Abstract
An integral form of the energy conservation equation has been derived from the first principle for low Mach number conditions for statistically steady premixed flame-wall interaction within turbulent boundary layers. The validity of this equation has been demonstrated based on three-dimensional Direct Numerical Simulation data of statistically stationary oblique quenching of a turbulent premixed V-shaped flame in a channel flow configuration as a result of its interaction with an inert isothermal wall. It has been found that the wall heat flux and the integral of chemical heat release in the wall normal direction within the turbulent thermal boundary layer are the major contributors in the energy integral equation, and their difference is accounted for by the advection contribution. The magnitudes of the wall heat flux increase, and integral of heat release rate across the thermal boundary layer decrease with increasing distance from the leading edge of the boundary layer as a result of flame quenching. The integral form of the energy conservation equation has been utilised to demonstrate that the Nusselt number (or Stanton number) for wall heat transfer is intrinsically related to the turbulent burning velocity in the case of flame-wall interaction within turbulent boundary layers. A Flame Surface Density based reaction rate closure, modified to account for the near-wall behaviour, has been utilised to estimate the mean Nusselt number in the case of flame-wall interaction within turbulent boundary layers, which revealed that the modelling limitations of the mean reaction rate closure may give rise to inaccuracies in the estimation of the mean Nusselt number. By contrast, the measurements of mean velocity, temperature, and wall heat flux can be utilised to estimate the turbulent burning velocity within the turbulent boundary layer using the newly derived energy integral equation.
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