Fastest Fish Shapes and Optimal Supercavitating and Hypersonic Bodies of Revolution

Abstract

Background. The best swimmers have a streamlined shape that provides a flow pattern without boundary layer separation and delays the laminar-to-turbulent transition. Their shape itself could be the reason of small drag and high locomotion velocity. The fastest fish, e.g., sailfish, swordfish, black marlin, etc. have another feature of their shape – a very sharp nose – rostrum, the purpose of which remains unclear. Popular belief that the rostrum is used by these predators to pierce their prey is often disputed. Objective. In this study, we analyze the hydrodynamic aspects of the rostrum presence and the possible use of similar hulls for supercavitating underwater vehicles and fast penetration into water. We illustrate that shapes with the very sharp nose could be useful for hypersonic motion in order to eliminate overheating of the vehicle fuselage. Methods. We use the known exact solutions of the Euler equations for the incompressible fluid to simulate the pressure distribution on the bodies of revolution with a sharp nose. The slender body theory is used to simulate the supercavitation and the axisymmetric air flows at high Mach numbers. Results. Bodies of revolution with a rostrum similar to trunks of the fastest fish (sailfish, swordfish, black marlin) and corresponding pressure ant temperature coefficients were calculated. The proposed shapes ensure no stagnation points and no high pressures and temperatures on their noses at sub- and supersonic speeds both in water and air. The drag on such bodies of revolution was estimated for attached, supercavitating and supersonic flow patterns. Conclusions. A method of calculation of axisymmetric bodies without stagnation points on their surface was proposed. This peculiarity of the shape allows diminishing the maximum pressure and temperature on the nose without a significant increase in drag. Such shapes with the sharp concave nose could be recommended for high-speed attached and supercavitating bodies of revolution and for the hypersonic motion.