate with a uniform velocity profile. The uniform velocity fluid hits the leading edge of the flat plate, and a laminar boundary layer begins to develop. The near-wall, subgrid-scale (SGS) model is used to perform Large Eddy Simulation (LES) of the incompressible developing, smooth-wall, flat-plate turbulent boundary layer. In this model, the stretched-vortex, SGS closure is utilized in conjunction with a tailored, near-wall model designed to incorporate anisotropic vorticity scales in the presence of the wall. The composite SGS-wall model is presently incorporated into a computer code suitable for the LES of developing flat-plate boundary layers. Presently this model is extended to the LES of the zero-pressure gradient, flat-plate turbulent boundary layer. LES solver using Smagorinsky and the One-equation LES turbulence models. Results show that the normalized mean velocity profile is in good agreement with the universal law-of-the-wall and previous published data. In order to ensure the quality of the numerical results a convergence study was performed.
Drag of a turbulent boundary layer with transverse 2D circular rods on the wall
Kamruzzaman, Md; Djenidi, L.; Antonia, R. A.; Talluru, K. M.
2015-06-01
In this paper, we present the results of a turbulent boundary layer developing over a rod-roughened wall with a spacing of ( is the spacing between two adjacent roughness elements, and is the rod diameter). Static pressure measurements are taken around a single roughness element to accurately determine the friction velocity, and the error in the origin, , which are the two prominent issues that surround rough-wall boundary layers. In addition, velocity measurements are taken at several streamwise locations using hot-wire anemometry to obtain from the momentum integral equation. Results showed that both methods give consistent values for , indicating that the contribution of the viscous drag over this rough wall is negligible. This supports the results of Perry et al. (J Fluid Mech 177:437-466, 1969) and Antonia and Luxton (J Fluid Mech 48(04):721-761, 1971) in a boundary layer and of Leonardi et al. (2003) in a channel flow but does not agree with those of Furuya et al. (J Fluids Eng 98(4):635-643, 1976). The results show that both and can be unambiguously measured on this particular rough wall. This paves the way for a proper comparison between the boundary layer developing over this wall and the smooth-wall turbulent boundary layer.
End-wall boundary layer measurements in a two-stage fan
Ball, C. L.; Reid, L.; Schmidt, J. F.
1983-01-01
Detailed flow measurements made in the casing boundary layer of a two-stage transonic fan are summarized. These measurements were taken at stations upstream of the fan, between all blade rows, and downstream of the last blade row. At the design tip speed of 429 m/sec the fan achieved a peak efficiency of 0.846 at a pressure ratio of 2.471. The boundary layer data were obtained at three weight flows at the design speed: one near choke flow, one near peak efficiency, and one near stall. Conventional boundary layer parameters were calculated from the data measured at each measuring station for each of the three flows. A classical two dimensional casing boundary layer was measured at the fan inlet and extended inward to approximately 15 percent of span. A highly three dimensional boundary layer was measured at the exit of each blade row and extended inward to approximately 10 percent of span. The steep radial gradient of axial velocity noted at the exit of the rotors was reduced substantially as the flow passed through the stators. This reduced gradient is attributed to flow mixing. The amount of flow mixing was reflected in the radial redistribution of total temperature as the flow passed through the stators. The data also show overturning of the tip flow at the stator exits that is consistent with the expected effect of the secondary flow field. The blockage factors calculated from the measured data show an increase in blockage across the rotors and a decrease across the stators.
A Cautionary Note on the Thermal Boundary Layer Similarity Scaling for the Turbulent Boundary Layer
Weyburne, David
2016-01-01
Wang and Castillo have developed empirical parameters for scaling the temperature profile of the turbulent boundary layer flowing over a heated wall in the paper X. Wang and L. Castillo, J. Turbul., 4, 1(2003). They presented experimental data plots that showed similarity type behavior when scaled with their new scaling parameters. However, what was actually plotted, and what actually showed similarity type behavior, was not the temperature profile but the defect profile formed by subtracting the temperature in the boundary layer from the temperature in the bulk flow. We show that if the same data and same scaling is replotted as just the scaled temperature profile, similarity is no longer prevalent. This failure to show both defect profile similarity and temperature profile similarity is indicative of false similarity. The nature of this false similarity problem is discussed in detail.
Analytical solution of conjugate turbulent forced convection boundary layer flow over plates
Directory of Open Access Journals (Sweden)
Joneydi Shariatzadeh Omid
2016-01-01
Full Text Available A conjugate (coupled forced convection heat transfer from a heated conducting plate under turbulent boundary layer flow is considered. A heated plate of finite thickness is cooled under turbulent forced convection boundary layer flow. Because the conduction and convection boundary layer flow is coupled (conjugated in the problem, a semi-analytical solution based on Differential Transform Method (DTM is presented for solving the non-linear integro-differential equation occurring in the problem. The main conclusion is that in the conjugate heat transfer case the temperature distribution of the plate is flatter than the one in the non-conjugate case. This feature is more pronounced under turbulent flow when compared with the laminar flow.
The Boundary Layer Interaction with Shock Wave and Expansion Fan
Institute of Scientific and Technical Information of China (English)
MaratA.Goldfeld; RomanV.Nestoulia; 等
2000-01-01
The results of experimental investigation of a turbulent boundary layer on compression and expansion surfaces are presented.They include the study of the shock wave and /or expansion fan action upon the boundary layer,boundary layer sepqartion and its relaxation.Complex events of paired interactions and the flow on compression convex-concave surfaces were studied.The posibility and conditions of the boundary layer relaminarization behind the expansion fan and its effect on the relaxation length are presented.Different model configurations for wide range conditions were investigated.Comparison of results for different interactions was carried out.
Nonparallel stability of boundary layers with pressure gradients and suction
Saric, W. S.; Nayfeh, A. H.
1977-01-01
An analysis is presented for the linear nonparallel stability of boundary layer flows with pressure gradients and suction. The effect of the boundary layer growth is included by using the method of multiple scales. The present analysis is compared with those of Bouthier and Gaster and the roles of the different definitions of the amplification rates are discussed. The results of these theories are compared with experimental data for the Blasius boundary layer. Calculations are presented for stability characteristics of boundary layers with pressure gradients and nonsimilar suction distributions.
Turbulent dispersion in cloud-topped boundary layers
Verzijlbergh, R. A.; Jonker, H. J. J.; Heus, T.; Vilöguerau de Arellano, J.
2009-02-01
Compared to dry boundary layers, dispersion in cloud-topped boundary layers has received less attention. In this LES based numerical study we investigate the dispersion of a passive tracer in the form of Lagrangian particles for four kinds of atmospheric boundary layers: 1) a dry convective boundary layer (for reference), 2) a "smoke" cloud boundary layer in which the turbulence is driven by radiative cooling, 3) a stratocumulus topped boundary layer and 4) a shallow cumulus topped boundary layer. We show that the dispersion characteristics of the smoke cloud boundary layer as well as the stratocumulus situation can be well understood by borrowing concepts from previous studies of dispersion in the dry convective boundary layer. A general result is that the presence of clouds enhances mixing and dispersion - a notion that is not always reflected well in traditional parameterization models, in which clouds usually suppress dispersion by diminishing solar irradiance. The dispersion characteristics of a cumulus cloud layer turn out to be markedly different from the other three cases and the results can not be explained by only considering the well-known top-hat velocity distribution. To understand the surprising characteristics in the shallow cumulus layer, this case has been examined in more detail by 1) determining the velocity distribution conditioned on the distance to the nearest cloud and 2) accounting for the wavelike behaviour associated with the stratified dry environment.
The onset of thermal instability of a two-dimensional hydromagnetic stagnation point flow
Energy Technology Data Exchange (ETDEWEB)
Amaouche, Mustapha; Bouda, Faical Nait [Laboratoire de physique theorique, Universite de Bejaia, Route de Targua Ouzemour Bejaia (Algeria); Sadat, Hamou [Laboratoire d' Etudes Thermiques, Universite de Poitiers, 40 Avenue du Recteur Pineau, 86022 Poitiers (France)
2005-10-01
The aim of the present paper is to examine the effects of a constant magnetic field on the thermal instability of a two-dimensional stagnation point flow. First, it is shown that a basic flow, described by an exact solution of the full Navier-Stokes equations exists under some conditions relating the orientation of the magnetic field in the plane of motion to the obliqueness of free stream. The stability of the basic flow is then investigated in the usual fashion by making use of the normal mode decomposition. The resulting eigenvalue problem is solved numerically by means of a pseudo spectral collocation method based upon Laguerre's functions. The use of this procedure is warranted by the exponential damping of disturbances far from the boundary layer and the appropriate distribution of the roots of Laguerre's polynomials to treat boundary layer problems. It is found through the calculation of neutral stability curves that magnetic field acts to increase the stability of the basic flow. (author)
Solution of the Falkner Skan equation for wedge by Adomian Decomposition Method
Alizadeh, Ebrahim; Farhadi, Mousa; Sedighi, Kurosh; Ebrahimi-Kebria, H. R.; Ghafourian, Akbar
2009-03-01
The Adomian Decomposition Method is employed in the solution of the two dimensional laminar boundary layer of Falkner-Skan equation for wedge. This work aims at the solution of momentum equation in the case of accelerated flow and decelerated flow with separation. The Adomian Decomposition Method is provided an analytical solution in the form of an infinite power series. The effect of Adomian polynomials terms is considered on accuracy of the results. The velocity profiles in boundary layer are obtained. Results show a good accuracy compared to the exact solution.
Control of the Transitional Boundary Layer
Belson, Brandt A.
This work makes advances in the delay of boundary layer transition from laminar to turbulent flow via feedback control. The applications include the reduction of drag over streamline bodies (e.g., airplane wings) and the decrease of mixing and heat transfer (e.g., over turbine blades in jet engines). A difficulty in many fields is designing feedback controllers for high-dimensional systems, be they experiments or high-fidelity simulations, because the required time and resources are too large. A cheaper alternative is to approximate the high-dimensional system with a reduced-order model and design a controller for the model. We implement several model reduction algorithms in "modred", an open source and publicly available library that is applicable to a wide range of problems. We use this library to study the role of sensors and actuators in feedback control of transition in the 2D boundary layer. Previous work uses a feedforward configuration in which the sensor is upstream of the actuator, but we show that the actuator-sensor pair is unsuitable for feedback control due to an inability to sense the exponentially-growing Tollmien-Schlichting waves. A new actuator-sensor pair is chosen that more directly affects and measures the TS waves, and as a result it is effective in a feedback configuration. Lastly, the feedback controller is shown to outperform feedforward controllers in the presence of unmodeled disturbances. Next, we focus on a specific type of actuator, the single dielectric barrier discharge (SDBD) plasma actuator. An array of these plasma actuators is oriented to produce stream-wise vorticity and thus directly cancel the structures with the largest transient growth (so-called stream-wise streaks). We design a feedback controller using only experimental data by first developing an empirical input-output quasi-steady model. Then, we design feedback controllers for the model such that the controllers perform well when applied to the experiment. Lastly, we
Directory of Open Access Journals (Sweden)
D. Pino
2011-12-01
Full Text Available Interpretation of observed diurnal carbon dioxide (CO_{2} mixing ratios near the surface requires knowledge of the local dynamics of the planetary boundary layer. In this paper, we quantify the relationship between the boundary layer dynamics and the CO_{2} budget in convective conditions through a newly derived set of analytical equations. From these equations, we are able to quantify how uncertainties in boundary layer dynamical variables or in the morning CO_{2} distribution in the mixed-layer or in the free atmosphere influence the bulk CO_{2} mixing ratio.
We find that the largest uncertainty incurred on the mid-day CO_{2} mixing ratio comes from the prescribed early morning CO_{2} mixing ratios in the stable boundary layer, and in the free atmosphere. Errors in these values influence CO_{2} mixing ratios inversely proportional to the boundary layer depth (h, just like uncertainties in the assumed initial boundary layer depth and surface CO_{2} flux. The influence of uncertainties in the boundary layer depth itself are one order of magnitude smaller. If we "invert" the problem and calculate CO_{2} surface exchange from observed or simulated CO_{2} mixing ratios, the sensitivities to errors in boundary layer dynamics also invert: they become linearly proportional to the boundary layer depth.
We demonstrate these relations for a typical well characterized situation at the Cabauw tower in the Netherlands, and conclude that knowledge of the temperature and carbon dioxide vertical profiles in the early morning are of vital importance to correctly interpret observed CO_{2} mixing ratios during midday.
Pino, D.; Vilà-Guerau de Arellano, J.; Peters, W.; Schröter, J.; van Heerwaarden, C. C.; Krol, M. C.
