A novel approach to modelling highly compressible and reactive flows is formulated to provide high resolution closure of turbulent-scale reaction rates in the presence of very rapid transients in pressure and energy. For such flows, treatment of turbulent-micro scales are generally unattainable through traditional modelling techniques. To address this, the modelling strategy developed here is based on the Linear Eddy Model for Large Eddy Simulation (LEM-LES);​ a technique which has only previously been applied to weakly compressible flows. In the current formulation of the Compressible LEM-LES (CLEM-LES), special treatment of the energy balance on the model subgrid is accounted for in order for the model reaction rates to respond accordingly to strong shocks and rapid expansions, both of which may be present in reactive and supersonic flow fields.

In the current study, the model implemented is verified and validated for various 1D and 2D flow configurations in a compressible Adaptive Mesh Refinement (AMR) framework. In 1D test cases, laminar and turbulent flame speeds and structure have been reproduced. Also, detonation speeds and initiation events are also captured with the model. For 2D model validation, unsteady and turbulent detonation propagation and initiation events, in a narrow channel, are simulated. Both test cases involve premixed methane-oxygen mixture at low pressures. The model is found to capture well the two-dimensional detonation cellular structure, behaviour, and initiation events that are observed in corresponding shock tube experiments. Furthermore, the effect of turbulent mixing rates is investigated though a single tuning constant. It was found that by increasing the intensity of turbulent fluctuations present, detonations exhibit larger and more irregular cell structures. Furthermore, the intensity of turbulent fluctuations is found to also have an effect on initiation events.