Numerical Modeling of the Thermodynamic Effects of Cavitation

Abstract

A Navier-Stokes solver based on artificial compressibility and pseudo-time stepping, coupled with the energy equation, is used to model the thermodynamic effects of cavitation in cryogenic fluids. The analysis is restricted to partial sheet cavitation in two-dimensional cascades. Thermodynamic effects of cavitation assume significance in cryogenic fluids because these fluids are generally operated close to the critical point and also because of the strong dependence of the vapor pressure on the temperature. The numerical approach used is direct and fully nonlinear, that is, the cavity profile evolves as part of the solution for a specified cavitation pressure. This precludes the necessity of specifying the cavity length or the location of the inception point. Numerical solutions are presented for two-dimensional flow problems and validated with experimental measurements. Predicted temperature depressions are also compared with measurements for liquid hydrogen and nitrogen. The cavitation procedure presented is easy to implement in engineering codes to provide satisfactory predictions of cavitation. The flexibility of the formulation also allows extension to more complex flows and/or geometries.

Numerical simulation of unsteady three-dimensional sheet cavitation

“…For the aft part of the cavity sheet, where the distinction between liquid and vapor is not so clear, some wake model must be introduced. Examples are, amongst others: Furness & Hutton [76], Chen & Heister [37], Deshpande et al [59], Hirschi et al [92], Sussman et al [187], Van der Pijl [205] and Dijkhuizen [61]. These methods do not allow the description of the unsteady behavior of pulsating cavities, including phenomena like the re-entrant jet, cavity breakdown or vapor cloud shedding.…”

The Numerical Analysis of the Effect of Flow Properties on the Thermodynamic Effect of Cavitation

“…The computational domain was re-grided accordingly over the hydrofoil/cavity surface. 5) In this paper, grid updating was accomplished every 10 steps. The growth of the cavity stops if the pressure differences between gas and liquid equals the surface tension.…”

“…In the paper of Deshpande et al, the normal velocity was determined by the Method of Characteristics, but this condition cannot express the pressure balance on the cavity surface. 5) In this paper the normal velocity on the cavity surface was determined to simulate the growth of the cavity by the balance among liquid pressure p ' , gas pressure p g and the surface tension ( at the cavity surface, where denotes the surface tension coefficient and ( denotes the curvature of the interface. The process of the simulation is as follows:…”

“…4) Recently, Deshpande et al presented a numerical method for modeling of the thermodynamic effect of cavitation and applied it to the flow around a hydrofoil. 5) This method can express the characteristics of the thermodynamic effect of cavitation, though it is doubtful that the cavitation model can express the real phenomenon accurately. Tani et al 6) developed a cavitating flow solver, based upon bubble two-phase flow equations, including the energy conservation.…”

“…In this study, the sheet cavity around a two-dimensional hydrofoil was simulated by the method of Deshpande,5) the cavitation model being improved so as to be more accurate in order to analyze the effect of flow properties on the thermodynamic effect of cavitation. A Navier-Stokes solver based on artificial compressibility and pseudo-time stepping was used.…”