Difference between revisions of "Contrib/CompressibleMixingPhaseChangeFoam"

Revision as of 20:54, 28 December 2012

Solver for two fluids with phase change (for example - water <---> steam), pressure and temperature density dependence

Model Equations

Equation of state

Low-compressible fluid: $\rho = \rho_0 + \frac{\partial \rho}{\partial T} \Delta T + \frac{\partial \rho}{\partial p} \Delta p$

Ideal gas: $\rho=\frac{p}{(C_p/C_v)(R/M)T}$

By combining this equations, we can get general relation:

$\rho = \hat \rho + \frac{\partial \rho}{\partial p} \Delta p$

where $\hat \rho$ computed with respect to previous formulations

mixture density $\rho$ calculated as

$\rho = \alpha_l \rho_l + \alpha_v \rho_v$

Liquid volume transport

Let us consider transport of liquid (heavy phase) volume fraction $\alpha_l$ :

$\frac{\partial \alpha_l \rho_l}{\partial t} + \nabla \cdot \left ( \alpha_l \rho_l \mathbf{U} \right ) = \dot m_l$

By converting to volume fluxes we get:

$\frac {\partial \alpha_l}{\partial t} + \nabla \cdot \left ( \alpha_l \textbf{U} \right ) = \frac {\alpha_l}{\rho_l} \frac {d \rho_l}{dt} + \frac {\dot m_l}{\rho_l}$

Using equation of state, we can reformulate substantial derivative for density in terms of pressure for any phase:

$\frac {d \rho}{dt}= \frac {d \hat \rho} {dt} + \psi \frac {dp} {dt} + p \frac {d \psi}{dt}$

General rule for converting from mass to volume fluxes in transport equation

$\frac{\partial \alpha_i \rho_i \zeta}{\partial t} + \nabla \cdot \left ( \alpha_i \rho_i \textbf{U} \zeta \right ) = \rho_i \alpha_i \left ( \frac {\partial \zeta}{\partial t} + \nabla \cdot \left ( \textbf{U} \zeta \right ) \right ) + \zeta \alpha_l \frac {d \rho_i}{dt} + \zeta \rho_i \frac {d \alpha_i}{dt}$

Momentum equation (velocity prediction)

\frac {\partial \rho \textbf{U}}{\partial t}

* Phase change model
* Energy equation

Solver sources and tutorials located here

@@ Line 17: / Line 17: @@
 where <math>\hat \rho</math> computed with respect to previous formulations
+mixture density <math> \rho </math> calculated as
+<math>\rho =  \alpha_l \rho_l + \alpha_v \rho_v </math>
 * Liquid volume transport
 Let us consider transport of liquid (heavy phase) volume fraction <math>\alpha_l</math>:
@@ Line 63: / Line 69: @@
 \zeta \alpha_l \frac {d \rho_i}{dt}  + \zeta \rho_i \frac {d \alpha_i}{dt}
 </math>
+* Momentum equation (velocity prediction)
+\frac {\partial \rho \textbf{U}}{\partial t}
   * Phase change model
- * Momentum equation
   * Energy equation
 [http://www.os-cfd.ru/compressibleMixingPhaseChangeFoam/Solver.tgz Solver sources and tutorials located here]