THE ANALYTICAL SOLUTION OF PARTIAL CAVITATION OVER AN AXISYMMETRIC PROJECTILE AND OBTAINING OPTIMUM CAVITATOR PROPORTIONAL TO PROJECTIL

High speed submerged bodies, such as projectiles, are subjected to cavitation phenomena which often take place when velocity increases to an extent where pressure reduces to vapor pressure and, consequently, liquid changes into vapor. This phenomenon is often undesirable but sometimes it is useful because of the drag reduction, due to the lower viscosity of the vapor phase relative to that of the liquid. Thus, the formation of cavitation in submerged bodies is of interest as a drag reduction technique, and therefore, has attracted many researchers to study its characteristics. When the cavity covers the entire solid body, the phenomenon is called supercavitation. However, if the cavity length is smaller than that of the body, i.e., the cavity closes on the body, partial cavitation occurs. Partial cavitation may also occur during flight, when the maneuvering of a vehicle is necessary. In this paper, the partially cavitating flow over an axisymmetric projectile was studied in order to obtain the optimum cavitator. The procedure used for this purpose was based on the minimization of the total drag coefficient at a given cavitation number. The boundary element method (BEM), along with CFD simulations, was employed in obtaining the optimum cavitator. Using a parabolic relation with three geometric variables, a large number of cavitators for a certain projectile were created and the BEM method was used to solve the potential fluid flow. Next, the optimum cavitator was selected based on the goal function of the minimum total drag coefficient. To examine the optimization results, several cavitators with a total drag coefficient close to that of the optimum cavitator were simulated using a CFD program (Fluent V6.3). Finally, the optimum cavitator was selected, based on both BEM and CFD results. The simulations showed that for a given projectile at all cavitation numbers, the cavitator that generates a cavity covering the entire conical section of the body with a minimum drag coefficient is optimum. It was found that increasing the cavitation number causes the optimum cavitator to approach the disk cavitator.