0262 1762/06 © 2006 Elsevier Ltd. All rights reserved WORLD PUMPS January 200624

The net positive suction head(NPSH) is defined as thedifference between suctionpressure and vapour pressuremeasured at the pump suctionnozzle when the pump is running.In a reciprocating pump NPSH isrequired to push the suction valvefrom its seat and to overcome thefriction losses and accelerationhead within the liquid end.

The flow output from a recip-rocating pump is unsteady andthe pumped fluid is constantlyaccelerating and decel-erating. Acertain amount of energy, theacceleration head, is required toproduce the acceleration.

The acceleration head is often solarge that the net positive suctionhead required (NPSHR) cannot bemet. The acceleration head can bereduced by increasing the pipediameter, shortening suctionpiping, decreasing pump speed orusing a suction stabilizer. Whennet positive suction headavailable (NPSHA) becomes lowerthan net positive suction headrequired, or very close to it,cavitation will occur

‘Displacementmachine’A reciprocating pump is a‘displacement machine’. Atconstant speed, handling a givenliquid, reciprocating pumpsdeliver essentially constant flowregardless of system resistance.Volumetric efficiency falls withincreasing differential pressure.

Unlike centrifugal pumps theycan achieve high pressure at lowvelocities.

Another characteristic of areciprocating pump is thatcapacity is a function of speed andis relatively independent ofdischarge pressure.

All reciprocating pumps containone or more pumping elements(piston or plunger) that move intoand out of pumping chambers toproduce the pumping action.Each chamber contains at leastone suction and one dischargevalve (Figure 1).

PressureAs the pumping element iswithdrawn from the pumpingchamber, liquid within thechamber expands and thepressure decreases. Since mostliquids are relativelyincompressible, very littlemovement of the element isrequired to decrease the pressure. When the pressure decreasessufficiently below suctionpressure, the differential pressure(that is, suction pressure —chamber pressure), pushes openthe suction valve. This occurswhen the element is movingslightly, so that the valve opens gradually and smoothly as the velocity of the elementincreases. Liquid then flowsthrough the valve assembly andfollows the element on its suction stroke. As the element

decelerates near the end of thisstroke, the suction valve graduallyreturns to its seat. When theelement stops, the suction valvecloses.

The pumping element thenreverses and starts on itsdischarge stroke. The liquidtrapped in the pumping chamberis compressed until chamberpressure exceeds the dischargepressure by an amount sufficientto push the discharge valve awayfrom its seat.

With a power pump, the velocityof the element (piston or plunger)varies approximately as the sineof the angle of the crank throw.The velocity of the liquid in thepiping is proportional to plungervelocity.

Indicator diagram The graph between the pressurein the cylinder and volume sweptby the piston for one completerevolution is called the indicatordiagram.

The volume swept by the piston is equal to product of A(cross-sectional area of cylinder)and 2x (distance travelled by thepiston). Since A remains constantduring piston motion, the volumeswept by the piston isproportional to x. This means thatwe can substitute x for volumeswept by the piston. For hydraulicpumps it is convenient to takepressure head (p/w) in place ofpressure.

So, the indicator diagram (Figure 2) for a reciprocatingpump is a graph betweenpressure head in the cylinderagainst distance travelled by thepiston for one completerevolution of crank. If thepressure in the sump is taken asatmospheric, then the pressurehead in the cylinder during thesuction stroke will be constantand given by Equation 1.

Cavitation in reciprocating pumpsCavitation is a common occurrence, but is one of the least understood of all pumpingproblems. Here, Trinath Sahoo explains how acceleration head phenomena and net positivesuction head available are related to cavitation

s p e c i a l f o c u s I n d i a

Figure 1. A reciprocating pump

is a ‘displacementmachine’.

Suction valve

Suction pipePiston

Piston rodSump level

Delivery valveCylinder

Connecting rod

Crank

Reservoir levelDelivery pipe

h

hd

hs

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s p e c i a l f o c u s I n d i a

pressure head in cylinder = Pa/W – hs (absolute) (Equation 1)This can be represented by line abin Figure 2.

Pressure head in the pumpcylinder during the return ordelivery stroke must be hd metresof liquid above atmosphericpressure and is represented onthe indicator diagram by line cd.

