RANS predictions of a cavitating tip vortex 8th International Symposium on Cavitation Tuomas Sipilä*, Timo Siikonen** *VTT Technical Research Centre of Finland **Aalto University

Contents  Introduction  Validation case  Numerical methodology  FINFLO code  Cavitation model  Grid  Results  Conclusions

Introduction - Validation case  Potsdam propeller test case (PPTC) propeller:  Five bladed controllable pitch propeller with moderate skew.  Diameter D = m.  Test procedure consisted:  Measuring the open water performance curves.  LDV measurements of the propeller wake field in wetted conditions in uniform inflow.  Cavitation observations in several performance conditions in uniform inflow.  All tests are made by SVA Potsdam.  The test procedure is repeated with the RANS approach:  The effect of the empirical coefficients in Merkle’s mass-transrer model on a cavitating tip vortex is also investigated.  Simulation work is done under VTT’s self-funded project CFDShip.

Numerical approach – FINFLO Code  General purpose CFD code.  Multiblock cell-centered finite-volume code.  The RANS equations are solved by the pressure correction method.  No wall functions, y + ≈ 1.  Number of turbulence models.  In the present work Chien’s low Reynold’s number k-  and SST k-  models are utilized.  Several features are implemented in the code, including  Sliding mesh,  Over lapping grid,  Free surface,  Cavitation model.

Numerical approach – Cavitation model  The cavitation model is based on the continuity and momentum equations of the mixture of vapour and water.  The variation of pressure is calculated by summing the density weighted mass residuals of the gas and liquid phases together.  The velocity change is determined by combining the mass residual and the explicit momentum residual.  Merkle’s model is utilized for the mass transfer.

Numerical approach – Grid  One blade modelled due to the symmetry of the problem.  Simulations are performed at three grid levels  Total number of cells: fine level: 4.3 M; medium level: 0.5 M; coarse level 0.07 M.  The grid in the slipstream is created iteratively to concentrate cells to the tip vortex and blade wake locations.  The tip vortex has about 20 x 20 cells in its cross-section at the finest grid level. Surface grid on the blade and the grid in the slipstream at the finest grid level. The axial cut of the grid is colored by the axial wake component.

Results – Open water characteristics  The calculated propeller thrust, torque, and efficiency were within two percent of the measured ones over the simulated region.

Results – Non-cavitating tip vortex Propeller axial wake at x/D = 0.2 Top: LDV measurements (from SVA Potsdam); Bottom:k-  simulations Wake components at x/D = 0.2 at the radius of maximum axial velocity Top: LDV measurements, and k-  and SST k-  simulations; Bottom: grid density investigation of the k-  simulations

Results – Cavitating tip vortex Cavitation patterns at  n = from k-  simulations. Top: Isosurface  v = 1% colored by vapor volume fraction; Bottom: Isosurface  v = 1% colored by evaporation rate. Circumferential pressure distribution at the radius of the vortex core in the cavitating and non-cavitating tip vortices at x/D = 0.2. x/D=0.1 x/D=0.2 Cavitation observations in the tests (from SVA Potsdam)

Results – Cavitating tip vortex  The empirical coefficients C dest and C prod in Merkle’s mass-transfer formula were given the values of 100, 350, and 1000 resulting a 3 x 3 test matrix. Circumferential distribution of void fraction (left) and evaporation rate (right) at the radius of the vortex core in the cavitating tip vortices. The results are from the k-  simulations at the finest grid level.

Results – Cavitating tip vortex C prod = 100C prod = 1000 C dest = 100 C dest = 1000 Vapor volume fraction  v = 0.5 calculated with different values of the empirical coefficients C prod and C dest. Cavitation observations in the tests (from SVA Potsdam)

Conclusions  The global propeller performance is well predicted by the RANS approach.  The simulated tip vortex is very sensitive to the grid resolution.  The simulated velocity components in the tip vortex region are reasonably close to the measured ones.  The turbulence models affect significantly the pressure distribution in the rotational core of the tip vortex.  Low values of the empirical coefficient C prod deteriorate the convergence and the result of the cavitation simulations.  The convergences with high C prod and C dest values were less stable.  Simulated sheet cavitation on the blade is over-predicted since the mass-transfer model does not take into the account laminar separation.