Difference between revisions of "Contrib/CompressibleMixingPhaseChangeFoam"

Revision as of 20:28, 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

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:

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

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

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

* Phase change model
* Momentum equation
* Energy equation

Solver sources and tutorials located here

@@ Line 3: / Line 3: @@
 == 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
+Low-compressible fluid: <math>
+\rho = \rho_0 + \frac{\partial \rho}{\partial T} \Delta T + \frac{\partial \rho}{\partial p} \Delta p
+</math>
+Ideal gas: <math> \rho=\frac{p}{(C_p/C_v)(R/M)T}
+</math>
+By combining this equations, we can get general relation:
+\rho = \hat \rho + \frac{\partial \rho}{\partial p} \Delta p
 * Liquid volume transport
 Let us consider transport of liquid (heavy phase) volume fraction <math>\alpha_l</math>: