微观混和问题的研究——(Ⅵ)不同混和阶段的化学反应的描述

STUDIES ON MICROMIXING (Ⅵ) DESCRIPTION OF CHEMICAL REACTIONS IN THE DIFFEENT MIXING REGIONS

根据作者对混和区域的划分,进一步完整地给出了各区域中混和与化学反应过程的描述,这些描述均归结成一系列包含反应项的扩散方程或对流扩散方程的初值问题。对于简单瞬时反应,文中给出了精确解,据此可以估计各区域中化学反应的最大转化率以及反应区的位置和大小。对于竞争串联反应,当主反应为瞬时反应时,经过适当的变换,结合有关的解析解,可将无限区域上多个强非线性方程的初值问题化为有限区域上一个弱非线性方程的初、边值问题。

According to the time scales given in our series paper(Ⅳ), an infinite urbulent mixing field can be divided into three successive regions: dispersion controlling, micromixing controlling and macromixing controlling. In this paper, mixing and chemical reactions in all the three regions were described by several initial problems of nonlinear partial differential equations based on the formulation outlined in paper (Ⅲ) and (Ⅳ). For a simple instantaneous reaction, exact solutions of the equations were obtained. Thus maximum conversion in each of the regions, and the size and location of the reaction zone can be estimated. It was shown that the conversion of instantaneous reaction in the dispersion region depends strongly on the initial concentration ratio C_(AE) rather than the Schmidt number Sc, and is usually less than 5％ in case of C_(AE)<0. 1, while the size of reaction zone depends on C_(AE) and the dimensionless number Li. Under certain conditions (low C_(AE) and small Li), the reaction zone will extend from micromixing region to acromixing region. For the competitive-con- secutive reactions, if the first reaction can be regarded to be instantaneous, the description can be greatly simplified to one weak-nonlinear equation with finite domain through certain transformations and by making use of the analytical solutions.