# Calculating the velocity and pressure profiles across an axial fan

Hi,

This is my first post on the PhysicsFormus

I am trying to design an inlet and outlet for an axial fan and calculate velocity and pressure profiles in the duct. See the sketch attached. The ultimate goal is to carry out a CFD study but I was wondering if there is an analytical solution for a simplified case, so I can have some estimation. I did some research and was trying to apply "actuator disk theory" (linked), but I do not find the results believable (see spreadsheet attached, I simplified the problem to have a uniform section area).

Let me know if you have any suggestions on how to tackle this problem!

EDIT: Calculations and sketch attached, apologies for "Google-Driving" them first

Kind regards
Olek

#### Attachments

• basic_fan_calcs.xlsx
94.3 KB · Views: 215
• fan_scheme.JPG
14.2 KB · Views: 420
Last edited:

anorlunda
Staff Emeritus

#### Attachments

14.5 KB · Views: 736

View attachment 232412
Hi Anorlunda,

Apologies, somehow I missed this functionality... all attached "properly" now :)

Hi,

would anyone be able to advise on this? Let me know if there's anything that's not clear.

Thanks

russ_watters
Mentor
Hi,

would anyone be able to advise on this? Let me know if there's anything that's not clear.

Thanks
Welcome to PF!

Yeah, I guess I saw this two weeks ago and wasn't clear on what the goal is. I didn't do a detailed check of your math, but it looks like you are using the area/velocity relationship and kinetic energy to find power. That's fine except for two problems I see:
1. If V1 is zero, how can V2 be anything but zero?
2. You don't have an efficiency factor for the fan...and it won't be constant.

What are you trying to use this for? It is tough to know if you are on the right track not knowing what problem you are trying to solve.

I am trying to use this for calculating force acting on the walls of the inlet duct, resulting from low pressure in the fan inlet and ambient.
With the issues you pointed out:
1. I am happy to use V1=/0
2. I am happy to neglect efficiency at the beginning. I will be making a scaled model of this system, so will get some idea about efficiency vs speed from there.

Let me know what you think

russ_watters
Mentor
I am trying to use this for calculating force acting on the walls of the inlet duct, resulting from low pressure in the fan inlet and ambient.
I don't think I've ever heard of someone caring about this. Any reason it seems important to you?

For low speeds, the pressure is very close to atmospheric. You would need very high speeds for the pressure to matter more than the structure holding up its own weight. The pressure will also neither be consistent or easy to predict due to the angled transition. Definitely a job for CFD.

I am investigating the feasibility of a powered ground effect device on a road vehicle, as in Brabham BT46

I don't think I've ever heard of someone caring about this. Any reason it seems important to you?

For low speeds, the pressure is very close to atmospheric. You would need very high speeds for the pressure to matter more than the structure holding up its own weight. The pressure will also neither be consistent or easy to predict due to the angled transition. Definitely a job for CFD.

russ_watters
Mentor
I am investigating the feasibility of a powered ground effect device on a road vehicle, as in Brabham BT46
Oh; that appears to me to be a very different problem than the one you are solving. Powered ground effect would just be the opposite of a hovercraft. The pressure is generated by restricting the airflow through the skirt. The fan inlet/outlet is not an important factor.

Oh; that appears to me to be a very different problem than the one you are solving. Powered ground effect would just be the opposite of a hovercraft. The pressure is generated by restricting the airflow through the skirt. The fan inlet/outlet is not an important factor.
I understand that the pressure is generated by restricting the airflow, but I think the fan is important as the magnitude of pressure generated has to, somehow, depend on the power of the fan. I am trying to think about an analytical way to model this problem and find a solution that's at least an order of magnitude accurate.

russ_watters
Mentor
I understand that the pressure is generated by restricting the airflow, but I think the fan is important as the magnitude of pressure generated has to, somehow, depend on the power of the fan.
All fans have a performance curve, with airflow and pressure varying against each other based on the restriction. Restrict the inlet or outlet and airflow drops while pressure rises.

For this application, the only significant restriction should be the slot. At the slot, you have a certain velocity and associated velocity pressure. under the car, the velocity is low and you have essentially all static pressure.
I am trying to think about an analytical way to model this problem and find a solution that's at least an order of magnitude accurate.
The problem as I described above is actually pretty simple. I suggest picking some performance parameters and solving it with Bernoulli's equation. There are some little intricacies, but we can walk through them.

All fans have a performance curve, with airflow and pressure varying against each other based on the restriction. Restrict the inlet or outlet and airflow drops while pressure rises.

For this application, the only significant restriction should be the slot. At the slot, you have a certain velocity and associated velocity pressure. under the car, the velocity is low and you have essentially all static pressure.

The problem as I described above is actually pretty simple. I suggest picking some performance parameters and solving it with Bernoulli's equation. There are some little intricacies, but we can walk through them.
Thanks for taking your time to help with this.

It does sound simple, I am not sure though how to use the pressure value from the fan performance curve. I thought it's the pressure "built up" by the fan downstream? Which means I cannot use it for Bernoulli equation between the slot and the fan face?

If I do I get a calculation as the one attached (with a drawing, fan here), but I do not "like it" - it assumes only the slot is in the low pressure zone?

Thanks,

#### Attachments

• PGE_calcs.xlsx
255.2 KB · Views: 180
• CCF14112018.pdf
1.1 MB · Views: 216
Last edited: