This thesis represents a part of a wider research project concerning microprocess tech-nology and was carried out in the Laboratory of Process and Product Development. The
14 1. Introduction
author developed and applied mathematical models needed in this work. The publica-tions [54, 51, 16] are results of this collaboration.
In the mass transfer study of the microplate reactor, experiments were designed and the data collected by other group members. The author was in charge of parameter estimation of the interface mass transfer model. Experimental data for the hydrodynamic study were also designed and collected by collaborators. The author contributed the design of the structure of the new microplate.
Kinetic modeling and parameter estimation in the kinetic study were carried out by other collaborators. The author was solely responsible for modeling and simulating the mentioned subcases of micromixer performance and heat transfer in the tube. No exper-imental measurements were conducted in these cases.
The packed-bed column study was conducted entirely by the author himself.
The thesis introduces two key points. One is the methodology of reducing the dimension of the problem from three dimensions to two dimensions while maintaining the same level of accuracy as in a 3D model. This is presented in section 3.1.3. Another novel feature is the methodology to generate a complex geometry of the packed-bed column with the help of auxiliary rigid body dynamic simulation described in Chapter 5.
Chapter II
Modeling aspects
2.1 Modeling approaches
The modeling of physical phenomena always involves the question of what level of details a model should provide. There are always several modeling approaches for every case, each with a different level of details. Simple models based on averaged estimated values and/or partially computed analytic solutions for some ideal cases can give a quick and rough answer, but can not give detailed information. Comprehensive models give many small details, but require much more computational resources than the simple ones.
Therefore, the question of the level of details can be transformed into a question of what computational resources are available. Until recently, computational resources have been very limited and most of the calculations have had to be done using very simple models.
That is why comprehensive models such as CFD have been rarely used. Currently, however, very powerful computers and even more powerful supercomputers are available to the majority of researchers. Consequently, it is clear why the most comprehensive models becoming more and more popular, although simpler models are still handy when quick parameter estimation is needed.
Once the decision about the model has been made, one should decide how to solve the task. As mentioned above, comprehensive models require a great deal of extra work to formulate the task appropriately for numerical solution by computer. Basically, for-mulating a task for a computer means programming it using a programming language.
However, the programming itself could be a non-trivial task, especially when implement-ing numerous complex methods, which is often the case of CFD models. There are two ways to handle this programming: to do it by yourself or adopt the code of somebody else. Writing your own code, if done properly, usually results in a faster and more robust program, because off-site programs will not necessarily be optimized for each particular case. Programming overheads, i.e. the time required purely to write and debug the code, when implementing a complex model in some computer language could be very high.
A large number of smaller sub-steps should be taken to obtain a numerical solution for a modern CFD model. Geometry which represents a computational domain for the solution
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16 2. Modeling aspects
of PDEs should be specified. This already might be a non-trivial task if the real geometry is complex. Then the geometrical domain should be efficiently divided into large numbers (hundred of thousands or even tens of millions) of small volumes. Laws of physics should be appropriately formulated. Then, taking into account the connectivity between the volumes and approximation methods, the laws of physics should be discretized to obtain a set of unknown values (one or more for each elementary volume) which represents discretized version of flow variables, such as velocity, pressure, concentration, etc. A corresponding number of preferably linear equations should also be obtained. These equations then need to be efficiently solved, which might be a non-trivial task even if they are linear, because of their number.
These sub-steps and even larger number of smaller sub-sub-steps might take a great deal of time when implemented from the very beginning. It might take even longer than running the final code. Consequently, a second question arises: whether to develop the model from scratch or to adopt somebody else’s code. With ever-growing interest in numerical models, more and more new codes are developed. They cover an increasing amount of specific areas. Because of this, at some point in the future the question above might become irrelevant, because there will be written codes which implement every known model and combine all the necessary steps to obtain a numerical solution.
For the available code there are also two options: commercial or open-source code. In case of CFD there are many packages to meet almost any of the common researcher’s needs.
Commercial ANSYSCFXR TM[2], ANSYSFLUENTR TM[3] and similar packages, which are designed for engineers, still can be used for research when the model is just a tool, not the subject. For example, they can be used to study complex flow phenomena when the experiments are not affordable or can not give sufficiently comprehensive results.
When the model is the subject of research, such engineering software is not appropriate.
Although CFX and FLUENT have some built-in tools to setup up one’s own models, there exist packages which are more appropriate for modeling. OpenFOAM, a free, open-source package, is one of them. With the current level of maturity, OpenFOAM is becoming a de-facto standard in research and even engineering. Originally, OpenFOAM is just a set of libraries, containing routines and utilities to define, discretise and solve partial differential equations by a finite volume method. Such equations can arise from fluid dynamics, magnetodynamics, market dynamics, etc. OpenFOAM also includes the community-made solvers on top of mentioned libraries. This allows using it for a widening area of real-life engineering applications, yet having full flexibility to study and modify the models without too much effort.