Centrifugal Pumps Design and Application 2nd ed - Val S. Lobanoff, Robert R. Ross (Butterworth-Heinemann, 1992)

440 Centrifugal Pumps: Design and Application
tially greater than the induced level. Multiples of the resonant modes can
be excited; however, the multiple wave length resonances generally decrease
in severity at the higher multiples because more acoustic energy is
required to drive the higher frequency modes.
The acoustic resonances of piping systems for constant-speed pumps
can usually be adjusted to detune them from the pump operating speed
and vane-passing frequencies and avoid pulsation amplification. However,
if the pump is operated over a speed range, the frequency band of
the excitations is widened, requiring more careful placement of acoustic
resonances.
Actual piping systems are more complex than the simple quarter-wave
and half-wave elements. A typical piping system with tees, flow control
valves (restrictions) pipe size changes, vessels, etc., will have a complicated
pattern of pressure pulse reflection patterns (standing waves).
Some of the standing waves may be amplified and others, attenuated.
Each of the standing waves will have a particular acoustic length pertaining
to a pipe segment between two end conditions. Calculations of the
acoustic resonances of a complex piping system require the use of computer
codes to consider the acoustic interaction between the pump and its
piping system,
Instabilities. Hydraulic instabilities [14] can be a result of the dynamic
interaction of a centrifugal pump (particularly the head-flow characteristics)
and the acoustic response of the piping system. A centrifugal pump
operating at constant speed in a piping system may amplify or attenuate
pressure disturbances that pass through the pump. The action of the
pump in causing amplification or attenuation of this energy is quite complex,
but basically is dependent upon:
• The head curve slope and operating point
« System flow damping (in the piping)
» The existence of strong reactive resonances in the piping, particularly
if they coincide with vortex frequencies
• The location of the pump in the standing wave field (i.e., at a velocity
maximum rather than a pressure maximum)
» The compressibility (bulk modulus) of the liquid
Pulsations can be amplified by the piping system and cause a variety of
problems such as damage to pump internals, torsional reactions, cavitation,
vibrations at elbows, valves, or other restrictions. The amplitude of
the pulsation is dependent upon operating conditions such as speed, flow
rate, and losses (pressure drop) as well as fluid properties and acoustic