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Numerical simulation of a compressible vortex–wall interaction

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Abstract

The wall interaction of isolated compressible vortices generated from a short driver section shock tube has been simulated numerically by solving the Navier–Stokes equations in axisymmetric form. The dynamics of shock-free (incident shock Mach number \(M = 1.36\)) and shock-embedded \((M = 1.57)\) compressible vortices near the wall has been studied in detail. The AUSM+ scheme with a fifth-order upwind interpolation formula is used for the convective fluxes. Time integration is performed using a low dissipative and dispersive fourth-order six-stage Runge–Kutta scheme. The evolution of primary and wall vortices has been shown using the velocity field, vorticity field, and numerical schlierens. The vortex impingement, shocklets, wall vortices, and their lift-off are clearly identified from the wall pressure time history. It has been observed that the maximum vorticity of the wall vortices reaches close to 30 % of the primary vortex for \(M = 1.36\) and it reaches up to 60 % for \(M = 1.57\). The net pressure force on the wall due to incident shock impingement is dominant compared to the compressible vortex impingement and their evolution.

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Abbreviations

M :

Mach number of the incident shock

t :

Time; \(t = 0\) represents incident shock at shock tube exit

D :

Inner diameter of the shock tube (64 mm)

x :

Distance from the shock tube exit to wall (300 mm)

y :

Perpendicular distance from the symmetry line

PR :

Pressure ratio between the driver and driven sections

CRVR:

Counter rotating vortex ring

R :

Radius of the computational domain (640 mm)

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Acknowledgments

The authors gratefully acknowledge their access to the High Performance Computing Facility at CSIR-CMERI, Durgapur, for providing the necessary computational resources. The authors would like to thank the reviewers for their valuable comments to enhance the quality of the paper.

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Authors and Affiliations

  1. CSIR-Central Mechanical Engineering Research Institute, Durgapur, 713209, WB, India

    T. Murugan, S. De & S. Dutta

  2. Mechanical Engineering, NITK Surathkal, Karnataka, India

    A. Sreevatsa

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  1. T. Murugan
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  2. S. De
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  3. A. Sreevatsa
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  4. S. Dutta
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Correspondence to T. Murugan.

Additional information

Communicated by F. Lu and A. Higgins.

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Murugan, T., De, S., Sreevatsa, A. et al. Numerical simulation of a compressible vortex–wall interaction. Shock Waves 26, 311–326 (2016). https://doi.org/10.1007/s00193-015-0611-2

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  • DOI: https://doi.org/10.1007/s00193-015-0611-2

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