9. Turbulent Flows
9.1 Introduction
Most flows encountered in engineering practice are turbulent and therefore
require different treatment. Turbulent flows are characterized by the following
properties:
Turbulent flows are highly unsteady. A plot of the velocity as a function
of time at most points in the flow would appear random to an observer
unfamiliar with these flows. The word 'chaotic' could be used but it has
been given another definition in recent years.
They are three-dimensional. The time-averaged velocity may be a function
of only two coordinates, but the instantaneous field fluctuates rapidly in
all three spatial dimensions.
They contain a great deal of vorticity. Indeed, vortex stretching is one of
the principal mechanisms by which the intensity of turbulence is increased.
Turbulence increases the rate at which conserved quantities are stirred.
Stirring is a process in which parcels of fluid with differing concentrations
of a t least one of the conserved properties are brought into contact. The
actual mixing is accomplished by diffusion. Nonetheless, this process is
often called turbulent diffusion.
By means of the processes just mentioned, turbulence brings fluids of differing momentum content into contact. The reduction of the velocity gradients due to the action of viscosity reduces the kinetic energy of the flow; in
other words, mixing is a dissipative process. The lost energy is irreversibly
converted into internal energy of the fluid.
It has been shown in recent years that turbulent flows contain coherent
structures-repeatable and essentially deterministic events that are responsible for a large part of the mixing. However, the random component of turbulent flows causes these events to differ from each other in size, strength,
and time interval between occurrences, making study of them very difficult.
Turbulent flows fluctuate on a broad range of length and time scales. This
property makes direct numerical simulation of turbulent flows very difficult.
(See below.)
All of these properties are important. The effects produced by turbulence
may or may not be desirable, depending on the application. Intense mixing
9.1 Introduction
Most flows encountered in engineering practice are turbulent and therefore
require different treatment. Turbulent flows are characterized by the following
properties:
Turbulent flows are highly unsteady. A plot of the velocity as a function
of time at most points in the flow would appear random to an observer
unfamiliar with these flows. The word 'chaotic' could be used but it has
been given another definition in recent years.
They are three-dimensional. The time-averaged velocity may be a function
of only two coordinates, but the instantaneous field fluctuates rapidly in
all three spatial dimensions.
They contain a great deal of vorticity. Indeed, vortex stretching is one of
the principal mechanisms by which the intensity of turbulence is increased.
Turbulence increases the rate at which conserved quantities are stirred.
Stirring is a process in which parcels of fluid with differing concentrations
of a t least one of the conserved properties are brought into contact. The
actual mixing is accomplished by diffusion. Nonetheless, this process is
often called turbulent diffusion.
By means of the processes just mentioned, turbulence brings fluids of differing momentum content into contact. The reduction of the velocity gradients due to the action of viscosity reduces the kinetic energy of the flow; in
other words, mixing is a dissipative process. The lost energy is irreversibly
converted into internal energy of the fluid.
It has been shown in recent years that turbulent flows contain coherent
structures-repeatable and essentially deterministic events that are responsible for a large part of the mixing. However, the random component of turbulent flows causes these events to differ from each other in size, strength,
and time interval between occurrences, making study of them very difficult.
Turbulent flows fluctuate on a broad range of length and time scales. This
property makes direct numerical simulation of turbulent flows very difficult.
(See below.)
All of these properties are important. The effects produced by turbulence
may or may not be desirable, depending on the application. Intense mixing