Centrifugal Pumps

Department of EnergyFundamentals Handbook

MECHANICAL SCIENCEModule 3

Pumps

REFERENCES DOE-HDBK-1018/1-93 Pumps

REFERENCES

Babcock & Wilcox, Steam, Its Generations and Use, Babcock & Wilcox Co.

Cheremisinoff, N. P., Fluid Flow, Pumps, Pipes and Channels, Ann Arbor Science.

General Physics, Heat Transfer, Thermodynamics and Fluid Flow Fundamentals, GeneralPhysics Corporation.

Academic Program for Nuclear Power Plant Personnel, Volume III, Columbia, MD,General Physics Corporation, Library of Congress Card #A 326517, 1982.

Stewart, Harry L., Pneumatics & Hydraulics, Theodore Audel & Company.

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Pumps DOE-HDBK-1018/1-93 CENTRIFUGAL PUMPS

CENTRIFUGAL PUMPS

Centrifugal pumps are the most common type of pumps found in DOE facilities.Centrifugal pumps enjoy widespread application partly due to their ability tooperate over a wide range of flow rates and pump heads.

EO 1.1 STATE the purposes of the following centrifugal pumpcomponents:

a. Impellerb. Volutec. Diffuser

d. Packinge. Lantern Ringf. Wearing ring

EO 1.2 Given a drawing of a centrifugal pump, IDENTIFY thefollowing major components:

a. Pump casingb. Pump shaftc. Impellerd. Volutee. Stuffing box

f. Stuffing box glandg. Packingh. Lantern Ringi. Impeller wearing ringj. Pump casing wearing ring

I ntr oduction

Centrifugal pumps basically consist of a stationary pump casing and an impeller mounted on arotating shaft. The pump casing provides a pressure boundary for the pump and containschannels to properly direct the suction and discharge flow. The pump casing has suction anddischarge penetrations for the main flow path of the pump and normally has small drain and ventfittings to remove gases trapped in the pump casing or to drain the pump casing for maintenance.

Figure 1 is a simplified diagram of a typical centrifugal pump that shows the relative locationsof the pump suction, impeller, volute, and discharge. The pump casing guides the liquid fromthe suction connection to the center, or eye, of the impeller. The vanes of the rotating impellerimpart a radial and rotary motion to the liquid, forcing it to the outer periphery of the pumpcasing where it is collected in the outer part of the pump casing called the volute. The voluteis a region that expands in cross-sectional area as it wraps around the pump casing. The purposeof the volute is to collect the liquid discharged from the periphery of the impeller at highvelocity and gradually cause a reduction in fluid velocity by increasing the flow area. Thisconverts the velocity head to static pressure. The fluid is then discharged from the pumpthrough the discharge connection.

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CENTRIFUGAL PUMPS DOE-HDBK-1018/1-93 Pumps

Figure 1 Centrifugal Pump

Centrifugal pumps can also be constructed in a manner that results in two distinct volutes, eachreceiving the liquid that is discharged from a 180o region of the impeller at any given time.Pumps of this type are called double volute pumps (they may also be referred to a split volutepumps). In some applications the double volute minimizes radial forces imparted to the shaft andbearings due to imbalances in the pressure around the impeller. A comparison of single anddouble volute centrifugal pumps is shown on Figure 2.

Figure 2 Single and Double Volutes

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Diffuser

Figure 3 Centrifugal Pump Diffuser

Some centrifugal pumps containdiffusers. A diffuser is a set ofstationary vanes that surround theimpeller. The purpose of thediffuser is to increase theefficiency of the centrifugal pumpby allowing a more gradualexpansion and less turbulent areafor the liquid to reduce in velocity.The diffuser vanes are designed ina manner that the liquid exiting theimpeller will encounter an ever-increasing flow area as it passesthrough the diffuser. This increasein flow area causes a reduction inflow velocity, converting kineticenergy into flow pressure.

I mpeller Classif ication

Impellers of pumps are classified

Figure 4 Single-Suction and Double-Suction Impellers

based on the number of points thatthe liquid can enter the impellerand also on the amount ofwebbing between the impellerblades.

Impellers can be either single-suction or double-suction. Asingle-suction impeller allowsliquid to enter the center of theblades from only one direction. Adouble-suction impeller allowsliquid to enter the center of theimpeller blades from both sidessimultaneously. Figure 4 showssimplified diagrams of single anddouble-suction impellers.

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Impellers can be open, semi-open, or enclosed. The open impeller consists only of bladesattached to a hub. The semi-open impeller is constructed with a circular plate (the web) attachedto one side of the blades. The enclosed impeller has circular plates attached to both sides of theblades. Enclosed impellers are also referred to as shrouded impellers. Figure 5 illustratesexamples of open, semi-open, and enclosed impellers.

Figure 5 Open, Semi-Open, and Enclosed Impellers

The impeller sometimes contains balancing holes that connect the space around the hub to thesuction side of the impeller. The balancing holes have a total cross-sectional area that isconsiderably greater than the cross-sectional area of the annular space between the wearing ringand the hub. The result is suction pressure on both sides of the impeller hub, which maintainsa hydraulic balance of axial thrust.

Centr ifugal Pump Classif ication by Flow

Centrifugal pumps can be classified based on the manner in which fluid flows through the pump.The manner in which fluid flows through the pump is determined by the design of the pumpcasing and the impeller. The three types of flow through a centrifugal pump are radial flow, axialflow, and mixed flow.

Radial Flow Pumps

In a radial flow pump, the liquid enters at the center of the impeller and is directed outalong the impeller blades in a direction at right angles to the pump shaft. The impellerof a typical radial flow pump and the flow through a radial flow pump are shown inFigure 6.

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Axial Flow Pumps

Figure 6 Radial Flow Centrifugal Pump

In an axial flow pump, the impeller pushes the liquid in a direction parallel to the pumpshaft. Axial flow pumps are sometimes called propeller pumps because they operateessentially the same as the propeller of a boat. The impeller of a typical axial flow pumpand the flow through a radial flow pump are shown in Figure 7.

Figure 7 Axial Flow Centrifugal Pump

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Mix ed Flow Pumps

Mixed flow pumps borrow characteristics from both radial flow and axial flow pumps.As liquid flows through the impeller of a mixed flow pump, the impeller blades push theliquid out away from the pump shaft and to the pump suction at an angle greater than90o. The impeller of a typical mixed flow pump and the flow through a mixed flowpump are shown in Figure 8.

Figure 8 Mixed Flow Centrifugal Pump

Multi-Stage Centr ifugal Pumps

A centrifugal pump with a single impeller that can develop a differential pressure of more than150 psid between the suction and the discharge is difficult and costly to design and construct.A more economical approach to developing high pressures with a single centrifugal pump is toinclude multiple impellers on a common shaft within the same pump casing. Internal channelsin the pump casing route the discharge of one impeller to the suction of another impeller.Figure 9 shows a diagram of the arrangement of the impellers of a four-stage pump. The waterenters the pump from the top left and passes through each of the four impellers in series, goingfrom left to right. The water goes from the volute surrounding the discharge of one impeller tothe suction of the next impeller.

A pump stage is defined as that portion of a centrifugal pump consisting of one impeller and itsassociated components. Most centrifugal pumps are single-stage pumps, containing only oneimpeller. A pump containing seven impellers within a single casing would be referred to as aseven-stage pump or, or generally, as a multi-stage pump.

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Figure 9 Multi-Stage Centrifugal Pump

Centr ifugal Pump Components

Centrifugal pumps vary in design and construction from simple pumps with relatively few partsto extremely complicated pumps with hundreds of individual parts. Some of the most commoncomponents found in centrifugal pumps are wearing rings, stuffing boxes, packing, and lanternrings. These components are shown in Figure 10 and described on the following pages.

W earing Rings

Centrifugal pumps contain rotating impellers within stationary pump casings. To allowthe impeller to rotate freely within the pump casing, a small clearance is designed to bemaintained between the impeller and the pump casing. To maximize the efficiency of acentrifugal pump, it is necessary to minimize the amount of liquid leaking through thisclearance from the high pressure or discharge side of the pump back to the low pressureor suction side.

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Some wear or erosion will occur at the point where the impeller and the pump casing

Figure 10 Centrifugal Pump Components

nearly come into contact. This wear is due to the erosion caused by liquid leakingthrough this tight clearance and other causes. As wear occurs, the clearances becomelarger and the rate of leakage increases. Eventually, the leakage could becomeunacceptably large and maintenance would be required on the pump.

To minimize the cost of pump maintenance, many centrifugal pumps are designed withwearing rings. Wearing rings are replaceable rings that are attached to the impeller and/orthe pump casing to allow a small running clearance between the impeller and the pumpcasing without causing wear of the actual impeller or pump casing material. Thesewearing rings are designed to be replaced periodically during the life of a pump andprevent the more costly replacement of the impeller or the casing.

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Stuffing Box

In almost all centrifugal pumps, the rotating shaft that drives the impeller penetrates thepressure boundary of the pump casing. It is important that the pump is designed properlyto control the amount of liquid that leaks along the shaft at the point that the shaftpenetrates the pump casing. There are many different methods of sealing the shaftpenetration of the pump casing. Factors considered when choosing a method include thepressure and temperature of the fluid being pumped, the size of the pump, and thechemical and physical characteristics of the fluid being pumped.

