1 fan vs 2 fans vs large fans (theory)

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datapappan
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1 fan vs 2 fans vs large fans (theory)

Post by datapappan » Thu Aug 12, 2010 3:05 am

Here's a rather theoretical post on fans, flow, pressure and noise, building on the sticky Are 2 fans noisier than 1 blowing the same CFM?
(In that topic I wrongfully posted some fauly conclusions, which I hope to rectify herein.)

Summary:
2 fans in parallel are more quiet than one (especially for less restricted air paths)
Larger fans are more quiet than smaller (especially for less restricted air paths)
2 small fans in parallell are more quiet than one large fan (especially for less restricted air paths)

Background (Fan and air path theory, skip if you know this already)
Figure 1 show the basic relationship between flow and pressure in a system with a fan pushing air through an air path (eg a PC case). At the operating point there's equilibrium between what head the fan can give and the pressure loss in the air path. (Flow rate on horizontal axis, pressure on vertical axis.)
Image
(Figure 1)

Figure 2 illustrates what happens to flow and pressure if you lower the voltage (and hence the RPM) to the fan. Both head and pressure loss is lowered in relation to the square of the flow rate.
Noise for the new op. point is lowered by [50 x log (RPM2/RPM1)], in this situation with only half of the RPM this calculates to 15 dB.
Image
(Figure 2)

1 fan vs 2 fans
Figure 3 shows the comparison between using two fans in parallel vs only one fan. Here the two fans work at half RPM, ie 15 dB less than at nominal RPM - but since they are two, you have to add them, which dB calculates as [ Lp + Lp = Lp + 3 dB ], equalling a 12 dB noise drop total.
With a single fan operating in the same point, voltage has to be lowered to 9.3 V, giving a noise drop of 5 dB. So, we can conclude that for this particular case 2 fans give less noise than one.
Image
(Figure 3)

Figure 3A shows what happens when impedance is variated - as impedance goes up, the single fan is going slower and slower to meet the operating point, whereas the two parallel fans are operating at the same speed in each case.
So, the analysis would be that noise drop for the single fan will increase as impedance is increased, finally matching and eventually superceding the noise of the two fans.
This would in this example happen when you can run the single fan at 7 V, and still meet the same operating point as the two fans. You can see that point, where the dashed curve intersects the solild curve of the parallell curves. This point is well above the stall area, where it's not recommended to use the fan at all (please don't ask me why, but I've read it somewhere). All in all, I think it's safe to say that 2 fans are less noisy than 1 fan.
Image
(Figure 3)

Small fans vs larger fans
Figure 4 finally gives the same comparison as before, but for an 80 mm and an 120 mm fan (for these products the 80 mm gives 19 dB(A), and the 120 mm gives 26 dB(A)).
The relation here is that the larger fan is quieter, more so as impedance lowers. Break-even would be with 120 fan at 8.3 V, but again this point is above the stall area (see figure 4A).
Image
(Figure 4)
Image
(Figure 4A)

2 small fans vs 1 large fan
Since it seems that 1 small fan is noisier than both 2 small fans in parallel, as well as 1 large fan, the natural question is, who wins in the battle between 2 small and 1 large fan?
Figure 5 shows how they compare, and also where the break-even occurs for these particular fans (2 80 mm at 19 dB = 22 dB; difference cf to 120 mm 26 - 22 dB = 4 dB, corresponding to 120 mm fan at 10V). The curves intersect at two points, one pretty high up in impedance, and on above the stall area.
So, the final winner is 2 small fans!
Image
(Figure 5)

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I hope this will shed some light on the recurring question of which setup gives the least noise. One question remains though: what's the real-life impedance of PC cases? I've made a tentative measure here at my office, giving 2 Pa pressure drop for the inlet grille at idle, and incidently the same on load, seems this Dell machine with quad CPU and graphics cool really well. What I read from other places is that impedance for cases are very low, so the conclusion is: 2 small fans are better than 1 large.

/d

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Disclaimer:
I have not taken into account any change in noise when the fan operates at higher pressures, nor the effect of lowered perceived noise when revving fans down (as per MikeC:s post).

datapappan
Posts: 199
Joined: Wed Nov 10, 2004 1:44 pm
Location: Sweden

Post by datapappan » Thu Aug 12, 2010 10:02 am

OK, now I'm going overboard with this...

The next natural question for me would be: if 2 fans ar better than one, aren't 3 or more even better?

Figure 6 and 6A shows 2, 3 and 4 fans (120 mm) @ 1/2, 1/3 and 1/4 of 12 volts, with their corresponding noise values. It also shows the curves for a single fan, undervolted to match the noise levels of those setups.
You can see that in the 1-3 Pascal pressure area, the 2 fan setup delivers more flow at the same noise level.
Image
(Figure 6)
Image
(Figure 6A)


Notes on this:
1. It's usually hard to start fans reliably below 5V. (You could limit the undervolting to 5V even for 3 and 4 fans, and find a new spot for break-even with the single fan - I guess the thery would hold true anyway, just at a slightly higher noise level.)
2. Noise levels below 5 dB are probably (and theoretically) drowned out by background noise (typically above 15 dB).
3. Undervolting severly limits fan head pressure, as you can see in fig 6A. The system curves I've put are supposedly true to typical PC case impedances, and won't cap the fan capacity (for CPU heatsinks and PSU innards we have a different story).

/d

tay
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Post by tay » Thu Aug 12, 2010 12:18 pm

Thumbs up to this type of analysis. Nice looking plots too.

nomoon
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Post by nomoon » Thu Aug 12, 2010 1:49 pm

Interesting. I like these kinds of topics. Mike Chen made a related posting here Are 2 fans noisier than 1 blowing the same CFM?. Mike measured the noise from two fans, and his measurements showed only a one db increase in noise instead of 3 db.

I made a comment here (Passive CPU cooling not necessarily the quietest solution). about the assumption that 2 identical noise sources will raise the noise by 3 db:
The 3 db assumption assumes a noise that is spread across a spectrum of wavelengths, where some wavelengths interfere constructively and others destructively at a fixed point in space. If I recall correctly, the 3 db increase will occur if the the noise power is spread across the spectrum in a white noise distribution. If you integrate power over the spectrum, the net increase will be 3 db. Here is a discussion by Mike Chin where he made measurements. I suspect that the apparent discrepancy with Mike's measurements is because of the spectral distribution of noise for the fan is not the same as for white noise. If fans produced white noise, then he might see the 3 db increase in noise when a second fan was added. The end result is that running multiple fans will often provide a quieter solution than running a single fan.

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