The effects of turbulent Reynolds number on the statistical behaviour of the displacement speed have been studied using\r\nthree-dimensional Direct Numerical Simulation of statistically planar turbulent premixed flames. The probability of finding\r\nnegative values of the displacement speed is found to increase with increasing turbulent Reynolds number when the Damk�¨ohler\r\nnumber is held constant. It has been shown that the statistical behaviour of the Surface Density Function, and its strain rate\r\nand curvature dependence, plays a key role in determining the response of the different components of displacement speed.\r\nIncreasing the turbulent Reynolds number is shown to reduce the strength of the correlations between tangential strain rate\r\nand dilatation rate with curvature, although the qualitative nature of the correlations remains unaffected. The dependence\r\nof displacement speed on strain rate and curvature is found to weaken with increasing turbulent Reynolds number when\r\neither Damk�¨ohler or Karlovitz number is held constant, but the qualitative nature of the correlation remains unaltered. The\r\nimplications of turbulent Reynolds number effects in the context of Flame Surface Density (FSD) modelling have also been\r\naddressed, with emphasis on the influence of displacement speed on the curvature and propagation terms in the FSD balance\r\nequation.
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