Numerical simulation of unsteady cavitating flows using a homogenous equilibrium model

Abstract

Numerical simulations of two-dimensional cavity flows around a flat plate normal to flow and flows through a 90 bent duct are performed to clarify unsteady behavior under various cavitation conditions. A numerical method applying a TVD-MacCormack scheme with a cavitation model based on a homogenous equilibrium model of compressible gas-liquid two-phase media proposed by the present authors, is applied to solve the cavitating flow. This method permits the simple treatment of the whole gas-liquid two-phase flow field including wave propagation and large interface deformation. Numerical results including detailed observations of unsteady cavity flows and comparisons of predicted results with experimental data are provided. IntroductionIt has become highly desirable in recent years for highspeed hydraulic machinery and equipment to provide reliable operation over a wide range of operating conditions and with improved performance. In the estimation of performance, the existence of unsteady cavity flow, which is considered to be a high-speed gas-liquid two-phase flow accompanied by cavitation, is a very important factor (Brennen 1994). Numerous attempts have been made to clarify the behavior of cavity flow using a range of gas-liquid two-phase flow models for numerical simulations, including Kubota et al. In these previous investigations, however, there has been no comprehensive application to the transient flow range from the subcavitation state to the supercavitation state. Okuda and Ikohagi (1996) contrived a cavitation model based on a homogenous equilibrium model taking account of the compressibility of the gas-liquid two-phase medium. A numerical method incorporating this model and MacCormack's predictor-corrector method (MacCormack 1982) has been proposed by the present authors (Okuda and Ikohagi 1996; Shin and Ikohagi 1997). The feature of this method is that the numerical simulation for an entire cavity flow field can be performed simply in a fixed mesh system without the need to capture the gas-liquid interface (e.g., Delannoy and Kueny 1990; Chen and Heister 1994) or perform a remeshing procedure. In addition, interfaces including a large change of density can be treated as a contact discontinuity from the viewpoint of a compressible fluid.The purpose of this paper is to verify the applicability of the authors' method to a wide range of cavity flow and to clarify the unsteady behavior of some kinds of cavitation.As numerical examples, external and internal two-dimensional (2-D) cavity flows around a flat plate orientated normal to flow, and flows through a 90 bent duct are simulated. Detailed cavity flow behavior including the cavity length and width, and the drag and pressure distributions for the above flow fields are investigated and compared with available experimental data. Equation of stateLet us consider a local volumetric element in a gas-liquid two-phase flow field containing an arbitrary void fraction (gas volume fraction) a as shown in Fig. 1a. This element is assumed to be a mathematically homoge...

Implementation of phase change thermodynamic probability for unsteady simulation of cavitating flows

“…For this reason, the obtained results are also compared with other cavitation simulation models such as the bubble dynamics model [19] and the State Equation model [25]. By this comparison, it is clear that the implied method improves the accuracy of cavitation simulations considerably.…”

“…In Figure 12, variations of average drag coefficient against cavitation number are presented. In this figure, the free stream prediction [26], the bubble dynamics model [19], the State Equation model [25] and experimental results by Waid [24] are presented together with the present numerical results.…”

“…Non-dimentional cavity length defined by = 0.5 for several cavitation numbers. Experimental data by Waid [24], State Equation model [25], Bubble Dynamics model [19].…”

Drag force on a flat plate in cavitating flows

“…In these situations, the re-entrant jet and vapor volume fraction distributions inside the cavity are much more complicated than sub-cavitation flows. The obtained results for cavity dimensions are compared with experimental results reported by Waid [25]. One of the basic objectives of this paper is to improve simulation of supercavitating flows.…”

“…11, variations of average drag coefficient against cavitation number are presented. In this figure, the free stream prediction [12], Shin et al numerical results [26] and experimental results by Waid [25] are presented together with present numerical results.…”