Difference between revisions of "Contrib/CompressibleMixingPhaseChangeFoam"
Mkraposhin (Talk | contribs) |
Mkraposhin (Talk | contribs) |
||
Line 1: | Line 1: | ||
Solver for two fluids with phase change (for example - water <---> steam), pressure and temperature density dependence | Solver for two fluids with phase change (for example - water <---> steam), pressure and temperature density dependence | ||
− | == Model Equations == | + | == Model Equations Derivation == |
* Equation of state | * Equation of state | ||
Low-compressible fluid: <math> | Low-compressible fluid: <math> | ||
Line 147: | Line 147: | ||
-\frac{1}{\rho_1 C_{p,1}} \nabla \cdot \kappa_1 \nabla T -\frac{1}{\rho_2 C_{p,2}} \nabla \cdot \kappa_2 \nabla T | -\frac{1}{\rho_1 C_{p,1}} \nabla \cdot \kappa_1 \nabla T -\frac{1}{\rho_2 C_{p,2}} \nabla \cdot \kappa_2 \nabla T | ||
= | = | ||
+ | </math> | ||
+ | |||
+ | <math> | ||
\left ( \frac{\alpha_1}{\rho_1 C_{p,1}} + \frac{\alpha_2}{\rho_2 C_{p,2}} \right ) \frac{d p}{d t} | \left ( \frac{\alpha_1}{\rho_1 C_{p,1}} + \frac{\alpha_2}{\rho_2 C_{p,2}} \right ) \frac{d p}{d t} | ||
+ \frac{p}{\rho_1 C_{p,1}}\frac{d \alpha_1}{d t} + \frac{p}{\rho_2 C_{p,2}}\frac{d \alpha_2}{d t} | + \frac{p}{\rho_1 C_{p,1}}\frac{d \alpha_1}{d t} + \frac{p}{\rho_2 C_{p,2}}\frac{d \alpha_2}{d t} | ||
+ \dot m_1 p \left (-\frac{1}{\rho_1 \rho_1 C_{p,1}} + \frac{1}{\rho_2 \rho_2 C_{p,2}}\right ) | + \dot m_1 p \left (-\frac{1}{\rho_1 \rho_1 C_{p,1}} + \frac{1}{\rho_2 \rho_2 C_{p,2}}\right ) | ||
</math> | </math> | ||
+ | |||
+ | * Linking liquid volume transport to pressure equation is done by introducing <math>+\alpha_1 \nabla \cdot \textbf{U}</math> and <math>-\alpha_1 \nabla \cdot \textbf{U}</math> at r.h.s of volume fraction balance equation. Then, <math>-\nabla \cdot \textbf{U}</math> replaced by value from pressure equation | ||
+ | |||
+ | <math> | ||
+ | \frac {\partial \alpha_l}{\partial t} + \nabla \cdot | ||
+ | \left ( | ||
+ | \alpha_l \textbf{U} | ||
+ | \right ) | ||
+ | = | ||
+ | \alpha_1 \nabla \cdot \textbf{U} + | ||
+ | \dot m_1 \left (\frac{1}{\rho_1} \alpha_1 - \left (\frac{1}{\rho_1} - \frac{1}{\rho_2} \right ) \right ) + | ||
+ | </math> | ||
+ | |||
+ | <math> | ||
+ | \alpha_1 \alpha_2 \left ( -\frac{1}{\rho_1} \frac{d \hat \rho_1}{d t} + \frac{1}{\rho_2} \frac{d \hat \rho_2}{d t}\right ) | ||
+ | +\alpha_1 \alpha_2 p \left ( -\frac{1}{\rho_1} \frac{d \psi_1}{d t} + \frac{1}{\rho_2} \frac{d \psi_2}{d t}\right ) | ||
+ | +\alpha_1 \alpha_2 \frac{d p}{d t}\left ( -\frac{\psi_1}{\rho_1} + \frac{\psi_2}{\rho_2} \right ) | ||
+ | </math> | ||
+ | |||
* Phase change model | * Phase change model | ||
[http://www.os-cfd.ru/compressibleMixingPhaseChangeFoam/Solver.tgz Solver sources and tutorials located here] | [http://www.os-cfd.ru/compressibleMixingPhaseChangeFoam/Solver.tgz Solver sources and tutorials located here] |
Revision as of 17:21, 30 December 2012
Solver for two fluids with phase change (for example - water <---> steam), pressure and temperature density dependence
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