Will Running Pumps Slower Help NPSH problem?
Dr. Lev Nelik, P.E., APICS
Pumping Machinery, LLC
If your immediate answer was yes, think again, as you might be surprised. Sometimes running the pumps faster can actually help avoid cavitation. How so?
To understand it, we need to first go back to the topic of affinity laws. As far as pump performance, the flow scales up or down directly with speed ratio, and the head as a square of that ratio. Consider Fig. 1. At 400 RPM, a pump’s BEP is at 90,000 gpm, and head at about 64 feet. As RPM drops in half, BEP flow halves as well (45,000 gpm), and head is reduced as (200/400)2 = 0.25 x 84 = 21 feet. In between (300 RPM) there is a similar relationship. So far, nothing spectacular.
The NPSHr curve scales similarly to head, i.e. as a squire of the speed RPM ratio. For most pumps, NPSHr curve stays mostly flat at low flow, then begins to slowly rise toward the BEP flow, and is taking off quickly past the BEP. It is difficult to mathematically describe the formula for the NPSHr curve. Fig. 2 shows four different shapes the NPSHr curve could have: linear (gradually and uniformly rising from zero towards higher flow, H=aQn, n=1), as a basic second order parabola (n=2), a third order cubic parabola (n=3), as well as a typical actual shape, which is a combination of all three, depending at which part of the flow segment (low flow, BEP region, and past the BEP) we are considering its behavior.
If behavior of the NPSHr versus flow was linear, then, as Fig. 3 shows, affinity law, as applied to the NPSHr curve, would scale down flow (directly with RPM) and the NPSHr (as a square of RPM), such that a lower speed NPSHr curve would sit entire below a higher speed curves. Thus, as BEP point would move to lower flow and lower heads, and so a BEP point on the NPSHr curve would move to lower flow and lower NPSHr. However, for a given value of the available NPSHA (32 feet in our example), a lower speed NPSHr curve would intersect the NPSHa line at a proportionally higher (percentage of corresponding BEP) flow. For example, at 400 RPM, this pump would be able to run out only to 72% of the BEP flow, at 300 RPM the pump can run out to 124% flow, and at 200 RPM even higher, to 233% flow. If the actual pump had such linear shape of the NPSHR curve with flow, then running the pump slower, against a given limitation of the NPSHA, would indeed help cavitation problem. Thus, at 400 RPM the pump could run out to 65,000 gpm, while at 200 RPM - way more, to 105,000 gpm – which is probably what you intuitively thought when you answered “yes” to a question at the beginning of the article.
Unfortunately, this is not how actual pumps behave as far as the shape of their NPSHr curves.
Consider one more example, if NPSHr is not a liner function of flow, but a regular parabola (n=2), as shown on Fig. 4. Here, the NPSHr curve does not change with speed at all, because the affinity laws (quadratic in nature) reduce the flow and head curve at the same rate as the NPSHr curve points scale down. Now, point “X’ (running out of NPSHA) is at the same flow (80,000 gpm), but it is 89% of the BEP at 400 RPM, 119% of the BEP at 300 RPM, and 178% of the BEP at 200 RPM. So now, running pumps slower or faster does not change things – either way, an 80,000 gpm is the limit, beyond which we run out of NPSHA, at any speed.
But what if the NPSHr behaves much “faster rising” as compared to the affinity laws scaling of flow and NPSHr points? On Fig. 5, a 400 RPM allows us to run out to 98% of the BEP flow, to about 86,000 gpm, while at lower speed (200 RPM), we can only run out to 65,000 gpm, which is 143% of the BEP at low speed.
The actual pump NPSHr curves behave closer to the cubic parabola, and even faster rising curve beyond the BEP, a phenomenon called “NPSHr stonewalling”, as shown on Fig. 6. Here, a faster running pump allows flow to roughly 95,000 gpm (103% of BEP flow at that speed), while at 200 RPM it will cavitate even below 60,000 gpm, a 129% of the 200-RPM flow. Thus, if, say, a 80,000 gpm flow was desired, speeding the pump up to 400 RPM will help, while at 200 ROM, or even 300 RPM, it will cause cavitation.
Surprised? Well, the answer to this counter-intuitive behavior, again, is in the shape of the NPSHr curve past the BEP point. So, why is NPSHr stonewalls past the BEP, but is relatively well behaved, even flat below the BEP? We will answer this question the next time.
As usual, a parting quiz: is NPSHr curve truly flat below the BEP flow? Give it a shot and a correct answer – for a free admission pass to the next Pump School session.
To learn more, sign up for one of the upcoming Pump School 2-day sessions, schedule of which is posted at Pumps & Systems News section, or at www.pumpingmachinery.com/pump_school/pump_school.htm.
Dr. Lev Nelik, P.E., APICS
Pumping Machinery, LLC
Pump School Training Services