One of the simplest types of shaft seal is the stuffing box. The stuffing box is acylindrical space in the pump casing surrounding the shaft. Rings of packing materialare placed in this space. Packing is material in the form of rings or strands that is placedin the stuffing box to form a seal to control the rate of leakage along the shaft. Thepacking rings are held in place by a gland. The gland is, in turn, held in place by studswith adjusting nuts. As the adjusting nuts are tightened, they move the gland in andcompress the packing. This axial compression causes the packing to expand radially,forming a tight seal between the rotating shaft and the inside wall of the stuffing box.

The high speed rotation of the shaft generates a significant amount of heat as it rubsagainst the packing rings. If no lubrication and cooling are provided to the packing, thetemperature of the packing increases to the point where damage occurs to the packing,the pump shaft, and possibly nearby pump bearings. Stuffing boxes are normallydesigned to allow a small amount of controlled leakage along the shaft to providelubrication and cooling to the packing. The leakage rate can be adjusted by tighteningand loosening the packing gland.

L anter n Ring

It is not always possible to use a standard stuffing box to seal the shaft of a centrifugalpump. The pump suction may be under a vacuum so that outward leakage is impossibleor the fluid may be too hot to provide adequate cooling of the packing. These conditionsrequire a modification to the standard stuffing box.

One method of adequately cooling the packing under these conditions is to include alantern ring. A lantern ring is a perforated hollow ring located near the center of thepacking box that receives relatively cool, clean liquid from either the discharge of thepump or from an external source and distributes the liquid uniformly around the shaft toprovide lubrication and cooling. The fluid entering the lantern ring can cool the shaft andpacking, lubricate the packing, or seal the joint between the shaft and packing againstleakage of air into the pump in the event the pump suction pressure is less than that ofthe atmosphere.

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Mechanical Seals

In some situations, packing material is not adequate for sealing the shaft. One commonalternative method for sealing the shaft is with mechanical seals. Mechanical sealsconsist of two basic parts, a rotating element attached to the pump shaft and a stationaryelement attached to the pump casing. Each of these elements has a highly polishedsealing surface. The polished faces of the rotating and stationary elements come intocontact with each other to form a seal that prevents leakage along the shaft.

Summary

The important information in this chapter is summarized below.

Centrifugal Pumps Summary

The impeller contains rotating vanes that impart a radial and rotary motion to theliquid.

The volute collects the liquid discharged from the impeller at high velocity andgradually causes a reduction in fluid velocity by increasing the flow area, convertingthe velocity head to a static head.

A diffuser increases the efficiency of a centrifugal pump by allowing a more gradualexpansion and less turbulent area for the liquid to slow as the flow area expands.

Packing material provides a seal in the area where the pump shaft penetrates thepump casing.

Wearing rings are replaceable rings that are attached to the impeller and/or thepump casing to allow a small running clearance between the impeller and pumpcasing without causing wear of the actual impeller or pump casing material.

The lantern ring is inserted between rings of packing in the stuffing box to receiverelatively cool, clean liquid and distribute the liquid uniformly around the shaft toprovide lubrication and cooling to the packing.

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Pumps DOE-HDBK-1018/1-93 CENTRIFUGAL PUMP OPERATION

CENTRIFUGAL PUMP OPERATION

Improper operation of centrifugal pumps can result in damage to the pump andloss of function of the system that the pump is installed in. It is helpful to knowwhat conditions can lead to pump damage to allow better understanding of pumpoperating procedures and how the procedures aid the operator in avoiding pumpdamage.

EO 1.3 DEFINE the following terms:

a. Net Positive SuctionHead Available

b. Cavitation

c. Gas bindingd. Shutoff heade. Pump runout

EO 1.4 STATE the relationship between net positive suction headavailable and net positive suction head required that isnecessary to avoid cavitation.

EO 1.5 LIST three indications that a centrifugal pump may becavitating.

EO 1.6 LIST five changes that can be made in a pump or itssurrounding system that can reduce cavitation.

EO 1.7 LIST three effects of cavitation.

EO 1.8 DESCRIBE the shape of the characteristic curve for acentrifugal pump.

EO 1.9 DESCRIBE how centrifugal pumps are protected fromthe conditions of dead heading and pump runout.

I ntr oduction

Many centrifugal pumps are designed in a manner that allows the pump to operate continuouslyfor months or even years. These centrifugal pumps often rely on the liquid that they arepumping to provide cooling and lubrication to the pump bearings and other internal componentsof the pump. If flow through the pump is stopped while the pump is still operating, the pumpwill no longer be adequately cooled and the pump can quickly become damaged. Pump damagecan also result from pumping a liquid whose temperature is close to saturated conditions.

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CENTRIFUGAL PUMP OPERATION DOE-HDBK-1018/1 Pumps

Cavitation

The flow area at the eye of the pump impeller is usually smaller than either the flow area of thepump suction piping or the flow area through the impeller vanes. When the liquid being pumpedenters the eye of a centrifugal pump, the decrease in flow area results in an increase in flowvelocity accompanied by a decrease in pressure. The greater the pump flow rate, the greater thepressure drop between the pump suction and the eye of the impeller. If the pressure drop islarge enough, or if the temperature is high enough, the pressure drop may be sufficient to causethe liquid to flash to vapor when the local pressure falls below the saturation pressure for thefluid being pumped. Any vapor bubbles formed by the pressure drop at the eye of the impellerare swept along the impeller vanes by the flow of the fluid. When the bubbles enter a regionwhere local pressure is greater than saturation pressure farther out the impeller vane, the vaporbubbles abruptly collapse. This process of the formation and subsequent collapse of vaporbubbles in a pump is called cavitation.

Cavitation in a centrifugal pump has a significant effect on pump performance. Cavitationdegrades the performance of a pump, resulting in a fluctuating flow rate and discharge pressure.Cavitation can also be destructive to pumps internal components. When a pump cavitates, vaporbubbles form in the low pressure region directly behind the rotating impeller vanes. These vaporbubbles then move toward the oncoming impeller vane, where they collapse and cause a physicalshock to the leading edge of the impeller vane. This physical shock creates small pits on theleading edge of the impeller vane. Each individual pit is microscopic in size, but the cumulativeeffect of millions of these pits formed over a period of hours or days can literally destroy a pumpimpeller. Cavitation can also cause excessive pump vibration, which could damage pumpbearings, wearing rings, and seals.

A small number of centrifugal pumps are designed to operate under conditions where cavitationis unavoidable. These pumps must be specially designed and maintained to withstand the smallamount of cavitation that occurs during their operation. Most centrifugal pumps are not designedto withstand sustained cavitation.

Noise is one of the indications that a centrifugal pump is cavitating. A cavitating pump cansound like a can of marbles being shaken. Other indications that can be observed from a remoteoperating station are fluctuating discharge pressure, flow rate, and pump motor current. Methodsto stop or prevent cavitation are presented in the following paragraphs.

Net Positive Suction Head

To avoid cavitation in centrifugal pumps, the pressure of the fluid at all points within the pumpmust remain above saturation pressure. The quantity used to determine if the pressure of theliquid being pumped is adequate to avoid cavitation is the net positive suction head (NPSH).The net positive suction head available (NPSHA) is the difference between the pressure at thesuction of the pump and the saturation pressure for the liquid being pumped. The net positivesuction head required (NPSHR) is the minimum net positive suction head necessary to avoidcavitation.

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The condition that must exist to avoid cavitation is that the net positive suction head availablemust be greater than or equal to the net positive suction head required. This requirement can bestated mathematically as shown below.

NPSHA ≥ NPSHR

A formula for NPSHA can be stated as the following equation.

NPSHA = Psuction - Psaturation

When a centrifugal pump is taking suction from a tank or other reservoir, the pressure at thesuction of the pump is the sum of the absolute pressure at the surface of the liquid in the tankplus the pressure due to the elevation difference between the surface of liquid in the tank andthe pump suction less the head losses due to friction in the suction line from the tank to thepump.

NPSHA = Pa + Pst - hf - Psat

Where:

NPSHA = net positive suction head availablePa = absolute pressure on the surface of the liquidPst = pressure due to elevation between liquid surface and pump suctionhf = head losses in the pump suction pipingPsat = saturation pressure of the liquid being pumped

Pr eventing Cavitation

If a centrifugal pump is cavitating, several changes in the system design or operation may benecessary to increase the NPSHA above the NPSHR and stop the cavitation. One method forincreasing the NPSHA is to increase the pressure at the suction of the pump. For example, if apump is taking suction from an enclosed tank, either raising the level of the liquid in the tank orincreasing the pressure in the space above the liquid increases suction pressure.

It is also possible to increase the NPSHA by decreasing the temperature of the liquid beingpumped. Decreasing the temperature of the liquid decreases the saturation pressure, causingNPSHA to increase. Recall from the previous module on heat exchangers that large steamcondensers usually subcool the condensate to less than the saturation temperature, calledcondensate depression, to prevent cavitation in the condensate pumps.

