Incompressible flow: mechanical energy terms

Pinaki Bhattacharya

Hello

I am simulating: 1. an unsteady incompressible flow, 2. in a pipe with a constriction, 3. using hex meshes.

I want to ensure that the mechanical energy equation is balanced to some degree of accuracy.

Note that there is NO THERMAL ENERGY involved. By mechanical energy equation I mean the equation you get when you take the dot product of the velocity (vector) with the momentum (vector) equation.

Now if my momemtum equation converges, how much can I expect the energy equation to balance?

I want to know if 1. anyone has tried this before in FLUENT, and what results did you get? 2. some particular solution strategy (refining/adapting grid, or making time step smaller) helped in getting a good balance? 3. there is any inherent problem in FLUENT that I can not get more than some level of accuracy?

I am using UDFs to calculate all the terms in the equation. I have written the equation as an integral over the whole fluid domain. So only surface integrals of pressure power and advected power over the inlet and outlet, and volume integral of energy dissipation matter. I compute these at every time step, and sum them up to get the integral. This should equal the time-rate of change of k.e. integrated over the volume, which I compute from a simple central difference in time (of the integral).

I find the sum of the power terms to be much larger than the rate of energy change in the domain. And the error is way off! I don't know what I can change to bring the difference down.

I will appreciate your help.

Thanks much in advance.