Simulation of Wave-Flow-Cavitation Interaction Using a Compressible Homogenous Flow Method

A numerical method based on a homogeneous single-phase flow model is presented to simulate the interaction between pressure wave and flow cavitation.To account for compressibility effects of liquid water,cavitating flow is assumed to be compressible and governed by time-dependent Euler equations with proper equation of state(EOS).The isentropic one-fluid formulation is employed to model the cavitation inception and evolution,while pure liquid phase is modeled by Tait equation of state.Because of large stiffness of Tait EOS and great variation of sound speed in flow field,some of conventional compressible gasdynamics solvers are unstable and even not applicable when extended to calculation of flow cavitation.To overcome the difficulties,a Godunov-type,cell-centered finite volume method is generalized to numerically integrate the governing equations on triangular mesh.The boundary is treated specially to ensure stability of the approach.The method proves to be stable,robust,accurate,time-efficient and oscillation-free.Novel numerical experiments are designed to investigate unsteady dynamics of the cavitating flow impacted by pressure wave,which is of great interest in engineering applications but has not been studied systematically so far.Numerical simulation indicates that cavity over cylinder can be induced to collapse if the object is accelerated suddenly and extremely high pressure pulse results almost instantaneously.This,however,may be avoided by changing the traveling speed smoothly.The accompanying huge pressure increasemay damage underwater devices.However,cavity formed at relatively high upstream speed may be less distorted or affected by shock wave and can recover fully from the initial deformation.It is observed that the cavitating flow starting from a higher freestream velocity is more stable and more resilient with respect to perturbation than the flow with lower background speed.These findings may shed some light on how to control cavitation development to avoid possible damage to operating devices.

Numerical Investigation of Cavitation Interacting with Pressure Wave

A computational fluid dynamics solver based on homogeneous cavitation model is employed to compute the two-phase cavitating flow.The model treats the two-phase regime as the homogeneous mixture of liquid and vapour which are locally assumed to be under both kinetic and thermodynamic equilibrium.As our focus is on pressure wave formation,propagation and its impact on cavitation bubble,the compressibility effects of liquid water have to be accounted for and hence the flow is considered to be compressible.The cavitating flow disturbed by the introduced pressure wave is simulated to investigate the unsteady features of cavitation due to the external perturbations.It is observed that the cavity becomes unstable,locally experiencing deformation or collapse,which depends on the shock wave intensity and freestream flow speed.

An Interface-Capturing Method for Resolving Compressible Two-Fluid Flows with General Equation of State

In this study,a stable and robust interface-capturing method is developed to resolve inviscid,compressible two-fluid flows with general equation of state(EOS).The governing equations consist of mass conservation equation for each fluid,momentum and energy equations for mixture and an advection equation for volume fraction of one fluid component.Assumption of pressure equilibrium across an interface is used to close the model system.MUSCL-Hancock scheme is extended to construct input states for Riemann problems,whose solutions are calculated using generalized HLLC approximate Riemann solver.Adaptive mesh refinement(AMR)capability is built into hydrodynamic code.The resulting method has some advantages.First,it is very stable and robust,as the advection equation is handled properly.Second,general equation of state can model more materials than simple EOSs such as ideal and stiffened gas EOSs for example.In addition,AMR enables us to properly resolve flow features at disparate scales.Finally,this method is quite simple,time-efficient and easy to implement.