Evaluation of Combustion Models for High Speed $H_2/$Air Confined Mixing Layer Using DNS Data

The capability of empirical combustion models to predict the mean reaction rate for supersonic mixing layer is evaluated by using the stored time series data of direct numerical simulations (DNS). The confined supersonic $H_2/$air mixing layer-the prototype representation of the scramjet combustor flow field-is taken as the test case. The reaction rate profiles of various species obtained from the DNS results are compared with the reaction rate profiles obtained from these combustion models. The combustion models based on fast chemistry approximation are seen to predict the peak mean reaction rate much higher (about two orders of magnitude) compared to DNS data, particularly in the mixing layer region where the reaction is taking place. The Eddy Dissipation Concept (EDC) based combustion models for finite rate chemistry suggested by Magnussen and coworkers predict the mean reaction rate of all the major and minor species extremely well. The EDC model with detailed full chemistry (FC) and finite rate single-step chemistry (SSC) captures all essential features of reaction rate profile distribution with similar order of magnitude peak values, although a thinner reaction zone is predicted. The comparisons of mean reaction rates with different hydrogen and air stream temperatures reveal that the model can predict the mean reaction rate for practical scramjet combustor flow field. The model is also seen to predict the mean reaction rate well at a location close to the occurrence of ignition. A modification of this model allowing a nonunity Schmidt number, a feature very important for the flow involving hydrogen, shows little improvement in the prediction of the reaction rates. It is inferred that for hypervelocity reactive flows for which heat release due to chemistry is counteracted by significant enthalpy change due to gas dynamics, the finite rate EDC model with fine tuning for reaction zone width may be adequate to describe full chemistry effect