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.

In 1808 Thomas Young introduced his Croonian lecture to the Royal Society on the function of the heart and arteries with the words:

For Young this was a natural approach to physiology; like many other scientists in the nineteenth century, he paid scant attention to the distinction between biological and physical science. Indeed, during his lifetime he was both a practising physician and a professor of physics; and, although he is remembered today mainly for his work on the wave theory of light and because the elastic modulus of materials is named after him, he also wrote authoritatively about optic mechanisms, colour vision, and the blood circulation, including wave propagation in arteries.

This polymath tradition seems to have been particularly strong among the early students of the circulation, as names like Borelli, Hales, Bernoulli, Euler, Poiseuille, Helmholtz, Fick, and Frank testify; but, as science developed, so did specialization and the study of the cardiovascular system became separated from physical science.

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.

This chapter deals with the mechanisms of flow in the larger systemic arteries. The pulmonary arteries are specifically excluded, because they have special properties and are dealt with separately; thus, we are concerned here with the aorta and its branches, which supply oxygenated blood to the organs of the body. As in other parts of the book, we take the vascular system of the dog as our primary example because it has been so widely studied experimentally; but we will refer to the situation in the human wherever specific differences of function or structure appear important. Again, we do not deal with active physiological processes, such as reflexes or mechanisms of vasoconstriction which may alter the flow or distribution of blood, but concentrate upon the physical properties of the system which are changed when such processes act.

This book deals with the arterial part of the systemic circulation in two parts: the arteries in this chapter and the microcirculation in Chapter 13. First, therefore, we must describe how and why this subdivision is made, and then we shall provide a brief description of the anatomy and structure of systemic arteries, and of pressures and flows which occur within them. Thereafter we shall introduce the fundamental mechanics which govern events and then successively add the complicating or modifying features which bring us nearer to a complete description of the pressure and flow in the arteries; in doing this, we shall repeatedly refer to the mechanics described earlier in the book.

We saw in Chapter 1 how real materials, in particular fluids, can be regarded as continuous if the distances over which their gross properties (like density) change is much larger than the molecular spacing. They can then be split up into small elements, to each of which the laws of particle mechanics can be applied. We have also set down those laws. Before applying them, however, we must know what forces act on such an element. As with the body sliding along the table (Fig. 2.7), the forces experienced by a representative fluid element are of two kinds: long-range and short-range.

The forces which act at long range, the body forces, are experienced by all fluid elements; the two most common examples are gravitational and electromagnetic in origin. The electromagnetic force on an element depends on quantities like its electrical charge, but the gravitational force, i.e. the weight of the element, depends only on its mass; this is the only example of body force to be considered from now on. If a fluid element P which occupies the point x at a certain time t has volume V and if the fluid in the neighbourhood of x at that time has density ρ, then the gravitational force on the element is ρVg.

Stress

Short-range forces are exerted on the element P by those other elements with which it is in contact, and by no other. They consist of all the intermolecular forces exerted by molecules just outside the surface of P on the molecules just inside.

The pulmonary circulation conveys the entire output of the right ventricle via the pulmonary arteries to the alveolar capillaries and returns the blood, via the pulmonary veins, to the left atrium. The lung has a second, though far smaller, circulation, the bronchial circulation. This arises from the thoracic aorta, supplies systemic arterial blood to the lung, has some interconnections (anastomoses) with the pulmonary microcirculation and drains into the systemic venous system.

The pulmonary circulation differs from the systemic circulation in several important respects. For example, it is a low-pressure, low-resistance system; the time-average excess pressure in the pulmonary arteries is only about 2 × 103 Nm−2 (15mm Hg or 20cm H2O), or approximately one-sixth of that in the systemic arteries, while the total blood flow rate through the lungs is the same as that through the systemic circulation. Further differences are that the pulmonary arteries have much thinner walls than the systemic arteries, and the pulmonary vascular bed is apparently not regionally specialized. In addition, vasomotor control in the pulmonary vessels is believed to be relatively unimportant under normal conditions; unlike the systemic arteries and veins, the vessels do not undergo large active changes in their dimensions.

The main function of the lungs is the exchange of oxygen and carbon dioxide between the air and the blood. However, any gas for which there is a difference in partial pressure between pulmonary capillary blood and alveolar gas will diffuse across the alveolar capillary membrane.