If the head losses in the pump suction piping can be reduced, the NPSHA will be increased.Various methods for reducing head losses include increasing the pipe diameter, reducing thenumber of elbows, valves, and fittings in the pipe, and decreasing the length of the pipe.

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It may also be possible to stop cavitation by reducing the NPSHR for the pump. The NPSHR isnot a constant for a given pump under all conditions, but depends on certain factors. Typically,the NPSHR of a pump increases significantly as flow rate through the pump increases.Therefore, reducing the flow rate through a pump by throttling a discharge valve decreasesNPSHR. NPSHR is also dependent upon pump speed. The faster the impeller of a pump rotates,the greater the NPSHR. Therefore, if the speed of a variable speed centrifugal pump is reduced,the NPSHR of the pump decreases. However, since a pump's flow rate is most often dictatedby the needs of the system on which it is connected, only limited adjustments can be madewithout starting additional parallel pumps, if available.

The net positive suction head required to prevent cavitation is determined through testing by thepump manufacturer and depends upon factors including type of impeller inlet, impeller design,pump flow rate, impeller rotational speed, and the type of liquid being pumped. Themanufacturer typically supplies curves of NPSHR as a function of pump flow rate for a particularliquid (usually water) in the vendor manual for the pump.

Centr ifugal Pump Character istic Cur ves

For a given centrifugal pump operating at a constant speed, the flow rate through the pump is

Figure 11 Centrifugal Pump Characteristic Curve

dependent upon the differential pressure or head developed by the pump. The lower the pumphead, the higher the flow rate. A vendor manual for a specific pump usually contains a curveof pump flow rate versus pump head called a pump characteristic curve. After a pump isinstalled in a system, it is usually tested to ensure that the flow rate and head of the pump arewithin the required specifications. A typical centrifugal pump characteristic curve is shown inFigure 11.

There are several terms associated with the pump characteristic curve that must be defined.Shutoff head is the maximum head that can be developed by a centrifugal pump operating at aset speed. Pump runout is the maximum flow that can be developed by a centrifugal pumpwithout damaging the pump. Centrifugal pumps must be designed and operated to be protectedfrom the conditions of pump runout or operating at shutoff head. Additional information maybe found in the handbook on Thermodynamics, Heat Transfer, and Fluid Flow.

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Centr ifugal Pump Pr otection

A centrifugal pump is dead-headed when it is operated with no flow through it, for example, witha closed discharge valve or against a seated check valve. If the discharge valve is closed andthere is no other flow path available to the pump, the impeller will churn the same volume ofwater as it rotates in the pump casing. This will increase the temperature of the liquid (due tofriction) in the pump casing to the point that it will flash to vapor. The vapor can interrupt thecooling flow to the pump's packing and bearings, causing excessive wear and heat. If the pumpis run in this condition for a significant amount of time, it will become damaged.

When a centrifugal pump is installed in a system such that it may be subjected to periodic shutoffhead conditions, it is necessary to provide some means of pump protection. One method forprotecting the pump from running dead-headed is to provide a recirculation line from the pumpdischarge line upstream of the discharge valve, back to the pump's supply source. Therecirculation line should be sized to allow enough flow through the pump to prevent overheatingand damage to the pump. Protection may also be accomplished by use of an automatic flowcontrol device.

Centrifugal pumps must also be protected from runout. Runout can lead to cavitation and canalso cause overheating of the pump's motor due to excessive currents. One method for ensuringthat there is always adequate flow resistance at the pump discharge to prevent excessive flowthrough the pump is to place an orifice or a throttle valve immediately downstream of the pumpdischarge. Properly designed piping systems are very important to protect from runout.

Gas Binding

Gas binding of a centrifugal pump is a condition where the pump casing is filled with gases orvapors to the point where the impeller is no longer able to contact enough fluid to functioncorrectly. The impeller spins in the gas bubble, but is unable to force liquid through the pump.This can lead to cooling problems for the pump's packing and bearings.

Centrifugal pumps are designed so that their pump casings are completely filled with liquidduring pump operation. Most centrifugal pumps can still operate when a small amount of gasaccumulates in the pump casing, but pumps in systems containing dissolved gases that are notdesigned to be self-venting should be periodically vented manually to ensure that gases do notbuild up in the pump casing.

Pr iming Centr ifugal Pumps

Most centrifugal pumps are not self-priming. In other words, the pump casing must be filled withliquid before the pump is started, or the pump will not be able to function. If the pump casingbecomes filled with vapors or gases, the pump impeller becomes gas-bound and incapable ofpumping. To ensure that a centrifugal pump remains primed and does not become gas-bound,most centrifugal pumps are located below the level of the source from which the pump is to takeits suction. The same effect can be gained by supplying liquid to the pump suction underpressure supplied by another pump placed in the suction line.

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Summary


Centrifugal Pump Operation Summary

There are three indications that a centrifugal pump is cavitating.NoiseFluctuating discharge pressure and flowFluctuating pump motor current

Steps that can be taken to stop pump cavitation include:Increase the pressure at the suction of the pump.Reduce the temperature of the liquid being pumped.Reduce head losses in the pump suction piping.Reduce the flow rate through the pump.Reduce the speed of the pump impeller.

Three effects of pump cavitation are:Degraded pump performanceExcessive pump vibrationDamage to pump impeller, bearings, wearing rings, and seals

To avoid pump cavitation, the net positive suction head available must be greaterthan the net positive suction head required.

Net positive suction head available is the difference between the pump suctionpressure and the saturation pressure for the liquid being pumped.

Cavitation is the process of the formation and subsequent collapse of vapor bubblesin a pump.

Gas binding of a centrifugal pump is a condition where the pump casing is filledwith gases or vapors to the point where the impeller is no longer able to contactenough fluid to function correctly.

Shutoff head is the maximum head that can be developed by a centrifugal pumpoperating at a set speed.

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Centrifugal Pump Operation Summary (Cont.)

Pump runout is the maximum flow that can be developed by a centrifugal pumpwithout damaging the pump.

The greater the head against which a centrifugal pump operates, the lower the flowrate through the pump. The relationship between pump flow rate and head isillustrated by the characteristic curve for the pump.

Centrifugal pumps are protected from dead-heading by providing a recirculationfrom the pump discharge back to the supply source of the pump.

Centrifugal pumps are protected from runout by placing an orifice or throttle valveimmediately downstream of the pump discharge and through proper piping systemdesign.

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POSITIVE DISPLACEMENT PUMPS DOE-HDBK-1018/1-93 Pumps

POSITIVE DISPLACEMENT PUMPS

Positive displacement pumps operate on a different principle than centrifugalpumps. Positive displacement pumps physically entrap a quantity of liquid at thesuction of the pump and push that quantity out the discharge of the pump.

EO 2.1 STATE the difference between the flow characteristics ofcentrifugal and positive displacement pumps.

EO 2.2 Given a simplified drawing of a positive displacement pump,CLASSIFY the pump as one of the following:

a. Reciprocating piston pumpb. Gear-type rotary pumpc. Screw-type rotary pumpd. Lobe-type rotary pump

e. Moving vane pumpf. Diaphragm pump

EO 2.3 EXPLAIN the importance of viscosity as it relates to theoperation of a reciprocating positive displacement pump.

EO 2.4 DESCRIBE the characteristic curve for a positivedisplacement pump.

EO 2.5 DEFINE the term slippage.

EO 2.6 STATE how positive displacement pumps are protectedagainst overpressurization.

I ntr oduction

A positive displacement pump is one in which a definite volume of liquid is delivered for eachcycle of pump operation. This volume is constant regardless of the resistance to flow offeredby the system the pump is in, provided the capacity of the power unit driving the pump or pumpcomponent strength limits are not exceeded. The positive displacement pump delivers liquid inseparate volumes with no delivery in between, although a pump having several chambers mayhave an overlapping delivery among individual chambers, which minimizes this effect. Thepositive displacement pump differs from centrifugal pumps, which deliver a continuous flow forany given pump speed and discharge resistance.

Positive displacement pumps can be grouped into three basic categories based on their designand operation. The three groups are reciprocating pumps, rotary pumps, and diaphragm pumps.

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Pumps DOE-HDBK-1018/1-93 POSITIVE DISPLACEMENT PUMPS

Pr inciple of Oper ation

All positive displacement pumps operate on the same basic principle. This principle can be mosteasily demonstrated by considering a reciprocating positive displacement pump consisting of asingle reciprocating piston in a cylinder with a single suction port and a single discharge port asshown in Figure 12. Check valves in the suction and discharge ports allow flow in only onedirection.

During the suction stroke, the piston moves to the left, causing the check valve in the suction

Figure 12 Reciprocating Positive Displacement Pump Operation

line between the reservoir and the pump cylinder to open and admit water from the reservoir.During the discharge stroke, the piston moves to the right, seating the check valve in the suctionline and opening the check valve in the discharge line. The volume of liquid moved by thepump in one cycle (one suction stroke and one discharge stroke) is equal to the change in theliquid volume of the cylinder as the piston moves from its farthest left position to its farthestright position.

Recipr ocating Pumps

Reciprocating positive displacement pumps are generally categorized in four ways: direct-actingor indirect-acting; simplex or duplex; single-acting or double-acting; and power pumps.

