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Understanding Transport Phenomena Concepts in Chemical Engineering with COMSOL Multiphysics®

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Understanding Transport Phenomena Concepts in Chemical Engineering with COMSOL Multiphysics® Understanding Transport Phenomena Concepts in Chemical Engineering with COMSOL Multiphysics® Erick S. Vasquez* Department of Chemical and Materials Engineering, University of Dayton, Dayton, OH, USA *Corresponding author: [email protected] ABSTRACT Transport Phenomena in Chemical Engineering 1. Introduction involves three key aspects: Momentum, Heat and Mass Transport. These areas are described by Momentum, heat, and mass transfer are the three core differential equations which are solved for a concepts involved in Transport Phenomena. In particular problem using independent or a set of Chemical Engineering, the fundamental concepts are combined equations (e.g., water flowing in a heated usually taught using the traditional BS&L textbook.1,2 pipe). At an undergraduate level class, the advanced Typically, at an undergraduate level in our institution, mathematics of partial differential equations, tensors this subject is divided into two courses and a and the specific applications of conservations laws complementary laboratory. The first course involves for a differential element are challenging concepts to 1-D and steady-state problems for the Navier-Stokes understand. Nonetheless, Transport phenomena equation and the equation of energy, and Fick’s 2nd represent the basis of Chemical Engineering law of Diffusion at steady state for Newtonian fluids. fundamentals. For example, fluid velocity The second course involves unsteady state problems distribution, temperature distribution, and fluxes which are also solved mathematically with changes in (momentum flux, heat flux, and Mass/Molar Fluxes) one dimension. For example, when using the error are core concepts in Chemical Engineering. function to predict heating of a semi-infinite slab. In Although analytical solutions exist for very the second course, additional emphasis is placed on simplified problems that are solved in class using interphase transport processes and turbulent flow. mathematics, the students are usually eager to Lastly, the Transport Phenomena Laboratory understand the effect of velocity change in more than involves measurements of flow, temperature, and one dimension and/or with respect to time. In this mass concentration using a variety of work, a unique approach is presented to develop an instrumentation. applied Transport Phenomena course that involves Recently, it has been shown that coupling computer simulations using COMSOL Multiphysics®. The simulations with theory lead to a better understanding specific models from the applications library used for of a topic.3,4 Due to the required use of PDEs and enhancing students learning are (a) shell and tube various assumptions needed to solve Transport heat exchanger and (b) flow past a cylinder. phenomena problems, COMSOL Multiphysics® is a Additionally, the Fluid Flow module, Heat Transfer potential tool that can enhance students’ learning of module, and Chemicals species Transport modules this topic. In fact, other researchers have already are used to understand laminar/turbulent flow in a focused on the implementation of COMSOL pipe. As an outcome, it is expected that a Multiphysics® to foster Transport Phenomena combination of analytical solutions and their understanding.5–8 representation in COMSOL Multiphysics® can be In this study, simple and easy-to-solve problems, utilized to enhance students’ learning. A survey has including models from the application library, were been developed to be used in the assessment of implemented at the end of the second Transport learning outcomes from this class. Phenomena course at an undergraduate level. During The ultimate goal is to develop a project-based a traditional lecture, analytical solutions of ODEs and course so that the students can obtain a practical PDEs are presented using a sequence of steps until a understanding of Transport Phenomena and connect problem is solved. Hence, the students found a the importance of computational tools in many connection between the steps shown in class and on Chemical Engineering processes. setting up a study with the software interface. Students’ surveys were used to assess the Keywords: Engineering Education, Transport understanding of transport phenomena after computer Phenomena, Student Creativity, Hands-on simulations, and a preliminary discussion of these learning. results along with the survey questions is discussed. Excerpt from the Proceedings of the 2017 COMSOL Conference in Boston COMSOL Multiphysics® is a powerful tool for Continuity Equation solving a multitude of research projects; here, it is 휌∇. (퐮) = 0 (1) shown that it can also be used to motivate students to understand the concepts of Momentum, Heat, and Navier-Stokes Equation Mass Transport at an undergraduate level. Also, it 휌(퐮. ∇)퐮 = ∇.