Scalar dissipation rate statistics in turbulent swirling jets

V Stetsyuk,A M K P Taylor,Y Hardalupas,N Soulopoulos

doi:10.1063/1.4954657

V Stetsyuk, A M K P Taylor + Show 2 more

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https://doi.org/10.1063/1.4954657

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Abstract

The scalar dissipation rate statistics were measured in an isothermal flow formed by discharging a central jet in an annular stream of swirling air flow. This is a typical geometry used in swirl-stabilised burners, where the central jet is the fuel. The flow Reynolds number was 29 000, based on the area-averaged velocity of 8.46 m/s at the exit and the diameter of 50.8 mm. The scalar dissipation rate and its statistics were computed from two-dimensional imaging of the mixture fraction fields obtained with planar laser induced fluorescence of acetone. Three swirl numbers, S, of 0.3, 0.58, and 1.07 of the annular swirling stream were considered. The influence of the swirl number on scalar mixing, unconditional, and conditional scalar dissipation rate statistics were quantified. A procedure, based on a Wiener filter approach, was used to de-noise the raw mixture fraction images. The filtering errors on the scalar dissipation rate measurements were up to 15%, depending on downstream positions from the burner exit. The maximum of instantaneous scalar dissipation rate was found to be up to 35 s−1, while the mean dissipation rate was 10 times smaller. The probability density functions of the logarithm of the scalar dissipation rate fluctuations were found to be slightly negatively skewed at low swirl numbers and almost symmetrical when the swirl number increased. The assumption of statistical independence between the scalar and its dissipation rate was valid for higher swirl numbers at locations with low scalar fluctuations and less valid for low swirl numbers. The deviations from the assumption of statistical independence were quantified. The conditional mean of the scalar dissipation rate, the standard deviation of the scalar dissipation rate fluctuations, the weighted probability of occurrence of the mean conditional scalar dissipation rate, and the conditional probability are reported.

Highlights

The dissipation rate, which is identified as a characteristic diffusion time scale imposed by the mixing field,[1] requires modelling in essentially all computational models for non-premixed combustion
Time averaging was performed for N = 5000 and for N = 1500, which demonstrated similar results. This indicated that mixture fraction statistics were sufficiently converged for a smaller number of instantaneous images (N = 1500)
We report that the probability density functions of the scalar dissipation rate are negatively skewed, but become almost symmetrical when a well-mixed flow regime is observed, i.e., S = 1.07 at y/Df = 5, 7

Summary

Introduction

The dissipation rate, which is identified as a characteristic diffusion time scale imposed by the mixing field,[1] requires modelling in essentially all computational models for non-premixed combustion. The scalar dissipation rate can be used, for instance, in a PDF-flamelet approach in which species mass fraction, mean reaction rate, temperature, etc., are pre-computed as a function of two variables, namely mixture fraction and the scalar dissipation rate and stored in a library. The scalar dissipation rate was identified as the criterion that was able to predict the local extinction phenomenon of diffusion flames. It was pointed out that local extinction of diffusion flames occurred where the conditional dissipation rate exceeded a critical quenching value and global extinction took place when the cumulative probability of the conditional dissipation rate exceeded a critical threshold..

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