Evaluation of mixture-fraction-based turbulent-reaction-rate model assumptions for high-pressure reactive flows

Several assumptions of atmospheric-pressure (atmospheric-p) single-phase turbulent reaction rate models are examined for high-p reactive flows having turbulent characteristics. The study uses a Direct Numerical Simulation (DNS) database described elsewhere (Bellan, 2017). This database was obtained with a model combining multi-species mixing under high- p conditions, a real-gas equation of state (EOS) and a single-step chemical reaction. The database, created in the configuration of a temporal mixing layer, probes the effect of the initial Reynolds number, Re0, of the initial pressure, p0, and of the initial composition of the two mixing-layer streams. The reaction is initiated in a turbulent flow and in each simulation the computations are pursued past a time when a maximum average-volumetric p is attained, tpp*. The examination of the vorticity and enstrophy equations at a time before reaction initiation and also at tpp* highlights the pivotal role of the high density-gradient magnitude regions (Bellan, 2017) in producing turbulence and the crucial role at tpp* of the baroclinic effect representing the misalignments of gradients of thermodynamic variables. Compared to the classical mixture fraction equation, the results show that the mixture fraction obeys an equation in which there is an additional diffusion term having a larger r.m.s. magnitude than that of the mixture-fraction typical diffusion term. An assessment of the Conditional Source-term Estimation (CSE) model assumptions found that, using an accurate mixture fraction probability density function (PDF), one can obtain a very good representation of the turbulent reaction rate in the most intense reaction regions, however the quality of the predictions of CSE deteriorated significantly when a common model for the PDF, the β -PDF, was used despite the β-PDF being constructed with the accurate moments extracted from the DNS. In the regions of minimal reaction, the CSE model using the exact PDF extracted from the DNS does not provide an accurate representation of the turbulent reaction rate, a fact which is attributed to the combined effect of lack of correlation between fluctuations of the reaction rate and of the mixture fraction, and to the strong correlation of the thermodynamic variables through the real-gas EOS in regions of colder and denser fluid.