A Numerical Study of Separating Supersonic Laminar Boundary Layers

1973 ◽  
Vol 40 (3) ◽  
pp. 679-684 ◽  
Author(s):  
M. J. Werle ◽  
G. D. Senechal
Keyword(s):  
Numerical Study ◽  
Supersonic Boundary Layer ◽  
Cold Wall ◽  
Governing Equations ◽  
Flat Plates ◽  
Number Range ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers ◽  
Implicit Finite Difference ◽  
Supersonic Laminar

A numerical study has been made of the nature of the solution to the supersonic boundary-layer equations when the flow separates from the surface. To this end, implicit finite-difference solutions to the governing equations were obtained for linearly and quadratically retarded flows over flat plates for a Mach number range of 2–15. Both extremely hot and cold-wall conditions are considered. The resutls of this study give strong evidence that all noninteracting flows are singular at separation.

Numerical Study of Non-Newtonian Maxwell Fluid in the Region of Oblique Stagnation Point Flow over a Stretching Sheet

2015 ◽  
Vol 32 (2) ◽  
pp. 175-184 ◽  
Author(s):  
T. Javed ◽  
A. Ghaffari
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Numerical Study ◽  
Maxwell Fluid ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Parameter Ratio ◽  
Two Dimensional Flow

AbstractIn this article, a numerical study is carried out for the steady two-dimensional flow of an incompressible Maxwell fluid in the region of oblique stagnation point over a stretching sheet. The governing equations are transformed to dimensionless boundary layer equations. After some manipulation a system of ordinary differential equations is obtained, which is solved by using parallel shooting method. A comparison with the previous studies is made to show the accuracy of our results. The effects of involving parameters are discussed in detail and the streamlines are drawn to predict the flow pattern of the fluid. It is observed that increasing velocities ratio parameter (ratio of straining to stretching velocity) helps to decrease the boundary layer thickness. Furthermore, the velocity of fluid increases by increasing the obliqueness parameter.

Fluid Flow and Mixed Convection Transport From a Moving Plate in Rolling and Extrusion Processes

1988 ◽  
Vol 110 (3) ◽  
pp. 655-661 ◽  
Author(s):  
M. V. Karwe ◽  
Y. Jaluria
Keyword(s):  
Numerical Study ◽  
Hot Extrusion ◽  
Physical Parameters ◽  
Manufacturing Processes ◽  
Heated Plate ◽  
Governing Equations ◽  
Moving Plate ◽  
Boundary Layer Equations ◽  
Temperature And Flow Fields ◽  
Finite Difference Techniques

The heat transfer arising due to the movement of a continuous heated plate in processes such as hot rolling and hot extrusion has been studied. Of particular interest were the resulting temperature distribution in the solid and the proper imposition of the boundary conditions at the location where the material emerges from a furnace or die. These considerations are important in the simulation and design of practical systems. A numerical study of the thermal transport process has been carried out, assuming a two-dimensional steady circumstance. The boundary layer equations, as well as full governing equations including buoyancy effects, are solved employing finite difference techniques. The effect of various physical parameters, which determine the temperature and flow fields, is studied in detail. The significance of these results in actual manufacturing processes is discussed.

Starting vortex, separation bubbles and stall: a numerical study of laminar unsteady flow around an airfoil

1975 ◽  
Vol 67 (2) ◽  
pp. 227-256 ◽  
Author(s):  
Unmeel B. Mehta ◽  
Zalman Lavan
Keyword(s):  
Numerical Study ◽  
Separation Bubble ◽  
Governing Equations ◽  
Implicit Finite Difference Scheme ◽  
Vortex Separation ◽  
Initial Generation ◽  
Relaxation Procedure ◽  
Implicit Finite Difference ◽  
Incipient Separation ◽  
Successive Relaxation

The stalling characteristics of an airfoil in laminar viscous incompressible fluid are investigated. The governing equations in terms of the vorticity and stream function are solved using an implicit finite-difference scheme and point successive relaxation procedure. The development of the impulsively started flow, the initial generation of circulation, and the behaviour of the forces at large times are studied.Following the impulsive start, the lift is at first very large and then it rapidly drops. The subsequent growth of circulation and lift is associated with the starting vortex. After incipient separation, the lift increases owing to enlargement of the separation bubble and intensification of the flow rotation in it. The extension of this bubble beyond the trailing edge causes it to rupture and brings about the stalling characteristics of the airfoil. Subsequently, new bubbles are formed near the upper surface of the airfoil and are swept away. The behaviour of the lift acting on the airfoil is explained in terms of the strength and sense of these bubbles. The lift increases when attached clockwise bubbles grow and when counterclockwise bubbles are swept away and vice versa.

scholarly journals Effects of Conduction Variation on MHD Natural Convection Flow Along a vertical Flat Plate

2016 ◽  
Vol 34 ◽  
pp. 63-73
Author(s):  
AKM Safiqul Islam ◽  
MA Alim ◽  
Md Rezaul Karim ◽  
ATM M Rahman
Keyword(s):  
Flat Plate ◽  
Linear Equations ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Governing Equations ◽  
Free Convection Flow ◽  
Boundary Layer Equations ◽  
Implicit Finite Difference ◽  
Non Linear Equations ◽  
Vertical Flat Plate

