Modeling temperature and species fluctuations in turbulent, reacting flow

Assessment of Turbulence-Chemistry Interactions in Missile Exhaust Plume Signature Analysis

“…Consistent with work of Gaffhey, et al 5 , the marginal pdf s P p , Pr and PQ were specified as follows. A delta function was assumed for the marginal pdf of density so that P p = A(p -p).…”

“…Other models do exist to more generally account for turbulence-chemistry interactions that are applicable to compressible flows. Among the most comprehensive techniques are the assumed probabilitydensity-function (pdf) method 5 and the compressible extension of the pdf evolution equation method '. Though providing a more accurate description of the higher order statistics of the turbulent scalar fields, the pdf evolution equation method has not been shown to yield significantly better results than the assumed pdf method when applied to compressible flows.…”

Methods for Prediction of High-Speed Reacting Flows in Aerospace Propulsion

“…In one approach discussed earlier with the VULCAN code, interactions between the turbulence field and chemistry were modeled with an assumed beta PDF to account for the effects of temperature fluctuations on chemical reaction rates and a multivariate assumed beta PDF to account for the effect of species fluctuations on species production [94,95]. Issues associated with cross correlations of temperature and species, not considered in the previous works, were accounted for using a new assumed PDF approach [150].…”

“…Coupling between the turbulence and chemistry fields was also accounted for with Gaussian or beta assumed probability density functions to account for temperature variance effects on forward and backward kinetic rate coefficients in the chemistry model [94]. Turbulence effects on the species production rates were also accounted for by modeling the sum of the species variances using a multivariate assumed probability density function [95]. The LARCK code was validated against a number of 2-and 3-D unit problems such as flat plate flow [96], highMach-number compression ramp flow, and Mach 3 corner flow.…”

“…Turbulence models used in the code included the k-ϵ and k-ω models previously used in the LARCK code as well improved turbulent kinetic energy models that were being developed in parallel with VULCAN. Interactions between the turbulence field and chemistry were modeled with an assumed beta probability density function (PDF) to account for the effects of temperature fluctuations on chemical reaction rates and a multivariate assumed beta PDF to account for the effect of species fluctuations on species production [94,95]. However, the statistical dependence among the scalars was not accounted for by these models.…”