Home  Blog How to Set the “Reference Density” for Buoyancy-Driven Flows
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How to Set the “Reference Density” for Buoyancy-Driven Flows |
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Buoyancy-driven flows are those
in which density variations cause the fluid motion. Examples
include low-pressure mixing of gases and natural convection heat
transfer. In CFD-ACE+, you must activate Gravity on the MO/Shared
tab if you want to capture buoyancy effects. Gravity is Off
by default because hydrostatic pressure variations do not contribute to
fluid motion in steady flows, and because the effect of hydrostatic
pressure variation on fluid density is usually small (non-existent for
incompressible fluids).
Once you’ve activated it, an additional input option appears, asking
you to choose how the “Reference Density” is to be
calculated. This tip explains what reference density means
and what you need to know to choose the right option.
The acceleration due to gravity of a fluid in any given control volume
is –ρg. In CFD-ACE+,
ρ = ρ0 + ρ',
where ρ0
is the
reference
density, and the gravitational body force is
implemented as -ρ'g. Omitting the ρ0g
term in
the
momentum equation produces a pressure field p*, as follows:
p*
= p - ρ0gy
In other words, the hydrostatic pressure variation is omitted.
This formulation is useful because it simplifies the specification of
pressure boundary conditions.
Consider buoyant flow along a heated wall, as shown below in Figure
1. The pressure along the open boundary should vary linearly with
height, but in order to specify this variation we would have to use a
profile boundary condition or a user subroutine. By omitting the ρ0g term, we are able
to specify a constant pressure on all 3
open boundaries and set up this type of problem with ease.
Figure 1
The only drawback to this
formulation is that you can no longer see hydrostatic pressure
variations in CFD-VIEW, only those pressure differences due to the
velocity field.
There are two ways to specify the reference density, ‘Automatic’ and
‘User-Specify’. The Automatic option behaves one of two ways,
depending on whether the system is open or closed. For open
systems such as the example above, reference density is calculated from
the initial solution as the average density over all inlet/outlet
boundaries. For closed systems, such as a box heated on one side
only, ρ0 is the average density over the
entire domain.
The Automatic reference density option is not appropriate for every
problem involving gravity, only for buoyant flows where the driving
forces for fluid motion are density differences. For unstable
transient cases where
the weight of the fluid causes fluid motion, the ‘User Specify’ option
should
be chosen and the reference density set to zero. In addition, the
initial pressure field must include the hydrostatic pressure variation,
i.e. must be physically realizable. Most likely you would need a
UINIT user subroutine for such cases.
In general, there is no harm in using the Automatic reference density
option. However, if there is any doubt, choose the ‘User-Specify’
option and set the reference density to zero, while paying special
attention to any pressure boundary conditions, i.e. don’t forget to
include hydrostatic variations. Also, be aware that an
initial guess of p = 0 everywhere may be very harsh for steady-state
cases and can cause
convergence problems. Increased velocity relaxation and/or a
better initialization of the pressure field can get around such
problems.
If you have any questions about this feature or would like us to
discuss some other topic in the future, please let us know.
Ed Blosch, Ph.D.
Lead Engineer
ESI Group
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