Baroclinic vortex sheet production by shocks and expansion waves |
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Authors: | V Kilchyk R Nalim C Merkle |
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Institution: | (1) Central Mechanical Engineering Research Institute (CMERI), Durgapur, West Bengal, India;(2) Department of Aerospace Engineering, IIT Kanpur, Kanpur, Uttar Pradesh, 208016, India |
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Abstract: | Vortex sheet production by shocks and expansion waves refracting at a density discontinuity was examined and compared using
an analytical solution and numerical simulations. The analytical solution showed that with a small exception, vortex sheet
strength is generally stronger in fast/slow shock refractions. In contrast, expansion waves generated a stronger vortex sheet
in slow/fast refractions. This difference results in larger vorticity deposited by shocks in fast/slow refractions and by
expansion waves in slow/fast refractions. Shock refractions become irregular and the analytical solution fails when either
incident, transmitted or reflected shock, exceeded the angle limit for an attached shock. To investigate vortex sheet production
outside the range of analytical solutions and to verify the applicability of the planar-interface analytical solution to a
curved interface, shock refraction through a sinusoidal interface was numerically simulated in the shock frame of reference.
It is found that variation in the local incidence angle along the curved interface creates pressure waves that affect the
level of deposited vorticity. This contributes to the difference between predictions from local analysis and numerical computation.
Furthermore, an interesting behavior of the shock and expansion wave-deposited vorticity in supersonic ramp flow was discovered.
When the high- and low-density streams were swapped, while keeping the incident flow Mach numbers constant, a vortex sheet
of equal magnitude but of opposite sign was generated. |
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