A simple algebraic model for the Favre averaged scalar dissipation rate, c, in high Damkohler number premixed flames is obtained from its transport equation by balancing the leading order terms. Recently proposed models for the dominant terms in the transport equation are revisited and revised. The algebraic model incorporates essential physics of turbulent premixed flames, namely, dilatation rate, its influence on turbulence-scalar interaction, chemical reactions, and dissipation processes. A realizability analysis is carried out to show that the algebraic model is always unconditionally realizable. The model predictions of dissipation rate are compared with the DNS results, and the agreement is good over a range of flame conditions. Application of the Kolmogorov-Petrovski-Piskunov (KPP) theorem along with the above algebraic model gives an expression for the turbulent flame speed. Its prediction compares well with a range of experimental data with no modifications to the model constants.

Scalar dissipation rate is a central quantity in turbulent flame modeling as it is closely related to the reaction rate. It is well known that turbulence-scalar interaction plays a vital role in turbulent flows with scalar mixing and thus on the scalar dissipation rate. This interaction process is characterized by the tensor inner product between the scalar gradient vector and the turbulence strain rate tensor and it is found to depend strongly on the Damköhler number, Da. Two direct numerical simulation data sets are analyzed in detail in order to understand the physics of Da dependence. The well known alignment of scalar gradient with the most compressive principal strain rate resulting in production of the scalar gradient by turbulence is observed for low $(\mathrm{Da}<1)$ Damköhler number flame, whereas the turbulence dissipates the scalar gradient in high Da flame. This dissipation of the scalar gradient in the high Da flame is because of its preferential alignment with the most extensive principal strain rate. Even for $\mathrm{Da}<1$ flame, in the regions of intense heat release the scalar gradient has a tendency to align with the most extensive strain rate. This distinct change is because of strong competition between chemical strain rate, due to dilatation from the flame front and the local fluid dynamic strain rate. The alignment characteristics affect flame normal and tangential strain rate statistics. The flame normal strain rate is found to be positive throughout the flame brush when $\mathrm{Da}>1$ , whereas it is predominantly negative when $\mathrm{Da}<1$ . Despite this difference the mean tangential strain rate remains positive yielding flame surface area production. However, the production results via different physical mechanisms. Possible implications of these differences on the modeling of turbulent premixed flames are identified and explained.

A strategy to extract turbulence structures from direct numerical simulation (DNS) data is described along with a systematic analysis of geometry and spatial distribution of the educed structures. A DNS dataset of decaying homogeneous isotropic turbulence at Reynolds number ${\mathit{Re}}_{\lambda } = 141$ is considered. A bandpass filtering procedure is shown to be effective in extracting enstrophy and dissipation structures with their smallest scales matching the filter width, $L$ . The geometry of these educed structures is characterized and classified through the use of two non-dimensional quantities, ‘planarity’ and ‘filamentarity’, obtained using the Minkowski functionals. The planarity increases gradually by a small amount as $L$ is decreased, and its narrow variation suggests a nearly circular cross-section for the educed structures. The filamentarity increases significantly as $L$ decreases demonstrating that the educed structures become progressively more tubular. An analysis of the preferential alignment between the filtered strain and vorticity fields reveals that vortical structures of a given scale $L$ are most likely to align with the largest extensional strain at a scale 3–5 times larger than $L$ . This is consistent with the classical energy cascade picture, in which vortices of a given scale are stretched by and absorb energy from structures of a somewhat larger scale. The spatial distribution of the educed structures shows that the enstrophy structures at the $5\eta $ scale (where $\eta $ is the Kolmogorov scale) are more concentrated near the ones that are 3–5 times larger, which gives further support to the classical picture. Finally, it is shown by analysing the volume fraction of the educed enstrophy structures that there is a tendency for them to cluster around a larger structure or clusters of larger structures.

The interaction of turbulence with progress variable, $c$ , field in a premixed flame is studied. This interaction is characterized by the correlation $\overline{c_{,i}{e}_{ij}{c}_{,j}}$ , where the overbar denotes an appropriate averaging process, $c_{,i}$ is the gradient of $c$ in spatial direction $i$ and $e_{ij}$ 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, $\Sigma$ , 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.