The purpose of this chapter is to explain the input needed to solve CFD problems, e.g. CAD geometry, computational mesh, material properties, boundary conditions etc. The difficulty and accuracy of CFD simulations for various applications, such as laminar and turbulent flows, single-phase and multiphase flows and reactive systems are discussed briefly.

Modelling in engineering

Traditional modelling in engineering is heavily based on empirical or semi-empirical models. These models often work very well for well-known unit operations, but are not reliable for new process conditions. The development of new equipment and processes is dependent on the experience of experts, and scaling up from laboratory to full scale is very time-consuming and difficult. New design equations and new parameters in existing models must be determined when changing the equipment or the process conditions outside the validated experimental database. A new trend is that engineers are increasingly using computational fluid dynamics (CFD) to analyse flow and performance in the design of new equipment and processes. CFD allows a detailed analysis of the flow combined with mass and heat transfer. Modern CFD tools can also simulate transport of chemical species, chemical reactions, combustion, evaporation, condensation and crystallization.

Computational fluid dynamics (CFD) has become an indispensable tool for engineers. CFD simulations provide insight into the details of how products and processes work, and allow new products to be evaluated in the computer, even before prototypes have been built. It is also successfully used for problem shooting and optimization. The turnover time for a CFD analysis is continuously being reduced since computers are becoming ever more powerful and software uses ever more efficient algorithms. Low cost, satisfactory accuracy and short lead times allow CFD to compete with building physical prototypes, i.e. ‘virtual prototyping’.

There are many commercial programs available, which have become easy to use, and with many default settings, so that even an inexperienced user can obtain reliable results for simple problems. However, most applications require a deeper understanding of fluid dynamics, numerics and modelling. Since no models are universal, CFD engineers have to determine which models are most appropriate to the particular case. Furthermore, this deeper knowledge is required since it gives the skilled engineer the capability to judge the potential lack of accuracy in a CFD analysis. This is important since the analysis results are often used to make decisions about what prototypes and processes to build.

The purpose of this chapter is to give an introduction to problems faced by engineers wanting to use CFD for detailed modelling of turbulent reactive flows. After reading this chapter you should be able to describe the physical process of turbulent mixing and know why this can have an effect on the outcome of chemical reactions, e.g. combustion. The problem arises when the grid and time resolution is not sufficient to resolve the concentration and the average concentration in the cells is a poor estimation of the actual concentration as shown in Figure 5.1. The local concentration changes fast, and we need models that can predict the space- and time-average reaction rate in each computational cell.

The average concentration in a computational cell can be used to describe macromixing (large-scale mixing) in the reactor and is relatively straightforward to model. The concentration fluctuations, on the other hand, can be used to describe micromixing (small-scale mixing on the molecular level). To quantify micromixing, the variance of the concentration fluctuations is used. Chemical reactions can take place only at the smallest scales of the flow, after micromixing has occurred, because reactions occur only as molecules meet and interact. An expression for the instantaneous rate of chemical reactions is often known for homogeneous mixtures. However, the average rate of chemical reactions in a reactor subject to mixing will depend also on the rate of micromixing.

Computational fluid dynamics does not provide an exact solution to all problems, but is in many cases a reliable tool that can provide useful results when it is employed by an experienced user. An inexperienced user, on the other hand, may obtain very nice graphs that are very far from being a prediction of the stated problem. Some of the problems arise from the many default settings in commercial CFD codes, since the user may obtain results without knowing what the code is doing by accepting settings that are not appropriate for the specific problem. The user must make an active decision regarding each setting due to the fact that many problems can arise from a user failing to understand what the proper settings should be. This chapter provides some guidelines that can help a new user to avoid the most common mistakes. Many more recomendations selected by experienced CFD users can be found in the ‘Best Practice Guidelines’ for single-phase flows [20] and for dispersed multiphase flows [21] by the European Research Community on Flow Turbulence and Combustion (ERCOFTAC).

A CFD simulation contains both errors and uncertainties. An error is defined as a recognizable deficiency that is not due to a lack of knowledge, whereas an uncertainty is a potential deficiency that is due to a lack of knowledge.

Polymers are remarkable molecules with a particularly rich behavior and a wealth of interesting properties. Statistical mechanical arguments may be used to understand these properties. In this chapter, we present an elementary theory of polymer configurations and polymer dynamics. We also offer a brief exposition of the theory of Brownian dynamics. This is a powerful theoretical formalism for studying the motion of molecules in a solution.

Polymers

The study of conformations and conformational motions of flexible polymer chains in solution is of great scientific and technological importance. Understanding the physics of macromolecules at the molecular level helps the synthesis and design of commercial products. It also provides insight into the structure and functions of biological systems. Flexible polymers have therefore been the subject of extensive theoretical treatments, a wide variety of experiments, and computer simulations (see Further reading at the end of the chapter).

Historically, theoretical treatments have resorted to simple phenomenological models of polymeric materials. In the framework of statistical mechanics, polymeric chains are at a first stage considered to consist of independent elements or segments. The principal property of macromolecular behavior taken into account with this representation is the flexibility of the chains. With non-interacting monomeric units having uncorrelated directions, it is straightforward to show that the chains acquire random-walk behavior.