Multi-Scale Modeling of the Dynamics of a Fibrous Reactor: Use of an Analytical Solution at the Micro-Scale to Avoid the Spatial Discretization of the Intra-Fiber Space
Multi-Scale Modeling of the Dynamics of a Fibrous Reactor: Use of an Analytical Solution at the Micro-Scale to Avoid the Spatial Discretization of the Intra-Fiber Space
复制标题
纤维反应器动力学的多尺度建模：使用微尺度的分析解决方案来避免纤维内空间的空间离散化
作者：
A. Dobri;T. Papathanasiou
在现实的异质系统中，以考虑宏观尺度（悬浮流体）和微观尺度（悬浮颗粒）中感兴趣的量的演变的方式对现实异质系统中的时间依赖性传输和反应进行直接建模，目前远远超出了现代超级计算的能力。这是可以理解的，因为即使是像这样的简单系统也很容易包含超过 107 个粒子，其长度和时间尺度与宏观尺度相差几个数量级。虽然通过对代表性模型系统应用直接数值求解可以获得很多好处，但当要对大型、现实系统的性能进行建模时，直接方法是不切实际的。在这项研究中，我们推导并分析了适用于纤维反应器的“混合”模型。该模型考虑了本体液体中的对流/扩散，以及纤维内的扩散和反应。我们方法的本质是，基于完善的理论，半解析地处理纤维内空间中的扩散和（一阶）反应。因此，纤维内传输和反应的问题被简化为一组易于求解的 n 0 ODE，其中 n 0 是在不求助于近似的情况下评估的贝塞尔展开式中的项数；该集合与宏观尺度的数值模型逐点耦合。当后者使用 N 个节点进行离散化时，系统的总体“混合”模型由 N ( 2 + n 0 ) 个 ODE 系统组成，这很容易在普通工作站上求解。提出并讨论了参数分析。
Direct modeling of time-dependent transport and reactions in realistic heterogeneous systems, in a manner that considers the evolution of the quantities of interest in both, the macro-scale (suspending fluid) and the micro-scale (suspended particles), is currently well beyond the capabilities of modern supercomputing. This is understandable, since even a simple system such as this can easily contain over 107 particles, whose length and time scales differ from those of the macro-scale by several orders of magnitude. While much can be gained by applying direct numerical solution to representative model systems, the direct approach is impractical when the performance of large, realistic systems is to be modeled. In this study we derive and analyze a “hybrid” model that is suitable for fibrous reactors. The model considers convection/diffusion in the bulk liquid, as well as intra-fiber diffusion and reaction. The essence of our approach is that diffusion and (first-order) reaction in the intra-fiber space are handled semi-analytically, based on well-established theory. As a result, the problem of intra-fiber transport and reaction is reduced to an easily solvable set of n 0 ODEs, where n 0 is the number of terms in the Bessel expansion evaluated without recourse to approximation; this set is coupled, point-wise, with a numerical model of the macro-scale. When the latter is discretized using N nodes, the total “hybrid” model for the system consists of a system of N ( 2 + n 0 ) ODEs, which is easily solvable on a modest workstation. Parametric analyses are presented and discussed.