A numerical approach to address the acoustic stiffness in cavitating flows

Abstract

A numerical approach based on preconditioning and dual-time stepping (DTS) is proposed to simulate cavitating flows at low Mach numbers. The methodology is based on a fully-compressible homogeneous mixture model and finite rate mass transfer as discussed in Gnanaskandan and Mahesh (2015). The method has shown promising results for capturing the large-scale cavitation in developed cavitation regimes (e.g. Bhatt and Mahesh, 2020; Gnanaskandan and Mahesh, 2016a). Small-scale vapor regions in the incipient cavitation, cavitation inception and wetted conditions are sensitive to free-stream nuclei content (e.g. Hsiao and Chahine, 2005; Bhatt and Mahesh, 2019, 2020). In these regimes, lower values of free-stream nuclei are necessary than what is typically prescribed in homogeneous mixture models that use a fully-compressible formulation. While important for the physical modeling, lower values of free-stream nuclei lead to acoustic stiffness. The goal of the present work is to present a numerical approach to enable such low free-stream nuclei calculations in an accurate manner and in a reasonable amount of time. The key aspects of the numerical approach are: (i) preconditioning applied to the cavitating flow equations in a fully-compressible (density-based) solver, (ii) modifications based on the all-speed Roe-type scheme to the characteristic-based filtering, and (iii) implementation in parallel and on unstructured grids that allow the simulation of complex problems. The numerical formulation of the time-derivative preconditioning matrix, the DTS framework, and modification to the shock-capturing are discussed. A proper conditioning of the preconditioned system of equations is obtained. The methodology is demonstrated for the unsteady flow over a cylinder under wetted and cavitation inception conditions, and LES of flow over a propeller under wetted conditions. Overall, a significant saving in total run-time as compared to the original solver is obtained, without compromising accuracy.