Why NPSHR Changes With Impeller Diameter?

Introduction

Confusion sometimes results when reviewing published NPSHR curves.  This is especially true when faced with trimming the impeller diameter to match changing operating conditions.  A well known fact is that the head-flow relationship varies with the diameter.  This can be accurately approximated by the affinity laws.  However, what happens to the NPSHR-flow relationship when the diameter changes?  This relationship is frequently over looked and can lead to pump cavitation.  This Tip of the Month examines the relationship of NPSHR to the impeller diameter and clarifies other misconceptions regarding pump NPSHR curves.

Background

Pump performance may be shown for a single impeller or a range of impeller diameters.  In the latter case the pump performance may be shown as multiple curves from the maximum to the minimum diameter, and may show several intermediate impeller sizes.  In addition, the pump performance characteristics may show curves for NPSHR, efficiency and required power.   The representation of the pump performance varies widely depending on many factors and can lead to design errors and possible confusion.

An example of a typical pump performance curve frequently seen in publications is shown in Figure 1.  The pump flow rate is plotted on the horizontal axis, and the head and NPSHR curves, which are a function of flow rate, plotted on the vertical axles.  Note that a single-line NPSHR curve starts at the no-flow condition and continually rises to the maximum flow rate.  For several reasons that will be discussed later, this type of NPSHR curve is incorrect and can lead to design errors and possible cavitation problems.

Pump cavitation is a complex subject and the topic of many technical papers and books.  However, it is widely accepted that this phenomenon begins at the pump inlet.  It basically results from the increased velocity and reduced pressure as the fluid enters the impeller.  If the fluid static pressure drops below the vapor pressure, gas bubbles form and later collapse as the fluid flows along the impeller vanes.  These vapor bubbles can have a significant effect on the head produced by the pump.

It is important to note that fluid temperature also plays an important part in pump cavitation.  Obviously, the fluid vapor pressure will vary with temperature.  The fluid temperature will also vary with pump efficiency.  Temperature rise due to pump efficiency is not significant in the high to mid-range flow rates, however, can be very significant at low flow rates.  This is why pump NPSHR values are not given at low flow conditions.

Figure 1 – Pump Performance Curve for a Range of Impeller Diameters

Another important factor in pump cavitation is the fluid velocity.  Fluid entering a pump will continually increase in velocity as it passes to the impeller eye.  This increase in velocity causes a drop in the fluid static pressure and is analogous to lift on an airfoil.   At high to mid-range flow rates the incoming fluid velocity and the impeller rotational velocity are compatible and contributes to stable flow through the pump.  However at low flow rates the entering velocity is well below the rotational velocity and may cause the fluid to “recirculation” at the impeller inlet.  Fluid recirculation is another form of pump cavitation.   This is another reason why NPSHR is not given at low flow rates.

NPSHR Testing

Understanding how NPSHR tests are conducted and how the impeller diameter influences the produced head will help eliminate confusion and possible errors.  Pump manufacturers determine the characteristic shape of the NPSHR curve for each impeller through carefully controlled shop testing, hydraulic modeling and computer simulation.  Hydraulic Institute Standard 1.6 gives strict guidelines for conducting shop testing and is used by most pump manufactures.  Pumps are normally connected to closed-loop piping circuit where water flows from a suction tank (or sump) through the pump and then back to the tank. The discharge flow rate, temperature and pressure are carefully measured and controlled throughout the test.    Basically the test is conducted at a fixed flow rate and speed while the suction pressure is reduced.   By reducing the suction pressure a point is reached when the water begins to vaporize thus causing the pump to cavitate.  The characteristic “cavitation” point is the flow rate that is exhibited by a small drop in head.  The test is conducted again at another fixed flow rate and again the resulting suction pressure and flow rate value are recorded at the “cavitation” point.  Once the series of tests are completed, a smooth line is drawn through the recorded data and plotted.   Figure 2 illustrates a typical series of test results and the resulting NPSHR curve.

Figure 2 – NPSHR Test Curve

A pump cavitation point can be difficult to define.  The formation of vapor bubbles is a gradual process, starting slowly and increasing with flow rate.  The API-610 defines the cavitation point as a three percent drop in head.  This is not to say that pump cavitation does not occur at smaller values, it is just difficult to accurately measure at smaller values.     To obtain a single point it is necessary to run a pump for a period of time and allow the testing circuit to stabilize to the reducing suction pressure.  Remember, vapor bubbles are forming and instruments need time to react to the fluid dynamics.

Impeller Diameter and Head Relationship

Larger pump impellers produce greater values of head for a given speed.   This is because the head is proportional to the tip speed.  The relationship of head to tip speed can be approximated by Equation 1.

(Eq. 1)

Tip velocity can also be related to impeller diameter and rotating speed by Equation 2.

(Eq. 2)

From Equations 1 and 2 it can be seen that changes in impeller diameter will have a direct effect on the pump head.  For example, reducing the impeller diameter will lower the pump head by a factor of four.   Since the cavitation point is identified by a three percent drop in pump head, it is logical that any change in impeller diameter will have a direct effect on the NPSHR value.  For this reason, most pump manufacturers provide a single NPSHR curve for a given impeller diameter.  Figures 3 and 4 are typical pump performance curves for a range of impeller diameters.  Note that a separate NPSHR curve is given for each diameter.

Figure 3 – Typical Pump Performance Curve for a Range of Diameters

Figure 4 – Optional Pump Performance Curve for a Range of Diameters

Conclusions

The following conclusions can be reached from the previous discussion.

1. Each impeller will have a characteristic NPSHR curve.  It will depend on many design factors including the diameter.
2. At a given flow rate, the NPSHR increases as the impeller diameter is reduced.
3. The NPSHR is never tested at the shut-off point.  The fluid temperature continually rises as the flow rates decreases.  This prevents the system from stabilizing sufficiently to obtain accurate measurements.
4. Pumps may cavitate at low flow rates due to recirculation of fluid at the impeller eye.
5. The shape of the NPSHR curve is a U-shape.  There is a slight rise in values as the flow is reduced and again at higher values.  The NPSHR is lowest in the mid-range values.

By: Joe Honeywell

Legend

A          Conversion constant = 720 ft/sec (600 m/s)

D          Impeller diameter, inches (cm)

H          Total pump head, ft (m)

g          Gravitational constant, 32.17 ft/sec² (9.81 m/s²)

n          Rotational speed, rev/min

V          Impeller tip velocity, ft/sec (m/s)

References

1. American Petroleum Institute Standard 610, Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries, 10^th Ed.
2. Hydraulic Institute Standard 1.6, Centrifugal Pump Tests, 2000
3. Terry Henshaw, Pumps and Systems, May 2009