A hybrid LES (Large Eddy Simulation)/assumed sub-grid PDF (Probability Density Function) model for supersonic turbulent combustion

A hybrid LES (Large Eddy Simulation)/assumed sub-grid PDF (Probability Density Function) closure model has been developed for supersonic turbulent combustion. Scalar transport equations for all species in a given chemical kinetic mechanism were solved, which are necessary in the supersonic combustion where the non-equilibrium chemistry is essentially involved. The clipped Gaussian PDF of temperature and multivariate β PDF of composition were used to close the sub-grid chemical sources that appear in the conservation equations. The sub-grid variances of temperature and composition were constructed based on scale similarity approach. A semi-implicit approach based on the PDF model was proposed to tackle the resulting numerical stiffness associated with finite rate chemistry. The model was applied to simulate a supersonic, coaxial H2-air burner, where both the mean and rms (root mean square) results were compared with the experimental data. In general, good agreements were achieved, which indicated that the present sub-grid PDF method could work well in simulating supersonic turbulent combustion. Moreover, the calculation showed that the sub-grid fluctuations of temperature and major species in the combustion region were of the order of 10%–20% of their rms, while the sub-grid fluctuation of hydroxyl might be as high as 40%–50% of its rms.