Modeling Hydrodynamic Nonequilibrium in Cavitating Flows

Abstract

A nonlinear numerical model has been developed to assess nonequilibrium effects in cavitating flows. The numerical implementation involves a two-phase treatment with the use of a pseudo-density which varies between the liquid and gas/vapor extremes. A new constitutive equation for the pseudo-density is derived based on the bubble response described by a modified form of the Rayleigh-Plesset equation. Use of this constitutive equation in a numerical procedure permits the assessment of nonequilibrium effects. This scheme provides a quantitative description of scaling effects in cavitated flows. With minimal modifications, the model can also be used for bubbly two-phase flows.

Fluid dynamics of acoustic and hydrodynamic cavitation in hydraulic power systems

“…The Rayleigh-Plesset equation accounts for the effects of inertia, viscosity and the surface tension of the bubbles, and it can be incorporated in one-, two-and three-dimensional partial differential equation models to simulate cavitating flows [53,101,102]. As the Rayleigh-Plesset equation causes the bubble growth and collapse rates to be time dependent, it is suitable for the simulation of transient structures in cavitation flows.…”

“…The reasons for these discrepancies are: secondary-scale effects related to micro-geometrical differences, which are caused by wall roughness [28] and by details of the nozzle geometry, such as roundness at the nozzle inlet [47,48] and nozzle conicity, or the K-factor of the hole [48,49]; local-flow motion, which is related to the influence of the viscous stresses on the tensile strength of a liquid [50,51] (the classic definition of cavitation inception is based on observations of liquid rupturing under static or quasi-static conditions [9], that is, when the static pressure in the liquid phase is much higher than the viscous stresses caused by the flow, but, if this is not the case, the tensile strength can be affected by the viscous stresses) and to the turbulent and transient nature of hydrodynamic cavitation [52][53][54][55]; liquid quality, which is characterized by means of the radius and density of the undissolved-gas microbubbles in the fluid as well as by the concentration of dissolved gas in the liquid phase [9,56]. In other words, the scale effects associated with the micro-geometry of the system, the local flow phenomena and the liquid quality should have a negligible effect on the considered tests in order to make equation (2.1) valid.…”

“…CN is sometimes replaced by the following dimensionless number, which is a special form of the Euler number [53,69]:…”

Numerical simulation of unsteady three-dimensional sheet cavitation

“…where the total specific enthalpy H is equal to 38) with the total specific energy E defined in equation (3.19). The speed of sound c is defined in equation (3.25).…”

Investigation of Cavitation Models for Steady and Unsteady Cavitating Flow Simulation

“…For solving the density of the liquid/vapor mixture in the cavitating flow, two main approaches are utilized: barotropic equation of state and transport equations. In the first approach proposed by Delannoy and Kueny in 1990, the local mixture density (ρ m ) is assumed to depend only on the local pressure: ρ m = f(p) in the barotropic equation of state [16,17]. Recent experimental results showed that the vorticity is important in cavitating flow, particularly in the cavity closure region [18].…”