Analytical Solutions of the Balance Equation for the Scalar Variance in One-Dimensional Turbulent Flows under Stationary Conditions

Abstract

This study presents 1D analytical solutions for the ensemble variance of reactive scalars in one-dimensional turbulent flows, in case of stationary conditions, homogeneous mean scalar gradient and turbulence, Dirichlet boundary conditions, and first order kinetics reactions. Simplified solutions and sensitivity analysis are also discussed. These solutions represent both analytical tools for preliminary estimations of the concentration variance and upwind spatial reconstruction schemes for CFD (Computational Fluid Dynamics)—RANS (Reynolds-Averaged Navier-Stokes) codes, which estimate the turbulent fluctuations of reactive scalars.