A Coordinate Transformation for Unsteady Boundary Layer Equations
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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.
Analysis of Laminar Boundary Layer Equations
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R. Yesman
2012-01-01
Full Text Available The paper proposes methodology for analysis and calculation of laminar fluid flow processes in a boundary layer.The presented dependences can be used for practical calculations while power carriers of various application are moving in the channels of heat and power devices.
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.
Numerical analysis of Weyl's method for integrating boundary layer equations
Najfeld, I.
1982-01-01
A fast method for accurate numerical integration of Blasius equation is proposed. It is based on the limit interchange in Weyl's fixed point method formulated as an iterated limit process. Each inner limit represents convergence to a discrete solution. It is shown that the error in a discrete solution admits asymptotic expansion in even powers of step size. An extrapolation process is set up to operate on a sequence of discrete solutions to reach the outer limit. Finally, this method is extended to related boundary layer equations.
Perfectly-matched-layer boundary integral equation method for wave scattering in a layered medium
Lu, Wangtao; Qian, Jianliang
2016-01-01
For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation conditions. For scattering problems in a layered medium, standard BIE methods based on the Green's function of the background medium must evaluate the expensive Sommefeld integrals. Alternative BIE methods based on the free-space Green's function give rise to integral equations on unbounded interfaces which are not easy to truncate, since the wave fields on these interfaces decay very slowly. We develop a BIE method based on the perfectly matched layer (PML) technique. The PMLs are widely used to suppress outgoing waves in numerical methods that directly discretize the physical space. Our PML-based BIE method uses the Green's function of the PML-transformed free space to define the boundary integral operators. The method is efficient, since the Green's function of the PML-tran...
Ardema, M. D.; Yang, L.
1985-01-01
A method of solving the boundary-layer equations that arise in singular-perturbation analysis of flightpath optimization problems is presented. The method is based on Picard iterations of the integrated form of the equations and does not require iteration to find unknown boundary conditions. As an example, the method is used to develop a solution algorithm for the zero-order boundary-layer equations of the aircraft minimum-time-to-climb problem.
Tetervin, Neal; Lin, Chia Chiao
1951-01-01
A general integral form of the boundary-layer equation, valid for either laminar or turbulent incompressible boundary-layer flow, is derived. By using the experimental finding that all velocity profiles of the turbulent boundary layer form essentially a single-parameter family, the general equation is changed to an equation for the space rate of change of the velocity-profile shape parameter. The lack of precise knowledge concerning the surface shear and the distribution of the shearing stress across turbulent boundary layers prevented the attainment of a reliable method for calculating the behavior of turbulent boundary layers.
Boundary Layer Equations and Lie Group Analysis of a Sisko Fluid
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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.
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.
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.
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.
Non-perturbative solution of free-convective boundary-layer equation by Adomian decomposition method
Energy Technology Data Exchange (ETDEWEB)
Kechil, Seripah Awang [Department of Mathematics, Universiti Teknologi MARA, 40450 Shah Alam Selangor (Malaysia); Hashim, Ishak [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor (Malaysia)]. E-mail: ishak_h@ukm.my
2007-03-19
A free-convective boundary layer flow modeled by a system of nonlinear ordinary differential equations is considered. The system is solved using the Adomian decomposition method (ADM) which yields an analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The analytical solutions and the pertinent features of the illustrations show the efficiency of the method.
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.
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.
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...
Transient Growth Analysis of Compressible Boundary Layers with Parabolized Stability Equations
Paredes, Pedro; Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan
2016-01-01
The linear form of parabolized linear stability equations (PSE) is used in a variational approach to extend the previous body of results for the optimal, non-modal disturbance growth in boundary layer flows. This methodology includes the non-parallel effects associated with the spatial development of boundary layer flows. As noted in literature, the optimal initial disturbances correspond to steady counter-rotating stream-wise vortices, which subsequently lead to the formation of stream-wise-elongated structures, i.e., streaks, via a lift-up effect. The parameter space for optimal growth is extended to the hypersonic Mach number regime without any high enthalpy effects, and the effect of wall cooling is studied with particular emphasis on the role of the initial disturbance location and the value of the span-wise wavenumber that leads to the maximum energy growth up to a specified location. Unlike previous predictions that used a basic state obtained from a self-similar solution to the boundary layer equations, mean flow solutions based on the full Navier-Stokes (NS) equations are used in select cases to help account for the viscous-inviscid interaction near the leading edge of the plate and also for the weak shock wave emanating from that region. These differences in the base flow lead to an increasing reduction with Mach number in the magnitude of optimal growth relative to the predictions based on self-similar mean-flow approximation. Finally, the maximum optimal energy gain for the favorable pressure gradient boundary layer near a planar stagnation point is found to be substantially weaker than that in a zero pressure gradient Blasius boundary layer.
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.
Computation of Boundary Layers
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József Dénes
2004-11-01
Full Text Available This paper is the first part of a series of studies where we examine several methods for the solution of the boundary layer equation of the fluid mechanics. The first of these is the analytical or rather quasi analytical method due to Blasius. This method reduces a system of partial differential equations to a system of ordinary differential equations and these in turn are solved by numerical methods since no exact solution of the Blasius type equations is known. We determind all the Blasius equation neccessary for up to 11-th order approximation. Our further aim to study the finite difference numerical solutions of the boundary layer equation and some of the methods applying weighted residual principles and by comparing these with the ”exact” solutions arrived at by Blasius method develop a quick reliable method for solving the boundary layer equation.
Langel, Christopher Michael
A computational investigation has been performed to better understand the impact of surface roughness on the flow over a contaminated surface. This thesis highlights the implementation and development of the roughness amplification model in the flow solver OVERFLOW-2. The model, originally proposed by Dassler, Kozulovic, and Fiala, introduces an additional scalar field roughness amplification quantity. This value is explicitly set at rough wall boundaries using surface roughness parameters and local flow quantities. This additional transport equation allows non-local effects of surface roughness to be accounted for downstream of rough sections. This roughness amplification variable is coupled with the Langtry-Menter model and used to modify the criteria for transition. Results from flat plate test cases show good agreement with experimental transition behavior on the flow over varying sand grain roughness heights. Additional validation studies were performed on a NACA 0012 airfoil with leading edge roughness. The computationally predicted boundary layer development demonstrates good agreement with experimental results. New tests using varying roughness configurations are being carried out at the Texas A&M Oran W. Nicks Low Speed Wind Tunnel to provide further calibration of the roughness amplification method. An overview and preliminary results are provided of this concurrent experimental investigation.
Institute of Scientific and Technical Information of China (English)
Muhammet Y(u)r(u)soy
2004-01-01
Two dimensional equations of steady motion for third order fluids are expressed in a special coordinate system generated by the potential flow corresponding to an inviscid fluid. For the inviscid flow around an arbitrary object, the streamlines are the phicoordinates and velocity potential lines are psi-coordinates which form an orthogonal curvilinear set of coordinates. The outcome, boundary layer equations, is then shown to be independent of the body shape immersed into the flow. As a first approximation, assumption that second grade terms are negligible compared to viscous and third grade terms. Second grade terms spoil scaling transformation which is only transformation leading to similarity solutions for third grade fluid. By using Lie group methods, infinitesimal generators of boundary layer equations are calculated. The equations are transformed into an ordinary differential system. Numerical solutions of outcoming nonlinear differential equations are found by using combination of a Runge-Kutta algorithm and shooting technique.
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
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.
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.
Directory of Open Access Journals (Sweden)
D. Diederen
2015-06-01
Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
Approximate Analytical Solutions for a Class of Laminar Boundary-Layer Equations
Institute of Scientific and Technical Information of China (English)
Seripah Awang Kechil; Ishak Hashim; Sim Siaw Jiet
2007-01-01
A simple and efficient approximate analytical technique is presented to obtain solutions to a class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the decomposition method which yields a general analytic solution in the form of a convergent infinite series with easily computable terms. Comparative study is carried out to show the accuracy and effectiveness of the technique.
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.
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.
Hanasoge, S M; Gizon, L
2010-01-01
Perfectly matched layers are a very efficient and accurate way to absorb waves in media. We present a stable convolutional unsplit perfectly matched formulation designed for the linearized stratified Euler equations. However, the technique as applied to the Magneto-hydrodynamic (MHD) equations requires the use of a sponge, which, despite placing the perfectly matched status in question, is still highly efficient at absorbing outgoing waves. We study solutions of the equations in the backdrop of models of linearized wave propagation in the Sun. We test the numerical stability of the schemes by integrating the equations over a large number of wave periods.
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).
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.
Calculation methods for compressible turbulent boundary layers, 1976
Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.
1977-01-01
Equations and closure methods for compressible turbulent boundary layers are discussed. Flow phenomena peculiar to calculation of these boundary layers were considered, along with calculations of three dimensional compressible turbulent boundary layers. Procedures for ascertaining nonsimilar two and three dimensional compressible turbulent boundary layers were appended, including finite difference, finite element, and mass-weighted residual methods.
Calculation methods for compressible turbulent boundary layers
Bushnell, D. M.; Cary, A. M., Jr.; Harris, J. E.
1976-01-01
Calculation procedures for non-reacting compressible two- and three-dimensional turbulent boundary layers were reviewed. Integral, transformation and correlation methods, as well as finite difference solutions of the complete boundary layer equations summarized. Alternative numerical solution procedures were examined, and both mean field and mean turbulence field closure models were considered. Physics and related calculation problems peculiar to compressible turbulent boundary layers are described. A catalog of available solution procedures of the finite difference, finite element, and method of weighted residuals genre is included. Influence of compressibility, low Reynolds number, wall blowing, and pressure gradient upon mean field closure constants are reported.
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
Modeling the urban boundary layer
Bergstrom, R. W., Jr.
1976-01-01
A summary and evaluation is given of the Workshop on Modeling the Urban Boundary Layer; held in Las Vegas on May 5, 1975. Edited summaries from each of the session chairpersons are also given. The sessions were: (1) formulation and solution techniques, (2) K-theory versus higher order closure, (3) surface heat and moisture balance, (4) initialization and boundary problems, (5) nocturnal boundary layer, and (6) verification of models.
Boundary transfer matrices and boundary quantum KZ equations
Energy Technology Data Exchange (ETDEWEB)
Vlaar, Bart, E-mail: Bart.Vlaar@nottingham.ac.uk [School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD (United Kingdom)
2015-07-15
A simple relation between inhomogeneous transfer matrices and boundary quantum Knizhnik-Zamolodchikov (KZ) equations is exhibited for quantum integrable systems with reflecting boundary conditions, analogous to an observation by Gaudin for periodic systems. Thus, the boundary quantum KZ equations receive a new motivation. We also derive the commutativity of Sklyanin’s boundary transfer matrices by merely imposing appropriate reflection equations, in particular without using the conditions of crossing symmetry and unitarity of the R-matrix.
Narayanswami, N.; Horstman, C. C.; Knight, D. D.
1993-01-01
A 3D hypersonic crossing shock wave/turbulent boundary layer interaction is examined numerically. The test geometry consists of a pair of opposing sharp fins of angle alpha = 15 deg mounted on a flat plate. The freestream Mach number is 8.28. Two theoretical models are evaluated. The full 3D Reynolds-averaged Navier-Stokes equations are solved using the Baldwin-Lomax algebraic turbulent eddy viscosity model and the Rodi turbulence model. Computed results for both cases show good agreement with experiment for flat plate surface pressure and for pitot pressure and yaw angle profiles in the flowfield. General agreement is obtained for surface flow direction. Fair to poor agreement is obtained for surface heat transfer, indicating a need for more accurate turbulence models. The overall flowfield structure is similar to that observed in previous crossing shock interaction studies.
Boundary-layer linear stability theory
Mack, L. M.
1984-06-01
reached a stage of development which permit the direct solution of the primary differential equations, numerical results were obtained from the linear theory during the next 10 years for many different boundary layer flows: three dimensional boundary layers; free convention boundary layers; compressible boundary layers; boundary layers on compliant walls; a recomputation of Falkner-Skan flows; unsteady boundary layers; and heated wall boundary layers.
Boundary Layer Control on Airfoils.
Gerhab, George; Eastlake, Charles
1991-01-01
A phenomena, boundary layer control (BLC), produced when visualizing the fluidlike flow of air is described. The use of BLC in modifying aerodynamic characteristics of airfoils, race cars, and boats is discussed. (KR)
A Boundary Integral Equation Approach for Boundary Problem of Laplace Equation
Institute of Scientific and Technical Information of China (English)
SUNJian-she; YELiu-qing
2003-01-01
Using the second Green formula, the boundary problem of Laplace equation satisfied by potential function of static electric field is transformed to the problem of the boundary integral equation,and then a boundary integral equation approach is established by partitioning boundary using linear boundary element.
Boundary-layer theory for blast waves
Kim, K. B.; Berger, S. A.; Kamel, M. M.; Korobeinikov, V. P.; Oppenheim, A. K.
1975-01-01
It is profitable to consider the blast wave as a flow field consisting of two regions: the outer, which retains the properties of the inviscid solution, and the inner, which is governed by flow equations including terms expressing the effects of heat transfer and, concomitantly, viscosity. The latter region thus plays the role of a boundary layer. Reported here is an analytical method developed for the study of such layers, based on the matched asymptotic expansion technique combined with patched solutions.
Byatt-Smith, J. G.
2000-01-01
Nekrasov's integral equation describing water waves of permanent form, determines the angle phi that the wave surface makes with the horizontal. The independent variable s is a suitably scaled velocity potential, evaluated at the free surface, with the origin corresponding to the crest of the wave. For all waves, except for amplitudes near the maximum, phi satisfies the inequality mod(phi) is less than pi/6. It has been shown numerically and analytically, that as the wave amplitude approaches...
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...
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...
High enthalpy hypersonic boundary layer flow
Yanow, G.
1972-01-01
A theoretical and experimental study of an ionizing laminar boundary layer formed by a very high enthalpy flow (in excess of 12 eV per atom or 7000 cal/gm) with allowance for the presence of helium driver gas is described. The theoretical investigation has shown that the use of variable transport properties and their respective derivatives is very important in the solution of equilibrium boundary layer equations of high enthalpy flow. The effect of low level helium contamination on the surface heat transfer rate is minimal. The variation of ionization is much smaller in a chemically frozen boundary layer solution than in an equilibrium boundary layer calculation and consequently, the variation of the transport properties in the case of the former was not essential in the integration. The experiments have been conducted in a free piston shock tunnel, and a detailed study of its nozzle operation, including the effects of low levels of helium driver gas contamination has been made. Neither the extreme solutions of an equilibrium nor of a frozen boundary layer will adequately predict surface heat transfer rate in very high enthalpy flows.
Reaction diffusion equations with boundary degeneracy
Directory of Open Access Journals (Sweden)
Huashui Zhan
2016-03-01
Full Text Available In this article, we consider the reaction diffusion equation $$ \\frac{\\partial u}{\\partial t} = \\Delta A(u,\\quad (x,t\\in \\Omega \\times (0,T, $$ with the homogeneous boundary condition. Inspired by the Fichera-Oleinik theory, if the equation is not only strongly degenerate in the interior of $\\Omega$, but also degenerate on the boundary, we show that the solution of the equation is free from any limitation of the boundary condition.
Numerical simulation of turbulent atmospheric boundary layer flows
Energy Technology Data Exchange (ETDEWEB)
Bennes, L.; Bodnar, T.; Kozel, K.; Sladek, I. [Czech Technical Univ., Prague (Czech Republic). Dept. of Technical Mathematics; Fraunie, P. [Universite Toulon et du Var, La Garde (France). Lab. de Sondages Electromagnetiques de l' Environment Terrestre
2001-07-01
The work deals with the numerical solution of viscous turbulent steady flows in the atmospheric boundary layer including pollution propagation. For its description we use two different mathematical models: - a model based on the Reynolds averaged Navier-Stokes equations for incompressible flows - a model based on a system of boundary layer equations. These systems are completed by two transport equations for the concentration of passive pollutants and the potential temperature in conservative form, respectively, and by an algebraic turbulence model. (orig.)
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
Nonlinear Transient Growth and Boundary Layer Transition
Paredes, Pedro; Choudhari, Meelan M.; Li, Fei
2016-01-01
Parabolized stability equations (PSE) are used in a variational approach to study the optimal, non-modal disturbance growth in a Mach 3 at plate boundary layer and a Mach 6 circular cone boundary layer. As noted in previous works, the optimal initial disturbances correspond to steady counter-rotating streamwise vortices, which subsequently lead to the formation of streamwise-elongated structures, i.e., streaks, via a lift-up effect. The nonlinear evolution of the linearly optimal stationary perturbations is computed using the nonlinear plane-marching PSE for stationary perturbations. A fully implicit marching technique is used to facilitate the computation of nonlinear streaks with large amplitudes. To assess the effect of the finite-amplitude streaks on transition, the linear form of plane- marching PSE is used to investigate the instability of the boundary layer flow modified by spanwise periodic streaks. The onset of bypass transition is estimated by using an N- factor criterion based on the amplification of the streak instabilities. Results show that, for both flow configurations of interest, streaks of sufficiently large amplitude can lead to significantly earlier onset of transition than that in an unperturbed boundary layer without any streaks.
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.
Green House Gases Flux Model in Boundary Layer
Nurgaliev, Ildus
Analytical dynamic model of the turbulent flux in the three-layer boundary system is presented. Turbulence is described as a presence of the non-zero vorticity. The generalized advection-diffusion-reaction equation is derived for an arbitrary number of components in the flux. The fluxes in the layers are objects for matching requirements on the boundaries between the layers. Different types of transport mechanisms are dominant on the different levels of the layers.
BOUNDARY CONTROL OF MKDV-BURGERS EQUATION
Institute of Scientific and Technical Information of China (English)
TIAN Li-xin; ZHAO Zhi-feng; WANG Jing-feng
2006-01-01
The boundary control of MKdV-Burgers equation was considered by feedback control on the domain [0,1]. The existence of the solution of MKdV-Burgers equation with the feedback control law was proved. On the base, priori estimates for the solution was given. At last, the existence of the weak solution of MKdV-Burgers equation was proved and the global-exponential and asymptotic stability of the solution of MKdV-Burgers equation was given.
Absorbing layers for the Dirac equation
Energy Technology Data Exchange (ETDEWEB)
Pinaud, Olivier, E-mail: pinaud@math.colostate.edu
2015-05-15
This work is devoted to the construction of perfectly matched layers (PML) for the Dirac equation, that not only arises in relativistic quantum mechanics but also in the dynamics of electrons in graphene or in topological insulators. While the resulting equations are stable at the continuous level, some care is necessary in order to obtain a stable scheme at the discrete level. This is related to the so-called fermion doubling problem. For this matter, we consider the numerical scheme introduced by Hammer et al. [19], and combine it with the discretized PML equations. We state some arguments for the stability of the resulting scheme, and perform simulations in two dimensions. The perfectly matched layers are shown to exhibit, in various configurations, superior absorption than the absorbing potential method and the so-called transport-like boundary conditions.
Iterative solution of Hermite boundary integral equations
Energy Technology Data Exchange (ETDEWEB)
Gray, Leonard J [ORNL; Nintcheu Fata, Sylvain [ORNL; Ma, Ding [ORNL
2008-01-01
An efficient iterative method for the solution of the linear equations arising from a Hermite boundary integral approximation has been developed. Along with equations for the boundary unknowns, the Hermite system incorporates equations for the first-order surface derivatives (gradient) of the potential, and is therefore substantially larger than the matrix for a corresponding linear approximation. However, by exploiting the structure of the Hermite matrix, a two-level iterative algorithm has been shown to provide a very efficient solution algorithm. In this approach, the boundary function unknowns are treated separately from the gradient, taking advantage of the sparsity and near-positive definiteness of the gradient equations. In test problems, the new algorithm significantly reduced computation time compared to iterative solution applied to the full matrix. This approach should prove to be even more effective for the larger systems encountered in three-dimensional analysis, and increased efficiency should come from pre-conditioning of the non-sparse matrix component.
Bending Boundary Layers in Laminated-Composite Circular Cylindrical Shells
Nemeth, Michael P.; Smeltzer, Stanley S., III
2000-01-01
A study of the attenuation of bending boundary layers in balanced and unbalanced, symmetrically and unsymmetrically laminated cylindrical shells is presented for nine contemporary material systems. The analysis is based on the linear Sanders-Koiter shell equations and specializations to the Love-Kirchhoff shell equations and Donnell's equations are included. Two nondimensional parameters are identified that characterize the effects of laminate orthotropy and anisotropy on the bending boundary-layer decay length in a very general manner. A substantial number of structural design technology results are presented for a wide range of laminated-composite cylinders. For all laminates considered, the results show that the differences between results obtained with the Sanders-Koiter shell equations, the Love-Kirchhoff shell equations, and Donnell's equations are negligible. The results also show that the effect of anisotropy in the form of coupling between pure bending and twisting has a negligible effect on the size of the bending boundary-layer decay length of the balanced, symmetrically laminated cylinders considered. Moreover, the results show that coupling between the various types of shell anisotropies has a negligible effect on the calculation of the bending boundary-layer decay length in most cases. The results also show that, in some cases, neglecting the shell anisotropy results in underestimating the bending boundary-layer decay length and, in other cases, results in an overestimation.
Instability of the stable boundary layer?
Wiel, van de B.J.H.; Moene, A.F.; Steeneveld, G.J.; Holtslag, A.A.M.
2006-01-01
Many observations of artic boundary layers and nighttime boundary layers in general show low temperatures and weak winds near the surface. These weak wind conditions coincide with extremely low intensities of turbulence. As a result, the upper part of the boundary seems to be de-coupled from the sur
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.
Ouwersloot, H.G.; Arellano, de J.V.G.
2013-01-01
In Ouwersloot and Vila-Guerau de Arellano (Boundary-Layer Meteorol. doi: 10. 1007/s10546-013-9816-z, 2013, this issue), the analytical solutions for the boundary-layer height and scalar evolutions are derived for the convective boundary layer, based on the prognostic equations of mixed-layer slab mo
Numerical simulation of tsunami-scale wave boundary layers
DEFF Research Database (Denmark)
Williams, Isaac A.; Fuhrman, David R.
2016-01-01
, 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...... 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...
On Cauchy conditions for asymmetric mixed convection boundary layer flows
Energy Technology Data Exchange (ETDEWEB)
Amaouche, Mustapha [Laboratoire de Physique Theorique, Universite de Bejaia (Algeria); Kessal, Mohand [Departement Transport et Equipement Petrolier, Faculte des Hydrocarbures et de la Chimie, Universite de Boumerdes, 35000, Boumerdes (Algeria)
2003-06-01
The fundamental question of how and where does an asymmetric mixed convection boundary layer flow around a heated horizontal circular cylinder begin to develop is raised. We first transform the classical boundary layer equations by using an integral method of Karman-Pohlhausen type and obtain two coupled equations governing the evolutions of the dynamic and thermal boundary layers. Because of its global character, the implemented method allows to bypass the difficulty of downstream-upstream interactions. Cauchy conditions characterizing the starting of the boundary layers are found; they are obtained in a surprisingly simple manner for the limiting cases corresponding to Pr=1, Pr{yields}0 and Pr{yields}{infinity}. Otherwise, these conditions can be found by using a prediction correction algorithm. Some numerical experiments are finally performed in order to illustrate the theory. (authors)
Boundary value problems and partial differential equations
Powers, David L
2005-01-01
Boundary Value Problems is the leading text on boundary value problems and Fourier series. The author, David Powers, (Clarkson) has written a thorough, theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Professors and students agree that the author is a master at creating linear problems that adroitly illustrate the techniques of separation of variables used to solve science and engineering.* CD with animations and graphics of solutions, additional exercises and chapter review questions* Nearly 900 exercises ranging in difficulty* Many fully worked examples
Microgravity Effects on Plant Boundary Layers
Stutte, Gary; Monje, Oscar
2005-01-01
The goal of these series of experiment was to determine the effects of microgravity conditions on the developmental boundary layers in roots and leaves and to determine the effects of air flow on boundary layer development. It is hypothesized that microgravity induces larger boundary layers around plant organs because of the absence of buoyancy-driven convection. These larger boundary layers may affect normal metabolic function because they may reduce the fluxes of heat and metabolically active gases (e.g., oxygen, water vapor, and carbon dioxide. These experiments are to test whether there is a change in boundary layer associated with microgravity, quantify the change if it exists, and determine influence of air velocity on boundary layer thickness under different gravity conditions.
Blow-up and control of marginally separated boundary layers.
Braun, Stefan; Kluwick, Alfred
2005-05-15
Interactive solutions for steady two-dimensional laminar marginally separated boundary layers are known to exist up to a critical value Gamma(c) of the controlling parameter (e.g. the angle of attack of a slender airfoil) Gamma only. Here, we investigate three-dimensional unsteady perturbations of such boundary layers, assuming that the basic flow is almost critical, i.e. in the limit Gamma(c)-Gamma-->0. It is then shown that the interactive equations governing such perturbations simplify significantly, allowing, among others, a systematic study of the blow-up phenomenon observed in earlier investigations and the optimization of devices used in boundary-layer control.
Investigation of Laminar Boundary Layer on Airfoil
林, 秀千人; 佐々木, 壮一; 児玉, 好雄; 清水, 光昭
1999-01-01
The development of the laminar boundary layer on the NACA symmetrical airfoils and the separation of it are simulated by using the boundary layer theory and discrete vortex method. The arrangement of the discrete vortices on the airfoil affects on the separation position very much because the separation is sensitive to the velocity gradient of the main flow. It needs the very small increment 1/500 in boundary layer simulation to get the exact position of the separation. The simulation of both...
THE INTERIOR LAYER SOLUTION TO NONLOCAL REACTION DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
An initial boundary value problem of semilinear nonlocal reaction diffusion equations is considered.Under some suitable conditions,using the asymptotic theory,the existence and asymptotic behavior of the interior layer solution to the initial boundary value problem are studied.
Cyclone separator having boundary layer turbulence control
Krishna, Coimbatore R.; Milau, Julius S.
1985-01-01
A cyclone separator including boundary layer turbulence control that is operable to prevent undue build-up of particulate material at selected critical areas on the separator walls, by selectively varying the fluid pressure at those areas to maintain the momentum of the vortex, thereby preventing particulate material from inducing turbulence in the boundary layer of the vortical fluid flow through the separator.
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
Experimental investigation of wave boundary layer
DEFF Research Database (Denmark)
Sumer, B. Mutlu
2003-01-01
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......-dominated regime, is covered. Processes such as turbulence reduction/re-laminarization, and increase/decrease in the bed shear stress are presented. The fifth section considers various effects on the wave boundary layer such as the non-uniformity (that due to change in the boundary roughness and that due to change...
A method used to determine the upper thermal boundary of subgrade based on boundary layer theory
Institute of Scientific and Technical Information of China (English)
QingBo Bai; Xu Li; YaHu Tian
2015-01-01
In the numerical simulation of long-term subgrade temperature fields, the daily variation of soil temperature at a certain depthh is negligible. Such phenomenon is called the "boundary layer theory." Depthh is defined as the boundary layer thickness and the soil temperature athis approximately equal to a temperature increment plus the average atmosphere temperature. In the past, the boundary layer thickness and temperature increment were usually extracted from monitored data in the field. In this paper, a method is proposed to determinate the boundary layer thickness and temperature incre-ment. Based on the typical designs of highway or railway, the theoretical solution of boundary layer thickness is inferred and listed. Further, the empirical equation and design chart for determining the temperature increment are given in which the following factors are addressed, including solar radiation, equivalent thermal diffusivity and convective heat-transfer coefficient. Using these equations or design charts, the boundary layer thickness and temperature increment can be easily determined and used in the simulation of long-term subgrade temperature fields. Finally, an example is conducted and used to verify the method. The result shows that the proposed method for determining the upper thermal boundary of subgrade is accurate and practical.
A NOVEL BOUNDARY INTEGRAL EQUATION METHOD FOR LINEAR ELASTICITY--NATURAL BOUNDARY INTEGRAL EQUATION
Institute of Scientific and Technical Information of China (English)
Niu Zhongrong; Wang Xiuxi; Zhou Huanlin; Zhang Chenli
2001-01-01
The boundary integral equation (BIE) of displacement derivatives is put at a disadvantage for the difficulty involved in the evaluation of the hypersingular integrals. In this paper, the operators δij and εij are used to act on the derivative BIE. The boundary displacements, tractions and displacement derivatives are transformed into a set of new boundary tensors as boundary variables. A new BIE formulation termed natural boundary integral equation (NBIE) is obtained. The NBIE is applied to solving two-dimensional elasticity problems. In the NBIE only the strongly singular integrals are contained. The Cauchy principal value integrals occurring in the NBIE are evaluated. A combination of the NBIE and displacement BIE can be used to directly calculate the boundary stresses. The numerical results of several examples demonstrate the accuracy of the NBIE.
Plasma boundary layer and magnetopause layer of the earth's magnetosphere
International Nuclear Information System (INIS)
IMP 6 observations of the plasma boundary layer (PBL) and magnetopause layer (MPL) of the earth's magnetosphere indicate that plasma in the low-latitude portion of the PBL is supplied primarily by direct transport of magnetosheath plasma across the MPL and that this transport process is relatively widespread over the entire sunward magnetospheric boundary
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).
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
The BIE (boundary integral equation) method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applyiing the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are most important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The BIE method is based on the numerical solution of a set of integral constraint equations which couple boundary tractions (stresses) to boundary displacements. Thus the dimensionality of the problem is reduced by one; only boundary geometry and data are discretized. Stresses at any set of selected interior points are computed following the boundary solution without any further numerical approximations. Thus, the BIE method has inherently greater resolution capability for stress gradients than does the finite element method. Conversely, the BIE method is not efficient for problems involving significant inhomogeneity such as in multi-thin-layered materials, or in elastoplasticity. Some progress in applying the BIE method to the latter problem has been made but much more work remains. Further, the BIE method is only optional for problems with significant stress risers, and only when boundary stresses are more important. Interior stress calculations are expensive, per point, and can drive the solution costs up rapidly. The current report summarizes some of the advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referring some of the much broader developmental effort. (Auth.)
Boundary Layer on a Moving Wall with Suction and Injection
Institute of Scientific and Technical Information of China (English)
Anuar Ishak; Roslinda Nazar; Ioan Pop
2007-01-01
@@ We investigate the boundary-layer flow on a moving permeable plate parallel to a moving stream. The governing equations are solved numerically by a finite-difference method. Dual solutions are found to exist when the plate and the free stream move in the opposite directions.
Boundary Layer Flow Over a Moving Wavy Surface
Hendin, Gali; Toledo, Yaron
2016-04-01
Boundary Layer Flow Over a Moving Wavy Surface Gali Hendin(1), Yaron Toledo(1) January 13, 2016 (1)School of Mechanical Engineering, Tel-Aviv University, Israel Understanding the boundary layer flow over surface gravity waves is of great importance as various atmosphere-ocean processes are essentially coupled through these waves. Nevertheless, there are still significant gaps in our understanding of this complex flow behaviour. The present work investigates the fundamentals of the boundary layer air flow over progressive, small-amplitude waves. It aims to extend the well-known Blasius solution for a boundary layer over a flat plate to one over a moving wavy surface. The current analysis pro- claims the importance of the small curvature and the time-dependency as second order effects, with a meaningful impact on the similarity pattern in the first order. The air flow over the ocean surface is modelled using an outer, inviscid half-infinite flow, overlaying the viscous boundary layer above the wavy surface. The assumption of a uniform flow in the outer layer, used in former studies, is now replaced with a precise analytical solution of the potential flow over a moving wavy surface with a known celerity, wavelength and amplitude. This results in a conceptual change from former models as it shows that the pressure variations within the boundary layer cannot be neglected. In the boundary layer, time-dependent Navier-Stokes equations are formulated in a curvilinear, orthogonal coordinate system. The formulation is done in an elaborate way that presents additional, formerly neglected first-order effects, resulting from the time-varying coordinate system. The suggested time-dependent curvilinear orthogonal coordinate system introduces a platform that can also support the formulation of turbulent problems for any surface shape. In order to produce a self-similar Blasius-type solution, a small wave-steepness is assumed and a perturbation method is applied. Consequently, a
Characterization of internal boundary layer capacitors
International Nuclear Information System (INIS)
Internal boundary layer capacitors were characterized by scanning transmission electron microscopy and by microscale electrical measurements. Data are given for the chemical and physical characteristics of the individual grains and boundaries, and their associated electric and dielectric properties. Segregated internal boundary layers were identified with resistivities of 1012-1013 Ω-cm. Bulk apparent dielectric constants were 10,000-60,000. A model is proposed to explain the dielectric behavior in terms of an equivalent n-c-i-c-n representation of ceramic microstructure, which is substantiated by capacitance-voltage analysis
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.
THE CORNER LAYER SOLUTION TO ROBIN PROBLEM FOR REACTION DIFFUSION EQUATION
Institute of Scientific and Technical Information of China (English)
无
2012-01-01
A class of Robin boundary value problem for reaction diffusion equation is considered. Under suitable conditions, using the theory of differential inequalities the existence and asymptotic behavior of the corner layer solution to the initial boundary value problem are studied.
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.
DEFF Research Database (Denmark)
Chivaee, Hamid Sarlak; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
2012-01-01
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......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...
Linear Stability of the boundary layer under a solitary wave
Verschaeve, Joris C G
2013-01-01
A theoretical and numerical analysis of the linear stability of the boundary layer flow under a solitary wave is presented. In the present work, the nonlinear boundary layer equations are solved. The result is compared to the linear boundary layer solution in Liu et al. (2007) reveal- ing that both profiles are disagreeing more than has been found before. A change of frame of reference has been used to allow for a classical linear stability analysis without the need to redefine the notion of stability for this otherwise unsteady flow. For the linear stability the Orr-Sommerfeld equation and the parabolic stability equation were used. The results are compared to key results of inviscid stability theory and validated by means of a direct numerical simulation using a Legendre-Galerkin spectral ele- ment Navier-Stokes solver. Special care has been taken to ensure that the numerical results are valid. Linear stability predicts that the boundary layer flow is unstable for the entire parameter range considered, conf...
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.
Boundary Layer Cloudiness Parameterizations Using ARM Observations
Energy Technology Data Exchange (ETDEWEB)
Bruce Albrecht
2004-09-15
This study used DOE ARM data and facilities to: (1) study macroscopic properties of continental stratus clouds at SGP and the factors controlling these properties, (2) develop a scientific basis for understanding the processes responsible for the formation of boundary layer clouds using ARM observations in conjunction with simple parametric models and LES, and (3) evaluate cumulus cloud characteristics retrieved from the MMCR operating at TWP-Nauru. In addition we have used high resolution 94 GHz observations of boundary layer clouds and precipitation to: (1) develop techniques for using high temporal resolution Doppler velocities to study large-eddy circulations and turbulence in boundary layer clouds and estimate the limitations of using current and past MMCR data for boundary layer cloud studies, (2) evaluate the capability and limitations of the current MMCR data for estimating reflectivity, vertical velocities, and spectral under low- signal-to-noise conditions associated with weak no n-precipitating clouds, (3) develop possible sampling modes for the new MMCR processors to allow for adequate sampling of boundary layer clouds, and (4) retrieve updraft and downdraft structures under precipitating conditions.
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.
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.
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)
Free Boundary Value Problems for Abstract Elliptic Equations and Applications
Institute of Scientific and Technical Information of China (English)
Veli SHAKHMUROV
2011-01-01
The free boundary value problems for elliptic differential-operator equations are studied.Several conditions for the uniform maximal regularity with respect to boundary parameters and the Fredholmness in abstract Lp-spaces are given.In application,the nonlocal free boundary problems for finite or infinite systems of elliptic and anisotropic type equations are studied.
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.
