A turbulent diffusion coefficient model of micro-mixing jet flow based on deep learning

Jet-in-crossflow is a typical form in a micro-mixing combustor, and the RANS (Reynolds average Navier–Stokes) method remains an effective tool for obtaining flow field information in its initial design stage. However, based on the gradient diffusion hypothesis, the traditional RANS method used an analogy approach to model the turbulent mass diffusion (Dt) by setting a constant turbulent Schmidt number (Sct), which is not suitable for micro-mixing conditions with strong density variations. Therefore, some scholars proposed Dt/Sct models by relating the Dt to the turbulent kinetic energy and its dissipation rate. Besides the velocity field data, the Dt was also considered to be connected with the mass fraction field. Some new models were given by establish transport equations for the turbulent scalar flux or the item related to the mass fraction. To further analysis the affecting factors to the Dt, and modeling it appropriately, this paper is conducted by the results of large eddy simulation data and a combination of a deep learning method and the Shapley additive explanations method. The results indicated that the mass fraction gradient (∇ω), mass fraction (ω), velocity (V), strain rate (S), and turbulent kinetic energy (k) are the primary features influencing Dt. In light of the efficiency of the calculation and the availability of data, a simplified deep learning model with fewer input features was developed for use in the RANS calculation. Subsequent validation of the proposed model was conducted within a micro-tube case and a four fuel channels case, utilizing the proposed multilayer perceptron-based turbulent diffusion coefficient models. In comparison with the previous Dt/Sct models in the RANS method, the current deep learning model enhances the accuracy of RANS results under micro-mixing conditions.