### Shape optimization of axisymmetric cavitators in supercavitating flows, using the NSGA II algorithm

Abstract

The reduction of energy consumption for high speed submersible bodies is an important challenge in hydrodynamic researches.
Supercavitation is a hydrodynamic process in which a submerged body gets enveloped in a layer of gas. As the density and
viscosity of the gas is much lower than that of seawater, skin friction drag can be reduced considerably. If the nose of
the body (cavitator) has a proper shape, the attendant pressure drag remains at a very low value, so the overall body drag
reduces significantly. Total drag force acting on the supercavitating self-propelled projectiles dictates the amount of fuel
consumption and thrust requirements for the propulsion system to maintain a required cavity at the operating speed. Therefore,
any reduction in the drag coefficient, by modifying the shape of the cavitator to achieve optimal shape, will lead to a decrease
of this force. The main objective of this study is to optimize the axisymmetric cavitator shape in order to decrease the drag
coefficient of a specified after-body length and body velocity in the axisymmetric supercavitating potential flow. To achieve
this goal, a multi-objective optimization problem is defined. NSGA II, which stands for Non-dominated Sorting Genetic Algorithm,
is used as the optimization method in this study. Design parameters and constraints are obtained according to the supercavitating
flow characteristics and cavitator modeling. Then objective functions will be generated using the Linear Regression Method. The
results of the NSGA II algorithm are compared with those generated by the weighted sum method as a classic optimization method.
The predictions of the NSGA II algorithm seem to be excellent. As a result, the optimal cavitator's shapes are similar to a cone.