Probability Calculations for Turbulent Jet Flows with Mixing and Reaction of NO and O₃

Abstract

Calculations are performed for non-premixed, chemically reacting axisymmetric and plane jets involving NO and O₃. The jet carries NO diluted with N₂ into the stagnant surrounding containing traces of O₃ in the carrier gas N₂. The concentrations of the reactants and products are determined from Monte Carlo solutions of the joint PDF equation of two scalars (Shvab-Zeldovich variables). The hydrodynamics are determined from the continuity equation, time averaged momentum equations and a two-equation model for turbulence. In order to compare the Monte Carlo calculations and to estimate the effects of concentration fluctuations on the reaction rate, finite-difference calculations were made on the averaged transport equations for the same two Shvab-Zeldovich variables, with neglect of second-order effects on the reaction rate. It is noted that for the passive scalar (first Shvab-Zeldovich variable) mean transport calculations are advantageous, where the joint PDF formulation has the advantage of closing the source term for the reactive scalar (second Shvab-Zeldovieh variable). This paper contains mean velocity profiles, turbulence scales, the mean and all the second-order moments of scalars calculated from joint PDF formulation.