2012-03-01
Interpretation of observed diurnal carbon dioxide (CO2) mixing ratios near the surface requires knowledge of the local dynamics of the planetary boundary layer. In this paper, we study the relationship between the boundary layer dynamics and the CO2 budget in convective conditions through a newly derived set of analytical equations. From these equations, we are able to quantify how uncertainties in boundary layer dynamical variables or in the morning CO2 distribution in the mixed-layer or in the free atmosphere (FA) influence the bulk CO2 mixing ratio. We find that the largest uncertainty incurred on the mid-day CO2 mixing ratio comes from the prescribed early morning CO2 mixing ratios in the stable boundary layer, and in the free atmosphere. Errors in these values influence CO2 mixing ratios inversely proportional to the boundary layer depth (h), just like uncertainties in the assumed initial boundary layer depth and surface CO2 flux. The influence of uncertainties in the boundary layer depth itself is one order of magnitude smaller. If we "invert" the problem and calculate CO2 surface exchange from observed or simulated CO2 mixing ratios, the sensitivities to errors in boundary layer dynamics also invert: they become linearly proportional to the boundary layer depth. We demonstrate these relations for a typical well characterized situation at the Cabauw site in The Netherlands, and conclude that knowledge of the temperature and carbon dioxide profiles of the atmosphere in the early morning are of vital importance to correctly interpret observed CO2 mixing ratios during midday.
Methods for determining the height of the atmospheric boundary layer
Energy Technology Data Exchange (ETDEWEB)
Sugiyama, Gayle [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Nasstrom, John S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
1999-02-01
The Atmospheric Release Advisory Capability (ARAC) is an operational emergency response program which provides real-time dose assessments of airborne pollutant releases. This report reviews methodologies for determining the height of the atmospheric boundary layer (ABL), which were investigated for use in the next generation of ARAC diagnostic and dispersion models. The ABL height, h_{ABL}, is an essential parameter in atmospheric dispersion modeling, controlling the extent of the vertical mixing of pollutants near the surface. Although eventually instrumentation (radiosonde, lidar, sodar, etc.) may provide accurate means for determining h_{ABL}, at present the availability of such data is too limited to provide a general capability for ARAC. The current operational ARAC diagnostic models use a fixed value of h_{ABL} for any given time. ARAC's new models support a horizontally-varying atmospheric boundary layer height, which is used to generate meteorological (mean wind, temperature, etc.) and turbulence fields. The purpose of the present work is to develop methods to derive the ABL height for all atmospheric stability regimes. One of our key requirements is to provide approaches which are applicable to routinely available data, which may be of limited temporal and spatial resolution. The final objective is to generate a consistent set of meteorological and turbulence or eddy diffusivity fields to drive the new ARAC dispersion model. A number of alternative definitions of the atmospheric boundary layer exist, leading to different approaches to deriving h_{ABL}. The definitions are based on either the turbulence characteristics of the atmosphere or the vertical structure of one or more meteorological variables. Most diagnostic analyses determine h_{ABL} from profiles of temperature or occasionally wind. A class of methods of considerable current interest are based on Richardson number criteria. Prognostic methods
Shock-Wave Boundary Layer Interactions
1986-02-01
proprietes de la couche limite subissent au cours de I’interaction; les methodes integrales ou aux differences finies qui permettent le calcul continu de...interesse par la recherche d’une plus ample information. CONTENTS Page PREFACE »’ INTRODUCTION 1 PART I: A PHYSICAL DESCRIPTION OF SHOCK-WAVE/BOUNDARY...References 105 109 PART II: METHODS OF CALCULATION GLOBAL METHODS 1.1 Introductory Remarks 109 1.2 Two-Dimensional Interactions HO 1.2.1
Osserman, Robert
2011-01-01
The basic component of several-variable calculus, two-dimensional calculus is vital to mastery of the broader field. This extensive treatment of the subject offers the advantage of a thorough integration of linear algebra and materials, which aids readers in the development of geometric intuition. An introductory chapter presents background information on vectors in the plane, plane curves, and functions of two variables. Subsequent chapters address differentiation, transformations, and integration. Each chapter concludes with problem sets, and answers to selected exercises appear at the end o
Juday, Richard D. (Inventor)
1992-01-01
A two-dimensional vernier scale is disclosed utilizing a cartesian grid on one plate member with a polar grid on an overlying transparent plate member. The polar grid has multiple concentric circles at a fractional spacing of the spacing of the cartesian grid lines. By locating the center of the polar grid on a location on the cartesian grid, interpolation can be made of both the X and Y fractional relationship to the cartesian grid by noting which circles coincide with a cartesian grid line for the X and Y direction.
Large Eddy Simulation of Transitional Boundary Layer
Sayadi, Taraneh; Moin, Parviz
2009-11-01
A sixth order compact finite difference code is employed to investigate compressible Large Eddy Simulation (LES) of subharmonic transition of a spatially developing zero pressure gradient boundary layer, at Ma = 0.2. The computational domain extends from Rex= 10^5, where laminar blowing and suction excites the most unstable fundamental and sub-harmonic modes, to fully turbulent stage at Rex= 10.1x10^5. Numerical sponges are used in the neighborhood of external boundaries to provide non-reflective conditions. Our interest lies in the performance of the dynamic subgrid scale (SGS) model [1] in the transition process. It is observed that in early stages of transition the eddy viscosity is much smaller than the physical viscosity. As a result the amplitudes of selected harmonics are in very good agreement with the experimental data [2]. The model's contribution gradually increases during the last stages of transition process and the dynamic eddy viscosity becomes fully active and dominant in the turbulent region. Consistent with this trend the skin friction coefficient versus Rex diverges from its laminar profile and converges to the turbulent profile after an overshoot. 1. Moin P. et. al. Phys Fluids A, 3(11), 2746-2757, 1991. 2. Kachanov Yu. S. et. al. JFM, 138, 209-247, 1983.
Turbulent Plasmaspheric Boundary Layer: Observables and Consequences
Mishin, Evgeny
2014-10-01
In situ satellite observations reveal strong lower hybrid/fast magnetosonic turbulence and broadband hiss-like VLF waves in the substorm subauroral geospace at and earthward of the electron plasmasheet boundary. These coincide with subauroral ion drifts/polarization streams (SAID/SAPS) in the plasmasphere and topside ionosphere. SAID/SAPS appear in ~10 min after the substorm onset consistent with the fast propagation of substorm injection fronts. The SAID channel follows the dispersionless cutoff of the energetic electron flux at the plasmapause. This indicates that the cold plasma maintains charge neutrality within the channel, thereby short-circuiting the injected plasma jet (injection fronts over the plasmasphere. Plasma turbulence leads to the circuit resistivity and magnetic diffusion as well as significant electron heating and acceleration. As a result, a turbulent boundary layer forms between the inner edge of the electron plasmasheet and plasmasphere. The SAID/SAPS-related VLF emissions appear to constitute a distinctive subset of substorm/storm-related VLF activity in the region co-located with freshly injected energetic ions inside the plasmasphere. Significant pitch-angle diffusion coefficients suggest that substorm SAID/SAPS-related VLF waves could be responsible for the alteration of the outer radiation belt boundary during (sub)storms. Supported by the Air Force Office of Scientific Research.
Boundary-layer effects in droplet splashing
Riboux, Guillaume; Gordillo, José Manuel
2017-07-01
A drop falling onto a solid substrate will disintegrate into smaller parts when its impact velocity V exceeds the so-called critical velocity for splashing, i.e., when V >V* . Under these circumstances, the very thin liquid sheet, which is ejected tangentially to the solid after the drop touches the substrate, lifts off as a consequence of the aerodynamic forces exerted on it. Subsequently, the growth of capillary instabilities breaks the toroidal rim bordering the ejecta into smaller droplets, violently ejected radially outward, provoking the splash [G. Riboux and J. M. Gordillo, Phys. Rev. Lett. 113, 024507 (2014)], 10.1103/PhysRevLett.113.024507. In this contribution, the effect of the growth of the boundary layer is included in the splash model presented in Phys. Rev. Lett. 113, 024507 (2014), 10.1103/PhysRevLett.113.024507, obtaining very good agreement between the measured and the predicted values of V* for wide ranges of liquid and gas material properties, atmospheric pressures, and substrate wettabilities. Our description also modifies the way at when the liquid sheet is first ejected, which can now be determined in a much more straightforward manner than that proposed in Phys. Rev. Lett. 113, 024507 (2014), 10.1103/PhysRevLett.113.024507.
Turbulence in the Stable Atmospheric Boundary Layer
Fernando, Harindra; Kit, Eliezer; Conry, Patrick; Hocut, Christopher; Liberzon, Dan
2016-11-01
During the field campaigns of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) Program, fine-scale measurements of turbulence in the atmospheric boundary layer (ABL) were made using a novel sonic and hot-film anemometer dyad (a combo probe). A swath of scales, from large down to Kolmogorov scales, was covered. The hot-film was located on a gimbal within the sonic probe volume, and was automated to rotate in the horizontal plane to align with the mean flow measured by sonic. This procedure not only helped satisfy the requirement of hot-film alignment with the mean flow, but also allowed in-situ calibration of hot-films. This paper analyzes a period of nocturnal flow that was similar to an idealized stratified parallel shear flow. Some new phenomena were identified, which included the occurrence of strong bursts in the velocity records indicative of turbulence generation at finer scales that are not captured by conventional sonic anemometers. The spectra showed bottleneck effect, but its manifestation did not fit into the framework of previous bottleneck-effect theories and was unequivocally related to bursts of turbulence. The measurements were also used to evaluate the energetics of stratified shear flows typical of the environment. ONR # N00014-11-1-0709; NSF # AGS-1528451; ISF 408/15.
Compressibility Effects in Turbulent Boundary Layers
Institute of Scientific and Technical Information of China (English)
CAO Yu-Hui; PEI Jie; CHEN Jun; SHE Zhen-Su
2008-01-01
Local cascade (LC) scheme and space-time correlations are used to study turbulent structures and their convection behaviour in the near-wall region of compressible boundary layers at Ma = 0.8 and 1.3. The convection velocities of fluctuating velocity components u (streamwise) and v (vertical) are investigated by statistically analysing scale-dependent ensembles of LC structures. The results suggest that u is convected with entropy perturbations while v with an isentropic process. An abnormal thin layer distinct from the conventional viscous sub-layer is discovered in the immediate vicinity of the wall (y+≤1) in supersonic flows. While in the region 1 ＜ y+ ＜ 30,streamwise streaks dominate velocity, density and temperature fluctuations, the abnormal thin layer is dominated by spanwise streaks in vertical velocity and density fluctuations, where pressure and density fluctuations are strongly correlated. The LC scheme is proven to be effective in studying the nature of supersonic flows and compressibility effects on wall-bounded motions.
Effects of air pollution on thermal structure and dispersion in an urban planetary boundary layer
Viskanta, R.; Johnson, R. O.; Bergstrom, R. W.
1977-01-01
The short-term effects of urbanization and air pollution on the transport processes in the urban planetary boundary layer (PBL) are studied. The investigation makes use of an unsteady two-dimensional transport model which has been developed by Viskanta et al., (1976). The model predicts pollutant concentrations and temperature in the PBL. The potential effects of urbanization and air pollution on the thermal structure in the urban PBL are considered, taking into account the results of numerical simulations modeling the St. Louis, Missouri metropolitan area.
Stability of solutions in boundary layer flow and heat transfer over a stretching cylinder
Najib, Najwa; Bachok, Norfifah; Arifin, Norihan Md.
2017-08-01
The boundary layer flow and heat transfer in viscous fluid passing through a stretching cylinder with present of mass suction are investigated. The governing equations of boundary layer in the form of partial differential equation are transformed into ordinary differential equations using appropriate similarity variables. The systems of ordinary differential equations are then reduced to first order system before being solved numerically. The results for skin friction coeffiecient, local Nusselt number, velocity and temperature profiles are presented. The effects of mass suction with different values of curvature parameter on the flow and heat transfer characteristics indicate that the dual solutions are found to exist. The stability analysis is performed to verify which solution (first or second solution) is linearly stable and thus the physical meaning is realizable. In the presence of mass suction, the dual solutions exist along stretching cylinder.
Hydrodynamic resistance of concentration polarization boundary layers in ultrafiltration
Wijmans, J.G.; Nakao, S.; Berg, van den J.W.A.; Troelstra, F.R.; Smolders, C.A.
1985-01-01
The influence of concentration polarization on the permeate flux in the ultrafiltration of aqueous Dextran T70 solutions can be described by (i) the osmotic pressure model and (ii) the boundary layer resistance model. In the latter model the hydrodynamic resistance of the non-gelled boundary layer i
Numerical Solution of Boundary Layer MHD Flow with Viscous Dissipation
Directory of Open Access Journals (Sweden)
S. R. Mishra
2014-01-01
Full Text Available The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper.
Excimer emission from cathode boundary layer discharges
Moselhy, Mohamed; Schoenbach, Karl H.
2004-02-01
The excimer emission from direct current glow discharges between a planar cathode and a ring-shaped anode of 0.75 and 1.5 mm diameter, respectively, separated by a gap of 250 μm, was studied in xenon and argon in a pressure range from 75 to 760 Torr. The thickness of the "cathode boundary layer" plasma, in the 100 μm range, and a discharge sustaining voltage of approximately 200 V, indicates that the discharge is restricted to the cathode fall and the negative glow. The radiant excimer emittance at 172 nm increases with pressure and reaches a value of 4 W/cm2 for atmospheric pressure operation in xenon. The maximum internal efficiency, however, decreases with pressure having highest values of 5% for 75 Torr operation. When the discharge current is reduced below a critical value, the discharge in xenon changes from an abnormal glow into a mode showing self-organization of the plasma. Also, the excimer spectrum changes from one with about equal contributions from the first and second continuum to one that is dominated by the second continuum emission. The xenon excimer emission intensity peaks at this discharge mode transition. In the case of argon, self-organization of the plasma was not seen, but the emission of the excimer radiation (128 nm) again shows a maximum at the transition from abnormal to normal glow. As was observed with xenon, the radiant emittance of argon increases with pressure, and the efficiency decreases. The maximum radiant emittance is 1.6 W/cm2 for argon at 600 Torr. The maximum internal efficiency is 2.5% at 200 Torr. The positive slope of the current-voltage characteristics at maximum excimer emission in both cases indicates the possibility of generating intense, large area, flat excimer lamps.
Hydrodynamic aspects of premixed flame stripes in two-dimensional stagnation-point flows
Energy Technology Data Exchange (ETDEWEB)
Lee, H.; Sohrab, S.H. [Northwestern Univ., Evanston, IL (United States). Dept. of Mechanical Engineering
1995-06-01
The behavior of cellular premixed flames of rich butane-air in the two-dimensional stagnation-point flow configuration has been investigated. It is found that the stretching of the cellular flame results in the alignment f the ridge (extinction) and the trough (combustion) zones of the individual cells such as to form a series of parallel flame stripes. The number of flame stripes as a function of the equivalence ratio for three different mean velocities at the nozzle have been determined. Through the introduction of a generalized form of the stream function periodic velocity fields are obtained as the exact solutions of the Euler equation for the nonreactive finite-jet two-dimensional stagnation flow. The predicted periodic velocity profiles are confirmed by the experimental observation of the streamlines in nonreactive flow made visible by laser-sheet lighting. The observed average size of the flame stripes is found to be in good agreement with the predicted value. Similar periodic velocity profiles are also obtained for the viscous flow within the laminar boundary layer by treatment of the unsteady vorticity equation first described by Taylor. The results support an earlier prediction by Williams that cellular flame structures that are affected mainly by diffusive-thermal phenomena may in fact be initiated by the hydrodynamic instability.
Numerical study of wingtip shed vorticity reduction by wing Boundary Layer Control
Posada, Jose Alejandro
Wingtip vortex reductions have been obtained by Boundary Layer Control application to an AR=1.5 rectangular wing using a NACA 0012 airfoil. If wingtip shed vorticity could be reduced significantly, then so would induced drag resulting in improved cruise fuel economy. Power savings would be even more impressive at low flight speed or in climb. A two dimensional wing produces lift without wingtip vorticity. Its bound vorticity, Gamma, equals the contour integral of the boundary layer vorticity gamma or Gamma = ∮gamma · dl. Where the upper and lower boundary layers meet at the cusped TE, their local static pressure pu=pl then the boundary layer outer edge inviscid velocity Vupper=Vlower and gammalower=-gamma upper. This explains the 2-D wing self cancellation of the upper and lower surface boundary layer vorticity when they meet upon shedding at the trailing edge. In finite wings, the presence of spanwise pressure gradients near the wing tips misaligns gammalower and gammaupper at the wingtip TE preventing the upper and lower surface boundary layers from completely canceling each other. To prevent them from generating wing tip vortices, the local boundary layers need to be captured in suction slots. Once vorticity is captured, it can be eliminated by viscous mixing prior to venting over board. The objective of this dissertation was to use a commercial Computational Fluid Dynamics code (Fluent) to search for the best configuration to locate BLC suction slots to capture non-parallel boundary layer vorticity prior to shedding near the wingtips. The configuration selected for running the simulations was tested by trying to duplicate a 3D wing for which sufficient experimental and computational models by others are available. The practical case selected was done by Chow et al in the 32 x 48 in. low speed wind tunnel at the Fluid Mechanics Laboratory of NASA Ames Research Center, and computationally analyzed by Dacles-Mariani et al, and Khim and Rhee. The present
Two-Dimensional Stagnation-Point Velocity-Slip Flow and Heat Transfer over Porous Stretching Sheet
Directory of Open Access Journals (Sweden)
FEROZ AHMED SOOMRO
2016-10-01
Full Text Available Present paper investigates 2D (Two-Dimensional stagnation-point velocity-slip flow over porous stretching sheet. The governing non-linear PDEs (Partial Differential Equations are non-dimensionlized by using the similarity transformation technique that results into coupled non-linear ODEs (Ordinary Differential Equations. Such ODEs are then solved by using shooting technique with fourth-order Runge-Kutta method. Since the behavior of boundary layer stagnation-point flow depends on the rate of cooling and stretching. Therefore, the main objective of this paper is to analyze the effects of different working parameters on shear stress, heat transfer, velocity and temperature of fluid. The results revealed that the velocity-slip has significant effect on the fluid flow as well as on the heat transfer. The numerical results are also compared with existing work for no-slip condition and found to have good agreement with improved asymptotic behavior.
Two-dimensional capillary origami
Energy Technology Data Exchange (ETDEWEB)
Brubaker, N.D., E-mail: nbrubaker@math.arizona.edu; Lega, J., E-mail: lega@math.arizona.edu
2016-01-08
We describe a global approach to the problem of capillary origami that captures all unfolded equilibrium configurations in the two-dimensional setting where the drop is not required to fully wet the flexible plate. We provide bifurcation diagrams showing the level of encapsulation of each equilibrium configuration as a function of the volume of liquid that it contains, as well as plots representing the energy of each equilibrium branch. These diagrams indicate at what volume level the liquid drop ceases to be attached to the endpoints of the plate, which depends on the value of the contact angle. As in the case of pinned contact points, three different parameter regimes are identified, one of which predicts instantaneous encapsulation for small initial volumes of liquid. - Highlights: • Full solution set of the two-dimensional capillary origami problem. • Fluid does not necessarily wet the entire plate. • Global energy approach provides exact differential equations satisfied by minimizers. • Bifurcation diagrams highlight three different regimes. • Conditions for spontaneous encapsulation are identified.
Scaling properties of the mean wall-normal velocity in zero-pressure-gradient boundary layers
Wei, Tie; Klewicki, Joseph
2016-12-01
The scaling properties of the mean wall-normal velocity V (x ,y ) in zero-pressure-gradient laminar and turbulent boundary-layer flows are investigated using numerical simulation data, physical experiment data, and integral analyses of the governing equations. The maximum mean wall-normal velocity V∞ and the boundary-layer thickness δ are evidenced to be the proper scaling for V over most if not all of the boundary layer. This is different from the behavior of the mean streamwise velocity U or the turbulent shear stress T =-ρ , which depend on different characteristic length scales in the regions near and away from the surface, respectively. The reason for this apparent difference in scaling behaviors is described physically relative to the downstream development of the U velocity profile and the mechanisms of boundary-layer growth. Insights pertaining to this are further surmised from an analytical relationship for the ratio of the displacement to momentum thickness, i.e., shape factor H . Integral analyses using the continuity and mean momentum equation show that U∞V∞/uτ2=H , where uτ is the friction velocity. Both the laminar similarity solution and direct numerical simulation data in post-transitional flows convincingly support this relation. Over the transitional regime, data of sufficiently high quality are lacking to check if this relation remains valid.
Receptivity and Forced Response to Acoustic Disturbances in High-Speed Boundary Layers
Balakumar, P.; King, Rudolph A.; Chou, Amanda; Owens, Lewis R.; Kegerise, Michael A.
2016-01-01
Supersonic boundary-layer receptivity to freestream acoustic disturbances is investigated by solving the Navier-Stokes equations for Mach 3.5 flow over a sharp flat plate and a 7-deg half-angle cone. The freestream disturbances are generated from a wavy wall placed at the nozzle wall. The freestream acoustic disturbances radiated by the wavy wall are obtained by solving the linearized Euler equations. The results for the flat plate show that instability modes are generated at all the incident angles ranging from zero to highly oblique. However, the receptivity coefficient decreases by about 20 times when the incident angle increases from zero to a highly oblique angle of 68 degrees. The results for the cone show that no instability modes are generated when the acoustic disturbances impinge the cone obliquely. The results show that the perturbations generated inside the boundary layer by the acoustic disturbances are the response of the boundary layer to the external forcing. The amplitude of the forced disturbances inside the boundary layer are about 2.5 times larger than the incoming field for zero azimuthal wavenumber and they are about 1.5 times for large azimuthal wavenumbers.
Equilibrium turbulent boundary layers with wall suction/blowing and pressure gradients
Patwardhan, Saurabh; Ramesh, O. N.
2012-11-01
Conditions for the equilibrium conditions in turbulent boundary layers with suction or blowing across a no slip wall and pressure gradients are derived from the governing equations. It is also shown that under these conditions the governing equations show self similarity in the conventional inner co-ordinates as well as ``laminar-like'' co-ordinates. The only turbulent boundary layer in ``perfect equilibrium'' known as sink flow turbulent boundary layer forms a subset of this more general equilibrium concept. Direct numerical simulations were carried out to investigate this hypothesis for the case of favourable pressure gradient with small blowing at the wall. Reynolds number invariance and complete self similarity of mean velocity profile and second order turbulence statistics is observed along the flow direction similar to the sink flow boundary layer. A comparison between the case with wall blowing and imposed favourable pressure gradient and the sink flow case for same value of pressure gradient parameter reveals a shift in log law in mean velocity profile and increase in peak turbulence intensities.
MHD Boundary Layer Flow of Dilatant Fluid in a Divergent Channel with Suction or Blowing
Institute of Scientific and Technical Information of China (English)
Krishnendu Bhattacharyya; G.C.Layek
2011-01-01
@@ An analysis is carried out to study a steady magnetohydrodynamic(MHD) boundary layer How 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 physical尔
Carling; Williams; Bowtell
1998-12-01
Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature's movement and the two-dimensional fluid flow of the surrounding water. The model creature is self-propelled; it follows a path determined by the forces acting upon it, as generated by its prescribed changing shape. The numerical solution has been obtained by applying coordinate transformations and then using finite difference methods. Results are presented showing the flow around the creature as it accelerates from rest in an enclosed tank. The kinematics and dynamics associated with the creature's centre of mass are also shown. For a particular set of body shape parameters, the final mean swimming speed is found to be 0.77 times the speed of the backward-travelling wave. The corresponding movement amplitude envelope is shown. The magnitude of oscillation in the net forward force has been shown to be approximately twice that in the lateral force. The importance of allowing for acceleration and deceleration of the creature's body (rather than imposing a constant swimming speed) has been demonstrated. The calculations of rotational movement of the body and the associated moment of forces about the centre of mass have also been included in the model. The important role of viscous forces along and around the creature's body and in the growth and dissolution of the vortex structures has been illustrated.
Lichtenberg, Mads; Nørregaard, Rasmus Dyrmose; Kühl, Michael
2017-03-01
The role of hyaline hairs on the thallus of brown algae in the genus Fucus is long debated and several functions have been proposed. We used a novel motorized set-up for two-dimensional and three-dimensional mapping with O2 microsensors to investigate the spatial heterogeneity of the diffusive boundary layer (DBL) and O2 flux around single and multiple tufts of hyaline hairs on the thallus of Fucus vesiculosus. Flow was a major determinant of DBL thickness, where higher flow decreased DBL thickness and increased O2 flux between the algal thallus and the surrounding seawater. However, the topography of the DBL varied and did not directly follow the contour of the underlying thallus. Areas around single tufts of hyaline hairs exhibited a more complex mass-transfer boundary layer, showing both increased and decreased thickness when compared with areas over smooth thallus surfaces. Over thallus areas with several hyaline hair tufts, the overall effect was an apparent increase in the boundary layer thickness. We also found indications for advective O2 transport driven by pressure gradients or vortex shedding downstream from dense tufts of hyaline hairs that could alleviate local mass-transfer resistances. Mass-transfer dynamics around hyaline hair tufts are thus more complex than hitherto assumed and may have important implications for algal physiology and plant-microbe interactions.
Two-dimensional optical spectroscopy
Cho, Minhaeng
2009-01-01
Discusses the principles and applications of two-dimensional vibrational and optical spectroscopy techniques. This book provides an account of basic theory required for an understanding of two-dimensional vibrational and electronic spectroscopy.
Geostrophic convective turbulence: The effect of boundary layers
Ostilla-Mónico, Rodolfo; Kunnen, Rudie P J; Verzicco, Roberto; Lohse, Detlef
2014-01-01
This Letter presents results of the first direct numerical simulations of rotating Rayleigh--B\\'enard convection in the so-called geostrophic regime, (hence very small Ekman numbers $\\mathcal{O}(10^{-7})$ and high Rayleigh numbers~$Ra=10^{10}$ and~$5\\cdot 10^{10}$), employing the \\emph{full} Navier--Stokes equations. In the geostrophic regime the criteria of very strong rotation and large supercriticality are met simultaneously, which is true for many geophysical and astrophysical flows. Until now, numerical approaches of this regime have been based on \\emph{reduced} versions of the Navier--Stokes equations (cf. Sprague \\emph{et al.} J. Fluid Mech., \\textbf{551}, 141 (2006)), omitting the effect of the viscous (Ekman) boundary layers. By using different velocity boundary conditions at the plates, we study the effect of these Ekman layers. We find that the formation of large-scale structures (Rubio \\emph{et al.} (Phys. Rev. Lett. \\textbf{112} (2014)), which indicates the presence of an inverse energy cascade, ...
