On the numerical simulation of a confined cavitating tip leakage vortex under geometrical and operational uncertainties

Abstract

The effects of operational and geometrical uncertainties on Tip Leakage Vortex (TLV) characteristics are investigated in the current research. Geometrical uncertainties are comprised of manufacturing tolerances or gradual geometry degradation over the time modeled by the Karhunen–Loève (KL) expansion. Operational uncertainties include randomness in operating temperature, inlet velocity, and pressure. These stochastic parameters are assumed to have a Beta probability distribution function with a standard deviation equal to measurement error. To perform Uncertainty Quantification (UQ) analysis, the non-intrusive polynomial chaos expansion is utilized. Moreover, Sobol’ indices obtain the contribution of each stochastic parameter on the quantity of interest. For numerical simulation of cavitating flow, the SST k−ω turbulence model and the Zwart mass transfer model were employed. It was observed that the cavitating tip leakage vortex flow as well as the lift and drag coefficients are profoundly affected by geometrical and operational uncertainties, which can also describe the discrepancies between numerical and experimental results. For instance, the deviation of vortices circulation, vortex core streamwise velocity, lift, and drag coefficients are more than 25%, 30%, 40%, and 70% of their mean value, respectively. Furthermore, results showed that the characteristics of TLV, like circulation and velocity field, are mostly influenced by operational uncertainties, while the vortex core position and viscous core radius are affected by geometrical randomness, specifically gap distance.