Interaction of two-dimensional spots with a heat releasing/absorbing shock wave: linear interaction approximation results

The canonical interaction between a two-dimensional weak Gaussian disturbance (entropy spot, density spot, weak vortex) with an exothermic/endothermic planar shock wave is studied via the linear interaction approximation. To this end, a unified framework based on an extended Kovásznay decomposition that simultaneously accounts for non-acoustic density disturbances along with a poloidal–toroidal splitting of the vorticity mode and for heat release is proposed. An extended version of Chu’s definition for the energy of disturbances in compressible flows encompassing multi-component mixtures of gases is also proposed. This new definition precludes spurious non-normal phenomena when computing the total energy of extended Kovásznay modes. Detailed results are provided for three cases, along with fully general expressions for mixed solutions that combine incoming vortical, entropy and density disturbances.

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Two-dimensional numerical study of planar shock-wave/moving-body interactions

Shock Waves ◽

10.1007/s00193-003-0219-9 ◽

2003 ◽

Vol 13 (5) ◽

pp. 395-408 ◽

Cited By ~ 2

Author(s):

C. Law ◽

B. W. Skews

Keyword(s):

Shock Wave ◽

Numerical Study ◽

Two Dimensional ◽

Planar Shock ◽

Moving Body ◽

Planar Shock Wave

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Application of a High-Resolution Compact Finite Difference Method to Computational Aeroacoustics of Compressible Flows

ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1, Symposia – Parts A, B, C, and D ◽

10.1115/ajk2011-15009 ◽

2011 ◽

Author(s):

Zhifeng Zuo ◽

Hiroshi Maekawa

Keyword(s):

Shock Wave ◽

High Resolution ◽

Flow Field ◽

Acoustic Wave ◽

Acoustic Waves ◽

Compressible Flows ◽

Compact Finite Difference Method ◽

Reflected Shock ◽

Planar Shock ◽

Planar Shock Wave

WCNS is an efficient high-resolution nonlinear scheme for solving flow-fields including discontinuity. In the present paper, a two-dimensional, unsteady, compressible flow field produced by the interaction between a strong planar shock wave and a strong vortex are simulated numerically using WCNS. The simulation shows the effects of the vortex on a planar shock and the production of acoustic waves by the shock-vortex interaction. At the early times of interaction, the shock wave is perturbed by the vortex and a precursor is produced; with the shock wave emerges from the vortex flow field, a Mach structure was generated and the secondary acoustic wave was formed by the interaction of the reflected shock (MR2) with the precursor. Both components of acoustic wave (the precursor and the second sound wave) propagate radially and have a quadrupolar nature. By this simulation, the ability of WCNS for computational aeroacoustic problems is confirmed.

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