A Cartesian Embedded Boundary Method for the Compressible Navier-Stokes Equations
Energy Technology Data Exchange (ETDEWEB)
Kupiainen, M; Sjogreen, B
2008-03-21
We here generalize the embedded boundary method that was developed for boundary discretizations of the wave equation in second order formulation in [6] and for the Euler equations of compressible fluid flow in [11], to the compressible Navier-Stokes equations. We describe the method and we implement it on a parallel computer. The implementation is tested for accuracy and correctness. The ability of the embedded boundary technique to resolve boundary layers is investigated by computing skin-friction profiles along the surfaces of the embedded objects. The accuracy is assessed by comparing the computed skin-friction profiles with those obtained by a body fitted discretization.
Temperature structure in the atmospheric boundary layer
Smedman, Ann-Sofi
2010-05-01
Temperature structure in the atmospheric boundary layer It is well established from experimental and theoretical studies that the temperature structure in the atmospheric boundary layer is depends on stability. During free convection conditions the flow is dominated by circular thermals but when stratification is becoming slightly unstable longitudinal roll structures that extend vertically throughout the entire boundary layer will be present. In close to neutral conditions on the unstable side (the UVCN regime) when the Obukhov length is much greater than the surface layer depth, it is observed that the structure of the surface layer turbulence does not accord with standard similarity theory. In particular the efficiency of the turbulent exchange of sensible and latent heat is observed to be more strongly enhanced than is consistent with the standard model. Also the profiles of dissipation of turbulent kinetic energy and temperature fluctuation variance are found to depend on the structure of the whole boundary layer (i.e. are non-local), indicating that a large-scale transport process is at work. At the same time, co-spectral analysis shows how the large scale eddy motions that determine the heat transport process near the surface are typically 1/5 of the surface layer depth. All these features are found to be similar in measurements at two marine sites, in the Baltic Sea and in Lake Ontario respectively and at several flat land sites ( around Uppsala and at the Island of Gotland), indicating that they are determined by the dynamics of the whole boundary layer rather than being simply dependent on the surface boundary conditions. The observed structures can also be interpreted as possible manifestations of a bifurcation of the large scale eddy structure towards a state in which there are quasi-steady longitudinal rolls and, on a smaller scale, unsteady detached eddies. Our interpretation of the results from the measurements is that, in the UVCN regime, the latter
Half-space Kinetic Equations with General Boundary Conditions
Li, Qin; Sun, Weiran
2015-01-01
We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary conditions. As in [LLS14], the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasi-optimality of the numerical scheme. The numerical method is validated by examples including a two-species transport equation, a multi-frequency transport equation, and the linearized BGK equation in 2D velocity space.
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.
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.
The free boundary Euler equations with large surface tension
Disconzi, Marcelo M.; Ebin, David G.
2015-01-01
We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then we prove that under natural assumptions, the solutions of the free boundary motion converge to solutions of the Euler equations in a domain with fixed boundary when the coefficient of surface tension tends to infinity.
The free boundary Euler equations with large surface tension
Disconzi, Marcelo M.; Ebin, David G.
2016-07-01
We study the free boundary Euler equations with surface tension in three spatial dimensions, showing that the equations are well-posed if the coefficient of surface tension is positive. Then we prove that under natural assumptions, the solutions of the free boundary motion converge to solutions of the Euler equations in a domain with fixed boundary when the coefficient of surface tension tends to infinity.
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
SOLVABILITY FOR NONLINEAR ELLIPTIC EQUATION WITH BOUNDARY PERTURBATION
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The solvability of nonlinear elliptic equation with boundary perturbation is considered. The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved.
Energy Technology Data Exchange (ETDEWEB)
Ishak, Anuar; Nazar, Roslinda [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Pop, Ioan [Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253 (Romania)
2008-07-01
The steady mixed convection boundary layer flow through a stable stratified medium adjacent to a vertical surface is investigated. The velocity outside the boundary layer and the surface temperature are assumed to vary linearly from the leading edge of the surface. The transformed ordinary differential equations are solved numerically by the Keller-box method. It is found that dual solutions exist, and the thermal stratification delays the boundary layer separation. (author)
Governing equations for vibrating constrained-layer damping sandwich plates and beams.
Yan, M.-J.; Dowell, E. H.
1972-01-01
A simple differential equation is derived to describe constrained-layer damping in nonsymmetric sandwich plates and beams composed of isotropic and homogeneous layers. The natural boundary conditions related to this equation are determined and some typical numerical results obtained by this equation are given. The equation is valid within the linear theories of elasticity and viscoelasticity in the absence of any constraints on thicknesses, positions, symmetries, and densities of the layers.
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.
Energy Technology Data Exchange (ETDEWEB)
Vlahostergios, Z. [Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, Karamanli str., Thessaloniki 54124 (Greece); Yakinthos, K. [Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, Karamanli str., Thessaloniki 54124 (Greece)], E-mail: kyros@eng.auth.gr; Goulas, A. [Laboratory of Fluid Mechanics and Turbomachinery, Department of Mechanical Engineering, Aristotle University of Thessaloniki, Karamanli str., Thessaloniki 54124 (Greece)
2009-08-15
We present an effort to model the separation-induced transition on a flat plate with a semi-circular leading edge, using a cubic non-linear eddy-viscosity model combined with the laminar kinetic energy. A non-linear model, compared to a linear one, has the advantage to resolve the anisotropic behavior of the Reynolds-stresses in the near-wall region and it provides a more accurate expression for the generation of turbulence in the transport equation of the turbulence kinetic energy. Although in its original formulation the model is not able to accurately predict the separation-induced transition, the inclusion of the laminar kinetic energy increases its accuracy. The adoption of the laminar kinetic energy by the non-linear model is presented in detail, together with some additional modifications required for the adaption of the laminar kinetic energy into the basic concepts of the non-linear eddy-viscosity model. The computational results using the proposed combined model are shown together with the ones obtained using an isotropic linear eddy-viscosity model, which adopts also the laminar kinetic energy concept and in comparison with the existing experimental data.
Wind and boundary layers in Rayleigh-Benard convection. Part 2: boundary layer character and scaling
van Reeuwijk, Maarten; Hanjalic, Kemo
2007-01-01
The effect of the wind of Rayleigh-Benard convection on the boundary layers is studied by direct numerical simulation of an L/H=4 aspect-ratio domain with periodic side boundary conditions for Ra={10^5, 10^6, 10^7} and Pr=1. It is shown that the kinetic boundary layers on the top- and bottom plate have some features of both laminar and turbulent boundary layers. A continuous spectrum, as well as significant forcing due to Reynolds stresses indicates undoubtedly a turbulent character, whereas the classical integral boundary layer parameters -- the shape factor and friction factor (the latter is shown to be dominated by the pressure gradient) -- scale with Reynolds number more akin to laminar boundary layers. This apparent dual behavior is caused by the large influence of plumes impinging onto and detaching from the boundary layer. The plume-generated Reynolds stresses have a negligible effect on the friction factor at the Rayleigh numbers we consider, which indicates that they are passive with respect to momen...
Wind and boundary layers in Rayleigh-Bénard convection. II. Boundary layer character and scaling.
van Reeuwijk, Maarten; Jonker, Harm J J; Hanjalić, Kemo
2008-03-01
The scaling of the kinematic boundary layer thickness lambda(u) and the friction factor C(f) at the top and bottom walls of Rayleigh-Bénard convection is studied by direct numerical simulation (DNS). By a detailed analysis of the friction factor, a new parameterisation for C(f) and lambda(u) is proposed. The simulations were made of an L/H=4 aspect-ratio domain with periodic lateral boundary conditions at Ra=(10(5), 10(6), 10(7), 10(8)) and Pr=1. The continuous spectrum, as well as significant forcing due to Reynolds stresses, clearly indicates a turbulent character of the boundary layer, while viscous effects cannot be neglected, judging from the scaling of classical integral boundary layer parameters with Reynolds number. Using a conceptual wind model, we find that the friction factor C(f) should scale proportionally to the thermal boundary layer thickness as C(f) proportional variant lambda(Theta)/H, while the kinetic boundary layer thickness lambda(u) scales inversely proportionally to the thermal boundary layer thickness and wind Reynolds number lambda(u)/H proportional variant (lambda(Theta)/H)(-1)Re(-1). The predicted trends for C(f) and lambda(u) are in agreement with DNS results.
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.
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.
DNS of compressible turbulent boundary layer around a sharp cone
Institute of Scientific and Technical Information of China (English)
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.
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.
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...... ground truth, as well as on urban turbulence and profiling (sodar, RASS, tethered balloon) were performed. Also tracer experiments with near-roof-level release and sampling were performed. In parallel to the experimental activities within BUBBLE, a meso-scale numerical atmospheric model, which contains...... a surface exchange parameterization, especially designed for urban areas was evaluated and further developed. Finally, the area of the full-scale tracer experiment which also contains several sites of other special projects during the IOP (street canyon energetics, satellite ground truth) is modeled using...
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.
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.
Submarine design optimization using boundary layer control
Christopher L Warren
1997-01-01
Several hull designs are studied with parametric based volume and area estimates to obtain preliminary hull forms. The volume and area study includes the effects of technologies which manifest themselves in the parametric study through stack length requirements. Subsequently, the hull forms are studied using a Reynolds Averaged Navier Stokes analysis coupled with a vortex lattice propeller design code. Optimization is done through boundary layer control analysis and through studies on the eff...
Coupled wake boundary layer model of windfarms
Stevens, Richard; Gayme, Dennice; Meneveau, Charles
2014-11-01
We present a coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a windfarm. The model couples the traditional, industry-standard wake expansion/superposition approach with a top-down model for the overall windfarm boundary layer structure. Wake models capture the effect of turbine positioning, while the top-down approach represents the interaction between the windturbine wakes and the atmospheric boundary layer. Each portion of the CWBL model requires specification of a parameter that is unknown a-priori. The wake model requires the wake expansion rate, whereas the top-down model requires the effective spanwise turbine spacing within which the model's momentum balance is relevant. The wake expansion rate is obtained by matching the mean velocity at the turbine from both approaches, while the effective spanwise turbine spacing is determined from the wake model. Coupling of the constitutive components of the CWBL model is achieved by iterating these parameters until convergence is reached. We show that the CWBL model predictions compare more favorably with large eddy simulation results than those made with either the wake or top-down model in isolation and that the model can be applied successfully to the Horns Rev and Nysted windfarms. The `Fellowships for Young Energy Scientists' (YES!) of the Foundation for Fundamental Research on Matter supported by NWO, and NSF Grant #1243482.
Boundary layer emission in luminous LMXBs
Gilfanov, M
2005-01-01
We show that aperiodic and quasiperiodic variability of bright LMXBs - atoll and Z- sources, on ~sec - msec time scales is caused primarily by variations of the boundary layer luminosity. The accretion disk emission is less variable on these time scales and its power density follows 1/f law, contributing to observed flux variation at low frequencies and low energies only. The kHz QPOs have the same origin as variability at lower frequencies - independent of the nature of the "clock", the actual luminosity modulation takes place on the NS surface. The boundary layer spectrum remains nearly constant during luminosity variations and can be represented by the Fourier frequency resolved spectrum. In the range of Mdot~(0.1-1)*Mdot_Edd it depends weakly on the global mass accretion rate and in the limit Mdot~Mdot_Edd is close to Wien spectrum with kT~2.4 keV. Its independence on the Mdot lends support to the suggestion by Inogamov & Sunyaev (1999) that the boundary layer is radiation pressure supported. Based on...
Pressure gradient influence in turbulent boundary layers
Reuther, Nico; Kaehler, Christian J.
2015-11-01
Understanding wall-bounded turbulence is still an ongoing process. Although remarkable progress has been made in the last decades, many challenges still remain. Mean flow statistics are well understood in case of zero pressure gradient flows. However, almost all turbulent boundary layers in technical applications, such as aircrafts, are subjected to a streamwise pressure gradient. When subjecting turbulent boundary layers to adverse pressure gradients, significant changes in the statistical behavior of the near-wall flow have been observed in experimental studies conducted however the details dynamics and characteristics of these flows has not been fully resolved. The sensitivity to Reynolds number and the dependency on several parameters, including the dependence on the pressure gradient parameter, is still under debate and very little information exists about statistically averaged quantities such as the mean velocity profile or Reynolds stresses. In order to improve the understanding of wall-bounded turbulence, this work experimentally investigates turbulent boundary layer subjected to favorable and adverse pressure gradients by means of Particle Image Velocimetry over a wide range of Reynolds numbers, 4200 statistics was found to increase significantly for a flow subjected to an adverse pressure gradient.
The Pauli equation with complex boundary conditions
Kochan, D; Novak, R; Siegl, P
2012-01-01
We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. A special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T.
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
Uddin, Mohammed J.; Khan, Waqar A.; Ahmed I Ismail
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 convert...
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.!
RADIATION BOUNDARY CONDITIONS FOR MAXWELL'S EQUATIONS: A REVIEW OF ACCURATE TIME-DOMAIN FORMULATIONS
Institute of Scientific and Technical Information of China (English)
Thomas Hagstrom; Stephen Lau
2007-01-01
We review time-domain formulations of radiation boundary conditions for Maxwell's equations, focusing on methods which can deliver arbitrary accuracy at acceptable computational cost. Examples include fast evaluations of nonlocal conditions on symmetric and general boundaries, methods based on identifying and evaluating equivalent sources, and local approximations such as the perfectly matched layer and sequences of local boundary conditions. Complexity estimates are derived to assess work and storage requirements as a function of wavelength and simulation time.
Testing outer boundary treatments for the Einstein equations
Rinne, Oliver; Scheel, Mark A
2007-01-01
Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a `reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests use a first-order generalized harmonic formulation of the Einstein equations. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of K...
The Pauli equation with complex boundary conditions
International Nuclear Information System (INIS)
We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin–magnetic interaction on the interplay between the type of boundary conditions and the spectrum. Special attention is paid to PT-symmetric boundary conditions with the physical choice of the time-reversal operator T. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’. (paper)
The Pauli equation with complex boundary conditions
Kochan, D.; Krejčiřík, D.; Novák, R.; Siegl, P.
2012-11-01
We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin-magnetic interaction on the interplay between the type of boundary conditions and the spectrum. Special attention is paid to {PT}-symmetric boundary conditions with the physical choice of the time-reversal operator {T}. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
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.
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)
Integral method for the calculation of three-dimensional, laminar and turbulent boundary layers
Stock, H. W.
1978-01-01
The method for turbulent flows is a further development of an existing method; profile families with two parameters and a lag entrainment method replace the simple entrainment method and power profiles with one parameter. The method for laminar flows is a new development. Moment of momentum equations were used for the solution of the problem, the profile families were derived from similar solutions of boundary layer equations. Laminar and turbulent flows at the wings were calculated. The influence of wing tapering on the boundary layer development was shown. The turbulent boundary layer for a revolution ellipsoid is calculated for 0 deg and 10 deg incidence angles.
The open boundary equation (discussion paper)
Diederen, D.; Savenije, H.H.G.; Toffolon, M.
2015-01-01
We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection) under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave
Thin-Layer Solutions of the Helmholtz and Related Equations
Ockendon, J. R.
2012-01-01
This paper concerns a certain class of two-dimensional solutions to four generic partial differential equations-the Helmholtz, modified Helmholtz, and convection-diffusion equations, and the heat conduction equation in the frequency domain-and the connections between these equations for this particular class of solutions.S pecifically, we consider thin-layer solutions, valid in narrow regions across which there is rapid variation, in the singularly perturbed limit as the coefficient of the Laplacian tends to zero.F or the wellstudied Helmholtz equation, this is the high-frequency limit and the solutions in question underpin the conventional ray theory/WKB approach in that they provide descriptions valid in some of the regions where these classical techniques fail.E xamples are caustics, shadow boundaries, whispering gallery, and creeping waves and focusing and bouncing ball modes.It transpires that virtually all such thin-layer models reduce to a class of generalized parabolic wave equations, of which the heat conduction equation is a special case. Moreover, in most situations, we will find that the appropriate parabolic wave equation solutions can be derived as limits of exact solutions of the Helmholtz equation.W e also show how reasonably well-understood thin-layer phenomena associated with any one of the four generic equations may translate into less well-known effects associated with the others.In addition, our considerations also shed some light on the relationship between the methods of matched asymptotic, WKB, and multiple-scales expansions. © 2012 Society for Industrial and Applied Mathematics.
Multilevel Model of Planetary Boundary-layer Suitable for use with Mesoscale Dynamic Models
DEFF Research Database (Denmark)
Busch, N. E.; Chang, S. W.; Anthes, R. A.
1976-01-01
In this paper a simple model of the planetary boundary layer (PBL) is proposed. The surface layer is modeled according to established similarity theory. Above the surface layer a prognostic equation for the mixing length is introduced. The time-dependent mixing length is a function of the PBL...
Numerical Solution for the Helmholtz Equation with Mixed Boundary Condition
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We consider the numerical solution for the Helmholtz equation in R2 with mixed boundary conditions. The solvability of this mixed boundary value problem is established by the boundary integral equation method. Based on the Green formula, we express the solution in terms of the boundary data. The key to the numerical realization of this method is the computation of weakly singular integrals. Numerical performances show the validity and feasibility of our method. The numerical schemes proposed in this paper have been applied in the realization of probe method for inverse scattering problems.
The large Reynolds number - Asymptotic theory of turbulent boundary layers.
Mellor, G. L.
1972-01-01
A self-consistent, asymptotic expansion of the one-point, mean turbulent equations of motion is obtained. Results such as the velocity defect law and the law of the wall evolve in a relatively rigorous manner, and a systematic ordering of the mean velocity boundary layer equations and their interaction with the main stream flow are obtained. The analysis is extended to the turbulent energy equation and to a treatment of the small scale equilibrium range of Kolmogoroff; in velocity correlation space the two-thirds power law is obtained. Thus, the two well-known 'laws' of turbulent flow are imbedded in an analysis which provides a great deal of other information.
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.
Cebeci, Tuncer
2005-01-01
This second edition of our book extends the modeling and calculation of boundary-layer flows to include compressible flows. The subjects cover laminar, transitional and turbulent boundary layers for two- and three-dimensional incompressible and compressible flows. The viscous-inviscid coupling between the boundary layer and the inviscid flow is also addressed. The book has a large number of homework problems.
On the Implementation of 3D Galerkin Boundary Integral Equations
Energy Technology Data Exchange (ETDEWEB)
Nintcheu Fata, Sylvain [ORNL; Gray, Leonard J [ORNL
2010-01-01
In this article, a reverse contribution technique is proposed to accelerate the construction of the dense influence matrices associated with a Galerkin approximation of singular and hypersingular boundary integral equations of mixed-type in potential theory. In addition, a general-purpose sparse preconditioner for boundary element methods has also been developed to successfully deal with ill-conditioned linear systems arising from the discretization of mixed boundary-value problems on non-smooth surfaces. The proposed preconditioner, which originates from the precorrected-FFT method, is sparse, easy to generate and apply in a Krylov subspace iterative solution of discretized boundary integral equations. Moreover, an approximate inverse of the preconditioner is implicitly built by employing an incomplete LU factorization. Numerical experiments involving mixed boundary-value problems for the Laplace equation are included to illustrate the performance and validity of the proposed techniques.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Vorona Yu.V.; Kara I.D.
2015-01-01
Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.
APPLICATION OF BOUNDARY INTEGRAL EQUATION METHOD FOR THERMOELASTICITY PROBLEMS
Directory of Open Access Journals (Sweden)
Vorona Yu.V.
2015-12-01
Full Text Available Boundary Integral Equation Method is used for solving analytically the problems of coupled thermoelastic spherical wave propagation. The resulting mathematical expressions coincide with the solutions obtained in a conventional manner.
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.
Halogen chemistry in the trosopheric boundary layer
Plane, John M. C.; Mahajan, Anoop; Oetjen, Hilke
Iodine and bromine chemistry can affect the lower troposphere in several important ways: (1), change the oxidizing capacity by destroying ozone and affecting the hydroxyl radical concentration; (2), react efficiently with dimethyl sulphide (in the marine boundary layer) and mercury (in the polar regions); and (3), form ultra-fine particles (iodine oxides are highly condensable), which may contribute to cloud condensation nuclei and hence affect climate. This paper will report measurements of IO, BrO, OIO and I2 , made by the technique of differential optical absorption spectroscopy (DOAS), in several contrasting environments: equatorial clean mid-ocean (Cape Verde); mid-latitude clean coastal (Mace Head, Ireland); polluted coastal (Roscoff, France); and the polar boundary layer (Halley Bay, Antarctica and Hudson Bay, Canada). Both IO and BrO are observed in all these locations at concentrations (> 1 pptv), and so have a major impact on (1) and (2) above. The concentrations of IO in coastal Antarctica, and coastlines rich in certain species of macro-algae, are large enough (> 10 pptv) to promote ultra-fine particle formation. Recently, the first satellite measurements of IO, using the SCIAMACHY instrument on ENVISAT, have been reported by two groups; their results will be compared with the ground-based measurements.
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.
Direct simulation of the turbulent boundary layer on a plate
Krupa, V. G.
2016-08-01
A numerical method for the integration of three-dimensional Navier-Stokes equations for compressible fluid as applied to direct numerical simulation is proposed. By way of example, the boundary layer on a plate is simulated. The computations were carried out for Reθ = 1500. The computational grid consisted of a half billion nodes. The flow region includes the laminar, transitional, and turbulent zones. The numerically obtained distributions of average velocity, friction, and pulsations are compared with experimental data and available numerical solutions.
Wave phenomena in a high Reynolds number compressible boundary layer
Bayliss, A.; Maestrello, L.; Parikh, P.; Turkel, E.
1987-01-01
The behavior of spatially unstable waves in a high Reynolds number compressible laminar boundary layer is investigated by solution of the laminar two-dimensional compressible Navier-Stokes equations (solved to fourth-order accuracy) over a flat plate with a fluctuating disturbance generated at the inflow. A significant nonlinear distortion is produced, in qualitative agreement with experimental data. It is shown that increasing compressibility can significantly stabilize the flow over a flat plate, and that the mechanism of phase cancellation is a viable mechanism for the control of growing disturbances.
Beloshapko, V. A.; Butuzov, V. F.
2016-08-01
For a singularly perturbed elliptic boundary value problem, an asymptotic expansion of the boundary-layer solution is constructed and justified in the case when the boundary layer consists of three zones with different behavior of the solution, which is caused by the multiplicity of the root of the degenerate equation.
Boundary value problems of discrete generalized Emden-Fowler equation
Institute of Scientific and Technical Information of China (English)
YU; Jianshe; GUO; Zhiming
2006-01-01
By using the critical point theory, some sufficient conditions for the existence of the solutions to the boundary value problems of a discrete generalized Emden-Fowler equation are obtained. In a special case, a sharp condition is obtained for the existence of the boundary value problems of the above equation. For a linear case, by the discrete variational theory, a necessary and sufficient condition for the existence, uniqueness and multiplicity of the solutions is also established.
Boundary Integral Equations and A Posteriori Error Estimates
Institute of Scientific and Technical Information of China (English)
YU Dehao; ZHAO Longhua
2005-01-01
Adaptive methods have been rapidly developed and applied in many fields of scientific and engineering computing. Reliable and efficient a posteriori error estimates play key roles for both adaptive finite element and boundary element methods. The aim of this paper is to develop a posteriori error estimates for boundary element methods. The standard a posteriori error estimates for boundary element methods are obtained from the classical boundary integral equations. This paper presents hyper-singular a posteriori error estimates based on the hyper-singular integral equations. Three kinds of residuals are used as the estimates for boundary element errors. The theoretical analysis and numerical examples show that the hyper-singular residuals are good a posteriori error indicators in many adaptive boundary element computations.
A NONLOCAL NONLINEAR BOUNDARY VALUE PROBLEM FOR THE HEAT EQUATIONS
Institute of Scientific and Technical Information of China (English)
YANJINHAI
1996-01-01
The existenoe and limit hehaviour of the solution for a kind of nonloeal noulinear boundary value condition on a part of the boundary is studied for the heat equation, which physicallymeans that the potential is the function of the total flux. When this part of boundary shrinks to a point in a certain way, this condition either results in a Dirac measure or simply disappears in the corresponding problem.
Khairullin, Ermek
2016-08-01
In this paper we consider a special boundary value problem for multidimensional parabolic integro-differential equation with boundary conditions that contains as a boundary condition containing derivatives of order higher than the order of the equation. The solution is sought in the form of a thermal potential of a double layer. Shows lemma of finding the limits of the derivatives of the unknown function in the neighborhood of the hyperplane. Using the boundary condition and lemma obtained integral-differential equation (IDE) of parabolic operators, whĐţre an unknown function under the integral contains higher-order space variables derivatives. IDE is reduced to a singular integral equation (SIE), when an unknown function in the spatial variables satisfies the Holder. The characteristic part is solved in the class of distribution function using method of transformation of Fourier-Laplace. Found an algebraic condition for the transition to the classical generalized solution. Integral equation of the resolvent for the characteristic part of SIE is obtained. Integro-differential equation is reduced to the Volterra-Fredholm type integral equation of the second kind by method of regularization. It is shown that the solution of SIE is a solution of IDE. Obtain a theorem on the solvability of the boundary value problem of multidimensional parabolic integro-differential equation, when a known function of the spatial variables belongs to the Holder class and satisfies the solvability conditions.
Boundary stabilization of wave equations with variable coefficients
Institute of Scientific and Technical Information of China (English)
FENG; Shaoji
2001-01-01
［1］Chen, G., Energy decay estimates and exact boundary value controllability for the wave equation in a bounded domain, J. Math. Pures. & Appl., 1979, 58: 249.［2］Komornik, V., Exact controllability and stabilization, Research in Applied Mathematics (Series Editors: Ciarlet, P. G., Lions, J.), New York: Masson/John Wiley copublication, 1994.［3］Komornik, V., Zuazua, E., A direct method for the boundary stabilization of the wave equation, J. Math. Pures. & Appl., 1990, 69: 33.［4］Lagnese, J., Decay of solutions of wave equations in a bounded region with boundary dissipation, J. Differential Equations, 1983, 50: 163.［5］Lasiecka, I., Triggiani, R., Uniform stabilization of the wave equation with Dirichlet or Neumann feedback control without geometrical conditions, Appl. Math. & Optim., 1992, 25: 189.［6］Wyler, A., Stability of wave equations with dissipative boundary conditions in a bounded domain, Differential and Integral Equations,1994, 7: 345.［7］Yao, P. F., On the observability inequality for exact controllability of wave equations with variable coefficients, SIAM J. Control & Optimization, 1999, 37, 5: 1568.［8］Wu, H., Shen, C. L., Yu, Y. L., Introduction to Riemannian Geometry (in Chinese), Beijing: Peking University Press, 1989.
On a stochastic Burgers equation with Dirichlet boundary conditions
Directory of Open Access Journals (Sweden)
Ekaterina T. Kolkovska
2003-01-01
Full Text Available We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.
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.
Modelling of the Evolving Stable Boundary Layer
Sorbjan, Zbigniew
2014-06-01
A single-column model of the evolving stable boundary layer (SBL) is tested for self-similar properties of the flow and effects of ambient forcing. The turbulence closure of the model is diagnostic, based on the K-theory approach, with a semi-empirical form of the mixing length, and empirical stability functions of the Richardson number. The model results, expressed in terms of local similarity scales, are universal functions, satisfied in the entire SBL. Based on similarity expression, a realizability condition is derived for the minimum allowable turbulent heat flux in the SBL. Numerical experiments show that the development of "horse-shoe" shaped, fixed-elevation hodographs in the interior of the SBL around sunrise is controlled by effects imposed by surface thermal forcing.
Geometric invariance of compressible turbulent boundary layers
Bi, Wei-Tao; Wu, Bin; She, Zhen-Su; Hussain, Fazle
2015-11-01
A symmetry based approach is applied to analyze the mean velocity and temperature fields of compressible, flat plate turbulent boundary layers (CTBL). A Reynolds stress length scale and a turbulent heat flux length scale are identified to possess the same defect scaling law in the CTBL bulk, which is solely owing to the constraint of the wall to the geometry of the wall-attached eddies, but invariant to compressibility and wall heat transfer. This invariance is called the geometric invariance of CTBL eddies and is likely the origin of the Mach number invariance of Morkovin's hypothesis, as well as the similarity of energy and momentum transports. A closure for the turbulent transport by using the invariant lengths is attainted to predict the mean velocity and temperature profiles in the CTBL bulk- superior to the van Driest transformation and the Reynolds analogy based relations for its sound physics and higher accuracy. Additionally, our approach offers a new understanding of turbulent Prandtl number.
Thermodynamically admissible boundary conditions for the regularized 13 moment equations
Energy Technology Data Exchange (ETDEWEB)
Rana, Anirudh Singh, E-mail: anirudh@uvic.ca [Department of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju, Gyeongnam 52828 (Korea, Republic of); Struchtrup, Henning, E-mail: struchtr@uvic.ca [Department of Mechanical Engineering, University of Victoria, Victoria, British Columbia V8W 2Y2 (Canada)
2016-02-15
A phenomenological approach to the boundary conditions for linearized R13 equations is derived using the second law of thermodynamics. The phenomenological coefficients appearing in the boundary conditions are calculated by comparing the slip, jump, and thermal creep coefficients with linearized Boltzmann solutions for Maxwell’s accommodation model for different values of the accommodation coefficient. For this, the linearized R13 equations are solved for viscous slip, thermal creep, and temperature jump problems and the results are compared to the solutions of the linearized Boltzmann equation. The influence of different collision models (hard-sphere, Bhatnagar–Gross–Krook, and Maxwell molecules) and accommodation coefficients on the phenomenological coefficients is studied.
Halogen chemistry in the marine boundary layer
Plane, J. M. C.; Gomez Martin, J. C.; Kumar, R.; Mahajan, A. S.; Oetjen, H.; Saunders, R. W.
2009-04-01
Important atmospheric sources of iodine include the air-sea exchange of biogenic iodocarbons, and the emission of I2 from macro-algae. The major source of bromine is the release of bromide ions from sea-salt aerosol. The subsequent atmospheric chemistry of these halogens (1), changes the oxidizing capacity of the marine boundary layer by destroying ozone and changing the hydroxyl radical concentration; (2), reacts efficiently with dimethyl sulphide and mercury (in the polar regions); and (3), leads to the formation of ultra-fine particles which may contribute to cloud condensation nuclei (CCN) and hence affect climate. This paper will report observations of IO, BrO, OIO and I2 made by the technique of differential optical absorption spectroscopy, in several contrasting marine environments: the equatorial mid-Atlantic (Cape Verde); mid-latitude clean coastal (Mace Head, Ireland); polluted coastal (Roscoff, France); and the polar marine boundary layer (Hudson Bay, Canada). Both IO and BrO are observed in all these locations at significant concentrations (> 1 pptv), and so have a major impact on (1) and (2) above. To complement the field campaigns we have also carried out wide-ranging laboratory investigation. A new study of OIO photochemistry shows that absorption in the visible bands between 490 and 630 nm leads to I atom production with a quantum yield of unity, which now means that iodine is a particularly powerful ozone-depleting agent. We have also studied the formation and growth kinetics of iodine oxide nano-particles, and their uptake of water, sulphuric acid and di-carboxylic organic acids, in order to model their growth to a size where they can act as CCN. Their ice-nucleating properties will also be reported.
NOVEL REGULARIZED BOUNDARY INTEGRAL EQUATIONS FOR POTENTIAL PLANE PROBLEMS
Institute of Scientific and Technical Information of China (English)
ZHANG Yao-ming; L(U) He-xiang; WANG Li-min
2006-01-01
The universal practices have been centralizing on the research of regularization to the direct boundary integal equations (DBIEs). The character is elimination of singularities by using the simple solutions. However, up to now the research of regularization to the first kind integral equations for plane potential problems has never been found in previous literatures. The presentation is mainly devoted to the research on the regularization of the singular boundaryintegral equations with indirect unknowns. A novel view and idea is presented herein, in which the regularized boundary integral equations with indirect unknowns without including the Cauchy principal value (CPV) and Hadamard-finite-part (HFP) integrals are established for the plane potential problems.With some numerical results, it is shown that the better accuracy and higher efficiency,especially on the boundary, can be achieved by the present system.
Plasma boundary layer with active surface. Pt. 1
International Nuclear Information System (INIS)
The space-charge boundary layer between plasma and wall which is normally (almost) homogeneous may become instable and may decay into largely independent spots of plasma-induced unipolar-like discharges. In Tokamaks the existence of such highly inhomogeneous boundary plasmas often has been found by observation of arc tracks and of ''hot spots'' a.s.o. In this way wall erosion and production rates of plasma impurities will be enhanced, and several special phenomena of intense wall erosion (like ''carbon blooming'') may be traced back to such effects. In this paper the influence of electron emission from the wall (i.e. of an ''active'' surface) on the parameter of the space charge sheath is investigated, applying simple balance equations, as a first step towards an explanation of the transition from a homogeneous into an inhomogeneous boundary layer. Several variations of such models are calculated, using typical plasma parameters. Essential result is the dependence of the sheath potential and of the surface power density on the emission yield and on the net current density. Irrespective of the chosen constants the potential drop between plasma and wall turns out to become the higher the lower is the electron emission and the higher is the net current. Opposite is the dependence of the energy flux to the wall which, however, passes a minimum and increases rapidly again near the maximum net current jmax (with jmax∼jis(γ-1), where jis=ion saturation current, and γ=emission yield per ion). As a consequence, the wall loading is strongly enhanced as well in case of high negative net currents and intense electron emission, as near the maximum net current. This will be infavour of an instability of the boundary layer, resulting - with high probability - in the decay of the layer into plasma-induced arc spots. As a next step in this investigation of such plasma boundary layers a careful analysis of this transition is provided for, taking the specified conditions of the
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, ...
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.
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...
On an initial-boundary value problem for the nonlinear Schrödinger equation
Directory of Open Access Journals (Sweden)
Herbert Gajewski
1979-01-01
Full Text Available We study an initial-boundary value problem for the nonlinear Schrödinger equation, a simple mathematical model for the interaction between electromagnetic waves and a plasma layer. We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.
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.
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.
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
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 ...
On similarity and pseudo-similarity solutions of Falkner-Skan boundary layers
Guedda, Mohamed; Hammouch, Zakia
2006-01-01
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 incompressi...
Directory of Open Access Journals (Sweden)
Guotao Wang
2012-01-01
Full Text Available We study nonlinear impulsive differential equations of fractional order with irregular boundary conditions. Some existence and uniqueness results are obtained by applying standard fixed-point theorems. For illustration of the results, some examples are discussed.
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.
Solitons induced by boundary conditions from the Boussinesq equation
Chou, Ru Ling; Chu, C. K.
1990-01-01
The behavior of solitons induced by boundary excitation is investigated at various time-dependent conditions and different unperturbed water depths, using the Korteweg-de Vries (KdV) equation. Then, solitons induced from Boussinesq equations under similar conditions were studied, making it possible to remove the restriction in the KdV equation and to treat soliton head-on collisions (as well as overtaking collisions) and reflections. It is found that the results obtained from the KdV and the Boussinesq equations are in good agreement.
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.
Institute of Scientific and Technical Information of China (English)
任景莉; 葛渭高
2003-01-01
A boundary value problems f or functional differenatial equations, with nonlinear boundary condition, is studied by the theorem of differential inequality. Using new method to construct the upper solution and lower solution, sufficient conditions for the existence of the problems' solution are established. A uniformly valid asymptotic expansions of the solution is also given.
Abels, Helmut
2005-05-01
We study the generalized Stokes equations in asymptotically flat layers, which can be considered as compact perturbations of an infinite (flat) layer Ω _0 = mathbb{R}^{n - 1} × ( - 1,1). Besides standard non-slip boundary conditions, we consider a mixture of slip and non-slip boundary conditions on the upper and lower boundary, respectively. In this second part, we use pseudodifferential operator techniques to construct a parametrix to the reduced Stokes equations, which solves the system in Lq-Sobolev spaces, 1 calculus of the (reduced) Stokes operator.
