The effects of pressure treatment on the flamelet modeling of supersonic combustion

The flamelet method has been used extensively as an affordable turbulence-combustion interaction model that obviates the need to solve the evolution equations for the species mass fractions during a large-eddy or Reynolds-averaged Navier–Stokes calculation of a reactive flow field, leading to substantial savings in the simulation time and enabling modeling with relatively complex kinetic mechanisms. The canonical problem analyzed and stored in a look-up array in the flamelet procedure usually assumes some baseline fields; in particular, the pressure is often specified at a fixed value that is characteristic of the examined configuration. However, pressure in supersonic combustion has significant dynamical roles, unlike in low-Mach number or incompressible flows, and a constant pressure field will not be adequate for the former. To remedy this problem, reaction rate in the combustor is often assumed to scale squarely with pressure. This approach, which is probably acceptable for low-speed, high pressure combustors, is not suitable for dealing with the variable pressure conditions in supersonic combustion. This paper focuses on the assessment of the aforementioned scaling, in absolute sense, and also relative to an approach where pressure is added as a control parameter in the flamelet library. To achieve this, three classes of reactive systems with different levels of modeling complexities are investigated to show that representative chemical variables do not scale squarely with pressure. For the case of supersonic combustion, the scaling treatment in general leads to over-prediction of pressure and combustion and also tends to stabilize the flame. To the knowledge of the authors, no previous studies have reported on the issues addressed in the present paper.