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Dir ect-Acting and I ndir ect-Acting Pumps

Some reciprocating pumps are powered by prime movers that also have reciprocatingmotion, such as a reciprocating pump powered by a reciprocating steam piston. The pistonrod of the steam piston may be directly connected to the liquid piston of the pump or it maybe indirectly connected with a beam or linkage. Direct-acting pumps have a plunger on theliquid (pump) end that is directly driven by the pump rod (also the piston rod or extensionthereof) and carries the piston of the power end. Indirect-acting pumps are driven by meansof a beam or linkage connected to and actuated by the power piston rod of a separatereciprocating engine.

Simplex and Duplex Pumps

A simplex pump, sometimes referred to as a single pump, is a pump having a single liquid(pump) cylinder. A duplex pump is the equivalent of two simplex pumps placed side byside on the same foundation.

The driving of the pistons of a duplex pump is arranged in such a manner that when onepiston is on its upstroke the other piston is on its downstroke, and vice versa. Thisarrangement doubles the capacity of the duplex pump compared to a simplex pump ofcomparable design.

Single-Acting and Double-Acting Pumps

A single-acting pump is one that takes a suction, filling the pump cylinder on the stroke inonly one direction, called the suction stroke, and then forces the liquid out of the cylinderon the return stroke, called the discharge stroke. A double-acting pump is one that, as itfills one end of the liquid cylinder, is discharging liquid from the other end of the cylinder.On the return stroke, the end of the cylinder just emptied is filled, and the end just filledis emptied. One possible arrangement for single-acting and double-acting pumps is shownin Figure 13.

Power Pumps

Power pumps convert rotary motion to low speed reciprocating motion by reductiongearing, a crankshaft, connecting rods and crossheads. Plungers or pistons are driven bythe crosshead drives. Rod and piston construction, similar to duplex double-acting steampumps, is used by the liquid ends of the low pressure, higher capacity units. The higherpressure units are normally single-acting plungers, and usually employ three (triplex)plungers. Three or more plungers substantially reduce flow pulsations relative to simplexand even duplex pumps.

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Power pumps typically have high efficiency and are capable of developing very high pressures.

Figure 13 Single-Acting and Double-Acting Pumps

They can be driven by either electric motors or turbines. They are relatively expensive pumpsand can rarely be justified on the basis of efficiency over centrifugal pumps. However, they arefrequently justified over steam reciprocating pumps where continuous duty service is needed dueto the high steam requirements of direct-acting steam pumps.

In general, the effective flow rate of reciprocating pumps decreases as the viscosity of the fluidbeing pumped increases because the speed of the pump must be reduced. In contrast tocentrifugal pumps, the differential pressure generated by reciprocating pumps is independent offluid density. It is dependent entirely on the amount of force exerted on the piston. For moreinformation on viscosity, density, and positive displacement pump theory, refer to the handbookon Thermodynamics, Heat Transfer, and Fluid Flow.

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Rotary Pumps

Rotary pumps operate on the principle that a rotating vane, screw, or gear traps the liquid in thesuction side of the pump casing and forces it to the discharge side of the casing. These pumpsare essentially self-priming due to their capability of removing air from suction lines andproducing a high suction lift. In pumps designed for systems requiring high suction lift and self-priming features, it is essential that all clearances between rotating parts, and between rotatingand stationary parts, be kept to a minimum in order to reduce slippage. Slippage is leakage offluid from the discharge of the pump back to its suction.

Due to the close clearances in rotary pumps, it is necessary to operate these pumps at relativelylow speed in order to secure reliable operation and maintain pump capacity over an extendedperiod of time. Otherwise, the erosive action due to the high velocities of the liquid passingthrough the narrow clearance spaces would soon cause excessive wear and increased clearances,resulting in slippage.

There are many types of positive displacement rotary pumps, and they are normally grouped intothree basic categories that include gear pumps, screw pumps, and moving vane pumps.

Simple Gear Pump

There are several variations of

Figure 14 Simple Gear Pump

gear pumps. The simple gearpump shown in Figure 14consists of two spur gearsmeshing together and revolving inopposite directions within acasing. Only a few thousandthsof an inch clearance existsbetween the case and the gearfaces and teeth extremities. Anyliquid that fills the space boundedby two successive gear teeth andthe case must follow along withthe teeth as they revolve. Whenthe gear teeth mesh with the teethof the other gear, the spacebetween the teeth is reduced, andthe entrapped liquid is forced outthe pump discharge pipe. As thegears revolve and the teeth disengage, the space again opens on the suction side of thepump, trapping new quantities of liquid and carrying it around the pump case to thedischarge. As liquid is carried away from the suction side, a lower pressure is created,which draws liquid in through the suction line.

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With the large number of teeth usually employed on the gears, the discharge is relativelysmooth and continuous, with small quantities of liquid being delivered to the discharge linein rapid succession. If designed with fewer teeth, the space between the teeth is greater andthe capacity increases for a given speed; however, the tendency toward a pulsatingdischarge increases. In all simple gear pumps, power is applied to the shaft of one of thegears, which transmits power to the driven gear through their meshing teeth.

There are no valves in the gear pump to cause friction losses as in the reciprocating pump.The high impeller velocities, with resultant friction losses, are not required as in thecentrifugal pump. Therefore, the gear pump is well suited for handling viscous fluids suchas fuel and lubricating oils.

Other Gear Pumps

There are two types of gears used in gear pumps

Figure 15 Types of Gears Used In Pumps

in addition to the simple spur gear. One type isthe helical gear. A helix is the curve producedwhen a straight line moves up or down thesurface of a cylinder. The other type is theherringbone gear. A herringbone gear iscomposed of two helixes spiraling in differentdirections from the center of the gear. Spur,helical, and herringbone gears are shown inFigure 15.

The helical gear pump has advantages over thesimple spur gear. In a spur gear, the entirelength of the gear tooth engages at the sametime. In a helical gear, the point of engagementmoves along the length of the gear tooth as thegear rotates. This makes the helical gear operatewith a steadier discharge pressure and fewerpulsations than a spur gear pump.

The herringbone gear pump is also amodification of the simple gear pump. Itsprincipal difference in operation from the simplespur gear pump is that the pointed center sectionof the space between two teeth beginsdischarging before the divergent outer ends ofthe preceding space complete discharging. Thisoverlapping tends to provide a steadier dischargepressure. The power transmission from thedriving to the driven gear is also smoother andquieter.

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L obe Type Pump

Figure 16 Lobe Type Pump

The lobe type pump shown in Figure 16is another variation of the simple gearpump. It is considered as a simple gearpump having only two or three teeth perrotor; otherwise, its operation or theexplanation of the function of its parts isno different. Some designs of lobepumps are fitted with replaceable gibs,that is, thin plates carried in grooves atthe extremity of each lobe where theymake contact with the casing. The gibpromotes tightness and absorbs radialwear.

Scr ew-Type Positive Displacement Rotary Pump

There are many variations in the design of the screw type positive displacement, rotarypump. The primary differences consist of the number of intermeshing screws involved,the pitch of the screws, and the general direction of fluid flow. Two common designs arethe two-screw, low-pitch, double-flow pump and the three-screw, high-pitch, double-flowpump.

Two-Scr ew, L ow-Pitch, Scr ew Pump

The two-screw, low-pitch, screw pump consists of two screws that mesh with closeclearances, mounted on two parallel shafts. One screw has a right-handed thread, andthe other screw has a left-handed thread. One shaft is the driving shaft and drives theother shaft through a set of herringbone timing gears. The gears serve to maintainclearances between the screws as they turn and to promote quiet operation. Thescrews rotate in closely fitting duplex cylinders that have overlapping bores. Allclearances are small, but there is no actual contact between the two screws or betweenthe screws and the cylinder walls.

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The complete assembly and the usual flow

Figure 17 Two-Screw, Low-Pitch, Screw Pump

Figure 18 Three-Screw, High-Pitch, Screw Pump

path are shown in Figure 17. Liquid istrapped at the outer end of each pair ofscrews. As the first space between the screwthreads rotates away from the opposite screw,a one-turn, spiral-shaped quantity of liquid isenclosed when the end of the screw againmeshes with the opposite screw. As thescrew continues to rotate, the entrapped spiralturns of liquid slide along the cylinder towardthe center discharge space while the next slugis being entrapped. Each screw functionssimilarly, and each pair of screws dischargesan equal quantity of liquid in opposed streamstoward the center, thus eliminating hydraulicthrust. The removal of liquid from thesuction end by the screws produces areduction in pressure, which draws liquidthrough the suction line.

Thr ee-Scr ew, H igh-Pitch, Scr ew Pump

The three-screw, high-pitch, screw pump,shown in Figure 18, has many of the sameelements as the two-screw, low-pitch, screwpump, and their operations are similar.Three screws, oppositely threaded on eachend, are employed. They rotate in a triplecylinder, the two outer bores of whichoverlap the center bore. The pitch of thescrews is much higher than in the low pitchscrew pump; therefore, the center screw, orpower rotor, is used to drive the two outeridler rotors directly without external timinggears. Pedestal bearings at the base supportthe weight of the rotors and maintain theiraxial position. The liquid being pumpedenters the suction opening, flows throughpassages around the rotor housing, andthrough the screws from each end, in opposedstreams, toward the center discharge. Thiseliminates unbalanced hydraulic thrust. Thescrew pump is used for pumping viscousfluids, usually lubricating, hydraulic, or fueloil.

