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Rich December 16, 2009 15:01

Viscosity and the Energy Equation
Hello all:

I've managed to confuse myself and I hope someone can set me straight.

I'm trying to add a frictional term to an unsteady, quasi-one-dimensional CFD model. Looking through the literature--namely, Anderson in his "Modern Compressible Flow" book--I see that he applies the force of friction ONLY to the momentum equation. This confuses me, as forces that add or subtract power are pertinent to the energy equation. Indeed there are viscous stress terms in the derivation of the energy equation in the NS equations. Yet Anderson and others neglect the energy equation in this treatment.

In my simulation, when modifying the momentum equation only, I do in fact get the correct trends in both subsonic and supersonic cases. And modifying the energy equation in kind causes some of those trends to become incorrect. So indeed, the momentum equation is the only equation affected by the addition of friction. But the question is, why?

Clearly, the force of friction has to have a direct affect on the momentum equation, since that equation deals with forces on the fluid. But force times velocity gives power, and so I'd expect the force of friction to have an affect on the energy equation.

Perhaps the difference lies in the fact that the frictional force, as envisioned in the Q-1-D case, is applied to the bulk flow, always acting to decelerate the flow. Whereas the viscous forces envisioned when deriving the energy equation are applied only to the surface of any flow element, and act to distort the element, rather than inhibit its bulk motion.

Do I have it, or has my trolley jumped its tracks? I'll appreciate any comments any of you can offer.


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