Efficient Numerical Simulation of Unsteady Cavitating Flows Using Thermodynamic Tables

A computational method based on the Euler equations for unsteady flow is employed to predict the structure and dynamics of unsteady sheet cavitation as it occurs on stationary hydrofoils, placed in a steady uniform inflow. An equilibrium cavitation model is employed, which assumes local thermodynamic and mechanical equilibrium in the two-phase flow region. Furthermore, the phase transition does not depend on empirical constants in this model. In order to be able to predict the dynamics of the pressure waves, the fluid is considered as a compressible medium by adopting appropriate equations of state for the liquid phase, the two-phase mixture and the vapor phase of the fluid. When these thermodynamic relations are used directly in the computational method, it was found that over 90% of the computational time was spent by computations associated with these closure relations. Therefore, in this paper this approach is replaced by using precomputed thermodynamic tables, containing the same information. It will be shown that the thermodynamic functions for the liquid, vapor, and mixture phases are consistent and have unique values in all the phases. Accordingly, a unique table can be prepared for any of the thermodynamic variables {p,T,c,α}, i.e. pressure, temperature, speed of sound, and vapor void fraction, covering all three phases in each table. Based on uniqueness property of the tables, the thermodynamic state can be characterized without any need for determining the flow phase, although it has been stored in a table for post processing purposes (and for later viscous simulations). To show that this approach is beneficial, results on sheet cavitation for the NACA0015 hydrofoil will be presented. The results clearly show the shedding of a sheet cavity and the strong pressure pulses, originating from the collapse of shed vapor structures. The usage of the tables leads to a speed-up of the computations of approximately a factor of 10.