A data-driven Reynolds-number-dependent model for turbulent mean flow prediction in circular jets

Abstract

This paper proposes a data-driven turbulence model for predicting the mean flow in turbulent circular jets over a wide range of Reynolds numbers (Re). The main formulation is adapted from the well-known k-ϵ model (where k is the turbulent kinetic energy, and ϵ is the dissipation rate) with a set Re-dependent variation of the model constants. The k-ϵ model with Tam-Thies correction is applied with model constants optimized using data assimilation based on the ensemble Kalman filter to minimize the deviation between the model prediction and experimental data. The model constants of converging jets at Re = 10 700, 20 100, and 95 500 are fitted using logarithmic curves with respect to Re to obtain a universal formulation for predicting the jet mean flow under various flow conditions. The model using the fitted model constants, named the k-ϵ-Re model, can accurately predict the mean flow in both converging and orifice jets at various Re. While the k-ϵ-Re model is directly applied to the pipe jets, much better prediction can be obtained at high Reynolds numbers (Re ≥ 21 000 presently) compared with the default k-ϵ model. However, certain discrepancy with experimental data is observed at 5 ≤ x/D ≤ 15 at Re = 6000 and 16 000. Further improvement can be achieved by assimilating the fitting coefficients based on the pipe jet data. The k-ϵ-Re model is adequately generalizable and can predict the mean flow in different circular jets at a moderate or high Re ( ≥ 21 000), while further improvement can be obtained by the data assimilation and recalibration based on the specific nozzle type at a small Re.