Some Problems of Hydrodynamics for Sub- and Supersonic Motion in Water with Supercavitation

The paper contain analysis and advancing of the understanding level in the modern state of investigations as whole in new enough field of hydrodynamics for the super high suband supersonic speeds of the motion in water of prolate near to axisymmetric supercavitating bodies. The most important problems here from one hand are connected with appearance of key compressibility effects of water as compressible fluid for speeds compared with sonic speed in water o a ~ 1500m / s . This is shock waves. wave resistance, transonic effects and i.e. Another number of the problems is connected with appearance for super high speeds super high hydrodynamics stresses which can be over as compared to strength point of the strongest steels. So here it is need to account of stresses deformation state of moving bodies including influence of hydro elastics effects, resonance and i.e. The analysis base are ones of the hopeful and effective methods applied for development of classical supercavitation in incompressible fluid. This is application of simple heuristic model together with integral conservation laws, Similarity Theory, Slender Body Theory (SBT) on base Matched Asymptotic Expansion Method (MAEM) and another approximations usually used in the cavitation. NOMENCLATURE r, x, t Cylindrical coordinates, time r R(x, t) = Axisymmetric cavity form k k k R ,L ,λ Maximum radius, semi-length, aspect ratio of ordinary cavity for const σ = U∞ , P∞ ρ∞ Velocity, pressure, mass density at infinity