The quadrature-based semi-analytical solution for the conditional moment closure (SA-CMC) given in (A. D. Ilgun, A. Passalacqua, and R. O. Fox, “A quadrature-based conditional moment closure for mixing-sensitive reactions,” Chem. Eng. Sci., 226, 2020) eliminates the additional conditioning-space discretization in CMC applications by assuming that the mixture-fraction PDF is well represented by a β-PDF. A Gaussian quadrature provides the mixture-fraction abscissae, and the conditional scalar mean is expressed in terms of Jacobi polynomials. Here, by preserving the computational efficiency of SA-CMC, a novel quadrature-based moment method (QBMM-CMC) is developed for CMC applications, which does not assume the form of the mixture-fraction PDF. Remarkably, by solving the closed forms for the micromixing terms from CMC, exact expressions result for the mixture-fraction moments of any order. Thus, QBMM-CMC covers cases where the mixture-fraction PDF cannot be well represented by a β-PDF and can be applied to disperse multiphase flows with mass transfer (e.g., droplet evaporation). For single-phase and multiphase pure-mixing problems, the QBMM-CMC mixture-fraction moments are observed to deviate from the β-PDF. For single-phase mixing with and without dispersed-phase mass transfer, QBMM-CMC predictions for mixing-sensitive competitive-consecutive and parallel reactions are investigated parametrically.

在（AD Ilgun，A. Passalacqua和RO Fox）中给出的条件矩闭合（SA-CMC）的基于正交的半解析解，“混合敏感反应的基于矩的条件矩闭合”，化学工程Sci。，226，2020）通过假设混合物分数PDF由β-PDF很好地表示，消除了CMC应用中的附加条件空间离散化。高斯求积提供了混合分数横坐标，条件标量均值用Jacobi多项式表示。在这里，通过保持SA-CMC的计算效率，针对CMC应用开发了一种新颖的基于矩量的矩量法（QBMM-CMC），该方法不采用混合分数PDF的形式。显着地，通过解决封闭形式对于CMC中的微混合项，可以得到任意阶数的混合分数矩的精确表达式。因此，QBMM-CMC涵盖了混合级数PDF不能很好地用β-PDF表示的情况，并且可以应用于通过质量传递来分散多相流（例如，液滴蒸发）。对于单相和多相纯混合问题，观察到QBMM-CMC混合分数矩偏离β-PDF。对于有或没有分散相传质的单相混合，将对混合敏感的竞争连续反应和平行反应的QBMM-CMC预测进行参数研究。