Incompressible flow assumption in hydroacoustic predictions of marine propellers

Abstract

Incompressible flow assumption is an essential step that simplifies numerical simulations for objects inside flowing water. However, incompressibility assumption creates a conflicting situation for sound propagation as the propagation speed is given by c(0) = root dp/d rho where p denotes the pressure and rho denotes the density. When d rho = 0 is assumed to relieve simulations, speed of sound theoretically becomes infinite and therefore, induced pressures should be corrected with the acoustic analogy. This approach is called the hybrid method that combines hydrodynamic solver with hydroacoustic solver. Hydroacoustic solver adds compressibility effects to the incompressible hydrodynamic solver and uses hydrodynamic pressure to calculate acoustic pressure. Time step size is an important parameter to calculate acoustic pressure field in the fluid domain and an approach to determine the minimum value (for at least capturing the first blade passage frequency) is presented in this study. Another purpose of this paper is to investigate the effect of incompressibility on hydroacoustics and to analyze the necessity of utilising the famous Ffowcs Williams-Hawkings (FWH) equation for predicting marine propeller noise; both for cavitating and non-cavitating cases. Our results are in line with other researchers; hydrodynamic pressure is sufficient to assess the hydroacoustic performance of marine propellers in the near-field due to having very low acoustic Mach numbers. Near-field results from the hydrodynamic solver are then extrapolated to the far-field by adopting ITTC distance normalization equation. However; this equation, which is actually the inverse distance law, is only valid for point noise sources in stationary flow. It is found out that eliminating FWH equation by coupling the incompressible hydrodynamic solver with ITTC distance normalization equation fails to produce satisfactory results. For cavitating cases, numerical results in this study show that implementation of FWH is required even in the near-field.