Computational fluid dynamic modeling of cavitating flows.

摘要

Sheet cavitation on hydrofoils is analyzed in Euler and Navier-Stokes codes using a model analogous to velocity potential theories. The approach taken is to ensure compatibility with previous velocity potential models before implementing this model in Euler and Navier-Stokes codes. The Navier-Stokes model is augmented by the inclusion of the energy equation which allows modeling of the effect subcooling in the vicinity of the cavity interface to take into account the thermodynamic effects of cavitation in cryogenic fluids. Both a fully nonlinear and a linearized model are developed. In both models, the cavity length and inception point evolve as part of the solution. The nonlinear model uses the cavity surface as a streamline, so that the numerical grid must evolve with the solution. The linearized model uses the initial surface grid throughout the solution and enforces approximate boundary conditions on the airfoil surface in a linearized airfoil fashion to force the streamlines to divert around the cavitation bubble. The cavitation models developed provide extension to more complex geometries and flows than can be addressed by velocity potential models.; The primary emphasis in this thesis centers on two-dimensional computations. The generality of the formulation in the Euler and Navier-Stokes codes allows for representative three-dimensional calculations to be presented. Comparisons between velocity potential, Euler and Navier-Stokes implementations indicate they all produce fairly consistent predictions. Comparisons with experimental measurements also indicate that the predictions are qualitatively correct and give a reasonable first estimate of sheet cavitation effects for both cryogenic and non-cryogenic fluids. The three-dimensional calculations demonstrate the extension of the model to more complex flows. The added computational resources required by the cavitation model are minimal, as are the code modifications required to implement the model, indicating that these models are appropriate for incorporation in current generation turbomachinery codes for engineering predictions of sheet cavitation effects.