Modeling of turbulent reacting flows with probability density functions for scramjet applications

The objective of this investigation is to examine the use of probability density functions (PDF's) to account for turbulence-chemistry interactions in supersonic turbulent reacting flows. Various assumed PDF approaches (approaches where the form of the PDF is assumed a priori) are studied that model the effects of both temperature and composition fluctuations on the chemical source terms. A PDF approach which allows the PDF to evolve as the flowfield develops is also examined. The computational models are tested by examining two axisymmetric reacting free shear flows, as well as a three dimensional experimental supersonic combustion ramjet (scramjet) configuration. Comparisons are made with experimental data for each case considered. In general, the assumed and evolution PDF approaches yield comparable mean flow quantities, but larger differences are noted when comparing higher order correlations. The scramjet calculations compare well with wall pressure measurements and flow visualization. Heat transfer rates, however, are consistently underpredicted. The turbulent Prandtl number is shown to have a significant impact on the heat transfer rates and instream pitot pressure.