Dr. Ir. Harinaldi, M.EngMechanical Engineering Department

Faculty of Engineering University of Indonesia

Centrifugal PuMP

Pumping System in an IndustryPumping System in an Industry

Centrifugal Pump

Construction and ComponentConstruction and Component

CasingCasing

Volute- area enlarge along flow direction- create uniform velocity distributionDiffuser- large size centrifugal pump- guide vanes surround the impeller- fluid flow decelerated while

directed to enter the volute

Working PrinciplesWorking Principles

Fluid

Kineti

c ene

rgy

pressure

InstallationInstallation

iii Zg

Vg

p

2

2

Inlet head :

ooo Zg

Vg

p

2

2

Outlet head : Total head developed by the pump:

ioioio ZZ

gVV

gppH

2

22

outinfofis

s

hhhhHlossesHH

H = manometric headhfi = friction loss at inlethfi = friction loss at outlethin= inlet losshout = outlet loss

ImpellerImpellerTheoretical Assumptions: No tangential flow in

the blade passage Impeller blades are

infinitely thin No Velocity variation

across impeller width Analysis only at inlet

and outlet Radial inlet flow

21

22

21

22

21

22

1122

21 WWUUCCg

gCUCUEh xx

Flow Capacity/Flow Rate

Head and Flow Capacity H Head and Flow Capacity H -- QQTheoretical Head Rise / Euler Head

222111 22 bCrbCrQ rr

slip

2

'2

:

x

xs C

Cfactorslip

STODOLA PROPOSALeCx

STODOLA PROPOSALIf the number of blades is Z, and impeller circumference is 2r2 then the distance between blades is 2r2/Z = 2e/sin Then :

Other Slip FactorStodola 20o < < 30o

222

2

cot1sin1

UCZ rs

Buseman 30o < < 80o

122

222

222

and , offunction are and cot1

cot

rrZBAUC

UCBAr

rs

Stanitz 80o < < 90o

222 cot163.01

UCZ rs

ExampleExampleThe impeller of a centrifugal pump has backward-facing blades inclined at 30o to the tangent at impeller outlet. The blades are 20 mm in depth at the outlet, the impeller is 250 mm in diameter and it rotates at 1450 rpm. The flow rate through the pump is 0.028 m3/s and a slip factor of 0.77 may be assumed. Assume also the blades of infinitesimal thickness. Determine the theoretical and actual head developed by the impeller, and the number of impeller blades

Solution:Flow Capacity/Flow Rate

m/s 78.1

02.025.0028.0

2

2

222

222

r

r

r

r

CC

bDQCbCDQ

For ideal outlet velocity triangle = 30o

m/s 08.330tan/78.130tan22 oorx CW

m/s 92.1508.319

m/s 1960/145025.060

222

22

xx WUCNDU

Theoretical (Euler) head

(ans.) m 83.3081.9

92.1519

) (0 11122

E

inletatradiallyentersflowCg

CUCUE xxx

Actual head with slip

(ans.) m 74.2383.3077.0.. 2

'2

EECC

sN

xsx

Number of blade

(ans.) 815.830cot1978.1130sin177.0

cot1sin1 2222

ZZ

UCZoo

rs

Pump LossesPump Losses1. Mechanical friction power

loss, Pm

2. Impeller (Disc) friction power loss, Pi

3. Leakage and recirculation power loss, Pl

4. Casing power loss, Pc

Pump LossesPump Losses1. Mechanical friction power loss, Pm

Pump LossesPump Losses2. Impeller (Disc) friction power loss, Pi

Head loss : hiFlow rate : Qi

Pi = g Qi hi

Pump LossesPump Losses3. Leakage and recirculation power loss, Pl

Head across impeller : HiLeakage flow rate : q = Qi - Q Pl = g qi Hi

Pump LossesPump Losses4. Casing power loss, Pc

Head loss : hcFlow rate : Q Pc = g Qhc

Pump Losses Pump Losses HH--Q DiagramQ Diagram

EfficiencyEfficiency

so P

gQH inputpower shaft

pumpby developedpower FluidEfficiency Overall

iic H

HgQHgQH

loss Leakage-impellerby developedpower Fluidoutlet casingat power Fluid

inlet casingat power Fluidoutlet casingat power FluidEfficiency Casing

iv Q

QqQ

Q

impeller through rate Flowpump through rate FlowEfficiency Volumetric

EfficiencyEfficiency

ii

i

iii

iii hH

HhHgQ

HgQ

lossimpeller impellerby developedpower Fluidexitimpeller at power Fluid

impeller tosuppliedpower Fluidexitimpeller at power FluidEfficiencyImpeller

s

iiim P

HhgQ

shaft theinput toPower impeller tosuppliedpower FluidEfficiency Mechanical

EH

hHH

iiH

impellerby developed head lTheoreticapumpby developed head ActualEfficiency Hydraulic