Periodic solutions to nonlinear equations with oblique boundary conditions
Allergretto, Walter; Papini, Duccio
2012-01-01
We study the existence of positive periodic solutions to nonlinear elliptic and parabolic equations with oblique and dynamical boundary conditions and non-local terms. The results are obtained through fixed point theory, topological degree methods and properties of related linear elliptic problems with natural boundary conditions and possibly non-symmetric principal part. As immediate consequences, we also obtain estimates on the principal eigenvalue for non-symmetric elliptic ...
Traveling waves for a boundary reaction-diffusion equation
Caffarelli, L; Sire, Y
2011-01-01
We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for traveling wave solutions of a free boundary problem obtained as singular limit for the reaction-diffusion equation (the so-called high energy activation energy limit). This explicit formula, which is interesting in itself, also allows us to get an estimate on the decay at infinity of the traveling wave (which turns out to be faster than the usual exponential decay).
Characteristics of the boundary layer of magnetic clouds and a new definition of the cloud boundary
Institute of Scientific and Technical Information of China (English)
WEI; Fengsi(魏奉思); LIU; Rui(刘睿); FAN; Quanlin(范全林); FENG; Xueshang(冯学尚)
2003-01-01
Based on the analysis of the boundaries of 70 magnetic clouds from 1967 to 1998, and relatively complete spacecraft observations, it is indicated that the magnetic cloud boundaries are boundary layers formed through the interaction between the magnetic clouds and the ambient medium. Most of the outer boundaries of the layers, with relatively high proton temperature, density and plasma β, are magnetic reconnection boundaries, while the inner boundaries, with low proton temperature, proton density and plasma β, separate the main body of magnetic clouds, which has not been affected by the interaction, from the boundary layers. The average time scale of the front boundary layer is 1.7 h and that of the tail boundary layer 3.1 h. It is also found that the magnetic probability distribution function undergoes significant changes across the boundary layers. This new definition, supported by the preliminary numerical simulation in principle, could qualitatively explain the observations of interplanetary magnetic clouds, and could help resolve the controversy in identifying the boundaries of magnetic clouds. Our concept of the boundary layer may provide some understanding of what underlies the observations, and a fresh train of thought in the interplanetary dynamics research.
Coleman-Gurtin type equations with dynamic boundary conditions
Gal, Ciprian G.; Shomberg, Joseph L.
2015-02-01
We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory. As a special case, we investigate the well-posedness of systems which consist of Coleman-Gurtin type equations subject to dynamic boundary conditions, also with memory. Nonlinear terms are defined on the interior of the domain and on the boundary and subject to either classical dissipation assumptions, or to a nonlinear balance condition in the sense of Gal (2012). Additionally, we do not assume that the interior and the boundary share the same memory kernel.
Institute of Scientific and Technical Information of China (English)
MO Jia-qi
2008-01-01
In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Institute of Scientific and Technical Information of China (English)
Jingsun Yao; Jiaqi Mo
2005-01-01
The nonlinear nonlocal singularly perturbed initial boundary value problems for reaction diffusion equations with a boundary perturbation is considered. Under suitable conditions, the outer solution of the original problem is obtained. Using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed. And then using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied. Finally the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.
Institute of Scientific and Technical Information of China (English)
MO Jia-qi; WANG Hui; LIN Wan-tao
2005-01-01
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.
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...
Bhupesh Kumar Mahatha; Raj Nandkeolyar; Goutam Kumar Mahato; Precious Sibanda
2016-01-01
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 Spect...
Direct numerical simulation of turbulent thermal boundary layers
Kong, Hojin; Choi, Haecheon; Lee, Joon Sik
2000-10-01
In this paper, a method of generating realistic turbulent temperature fluctuations at a computational inlet is proposed and direct numerical simulations of turbulent thermal boundary layers developing on a flat plate with isothermal and isoflux wall boundary conditions are carried out. Governing equations are integrated using a fully implicit fractional-step method with 352×64×128 grids for the Reynolds number of 300, based on the free-stream velocity and the inlet momentum thickness, and the Prandtl number of 0.71. The computed Stanton numbers for the isothermal and isoflux walls are in good agreement with power-law relations without transient region from the inlet. The mean statistical quantities including root-mean-square temperature fluctuations, turbulent heat fluxes, turbulent Prandtl number, and skewness and flatness of temperature fluctuations agree well with existing experimental and numerical data. A quadrant analysis is performed to investigate the coherence between the velocity and temperature fluctuations. It is shown that the behavior of the wall-normal heat flux is similar to that of the Reynolds shear stress, indicating close correlation between the streamwise velocity and temperature. The effect of different thermal boundary conditions at the wall on the near-wall turbulence statistics is also discussed.
Transition Delay in Hypersonic Boundary Layers via Optimal Perturbations
Paredes, Pedro; Choudhari, Meelan M.; Li, Fei
2016-01-01
The effect of nonlinear optimal streaks on disturbance growth in a Mach 6 axisymmetric flow over a 7deg half-angle cone is investigated in an e ort to expand the range of available techniques for transition control. Plane-marching parabolized stability equations are used to characterize the boundary layer instability in the presence of azimuthally periodic streaks. The streaks are observed to stabilize nominally planar Mack mode instabilities, although oblique Mack mode disturbances are destabilized. Experimentally measured transition onset in the absence of any streaks correlates with an amplification factor of N = 6 for the planar Mack modes. For high enough streak amplitudes, the transition threshold of N = 6 is not reached by the Mack mode instabilities within the length of the cone, but subharmonic first mode instabilities, which are destabilized by the presence of the streaks, reach N = 6 near the end of the cone. These results suggest a passive flow control strategy of using micro vortex generators to induce streaks that would delay transition in hypersonic boundary layers.
Numerical solutions of telegraph equations with the Dirichlet boundary condition
Ashyralyev, Allaberen; Turkcan, Kadriye Tuba; Koksal, Mehmet Emir
2016-08-01
In this study, the Cauchy problem for telegraph equations in a Hilbert space is considered. Stability estimates for the solution of this problem are presented. The third order of accuracy difference scheme is constructed for approximate solutions of the problem. Stability estimates for the solution of this difference scheme are established. As a test problem to support theoretical results, one-dimensional telegraph equation with the Dirichlet boundary condition is considered. Numerical solutions of this equation are obtained by first, second and third order of accuracy difference schemes.
Institute of Scientific and Technical Information of China (English)
MO Jiaqi; WANG Hui; LIN Wantao
2006-01-01
The perturbed boundary undercurrent is an exceptional event in the tropical atmosphere and ocean. It is a complicated nonlinear system. Its appearance badly affects not only natural conditions such as climate and environment,but also global economic development and human living, and brings about many calamities. Thus there is very attractive study on its rules in the international academic circles. Many scholars made more studies on its local and whole behaviors using different methods, such as self-anamnestic principle, Fokker-Plank Equation method, higher order singular pedigree and predictable study, rapid change on boundary, indeterminate adaptive control, multi-cogradient method and so on. Nonlinear perturbed theory and approximate method are very attractive studies in the international academic circles. Many scholars considered a class of nonlinear problems for the ordinary differential equation, the reaction diffusion equations, the boundary value of elliptic equation, the initial boundary value of hyperbolic equation, the shock layer solution of nonlinear equation and so on. In this paper, a class of perturbed mechanism for the western boundary undercurrents in the equator Pacific is considered. Under suitable conditions, using a homotopic mapping theory and method, we obtain a simple and rapid arbitrary order approximate solution for the corresponding nonlinear system. For example, a special case shows that using the homotopic mapping method, there is a high accuracy for the computed value.It is also provided from the results that the solution for homotopic mapping solving method can be used for analyzing operator for perturbed mechanism of western boundary undercurrents in the equator Pacific.
QUENCHING ON BOUNDARY TO THE NEWTON FILTRATION EQUATION (Ⅰ)
Institute of Scientific and Technical Information of China (English)
段志文; 谢春红; 卢伟明
2003-01-01
This paper discusses the global existence and quenching of the solution to the Newton filtration equation with the nonlinear boundary condition.The authors also discuss the profile of the quenching solution in the quenching time and obtain the quenching rate of the quenching solution.
Positive Solutions for Nonlinear Differential Equations with Periodic Boundary Condition
Directory of Open Access Journals (Sweden)
Shengjun Li
2012-01-01
Full Text Available We study the existence of positive solutions for second-order nonlinear differential equations with nonseparated boundary conditions. Our nonlinearity may be singular in its dependent variable. The proof of the main result relies on a nonlinear alternative principle of Leray-Schauder. Recent results in the literature are generalized and significantly improved.
High frequency ground temperature fluctuation in a Convective Boundary Layer
Garai, A.; Kleissl, J.; Lothon, M.; Lohou, F.; Pardyjak, E.; Saïd, F.; Cuxart, J.; Steeneveld, G.J.; Yaguë, C.; Derrien, S.; Alexander, D.; Villagrasa, D.M.
2012-01-01
To study influence of the turbulent structures in the convective boundary layer (CBL) on the ground temperature, during the Boundary Layer Late Afternoon and Sunset Turbulence (BLLAST) observational campaign, high frequency ground temperature was recorded through infra-red imagery from 13 June - 8 J
Institute of Scientific and Technical Information of China (English)
Mo Jiaqi
2007-01-01
A class of nonlinear initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions and using the theory of differential inequalities the asymptotic solution of the initial boundary value problems is studied.
On the wave equation with semilinear porous acoustic boundary conditions
Graber, Philip Jameson
2012-05-01
The goal of this work is to study a model of the wave equation with semilinear porous acoustic boundary conditions with nonlinear boundary/interior sources and a nonlinear boundary/interior damping. First, applying the nonlinear semigroup theory, we show the existence and uniqueness of local in time solutions. The main difficulty in proving the local existence result is that the Neumann boundary conditions experience loss of regularity due to boundary sources. Using an approximation method involving truncated sources and adapting the ideas in Lasiecka and Tataru (1993) [28], we show that the existence of solutions can still be obtained. Second, we prove that under some restrictions on the source terms, then the local solution can be extended to be global in time. In addition, it has been shown that the decay rates of the solution are given implicitly as solutions to a first order ODE and depends on the behavior of the damping terms. In several situations, the obtained ODE can be easily solved and the decay rates can be given explicitly. Third, we show that under some restrictions on the initial data and if the interior source dominates the interior damping term and if the boundary source dominates the boundary damping, then the solution ceases to exists and blows up in finite time. Moreover, in either the absence of the interior source or the boundary source, then we prove that the solution is unbounded and grows as an exponential function. © 2012 Elsevier Inc.
Gravity actions, boundary terms and second-order field equations
International Nuclear Information System (INIS)
The Lovelock action is a natural generalization of the Einstein-Hilbert gravity action in higher (more than four) dimensions. Certain boundary terms have to be added to this action because of various reasons which we briefly review. Dimensional reduction of the Lovelock action leads to a generalized Einstein-Yang-Mills (+ scalar field or σ-models) action in lower dimensions. Since the field equations derived from the Lovelock action are of second order only, the same holds for the dimensionally reduced action. The necessary boundary terms for the latter action are then obtained by dimensional reduction of the boundary terms in the Lovelock action. We consider reduction from n to n-1 dimensions in some detail and obtain generalizations of Horndeski's non-minimally coupled Einstein-Maxwell action with second-order field equations in more than four dimensions. (orig./HSI)
Solving wave equation with spectral methods and nonreflecting boundary conditions
Novák, J; Novak, Jerome; Bonazzola, Silvano
2002-01-01
A multidomain spectral method for solving wave equations is presented. This method relies on the expansion of functions on basis of spherical harmonics $(Y_l^m(\\theta, \\phi))$ for the angular dependence and of Chebyshev polynomials $T_n(x)$ for the radial part. The spherical domains consist of shells surrounding a nucleus and cover the space up to a finite radius $R$ at which boundary conditions are imposed. Time derivatives are estimated using standard finite-differences second order schemes, which are chosen to be implicit to allow for (almost) any size of time-step. Emphasis is put on the implementation of absorbing boundary conditions that allow for the numerical boundary to be completely transparent to the physical wave. This is done using a multipolar expansion of an exact boundary condition for outgoing waves, which is truncated at some point. Using an auxiliary function, which is solution of a wave equation on the sphere defining the outer boundary of the numerical grid, the absorbing boundary conditi...
Local boundary layer scales in turbulent Rayleigh-Benard convection
Scheel, Janet D
2014-01-01
We compute fully local boundary layer scales in three-dimensional turbulent Rayleigh-Benard convection. These scales are directly connected to the highly intermittent fluctuations of the fluxes of momentum and heat at the isothermal top and bottom walls and are statistically distributed around the corresponding mean thickness scales. The local boundary layer scales also reflect the strong spatial inhomogeneities of both boundary layers due to the large-scale, but complex and intermittent, circulation that builds up in closed convection cells. Similar to turbulent boundary layers, we define inner scales based on local shear stress which can be consistently extended to the classical viscous scales in bulk turbulence, e.g. the Kolmogorov scale, and outer scales based on slopes at the wall. We discuss the consequences of our generalization, in particular the scaling of our inner and outer boundary layer thicknesses and the resulting shear Reynolds number with respect to Rayleigh number. The mean outer thickness s...
Partial differential equations & boundary value problems with Maple
Articolo, George A
2009-01-01
Partial Differential Equations and Boundary Value Problems with Maple presents all of the material normally covered in a standard course on partial differential equations, while focusing on the natural union between this material and the powerful computational software, Maple. The Maple commands are so intuitive and easy to learn, students can learn what they need to know about the software in a matter of hours- an investment that provides substantial returns. Maple''s animation capabilities allow students and practitioners to see real-time displays of the solutions of partial differential equations. Maple files can be found on the books website. Ancillary list: Maple files- http://www.elsevierdirect.com/companion.jsp?ISBN=9780123747327 Provides a quick overview of the software w/simple commands needed to get startedIncludes review material on linear algebra and Ordinary Differential equations, and their contribution in solving partial differential equationsIncorporates an early introduction to Sturm-L...
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.
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.
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 ...
Study of effect of a smooth hump on hypersonic boundary layer instability
Park, Donghun; Park, Seung O.
2016-05-01
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.
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.
Role of boundary layer processes on the mixed layer CO2-budget
D. Pino; Vilà-Guerau de Arellano, J.
2010-01-01
The diurnal and vertical variability of temperature, humidity and specially CO2 in the atmospheric boundary layer is studied by combining detailed observations taken at Cabauw (The Netherlands), Large-Eddy simulations (LES) and mixed layer theory. The research focus on the role played by the entrainment and other boundary layer driven processes on the distribution and diurnal evolution of CO2 in the boundary layer. The relative importance of this entrained air to ventilate CO2 will be analyze...
Corrections for attached sidewall boundary-layer effects in 2-dimensional airfoil testing
Murthy, A. V.
1985-01-01
The problems of sidewall boundary-layer effects in airfoil testing is treated by considering the changes in the flow area due to boundary-layer thinning under the influence of the airfoil flowfield. Using von Karman's momentum integral equation, it is shown that the sidewall boundary-layer thickness in the region of the airfoil can reduce to about half the undisturbed value under the conditions prevailing in testing of supercritical airfoils. A Mach number correction due to this increased width of the flow passage is proposed. Using the small disturbance approximation, the effect of the sidewall boundary-layers is shown to be equivalent to a change in the test Mach number and also in the airfoil thickness. Comparison of the results of this approach with other similarity rules and correlation of the experimental data demonstrate the applicability of the analysis presented from low speeds to transonic speeds.
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.
Characterization of the Martian Convective Boundary Layer
Martínez, Germán; Valero Rodríguez, Francisco; Vázquez Martínez, Luis
2009-01-01
The authors have carried out an extensive characterization of the Martian mixed layer formed under convective conditions. The values of the mixed layer height, convective velocity scale, convective temperature scale, mean temperature standard deviation, mean horizontal and vertical velocity standard deviations, and mean turbulent viscous dissipation rate have been obtained during the strongest convective hours for the mixed layer. In addition, the existing database of the surface layer has be...
Maxwell boundary conditions imply non-Lindblad master equation
Bamba, Motoaki; Imoto, Nobuyuki
2016-09-01
From the Hamiltonian connecting the inside and outside of a Fabry-Pérot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to the connecting Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in the framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultrastrong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical electrodynamics.
Maxwell boundary conditions impose non-Lindblad master equation
Bamba, Motoaki
2016-01-01
From the Hamiltonian connecting the inside and outside of an Fabry-Perot cavity, which is derived from the Maxwell boundary conditions at a mirror of the cavity, a master equation of a non-Lindblad form is derived when the cavity embeds matters, although we can transform it to the Lindblad form by performing the rotating-wave approximation to that Hamiltonian. We calculate absorption spectra by these Lindblad and non-Lindblad master equations and also by the Maxwell boundary conditions in framework of the classical electrodynamics, which we consider the most reliable approach. We found that, compared to the Lindblad master equation, the absorption spectra by the non-Lindblad one agree better with those by the Maxwell boundary conditions. Although the discrepancy is highlighted only in the ultra-strong light-matter interaction regime with a relatively large broadening, the master equation of the non-Lindblad form is preferable rather than of the Lindblad one for pursuing the consistency with the classical elec...
A spectral boundary integral equation method for the 2D Helmholtz equation
International Nuclear Information System (INIS)
In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the non-smoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the non-smoothness of the integral kernels in the spectral implementation. The present method is robust for a general smooth boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. Numerical examples of wave scattering are given in which the exponential accuracy of the present numerical method is demonstrated. 15 refs., 3 figs., 4 tabs
ON A PARABOLIC FREE BOUNDARY EQUATION MODELING PRICE FORMATION
MARKOWICH, P. A.
2009-10-01
We discuss existence and uniqueness of solutions for a one-dimensional parabolic evolution equation with a free boundary. This problem was introduced by Lasry and Lions as description of the dynamical formation of the price of a trading good. Short time existence and uniqueness is established by a contraction argument. Then we discuss the issue of global-in-time-extension of the local solution which is closely related to the regularity of the free boundary. We also present numerical results. © 2009 World Scientific Publishing Company.
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.
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.
Krishnendu Bhattacharyya; Layek, G. C.
2014-01-01
A numerical investigation is made to study the thermal boundary layer for flow of incompressible Newtonian fluid over an exponentially stretching sheet with an exponentially moving free stream. The governing partial differential equations are transformed into self-similar ordinary differential equations using similarity transformations in exponential forms. Then those are solved numerically by shooting technique using Runge-Kutta method. The study reveals that the momentum boundary layer thic...
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.
Assessment of a transitional boundary layer theory at low hypersonic Mach numbers
Shamroth, S. J.; Mcdonald, H.
1972-01-01
An investigation was carried out to assess the accuracy of a transitional boundary layer theory in the low hypersonic Mach number regime. The theory is based upon the simultaneous numerical solution of the boundary layer partial differential equations for the mean motion and an integral form of the turbulence kinetic energy equation which controls the magnitude and development of the Reynolds stress. Comparisions with experimental data show the theory is capable of accurately predicting heat transfer and velocity profiles through the transitional regime and correctly predicts the effects of Mach number and wall cooling on transition Reynolds number. The procedure shows promise of predicting the initiation of transition for given free stream disturbance levels. The effects on transition predictions of the pressure dilitation term and of direct absorption of acoustic energy by the boundary layer were evaluated.
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.
Size distributions of boundary-layer clouds
Energy Technology Data Exchange (ETDEWEB)
Stull, R.; Berg, L.; Modzelewski, H. [Univ. of Wisconsin, Madison, WI (United States)
1996-04-01
Scattered fair-weather clouds are triggered by thermals rising from the surface layer. Not all surface layer air is buoyant enough to rise. Also, each thermal has different humidities and temperatures, resulting in interthermal variability of their lifting condensation levels (LCL). For each air parcel in the surface layer, it`s virtual potential temperature and it`s LCL height can be computed.
Galerkin Boundary Integral Analysis for the 3D Helmholtz Equation
Energy Technology Data Exchange (ETDEWEB)
Swager, Melissa [Emporia State University; Gray, Leonard J [ORNL; Nintcheu Fata, Sylvain [ORNL
2010-01-01
A linear element Galerkin boundary integral analysis for the three-dimensional Helmholtz equation is presented. The emphasis is on solving acoustic scattering by an open (crack) surface, and to this end both a dual equation formulation and a symmetric hypersingular formulation have been developed. All singular integrals are defined and evaluated via a boundary limit process, facilitating the evaluation of the (finite) hypersingular Galerkin integral. This limit process is also the basis for the algorithm for post-processing of the surface gradient. The analytic integrations required by the limit process are carried out by employing a Taylor series expansion for the exponential factor in the Helmholtz fundamental solutions. For the open surface, the implementations are validated by comparing the numerical results obtained by using the two different methods.
EFFECTS OF NONPARALLELISM ON THE BOUNDARY LAYER STABILITY
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The nonparallel effects on the stability of the boundary layer flow was investigated using the Parabolie Stability Equations (PSE). In order to improve the accuracy of the calculation which is very important for the investigation of stability, higher order expansions in orthogonal functions in normal direction and the effective algebraic mapping to deal with the problem of infinite region were used and the way to collocate the boundary point based on its characteristics was adopted. With the effective control of step size in the marching procedure, the special condition was satisfied, and the stability of calculation was assured. From the curves of the neutral stability, the growth rate, the amplitude variation and disturbed velocity profile, the effects of the nonparallelism were given accurately and analyzed detailedly. It is found that the nonparallelism of the flow amplifies the amplitude and growth rate of disturbances, especially for three-dimensional disturbances, even can change the sign of flow stability from stability to instability for some cases. Computed results are in good agreement with the classical experimental results.
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.
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.
Directory of Open Access Journals (Sweden)
Sulym Heorhiy
2016-03-01
Full Text Available This paper studies a thermoelastic anisotropic bimaterial with thermally imperfect interface and internal inhomogeneities. Based on the complex variable calculus and the extended Stroh formalism a new approach is proposed for obtaining the Somigliana type integral formulae and corresponding boundary integral equations for a thermoelastic bimaterial consisting of two half-spaces with different thermal and mechanical properties. The half-spaces are bonded together with mechanically perfect and thermally imperfect interface, which model interfacial adhesive layers present in bimaterial solids. Obtained integral equations are introduced into the modified boundary element method that allows solving arbitrary 2D thermoelacticity problems for anisotropic bimaterial solids with imperfect thin thermo-resistant inter-facial layer, which half-spaces contain cracks and thin inclusions. Presented numerical examples show the effect of thermal resistance of the bimaterial interface on the stress intensity factors at thin inhomogeneities.
Singular-boundary reductions of type-Q ABS equations
Atkinson, James; Joshi, Nalini
2011-01-01
We study the fully discrete elliptic integrable model Q4 and its immediate trigonometric and rational counterparts (Q3, Q2 and Q1). Singular boundary problems for these equations are systematised in the framework of global singularity analysis. We introduce a technique to obtain solutions of such problems, in particular constructing the exact solution on a regular singularity-bounded strip. The solution technique is based on the multidimensional consistency and uses new insights into these eq...
Reactive boundary layers in metallic rolling contacts
International Nuclear Information System (INIS)
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 of the
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
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.
A boundary matching micro/macro decomposition for kinetic equations
Lemou, Mohammed
2010-01-01
We introduce a new micro/macro decomposition of collisional kinetic equations which naturally incorporates the exact space boundary conditions. The idea is to write the distribution fonction $f$ in all its domain as the sum of a Maxwellian adapted to the boundary (which is not the usual Maxwellian associated with $f$) and a reminder kinetic part. This Maxwellian is defined such that its 'incoming' velocity moments coincide with the 'incoming' velocity moments of the distribution function. Important consequences of this strategy are the following. i) No artificial boundary condition is needed in the micro/macro models and the exact boundary condition on $f$ is naturally transposed to the macro part of the model. ii) It provides a new class of the so-called 'Asymptotic preserving' (AP) numerical schemes: such schemes are consistent with the original kinetic equation for all fixed positive value of the Knudsen number $\\eps$, and if $\\eps \\to 0 $ with fixed numerical parameters then these schemes degenerate into ...
Boundary Layer Flow over a Continuously Moving Thin Needle in a Parallel Free Stream
Institute of Scientific and Technical Information of China (English)
Anuar Ishak; Roslinda Nazar; Ioan Pop
2007-01-01
We investigate the boundary-layer flow on a moving isothermal thin needle parallel to a moving stream. The governing equations are solved numerically by a finite-difference method. Dual solutions are found to exist when the needle and the free stream move in the opposite directions.
STUDY ON THE TRANSPORT MECHANISM IN THE ANODE BOUNDARY LAYER OF WELDING ARGON ARC
Institute of Scientific and Technical Information of China (English)
C.S. Wu; J.Q. Gao
2001-01-01
The anode region of welding arc is divided into three subzones: the anode boundary layer, the presheath and the sheath. A model is established for analyzing the transport mechanisms in the anode boundary layer. The computer program is designed and the governing equations of the dominating processes with the boundary conditions taken from the solutions of LTE plasmas are solved by applying the Runge-Kutta procedure.One parameter θ, the ratio of the heavy particle temperature at the free-fall edge to the anode surface temperature, is introduced into this study. The results indicate that when the parameter θ is of the value 6 the predicted heat flux at the anode surface matches the measured one. Based on the model, various plasma properties in the boundary layer can be obtained. The calculated results are in good agreement with the measurements.
Change of Surface Roughness and Planetary Boundary Layer
DEFF Research Database (Denmark)
Jensen, Niels Otto
1978-01-01
The ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found to compare quite well with recent ...... numerical results from higher-order closure models, it is found that, even at a downwind distance such that the internal boundary layer has grown to the full height of the planetary boundary layers, the surface stress still considerably exceeds the equilibrium value......The ratio between upstream and far downstream surface friction velocities relative to a change in surface roughness is given on the basis of results from surface Rossby number similarity theory. By simple theories for the internal boundary layer, which are found to compare quite well with recent...
Spatially Developing Secondary Instabilities in Compressible Swept Airfoil Boundary Layers
Li, Fei; Choudhari, Meelan M.
2011-01-01
Two-dimensional eigenvalue analysis is used on a massive scale to study spatial instabilities of compressible shear flows with two inhomogeneous directions. The main focus of the study is crossflow dominated swept-wing boundary layers although the methodology can also be applied to study other type of flows, such as the attachment-line flow. Certain unique aspects of formulating a spatial, two-dimensional eigenvalue problem for the secondary instability of finite amplitude crossflow vortices are discussed, namely, fixing the spatial growth direction unambiguously through a non-orthogonal formulation of the linearized disturbance equations. A primary test case used for parameter study corresponds to the low-speed, NLF-0415(b) airfoil configuration as tested in the ASU Unsteady Wind Tunnel, wherein a spanwise periodic array of roughness elements was placed near the leading edge in order to excite stationary crossflow modes with a specified fundamental wavelength. The two classes of flow conditions selected for this analysis include those for which the roughness array spacing corresponds to either the naturally dominant crossflow wavelength, or a subcritical wavelength that serves to reduce the growth of the naturally excited dominant crossflow modes. Numerical predictions are compared with the measured database, both as indirect validation for the spatial instability analysis and to provide a basis for comparison with a higher Reynolds number, supersonic swept-wing configuration. Application of the eigenvalue analysis to the supersonic configuration reveals that a broad spectrum of stationary crossflow modes can sustain sufficiently strong secondary instabilities as to potentially cause transition over this configuration. Implications of this finding for transition control in swept wing boundary layers are examined.
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.
Edwards, S.; Reuther, J.; Chattot, J. J.
The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjoint approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to a target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speeds.
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.
Tropical boundary layer equilibrium in the last ice age
Betts, Alan K.; Ridgway, W.
1992-01-01
A radiative-convective boundary layer model is used to assess the effect of changing sea surface temperature, pressure, wind speed, and the energy export from the tropics on the boundary layer equilibrium equivalent potential temperature. It remains difficult to reconcile the observations that during the last glacial maximum (18,000 yr BP) the snowline on the tropical mountains fell 950 m, while the tropical sea surface temperatures fell only 1-2 K.
Theoretical investigation on shocklets in compressible boundary layers
Institute of Scientific and Technical Information of China (English)
袁湘江; 刘智勇; 沈洁; 李国良
2014-01-01
By the shock relationships, the wavy characteristics and the forming condi-tions of a shock wave are analyzed. The wavy characteristics of an Euler system are stud-ied theoretically. The present research focuses on the wavy characteristics of Tollmien-Schlichting (T-S) waves, the excitation conditions of shocklets in compressible boundary layers, and the viscous effect on shock. The possibility of existence of shocklets in the compressible boundary layer and the physical mechanism of formation are theoretically interpreted.
LES model intercomparisons for the stable atmospheric boundary layer
Moene, A.F.; Baas, P.; Bosveld, F.C.; Basu, S.
2011-01-01
Model intercomparisons are one possible method to gain confidence in Large-Eddy Simulation (LES) as a viable tool to study turbulence in the atmospheric boundary-layer. This paper discusses the setup and some results of two intercomparison cases focussing on the stably stratified nocturnal boundary-
Hydrodynamic structure of the boundary layers in a rotating cylindrical cavity with radial inflow
Herrmann-Priesnitz, Benjamín; Calderón-Muñoz, Williams R.; Salas, Eduardo A.; Vargas-Uscategui, Alejandro; Duarte-Mermoud, Manuel A.; Torres, Diego A.
2016-03-01
A flow model is formulated to investigate the hydrodynamic structure of the boundary layers of incompressible fluid in a rotating cylindrical cavity with steady radial inflow. The model considers mass and momentum transfer coupled between boundary layers and an inviscid core region. Dimensionless equations of motion are solved using integral methods and a space-marching technique. As the fluid moves radially inward, entraining boundary layers develop which can either meet or become non-entraining. Pressure and wall shear stress distributions, as well as velocity profiles predicted by the model, are compared to numerical simulations using the software OpenFOAM. Hydrodynamic structure of the boundary layers is governed by a Reynolds number, Re, a Rossby number, Ro, and the dimensionless radial velocity component at the periphery of the cavity, Uo. Results show that boundary layers merge for Re > 0.1, and boundary layers become predominantly non-entraining for low Ro, low Re, and high Uo. Results may contribute to improve the design of technology, such as heat exchange devices, and turbomachinery.
Structure and Growth of the Marine Boundary Layer
Mccumber, M.
1984-01-01
LANDSAT visible imagery and a one-dimensional Lagrangian boundary layer model were used to hypothesize the nature and the development of the marine boundary layer during a winter episode of strong seaward cold air advection. Over-water heating and moistening of the cold, dry continental air is estimable from linear relations involving horizontal gradients of the near-surface air temperature and humidity. A line of enhanced convection paralleling the Atlantic U.S. coast from south of New York Bay to the vicinity of Virginia Beach, VA was attributed to stronger convergence at low levels. This feature was characterized as a mesoscale front. With the assistance of a three-dimensional mesoscale boundary layer model, initialized with data obtained from the MASEX, the marine boundary layer can be mapped over the entire Atlantic coastal domain and the evolution of the boundary layer can be studied as a function of different characteristics of important surface level forcings. The effects on boundary layer growth due to the magnitude and pattern of sea surface temperature, to the shape of the coastline, and to atmospheric conditions, such as the orientation of the prevailing wind are examined.
Turbulent Boundary Layer at Large Re
Directory of Open Access Journals (Sweden)
Horia DUMITRESCU
2016-03-01
Full Text Available The fluids as deformable bodies without own shape, when starting from rest, experience interactions between the flowing fluid and the physical surfaces marking the bounds of flow. These interactions are a kind of impact process where there is a momentum exchange between two colliding bodies, i.e. the flow and its boundary surfaces. Within a short time of contact a post-impact shear flow occurs where two main effects are triggered off by the flow-induced collision: dramatic redistribution of the momentum and the boundary vorticity followed by the shear stress/viscosity change in the microstructure of the fluid which at the beginning behaves as linear reactive medium and latter as nonlinear dispersive medium. The disturbance of the starting flow induces the entanglement of the wall-bounded flow in the form of point-vortices or concentrated vorticity balls whence waves are emitted and propagated through flow field. The paper develops a wave mechanism for the transport of the concentrated boundary vorticity, directly related to the fascinating turbulence phenomenon, using the torsion concept of vorticity filaments associated with the hypothesis of thixotropic/nonlinear viscous fluid.
Numerical simulations of coupled sea waves and boundary layer dynamics
Chalikov, D.
2009-04-01
potential equations, while an atmospheric model is based on Reynolds equations with 2nd order closing. Hundreds of long-term numerical experiments for different initial wave spectra were carried out to investigate statistical structure of the wave boundary layer (WBL) and particularly, for construction of effective beta-function, taking into account real shapes of waves, occasional separation of boundary layer and the effect of parameterized wave breaking. Naturally, beta-function determined in such a way, has a wide scatter, however extensive statistics allows to derive that function with high accuracy. Data on vertical distribution of spectral components of wave-produced momentum flux are used for construction of 1-D model of WBL. It is shown, that most of the momentum flux to waves is concentrated in a high wave number part of spectrum where dispersion relation is actually not valid. Wind waves form rough surface, so all of the momentum flux is absorbed by waves, while local tangent stress is negligibly small. The approach allows to investigate WBL structure for arbitrary wind conditions and wave spectra. It is shown that wide scatter for drag coefficient can be easily explained by different wave conditions. For example, decrease of effective surface roughness at storm winds can be explained by dumping of high-frequency waves by foam.
A Nonlinear Singularly Perturbed Problem for Reaction Diffusion Equations with Boundary Perturbation
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2005-01-01
A nonlinear singularly perturbed problems for reaction diffusion equation with boundary perturbation is considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems of reaction diffusion equations is studied using the theory of differential inequalities.
Energy Technology Data Exchange (ETDEWEB)
Ishak, Anuar [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia); Nazar, Roslinda [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia)], E-mail: rmn72my@yahoo.com; Pop, Ioan [Faculty of Mathematics, University of Cluj, R-3400 Cluj, CP 253 (Romania)
2008-03-31
The mixed convection boundary layer flow through a stable stratified porous medium bounded by a vertical surface is investigated. The external velocity and the surface temperature are assumed to vary as x{sup m}, where x is measured from the leading edge of the vertical surface and m is a constant. Numerical solutions for the governing Darcy and energy equations are obtained. The results indicate that the thermal stratification significantly affects the surface shear stress as well as the surface heat transfer, besides delays the boundary layer separation.
Unsteady compressible boundary layer flow over a circular cone near aplane of symmetry
Chamkha, AJ; Takhar, HS; G. Nath
2005-01-01
An analysis has been performed to study the unsteady laminar compressible boundary layer governing the hypersonic flow over a circular cone at an angle of attack near a plane of symmetry with either in flow or out flow in the presence of suction. The flow is assumed to be steady at time t= 0 and at t > 0 it becomes unsteady due to the time-dependent free stream velocity which varies arbitrarily with time. The nonlinear coupled parabolic partial differential equations under boundary layer a...
Plasma boundary layer and magnetopause layer of the earth's magnetosphere
Energy Technology Data Exchange (ETDEWEB)
Eastman, T.E.
1979-06-01
IMP 6 observations of the plasma boundary layer (PBL) and magnetopause layer (MPL) of the earth's magnetosphere indicate that plasma in the low-latitude portion of the PBL is supplied primarily by direct transport of magnetosheath plasma across the MPL and that this transport process is relatively widespread over the entire sunward magnetospheric boundary.