Effect of a bulge on the subharmonic instability of boundary layers
Nayfeh, Ali H.; Ragab, Saad A.; Masad, Jamal A.
1990-01-01
The influence of a two-dimensional hump on the three-dimensional (3-D) subharmonic secondary instability on a flat plate is investigated. The mean flow is calculated by using interacting boundary layers, thereby accounting for the viscid/inviscid interaction. The primary wave is taken in the form of a two-dimensional (2-D) Tollmien-Schlichting (T-S) wave. The secondary wave is taken in the form of a 3-D subharmonic wave. The results show that increasing the hump height results in an increase in the amplification factors of the primary and subharmonic waves. When the hump causes separation, the growth rates of both the primary and subharmonic waves are considerably larger than those obtained in the case of no separation.
UNSTEADY BOUNDARY LAYER FLOW ALONG A STRETCHING CYLINDER AN ANALYTICAL SOLUTION
Directory of Open Access Journals (Sweden)
M. Y. Akl
2014-01-01
Full Text Available The axisymetric laminar boundary layer unsteady flow along a continuously stretching cylinder immersed in a viscous and incompressible fluid is studied. The governing partial boundary layer equations in cylindrical form are first transformed into ordinary differential equations these equations are solved analytically using the optimal modified Homotopy Asymptotic method in order to get a closed form solution for the dimensionless functions f and è. The main object of this study is to investigate the effect of an unsteady motion of a stretching cylinder on the flow and heat transfer characteristics such as surface skin friction and surface heat flux. These characteristics have a direct effect on the quality of the final product of the fiber manufacturing and extrusion processes. Considerable effects were found for the dynamic parameter (γ, the curvature parameter (ρ and the prandtl number (pr on the velocity and the heat transfer.
Institute of Scientific and Technical Information of China (English)
唐登斌; 夏浩
2002-01-01
The nonlinear evolution problem in nonparallel boundary layer stability was studied. The relative parabolized stability equations of nonlinear nonparallel boundary layer were derived. The developed numerical method, which is very effective, was used to study the nonlinear evolution of T-S disturbance wave at finite amplitudes. Solving nonlinear equations of different modes by using predictor-corrector and iterative approach, which is uncoupled between modes, improving computational accuracy by using high order compact differential scheme, satisfying normalization condition, determining tables of nonlinear terms at different modes, and implementing stably the spatial marching, were included in this method. With different initial amplitudes, the nonlinear evolution of T-S wave was studied. The nonlinear nonparallel results of examples compare with data of direct numerical simulations (DNS) using full Navier- Stokes equations.
Crouseilles, Nicolas; Lemou, Mohammed; Méhats, Florian; Zhao, Xiaofei
2017-10-01
In this work, we focus on the numerical resolution of the four dimensional phase space Vlasov-Poisson system subject to a uniform strong external magnetic field. To do so, we consider a Particle-in-Cell based method, for which the characteristics are reformulated by means of the two-scale formalism, which is well-adapted to handle highly-oscillatory equations. Then, a numerical scheme is derived for the two-scale equations. The so-obtained scheme enjoys a uniform accuracy property, meaning that its accuracy does not depend on the small parameter. Several numerical results illustrate the capabilities of the method.
Turbulence models and Reynolds analogy for two-dimensional supersonic compression ramp flow
Wang, Chi R.; Bidek, Maleina C.
1994-01-01
Results of the application of turbulence models and the Reynolds analogy to the Navier-Stokes computations of Mach 2.9 two-dimensional compression ramp flows are presented. The Baldwin-Lomax eddy viscosity model and the kappa-epsilon turbulence transport equations for the turbulent momentum flux modeling in the Navier-Stokes equations are studied. The Reynolds analogy for the turbulent heat flux modeling in the energy equation was also studied. The Navier-Stokes equations and the energy equation were numerically solved for the flow properties. The Reynolds shear stress, the skin friction factor, and the surface heat transfer rate were calculated and compared with their measurements. It was concluded that with a hybrid kappa-epsilon turbulence model for turbulence modeling, the present computations predicted the skin friction factors of the 8 deg and 16 deg compression ramp flows and with the turbulent Prandtl number Pr(sub t) = 0.93 and the ratio of the turbulent thermal and momentum transport coefficients mu(sub q)/mu(sub t) = 2/Prt, the present computations also predicted the surface heat transfer rates beneath the boundary layer flow of the 16 compression ramp.
Boundary Layer Ventilation Processes During a High Pressure Event
Gray, S. L.; Dacre, H. F.; Belcher, S. E.
2006-12-01
It is often assumed that ventilation of the atmospheric boundary layer is weak during high pressure events. But is this always true? Here we investigate the processes responsible for ventilation of the atmospheric boundary layer during a high pressure event that occured on the 9 May 2005 using the UK Met Office Unifed Model. Pollution sources are represented by the constant emission of a passive tracer everywhere over land. The ventilation processes observed include a sea breeze circulation, turbulent mixing across the top of the boundary layer followed by large-scale ascent, and shallow convection. Vertical distributions of tracer are validated with AMPEP (Aircraft Measurement of chemical Processing Export fluxes of Pollutants over the UK) CO aircraft measurements and are shown to agree impressively well. Budget calculations of tracers are performed in order to determine the relative importance of these ventilation processes. The sea breeze circulation was found to ventilate 26% of the boundary layer tracer by sunset of which 2% was above 2km. A combination of the sea breeze circulation and turbulent mixing ventilated 46% of the boundary layer tracer, of which 10% was above 2km. Finally, the sea breeze circulation, turbulent mixing and shallow convection processes together ventilated 52% of the tracer into the free troposphere, of which 26% was above 2km. Hence this study shows that signicant ventilation of the boundary layer can occur during high pressure events; turbulent mixing and convection processes can double the amount of pollution ventilated from the boundary layer.
Diffusive boundary layers over varying topography
Dell, R. W.
2015-03-25
Diffusive bottom boundary layers can produce upslope flows in a stratified fluid. Accumulating observations suggest that these boundary layers may drive upwelling and mixing in mid-ocean ridge flank canyons. However, most studies of diffusive bottom boundary layers to date have concentrated on constant bottom slopes. We present a study of how diffusive boundary layers interact with various idealized topography, such as changes in bottom slope, slopes with corrugations and isolated sills. We use linear theory and numerical simulations in the regional ocean modeling system (ROMS) model to show changes in bottom slope can cause convergences and divergences within the boundary layer, in turn causing fluid exchanges that reach far into the overlying fluid and alter stratification far from the bottom. We also identify several different regimes of boundary-layer behaviour for topography with oceanographically relevant size and shape, including reversing flows and overflows, and we develop a simple theory that predicts the regime boundaries, including what topographies will generate overflows. As observations also suggest there may be overflows in deep canyons where the flow passes over isolated bumps and sills, this parameter range may be particularly significant for understanding the role of boundary layers in the deep ocean.
MacRorie, Michael
1995-01-01
The interaction between convecting spanwise vortices and a flat plate turbulent boundary layer was studied experimentally. The results are relevant to the flow downstream of unsteady airfoils or spoilers. Vortices were generated with a rapidly pitched airfoil upstream of a test plate leading edge in a low-speed wind tunnel. By varying the height of the vortex generator the degree to which the vortices interacted with the test plate was controlled. Dynamic stall vortices of both positive and negative circulation were studied with Reynolds numbers (Gamma/upsilon ) of 9300 and 7400 respectively. The free-stream velocity was 5.9 m/s for all cases and the boundary layer momentum thickness Reynolds number was 480 at the primary measurement station. The measurement techniques were hot -wire anemometry (single and cross wire) and smoke-wire visualization. The results focus on two distinct aspects of the flow, first is the decay and diffusion rates of the vortices. Only in the case where a negative circulation vortex impinges directly on the leading edge does surface interaction significantly increase the vortex decay/diffusion rate. The second aspect is the response of the turbulent boundary layer to the convecting vortices. Wall shear stress measurements show that the passage of a positive circulation vortex results in an increase in wall shear after a delay-time, while the negative circulation vortices result in a decrease in wall shear. An application of log-law scaling to the ensemble-averaged mean flow was found to produce a velocity scale which resembles one based on measured wall shear stress but is offset by a phase lag. The ratio of turbulent shear stress to the two-dimensional turbulent kinetic energy was generally not constant, although it did show a constant value across the boundary layer at different phases of the interaction.
Stable Boundary Layer Education (STABLE) Final Campaign Summary
Energy Technology Data Exchange (ETDEWEB)
Turner, David D. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2016-03-01
The properties of, and the processes that occur in, the nocturnal stable boundary layer are not well understood, making it difficult to represent adequately in numerical models. The nocturnal boundary layer often is characterized by a temperature inversion and, in the Southern Great Plains region, a low-level jet. To advance our understanding of the nocturnal stable boundary layer, high temporal and vertical resolution data on the temperature and wind properties are needed, along with both large-eddy simulation and cloud-resolving modeling.
Boundary-layer predictions for small low-speed contractions
Mehta, Rabindra D.; Bell, James H.
1989-01-01
The present scheme for the prediction of boundary-layer development in small, low-speed wind tunnel contraction sections proceeds by calculating the wall pressure distributions, and hence the wall velocity distributions, by means of a three-dimensional potential-flow method. For the family of contractions presently treated, the assumption of a laminar boundary layer appears to be justified; the measured boundary layer momentum thicknesses at the exit of the four contractions were found to lie within 10 percent of predicted values.
Investigation of Shock-Induced Laminar Separation Bubble in a Supersonic Boundary Layer
Sivasubramanian, Jayahar; Fasel, Hermann
2015-11-01
The interaction between an impinging oblique shock and a laminar boundary-layer on a flat plate is investigated using DNS. In particular, the two-dimensional separation bubble resulting from the shock/boundary-layer interaction (SBLI) at freestream Mach number of 2.0 is investigated in detail. The flow parameters used for the present investigation match the laboratory conditions in the experiments by Hakkinen et al. The skin friction and pressure distribution from the simulations are compared to the experimental measurements and numerical results available in the literature. Our results confirm the asymmetric nature of the separation bubble as reported in the literature. In addition to the steady flow field calculations, the response to low-amplitude disturbances is investigated in order to study the linear stability behavior of the separation bubble. For comparison, both the development of two-dimensional and three-dimensional (oblique) disturbances are studied with and without the impinging oblique shock. Furthermore, the effects of the shock incidence angle and Reynolds number are also investigated. Finally, three-dimensional simulations were performed in order to explore the laminar-turbulent transition process in the presence of a laminar separation bubble. Funded by the Air Force Office of Scientific Research under grant FA9550-14-1-0195.
leMesurier, Brenton John; Christiansen, Peter Leth; Gaididei, Yuri B; Rasmussen, Jens Juul
2004-10-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrödinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrödinger equation in the critical dimension 2 and can lead to a stable oscillating beam. This is observed to involve a splitting of the beam into an inner part that is oscillatory and of subcritical power and an outer dispersing part. An analysis is given in terms of the rate competition between the linear and nonlinear focusing effects, radiation losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials.
Nonlinear Excitation of Inviscid Stationary Vortex in a Boundary-Layer Flow
Choudhari, Meelan; Duck, Peter W.
1996-01-01
We examine the excitation of inviscid stationary crossflow instabilities near an isolated surface hump (or indentation) underneath a three-dimensional boundary layer. As the hump height (or indentation depth) is increased from zero, the receptivity process becomes nonlinear even before the stability characteristics of the boundary layer are modified to a significant extent. This behavior contrasts sharply with earlier findings on the excitation of the lower branch Tollmien-Schlichting modes and is attributed to the inviscid nature of the crossflow modes, which leads to a decoupling between the regions of receptivity and stability. As a result of this decoupling, similarity transformations exist that allow the nonlinear receptivity of a general three-dimensional boundary layer to be studied with a set of canonical solutions to the viscous sublayer equations. The parametric study suggests that the receptivity is likely to become nonlinear even before the hump height becomes large enough for flow reversal to occur in the canonical solution. We also find that the receptivity to surface humps increases more rapidly as the hump height increases than is predicted by linear theory. On the other hand, receptivity near surface indentations is generally smaller in comparison with the linear approximation. Extension of the work to crossflow receptivity in compressible boundary layers and to Gortler vortex excitation is also discussed.
The stabilizing role of anisotropy in the free stream on boundary layer development
Frohnapfel, Bettina
2005-11-01
An experimental study on the transition of a flat plate boundary layer was conducted in the large wind tunnel of the chair of fluid dynamics (LSTM) in Erlangen, Germany. Although this is not an especially designed transition tunnel it was possible to maintain a stable laminar regime up to Rex=4x10^6, one of the highest transition Reynolds numbers achieved in a flat plate boundary layer. It is argued that this was possible due to a stabilizing effect originating from the high anisotropy level in the free stream disturbances that exists in the tunnel. Based on a statistical analysis of the dynamical equations for small axisymmetric disturbances, the influence of anisotropy on the dynamics of those disturbances in a laminar boundary layer was studied. The derived transition criterion is formulated in terms of a transition Reynolds number - based on intensity and Taylor length scale of the disturbances - that shows a dependency on the anisotropy level of the free stream disturbances. In this respect all available existing measurements on natural boundary layer transition at high Reynolds numbers were analyzed.