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Rotary Moving Vane Pump

The rotary moving vane pump shown in Figure 19 is another type of positive displacementpump used. The pump consists of a cylindrically bored housing with a suction inlet on oneside and a discharge outlet on the other. A cylindrically shaped rotor with a diametersmaller than the cylinder is driven about an axis placed above the centerline of the cylinder.The clearance between rotor and cylinder is small at the top but increases at the bottom.The rotor carries vanes that move in and out as it rotates to maintain sealed spaces betweenthe rotor and the cylinder wall. The vanes trap liquid or gas on the suction side and carryit to the discharge side, where contraction of the space expels it through the discharge line.The vanes may swing on pivots, or they may slide in slots in the rotor.

Figure 19 Rotary Moving Vane Pump

Diaphr agm Pumps

Diaphragm pumps are also classified as positive displacement pumps because the diaphragm actsas a limited displacement piston. The pump will function when a diaphragm is forced intoreciprocating motion by mechanical linkage, compressed air, or fluid from a pulsating, externalsource. The pump construction eliminates any contact between the liquid being pumped and thesource of energy. This eliminates the possibility of leakage, which is important when handlingtoxic or very expensive liquids. Disadvantages include limited head and capacity range, and thenecessity of check valves in the suction and discharge nozzles. An example of a diaphragmpump is shown in Figure 20.

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Figure 20 Diaphragm Pump

Positive Displacement Pump Character istic Cur ves

Positive displacement pumps deliver a definite volume of

Figure 21 Positive Displacement Pump

Characteristic Curve

liquid for each cycle of pump operation. Therefore, theonly factor that effects flow rate in an ideal positivedisplacement pump is the speed at which it operates. Theflow resistance of the system in which the pump isoperating will not effect the flow rate through the pump.Figure 21 shows the characteristic curve for a positivedisplacement pump.

The dashed line in Figure 21 shows actual positivedisplacement pump performance. This line reflects thefact that as the discharge pressure of the pump increases,some amount of liquid will leak from the discharge of thepump back to the pump suction, reducing the effectiveflow rate of the pump. The rate at which liquid leaksfrom the pump discharge to its suction is called slippage.

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Positive Displacement Pump Pr otection

Positive displacement pumps are normally fitted with relief valves on the upstream side of theirdischarge valves to protect the pump and its discharge piping from overpressurization. Positivedisplacement pumps will discharge at the pressure required by the system they are supplying.The relief valve prevents system and pump damage if the pump discharge valve is shut duringpump operation or if any other occurrence such as a clogged strainer blocks system flow.

Summary


Positive Displacement Pumps Summary

The flow delivered by a centrifugal pump during one revolution of the impeller dependsupon the head against which the pump is operating. The positive displacementpump delivers a definite volume of fluid for each cycle of pump operationregardless of the head against which the pump is operating.

Positive displacement pumps may be classified in the following ways:Reciprocating piston pumpGear-type rotary pumpLobe-type rotary pumpScrew-type rotary pumpMoving vane pumpDiaphragm pump

As the viscosity of a liquid increases, the maximum speed at which a reciprocatingpositive displacement pump can properly operate decreases. Therefore, as viscosityincreases, the maximum flow rate through the pump decreases.

The characteristic curve for a positive displacement pump operating at a certainspeed is a vertical line on a graph of head versus flow.

Slippage is the rate at which liquid leaks from the discharge of the pump back tothe pump suction.

Positive displacement pumps are protected from overpressurization by a relief valveon the upstream side of the pump discharge valve.

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Centrifugal Pumps (3 PDH)

Course No. M-3005

Introduction

The centrifugal pump is second only to the electric motor as the most widely used type of rotating mechanical equipment in the world. It is not surprising that this is true in the typical nuclear or fossil fuel power plant, refinery, petrochemical, or chemical complex, where the use of centrifugal pumps is so prevalent. Since this is where the process design engineer plies his or her wares, it is necessary that engineers be familiar with the theory and application of centrifugal pumps.

The portion of this lesson on pump system curves was adapted from "A Pump Handbook for Salesmen", written by D. B. Barta, now retired from the Ingersoll Rand Company. This handbook was never published, and was informally distributed within the Ingersoll Rand Company as part of a training program.

You may notice some inconsistencies in the symbol definitions in different parts of the text. For instance, the symbol ω is used for rotational speed (rpm) in some cases, while the symbol N is used for rpm in conjunction with the pump affinity laws, because the affinity laws always seem to use that symbol. I have tried to define, or possibly redefine, the symbols used for each set of equations.

The Centrifugal Pump

Centrifugal pumps offer important advantages over other types of pumps. Since they operate at considerably higher speeds, they are smaller and lighter. The suction and discharge flows are smooth and relatively free from pulsations. Because there is a maximum differential pressure which they can develop known as the shutoff differential pressure, discharge piping can be designed without the necessity of relief valves and the pump can be started against closed discharge shutoff or check valves. Since there are not as many wearing parts, maintenance and downtime are lower than for other types of pumps.

On the other hand, centrifugal pumps do not perform well at low flows or high viscosities. For applications under these conditions, it is frequently better to use a rotary or reciprocating pump. The centrifugal pump consists of a casing to contain the liquid being pumped, an impeller which rotates thus transferring energy to the pumped liquid, a shaft to which the impeller is attached, a stuffing box containing a mechanical seal or packing to prevent leakage at the point where the shaft passes through the casing, bearings to support the shaft, a coupling to connect the pump shaft to the driver shaft and a driver, which is normally either an electric motor or a steam turbine, although engines and gas turbines are occasionally used to drive pumps. Sometimes a gear increaser or decreaser is used between the pump and drive to obtain a desired pump speed. Liquid enters the casing through the suction nozzles and is propelled outward toward the discharge nozzle by the rotating impeller. As the liquid passes from the center of the impeller to the periphery, its angular momentum is increased. After leaving the impeller, the velocity, which was created in the impeller, is converted or diffused into a pressure increase by decelerating the liquid in the outer zone of the casing known as the diffuser, or volute.

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Performance Parameters

When specifying a centrifugal pump, it is necessary to provide information on its performance characteristics in units that are universally understood and agreed upon. Generally speaking, these are as follows:

Flow Flow through a pump is generally understood as the volumetric Flow, rather than the weight or mass flow, and normally is expressed in U. S. gallons per minute (gpm). cubic meters per second (1 cu.m/min = 4.4 gal/sec), or on large capacity pumps in cubic feet per second (cfs) (one cfs = 449gpm). Specific gravity Specific gravity is the standard method of expressing the density of the liquid being pumped, and is generally understood to be the ratio of the density of the liquid to the density of the water at standard conditions.

Suction Pressure Suction pressure is the pressure at the suction nozzle of the pump expressed in pounds per square inch gauge.

Discharge Pressure Discharge pressure is the pressure at the discharge nozzle of the pump expressed in pounds per square inch gauge. Differential Pressure Differential pressure is the difference between the discharge pressure and the suction pressure measured in pounds per square inch.

Differential Head (Also known as Total Dynamic Head or TDH) Differential head is the energy per unit weight necessary to create the pump differential pressure. Its true unit of measure is foot-pounds per pound; however, if one cancels out the pounds in both the numerator and denominator, the result is the generally accepted unit of measure for head which is simply feet. From this it can be deduced that the head could also be interpreted as the height of a static column of liquid which would have a pressure at its base equal to the differential pressure of the pump.

A formula relating the differential pressure, the specific gravity and the differential head can be derived by applying the first law of thermodynamics as follows: h1 + v1

2 /2g + p1/γ + Q + w = h2 + v22 /2g + p2 /γ

where: h =elevation v = velocity

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g = gravitational constant w = work per unit weight which by definition is the differential head. Q = heat transfer p = pressure γ = specific weight Subscripts 1 and 2 indicate suction and discharge conditions respectively. If we assume that the elevation and velocity at the suction and discharge are the same and that the heat transfer, Q, is negligible, the first law can be simplified to the following: w = (p2 - p1) / γ = H

where H is the differential head. Since we wish to express H in feet, (p2 - p1) must be in pounds per square foot, and the specific weight must be in pounds per cubic foot. Noting from our previous definition of specific gravity, that the specific weight equals the specific gravity times the specific weight of water at standard conditions, we have: H = ∆p lb/in2 x 144 in2/ ft2

Specific gravity x 62.4 lb/cu ft H = 2.31 ∆p Specific gravity (sg) Where H is in feet and p1 and p2 are in psig. Net Positive Suction Head (NPSH) The suction pressure, expressed in feet of liquid, required at the eye of the impeller to prevent cavitation. This required NPSH (NPSHr) is usually determined by a test performed by the pump manufacturer. The available NPSH (NPSHa) is a function of the system design and operation, and must exceed the NPSHr or else cavitation will occur. Hydraulic Horsepower The hydraulic horsepower of a pump is the work which would ideally be required to produce the pressure rise in the pumped liquid. Recalling our definition of head as the energy per unit mass necessary to create the pump differential pressure, we can easily calculate the horsepower for a given flow and differential head by multiplying the head times the flow in pounds per minute and dividing the result by 33,000 foot pounds per minute per horsepower. Noting that the flow in pounds per minute is 8.33 lb per gal x sg. x gpm (where 8. 33 lb per gal is the density of water at standard conditions), we have:

Hydraulic Horsepower = 8.33 lb per gal.x sg x gpm x feet of head 33,000 ft lb per HP min

Hydraulic Horsepower = sg x gpm x head 3,960 If we substitute 2.31 (p1- p2)/sg for the head, we have:

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(4) Hydraulic Horsepower = gpm (p1- p2) 1,714

Brake Horsepower Brake horsepower is the actual horsepower transmitted to the pump by the driver through the shaft coupling. In order to accurately measure the brake horsepower, it is necessary to measure the speed (rpm) and torque at the coupling. If these two values are known, the brake horsepower can then be calculated as follows:

Brake horsepower = work in foot pounds per minute / 33,000 Work = Force x Distance Force = Torque / Radius Distance = 2π Radius x rpm x time Work = (Torque / Radius) x 2π Radius x rpm x time Work per min. = 2π x torque x rpm Brake HP = (2π x torque x rpm) / 33,000 Brake HP = (torque x rpm) / 5,250 Since instruments to measure torque at shaft couplings are expensive and rarely available except in test facilities, brake horsepower is frequently approximated by measuring the energy consumption of the driver. For a steam turbine, this would be the steam flow; for an electric motor, the amps, and for an engine or gas turbine, the fuel consumption. Efficiency Efficiency is the ratio of the hydraulic horsepower to the brake horsepower. Efficiency (η) = hydraulic HP / brake HP, therefore: Brake horsepower BHP = ( sg x gpm x head) / 3,690 x η Specific Speed It is obviously not possible in this short summary to discuss the theory of dimensionless parameters in great depth. For our purposes it is sufficient to state that it seems intuitively logical that if any complex natural phenomenon can be described by a parameter calculated from variables, which could logically affect it, then it should be dimensionless, since nature should be completely oblivious to the man made concept of dimensions. If we apply this principal to centrifugal pumps we can see that the flow, the differential head and the speed are the variables which could be expected to describe pump performance. One could argue that a dimension describing the pump size should be added to this list. We will therefore recognize the validity of this argument by stipulating that the dimensionless parameters which result from flow, differential head and speed should be applied to dimensionally similar machines. The parameter which follows from this reasoning is known as the specific speed and is calculated as follows: Ns = N Q1/2/ H3/4 Where

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Q = flow in gpm H = head in feet N = pump speed

The number that results from this formula is not the same number which would result if the dimensions were consistent. In order to make the dimensions consistent, we would multiply by the appropriate constants. Therefore, the conclusions drawn from specific speed calculated with standard parameters and inconsistent units would be the same as if the dimensions were consistent. Follow that? Words can be tricky as well as math! The concept of specific speed was originally defined as the speed which is required to produce a head of one foot at a flow of one gallon per minute in a machine that is dimensionally similar, but smaller. The concept is extended to state that at a given value of specific speed, the operating conditions are such that similar flow conditions can exist in geometrically similar machines. This is analogous to the concept of using the Reynolds number to predict fluid flow characteristics. As a result of empirical tests which have been performed on a number of pumps, the curves shown in Figure 2 have developed. These curves show a plot of efficiency versus specific speed for various types of centrifugal pumps.

Figure 2 Two points can be drawn from Figure 2; first, low specific speed pumps have very high radial flow components and high specific speed pumps have high or totally axial flow components.

Second, the most efficient pumps fall in the specific speed range of 2000 to 2500. Although, strictly speaking, only the pumps with predominately radial flow components should be classified as centrifugal; in practice all pumps with rotating impellers, regardless of specific speed, are

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categorized as centrifugal pumps. Performance Curves The essence of the pump application to an engineer's work is to select the optimum commercially available pump for a given set of hydraulic conditions. Of fundamental importance to this task is the understanding of how to use and interpret the pump performance curves which are found in manufacturers’ catalogs. A typical catalog performance curve will consist of curves of head versus flow for various impeller diameters, lines of constant horsepower and efficiency superimposed on the head/flow coordinates and a plot of net positive suction head required (NPSHr) versus flow.

Figure 3 A typical example of such curves is shown in Figure 3. It should be noted that the pump curves which we are discussing here, and which comprise the vast majority of curves normally encountered, are drawn for a fixed speed which usually coincides with a standard motor speed.

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An understanding of the theoretical basis for these performance curves will prove a valuable asset in solving pump application problems. Let us begin our discussion of performance curves with the equation which is the theoretical basis for the performance of all turbo machines, the Euler turbine equation. Consider the generalized turbo machine rotor in Figure 4.The rotor rotates about its axis with an angular velocity N.

Figure 4 Fluid enters the impeller at a point near the axis, travels through the impeller following an undefined path and exits at the periphery of the impeller. Let us assume that steady state conditions apply; that is, that the angular velocity and flow through the impeller are constant, there is no heat transfer and fluid velocity magnitudes and directions do not change with time. Let us also assume that the velocity at any point at a given radius from the rotor axis is the same at any point on the circumference described by that radius. This means that at any radius the velocity of the fluid can be described by a vector at a point. Consider now the velocity of the fluid at the point where it enters the impeller near its axis and at the point where it exits the impeller at its periphery. In both cases the velocity can be resolved into three components, one parallel to the axis (the axial component) one perpendicular to the axis (the radial component) and one in the plane of the impeller and perpendicular to the axial and radial components, (the tangential component).

Recall from Newton's law that a change in momentum (in this case velocity since the mass is a constant) results in a force being exerted in the direction of the change of momentum. Thus, we see that if there is a change in axial momentum as the fluid travels through the impeller, then an axial force will result. Similarly, a change in radial momentum will result in a radial force. In an actual pump, the two forces just mentioned do not contribute to energy transfer but rather produce forces which must be absorbed by bearings; the axial force by a thrust bearing and the radial force by journal bearings.

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The tangential component of the momentum (velocity) vector is the one which is most significant in describing pump performance since it is the increase in tangential momentum, created by torque, exerted on the fluid by the impeller which causes the increase in pressure. Recalling that momentum is the product of mass and velocity we would have: M = mV Where: M = tangential momentum m = mass V = tangential velocity m = Qt/g where: Q = weight flow (Ib/sec)

g = 32.2 ft/sec t = time (sec) then: M = (Qt x V) /g From Newton's law, force is equal to the time rate of change of momentum

Force= (Qt x V) / g x t Force= QV / g Torque = Force x Radius Force = Torque / Radius = QV / g Torque = (QV/g) x Radius Work = Force x Distance Work = Force x 2π Radius x ωt, where ω is rpm Work = 2πωt x Torque Work = 2πωt x QV / g x Radius

Notice that 2πωt x radius is the tangential velocity of the impeller, or U. Then Work = (UVQt) / g, noting that head was defined as the energy (or work per unit mass) to create the pressure rise. Thus, Work = (UVQt) / g. And since mass = Qt, (Work / Mass) = head = UV/g. In order to develop a relationship between the head and the flow, we must consider a diagram relating the fluid and impeller velocity vectors at the point where the fluid exits from the impeller.

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Figure 5 Referring to Figure 5 we see that V, the tangential component of the fluid velocity is equal to U, the tangential velocity of the rotor, minus the tangential component of the velocity of the fluid relative to the impeller, Vru Head = (U/g) x (U-Vru) We also note from the vector diagram that Vru equals the radial component of the relative velocity, Vr(radial) times the cotangent of β, the angle between a tangent to the impeller vane and a tangent to the periphery of the impeller. Vru = Vr(radial) x cot β

Then H = ( U / g ) ( U – Vr cot β ) We now note that the flow through the pump, from the law of continuity, is equal to the discharge area (A) at the periphery of the impeller times the radial component of the relative velocity: Q = AVr(radial) Then Vr(radial) =Q/A Substituting into our formula above for head we have:

H = (U2/g) – (U cot β/ g A) Q Note that for a given pump operating at a particular rpm, U, β/g A We then have finally: Head = K1- K2Q where K1 = U2/g,

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and K2 = U cot β/ area x g

K1 and K2 are constants. Note that K2 determines the slope of the head capacity curve and is dependent on the cotangent of β. If β is equal to 90o, cot β equals zero and the head is a constant.

This of course is an idealized treatment; in actual practice the hydraulic losses must also be subtracted. This is the reason for the characteristic head-capacity curve as shown in Figure 3. instead of the straight line. ~~ This explains the very flat performance curves that straight vaned pumps normally have. On the other hand as β decreases cot β increases, therefore so does the slope of the head capacity curve. Curve slopes for several values of β are shown in Figure 6.

