Validity of an assumed PDF combustion model for SCRAMJET applications

The assumed PDF approach of Girimaji is a well-known method to describe mix- ing processes or combustion with turbulence-chemistry interaction. Its advantages are a realistic shape of the multivariate species distribution, which can be analytically determined as well as the inexpensive way to calculate the temperature and species variances. Compared to sophisticated methods like transported PDF in combination with LES, this assumed PDF method is extremely fast and especially suited for engineering applications. In this paper the physical validity of the approach of Girimaji is investigated for the case of supersonic combustion. The flame regime diagram for supersonic combustion is discussed and an extension of this region is proposed. The assumed PDF approach is used together with a detailed 9-species H₂-air mechanism of Jachimowski. This combination allows an exact calculation of many effects which occure in non-premixed combustion, like ignition, quenching or reignition. Mixing is the crucial factor in SCRAMJET engines and this process is described by the multivariate β-PDF for species mass fractions. Deficiencies of this moment closure method are evaluated. Independent of a real flow, the influence of fluctuations of temperature and species are investigated. It is shown that in all cases species fluctuations slow down the chemistry compared to combustion without turbulence-chemistry interaction. Fluctuation diagrams are presented that illustrates the change in the ignition delay time with fluctuations relative to the laminar ignition delay time. This work is part of the German SCRAMJET project.