Development of Practical Method for Prediction of Cavitation Erosion with Turbulent Flow using Computational Fluid Dynamics

Abstract

Cavitation erosion can be observed on hydraulic mechanical devices and has long been studies, yet a difficult research subject for many years. In the present study, a practical method to predict cavitation erosion, which caused a critical damage on hydraulic machineries, was developed. Impact and critical velocities were defined to develop a practical method for the prediction of cavitation erosion. When the impact velocity was larger than the critical velocity, it was predicted that cavitation erosion could be observed. To close the practical method, the computational fluid dynamics (CFD) was introduced. To simulate cavitating flows using CFD, pressure-based incompressible and isothermal compressible flow solvers based on a cell-centered finite volume method were developed using the open source libraries, respectively. Time derivative terms were discretized using the first-order accurate backward implicit scheme Second order accurate discretized scheme was applied it to the convection and diffusion terms. To validate the developed solvers, incompressible and isothermal compressible cavitating flows were studied carefully and validated against existing experimental data. An incompressible flow with sheet, super, and cloud cavitations were simulated. A sheet cavitating flow around a hemispherical head-form body was simulated, and selected cavitation and turbulence models. A sheet cavitating flow around a modified NACA66 section (Brockett, 1966) was simulated and tested for various condensation and evaporation model constants. From the simulation of sheet cavitation, model constants were selected carefully. A super-cavitating flow behind a wedge-shaped cavitator was simulated. The computed cavity lengths on the body were compared with an analytic solution and numerical results using a potential flow solver. Fairly good agreement was observed in the three-way comparison. And then, a super cavitating flow around a body equipped with a cavitator was simulated and validated by comparisons with existing experimental data. A cloud cavitating flow around a three-dimensional twisted hydrofoil (Foeth, 2008) was simulated, and the cavity shedding dynamics by a re-entrant jet and a side entrant jet were investigated in terms of the cavity shedding cycles. The computed lift force and Strouhal number were compared against existing experimental data. From the results, the developed solver predicted well the incompressible cavitating flows. An isothermal compressible sheet cavitating flow around a hemispherical head-form body was simulated. The cavity shedding behavior, length of a re-entrant jet, drag history, and Strouhal number were investigated. Based on the results, it was confirmed that computations of the cavitating flow including compressibility effects improved the reproduction of cavitation dynamics. Thus, the isothermal compressible cavitating flow solver was selected to simulate the flow with cavitation erosion. To close the practical method for the prediction of cavitation erosion, cavitating flows with erosion in a converging-diverging nozzle (Keil et al., 2011) and around a hydrofoil (Dular and Coutier-Delgosha, 2009) were simulated by developed and validated code. From the simulations, the cavitation erosion coefficients were calculated. Based on the CFD results, the cavitation erosion coefficient was derived by a metamodeling and curve fitting methods. A kriging metamodel, which had an advantage in a non-linear problem, was selected. The cavitation erosion coefficient surface, which consisted of the cavitation and Reynolds numbers, was introduced by the kriging metamodel. In a curve fitting method, the cavitation erosion coefficient was formulated as the function of the cavitation and Reynolds numbers. A function of the cavitation number was formulated as an exponential function, while, a function of the Reynolds number was formulated as a log function for a slight change at high Reynolds number. A cavitating flow in an axisymmetric nozzle followed by radial divergence (Franc, 2009) was simulated to validate the developed practical method. Predicted damage extent showed acceptable agreement with the existing experimental data. For the application to a propeller, a cavitating flow around a propeller was simulated. Predicted damage extent showed similar with damaged full-scale propeller blade. The developed practical method helps predict cavitation erosion observed on the blades of pumps, turbines, and propellers. The prediction method including a bubble cavitation, fatigue of a material, high Reynolds number, and cavity shedding cycle is needed.