The transport of turbulence in non-reacting and reacting shear layers is investigated using direct numerical simulations (DNS). The present DNS code solves non-dimensional transport equations for total mass, momentum, energy, and reactant mass fractions. The combustion is simulated by a single-step, second-order reaction with an Arrhenius reaction rate. The transport equations are solved using a low Mach number approximation where the effects of heat release are accounted for through variable density. The numerical formulation is characterized by a third-order Runge-Kutta time integration, eleventh-order finite-difference spatial derivatives, and a fully consistent fractional-step method for the solution of the momentum equation.
Three-dimensional simulations of one non-reacting shear layer and one reacting shear layer were performed to generate databases for statistical analysis. Transverse budgets of turbulence kinetic energy reveal that the turbulent transport and pressure transport terms have a unique role in the energy balance in that they have different algebraic signs in different regions of the layer. In the non-reacting shear layer, the pressure transport term tends to balance the turbulent transport term. In the reacting shear layer, however, a flip in the pressure transport term is observed and the resulting behavior is similar to the turbulent transport. The pressure transport term for both cases is examined in detail and the flip is attributed to the heat release through correlations with the reaction rate.
The DNS results are compared with the standard k-? model for production and turbulent transport. When calculated with the standard eddy viscosity closure coefficient, the Boussinesq approximation accurately predicts the production for the non-reacting shear layer but overpredicts it for the reacting shear layer. The calculation of the Boussinesq approximation also shows that the dilatation dissipation is small compared to the solenoidal dissipation. The evaluation of the gradient-diffusion approximation indicates that, in general, the sum of the pressure transport and turbulent transport terms behaves as a gradient-diffusion process for both the non-reacting and reacting shear layers. It is shown that including the pressure transport in the gradient-diffusion approximation makes the model more accurate for the non-reacting shear layer and less accurate for the reacting shear layer.