Turbulent kinetic energy evolution in turbulent boundary layers during head-on interaction of premixed flames with inert walls for different thermal boundary conditions

Abstract

The statistical behaviour of turbulent kinetic energy, and its transport in turbulent boundary layers during premixed flame-wall interaction for isothermal and adiabatic chemically inert walls have been analysed using a Direct Numerical Simulation (DNS) database. The terms due to the mean velocity gradient (commonly known as the production term) and viscous dissipation remain leading order contributors to the turbulent kinetic energy transport when the flame is away from the wall, similar to that in the corresponding non-reacting turbulent boundary layer, but in addition to these terms, the pressure dilatation and pressure transport contributions play leading order roles when the flame interacts with the wall. It has been found that the gradient hypothesis-based Reynolds stress closures in the context of the k−ε model may yield an inaccurate prediction of the mean velocity gradient term due to the counter-gradient behaviour of Reynolds stresses in the premixed flame cases considered in this analysis. The thermal boundary condition at the wall does not have a major influence apart from a higher wall friction velocity for adiabatic boundary condition than in the case of isothermal boundary condition. The assumption of local equilibrium of production and dissipation of turbulent kinetic energy has been found to be rendered invalid when the flame is either near to the wall or interacting with the wall. This invalidates the conventional log-law for mean streamwise velocity variation, and the wall functions derived based on production-dissipation balance equipped by the usual gradient hypothesis in the context of the standard k−ε model for premixed flame-wall interaction in turbulent boundary layers. Therefore, improved wall functions are necessary for Reynolds averaged Navier-Stokes simulations of premixed flame-wall interaction in turbulent boundary layers.