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Numerical simulation and PIV study of compressible vortex ring evolution

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Abstract

Formation and evolution of a compressible vortex ring generated at the open end of a short driver section shock tube has been simulated numerically for pressure ratios (PR) of 3 and 7 in the present study. Numerical study of compressible vortex rings is essential to understand the complicated flow structure and acoustic characteristics of many high Mach number impulsive jets where simultaneously velocity, density and pressure fields are needed. The flow development, incident shock formation, shock diffraction, vortex ring formation and its evolution are simulated using the AUSM+ scheme. The main focus of the present study is to evaluate the time resolved vorticity field of the vortex ring and the shock/expansion waves in the starting jet for short driver section shock tubes—a scenario where little data are available in existing literature. An embedded shock and a vortex induced shock are observed for PR =  7. However the vortex ring remains shock free, compact and unaffected by the trailing jet for PR =  3. Numerical shadowgraph shows the evolution of embedded shock and shock/expansion waves along with their interactions. The velocity and vorticity fields obtained from simulation are validated with the particle image velocimetry results and these data match closely. The translational velocity of the vortex ring, velocity across the vortex and the centre line velocity of the jet obtained from simulation also agree well with the experimental results.

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Abbreviations

M :

Mach number of the incident shock

U b :

Velocity behind the incident shock

U r :

Vortex ring translational velocity

u, v :

x, y component of velocities

t :

Time; t =  0 represents incident shock at shock tube exit

D :

Inner diameter of the shock tube

PR:

Pressure ratio between the driver and driven section

V s :

Shock speed

a :

Local speed of sound

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Authors and Affiliations

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

    T. Murugan & S. De

  2. Department of Aerospace Engineering, IIT, Kanpur, 208016, UP, India

    C. L. Dora & D. Das

Authors
  1. T. Murugan
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  2. S. De
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  3. C. L. Dora
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  4. D. Das
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Corresponding author

Correspondence to T. Murugan.

Additional information

Communicated by M. Brouillette.

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Murugan, T., De, S., Dora, C.L. et al. Numerical simulation and PIV study of compressible vortex ring evolution. Shock Waves 22, 69–83 (2012). https://doi.org/10.1007/s00193-011-0344-9

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  • DOI: https://doi.org/10.1007/s00193-011-0344-9

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