regionCoupledMassTransferVelocityValue

Overview

regionCoupledMassTransferVelocityValue is the Dirichlet (jump) half of the partitioned velocity coupling across a sharp liquid-vapour interface with phase change. It acts on a volVectorField (U) and derives from genericRegionCoupledJump<vector>, i.e. from fixedValue. The patch value is the interpolated neighbour velocity plus the jump in normal velocity that a mass flux $\dot m$ produces between two phases of different density. The partner condition on the other side is regionCoupledMassTransferVelocityFlux. The BC needs both a capillaryInterface and a massTransferInterface on the same patch pair, and the pressure is coupled by regionCoupledMassTransferPressureValue and (inferred) regionCoupledPressureFlux. It is the phase-change counterpart of regionCoupledVelocityValue.

Mathematical Formulation

“own” is the side the BC sits on and “nbr” the other side. $\mathcal{I}_{\text{nbr}\to\text{own}}$ is the patch-to-patch interpolation. $\mathbf{n}_\varepsilon$ is the local patch normal if the local region is meshA of the capillaryInterface, and its negative otherwise. In both cases it points out of region A.

followed by relaxation, $\mathbf{U}^{k} = \mathbf{U}^{k-1} + \omega\,(\mathbf{U}^{*} - \mathbf{U}^{k-1})$.

Unlike regionCoupledVelocityValue, no surface-velocity or mesh-velocity correction of the normal component is applied. That version is still in the source but commented out.

The diffusive momentum flux handed to regionCoupledMassTransferVelocityFlux is the same as for regionCoupledVelocityValue: $\mu_\text{own}$ times the tangential part of the face-normal gradient (normal component removed in the vector snGrad() of genericRegionCoupledJump).

Implementation

updateCoeffs() is the generic one of genericRegionCoupledJump: return if updated or coupled no; call update() on the first interfaceType; interpolate the neighbour U (looked up by the local field name); add valueJump(); relax; call fixedValue::updateCoeffs().

valueJump():

• finds the capillaryInterface and the massTransferInterface by type name on this patch (rgInterface(<type>)), independent of their order in interfaceType;
• interpolates mDotS() from the neighbour side;
• reads rho of both regions from transportProperties;
• refCasts the neighbour U patch field to genericRegionCoupledFlux<vector> and uses its values only for a diagnostic line;
• prints U Dirichlet boundary contributions: ... (integrated volume fluxes of the neighbour velocity, of the jump term and of mesh motion plus $\dot m/\rho$) on every call.

Only the interface listed first in interfaceType is update()d by this BC. With (capillaryInterface massTransferInterface) the massTransferInterface is not corrected here. $\dot m$ is only recomputed when a BC that lists massTransferInterface first (e.g. regionCoupledPhaseChangeHeatFlux on T) is updated. Otherwise it stays at its initial value of zero.

The class has two more functions that are not used in the solution:

• updatePhi() would set the boundary phi to the negated interpolated neighbour flux plus $\pm(1/\rho_\text{own}-1/\rho_\text{nbr})\dot m\,|\mathbf{S}_f|$. The call in the base class is commented out.
• The member correctClosedVolumePhi(phi, U, p, rAU) would correct the interface flux to the net volume flux $-\dot m/\rho\,|\mathbf{S}_f|$. It is never called. The global correctClosedVolumePhi() used by icoFluid and interTrackFluid (closedVolume on) recognises this BC, but forces the net volume flux through the patch to zero.

The U jump residual is evaluated on this BC if the side-A U patch is not jump-derived (as in the intended setup): $\lVert\mathbf{U}_\text{own} - \mathcal{I}(\mathbf{U}_\text{nbr}) - \text{valueJump}\rVert_2$, normalised as in genericRegionCoupledJump.

Dictionary Entries

rho (and mu) must be present in transportProperties of both regions.

Usage

No tutorial uses this BC. The entry below follows massTransferInterface and has not been run. Side B (second in coupledPatchPair):

// 0/fluidB/U
interfaceShadow
{
    type                    regionCoupledMassTransferVelocityValue;
    interfaceType           (capillaryInterface massTransferInterface);
    secondOrder             false;
    nonOrthCorr             false;
    value                   uniform (0 0 0);
}

Partner on side A:

// 0/fluidA/U
interface
{
    type                    regionCoupledMassTransferVelocityFlux;
    interfaceType           (capillaryInterface massTransferInterface);
    secondOrder             false;
    nonOrthCorr             false;
    value                   uniform (0 0 0);
}

regionInterfaceProperties (excerpt):

fluidAfluidB
{
    interfaceType (capillaryInterface massTransferInterface);

    coupledPatchPair
    (
        (fluidA interface)
        (fluidB interfaceShadow)
    );

    coupledFields
    (
        pUPimple
        T
    );

    capillaryInterfaceCoeffs    { sigma sigma [1 0 -2 0 0 0 0] 0.07232; }
    massTransferInterfaceCoeffs { hlv hlv [0 2 -2 0 0 0 0] 2.257e6; TSat TSat [0 0 0 1 0 0 0] 373.15; }
}

The full case setup, including the T coupling that drives $\dot m$, is in massTransferInterface.

Known Limitations

• Untested, no tutorial. The interface-tracking region type it was written for (interTrackFluid) is disabled in src/multiRegionSystem/Make/files.
• $\dot m$ is only updated through another BC. See Implementation.
• Must sit on side B (inferred). mDotS() lives on the side-A faMesh and is interpolated “from the neighbour”.
• Neighbour must be flux-derived. The neighbour U patch field is refCast to genericRegionCoupledFlux<vector> (for a log line only); any other type aborts.
• Closed-volume correction ignores phase change. With closedVolume on, the global correctClosedVolumePhi() forces zero net volume flux through this patch, which contradicts a non-zero $\dot m$ (inferred).
• No normal mesh-velocity term. The normal velocity is not tied to the mesh motion as in regionCoupledVelocityValue (inferred from the commented-out code; intent unclear).
• Log output on every call; diffusivity and neighbourFieldName are ignored.

Tutorials

References

• Alkfri, A., Habes, C., Marschall, H., multiRegionFoam: A Unified Multiphysics Framework for Multi-Region Coupled Continuum-Physical Problems, Engineering with Computers, 2023. DOI: 10.1007/s00366-024-01974-4