A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section

Abstract

A new cavity model that can explain the interaction between viscous effects including vortices and cavitation bubbles is presented in this study. This model, which is named a bubble two-phase flow (BTF) model, treats the inside and outside of a cavity as one continuum by regarding the cavity as a compressible viscous fluid whose density changes greatly. Navier–Stokes equations including cavitation bubble clusters are solved in finite-difference form by a time-marching scheme, where the growth and collapse of a bubble cluster is given by a modified Rayleigh's equation. Computation was made on a two-dimensional flow field around a hydrofoil NACA0015 at angles of attack of 8° and 20°. The Reynolds number was 3 × 105. The experiments were also performed at the same Reynolds number for comparison. The computed results by the BTF cavity model can express the feature of cloud-type cavitation shed from the trailing edge of the attached cavities when the angle of attack is 8°. It shows the mechanism of cavitation cloud generation and large-scale vortices. The boundary layer separates at the cavity leading edge. Then it rolls up and produces the cavitation cloud. In other words, the instability of the shear layer may produce the cavitation cloud. When the angle of attack is 20°, the flow was fully separated from the leading edge of the hydrofoil and vortex cavitation occurs in the separated region. The BTF cavity model can also express the generation of such vortex cavitation and the effect of cavitation nuclei in the uniform flow.

Numerical simulation of a collapsing bubble subject to gravity

“…Even though modifications of the Rayleigh Plesset equation have been formulated over time, in order to address issues arising from simplifications in the original derivation, such as compressibility effects 2 , or bubble interactions 3 , still the main assumption of spherically symmetric bubble evolution remains.…”

Numerical and experimental investigations on the cavitating flow in a cascade of hydrofoils

“…Vaporisation and condensation of the fluid are managed by using barotropic state law, mass transfer equation or bubble dynamic model. Besides applications of different models to quasi-steady cavitating flow, some studies focused on unsteady cloud cavitation phenomenon in Venturi type ducts Kueny, 1990, Reboud et al, 1998] or around hydrofoils in cavitation tunnels [Kubota et al 1992, Reboud and Delannoy, 1994, Song and He, 1998, Sauer and Schnerr 2000. Numerical simulation of the stabilising effect of small obstacle placed in the cavitation sheet area [Hofmann et al 1999], shows the ability of such model to catch localised hydrodynamic effects.…”

Review of numerical models of cavitating flows with the use of the homogeneous approach

“…The initial value of the bubble radius, R, just as in Kubota model [12], was set to 1 × 10 −6 m and the value of the nucleation site of volume fraction, α nuc , to 5 × 10 −4 . The Zwart et al model is intended for three-dimensional unsteady cavitating flows.…”