Numerical simulation of a cavitating line vortex in a converging-diverging nozzle

Abstract

Tip vortex cavitation was previously identified as a source of the broadband noise emitted by ships underwater. This leads to unwanted noise and vibrations on board, which reduces passenger comfort, and increases the underwater signature of naval ships. The influence of different cavitation regimes on propellers and boundary layer transition on wings, has led to studies that isolate the cavitating tip vortex. This is done by using a converging-diverging nozzle (Venturi tube) geometry, combined with a suitable inflow condition to simulate a cavitating line vortex. The currently available computational power allowed for a comparative study of SRS methods (i.e. the IDDES model) and RANS models (i.e. the k − ω SST and EARSM) in wetted and cavitating vortex conditions. Both the general flow field, as well as the dynamics of the cavity deformations in the vortex were analyzed in this thesis. The geometry was selected based on the available experimental validation data for the wetted flow case, whereby preliminary studies determined the inflow and outflow lengths of the domain. A Lamb-Oseen tangential velocity profile was specified at the inlet. The vortex strength and viscous core size were tuned to obtain similar inflow conditions as in the experimental measurements, which used a fixed-blade swirl generator to generate the line vortex. The flow field in the wetted vortex case demonstrated an excessive amount of viscous diffusion of the vortex for both RANS models.This was caused by the overproduction of modeled turbulent kinetic energy at the viscous core edge. EARSM resuls were verified in a grid- and time step refinement study, however the large modeling error in the viscous core prevented the validation of the results. The IDDES model results were closer to the experimental reference, but were obtained with an almost laminar flow field. Modeled turbulence was mostly dissipated and no resolved velocity fluctuations were present in the flow at the measurement section. In the cavitating vortex simulations, numerical diffusion of the EARSM led to a more diffuse vapor core interface and a more downstream development of the vortex cavity compared to IDDES, where the flow field remained predominantly laminar at the measurement section. Both EARSM and IDDES predicted a solid-body rotation of the vapor core, combined with an increase of radial velocity towards the vapor core edge. The non-negligible radial velocity resulted in a conical cavity shape. The velocity profile of the simulated line vortex therefore did not correspond to that of a cavitating Lamb-Oseen vortex (which assumes no radial velocity components), such that the simulated line vortex was not representative of a cavitating tip vortex. he sheet cavities originating from sharp edges at the front and end of the Venturi throat strongly influenced the flow field and cavity dynamics. The developed front sheet cavity determined the streamwise inception of the vapor core of the vortex. Periodic shedding and collapse of the irregular downstream sheet cavity caused axial and radial contractions of the vapor core
as well as a noncircular deformation of the cavity cross-section. No traveling or standing Kelvin waves could be identified on the cavity interface using the developed post-processing and spectral analysis tool. The identified cross-sectional deformation did not correspond to cavity deformation modes defined in previous research and none of the other deformation modes were found to occur. Grid-dependent solutions, numerical noise and large wavenumber resolution indicated that a finer grid is required and that the analyzed length of the cavity should increase to improve the quality of numerical analyses of simulated cavity dynamics.