Douken, (sed2),
If I may. He's saying, when mfgrs give a minimum flow, it is customary for them to give that value as a percentage of BEP rated flow, so I think the question is, "what is the pump's minimum flow at a reduced rpm setting".
Douken, yes, its typically assumed to follow the reduced equivalent "BEP-eq" at a lower RPM.
I think that its true in general, but have doubts as to how far down into the lower flows that the affinity laws can be extended. I think other factors can enter at lower flows that obviously would cause "minimum flows" to approach some limiting value > 0. The lubrication effect, for example, as well as some others.
Pumps components are hydraulically optimized for BEP conditions, which define the differential head and the flowrate, so if one wants to deviate from the BEP condition, one should try to evaluate possible effects. As I understand this, determining a minimum flowrate should be based on 3 primary factors, temperature, lubrication and unbalanced forces.
Pumps components are hydraulically optimized for BEP conditions, which define the differential head and the flowrate, so we should assume that any deviation from that operating point will result in reduced performance in one respect or another.
The reduced performance in terms of lubrication should be evaluated. At reduced rpm, will there be reduced lubrication? Flow through the pump is reduced linearly with rpm, so yes it is possible that lubrication will be reduced as well, depending on the type of lubrication provided for the particular pump. If lubrication is dependent on internal flowrate, beware. However, as rpm is reduced, it is possible that friction is reduced. If friction is reduced by the square of the speed, a net gain in lubrication effects could be possible.
The reduced performance, in the case of pressure imbalance might best be correlated to increased bearing wear, for example, due to higher thrusts in the axial direction, and increased lateral loads to the shaft. In the case of a variation in RPM, one should therefore examine the resulting force imbalances in relation to their values at BEP. Are imbalanced forces reduced proportionally with reduced rpm? No. Discharge pressure would most likely be reduced by the square of the speed, and assuming suction pressure remained more or less constant, a higher net thrust force could be developed towards the discharge end, unless the pump somehow compensated for the change in the differential pressure at the new operating point.
Lastly, temperature build-up at lower flowrates should be evaluated. Temperature is a function of both hydraulic efficiency and the cooling effect of fluid flow through the pump. At a lower rpm a lower product flowrate with consequent lesser cooling action would be expected. Efficiency may also vary. While efficiency is generally assumed to follow the pump affinity law, that may not be entirely the case, since pumps with higher BEP rpms typically reach higher efficiencies, should not some reduction in efficiency somehow be expected to occur with a VSD reduced rpm? I expect that there is some, but have not tried to evaluate how to predict what it would be. In any case, at very low flows, in the range of what would be a typical "minimum flow" region, the affinity laws might not be entirely valid for correlating efficiency, so I'm hesitant to push a possible analytical solution, but believe it could be at least partially evaluated with a heat balance calculation. If you assumed that efficiency followed the affinity laws, the mfgr's minimum BEP flowrate would follow the "BEPr" flow wher r=> BEP op point at a reduced rpm. There does appear to be a limitation to the validity of the assumption that efficiency follows affinity laws, since the frictional component of power at shutoff on the BEP curve is not entirely dependent on rated rpm. The static friction component of total friction, would not necessarily change in total proportion to lower rpm's, so caution at low flows would be prudent.
I would really like to hear from some pump designers on this subject myself, but until they say otherwise, then I certainly beleive you are correct, at least until you approach the limitations I listed above.
