Difference between revisions of "Contrib/CompressibleMixingPhaseChangeFoam"
Mkraposhin (Talk | contribs) (→Model Equations Derivation) |
Mkraposhin (Talk | contribs) (→Model Equations Derivation) |
||
Line 111: | Line 111: | ||
<math> | <math> | ||
\frac{\partial \alpha_1 \rho_1 e_1} {\partial t} + | \frac{\partial \alpha_1 \rho_1 e_1} {\partial t} + | ||
− | \nabla \cdot \left ( \alpha_1 \rho_1 e_1 \textbf{U} \right ) | + | \nabla \cdot \left ( \alpha_1 \rho_1 e_1 \textbf{U} \right ) + \nabla \cdot \textbf{q}_1 |
= | = | ||
-\alpha_1 p \nabla \cdot \textbf{U} | -\alpha_1 p \nabla \cdot \textbf{U} | ||
Line 126: | Line 126: | ||
\frac {\partial \alpha_1 p}{\partial t} + \nabla \cdot \left ( \alpha_1 p \textbf{U} \right ) | \frac {\partial \alpha_1 p}{\partial t} + \nabla \cdot \left ( \alpha_1 p \textbf{U} \right ) | ||
\right ) | \right ) | ||
− | + | + \nabla \cdot \textbf{q}_1 | |
= | = | ||
-\alpha_1 p \nabla \cdot \textbf{U}+ | -\alpha_1 p \nabla \cdot \textbf{U}+ |
Revision as of 18:47, 15 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
2 Model Equations Summary
3 Tutorial cases
- Case #1 - Water Evaporation in Cavity