Second-order modeling of a passive scalar in a turbulent shear flow

A realizability concept for the scalar flux is described and a new model form of the pressure correlation term in the passive scalar flux equations is carefully derived based on realizability. A modeled scalar dissipation equation is proposed based on the idea that the ratio of mechanical time scale to scalar time scale tends toward an equilibrium value during the evolution of turbulence. As test flows, we consider the slightly heated plane and axisymmetric jets so that the temperature can be treated as a passive scalar. The calculations show that the profiles of mean velocity, mean temperature, shear stress, component energies, temperature variance, heat flux and dissipations of turbulent energy, and temperature variance approach self-preservation. The results are compared with existing measurements.