Investigation of a Method for the General Analysis of Time Dependent Two-Dimensional Laminar Boundary Layers

1968 ◽  
Vol 90 (4) ◽  
pp. 563-570 ◽  
Author(s):  
S. J. Koob ◽  
D. E. Abbott
Keyword(s):  
Boundary Layers ◽  
Transient Flow ◽  
Order Approximation ◽  
Method Of Lines ◽  
Skin Friction Coefficient ◽  
Time Dependent ◽  
Two Dimensional ◽  
Weighted Residuals ◽  
Boundary Layer Equations ◽  
Laminar Boundary Layers

A method is given for the analysis of time dependent two-dimensional incompressible laminar boundary layers. The technique is a combination of the method of weighted residuals and the method of lines, and reduces the boundary-layer equations to an Nth order approximation in terms of a system of ordinary differential equations. The method is demonstrated by solving the transient flow over a semi-infinite flat plate and the results are compared with known asymptotic solutions. For a third approximation, the steady-state skin friction coefficient given by the present method agrees with the Blasius solution within 0.1 percent.

Laminar boundary layers behind detonation waves

1983 ◽  
Vol 387 (1793) ◽  
pp. 331-349 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Flow Analysis ◽  
Time Dependent ◽  
Detonation Waves ◽  
Planar Geometry ◽  
Laminar Boundary Layers ◽  
Spherical Detonation ◽  
Layer Flow

New solutions are presented for non-stationary boundary layers induced by planar, cylindrical and spherical Chapman-Jouguet (C-J) detonation waves. The numerical results show that the Prandtl number ( Pr ) has a very significant influence on the boundary-layer-flow structure. A comparison with available time-dependent heat-transfer measurements in a planar geometry in a 2H 2 + O 2 mixture shows much better agreement with the present analysis than has been obtained previously by others. This lends confidence to the new results on boundary layers induced by cylindrical and spherical detonation waves. Only the spherical-flow analysis is given here in detail for brevity.

Effects of Curvature on Laminar Boundary Layers in Sink-Type Flows

1969 ◽  
Vol 91 (3) ◽  
pp. 353-358 ◽  
Author(s):  
W. A. Gustafson ◽  
I. Pelech
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Momentum Equation ◽  
Similarity Solutions ◽  
Momentum Thickness ◽  
Two Dimensional ◽  
Thickness Increase ◽  
Laminar Boundary Layers ◽  
Converging Channel ◽  
Special Case

The two-dimensional, incompressible laminar boundary layer on a strongly curved wall in a converging channel is investigated for the special case of potential velocity inversely proportional to the distance along the wall. Similarity solutions of the momentum equation are obtained by two different methods and the differences between the methods are discussed. The numerical results show that displacement and momentum thickness increase linearly with curvature while skin friction decreases linearly.

A Reference Temperature Method for Compressible Laminar Boundary Layers

1973 ◽  
Vol 2 (4) ◽  
pp. 201-204
Author(s):  
R. Camarero
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Reference Temperature ◽  
Integral Approach ◽  
Pressure Gradients ◽  
Two Dimensional ◽  
Laminar Boundary Layers ◽  
Temperature Method ◽  
Compressibility Effects

A calculation procedure for the solution of two-dimensional and axi-symmetric laminar boundary layers in compressible flow has been developed. The method is an extension of the integral approach of Tani to include compressibility effects by means of a reference temperature. Arbitrary pressure gradients and wall temperature can be specified. Comparisons with experiments obtained for supersonic flows over a flat plate indicate that the method yields adequate results. The method is then applied to the solution of the boundary layer on a Basemann inlet.

Near-similarity approximation for compressible, laminar boundary layers on adiabatic walls

1997 ◽  
Vol 211 (5) ◽  
pp. 285-294 ◽  
Author(s):  
H P Horton
Keyword(s):  
Differential Equations ◽  
Boundary Layers ◽  
Constant Pressure ◽  
Boundary Layer Stability ◽  
Temperature Profiles ◽  
Two Dimensional ◽  
Careful Choice ◽  
Laminar Boundary Layers ◽  
Gradient Parameter ◽  
Prandtl Numbers

Two-dimensional, compressible, laminar boundary layers with zero heat transfer and a constant pressure gradient parameter are considered. Although it is well known that exact similarity is, in general, only possible when the Prandtl number is equal to unity, it is shown here that, at least for Prandtl numbers in the range from 0.5 to 2.0, a careful choice of transformation gives partial differential equations in which the streamwise derivatives are practically negligible, irrespective of Mach number. The set of ordinary differential equations which results from setting the streamwise derivatives to zero is proposed as a useful approximation for generating families of velocity and temperature profiles, for use in database methods for analysing boundary layer stability, for example.

Triple-deck solutions for supersonic flows past flared cylinders

1987 ◽  
Vol 179 ◽  
pp. 469-487 ◽  
Author(s):  
Ph. Gittler ◽  
A. Kluwick
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Asymptotic Expansions ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Hysteresis Phenomenon ◽  
Two Dimensional ◽  
Planar Flow ◽  
Laminar Boundary Layers ◽  
External Flows

Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and supersonic external flows is investigated in the limit of large Reynolds numbers. Numerical solutions to the interaction equations are presented for flare angles α that are moderately large. If α > 0 the boundary layer separates upstream of the corner and the formation of a plateau structure similar to the two-dimensional case is observed. In contrast to the case of planar flow, however, separation can occur also if α < 0, owing to the axisymmetric effect of overexpansion and recompression. The separation point then is located downstream of the corner and, most remarkable, a hysteresis phenomenon is observed.

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