Surrogate based optimization approach for the calibration of cavitation models

The accuracy of CFD simulations is heavily influenced by the empirical coefficients employed by the mathematical models adopted to describe different physical phenomena. While for many models, e.g. turbulence models, the choice of these coefficients can be delegated to the state of art, no extensive guidelines are present for cavitation models. These models have an empirical nature, and the set of constants has a great impact on the results, requiring a careful choice. A possible approach for their automatic selection can be represented by optimization strategies. Most of the research regarding the optimization of these coefficients focuses on searching values that are optimal only for a specific case: the results don't allow to infer a set of values that can be considered optimal for different geometries and/or different operating conditions. This paper aims to describe a methodology based on a surrogate based approximate optimization for the choice of the empirical constants of the Kunz cavitation model, which can be used for the prediction of the cavitation on centrifugal pumps. The main idea is to optimize the set of constants on three geometries representative of the impeller blades of a centrifugal pump, i.e. the hemispherical (1/2 caliber), ellipsoidal (2:1) head-form bodies of Rouse and McNown, and the NACA0009 hydrofoil. The optimal values are identified through a sequential approximate optimization. The constants values are validated on two different test cases: a blunt (0 caliber) head-form body, and a real centrifugal pump. The proposed optimization strategy allows to reach a faster convergence with respect to other algorithms available in literature, and considers a wider set of test cases to find the optimal empirical coefficients, which guarantee good accuracy for many (five) test cases, characterized by different fluid dynamic conditions (cavitation and Reynolds numbers).