At the end of the suction strokethe pressure head must jumpfrom suction head hs to deliveryhead hd before the beginning ofthe delivery stroke. This jump isrepresented by line bc. Similarly,at the end of the delivery stroke,the pressure head must fall fromhd to suction head hs, before thestart of the suction stroke. This isshown in the figure by line da. Inthis way, quadrilateral abcdrepresents the indicator diagram(Figure 2).

Effect of accelerationIt is obvious that in thereciprocating motion underconsideration, the velocity ofthe piston is not uniform at allpoints. It is zero at the end ofeach stroke, and reaches amaximum at the centre — if the motion of the piston isassumed to be simple harmonicin character.

Starting from point IDC after timet, the crank and piston are in theposition that is shown in thediagram (Figure 3). Let θ bethe regular distance travelled bythe crank. Then the distancetravelled by the piston is given byEquation 2.

x = r – rcosθ= r – rcosωt (Equation 2)

By differentiating x with respectto time t we obtain the velocity ofthe piston (Equation 3).

dx/dt = rωsinωt = rωsinθ(Equation 3)

Since the quantity of liquidflowing from the pipe to thecylinder, or from the cylinder tothe pipe is the same at any time,the velocity of water in the pipe isequal to the velocity of the piston(r is the radius of crank; and L = 2r,is the length of stroke).

Velocity of water in the pipe is:

= (A/a)r ωsinωt = (A/a)r ωsinθ(Equation 4)

where A is the area of cross-section of the cylinder and a is thearea of the cross-section of thepipe. Differentiating once againwith respect to time, we obtainthe acceleration of the water:

= (A/a)rω2cosωt = (A/a)rω2cosθ(Equation 5)

The mass of the water to beaccelerated is:

= wal/g (Equation 6)

where l = length of pipe.

The force required to acceleratethe water in the pipe is:

F = (wal/g)(A/a)rω2cosωt(Equation 7)

The intensity of pressure causedby the acceleration is given by:

P = F/a = (wlA/ga)rω2cosωt(Equation 8)

Pressure head (Figure 4) oracceleration head ha

= p/w = (l/g)(A/a)rω2cosωt(Equation 9)

It is clear from these equationsthat the acceleration headrequired by the pump is maximumat the beginning of each strokewhen θ = 0º, zero in the middle θ =90º, and a maximum negative atthe end of each stroke, when θ =180º. The magnitude of maximumacceleration is:

= (l/g)(A/a)rω2 (Equation 10)

that is, when cosωt = 1, (θ = 0º).

Effect of pipe frictionThe pump also provides pressureto overcome loss of fluid headbecause of friction:

hf = (4flv2/2gd) (Equation 11)

where f is Darcey’s coefficient offriction.

hfs = [4fls(Arωsinθ)2]/2gds(Equation 12)

hfg = [4fld(Arωsinθ)2]/2gdd(Equation 13)

From the above equation, it isclear that loss of head because offriction is zero at the beginningand end of each stroke when θ = 0º or θ = 180º, and a maximumat θ = 90º of each stroke.

hf(max) = [4fls(Arω)2]/2gds(Equation 14)

DiscussionWhen net positive pressure headat the inlet falls below vapourpressure head (Pv /w) thencavitation occurs.

From the diagram shown inFigure 5 we can see that the pointof lowest pressure during suctionstroke is a’, that is, at the

ab

cd

o o'

Datum

Length of strokepaw

pw

hd

hs

L.D.Cxx

O.D.CI.D.C

ω

r

θ

l

Figure 2. Theindicator diagram.

Figure 3. Rotarymotion convertedinto reciprocatingmotion.

WORLD PUMPS January 200626

s p e c i a l f o c u s I n d i a

beginning of the suction stroke.Hence, cavitation during thesuction stroke — if it occurs — islikely to occur at the beginning ofthe suction stroke, and willobviously occur at the highestpoint of suction pipe, that is,where the suction pipe meets thepump cylinder.

Net positive pressure head at thepoint a’ is:

= Pa/w – hs – has(max) (Equation 15)

= Pa/w – hs – ls/g(A/as)rω2

(Equation 16)

Cavitation will start to occur whenthis value falls below vapourpressure head (Pv /w). This meansthat cavitation puts a limit on thesuction height of pump suctionpipe length and the speed of thepump, because acceleration headis proportional to ω2.

