scholarly journals Similarity Solutions of the MHD Boundary Layer Flow Past a Constant Wedge within Porous Media

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ramesh B. Kudenatti ◽  
Shreenivas R. Kirsur ◽  
Achala L. Nargund ◽  
N. M. Bujurke
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Similarity Solutions ◽  
Positive Pressure ◽  
Boundary Layer Equations ◽  
Similarity Transformations ◽  
Wide Range

The two-dimensional magnetohydrodynamic flow of a viscous fluid over a constant wedge immersed in a porous medium is studied. The flow is induced by suction/injection and also by the mainstream flow that is assumed to vary in a power-law manner with coordinate distance along the boundary. The governing nonlinear boundary layer equations have been transformed into a third-order nonlinear Falkner-Skan equation through similarity transformations. This equation has been solved analytically for a wide range of parameters involved in the study. Various results for the dimensionless velocity profiles and skin frictions are discussed for the pressure gradient parameter, Hartmann number, permeability parameter, and suction/injection. A far-field asymptotic solution is also obtained which has revealed oscillatory velocity profiles when the flow has an adverse pressure gradient. The results show that, for the positive pressure gradient and mass transfer parameters, the thickness of the boundary layer becomes thin and the flow is directed entirely towards the wedge surface whereas for negative values the solutions have very different characters. Also it is found that MHD effects on the boundary layer are exactly the same as the porous medium in which both reduce the boundary layer thickness.

Experimental Investigation of a Turbulent Compressible Boundary Layer

2009 ◽  
Author(s):  
Todd Reedy
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Pressure Gradient ◽  
Static Pressure ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Experimental Results ◽  
Compressible Boundary Layer ◽  
Law Of The Wall ◽  
Displacement Thickness

A turbulent compressible boundary layer in a nominally Mach 4.2 flow was investigated experimentally. Pitot, wall-static pressure, total pressure and temperature measurements were utilized to determine Mach number, temperature, and velocity profiles within the boundary layer. An adverse pressure gradient was observed, resulting in non-uniform flow in the streamwise direction of the test section during development. Alterations were made to the tunnel top and bottom walls to account for the growing boundary layer displacement thickness, resulting in a much improved, uniform Mach number in the freestream and boundary layer. The existence of a slight adverse pressure gradient remained. Flow visualization was conducted via the Schlieren imaging technique. Experimental results were compared against turbulent compressible flow theory and were found to be in excellent agreement, based on an extension of the law-of-the-wall and law-of-the-wake. Velocity profiles and boundary layer thicknesses of the theoretical and experimental results aligned satisfactorily.

Separated Turbulent Boundary Layer Under Unsteady Adverse Pressure Gradients: DNS and RANS

2014 ◽  
Author(s):  
Junshin Park
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Eddy Viscosity ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Navier Stokes ◽  
Pressure Gradients ◽  
Recirculation Bubble ◽  
Rans Models

Predicitve capabilities of Reynolds Averaged Navier-Stokes (RANS) techniques have been assessed using SST k–ω model and Spalart-Allmaras model by comparing its results with direct numerical simulation (DNS) results. It has been shown that Spalart-Allmaras and SST k–ω model predict an earlier separation point and a bigger recirculation bubble as compared to the DNS result. Velocity profiles predicted by RANS for both models closely match with DNS results for the steady adverse pressure gradient case. However, the RANS fail to predict correct velocity profiles for unsteady adverse pressure gradients not only for inside the bubble but also after the reattachment zone. To provide the backgrounds for improving RANS models, these differences are explained with Reynolds stress and eddy viscosity which differ between the steady and unsteady adverse pressure gradient RANS cases.

Supplementary Boundary-Layer Approximations for Turbulent Flow

1989 ◽  
Vol 111 (4) ◽  
pp. 420-427 ◽  
Author(s):  
L. C. Thomas ◽  
S. M. F. Hasani
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Pressure Gradient ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Wide Range ◽  
The Mean ◽  
Wall Shear

Approximations for total stress τ and mean velocity u are developed in this paper for transpired turbulent boundary layer flows. These supplementary boundary-layer approximations are tested for a wide range of near equilibrium flows and are incorporated into an inner law method for evaluating the mean wall shear stress τ0. The testing of the proposed approximations for τ and u indicates good agreement with well-documented data for moderate rates of blowing and suction and pressure gradient. These evaluations also reveal limitations in the familiar logarithmic law that has traditionally been used in the determination of wall shear stress for non-transpired boundary-layer flows. The calculations for τ0 obtained by the inner law method developed in this paper are found to be consistent with results obtained by the modern Reynolds stress method for a broad range of near equilibrium conditions. However, the use of the proposed inner law method in evaluating the mean wall shear stress for early classic near equilibrium flow brings to question the reliability of the results for τ0 reported for adverse pressure gradient flows in the 1968 Stanford Conference Proceedings.

