Rather than forcing the dispersed-phase velocity -> the continuous-phase
velocity as the phase-fraction -> 0 the velocity is now calculated from
a balance of pressure, buoyancy and drag forces. The advantage is now
liquid or particles are not carried out of bubble-column of
fluidised-beds by the fictitious drag caused by forcing the
phase-velocities becoming equal in the limit.
nLimiterIter: Number of iterations during limiter construction
3 (default) is sufficient for 3D simulations with a Courant number 0.5 or so
For larger Courant numbers larger values may be needed but this is
only relevant for IMULES and CMULES
smoothLimiter: Coefficient to smooth the limiter to avoid "diamond"
staggering patters seen in regions of low particle phase-fraction in
fluidised-bed simulations.
The default is 0 as it is not needed for all simulations.
A value of 0.1 is appropriate for fluidised-bed simulations.
The useful range is 0 -> 0.5.
Values larger than 0.5 may cause excessive smearing of the solution.
This formulation provides C-grid like pressure-flux staggering on an
unstructured mesh which is hugely beneficial for Euler-Euler multiphase
equations as it allows for all forces to be treated in a consistent
manner on the cell-faces which provides better balance, stability and
accuracy. However, to achieve face-force consistency the momentum
transport terms must be interpolated to the faces reducing accuracy of
this part of the system but this is offset by the increase in accuracy
of the force-balance.
Currently it is not clear if this face-based momentum equation
formulation is preferable for all Euler-Euler simulations so I have
included it on a switch to allow evaluation and comparison with the
previous cell-based formulation. To try the new algorithm simply switch
it on, e.g.:
PIMPLE
{
nOuterCorrectors 3;
nCorrectors 1;
nNonOrthogonalCorrectors 0;
faceMomentum yes;
}
It is proving particularly good for bubbly flows, eliminating the
staggering patterns often seen in the air velocity field with the
previous algorithm, removing other spurious numerical artifacts in the
velocity fields and improving stability and allowing larger time-steps
For particle-gas flows the advantage is noticeable but not nearly as
pronounced as in the bubbly flow cases.
Please test the new algorithm on your cases and provide feedback.
Henry G. Weller
CFD Direct
Improves stability and convergence of systems in which drag dominates
e.g. small particles in high-speed gas flow.
Additionally a new ddtPhiCorr strategy is included in which correction
is applied only where the phases are nearly pure. This reduces
staggering patters near the free-surface of bubble-column simulations.
Allows the specification of a reference height, for example the height
of the free-surface in a VoF simulation, which reduces the range of p_rgh.
hRef is a uniformDimensionedScalarField specified via the constant/hRef
file, equivalent to the way in which g is specified, so that it can be
looked-up from the database. For example see the constant/hRef file in
the DTCHull LTSInterFoam and interDyMFoam cases.
This is an experimental feature demonstrating the potential of MULES to
create bounded solution which are 2nd-order in time AND space.
Crank-Nicolson may be selected on U and/or alpha but will only be fully
2nd-order if used on both within the PIMPLE-loop to converge the
interaction between the flux and phase-fraction. Note also that
Crank-Nicolson may not be used with sub-cycling but all the features of
semi-implicit MULES are available in particular MULESCorr and
alphaApplyPrevCorr.
Examples of ddt specification:
ddtSchemes
{
default Euler;
}
ddtSchemes
{
default CrankNicolson 0.9;
}
ddtSchemes
{
default none;
ddt(alpha) CrankNicolson 0.9;
ddt(rho,U) CrankNicolson 0.9;
}
ddtSchemes
{
default none;
ddt(alpha) Euler;
ddt(rho,U) CrankNicolson 0.9;
}
ddtSchemes
{
default none;
ddt(alpha) CrankNicolson 0.9;
ddt(rho,U) Euler;
}
In these examples a small amount of off-centering in used to stabilize
the Crank-Nicolson scheme. Also the specification for alpha1 is via the
generic phase-fraction name to ensure in multiphase solvers (when
Crank-Nicolson support is added) the scheme is identical for all phase
fractions.
