Unstable Curves

April 22, 2003
Pump Performance

A "stable" curve is very important for a pump operation, especially for pumps operating in parallel. The higher the energy level and the more critical an installation is, the more this could become an issue. American Petroleum Institute (API) spec 610 even states that "pumps that have stable head/capacity curves (continuous rise to shutoff) are preferred for all applications and are required when parallel operation is specified. When parallel operation is specified, the head rise shall be at least 10 percent of the head at rated capacity [H-Q]...." (See Figure 1.)

A centrifugal pump operates at the intersection point of a pump curve and system curve. A system curve is a parabola starting from zero in case of mainly friction losses (long pipe with restrictions such as valves, fittings, etc.) or a parallel line in case of mainly static head (pumping up to a vessel). It also can be a combination of both. (See Figure 2.)

If the pump curve is stable, there always is a unique point (A) an intersection of a pump curve and system curve. If the pump curve is unstable, the region between B and F has two possibilities at either flow Qb or Qf. (See Figure 3.)

Imagine a parallel operation, with two pumps piped to a common header. Suppose Pump 1 is running and Pump 2 is idle, ready to be brought online. The starting of a pump usually is done near the shut-off (valve just slightly cranked open) in order to minimize motor load. If Pump 1 is running in a "funny" region, for example, at point C (where the curve is unstable), the system head is Hc, (i.e., higher than the shutoff head Hf, which is what Pump-2 will generate at first when it starts). Therefore, Pump 2 cannot open the check valve, which is held closed by the higher pressure Hc imposed by the already-running Pump 2. (See Figure 4.)

Imagine next that several pumps already are running in parallel. Since they discharge to a common header, their discharge head must be the same. However, each pump may have different flows--either Qc, or Qe. If a plant operator wants to increase the total flow and opens the discharge valve more, Pump 1 will increase its flow, and its head will decrease (Qcc, Hcc). The new system head Hcc now will "push" Pump 2 to lower flow (Qee). Eventually, a "stronger" pump may completely "take out" the weaker pump to near or at the shut-off head. The operator, only noticing a total increase in flow, would not even know of this happening, while Pump 2 "unexplainably" begins to vibrate, shake and possibly fail. (See Figure 5.)

As an excellent source of reference on this, a book by A.F. Stepanoff, Centrifugal and Axial Flow Pumps, (John Wiley publication, 2nd Edition, page 293) offers a more detailed explanation of unstable curves. The author also addresses the system conditions that would contribute to or further aggravate the situation.

*                The mass of water must be free to oscillate, a typical scenario in boiler feed applications.

*                There must be a member in the system that can store and give back the pressure energy or act as a spring in a water system. In a boiler feed pump cycle, the elastic steam cushion in the boiler also serves the same purpose. Long piping also can do the same.

Stepanoff also provides recommendations.

*                Bypassing part of the capacity to the suction supply tank.

*                Automatic capacity governor near the boiler with very slight throttling at the pump to stop H-Q swings.

*                Braced piping, except for the provision for heat expansion.

*                Avoid operation near critical point.

For higher specific-speed pumps such as axial flow pumps, the instability happens at flows substantially closer to its best efficiency point (BEP), as compared to lower specific speed pumps (such as boiler feed). However, this instability is local, and the curve continues to rise again after the local region of instability. (See Figure 6.)

The "best" designs with regard to efficiency often end up with unstable curves. Such is the nature of hydraulics and pumping machinery. A better and more practical compromise is not to "push" the efficiency overly high at a single best efficiency point but to have a more "balanced" design where efficiency still may be good overall but the curve is stable. This is because, in practice, it is almost impossible to limit a pump operation to a very near region of flow.

All pumps, regardless of their energy level, may experience these difficulties with curve instability. However, small pumps such as inexpensive commercial units or even small pumps for chemicals such as ANSI usually either do not operate in parallel too often or, if they do, can be started with a more open valve. Since the energy level is small enough and the duration is short as compared to a much more powerful unit such as boiler feed pump or circulating vertical pumps, there seldom is a problem with these pumps.

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