Article #8:
Unstable Curves – Tell Me More!
This Article was
initiated as a response to a question from one of our readers:
Can you tell me more about unstable curves? Optimal designs of
centrifugal pumps result in unstable curves (near to dead head), but in which
cases is this creating a problem, and what can you do to resolve other than
re-designing the pump?
Walter A. Koch
VERDER Group, Liquids Division,
Dear Walter:
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. API 610 even states that “…pumps that have
stable head/capacity curves (continuous rise to shutoff) are preffered 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…”
Fig. 1 Stable (left)
and Unstable (right) H-Q curves
A centrifugal pump
operates at the intersection point of a pump curve and a 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). Or, it can also be a
combination of both:
Fig. 2 A pump operates at the intersection of a pump
H-Q curve and a system curve…
If the pump curve is stable,
there is always a unique point (“A”) – an intersection of a pump curve and a
system curve. If the pump curve is unstable, the region between “B” and
“F” has two possibilities – at either flow Qb, or Qf :
Fig. 3 Stable
curve (left) has a single definition of an intersection between a pump curve
and a system curve. Unstable curve (right) has two flows where a pump can
operate, at the same head.
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 on-line. Starting of a pump is usually
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, say at point “C” (where
curve is unstable), the system head is Hc, - i.e. higher then the shutoff head
Hf, which is what Pump-2 will generate at first, when it starts. Therefore
Pump-2 can not open the check valve, which is held closed by the higher
pressure Hc – imposed by the already-running Pump-2.
Fig. 4 Two
pumps in parallel – pump P2 is having trouble starting…
Imagine next that
several pumps are already 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 will
now “push” the 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. Operator, only noticing a total increase in flow, would not even
know of this happening, - while the Pump-2 “unexplainably” begins to vibrate,
shake, and possibly fail:
Fig. 5 Pump P1
is forcing pump P2 out… Not a nice thing…
An excellent source
of reference on this, with a more detailed explanation of unstable curves, is
in a book (a “classic”!) by A.F. Stepanoff, “Centrifugal and axial Flow Pumps”,
John Wiley publication, 2nd Edition, page 293. There, 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
which 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 same purpose. Long piping can also do the same.
Stepanoff also
provides recommendations:
By-passing 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 (see separate article on Ns and Nss definitions), such as axial
flow pumps, the instability happens at flows substantially closer to 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:
Fig. 6 High
specific-speed (Ns) pumps have instability starting much closer to BEP, as
compared to lower specific-speed units
As the reader has
pointed out, and it is true - that the “best” designs, with regard to
efficiency, often end up with unstable curves. Such is the nature of
hydraulics! - of the pumping machinery.
A better and more practical compromise is not to “push” the efficiency overly
high at a single BEP (best efficiency) point, but to have a more “balanced”
design, where efficiency may still 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. As a practical matter, small pump, however, 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, they can be
started at more open valve. Since the energy level is small enough, and the
duration is short, as compared to a much more powerful units (such as boiler
feed pump, circulating vertical pumps, etc.), there is seldom (but could
happen!) a problem with these pumps.
By note to the
readers – we welcome any additional comments on the subject. If anyone would
like to expand or add on a personal experience regarding curves instability and
practical ways of how it was handled – please let us know, so that we can add
your contribution in the next edition.