Response of neutral boundary-layers to changes of roughness
DEFF Research Database (Denmark)
Sempreviva, Anna Maria; Larsen, Søren Ejling; Mortensen, Niels Gylling;
1990-01-01
stratification, and the surface roughness is the main parameter. The analysis of wind data and two simple models, a surface layer and a planetary boundary layer (PBL) model, are described. Results from both models are discussed and compared with data analysis. Model parameters have been evaluated and the model......When air blows across a change in surface roughness, an internal boundary layer (IBL) develops within which the wind adapts to the new surface. This process is well described for short fetches, > 1 km. However, few data exist for large fetches on how the IBL grows to become a new equilibrium...... boundary layer where again the drag laws can be used to estimate the surface wind. To study this problem, data have been sampled for two years from four 30-m meteorological masts placed from 0 to 30 km inland from the North Sea coast of Jutland in Denmark. The present analysis is limited to neutral...
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....
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...... spots, isolated arrowhead-shaped areas close to the bed in an otherwise laminar boundary layer where the flow ‘bursts’ with violent oscillations. The emergence of the turbulent spots marks the onset of turbulence. Turbulent spots cause single or multiple violent spikes in the bed shear stress signal......) 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...
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.
Definition of Turbulent Boundary-Layer with Entropy Concept
Directory of Open Access Journals (Sweden)
Zhao Rui
2016-01-01
Full Text Available The relationship between the entropy increment and the viscosity dissipation in turbulent boundary-layer is systematically investigated. Through theoretical analysis and direct numerical simulation (DNS, an entropy function fs is proposed to distinguish the turbulent boundary-layer from the external flow. This approach is proved to be reliable after comparing its performance in the following complex flows, namely, low-speed airfoil flows with different wall temperature, supersonic cavity-ramp flow dominated by the combination of free-shear layer, larger recirculation and shocks, and the hypersonic flow past an aeroplane configuration. Moreover, fs is deduced from the point of energy, independent of any particular turbulent quantities. That is, this entropy concept could be utilized by other engineering applications related with turbulent boundary-layer, such as turbulence modelling transition prediction and engineering thermal protection.
Tokamak plasma shape identification based on the boundary integral equations
International Nuclear Information System (INIS)
A necessary condition for tokamak plasma shape identification is discussed and a new identification method is proposed in this article. This method is based on the boundary integral equations governing a vacuum region around a plasma with only the measurement of either magnetic fluxes or magnetic flux intensities. It can identify various plasmas with low to high ellipticities with the precision determined by the number of the magnetic sensors. This method is applicable to real-time control and visualization using a 'table-look-up' procedure. (author)
Periodic and Boundary Value Problems for Second Order Differential Equations
Indian Academy of Sciences (India)
Nikolaos S Papageorgiou; Francesca Papalini
2001-02-01
In this paper we study second order scalar differential equations with Sturm–Liouville and periodic boundary conditions. The vector field (, , ) is Caratheodory and in some instances the continuity condition on or is replaced by a monotonicity type hypothesis. Using the method of upper and lower solutions as well as truncation and penalization techniques, we show the existence of solutions and extremal solutions in the order interval determined by the upper and lower solutions. Also we establish some properties of the solutions and of the set they form.
Vortex Generators to Control Boundary Layer Interactions
Babinsky, Holger (Inventor); Loth, Eric (Inventor); Lee, Sang (Inventor)
2014-01-01
Devices for generating streamwise vorticity in a boundary includes various forms of vortex generators. One form of a split-ramp vortex generator includes a first ramp element and a second ramp element with front ends and back ends, ramp surfaces extending between the front ends and the back ends, and vertical surfaces extending between the front ends and the back ends adjacent the ramp surfaces. A flow channel is between the first ramp element and the second ramp element. The back ends of the ramp elements have a height greater than a height of the front ends, and the front ends of the ramp elements have a width greater than a width of the back ends.
Direct simulation of turbulent supersonic boundary layers by an extended temporal approach
Maeder, Thierry; Adams, Nikolaus A.; Kleiser, Leonhard
2001-02-01
The present paper addresses the direct numerical simulation of turbulent zero-pressure-gradient boundary layers on a flat plate at Mach numbers 3, 4.5 and 6 with momentum-thickness Reynolds numbers of about 3000. Simulations are performed with an extended temporal direct numerical simulation (ETDNS) method. Assuming that the slow streamwise variation of the mean boundary layer is governed by parabolized Navier Stokes equations, the equations solved locally in time with a temporal DNS are modified by a distributed forcing term so that the parabolized Navier Stokes equations are recovered for the spatial average. The correct mean flow is obtained without a priori knowledge, the streamwise mean-flow evolution being approximated from its upstream history. ETDNS reduces the computational effort by up to two orders of magnitude compared to a fully spatial simulation.
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.
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.
Neumann, B. J.
1983-07-01
One objective of the Advanced Undersea Vehicle (AUV) program is to design a low drag vehicle. The approach in this investigation is boundary layer control by means of an annular suction slot located on the afterbody. Although wind tunnel data showed significant reduction in propulsive power over conventional shapes, an attempt was made to achieve further reduction by means of forebody shaping. Two methods were used to vary the geometric parameters for this analysis. The direct method, based on the mathematical development of the Series 58 bodies, allows the definition of a shape by a fifth-order polynomial based on the four fundamental parameters of fineness ratio, nose radius of curvature, location of maximum thickness, and prismatic coefficient. The inverse method allows various velocity distributions to define the body shape. The shapes derived by this method have flat velocity distributions and show similar trends to the polynomial shapes (about 3-percent reduction in propulsive power). The range of fineness ratios analyzed was from 1 to 10 at a volume-based Reynolds number of 3.2 million. In the range of 2.5 to 8, fineness ratio did not affect propulsive power more than 6 percent. A maximum improvement of 3 percent as shown by varying the meridian section.
A numerical solution of a singular boundary value problem arising in boundary layer theory.
Hu, Jiancheng
2016-01-01
In this paper, a second-order nonlinear singular boundary value problem is presented, which is equivalent to the well-known Falkner-Skan equation. And the one-dimensional third-order boundary value problem on interval [Formula: see text] is equivalently transformed into a second-order boundary value problem on finite interval [Formula: see text]. The finite difference method is utilized to solve the singular boundary value problem, in which the amount of computational effort is significantly less than the other numerical methods. The numerical solutions obtained by the finite difference method are in agreement with those obtained by previous authors. PMID:27026894
Heterogeneous evaporation across a turbulent internal boundary layer
Shahraeeni, Ebrahim; Vanderborght, Jan; Vereecken, Harry
2014-05-01
In local evaporation from sufficiently uniform and large surfaces, horizontal advection close to the changes in surface condition is not significant. Under natural condition, this assumption is often invalid and horizontal inhomogeneity is important. When partially saturated air flows from a uniform dry land surface over a wet surface, all lower boundary conditions of transport equations change abruptly. Also surface humidity and roughness are likely to be different from their upwind values. Due to these changes, the velocity profile and turbulence structure of the airflow must readjust. The vertical profiles are no longer in equilibrium and the horizontal gradients do not equal to zero. When there is more than one of these changes in the domain of interest, the interaction between different patches with a contrast in roughness, temperature or surface water content is also important. Rigorous experimental and numerical analysis of turbulent transfer of mass and momentum in the so-called internal boundary layer (the region affected by such step changes in surface condition) is the aim of this work. A combination of numerical simulations using in-house codes and commercial softwares and experimental measurements in the environmental wind tunnel is performed. We are specifically interested in correct depiction of roughness, in a more accurate representation of the turbulent velocity profile and in a better description of turbulent diffusion close to the interface. A series of simplifying assumptions in the classical representation of this problem are investigated and a sensitivity analysis is performed to identify the contribution of neglected terms. We are also interested in the parameterization of the heat and mass exchange processes for the case with different wet patches in a background of dry soil, which is of interest in several field scale applications.
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. PMID:23166688
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.
Modelling Scalar Skewness in Cloudy Boundary Layers
Mironov, Dmitrii; Machulskaya, Ekaterina; Naumann, Ann Kristin; Seifert, Axel; Mellado, Juan Pedro
2015-04-01
Following the pioneering work of Sommeria and Deardorff (1977), statistical cloud schemes are widely used in numerical weather prediction (NWP) and climate models to parameterize the effect of shallow clouds on turbulent mixing and radiation fluxes. Statistical cloud schemes compute the cloud fraction, the amount of cloud condensate and the effect clouds on the buoyancy flux in a given atmospheric-model grid box. This is done with due regard for the sub-grid scale (SGS) fluctuations of temperature and humidity (and possibly the vertical velocity), thus providing an important coupling between cloudiness and the SGS mixing processes. The shape of the PDF of fluctuating fields is assumed, whereas the PDF moments should be provided to the cloud scheme as an input. For non-precipitation clouds, the mixing schemes are usually formulated in terms of quasi-conservative variable, e.g. the liquid (total) water potential temperature and the total water specific humidity. Then, the cloud schemes are conveniently cast in terms of the linearized saturation deficit, referred to as the "s" variable (Mellor 1977), that accounts for the combined effect of the two scalars. If a simple two-parameter single-Gaussian PDF is used, the only "turbulence" parameter to be provided to the cloud scheme is the variance of s. The single-Gaussian PDF ignores the skewed nature of SGS motions and fails to describe many important regimes, e.g. shallow cumuli. A number of more flexible skewed PDFs have been proposed to date. A three-parameter PDF, based on a double-Gaussian distribution and diagnostic relations between some PDF parameters derived from LES and observational data (Naumann et al. 2013), appears to be a good compromise between physical realism and computational economy. A crucial point is that the cloud schemes using non-Gaussian PDFs require the scalar skewness as an input. Using rather mild non-restrictive assumptions, we develop a transport equation for the s-variable triple
Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability Over Cones
Kara, Kursat; Balakumar, Ponnampalam; Kandil, Osama A.
2011-01-01
The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate weighted-essentially-non-oscillatory scheme. A third-order accurate total-variation-diminishing Runge-Kutta scheme is employed for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. The appearance of instability waves near the nose region and the receptivity of the boundary layer with respect to slow mode acoustic waves are investigated. Computations confirm the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary-layer transition. The current solutions, compared with experimental observations and other computational results, exhibit good agreement.
Turbulent boundary-layer structure of flows over freshwater biofilms
Walker, J. M.; Sargison, J. E.; Henderson, A. D.
2013-12-01
The structure of the turbulent boundary-layer for flows over freshwater biofilms dominated by the diatom Tabellaria flocculosa was investigated. Biofilms were grown on large test plates under flow conditions in an Australian hydropower canal for periods up to 12 months. Velocity-profile measurements were obtained using LDV in a recirculating water tunnel for biofouled, smooth and artificially sandgrain roughened surfaces over a momentum thickness Reynolds number range of 3,000-8,000. Significant increases in skin friction coefficient of up to 160 % were measured over smooth-wall values. The effective roughnesses of the biofilms, k s, were significantly higher than their physical roughness measured using novel photogrammetry techniques and consisted of the physical roughness and a component due to the vibration of the biofilm mat. The biofilms displayed a k-type roughness function, and a logarithmic relationship was found between the roughness function and roughness Reynolds number based on the maximum peak-to-valley height of the biofilm, R t. The structure of the boundary layer adhered to Townsend's wall-similarity hypothesis even though the scale separation between the effective roughness height and the boundary-layer thickness was small. The biofouled velocity-defect profiles collapsed with smooth and sandgrain profiles in the outer region of the boundary layer. The Reynolds stresses and quadrant analysis also collapsed in the outer region of the boundary layer.
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.
Highly buoyant bent-over plumes in a boundary layer
Tohidi, Ali; Kaye, Nigel B.
2016-04-01
Highly buoyant plumes, such as wildfire plumes, in low to moderate wind speeds have initial trajectories that are steeper than many industrial waste plumes. They will rise further into the atmosphere before bending significantly. In such cases the plume's trajectory will be influenced by the vertical variation in horizontal velocity of the atmospheric boundary layer. This paper examined the behavior of a plume in an unstratified environment with a power-law ambient velocity profile. Examination of previously published experimental measurements of plume trajectory show that inclusion of the boundary layer velocity profile in the plume model often provides better predictions of the plume trajectory compared to algebraic expressions developed for uniform flow plumes. However, there are many cases in which uniform velocity profile algebraic expressions are as good as boundary layer models. It is shown that it is only important to model the role of the atmospheric boundary layer velocity profile in cases where either the momentum length (square root of source momentum flux divided by the reference wind speed) or buoyancy length (buoyancy flux divided by the reference wind speed cubed) is significantly greater than the plume release height within the boundary layer. This criteria is rarely met with industrial waste plumes, but it is important in modeling wildfire plumes.
Stabilization of boundary layer streaks by plasma actuators
International Nuclear Information System (INIS)
A flow's transition from laminar to turbulent leads to increased levels of skin friction. In recent years, dielectric barrier discharge actuators have been shown to be able to delay the onset of turbulence in boundary layers. While the laminar to turbulent transition process can be initiated by several different instability mechanisms, so far, only stabilization of the Tollmien–Schlichting path to transition has received significant attention, leaving the stabilization of other transition paths using these actuators less explored. To fill that void, a bi-global stability analysis is used here to examine the stabilization of boundary layer streaks in a laminar boundary layer. These streaks, which are important to both transient and by-pass instability mechanisms, are damped by the addition of a flow-wise oriented plasma body force to the boundary layer. Depending on the magnitude of the plasma actuation, this damping can be up to 25% of the perturbation's kinetic energy. The damping mechanism appears to be due to highly localized effects in the immediate vicinity of the body force, and when examined using a linearized Reynolds-averaged Navier–Stokes energy balance, indicate negative production of the perturbation's kinetic energy. Parametric studies of the stabilization have also been performed, varying the magnitude of the plasma actuator's body force and the spanwise wavenumber of the actuation. Based on these parametric studies, the damping of the boundary layer streaks appears to be linear with respect to the total amount of body force applied to the flow. (paper)
Uranus evolution models with simple thermal boundary layers
Nettelmann, Nadine; Redmer, Ronald; Fortney, Jonathan J.; Hamel, Sebastien; Bethkenhagen, Mandy
2016-04-01
The strikingly low luminosity of Uranus imposes a long-standing challenge to our understanding of Ice Giant planets. Similar to the Earth, Uranus appears to evolve in equilibrium with the solar incident flux (Teq). Here we present the first Uranus structure and evolution models that are constructed to agree with both the observed low luminosity and the gravity field data. Our models make use of modern ab initio equations of state at high pressures for the icy components water, methane, and ammonia. We argue that the transition between the ice/rock-rich interior and the H/He-rich outer envelope should be stably stratified. Therefore, we introduce a simple thermal boundary layer (TBL) and adjust it to reproduce the luminosity. Due to this TBL, the deep interior of the Uranus models are up to a factor 3 warmer than adiabatic models, necessitating the presence of rocks there with a possible I:R of 1 x solar. Furthermore, we also allow for an equilibrium evolution (Teff ~ Teq) that begun prior to the present day, which would therefore no longer constitute a "special time" in Uranus' evolution. Once Teff ~ Teq happens, a shallow, subadiabatic zone in the atmosphere begins to develop. Its depth is adjusted to meet the luminosity constraint. This work provides a simple foundation for future Ice Giant structure and evolution models, that can be improved by properly treating the heat and particle fluxes in the diffusive zones.
The numerical solution of the boundary inverse problem for a parabolic equation
Vasil'ev, V. V.; Vasilyeva, M. V.; Kardashevsky, A. M.
2016-10-01
Boundary inverse problems occupy an important place among the inverse problems of mathematical physics. They are connected with the problems of diagnosis, when additional measurements on one of the borders or inside the computational domain are necessary to restore the boundary regime in the other border, inaccessible to direct measurements. The boundary inverse problems belong to a class of conditionally correct problems, and therefore, their numerical solution requires the development of special computational algorithms. The paper deals with the solution of the boundary inverse problem for one-dimensional second-order parabolic equations, consisting in the restoration of boundary regime according to measurements inside the computational domain. For the numerical solution of the inverse problem it is proposed to use an analogue of a computational algorithm, proposed and developed to meet the challenges of identification of the right side of the parabolic equations in the works P.N.Vabishchevich and his students based on a special decomposition of solving the problem at each temporal layer. We present and discuss the results of a computational experiment conducted on model problems with quasi-solutions, including with random errors in the input data.
Mixed convection boundary layer flow over a vertical cylinder with prescribed surface heat flux
Energy Technology Data Exchange (ETDEWEB)
Ishak, Anuar [School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor (Malaysia)], E-mail: anuar_mi@ukm.my
2009-05-15
The steady mixed convection boundary layer flow along a vertical cylinder with prescribed surface heat flux is investigated in this study. The free stream velocity and the surface heat flux are assumed to vary linearly with the distance from the leading edge. Both the case of the buoyancy forces assisting and opposing the development of the boundary layer are considered. Similarity equations are derived, their solutions being dependent on the mixed convection parameter, the curvature parameter, as well as of the Prandtl number. Dual solutions are found to exist for both buoyancy assisting and opposing flows. It is also found that the boundary layer separation is delayed for a cylinder compared to a flat plate.
DEFF Research Database (Denmark)
Kristensen, Leif; Lenschow, Donald H.; Gurarie, David;
2010-01-01
We have developed a simple, steady-state, one-dimensional second-order closure model to obtain continuous profiles of turbulent fluxes and mean concentrations of non-conserved scalars in a convective boundary layer without shear. As a basic tool we first set up a model for conserved species...... with standard parameterizations. This leads to formulations for profiles of the turbulent diffusivity and the ratio of temperature-scalar covariance to the flux of the passive scalar. The model is then extended to solving, in terms of profiles of mean concentrations and fluxes, the NO x –O3 triad problem...... layer, the problem reduces to solving two differential equations for the concentration and the flux of NO2. The boundary conditions are the three surface fluxes and the fluxes at the top of the boundary layer, the last obtained from the entrainment velocity, and the concentration differences between...
Shear Force Distribution and Heat Transfer in Laminar Boundary Layer Flows for Power Law Fluid
Institute of Scientific and Technical Information of China (English)
郑连存; 张欣欣
2002-01-01
Analytical and numerical solutions are presented for the momentum and energy laminar boundary layer equations in power law fluids utilizing a similarity transformation and the shooting technique. The results indicated that for power law exponents 0＜n≤1, the skin friction σ decreases with increasing n, and the dimensionless shear force decreases with increasing dimensionless velocity t. When Pr=1, the velocity distribution in the viscous boundary layer is the same as the temperature distribution in the thermal boundary layer and δ＝δT. For Pr＞1, the increase of the viscous diffusion exceeds that of thermal diffusion with increasing Pr, i.e., δT(t)＜δ(t). The thermal diffusion ratio increases with increasing n(0＜n≤1).
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.
Particle motion inside Ekman and Bödewadt boundary layers
Duran Matute, Matias; van der Linden, Steven; van Heijst, Gertjan
2014-11-01
We present results from both laboratory experiments and numerical simulations of the motion of heavy particles inside Ekman and Bödewadt boundary layers. The particles are initially at rest on the bottom of a rotating cylinder filled with water and with its axis parallel to the axis of rotation. The particles are set into motion by suddenly diminishing the rotation rate and the subsequent creation of a swirl flow with the boundary layer above the bottom plate. We consider both spherical and non-spherical particles with their size of the same order as the boundary layer thickness. It was found that the particle trajectories define a clear logarithmic spiral with its shape depending on the different parameters of the problem. Numerical simulations show good agreement with experiments and help explain the motion of the particles. This research is funded by NWO (the Netherlands) through the VENI Grant 863.13.022.
Vertical pressure gradient and particle motions in wave boundary layers
DEFF Research Database (Denmark)
Jensen, Karsten Lindegård
The present study covers both a numerical and experimental investigation of the processes in the oscillatory boundary layer. In the first part a direct numerical simulation (DNS) is conducted to study the vertical pressure gradient, and its role in relation to laminar to turbulent transition...... and its role in the fully turbulent boundary layer. The pressure in the flow is obtained from the flow fields of the oscillatory boundary layer. What differs, the vertical pressure gradient, from other turbulent quantities, like e.g. velocity fluctuations is that it can detect newly generated turbulence....... This is in contrast to velocity fluctuations that are diffusive, so they can also contain residual turbulence from the previous half cycle until they are dissipated. Furthermore, the magnitude of the mean value of conditionally averaged vertical pressure gradient (for −∂p∗/∂x∗ 2 > 0) is compared to the submerged...
On the interaction between turbulence grids and boundary layers
Directory of Open Access Journals (Sweden)
Irps Thomas
2016-01-01
Full Text Available Turbulence grids are widely used in wind tunnels to produce representative turbulence levels when testing aerodynamic phenomena around models. Although the purpose of the grid is to introduce a desired turbulence level in the freestream flow, the wall boundary layers of the tunnel are subjected to modification due to the presence of such grids. This could have major implications to the flow around the models to be tested and hence there is a need to further understand this interaction. The study described in this paper examines wind tunnel wall boundary layer modification by turbulence grids of different mesh sizes and porosities to understand the effect of these parameters on such interaction. Experimental results are presented in the form of pressure loss coefficients, boundary layer velocity profiles and the statistics of turbulence modification.
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.
Bypass transition and spot nucleation in boundary layers
Kreilos, Tobias; Schlatter, Philipp; Duguet, Yohann; Henningson, Dan S; Eckhardt, Bruno
2016-01-01
The spatio-temporal aspects of the transition to turbulence are considered in the case of a boundary layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence with the nonlinear concept of a transition threshold, a physically motivated model suggests a spatial distribution of spot nucleation events. To describe the evolution of turbulent spots a probabilistic cellular automaton is introduced, with all parameters directly fitted from numerical simulations of the boundary layer. The nucleation rates are then combined with the cellular automaton model, yielding excellent quantitative agreement with the statistical characteristics for different free-stream turbulence levels. We thus show how the recent theoretical progress on transitional wall-bounded flows can be extended to the much wider class of spatially developing boundary-layer flows.
Bypass transition and spot nucleation in boundary layers
Kreilos, Tobias; Khapko, Taras; Schlatter, Philipp; Duguet, Yohann; Henningson, Dan S.; Eckhardt, Bruno
2016-08-01
The spatiotemporal aspects of the transition to turbulence are considered in the case of a boundary-layer flow developing above a flat plate exposed to free-stream turbulence. Combining results on the receptivity to free-stream turbulence with the nonlinear concept of a transition threshold, a physically motivated model suggests a spatial distribution of spot nucleation events. To describe the evolution of turbulent spots a probabilistic cellular automaton is introduced, with all parameters directly obtained from numerical simulations of the boundary layer. The nucleation rates are then combined with the cellular automaton model, yielding excellent quantitative agreement with the statistical characteristics for different free-stream turbulence levels. We thus show how the recent theoretical progress on transitional wall-bounded flows can be extended to the much wider class of spatially developing boundary-layer flows.
Institute of Scientific and Technical Information of China (English)
Gui-Qiang Chen; Dan Osborne; Zhongmin Qian
2009-01-01
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in RN with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-fiat boundary. We observe that, under the nonhomogeneons boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition (without the incompressibility condition), which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in RN(n≥3) with nonhomogeneous vorticity boundary condition converge in L2 to the corresponding Euler equations satisfying the kinematic condition.
Indian Academy of Sciences (India)
M Tajuddin; G Narayan Reddy
2005-08-01
A transcendental equation is derived relating wave number and phase velocity of propagation of waves in a partially saturated layered half-space under plane strain conditions. The period equation is derived and discussed for two types of boundaries, permeable and impermeable. In the limiting cases, the problem reduces to more simpliﬁed forms as discussed by earlier researchers.
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...
Numerical modeling of the transitional boundary layer over a flat plate
Ivanov, Dimitry; Chorny, Andrei
2015-11-01
Our example is connected with fundamental research on understanding how an initially laminar boundary layer becomes turbulent. We have chosen the flow over a flat plate as a prototype for boundary-layer flows around bodies. Special attention was paid to the near-wall region in order to capture all levels of the boundary layer. In this study, the numerical software package OpenFOAM has been used in order to solve the flow field. The results were used in a comparative study with data obtained from Large Eddy Simulation (LES). 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. In current study the time discretization is based on a second order Crank-Nicolson/Adams-Bashforth method. LES solver using Smagorinsky and the one-equation LES turbulence models. The transition models significantly improve the prediction of the onset location compared to the fully turbulent models.LES methods appear to be the most promising new tool for the design and analysis of flow devices including transition regions of the turbulent flow.
Boundary value problemfor multidimensional fractional advection-dispersion equation
Directory of Open Access Journals (Sweden)
Khasambiev Mokhammad Vakhaevich
2015-05-01
Full Text Available In recent time there is a very great interest in the study of differential equations of fractional order, in which the unknown function is under the symbol of fractional derivative. It is due to the development of the theory of fractional integro-differential theory and application of it in different fields.The fractional integrals and derivatives of fractional integro-differential equations are widely used in modern investigations of theoretical physics, mechanics, and applied mathematics. The fractional calculus is a very powerful tool for describing physical systems, which have a memory and are non-local. Many processes in complex systems have nonlocality and long-time memory. Fractional integral operators and fractional differential operators allow describing some of these properties. The use of the fractional calculus will be helpful for obtaining the dynamical models, in which integro-differential operators describe power long-time memory by time and coordinates, and three-dimensional nonlocality for complex medium and processes.Differential equations of fractional order appear when we use fractal conception in physics of the condensed medium. The transfer, described by the operator with fractional derivatives at a long distance from the sources, leads to other behavior of relatively small concentrations as compared with classic diffusion. This fact redefines the existing ideas about safety, based on the ideas on exponential velocity of damping. Fractional calculus in the fractal theory and the systems with memory have the same importance as the classic analysis in mechanics of continuous medium.In recent years, the application of fractional derivatives for describing and studying the physical processes of stochastic transfer is very popular too. Many problems of filtration of liquids in fractal (high porous medium lead to the need to study boundary value problems for partial differential equations in fractional order.In this paper the
Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers
Abramov, Rafail V
2016-01-01
In the current work we propose a diffusive modification of the Boltzmann equation. This naturally leads to the corresponding diffusive fluid dynamics equations, which we numerically investigate in a simple Couette flow setting. This diffusive modification is based on the assumption of the "imperfect" model collision term, which is unable to track all collisions in the corresponding real gas particle system. The effect of missed collisions is then modeled by an appropriately scaled long-term homogenization process of the particle dynamics. The corresponding diffusive fluid dynamics equations are produced in a standard way by closing the hierarchy of the moment equations using either the Euler or the Grad closure. In the numerical experiments with the Couette flow, we discover that the diffusive Euler equations behave similarly to the conventional Navier-Stokes equations, while the diffusive Grad equations additionally exhibit Knudsen-like velocity boundary layers. We compare the simulations with the correspond...
Numerical Modeling of the Evolving Stable Boundary Layer
Sorbjan, Z.
2013-12-01
A single-column model of the evolving stable boundary layer is tested for the consistency of turbulence parameterization, self-similar properties of the flow, and effects of ambient forcing. The turbulence closure of the model is based on the K-theory approach, with stability functions based on empirical data, and a semi-empirical form of the mixing length. The model has one internal, governing stability parameter, the Richardson number Ri, which dynamically adjusts to the boundary conditions and to external forcing. Model results, expressed in terms of local similarity scales, are universal functions of the Richardson number, i.e. they are satisfied in the entire stable boundary layer, for all instants of time, and all kinds of external forcing. Based on similarity expression, a realizability condition is derived for the minimum turbulent heat flux in the stable boundary layer. Numerical experiments show that the development of 'horse-shoe' shaped, 'fixed-elevation' wind hodographs in the interior of the stable boundary layer are solely caused by effects imposed by surface thermal forcing, and are not related to the inertial oscillation mechanism.
Non-Equilibrium Effects on Hypersonic Turbulent Boundary Layers
Kim, Pilbum
Understanding non-equilibrium effects of hypersonic turbulent boundary layers is essential in order to build cost efficient and reliable hypersonic vehicles. It is well known that non-equilibrium effects on the boundary layers are notable, but our understanding of the effects are limited. The overall goal of this study is to improve the understanding of non-equilibrium effects on hypersonic turbulent boundary layers. A new code has been developed for direct numerical simulations of spatially developing hypersonic turbulent boundary layers over a flat plate with finite-rate reactions. A fifth-order hybrid weighted essentially non-oscillatory scheme with a low dissipation finite-difference scheme is utilized in order to capture stiff gradients while resolving small motions in turbulent boundary layers. The code has been validated by qualitative and quantitative comparisons of two different simulations of a non-equilibrium flow and a spatially developing turbulent boundary layer. With the validated code, direct numerical simulations of four different hypersonic turbulent boundary layers, perfect gas and non-equilibrium flows of pure oxygen and nitrogen, have been performed. In order to rule out uncertainties in comparisons, the same inlet conditions are imposed for each species, and then mean and turbulence statistics as well as near-wall turbulence structures are compared at a downstream location. Based on those comparisons, it is shown that there is no direct energy exchanges between internal and turbulent kinetic energies due to thermal and chemical non-equilibrium processes in the flow field. Instead, these non-equilibria affect turbulent boundary layers by changing the temperature without changing the main characteristics of near-wall turbulence structures. This change in the temperature induces the changes in the density and viscosity and the mean flow fields are then adjusted to satisfy the conservation laws. The perturbation fields are modified according to
Conference on Boundary and Interior Layers : Computational and Asymptotic Methods
2015-01-01
This volume offers contributions reflecting a selection of the lectures presented at the international conference BAIL 2014, which was held from 15th to 19th September 2014 at the Charles University in Prague, Czech Republic. These are devoted to the theoretical and/or numerical analysis of problems involving boundary and interior layers and methods for solving these problems numerically. The authors are both mathematicians (pure and applied) and engineers, and bring together a large number of interesting ideas. The wide variety of topics treated in the contributions provides an excellent overview of current research into the theory and numerical solution of problems involving boundary and interior layers. .
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 w...... the friction coefficient. Other features related to the bed shear stress, such as transition, the friction factor and phase lead are discussed. The range of the Reynolds number studied is 10.000 - 2.000.000...
Passive and active control of boundary layer transition
Nosenchuck, Daniel Mark
It is well known that laminar-turbulent boundary layer transition is initiated by the formation of Tollmien-Schlichting laminar instability waves. The amplification rates of these waves are strongly dependent on the shape of the boundary layer velocity profile. Consequently, the transition process can be controlled by modifying the velocity profile. This can be accomplished by controlling the pressure gradient (dp/dx), using boundary layer suction, installing surface roughness elements, or by surface heating or cooling. Methods used to modify the transition process through changes in the mean velocity profile are called "passive" in this paper. There exists a large set of experiments and theory on the application of passive methods for boundary layer control. In the present work only surface heating will be addressed.Transition measurements were made on a heated flat plate in water. Results are presented for several plate wall temperature distributions. An increase by a factor of 2.5 in transition Reynolds number was observed for a 5°C isothermal wall overheat. Buoyancy effects on transition were minimal due to the small Richardson and Grashof numbers encountered in the experiments.The amplification of laminar instability waves is comparatively to process, taking place over many boundary layer thicknesses. After the slow amplification of the laminar instability waves, transition occurs by a strong three dimensional dynamic instability. It appears possible to attenuate (or reinforce) the instability waves by introducing amplitude-and phase-controlled perturbations into the laminar boundary layer using feedback control system. This method is called "active" control and forms the larger part of the research reported in this thesis.A combination of sensors, activators and feedback control electronics is required for active control. The sensors used in the experiments are flush-mounted hot film wall shear robes. A new type of activator was developed using thin, flush
Lower Atmospheric Boundary Layer Experiment (LABLE) Final Campaign Report
Energy Technology Data Exchange (ETDEWEB)
Klein, P [University of Oklahoma - School of Meteorology; Bonin, TA; Newman, JF [National Renewable Energy Laboratory; Turner, DD [National Oceanic and Atmospheric Administration; Chilson, P [University of Oklahoma; Blumberg, WG [University of Oklahoma; Mishra, S; Wainwright, CE; Carney, M [University of Oklahoma - School of Meteorology; Jacobsen, EP [University of Oklahoma; Wharton, S [Lawrence Livermore National Laboratory
2015-11-01
The Lower Atmospheric Boundary Layer Experiment (LABLE) included two measurement campaigns conducted at the Atmospheric Radiation Measurement (ARM) Southern Great Plains site in Oklahoma during 2012 and 2013. LABLE was designed as a multi-phase, low-cost collaboration among the University of Oklahoma, the National Severe Storms Laboratory, Lawrence Livermore National Laboratory, and the ARM program. A unique aspect was the role of graduate students in LABLE. They served as principal investigators and took the lead in designing and conducting experiments using different sampling strategies to best resolve boundary-layer phenomena.
Axisymmetric fundamental solutions for a finite layer with impeded boundaries
Institute of Scientific and Technical Information of China (English)
程泽海; 陈云敏; 凌道盛; 唐晓武
2003-01-01
Axisymmetric fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary-value problems involving unit point loading and ring loading in the vertical. The solutions are extended to circular distributed and strip distributed normal load. The computation and analysis of settlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.
Axisymmetric fundamental solutions for a finite layer with impeded boundaries
Institute of Scientific and Technical Information of China (English)
程泽海; 陈云敏; 凌道盛; 唐晓武
2003-01-01
Axisymmetrie fundamental solutions that are applied in the consolidation calculations of a finite clay layer with impeded boundaries were derived. Laplace and Hankel integral transforms were utilized with respect to time and radial coordinates, respectively in the analysis. The derivation of fundamental solutions considers two boundary-value problems involving unit point loading and ring loading in the vertical. The solut-ions are extended to circular distributed and strip distributed normal load. The computation and analysis of set-tlements, vertical total stress and excess pore pressure in the consolidation layer subject to circular loading are presented.
Oscillations of the Boundary Layer and High-frequency QPOs
Directory of Open Access Journals (Sweden)
Blinova A. A.
2014-01-01
Full Text Available We observed persistent high-frequency oscillations of the boundary layer near an accreting, weakly-magnetized star in global 3D MHD simulations. The tilted dipole magnetic field is not strong enough to open a gap between the star and the disk. Instead, it forms a highly-wrapped azimuthal field near the surface of the star which slows down rotation of the disk matter, while a small tilt of the field excites oscillations of the boundary layer with a frequency below the Keplerian frequency. This mechanism may be responsible for the high-frequency oscillations in accreting neutron stars, white dwarfs and classical T Tauri stars.
Directory of Open Access Journals (Sweden)
M. RAHIMI EOSBOEE,
2010-12-01
Full Text Available In this study magnetohydrodynamics (MHD boundary layer flow of an upper-convected Maxwell fluid has been investigated. Similarity transformation has been used to reduce the governing differential equations into an ordinary non-linear differential equation. homotopy perturbation Method (HPM has applied to solve this developed nonlinear equation. In this article firstly, the basic idea of the HPM for solving nonlinear differential equations is briefly ntroduced and then it is employed to derive solution of nonlinear governing equation of MHD boundary layer flow with highly nonlinear term. The obtained results from HPM have been compared with numerical Boundary Value problem Method (BVP to verify the accuracy of the proposed method. The effects of the Hartman number (M and Deborah number (β for various conditions have been shown through graphs.
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.
Acoustic Radiation From a Mach 14 Turbulent Boundary Layer
Zhang, Chao; Duan, Lian; Choudhari, Meelan M.
2016-01-01
Direct numerical simulations (DNS) are used to examine the turbulence statistics and the radiation field generated by a high-speed turbulent boundary layer with a nominal freestream Mach number of 14 and wall temperature of 0:18 times the recovery temperature. The flow conditions fall within the range of nozzle exit conditions of the Arnold Engineering Development Center (AEDC) Hypervelocity Tunnel No. 9 facility. The streamwise domain size is approximately 200 times the boundary-layer thickness at the inlet, with a useful range of Reynolds number corresponding to Re 450 ?? 650. Consistent with previous studies of turbulent boundary layer at high Mach numbers, the weak compressibility hypothesis for turbulent boundary layers remains applicable under this flow condition and the computational results confirm the validity of both the van Driest transformation and Morkovin's scaling. The Reynolds analogy is valid at the surface; the RMS of fluctuations in the surface pressure, wall shear stress, and heat flux is 24%, 53%, and 67% of the surface mean, respectively. The magnitude and dominant frequency of pressure fluctuations are found to vary dramatically within the inner layer (z/delta 0.acoustic. The dominant frequency of the pressure spectrum shows a significant dependence on the freestream Mach number both at the wall and in the free stream.
