Exploring tubular steady‐state laminar flow reactors with orthogonal collocation
André Von‐Held Soares, Lizandro de Sousa Santos, Housam Binous, Abdullah A. Shaikh, Ahmed Bellagi
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Abstract
The laminar flow reactor (LFR) is one of the most comprehensive problems in chemical reaction engineering, as its modeling involves mass, heat, and momentum conservation equations coupled with chemical reaction rate equations. It is relatively easy to grasp its basic operation, but the solution of the problem is far from trivial. Although there are analytical solutions that simplify the problem, students and tutors must use efficient numerical strategies to appropriately solve some LFR problems. In the present investigation, we solve several different cases of two‐dimensional cylindrical LFR, beginning with the isothermal case, as a benchmark. Calculations were performed using the Chebyshev orthogonal collocation technique by custom scripts in Scilab, Mathematica© , and Matlab®, and were compared with solutions available from the ECRE Version of COMSOL®, which was used as the reference, as well as available analytical solutions in the literature. After analyzing the case of the isothermal LFR with Newtonian fluid, we explored non‐Newtonian fluids, including Carreau and Bingham fluids, whose LFR results are not available in the preceding literature. For Newtonian fluids, besides (a) the isothermal case, we also explore other three nonisothermal design cases: (b) cooling jacket with a fixed heat exchange coefficient at the wall, (c) adiabatic operation, (d) nonisothermal LFR with isothermal wall. Through a performance criterion, the different operation models are compared and we show that nonisothermal design cases perform better than the isothermal case. Computation times, for different scenarios, are quite short and taking 25 nodal points or more suffice for an accurate and timely solution of the more complex problem Case (b). The numerical modeling approach is useful from a pedagogical standpoint, as one can compare numerical results with classical assumptions, and progress from a more restrictive conceptual model (segregated flow) to an array of different kinds of operation with the LFR in which one needs to consider diffusion and temperature distribution.
利用正交配置探索管式稳态层流反应器
层流反应器(LFR)是化学反应工程中最复杂的问题之一,因为其建模涉及质量、热量和动量守恒方程以及化学反应速率方程。要掌握其基本操作相对容易,但问题的解决却绝非易事。虽然有简化问题的解析解,但学生和导师必须使用高效的数值策略才能恰当地解决一些 LFR 问题。在本研究中,我们首先以等温情况为基准,求解了二维圆柱形 LFR 的几种不同情况。计算是通过 Scilab、Mathematica© 和 Matlab® 中的自定义脚本使用切比雪夫正交配位技术进行的,并与作为参考的 COMSOL® ECRE 版本提供的解决方案以及文献中提供的分析解决方案进行了比较。在分析了牛顿流体的等温低温流体阻力分析之后,我们又研究了非牛顿流体,包括 Carreau 和 Bingham 流体,这些流体的低温流体阻力分析结果在之前的文献中没有出现过。对于牛顿流体,除了 (a) 等温情况外,我们还探讨了其他三种非等温设计情况:(b) 壁面热交换系数固定的冷却套,(c) 绝热运行,(d) 壁面等温的非等温低温循环流化床。通过性能标准,我们对不同的运行模式进行了比较,结果表明,非等温设计方案的性能优于等温方案。不同情况下的计算时间都很短,25 个节点或更多节点足以准确及时地解决更复杂的问题(b)。从教学角度来看,数值建模方法非常有用,因为人们可以将数值结果与传统假设进行比较,并从限制性较强的概念模型(隔离流)发展到一系列需要考虑扩散和温度分布的低温冷凝器的不同运行方式。
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