Determination of the induced Drag for a rectangular wing
 

Hello,
I am currently working at an Optimization for Wingtip Fences for a rectangular wing in subsonic (incompressible) flows. For my seminar paper one task is to determine the separate drag forces.

To determine the induced drag I watch the losses of momentum in the control volume.

Di = [(Pressure@IN)-(Pressure@OUT)] dy dz = 0.5*(Density)*(v^2+w^2) dy dz

Expression in Post: "0.5*Density*areaInt((Velocity v)^2+(Velocity w)^2)@OUT"

where v and w are the induced velocities in a yz-Plane (Trefftz), very far behind the wing.

I have observed, that the viscosity of the used gas (air at 25°C) has no large influence at the so calculated drag. Additional to that, I determined the zeroliftdrag (nearly the parasitic drag) and subtracted it from the general wingdrag to become a guess for the induced drag.

My question: Why are the results for the induced drag so different for the different ways of calculation?

Thank you very much!

This approach appears to be very sensitive to the global imbalances. Try converging to tighter imbalances and see if that improves things.

Hi ghorrocks,
thx for your fast answer! I'm an absolute newcomer in cfd-practice. What do you mean with "converging to tighter imbalances". I have choosen a huge control volume sourrounding the wing (wingdept x 100 x100 x 800) and for first evaluations a rough unstructured grid. For better results I will refine the Mesh with Prism Layers around the wing.

Is the formulation of my expression:

"0.5*Density*areaInt((Velocity v)^2+(Velocity w)^2)@OUT"

equal to the above shown formula?
Attachment 38546

Attachment 38547

Your results are going to be very inaccurate without this.

And while you are at it, you transition very quickly from fine mesh on the wing to coarse mesh further away. This will also be a problem, especially if you are trying to pick up small differences in the momentum field. Have a look in the literature at the sort of meshed they use - you will find the transition is much gentler, and they usually have a tail of fine mesh in the wake region (which is where your momentum deficit will exist).