Direct Numerical Simulation (DNS) is used to study non-constant density reacting turbulent Couette flow. The turbulent boundary layer sweep, which is the main mechanism in turbulent production, pushes the flame toward the wall, increasing the wall heat flux. At the same time, the first and the third quadrants of the Reynolds stresses become dominant at the wall. Low speed streaks decrease the stretch on the flame increasing the heat wall flux. High speed streaks increase the stretch on the flame reducing the wall heat flux. Streamwise vortices convect the flame toward the wall increasing the wall heat flux. Studying the instantaneous wall heat flux reveals that the wall heat flux of 1.25 times its laminar value repeats itself every 3.2 outer time units (based on mean velocity and channel half width). A wall heat flux of 1.4 times its laminar value repeats itself every 120 outer time units. The streamwise mean velocity and mean temperature compare well with the law of the wall. The integral length scale, which is within the order of the channel width for the approaching turbulence, becomes within the order of the flame thickness. Overall the flame reduces the turbulent kinetic energy (k). The budget of turbulent kinetic energy is also studied. The pressure term is the main mechanism for turbulent production in the flame. The viscous dissipation term in the k equation is dominated by the dilatational dissipation in the reaction zone. Due to the heat release, the production terms in the k equation become a loss for k close to the wall. The budget of the Reynolds stresses is studied also. The Bray Moss and Libby (BML) model is also compared with DNS data. Due the non-adiabaticity at the wall, the BML model does not give the correct quantitative value of the turbulent scalar flux close to the wall. The BML model for the flame surface density $(\Sigma )$ is also considered. The existing models for $\Sigma$ and reaction rate are modified close to the wall. The suggested models compare well with the DNS data.
Al-Shaalan, T. M. Studying Reacting Turbulent Couette Flow Using Direct Numerical Simulations. University of Wisconsin-Madison, 1997.