Numerical Simulation Of The High-speed Compressible Supercavitating Flows Around A Symmetrical Body

The high-speed supercavitating vehicle is a new type of underwater weapon with a significant reduction of drag.The speed of supercavitating projectile can reach transonic and supersonic.Compared with the general projectile,many complicated hydro-dynamic problems must be considered such as compressibility of water,unsteady flow,multiphase flow,phase transition,turbulent flow and so on,because of the super-high speed.It is necessary to develop a reasonable model to study this problem accurately which can be used to analyze the supercavitating flows in subsonic,transonic and supersonic conditions.The main contents and findings are as follows:(1)Equations of compressible potential flow were established based on the potential flow and the slender body theory.The results shown that the supercavity shape is spheroidicity.Whether in subsonic or supersonic condition,supercavity length and bubble radius increases gradually with the increase of speed.But the growth gradient in subsonic region is greater than supersonic region,which indicates that supercavity shape changes less in supersonic range.The compressibility of water lead to the asymmetry of the supercavity shape.As the Mach number increases,the maximum bubble radius moves forward,and the asymmetry becomes greater.(2)The model to simulate the high-speed compressible supercavitating flows was developed based on the Navier-Stokes equations.And then the feasibility of the multiphase model,the turbulence model and the cavitation model was discussed.Adding the Tait equation and the effective sound speed in water into CFD software through the function of UDF,the simulation of the compressibility of water was realized.The results of simulation fitted well with the experimental phenomenon.At the same time,the necessity of the consideration of water compressibility was discussed by comparing the numerical results of incompressible water.(3)The impact of projectile speed on high-speed compressible supercavitating flows was discussed under the condition of subsonic,transonic and supersonic.Based on the numerical calculation method,the result shown that with the increase of speed,the compressibility of water becomes prominent and the gradient and maximum of pressure and density increase.Especially at supersonic,pressure and density distribution shows the shock wave characteristics;The supercavity shape becomes close to the projectile body by speed increasing.In aspect of hydrodynamic characteristics,as time passes by,the cavity is developing to surround the whole projectile,which leads to a significant reduction of drag;And with the increase of speed,the drag become large.Under the same condition,the drag of compressible setting is larger than the results of incompressible setting.(4)Equations to describe the water parameters ahead and behind the shock wave in low-supersonic flow was inferred.For any shock wave,a certain shock wave intensity is corresponding to a certain density ratio,and this relationship has nothing to do with the shock angle.The simulation results coincided well with the theory,which proved that the numerical simulation method is reasonable to predict high-speed compressible supercavitating flows.