Favre averaged Navier-Stokes equations
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for a compressible fluid can be written as: | for a compressible fluid can be written as: | ||
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- | <math> | + | |
\frac{\partial \rho}{\partial t} + | \frac{\partial \rho}{\partial t} + | ||
\frac{\partial}{\partial x_j}\left[ \rho u_j \right] = 0 | \frac{\partial}{\partial x_j}\left[ \rho u_j \right] = 0 |
Revision as of 08:09, 5 September 2005
The instantaneous continuity equation, momentum equation and energy equation for a compressible fluid can be written as:
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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.