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In order to ensure temperature consistency between the phases it is necessary to
solve for the mixture temperature rather than the mixture energy or phase
energies which makes it very difficult to conserve energy. The new temperature
equation is a temperature correction on the combined phase energy equations
which will conserve the phase and mixture energies at convergence. The
heat-flux (Laplacian) term is maintained in mixture temperature form so
heat-transfer boundary conditions, in particular for CHT, remain in terms of the
mixture kappaEff. The fvModels are applied to the phase energy equations and
the implicit part converted into an implicit term in the temperature correction
part of the equation to improve convergence and stability.
This development has required some change to the alphaEqn.H and interFoam has
been updated for consistency in preparation for conversion into the
solvers::incompressibleVoF modular module.
All compressibleVoF fvModels and tutorial cases have been updated for the above
change. Note that two entries are now required for the convection terms in the
temperature equation, one for explicit phase energy terms and another for the
implicit phase temperature correction terms, e.g.
tutorials/modules/compressibleVoF/ballValve
div(alphaRhoPhi,e) Gauss limitedLinear 1;
div(alphaRhoPhi,T) Gauss upwind;
In the above the upwind scheme is selected for the phase temperature correction
terms as they are corrections and will converge to a zero contribution. However
there may be cases which converge better if the same scheme is used for both the
energy and temperature terms, more testing is required.
Reference:
Figueiredo, R. A., Oishi, C. M., Afonso, A. M., Tasso, I. V. M., &
Cuminato, J. A. (2016).
A two-phase solver for complex fluids: Studies of the Weissenberg effect.
International Journal of Multiphase Flow, 84, 98-115.
In compressibleInterFoam with momentumTransport simulationType set to
twoPhaseTransport separate stress models (laminar, non-Newtonian, LES or RAS)
are instantiated for each of the two phases allowing for different modeling for
the phases.
This example case uses:
- phases "air" and "liquid"
- air phase
- constant/momentumTransport.air:
- stress model set to laminar, Newtonian
- constant/physicalProperties.air:
- transport set to const (Newtonian)
- mu (dynamic viscoity) = 1.84e-5
- liquid phase
- constant/momentumTransport.liquid:
- stress model set to laminar, Maxwell non-Newtonian
- nuM (kinematic viscosity) = 0.01476
- lambda = 0.018225
- constant/physicalProperties.liquid
- transport set to const (Newtonian)
- mu (dynamic viscoity) = 1.46
Liquid phase properties were calculated from the relations given in the paper:
- rho = 890 kg/m^3
- mu = mu_{s} + mu_{p} = 146 poise = 14.6 Pa.s
s = solvent (Newtonian), p = polymer (Maxwell)
- mu_{s}/mu_{p} = 1/9
=> mu_{s} = 14.6/10 = 1.46 Pa.s
=> nu_{p} = nuM = (9/10)*14.6/890 = 0.01476 m^2/s
compressibleInterFoam solves the energy equation, despite not being needed in
this example. The case is simply initialised at a uniform temperature of 300K
throughout the domain and at the atmosphere boundary.