A three-dimensional Direct Numerical Simulation of an open turbulent jet spray flame representing a laboratory-scale burner configuration has been used to analyse the statistical behaviours of the magnitude of reaction progress variable gradient $$\left| {\nabla c} \right|$$ ∇ c [alternatively known as the Surface Density Function (SDF)] and the strain rates, which affect its evolution. The flame has been found to exhibit fuel-lean combustion close to the jet exit, but fuel-rich conditions have been obtained further downstream due to the evaporation of fuel droplets, which leads to the reduction in the mean value of the SDF in the downstream direction. This change in mixture composition in the axial direction has implications on the statistical behaviours of the SDF and the strain rates affecting its evolution. The mean value of dilatation rate remains positive, whereas the mean normal strain rate assumes positive values where the effects of heat release are strong but becomes negative towards both unburned and burned gas sides. The mean values of dilatation rate, normal strain rate and tangential strain rate decrease downstream of the jet exit. However, the mean behaviours of displacement speed and its components do not change significantly away from the jet exit. The mean values of normal strain rate arising from flame propagation remain positive and thus act to thicken the flame. The mean tangential strain rate due to flame propagation (alternatively the curvature stretch rate) remains negative throughout the flame at all axial locations investigated. The mean effective normal strain rate assumes positive values throughout the flame and it increases in the downstream direction for the present case, which is consistent with the reduction in the peak mean value of the SDF in the axial direction. The mean effective tangential strain rate (alternatively stretch rate) assumes negative values throughout the flame at all axial locations.

中文翻译：

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开放湍流喷射火焰中表面密度函数的演变

代表实验室规模燃烧器配置的开放式湍流喷射火焰的三维直接数值模拟已被用于分析反应进程变量梯度 $$\left| 幅度的统计行为。{\nabla c} \right|$$ ∇ c [也称为表面密度函数 (SDF)] 和影响其演化的应变率。已发现火焰在靠近射流出口处表现出贫燃料燃烧，但由于燃料液滴的蒸发，在更远的下游获得了富燃料条件，这导致下游 SDF 的平均值降低方向。轴向方向上混合物成分的这种变化对 SDF 的统计行为和影响其演变的应变率有影响。膨胀率的平均值保持为正值，而平均法向应变率假定为正值，其中放热的影响很强，但对未燃烧和已燃烧的气体侧都变为负值。膨胀率、法向应变率和切向应变率的平均值在射流出口下游减小。然而，位移速度及其分量的平均行为在远离射流出口处没有显着变化。由火焰传播引起的法向应变率的平均值保持为正值，从而起到加厚火焰的作用。由于火焰传播的平均切向应变率（或者曲率拉伸率）在整个火焰中在所研究的所有轴向位置保持为负。平均有效法向应变率在整个火焰中假定为正值，并且在当前情况下在下游方向上增加，这与轴向方向上 SDF 峰值平均值的减少一致。平均有效切向应变率（或者拉伸率）在整个火焰的所有轴向位置均假定为负值。