Second Order Boundary Layer Solutions on a Curved Surface

1972 ◽  
Vol 94 (3) ◽  
pp. 649-654 ◽  
Author(s):  
W. F. Van Tassell ◽  
D. B. Taulbee
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Order Effect ◽  
Second Order ◽  
Two Dimensional ◽  
First Order ◽  
Boundary Layer Equations ◽  
Similar Solutions ◽  
Nonsimilar Solutions ◽  
Different Altitudes

Solutions of the second order longitudinal curvature boundary layer equations near the stagnation point of a two-dimensional circular cylinder are presented. Four cases corresponding to 1 first order locally similar solutions, 2 first order nonsimilar solutions, 3 second order locally similar solutions, and 4 second order nonsimilar solutions are considered. For each of the four cases, results for four different altitudes are given. The only second order effect considered is longitudinal curvature. Based on the numerical results, it is concluded that similarity and curvature assumptions can alter the skin friction calculations significantly. The heat transfer calculations are much less sensitive to the various assumptions, at least for the cases studied in this paper.

On the nature of unsteady three-dimensional laminar boundary-layer separation

1978 ◽  
Vol 88 (2) ◽  
pp. 241-258 ◽  
Author(s):  
James C. Williams
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Boundary Layer Separation ◽  
The Body ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Unsteady Separation ◽  
Similar Solutions

Solutions have been obtained for a family of unsteady three-dimensional boundary-layer flows which approach separation as a result of the imposed pressure gradient. These solutions have been obtained in a co-ordinate system which is moving with a constant velocity relative to the body-fixed co-ordinate system. The flows studied are those which are steady in the moving co-ordinate system. The boundary-layer solutions have been obtained in the moving co-ordinate system using the technique of semi-similar solutions. The behaviour of the solutions as separation is approached has been used to infer the physical characteristics of unsteady three-dimensional separation.In the numerical solutions of the three-dimensional unsteady laminar boundary-layer equations, subject to an imposed pressure distribution, the approach to separation is characterized by a rapid increase in the number of iterations required to obtain converged solutions at each station and a corresponding rapid increase in the component of velocity normal to the body surface. The solutions obtained indicate that separation is best observed in a co-ordinate system moving with separation where streamlines turn to form an envelope which is the separation line, as in steady three-dimensional flow, and that this process occurs within the boundary layer (away from the wall) as in the unsteady two-dimensional case. This description of three-dimensional unsteady separation is a generalization of the two-dimensional (Moore-Rott-Sears) model for unsteady separation.

A note on expansions for the two-dimensional, compressible, laminar boundary layer equations near a point of zero skin friction

1983 ◽  
Vol 94 (1-2) ◽  
pp. 93-96 ◽  
Author(s):  
G. Wilks
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Two Dimensional ◽  
Transfer Coefficients ◽  
Boundary Layer Equations ◽  
Heat Transfer Coefficients

SynopsisThe first non-arbitrary coefficient, α12, of the Buckmaster expansions is evaluated in the context of the extended Goldstein-Stewartson theory. Leading terms of the next order contributions to the skin friction and heat transfer coefficients are also obtained.

Approximate Solutions of the Unsteady Boundary-Layer Equations

1976 ◽  
Vol 43 (3) ◽  
pp. 396-398 ◽  
Author(s):  
A. Bianchini ◽  
L. de Socio ◽  
A. Pozzi
Keyword(s):  
Boundary Layer ◽  
Linear Partial Differential Equation ◽  
Approximate Solutions ◽  
Scale Function ◽  
Unsteady Boundary Layer ◽  
First Order ◽  
Boundary Layer Equations ◽  
Approximate Integral ◽  
Similar Solutions ◽  
Approximate Integral Method

An approximate integral method is proposed for solving the unsteady laminar boundary-layer equations. The essence of the method is to assume a similar solution for the velocity profile even in those situations where similar solutions do not exist, and then to find a suitable scale function for the similarity variable. The scale function is the solution to a simple first-order linear partial differential equation. This solution is determined in closed form. Satisfactory results were obtained in comparison with more sophisticated and time-consuming procedures.

Self-similar solutions to the second-order incompressible boundary-layer equations

1970 ◽  
Vol 40 (2) ◽  
pp. 343-360 ◽  
Author(s):  
M. J. Werle ◽  
R. T. Davis
Keyword(s):  
Boundary Layer ◽  
Numerical Solutions ◽  
Second Order ◽  
Closed Form Solutions ◽  
Boundary Layer Equations ◽  
Incompressible Boundary Layer ◽  
Incompressible Boundary ◽  
Self Similar ◽  
Displacement Speed ◽  
Similar Solutions

Solutions are obtained for the self-similar form of the incompressible boundary-layer equations for all four second-order contributors, i.e. vorticity interaction, displacement speed, longitudinal and transverse curvature. These results are found to contain all previous self-similar solutions as members of the much larger family of solutions presented here. Numerical solutions are presented for a large number of cases, and several closed form solutions, which may have special significance for the separation problem, are also discussed.

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