Unstable Curves

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

*                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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