Effects of Nose Bluntness on Stability of Hypersonic Boundary Layers over Blunt Cone
Kara, K.; Balakumar, P.; Kandil, O. A.
2007-01-01
Receptivity and stability of hypersonic boundary layers are numerically investigated for boundary layer flows over a 5-degree straight cone at a free-stream Mach number of 6.0. To compute the shock and the interaction of shock with the instability waves, we solve the Navier-Stokes equations in axisymmetric coordinates. The governing equations are solved using the 5th-order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. Generation of instability waves from leading edge region and receptivity of boundary layer to slow acoustic waves are investigated. Computations are performed for a cone with nose radii of 0.001, 0.05 and 0.10 inches that give Reynolds numbers based on the nose radii ranging from 650 to 130,000. The linear stability results showed that the bluntness has a strong stabilizing effect on the stability of axisymmetric boundary layers. The transition Reynolds number for a cone with the nose Reynolds number of 65,000 is increased by a factor of 1.82 compared to that for a sharp cone. The receptivity coefficient for a sharp cone is about 4.23 and it is very small, approx.10(exp -3), for large bluntness.
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.
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
Toward Convective Boundary Layer Parameterization: A Scalar Transport Module.
Wyngaard, John C.
1984-06-01
Recent results from large-eddy simulations indicate that the eddy diffusivity for scalar diffusion through the top of a convective boundary layer is different from that for diffusion through the bottom. From this, one can show that the eddy diffusivity is not well behaved in general and can have singularities.As an alternative to the high-resolution approach using eddy-diffusivity closure, we propose an improved integral method for calculating scalar transport in the convective boundary layer. Based on an analytical parameterization for the mean scalar profile, it is computationally as simple as the familiar `mixed-layer' integral method but is physically more realistic, allowing a mean scalar gradient within the mixed layer. We present sample results for the evolution of humility, CO and O3 profiles during the day.
International Nuclear Information System (INIS)
The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t-J model are studied in the framework of the boundary QISM. Diagonal boundary K-matrices are found and four classes of integrable boundary terms are determined. (author)
Chitta, Subhashini; Steinhoff, John
2015-11-01
This paper describes the use of Vorticity Confinement (VC) to efficiently treat complex blunt bodies with thin shed vortex sheets and attached boundary layers. Because these flows involve turbulence in the vortical regions, there is currently no ab initio method to treat them on current or foreseeable computers. In fact, in spite of years of turbulence modeling efforts (such as LES or RANS), serious flaws in aerodynamic design involving vortex shedding may still be left undetected until the expensive prototype or production stage. Our basic premise is that, for a class of real-world problems requiring simulating ensembles of flow conditions for overall accuracy, conventional turbulence models suffer cost constraints. For these reasons, VC is used to rapidly simulate many operating conditions, as is often done in expensive testing programs for flying prototypes, and in realistic simulations. To achieve dramatically lower computational cost, VC treats the entire flow in a uniform, coarse grid with solid surfaces ``immersed'' in the grid so that they can be quickly generated for many configurations with no requirement for adaptive or conforming fine grids. Also, the VC method has the efficiency of panel methods, but the generality and ease of use of Euler equation methods. We would like to thank Dr. Frank Caradonna for his suggestions and support.
Hussain Ahmad; Tariq Javed; Abuzar Ghaffari
2016-01-01
In the present article, radiation effect on mixed convection boundary layer flow of a viscoelastic fluid over a horizontal circular cylinder with constant heat flux has been numerically analyzed. The governing boundary layer equations are transformed to dimensionless nonlinear partial differential equations. The equations are solved numerically by using Keller-box method. The computed results are in excellent agreement with the previous studies. Skin friction coefficient and Nusselt number ar...
THREE POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Mujeeb ur Rehman; Rahmat Ali Khan; Naseer Ahmad Asif
2011-01-01
In this paper,we study existence and uniqueness of solutions to nonlinear three point boundary value problems for fractional differential equation of the type cDδ0+u(t) =f(t,u(t),cDσ0+u(t)),t ∈[0,T],u(0) =αu(η),u(T) =βu(η),where1 ＜δ＜2,0＜σ＜ 1,α,β∈R,η∈(0,T),αη(1-β)+(1-α)(T-βη) ≠0 and cDoδ+,cDσ0+ are the Caputo fractional derivatives.We use Schauder fixed point theorem and contraction mapping principle to obtain existence and uniqueness results.Examples are also included to show the applicability of our results.
RESTRICTED NONLINEAR APPROXIMATION AND SINGULAR SOLUTIONS OF BOUNDARY INTEGRAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Reinhard Hochmuth
2002-01-01
This paper studies several problems, which are potentially relevant for the construction of adaptive numerical schemes. First, biorthogonal spline wavelets on [0,1 ] are chosen as a starting point for characterizations of functions in Besov spaces B , (0,1) with 0＜σ＜∞ and (1+σ)-1＜τ＜∞. Such function spaces are known to be related to nonlinear approximation. Then so called restricted nonlinear approximation procedures with respect to Sobolev space norms are considered. Besides characterization results Jackson type estimates for various tree-type and tresholding algorithms are investigated. Finally known approximation results for geometry induced singularity functions of boundary integeral equations are combined with the characterization results for restricted nonlinear approximation to show Besov space regularity results.
Advanced applications of boundary-integral equation methods
International Nuclear Information System (INIS)
Numerical analysis has become the basic tool for both design and research problems in solid mechanics. The need for accuracy and detail, plus the availablity of the high speed computer has led to the development of many new modeling methods ranging from general purpose structural analysis finite element programs to special purpose research programs. The boundary-integral equation (BIE) method is based on classical mathematical techniques but is finding new life as a basic stress analysis tool for engineering applications. The paper summarizes some advanced elastic applications of fracture mechanics and three-dimensional stress analysis, while referencing some of the much broader developmental effort. Future emphasis is needed to exploit the BIE method in conjunction with other techniques such as the finite element method through the creation of hybrid stress analysis methods. (Auth.)
Directory of Open Access Journals (Sweden)
Ivanović Dečan
2005-01-01
Full Text Available Through the porous contour in perpendicular direction, the fluid of the same properties as incompressible fluid in basic flow, has been injected or ejected with velocity who is a function of the contour longitudinal coordinate and time. The corresponding equations of unsteady boundary layer, by introducing the appropriate variable transformations, momentum and energy equations and two similarity parameters sets, are transformed into generalized form. These parameters are expressing the influence of the outer flow velocity, the injection or ejection velocity and the flow history in boundary layer, on the boundary layer characteristics. Obtained generalized solutions are used to calculate the distributions of velocity, and shear stress in laminar-turbulent transition of unsteady incompressible boundary layer on different porous contours: circular cylinder, thin elliptical cylinder and aerofoil, whose centers velocities changes in time as a degree functions. The ejection of fluid postpones the boundary layer separation, i.e. laminar-turbulent transition, and vice versa the injection of fluid favors the separation. Boundary layer characteristics are found directly, no further numerical integration of momentum equation.
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
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 growth of turbulent regions in laminar boundary layers
Gad-El-hak, M.; Riley, J. J.; Blackwelder, R. F.
1981-01-01
Turbulent spots evolving in a laminar boundary layer on a nominally zero pressure gradient flat plate are investigated. The plate is towed through an 18 m water channel, using a carriage that rides on a continuously replenished oil film giving a vibrationless tow. Turbulent spots are initiated using a solenoid valve that ejects a small amount of fluid through a minute hole on the working surface. A novel visualization technique that utilizes fluorescent dye excited by a sheet of laser light is employed. Some new aspects of the growth and entrainment of turbulent spots, especially with regard to lateral growth, are inferred from the present experiments. To supplement the information on lateral spreading, a turbulent wedge created by placing a roughness element in the laminar boundary layer is also studied both visually and with probe measurements. The present results show that, in addition to entrainment, another mechanism is needed to explain the lateral growth characteristics of a turbulent region in a laminar boundary layer. This mechanism, termed growth by destabilization, appears to be a result of the turbulence destabilizing the unstable laminar boundary layer in its vicinity. To further understand the growth mechanisms, the turbulence in the spot is modulated using drag-reducing additives and salinity stratification.
Vortex Generator Induced Flow in a High Re Boundary Layer
DEFF Research Database (Denmark)
Velte, Clara Marika; Braud, C.; Coudert, S.;
2014-01-01
Stereoscopic Particle Image Velocimetry measurements have been conducted in cross-planes behind three different geometries of Vortex Generators (VGs) in a high Reynolds number boundary layer. The VGs have been mounted in a cascade producing counter-rotating vortices and the downstream flow...
Vortex Generator Induced Flow in a High Re Boundary Layer
DEFF Research Database (Denmark)
Velte, Clara Marika; Braud, C.; Coudert, S.;
2012-01-01
Stereoscopic Particle Image Velocimetry measurements have been conducted in cross-planes behind three different geometries of Vortex Generators (VGs) in a high Reynolds number boundary layer. The VGs have been mounted in a cascade producing counter-rotating vortices and the downstream flow...
CISM Course on Recent Advances in Boundary Layer Theory
1998-01-01
Recent advances in boundary-layer theory have shown how modern analytical and computational techniques can and should be combined to deepen the understanding of high Reynolds number flows and to design effective calculation strategies. This is the unifying theme of the present volume which addresses laminar as well as turbulent flows.
A parametric study of adverse pressure gradient turbulent boundary layers
International Nuclear Information System (INIS)
There are many open questions regarding the behaviour of turbulent boundary layers subjected to pressure gradients and this is confounded by the large parameter space that may affect these flows. While there have been many valuable investigations conducted within this parameter space, there are still insufficient data to attempt to reduce this parameter space. Here, we consider a parametric study of adverse pressure gradient turbulent boundary layers where we restrict our attention to the pressure gradient parameter, β, the Reynolds number and the acceleration parameter, K. The statistics analyzed are limited to the streamwise fluctuating velocity. The data show that the mean velocity profile in strong pressure gradient boundary layers does not conform to the classical logarithmic law. Moreover, there appears to be no measurable logarithmic region in these cases. It is also found that the large-scale motions scaling with outer variables are energised by the pressure gradient. These increasingly strong large-scale motions are found to be the dominant contributor to the increase in turbulence intensity (scaled with friction velocity) with increasing pressure gradient across the boundary layer.
DNS of stratified spatially-developing turbulent thermal boundary layers
Araya, Guillermo; Castillo, Luciano; Jansen, Kenneth
2012-11-01
Direct numerical simulations (DNS) of spatially-developing turbulent thermal boundary layers under stratification are performed. It is well known that the transport phenomena of the flow is significantly affected by buoyancy, particularly in urban environments where stable and unstable atmospheric boundary layers are encountered. In the present investigation, the Dynamic Multi-scale approach by Araya et al. (JFM, 670, 2011) for turbulent inflow generation is extended to thermally stratified boundary layers. Furthermore, the proposed Dynamic Multi-scale approach is based on the original rescaling-recycling method by Lund et al. (1998). The two major improvements are: (i) the utilization of two different scaling laws in the inner and outer parts of the boundary layer to better absorb external conditions such as inlet Reynolds numbers, streamwise pressure gradients, buoyancy effects, etc., (ii) the implementation of a Dynamic approach to compute scaling parameters from the flow solution without the need of empirical correlations as in Lund et al. (1998). Numerical results are shown for ZPG flows at high momentum thickness Reynolds numbers (~ 3,000) and a comparison with experimental data is also carried out.
Boundary-Layer Wind Structure in a Landfalling Tropical Cyclone
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this study, a slab boundary layer model with a constant depth is used to analyze the boundary-layer wind structure in a landfalling tropical cyclone. Asymmetry is found in both the tangential and radial components of horizontal wind in the tropical cyclone boundary layer at landfall. For a steady tropical cyclone on a straight coastline at landfall, the magnitude of the radial component is greater in the offshoreflow side and the tangential component is greater over the sea, slightly offshore, therefore the greater total wind speed occurs in the offshore-flow side over the sea. The budget analysis suggests that: (1) a greater surface friction over land produces a greater inflow and the nonlinear effect advects the maximum inflow downstream, and (2) a smaller surface friction over the sea makes the decrease of the tangential wind component less than that over land. Moreover, the boundary layer wind structures in a tropical cyclone are related to the locations of the tropical cyclone relative to the coastline due to the different surface frictions. During tropical cyclone landfall, the impact of rough terrain on the cyclone increases, so the magnitude of the radial component of wind speed increases in the offshore-flow side and the tangential component outside the radius of maximum wind speed decreases gradually.
Drizzle and Turbulence Variability in Stratocumulus-topped Boundary Layers
Kollias, P.; Luke, E. P.; Szyrmer, W.
2015-12-01
Marine stratocumulus clouds frequently produce light precipitation in the form of drizzle. The drizzle rate at the cloud base (RCB) dictates the impact of drizzle on the boundary layer turbulence and cloud organization. Here, synergistic observations from the US Department of Energy Atmospheric Radiation Measurement (ARM) program Eastern North Atlantic (ENA) site located on Graciosa Island in the Azores are used to investigate the relationship between RCB, and boundary layer turbulence and dynamics. The ARM ENA site is a heavily instrumented ground-based facility that offers new measurement capabilities in stratocumulus-topped boundary layers (STBL). The RCB is retrieved using a radar-lidar algorithm. The STBL turbulent structure is characterized using the Doppler lidar and radar observations. The profiling radar/lidar/radiometer observations are used to describe the cloud fraction and morphology. Finally, surface-based aerosol number concentration measurements are used to investigate the connection between the boundary layer turbulence, cloud morphology and aerosol loading. Preliminary correlative relationships between the aforementioned variables will be shown.
Passive Control of Supersonic Rectangular Jets through Boundary Layer Swirl
Han, Sang Yeop; Taghavi, Ray R.; Farokhi, Saeed
2013-06-01
Mixing characteristics of under-expanded supersonic jets emerging from plane and notched rectangular nozzles are computationally studied using nozzle exit boundary layer swirl as a mean of passive flow control. The coupling of the rectangular jet instability modes, such as flapping, and the swirl is investigated. A three-dimensional unsteady Reynolds-Averaged Navier-Stokes (RANS) code with shock adaptive grids is utilized. For plane rectangular nozzle with boundary layer swirl, the flapping and spanwise oscillations are captured in the jet's small and large dimensions at twice the frequencies of the nozzles without swirl. A symmetrical oscillatory mode is also observed in the jet with double the frequency of spanwise oscillation mode. For the notched rectangular nozzle with boundary layer swirl, the flapping oscillation in the small jet dimension and the spanwise oscillation in the large jet dimension are observed at the same frequency as those without boundary layer swirl. The mass flow rates in jets at 11 and 8 nozzle heights downstream of the nozzles increased by nearly 25% and 41% for the plane and notched rectangular nozzles respectively, due to swirl. The axial gross thrust penalty due to induced swirl was 5.1% for the plane and 4.9% for the notched rectangular nozzle.
Hair receptor sensitivity to changes in laminar boundary layer shape
Energy Technology Data Exchange (ETDEWEB)
Dickinson, B T, E-mail: btdickinson@lifetime.oregonstate.ed [Air Force Research Laboratory, Munitions Directorate, Eglin Air Force Base, FL 32542 (United States)
2010-03-15
Biologists have shown that bat wings contain distributed arrays of flow-sensitive hair receptors. The hair receptors are hypothesized to feedback information on airflows over the bat wing for enhanced stability or maneuverability during flight. Here, we study the geometric specialization of hair-like structures for the detection of changes in boundary layer velocity profiles (shapes). A quasi-steady model that relates the flow velocity profile incident on the longitudinal axis of a hair to the resultant moment and shear force at the hair base is developed. The hair length relative to the boundary layer momentum thickness that maximizes the resultant moment and shear-force sensitivity to changes in boundary layer shape is determined. The sensitivity of the resultant moment and shear force is shown to be highly dependent on hair length. Hairs that linearly taper to a point are shown to provide greater output sensitivity than hairs of uniform cross-section. On an order of magnitude basis, the computed optimal hair lengths are in agreement with the range of hair receptor lengths measured on individual bat species. These results support the hypothesis that bats use hair receptors for detecting changes in boundary layer shape and provide geometric guidelines for artificial hair sensor design and application.
Hair receptor sensitivity to changes in laminar boundary layer shape.
Dickinson, B T
2010-03-01
Biologists have shown that bat wings contain distributed arrays of flow-sensitive hair receptors. The hair receptors are hypothesized to feedback information on airflows over the bat wing for enhanced stability or maneuverability during flight. Here, we study the geometric specialization of hair-like structures for the detection of changes in boundary layer velocity profiles (shapes). A quasi-steady model that relates the flow velocity profile incident on the longitudinal axis of a hair to the resultant moment and shear force at the hair base is developed. The hair length relative to the boundary layer momentum thickness that maximizes the resultant moment and shear-force sensitivity to changes in boundary layer shape is determined. The sensitivity of the resultant moment and shear force is shown to be highly dependent on hair length. Hairs that linearly taper to a point are shown to provide greater output sensitivity than hairs of uniform cross-section. On an order of magnitude basis, the computed optimal hair lengths are in agreement with the range of hair receptor lengths measured on individual bat species. These results support the hypothesis that bats use hair receptors for detecting changes in boundary layer shape and provide geometric guidelines for artificial hair sensor design and application.
On the Effects of Surface Roughness on Boundary Layer Transition
Choudhari, Meelan M.; Li, Fei; Chang, Chau-Lyan; Edwards, Jack
2009-01-01
Surface roughness can influence laminar-turbulent transition in many different ways. This paper outlines selected analyses performed at the NASA Langley Research Center, ranging in speed from subsonic to hypersonic Mach numbers and highlighting the beneficial as well as adverse roles of the surface roughness in technological applications. The first theme pertains to boundary-layer tripping on the forebody of a hypersonic airbreathing configuration via a spanwise periodic array of trip elements, with the goal of understanding the physical mechanisms underlying roughness-induced transition in a high-speed boundary layer. The effect of an isolated, finite amplitude roughness element on a supersonic boundary layer is considered next. The other set of flow configurations examined herein corresponds to roughness based laminar flow control in subsonic and supersonic swept wing boundary layers. A common theme to all of the above configurations is the need to apply higher fidelity, physics based techniques to develop reliable predictions of roughness effects on laminar-turbulent transition.
Two Phases of Coherent Structure Motions in Turbulent Boundary Layer
Institute of Scientific and Technical Information of China (English)
LIU Jian-Hua; JIANG Nan
2007-01-01
Two phases of coherent structure motion are acquired after obtaining conditional phase-averaged waveforms for longitudinal velocity of coherent structures in turbulent boundary layer based on Harr wavelet transfer. The correspondences of the two phases to the two processes (i.e. ejection and sweep) during a burst are determined.
STUDIES ON RETRIEVAL OF THE TURBULIVITY OF ATMOSPHERIC BOUNDARY LAYER
Institute of Scientific and Technical Information of China (English)
WANG Ting-fang; HUANG Si-xun; XIANG Jie
2006-01-01
The variational adjoint method was applied to retrieving the turbulivity of the atmospheric Ekman boundary layer along with the regularization principle. The validity of the method was verified by using the idealized data, and then the turbulivity profile and the geostrophic wind profile were retrieved through it for real observational wind filed data.
Convective boundary layers driven by nonstationary surface heat fluxes
Van Driel, R.; Jonker, H.J.J.
2011-01-01
In this study the response of dry convective boundary layers to nonstationary surface heat fluxes is systematically investigated. This is relevant not only during sunset and sunrise but also, for example, when clouds modulate incoming solar radiation. Because the time scale of the associated change
Flow visualization of swept wing boundary layer transition
Serpieri, J.; Kotsonis, M.
2015-01-01
In this work the flow visualization of the transition pattern occurring on a swept wing in a subsonic flow is presented. This is done by means of fluorescent oil flow technique and boundary layer hot-wire scans. The experiment was performed at Reynolds number of 2:15 . 106 and at angle of attack of
Boundary Layer Flows in Porous Media with Lateral Mass Flux
DEFF Research Database (Denmark)
Nemati, H; H, Bararnia; Noori, F;
2015-01-01
Solutions for free convection boundary layers on a heated vertical plate with lateral mass flux embedded in a saturated porous medium are presented using the Homotopy Analysis Method and Shooting Numerical Method. Homotopy Analysis Method yields an analytic solution in the form of a rapidly...
Spatially developing turbulent boundary layer on a flat plate
Lee, J H; Hutchins, N; Monty, J P
2012-01-01
This fluid dynamics video submitted to the Gallery of Fluid motion shows a turbulent boundary layer developing under a 5 metre-long flat plate towed through water. A stationary imaging system provides a unique view of the developing boundary layer as it would form over the hull of a ship or fuselage of an aircraft. The towed plate permits visualisation of the zero-pressure-gradient turbulent boundary layer as it develops from the trip to a high Reynolds number state ($Re_\\tau \\approx 3000$). An evolving large-scale coherent structure will appear almost stationary in this frame of reference. The visualisations provide an unique view of the evolution of fundamental processes in the boundary layer (such as interfacial bulging, entrainment, vortical motions, etc.). In the more traditional laboratory frame of reference, in which fluid passes over a stationary body, it is difficult to observe the full evolution and lifetime of turbulent coherent structures. An equivalent experiment in a wind/water-tunnel would requ...
A Fast Spectral Galerkin Method for Hypersingular Boundary Integral Equations in Potential Theory
Energy Technology Data Exchange (ETDEWEB)
Nintcheu Fata, Sylvain [ORNL; Gray, Leonard J [ORNL
2009-01-01
This research is focused on the development of a fast spectral method to accelerate the solution of three-dimensional hypersingular boundary integral equations of potential theory. Based on a Galerkin approximation, the Fast Fourier Transform and local interpolation operators, the proposed method is a generalization of the Precorrected-FFT technique to deal with double-layer potential kernels, hypersingular kernels and higher-order basis functions. Numerical examples utilizing piecewise linear shape functions are included to illustrate the performance of the method.
Energy Technology Data Exchange (ETDEWEB)
Tokuda, Shinji [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Watanabe, Tomoko
1996-08-01
The matching problem in resistive MagnetoHydroDynamic stability analysis by the asymptotic matching method has been reformulated as an initial-boundary value problem for the inner-layer equations describing the plasma dynamics in the thin layer around a rational surface. The third boundary conditions at boundaries of a finite interval are imposed on the inner layer equations in the formulation instead of asymptotic conditions at infinities. The finite difference method for this problem has been applied to model equations whose solutions are known in a closed form. It has been shown that the initial value problem and the associated eigenvalue problem for the model equations can be solved by the finite difference method with numerical stability. The formulation presented here enables the asymptotic matching method to be a practical method for the resistive MHD stability analysis. (author)
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.
Series Solution for Unsteady Boundary-Layer Flows Due to Impulsively Stretching Plate
Institute of Scientific and Technical Information of China (English)
Seripah Awang Kechil; Ishak Hashim
2007-01-01
@@ The third-order nonlinear partial differential equation modelling the unsteady boundary-layer flows caused by an impulsively stretching flat plate is solved by using the Adomian decomposition method (ADM). The ADM yields analytic solution in the form of a rapidly convergent infinite series with easily computable terms. The series solution using the ADM for the unsteady flows is presented for the first time.
Weyburne, David
2015-01-01
The use of the defect profile instead of the experimentally observed velocity profile for the search for similarity parameters has become firmly imbedded in the turbulent boundary layer literature. However, a search of the literature reveals that there are no theoretical reasons for this defect profile preference over the more traditional velocity profile. In the report herein, we use the flow governing equation approach to develop similarity criteria for the two profiles. Results show that t...
A turbulence model for steady and unsteady boundary layers in strong pressure gradients
Hytopoulos, Evangelos
1994-01-01
A new turbulence model designed for two-dimensional, steady and unsteady boundary layers in strong adverse pressure gradients is described. The model is developed in a rational way based on an understanding of the flow physics obtained from recent experimental observations. The turbulent shear stress is given by a mixing length model, but the variation of the mixing length in the outer region is not constant; it varies according to an integral form of the turbulence kinetic-energy equation. T...
On the Study of Viscoelastic Walters' B Fluid in Boundary Layer Flows
Directory of Open Access Journals (Sweden)
Seyed Ali Madani Tonekaboni
2012-01-01
Full Text Available Viscoelastic Walters' B fluid flows for three problems, stagnation-point flow, Blasius flow, and Sakiadis flow, have been investigated. In each problem, Cauchy equations are changed to a nondimensional differential equations using stream functions and with assumption of boundary layer flow. The fourth-order predictor-corrector finite-difference method for solving these nonlinear differential equations has been employed. The results that have been obtained using this method are compared with the results of the last studies, and it is clarified that this method is more accurate. It is also shown that the results of last study about Sakiadis flow of Walter's B fluid are not true. In addition, the effects of order of discretization in the boundaries are investigated. Moreover, it has been discussed about the valid region of Weissenberg numbers for the second-order approximation of viscoelastic fluids in each case of study.
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.
New Theories on Boundary Layer Transition and Turbulence Formation
Directory of Open Access Journals (Sweden)
Chaoqun Liu
2012-01-01
Full Text Available This paper is a short review of our recent DNS work on physics of late boundary layer transition and turbulence. Based on our DNS observation, we propose a new theory on boundary layer transition, which has five steps, that is, receptivity, linear instability, large vortex structure formation, small length scale generation, loss of symmetry and randomization to turbulence. For turbulence generation and sustenance, the classical theory, described with Richardson's energy cascade and Kolmogorov length scale, is not observed by our DNS. We proposed a new theory on turbulence generation that all small length scales are generated by “shear layer instability” through multiple level ejections and sweeps and consequent multiple level positive and negative spikes, but not by “vortex breakdown.” We believe “shear layer instability” is the “mother of turbulence.” The energy transferring from large vortices to small vortices is carried out by multiple level sweeps, but does not follow Kolmogorov's theory that large vortices pass energy to small ones through vortex stretch and breakdown. The loss of symmetry starts from the second level ring cycle in the middle of the flow field and spreads to the bottom of the boundary layer and then the whole flow field.
Transparent boundary conditions for the wave equation in one dimension and for a Dirac-like equation
Directory of Open Access Journals (Sweden)
M. Pilar Velasco
2015-11-01
Full Text Available We present a method to achieve transparent boundary conditions for the one-dimensional wave equation, and show its numerical implementation using a finite-difference method. We also present an alternative method for building the same transparent boundary conditions using a Dirac-like equation and a Spinor-like formalism. Finally, we extend our method to the three-dimensional wave equation with radial symmetry.
Minimum Wind Dynamic Soaring Trajectories under Boundary Layer Thickness Limits
Bousquet, Gabriel; Triantafyllou, Michael; Slotine, Jean-Jacques
2015-11-01
Dynamic soaring is the flight technique where a glider, either avian or manmade, extracts its propulsive energy from the non-uniformity of horizontal winds. Albatrosses have been recorded to fly an impressive 5000 km/week at no energy cost of their own. In the sharp boundary layer limit, we show that the popular image, where the glider travels in a succession of half turns, is suboptimal for travel speed, airspeed, and soaring ability. Instead, we show that the strategy that maximizes the three criteria simultaneously is a succession of infinitely small arc-circles connecting transitions between the calm and windy layers. The model is consistent with the recordings of albatross flight patterns. This lowers the required wind speed for dynamic soaring by over 50% compared to previous beliefs. In the thick boundary layer limit, energetic considerations allow us to predict a minimum wind gradient necessary for sustained soaring consistent with numerical models.
Cengizci, Süleyman; Atay, Mehmet Tarık; Eryılmaz, Aytekin
2016-01-01
This paper is concerned with two-point boundary value problems for singularly perturbed nonlinear ordinary differential equations. The case when the solution only has one boundary layer is examined. An efficient method so called Successive Complementary Expansion Method (SCEM) is used to obtain uniformly valid approximations to this kind of solutions. Four test problems are considered to check the efficiency and accuracy of the proposed method. The numerical results are found in good agreement with exact and existing solutions in literature. The results confirm that SCEM has a superiority over other existing methods in terms of easy-applicability and effectiveness. PMID:27006888
Scattering for wave equations with dissipative terms in layered media
Directory of Open Access Journals (Sweden)
Mitsuteru Kadowaki
2011-05-01
Full Text Available In this article, we show the existence of scattering solutions to wave equations with dissipative terms in layered media. To analyze the wave propagation in layered media, it is necessary to handle singular points called thresholds in the spectrum. Our main tools are Kato's smooth perturbation theory and some approximate operators.
A Multi-Layer Extension of the Stochastic Heat Equation
O'Connell, Neil; Warren, Jon
2016-01-01
Motivated by recent developments on solvable directed polymer models, we define a `multi-layer' extension of the stochastic heat equation involving non-intersecting Brownian motions. By developing a connection with Darboux transformations and the two-dimensional Toda equations, we conjecture a Markovian evolution in time for this multi-layer process. As a first step in this direction, we establish an analogue of the Karlin-McGregor formula for the stochastic heat equation and use it to prove a special case of this conjecture.
The height of the atmospheric boundary layer during unstable conditions
Energy Technology Data Exchange (ETDEWEB)
Gryning, S.E.
2005-11-01
The height of the convective atmospheric boundary layer, also called the mixed-layer, is one of the fundamental parameters that characterise the structure of the atmosphere near the ground. It has many theoretical and practical applications such as the prediction of air pollution concentrations, surface temperature and the scaling of turbulence. However, as pointed out by Builtjes (2001) in a review paper on Major Twentieth Century Milestones in Air Pollution Modelling and Its Application, the weakest point in meteorology data is still the determination of the height of the mixed-layer, the so-called mixing height. A simple applied model for the height of the mixed-layer over homogeneous terrain is suggested in chapter 2. It is based on a parameterised budget for the turbulent kinetic energy. In the model basically three terms - the spin-up term and the production of mechanical and convective turbulent kinetic energy - control the growth of the mixed layer. The interplay between the three terms is related to the meteorological conditions and the height of the mixed layer. A stable layer, the so-called entrainment zone, which is confined between the mixed layer and the free air above, caps the mixed layer. A parameterisation of the depth of the entrainment zone is also suggested, and used to devise a combined model for the height of the mixed layer and the entrainment zone. Another important aspect of the mixed layer development exists in coastal areas where an internal boundary layer forms downwind from the coastline. A model for the growth of the internal boundary layer is developed in analogy with the model for mixed layer development over homogeneous terrain. The strength of this model is that it can operate on a very fine spatial resolution with minor computer resources. Chapter 3 deals with the validation of the models. It is based in parts on data from the literature, and on own measurements. For the validation of the formation of the internal boundary layer
Shear Capacity as Prognostic of Nocturnal Boundary Layer Regimes
van Hooijdonk, Ivo; Donda, Judith; Bosveld, Fred; Moene, Arnold; Clercx, Herman; van de Wiel, Bas
2015-04-01
After sunset the surface temperature can drop rapidly in some nights and may lead to ground frost. This sudden drop is closely related to the occurrence of fundamentally different behaviour of turbulence in the nocturnal boundary layer. Recent theoretical findings predict the appearance of two different regimes: the continuously turbulent (weakly stable) boundary layer and the relatively 'quiet' (very stable) boundary layer. Field observations from a large number of nights (approx. 4500 in total) are analysed using an ensemble averaging technique. The observations support the existence of these two fundamentally different regimes: weakly stable (turbulent) nights rapidly reach a steady state (within 2-3 hours). In contrast, very stable nights reach a steady state much later after a transition period (2-6 hours). During this period turbulence is weak and non-stationary. To characterise the regime a new parameter is introduced: the Shear Capacity. This parameter compares the actual shear after sunset with the minimum shear needed to sustain continuous turbulence. In turn, the minimum shear is dictated by the heat flux demand at the surface (net radiative cooling), so that the Shear Capacity combines flow information with knowledge on the boundary condition. It is shown that the Shear Capacity enables prediction of the flow regimes. The prognostic strength of this non-dimensional parameter appears to outperform the traditional ones like z/L and Ri as regime indicator.
Noncontinuous data boundary value problems for Schr(o)dinger equation in Lipschitz domains
Institute of Scientific and Technical Information of China (English)
TAO Xiangxing
2006-01-01
The noncontinuous data boundary value problems for Schr(o)dinger equations in Lipschitz domains and its progress are pointed out in this paper.Particularly,the Lp boundary value problems with p＞1,and Hp boundary value problems with p＜1 have been studied.Some open problems about the Besov-Sobolev and Orlicz boundary value problems are given.
Random Boundary Simulation of Pumping Groundwater on Two-layer Soft Soil Structure with Porous Media
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Based on random theory,fluid dynamics,porous media and soil mechanics,the porosity and random characteristic of the two-layer soft soil in Wuhan region were studied in this paper.The random seepage coefficient on the two-layer soft soil was analyzed,and the seepage model and its random distribution function were given.The groundwater flow differential equations related to the two layer soft soil structure were also established.The evaluation procedure of effect boundary on the pumping water in deep foundation pit was put forward.Moreover,with an engineering example,the probability distribution on random boundary prediction for pumping water of foundation pit was computed.
Institute of Scientific and Technical Information of China (English)
Jia-qi Mo; Wan-tao Lin
2006-01-01
A class of nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, the asymptotic behavior of solution for the initial boundary value problems is studied using the theory of differential inequalities.
Institute of Scientific and Technical Information of China (English)
OuyangCheng; MoJiaqi
2005-01-01
The nonlinear singularly perturbed problems for reaction diffusion equations with boundary perturbation are considered. Under suitable conditions, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems is studied.
LIMIT BEHAVIOUR OF SOLUTIONS TO EQUIVALUED SURFACE BOUNDARY VALUE PROBLEM FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
LI Fengquan
2002-01-01
In this paper, we discuss the limit behaviour of solutions to equivalued surface boundary value problem for parabolic equations when the equivalued surface boundary shrinks to a point and the space dimension of the domain is two or more.
A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations
Alikhanov, A A
2011-01-01
We consider boundary value problems of the first and third kind for the diffusionwave equation. By using the method of energy inequalities, we find a priori estimates for the solutions of these boundary value problems.
An initial-boundary value problem for three-dimensional Zakharov-Kuznetsov equation
Faminskii, Andrei V.
2016-02-01
An initial-boundary value problem with homogeneous Dirichlet boundary conditions for three-dimensional Zakharov-Kuznetsov equation is considered. Results on global existence, uniqueness and large-time decay of weak solutions in certain weighted spaces are established.
SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT
Institute of Scientific and Technical Information of China (English)
MoJiaqi
2002-01-01
The singularly perturbed elliptic equation boundary value problem with a curve of turning point is considered. Using the method of multiple scales and the comparison theorem,the asymptotic behavior of solution for the boundary value problem is studied.
RESEARCH ON THE FLOW STABILITY IN A CYLINDRICAL PARTICLE TWO-PHASE BOUNDARY LAYER
Institute of Scientific and Technical Information of China (English)
林建忠; 聂德明
2003-01-01
Based on the momentum and constitutive equations, the modified Orr-Sommerfeld equation describing the flow stability in a cylindrical particle two-phase flow was derived. For a cylindrical particle two-phase boundary layer, the neutral stability curves and critical Reynolds number were given with numerical simulation. The results show that the cylindrical particles have a suppression effect on the flow instability, the larger the particle volume fraction and the particle aspect-ratio are, the more obvious the suppression effect is.