Priimak, Dmitri
2014-01-01
We present finite differences numerical algorithm for solving 2D spatially homogeneous Boltzmann transport equation for semiconductor superlattices (SL) subject to time dependant electric field along SL axis and constant perpendicular magnetic field. Algorithm is implemented in C language targeted to CPU and in CUDA C language targeted to commodity NVidia GPUs. We compare performance and merits of one implementation versus another and discuss various methods of optimization.
Influences on the Height of the Stable Boundary Layer as seen in LES
Energy Technology Data Exchange (ETDEWEB)
Kosovic, B; Lundquist, J
2004-06-15
Climate models, numerical weather prediction (NWP) models, and atmospheric dispersion models often rely on parameterizations of planetary boundary layer height. In the case of a stable boundary layer, errors in boundary layer height estimation can result in gross errors in boundary-layer evolution and in prediction of turbulent mixing within the boundary layer.
Boundary layer flow and heat transfer to Carreau fluid over a nonlinear stretching sheet
Directory of Open Access Journals (Sweden)
Masood Khan
2015-10-01
Full Text Available This article studies the Carreau viscosity model (which is a generalized Newtonian model and then use it to obtain a formulation for the boundary layer equations of the Carreau fluid. The boundary layer flow and heat transfer to a Carreau model over a nonlinear stretching surface is discussed. The Carreau model, adequate for many non-Newtonian fluids, is used to characterize the behavior of the fluids having shear thinning properties and fluids with shear thickening properties for numerical values of the power law exponent n. The modeled boundary layer conservation equations are converted to non-linear coupled ordinary differential equations by a suitable transformation. Numerical solution of the resulting equations are obtained by using the Runge-Kutta Fehlberg method along with shooting technique. This analysis reveals many important physical aspects of flow and heat transfer. Computations are performed for different values of the stretching parameter (m, the Weissenberg number (We and the Prandtl number (Pr. The obtained results show that for shear thinning fluid the fluid velocity is depressed by the Weissenberg number while opposite behavior for the shear thickening fluid is observed. A comparison with previously published data in limiting cases is performed and they are in excellent agreement.
Two-Dimensional Toda-Heisenberg Lattice
Directory of Open Access Journals (Sweden)
Vadim E. Vekslerchik
2013-06-01
Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.
Bristled shark skin: a microgeometry for boundary layer control?
Energy Technology Data Exchange (ETDEWEB)
Lang, A W; Hidalgo, P; Westcott, M [Aerospace Engineering and Mechanics Department, University of Alabama, Box 870280, Tuscaloosa, AL 35487 (United States); Motta, P [Biology Department, University of South Florida, 4202 East Fowler Avenue, Tampa, FL 33620 (United States)], E-mail: alang@eng.ua.edu
2008-12-01
There exists evidence that some fast-swimming shark species may have the ability to bristle their scales during fast swimming. Experimental work using a water tunnel facility has been performed to investigate the flow field over and within a bristled shark skin model submerged within a boundary layer to deduce the possible boundary layer control mechanisms being used by these fast-swimming sharks. Fluorescent dye flow visualization provides evidence of the formation of embedded cavity vortices within the scales. Digital particle image velocimetry (DPIV) data, used to evaluate the cavity vortex formation and boundary layer characteristics close to the surface, indicate increased momentum in the slip layer forming above the scales. This increase in flow velocity close to the shark's skin is indicative of boundary layer control mechanisms leading to separation control and possibly transition delay for the bristled shark skin microgeometry.
Magnetic Structure of the Magnetopause Boundary Layer for Open Magnetosphere
Ma, Yonghui; Shen, Chao; Zeng, Gang
2017-04-01
Using Cluster and Magnetospheric MultiScale (MMS) spacecraft 4 point magnetic field measurements, we analyzed the magnetic structure of magnetopause boundary layer of the open magnetosphere. It is indicated that the magnetopause boundary layer is very thin under strong magnetic shear and the thickness is usually 0.1 Re. We found that the Rotational Discontinuity (RD) is very important structure at magnetopause when the Interplanetary Magnetic Field (IMF) is southward. Within the boundary layer, the magnetic field has a large rotation. Using curvature calculation method, we got that the minimum curvature radius of magnetic field of RD is 0.02 - 0.1Re, implying that the magnetosphere is open when the IMF is southward. Advanced research showed that the field-aligned currents are common in the magnetopause boundary layer.
Simulation of Wind turbines in the atmospheric boundary layer
DEFF Research Database (Denmark)
Chivaee, Hamid Sarlak; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
Large eddy simulation of an arbitrary wind farm is studied in the neutral and thermally stratified atmospheric boundary Layer. Large eddy simulations of industrial flows usually requires full resolution of the flow near the wall and this is believed to be one of the main deficiencies of LES because...... layer. In the current study, another approach has been implemented to simulate the flow in a fully developed wind farm boundary layer. The approach is based on Immersed Boundary Method and involves implementation of an arbitrary prescribed initial boundary layer. An initial boundary layer is enforced...... height and the flow development is seen based on the temperature variations and wind turbine wake generations and interactions of wakes occurs as soon as the wakes of the upwind turbine reach the downwind turbines. References: [1] U. Piomelli, Wall-layer models for large-eddy simulations, Progress...
Microprobe of structure of crystal/liquid interface boundary layers
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The molecular structures and its evolutive regularities within the boundary layers in the crystal growth of KDP and DKDP have been studied in real time by using holography and Raman microprobe. The experiments show that the molecular structure of mother solution within the boundary layers is distinctly different from that of the solutions alone. In this paper, the effects of cations within the boundary layers on the structure of solution are considered. Within the characteristic boundary layers, the effects of cations cause the changes in O-P-O bond angle, electronic density redistribution of the phosphate groups, and significant changes in the bond intensity, thus leading to the breaking of partial hydrogen bonds of the phosphate associations, the readjustment of geometry of anionic phosphate groups and desolvation, and the forming of the smectic ordering structure of the anions_cations. Finally, the crystallization unit of anion_cation should be formed at the proximate interface.
DEFF Research Database (Denmark)
Fuhrman, David R.; Fredsøe, Jørgen; Sumer, B. Mutlu
2009-01-01
A numerical model solving incompressible Reynolds-averaged Navier-Stokes equations, combined with a two-equation k-omega turbulence closure, is used to study converging-diverging effects from a sloping bed on turbulent (oscillatory) wave boundary layers. Bed shear stresses from the numerical model...
A numerical-physical planetary boundary layer model
Padro, Jacob
1983-07-01
A numerical-physical model for the planetary boundary layer has been formulated for the purpose of predicting the winds, temperatures and humidities in the lowest 1600 m of the atmosphere. An application of the model to the synoptic situation of 30 August, 1972, demonstrates its ability to produce useful forecasts for a period of 24 h. Results are illustrated in terms of horizontal maps and time-height sections of winds and temperatures. The model is divided in the vertical direction into three layers that are governed, respectively, by different physical formulations. At the lowest level, which is the surface of the earth, forecasts of temperature and humidity are computed from empirical relations. In the first layer, the surface layer, application is made of the similarity theories of Monin-Obukhov, Monin-Kazanski and Businger’s form of the universal functions. The second layer, the Ekman layer, is 1550 m deep and is governed by diagnostic momentum and time-dependent thermodynamic and humidity equations. External input to the model are large-scale pressure gradients and middle-level cloudiness. Cressman’s objective analysis procedure is applied to conventional surface and upper air data over a horizontal region of about 2500 km by 2500 km, centered about Lake Ontario. With a grid distance of 127 km and a time interval of 30 min, the computer time required on Control Data Cyber 76 for a 24 h forecast for the case study is less than two minutes.
Wave mediated angular momentum transport in astrophysical boundary layers
Hertfelder, Marius
2015-01-01
Context. Disk accretion onto weakly magnetized stars leads to the formation of a boundary layer (BL) where the gas loses its excess kinetic energy and settles onto the star. There are still many open questions concerning the BL, for instance the transport of angular momentum (AM) or the vertical structure. Aims. It is the aim of this work to investigate the AM transport in the BL where the magneto-rotational instability (MRI) is not operating owing to the increasing angular velocity $\\Omega(r)$ with radius. We will therefore search for an appropriate mechanism and examine its efficiency and implications. Methods. We perform 2D numerical hydrodynamical simulations in a cylindrical coordinate system $(r, \\varphi)$ for a thin, vertically inte- grated accretion disk around a young star. We employ a realistic equation of state and include both cooling from the disk surfaces and radiation transport in radial and azimuthal direction. The viscosity in the disk is treated by the {\\alpha}-model; in the BL there is no v...
Numerical simulation of boundary layers. Part 1: Weak formulation and numerical method
Spalart, P. R.
1986-01-01
A numerical method designed to solve the time-dependent, three-dimensional, incompressible Navier-Stokes equations in boundary layers is presented. The fluid domain is the half-space over a flat plate, and periodic conditions are applied in the horizontal directions. The discretization is spectral. The basis functions are divergence-free and a weak formulation of the momentum equation is used, which eliminates the pressure term. An exponential mapping and Jacobi polynomials are used in the semi-infinite direction, with the irrotational component receiving special treatment. Issues related to the accuracy, stability and efficiency of the method are discussed. Very fast convergence is demonstrated on some model problems with smooth solutions. The method has also been shown to accurately resolve the fine scales of transitional and turbulent boundary layers.
Miner, E. W.; Lewis, C. H.
1972-01-01
An implicit finite difference method has been applied to tangential slot injection into supersonic turbulent boundary layer flows. In addition, the effects induced by the interaction between the boundary layer displacement thickness and the external pressure field are considered. In the present method, three different eddy viscosity models have been used to specify the turbulent momentum exchange. One model depends on the species concentration profile and the species conservation equation has been included in the system of governing partial differential equations. Results are compared with experimental data at stream Mach numbers of 2.4 and 6.0 and with results of another finite difference method. Good agreement was generally obtained for the reduction of wall skin friction with slot injection and with experimental Mach number and pitot pressure profiles. Calculations with the effects of pressure interaction included showed these effects to be smaller than effects of changing eddy viscosity models.
Analytic Study of Magnetohydrodynamic Flow and Boundary Layer Control Over a Wedge
Institute of Scientific and Technical Information of China (English)
M. Chandrasekar; S. Baskaran
2008-01-01
A genuine variational principle developed by Gyarmati, in the field of thermodynamics of irreversible processes unifying the theoretical requirements of technical, environmental and biological sciences is employed to study the effects of uniform suction and injection on MHD flow adjacent to an isothermal wedge with pressure gradient in the presence of a transverse magnetic field. The velocity distribution inside the boundary layer has been considered as a simple polynomial function and the variational principle is formulated. The Euler-Lagrange equation is reduced to a simple polynomial equation in terms of momentum boundary layer thickness. The velocity profiles, displacement thickness and the coefficient of skin friction are calculated for various values of wedge angle parameter m, magnetic parameter ε and suction/injection parameter H. The present results are compared with known available results and the comparison is found to be satisfactory. The present study establishes high accuracy of results obtained by this variational technique.
On the Coupling Between a Supersonic Turbulent Boundary Layer and a Flexible Structure
Frendi, Abdelkader
1996-01-01
A mathematical model and a computer code have been developed to fully couple the vibration of an aircraft fuselage panel to the surrounding flow field, turbulent boundary layer and acoustic fluid. The turbulent boundary layer model is derived using a triple decomposition of the flow variables and applying a conditional averaging to the resulting equations. Linearized panel and acoustic equations are used. Results from this model are in good agreement with existing experimental and numerical data. It is shown that in the supersonic regime, full coupling of the flexible panel leads to lower response and radiation from the panel. This is believed to be due to an increase in acoustic damping on the panel in this regime. Increasing the Mach number increases the acoustic damping, which is in agreement with earlier work.
A note on boundary-layer friction in baroclinic cyclones
Boutle, I A; Belcher, S E; Plant, R S
2008-01-01
The interaction between extratropical cyclones and the underlying boundary layer has been a topic of recent discussion in papers by Adamson et. al. (2006) and Beare (2007). Their results emphasise different mechanisms through which the boundary layer dynamics may modify the growth of a baroclinic cyclone. By using different sea-surface temperature distributions and comparing the low-level winds, the differences are exposed and both of the proposed mechanisms appear to be acting within a single simulation.
CONTINUOUS WAVELET TRANSFORM OF TURBULENT BOUNDARY LAYER FLOW
Institute of Scientific and Technical Information of China (English)
LIU Ying-zheng; KE Feng; CHEN Han-ping
2005-01-01
The spatio-temporal characteristics of the velocity fluctuations in a fully-developed turbulent boundary layer flow was investigated using hotwire. A low-speed wind tunnel was established. The experimental data was extensively analyzed in terms of continuous wavelet transform coefficients and their auto-correlation. The results yielded a potential wealth of information on inherent characteristics of coherent structures embedded in turbulent boundary layer flow. Spatial and temporal variations of the low- and high- frequency motions were revealed.
