Straining and scalar dissipation on material surfaces in turbulence: Implications for flamelets

Direct numerical simulations of turbulence are used to examine the straining on material surfaces, and the behavior of thin diffusive layers. The results are related to questions arising in the study of turbulent premixed and diffusion flames in the flamelet regime. The simulations are of constant-density, homogeneous, isotropic turbulence, with artificial forcing of the velocity field to maintain statistical stationarity. Taylor-scale Reynolds numbers (Rλ) up to 93 are achieved. It is found that the total rate-of-strain a in the tangent plane of a material surface is positive (i.e., extensive) with 80% probability. This straining causes the area of the surface to double every 2.5 Kolmogorov time scales (τη). A premixed flamelet can be viewed as a surface that propagates at a speed w (i.e., the local laminar flame speed) relative to the fluid ahead. It is shown that the distance z between such a propagating surface and an initially coincident material surface remains small if w is small compared to the Kolmogorov velocity scale. For this case, the statistics of z are characterized. Subject to certain assumptions, the thin diffusive layers between blobs of fluid of different concentration adopt a self-similar form (at least for small times). It is found that the scalar dissipation χ0 in the center of these layers is approximately log-normally distributed. The mean thickness of these layers is approximately 2 Batchelor scales, and is less than 5 Batchelor scales with 98% probability. The joint probability density of χ0 and a shows that χ0 fluctuates significantly about its quasi-static value based on a (for a > 0). The integral time scales of a and χ0 are found to be approximately τη and 4τη, respectively. None of the results obtained shows significant Reynolds-number dependence when normalized by the Kolmogorov scales.