Chakraborty Nilanjan, Klein Markus
Newcastle University, Newcastle Upon Tyne, UK.
University of the Bundeswehr Munich, Neubiberg, Germany.
Flow Turbul Combust. 2025;115(2):917-926. doi: 10.1007/s10494-025-00670-7. Epub 2025 Jun 12.
A scaling relation has been derived to link the fractal dimension of a flame surface with the ratio of the normalised 3D flame surface area to its 2D counterpart. This derivation assumes an isotropic distribution of angles between the measurement plane and the flame's normal vector, as well as a uniform distribution of angles between the principal direction and the flame's tangent vector. The validity of the newly derived relation was assessed using an existing Direct Numerical Simulation (DNS) database of statistically planar turbulent premixed flames, encompassing a range of different Karlovitz numbers. The DNS data-based assessment revealed that the newly derived relations are reasonably accurate for the thin reaction zones regime flames, with the precision of predictions based on isotropy improving, as the Karlovitz number increases. Moreover, 2D measurements of the flame surface fractal dimension and the flame wrinkling factor can be effectively used to predict the actual 3D flame wrinkling factor for flames with Karlovitz numbers much greater than unity. Alternatively, the ratio of the 3D wrinkling factor to its 2D counterpart can provide a reasonable estimate of the 3D fractal dimension for flames in the thin reaction zones regime. The newly derived relations provide an estimation for the value of fractal dimension in the limit of high Karlovitz number using an alternative route.
已推导出一种标度关系，以将火焰表面的分形维数与归一化三维火焰表面积与其二维对应物的比率联系起来。该推导假设测量平面与火焰法向矢量之间的角度呈各向同性分布，以及主方向与火焰切向矢量之间的角度呈均匀分布。使用现有的统计平面湍流预混火焰直接数值模拟（DNS）数据库评估了新推导关系的有效性，该数据库涵盖了一系列不同的卡尔洛维茨数。基于DNS数据的评估表明，新推导的关系对于薄反应区火焰是相当准确的，随着卡尔洛维茨数的增加，基于各向同性的预测精度会提高。此外，对于卡尔洛维茨数远大于1的火焰，火焰表面分形维数和火焰皱折因子的二维测量可有效地用于预测实际的三维火焰皱折因子。或者，三维皱折因子与其二维对应物的比率可为薄反应区火焰的三维分形维数提供合理估计。新推导的关系使用另一种途径对高卡尔洛维茨数极限下的分形维数值进行了估计。
