Interaction of turbulence and scalar fields in premixed flames

The interaction of turbulence with progress variable, c, field in a premixed flame is studied. This interaction is characterized by the correlation c,ieijc,j¯, where the overbar denotes an appropriate averaging process, c,i is the gradient of c in spatial direction i and eij is the turbulence strain rate. The importance of this term is recognized via a transport equation for the square of the magnitude of the scalar gradient in turbulent premixed flames. It is also shown that the above correlation forms a natural part of the tangential strain rate which appears in the flame surface density, Σ, equation. It is well known that this correlation is negative signifying the scalar gradient production by incompressible turbulence via the preferential alignment of the scalar gradient with the most compressive principal strain rate. This physical picture is commonly adopted for turbulent premixed flames also. Contrary to this, analyses of direct numerical simulation data for a turbulent premixed flame having flamelet combustion characteristics show the preferential alignment of the scalar gradient with the most extensive principal strain rate. This preferential alignment is because of flame influence on the flow via dilation. The above alignment pulls the isoscalar surfaces from each other yielding positive values for the above correlation inside the flame brush. Thus the turbulence, in addition to the molecular dissipation process, dissipates the scalar gradients in premixed flames when the Damköhler number (Da) is large. These dissipation processes are counteracted by chemical reactions which produce the scalar gradients. A simple RANS model for the above correlation is obtained by decomposing it into contributions from flame front and nonflame front regions of the flow as suggested by the DNS results. The model obtained here involves Da and represents the dissipation of the scalar gradients by the turbulence when Da is larger than unity. This model also recovers the production of the scalar gradient by the turbulence when Da is less than unity. Comparison of this model prediction with the DNS data of large Da flame is reasonable. The turbulence-scalar interaction in low and moderate Damköhler number flames still needs to be explored.