Flow-flame interaction in a closed chamber

Numerous studies of flame interaction with a single vortex and recent simulations of burning in vortex arrays in open tubes demonstrated the same tendency for the turbulent burning rate Urms2/3, where Urms is the root-mean-square velocity and is the vortex size. Here, it is demonstrated that this tendency is not universal for turbulent burning. Flame interaction with vortex arrays is investigated for the geometry of a closed burning chamber by using direct numerical simulations of the complete set of gas-dynamic combustion equations. Various initial conditions in the chamber are considered, including gas at rest and several systems of vortices of different intensities and sizes. It is found that the burning rate in a closed chamber (inverse burning time) depends strongly on the vortex intensity; at sufficiently high intensities it increases with Urms approximately linearly in agreement with the above tendency. On the contrary, dependence of the burning rate on the vortex size is nonmonotonic and qualitatively different from the law 2/3. It is shown that there is an optimal vortex size in a closed chamber, which provides the fastest total burning rate. In the present work, the optimal size is six times smaller than the chamber height.