The principal component of areciprocating pump’s NPSHR is thepressure differential required toopen the suction valve. Therefore,NPSHR, expressed in pressureterms, increases with pump speedand valve closing force. The netpositive suction head is defined asthe difference be-tween suctionpressure and vapour pressure,measured at the pump suctionnozzle when the pump is running.

In a reciprocating pump, NPSH isrequired to push the suction valvefrom its seat and to overcome thefriction losses and accelerationhead within the liquid end. This isbecause, a significant portion ofthe required NPSH is used to openthe valve (particularly at lowpump speeds), and because this isa pressure rather than a headrequirement (NPSHR). For areciprocating pump this is

normally expressed in pressureunits. For example, if a powerpump requires 2 psi of NPSH whenpumping water, it will also require2 psi NPSH for propane.

As the suction valve is keptvertical, the valve can operatewithout a spring if the pumpspeed is kept low. The NPSHrequirement for a bigger plungerand higher speed is greater thanthat of a smaller plunger and thelower speed, when tested withthe same fluid. 9The speed of thepump is limited by the ability ofthe suction valve to ‘keep up’ withthe plunger. If a higher speed isdesired, stiffer springs areneeded.

NPSH testPower pump NPSH tests areperformed by holding the pumpspeed and discharge pressureconstant and varying the NPSHAin the system.

The capacity remains constant forall NPSHA values above a certainpoint. As NPSHA is reduced belowthis point, capacity begins to fall.A 3% capacity drop is the criteriafor defining NPSHR.

RemediesThere are a number of ways toincrease NPSHA. These are: • enlarge the diameter of

suction line;• reduce the length of suction

line by moving the pump closerto the suction vessel;

• install a suction bottle; • elevate the suction vessel or

level of liquid; and • reduce the speed of the power

pump, or select a larger pumprunning at a lower speed.

Rotating speed One of the most importantparameters for power pumps isthe maximum allowable speed. The velocity variation in thepiping for a triplex pump is 25%,regardless of the pump size orspeed. For the same capacity, asmaller pump, running faster, willproduce the same maximum andminimum flow rates and morepulses per second. Since theacceleration head increases indirect proportion to frequency,doubling the pump speed doublesthe acceleration head, therebyreducing NPSHA from the system.Also doubling the speed requiresa stiffer valve spring, therebyincreasing NPSHR. As previouslystated, if NPSHA drops belowNPSHR, cavitation will occur.

The speed of the pump is limitedby the ability of the suction valveto ‘keep up’ with the plunger.When there is no spring to pushthe valve back onto its seat,gravity is the only force acting toclose the valve against theexisting fluid. If the pump isrunning too fast the valve will stillbe off its seat when the plungerreverses and starts to re-enter thepumping chamber. The liquid will then momentarily flowbackwards through the seat, andthe valve will be slammed onto itsseat, sending a shock wave to thesuction manifold and piping.

The pressure in the pumpingchamber will quickly exceeddischarge pressure, and thedischarge valve will be drivenfrom its seat. A shock wave will betransmitted from the pumpingchamber, though the dischargemanifold to the discharge line.

Valve spring factor

At low speeds (100 rpm or less)the characteristics of the suctionvalve spring are of littleconsequence, and a low suctionpressure can be tolerated.

Many low-speed pumps operatewithout the valve spring. Thepump suction pressure require-ment depends on the pump speedand the valve spring rate. Thevolumetric efficiency of the pumpimproves when the pump isrunning at low rpm and the valvehas a higher spring rate.

Datum

hd

hshs has(max)

has(max)

had(max)

had(max)

a b

b'

d'

c

c'

d

a

a'

o o'

paw

Figure 4. Theindicator diagramwith acceleration.

The higher spring rate increasesefficiency at the cost of highersuction pressure. Lower suctionpressure diminishes the volu-metric effici-ency. A higher valvespring rate increases theefficiency.

When stiffer springs are added tothe suction valves, the springforce and the valve weight mustbe overcome to open the suctionvalve, so NPSHR increases. Thesesprings return the valves to theirseats quickly so that operation issmooth at higher speeds. Lightsprings should be used for a lowpressure and low speed, whileheavy springs should be used fora high speed and high pressure.

