A direct numerical simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of\r\ndifferent turbulent Reynolds numbers has been used to assess the performance of algebraic flame surface density (FSD) models\r\nbased on a fractal representation of the flame wrinkling factor. The turbulent Reynolds number Ret has been varied by modifying\r\nthe Karlovitz number Ka and the Damk�¨ohler number Da independently of each other in such a way that the flames remain\r\nwithin the thin reaction zones regime. It has been found that the turbulent Reynolds number and the Karlovitz number both\r\nhave a significant influence on the fractal dimension, which is found to increase with increasing Ret and Ka before reaching an\r\nasymptotic value for large values of Ret and Ka. A parameterisation of the fractal dimension is presented in which the effects of\r\nthe Reynolds and the Karlovitz numbers are explicitly taken into account. By contrast, the inner cut-off scale normalised by the\r\nZelâ��dovich flame thickness ?i/dz does not exhibit any significant dependence on Ret for the cases considered here. The performance\r\nof several algebraic FSD models has been assessed based on various criteria. Most of the algebraic models show a deterioration in\r\nperformance with increasing the LES filter width.
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