Equivalent fan sizing: Volumetric flow versus static pressure

[pipe2null]

I've struck out trying to figure out the required "Static Pressure" and "Volumetric flow" ratings for replacement fans to order as I rip out existing thermal management hardware in a piece of equipment I'm retrofitting.  Why?  Because I need a noise reduction from the current 90dBA down to a more pleasant 30ish dBA.  I do not know what numbers the original designers were working within, what ambient temps were assumed, nor have I found a datasheet on the primary Broadcom ASIC to know the safe operating temperature range.

The equipment has 2 part density fan cooling scenarios, same piece of equipment, and the OEM designers used the exact same fan model for both:
Nidec W40S12BS4A5-07
- 40mm x 40mm x 28mm
- 26.5 CFM volumetric flow
- 475 Pa static pressure

Scenario 1:
For the main board cooling, originally designed with a 1x5 array of Nidec fans, I'm replacing with (2x) 120mm x 120mm fans mounted and duct-ed into the chassis bays previously used by the 5 hot swap Nidec fans.  The original airflow design has very low impedance on both sides of the Nidec fans, low part density/etc, so I am assuming my replacement fans need to provide the max CFM of the original Nidecs at zero static pressure delta, so my new fans need 5x26.5CFM/2= 66.25 CFM minimum each.

BUT the cross sectional area of the 2x fan intake (fan blade OD= 110mm ID=40mm) gets reduced down to 5x ducts (appx 38mm x 36mm each).  The reduction ratio is about 6:1 with a 90 degree air flow direction change.  Which tells me that the "Static Pressure" rating for my replacement fans is probably an important consideration. 

So I think my replacement fan minimum spec should be 66.25CFM at the point of the P-Q curve that has Static Pressure rating equivalent to the pressure drop of my 6:1 reducing duct.  I've looked around, but I've not found the correct way to calculate this (or I didn't understand the equations well enough to use them).



Scenario 2:  The original power supply fan is exactly the same Nidec as all the other fans.  The difference in this scenario is the part density of the power supply is significantly higher than the main board.

I don't know what to do for this scenario.  With the higher part density, I think the Static Pressure rating of the original fans would probably be more important to stick with for my replacement than the volumetric flow of the original Nidec fan.  But 475Pa is pretty significant, and most quiet fans I've seen so far do not come anywhere close to this static pressure rating.




My proof of concept (the red plastic part in the first pic) works, replacing the 5x fans for cooling the main board reduced noise from 80dBA to 60dBA.  Replacing the PSU fan should further reduce noise to around 30dBA.  BUT the cheapo substandard fans I had laying around on a shelf are not beefy enough and I got a 10+ degree C temperature rise compared to stock fans with the equipment running at idle.  I could not find the datasheet for the Broadcom IC to know what the safe temperature range is, so I need to get beefier fans, but also need to get the quietest fans possible that still meet spec requirements (when I don't have the original spec requirements available).

I would appreciate direction on this to get across the finish line on my retrofit.  On a side note, if you have any book recommendations for this kind of thermal design, I'd appreciate it as reference for future projects.  Thanks!

[Gregg]

An inexpensive dual port digital manometer could tell you the stock fan’s static pressure in normal operation but placing the ports for measurement can be really tricky to get actual accurate pressure differential in situ.
https://www.amazon.com/dp/B07BDGWZLJ

[mag_therm]

The way I replaced a noisy  fan in old Spectrum Analyser, was to measure two heatsinks  and exit air with a thermocouple before starting, then measure again in same place after new fan was in.
I replaced an old type 4.25 by 1.5 inch muffin fan rated at 115 CFM and 47dBA
with a thinner fan 4.25 by 1 inch rated at 80 CFM and 30 dBA

One temperature rise was only about 7 Celsius with the old fan, and about the same with the new fan.
Unfortunately, the new fan, while sounding slightly less noisy overall, has an annoying high pitched resonance so I am not pleased with the afternoon's struggle to get the old one out and the new one in.

[pipe2null]

Good advice, thanks

Scenario 2: PSU fan measurement/replacement

I had to scratch my head on this for a long while, but I think I figured a way to indirectly measure the static pressure difference across the fan.  The PSU is dense and fully enclosed, so the only locations measurements can be feasibly taken is at the air intake and exhaust.

*If* I'm correct, please correct me if not:
delta P(total) = P(exhaust) - P(intake) = P(fan static pressure) - P(impedance pressure drop from airflow through PSU)
volumetric air flow (intake) = volumetric air flow (exhaust)

Measurement 1 (M1):
Use manometer to get delta P(total) and use anemometer to measure airflow into PSU fan intake.

Measurement 2 (M2):
Use an external "helper fan" to pre-accelerate airflow into the PSU fan's intake.  Use manometer and anemometer same as with Measurement 1.

Potentially incorrect theory, please correct if wrong:
I'm thinking that the pre-accelerated airflow should make the pressure difference across the internal PSU fan to be approximately zero, so the measured delta P(total) would only be the P(impedance pressure drop from airflow through PSU) scaled by anemometer reading difference between the 2 measurements.

So the calculation would be, please correct if wrong:
P(static fan pressure) = P(M1 total) + P(M2 total) * ( CFM(M1) / CFM(M2) )


For Scenario 1, if I am correct that my replacement fan only needs to provide enough static pressure to overcome the reduction in duct size and the 90 degree airflow direction change, I suppose I might be able to measure the impedance of the duct similarly to Scenario 2, but there should be a simple calculation for that rather than the somewhat complex method of measuring it.
I've dug around but the equations I've found are either extremely high level HVAC related or deep down into fluid dynamics where the "internet factoid explanation" mentions various constants but not really what they are or how you're supposed to use them to get a practical result.  Or even if those equations could be applied to a non-circular duct/orifice/etc.


Does this seem vaguely in the right ballpark?  I'm trying to make sure I understand this since I need to repeat the exercise on several other pieces of equipment, each with their own unique challenges...  heh.  Thanks

[mag_therm]

Your final function:
turbulent incompressible  flow the pressure drop is proportional to the square of the flow velocity

delta_p = K * flow_velocity_mean ^ 2

Where K contains friction coefficients, density etc

So you need 4 times of a pressure increase to double the flow.
Further, the flow velocity will probably be non linear over your aperture.

And then the heatsink temperature rises are not linearlly varying with the flow.

Since you have a number of "similar but  different" cases,
I wonder if this  economically  solved as a 2D simplification in a fluid dynamic FEM coupled to a thermal FEM.

Or perhaps build a cardboard model to try the  different fans.
I don't think simple analytical estimations are going to be very accurate.