A novel subgrid-scale stress model considering the influence of combustion on turbulence: <i>A priori</i> and <i>a posteriori</i> assessment

Most classical turbulence models were proposed and developed based on non-reacting flows without considering the effects of combustion on turbulence. The flow structure in turbulent combustion is more complex, creating challenges to the applicability of traditional turbulence models. Given this, a novel flame surface and k-equation-based gradient model (FKGM) considering combustion effects is proposed for the modeling of the subgrid-scale (SGS) stress in large eddy simulation (LES). The SGS stress is calculated based on the SGS kinetic energy (kSGS) and normalized velocity gradient. The velocity gradient incorporates first-order gradients at multiple stencil locations and considers the anisotropy of the stress near the flame surface. The FKGM model is first validated by the a priori analysis based on the direct numerical simulation (DNS) database of a premixed swirling flame. The closure terms of the kSGS equation are well validated, and the predicted SGS stress using the FKGM model achieves good agreement with the filtered DNS results. In the a posteriori LES study, the FKGM model demonstrates better performance compared with the traditional dynamic Smagorinsky model and velocity gradient model, providing more accurate predictions for mean and fluctuation velocities. The error analysis for SGS kinetic energy is further conducted by comparing the LES results with the DNS data, and the results indicate that the underestimation of the generation term of the kSGS equation is the main source of error.