Numerical analysis of scalar dissipation length-scales and their scaling properties

Scalar dissipation rate, $\chi $, is fundamental to the description of scalar-mixing in turbulent non-premixed combustion. Most contributions to the statistics for $\chi $ come from the finest turbulent mixing-scales and thus its adequate characterisation requires good resolution. Reliable $\chi $-measurement is complicated by the trade-off between higher resolution and greater signal-to-noise ratio. Thus, the present numerical study utilises the error-free mixture fraction, Z, and fluid mechanical data from the turbulent reacting jet DNS of Pantano (2004). The aim is to quantify the resolution requirements for $\chi $-measurement in terms of easily measurable properties of the flow like the integral-scale Reynolds number, $Re_\delta $, using spectral and spatial-filtering [cf. Barlow and Karpetis (2005)] analyses. Analysis of the 1-D cross-stream dissipation spectra enables the estimation of the dissipation length scales. It is shown that these spectrally-computed scales follow the expected Kolmogorov scaling with $Re_\delta ^{-0.75} $. The work also involves local smoothening of the instantaneous $\chi $-field over a non-overlapping spatial-interval (filter-width, $w_f )$, to study the smoothened $\chi $-value as a function of $w_f $, as $w_f $ is extrapolated to the smallest scale of interest. The dissipation length-scales thus captured show a stringent $Re_\delta ^{-1} $ scaling, compared to the usual Kolmogorov-type. This concurs with the criterion of 'resolution adequacy' of the DNS, as set out by Sreenivasan (2004) using the theory of multi-fractals.