On the spatial length scales of scalar dissipation in turbulent jet flames

Spatial length scales of the rate of dissipation, χ, of fluctuations of a conserved scalar, Z, are inferred numerically using a DNS database of a turbulent planar jet flame. The Taylor-scale Reynolds numbers lie in the range of 38 to 58 along the centreline of the simulated jet flame. Three different methods are used to study the spatial length scales associated with χ. First, analysis of the one-dimensional dissipation spectra shows an expected Re_δ^-3/4 (Kolmogorov) scaling with the outer-scale Reynolds number, Re_δ. Secondly, thin sheet-like three-dimensional scalar dissipation structures have been investigated directly. Such structures were identified within the computational domain using level-sets of the χ-field, and their thicknesses were subsequently computed. The study shows, in accordance with experimental studies, that the captured dissipation-layer thickness also shows a Kolmogorov scaling with Re_δ. Finally, spatial filters of varying widths were applied to the instantaneous Z field in order to model the averaging effect that takes place with some experimental measurement techniques. The filtered scalar dissipation rate was then calculated from the filtered scalar field. The peaks in the instantaneous filtered χ-profiles are observed to decrease exponentially with increasing filter width, yielding estimates of the true value of χ. Unlike the dissipation length scales obtained from the spectral analysis and the level-set method, the length-scale estimates from the spatial-filtering method are found to be proportional to Re_δ^-1. This is consistent with the small-scale intermittency of χ which cannot be captured by techniques that just resolve the conventional Batchelor/Obukhov - Corrsin scale. These results have implications when considering resolution requirements for measuring scalar dissipation length scales in experimental flows.