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International Journal of Aerospace Engineering
Volume 2017, Article ID 8532507, 7 pages
https://doi.org/10.1155/2017/8532507
Research Article

Spatial-Temporal Instability of an Inviscid Shear Layer

School of Astronautics, Beihang University, Beijing 100191, China

Correspondence should be addressed to Li-jun Yang; moc.361@77051362431

Received 23 November 2016; Revised 11 March 2017; Accepted 22 March 2017; Published 9 April 2017

Academic Editor: Corin Segal

Copyright © 2017 Qing-fei Fu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this work, we explore the transition of absolute instability and convective instability in a compressible inviscid shear layer, through a linear spatial-temporal instability analysis. From linearized governing equations of the shear layer and the ideal-gas equation of state, the dispersion relation for the pressure perturbation was obtained. The eigenvalue problem for the evolution of two-dimensional perturbation was solved by means of shooting method. The zero group velocity is obtained by a saddle point method. The absolute/convective instability characteristics of the flow are determined by the temporal growth rate at the saddle point. The absolute/convective nature of the flow instability has strong dependence on the values of the temperature ratio, the velocity ratio, the oblique angle, and number. A parametric study indicates that, for a great value of velocity ratio, the inviscid shear layer can transit to absolute instability. The increase of temperature ratio decreases the absolute growth rate when the temperature ratio is large; the effect of temperature ratio is opposite when the temperature ratio is relatively small. The obliquity of the perturbations would cause the increase of the absolute growth rate. The effect of number is different when the oblique angle is great and small. Besides, the absolute instability boundary is found in the velocity ratio, temperature ratio, and number space.