1 Direct Calculations of Cavitating Flows by the Space-Time CE/SE Method Jian-Rong Qin 1 , S.T. John Yu 2 Zeng-Chan Zhang, 3 Ming-Chia Lai 4 Mechanical Engineering Department Wayne State University Detroit, MI 48202 1 Senior Engineer, Siemens Automotive, Email: Michael.qin@at.siemens.com 2 Associate Professor, AIAA member, Email:styu@me1.eng.wayne.edu, http://141.217.13.61/ 3 Research associate, AIAA member, Email:zhangzc@me1.eng.wayne.edu 4 Professor, AIAA member, Email:lai@me1.eng.wayne.edu Abstract This paper reports one- and two-dimensional simulations of cavitating flows by the Space-Time Conservation Element and Solution Element (CE/SE) method. A continuum cavitation model based on specifying the speed of sound of two-phase flows is employed. The CE/SE method is a viable CFD method for flows at wide range of Mach numbers. The method is explicit and is suitable for time accurate simulations. Moreover, without using a Riemann solver or a reconstruction procedure, the logic and operation count is simple and efficient for sharp resolution of evolving liquid/vapor interfaces. To validate the present model, three cavitating flows are simulated: the one-dimensional simulation of the water- hammer effect, flows over a hydrofoil, and flows through a high-pressure fuel injector. Numerical results show salient features of cavitations commonly observed in experiments, including, reentrant jet, hydraulic flip, and cyclical cavitations. The numerical results compare favorably with previously reported data. 1. Introduction Many researchers investigated cavitations by numerical simulations [4-10]. The challenges are twofold: (1) viable modeling for complex flow physics involved, and (2) development of robust and accurate numerical methods for the unsteady two-phase flows. Owing to the complex physics involved in the cavitating flows, in spite of many excellent studies, the underpinning flow physics of cavitation is still not fully understood. Flow features of cavitating flows are liquid/vapor phase change, high gradients of flow variables, and unsteadiness. When cavitations take place, bubbly clouds are often observed in the lee of the cavity. The clouds interact with vortices and form vortex cavitations. Both cavitation cloud and vortex cavitation consist of many bubbles of different sizes. The bubble clusters grow, collapse, interact with each other, and exchange mass, momentum, and heat with the surrounding liquid, and the physical processes are extremely complex. To simulate cavitations by resolving each tiny bubble is beyond the computational capabilities currently available. Therefore, viable cavitation models, which simulate salient features of cavitations macroscopically, must to be employed. Many approaches exist. In this present paper, a simple continuum method is adopted. We treat cavitating fluid as a homogeneous mixture of liquid and vapor rather than identifying the liquid/vapor interface. The interface is inferred from the value of the mixture density (or a void fraction). No wake model is required in the lee of cavities. Since we don’t need to calculate for a distinct interface, time-accurate simulation of evolving cavitations is efficient. We use a pseudo-density in the model. The value of the pseudo-density varies between the liquid and vapor extremes. To close the system, a constitutive relation is