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The interaction region in the boundary layer of a shock tube

Published online by Cambridge University Press:  29 March 2006

S. D. Ban  and
G. Kuerti
S. D. Ban
Affiliation:
Fluid and Gas Dynamics Division, Battelle Memorial Institute, Columbus, Ohio
G. Kuerti
Affiliation:
Case Western Reserve University, Cleveland, Ohio
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Abstract

Velocity and temperature boundary layers developed on a plane wall by ideal shock-tube flow are considered for weak shock and expansion waves. Analytically, the boundary layer consists of three regions, bounded by (1) expansion-wave head, (2) diaphragm location, (3) contact discontinuity, (4) shock. The flow fields (1, 2) and (3, 4) are, essentially, known. In the interaction region (2, 3), these flow fields merge, the governing equations are ‘singular parabolic’ and admit boundary conditions usually associated with elliptic equations. It is convenient to replace the weak expansion wave in the main flow by a line discontinuity. A consistent linearization scheme can now be devised to obtain the solution in the three regions. In (2, 3), the resulting linear singular parabolic equations for the first-order solutions are solved successfully by an iterative finite difference method, normally applied to elliptic equations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 38 , Issue 1 , 14 August 1969 , pp. 109 - 125
Copyright
© 1969 Cambridge University Press

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