Provides a clear, concise, and self-contained introduction to Computational Fluid Dynamics (CFD)
This comprehensively updated new edition covers the fundamental concepts and main methods of modern Computational Fluid Dynamics (CFD). With expert guidance and a wealth of useful techniques, the book offers a clear, concise, and accessible account of the essentials needed to perform and interpret a CFD analysis.
The new edition adds a plethora of new information on such topics as the techniques of interpolation, finite volume discretization on unstructured grids, projection methods, and RANS turbulence modeling. The book has been thoroughly edited to improve clarity and to reflect the recent changes in the practice of CFD. It also features a large number of new end-of-chapter problems.
All the attractive features that have contributed to the success of the first edition are retained by this version. The book remains an indispensable guide, which:
Introduces CFD to students and working professionals in the areas of practical applications, such as mechanical, civil, chemical, biomedical, or environmental engineering
Focuses on the needs of someone who wants to apply existing CFD software and understand how it works, rather than develop new codes
Covers all the essential topics, from the basics of discretization to turbulence modeling and uncertainty analysis
Discusses complex issues using simple worked examples and reinforces learning with problems
Is accompanied by a website hosting lecture presentations and a solution manual
Essential Computational Fluid Dynamics, Second Edition is an ideal textbook for senior undergraduate and graduate students taking their first course on CFD. It is also a useful reference for engineers and scientists working with CFD applications.
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CFD (Computational Fluid Dynamics) is a set of numerical methods applied to obtain approximate solutions of problems of fluid dynamics and heat transfer.
According to this definition, CFD is not a science on its own but a way to apply the methods of one discipline (numerical analysis) to another (heat and mass transfer). We will deal with details later. Right now, a brief discussion is in order of why exactly we need CFD.
A distinctive feature of the science of fluid flow and heat and mass transfer is the approach it takes toward description of physical processes. Instead of bulk properties, such as momentum or angular momentum of a body in mechanics or total energy or entropy of a system in thermodynamics, the analysis focuses on distributed properties. We try to determine the entire fields such as temperature
, velocity
, density
, etc.1 Even when an integral characteristic, such as the friction coefficient or the net rate of heat transfer, is the ultimate goal of the analysis, it is derived from distributed fields.
The approach is very attractive by virtue of the level of details it provides. Evolution of the entire temperature distribution within a body can be determined. The effect of internal processes of a fluid flow such as motion, rotation, and deformation of minuscule fluid particles can be taken into account. Of course, the opportunities come at a price, most notably in the form of dramatically increased complexity of the governing equations. Except for a few strongly simplified models, the equations for distributed properties are partial differential equations, often nonlinear.
As an example of complexity, let us consider a seemingly simple task of mixing and dissolving sugar in a cup of hot coffee. An innocent question of how long would it take to completely dissolve the sugar leads to a very complex physical problem that includes a possibly turbulent twoâphase (coffee and sugar particles) flow with variable physical properties and a chemical reaction (dissolving). Heat transfer (within the cup and between the cup and surroundings) is also of importance because temperature strongly affects the rate of the reaction. No simple solution of the problem exists. Of course, we can rely on the experience acquired after repeating the process daily (perhaps more than once) for many years. We can also add a couple of extra, possibly unnecessary, stirs. If, however, the task in question is more serious â for example, optimizing an oil refinery or designing a new aircraft â relying on everyday experience or excessive effort is not an option. We must find a way to understand and predict the process.
Generally, we can distinguish between three approaches to solving fluid flow and heat transfer problems:
Theoretical approach: Finding analytical solutions of governing equations or arriving to conclusions on the basis of some theoretical considerations.
Experimental approach: Staging an experiment using a model of the real object.
Numerical approach: Using computational procedures to find a solution of the governing equations.
Let us look at these approaches in more detail.
Theoretical Approach. The approach has a crucial advantage of providing exact solutions. Among the disadvantages, the most important is that analytical solutions are only possible for a very limited class of problems, typically formulated in an artificial, idealized way. One example is the HagenâPoiseuille solution for a flow in an infinitely long pipe (see Figure 1.1). The steadyâstate laminar velocity profile is
where
is the velocity,
is the pipe radius,
is the constant pressure gradient that drives the flow, and
is the dynamic viscosity of the fluid. The solution is, indeed, simple and gives insight into the nature of flows in pipes and ducts, so its inclusion into all textbooks of fluid dynamics is not surprising. At the same time, the solution is correct only if the pipe is infinitely long,2 temperature is constant, and the fluid is perfectly incompressible. Furthermore, even if we were able to build such a pipe and find some use for it, the solution would be correct only at Reynolds numbers
(
is the density of the fluid) below, approximately, 1200. Above this limit, the flow would take fully threeâdimensional and timeâdependent transitional or turbulent form, for which no analytical solution is possible.
Figure 1.1 Laminar flow in an infinite pipe.
It can also be noted that derivation of analytical solutions often requires substantial mathematical skills, which are not among the strongest traits of many modern engineers and scientists, especially if compared to the situation of 30 or 40 years ago. Several reasons can be named for the deterioration of such skills, one, no doubts, being development of computers and numerical methods, including the CFD.
Experimental approach: Wellâknown examples are the wind tunnel experiments, which help to design and optimize the external shapes of airplanes (also of ships, cars, buildings, and other objects). Another example is illustrated in Figure 1.2. The main disadvantages of the experimental approach are the technical difficulty (sometimes it takes several years before an experiment is set up and all technical problems are resolved) and high cost.
Figure 1.2 The experiment for studying thermal convection at the Ilmenau University of Technology, Germany. Turbulent convection similar to the convection observed in the atmosphere of Earth or Sun is simulated by air motion within a large barrel with thermally insulated walls and uniformly heated bottom.
Numerical (computational) approach: Here, again, we employ our ability to describe almost any fluid flow or heat transfer process as a solution of a set of partial differential equations. An approximation to this solution is found by a computer executing an algorithm. This approach is not problemâfree either. We will discuss the problems throughout the book. The computational approach, however, beats the analytical and experimental methods in some very imp...
