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Three-dimensional unsteady cavitating flow around a NACA0015 hydrofoil fixed between the sidewalls was simulated and the mechanism of U-shaped cloud cavity formation was clarified. A local homogeneous model was used for the modeling of the vaporliquid two-phase medium. The compressible two-phase Navier-Stokes equations as the governing equations were solved. To describe the phase change between water and vapor, the mass transfer model based on the theory of evaporation/condensation on a plane interface was introduced. The cell-centered finite volume method was employed to discretize the governing equations. Assuming turbulent flow, the turbulent eddy viscosity coefficient was computed by using the Baldwin-Lomax model with the Degani-Schiff modification. As a result, even in the case of cavitating flow without sidewalls, the shed cloud cavities has slightly 3D structure, which was not so much large as extending across the whole spanwise direction. On the other hand, in the case of cavitating flow with sidewalls, the end of sheet cavities bows in the spanwise direction because of the development of boundary layer near both sidewalls. After that, due to the occurring of the reentrant jet towards the mid-span region, the sheet cavities breaks off from mid-span region near the leading edge of the hydrofoil, and became the vortical cloud cavities, which have the large-scale U-shaped structure.

Abstract2-D unsteady cavity flows through hydrofoils in cascade which is the most fundamental element of turbomachinery are numerically calculated. In particular, attention was paid to instability phenomena of the sheet cavity in transient cavitation condition and the mechanism of break-off phenomenon was examined. A TVD MacCormack's scheme employing a locally homogeneous model of compressible gas-liquid two-phase media was applied to analyze above cavity flows. The present method permits us to treat the whole cavitating/noncavitating unsteady flow field. By analyzing numerical results in detail, it became clear that there are at least two mechanisms in the break-off phenomena of sheet cavity; one is that re-entrant jets play a dominant role in such a break-off phenomenon, and the other is that pressure waves propagating inside the cavity bring about an another type of break-off phenomenon accompanied with cavity surface waves.

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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...