Couette flow between cylinders - Windage Loss Calculation
 

Hello everybody,

These days, I am dealing with the simulation of fluid flow between two cylinders with the help of CFX software program. In fact, I need to calculate the windage loss energy generated between cylinders. The pictures of geometry and grid are both attached.

To be more elaborate,
The inner cylinder is rotating with 5800(Rpm) and the outer cylinder is stationary. Some specifications are as below;

(Length of cylinders= 11.42 cm, Airgap = 0.063 cm, Rotor Radius=10 cm, fluid = air @ 25 C)

About the setup that I applied in this simulation, I should say,
Total Energy - SST turbulence model - viscose work term is activated

About Boundary Conditions:

inlet mass flow (0.001 kg/s) (Honestly, I used a tiny inlet flow rate for the sake of convergence and I suppose there is no axial flow because the amount of inlet flow is not tangible)

Opening boundary condition for the outlet.

Moving wall --> inner cylinder
no Slip wall --> outer cylinder

After the simulation of fluid flow, I calculated the windage loss which equal (Torque * rotational velocity)

P=TΩ = 0.03743 (N.m) * 607.3746 (rad/s) = 22.7340 (watt)

However, this power loss (22.7) does not equal the power loss calculated by empirical equations. According to windage correlations we have :

W=πC_d ρR^4 Ω^3 L
1/√(C_d )=2.04+1.768 Ln(Re√(C_d ))

the picture of this formula is attached.
Actually, as per this correlation the windage loss in this case is supposed to be 71.7 (Watt).
The origin of this discrepancy is really worrying me.

Please let me know if you have any idea about this problem.

With Best Regards
Sasan Ghomi

First of all - empirical equations are rarely "accurate". They are usually approximations only. So make sure you are aware of exactly how accurate the empirical relation you are comparing to actually is.

The rest of your question is about accuracy, which is an FAQ: https://www.cfd-online.com/Wiki/Ansy..._inaccurate.3F

In your case things to look at include:
* The effect of your inlet and outlet boundary condition
* Whether you need to model the region outside the ring to get the edge effects correct
* Mesh, convergence tolerance and time step size sensitivity check
* Effect of turbulence model
* Effect of simplifying assumptions you have made: smooth surfaces versus rough, constant properties ideal gas (I assume this is what you used) versus real gas with variable properties