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Asymmetric characteristics of the shock bifurcation in the reflected shock/boundary layer interaction

Yang Zhang, Jianfeng Zou, Jiahua Xie, Xiaoyue Li, Zhenhai Ma, Yao Zheng

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 11 October 2018

Issue publication date: 19 October 2018

189

Abstract

Purpose

When a reflected shock interacts with the boundary layer in a shock tube, the shock bifurcation occurs near the walls. Although the study of the shock bifurcation has been carried out by many researchers for several decades, little attention has been devoted to investigate the instability pattern of the bifurcation. This research work aims to successfully capture the asymmetry of the whole flow field, and attempt to achieve the instability mechanism of the shock bifurcation by a direct numerical simulation of the reflected shock wave/boundary layer interaction at Ma = 1.9. In addition, the reason for the formation of the bifurcated structure is also explored.

Design/methodology/approach

The spatial and temporal evolution of the shock bifurcation is obtained by solving the two-dimensional compressible Navier–Stokes equations using a seventh-order accurate weighted essentially non-oscillatory (WENO) scheme and a three-step Runge–Kutta time advancing approach.

Findings

The results show that the formation of shock bifurcation is mainly because of the shock/gradient field interaction, and the height of the bifurcated foot increases with the growth of the shock intensity and the gradient field. The unsteady asymmetry of the upper and bottom shock bifurcated structures is because of the vortex shedding with high frequency in the rear recirculation zone, which leads to the fluctuation of the recirculation area. The vortex shedding process behind the bifurcated structure closely resembles the Karman vortex street formed by the flow around the cylinder. The dimensionless vortex shedding frequency varies between 0.01 and 0.02. In comparison to the scenario at Ma = 1.9, the occurring time of instability is delayed and the upper and bottom bifurcated feet intersect in a relatively short time at Ma = 3.5. The region behind the bifurcated shock is a transitional flow field containing obvious cell structures and “isolated islands.”

Originality/value

This paper discovers an unsteady flow pattern of the shock bifurcation, and the mechanism of this instability in the reflected shock/boundary layer interaction is revealed in detail.

Keywords

Acknowledgements

The authors are grateful to Dr Li from the Institute of Mechanics in Chinese Academy of Sciences for valuable discussion on DNS code. The National Supercomputing Center of Tianhe in Guangzhou provides efficient computing resources for simulations in this paper. Financial support from the National Natural Science Foundations of China (Grant N0. 11372276, 11432013, 11372278) is sincerely acknowledged.

Citation

Zhang, Y., Zou, J., Xie, J., Li, X., Ma, Z. and Zheng, Y. (2018), "Asymmetric characteristics of the shock bifurcation in the reflected shock/boundary layer interaction", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 10, pp. 2357-2377. https://doi.org/10.1108/HFF-09-2017-0376

Publisher

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Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

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