“But never have I been a blue calm sea, I have always been a storm.”
Fleetwood Mac, Storms (1979).
The previous chapters provide some general principles for CFD, from the governing equations and common models, to numerical methods, boundary conditions, algorithms and solvers.
Since the book is about general principles, it does not generally cover complex physical modelling. The exception is turbulence which need to be addressed since it is so common in ﬂuid ﬂow and therefore a critical part of most CFD simulations.
Turbulence is illustrated by a plume of smoke below. The smoke rises vertically from the base, initially tracing a relatively straight, narrow path, characteristic of laminar ﬂow. At some point, there is an abrupt transition to turbulent ﬂow in which ﬂuid particles follow curved paths which cross one another in a disorderly, irregular manner, causing and to ﬂuctuate randomly in time.
Turbulent ﬂow evidently involves signiﬁcant mixing of the ﬂuid which is an important consideration in many CFD problems. For example, it directly aﬀects the rate of pollutant dispersion and the rate of reaction of a chemical process. It causes heat to diﬀuse more rapidly. Similarly, mixing aﬀects momentum diﬀusion and, consequently, the aerodynamic forces within a ﬂuid and surrounding vehicles, wind turbines, buildings, etc.
Turbulence is a vast subject with an abundance of textbooks for various levels of expertise. As an introduction to turbulence, this chapter aims to provide:
- a short description of the nature of turbulence;
- an understanding of its importance in analysis and particular challenges it presents in CFD;
- the basic concepts of turbulence modelling to lay the groundwork for the models presented in Chapter 7.
6.2 A picture of turbulence
6.3 Vorticity transport
6.4 Boundary layers
6.5 Boundary layer separation
6.6 Scales of turbulence
6.7 Energy cascade
6.8 The cost of simulating turbulence
6.9 Reynolds-averaged simulation
6.10 The nature of viscosity
6.11 Turbulent mixing
6.12 Mixing length
6.13 Turbulent kinetic energy
6.14 Turbulent dissipation rate
6.15 Summary of turbulence