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Cumulative effects of weak pressure waves during the induction period of a thermal explosion in a closed cylinder

Published online by Cambridge University Press:  21 April 2006

R. Klein  and
N. Peters
R. Klein
Affiliation:
Institut für Allegemeine Mechanik, RWTH Aachen, West Germany
N. Peters
Affiliation:
Institut für Allegemeine Mechanik, RWTH Aachen, West Germany
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Abstract

It is shown that the accumulation of small-amplitude gasdynamic perturbations is able to accelerate the process of self-ignition of a homogeneous explosive mixture. For analytical simplicity, the chemical kinetics are represented by a one-step irreversible reaction with a large activation energy. A one-dimensional piston-cylinder geometry is considered, which allows a slow compression of the gas during the induction period. It is assumed that the rates of temperature increase due to the reaction and due to the compression are comparable. A two-timescale asymptotic expansion for small Mach numbers is performed considering the distinguished limit ME = O(1), where E is the non-dimensional activation energy, and M is the Mach number based on a characteristic speed of the gas motion. Gasdynamic-chemical interaction is observed at the second order, where the secular equations describing the evolution on the slow timescale explicitly show a cumulative influence.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 187 , February 1988 , pp. 197 - 230
Copyright
© 1988 Cambridge University Press

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