Supersonic combustion modelling using the conditional moment closure approach

This work presents a novel algorithm for supersonic combustion modelling. The method involved coupling the Conditional Moment Closure (CMC) model to a fully compressible, shock capturing, high-order flow solver, with the intent of modelling a reacting hydrogen-air, supersonic jet. Firstly, a frozen chemistry case was analysed to validate the implementation of the algorithm and the ability for CMC to operate at its frozen limit. Accurate capturing of mixing is crucial as the mixing and combustion time scales for supersonic flows are on the order of milliseconds. The results of this simulation were promising even with an unexplainable excess velocity decay of the jet core. Hydrogen mass fractions however, showed fair agreement to the experiment. The method was then applied to the supersonic reacting case of ONERA. The results showed the method was able to successfully capture chemical non-equilibrium effects, as the lift-off height and autoignition time were reasonably captured. Distributions of reactive scalars were difficult to asses as experimental data was deemed to be very inaccurate. As a consequence, published numerical results for the same test case were utilised to aid in analysing the results of the presented simulations. Due to the primary focus of the study being to assess non-equilibrium effects, the clustering of the computational grid lent itself to smeared and lower magnitude wall pressure distributions. Nevertheless, the wall pressure distributions showed good qualitative agreement to experiment. The primary conclusions from the study were that the CMC method is feasible to model supersonic combustion. However, a more detailed analysis of sub-models and closure assumptions must be conducted to assess the feasibility on a more fundamental level. Also, from the results of both the frozen chemistry and the reacting case, the effects of assuming constant species Lewis number was visible.