网络反应器上反应-平流-扩散系统输出组成的确定
Determination of output composition in reaction-advection-diffusion systems on network reactors
AI总结：
研究开放网络反应器中反应-输运过程的输出组成问题，提出基于时间无关偏微分方程边值问题的求解方法，并为网络状反应器推导出输出组成的显式公式。
摘要：
我们考虑开放反应器中的反应-输运过程，在该反应器中，涉及多种气体和固体催化剂的一阶反应系统可以在局部活性区域发生。反应产物从反应器流入真空条件，并在出口边界处被收集。输出组成问题（OCP）是确定反应器完全排空后所收集气体的组成（摩尔分数）。我们以一组时间无关偏微分方程的边值问题的形式提供了该问题的解。然后我们考虑网络状反应器，它可以近似为由一系列节点和一维分支组成的网络，反应在节点处发生。对于这些反应器，能够以简单有效的方式求解OCP，给出输出组成作为反应系数和与系统几何构型相关参数的函数的显式公式。给出了几个例子来说明该方法。
英文摘要：
We consider reaction-transport processes in open reactors in which systems of first order reactions involving a number of gas species and solid catalysts can occur at localized active regions. Reaction products flow out of the reactor into vacuum conditions and are collected at an exit boundary. The output composition problem (OCP) is to determine the composition (molar fractions) of the collected gas after the reactor is fully emptied. We provide a solution to this problem in the form of a boundary-value problem for a system of time-independent partial differential equations. We then consider network-like reactors, which can be approximated by a network consisting of a collection of nodes and 1-dimensional branches, with reactions taking place at nodes. For these, it is possible to solve the OCP in a simple and effective way, giving explicit formulas for the output composition as a function of the reaction coefficients and parameters associated with the geometric configuration of the system. Several examples are given to illustrate the method.
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