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9. Turbulent Flows
On solid walls, no slip boundary conditions, which have been described in
Chaps. 7 and 8 may be used. One must bear in mind that a t boundaries of
this type the turbulence tends to develop small but very important structures
('streaks') that require very fine grids especially in the direction normal the
wall and, to a lesser extent, in the spanwise direction (the direction normal
to both the wall and the principal flow direction).
Symmetry boundary conditions, which are often used in RANS computations to reduce the size of the domain are usually not applicable in DNS or
LES because, although the mean flow may be symmetric about some particular plane, the instantaneous flow is not and important physical effects may
be removed by application of conditions of this type. Symmetry conditions
have, however, been used to represent free surfaces.
Despite all attempts to make the initial and boundary conditions as realistic as possible, a simulation must be run for some time before the flow
develops all of the correct characteristics of the physical flow. This situation
derives from the physics of turbulent flows so there is little one can do to
speed up the process; one possibility is mentioned below. As we have noted,
the eddy turnover time scale is the key time scale of the problem. In many
flows, it can be related to a time scale characteristic of the flow as a whole
i.e. a mean flow time scale. However, in separated flows, there are regions
that communicate with the remainder of the flow on a very long time scale
and the development process can be very slow, making very long run times
necessary.
The best way to ascertain that flow development is complete is to monitor
some quantity, preferably one that is sensitive to the parts of the flow that
are slow to develop; the choice depends on the flow being simulated. As an
example, one might measure a spatial average of the skin friction in the
recirculating region of a separated flow as a function of time. Initially, there
is usually a systematic increase or decrease of the monitored quantity; when
the flow becomes fully developed, the value will show statistical fluctuations
with time. After this point, statistical average results (for example, for the
mean velocity or its fluctuations) may be obtained by averaging over time
and/or a statistically homogeneous coordinate in the flow. In so doing it is
important to remember that, because turbulence is not purely random, the
sample size is not the same as the number of points used in the averaging
process. A conservative estimate is to assume that each volume of diameter
equal to the integral scale (and each time period equal to the integral time
scale) represents only a single sample.
The development process can be sped up by using a coarse grid initially.
When the flow is developed on that grid, the fine grid can be introduced. If
this is done, some waiting is still necessary for the flow to develop on the fine
grid but it may be smaller than the time that would have been required had
the fine grid been used throughout the simulation.
9. Turbulent Flows
On solid walls, no slip boundary conditions, which have been described in
Chaps. 7 and 8 may be used. One must bear in mind that a t boundaries of
this type the turbulence tends to develop small but very important structures
('streaks') that require very fine grids especially in the direction normal the
wall and, to a lesser extent, in the spanwise direction (the direction normal
to both the wall and the principal flow direction).
Symmetry boundary conditions, which are often used in RANS computations to reduce the size of the domain are usually not applicable in DNS or
LES because, although the mean flow may be symmetric about some particular plane, the instantaneous flow is not and important physical effects may
be removed by application of conditions of this type. Symmetry conditions
have, however, been used to represent free surfaces.
Despite all attempts to make the initial and boundary conditions as realistic as possible, a simulation must be run for some time before the flow
develops all of the correct characteristics of the physical flow. This situation
derives from the physics of turbulent flows so there is little one can do to
speed up the process; one possibility is mentioned below. As we have noted,
the eddy turnover time scale is the key time scale of the problem. In many
flows, it can be related to a time scale characteristic of the flow as a whole
i.e. a mean flow time scale. However, in separated flows, there are regions
that communicate with the remainder of the flow on a very long time scale
and the development process can be very slow, making very long run times
necessary.
The best way to ascertain that flow development is complete is to monitor
some quantity, preferably one that is sensitive to the parts of the flow that
are slow to develop; the choice depends on the flow being simulated. As an
example, one might measure a spatial average of the skin friction in the
recirculating region of a separated flow as a function of time. Initially, there
is usually a systematic increase or decrease of the monitored quantity; when
the flow becomes fully developed, the value will show statistical fluctuations
with time. After this point, statistical average results (for example, for the
mean velocity or its fluctuations) may be obtained by averaging over time
and/or a statistically homogeneous coordinate in the flow. In so doing it is
important to remember that, because turbulence is not purely random, the
sample size is not the same as the number of points used in the averaging
process. A conservative estimate is to assume that each volume of diameter
equal to the integral scale (and each time period equal to the integral time
scale) represents only a single sample.
The development process can be sped up by using a coarse grid initially.
When the flow is developed on that grid, the fine grid can be introduced. If
this is done, some waiting is still necessary for the flow to develop on the fine
grid but it may be smaller than the time that would have been required had
the fine grid been used throughout the simulation.