Efficiency RelationEfficiency Relation

icH

mvHmvico

Pump Shaft Power, Pump Shaft Power, PPss

QHqHQhQhgPP iciims

Driven Motor Shaft Power, Driven Motor Shaft Power, PPMM

Transmission Efficiency, Transmission Efficiency, TT

MTs PP T

SM

PP

PumpPump’’s Characteristic Curves Characteristic Curve

QKKEgAQUUE

21

222

cot

sN QKKE 21

flowratedesignisQwhere

QQKh

D

Dshock

:

23

24QKhf

Effect of Flow Rate VariationEffect of Flow Rate VariationInlet velocity

Outlet velocityQ ; H Q ; H

Effect of Blade Outlet AngleEffect of Blade Outlet Angle2222 cot rx CUC

bQaHgAQUgUE

gCUUE r

2222

2222

cot

cot

ofor 90 2

ofor 90 2 aH

ofor 90 2 bQaH

Effect of Blade Outlet AngleEffect of Blade Outlet AngleTheoretical characteristic curves

Actual characteristic curves

Flow in the Discharge CasingFlow in the Discharge CasingVolute Casing

Function:1. Collector2. Diffuser

Deviation in capacity from the design condition will result in a radial thrust (P):

222

136.0:

495

DQQKwhere

BKHDP

Function:P = radial force (N)H = Head (m)D2 = peripheral diameter (m)B2 = impeller width (m)Circular section to

reduce losses due to friction and impact

Flow in the Discharge CasingFlow in the Discharge CasingVaneless Diffuser

Flow in the Discharge CasingFlow in the Discharge CasingVaneless Diffuser Continuity:

222222 rrr CbrCrbACm rbCbrC rr 2222

Conservation of angular momentum:

rxxx CCusuallyrrCC 22

Then: xCC

rrCC x 22 Radius, r Outlet kinetic energi

'tan'tan 222 consCC rx

drrd

'tan

22 ln'tan rr Then:

diffuserofangle

Flow in the Discharge CasingFlow in the Discharge CasingVaned Diffuser

Number of vanes on the diffuser ring:

Greater number better diffusion but more friction loss

Square cross section of diffuser channel max rh

Number of diffuser vanes have no common factor with the number of impeller

Higher rate Shorter length Higher efficiency

Able to diffuse the outlet kinetic energy at:

Flow in the Discharge CasingFlow in the Discharge CasingContribution of each section of the pump to total head

Cavitation in PumpsCavitation in PumpsVapour bubbles formation of the liquid as the local absolute static pressure of a liquid falls below the vapour pressure occurs mainly at the suction side (at the eye of impeller as the

velocity increases and pressure decreases) Local pitting of impeller cavitation erosion Noise Decrease pump efficiency

Net Positive Suction Head (NPSH)Net Positive Suction Head (NPSH)The difference of total suction head in the impeller inlet side (impeller eye) above the vapour pressure

absolutearepressuresallg

pg

Vg

pNPSH vapii 2

2

A measure of the energy available on the suction side of the pump

A measure to indicate the occurrence of cavitation

Cavitation Parameter (Toma Cavitation Number)

Hg

pg

Vg

p

pumpbyDevelopedHeadNPSH

vapii

2

2

NPSH Required (NPSHR) Net Suction Head as required by the pump

in order to prevent cavitation for safe and reliable operation of the pump.

The required NPSHR for a particular pump is in general determined experimentally by the pump manufacturer (will vary depending on the size and speed of the pump) and a part of the documentation of the pump.

Net Positive Suction Head (NPSH)Net Positive Suction Head (NPSH)

Measurement of NPSHR by 3% head reduction

Example of pump documentation

NPSH Available (NPSHA) The Net Positive Suction Head

made available the suction system for the pump.

The NPSHA can be determined during design and construction, or determined experimentally from the actual physical system and calculated with the Energy Equation

Net Positive Suction Head (NPSH)Net Positive Suction Head (NPSH)

Energy at 1 = Energy at 2 + Energy lost between 1 and 2

inletinlet losseszg

pg

Vg

plosessg

Vg

pzg

p1

12

222

221

1

22

At inlet p2 = pi ; V2 = Vi and lossesinlet = hin + hfi, then:NPSH available at impeller inlet :

fiivap

A hhzg

pg

pNPSH 11

To avoid cavitation in a pump operationCavitation ~ NPSHCavitation ~ NPSH

RA NPSHNPSH RA or

Suction Specific SpeedSuction Specific SpeedA function due to cavitation that influences the efficiency

4/3

2/1

NPSHgNQN suc

Dimensionless suction specific speed

sucNf ,

4/34/3

4/3

H

NPSHNN

suc

s

Cavitation parameter

212

212

212

1 DDNNNPSHNPSH

Similarity Laws

ExampleExampleWhen a laboratory test was carried out on a pump, it was found that, for a pump total head of 36 m at discharde of 0.05 m3/s, cavitation began when the sum of the static pressure plus the velocity head at inlet was reduced to 3.5 m. The atmospheric pressure was 750 mmHg and the vapour pressure of water 1.8 kPa. If the pump is to operate at a location where atmospheric pressure is reduced to 620 mmHg and the vapour pressure of water is 830 Pa, what is the value of the cavitation parameter when the pump develops the same total head and discharge? Is it necessary to reduce the height of the pump above the supply, and if so by how much?