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23.3.5 Energy Equation

The energy equation, also shared among the phases, is shown below.

 \frac{\partial}{\partial t} (\rho E) + \nabla \cdot ({\vec v... ... + p)) = \nabla \cdot \left(k_{\rm eff} \nabla T \right) + S_h (23.3-8)

The VOF model treats energy, $E$, and temperature, $T$, as mass-averaged variables:

 E = \frac{\displaystyle\sum_{q=1}^n \alpha_q \rho_q E_q} {\displaystyle\sum_{q=1}^n \alpha_q \rho_q} (23.3-9)

where $E_q$ for each phase is based on the specific heat of that phase and the shared temperature.

The properties $\rho$ and $k_{\rm eff}$ (effective thermal conductivity) are shared by the phases. The source term, $S_h$, contains contributions from radiation, as well as any other volumetric heat sources.

As with the velocity field, the accuracy of the temperature near the interface is limited in cases where large temperature differences exist between the phases. Such problems also arise in cases where the properties vary by several orders of magnitude. For example, if a model includes liquid metal in combination with air, the conductivities of the materials can differ by as much as four orders of magnitude. Such large discrepancies in properties lead to equation sets with anisotropic coefficients, which in turn can lead to convergence and precision limitations.

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Up: 23.3 Volume of Fluid
Next: 23.3.6 Additional Scalar Equations
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