A quantity called “the conserved scalar” is very important in the modeling of turbulent reactive flows in large eddy simulations because, if it can be defined, it numerically simplifies the solution of the conservation equations by confining the reaction term to a single-species equation. This conserved scalar is assumed to have the statistics of a beta probability distribution function, and is thus determined by its first two moments of the distribution. The mean is computed as part of the general solution of the governing equations. However, the second moment, which is the variance at the scale smaller than that of the grid used for computation, is not known. For subcritical-pressure flows, an equation is usually derived for the scalar variance, and since all terms of the equation are not calculable from the solution of the governing equations, some of these terms are modeled and the scalar variance equation is then solved. The problem is that under supercritical conditions the scalar variance equation is considerably more complex, a fact that begs the question whether the same meth odology can be used for the important applications where the pressure is very high with respect to the critical point.
The scalar variance equation was derived under supercritical conditions, its terms were analyzed, and it was shown that new terms never modeled before are now important. Two methods were devised to model accurately the scalar variance and filtered, non-linear functions of it, such as the dissipation.
A database of direct numerical simulation was used to: (1) examine the magnitude of the new terms in the subgrid scalar variance equation, (2) inquire whether the scalar has a probability distribution function of presumed shape, (3) develop directly two models for the subgrid scalar variance, and (4) show how these models portray non-linear functions of the conserved scalar when the scalar is assumed to have a presumed probability distribution shape.