CJO - Abstract - Nonlinear distortion of travelling waves in variable-area ducts with base flow: a quasi-one-dimensional analysis

Journal of Fluid Mechanics (2005), 536 : 347-366 Cambridge University Press

Copyright © 2005 Cambridge University Press

doi:10.1017/S002211200500491X

Published online by Cambridge University Press 26 Jul 2005

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Nonlinear distortion of travelling waves in variable-area ducts with base flow: a quasi-one-dimensional analysis

MANAV TYAGI ^a1 and R. I. SUJITH ^a2^c1
^a1 Department of Mechanical Engineering, Indian Institute of Technology, Madras, Chennai 600036, India
^a2 Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India

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Abstract

This paper presents an investigation of the nonlinear steepening of a gasdynamic disturbance propagating in a steady non-uniform base flow. The base flow is the steady compressible flow of a gas in a variable-area duct. The quasi-one-dimensional continuity, momentum and energy equations for the unsteady disturbance in homentropic flow are solved using the method of characteristics (wave front expansion technique). A closed-form solution for the slope of the disturbance at the wave front is obtained. The solution admits singularity for a compressive disturbance, which is responsible for the formation of shock in the flow. The solution is general and is applicable in any range of Mach number of the base flow. A special case of the steady gas flow in a convergent–divergent duct (C-D nozzle), where the flow makes a transition from subsonic to supersonic and vice versa, is investigated.

(Published Online July 26 2005)
(Received November 12 2003)
(Revised February 24 2005)

Correspondence:
^c1 Author to whom correspondence should be addressed. sujith@iitm.ac.in