An Approximate Method for the Solution of a Class of Nonsimilar Laminar Boundary Layer Equations

1976 ◽  
Vol 98 (2) ◽  
pp. 292-296 ◽  
Author(s):  
G. Nath
Keyword(s):  
Boundary Layer ◽  
Velocity Distribution ◽  
Approximate Method ◽  
Laminar Boundary Layer ◽  
Boundary Layer Flows ◽  
Freestream Velocity ◽  
Boundary Layer Equations ◽  
Transverse Curvature ◽  
Layer Velocity ◽  
Good Agreement

An approximate method is developed for locally nonsimilar laminar boundary layer flows. This method is applicable to several boundary layer velocity problems where the nonsimilarity stems from the freestream velocity distribution and the transverse curvature. The results are compared with those obtained by other methods and, except in the neighborhood of the point of separation, they are in good agreement.

Singularities in solutions of the three-dimensional laminar-boundary-layer equations

1985 ◽  
Vol 160 ◽  
pp. 257-279 ◽  
Author(s):  
James C. Williams
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Unsteady Boundary Layer ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
New Type ◽  
Steady Laminar

The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that there may be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations.A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle.

Approximate Calculations of the Incompressible Laminar Boundary Layer

1967 ◽  
Vol 18 (3) ◽  
pp. 259-272 ◽  
Author(s):  
M. R. Head ◽  
N. Hayasi
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Approximate Method ◽  
Laminar Boundary Layer ◽  
Calculation Method ◽  
Close Agreement ◽  
Computer Solution ◽  
Three Solutions ◽  
Recent Calculation ◽  
Good Agreement

SummaryA recent calculation method proposed by Curle has been applied to the flow U=U0ξe-ξ for which a computer solution exists. An earlier approximate method due to Head, presented here in a simplified form, has been applied to the same problem. All three solutions are found to be in close agreement. A further problem, already examined by Curle, is treated by Head’s method. Again the results are in good agreement with each other and with an exact solution obtained subsequently.

Jeffery-Hamel boundary-layer flows over curved beds

1988 ◽  
Vol 186 ◽  
pp. 583-597 ◽  
Author(s):  
P. M. Eagles
Keyword(s):  
Boundary Layer ◽  
Flow Field ◽  
Film Flow ◽  
Local Approximation ◽  
Main Stream ◽  
Streamwise Direction ◽  
Boundary Layer Flows ◽  
Boundary Layer Equations ◽  
First Approximation ◽  
Local Value

We find certain exact solutions of Jeffery-Hamel type for the boundary-layer equations for film flow over certain beds. If β is the angle of the bed with the horizontal and S is the arclength these beds have equation sin β = (const.)S−3, and allow a description of flows on concave and convex beds. The velocity profiles are markedly different from the semi-Poiseuille flow on a plane bed.We also find a class of beds in which the Jeffery-Hamel flows appear as a first approximation throughout the flow field, which is infinite in streamwise extent. Since the parameter γ specifying the Jeffery-Hamel flow varies in the streamwise direction this allows a description of flows over curved beds which are slowly varying, as described in the theory, in such a way that the local approximation is that Jeffery-Hamel flow with the local value of γ. This allows the description of flows with separation and reattachment of the main stream in some cases.

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