Chicken or Egg - Porous Body or Fan Rotation Controls the Flow in a tube
 

Hello Everyone,

Following query has been quite troubling for me to get an answer. Probably the experts in here should be able to guide me on it.

Have a circular tube, with a porous body and a 3D Axial Fan, as shown in the attached figure.

3D Fan zone is a rotating domain with an rpm attached to it and the porous body has the inertial components attached in the definition of porous zone.

Now herein my grey cells give up.


Let's say

For a fixed rpm of 1000, and an inertial coefficient of 50, the flow from the tube is 200 m3/s

Now for the "same rpm", and an "increase" in inertial coefficent above 50, the flow from the tube "drops/decreases" to less than 200 m3/s


Was under the impression that it is the fan rpm that is controlling the flow through the tube.

Believe that when we provide "frame motion" to the rotating domain, its only the forces that gets transferred to the fluid. Shouldn't this also control the suction and hence the flow through the tube ?


Not sure what I am missing in the understanding of the physics in here.


Appreciate all your guidance and insights on the topic.

Look up "fan curve".
By increasing the inertial coefficient of the porous block, you increase the pressure drop from said porous material. Working against a higher pressure difference, the fan can't provide the same volume flow rate.
Maybe it's more intuitive if you picture the 2 extremes of a fan curve:
1) for a porous block with infinite flow resistance (i.e. a wall), the volume flow rate will obviously be 0. All the fan does in this case is create a low pressure zone between the porous block and the fan.
2) for the porous block with zero flow resistance, the fan does not have to do any of the work sucking the fluid through the porous material. All energy it transfers to the fluid by spinning at 1000 rpm goes into kinetic energy (if we ignore losses other than the porous block for now) and thus it provides the maximum volume flow rate at zero pressure difference.

Giving your porous block resistance values between 0 and infinity, you arrive at different operating points on the fan curve with varying volume flow rates. Despite spinning the fan at a constant rpm.
Side-note: the power required to spin the fan at 1000 rpm will also be different, depending on which operating point you land on.

Hi,
Thanks for the insights into the flow concepts of Porous zone and Fan Operation.

In effect, it is the porous body that controls the flow through the tube, and the fan rotation adds energy to the fluid. Can we make this valid assumption of the features within the tube flow above ?

Apreciate the guidance about it.

I would not frame it as an either/or problem. It is not the chicken or the egg, but instead both components negotiating an equilibrium.
Both the porous zone and the fan determine the volume flow rate in your case.
Instead of increasing the flow resistance of the porous block, you could have used a weaker fan, still spinning at 1000 rpm. The result would be the same: lower volume flow rate.

Different analogy: what determines the terminal velocity of a 1cm diameter sphere, in 9.81m/s² gravity? Is it the properties of the surrounding fluid? Or is it the density of the sphere? Of course it is both. The sphere accelerates until the force of gravity matches the drag force.