Mixing time scale analysis of the Partially Stirred Reactor model for high-speed turbulent combustion of hydrogen in vitiated air

Abstract

Scramjet engines represent one of the most promising alternatives to power hypersonic vehicles, although the peculiarities of supersonic combustion raise many challenges. Computational Fluid Dynamics (CFD) simulations can be used to model highly turbulent reactive flows in such complex configurations and avoid expensive experimental campaigns. A particularly challenging aspect when dealing with numerical simulations of turbulent combustion is accurately modelling the interactions between chemistry and turbulence. These interactions can play a significant role in supersonic flows and require an appropriate closure since the conditions encountered in supersonic flows differ from those of conventional combustion devices. For this reason, an assessment of the role of turbulence-chemistry interactions in supersonic combustion is needed. This work evaluates the performance of the Partially-Stirred Reactor (PaSR) closure of the mean chemical source term by performing Reynolds-Averaged Navier–Stokes (RANS) simulations of two selected test cases, namely, the Burrows and Kurkov combustor and the German Aerospace Centre (DLR) scramjet. The PaSR approach requires the definitions of two important quantities: mixing and chemical time scales. While the chemical time scale is related to finite-rate chemistry, supersonic flow conditions can affect the most appropriate definition of the mixing time scale. For this reason, several formulations of the mixing time scale are tested in this work. The PaSR model is validated against experimental data and also compared to the finite-rate approach without turbulence-chemistry interactions (FR/No-TCI) and the Eddy Dissipation Concept (EDC). In the Burrows and Kurkov test case, the PaSR model can accurately predict the main quantities of interest (e.g., temperature and chemical compositions), showing better results than the FR/No-TCI and similar to the EDC model. The validation on the DLR case confirms these trends and highlights the importance of accounting for turbulence-chemistry interaction in supersonic combustion modelling. However, the EDC model is not able to predict a stable ignited flame in the DLR combustor. The presence of recirculation zones near the strut injector of the DLR scramjet can explain the better performance of the PaSR model versions employing the integral-based and geometric mean formulations, which estimate comparable values of the mixing time but higher than those of other time scale approaches considered in this work.