NPSH

In a hydraulic circuit, net positive suction head (NPSH) may refer to one of two quantities in the analysis of cavitation:

1. The Available NPSH (NPSH_A): a measure of how close the fluid at a given point is to flashing, and so to cavitation.
2. The Required NPSH (NPSH_R): the head value at a specific point (e.g. the inlet of a pump) required to keep the fluid from cavitating.

NPSH is particularly relevant inside centrifugal pumps and turbines, which are parts of a hydraulic system that are most vulnerable to cavitation. If cavitation occurs, the drag coefficient of the impeller vanes will increase drastically - possibly stopping flow altogether - and prolonged exposure will damage the impeller.

NPSH in a Pump

A simple hydraulic pumping circuit. Point 0 is the free suction surface, and point i is the inlet of the impeller.

In a pump, cavitation will first occur at the inlet of the impeller.^[1] Denoting the inlet by i, the NPSH_A at this point is defined as:

$NPSH_A = \left( \frac{p_i}{\rho g} + \frac{V_i^2}{2 g} \right) - \frac{p_{v}}{\rho g}$

where $p_i$ is the absolute pressure at the inlet, $V_i$ is the average velocity at the inlet, $\rho$ is the fluid density, $g$ is the acceleration of gravity and $p_v$ is the vapour pressure of the fluid.

Applying Bernoulli's principle from the suction free surface 0 to the pump inlet i, under the assumption that the kinetic energy at 0 is negligible, that the fluid is inviscid, and that the fluid density is constant:

$\frac{p_{0}}{\rho g} + z_{0} = \frac{p_i}{\rho g} + \frac{V_i^2}{2 g} + z_i + h_f$

Using the above application of Bernoulli to eliminate the velocity term and local pressure terms in the definition of NPSH_A:

$NPSH_A = \frac{p_{0}}{\rho g} - \frac{p_{v}}{\rho g} - ( z_i - z_{0} ) - h_f$

This is the standard expression for the Available NPSH at point. Cavitation will occur at the point i when the Available NPSH is less than the NPSH required to prevent cavitation (NPSH_R). For simple impeller systems, NPSH_R can be derived theoretically,^[2] but very often it is determined empirically.^[3]Note NPSH_A and NPSH_R are in absolute units and usually expressed in "ft abs" not "psia".

Experimentally, NPSH_R is often defined as the NPSH₃, the point at which the head output of the pump decreases by 3% at a given flow due to reduced hydraulic performance. On multi-stage pumps this is limited to a 3% drop in the first stage head.^[4]

NPSH in a Turbine

The calculation of NPSH in a reaction turbine is different to the calculation of NPSH in a pump, because the point at which cavitation will first occur is in a different place. In a reaction turbine, cavitation will first occur at the outlet of the impeller, at the entrance of the draft tube.^[5] Denoting the entrance of the draft tube by e, the NPSH_A is defined in the same way as for pumps:

$NPSH_A = \left( \frac{p_e}{\rho g} + \frac{V_e^2}{2 g} \right) - \frac{p_{v}}{\rho g}$^[6]

Applying Bernoulli's principle from the draft tube entrance e to the lower free surface 0, under the assumption that the kinetic energy at 0 is negligible, that the fluid is inviscid, and that the fluid density is constant:

$\frac{p_e}{\rho g} + \frac{V_e^2}{2 g} + z_e = \frac{p_{0}}{\rho g} + z_{0} + h_f$

Using the above application of Bernoulli to eliminate the velocity term and local pressure terms in the definition of NPSH_A:

$NPSH_A = \frac{p_{0}}{\rho g} - \frac{p_{v}}{\rho g} - ( z_e - z_{0} ) + h_f$

Note that, in turbines minor losses ($h_f$) alleviate the effect of cavitation - opposite to what happens in pumps.

NPSH design considerations

Vapour pressure is strongly dependent on temperature, and thus so will both NPSH_R and NPSH_A. Centrifugal pumps are particularly vulnerable especially when pumping heated solution near the vapor pressure, whereas positive displacement pumps are less affected by cavitation, as they are better able to pump two-phase flow (the mixture of gas and liquid), however, the resultant flow rate of the pump will be diminished because of the gas volumetrically displacing a disproportion of liquid. Careful design is required to pump high temperature liquids with a centrifugal pump when the liquid is near its boiling point.

