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Centrifugal Pump Performance Experiment Instructors: Dr. Cyders, 294A Stocker, [email protected] Dr. Ghasvari, 249B Stocker, [email protected] Spring 2014

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Part I. • General topics on Pumps • Categories of Pumps • Pump curve • Cavitation • NSPH

Pumps – Basic definitions to describe pumps and pumping pipe circuits – Positive displacement pumps and centrifugal pumps – The ‘Pump Curve’ – Net Positive Suction Head

Pump analysis: energy equation P1 V12 P2 V2 2 z1 z2 h friction hpump g 2g g 2g Q 1

2

• Shaft work delivered by pump is translated into a pressure rise across the pump: P2 > P1 • How does hpump vary with Q? – Typically data is gathered from experiments by manufacturer and is presented in dimensional form (pump curve)

Definitions in a typical pump system: • Liquid flows from the P1 V12 P2 V2 2 z1 z2 h friction hpump suction side to the g 2g g 2g discharge side • Suction head is head P available just before hs zs s h fs g pump, hs: • Discharge head is head at Pd h z h d d the exit from pump, hd: g fd • Pump head, hp: hp hd hs = head required from pump • Flow rates affect terms hfd & hfs

Positive Displacement Pumps • Properties of a PD pump: – Pumps fluid by varying the dimension of an inner chamber. Volumetric flow rate determined size of chamber + RPM of pump. – Nearly independent of back pressure. • Application for metering fluids (example, chemicals into a process, etc.)

– Develops the required head to meet the specified flow rate • Head limit is due to mechanical limitations (design/metallurgy). Catastrophic failure at limit. • High pressure applications

– Able to handle high viscosity fluids. – Often produces a pulsed flow

Types of Positive Displacement Pumps A. B. C. D. E. F. G. H.

Reciprocating piston (steam pumps) External gear pump Double-screw pump Sliding vane Three lobe pump Double circumferential piston Flexible tube squeegee Internal gear

Positive Displacement Pumps

Centrifugal pumps • Characteristics – Typically higher flow rates than PDs. – Comparatively steady discharge. – Moderate to low pressure rise. – Large range of flow rate operation. – Sensitive to fluid viscosity.

Efficiency of centrifugal pumps: • From the energy equation, pumps increase the pressure head • The power delivered to the water (water horse power) is given by • The power delivered by the motor to the shaft (breaking horse power) is given by • Therefore, efficiency is: Note: 1HP = 746W

P1 V12 P2 V2 2 z z h h g 2 g 1 g 2 g 2 friction pump

H

P g

Pw QP Pw gQH

Pbhp T

Pw gQH PBHP T

Centrifugal pumps – pump curves • Real pumps are never ‘ideal’ and the performance of the pumps are determined experimentally by the manufacturer and typically given in terms of graphs or pump curves. • Typically performance is given by curves of: • Head versus capacity • Power versus capacity • NPSH versus capacity – As Q increases the head developed by the screen decreases. – Maximum head is at zero capacity – The maximum capacity of the pump is at the point where no head is developed.

Centrifugal pumps – Sample Pump Curve • • •

3500 is the RPM Impeller size 6¼ to 8¾ in. are shown Maximum efficiency is ~50%. –

•

Maximum normal capacity line –

•

–

H pump

4

2

Remember to correct for density using previous equation

Operating line (system curve) –

2 P2 P1 L Q z2 z1 f hm g D 2 g D2

Max sphere 1¼” This pump is designed for slurries / suspensions and can pass particles up to 1¼”. This is why efficiency is relatively low.

Motor horse power. –

•

Should not operate in the region to the right of the line because pump can be unstable.

Semi-open impeller – –

•

Note that pumps can operate at 80-90% eff.

This is dependent on the system you are putting the pump into. It is a plot from the energy equation. That is, analyze the system to determine the pump head required as a function of flow rate through the pump … This will form the system line.

Pump cavitation and NSPH • Cavitation should be avoided due to erosion damage to pump parts and noise. • Cavitation occurs when P < Pv somewhere in the pump • Since pump increases pressure, to prevent cavitation we ensure suction head is large enough compared to vapour pressure Pv • Net positive suction head • Often we evaluate NPSH using energy equation and reference values – don’t measure Pinlet

NPSH zs

Ps Pv h fs g

NSPHrequired • Manufacturers determine conservatively how much NPSH is needed to avoid cavitation in the pump – Systematic experimental testing

• NSPHrequired (NPSHR) is plotted on pump chart – Caution: different axis scale is common – read carefully