DNS of compressible turbulent boundary layer over a blunt wedge
Institute of Scientific and Technical Information of China (English)
LI Xinliang; FU Dexun; MA Yanwan
2005-01-01
Direct numerical simulation of spatially evolving compressible boundary layer over a blunt wedge is performed in this paper. The free-stream Mach number is 6 and the disturbance source produced by wall blowing and suction is located downstream of the sound-speed point. Statistics are studied and compared with the results in incompressible flat-plate boundary layer. The mean pressure gradient effects on the vortex structure are studied.
A Compilation of Unsteady Turbulent Boundary Layer Experimental Data,
1981-11-01
HIRSCH KITAet ai, GOSTELOW EHERENSBERGER LU HO & CHEN KOBASHI & HAYAKAWA MAINARDI & PANDAY MARVIN* LORBER & COVERT MIZUSHINA I SAXENA RAMAPRIAN & TU...Laminar Boundary Layer by a Moving Belt. AIAA Paj_2r 69-40, New York, N.Y., 1969. (LT) Mainardi , H. and Panday, P. K.: A Study of Turbulent Pulsating...Flow in a (-cular Pipe. Eurovisc 77 - Unsteady Turbulent Boundary Layers and Shear Flows, Toulouse, France, Jar,. 2977. (TE-D) Mainardi , H. and Panday
Boundary Layer to a System of Viscous Hyperbolic Conservation Laws
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we investigate the large-time behavior of solutions to the initial-boundary value problem for nxn hyperbolic system of conservation laws with artificial viscosity in the half line (0, ∞). We first show that a boundary layer exists if the corresponding hyperbolic part contains at least one characteristic field with negative propagation speed. We further show that such boundary layer is nonlinearly stable under small initial perturbation. The proofs are given by an elementary energy method.
Boundary layer effects on liners for aircraft engines
Gabard, Gwénaël
2016-10-01
The performance of acoustic treatments installed on aircraft engines is strongly influenced by the boundary layer of the grazing flow on the surface of the liner. The parametric study presented in this paper illustrates the extent of this effect and identifies when it is significant. The acoustic modes of a circular duct with flow are calculated using a finite difference method. The parameters are representative of the flow conditions, liners and sound fields found in current turbofan engines. Both the intake and bypass ducts are considered. Results show that there is a complex interplay between the boundary layer thickness, the direction of propagation and the liner impedance and that the boundary layer can have a strong impact on liner performance for typical configurations (including changes of the order of 30 dB on the attenuation of modes associated with tonal fan noise). A modified impedance condition including the effect of a small but finite boundary layer thickness is considered and compared to the standard Myers condition based on an infinitely thin boundary layer. We show how this impedance condition can be implemented in a mode calculation method by introducing auxiliary variables. This condition is able to capture the trends associated with the boundary layer effects and in most cases provides improved predictions of liner performance.
Unsteady Boundary-Layer Flow over Jerked Plate Moving in a Free Stream of Viscoelastic Fluid
Directory of Open Access Journals (Sweden)
Sufian Munawar
2014-01-01
Full Text Available This study aims to investigate the unsteady boundary-layer flow of a viscoelastic non-Newtonian fluid over a flat surface. The plate is suddenly jerked to move with uniform velocity in a uniform stream of non-Newtonian fluid. Purely analytic solution to governing nonlinear equation is obtained. The solution is highly accurate and valid for all values of the dimensionless time 0≤τ<∞. Flow properties of the viscoelastic fluid are discussed through graphs.
Institute of Scientific and Technical Information of China (English)
Xuehui Chen; Liancun Zheng; Xinxin Zhang
2006-01-01
An efficient Adomian analytical decomposition technique for studying the momentum and heat boundary layer equations with exponentially stretching surface conditions was presented and an approximate analytical solution was obtained, which can be represented in terms of a rapid convergent power series with elegantly computable terms. The reliability and efficiency of the approximate solution were verified using numerical solutions in the literature. The approximate solution can be successfully applied to provide the values of skin friction and the temperature gradient coefficient.
Low Ozone in the Marine Boundary Layer of the Tropical Pacific Ocean
Singh, Hanwant B.; Gregory, G. L.; Andesrson, B.; Browell, E.; Sachse, G. W.; Davis, D. D.; Crawford, J.; Bradshaw, J. D.; Talbot, R.; Blake, D. R.; Lawless, James G. (Technical Monitor)
1994-01-01
Aircraft measurements of ozone, its key precursors, and a variety of chemical tracers were made in the troposphere of the western and central Pacific in October 1991. These data are presented and analyzed to examine the occurrence of low ozone concentrations in the remote marine boundary layer of the tropical and equatorial Pacific Ocean. The data from these flights out of Guam, covering an area extending from the equator to 20 N and from south of the Philippines to Hawaii, show average O3 concentrations as low as 8-9 ppb (ppb=10(exp-9)v/v) at altitudes of 0.3-0.5 km in the boundary layer. Individual measurements as low as 2-5 ppb were recorded. Low O3 concentrations do not always persist in space and time. High O3, generally associated with the transport of upper tropospheric air, was also encountered in the boundary layer. In practically all cases, O3 increased to values as large as 25-30 ppb within 2 km above the boundary layer top. Steady state model computations are used to suggest that these low O3 concentrations are a result of net photochemical O3 destruction in a low NO environment, sea-surface deposition, and extremely low net entrainment rates (1-2 mm per second) from the free troposphere. Day/night measurements of ethane, propane, gaseous and aerosol Cl suggest that daytime (morning) Cl atom concentrations in the vicinity of 10(exp 5) molecules per cubic centimeter may be present in the marine boundary layer. This Cl atom abundance can be rationalized only if sea salt aerosols can release free chlorine (Cl2) to the gas phase in the presence of sun light (and possibly O3). These Cl atom concentrations, however, are still insufficient and Cl (or Br) chemistry is not likely to be an important cause of the observed low O3.
On the impact of adverse pressure gradient on the supersonic turbulent boundary layer
Wang, Qian-Cheng; Wang, Zhen-Guo; Zhao, Yu-Xin
2016-11-01
By employing the particle image velocimetry, the mean and turbulent characteristics of a Mach 2.95 turbulent boundary layer are experimentally investigated without the impact of curvature. The physical mechanism with which the streamwise adverse pressure gradient affects the supersonic boundary layer is revealed. The data are compared to that of the concave boundary layer with similar streamwise distributions of wall static pressure to clarify the separate impacts of the adverse pressure gradient and the concave curvature. The logarithmic law is observed to be well preserved for both of the cases. The dip below the logarithmic law is not observed in present investigation. Theoretical analysis indicates that it could be the result of compromise between the opposite impacts of the compression wave and the increased turbulent intensity. Compared to the zero pressure gradient boundary layer, the principal strain rate and the turbulent intensities are increased by the adverse pressure gradient. The shear layer formed due the hairpin packets could be sharpened by the compression wave, which leads to higher principal strain rate and the associated turbulent level. Due to the additional impact of the centrifugal instability brought by the concave wall, even higher turbulent intensities than that of the adverse pressure gradient case are introduced. The existence of velocity modes within the zero pressure gradient boundary layer suggests that the large scale motions are statistically well organized. The generation of new velocity modes due to the adverse pressure gradient indicates that the turbulent structure is changed by the adverse pressure gradient, through which more turbulence production that cannot be effectively predicted by the Reynolds-stress transport equations could be brought.
Reactive boundary layers in metallic rolling contacts
Energy Technology Data Exchange (ETDEWEB)
Burbank, John
2016-05-01
more thorough investigation into the effects of residual austenite on the properties of this material. The high-performance alternative steels, 36NiCrMoV1-5-7 (hot working steel) and 45SiCrMo6 (spring steel), were heat treated as recommended by their respective manufacturers, and were not case-hardened. The selection of materials with and materials without case-hardening allows for an investigation into whether or not case-hardening is even necessary to deliver acceptable friction behaviour and wear performance. Elemental analyses were conducted by multiple methods to ensure accurate results. Residual austenite contents of the steels and the depth profiles of residual stresses were determined by X-Ray diffraction (XRD), for 20MnCr5 ranging from approximately 6 - 14 vol.%, and under 2 vol.% for the alternative alloys. Hardness profiles were taken from the testing surfaces into the material core. The carburization of 20MnCr5 led to higher hardness and the greater concentration of carbon in the carburization zone more representative of a hardened SAE E52100, or 100Cr6/102Cr6, than of a non-case-hardened 20MnCr5. Residual stresses from machining and case-hardening were measured directly at the sample surface. The high-performance steels fulfilled manufacturer expectations in terms of elemental content, with hardness values between 50 - 55 HRC and strongly martensitic microstructure character. With characterization of the chosen materials complete, the materials could then be subjected to pre-conditioning. The first pre-conditioning method involved targeted generation of cold work hardening as induced boundary layers to protect the contact zone against wear. Work hardening was identified both by variations in residual stress profiles, i.e. the introduction of beneficial compressive residual stresses, and hardness increases in the contact zone, providing enhanced wear resistance. Parameters for work hardening were further optimized to reduce damage to the surface substrates
Directory of Open Access Journals (Sweden)
T. M. Ajayi
2017-01-01
Full Text Available The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases in Rex1/2Cfx is guaranteed with St when magnitude of β is large. Rex1/2Cfx decreases with Ec and m.
Mobility anisotropy of two-dimensional semiconductors
Lang, Haifeng; Zhang, Shuqing; Liu, Zhirong
2016-12-01
The carrier mobility of anisotropic two-dimensional semiconductors under longitudinal acoustic phonon scattering was theoretically studied using deformation potential theory. Based on the Boltzmann equation with the relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was derived, showing that the influence of effective mass on mobility anisotropy is larger than those of deformation potential constant or elastic modulus. Parameters were collected for various anisotropic two-dimensional materials (black phosphorus, Hittorf's phosphorus, BC2N , MXene, TiS3, and GeCH3) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio is overestimated by the previously described method.
Schoenauer, W.; Daeubler, H. G.; Glotz, G.; Gruening, J.
1986-01-01
An implicit difference procedure for the solution of equations for a chemically reacting hypersonic boundary layer is described. Difference forms of arbitrary error order in the x and y coordinate plane were used to derive estimates for discretization error. Computational complexity and time were minimized by the use of this difference method and the iteration of the nonlinear boundary layer equations was regulated by discretization error. Velocity and temperature profiles are presented for Mach 20.14 and Mach 18.5; variables are velocity profiles, temperature profiles, mass flow factor, Stanton number, and friction drag coefficient; three figures include numeric data.
Institute of Scientific and Technical Information of China (English)
Chandaneswar Midya
2012-01-01
An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible Buid over a linearly shrinking surface is presented. The Row is permeated by an externally applied magnetic Geld normal to the plane of the flow. The equations governing the Row and concentration Reid are reduced into a set of nonlinear ordinary differential equations using similarity variables. Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall mass flux (PMF) as boundary conditions. The study reveals that the concentration over a shrinking sheet is signiRcantly different from that of a stretching surface. It s found that te solute boundary layer thickness is enhanced with the increasing values of the Schmidt number and the power-law index parameter, but decreases with enhanced vaJues of magnetic and reaction rate parameters for the PSC case. For the PMF case, the solute boundary layer thickness decreases with the increase of the Schmidt number, magnetic and reaction rate parameter for power-law index parameter n = 0. Negative solute boundary layer thickness is observed for the PMF case when n = 1 and 2, and these facts may not be realized in real-world applications.%An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible fluid over a linearly shrinking surface is presented.The flow is permeated by an externally applied magnetic field normal to the plane of the flow.The equations governing the flow and concentration field are reduced into a set of nonlinear ordinary differential equations using similarity variables.Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall
CFD simulation of neutral ABL flows; Atmospheric Boundary Layer
Energy Technology Data Exchange (ETDEWEB)
Xiaodong Zhang
2009-04-15
This work is to evaluate the CFD prediction of Atmospheric Boundary Layer flow field over different terrains employing Fluent 6.3 software. How accurate the simulation could achieve depend on following aspects: viscous model, wall functions, agreement of CFD model with inlet wind velocity profile and top boundary condition. Fluent employ wall function roughness modifications based on data from experiments with sand grain roughened pipes and channels, describe wall adjacent zone with Roughness Height (Ks) instead of Roughness Length (z{sub 0}). In a CFD simulation of ABL flow, the mean wind velocity profile is generally described with either a logarithmic equation by the presence of aerodynamic roughness length z{sub 0} or an exponential equation by the presence of exponent. As indicated by some former researchers, the disagreement between wall function model and ABL velocity profile description will result in some undesirable gradient along flow direction. There are some methods to improve the simulation model in literatures, some of them are discussed in this report, but none of those remedial methods are perfect to eliminate the streamwise gradients in mean wind speed and turbulence, as EllipSys3D could do. In this paper, a new near wall treatment function is designed, which, in some degree, can correct the horizontal gradients problem. Based on the corrected model constants and near wall treatment function, a simulation of Askervein Hill is carried out. The wind condition is neutrally stratified ABL and the measurements are best documented until now. Comparison with measured data shows that the CFD model can well predict the velocity field and relative turbulence kinetic energy field. Furthermore, a series of artificial complex terrains are designed, and some of the main simulation results are reported. (au)
Institute of Scientific and Technical Information of China (English)
A.S.J.AL-SAIF; 朱正佑
2003-01-01
The traditional differential quadrature method was improved by using the upwind difference scheme for the convectiveterms to solve the coupled two-dimensional incompressible Navier-stokes equations and heat equation. The new method was comparedwith the conventional differential quadrature method in the aspects of convergence and accuracy. The results show that the newmethod is more accurate, and has better convergence than the conventional differential quadrature method for numerically computingthe steady-state solution.