The violent collapse of the cavitation bubble creates a shock wave that can carve material from internal pump components (usually the leading edge of the impeller) and creates noise often described as "pumping gravel". Additionally, the inevitable increase in vibration can cause other mechanical faults in the pump and associated equipment.

Relationship to other cavitation parameters

The NPSH appears in a number of other cavitation-relevant parameters. The suction head coefficient is a dimensionless measure of NPSH:

$C_{NPSH} = \frac{g NPSH}{n^2 D^2}$

Where $n$ is the angular velocity (in rad/s) of the turbomachine shaft, and $D$ is the turbomachine impeller diameter. The Thoma cavitation number is defined as:

$\sigma = \frac{NPSH}{H}$

Where $H$ is the head across the turbomachine.

Some general NPSH Examples

(based on sea level).

Example 1: A tank with a liquid level 2 metres above the pump intake, plus the atmospheric pressure of 10 metres, minus a 2 metre friction loss into the pump (say for pipe & valve loss), minus the NPSHR curve (say 2.5 metres) of the pre-designed pump (see the manufacturers curve) = an NPSHA (available) of 7.5 metres. (not forgetting the flow duty). This equates to 3 times the NPSH required. This pump will operate well so long as all other parameters are correct.

Remember that (+ or -) flow duty will change the reading on the pump manufacture NPSHR curve. The lower the flow, the lower the NPSHR, and vice versa.

Lifting out of a well will also create negative NPSH; however remember that atmospheric pressure at sea level is 10 metres! This helps us, as it gives us a bonus boost or “push” into the pump intake. (Remember that you only have 10 metres of atmospheric pressure as a bonus and nothing more!).

Example 2: A well or bore with an operating level of 5 metres below the intake, minus a 2 metre friction loss into pump (pipe loss), minus the NPSHR curve (say 2.4 metres) of the pre-designed pump = an NPSHA (available) of (negative) -9.4 metres. NOW we add the atmospheric pressure of 10 metres. We have a positive NPSHA of 0.6 metres. (minimum requirement is 0.6 metres above NPSHR), so the pump should lift from the well.

Now we will try the situation from example 2 above, but will pump 70 degrees Celsius (158F) water from a hot spring, creating negative NPSH.

Example 3: A well or bore running at 70 degrees Celsius (158F) with an operating level of 5 metres below the intake, minus a 2 metre friction loss into pump (pipe loss), minus the NPSHR curve (say 2.4 metres) of the pre-designed pump, minus a temperature loss of 3 metres/10 feet = an NPSHA (available) of (negative) -12.4 metres. NOW we add the atmospheric pressure of 10 metres and we have a negative NPSHA of -2.4 metres remaining.

Remembering that the minimum requirement is 600 mm above the NPSHR therefore this pump will not be able to pump the 70 degree Celsius liquid and will cavitate and lose performance and cause damage. To work efficiently, the pump must be buried in the ground at a depth of 2.4 metres plus the required 600 mm minimum, totalling a total depth of 3 metres into the pit. (3.5 metres to be completely safe).

A minimum of 600 mm (0.06 bar) and a recommended 1.5 metre (0.15 bar) head pressure “higher” than the NPSHR pressure value required by the manufacturer is required to allow the pump to operate properly.

Serious damage may occur if a large pump has been sited incorrectly with an incorrect NPSHR value and this may result in a very expensive pump or installation repair.

NPSH problems may be able to be solved by changing the NPSHR or by re-siting the pump.

If an NPSHA is say 10 bar then the pump you are using will deliver exactly 10 bar more over the entire operational curve of a pump than its listed operational curve.

Example: A pump with a max. pressure head of 8 bar (80 metres) will actually run at 18 bar if the NPSHA is 10 bar.

i.e.: 8 bar (pump curve) plus 10 bar NPSHA = 18 bar.

This phenomenon is what manufacturers use when they design multistage pumps, (Pumps with more than one impeller). Each multi stacked impeller boosts the previous impeller to raise the pressure head. Some pumps can have up to 150 stages or more, in order to boost heads up to hundreds of metres.

References

1. Frank M. White Fluid Mechanics, 7th Ed., p. 771
2. Paresh Girdhar, Octo Moniz, Practical Centrifugal Pumps, p. 68
3. Frank M. White Fluid Mechanics, 7th Ed., p . 771
4. http://www.pumps.org/content_detail.aspx?id=1770
5. Cavitation in reaction turbines, http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/machine/ui/Course_home-lec31.htm
6. Frank M. White Fluid Mechanics, 7th Ed., p. 771