This paper reports free convection flow along a vertical flat plate with conduction variation on magneto hydrodynamic (MHD) effects. The governing equations with associated boundary conditions reduce to local non-similarity boundary layer equations for this phenomenon are converted to dimensionless forms using a suitable transformation. The transformed non-linear equations are then solved using the implicit finite difference method together with Keller-box technique. Numerical results of the velocity and temperature profiles, skin friction and surface temperature profiles for different values of the magnetic parameter, the Prandtl number and the conduction variation parameters are presented graphically. Detailed discussion is given for the effect of the aforementioned parameters.GANIT J. Bangladesh Math. Soc.Vol. 34 (2014) 63-73

A Numerical Study of Laminar Combined Convective Flow over Flat Plates

1973 ◽  
Vol 95 (1) ◽  
pp. 60-63 ◽  
Author(s):  
P. H. Oosthuizen ◽  
R. Hart
Keyword(s):  
Heat Flux ◽  
Convective Flow ◽  
Flux Distribution ◽  
Numerical Study ◽  
Longitudinal Component ◽  
Forced Flow ◽  
Uniform Heat Flux ◽  
Heat Flux Distribution ◽  
Flat Plates ◽  
Boundary Layer Equations

The boundary-layer equations for combined forced- and free-convective flow over flat plates have been numerically solved using a simple implicit finite-difference scheme. The method of analysis has been developed for flow over plates for which either the surface temperature distribution or the surface heat-flux distribution is arbitrarily specified. Both assisting flow, in which the longitudinal component of the buoyancy force is in the same direction as the forced flow, and opposing flow, in which it is opposite in direction to the forced flow, have been considered. Numerical results have been obtained for plates having a uniform temperature and a uniform heat-flux distribution, and for fluids with Prandtl numbers of 0.7, 3, and 10.

On supersonic laminar boundary layers near convex corners

1970 ◽  
Vol 319 (1538) ◽  
pp. 289-305 ◽  
Keyword(s):  
Boundary Layer ◽  
Initial Pressure ◽  
Supersonic Boundary Layer ◽  
Relative Pressure ◽  
Laminar Boundary Layers ◽  
Numerical Studies ◽  
Flow Through ◽  
Corner Turning ◽  
Supersonic Laminar ◽  
Pressure Fall

The structure of a laminar supersonic boundary layer is examined near a convex corner, turning the flow through an angle α *, on the assumption that α * Re ½ ~ 1 where Re is the Rey­nolds number of the flow. In common with related problems already examined, the boundary layer takes on the character of a triple-deck with the initial pressure fall occurring upstream of the corner. Numerical studies show that as α * Re ½ increases so does the proportion of the total pressure fall which occurs upstream of the corner and an analysis is given which strongly suggests that as α * Re ½ -> ∞ the relative pressure fall downstream of the corner vanishes. The theory is carried over to include angles α * which are small but finite [ α * ≪ 1, α * Re t ≫ 1 for all t > 0] and an earlier theory, due to Matveeva and Neiland, is made uniformly valid and completed. Comparisons with experiment are made which, while not being decisive, are encouraging.

Numerical Study of Natural Convection in a Partitioned Cavity

2008 ◽  
Author(s):  
M. Pirmohammadi ◽  
M. Ghassemi ◽  
G. A. Sheikhzadeh
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Numerical Study ◽  
Temperature Gradients ◽  
Cold Wall ◽  
Governing Equations ◽  
Square Cavity ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Energy Equations

The purpose of this study is to investigate the effect of insulated horizontal baffle placed at the hot wall of a differentially heated square cavity. The vertical walls are at different temperatures while the horizontal walls are adiabatic. In our formulation of governing equations, mass, momentum and the energy equations are applied to the cavity and the baffles. To solve the governing differential equations a finite volume code based on Patankar’s SIMPLER method is utilized [1]. The Results are presented for Rayleigh number from 104 up to 106 and are in form of streamlines, isotherms and Nusselt number. The baffle causes that at low Rayleigh number the horizontal isotherms are replaced by nearly vertical ones, specially around the baffle. Also it is found that thermal boundary layers are thickened, and the temperature gradients at the cold wall are reduced from their values for the case without baffle and this implies that a reduction in the heat transfer through the cavity occurs.

scholarly journals Natural Convection Flow with Combined Buoyancy Effects Due to Thermal and Mass Diffusion in a Thermally Stratified Media

2004 ◽  
Vol 9 (1) ◽  
pp. 89-102 ◽  
Author(s):  
S. C. Saha ◽  
M. A. Hossain
Keyword(s):  
Numerical Study ◽  
Vertical Surface ◽  
Stratified Medium ◽  
Graphical Form ◽  
Convection Flow ◽  
Stratified Media ◽  
Governing Equations ◽  
Natural Convection Flow ◽  
Implicit Finite Difference ◽  
Similarity Method

We present here a numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium. The governing equations of mass, momentum, energy and species are non-dimensionalized. These equations have been solved by using an implicit finite difference method and local non-similarity method. The results show many interesting aspects of complex interaction of the two buoyant mechanisms that have been shown in both the tabular as well as graphical form.

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