Applying and optimizing Gene Expression Programming (GEP) applied to URANS modelling of cloud cavitating flows

Cavitation is characterized by formation of vapor bubbles when the liquid pressure falls below the vapor pressure. These bubbles travel with high velocities and burst upon exiting the low-pressure region, generating performance-degrading effects like shock, noise and vibration. Alternatively, cavitation has also been utilized for non-invasive surgical procedures and jet-drilling for the hydrocarbon industry. Thus, cavitation needs to be studied more using both experiments and numerical methods. Modelling an unsteady flow like cloud cavitating flows (where clouds of cavitating bubbles form and detach from the wall periodically) requires coupling of a cavitation and turbulence model, generally a URANS model due to its lower computational costs. However, recent studies show URANS models having considerable discrepancies when the turbulence properties are compared with experiments on a local scale. To overcome these drawbacks, Gene Expression Programming (GEP), a branch of machine learning based on an iterative survival-of-the-fittest concept is applied here. GEP is utilized specifically to correct the Boussinesq approximation, a standard assumption to compute Reynolds stress tensors in a URANS model. Here the Reynolds stress tensors are computed as a function of time-averaged velocities in X and Y directions, the void fraction and the Reynolds stress tensor values provided by experiments and traditional URANS models. However, GEP itself has several underlying factors like the population size, the number of generations, mutation index etc. that increase the variability of the "ideal" solution and its uncertainty. A dataset of solutions provided by GEP, separated by coefficients is created and a regularized linear regression technique is applied to it. This optimizes the solution coefficients to reduce the dependence on the inherent GEP factors and thus provide a stable, general relation to ameliorate the approximation. Employing this approach substantially improves the Reynolds stress modeling as compared to the URANS cases.