Plunger size Generally, in reciprocating pumpsthe size of the plunger can bechanged. The larger clearancethat results from using a smallerdiameter plunger lowersvolumetric efficiency. However,for the same rotational speedand service conditions NPSHRrises if the plunger size isincreased.

Entrained gas Reciprocating pumps will com-press gas, but the pressuredeveloped is limited by theusually large clearance volume.Unless the pump can dischargesome gas during each stroke, itwill not clear itself.

A second and potentially moreserious problem arises if the pumpis able to raise the pressuresufficiently to force the gas intothe liquid solution. Should thishappen, the sudden change involume can produce a destructivepressure pulsation.

When the liquid contains air or isexposed to gas other than its ownvapour, the vapour pressure of thesolution increases. The HydraulicInstitute, based in the USA,recommends an NPSH margin of 3 psi for power pumps in systemswhere the pumpage has beenexposed to a gas other than theliquid’s own vapour. To minimizethe problem of dissolved air, theNPSH tests are performed withwater near its boiling point, in thesuction vessel.

The stuffing box packing is asource of air ingress when thesuction pressure is belowatmospheric pressure. In that case,air is drawn through the stuffingbox packing into the pumpingchamber on the suction stroke. Airingress will cause a drop incapacity and make the pumpoperate noisily.

Differential pressureWhen a pump operates with a lowdifferential pressure the effect ofcavitation is difficult to detect.However, when a pump handlesliquid with a high dischargepressure, the effect of cavitation ismore pronounced.

Liquid properties When reciprocating pumps areused in viscous service, there is acorresponding decrease in themaximum allowable speed atwhich they are able to operatesatisfactorily. A decrease in thespeed reduces the volumetric flow.This decease limits the flow range. Increasing viscosity has twoeffects. Firstly, the motion of thevalves is impeded. At constantspeed this leads to greater valveleakage, hence, lower volumetricefficiency. Alternatively, for agiven volumetric efficiency, thepump speed must be reduced asviscosity increases.

The second effect is increasedhead loss through the suctionvalve and post, resulting in higherNPSHR. The extent of this effectincreases with pump designpressure.

Pumps with a high fluid temp-erature must be run at a reducedspeed in order for them tooperate properly.

Suction line The suction line is sized to limit thefluid velocity 1-3 ft/s. This lowvelocity reduces the accelerationhead of the system, maximizingNPSHA of the pump. The longradius elbow minimizes pressuredrop and maximizes the NPSHA.

The eccentric reducer decreasesthe line size from the largersuction pipe diameter, drawn tothe inlet size of the pump. Thisreducer is orientated in such a way

that air pockets cannot form inthe pipe. The suction stabilizerusually contains internal partssuch as a bladder, diaphragms,choke tubes or baffles. It is used infront of the pump to reduce thepressure pulsation in the pipe andacceleration head in the system.

Suction stabilizer

Suction stabilizers greatlydecrease the pulsation that ispassed on through the pipingsystem, or even the pulsation thatis reflected back to the pump.

Generally, these are pressurizedvessels or containers with agas–liquid interface. Some have adirect interface, others use anelastomeric sheet to keep themseparated. The energy from thepressure pluses is partiallyabsorbed and the peaks on thepulsation curves are reduced.

Using a pulsation dampenerreduces acceleration head andfriction losses (to minimizeNPSHA) when installed as asuction stabilizer in the suctionpiping. Using a suction stabilizerproduces steady flow and reduceshigh pressure fluctuations in thepipe system.

ConclusionThe NPSHA must be greater thanthe NPSHR, for the pump todeliver its rated flow. When theNPSHA is below the NPSHR, thepump’s capacity is reduced. Insevere cases, the shocks associatedwith the vapour collapse (asudden reduction in pumped fluidvolume) can cause major parts of apump to fracture. ■

CONTACT:Trinath Sahoo Deputy maintenance manager (FOB) Indian Oil Corp Ltd , Haldia Refrinery Dist-Midnapore, West Bengal India, 721606 Email: sahoot@iocl.co.in

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s p e c i a l f o c u s I n d i a

Figure 5. Theindicatordiagram withacceleration andfriction.

hd

hfd (max)

hfs (max)

had(max)

(max) a'

ba

d

e

b'

c'

c

has

hs

d'