Boundary Conditions for the Turbulent Mixing Layer Between Two Parallel Streams

1974 ◽  
Vol 41 (1) ◽  
pp. 25-28 ◽  
Author(s):  
T. E. Unny ◽  
Norio Hayakawa
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Boundary Conditions ◽  
Eddy Viscosity ◽  
Outer Boundary ◽  
Mixing Layer ◽  
Turbulent Mixing Layer ◽  
Boundary Layer Problem ◽  
Finite Distance ◽  
Layer Problem

The boundary conditions of the boundary-layer problem between two parallel turbulent streams are investigated solving higher-order terms of the inner and outer boundary-layer expansion. It is shown that the assumption that the eddy viscosity is proportional to longitudinal distance x fails to yield the third boundary condition of the boundary-layer problem. In this paper this boundary condition has been derived based on the consideration that the eddy viscosity attains a constant value at large but finite distance. The result applies to compressible as well as incompressible flow.

Local Nonsimilarity Solutions for Boundary Layers at Lubricated Walls

1984 ◽  
Vol 51 (1) ◽  
pp. 204-205 ◽  
Author(s):  
H. I. Andersson
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Boundary Layers ◽  
Solution Method ◽  
Slip Flow ◽  
Boundary Layer Problem ◽  
Lubricating Film ◽  
Flow Boundary ◽  
Layer Problem

The effect of the lubricating film is accounted for by a slip flow boundary condition, and the nonsimilar boundary layer problem is solved by a local nonsimilarity solution method.

Nonlinear Theory for Flexural Motions of Thin Elastic Plate—Part 2: Boundary-Layer Theory Near the Edge

1981 ◽  
Vol 48 (2) ◽  
pp. 383-390 ◽  
Author(s):  
N. Sugimoto
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Elastic Plate ◽  
Order Theory ◽  
Higher Order ◽  
Boundary Layer Theory ◽  
Thin Elastic Plate ◽  
Boundary Layer Problem ◽  
Higher Order Theory ◽  
Layer Problem

This paper deals with, as a continuation of Part 1 of this series, the boundary-layer theory for flexural motions of a thin elastic plate. In the framework of the higher-order theory developed in Part 1, three independent boundary conditions at the edge of the plate are too many to be imposed on the essentially fourth order differential equations. To overcome this difficulty, a boundary layer appearing in a narrow region adjacent to the edge is introduced. Using the matched asymptotic expansion method, uniformly valid solutions for a full plate problem are sought. The boundary-layer problem consists of the torsion problem and the plane problem. Three types of the edge conditions are treated, the built-in edge, the free edge, and the hinged edge. Depending on the type of edge condition, the nature of the boundary layer is characterized. After solving the boundary-layer problem, “reduced” boundary conditions relevant to the higher-order theory are established.

Numerical Study of Boundary Layers With Reverse Wedge Flows Over a Semi-Infinite Flat Plate

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
R. Ahmad ◽  
K. Naeem ◽  
Waqar Ahmed Khan
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Numerical Study ◽  
Boundary Layer Equation ◽  
Wedge Angle ◽  
Adverse Pressure Gradient ◽  
Problem Solution ◽  
Weighted Residual Method ◽  
Boundary Layer Problem ◽  
Layer Problem

This paper presents the classical approximation scheme to investigate the velocity profile associated with the Falkner–Skan boundary-layer problem. Solution of the boundary-layer equation is obtained for a model problem in which the flow field contains a substantial region of strongly reversed flow. The problem investigates the flow of a viscous liquid past a semi-infinite flat plate against an adverse pressure gradient. Optimized results for the dimensionless velocity profiles of reverse wedge flow are presented graphically for different values of wedge angle parameter β taken from 0≤β≤2.5. Weighted residual method (WRM) is used for determining the solution of nonlinear boundary-layer problem. Finally, for β=0 the results of WRM are compared with the results of homotopy perturbation method.

On a Boundary Layer Problem

2002 ◽  
Vol 108 (4) ◽  
pp. 369-398 ◽  
Author(s):  
R. Wong ◽  
Heping Yang
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Problem ◽  
Layer Problem

The boundary layer over an impulsively started flat plate

1969 ◽  
Vol 310 (1502) ◽  
pp. 401-414 ◽  
Keyword(s):  
Boundary Layer ◽  
Leading Edge ◽  
Surface Shear Stress ◽  
Unsteady State ◽  
Similarity Condition ◽  
Surface Shear ◽  
Boundary Layer Problem ◽  
Independent Variables ◽  
Selection Of ◽  
Layer Problem

A numerical solution has been obtained for the development of the flow from the initial unsteady state described by Rayleigh to the ultimate steady state described by Blasius. The usual formulation of the problem in two independent variables is dropped, and three independent variables, in space and time, are reverted to. The boundary-layer problem is unconventional in that the boundary conditions are not completely known. Instead, it is known that the solution should satisfy a similarity condition, and use is made of this to obtain a solution by iteration. A finite-difference technique of a mixed, explicit-implicit, type is employed. The iteration converges rapidly. It is terminated where the maximum errors are estimated to be about 0.04%. A selection of the results for the velocity profiles and the surface shear stress is presented. One striking feature is the rapidity of the transition from the Rayleigh to the Blasius state. The change is practically complete, at a given station on the plate, by the time the plate has moved a distance equal to four times the distance from the station to the leading edge of the plate.

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