12 Replies Latest reply on Aug 25, 2016 3:29 PM by Bill McEachern

# Kutta Joukowski theorem for flow over a rotating cylinder

Hi,

I try to simulate the flow over a rotating cylinder in order to prove the Magnus effect. The diameter is 1 meter, length is 5 m, velocity is 40 m/s, the cylinder turns 90 rpm and the density is 1.2 kg/m3 so just in normal air. I used a computational domain in 2D with a width of 10 cms so, 1/50th of the total length of the cylinder.

Because i want to simulate the flow around the cilinder i don't use a rotating region but i define a real wall as a boundary condition with the velocity and rotational speed; I defined a local and global mesh (see files included).

When i calculate the lift by hand (Kutta Joukowski theorem from Lift of a Rotating Cylinder from the NASA site) the results are a lift force of 3552  N but when I use flow simulation and multiply the calculated 0.485 N with 50 (the comp. domain was 1/50 of the exact size) I only get a lousy 24.3 N.

So i guess i'm doing something totally wrong.

can anyone help me?

thx

Theo

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

I haven't looked at your model yet, but I'm not sure about your math. When I calculate the theoretical lift according to the simplified theorem, I only get 711 N/m, this is the equation I used: Wolfram|Alpha: Computational Knowledge Engine

Your calculate force from the model is .485 N / 10cm  = 4.85 N/m. So still pretty far off, but different numbers from what you have.

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

your result is equal to mine.

My total lift for a 5 meter long beam is 3552 N, yours 711*5 = 3555 N. (manually calculated using the NASA site)

So our results differ 3 N.

the result from the flow software is 0.485 N per 10 cms computational domain

So.485*50 = 24.3 total lift

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

There are some errors in your setup I can see.

Where you are setting your real wall condition, you are giving a translation and a rotation about the wrong axis.

First of all you don't need to translate the wall, because you already set the fluid to be moving at 40m/s in the project settings. So in the real wall settings the translation value should be 0 m/s.

Your rotation should be set around the z-axis, which is the longitudinal axis of your cylinder, it's currently set about the x-axis.

I changed these settings and came up with a lift value of 160 N/m, which is not correct according to theory but at least it's going in the right direction.

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

aarghh

oh my god, that was stupid. I will also change the mesh and see what i get

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

i'm starting to changing the refinement criteria in de calculation control options and the values are going up. i keep you informed

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

Hi,

I changed the size of the mesh and the refinement of the calculation control options and the values are rising, so that is positive but there is no convergence in the solution. Do you know how to achieve this? • ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

This may be due to vortex shedding in the wake, which causes alternating lift forces on your blunt body. It's possible the physics code is simply not up to the task of simulating this theorem, you may want your VAR to take this up with SolidWorks.

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

you can use the Strohal number and get the frequency, first thing would be to check if you are in the right R'number range to see if vortex shedding is a possibility. See Hoerner, Dynamic Drag.

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

The R# is ~2.5x10^6. If I remember my theory correctly the only time you don't see vortex shedding in potential flow is at extremely low R#s, up to 10-50.

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

Hoerner says max R'number ~80k for the upper limit if recollection serves. This is not, structly speaking,  potential flow.

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

You're right, that wasn't the right term to use. I should have wrote "incompressible flow", that's the flow regime I meant.

• ###### Re: Kutta Joukowski theorem for flow over a rotating cylinder

figured you knew that but others might not understand the difference, hence the strictly speaking bit..