• Plot NPSH vs NSPHrequired to give safe operating range of pump

Qmax

Q

Part II. • Dimensional analysis • Affinity Laws

Dimensionless pump performance

• Previous part: everything dimensional – Terminology used in pump systems – Pump performance charts – NPSH and avoiding cavitation (NPSH vs NPSHR)

• This part : – Discuss how centrifugal pumps might be scaled – Best efficiency point – Examples

Dimensionless Pump Performance • For geometrically similar pumps we expect similar dimensionless performance curves • Dimensionless groups? Q CQ

nD – Capacity coefficient gH CH 2 2 – Head coefficient n D – Power coefficient – Efficiency g NPSH C NPSH – NPSH? n2 D 2 3

CP

Pbh

n3 D 5

• What to use for n (units 1/time): rad/s (), rpm, rps

CH CQ C

Dimensional Analysis • If two pumps are geometrically similar, and • The independent ’s are similar, i.e., CQ,A = CQ,B ReA = ReB A/DA = B/DB • Then the dependent ’s will be the same CH,A = CH,B CP,A = CP,B

Affinity Laws • For two homologous states A and B, we can use variables to develop ratios (similarity rules, affinity laws, scaling laws). CQ , A CQ , B

Q D B B B QA A DA

3

• Useful to scale from model to prototype • Useful to understand parameter changes, e.g., doubling pump speed.

Dimensional Analysis: ideal situation • If plotted in nondimensional form, all curves of a family of geometrically similar pumps should collapse onto one set of nondimensional pump performance curves • From this we identify the best efficiency point BEP • Note: Reynolds number and roughness can often be neglected

Dimensionless Pump Performance • In reality we never achieve true similarity – –

E.g. manufacturers put different impeller into same housing Following figure illustrates a typical example of 2 pumps that are ‘close’ to similar

• Note: • See that at BEP: max = 088 • From which we get * CQ* , CH* , CHS , C* x • From which you can calculate Q, H, NPSH, P

Part III. • More on Centrifugal Pumps • Pump selection

Pump selection • Previous part : – Other types of pumps – Centrifugal and axial ducted – Pump specific speed

• This part Non-dimensional Pi Groups for pumps – Application to optimize pump speed (BEP) – Scaling between pumps

CNPSH

g NPSH n2 D 2

CP

Pbh

n3 D 5

CH

gH n2 D2

CQ

Q nD3

Dynamic Pumps • Dynamic Pumps include – centrifugal pumps: fluid enters axially, and is discharged radially. – mixed--flow pumps: fluid enters axially, and leaves at an angle between radially and axially. – axial pumps: fluid enters and leaves axially.

Centrifugal Pumps • Snail--shaped scroll • Most common type of pump: homes, autos, industry.

Centrifugal Pumps

Centrifugal Pumps: Blade Design

Centrifugal Pumps: Blade Design

Vector analysis of leading and trailing edges.

Centrifugal Pumps: Blade Design

Blade number affects efficiency and introduces circulatory losses (too few blades) and passage losses (too many blades)

Axial Pumps

Open vs. Ducted Axial Pumps

Open Axial Pumps

Blades generate thrust like wing generates lift.

Propeller has radial twist to take into account for angular velocity (=r)

Ducted Axial Pumps • Tube Axial Fan: Swirl downstream • Counter-Rotating AxialFlow Fan: swirl removed. Early torpedo designs • Vane Axial-Flow Fan: swirl removed. Stators can be either pre-swirl or postswirl.

Pump Specific Speed

Pump Specific Speed is used to characterize the operation of a pump at BEP and is useful for preliminary pump selection.

Centrifugal pumps-specific speed Use Dimensionless ‘specific speed’ to help choose. Dimensionless speed is derived by eliminating diameters in Cq and Ch at the BEP.

Proper Lazy

N s'

CQ*

1 2

CH *

3 4

gH n Q*

* 3/ 4

1

Ns

Rpm(Gal / min) 2

H ( ft )

1/ 2

3/ 4

N s 17,182 N s'

What we covered: • Characteristics of positive displacement and centrifugal pumps • Terminology used in pump systems • Head vs flow rate: pump performance charts • NPSH and avoiding cavitation (NPSH vs NPSHR) • Examples

What we covered: • Today we – Developed dimensionless pump variables – Extrapolate existing pump curve to different pump speeds, diameters, and densities – Examples

CQ

Q nD3

CH

gH n2 D2 Pbh

CP CNPSH

n3 D 5

g NPSH n2 D 2

What we covered • Today we: – Examined axial, mixed, radial ducted and open pump designs – Used specific speed to determine which type is optimal

