Difference between revisions of "Contrib/CompressibleMixingPhaseChangeFoam"
Mkraposhin (Talk | contribs) |
Mkraposhin (Talk | contribs) (→Model Equations Derivation) |
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- \nabla \cdot \textbf{q}_1 | - \nabla \cdot \textbf{q}_1 | ||
= | = | ||
+ | -\alpha_1 p \nabla \cdot \textbf{U}+ | ||
\dot m_1 h_1 - \dot m_1 \frac{p}{\rho_1} | \dot m_1 h_1 - \dot m_1 \frac{p}{\rho_1} | ||
</math> | </math> | ||
Line 141: | Line 142: | ||
\frac{1}{\rho_1 C_{p,1}} | \frac{1}{\rho_1 C_{p,1}} | ||
\left ( | \left ( | ||
− | \frac { | + | \alpha_1 \frac {d p}{d t} + p \frac {d \alpha_1}{d t} |
\right ) | \right ) | ||
</math> | </math> |
Revision as of 16:04, 6 January 2013
Solver for two fluids with phase change (for example - water <---> steam), pressure and temperature density dependence
1 Model Equations Derivation
- Equation of state
Low-compressible fluid:
Ideal gas:
By combining this equations, we can get general relation:
where computed with respect to previous formulations
mixture density calculated as
Here, and afterthere indices:
1,l,f - for liquid (heavy media with low compressibility)
2,g,s - for gas (light media (like steam) with big compressibility)
without index - mixture variable (or all variables local to some phase)
- Liquid volume transport
Let us consider transport of liquid (heavy phase) volume fraction :
By converting to volume fluxes we get:
Using equation of state, we can reformulate substantial derivative for density in terms of pressure for any phase:
- General rule for converting from mass to volume fluxes in transport equation
- Momentum equation (velocity prediction)
by substituting piezometric pressure we get:
- Pressure equation obtained by summation of equation for volume phase fraction of liquid and gas phases:
- Energy equation
Energy equation for mixture temperature obtained from sum of energy equations for each phase. Consider energy equation for phase-1:
by converting to enthalpies we get:
By substituting temperature instead of enthalpy, after conversion to volume fluxes we get equation for temperature (divided by )
By combining equations of phases, we get energy balance for mixture:
- Linking liquid volume transport to pressure equation is done by introducing and at r.h.s of volume fraction balance equation. Then, replaced by value from pressure equation
- Phase change model