Multi-species, mass-transfer and reaction support and multi-phase
structure provided by William Bainbridge.

Integration of the latest p-U and face-p_U algorithms with William's
multi-phase structure is not quite complete due to design
incompatibilities which needs further development.  However the
integration of the functionality is complete.

The results of the tutorials are not exactly the same for the
twoPhaseEulerFoam and reactingTwoPhaseEulerFoam solvers but are very
similar.  Further analysis in needed to ensure these differences are
physical or to resolve them; in the meantime the twoPhaseEulerFoam
solver will be maintained.

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

Updated tutorials to converge pressure during PIMPLE loop to avoid
phase-fraction unboundedness which limits thermodynamics convergence.

Reduces or eliminates staggering patterns due to cell-force imbalances
Resolves bug-report http://www.openfoam.org/mantisbt/view.php?id=1363

BUG: twoPhaseEulerFoam: removed multiple of the continuous phase fraction from force and heat transfer models

twoPhaseEulerFoam: Remove k from the Reynolds stress because there is only a single pressure in the system
and to avoid the generation of flow from the gradient of k the pressure gradient must balance the k term in
each U equation