Compressible Boundary-Layer Equations Solved by the Method of Parametric Differentiation

AIAA Journal ◽  
1972 ◽  
Vol 10 (8) ◽  
pp. 1085-1086 ◽  
Author(s):  
C. L. NARAYANA ◽  
P. RAMAMOORTHY
Keyword(s):  
Boundary Layer ◽  
Compressible Boundary Layer ◽  
Boundary Layer Equations

Compressible Boundary Layer-Inviscid Flow Interactions in Entrance Region of Internal Flows

1967 ◽  
Vol 89 (4) ◽  
pp. 281-288 ◽  
Author(s):  
V. D. Blankenship ◽  
P. M. Chung
Keyword(s):  
Boundary Layer ◽  
Shock Tube ◽  
Inviscid Flow ◽  
Perturbation Parameter ◽  
Entrance Region ◽  
Compressible Boundary Layer ◽  
Internal Flows ◽  
Flow Equations ◽  
Boundary Layer Equations ◽  
Interaction Problem

The coupling between the inviscid flow and the compressible boundary layer in the developing entrance region for internal flows is analyzed by solving the particular inviscid flow-boundary layer interaction problem. The interaction problem is solved by postulating certain series forms of solutions for the inviscid region and the boundary layer. The boundary-layer equations and inviscid-flow equations are perturbed to third order and each generated equation is solved numerically. In order to preserve the universality of each of the perturbed boundary-layer equations, the perturbation parameter is described by an integral equation which is also solved in series form. The final results describing the interaction problem are then constructed for any given conditions by forming the three series to a consistent order of magnitude. This technique of coordinate perturbation is generalized to show how it may be applied to the entrance regions of pipe flows, including mass injection or suction, and also to the laminar boundary layers in shock tube flows. It demonstrates analytically the manner in which the boundary layer and inviscid flow interact and create a streamwise pressure gradient. In particular, the interaction problem which occurs in shock tube flows is solved in detail by the use of this generalized method, as an example.

On the laminar compressible boundary layer induced by the passage of a plane shock wave over a flat wall

1967 ◽  
Vol 63 (3) ◽  
pp. 889-907 ◽  
Author(s):  
J. A. D. Ackroyd
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Prandtl Number ◽  
Plane Shock Wave ◽  
Plane Shock ◽  
Compressible Boundary Layer ◽  
Empirical Relationships ◽  
Flat Wall ◽  
Boundary Layer Equations ◽  
Semi Empirical

SummaryThe laminar compressible boundary layer induced by the passage of a plane shock wave over a flat wall is examined in detail. Use is made of the empirical viscosity-temperature relationship μ ∝ Tω. The boundary-layer equations are solved numerically for various values of the index ω, Prandtl number and shock strengths. The resulting solutions are then used to construct simple semi-empirical relationships for some of the more important boundary-layer parameters.

scholarly journals Finite-volume solution of the compressible boundary-layer equations

AIAA Journal ◽  
1987 ◽  
Vol 25 (4) ◽  
pp. 525-526
Author(s):  
Bernard Loyd ◽  
Earll M. Murman
Keyword(s):  
Boundary Layer ◽  
Finite Volume ◽  
Compressible Boundary Layer ◽  
Boundary Layer Equations

The behaviour of similar solutions in a compressible boundary layer

1968 ◽  
Vol 34 (2) ◽  
pp. 337-342 ◽  
Author(s):  
J. B. Mcleod ◽  
J. Serrin
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Compressible Boundary Layer ◽  
Rigorous Proof ◽  
Velocity Overshoot ◽  
Boundary Layer Equations ◽  
Mathematical Properties ◽  
Model Fluid ◽  
Similar Solutions

This paper discusses the mathematical properties of similar solutions of the boundary-layer equations in a compressible model fluid, under assumptions first introduced by Stewartson and by Li & Nagamatsu. Assuming a favourable pressure gradient and that backflow is not present, our results include (among other things) a rigorous proof that velocity overshoot occurs in the boundary layer if the wall is heated, and that this is true whether or not suction, blowing or slipping occurs at the wall; while, conversely, velocity overshoot does not occur when the wall is cooled and the amount of slipping at the wall is suitably restricted.

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