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

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434 <strong>Centrifugal</strong> <strong>Pumps</strong>: <strong>Design</strong> <strong>and</strong> <strong>Application</strong><br />

Generation Mechanism<br />

Table 18-1<br />

Pulsation Sources<br />

Excitation Frequencies<br />

1. <strong>Centrifugal</strong> / = *£<br />

Compressors & <strong>Pumps</strong><br />

/ = sg* B = Number of Blades<br />

/ = asf. v = Number of Volutes<br />

or Diffuser Vanes<br />

2. Flow Excit<strong>ed</strong><br />

A. Flow through / = Sjj S = Strouhal Number<br />

Restrictions = .2 to .5<br />

01 Across V = Flow Velocity, ft/sec<br />

Obstructions<br />

D = Restriction<br />

diameter, ft<br />

B. Flow Past Stubs / = Sg S = .2 to .5<br />

C. Flow Turbulence / = 0 - 30 Hz<br />

Due to Quasi<br />

(Typically)<br />

Steady Flow<br />

D. Cavitation <strong>and</strong> Broad B<strong>and</strong><br />

Flashing<br />

Even with the pump operating at its best efficiency point <strong>and</strong> proper<br />

conditions (NPSH, etc.) pulsations may be generat<strong>ed</strong> by high-flow velocities<br />

<strong>and</strong> turbulence at the vane tips or at the cutwater. As operating conditions<br />

deviate from the design conditions, more sources may come into<br />

play such as cavitation, recirculation, flow instabilities, etc.<br />

These pulsations can interact with the hydraulic or acoustic natural frequencies<br />

of the piping system to amplify the pulsation. Acoustic natural<br />

frequencies in piping systems are a function of the fluid properties, the<br />

piping, <strong>and</strong> pump geometry. The acoustic interaction can be compar<strong>ed</strong> to<br />

the action of an organ pipe resonance where turbulence produc<strong>ed</strong> at the<br />

lip is amplifi<strong>ed</strong> into an audible tone. Similarly, pulsations from the pump<br />

are amplifi<strong>ed</strong> into pressure pulsations that react at elbows, restrictions,<br />

clos<strong>ed</strong> valves, <strong>and</strong> piping size changes to cause dynamic shaking forces.<br />

This conversion of hydraulic energy into mechanical forces can result in<br />

vibrations of the pump, piping, <strong>and</strong> their support structure.<br />

In the design stage, the acoustical natural frequencies of piping systems<br />

can be calculat<strong>ed</strong> using either digital [13] or analog [14] modeling

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