Rapid Laminar Boundary-Layer Calculations by Piecewise Application of Similar Solutions

1956 ◽  
Vol 23 (10) ◽  
pp. 901-912 ◽  
Author(s):  
A. M. O. SMITH
Keyword(s):  
Boundary Layer ◽  
Laminar Boundary Layer ◽  
Similar Solutions

Similar and Asymptotic Solutions of the Incompressible Laminar Boundary Layer Equations with Suction

1967 ◽  
Vol 18 (2) ◽  
pp. 103-120 ◽  
Author(s):  
M. Zamir ◽  
A. D. Young
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Asymptotic Solution ◽  
Laminar Boundary Layer ◽  
Incompressible Flow ◽  
Suction Parameter ◽  
Suction Velocity ◽  
Boundary Layer Equations ◽  
Wide Range ◽  
Similar Solutions

SummarySimilar solutions of the boundary layer equations for incompressible flow with external velocity u1 ∞ xm and suction velocity υw ∞ x(m-1)/2 are obtained for negative values of m, in the range −0-1 to −0-9, and a wide range of suction quantities.The results are used, in combination with, existing solutions for positive m, to provide a guide to the ranges of m and suction parameter [(υw/u1√x] for which a general form of the classical asymptotic solution can be regarded as a good approximation to the exact solution.It is shown that the values of both m and suction parameter are generally important in this comparison, but for values of the latter greater than about 8 the approximation is a very good one for all values of m considered. For m≃−0·14 the approximation is good (i.e. the error is less than about 1 per cent) down to values of the suction parameter as low as 1·0.

The Calculation of Heat Transfer Coefficients from Skin Friction Coefficients in the Compressible Laminar Boundary Layer on an Aerofoil

1968 ◽  
Vol 19 (3) ◽  
pp. 243-253 ◽  
Author(s):  
R. E. Luxton
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Laminar Boundary Layer ◽  
Strong Dependence ◽  
Transfer Coefficients ◽  
Friction Coefficients ◽  
Heat Transfer Coefficients ◽  
Similar Solutions

SummaryIn this note a relation is established between the correlation parameters obtained by Cohen and Reshotko from similar solutions of the compressible laminar boundary layer, and the Pohlhausen-type pressure gradient parameter used in the approximate methods devised by Luxton and Young. A simple graphical procedure is presented to allow heat transfer coefficients to be obtained from known skin friction coefficients in the presence of a pressure gradient. In view of the restrictions of the similar solutions it cannot be claimeda priorithat the method gives accurate results. It does, however, reflect the strong dependence of the heat-transfer skin-friction relation on the pressure gradient and, by reference to calculated results published previously, it is suggested that the method may give adequate accuracy under quite severe conditions.

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.

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