Favre averaged Navier-Stokes equations
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The total energy <math>e_0</math> is defined by: | The total energy <math>e_0</math> is defined by: | ||
+ | <span id="total_energy"> | ||
<math> | <math> | ||
e_0 \equiv e + \frac{u_k u_k}{2} | e_0 \equiv e + \frac{u_k u_k}{2} | ||
</math> | </math> | ||
+ | </span> | ||
Note that the | Note that the |
Revision as of 08:03, 5 September 2005
The instantaneous continuity equation, momentum equation and energy equation for a compressible fluid can be written as:
For a Newtonian fluid, assuming Stokes Law for mono-atomic gases, the viscous stress is given by:
Where the trace-less viscous strain-rate is defined by:
The heat-flux, , is given by Fourier's law:
Where the laminar Prandtl number is defined by:
To close these equations it is also necessary to specify an equation of state. Assuming a calorically perfect gas the following relations are valid:
Where and are constant.
The total energy is defined by:
Note that the corresponding expression~\ref{eq:fav_total_energy} for Favre averaged turbulent flows contains an extra term related to the turbulent energy.