Part IV. • • • •

Lab procedure Venturi Measurements Summary of equations and calculation way Preparing graphs

Lab Objectives • Understand operation of a dc motor • Analyze fluid flow using – Centrifugal pump – Venturi flow meter

• Evaluate pump performance as a function of impeller (shaft) speed – Develop pump performance curves – Assess efficiencies

Lab Set-up Paddle meter

Valve Venturi (P) Dynamometer

E

I Pout

Pump

Motor T

Water Tank

Pin

D.C motor

•Armature or rotor •Commutator •Brushes •Axle •Field magnet •DC power supply

Figure 1. dc motor (howstuffworks.com)

Centrifugal pump operation • Rotating impeller delivers energy to fluid • Governing equations or Affinity Laws relate pump speed to: – Flow rate, Q – Pump head, Hp – Fluid power, P

24

1400

0.6

22 20

1200

0.5

Head (m)

14

800

12 10

600

operating point

8

400

6

pump head 1709 rpm 200 fluid power 1709 rpm pump efficiency 1709 rpm system load - head

4 2 0 0.000

fluid power (W)

1000

16

0.002

0.004

0.006

0.008 3

Flow Rate (m /s)

0.010

0 0.012

pump efficiency,

18 0.4

0.3

0.2

0.1

0.0

Pump Affinity Laws • NQ • N2 Hp • N3 P

N1 Q1 N 2 Q2 2

H p1 N1 H p2 N2 3

N1 P1 P2 N2

Determination of Pump Head Pout Pin V22 V12 Hp Z 2 Z1 g 2g Pout Pin Hp g

Determination of Flow Rate • Use Venturi meter to determine Q • Fluid is incompressible (const. ) Q = Vfluid Area

Venturi Meter

• • • •

As V , kinetic energy T = 0 Height = 0 Pv or P

Calculate Q from Venturi data

Q Cd A2V2 • • • •

V1 = inlet velocity V2 = throat velocity A1 = inlet area A2 = throat area

Throat Velocity 2 2 V1 P1 V2 P2 Z1 Z2

2g

Z 0

g

g

2g

A2 V1 V2 V2 B 2 A1 .

.

P P1 P2

m 1 m 2 A v

V2 f (P, B, )

Discharge Coefficient B Cd 0.907 6.53 ReD ReD

V1D1

D2 B D1

A2 2 V1 V2 V2 B A1

Solve for Q • Use MS EXCEL (or Matlab) • Calculate throat velocity • Calculate discharge coefficient using Reynold’s number and throat velocity • Calculate throat area • Solve for Q

Power and Pump Efficiency • Assumptions – Q 0 – No change in elevation – No change in pipe diameter – Incompressible fluid – T = 0

• Consider 1st Law (as a rate eqn.)

1 2 2 Q W m h2 h1 V2 V1 g Z 2 Z1 2

Pump Power Derivation h u Pv

h2 h1 m u2 P2v u1 P1v W m vP2 P1 W m v AV Q m

W QP2 P1

Efficiencies

output QP2 P1 pump input T T motor EI QP2 P1 overall EI

Summary of Lab Requirements • • • • •

Plots relating Hp, P, and pump to Q Plot relating P to pump Regression analyses Uncertainty of overall (requires unc. of Q) Compare Hp, P, Q for two N’s – For fully open valve position – WRT affinity laws

Pump Head (m)

905 rpm 1099 rpm 1303 rpm 1508 rpm 1709 rpm

3

Flow Rate (m /s)

Power Delevered to Fluid (W)

905 rpm 1099 rpm 1303 rpm 1508 rpm 1709 rpm

3

Flow Rate (m /s)

pump efficiency

905 rpm 1099 rpm 1303 rpm 1508 rpm 1709 rpm

3

Flow Rate (m /s)

Pump Efficiency

905 rpm 1099 rpm 1303 rpm 1508 rpm 1709 rpm

pump power delivered to fluid (W)

Start-up Procedure 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Fill pvc tube with water (3/4 full) Bleed pump Switch breaker to “on” Push main start button Make sure variac is turned counterclockwise Make sure throttle valve is fully open Turn lever to “pump” Push “reset” button Push “start” button Adjust variac to desired rpm using tach.

Pump lab raw data Shaft speed (rpm)

DC voltage (volts)

DC current (amps)

Inlet Pressure (in Hg)

Outlet Pressure (kPa)

Venturi DP (kPa)

Dyna (lbs)

Shut-down Procedure 1. 2. 3. 4. 5. 6.

Fully open throttle valve Turn variac fully counterclockwise Push pump stop button Turn pump lever to “off” Push main stop button Switch breaker to “off”

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