Edge Plasma Boundary Layer Generated By Kink Modes in Tokamaks
International Nuclear Information System (INIS)
This paper describes the structure of the electric current generated by external kink modes at the plasma edge using the ideally conducting plasma model. It is found that the edge current layer is created by both wall touching and free boundary kink modes. Near marginal stability, the total edge current has a universal expression as a result of partial compensation of the (delta)-functional surface current by the bulk current at the edge. The resolution of an apparent paradox with the pressure balance across the plasma boundary in the presence of the surface currents is provided.
Turbulence spectra of the FIRE stratocumulus-topped boundary layers
Young, G. S.; Nucciarone, J. J.; Albrecht, Bruce A.
1990-01-01
There are at least four physical phenomena which contribute to the FIRE boundary layer turbulence spectra: boundary layer spanning eddies resulting from buoyant and mechanical production of turbulent kinetic energy (the microscale subrange); inertial subrange turbulence which cascades this energy to smaller scales; quasi-two dimensional mesoscale variations; and gravity waves. The relative contributions of these four phenomena to the spectra depend on the altitude of observation and variable involved (vertical velocity, temperature and moisture spectra are discussed). The physical origins of these variations in relative contribution are discussed. As expected from the theory (Kaimal et al., 1976), mixed layer scaling of the spectra (i.e., nondimensionalizing wavelength by Z(sub i) and spectral density by Z(sub i) and the dissipation rates) is successful for the microscale subrange and inertial subrange but not for the mesoscale subrange. The most striking feature of the normalized vertical velocity spectra is the lack of any significant mesoscale contribution. The spectral peak results from buoyant and mechanical production on scales similar to the boundary layer depth. The decrease in spectral density at larger scales results from the suppression of vertical velocity perturbations with large horizontal scales by the shallowness of the atmosphere. The spectral density also decreases towards smaller scales following the well known inertial subrange slope. There is a significant variation in the shape of the normalized spectra with height.
The nonlinear evolution of inviscid Goertler vortices in three-dimensional boundary layers
Blackaby, Nicholas; Dando, Andrew; Hall, Philip
1995-09-01
The nonlinear development of inviscid Gortler vortices in a three-dimensional boundary layer is considered. We do not follow the classical approach of weakly nonlinear stability problems and consider a mode which has just become unstable. Instead we extend the method of Blackaby, Dando, and Hall (1992), which considered the closely related nonlinear development of disturbances in stratified shear flows. The Gortler modes we consider are initially fast growing and we assume, following others, that boundary-layer spreading results in them evolving in a linear fashion until they reach a stage where their amplitudes are large enough and their growth rates have diminished sufficiently so that amplitude equations can be derived using weakly nonlinear and non-equilibrium critical-layer theories. From the work of Blackaby, Dando and Hall (1993) is apparent, given the range of parameters for the Gortler problem, that there are three possible nonlinear integro-differential evolution equations for the disturbance amplitude. These are a cubic due to viscous effects, a cubic which corresponds to the novel mechanism investigated in this previous paper, and a quintic. In this paper we shall concentrate on the two cubic integro-differential equations and in particular, on the one due to the novel mechanism as this will be the first to affect a disturbance. It is found that the consideration of a spatial evolution problem as opposed to temporal (as was considered in Blackaby, Dando, and Hall, 1992) causes a number of significant changes to the evolution equations.
Monotone iterative technique for fractional differential equations with periodic boundary conditions
Directory of Open Access Journals (Sweden)
J. D. Ramírez
2009-01-01
Full Text Available In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.
Monotone iterative technique for fractional differential equations with periodic boundary conditions
J. D. Ramírez; A. S. Vatsala
2009-01-01
In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary con...
Quano, Y H
2001-01-01
The $A^{(1)}_{n-1}$-face model with boundary reflection is considered on the basis of the boundary CTM bootstrap. We construct the fused boundary Boltzmann weights to determine the normalization factor. We derive difference equations of the quantum Knizhnik-Zamolodchikov type for correlation functions of the present model. The simplest difference equations are solved the in the case of the free boundary condition.
Self-similar analysis of fluid flow and heat-mass transfer of nanofluids in boundary layer
Avramenko, A. A.; Blinov, D. G.; Shevchuk, I. V.
2011-08-01
Processes of heat, momentum, and concentration transport in a boundary layer of a nanofluid near a flat wall were studied. The study was performed by means of numerical analysis of boundary layer equations in a self-similar form. Self-similar forms of these equations were obtained based on symmetry properties (Lie groups). In doing so, dependence of physical properties (viscosity, thermal conductivity, and diffusion coefficient) on concentration of nanofluids and temperature were taken into account. Effects of concentration of the nano-particles on velocity and temperature profiles, as well as on the relative Nusselt numbers and skin-friction coefficients, were elucidated.
Directory of Open Access Journals (Sweden)
Khairy Zaimi
2015-01-01
Full Text Available This paper concerns with the boundary layer flow and heat transfer over a permeable stretching/shrinking sheet in a viscous fluid, with the bottom surface of the plate is heated by convection from a hot fluid. The partial differential equations governing the flow and heat transfer are converted into ordinary differential equations using a similarity transformation, before being solved numerically. The effects of the suction, convection and stretching/shrinking parameters on the skin friction coefficient and the local Nusselt number are examined and graphically illustrated. Dual solutions are found to exist for a certain range of the suction and stretching/shrinking parameters. The numerical results also show that suction widens the range of the stretching/shrinking parameter for which the solution exists.
A Thermal Plume Model for the Martian Convective Boundary Layer
Colaïtis, Arnaud; Hourdin, Frédéric; Rio, Catherine; Forget, François; Millour, Ehouarn
2013-01-01
The Martian Planetary Boundary Layer [PBL] is a crucial component of the Martian climate system. Global Climate Models [GCMs] and Mesoscale Models [MMs] lack the resolution to predict PBL mixing which is therefore parameterized. Here we propose to adapt the "thermal plume" model, recently developed for Earth climate modeling, to Martian GCMs, MMs, and single-column models. The aim of this physically-based parameterization is to represent the effect of organized turbulent structures (updrafts and downdrafts) on the daytime PBL transport, as it is resolved in Large-Eddy Simulations [LESs]. We find that the terrestrial thermal plume model needs to be modified to satisfyingly account for deep turbulent plumes found in the Martian convective PBL. Our Martian thermal plume model qualitatively and quantitatively reproduces the thermal structure of the daytime PBL on Mars: superadiabatic near-surface layer, mixing layer, and overshoot region at PBL top. This model is coupled to surface layer parameterizations taking ...
Tatsii, R. M.; Pazen, O. Yu.
2016-03-01
A constructive scheme for the construction of a solution of a mixed problem for the heat conduction equation with piecewise-continuous coefficients coordinate-dependent in the final interval is suggested and validated in the present work. The boundary conditions are assumed to be most general. The scheme is based on: the reduction method, the concept of quasi-derivatives, the currently accepted theory of the systems of linear differential equations, the Fourier method, and the modified method of eigenfunctions. The method based on this scheme should be related to direct exact methods of solving mixed problems that do not employ the procedures of constructing Green's functions or integral transformations. Here the theorem of eigenfunction expansion is adapted for the case of coefficients that have discontinuity points of the 1st kind. The results obtained can be used, for example, in investigating the process of heat transfer in a multilayer slab under conditions of ideal thermal contact between the layers. A particular case of piecewise-continuous coefficients is considered. A numerical example of calculation of a temperature field in a real four-layer building slab under boundary conditions of the 3rd kind (conditions of convective heat transfer) that model the phenomenon of fire near one of the external surfaces is given.
The effect of a shear boundary layer on the stability of a capillary jet
Ganan-Calvo, Alfonso; Montanero, Jose M.; Herrada, Miguel A.
2014-11-01
The generic stabilization effect of a shear boundary layer over the free surface of a capillary jet is here studied from analytical (asymptotic), numerical and experimental approaches. In first place, we show the consistency of the proposed asymptotic analysis by a linear stability (numerical) analysis of the Navier-Stokes equations for a finite boundary layer thickness. We show how the convective-to-absolute instability transition departs drastically from the flat velocity profile case as the axial coordinate becomes closer to the origin of the boundary layer development. For large enough axial distances from that origin, Rayleigh's dispersion relation is recovered. A collection of experimental observations is analyzed from the perspective provided by these results. We propose a systematic framework to the dynamics of capillary jets issued from a nozzle, either by direct injection into a quiescent atmosphere or in a co-flow (e.g. gas flow-focused jets), which exhibit peculiarities now definitely attributable in first order to the formation of shear boundary layers. Partial support from the Ministry of Economy and Competitiveness, Junta de Extremadura, and Junta de Andalucia (Spain) through Grant Nos. DPI2010-21103, GR10047, P08-TEP-04128, and TEP-7465, respectively, is gratefully acknowledged.
Acoustic Receptivity of Mach 4.5 Boundary Layer with Leading- Edge Bluntness
Malik, Mujeeb R.; Balakumar, Ponnampalam
2007-01-01
Boundary layer receptivity to two-dimensional slow and fast acoustic waves is investigated by solving Navier-Stokes equations for Mach 4.5 flow over a flat plate with a finite-thickness leading edge. Higher order spatial and temporal schemes are employed to obtain the solution whereby the flat-plate leading edge region is resolved by providing a sufficiently refined grid. The results show that the instability waves are generated in the leading edge region and that the boundary-layer is much more receptive to slow acoustic waves (by almost a factor of 20) as compared to the fast waves. Hence, this leading-edge receptivity mechanism is expected to be more relevant in the transition process for high Mach number flows where second mode instability is dominant. Computations are performed to investigate the effect of leading-edge thickness and it is found that bluntness tends to stabilize the boundary layer. Furthermore, the relative significance of fast acoustic waves is enhanced in the presence of bluntness. The effect of acoustic wave incidence angle is also studied and it is found that the receptivity of the boundary layer on the windward side (with respect to the acoustic forcing) decreases by more than a factor of 4 when the incidence angle is increased from 0 to 45 deg. However, the receptivity coefficient for the leeward side is found to vary relatively weakly with the incidence angle.
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.
Infrared propagation in the air-sea boundary layer
Larsen, R.; Preedy, K. A.; Drake, G.
1990-03-01
Over the oceans and other large bodies of water the structure of the lowest layers of the atmosphere is often strongly modified by evaporation of water vapor from the water surface. At radio wavelengths this layer will usually be strongly refracting or ducting, and the layer is commonly known as the evaporation duct. However, the refractive index of air at infrared wavelengths differs from that at radio wavelengths, and the effects of the marine boundary layer on the propagation of infrared radiation are examined. Meteorological models of the air-sea boundary layer are used to compute vertical profiles of temperature and water-vapor pressure. From these are derived profiles of atmospheric refractive index at radio wavelengths and at infrared wavelengths in the window regions of low absorption. For duct propagation to occur it is necessary that the refractivity of air decreases rapidly with increasing height above the surface. At radio wavelengths this usually occurs when there is a strong lapse of water vapor pressure with increasing height. By contrast, at infrared wavelengths the refractive index is almost independent of water vapor pressure, and it is found that an infrared duct is formed only when there is a temperature inversion.
Bandgap tunability at single-layer molybdenum disulphide grain boundaries
Huang, Yu Li
2015-02-17
Two-dimensional transition metal dichalcogenides have emerged as a new class of semiconductor materials with novel electronic and optical properties of interest to future nanoelectronics technology. Single-layer molybdenum disulphide, which represents a prototype two-dimensional transition metal dichalcogenide, has an electronic bandgap that increases with decreasing layer thickness. Using high-resolution scanning tunnelling microscopy and spectroscopy, we measure the apparent quasiparticle energy gap to be 2.40±0.05 eV for single-layer, 2.10±0.05 eV for bilayer and 1.75±0.05 eV for trilayer molybdenum disulphide, which were directly grown on a graphite substrate by chemical vapour deposition method. More interestingly, we report an unexpected bandgap tunability (as large as 0.85±0.05 eV) with distance from the grain boundary in single-layer molybdenum disulphide, which also depends on the grain misorientation angle. This work opens up new possibilities for flexible electronic and optoelectronic devices with tunable bandgaps that utilize both the control of two-dimensional layer thickness and the grain boundary engineering.
Flight Experiment Verification of Shuttle Boundary Layer Transition Prediction Tool
Berry, Scott A.; Berger, Karen T.; Horvath, Thomas J.; Wood, William A.
2016-01-01
Boundary layer transition at hypersonic conditions is critical to the design of future high-speed aircraft and spacecraft. Accurate methods to predict transition would directly impact the aerothermodynamic environments used to size a hypersonic vehicle's thermal protection system. A transition prediction tool, based on wind tunnel derived discrete roughness correlations, was developed and implemented for the Space Shuttle return-to-flight program. This tool was also used to design a boundary layer transition flight experiment in order to assess correlation uncertainties, particularly with regard to high Mach-number transition and tunnel-to-flight scaling. A review is provided of the results obtained from the flight experiment in order to evaluate the transition prediction tool implemented for the Shuttle program.
Coherent structures in wave boundary layers. Part 2. Solitary motion
DEFF Research Database (Denmark)
Sumer, B. Mutlu; Jensen, Palle Martin; Sørensen, Lone B.;
2010-01-01
in an oscillating water tunnel. Two kinds of measurements were made: bed shear stress measurements and velocity measurements. The experiments show that the solitary-motion boundary layer experiences three kinds of flow regimes as the Reynolds number is increased: (i) laminar regime; (ii) laminar regime where...... the boundary-layer flow experiences a regular array of vortex tubes near the bed over a short period of time during the deceleration stage; and (iii) transitional regime characterized with turbulent spots, revealed by single/multiple, or, sometimes, quite dense spikes in the bed shear stress traces....... Supplementary synchronized flow visualization tests confirmed the presence of the previously mentioned flow features. Information related to flow resistance are also given in the paper....
Full-Scale Spectrum of Boundary-Layer Winds
DEFF Research Database (Denmark)
Larsén, Xiaoli Guo; Larsen, Søren Ejling; Lundtang Petersen, Erik
2016-01-01
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 to10 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...... 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 statistics in the boundary layer....
Directory of Open Access Journals (Sweden)
anjali devi
2015-01-01
Full Text Available The effects of nonlinear radiation on hydromagnetic boundary layer flow and heat transfer over a shrinking surface is investigated in the present work. Using suitable similarity transformations, the governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations. The resultant equations which are highly nonlinear are solved numerically using Nachtsheim Swigert shooting iteration scheme together with Fourth Order Runge Kutta method. Numerical solutions for velocity, skin friction coefficient and temperature are obtained for various values of physical parameters involved in the study namely Suction parameter, Magnetic parameter, Prandtl number, Radiation parameter and Temperature ratio parameter. Numerical values for dimensionless rate of heat transfer are also obtained for various physical parameters and are shown through tables. The analytical solution of the energy equation when the radiation term is taken in linear form is obtained using Confluent hypergeometric function.
Boundary integral equation methods and numerical solutions thin plates on an elastic foundation
Constanda, Christian; Hamill, William
2016-01-01
This book presents and explains a general, efficient, and elegant method for solving the Dirichlet, Neumann, and Robin boundary value problems for the extensional deformation of a thin plate on an elastic foundation. The solutions of these problems are obtained both analytically—by means of direct and indirect boundary integral equation methods (BIEMs)—and numerically, through the application of a boundary element technique. The text discusses the methodology for constructing a BIEM, deriving all the attending mathematical properties with full rigor. The model investigated in the book can serve as a template for the study of any linear elliptic two-dimensional problem with constant coefficients. The representation of the solution in terms of single-layer and double-layer potentials is pivotal in the development of a BIEM, which, in turn, forms the basis for the second part of the book, where approximate solutions are computed with a high degree of accuracy. The book is intended for graduate students and r...
Turbulence Scales Simulations in Atmospheric Boundary Layer Wind Tunnels
Elena-Carmen Teleman; Radu Silion; Elena Axinte; Radu Pescaru
2008-01-01
The simulation of the air flow over models in atmospheric boundary layer tunnels is a research domain based on advanced scientific technologies imposed by the necessity of studying the turbulent fluid movements in the proximity of the Earth’s surface. The experiment presented herein is developed in the wind tunnel from the Laboratory of Structural Aerodynamics of the Faculty of Civil Engineering and Building Services in Iassy. Measurements necessary for the determination of the turbulence sca...
Ozone in the Atlantic Ocean marine boundary layer
Patrick Boylan; Detlev Helmig; Samuel Oltmans
2015-01-01
Abstract In situ atmospheric ozone measurements aboard the R/V Ronald H. Brown during the 2008 Gas-Ex and AMMA research cruises were compared with data from four island and coastal Global Atmospheric Watch stations in the Atlantic Ocean to examine ozone transport in the marine boundary layer (MBL). Ozone measurements made at Tudor Hill, Bermuda, were subjected to continental outflow from the east coast of the United States, which resulted in elevated ozone levels above 50 ppbv. Ozone measurem...
Defects and boundary layers in non-Euclidean plates
Gemmer, John
2012-01-01
We investigate the behaviour of non-Euclidean plates with constant negative Gaussian curvature using the F\\"oppl-von K\\'arm\\'an reduced theory of elasticity. Motivated by recent experimental results, we focus on annuli with a periodic profile. We prove rigorous upper and lower bounds for the elastic energy that scales like the thickness squared. We also investigate the scaling with thickness of boundary layers where the stretching energy is concentrated with decreasing thickness.
Pressure gradient effect in natural convection boundary layers
Higuera Antón, Francisco; Liñán Martínez, Amable
1993-01-01
The high Grashof number laminar natural convection flow around the lower stagnation point of a symmetric bowl- shaped heated body is analyzed. A region is identified where the direct effect on the flow of the component of the buoyancy force tangential to the body surface is comparable to the indirect effect of the component normal to the surface, which acts through the gradient of the nonuniform pressure that it induces in the boundary layer. Analysis of this region provides a description ...
Grey zone simulations of the morning convective boundary layer development
Efstathiou, G. A.; Beare, R. J.; Osborne, S.; Lock, A. P.
2016-05-01
Numerical simulations of two cases of morning boundary layer development are conducted to investigate the impact of grid resolution on mean profiles and turbulent kinetic energy (TKE) partitioning from the large eddy simulation (LES) to the mesoscale limit. Idealized LES, using the 3-D Smagorinsky scheme, is shown to be capable of reproducing the boundary layer evolution when compared against measurements. However, increasing grid spacing results in the damping of resolved TKE and the production of superadiabatic temperature profiles in the boundary layer. Turbulence initiation is significantly delayed, exhibiting an abrupt onset at intermediate resolutions. Two approaches, the bounding of vertical diffusion coefficient and the blending of the 3-D Smagorinsky with a nonlocal 1D scheme, are used to model subgrid diffusion at grey zone resolutions. Simulations are compared against the coarse-grained fields from the validated LES results for each case. Both methods exhibit particular strengths and weaknesses, indicating the compromise that needs to be made currently in high-resolution numerical weather prediction. The blending scheme is able to reproduce the adiabatic profiles although turbulence is underestimated in favor of the parametrized heat flux, and the spin-up of TKE remains delayed. In contrast, the bounding approach gives an evolution of TKE that follows the coarse-grained LES very well, relying on the resolved motions for the nonlocal heat flux. However, bounding gives unrealistic static instability in the early morning temperature profiles (similar to the 3-D Smagorinsky scheme) because model dynamics are unable to resolve TKE when the boundary layer is too shallow compared to the grid spacing.
Iodine monoxide in the Western Pacific marine boundary layer
Directory of Open Access Journals (Sweden)
K. Großmann
2012-10-01
Full Text Available A latitudinal cross-section and vertical profiles of iodine monoxide (IO are reported from the marine boundary layer of the Western Pacific. The measurements were taken using Multi-Axis Differential Optical Absorption Spectroscopy (MAX-DOAS during the TransBrom cruise of the German research vessel Sonne, which led from Tomakomai, Japan (42° N, 141° E through the Western Pacific to Townsville, Australia (19° S, 146° E in October 2009. In the marine boundary layer within the tropics (between 20° N and 5° S, IO mixing ratios ranged between 1 and 2.2 ppt, whereas in the subtropics and at mid-latitudes typical IO mixing ratios were around 1 ppt in the daytime. The profile retrieval reveals that the bulk of the IO was located in the lower part of the marine boundary layer. Photochemical simulations indicate that the organic iodine precursors observed during the cruise (CH_{3}I, CH_{2}I_{2}, CH_{2}ClI, CH_{2}BrI are not sufficient to explain the measured IO mixing ratios. Reasonable agreement between measured and modelled IO can only be achieved, if an additional sea-air flux of inorganic iodine (e.g. I_{2} is assumed in the model. Our observations add further evidence to previous studies that reactive iodine is an important oxidant in the marine boundary layer.
Glyoxal observations in the global marine boundary layer
Mahajan, Anoop S.; Prados-Roman, Cristina; Hay, Timothy D.; Lampel, Johannes; Pöhler, Denis; Groβmann, Katja; Tschritter, Jens; Frieß, Udo; Platt, Ulrich; Johnston, Paul; Kreher, Karin; Wittrock, Folkard; Burrows, John P; Plane, John M. C.; Saiz-Lopez, Alfonso
2014-01-01
Glyoxal is an important intermediate species formed by the oxidation of common biogenic and anthropogenic volatile organic compounds such as isoprene, toluene and acetylene. Although glyoxal has been shown to play an important role in urban and forested environments, its role in the open ocean environment is still not well understood, with only a few observations showing evidence for its presence in the open ocean marine boundary layer (MBL). In this study, we report observations of glyoxal f...
Using UAV's to Measure the Urban Boundary Layer
Jacob, R. L.; Sankaran, R.; Beckman, P. H.
2015-12-01
The urban boundary layer is one of the most poorly studied regions of the atmospheric boundary layer. Since a majority of the world's population now lives in urban areas, it is becoming a more important region to measure and model. The combination of relatively low-cost unmanned aerial vehicles and low-cost sensors can together provide a new instrument for measuring urban and other boundary layers. We have mounted a new sensor and compute platform called Waggle on an off-the-shelf XR8 octo-copter from 3DRobotics. Waggle consists of multiple sensors for measuring pressure, temperature and humidity as well as trace gases such as carbon monoxide, nitrogen dioxide, sulfur dioxide and ozone. A single board computer running Linux included in Waggle on the UAV allows in-situ processing and data storage. Communication of the data is through WiFi or 3G and the Waggle software can save the data in case communication is lost during flight. The flight pattern is a deliberately simple vertical ascent and descent over a fixed location to provide vertical profiles and so flights can be confined to urban parks, industrial areas or the footprint of a single rooftop. We will present results from test flights in urban and rural areas in and around Chicago.
Wave boundary layer over a stone-covered bed
DEFF Research Database (Denmark)
Dixen, Martin; Hatipoglu, Figen; Sumer, B. Mutlu;
2008-01-01
This paper summarizes the results of an experimental investigation on wave boundary layers over a bed with large roughness, simulating stone/rock/armour block cover on the sea bottom. The roughness elements used in the experiments were stones the size of 1.4cm and 3.85cm in one group of experiments...... and regular ping-pong balls the size 3.6cm in the other. The orbital-motion-amplitude-to-roughness ratio at the bed was rather small, in the range a/ks=0.6-3. The mean and turbulence properties of the boundary-layer flow were measured. Various configurations of the roughness elements were used in the ping...... for small values of a/ks. The results further show that the phase lead of the bed friction velocity over the surface elevation does not seem to change radically with a/ks, and found to be in the range 12°-23°. Furthermore the results show that the boundary-layer turbulence also is not extremely sensitive...
Coupled wake boundary layer model of wind-farms
Stevens, Richard J A M; Meneveau, Charles
2014-01-01
We present and test a coupled wake boundary layer (CWBL) model that describes the distribution of the power output in a wind-farm. The model couples the traditional, industry-standard wake expansion/superposition approach with a top-down model for the overall wind-farm boundary layer structure. The wake expansion/superposition model captures the effect of turbine positioning, while the top-down portion adds the interaction between the wind-turbine wakes and the atmospheric boundary layer. Each portion of the model requires specification of a parameter that is not known a-priori. For the wake model the wake expansion coefficient is required, while the top-down model requires an effective span-wise turbine spacing within which the model's momentum balance is relevant. The wake expansion coefficient is obtained by matching the predicted mean velocity at the turbine from both approaches, while the effective span-wise turbine spacing depends on turbine positioning and thus can be determined from the wake expansion...
Some characteristics of bypass transition in a heated boundary layer
Sohn, K. H.; Reshotko, E.; O'Brien, J. E.
Experimental measurements of both mean and conditionally sampled characteristics of laminar, transitional and low Reynolds number turbulent boundary layers on a heated flat plate are presented. Measurements were obtained in air over a range of freestream turbulence intensities from 0.3 percent to 6 percent with a freestream velocity of 30.5 m/s and zero pressure gradient. Conditional sampling performed in the transitional boundary layers indicate the existence of a near-wall drop in intermittency, especially pronounced at low intermittencies. Nonturbulent intervals were observed to possess large levels of low-frequency unsteadiness, and turbulent intervals had peak intensities as much as 50 percent higher than were measured at fully turbulent stations. Heat transfer results were consistent with results of previous researches and Reynolds analogy factors were found to be well predicted by laminar and turbulent correlations which accounted for unheated starting length. A small dependence of the turbulent Reynolds analogy factors on freestream turbulence level was observed. Laminar boundary layer spectra indicated selective amplification of unstable frequencies. These instabilities appear to play a dominant role in the transition process only for the lowest freestream turbulence level studied, however.
Manipulation of Turbulent Boundary Layers Using Synthetic Jets
Berger, Zachary; Gomit, Guillaume; Lavoie, Philippe; Ganapathisubramani, Bharath
2015-11-01
This work focuses on the application of active flow control, in the form of synthetic jet actuators, of turbulent boundary layers. An array of 2 synthetic jets are oriented in the spanwise direction and located approximately 2.7 meters downstream from the leading edge of a flat plate. Actuation is applied perpendicular to the surface of the flat plate with varying blowing ratios and reduced frequencies (open-loop). Two-component large window particle image velocimetry (PIV) was performed at the University of Southampton, in the streamwise-wall-normal plane. Complementary stereo PIV measurements were performed at the University of Toronto Institute for Aerospace Studies (UTIAS), in the spanwise-wall-normal plane. The freestream Reynolds number is 3x104, based on the boundary layer thickness. The skin friction Reynolds number is 1,200 based on the skin friction velocity. The experiments at Southampton allow for the observation of the control effects as the flow propagates downstream. The experiments at UTIAS allow for the observation of the streamwise vorticity induced from the actuation. Overall the two experiments provide a 3D representation of the flow field with respect to actuation effects. The current work focuses on the comparison of the two experiments, as well as the effects of varying blowing ratios and reduced frequencies on the turbulent boundary layer. Funded Supported by Airbus.
Institute of Scientific and Technical Information of China (English)
A.S. BERDYSHEV; A. CABADA; B.Kh. TURMETOV
2014-01-01
This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.
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.
Receptivity of the Boundary Layer to Vibrations of the Wing Surface
Bernots, Tomass; Ruban, Anatoly; Pryce, David; Laminar Flow Control UK Group Team
2014-11-01
In this work we study generation of Tollmien-Schlichting (T-S) waves in the boundary layer due to elastic vibrations of the wing surface. The flow is investigated based on the asymptotic analysis of the Navier-Stokes equations at large values of the Reynolds number. It is assumed that in the spectrum of the wing vibrations there is a harmonic which comes in resonance with the T-S wave on the lower branch of the stability curve. It was found that the vibrations of the wing surface produce pressure perturbations in the flow outside the boundary layer which can be calculated with the help of the piston theory. As the pressure perturbations penetrate into the boundary layer, a Stokes layer forms on the wing surface which appears to be influenced significantly by the compressibility of the flow, and is incapable of producing the T-S waves. The situation changes when the Stokes layer encounters an roughness; near which the flow is described using the triple-deck theory. The solution of the triple-deck problem can be found in an analytic form. Our main concern is with the flow behaviour downstream of the roughness and, in particular, with the amplitude of the generated Tollmien-Schlichting waves. This research was performed in the Laminar Flow Control Centre (LFC-UK) at Imperial College London. The centre is supported by EPSRC, Airbus UK and EADS Innovation Works.
Institute of Scientific and Technical Information of China (English)
S PANIGRAHI; M REZA; A K MISHRA
2014-01-01
Suﬃcient conditions are found for the existence of similar solutions of the mixed convection flow of a Powell-Eyring fluid over a nonlinear stretching permeable sur-face in the presence of magnetic field. To achieve this, one parameter linear group trans-formation is applied. The governing momentum and energy equations are transformed to nonlinear ordinary differential equations by use of a similarity transformation. These equations are solved by the homotopy analysis method (HAM) to obtain the approximate solutions. The effects of magnetic field, suction, and buoyancy on the Powell-Eyring fluid flow with heat transfer inside the boundary layer are analyzed. The effects of the non-Newtonian fluid (Powell-Eyring model) parametersεandδ on the skin friction and local heat transfer coeﬃcients for the cases of aiding and opposite flows are investigated and discussed. It is observed that the momentum boundary layer thickness increases and the thermal boundary layer thickness decreases with the increase inεwhereas the momentum boundary layer thickness decreases and thermal boundary layer thickness increases with the increase in δ for both the aiding and opposing mixed convection flows.
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.
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.
Influence of rigid boundary on the propagation of torsional surface wave in an inhomogeneous layer
Indian Academy of Sciences (India)
Shishir Gupta; Rehena Sultana; Santimoy Kundu
2015-02-01
The present work illustrates a theoretical study on the effect of rigid boundary for the propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. It is believed that the inhomogeneity in the half space arises due to hyperbolic variation in shear modulus and density whereas the layer has linear variation in shear modulus and density. The dispersion equation has been obtained in a closed form by using Whittaker’s function, which shows the variation of phase velocity with corresponding wave number. Numerical results show the dispersion equations, which are discussed and presented by means of graphs. Results in some special cases are also compared with existing solutions available from analytical methods, which show a close resemblance. It is also observed that, for a layer over a homogeneous half space, the velocity of torsional waves does not coincide with that of Love waves in the presence of the rigid boundary, whereas it does at the free boundary. Graphical user interface (GUI) software has been developed using MATLAB 7.5 to generalize the effect of various parameter discussed.
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.
2016-08-01
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.
International Nuclear Information System (INIS)
In this paper, the combined effects of radiation, temperature dependent viscosity, suction and injection on thermal boundary layer over a permeable flat plate with a convective heat exchange at the surface are investigated. By taking suitable similarity variables, the governing boundary layer equations are transformed into a boundary value problem of coupled nonlinear ordinary differential equations and solved numerically using the shooting technique with sixth-order Runge-Kutta integration scheme. The solutions for the velocity and temperature distributions together with the skin friction coefficient and Nusselt number depend on six parameters: Prandtl number Pr, Brinkmann number Br, the radiation parameter Ra, the viscosity variation parameter a, suction/injection parameter fw and convection Biot number Bi. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters on thermal boundary layer. The thermal boundary layer thickens with a rise in the local temperature as the viscous dissipation, wall injection, and convective heating each intensifies, but decreases with increasing suction and thermal radiation. For fixed Pr, Ra, Br and Bi, both the skin friction coefficient and the Nusselt number increase with a decrease in fluid viscosity and an increase in suction. A comparison with previously published results on special case of the problem shows excellent agreement
THE INTERIOR LAYER FOR A NONLINEAR SINGULARLY PERTURBED DIFFERENTIAL-DIFFERENCE EQUATION
Institute of Scientific and Technical Information of China (English)
Wang Aifeng; Ni Mingkang
2012-01-01
In this article,the interior layer for a second order nonlinear singularly perturbed differential-difference equation is considered.Using the methods of boundary function and fractional steps,we construct the formula of asymptotic expansion and point out that the boundary layer at t =0 has a great influence upon the interior layer at t =σ.At the same time,on the basis of differential inequality techniques,the existence of the smooth solution and the uniform validity of the asymptotic expansion are proved.Finally,an example is given to demonstrate the effectiveness of our result.The result of this article is new and it complements the previously known ones.
Directory of Open Access Journals (Sweden)
Freidooni Mehr N.
2012-01-01
Full Text Available In this paper, the semi-analytical/numerical technique known as the homotopy analysis method (HAM is employed to derive solutions for the laminar axisymmetric mixed convection boundary-layer nanofluid flow past a vertical cylinder. The similarity solutions are employed to transform the parabolic partial differential conservation equations into system of nonlinear, coupled ordinary differential equations, subject to appropriate boundary conditions. A comparison has been done to verify the obtained results with the purely numerical results of Grosan and Pop (2011 with excellent correlation achieved. The effects of nanoparticle volume fraction, curvature parameter and mixed convection or buoyancy parameter on the dimensionless velocity and temperature distributions, skin friction and wall temperature gradients are illustrated graphically. HAM is found to demonstrate excellent potential for simulating nanofluid dynamics problems. Applications of the study include materials processing and also thermal enhancement of energy systems.
Hussanan, Abid; Zuki Salleh, Mohd; Tahar, Razman Mat; Khan, Ilyas
2014-01-01
In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform method and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.
Numerical study of the anode boundary layer in atmospheric pressure arc discharges
Semenov, I. L.; Krivtsun, I. V.; Reisgen, U.
2016-03-01
The anode boundary layer in atmospheric pressure arc discharges is studied numerically on the basis of the hydrodynamic (diffusion) equations for plasma components. The governing equations are formulated in a unified manner without the assumptions of thermal equilibrium, ionization equilibrium or quasi-neutrality. For comparison, a quasi-neutral model of the anode layer is also considered. The numerical computations are performed for an argon arc at typical values of the current density in anode layers (500-2000 A cm-2). The results of numerical modelling show that the common collisionless model of the sheath fails to describe the sheath region for the problem under consideration. For this reason, a detailed analysis of the anode sheath is performed using the results of unified modelling. In addition, the distributions of plasma parameters in the anode layer are analysed and the basic characteristics of the layer (anode voltage drop, sheath voltage drop, anode layer thickness, sheath thickness, heat flux to the anode) are calculated. Our results are found to be in good agreement with the existing theoretical predictions and experimental data. The dependence of the anode layer characteristics on the current density is also discussed.
CFD Modeling of Non-Neutral Atmospheric Boundary Layer Conditions
DEFF Research Database (Denmark)
Koblitz, Tilman
For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important to the atmo......For wind resource assessment, the wind industry is increasingly relying on Computational Fluid Dynamics models that focus on modeling the airflow in a neutrally stratified surface-layer. Physical processes like the Coriolis force, buoyancy forces and heat transport, that are important...... to the atmospheric boundary-layer, are mostly ignored so far. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include atmospheric stability and the Coriolis effect. Within the present work a RANS model framework is developed and implemented...
Grain-boundary layering transitions and phonon engineering
Rickman, J. M.; Harmer, M. P.; Chan, H. M.
2016-09-01
We employ semi-grand canonical Monte Carlo simulation to investigate layering transitions at grain boundaries in a prototypical binary alloy. We demonstrate the existence of such transitions among various interfacial states and examine the role of elastic fields in dictating state equilibria. The results of these studies are summarized in the form of diagrams that highlight interfacial state coexistence in this system. Finally, we examine the impact of layering transitions on the phononic properties of the system, as given by the specific heat and, by extension, the thermal conductivity. Thus, it is suggested that by inducing interfacial layering transitions via changes in temperature or pressure, one can thereby engineer thermodynamic and transport properties in materials.
