Simulation of Non-Premixed, Supersonic Combustion using the Discontinuous Galerkin Method on Fully Unstructured Grids

In this study, three-dimensional simulations of a reacting hydrogen jet in supersonic crossflow using a structure-preserving discontinuous Galerkin (DG) formulation are examined. The hydrogen jet, with a momentum flux ratio of five, is injected into a high enthalpy crossflow. The sensitivities of the solution to the grid element size and polynomial order are investigated to determine an accurate and computationally efficient approach to simulating high-speed airbreathing propulsion vehicles. The results demonstrate that DG(p = 2) solutions, which are nominally third-order accurate in smooth regions of the flow, show reasonable agreement with existing experimental results. The separation shock formation behind the jet is found to be heavily grid dependent and necessary for accurate simulations of the reacting jet in supersonic crossflow. It is determined that the highest resolution cell and polynomial order is required to capture the upstream separation shock and consequently the flame stabilization point. The mixing and combustion mode is also determined using the flame index and demonstrates the flow is heavily skewed towards a non-premixed diffusion mode which is consistent with previously run simulations of this case using traditional finite volume schemes and sub grid scale modeling approaches. Beyond this analysis, given the prevalent use of structured hexahedral meshes in the computation of realistic high-speed, chemically reacting flows, the novelty of this work lies in demonstrating accurate simulation of such a flow on a fully unstructured tetrahedral mesh. This highlights the potential of these methods to handle both complicated geometries and complex physics.