Fan Laws / Affinity Laws

[Rick99]

I see some engineers use a 2.5 exponent for calculating horsepower using the affinity laws instead of 3.0 to account for inefficiencies not captured in the fan laws.

Is there a technical reference for taking this position?

 

[Ryno]

I can not find a reference for fan affinity law using 2.5 as the power versus 3. Fan laws are simplications of the similarity laws, but even using these, I can not find how to get a power of 2.5.

 

[PacificSteve]

No real reference that I have ever heard of. I happen to like and use the 2.5. Some people have a problem with this...saying that a 2.5 exponent "doesn't make sense". They use 2.0, which greatly underestimates the potential for savings using variable speed drives. A good guess is better than a bad guess.

Steve

 

[electricpete]

I've never heard of it but I can guess a rationale for this approach.

As pump speed increases for a fixed fluid system load, both the dp and flow-rate increase. But both dp and flow-rate contribute to internal losses which reduce the pump output below ideal. The increased dp causes increased internal leakage which reduces external flow below ideal. The increased flow causes increased headloss within the pump components which decreases pump flange dp below ideal.

Just a guess. Is this similar to the rationale that you have heard or are there other reasons for this adjustment?

 

[Rick99]

Since posting the question in July, I have found the following information:

The affinity laws are valid only under constant efficiency conditions. When an impeller diameter is cut it increases the radial clearance between the impeller and the volute. This results to increased losses due to recirculation. Changes in pump speed, up or down, using a VFD results in similar changes in recirculation losses, as well as changes in operating efficiency.

The affinity laws are most commonly used to derive energy-savings estimates from vsd-controlled devices in comparison with other types of control devices. However, the affinity laws are the frequent subject of debates. The argument is that in an actual situation, the energy savings of a fan or a pump with vsd control are not proportional to the cubic relationship of the speed.

Many individuals argue that it is more of a square relationship, to be conservative. Others would use a 2.x exponent, where 0 = x = 9. The value of x depends on the user, and is often based on the experience of the engineer doing the calculations. There are not hard facts to justify the figure, and there is no consensus on what the exponent should be.

Credit to: Tumin Chan, for R.G. Vanderweil Engineers, Inc. (Boston)