Modeling turbulent/chemistry interactions using assumed pdf methods

Influence of reaction mechanisms, grid spacing, and inflow conditions on the numerical simulation of lifted supersonic flames

“…The reaction mechanisms tested are summarized in Table I, where the numbers of species and reactions involved as well as the ranges of validation (concerning pressure, temperature, and stoichiometric ratio ) are indicated. With the exception of the skeletal Jachimowski scheme [4] and the one-step mechanism of Marinov et al [8] The 1988 Jachimowski mechanism [1] (9-species, 20-steps) is one of the most widely used kinetic schemes in supersonic combustion [3,[9][10][11][12][13][14]. The original mechanism has been slightly modified as presented by Wilson and MacCormack [3].…”

DNS, LES and Stochastic Modeling of Turbulent Reacting Flows

“…Even with the assumption of statistical independence of the reacting species and the temperature, the question of the local scalar range imposes a severe restriction on the validity of this approximation. For example, it is demonstrated by Gaffney et al (1992) that in the modeling of a reacting turbulent shear flow, depending on the a priori choice of the magnitudes of the local scalar bounds the predicted results can be altered significantly. Obviously, this problem is!…”

“…The most obvious means is to implement the multivariate form of the PE The direct analog of the Beta U density is the Dibichlet frequency Narumi, 1923;. The application of this density in modeling of multiple species reactions has been discussed by ; ; Gaffney et aL (1992). However, the I use of the Dirichlet frequency cannot be justified for modeling of reacting flows in a general sense .…”

“…In those cases, the use of the Beta density can be justified. In fact, in non-homogeneous flows it is easier to use this density, at least until further development of the AMC for practical applications (see ; Gaffney et al (1992)). The extension of all of the three models in describing multi-scalar mixing is possible.…”

“…In regard to this last issue, it must be indicated that the Beta density has been extensively used for the modeling of nonhomogeneous reacting systems (e.g. ; Jones and Priddin (1978); ; ; Peters (1984); ; Gaffney et al (1992); for recent reviews, see Priddin (1991)). Due to their special mathematical properties, the Beta and/or the Dirichlet frequencies yield relatively simple analytical solutions for the higher order statistics of the reacting fields.…”