Tumin, Anatoli
2015-11-01
Zavol'skii and Reutov (1983), Luchini (2008, 2010), Fedorov (2010, 2012, 2014) explored potential role of kinetic fluctuations (KF) in incompressible and calorically perfect gas boundary layer flows. The results indicate that role of KF is comparable with other disturbance sources in flight experiments and in quiet wind tunnels. The analysis is based on the Landau and Lifshitz (1957) concept of fluctuating hydrodynamics representing the dissipative fluxes as an average and fluctuating parts. We are extending analysis of the receptivity problem to the fluctuating dissipative fluxes in chemically reacting nonequilibrium boundary layer flows of binary mixtures. There are new terms in the energy, and the species equations. The species conservation equation includes the dissipative diffusion flux and the species generation due to dissociation. The momentum equation includes fluctuating stress tensor. The energy equation includes fluctuating heat flux, energy flux due to diffusion of the species, and fluctuating dissipative flux due to viscosity. The effects are compared for the cases stemming from constraints of the HTV project (Klentzman and Tumin, AIAA Paper 2013-2882). Supported by AFOSR.
Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations
Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping
2016-07-01
We consider numerical boundary conditions for high order finite difference schemes for solving convection-diffusion equations on arbitrary geometry. The two main difficulties for numerical boundary conditions in such situations are: (1) the wide stencil of the high order finite difference operator requires special treatment for a few ghost points near the boundary; (2) the physical boundary may not coincide with grid points in a Cartesian mesh and may intersect with the mesh in an arbitrary fashion. For purely convection equations, the so-called inverse Lax-Wendroff procedure [28], in which we convert the normal derivatives into the time derivatives and tangential derivatives along the physical boundary by using the equations, has been quite successful. In this paper, we extend this methodology to convection-diffusion equations. It turns out that this extension is non-trivial, because totally different boundary treatments are needed for the diffusion-dominated and the convection-dominated regimes. We design a careful combination of the boundary treatments for the two regimes and obtain a stable and accurate boundary condition for general convection-diffusion equations. We provide extensive numerical tests for one- and two-dimensional problems involving both scalar equations and systems, including the compressible Navier-Stokes equations, to demonstrate the good performance of our numerical boundary conditions.
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.
Temperature boundary layer on a rotating surface - the problem of the constant temperature wall
Directory of Open Access Journals (Sweden)
Pavlović Miloš D.
2006-01-01
Full Text Available Introducing the group of Loitskanskii [1] form-parameters and transformations of Saljnikov [2], the set of governing equations of the in compressible laminar temperature boundary layer was transformed in the universal form, with Prandtl number as parameter, for the case of the constant wall temperature. Using the universal results for air (Pr=0.72 the procedure for calculation of the Nusselt number (dimensionless heat transfer coefficient on the particular contour (airfoil NACA 0010-34 was developed. The dimensionless temperature profiles within the boundary layer were presented also. The parameter of rotation Ω0, as well as Eckert number, was varied, and their influences on the heat transfer from the surface to the working fluid were presented and analyzed. .
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.
Application of a transitional boundary-layer theory in the low hypersonic Mach number regime
Shamroth, S. J.; Mcdonald, H.
1975-01-01
An investigation is made to assess the capability of a finite-difference boundary-layer procedure to predict the mean profile development across a transition from laminar to turbulent flow in the low hypersonic Mach-number regime. The boundary-layer procedure uses an integral form of the turbulence kinetic-energy equation to govern the development of the Reynolds apparent shear stress. The present investigation shows the ability of this procedure to predict Stanton number, velocity profiles, and density profiles through the transition region and, in addition, to predict the effect of wall cooling and Mach number on transition Reynolds number. The contribution of the pressure-dilatation term to the energy balance is examined and it is suggested that transition can be initiated by the direct absorption of acoustic energy even if only a small amount (1 per cent) of the incident acoustic energy is absorbed.
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.
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.
DEFF Research Database (Denmark)
Kirca, V. S. Ozgur; Sumer, B. Mutlu; Steffensen, Michael;
2016-01-01
The present research aims at getting an understanding of the process of dispersion of surface sediment in an oscillatory boundary layer, which may represent an idealised case of, for example, a stockpile area where excavated sediment is stockpiled temporarily (or permanently). The process is...... studied numerically, using a random-walk particle model with the input data for the mean and turbulence characteristics of the wave boundary layer picked up from a transitional two-equation k–ω Reynolds averaged Navier–Stokes model and plugged in the random-walk model. First, the flowmodel is validated...... against experimental data in the literature. Then, the random-walk dispersion model is run for different oscillatory flow cases and for a number of steady flow cases for comparison. The primary sediment grains of concern are fine sediments (with low fall velocity), which would stay in suspension for most...
Initial-boundary value problems for a class of nonlinear thermoelastic plate equations
Institute of Scientific and Technical Information of China (English)
Zhang Jian-Wen; Rong Xiao-Liang; Wu Run-Heng
2009-01-01
This paper studies initial-boundary value problems for a class of nonlinear thermoelastic plate equations. Under some certain initial data and boundary conditions,it obtains an existence and uniqueness theorem of global weak solutions of the nonlinear thermoelstic plate equations,by means of the Galerkin method. Moreover,it also proves the existence of strong and classical solutions.
REGULARITY THEORY FOR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The objective of this paper is to consider the theory of regularity of systems of partial differential equations with Neumann boundary conditions. It complements previous works of the authors for the Dirichlet case. This type of problem is motivated by stochastic differential games. The Neumann case corresponds to stochastic differential equations with reflection on boundary of the domain.
Well-posed initial-boundary value problems for the Zakharov-Kuznetsov equation
Directory of Open Access Journals (Sweden)
Andrei V. Faminskii
2008-09-01
Full Text Available This paper deals with non-homogeneous initial-boundary value problems for the Zakharov-Kuznetsov equation, which is one of the variants of multidimensional generalizations of the Korteweg-de Vries equation. Results on local and global well-posedness are established in a scale of Sobolev-type spaces under natural assumptions on initial and boundary data.
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.
Edge states for the turbulence transition in the asymptotic suction boundary layer
Kreilos, Tobias; Schneider, Tobias M; Eckhardt, Bruno
2013-01-01
We demonstrate the existence of an exact invariant solution to the Navier-Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer we demonstrate that the periodic orbit emerges in a saddle-node infinite-period (SNIPER) bifurcation of two symmetry-related travelling wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwi...
DNS of a spatially developing turbulent boundary layer with passive scalar transport
Energy Technology Data Exchange (ETDEWEB)
Li Qiang [Linne Flow Centre, KTH Mechanics, Osquars Backe 18, SE-100 44 Stockholm (Sweden)], E-mail: qiang@mech.kth.se; Schlatter, Philipp; Brandt, Luca; Henningson, Dan S. [Linne Flow Centre, KTH Mechanics, Osquars Backe 18, SE-100 44 Stockholm (Sweden)
2009-10-15
A direct numerical simulation (DNS) of a spatially developing turbulent boundary layer over a flat plate under zero pressure gradient (ZPG) has been carried out. The evolution of several passive scalars with both isoscalar and isoflux wall boundary condition are computed during the simulation. The Navier-Stokes equations as well as the scalar transport equation are solved using a fully spectral method. The highest Reynolds number based on the free-stream velocity U{sub {infinity}} and momentum thickness {theta} is Re{sub {theta}}=830, and the molecular Prandtl numbers are 0.2, 0.71 and 2. To the authors' knowledge, this Reynolds number is to date the highest with such a variety of scalars. A large number of turbulence statistics for both flow and scalar fields are obtained and compared when possible to existing experimental and numerical simulations at comparable Reynolds number. The main focus of the present paper is on the statistical behaviour of the scalars in the outer region of the boundary layer, distinctly different from the channel-flow simulations. Agreements as well as discrepancies are discussed while the influence of the molecular Prandtl number and wall boundary conditions is also highlighted. A Pr scaling for various quantities is proposed in outer scalings. In addition, spanwise two-point correlation and instantaneous fields are employed to investigate the near-wall streak spacing and the coherence between the velocity and the scalar fields. Probability density functions (PDF) and joint probability density functions (JPDF) are shown to identify the intermittency both near the wall and in the outer region of the boundary layer. The present simulation data will be available online for the research community.
On a problem for wave equation with data on the whole boundary
Yessirkegenov, Nurgissa
2016-08-01
In this paper we propose a new formulation of boundary value problem for a one-dimensional wave equation in a rectangular domain in which boundary conditions are given on the whole boundary. We prove the well-posedness of boundary value problem in the classical and generalized senses. In order to substantiate the well-posedness of this problem it is necessary to have an effective representation of the general solution of the problem. In this direction we obtain a convenient representation of the general solution for the wave equation in a rectangular domain based on d'Alembert classical formula. The constructed general solution automatically satisfies the boundary conditions by a spatial variable. Further, by setting different boundary conditions according to temporary variable, we get some functional or functional-differential equations. Thus, the proof of the well-posedness of the formulated problem is reduced to question of the existence and uniqueness of solutions of the corresponding functional equations.
Three-dimensional instability analysis of boundary layers perturbed by streamwise vortices
Martín, Juan A.; Paredes, Pedro
2016-08-01
A parametric study is presented for the incompressible, zero-pressure-gradient flat-plate boundary layer perturbed by streamwise vortices. The vortices are placed near the leading edge and model the vortices induced by miniature vortex generators (MVGs), which consist in a spanwise-periodic array of small winglet pairs. The introduction of MVGs has been experimentally proved to be a successful passive flow control strategy for delaying laminar-turbulent transition caused by Tollmien-Schlichting (TS) waves. The counter-rotating vortex pairs induce non-modal, transient growth that leads to a streaky boundary layer flow. The initial intensity of the vortices and their wall-normal distances to the plate wall are varied with the aim of finding the most effective location for streak generation and the effect on the instability characteristics of the perturbed flow. The study includes the solution of the three-dimensional, stationary, streaky boundary layer flows by using the boundary region equations, and the three-dimensional instability analysis of the resulting basic flows by using the plane-marching parabolized stability equations. Depending on the initial circulation and positioning of the vortices, planar TS waves are stabilized by the presence of the streaks, resulting in a reduction in the region of instability and shrink of the neutral stability curve. For a fixed maximum streak amplitude below the threshold for secondary instability (SI), the most effective wall-normal distance for the formation of the streaks is found to also offer the most stabilization of TS waves. By setting a maximum streak amplitude above the threshold for SI, sinuous shear layer modes become unstable, as well as another instability mode that is amplified in a narrow region near the vortex inlet position.
Boundary Conditions for 2D Boussinesq-type Wave-Current Interaction Equations
Directory of Open Access Journals (Sweden)
Mera M.
2011-01-01
Full Text Available This research focuses on the development of a set of two-dimensional boundary conditions for specific governing equations. The governing equations are existing Boussinesqtype equations which is capable of simulating wave-current interaction. The present boundary conditions consist of for waves only case and for currents only case. To simulate wave-current interaction, the two kinds of the present boundary conditions are then combined. A numerical model based on both the existing governing equations and the present boundary conditions is applied to simulation of currents only and of wave-current interaction propagating over a basin with a submerged shoal. The results of the numerical model show that the present boundary conditions go well with the existing Boussinesq-type wave-current interaction equations.
An ODE for boundary layer separation on a sphere and a hyperbolic space
Chan, Chi Hin; Czubak, Magdalena; Yoneda, Tsuyoshi
2014-07-01
Ma and Wang derived an equation linking the separation location and times for the boundary layer separation of incompressible fluid flows. The equation gave a necessary condition for the separation (bifurcation) point. The purpose of this paper is to generalize the equation to other geometries, and to phrase it as a simple ODE. Moreover we consider the Navie-Stokes equation with the Coriolis effect, which is related to the presence of trade winds on Earth. A ∂-singular point (bifurcation point) occurs at t0 iff a function α1(t) satisfies α1(t0)=0. The above result is a generalization of [10] which is considered in the Euclidean space R2. We can regard α1(t), α2(t) and α3(t) as a part of the inflow profile. However η(t) is not. Let us be more precise. Choose p˜∈∂K close to p0∈∂K, and let K˜≔{p∈M-K:d(p,p˜)0. It is reasonable to assume uθ does not grow polynomially for the r direction (this is due to the observation of the "boundary layer", since the flow should be a uniform one away from the boundary). Thus, it should be reasonable to focus on the following two cases: (Poiseuille type profile) -k2α1(t)+2kα2(t)0, α2(t)0, α3(t)0 and dp=Δu on the boundary. Our method can be applied to geophysics, in particular, to the "trade winds" on Earth. The trade winds are the easterly surface winds that can be found in the tropics, within the lower portion of the Earth's atmosphere near the equator. The Coriolis effect is responsible for deflecting the surface air, which flows from subtropical high-pressure belts towards the Equator, towards the west in both hemispheres. In the corollary below, we consider the Navie-Stokes equation with the Coriolis effect on a rotating sphere. The equation is
Partial differential equations IX elliptic boundary value problems
Egorov, Yu; Shubin, M
1997-01-01
This EMS volume gives an overview of the modern theory of elliptic boundary value problems. The contribution by M.S. Agranovich is devoted to differential elliptic boundary problems, mainly in smooth bounded domains, and their spectral properties. This article continues his contribution to EMS 63. The contribution by A. Brenner and E. Shargorodsky concerns the theory of boundary value problems for elliptic pseudodifferential operators. Problems both with and without the transmission property, as well as parameter-dependent problems are considered. The article by B. Plamenevskij deals with general differential elliptic boundary value problems in domains with singularities.
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
On the partially reacted boundary layer in rate sticks
Partom, Y.
2014-05-01
Using our temperature dependent reactive flow model (TDRR) to simulate detonation in a rate stick, we observe that a partially reacted layer (PRL) is formed near the boundary. We are not aware that such a PRL has been observed in tests, and this is why we regarded it in the past as a numerical artifact. Assuming that such an artefact may be caused by the finite rise time of the detonation shock, we showed in [1] how it can be eliminated by delaying the outward boundary motion for a length of time comparable with the shock rise time. Here we revisit the PRL problem. We first show that it is not a numerical artifact but a real phenomenon. We do this by repeating the reactive flow run with a finer mesh. By looking at the PRL structure, we see that doubling the resolution affects the PRL only slightly. We then conjecture that the PRL formation has to do with the finite duration of the reaction process (or the finite extent of the reaction zone). By the time the boundary rarefaction reaches a cell near the boundary, it may be only partially reacted, and its reaction may therefore be cut off. To establish our conjecture we show how the PRL structure changes with the reaction duration.
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
Arnold, Douglas N.; Nicolae Tarfulea
2007-01-01
Specifying boundary conditions continues to be a challenge in numerical relativity in order to obtain a long time convergent numerical simulation of Einstein's equations in domains with artificial boundaries. In this paper, we address this problem for the Einstein--Christoffel (EC) symmetric hyperbolic formulation of Einstein's equations linearized around flat spacetime. First, we prescribe simple boundary conditions that make the problem well posed and preserve the constraints. Next, we indi...
INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEM FOR GINZBURG-LANDAU EQUATIONS
Institute of Scientific and Technical Information of China (English)
杨灵娥; 郭柏灵; 徐海祥
2004-01-01
Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.
National Aerospace Laboratory; 航空宇宙技術研究所
1996-01-01
The following topics were discussed: vortex shedding, laminar boundary layer measurement, vortex ring, turbulent flow measurement, high Reynolds number turbulence, pulsed flow, boundary layer instability, Ekman boundary layer, sound receptivity, Tollmien-Schlichting wave in supersonic boundary layer, flow field instability, turbulent flow pattern, vorticity distribution in shear flow, turbulence wedge, streamwise vortex mixing, thermal convection, oblique wave generation in boundary layer, in...
The Jovian boundary layer as formed by magnetic-anomaly effects
Dessler, A. J.
1979-01-01
A model is presented in which a plasma boundary layer of Jupiter is formed from plasma of internal origin. It is proposed that, unlike the Earth's boundary layer, which is thought to consist principally of solar wind plasma, Jupiter's boundary layer consists principally of sulphur and oxygen from the Io plasma torus, plus a small component of hydrogen from Jupiter's ionosphere. Fresh plasma is supplied to the boundary layer once each planetary rotation period by a convection pattern that rotates with Jupiter.
Radiative instabilities of atmospheric jets and boundary layers
International Nuclear Information System (INIS)
Complex flows occur in the atmosphere and they can be source of internal gravity waves. We focus here on the sources associated with radiative and shear (or Kelvin-Helmholtz) instabilities. Stability studies of shear layers in a stably stratified fluid concern mainly cases where shear and stratification are aligned along the same direction. In these cases, Miles (1961) and Howard (1961) found a necessary condition for stability based on the Richardson number: Ri ≥ 1/4. In this thesis, we show that this condition is not necessary when shear and stratification are not aligned: we demonstrate that a two-dimensional planar Bickley jet can be unstable for all Richardson numbers. Although the most unstable mode remains 2D, we show there exists an infinite family of 3D unstable modes exhibiting a radiative structure. A WKBJ theory is found to provide the main characteristics of these modes. We also study an inviscid and stratified boundary layer over an inclined wall with non-Boussinesq and compressible effects. We show that this flow is unstable as soon as the wall is not horizontal for all Froude numbers and that strongly stratified 3D perturbations behave exactly like compressible 2D perturbations. Applications of the results to the jet stream and the atmospheric boundary layer are proposed. (author)
Vertical ozone characteristics in urban boundary layer in Beijing.
Ma, Zhiqiang; Xu, Honghui; Meng, Wei; Zhang, Xiaoling; Xu, Jing; Liu, Quan; Wang, Yuesi
2013-07-01
Vertical ozone and meteorological parameters were measured by tethered balloon in the boundary layer in the summer of 2009 in Beijing, China. A total of 77 tethersonde soundings were taken during the 27-day campaign. The surface ozone concentrations measured by ozonesondes and TEI 49C showed good agreement, albeit with temporal difference between the two instruments. Two case studies of nocturnal secondary ozone maxima are discussed in detail. The development of the low-level jet played a critical role leading to the observed ozone peak concentrations in nocturnal boundary layer (NBL). The maximum of surface ozone was 161.7 ppbv during the campaign, which could be attributed to abundant precursors storage near surface layer at nighttime. Vertical distribution of ozone was also measured utilizing conventional continuous analyzers on 325-m meteorological observation tower. The results showed the NBL height was between 47 and 280 m, which were consistent with the balloon data. Southerly air flow could bring ozone-rich air to Beijing, and the ozone concentrations exceeded the China's hourly ozone standard (approximately 100 ppb) above 600 m for more than 12 h.
A Kind of Discrete Non-Reflecting Boundary Conditions for Varieties of Wave Equations
Institute of Scientific and Technical Information of China (English)
Xiu-min Shao; Zhi-ling Lan
2002-01-01
In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase media and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the construction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.
Three-Dimensional Waves in Tilt Thermal Boundary Layers
Institute of Scientific and Technical Information of China (English)
TAO Jian-Jun; YUAN Xiang-Jiang
2009-01-01
We numerically and theoretically study the stabilities of tilt thermal boundary layers immersed in stratified air. An interesting phenomenon is revealed: the stationary longitudinal-roll mode becomes unstable to some oscillating state even when the Grashof number is smaller than its corresponding critical value. By stability analysis, this phenomenon is explained in terms of a new three-dimensional wave mode. The effect of the tilt angle on the stability of the boundary flows is investigated. Since the new three-dimensional wave is found to be the most unstable mode when the title angle is between 30° and 64°, it is expected to play an important role in the transition to turbulence.
Allaerts, Dries; Meyers, Johan
2015-06-01
Under conventionally neutral conditions, the boundary layer is frequently capped by an inversion layer, which counteracts vertical entrainment of kinetic energy. Very large wind farms are known to depend on vertical entrainment to transport energy from above the farm towards the turbines. In this study, large eddy simulations of an infinite wind-turbine array in a conventionally neutral atmospheric boundary layer are performed. By carefully selecting the initial potential-temperature profile, the influence of the height and the strength of a capping inversion on the power output of a wind farm is investigated. Results indicate that both the height and the strength have a significant effect on the boundary layer flow, and that the height of the neutral boundary layer is effectively controlled by the capping inversion. In addition, it is shown that the vertical entrainment rate decreases for increasing inversion strength or height. In our infinite wind-farm simulations, varying the inversion characteristics leads to differences in power extraction on the order of 13% ± 0.2% (for increasing the strength from 2.5 to 10 K), and 31% ± 0.4% (for increasing the height from 500 to 1500 m). A detailed analysis of the mean kinetic-energy equation is included, showing that the variation in power extraction originates from the work done by the driving pressure gradient related to the boundary layer height and the geostrophic angle, while entrainment of kinetic energy from the free atmosphere does not play a significant role. Also, the effect of inversion strength on power extraction is energetically not related to different amounts of energy entrained, but explained by a difference in boundary layer growth, leading to higher boundary layers for lower inversion strengths. We further present a simple analytical model that allows to obtain wind-farm power output and driving power for the fully developed regime as function of Rossby number and boundary layer height.
Boundary singularities and characteristics of Hamilton–Jacobi equation
Melikyan, A.; Olsder, G.J.
2010-01-01
Boundary-value problems for first order PDEs are locally considered, when the classical sufficient condition for the solution existence does not hold, but a solution still exists, possibly defined on one or both sides of the boundary surface. We note three situations when such a surface (locally) ar
Comments on deriving the equilibrium height of the stable boundary layer
Steeneveld, G.J.; Wiel, van de B.J.H.; Holtslag, A.A.M.
2007-01-01
Recently, the equilibrium height of the stable boundary layer received much attention in a series of papers by Zilitinkevich and co-workers. In these studies the stable boundary-layer height is derived in terms of inverse interpolation of different boundary-layer height scales, each representing a p
Porosity of Free Boundaries in the Obstacle Problem for Quasilinear Elliptic Equations
Indian Academy of Sciences (India)
Jun Zheng; Zhihua Zhang; Peihao Zhao
2013-08-01
In this paper, we establish growth rate of solutions near free boundaries in the identical zero obstacle problem for quasilinear elliptic equations. As a result, we obtain porosity of free boundaries, which is naturally an extension of the previous works by Karp et al. (J. Diff. Equ. 164 (2000) 110–117) for -Laplacian equations, and by Zheng and Zhang (J. Shaanxi Normal Univ. 40(2) (2012) 11–13, 18) for -Laplacian type equations.
Solution of Moving Boundary Space-Time Fractional Burger’s Equation
Directory of Open Access Journals (Sweden)
E. A.-B. Abdel-Salam
2014-01-01
Full Text Available The fractional Riccati expansion method is used to solve fractional differential equations with variable coefficients. To illustrate the effectiveness of the method, the moving boundary space-time fractional Burger’s equation is studied. The obtained solutions include generalized trigonometric and hyperbolic function solutions. Among these solutions, some are found for the first time. The linear and periodic moving boundaries for the kink solution of the Burger’s equation are presented graphically and discussed.
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.
Large Eddy Simulation of Pollen Transport in the Atmospheric Boundary Layer
Chamecki, Marcelo; Meneveau, Charles; Parlange, Marc B.
2007-11-01
The development of genetically modified crops and questions about cross-pollination and contamination of natural plant populations enhanced the importance of understanding wind dispersion of airborne pollen. The main objective of this work is to simulate the dispersal of pollen grains in the atmospheric surface layer using large eddy simulation. Pollen concentrations are simulated by an advection-diffusion equation including gravitational settling. Of great importance is the specification of the bottom boundary conditions characterizing the pollen source over the canopy and the deposition process everywhere else. The velocity field is discretized using a pseudospectral approach. However the application of the same discretization scheme to the pollen equation generates unphysical solutions (i.e. negative concentrations). The finite-volume bounded scheme SMART is used for the pollen equation. A conservative interpolation scheme to determine the velocity field on the finite volume surfaces was developed. The implementation is validated against field experiments of point source and area field releases of pollen.
Effects of Joule Heating and Viscous Dissipation on MHD Marangoni Convection Boundary Layer Flow
Directory of Open Access Journals (Sweden)
Rohana Abdul Hamid
2011-09-01
Full Text Available An analysis is performed to study the effects of the Joule heating and viscous dissipation on the magnetohydrodynamics (MHD Marangoni convection boundary layer flow. The governing partial differential equations are reduced to a system of ordinary differential equations via the similarity transformations. Numerical results of the similarity equations are obtained using the Runge-Kutta-Fehlberg method. Effects of the magnetic field parameter, and the combined effects of the Joule heating and the viscous dissipation are investigated and the numerical results are tabulated in tables and figures. It is found that the magnetic field reduces the fluid velocity but increases the fluid temperature. On the other hand, the combined effects of the Joule heating and viscous dissipation have significantly influenced the surface temperature gradient.
Numerical modelling of pollution dispersion in 3D atmospheric boundary layer
Energy Technology Data Exchange (ETDEWEB)
Benes, L.; Bodnar, T.; Kozel, K. [Czech Technical Univ. of Prague (Czech Republic). Dept. of Technical Mathematics; Fraunie, Ph. [Univ. de Toulon et du Var, La Garde (France). Lab. de Sondages Electromagnetiques et Environnemental Terrestre
2002-07-01
The main goal of this work is to present the applicable models and numerical methods for solution of flow and pollution dispersion in 3D atmospheric boundary layer (ABL). Mathematical models are based on the system of Reynolds averaged Navier-Stokes equations and its simplifications. The sets of governing equations are completed by the transport equations for passive impurities and potential temperature. A simple algebraic turbulent closure model is used. The thermal stability phenomenon is taken into account. For each mathematical model a numerical scheme based on finite-difference or finite-volume discretization is proposed and discussed. Some results of numerical tests are presented for pollution dispersion from point sources and flows over simple geometries. (orig.)
Turbulent thermal boundary layers with temperature-dependent viscosity
International Nuclear Information System (INIS)
Highlights: • Turbulent thermal boundary layers with temperature-dependent viscosity are simulated. • Effect of temperature-dependent viscosity on the statistics of the scalar field. • An identity for the Stanton number is derived and analyzed. • Effect of temperature-dependent viscosity on the statistics of scalar transfer rate. • Modification of turbulent flow field leads to an enhanced scalar transfer rate. - Abstract: Direct numerical simulations (DNS) of turbulent boundary layers (TBLs) over isothermally heated walls were performed, and the influence of the wall-heating on the thermal boundary layers was investigated. The DNS adopt an empirical relation for the temperature-dependent viscosity of water. The Prandtl number therefore changes with temperature, while the Péclet number is constant. Two wall temperatures (Tw = 70 °C and 99 °C) were considered relative to T∞ = 30 °C, and a reference simulation of TBL with constant viscosity was also performed for comparison. In the variable viscosity flow, the mean and variance of the scalar, when normalized by the friction temperature deficit, decrease relative to the constant viscosity flow. A relation for the mean scalar which takes into account the variable viscosity is proposed. Appropriate scalings for the scalar fluctuations and the scalar flux are also introduced, and are shown to be applicable for both variable and constant viscosity flows. Due to the modification of the near-wall turbulence, the Stanton number and the Reynolds analogy factor are augmented by 10% and 44%, respectively, in the variable viscosity flow. An identity for the Stanton number is derived and shows that the mean wall-normal velocity and wall-normal scalar flux cause the increase in the heat transfer coefficient. Finally, the augmented near-wall velocity fluctuations lead to an increase of the wall-normal scalar flux, which contributes favorably to the enhanced heat transfer at the wall
Surface Temperature and Surface-Layer Turbulence in a Convective Boundary Layer
Garai, A.; Pardyjak, E.; Steeneveld, G.J.; Kleissl, J.
2013-01-01
Previous laboratory and atmospheric experiments have shown that turbulence influences the surface temperature in a convective boundary layer. The main objective of this study is to examine land-atmosphere coupled heat transport mechanism for different stability conditions. High frequency infrared im
Transition in Hypersonic Boundary Layers: Role of Dilatational Waves
Zhu, Yiding; Yuan, Huijing; Wu, Jiezhi; Chen, Shiyi; Lee, Cunbiao; Gad-el-Hak, Mohamed
2015-01-01
Transition and turbulence production in a hypersonic boundary layer is investigated in a Mach 6 quiet wind tunnel using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. It is found that the second instability acoustic mode is the key modulator of the transition process. The second mode experiences a rapid growth and a very fast annihilation due to the effect of bulk viscosity. The second mode interacts strongly with the first vorticity mode to directly promote a fast growth of the latter and leads to immediate transition to turbulence.
Large Eddy Simulation of the ventilated wave boundary layer
DEFF Research Database (Denmark)
Lohmann, Iris P.; Fredsøe, Jørgen; Sumer, B. Mutlu;
2006-01-01
to reproduce experimental results well. However, in case 1, the near-bed ensemble averaged velocity is underestimated during the acceleration stage, probably due to the Smagorinsky subgrid-scale model not being able to capture the physics well in that region. Also, there is a general overestimation......A Large Eddy Simulation (LES) of (1) a fully developed turbulent wave boundary layer and (2) case 1 subject to ventilation (i.e., suction and injection varying alternately in phase) has been performed, using the Smagorinsky subgrid-scale model to express the subgrid viscosity. The model was found...
STUDY OF SWEPT SHOCK WAVE AND BOUNDARY LAYER INTERACTIONS
Institute of Scientific and Technical Information of China (English)
1998-01-01
This paper presents briefly the recent progress on study of swept shock wave/boundary layer interactions with emphasis on application of zonalanalysis and correlation analysis to them. Based on the zonal analysis an overall framework of complicated interaction flow structure including both surface flowfield and space flowfield is discussed. Based on correlation analysis the conical interactions induced by four families of shock wave generators have been discussedin detail. Some control parameter and physical mechanism of conical interaction have been revealed. Finally some aspects of the problem and the prospects for future work are suggested.
Experiments on the active control of transitional boundary layers
Nelson, P. A.; Rioual, J.-L.; Fisher, M. J.
Experimental results are presented which demonstrate that the streamwise position of the transition region of a flat plate boundary layer can be actively controlled. The means of control is through the application of suction through the surface of the plate, a progressive increase in suction rate being capable of producing transition at progressively larger distances downstream from the plate leading edge. A simple digital feedback regulator based on an integral control law is shown to be most effective in regulating the position of transition, an error signal being derived from measurements of pressure fluctuations on the surface of the plate.
A wavenumber-frequency spectral model for atmospheric boundary layers
International Nuclear Information System (INIS)
Motivated by the need to characterize power fluctuations in wind farms, we study spatio-temporal correlations of a neutral atmospheric boundary layer in terms of the joint wavenumber-frequency spectrum of the streamwise velocity fluctuations. To this end, we perform a theoretical analysis of a simple advection model featuring the advection of small- scale velocity fluctuations by the mean flow and large-scale velocity fluctuations. The model is compared to data from large-eddy simulations (LES). We find that the model captures the trends observed in LES, specifically a Doppler shift of frequencies due to the mean flow as well as a Doppler broadening due to random sweeping effects
Lidar Scanning of Momentum Flux in the Marine Boundary Layer
DEFF Research Database (Denmark)
Pena Diaz, Alfredo; Mann, Jakob; Courtney, Michael;
Momentum flux measurements are important for describing the wind profile in the atmospheric boundary layer, modeling the atmospheric flow over water, the accounting of exchange processes between air and sea, etc. It is also directly related to the friction velocity, which is a velocity scale...... turbulence measurements from a sonic anemometer, showing high agreement. In this study, a conical scanning lidar is used to derive the momentum flux, which compares well to the estimations from the bulk-derived method, but it also shows a filtering effect due to the large spatial-averaging volume...
Role of the vertical pressure gradient in wave boundary layers
DEFF Research Database (Denmark)
Jensen, Karsten Lindegård; Sumer, B. Mutlu; Vittori, Giovanna;
2014-01-01
By direct numerical simulation (DNS) of the flow in an oscillatory boundary layer, it is possible to obtain the pressure field. From the latter, the vertical pressure gradient is determined. Turbulent spots are detected by a criterion involving the vertical pressure gradient. The vertical pressure...... gradient is also treated as any other turbulence quantity like velocity fluctuations and statistical properties of the vertical pressure gradient are calculated from the DNS data. The presence of a vertical pressure gradient in the near bed region has significant implications for sediment transport....
Notes on an Internal Boundary-Layer Height Formula
Savelyev, Sergiya.; Taylor, Petera.
The derivation of the Panofsky-Dutton internal boundary-layer(IBL) height formula has been revisited. We propose that the upwindroughness length (rather than downwind) should be used in theformula and that a turbulent vertical velocity (w) ratherthan the surface friction velocity (u*) should be considered asthe appropriate scaling for the rate of propagation ofdisturbances into the turbulent flow. A published set ofwind-tunnel and atmospheric data for neutral stratification hasbeen used to investigate the influence of the magnitude ofroughness change on the IBL height.
Injection-induced turbulence in stagnation-point boundary layers
Park, C.
1984-02-01
A theory is developed for the stagnation point boundary layer with injection under the hypothesis that turbulence is produced at the wall by injection. From the existing experimental heat transfer rate data obtained in wind tunnels, the wall mixing length is deduced to be a product of a time constant and an injection velocity. The theory reproduces the observed increase in heat transfer rates at high injection rates. For graphite and carbon-carbon composite, the time constant is determined to be 0.0002 sec from the existing ablation data taken in an arc-jet tunnel and a balistic range.
Research on Fractal-Scanning Path for Arbitrary Boundary Layer in Layered Manufacturing
Institute of Scientific and Technical Information of China (English)
阳佳; 宾鸿赞; 等
2002-01-01
The fractal curve is proposed as a novel scanning-path used in Layered Manufacturing.Aiming at a limitation that the fractal curve can only fill a square region,a method is developed to realize the trimming of fractal curve in arbitrary boundary layer by means of undging intersection points between parameterized arbitrary boundary and a FASS(space-filling,self-avoiding,simple and self-similar)fractal curve.Accordingly,the related algorithm concerning with determining intersection points has been investigated according to the recursion reature of the fractal curve,and in the process of the fractal curve traversed,the rule of udging intersection points is ascertained as well,so that the laser-scanning beam can “walk” along the fractal curve inside the desired boundary,and arbitrary contour components are fabricated.
International Nuclear Information System (INIS)
In this work, we solve analytically, without losing generality, the neutron diffusion equation for monoenergetic neutrons in a multilayered slab. To this end, we initially determine the solution of the neutron diffusion equation for a generic slab using standard results of second order linear ordinary differential equation with constant coefficients. The global solution for the multilayered slab is then determined applying the boundary condition and continuity of the flux and current at interface. Once the neutron flux is known, the albedo boundary condition is straightly obtained for an arbitrary number of layers in the baffle-reflecting regions, by just using the definition of albedo. We also present numerical simulation for the results neutron flux and comparison with the in literature. (author)
Bhattacharya, Ritthik; Stevens, Bjorn
2016-03-01
A two Turbulence Kinetic Energy (2TKE) model is developed to address the boundary layer "grey zone" problem. The model combines ideas from local and nonlocal models into a single energetically consistent framework. By applying the Reynolds averaging to the large eddy simulation (LES) equations that employ Deardorff's subgrid TKE, we arrive at a system of equations for the boundary layer quantities and two turbulence kinetic energies: one which encapsulates the TKE of large boundary-layer-scale eddies and another which represents the energy of eddies subgrid to the vertical grid size of a typical large-scale model. These two energies are linked via the turbulent cascade of energy from larger to smaller scales and are used to model the mixing in the boundary layer. The model is evaluated for three dry test cases and found to compare favorably to large eddy simulations. The usage of two TKEs for mixing helps reduce the dependency of the model on the vertical grid scale as well as on the free tropospheric stability and facilitates a smoother transition from convective to stable regimes. The usage of two TKEs representing two ranges of scales satisfies the prerequisite for modeling the boundary layer in the "grey zone": an idea that is explored further in a companion paper.
Atmospheric Boundary Layer Characteristics during BOBMEX-Pilot Experiment
Indian Academy of Sciences (India)
G S Bhat; S Ameenulla; M Venkataramana; K Sengupta
2000-06-01
The atmospheric boundary layer characteristics observed during the BOBMEX-Pilot experiment are reported. Surface meteorological data were acquired continuously through an automatic weather monitoring system and manually every three hours. High resolution radiosondes were launched to obtain the vertical thermal structure of the atmosphere. The study area was convectively active, the SSTs were high, surface air was warm and moist, and the surface air moist static energy was among the highest observed over the tropical oceans. The mean sea air temperature difference was about 1.25°C and the sea skin temperature was cooler than bucket SST by 0.5°C. The atmospheric mixed layer was shallow, fluctuated in response to synoptic conditions from 100 m to 900 m with a mean around 500 m.
