MODELING OF THE INFLUENCE OF MIXTURE FRACTION FLUCTUATIONS ON BURNING RATE IN PARTIALLY PREMIXED TURBULENT FLAMES

摘要

A common approach to modeling the influence of turbulent fluctuations in the mixture fraction f on the burning rate in a partially premixed flame consists of invoking a presumed Favre (mass-weighted) probability density function (PDF) (P) over tilde (f). In the present work, two issues relevant to such an approach are addressed. First, averaging of a dependence q(f), where q is an arbitrary quantity, e.g., the laminar flame speed S-L, requires modeling of the canonical PDF P(f) if q is not proportional to the density rho. Second, because the shape of (P) over tilde (f) is not known a priori in a typical case, the presumed PDF approach can be a predictive tool only if the mean quantities q(f) are weakly sensitive to the PDF shape. To study the two issues, dependencies of rho b(f) and SL(f), computed for gasoline surrogate-air mixtures under elevated temperatures and pressures, associated with the conditions in a gasoline direct injection spark ignition engine, are averaged invoking either beta function or double-Dirac delta function Favre or canonical PDFs. Moreover, a simpler approach is proposed to evaluate <(q(f))over bar>. The approach consists of expanding q(f) in Taylor series with respect to <((f-<(f)over tilde>))over bar>, followed by averaging. The mean quantities <(rho b(f))over bar> and <(S-L(f))over bar> obtained for various Favre first (f) over tilde and second rho f ''(2)/(rho) over bar moments using the aforementioned alternative methods are compared with each other and with rho b (f) over tilde and S-L(f) over tilde, respectively. The following conclusions are drawn. First, when averaging S-L(f) under conditions of the present study, the difference between the Favre and canonical beta-function PDFs may be disregarded for simplicity. Second, <(S-L(f))over bar> is sensitive to the shape of presumed PDF (P) over tilde (f) if the magnitude of turbulent fluctuations in the mixture fraction is sufficiently large. Third, if the magnitude of turbulent fluctuations in the mixture fraction is sufficiently low in order for the mean laminar flame speeds obtained invoking the beta-function and double-Dirac delta-function PDFs to be approximately equal to one another, then, <(S-L(f))over bar> can also be evaluated using the Taylor-expansion approach.