Stationary Boundary Layer: von Mises Variables

2018 ◽  
pp. 20-81
Author(s):  
O. A. Oleinik ◽  
V. N. Samokhin
Keyword(s):  
Boundary Layer ◽  
Stationary Boundary ◽  
Von Mises

To calculation of a stationary boundary layer under conditions of strong thermochemical nonequilibrium

2020 ◽  
Author(s):  
Yurii N. Grigoryev ◽  
Aleksey G. Gorobchuk ◽  
Igor V. Ershov
Keyword(s):  
Boundary Layer ◽  
Stationary Boundary

A simple derivation of Lighthill's heat transfer formula

1958 ◽  
Vol 3 (4) ◽  
pp. 357-360 ◽  
Author(s):  
H. W. Liepmann
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradients ◽  
Simple Derivation ◽  
Simple Argument ◽  
Boundary Layer Equations ◽  
Permit Application ◽  
Von Mises ◽  
Separating Flows ◽  
Operational Methods

In the following it will be shown that a simple argument based on the use of the energy integral equation of the laminar boundary layer permits the derivation of a heat transfer formula valid for non-uniform temperature distribution and non-zero pressure gradients. The formula is then shown to be identical in structure with Lighthill's (1950) well-known results. Lighthill obtained his formula by solving the boundary layer equations in the von Mises form using operational methods. An elegant way to obtain the same results using exact similarity consideration was given by Lagerstrom (not yet published). The derivation given here is probably the most simple-minded one and the method may be useful for other applications as well. Furthermore, it is shown that the approach can be slightly modified to permit application of the formula to flow near separation. The latter result is applied to the Falkner-Skan solution for just separating flows and is found to be in excellent agreement with the exact solutions.

Vortex decay above a stationary boundary

1967 ◽  
Vol 27 (1) ◽  
pp. 155-175 ◽  
Author(s):  
Albert I. Barcilon
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Swirling Flows ◽  
Rigid Boundary ◽  
Free Vortex ◽  
Stationary Boundary ◽  
Small Viscosity

An attempt is made to understand the decay of a free vortex normal to a stationary, infinite boundary. For rapidly swirling flows in fluids of small viscosity, thin boundary layers develop along the rigid boundary and along the axis, the axial boundary layer being strongly influenced by the behaviour of the plate boundary. An over-all picture of the flow is sought, with only moderate success in the region far from the origin. Near the origin, the eruption of the plate boundary layer into the axial boundary layer is studied.

On the Closed Motion of a Fluid in a Square Cavity

1965 ◽  
Vol 69 (650) ◽  
pp. 116-120 ◽  
Author(s):  
Ronald D. Mills
Keyword(s):  
Boundary Layer ◽  
Fluid Motion ◽  
Periodic Variation ◽  
Square Cavity ◽  
Boundary Layer Problem ◽  
The Core ◽  
Method Of Solution ◽  
Von Mises ◽  
Small Periodic ◽  
Layer Problem

SummaryThis paper is concerned with two-dimensional, incompressible fluid motion generated within a square cavity (a) by an outer stream and (b) by the action of a flat surface passing over one of its sides. This type of motion (“cavity flow”) is considered to consist of a boundary layer surrounding an inviscid “core.” A solution of a linearised form of von Mises’ equation is obtained for steady flow in the boundary layer for constant pressure and that of a small periodic variation around the walls of the cavity. From this analysis the vorticity imparted to the core is obtained. The motion in the core is then determined on the basis of the persistence of this value of the vorticity. Experimental results are given for (a) and (b) and compared with the theory. A method of solution of the non-linear boundary layer problem is indicated.

A Study of Linearized Approximations to the Boundary-Layer Equations

1965 ◽  
Vol 32 (4) ◽  
pp. 757-764 ◽  
Author(s):  
Joseph A. Schetz ◽  
Joseph Jannone
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Constant Pressure ◽  
Approximate Solutions ◽  
Physical Problem ◽  
Physical Plane ◽  
Qualitative And Quantitative ◽  
Boundary Layer Equations ◽  
Flow Problems ◽  
Von Mises

The general subject of linearized approximations to the boundary-layer equations is considered in terms of the behavior, both qualitative and quantitative, of the resulting approximate solutions. In this regard, two nonsimilar flow problems are treated by various methods which are based upon the linearized concept. The results are analyzed and compared both with each other and “exact” numerical solutions where available. Linearization in the von Mises plane is considered in some generality and typical results are compared with those obtained by the more conventional physical plane linearization technique. In particular, it is shown that the use of the total pressure rather than the velocity as the dependent variable has important advantages even for constant pressure flow problems when subjected to a linearized treatment in the von Mises plane. Finally, specific recommendations are made as to the approach best applied to a given type of physical problem.

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