Solver for two fluids with phase change (for example - water <---> steam), pressure and temperature density dependence Valid versions:
Contents
1 Model Equations Derivation
VALID OPENFOAM VERSION - 2.1.0
- 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 internal energy equation for phase-1:
By combining equations of phases, we get internal energy balance for mixture in temperatures:
Where - latent heat of evaporation
- 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
2 Implemented phase change models
- Phase change model Schnerr-Sauer
- Phase change model Zwart
- Phase change model Singhal
- Phase change model Merkle
- Phase change model Kunz
3 Model Source Code For OpenFOAM 2.1.0
Source code for solver located here
4 Tutorial cases
- Case #1 - cavitation on the hemispherical body
Problem description, initial and boundary conditions are shown on the figure
Volume fraction of liquid (water) is shown on the next figure Figure 1.2
- Case #2 - hot water flashing in the nozzle
Problem description, initial and boundary conditions are shown on the figure 2.1
Volume and mass fractions of vapour are shown on the figures 2.2 and 2.3 Pressure distribution is shown on figure 2.4 Velocity magnitude and Mach number for compressible case are shown on figures 2.5 and 2.6 Velocity magnitude for incompressible case is shown on the case 2.7 Temperature distribution is located of figure 2.8