Simulation of a high Reynolds number reactive transverse jet and the formation of a triple flame

Theoretical Background of the Hybrid VπLES Method for Flows with Variable Transport Properties

“…where u v old is the velocity induced by vortices generated in the previous time steps. The vortex identification criterion λ ci [5] is calculated at each cell using the velocity field (4). The cells at which λ ci > λ ci,min contain the vortex candidates which in principle can be converted to vortex particles.…”

“…First, one can assume that the whole density is represented only on the grid, i.e., we neglect the subgrid change of the density ρ v = 0 and the fine scale expansion velocity u ε (x, t) = 0. For instance, in the recent paper of Ghoniem's group on combustion [4] only the flow is calculated using the vortex particle method whereas all scalars including the density are computed on the grid. Then only the Equation (17) remains.…”

“…Within the second strategy the Equation (18) is taken into account in the computation of the velocity u ε (x, t) which is calculated from the expansion field ε v (see also the formula (8) in [4]):…”

“…Discretization of (22) using the expansion particles is given in [4] (see formula (15)-(17) on the page 971 in [4]).…”

“…In principle they are different, because vortex particles arise in areas of high vorticity whereas the expansion particles should correspond to the areas of high expansion rate characterized by the material derivatives of the density. Although in the paper [4] the same set of particles is used for vortex particles and expansion particles, in this paper we will consider a more general case introducing different particle sets.…”