[p퐈+휇(∇퐮+ (∇퐮)푇] + F (2) gives a first-hand experience to computational tools that complement the lectures and the laboratory experiments. Fourier’s law of Heat Conduction 퐪 = −푘∇퐓 (3) 2. Methods and Examples using COMSOL Multiphysics® Energy Equation 휕퐓 휌퐶 + 휌퐶 퐮.∇퐓+∇.퐪=Q+Q (4) 푝 휕푡 푝 ted COMSOL Multiphysics® v.5.2 was used for all the class examples. The students had complete access to Fick’s Laws the software and performed the simulations with 퐍 = −퐷 ∇푐 (5) guidance from the instructor simultaneously. The 풊 푖 푖 following examples were implemented during class 휕c 푖 + ∇. (−퐷 ∇푐 ) = 푅 (6) sessions [Note: * indicates a problem found in the 휕푡 푖 푖 푖 application library]: A. Flow in a pipe 4. Simulation Results and Major Transport B. Flow Between Parallel Plates Concepts Illustrated in Class. C. Heat Conduction through a plane D. Flow Past a Cylinder* 4.1 Flow in a pipe E. Transient Diffusion or Tubular Reactor*. Laminar flow was illustrated using flow in a pipe For Examples A-C, the students learned the selection (Fig. 1). For this example, a Newtonian fluid was of space dimension, setup boundary conditions, selected at a constant temperature. The primary goal steady vs. non-steady steady solutions, draw of this example consisted of identifying the velocity geometries, and define mesh types. This connection profile, the maximum velocity at the center of the also helped the students to identify the steps followed pipe, and the symmetry of the solution based on in-class for simplified problems. defining an average velocity at the entrance of the A project-type assignment was given to the students pipe. The same examples was solved in class based on the shell and tube heat exchanger* analytically. However, using simulations, students simulation at the end of the course. The assignment were able to see the importance of assumptions and consisted of changing one variable of their choice the effects on the results from a 3-D point of view. and compare it with the results provided originally. This assignment was left to connect concepts that are taught in following courses: Fluid Flow and Heat Transfer and the Chemical Engineering Unit Operations Laboratory. 3. Governing Equations and Numerical Model Stationary and Time-Dependent studies were implemented in the class. Laminar flow and Turbulent flow (k-ϵ) were used to demonstrate the Figure 1. A) Top view of a pipe with a maximum velocity different velocity profiles obtained in fluid flow. Heat of 2 m/s and B) isometric view of the velocity profile. transport was illustrated only using conduction through a wall. For Diffusion studies, transport of 4.2 Flow between parallel plates diluted species was utilized. Materials were selected A second concept illustrated with COMSOL from the applications library and are specified for Multiphysics® involves pressure drop between each example in the next sections. The primary parallel plates (Fig. 2). In this example, students equations used for each problem are the following: defined different boundary conditions such as inlet and outlet pressure and determine the velocity profile at different sections of the system. Overall, the Excerpt from the Proceedings of the 2017 COMSOL Conference in Boston students gained a better understanding of the After illustrating basic concepts and how to use relationship between pressure drop and fluid flow, COMSOL Multiphysics® in the classroom, the which is typically covered by the Hagen-Poiseuille students were introduced to transient/unsteady state equation for flow in a pipe. This example also studies using two examples. illustrated fluid flow transitions between laminar and turbulent velocity profiles based on the gap between 4.4 Flow past a cylinder the plates and the inlet pressure. The concepts of streamlines, boundary layers, eddies, and turbulent flow were explained using an example from the application library: Flow past a cylinder. The students demonstrated understanding on this topic after running the simulations (Fig.4). Moreover, the students also changed the size or the position of the cylinder to obtain a better idea of the effects of disturbances in fluid flow. While these topics enhanced students understanding, the most interesting outcome from this simulation was the generation of small video that showed the fluid flow Figure 2. A) Velocity magnitude for flow between parallel as a function of time. This example fulfilled the plates and B) Turbulent velocity profile (inset) and pressure expectations of students on getting a better drop illustration. understanding of transient fluid flow from a simulation point of view. Without experiments to confirm transitional regimes—laminar to turbulent 4.3 Heat conduction through a plane flow—simulations are an excellent alternative for
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