Development of a methodology for LES of Turbulent Cavitating Flows

Abstract

The objective of this dissertation is to develop a numerical methodology for large eddy simulation of multiphase cavitating flows on unstructured grids and apply it to study two cavitating flow problems. The multiphase medium is represented using a homogeneous mixture model that assumes thermal equilibrium between the liquid and vapor phases. We develop a predictor-corrector approach to solve the governing Navier Stokes equations for the liquid/vapor mixture, together with the transport equation for the vapor mass fraction. While a non-dissipative and symmetric scheme is used in the predictor step, a novel characteristic-based filtering scheme with a second order TVD filter is developed for the corrector step to handle shocks and material discontinuities in non-ideal gases and mixtures. Additionally, a sensor based on vapor volume fraction is proposed to localize dissipation to the vicinity of discontinuities. The scheme is first validated for one dimensional canonical problems to verify its accuracy in predicting jump conditions across material discontinuities and shocks. It is then applied to two turbulent cavitating flow problems - over a hydrofoil and over a wedge. Our results show that the simulations are in good agreement with experimental data for the above tested cases, and that the scheme can be successfully applied to RANS, LES and DNS methodologies. We first study cavitation over a circular cylinder at two different Reynolds numbers ($Re = 200 ~\rm{and}~ 3900$ based on cylinder diameter and free stream velocity) and four different cavitation numbers ($\sigma = 2.0, 1.0, 0.7 ~\rm{and}~ 0.5$). Large Eddy Simulation (LES) is employed at the higher Reynolds number and Direct Numerical Simulations (DNS) at the lower Reynolds number. %The unsteady characteristics of the flow are found to be altered significantly by cavitation. It is observed that the simulated cases fall into two different cavitation regimes: cyclic and transitional. Cavitation is seen to significantly influence the evolution of pressure, boundary layer and loads on the cylinder surface. The cavitated shear layer rolls up into vortices, which are then shed from the cylinder, similar to a single phase flow. However, the Strouhal number corresponding to vortex shedding decreases as the flow cavitates and vorticity dilatation is found to play an important role in this reduction. At lower cavitation numbers, the entire vapor cavity detaches from the cylinder leaving the wake cavitation--free for a small period of time. This low frequency cavity detachment is found to occur due to a propagating condensation front and is discussed in detail. The effect of initial void fraction is assessed. The speed of sound in the free stream is altered as a result and the associated changes in the wake characteristics are discussed in detail. LES of cavitating flow at $Re = 3900$ and $\sigma = 1.0$ is studied and a higher mean cavity length is obtained when compared to the cavitating flow at $Re = 200$ and $\sigma = 1.0$. The wake characteristics are compared to the single phase results at the same Reynolds number and it is observed that cavitation suppresses turbulence in the near wake and delays three dimensional breakdown of the vortices. LES of sheet to cloud cavitation over a wedge is performed at $Re = 200,000$ (based on the wedge height and free stream velocity) and $\sigma = 2.1$. The attached sheet cavity grows upto a length of $x/h = 2.0$, after which it breaks into a cloud cavity which is highly three--dimensional and vortical in nature. The mean and RMS void fraction profiles obtained inside the cavity are compared to experiment and good agreement is observed. The frequency of the shedding process is obtained from point spectra at several locations and the obtained frequency is found to agree with the experiment. It is observed that the mean pressure at the wedge apex does not fall below vapor pressure; however cavitation occurs there due to the unsteady pressure falling below vapor pressure. The maximum mean void fraction occurs in the sheet cavity and is about 0.5, while the cloud region has even lesser amount of void fraction. The velocity fluctuations immediately downstream of the cavity show dominant fluctuations in both the streamwise and spanwise directions, while only streamwise fluctuations are dominant inside the cavity region. The probability density function of void fraction examined at several locations inside the cavity show that the mean value obtained from time averaged data is very different from the most probable value of void fraction, indicating the considerable unsteadiness of the flow. The pressure waves produced on cloud collapse are found to display both wave--like behavior and highly intermittent small--scale behavior downstream of the wedge. The pressure waves also impinge on the growing sheet cavity and affect the shedding process significantly.