Comparison of Reynolds shear stress methods for RANS turbulence modelling of a cloud cavitation in a venturi

Cavitation is defined as the process when the local pressure of the fluid drops below the vapor pressure at a roughly constant temperature resulting in the formation of vapor cavities or bubbles. It leads to several performance degrading effects like noise, vibrations and there exists a need to investigate it experimentally & numerically to study the mechanisms behind it. On the numerical side, the flow is resolved using a cavitation model coupled with a turbulence model. For coupling of a cavitation model with a URANS turbulence model for a cloud cavitating flow (cavitating flow where main cloud cavity of vapor detaches from the main wall periodically and results in large scale clouds of bubbles), the Reynolds shear stress is expected to be dependent on the turbulent eddy viscosity since the velocity fluctuations are averaged out but it is shown in this study that both formulas yield different results. A 2D model of a venturi-type section is selected as the numerical model to study the flow using the multiphase solver, interPhaseChangeFoam available in OpenFOAM. Here,the Merkle cavitation model is used along with the k-omega Shear Stress Transport (SST) turbulence model.  The Reynolds stress data is plotted globally and at local probe stations using both methods- the time-averaged product of eddy viscosity and the velocity gradients and the time-averaged product of the subtraction of time-averaged velocity from the instantaneous velocity in each direction.The results of both methods are discussed and compared with experimental data obtained using X-ray high speed Particle-Image Velocimetry (PIV) experiments. On a local comparison, it is observed that both methods yield different results: the Reynolds shear stresses calculated using the eddy viscosity method shows a near linear profile at local stations regardless of the distance from the throat while the stress calculated using the time-averaged fluctuations agrees with experimental data close to the throat.