Numerical simulation of ultra-high speed supercavitating flows considering the effects of the water compressibility

The objective of this paper is to address the simulation of supercavitating flows around a slender body projectile at the sub-, trans- and supersonic speeds with the water compressibility effects considered. Based on the slender body theory (SBT) and the matched asymptotic expansion method (MAEM), the integro-differential equations for the cases of M_a<1 and M_a>1 are derived and solved. The results show that there is a good agreement of the supercavity shape for both the cases of M_a<1 and M_a>1 between the numerical simulation and the experimental results. The influence of Mach number on the supercavity length L, maximum radius R, slenderness λ, the corresponding growth rate of the supercavity length L˜, the growth rate of the maximum supercavity radius R˜_, and the position of the supercavity maximum section (PSMS) are discussed. It can be found that L˜ is much bigger than R˜, due to the large λ. It also concludes that the front part of the supercavity is thicker than the rear part, and the PSMS moves forward further at supersonic speed. Finally, the reason for the supercavity shape transition around M_a = 1 is illustrated and it may be the c_ause of the extension of perturbation zones at transonic speed.