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Bow shock stand-off distance for subsonic decelerating bodies


Projectile accelerations above \(500~\hbox {ms}^{-2}\) are commonly encountered in aerodynamic applications, but suitable validation data are rare in this regime. Experimental transonic velocity range data for a sphere decelerating under its own drag have been used to validate a numerical model for decelerating objects. The validated model is then used to explore the flow field ahead of objects decelerating from supersonic to subsonic Mach numbers. To model the non-inertial frame of the projectile, source terms were included in the momentum and energy equations in a computational fluid dynamics model. In decelerating cases, the bow shock formed in supersonic flight persists in the subsonic regime. The differences in the flow field between the steady and unsteady cases are explained using the concept of flow history. In the experiment, a tubular insert was present near the observation window in the ballistic range. The insert was numerically modelled, and it is shown that the resulting bow shock behaviour can be explained in terms of the Kantrowitz criterion, in conjunction with flow history. The RAE2822 aerofoil was used to explore the effects of shock overtaking and propagation during deceleration from supersonic to low subsonic Mach numbers. In this case, the bow shock wave persists from the initial supersonic speed to projectile Mach numbers lower than 0.4. The expansion wave and tail shock are shown to overtake the decelerating projectile and propagate forward, behind the bow shock.

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The very helpful information provided by T. Saito and his team is acknowledged with gratitude. One of the authors (I.M.A. Gledhill) acknowledges the generous grant of the CSIR (Council for Scientific and Industrial Research), South Africa, without which the collaboration could not have been accomplished. The financial assistance of the National Research Foundation (NRF) towards this research is hereby acknowledged. Opinions expressed, and conclusions arrived at, are those of the author and are not necessarily to be attributed to the NRF. ANSYS, ANSYS Workbench, AUTODYN, CFX, Fluent and any and all ANSYS, Inc., brand, product, service and feature names, logos and slogans are registered trademarks or trademarks of ANSYS, Inc., or its subsidiaries in the USA or other countries. All other brand, product, service and feature names, or trademarks are the property of their respective owners.

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Correspondence to I. M. A. Gledhill.

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Roohani, H., Gledhill, I.M.A., Mahomed, I. et al. Bow shock stand-off distance for subsonic decelerating bodies. Shock Waves 30, 115–129 (2020).

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  • Ballistic range
  • CFD
  • Bow shock
  • Stand-off distance
  • Acceleration aerodynamics
  • Flow history