In many publications and Euler-Euler codes the pressure-work term in the
total enthalpy is stated and implemented as -alpha*dp/dt rather than the
conservative form derived from the total internal energy equation
-d(alpha*p)/dt. In order for the enthalpy and internal energy equations
to be consistent this error/simplification propagates to the total
internal energy equation as a spurious additional term p*d(alpha)/dt
which is included in the OpenFOAM Euler-Euler solvers and causes
stability and conservation issues.
I have now re-derived the energy equations for multiphase flow from
first-principles and implemented in the reactingEulerFoam solvers the
correct conservative form of pressure-work in both the internal energy
and enthalpy equations.
Additionally an optional limiter may be applied to the pressure-work
term in either of the energy forms to avoid spurious fluctuations in the
phase temperature in regions where the phase-fraction -> 0. 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.
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