Improved Junction Body Flow Modeling Through Data-Driven Symbolic Regression

Abstract

A novel data-driven turbulence modeling framework is presented and applied to the problem of junction body flow. In particular, a symbolic regression approach is used to find nonlinear analytical expressions of the turbulent stress–strain coupling that are ready for implementation in computational fluid dynamics (CFD) solvers using Reynolds-averaged Navier–Stokes (RANS) closures. Results from baseline linear RANS closure calculations of a finite square-mounted cylinder with a Reynolds number of 11,000, based on diameter and freestream velocity, are shown to considerably overpredict the separated flow region downstream of the square cylinder, mainly because of the failure of the model to accurately represent the complex vortex structure generated by the junction flow. In the present study, a symbolic regression tool built on a gene expression programming technique is used to find a nonlinear constitutive stress–strain relationship. In short, the algorithm finds the most appropriate linear combination of basis functions and spatially varying coefficients that approximate the turbulent stress tensor from high-fidelity data. Here, the high-fidelity data, or the so-called training data, were obtained from a hybrid RANS/Large Eddy Simulation (LES) calculation also developed with symbolic regression that showed excellent agreement with direct numerical simulation data. The present study, therefore, also demonstrates that training data required for RANS closure development can be obtained using computationally more affordable approaches, such as hybrid RANS/LES. A procedure is presented to evaluate which of the individual basis functions that are available for model development are most likely to produce a successful nonlinear closure. A new model is built using those basis functions only. This new model is then tested, i.e., an actual CFD calculation is performed, on the well-known periodic hills case and produces significantly better results than the linear baseline model, despite this test case being fundamentally different from the training case. Finally, the new model is shown to also improve predictive accuracy for a surface-mounted cube placed in a channel at a cube height Reynolds number of 40,000 over traditional linear RANS closures.