Incompressible Laminar Boundary Layers on a Parabola at Angle of Attack: A Study of the Separation Point

1972 ◽  
Vol 39 (1) ◽  
pp. 7-12 ◽  
Author(s):  
M. J. Werle ◽  
R. T. Davis
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Angle Of Attack ◽  
Adverse Pressure Gradient ◽  
Boundary Layer Separation ◽  
Separation Point ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Type Singularity ◽  
Flow Experiences

The laminar boundary-layer equations were solved for incompressible flow past a parabola at angle of attack. Such flow experiences a region of adverse pressure gradient and thus can be employed to study the boundary-layer separation process. The present solutions were obtained numerically using both implicit and Crank-Nicolson-type difference schemes. It was found that in all cases the point of vanishing shear stress (the separation point) displayed a Goldstein-type singularity. Based on this evidence, it is concluded that a singularity is always present at separation independent of the mildness of the pressure gradient at that point.

Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients

1978 ◽  
Vol 89 (2) ◽  
pp. 305-342 ◽  
Author(s):  
B. A. Kader ◽  
A. M. Yaglom
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Local Equilibrium ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Experimental Information ◽  
Turbulent Boundary Layers ◽  
Stream Velocity ◽  
Pressure Gradients

Dimensional analysis is applied to the velocity profile U(y) of turbulent boundary layers subjected to adverse pressure gradients. It is assumed that the boundary layer is in moving or local equilibrium in the sense that the free-stream velocity U∞ and kinematic pressure gradient α = ρ−1dP/dx vary only slowly with the co-ordinate x. This assumption implies a rather complicated general equation for the velocity gradient dU/dy which may be considerably simplified for several specific regions of the flow. A general family of velocity profiles is derived from the simplified equations supplemented by some experimental information. This family agrees well with almost all existing data on velocity profiles in adverse-pressure-gradient turbulent boundary layers. It may be used for the derivation of a skin-friction law which predicts satisfactorily the values of the wall shear stress at any non-negative value of the pressure gradient. The variation of the boundary-layer thickness with x is also predicted by dimensional considerations.

Separation Criterion for Turbulent Boundary Layers Via Similarity Analysis

2004 ◽  
Vol 126 (3) ◽  
pp. 297-304 ◽  
Author(s):  
Luciano Castillo ◽  
Xia Wang ◽  
William K. George
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layers ◽  
Boundary Layer Equation ◽  
Outer Part ◽  
Adverse Pressure Gradient ◽  
Gradient Flows ◽  
Boundary Layer Equations ◽  
Gradient Parameter ◽  
Momentum Boundary Layer

By using the RANS boundary layer equations, it will be shown that the outer part of an adverse pressure gradient turbulent boundary layer tends to remain in equilibrium similarity, even near and past separation. Such boundary layers are characterized by a single and constant pressure gradient parameter, Λ, and its value appears to be the same for all adverse pressure gradient flows, including those with eventual separation. Also it appears from the experimental data that the pressure gradient parameter, Λθ, is also approximately constant and given by Λθ=0.21±0.01. Using this and the integral momentum boundary layer equation, it is possible to show that the shape factor at separation also has to within the experimental uncertainty a single value: Hsep≅2.76±0.23. Furthermore, the conditions for equilibrium similarity and the value of Hsep are shown to be in reasonable agreement with a variety of experimental estimates, as well as the predictions from some other investigators.

A Novel Similarity Transformation for the Boundary Layer Equations: Solution of Boundary Layer Flows Subjected to Exponential Outer Velocity Profiles

2011 ◽  
Vol 78 (4) ◽  
Author(s):  
S. J. Karabelas
Keyword(s):  
Boundary Layer ◽  
Power Law ◽  
Physical Interpretation ◽  
Incompressible Flows ◽  
Similarity Transformation ◽  
Adverse Pressure Gradient ◽  
Velocity Profiles ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
Similar Solutions

A new similarity transformation applies to the boundary layer equations, which govern laminar, steady, and incompressible flows. This transformation is proved to be more consistent and more complete than the well known Falkner–Skan transformation. It applies to laminar, incompressible, and steady boundary layer flows with a power-law ue(x)=cxm or exponential profile ue(x)=cemx of the outer velocity. This family of “similar solutions” is resolved for various values of the exponent m. A physical interpretation of these velocity profiles is presented, and conclusions are drawn regarding the tolerance of these boundary layers to flow separation under an adverse pressure gradient.

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