Figure 6 Affinity Laws As we mentioned at the beginning of our discussion of performance curves, most pump performance curves are drawn for a constant speed, usually a standard motor speed. Frequently, it is necessary to predict the performance of a pump at a speed other than that shown in the catalog performance curve. The affinity laws are relationships between the flow, head and power and the RPM for the same pump operating at different speeds, or for geometrically similar pumps operating at the same specific speed, which permits us to predict performance at different speeds. Using dimensionless parameter once again, it can be shown that: 1. With impeller diameter, D, held constant: Q1 / Q2 = N1 / N2 H1 / H2 = (N1 / N2)2 BHP1 / BHP2 = (N1 / N2)3

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2. With Speed held constant: Q1 / Q2 = D1 / D2 H1 / H2 =(D1 / D2)2 (BHP1 / BHP2) = (D1 / D2)3

Where: Q = Flow rate of the fluid

When the performance (Q1, H1, and BHP1) is known at some Particular speed (N1) or impeller diameter (D1), the affinity formulas can be used to estimate the performance at some other speed or diameter. The efficiency remains nearly constant for speed changes and for small changes in impeller diameter.

Net Positive Suction Head A pump characteristic which is of equal importance to the head-capacity curve is the NPSH or net positive suction head. In order to understand NPSH, we must first discuss the phenomenon of cavitation. Cavitation occurs when the pressure at the suction eye of the pump impeller drops below the vapor pressure of the liquid being pumped. This pressure drop causes gas bubbles to form which suddenly collapse as they flow into higher-pressure regions of the pump. The sudden collapse of the gas bubbles results in mechanical shock, which can cause severe pitting of the impeller vanes. Cavitation is normally characterized by noise, vibration and a reduction in head. The noise and vibration are obviously a result of the mechanical shock caused by the collapsing gas bubbles; however, the explanation for the drop in head is not so obvious. As the pressure at the eye of the impeller of a low or medium specific speed pump reaches the vapor pressure of the liquid being pumped, a band of vapor starts to form at the back side of the vane, and rapidly extends across the entire channel formed by the two adjacent impeller vanes. When this happens, the flow through the pump impeller for a given suction pressure cannot be increased by reducing the discharge pressure, since the pressure differential (and therefore the flow) between the suction and the area where vaporization is taking place is fixed. It is interesting to note that pumps with very high specific speeds (i.e. axial flow pumps) do not experience a sharp drop in head when cavitation takes place, but do experience a gradual drop off in head which increases as the cavitation becomes more severe. This is due to the fact that the blades do not overlap, and therefore do not form a definite channel which can be blocked by a band of the vaporized liquid. Cavitation has eluded a simple, elegant theoretical description which would allow calculating the conditions under which cavitation will take place without relying on empirical test data. However, there have been theoretical analyses made which use some empirical data and which do aid in understanding qualitatively the mechanism by which cavitation takes place. The most well known of these analyses is that using Thoma's cavitation constant. In order to develop Thoma's theory, we begin with Bernoulli's equation for a pump that is about to experience cavitation: Ha + hs = hL + hv + (c2/2g) + λ (w2/2g) , where:

Ha = pressure head of the liquid in the suction tank

Hs = static head of the liquid in the suction tank and piping above the pump suction nozzle

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hL = head loss in suction piping and pump suction hv = vapor pressure of pumped liquid expressed as head c = average absolute velocity of liquid through the impeller eye. λ (w2/2g ) = the local pressure drop below average pressure in the eye of the impeller when cavitation takes place (w is the average relative velocity and λ is an experimental coefficient).

The local pressure drop is frequently referred to as the dynamic depression, and results from the fact that there is a pressure differential between the two faces of an impeller vane. This pressure differential is a result of the reaction of the liquid being pumped to the torque being exerted on it by the impeller vanes. Thoma theorized that the sum of the velocity head and the dynamic depressions is proportional to the total head: (c2/2g) + (w2/2g) = Hσ where σ is known as Thoma's cavitation constant, and is less than one. If we assume the suction losses are negligible and substitute H for c2/2g + λ(w2/2g) in Bernoulli's equation we have:

σ = (Ha + hs- hv) / H

Since, as we have seen from the affinity laws, the head H varies as the square of the speed for the same pump at different speeds, or similar pumps at the same specific speed:

σ = 1 /[2gH (c2 + 2w2)] = a constant

This relationship is used primarily to determine the conditions at which very large pumps and hydraulic turbines will cavitate from model test results. Another approach that has been used to describe and study cavitation is the so-called suction specific speed:

Suction specific speed = N (gpm)1/2 / [(c2/2g) + σ (w2/2g)]3/4

The principal of suction specific speed was arrived at using the principle of dimensionless parameters in a fashion similar to the reasoning used to develop the concept of specific speed, which was discussed earlier in this section. By combining the formulas for specific speed, suction specific speed and Thoma cavitation constant we have: Specific speed / suction specific speed = (Thoma cavitation constant)3/4 It has been shown by correlating the results of tests done on single suction pumps at their best efficiency point, that the Thoma cavitation constant is related to the specific speed as follows:

σ = 6.3 (specific speed)4/3 / 106

If σ values for moderate specific speeds are calculated using the above formula, and then substituted into the formula:

Specific speed / suction specific speed = σ 3/4

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It will be seen that the suction specific speed will be approximately equal to 8000. Now return to the original subject of our discussion, NPSH. Consider Bernoulli's equation for a system that includes the suction vessel and piping as well as the inlet eye of the pump impeller:

Ha +hs = h1 + Hp + (c2/2g) + σ (w2/2g)

This equation is the same as the one used to start our discussion of Thoma's cavitation constant with the exception that Hp has been substituted for hv, where hp is defined as the pressure at the impeller inlet eye expressed as head. As was stated previously, if hp equals hv, cavitation will result. Therefore, the pumping system should be designed so that hp is always greater than hv. Rearranging the Bernoulli equation, which we have just written we have: hp = (Ha + hs - h1) - (c2/2g) + σ (w2/2g) If cavitation is to be avoided, Hp must be greater than hv therefore: (Ha + hs - h1) - (c2/2g) + σ (w2/2g) > hv or, (Ha + hs - h1) - hv > (c2/2g) + σ (w2/2g)

In a practical pump system design problem, the term on the left is called the Net Positive Suction Head Available (NPSHa), and is calculated just as shown in the left side of the inequality above. That is, the sum of the pressure head in the suction vessel and the static head of the liquid above the pump suction minus the suction system losses minus the vapor pressure. The term on the right is known as the net Positive Suction Head Required (NPSHr), and is a characteristic of the pump. In practice, no attempt is made to calculate the NPSHr by estimating fluid velocities inside the pump. Rather, the NPSHr is determined by testing each pump and noting the NPSH at which cavitation begins for flows throughout the operating range of the pump. The curve of NPSHr versus flow, which can be found in pump catalogs superimposed on the head capacity curve, is then plotted. Noting that: c2/2g + σ (w2/2g) = NPSHr, we have: (Ha + hs - h1) - hv > NPSHr See figure 7.

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Figure 7 Following the definition of NPSHr above, we can now rewrite the expression for suction specific speed as: Suction Specific Speed (Nss) =N (Q)1/2 / NPSHr3/4

For a properly designed commercially available pump, the suction specific speed will normally be between 8,000 and 12,000. The margin of NPSHa over NPSHr is a complicated decision and depends on many factors, including the liquid properties, size and h.p. of the pump, system operation, and control.

Radial Thrust Any discussion of radial thrust must begin with a discussion of the flow space in the casing around the periphery of the impeller. Most centrifugal pumps have a volute casing, shown in Figure 8.

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Figure 8 Notice that the outer boundary of the casing starts at point A, where it is separated from the impeller by a small clearance. From there it winds around the impeller in such a fashion that the flow area available to the liquid discharging from the impeller is constantly increasing. At Point B, it joins the diffuser section leading to the pump discharge. Point A, the close clearance point, is known as the tongue, or cut water. The flow passage A-B just before the diffuser and discharge is called the throat.

There are two schools of thought regarding the layout of the actual volute curve. One says that the volute should be laid out in such a fashion that the angular momentum of the liquid pumped is a constant at any point in the area around the periphery of the impeller. That is; velocity x radius = constant In practice, it has been found that this approach leads to excessive velocities at the smaller section areas of the volute, and that a better approach is to lay the volute out in such a way that the average velocity throughout the entire zone around the impeller is constant. This approach has been found to yield higher efficiencies and obviously implies that the curve be constructed in such a fashion that the flow area increases directly proportional to the angular displacement from the cutwater. The radial thrust on a pump impeller is the resultant of the pressure force acting on the impeller from the liquid in the volute. If the volute is designed so that the velocity is constant throughout, then in theory the pressure should be constant as well. In practice this is approximately true, at the best efficiency point, but not true at flows other than best efficiency. As the flow varies from shutoff to the end of the curve, the direction and magnitude of the radial thrust change constantly, passing through a minimum magnitude at the best efficiency point. Normally, the largest thrust

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loads are at shut off and low flow conditions. It is for this reason, among others, that it is not desirable to operate centrifugal pumps at very low flows, or at shut off.

In order to reduce some of the radial forces which act on a centrifugal pump impeller, double-volute casings are frequently used. Such a casing is illustrated in Figure 9.

