The present work aims at modeling the entire convection flux ρuW¯$\overline {\rho \mathbf {u}W}$ in the transport equation for a mean reaction rate ρW¯$\overline {\rho W}$ in a turbulent flow, which (equation) was recently put forward by the present authors. In order to model the flux, several simple closure relations are developed by introducing flow velocity conditioned to reaction zone and interpolating this velocity between two limit expressions suggested for the leading and trailing edges of the mean flame brush. Subsequently, the proposed simple closure relations for ρuW¯$\overline {\rho \mathbf {u}W}$ are assessed by processing two sets of data obtained in earlier 3D Direct Numerical Simulation (DNS) studies of adiabatic, statistically planar, turbulent, premixed, single-step-chemistry flames characterized by unity Lewis number. One dataset consists of three cases characterized by different density ratios and is associated with the flamelet regime of premixed turbulent combustion. Another dataset consists of four cases characterized by different low Damköhler and large Karlovitz numbers. Accordingly, this dataset is associated with the thin reaction zone regime of premixed turbulent combustion. Under conditions of the former DNS, difference in the entire, ρuW¯$\overline {\rho {u}W}$, and mean, ũρW¯$\tilde {u}\overline {\rho W}$, convection fluxes is well pronounced, with the turbulent flux, ρu′′W′′¯$\overline {\rho u^{\prime \prime }W^{\prime \prime }}$, showing countergradient behavior in a large part of the mean flame brush. Accordingly, the gradient diffusion closure of the turbulent flux is not valid under such conditions, but some proposed simple closure relations allow us to predict the entire flux ρuW¯$\overline {\rho \mathbf {u}W}$ reasonably well. Under conditions of the latter DNS, the difference in the entire and mean convection fluxes is less pronounced, with the aforementioned simple closure relations still resulting in sufficiently good agreement with the DNS data.

中文翻译：

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湍流平均反应速率输运方程中对流项闭合关系的DNS研究

目前的工作旨在模拟传输方程中的整个对流通量 ρuW¯$\overline {\rho \mathbf {u}W}$ 在湍流中的平均反应速率 ρW¯$\overline {\rho W}$ ，这是（方程）最近由本作者提出的。为了模拟通量，通过引入调节到反应区的流速并将该速度插入到为平均火焰刷的前缘和后缘建议的两个极限表达式之间，开发了几种简单的闭合关系。随后，对 ρuW¯$\overline {\rho \mathbf {u}W}$ 提出的简单闭合关系通过处理在早期 3D 直接数值模拟 (DNS) 绝热、统计平面、湍流研究中获得的两组数据进行评估，以统一路易斯数为特征的预混单步化学火焰。一个数据集由三个以不同密度比为特征的案例组成，并与预混湍流燃烧的火焰状态相关。另一个数据集由四个案例组成，其特征是不同的低 Damköhler 数和大 Karlovitz 数。因此，该数据集与预混湍流燃烧的薄反应区制度有关。在前DNS条件下，整体差异ρuW¯$\overline {\rho {u}W}$，均值ũρW¯$\tilde {u}\overline {\rho W}$，对流通量为很明显，随着湍流，ρu′′W′′¯$\overline {\rho u^{\prime \prime }W^{\prime \prime }}$，在大部分均值中显示出逆梯度行为火焰刷。因此，湍流的梯度扩散闭合在这种条件下是无效的，但是一些提议的简单闭包关系使我们能够相当好地预测整个通量 ρuW¯$\overline {\rho \mathbf {u}W}$。在后一种 DNS 的条件下，整体和平均对流通量的差异不太明显，上述简单的闭合关系仍然导致与 DNS 数据足够好的一致性。