Modeling temperature and species fluctuations in turbulent, reacting flow

Assumed Gaussian and β probability density functions (PDFs) for temperature are used with series expansions of the reaction-rate coefficients to compute the mean reaction-rate coefficients in a turbulent, reacting flow. The series-expansion/assumed PDF approach does not require any numerical integration, which substantially reduces computational cost with little loss of accuracy. An assumed multivariate β PDF for species is investigated for use in modeling the interaction of species fluctuations and chemical combustion. The multivariate β PDF is initially evaluated through a parametric study. Results of the parametric study indicate that species fluctuations can increase or decrease the magnitude of the species production term, depending on the type of reaction. The models are then tested on a two-dimensional high-speed turbulent reacting hydrogen-air mixing layer. For the conditions tested the numerical simulations indicate that the net effect of species fluctuations is to reduce the mean species production rate.