Added the interfacial pressure-work terms according to:
Ishii, M., Hibiki, T.,
Thermo-fluid dynamics of two-phase flow,
ISBN-10: 0-387-28321-8, 2006
While this is the most common approach to handling the interfacial
pressure-work it introduces numerical stability issues in regions of low
phase-fraction and rapid flow deformation. To alleviate this problem an
optional limiter may be applied to the pressure-work term in either of
the energy forms. This may specified in the
"thermophysicalProperties.<phase>" file, e.g.
pressureWorkAlphaLimit 1e-3;
which sets the pressure work term to 0 for phase-fractions below 1e-3.
For particularly unstable cases a limit of 1e-2 may be necessary.
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