The boundary layer over turbine blade models with realistic rough surfaces
McIlroy, Hugh M., Jr.
The impact of turbine blade surface roughness on aerodynamic performance and heat loads is well known. Over time, as the turbine blades are exposed to heat loads, the external surfaces of the blades become rough. Also, for film-cooled blades, surface degradation can have a significant impact on film-cooling effectiveness. Many studies have been conducted on the effects of surface degradation/roughness on engine performance but most investigations have modeled the rough surfaces with uniform or two-dimensional roughness patterns. The objective of the present investigation is to conduct measurements that will reveal the influence of realistic surface roughness on the near-wall behavior of the boundary layer. Measurements have been conducted at the Matched-Index-of-Refraction (MIR) Facility at the Idaho National Engineering and Environmental Laboratory with a laser Doppler velocimeter. A flat plate model of a turbine blade has been developed that produces a transitional boundary layer, elevated freestream turbulence and an accelerating freestream in order to simulate conditions on the suction side of a high-pressure turbine blade. Boundary layer measurements have been completed over a smooth plate model and over a model with a strip of realistic rough surface. The realistic rough surface was developed by scaling actual turbine blade surface data that was provided by U.S. Air Force Research Laboratory. The results indicate that bypass transition occurred very early in the flow over the model and that the boundary layer remained unstable throughout the entire length of the test plate; the boundary layer thickness and momentum thickness Reynolds numbers increased over the rough patch; and the shape factor increased over the rough patch but then decreased downstream of the patch relative to the smooth plate case; in the rough patch case the flow experienced two transition reversals with laminar-like behavior achieved by the end of the test plate; streamwise turbulence
The inner core thermodynamics of the tropical cyclone boundary layer
Williams, Gabriel J.
2016-10-01
Although considerable progress has been made in understanding the inner-core dynamics of the tropical cyclone boundary layer (TCBL), our knowledge of the inner-core thermodynamics of the TCBL remains limited. In this study, the inner-core budgets of potential temperature (θ), specific humidity ( q), and reversible equivalent potential temperature (θ _e) are examined using a high-resolution multilevel boundary layer model. The potential temperature budgets show that the heat energy is dominated by latent heat release in the eyewall, evaporative cooling along the outer edge of the eyewall, and upward surface fluxes of sensible and latent heat from the underlying warm ocean. It is shown that the vertical θ advection overcompensates the sum of radial advective warming from the boundary layer outflow jet and latent heating for the development of cooling in the eyewall within the TCBL. The moisture budgets show the dominant upward transport of moisture in the eyewall updrafts, partly by the boundary-layer outflow jet from the bottom eye region, so that the eyewall remains nearly saturated. The θ _e budgets reveal that the TCBL is maintained thermodynamically by the upward surface flux of higher-θ _e air from the underlying warm ocean, the radial transport of low-θ _e air from the outer regions of the TCBL, and the dry adiabatic cooling associated by eyewall updrafts. These results underscore the significance of vertical motion and the location of the boundary layer outflow jet in maintaining the inner core thermal structure of the TCBL.
An investigation of streaklike instabilities in laminar boundary layer flames
Miller, Colin; Finney, Mark; Forthofer, Jason; McAllister, Sara; Gollner, Michael
2016-11-01
Observations of coherent structures in boundary layer flames, particularly wildland fires, motivated an investigation on flame instabilities within a boundary layer. This experimental study examined streaklike structures in a stationary diffusion flame stabilized within a laminar boundary layer. Flame streaks were found to align with pre-existing velocity perturbations, enabling stabilization of these coherent structures. Thermocouple measurements were used to quantify streamwise amplification of flame streaks. Temperature mapping indicated a temperature rise in the flame streaks, while the region in between these streaks, the trough, decreased in temperature. The heat flux to the surface was measured with a total heat flux gauge, and the heat flux below the troughs was found to be higher at all measurement locations. This was likely a function of the flame standoff distance, and indicated that the flame streaks were acting to modify the spanwise distribution of heat flux. Instabilities in boundary layer combustion can have an effect on the spanwise distribution of heat transfer. This finding has significant implications for boundary layer combustion, indicating that instantaneous properties can vary significantly in a three-dimensional flow field.
Nonlinear optimal control of bypass transition in a boundary layer flow
Xiao, Dandan; Papadakis, George
2016-11-01
Bypass transition is observed in a flat-plate boundary-layer flow when high levels of free stream turbulence are present. This scenario is characterized by the formation of streamwise elongated streaks inside the boundary layer, their break down into turbulent spots and eventually fully turbulent flow. In the current work, we perform DNS simulations of control of bypass transition in a zero-pressure-gradient boundary layer. A non-linear optimal control algorithm is developed that employs the direct-adjoint approach to minimise a quadratic cost function based on the deviation from the Blasius velocity profile. Using the Lagrange variational approach, the distribution of the blowing/suction control velocity is found by solving iteratively the non-linear Navier-Stokes and its adjoint equations in a forward/backward loop. The optimisation is performed over a finite time horizon during which the Lagrange functional is to be minimised. Large values of optimisation horizon result in instability of the adjoint equations. The results show that the controller is able to reduce the turbulent kinetic energy of the flow in the region where the objective function is defined and the velocity profile is seen to approach the Blasius solution. Significant drag reduction is also achieved.
Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models
Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.
2016-10-01
We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.
Wind-US Code Contributions to the First AIAA Shock Boundary Layer Interaction Prediction Workshop
Georgiadis, Nicholas J.; Vyas, Manan A.; Yoder, Dennis A.
2013-01-01
This report discusses the computations of a set of shock wave/turbulent boundary layer interaction (SWTBLI) test cases using the Wind-US code, as part of the 2010 American Institute of Aeronautics and Astronautics (AIAA) shock/boundary layer interaction workshop. The experiments involve supersonic flows in wind tunnels with a shock generator that directs an oblique shock wave toward the boundary layer along one of the walls of the wind tunnel. The Wind-US calculations utilized structured grid computations performed in Reynolds-averaged Navier-Stokes mode. Four turbulence models were investigated: the Spalart-Allmaras one-equation model, the Menter Baseline and Shear Stress Transport k-omega two-equation models, and an explicit algebraic stress k-omega formulation. Effects of grid resolution and upwinding scheme were also considered. The results from the CFD calculations are compared to particle image velocimetry (PIV) data from the experiments. As expected, turbulence model effects dominated the accuracy of the solutions with upwinding scheme selection indicating minimal effects.
Institute of Scientific and Technical Information of China (English)
WANG Liang; FU Song
2009-01-01
Based on Reynolds-averaged Navier-Stokes approach, a laminar-turbulence transition model is proposed in this study that takes into account the effects of different instability modes associated with the variations in Mach numbers of compressible boundary layer flows. The model is based on k-ω-γ three-equation eddy-viscosity concept with k representing the fluctuating kinetic energy, ωthe specific dissipation rate and the intermittency factor γ.The particular features of the model are that: 1) k includes the non-turbulent, as well as turbulent fluctuations; 2) a transport equation for the intermittency factor γis proposed here with a source term set to trigger the transition onset; 3) through the introduction of a new length scale normal to wall, the present model employs the local variables only avoiding the use of the integral parameters, like the boundary layer thickness δ,which are often cost-ineffective with the modern CFD (Computational Fluid Dynamics) methods; 4) in the fully turbulent region, the model retreats to the well-known k-ωSST (Shear Stress Transport) model. This model is validated with a number of available experiments on boundary layer transitions including the incompressible, supersonic and hypersonic flows past flat plates, straight/flared cones at zero incidences, etc. It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Based on Reynolds-averaged Navier-Stokes approach,a laminar-turbulence transition model is proposed in this study that takes into account the effects of different instability modes associated with the variations in Mach numbers of compressible boundary layer flows.The model is based on k-ω-γ three-equation eddy-viscosity concept with k representing the fluctuating kinetic energy,ωthe specific dissipation rate and the intermittency factorγ.The particular features of the model are that:1)k includes the non-turbulent,as well as turbulent fluctuations;2)a transport equation for the intermittency factorγis proposed here with a source term set to trigger the transition onset;3)through the introduction of a new length scale normal to wall,the present model employs the local variables only avoiding the use of the integral parameters,like the boundary layer thicknessδ,which are often cost-ineffective with the modern CFD(Computational Fluid Dynamics)methods;4)in the fully turbulent region,the model retreats to the well-known k-ωSST(Shear Stress Transport)model.This model is validated with a number of available experiments on boundary layer transitions including the incompressible,supersonic and hypersonic flows past flat plates,straight/flared cones at zero incidences,etc.It is demonstrated that the present model can be successfully applied to the engineering calculations of a variety of aerodynamic flow transition.
Nonlinear stability of non-stationary cross-flow vortices in compressible boundary layers
Gajjar, J. S. B.
1995-01-01
The nonlinear evolution of long wavelength non-stationary cross-flow vortices in a compressible boundary layer is investigated and the work extends that of Gajjar (1994) to flows involving multiple critical layers. The basic flow profile considered in this paper is that appropriate for a fully three-dimensional boundary layer with O(1) Mach number and with wall heating or cooling. The governing equations for the evolution of the cross-flow vortex are obtained and some special cases are discussed. One special case includes linear theory where exact analytic expressions for the growth rate of the vortices are obtained. Another special case is a generalization of the Bassom & Gajjar (1988) results for neutral waves to compressible flows. The viscous correction to the growth rate is derived and it is shown how the unsteady nonlinear critical layer structure merges with that for a Haberman type of viscous critical layer.
Semenov, A. N.; Gaponov, S. A.
2016-10-01
The boundary layer receptivity process due to the interaction of three-dimensional slow acoustic disturbances is numerically investigated at a free stream Mach number of 2.0. Problem is solved in the linear approximation relatively excited disturbances by an acoustic wave. Numerical simulations were conducted with using the program complex Ansys. In general, matching the results of the approximate method (based on stability equations for low-frequency fluctuations) with direct numerical simulation data is satisfactory. Normalized solutions on the corresponding maxima of the velocity perturbations amplitudes are coincided well enough about a wall. The greatest discrepancy occurs in the area of the boundary layer edge where the approximation theory is inapplicable.
Viscous boundary layers of radiation-dominated, relativistic jets. I. The two-stream model
Coughlin, Eric R
2015-01-01
Using the relativistic equations of radiation hydrodynamics in the viscous limit, we analyze the boundary layers that develop between radiation-dominated jets and their environments. In this paper we present the solution for the self-similar, 2-D, plane-parallel two-stream problem, wherein the jet and the ambient medium are considered to be separate, interacting fluids, and we compare our results to those of previous authors. (In a companion paper we investigate an alternative scenario, known as the free-streaming jet model.) Consistent with past findings, we show that the boundary layer that develops between the jet and its surroundings creates a region of low-density material. These models may be applicable to sources such as super-Eddington tidal disruption events and long gamma-ray bursts.
Directory of Open Access Journals (Sweden)
Krishnendu Bhattacharyya
2014-01-01
Full Text Available A mathematical model of the steady boundary layer flow of nanofluid due to an exponentially permeable stretching sheet with external magnetic field is presented. In the model, the effects of Brownian motion and thermophoresis on heat transfer and nanoparticle volume friction are considered. Using shooting technique with fourth-order Runge-Kutta method the transformed equations are solved. The study reveals that the governing parameters, namely, the magnetic parameter, the wall mass transfer parameter, the Prandtl number, the Lewis number, Brownian motion parameter, and thermophoresis parameter, have major effects on the flow field, the heat transfer, and the nanoparticle volume fraction. The magnetic field makes enhancement in temperature and nanoparticle volume fraction, whereas the wall mass transfer through the porous sheet causes reduction of both. For the Brownian motion, the temperature increases and the nanoparticle volume fraction decreases. Heat transfer rate becomes low with increase of Lewis number. For thermophoresis effect, the thermal boundary layer thickness becomes larger.
Energy Technology Data Exchange (ETDEWEB)
Rauf, A., E-mail: raufamar@ciitsahiwal.edu.pk [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Siddiq, M.K. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Abbasi, F.M. [Department of Mathematics, Comsats Institute of Information Technology, Islamabad 44000 (Pakistan); Meraj, M.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan); Ashraf, M. [Centre for Advanced Studies in Pure and Applied Mathematics, Department of Mathematics, Bahauddin Zakariya University, Multan 63000 (Pakistan); Shehzad, S.A. [Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000 (Pakistan)
2016-10-15
The present work deals with the steady laminar three-dimensional mixed convective magnetohydrodynamic (MHD) boundary layer flow of Casson nanofluid over a bidirectional stretching surface. A uniform magnetic field is applied normal to the flow direction. Similarity variables are implemented to convert the non-linear partial differential equations into ordinary ones. Convective boundary conditions are utilized at surface of the sheet. A numerical technique of Runge–Kutta–Fehlberg (RFK45) is used to obtain the results of velocity, temperature and concentration fields. The physical dimensionless parameters are discussed through tables and graphs. - Highlights: • Mixed convective boundary layer flow of Casson nanofluid is taken into account. • Impact of magnetic field is examined. • Convective heat and mass conditions are imposed. • Numerical solutions are presented and discussed.
