Speaker
Description
This work is part of an extended programme to understand and formulate the flow physics of accelerating objects travelling in the transonic and subsonic speed ranges. Of these, deceleration generates the more interesting flow phenomena. The persistence of shocks ahead of objects decelerating from transonic speeds was for some time puzzling [1], but it is now clear that these are shocks formed at supersonic or transonic speeds which continue to propagate forward as the object decelerates behind them [2]. There is relatively little theoretical development of flow physics for cases of significant acceleration [3], and computational fluid dynamics (CFD) has largely been used to understand behaviour [2]. It is useful, however, to generate some basic physical descriptions under deceleration to determine whether such waves may cause damage, since they consist of a shock followed by an expansion wave in which the pressure drops below ambient. Previously, CFD models have been developed and validated by comparison with experimental results from ballistic ranges [4]. Using this model, we show that the flow behaviour behind the shock for significant acceleration cannot be adequately described by Bernoulli’s equation for compressible fluids because time-dependent terms are non-negligible. Therefore, the modified Friedlander blast wave profile is investigated, as a starting point for a more extensive description. It is shown that the modified Friedlander profile [5] does provide a reasonable approximation to the positive phase of the wave behind the shock front, in the region where p - p0 > 0 (where p is static pressure and p - p0 is the ambient pressure of the undisturbed air into which the wave is propagating). The Friedlander model provides a poor approximation in the negative phase p- p0 < 0. This is a novel step towards a better predictive model for shock waves generated by deceleration.
References
[1] Kikuchi T et al., 2017 Shock Standoff Distance over Spheres in Unsteady Flows In: Ben-Dor, G., et al. (eds) 30th International Symposium on Shock Waves 1. Springer, Cham. https://doi.org/10.1007/978-3-319-46213-4_45
[2] Roohani H et al., 2020 Bow shock stand-off distance for subsonic decelerating bodies Shock Waves 30 115–29 https://doi.org/10.1007/s00193-019-00921-3
[3] Gledhill I M A et al., 2016 Theoretical treatment of fluid flow for accelerating bodies Theor. Comp. Fluid Dyn. 30 449–67 https://doi.org/10.1007/s00162-016-0382-0
[4] Mahomed I et al., 2021 Numerical Investigation of a Ballistic Range Free Flight Model, International Journal of Aeronautical and Space Sciences, 22(6), 1293-1301
[5] Karlos V. et al., 2016. Analysis of the blast wave decay coefficient using the Kingery–Bulmash data, J. of Protective Structures, 7(3) 409–429 https://journals.sagepub.com/doi/10.1177/2041419616659572
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