Figure 9 In a double volute casing, a flow divider is introduced with its cutwater 1800 from the principal pump casing cut water. In this way the radial forces which build up in one half of the casing should be balanced by similar forces in the opposite half of the casing. In practice, complete radial balance is never achieved; however a substantial reduction in unbalanced radial force can be realized. Axial Thrust Of equal importance to the radial thrust is the axial thrust. Every pump from the smallest general service water pump to the largest multistage boiler feed pump must have some provision for restraining the shaft against axial movement, and counterbalancing axial force. In a simple single stage pump, shown diagrammatically in Figure 10, the axial forces are due to two causes:

1. The pressure difference across the back shroud of the impeller at the suction eye. 2. The dynamic effect of the liquid entering the impeller in an axial direction, and turning 90o as it changes

direction to flow in a radial direction through the impeller.

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Figure 10 Therefore, the thrust could be calculated as follows: Thrust = (eye area - shaft area)x (shroud pressure - suction pressure) minus [(Eye area) ( density) x (axial velocity)2/2g Two things should be noted about the above expression for thrust. First, the dynamic force acts in the opposite direction to the force caused by the pressure difference, and secondly the shroud pressure normally lies between the suction and discharge pressure and must be determined by testing. There are three traditional methods of reducing or counterbalancing the residual axial thrust on a centrifugal pump impeller. The most common method is to drill holes in the back shroud of the impeller in the area of the suction eye. This has the effect of relieving the pressure on the back shroud. However, it also permits liquid to flow from the discharge of the impeller, through the clearance between the back shroud and the pump casing, through the balance holes and back into the suction of the pump. It therefore results in inefficiencies due to recirculation and due to flow disturbances caused by the leakage flow from the balance holes mixing with the flow entering the suction of the pump. Another method of achieving axial balance frequently used on single stage overhung pumps is the use of radial ribs on the back shroud of the impeller. Without such ribs, the angular velocity of the liquid in the space between the back shroud of the impeller and the pump casing has been shown by testing to be one half the angular velocity of the impeller. The addition of radial ribs on the back shroud of the impeller increases the angular velocity of the liquid and thus decreases the pressure. There is a theoretical basis for this effect, however it is omitted here since it is very long and complex and not useful or necessary for pump application work . The last commonly used method of axial balance is the use of a balance piston and chamber. This type of axial balance is used almost exclusively on multistage pumps and is illustrated in Figure 11.

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Figure 11 A solid plate or "piston" which rotates with the shaft is mounted on the shaft at the discharge end of the pump. There is a close clearance labyrinth seal between the circumference of the balance piston and the pump casing, and a low-pressure chamber outboard of the balance piston. Since there is a leakage across the labyrinth from the high-pressure inboard side of the balance piston to the outboard low-pressure chamber, the chamber is normally piped either to the pump suction vessel or the pump suction itself, thus permitting the leakage to flow back into the pump suction. If the labyrinth seal is good, this will also serve to maintain the pressure in the chamber at a level slightly above pump suction pressure. Since the resultant force on the balance piston opposes the resultant pressure differential forces on the pump impellers, the balance piston serves as a very effective axial thrust balancing device. Another version utilizes a balance drum and bushing where the pressure breakdown is done in the vertical close clearance between the rotating balance drum face and the stationary balance drum bushing. System Curves A centrifugal pump always operates at the intersection of its Head-Capacity curve and the system curve. The system curve is a curve which shows how much head is required to make liquid flow through the system of piping, valves, etc. The head in the system is made up of three components:

1. Static Head 2. Pressure Head 3. Friction from entrance and exit head losses.

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Figure 12 In Figure 12, the static head is 70 feet, the pressure head is 60 feet, (26-0) x 2.31. The friction head through all the piping, valves and fittings is 18.9 feet when the flow is 1500 gpm. In drawing the system curve, Figure 13, the static head will not change with flow, so it is represented as a horizontal line AB. The pressure head does not change with flow either, so it is added to the static head and shown as a horizontal line CD. The friction head through a piping system, however, varies approximately as the square of the flow. So the friction at 500 gpm will be: (500 /1500)2 x 18.9 = 2.1 feet.(Point E), and the friction at 1000 GPM will be: (1000/1500) 2 x 18.9 = 8.4 ft (Point F)

Figure 13 These determine the system curve, CEFG. All system curves are drawn the same way. The

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pump curve has been overlaid on the system curve in Figure 12. Unless something is done to change either the pump curve or the system curve, the pump will operate at 1500 GPM (Point G) indefinitely. If the throttle valve in the pump discharge line is closed partially, it will add head loss to the system and the pump can be forced to operate at Point H, (1000GPM), Point J (500 GPM), or any other point on its curve. This is essentially bending the system curve by adding head loss, and is known as throttling control. It is the most common form of pump control, but is wasteful of power since the pressure throttled out across the valve (FH or EJ) is lost. Minimum Flow Requirements All centrifugal pumps have minimum flow requirements that must be met to prevent damage to the pump and/or the system. There are six distinct effects that an engineer applying centrifugal pumps must be aware of so that the system has adequate protection to prevent or minimize the consequences of operating at flows below the minimum requirement. 1. Excess heating of the pump due to its inefficiency. This is best illustrated by considering the operation against a closed discharge valve. In this case, all of the pump energy is added to the fluid inside the pump. It will eventually flash to a vapor, usually with detrimental effects to the pump. There is some minimum flow, above which this will not occur, and the pump will continue to operate satisfactorily. It is common, however, to start centrifugal pumps against a closed discharge valve to stabilize the pump as it comes up to speed. The discharge valve should be opened automatically or manually as soon as the pump is up to full speed. Care must be taken with high specific speed not to exceed the motor horsepower rating, because the horsepower vs. capacity curve rises sharply toward shut off. 2. Radial and axial thrust usually both increase as the flow is reduced, and there are limits set by the manufacturer to prevent shaft breakage and bearing failure. 3. Pumps with high suction specific speeds, usually above 12,000, have NPSH requirements that increase rather than continuing to decrease with decreasing flow. Since these pumps are normally applied where the NPSHa is marginal, it is possible to reach the point where the NPSHr exceeds the NPSHa and the pump begins to cavitate at low flows. 4. All pumps have a flow at which there is internal recirculation on the suction and discharge sides of the impeller. Depending on the size, HP, and service of the pump, this can be detrimental to the pump and/or the piping system. 5. On some pumps, in some systems, the suction and discharge pulsations increase at low flows. These can cause excessive piping motion and system upsets. These pulsations usually occur at a frequency equal to the number of impeller vanes x the running speed or some harmonic of this frequency. 6. There is usually noise associated with pump cavitation. Also the noise level usually increases as the flow is decreased because of the added turbulence and recirculation. Many times this is unacceptable because of its effect on personnel. It also manifests itself as increased vibration which can exceed acceptable limits. Each of the six areas may result in a different minimum flow requirement, so the pump manufacturer must specify what the minimum flow requirement is, so the system engineer can design a bypass or recirculation system that has adequate flow capacity. Centrifugal Pump Drives Centrifugal pumps lend themselves to direct connected drives. The great majority of them are driven by induction motors at speeds from 3600 RPM (2 pole-60HZ) down to as low as 300 RPM (24 pole-60HZ), and even lower on very large pumps. The second most common direct connected drives are steam turbines, especially in power plants, refineries, and chemical plants. Also widely used are diesel and gasoline engines, particularly where electric service is

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unavailable or very expensive, for example irrigation pumps. The low starting torque and lack of torque fluctuations generally make direct connected drives simple to engineer and relatively trouble free. Speed increasers are used many times with induction motors where speeds above two-pole speed (3600RPM @ 60HZ) are desirable, generally because of high system head requirements. A few manufacturers have single stage high speed (up to 25,000 RPM) pumps available with the speed increaser as an integral part of the pump. Speed decreasers are also used with induction motors and steam turbines, generally on larger low speed pumps where it is desirable to use lower cost higher speed motors, or mechanical drive turbines that operate most efficiently at speeds greater than 3000 RPM. When gasoline or diesel engines are used to drive vertical turbine pumps, they have right angle gears between the engine and pump, many times with a 1.1 ratio. For variable speed applications, fluid drives, eddy current couplings, wound rotor motors, variable voltage and frequency motors are available. On rubber lined and hard metal slurry pumps, it is common to use V-belt drives to obtain optimum pump speeds while using two or four pole electrical motors. Of course, steam turbines have the inherent advantage of variable speed, as do gas turbines.

Conclusion Much of today's engineering at the design and production levels is performed by computers using commercially-developed programs. This has taken much of the day-to-day "dog work" out of engineering, and has freed up engineers to do more challenging and creative tasks beyond computations. However, it is essential for an engineer to understand what the computer programs actually do, and even more enlightening to be able to trace the origins of a computer calculation back to the basics of F=MA and the first and second laws of thermodynamics. Only then does one really understand, for instance, why a pump performs at it does.

Fortunately, the derivations illustrated in this course are not performed every time an engineer specifies a pump! But once having studied these derivations, an engineer can use the streamlined computer solutions with some increased degree of confidence that he or she knows what the solutions are based upon.

Perhaps the most practical and useful tools to the mechaical engineer presented herein are: (1) The pump affinity laws (2) Understanding the significance of and how to calculate NPSH (3) Interpreting pump performance curves

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Centrifugal Pumps