Interactions between the thermal internal boundary layer and sea breezes
Energy Technology Data Exchange (ETDEWEB)
Steyn, D.G. [The Univ. of British Columbia, Dept. of Geography, Atmospheric Science Programme, Vancouver (Canada)
1997-10-01
In the absence of complex terrain, strongly curved coastline or strongly varying mean wind direction, the Thermal Internal Boundary Layer (TIBL) has well known square root behaviour with inland fetch. Existing slab modeling approaches to this phenomenon indicate no inland fetch limit at which this behaviour must cease. It is obvious however that the TIBL cannot continue to grow in depth with increasing fetch, since the typical continental Mixed Layer Depths (MLD) of 1500 to 2000 m must be reached between 100 and 200 km from the shoreline. The anticyclonic conditions with attendant strong convection and light winds which drive the TIBL, also drive daytime Sea Breeze Circulations (SBC) in the coastal zone. The onshore winds driving mesoscale advection of cool air are at the core of TIBL mechanisms, and are invariably part of a SBC. It is to be expected that TIBL and SBC be intimately linked through common mechanisms, as well as external conditions. (au)
The Dirichlet problem for the two-dimensional Helmholtz equation for an open boundary
Hayashi, Y.
1973-01-01
Development of a complete theory of the two-dimensional Dirichlet problem for an open boundary. It is shown that the solution of the Dirichlet problem for an open boundary requires the solution of a Fredholm integral equation of the first kind. Although a Fredholm integral equation of the first kind usually has no solution if the kernel is continuous, owing to the logarithmic singularity of the kernel, the equation in this case is converted to a singular integral equation with a Cauchy kernel. It is proven that the homogeneous adjoint equation of the singular integral equation has no nonzero solution. By virtue of this result, and with the aid of an existence theorem known in the theory of singular integral equations, the existence of solutions of the singular integral equation, and then of the unique solution of the Fredholm integral equation of the first kind is proved.
THE EFFECT OF BOUNDARY SHAPE ON BOUNDARY LAYER OF P-MODEL PLATEPROBLEMS WITH HARD SIMPLY SUPPORT
Institute of Scientific and Technical Information of China (English)
LILIKANG; CHENJIUHUA
1996-01-01
The paper shows that: for a unit circular plate: Reissner-Mindlin plate model with hardsimply support does not capture the boundary, layer behaviour for the bending moment whenthe load is independent of θ, where (r,θ) is the polar coordinates in plane. In contrast p-modelshows this boundary layer, which is proved theoretically and numerically. But for the case whenthe boundary is a straight line, the boundary layer for p-model is weak and disappears as thePlate thickness tends to zero.
KdV equation under periodic boundary conditions and its perturbations
Huang, Guan; Kuksin, Sergei
2013-01-01
In this paper we discuss properties of the KdV equation under periodic boundary conditions, especially those which are important to study perturbations of the equation. Next we review what is known now about long-time behaviour of solutions for perturbed KdV equations.
The KdV equation under periodic boundary conditions and its perturbations
Guan, Huang; Kuksin, Sergei
2014-09-01
In this paper we discuss properties of the Korteweg-de Vries (KdV) equation under periodic boundary conditions, especially those which are important for studying perturbations of the equation. We then review what is known about the long-time behaviour of solutions for perturbed KdV equations.
THE NAVIER-STOKES EQUATIONS IN STREAM LAYER AND ON STREAM SURFACE AND A DIMENSION SPLIT METHODS
Institute of Scientific and Technical Information of China (English)
李开泰; 黄艾香
2002-01-01
In this paper,we proposal stream surface and stream layer. By using classical tensor calculus, we derive 3-D Navier-Stokes Equations(NSE) in the stream layer under semigeodesic coordinate system, Navier-Stokes equation on the stream surface and 2-D Navier-Stokes equations on a two dimensional manifold. After introducing stream function on the stream surface, a nonlinear initial-boundary value problem satisfies by stream function is obtained, existence and uniqueness of its solution are proven. Based this theory we proposal a new method called "dimension split method" to solve 3D NSE.
Om, D.; Childs, M. E.
1983-01-01
An approximate integral viscous-inviscid interaction method is presented for calculating the development of a turbulent boundary layer subjected to a normal shock wave induced adverse pressure gradient in an internal axisymmetric flow. The inflow conditions and the downstream pressure are provided for the computation. In the supersonic region of shock pressure rise, the Prandtl-Meyer function is used to couple the viscous and inviscid flows. An analytical model for the coupling process is postulated and appropriate equations are defined. Downstream of the sonic point, one-dimensional inviscid flow is assumed for coupling with the viscous flow. The turbulent boundary layer is calculated using Green's integral lag-entrainment method. Comparisons of the solutions with the experimental data are made for interactions which are unseparated, near separation and separated. For comparison purposes, solutions to the time-dependent, mass-averaged, Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model are also shown. The computed results from the integral method show good agreement with experimental data for unseparated interactions and reasonable agreement with the trend of the viscous effects when the interaction becomes increasingly separated.
BOUNDARY VALUE PROBLEM TO DYNAMIC EQUATION ON TIME SCALE
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper we consider a nonlinear first-order boundary value problem on a time scale. The existence results of three positive solutions are obtained using fixed point theorems. Finally,examples are presented to illustrate the main results.
Sweeping Preconditioner for the Helmholtz Equation: Artificial Perfectly Matched Layers
Engquist, Björn
2010-01-01
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate $LDL^t$ factorization by eliminating the unknowns layer by layer starting from an absorbing layer. The central idea of this paper is to approximate the Schur complement matrices of the factorization using artificial perfectly matched layers (PMLs) introduced in the interior of the domain. Applying each Schur complement matrix is equivalent to solving a quasi-1D problem with a banded LU factorization in the 2D case and to solving a quasi-2D problem with a multifrontal method in the 3D case. The resulting preconditioner has linear application cost and the preconditioned iterative solver converges in a number of iterations that scales at most logarithmically with the number of unknowns. Numerical results are presented in both two and three dimensions to demonstrate the efficiency of thi...
Boundary integral equation method calculations of surface regression effects in flame spreading
Altenkirch, R. A.; Rezayat, M.; Eichhorn, R.; Rizzo, F. J.
1982-01-01
A solid-phase conduction problem that is a modified version of one that has been treated previously in the literature and is applicable to flame spreading over a pyrolyzing fuel is solved using a boundary integral equation (BIE) method. Results are compared to surface temperature measurements that can be found in the literature. In addition, the heat conducted through the solid forward of the flame, the heat transfer responsible for sustaining the flame, is also computed in terms of the Peclet number based on a heated layer depth using the BIE method and approximate methods based on asymptotic expansions. Agreement between computed and experimental results is quite good as is agreement between the BIE and the approximate results.
Application of Arnoldi method to boundary layer instability
Zhang, Yong-Ming; Luo, Ji-Sheng
2015-12-01
The Arnoldi method is applied to boundary layer instability, and a finite difference method is employed to avoid the limit of the finite element method. This modus operandi is verified by three comparison cases, i.e., comparison with linear stability theory (LST) for two-dimensional (2D) disturbance on one-dimensional (1D) basic flow, comparison with LST for three-dimensional (3D) disturbance on 1D basic flow, and comparison with Floquet theory for 3D disturbance on 2D basic flow. Then it is applied to secondary instability analysis on the streaky boundary layer under spanwise-localized free-stream turbulence (FST). Three unstable modes are found, i.e., an inner mode at a high-speed center streak, a sinuous type outer mode at a low-speed center streak, and a sinuous type outer mode at low-speed side streaks. All these modes are much more unstable than Tollmien-Schlichting (TS) waves, implying the dominant contribution of secondary instability in bypass transition. The modes at strong center streak are more unstable than those at weak side streaks, so the center streak is ‘dangerous’ in secondary instability. Project supported by the National Natural Science Foundation of China (Grant Nos. 11202147, 11332007, 11172203, and 91216111) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20120032120007).
Retrievals of boundary layer methane and isotope fractionation on Titan
Adamkovics, Mate; Lora, Juan M.; Mitchell, Jonathan L.
2016-10-01
The amount of methane in the boundary layer on Titan is an interesting diagnostic of whether or not it might be seeping out of the regolith. We know that kinetic fractionation of methane isotopes can be diagnostic of evaporation at the surface and condensation in the atmosphere. If a parcel is constrained to follow a moist adiabat while condensation occurs, we can predict the amount of fractionation that is expected (Ádámkovics & Mitchell, 2016). We will present our most recent efforts to measure boundary layer methane abundance and isotopic composition, which include our recently published Keck NIRSPAO observations from 17 July 2014 (Ádámkovics et al., 2016), as well as preliminary results from follow-up measurements made on 15 May 2016. Our measurements are tantalizingly close to being able to distinguish between different hydrological parameterizations of the polar regions in the Titan Atmospheric Model (Lora & Ádámkovics, 2016). We will discuss the systematic uncertainties that can be evaluated with the combination of these two datasets and the prospects for exceptionally high S/N observations via particularly deep integrations over multiple nights.
Characteristics of turbulent boundary layer flow over algal biofilm
Murphy, Elizabeth; Barros, Julio; Schultz, Michael; Steppe, Cecily; Flack, Karen; Reidenbach, Matthew
2015-11-01
Algal biofilms are an important fouling community on ship hulls, with severe economic consequences due to drag-induced increases in fuel use and cleaning costs. Here, we characterize the boundary layer flow structure in turbulent flow over diatomaceous slime, a type of biofilm. Diatomaceous slime composed of three species of diatoms commonly found on ship hulls was grown on acrylic test plates under shear stress. The slime averages 1.6 mm in thickness and has a high density of streamers, which are flexible elongated growths with a length on the order of 1- 2 mm located at the top of the biofilm that interact with the flow. Fouled acrylic plates were placed in a water tunnel facility specialized for detailed turbulent boundary layer measurements. High resolution Particle Image Velocimetry (PIV) data are analyzed for mean velocity profile as well as local turbulent stresses and turbulent kinetic energy (TKE) production, dissipation and transport. Quadrant analysis is used to characterize the impact of the instantaneous events of Reynolds shear stress (RSS) in the flow. To investigate the coherence of the large-scale motion in the flow two-point correlation analysis is employed. Funding provided by the Office of Naval Research and the National Science Foundation.
Hypersonic boundary-layer transition on a flared cone
Institute of Scientific and Technical Information of China (English)
Chuan-Hong Zhang; Qing Tang; Cun-Biao Lee
2013-01-01
Transition on a flared cone with zero angle of attack was studied in our newly established Mach 6 quiet wind tunnel (M6QT) via wall pressure measurement and flow visualization.High-frequency pressure transducers were used to measure the second-mode waves' amplitudes and frequencies.Using pulsed schlieren diagnostic and Rayleigh scattering technique,we got a clear evolution of the second-mode disturbances.The second-mode waves exist for a long distance,which means that the second-mode waves grow linearly in a large region.Strong Mach waves are radiated from the edge of the boundary layer.With further development,the second-mode waves reach their maximum magnitude and harmonics of the second-mode instability appear.Then the disturbances grow nonlinearly.The second modes become weak and merge with each other.Finally,the nonlinear interaction of disturbance leads to a relatively quiet zone,which further breaks down,resulting in the transition of the boundary layer.Our results show that transition is determined by the second mode.The quiet zone before the final breakdown is observed in flow visualization for the first time.Eventual transition requires the presence of a quiet zone generated by nonlinear interactions.
Using GPS Radio Occultation to study polar boundary layer properties
Ganeshan, M.; Wu, D. L.
2015-12-01
The sensitivity of GPS RO refractivity to moisture and temperature variations in polar regions is explored using radiosonde observations from the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment. A retrieval algorithm for the boundary layer inversion height and surface-based inversion (SBI) frequency is developed for dry atmospheric conditions (total precipitable water < 3.6 mm) that typically exist during polar winter, as well as in high-latitude, elevated regions such as eastern Antarctica and central Greenland. The algorithm is applied to the high-resolution refractivity profiles obtained over the polar Arctic region using the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) dataset for the period 2006-2013. The method is found useful for capturing the spatiotemporal variability in Arctic inversion properties. For the Arctic Ocean, the spatial patterns show a minimum inversion height (maximum SBI frequency) over the ice-covered Pacific sector similar to that observed in past studies. Monthly evolution of the inversion characteristics suggests a surface temperature control in the multi-year sea ice region, with the peak in SBI frequency occurring during the transition period from winter to spring. For central Greenland, the seasonal peak in SBI frequency occurs during winter. The diurnal variability in SBI frequency is forced mainly by solar heating, consistent with past observations. Despite some limitations, the RO refractivity profile is found quite useful for monitoring the Arctic boundary layer, and is able to capture the interannual variability of inversion characteristics.
Delaying natural transition of a boundary layer using smooth steps
Xu, Hui; Sherwin, Spencer J
2015-01-01
The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on the delay of the transition to turbulence. The interaction between the Tollmien-Schlichting (T-S) waves and the base flow over a single/two forward facing smooth steps is conducted by linear analysis indicating the amplitude of the T-S waves are attenuated in the boundary layer over a single smooth plate. Furthermore, we show that two smooth forward facing steps give rise to a further reduction of the amplitude of the T-S waves. A direct numerical simulation (DNS) is performed for the two smooth forward steps correlating favourably with the linear analysis and showing that for the investigated parameters, the K-type transition is inhibited whereas the turbulence onset of the H-type transition is postponed albeit not suppressed. Transition is indeed delayed and drag reduced for both these transition scenarios suggesting smooth forward facing steps could be leveraged as a passive flow control strategy to de...
Second Law Analysis of the Turbulent Flat Plate Boundary Layer
Directory of Open Access Journals (Sweden)
Dragos Isvoranu
2000-09-01
Full Text Available
Until now the second law analysis of turbulent flow relied only on the irreversibilities performed by the mean velocity and mean temperature gradients. Using the Reynolds decomposition of the volumetric entropy generation rate expression we found that the dissipation rates of both, turbulent kinetic energy and fluctuating temperature variance, also represent the irreversibilities of the flow. Applying the above results, the second law analysis of the turbulent boundary layer shows that the maximum values of the "mean motion irreversibilities" (generated by the mean velocity and mean temperature gradient are located at the wall, while the maximum values of the "turbulent irreversibilities" (performed by the dissipation rate of turbulent kinetic energy and fluctuating temperature variance are located in the buffer sublayer. As a consequence, for a given location on the plate, the integral values of the "mean motion irreversibilities" are approximately constant and the "turbulent irreversibilities" grow up with the boundary layer thickness.
A law of the wall for turbulent boundary layers with suction: Stevenson's formula revisited
Vigdorovich, Igor
2016-08-01
The turbulent velocity field in the viscous sublayer of the boundary layer with suction to a first approximation is homogeneous in any direction parallel to the wall and is determined by only three constant quantities — the wall shear stress, the suction velocity, and the fluid viscosity. This means that there exists a finite algebraic relation between the turbulent shear stress and the longitudinal mean-velocity gradient, using which as a closure condition for the equations of motion, we establish an exact asymptotic behavior of the velocity profile at the outer edge of the viscous sublayer. The obtained relationship provides a generalization of the logarithmic law to the case of wall suction.
Boundary Layer Ducting of Low-elevation GNSS Ocean Reflected Signals
DEFF Research Database (Denmark)
Høeg, Per; von Benzon, Hans-Henrik; Durgonics, Tibor
reflection zone (and broader received power spectra).The spectral analysis of the simulated surface reflected signals shows spectral structures that could be used for the extraction of parameters as, boundary layer height and atmosphere water vapor density, sea surface roughness, ocean wave heights......, and surface wind speed. The presented simulations will quantify how these parameters are derived from the observations. Our simulator uses a finite difference solution to the parabolic wave equation using the split stepsine transformation. The ocean surface is modeled through the use of an impedance model...
Direct spatial resonance in the laminar boundary layer due to a rotating-disk
Indian Academy of Sciences (India)
M Turkyilmazoglu; J S B Gajjar
2000-12-01
Numerical treatment of the linear stability equations is undertaken to investigate the occurrence of direct spatial resonance events in the boundary layer flow due to a rotating-disk. A spectral solution of the eigenvalue problem indicates that algebraic growth of the perturbations shows up, prior to the amplification of exponentially growing instability waves. This phenomenon takes place while the flow is still in the laminar state and it also tends to persist further even if the non-parallelism is taken into account. As a result, there exists the high possibility of this instability mechanism giving rise to nonlinearity and transition, long before the unboundedly growing time-amplified waves.
Time-domain implementation of an impedance boundary condition with boundary layer correction
Brambley, E. J.; Gabard, G.
2016-09-01
A time-domain boundary condition is derived that accounts for the acoustic impedance of a thin boundary layer over an impedance boundary, based on the asymptotic frequency-domain boundary condition of Brambley (2011) [25]. A finite-difference reference implementation of this condition is presented and carefully validated against both an analytic solution and a discrete dispersion analysis for a simple test case. The discrete dispersion analysis enables the distinction between real physical instabilities and artificial numerical instabilities. The cause of the latter is suggested to be a combination of the real physical instabilities present and the aliasing and artificial zero group velocity of finite-difference schemes. It is suggested that these are general properties of any numerical discretization of an unstable system. Existing numerical filters are found to be inadequate to remove these artificial instabilities as they have a too wide pass band. The properties of numerical filters required to address this issue are discussed and a number of selective filters are presented that may prove useful in general. These filters are capable of removing only the artificial numerical instabilities, allowing the reference implementation to correctly reproduce the stability properties of the analytic solution.
A formal derivation for the Blasius similarity solution for flat-plate boundary layer
Lin, Hao
2015-11-01
The Blasius solution is a classical solution for a laminar boundary layer attached to a semi-infinite flat plate. The key of the solution strategy is to reduce the boundary layer equations, which are PDEs, to a set of ODEs, using a similarity variable transform. Conceptually, the similarity suggests that the velocity profile in each transverse cross-section appears ``self-similar''. In many classical text books and typical classroom lectures on fluid mechanics, the existence of the similarity solution is argued heuristically. The similarity variable is defined a priori so as to collapse the PDEs. It appears somewhat mystical that the PDEs can be perfectly reduced via such an approach. Here we present a rigorous derivation for the existence of a similarity solution, which naturally arises from the fact that there is no apparent streamwise length scale for a semi-infinite plate. Conversely, a similarity solution cannot exist if the plate size is finite. This derivation can be useful in fluids education, in topics including similarity, scaling arguments, and boundary layer theory.
On the Impact of Wind Farms on a Convective Atmospheric Boundary Layer
Lu, Hao; Porté-Agel, Fernando
2015-10-01
With the rapid growth in the number of wind turbines installed worldwide, a demand exists for a clear understanding of how wind farms modify land-atmosphere exchanges. Here, we conduct three-dimensional large-eddy simulations to investigate the impact of wind farms on a convective atmospheric boundary layer. Surface temperature and heat flux are determined using a surface thermal energy balance approach, coupled with the solution of a three-dimensional heat equation in the soil. We study several cases of aligned and staggered wind farms with different streamwise and spanwise spacings. The farms consist of Siemens SWT-2.3-93 wind turbines. Results reveal that, in the presence of wind turbines, the stability of the atmospheric boundary layer is modified, the boundary-layer height is increased, and the magnitude of the surface heat flux is slightly reduced. Results also show an increase in land-surface temperature, a slight reduction in the vertically-integrated temperature, and a heterogeneous spatial distribution of the surface heat flux.
The effect of non-Newtonian viscosity on the stability of the Blasius boundary layer
Griffiths, P. T.; Gallagher, M. T.; Stephen, S. O.
2016-07-01
We consider, for the first time, the stability of the non-Newtonian boundary layer flow over a flat plate. Shear-thinning and shear-thickening flows are modelled using a Carreau constitutive viscosity relationship. The boundary layer equations are solved in a self-similar fashion. A linear asymptotic stability analysis, that concerns the lower-branch structure of the neutral curve, is presented in the limit of large Reynolds number. It is shown that the lower-branch mode is destabilised and stabilised for shear-thinning and shear-thickening fluids, respectively. Favourable agreement is obtained between these asymptotic predictions and numerical results obtained from an equivalent Orr-Sommerfeld type analysis. Our results indicate that an increase in shear-thinning has the effect of significantly reducing the value of the critical Reynolds number, this suggests that the onset of instability will be significantly advanced in this case. This postulation, that shear-thinning destabilises the boundary layer flow, is further supported by our calculations regarding the development of the streamwise eigenfunctions and the relative magnitude of the temporal growth rates.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper deals with boundary value problems for linear uniformly elliptic systems. First the general linear uniformly elliptic system of the first order equations is reduced to complex form, and then the compound boundary value problem for the complex equations of the first order is discussed. The approximate solutions of the boundary value problem are found by the variation-difference method, and the error estimates for the approximate solutions are derived.Finally the approximate method of the oblique derivative problem for linear uniformly elliptic equations of the second or der is introduced.
Local absorbing boundary conditions for nonlinear wave equation on unbounded domain.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2011-09-01
The numerical solution of the nonlinear wave equation on unbounded spatial domain is considered. The artificial boundary method is introduced to reduce the nonlinear problem on unbounded spatial domain to an initial boundary value problem on a bounded domain. Using the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and give the stability analysis of the resulting boundary conditions. Finally, several numerical examples are given to demonstrate the effectiveness of our method.
Boundary Shape Control of the Navier-Stokes Equations and Applications
Institute of Scientific and Technical Information of China (English)
Kaitai LI; Jian SU; Aixiang HUANG
2010-01-01
In this paper,the geometrical design for the blade's surface(s)in an impeller or for the profile of an aircraft,is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations.The objective function is the sum of a global dissipative function and the power of the fluid.The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations.The Euler-Lagrange equations of the optimal control problem are derived,which are an elliptic boundary value system of fourth order,coupled with the Navier-Stokes equations.The authors also prove the existence of the solution of the optimal control problem,the existence of the solution of the Navier-Stokes equations with mixed boundary conditions,the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the G(a)teaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.
Directory of Open Access Journals (Sweden)
Bingyu Shen
2015-10-01
Full Text Available This paper presents an investigation for magnetohydrodynamic (MHD viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.
Energy Technology Data Exchange (ETDEWEB)
Shen, Bingyu; Zheng, Liancun, E-mail: liancunzheng@ustb.edu.cn; Chen, Shengting [School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083 (China)
2015-10-15
This paper presents an investigation for magnetohydrodynamic (MHD) viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.
International Nuclear Information System (INIS)
This paper presents an investigation for magnetohydrodynamic (MHD) viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail
Bassom, Andrew P.; Hall, Philip
1990-01-01
Recently there has been much work devoted to considering some of the many and varied interaction mechanisms which may be operative in three-dimensional boundary layer flows. This paper is concerned with resonant triads of crossflow vortices. The effects of interactions upon resonant triads is examined where each member of the triad has the property of being linearly neutrally stable so that the importance of the interplay between modes can be relatively easily assessed. Modes within the boundary layer flow above a rotating disc are investigated because of the similarity between this disc flow and many important practical flows and, secondly, because the selected flow is an exact solution of the Navier-Stokes equations which makes its theoretical analysis especially attractive. It is demonstrated that the desired triads of linearly neutrally stable modes can exist within the chosen boundary layer flow. Evolution equations are obtained to describe the development of the amplitudes of these modes once the interaction mechanism is accounted for. It is found that the coefficients of the interaction terms within the evolution equations are, in general, given by quite intricate expressions although some elementary numerical work shows that the evaluation of these coefficients is practicable. The basis of the work lends itself to generalization to more complicated boundary layers, and effects of detuning or non-parallelism could be provided for within the asymptotic framework.
FOREWORD: International Conference on Planetary Boundary Layer and Climate Change
Djolov, G.; Esau, I.
2010-05-01
One of the greatest achievements of climate science has been the establisment of the concept of climate change on a multitude of time scales. The Earth's complex climate system does not allow a straightforward interpretation of dependences between the external parameter perturbation, internal stochastic system dynamics and the long-term system response. The latter is usually referred to as climate change in a narrow sense (IPCC, 2007). The focused international conference "Planetary Boundary Layers and Climate Change" has addressed only time scales and dynamical aspects of climate change with possible links to the turbulent processes in the Planetary Boundary Layer (PBL). Although limited, the conference topic is by no means singular. One should clearly understand that the PBL is the layer where 99% of biosphere and human activity are concentrated. The PBL is the layer where the energy fluxes, which are followed by changes in cryosphere and other known feedbacks, are maximized. At the same time, the PBL processes are of a naturally small scale. What is the averaged long-term effect of the small-scale processes on the long-term climate dynamics? Can this effect be recognized in existing long-term paleo-climate data records? Can it be modeled? What is the current status of our theoretical understanding of this effect? What is the sensitivity of the climate model projections to the representation of small-scale processes? Are there significant indirect effects, e.g. through transport of chemical components, of the PBL processes on climate? These and other linked questions have been addressed during the conference. The Earth's climate has changed many times during the planet's history, with events ranging from ice ages to long periods of warmth. Historically, natural factors such as the amount of energy released from the Sun, volcanic eruptions and changes in the Earth's orbit have affected the Earth's climate. Beginning late in the 18th century, human activities
Ferdows, M.
2012-01-01
Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed. 2012 M. Ferdows et al.
Directory of Open Access Journals (Sweden)
M. Ferdows
2012-01-01
Full Text Available Magnetohydrodynamic (MHD boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed.
Simulation of Wind turbines in the atmospheric boundary layer
DEFF Research Database (Denmark)
Chivaee, Hamid Sarlak; Sørensen, Jens Nørkær; Mikkelsen, Robert Flemming
the computational costs scale rapidly with Reynolds number and domain size[1]. An approach to overcome these deficiencies is to use a wall modeling near the walls and then use a coarser grid at the first grid level above the ground. This could be performed by using simplified Navier-Stokes equations in the boundary...... as well as turbulent inflow condition. For generating turbulent inflow, a model is used in which a turbulent plane is introduced in the domain and convected in each time step, using Taylor's frozen hypothesis. The results of different simulations are analysed and compared in terms of mean values...... and higher moments. As an example, figure (1) shows a 2D snapshot of stream-wise velocity contours (in SI units) in an infinite row of wind turbines simulated in stably stratified flow. Simulations are performed usind the in-house CFD code Ellipsys3D, which is a multi-block general purpose, parallelized...
Afzal, Bushra; Noor Afzal Team; Bushra Afzal Team
2014-11-01
The momentum and thermal turbulent boundary layers over a continuous moving sheet subjected to a free stream have been analyzed in two layers (inner wall and outer wake) theory at large Reynolds number. The present work is based on open Reynolds equations of momentum and heat transfer without any closure model say, like eddy viscosity or mixing length etc. The matching of inner and outer layers has been carried out by Izakson-Millikan-Kolmogorov hypothesis. The matching for velocity and temperature profiles yields the logarithmic laws and power laws in overlap region of inner and outer layers, along with friction factor and heat transfer laws. The uniformly valid solution for velocity, Reynolds shear stress, temperature and thermal Reynolds heat flux have been proposed by introducing the outer wake functions due to momentum and thermal boundary layers. The comparison with experimental data for velocity profile, temperature profile, skin friction and heat transfer are presented. In outer non-linear layers, the lowest order momentum and thermal boundary layer equations have also been analyses by using eddy viscosity closure model, and results are compared with experimental data. Retired Professor, Embassy Hotel, Rasal Ganj, Aligarh 202001 India.
Talpos, Simona; Apostol, Marian
2015-12-01
It is shown that the Reynolds equations for a turbulent flow over an unbounded flat surface in the presence of a constant pressure-gradient lead to a displaced logarithmic profile of the velocity distribution; the displaced logarithmic profile is obtained by assuming a constant production rate of turbulence energy. The displacement height measured on the (vertical) axis perpendicular to the surface is either positive or negative. For a positive displacement height the boundary layer exhibits an inversion, while for a negative displacement height the boundary layer is a direct one. In an inversion boundary layer the logarithmic velocity profile is disrupted into two distinct branches separated by a logarithmic singularity. The viscosity transforms this logarithmic singularity into a sharp edge, governed by a generalized Reynolds number. The associated temperature distribution is calculated, and the results are discussed in relation to meteorological boundary-layer jets and stratified layers. The effects of gravitation and atmospheric thermal or fluid-mixture concentration gradients ("external forcings") are also considered; it is shown that such circumstances may lead to various modifications of the boundary layers. A brief presentation of a similar situation is described for a circular pipe.
A Lagrangian Study of Southeast Pacific Boundary Layer Clouds
Painter, Gallia
concentration which extend far offshore into regions of normally very clean cloud. We use Lagrangian trajectories to investigate the source of the high droplet concentrations of the mesoscale "hooks", and evaluate whether boundary layer transport of coastal pollutants alone can account for their extent. We find that boundary layer trajectories past 85 W do not pass sufficiently close to the coastline to explain high aerosol concentrations offshore.
Institute of Scientific and Technical Information of China (English)
Xiao-jing LIU; Ji-zeng WANG; Xiao-min WANG; You-he ZHOU
2014-01-01
General exact solutions in terms of wavelet expansion are obtained for multi-term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ-ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.
The viscous boundary layer at the free surface of a rotating baroclinic fluid
Hide, R.
2011-01-01
The properties of the viscous boundary layer at the free surface of a rotating baroclinic fluid are analyzed and compared with those of the well-known Ekman boundary layer at a rigid surface. Although the ageostrophic components of the flow in the free surface boundary layer are weaker than in the Ekman layer, there are problems of practical interest in which their effects are not negligible.DOI: 10.1111/j.2153-3490.1964.tb00188.x
Uranus evolution models with simple thermal boundary layers
Nettelmann, N; Fortney, J J; Hamel, S; Yellamilli, S; Bethkenhagen, M; Redmer, R
2016-01-01
The strikingly low luminosity of Uranus (Teff ~ Teq) constitutes a long-standing challenge to our understanding of Ice Giant planets. Here we present the first Uranus structure and evolution models that are constructed to agree with both the observed low luminosity and the gravity field data. Our models make use of modern ab initio equations of state at high pressures for the icy components water, methane, and ammonia. Proceeding step by step, we confirm that adiabatic models yield cooling times that are too long, even when uncertainties in the ice:rock ratio (I:R) are taken into account. We then argue that the transition between the ice/rock-rich interior and the H/He-rich outer envelope should be stably stratified. Therefore, we introduce a simple thermal boundary and adjust it to reproduce the low luminosity. Due to this thermal boundary, the deep interior of the Uranus models are up to 2--3 warmer than adiabatic models, necessitating the presence of rocks in the deep interior with a possible I:R of $1\\tim...
INITIAL BOUNDARY VALUE PROBLEM FOR A DAMPED NONLINEAR HYPERBOLIC EQUATION
Institute of Scientific and Technical Information of China (English)
陈国旺
2003-01-01
In the paper, the existence and uniqueness of the generalized global solution and the classical global solution of the initial boundary value problems for the nonlinear hyperbolic equationare proved by Galerkin method and the sufficient conditions of blow-up of solution in finite time are given.
Uranus evolution models with simple thermal boundary layers
Nettelmann, N.; Wang, K.; Fortney, J. J.; Hamel, S.; Yellamilli, S.; Bethkenhagen, M.; Redmer, R.
2016-09-01
The strikingly low luminosity of Uranus (Teff ≃ Teq) constitutes a long-standing challenge to our understanding of Ice Giant planets. Here we present the first Uranus structure and evolution models that are constructed to agree with both the observed low luminosity and the gravity field data. Our models make use of modern ab initio equations of state at high pressures for the icy components water, methane, and ammonia. Proceeding step by step, we confirm that adiabatic models yield cooling times that are too long, even when uncertainties in the ice:rock ratio (I:R) are taken into account. We then argue that the transition between the ice/rock-rich interior and the H/He-rich outer envelope should be stably stratified. Therefore, we introduce a simple thermal boundary and adjust it to reproduce the low luminosity. Due to this thermal boundary, the deep interior of the Uranus models are up to 2-3 warmer than adiabatic models, necessitating the presence of rocks in the deep interior with a possible I:R of 1 × solar. Finally, we allow for an equilibrium evolution (Teff ≃ Teq) that begun prior to the present day, which would therefore no longer require the current era to be a "special time" in Uranus' evolution. In this scenario, the thermal boundary leads to more rapid cooling of the outer envelope. When Teff ≃ Teq is reached, a shallow, subadiabatic zone in the atmosphere begins to develop. Its depth is adjusted to meet the luminosity constraint. This work provides a simple foundation for future Ice Giant structure and evolution models, that can be improved by properly treating the heat and particle fluxes in the diffusive zones.
Randall, David A.; Abeles, James A.; Corsetti, Thomas G.
1985-04-01
The UCLA general circulation model (GCM) has been used to simulate the seasonally varying planetary boundary layer (PBL), as well as boundary-layer stratus and stratocumulus clouds. The PBL depth is a prognostic variable of the GCM, incorporated through the use of a vertical coordinate system in which the PBL is identified with the lowest model layer.Stratocumulus clouds are assumed to occur whenever the upper portion of the PBL becomes saturated, provided that the cloud-top entrainment instability does not occur. As indicated by Arakawa and Schubert, cumulus clouds are assumed to originate at the PBL top, and tend to make the PBL shallow by drawing on its mass.Results are presented from a three-year simulation, starting from a 31 December initial condition obtained from an earlier run with a different version of the model. The simulated seasonally varying climates of the boundary layer and free troposphere are realistic. The observed geographical and seasonal variations of stratocumulus cloudiness are fairly well simulated. The simulation of the stratocumulus clouds associated with wintertime cold-air outbreaks is particularly realistic. Examples are given of individual events. The positions of the subtropical marine stratocumulus regimes are realistically simulated, although their observed frequency of occurrence is seriously underpredicted. The observed summertime abundance of Arctic stratus clouds is also underpredicted.In the GCM results, the layer cloud instability appears to limit the extent of the marine subtropical stratocumulus regimes. The instability also frequently occurs in association with cumulus convection over land.Cumulus convection acts as a very significant sink of PBL mass throughout the tropics, and over the midlatitude continents in summer.Three experiments have been performed to investigate the sensitivity of the GCM results to aspects of the PBL and stratocumulus parameterizations. For all three experiments, the model was started from 1
A CLASS OF SINGULARLY PERTURBED INITIAL BOUNDARY PROBLEM FOR REACTION DIFFUSION EQUATION
Institute of Scientific and Technical Information of China (English)
Xie Feng
2003-01-01
The singularly perturbed initial boundary value problem for a class of reaction diffusion equation isconsidered. Under appropriate conditions, the existence-uniqueness and the asymptotic behavior of the solu-tion are showed by using the fixed-point theorem.
Otelbaev, Mukhtarbay; Koshanov, Bakytbek D.
2016-08-01
This paper describes the correct narrowing of the Navier-Stokes equations in a stationary three-dimensional cube and clarified the correct formulation of the boundary conditions for the pressure in the environment.
The Pressure Boundary Conditions for the Incompressible Navier—Stokes Equations Computation
Institute of Scientific and Technical Information of China (English)
YaosongCHEN; TaoJIANG
1996-01-01
This article devotes to the correct formulation of the pressure boundary conditions for the incompressible Navier-Stokes equation and gives the method of integration.The example has been shown for its feasibility.
Asymptotic behavior of solutions to nonlinear parabolic equation with nonlinear boundary conditions
Directory of Open Access Journals (Sweden)
Diabate Nabongo
2008-01-01
Full Text Available We show that solutions of a nonlinear parabolic equation of second order with nonlinear boundary conditions approach zero as t approaches infinity. Also, under additional assumptions, the solutions behave as a function determined here.