Thermochemical closure in high-speed flows

A model for the thermochemical closure in high-speed turbulent flows with nonpremixed reactants is presented, based on relatively lenient assumptions involving, inter alia, equilibrium chemistry, and the ratio density/pressure being pressure independent. The proposed approach is based on the introduction of a presumed joint pdf of the conserved scalar and an appropriately defined nondimensional enthalpy gap, for which plausible shapes are assumed. The model is applied to a test case concerning a supersonic hydrogen/vitiated air flame for a check of its consistency; results indicate good performance for both the mean and the rms of state quantities. The assumption of pressure independence is verified, and an indication of errors involved in overlooking thermochemical closure is also given. An extension to flows involving finite-rate chemistry and differential diffusion is also briefly presented, though requiring a quite extensive flamelet library.