Turbulent premixed flame propagation in the vicinity of a
wall is studied using a
three-dimensional constant-density simulation of flames propagating in
a channel. The
influence of the walls is investigated in terms of the flamelet approach,
where flamelet
speed and flame surface density transport are used to describe the flame.
The walls
have constant temperature and lead to flamelet quenching for
sufficiently small wall–flame distances. Starting from the
exact evolution equation for the surface density of
propagating interfaces (Trouvé & Poinsot 1994; Candel &
Poinsot 1990; Pope 1988), a
budget for the flame surface density equation is presented before,
during, and after the
interaction with the wall. Before the flame interacts with the wall,
flame propagation
is controlled by a balance between surface production and annihilation.
During the
interaction, high flame surface density gradients near the wall are responsible
for
the predominance of the transport terms. Closures of all terms of the flame
surface
density equation are proposed. These models are based on flamelet ideas
and take into
account wall effects. Enthalpy loss through the wall affects flamelet speed,
flamelet
annihilation and flame propagation. Decrease of turbulent scales
near the wall affects
turbulent diffusion and flame strain. This model is compared to DNS results
using
two types of tests: (i) a priori tests, where individual
terms of the modelled flame
surface density equation are compared to the terms of the exact interface
density
propagation equation, calculated with the DNS; (ii) a posteriori
tests, where the final
model is used to obtain total reaction rate, mean fuel mass fraction,
heat flux at the
wall and fuel mass fraction at the wall in the configuration used in the
DNS. For
both types of tests the model compares well with the DNS results.