Brandao, Filipe2023-05-122023-05-122023-03https://hdl.handle.net/11299/254130University of Minnesota Ph.D. dissertation. March 2023. Major: Aerospace Engineering and Mechanics. Advisor: Krishnan Mahesh. 1 computer file (PDF); xix, 173 pages.The objective of this dissertation is to develop numerical methodologies for large eddysimulation (LES) of multiphase cavitating flows over different cavitation regimes. Unstructured grids are considered to enable complex geometries to be considered. The dissertation has the following major components: (i) a compressible homogeneous approach for a mixture of water–vapor–gas is developed to study the effect of non–condensable gas on bluff–body cavitation. (ii) Incipient cavitation in the shear layer of a backstep is studied using incompressible simulations of the flow field coupled with a continuum equation for vapor volume fraction. (iii) The inception model is extended to account for multiple groups of bubbles of different sizes and used to investigate the effects of water quality on tip vortex inception. A numerical method based on the homogeneous mixture model, fully compressible formulation and finite rate mass transfer developed by Gnanaskandan and Mahesh [1] is extended to include the effects of non–condensable gas (NCG). We then investigate cavitation over a circular cylinder at two different Reynolds numbers (Re = 200 and 3900 based on cylinder diameter and free–stream velocity) and different cavitation numbers. Two different cavitation regimes are observed depending on free–stream pressure: cyclic and transitional. In the cyclic regime, the cavitated shear layer rolls up into vortices, which are then shed from the cylinder, forming the K´arm´an vortex street, similar to a single phase flow. In the transitional regime, a cavity is formed behind the cylinder, and is only detached after the passage of a condensation shock. As a consequence, there is a drastic drop in shedding frequency. Dynamic mode decomposition (DMD) is performed to explain this change in behavior. DMD reveals that cavitation delays the first transition of the Karman vortex street. The effects of the non–condensable gases on this flow is discussed for both regimes, and it is found that the gas decreases the strength of the condensation shock. It is observed that vapor and gas uniformly introduced in the free–stream, distributed themselves differently in the wake of cylinder depending upon local flow conditions, particularly at lower cavitation numbers as the pressure in the wake dropped below vapor pressure. Vapor and NCG distribution in the boundary layer suggest that cavitation as a mass transfer process only occurs inside a fine layer in the near–wall region, while the remaining boundary layer only undergoes expansion of both vapor and gas. The levels of free–stream void fraction are found to have an impact on the boundary–layer separation point. Vortex stretching and baroclinic torque are greatly reduced in the transitional regime compared to the cyclic regime. Next, the development of a method to simulate cavitation in the incipient regime is presented. The main idea is that since inception is a stochastic process that generates small amounts of vapor for short periods of time, the effects of these small regions of vapor on the liquid density and dynamics can be neglected. Therefore, vapor is treated as a passive scalar in an incompressible liquid. Thus, the equations solved are the incompressible Navier–Stokes equation along with a advection–diffusion equation with source terms for the transport of vapor. The scalar field, however, is advanced in time with a different time step than the one used to advance the velocity field. The model is used to investigate inception in the shear layer of a backward–facing step at Reτ = 1500 (based on skin friction velocity and boundary layer thickness). Statistics are computed for both pressure and vapor volume fraction, and the likelihood of inception is determined. The locations of the preferred sites for cavitation are compared to experimental results and good agreement is achieved. The effects of finite rate evaporation and condensation are revealed by the probability density functions of pressure and volume fraction. The flow topology is investigated and inception is found to occur in the core of the stretched tubular vortical structures with a rotation rate four times higher than the stretching rate. These cavitating tubular structures are elongated two to three times more in their most extensive principal direction than in their intermediate principal direction, and are most likely aligned with the streamwise direction. The model developed for cavitation inception is extended to account for multiple groups of bubbles of different sizes, effectively making it a polydisperse model. This allows us to investigate the effects of water quality on inception. The model is used to simulate inception in a tip vortex of an elliptic hydrofoil at 12 degrees angle of attack and Reynolds numbers of 9 × 105 and 1.4 × 106 based on root chord length and free–stream velocity. It was found that inception is strongly dependent on the amounts of nuclei in the freestream. When the flow is depleted of nuclei, inception is an intermittent event confined to a position very close to the hydrofoils tip. However, when the flow is rich in nuclei, a larger portion of the tip vortex cavitates, as well as part of the suction side very close to the leading edge of the hydrofoil. Probability density functions reveal that cavitation occurs in any region experiencing a pressure field lower than vapor pressure when the flow is rich in nuclei, while extremely low values of pressure (usually kPa of tension) are required to make a flow deplete of nuclei cavitate. The topology of a flow poor in nuclei was investigated and inception was found to occur in regions dominated by irrotational straining with high stretching rates. Particles were released from the hydrofoil tip and tracked. It is seen that at the higher Reynolds number, the particles are more likely to experience low pressures. However, the amount of time they are subject to very low pressures is shorter at the higher Reynolds number.enCavitationCompressible flowHomogenous mixture modelInceptionLarge eddy simulationThesis or Dissertation