Boundary Layer Flow and Heat Transfer of FMWCNT/Water Nanofluids over a Flat Plate
Directory of Open Access Journals (Sweden)
Mohammad Reza Safaei
2016-09-01
Full Text Available In the present study, the heat transfer and flow of water/FMWCNT (functionalized multi-walled carbon nanotube nanofluids over a flat plate was investigated using a finite volume method. Simulations were performed for velocity ranging from 0.17 mm/s to 1.7 mm/s under laminar regime and nanotube concentrations up to 0.2%. The 2-D governing equations were solved using an in-house FORTRAN code. For a specific free stream velocity, the presented results showed that increasing the weight percentage of nanotubes increased the Nusselt number. However, an increase in the solid weight percentage had a negligible effect on the wall shear stress. The results also indicated that increasing the free stream velocity for all cases leads to thinner boundary layer thickness, while increasing the FMWCNT concentration causes an increase in the boundary layer thickness.
Model Simulations of the Boundary-Layer Evolution over an Arid Andes Valley
Bischoff-Gauß, Inge; Kalthoff, Norbert; Khodayar, Samiro; Fiebig-Wittmaack, Melitta; Montecinos, Sonia
2008-09-01
The boundary layer of the Elqui valley in the arid north of Chile exhibits several interesting phenomena, such as a very shallow convective boundary layer (CBL) during the day. In the morning, warming is observed in and above the CBL, while the humidity decreases in the CBL. At midday, in and above the CBL of the valley, the temperature stagnates. In the afternoon in the CBL the temperature decreases and humidity increases, although the latent heat flux is very low. Because the characteristic features of the valley atmosphere are hard to interpret from observations alone, model simulations were applied. The simulations indicate that all components of the budget equations, i.e. the turbulent flux divergences, advection via the sea breeze, the upvalley and upslope wind systems, as well as subsidence, contribute to the evolution of the valley atmosphere.
Viscous boundary layers of radiation-dominated, relativistic jets. II. The free-streaming jet model
Coughlin, Eric R
2015-01-01
We analyze the interaction of a radiation-dominated jet and its surroundings using the equations of radiation hydrodynamics in the viscous limit. In a previous paper we considered the two-stream scenario, which treats the jet and its surroundings as distinct media interacting through radiation viscous forces. Here we present an alternative boundary layer model, known as the free-streaming jet model -- where a narrow stream of fluid is injected into a static medium -- and present solutions where the flow is ultrarelativistic and the boundary layer is dominated by radiation. It is shown that these jets entrain material from their surroundings and that their cores have a lower density of scatterers and a harder spectrum of photons, leading to observational consequences for lines of sight that look "down the barrel of the jet." These jetted outflow models may be applicable to the jets produced during long gamma-ray bursts and super-Eddington phases of tidal disruption events.
Analytical solutions for thermal forcing vortices in boundary layer and its applications
Institute of Scientific and Technical Information of China (English)
LIU Xiao-ran; LI Guo-ping
2007-01-01
Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.
Modeling of the thermal boundary layer in turbulent Rayleigh-Bénard convection
Emran, Mohammad; Shishkina, Olga
2016-11-01
We report modeling of the thermal boundary layer in turbulent Rayleigh-Bénard convection (RBC), which incorporates the effect of turbulent fluctuations. The study is based on the thermal boundary layer equation from Shishkina et al., and new Direct Numerical Simulations (DNS) of RBC in a cylindrical cell of the aspect ratio 1, for the Prandtl number variation of several orders of magnitude. Our modeled temperature profiles are found to agree with the DNS much better than those obtained with the classical Prandtl-Blasius or Falkner-Skan approaches. The work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh405/4 - Heisenberg fellowship and SFB963, Project A06.
1980-03-31
studying the effect of the gap between the airfoil tip and the channel wall. A fiber optics instrument ( Fotonic Sensor) was used to measure pre...dramatically better. Another significant result stems from the Fotonic Sensor tests. The data indicate that within a certain range the size of the gap
Boccio, J.; Economos, C.
1972-01-01
An analysis of the incompressible turbulent boundary layer, developing under the combined effects of mass transfer and pressure gradient, is presented in this paper. A strip-integral method is employed whereby two of the three governing equations are obtained by integrating the combined momentum and continuity equation to 50 percent and 100 percent, respectively, of the boundary-layer height. The latter equation is the usual momentum-integral equation; the former equation requires specification of shear. Accordingly, Clauser's equilibrium eddy-viscosity law is assumed valid at this point. The third and final equation is obtained by specifying that Stevenson's velocity profiles apply throughout the domain of interest, from which a skin-friction law can be derived. Comparisons of the numerical results with the experiments of McQuaid, which include combined effects of variable pressure gradient and mass transfer, show good agreement.
Wedin, Håkan; Cherubini, Stefania
2016-12-01
The asymptotic suction boundary layer (ASBL) is used for studying two permeability models, namely the Darcy and the Forchheimer model, the latter being more physically correct according to the literature. The term that defines the two apart is a function of the non-Darcian wall permeability {\\hat{K}}2 and of the wall suction {\\hat{V}}0, whereas the Darcian wall permeability {\\hat{K}}1 is common to the two models. The underlying interest of the study lies in the field of transition to turbulence where focus is put on two-dimensional nonlinear traveling waves (TWs) and their three-dimensional linear stability. Following a previous study by Wedin et al (2015 Phys. Rev. E 92 013022), where only the Darcy model was considered, the present work aims at comparing the two models, assessing where in the parameter space they cease to produce the same results. For low values of {\\hat{K}}1 both models produce almost identical TW solutions. However, when both increasing the suction {\\hat{V}}0 to sufficiently high amplitudes (i.e. lowering the Reynolds number Re, based on the displacement thickness) and using large values of the wall porosity, differences are observed. In terms of the non-dimensional Darcian wall permeability parameter, a, strong differences in the overall shape of the bifurcation curves are observed for a≳ 0.70, with the emergence of a new family of solutions at Re lower than 100. For these large values of a, a Forchheimer number {{Fo}}\\max ≳ 0.5 is found, where Fo expresses the ratio between the kinetic and viscous forces acting on the porous wall. Moreover, the minimum Reynolds number, {{Re}}g, for which the Navier-Stokes equations allow for nonlinear solutions, decreases for increasing values of a. Fixing the streamwise wavenumber to α = 0.154, as used in the study by Wedin et al referenced above, we find that {{Re}}g is lowered from Re ≈ 3000 for zero permeability, to below 50 for a = 0.80 for both permeability models. Finally, the stability of
The Coupling State of an Idealized Stable Boundary Layer
Acevedo, Otávio C.; Costa, Felipe D.; Degrazia, Gervásio A.
2012-10-01
The coupling state between the surface and the top of the stable boundary layer (SBL) is investigated using four different schemes to represent the turbulent exchange. An idealized SBL is assumed, with fixed wind speed and temperature at its top. At the surface, two cases are considered, first a constant temperature, 20 K lower than the SBL top, and later a constant 2 K h-1 cooling rate is assumed for 10 h after a neutral initial condition. The idealized conditions have been chosen to isolate the influence of the turbulence formulations on the coupling state, and the intense stratification has the purpose of enhancing such a response. The formulations compared are those that solve a prognostic equation for turbulent kinetic energy (TKE) and those that directly prescribe turbulence intensity as a function of atmospheric stability. Two TKE formulations are considered, with and without a dependence of the exchange coefficients on stability, while short and long tail stability functions (SFs) are also compared. In each case, the dependence on the wind speed at the SBL top is considered and it is shown that, for all formulations, the SBL experiences a transition from a decoupled state to a coupled state at an intermediate value of mechanical forcing. The vertical profiles of potential temperature, wind speed and turbulence intensity are shown as a function of the wind speed at the SBL top, both for the decoupled and coupled states. The formulation influence on the coupling state is analyzed and it is concluded that, in general, the simple TKE formulation has a better response, although it also tends to overestimate turbulent mixing. The consequences are discussed.
Effect of externally generated turbulence on wave boundary layer
DEFF Research Database (Denmark)
Fredsøe, Jørgen; Sumer, B. Mutlu; Kozakiewicz, A.
2003-01-01
This experimental study deals with the effect of externally generated turbulence on the oscillatory boundary layer to simulate the turbulence in the wave boundary layer under broken waves in the swash zone. The subject has been investigated experimentally in a U-shaped, oscillating water tunnel...... with a smooth bottom. Turbulence was generated ´externally´ as the flow in the oscillator was passed through a series of grids, that extended from the cover of the water tunnel to about mid-depth. Two different types of grid porosities were used. Direct measurements of the bed shear stress and velocity...... results. The mean and turbulence quantities in the outer flow region are increased substantially with the introduction of the grids. It is shown that the externally generated turbulence is able to penetrate the bed boundary layer, resulting in an increase in the bed shear stress, and therefore...
Localized travelling waves in the asymptotic suction boundary layer
Kreilos, Tobias; Schneider, Tobias M
2016-01-01
We present two spanwise-localized travelling wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwise-localized edge states previously found for this system. The vortical structures of the second solution are located in the free stream far above the laminar boundary layer and are supported by a secondary shear gradient that is created by a large-scale low-speed streak. The dynamically relevant eigenmodes of this solution are concentrated in the free stream, and the departure into turbulence from this solution evolves in the free stream towards the walls. For invariant solutions in free-stream turbulence, this solution thus shows that that the source of energy of the vortical structures can be a dynamical structure of the solution itself, instead of the laminar boundary layer.
Optical measurements of degradation in aircraft boundary layers
Kelsall, D.
1980-01-01
Visible wavelength measurements of the degradation of optical beams when transmitted through the thin aerodynamic boundary layers around an aircraft are reviewed. The measured results indicated degradation levels for the KC-135 airplanes between 0.10 to 0.13 lambda increasing to 0.18 lambda (rms wavefront distortion). For the Lear Jet, degradation with a 25 mm diameter optics was roughly 0.07 lambda. The corresponding infinite aperture degradation levels are also calculated. The corresponding measured correlation lengths of roughly 12 mm for the KC-135 aircraft and 6 mm for the Lear Jet scale to roughly 20 and 25 mm, respectively, for infinite apertures. These boundary layer correlation lengths do not appear to reflect the different boundary layer thicknesses on the two different aircraft.
Analysis of diabatic flow modification in the internal boundary layer
DEFF Research Database (Denmark)
Floors, Rogier; Gryning, Sven-Erik; Pena Diaz, Alfredo
2011-01-01
is controlled by a combination of both downstream and upstream stability and surface roughness conditions. A model based on a diffusion analogy is able to predict the internal boundary layer height well. Modeling the neutral and long-term wind profile with a 3 layer linear interpolation scheme gives good......Measurements at two meteorological masts in Denmark, Horns Rev in the sea and Høvsøre near the coastline on land, are used to analyze the behaviour of the flow after a smooth-to-rough change in surface conditions. The study shows that the wind profile within the internal boundary layer...... results at Høvsøre. Based on a comparison with a numerical model and the measurements, the constants in the interpolation scheme are slightly adjusted, which yields an improvement for the description of the wind profile in the internal boundary layer....
Boundary Layer Ventilation by Convection and Coastal Processes
Dacre, H.
2008-12-01
Several observational studies measuring aerosol in the atmosphere have found multiple aerosol layers located above the marine boundary layer. It is hypothesized that the existence of these layers is influenced by the diurnal variation in the structure of the upwind continental boundary layer. Furthermore, collision between a sea breeze and the prevailing wind can result in enhanced convection at the coast which can also lead to elevated layers of pollution. In this study we investigate the processes responsible for ventilation of the atmospheric boundary layer near the coast using the UK Met Office Unified Model. Pollution sources are represented by the constant emission of a passive tracer everywhere over land. The ventilation processes observed include shallow convection, a sea breeze circulation and coastal outflow. Vertical distributions of tracer at the coast are validated qualitatively with AMPEP (Aircraft Measurement of chemical Processing Export fluxes of Pollutants over the UK) CO aircraft measurements and are shown to agree well.
Boundary-layer control by electric fields A feasibility study
Mendes, R V
1998-01-01
A problem of great concern in aviation and submarine propulsion is the control of the boundary layer and, in particular, the methods to extend the laminar region as a means to decrease noise and fuel consumption. In this paper we study the flow of air along an airfoil when a layer of ionized gas and a longitudinal electric field are created in the boundary layer region. By deriving scaling solutions and more accurate numerical solutions we discuss the possibility of achieving significant boundary layer control for realistic physical parameters. Practical design formulas and criteria are obtained. We also discuss the perspectives for active control of the laminar-to-turbulent transition fluctuations by electromagnetic field modulation.