chapter 21 performance of fluid flow equipment

Chapter 21 Performance Curves forPerformance Curves for

Individual Unit Operations(Fluid Flow Equipment)

Department of Chemical EngineeringWest Virginia University

Copyright J. A. Shaeiwitz and R. Turton - 2012 1

OutlineOutline

• Flow in pipesFlow in pipes– laminar vs. turbulent

• NPSH• NPSH

• Pump and system curves– single vs. multiple pumps

– centrifugal vs. positive displacement

– compressors


OutlineOutline


• NPSH• NPSH



– compressors


Key RelationshipsKey Relationships

2

• Turbulent flow

22

4

2∝Δ⇒=Δ

mm

vPDfLvP frfrρ

&&

2

2

32

4==

mfL

Dm

Amv

ρπρ

&

&&

552

32 −∝Δ⇒=Δ DPDmfLP frfr ρπ&


Key RelationshipsKey Relationships

• Laminar flow

LLL

DPvDv Δ==

128321284

42

μππ

&

&

vDPD

LvD

LvP frfr ∝∝Δ⇒==Δ − and12832 442 πμμ &


Example 1Example 1

• Increase velocity by 25% ‐ turbulent flow ‐effect on ΔP

ld12

25.1

old1 new2

2 =

==

vv

2 22

1

∝Δ⇒=Δ vPDfLvP

v

frfrρ

5625.125.1 22

22

1

2 ===ΔΔ

vv

PP

D ff

11Δ vP


Example 2Example 2

• Double diameter – turbulent flow‐ effect on ΔP

2

old1 new2

2 =

==

DD

32 552

21

∝Δ⇒=Δ −DPDmfLP

D

frfrρπ

&

32103125.05.0 5

5

51

1

2 ====ΔΔ

DD

PP

Dρπ

3221Δ DP


OutlineOutline


• NPSH• NPSH



– compressors


NPSHNPSH

NPSH N P i i S i H d• NPSH = Net Positive Suction Head

• There is pressure drop upon entering pump, p p p g p p,before mechanism that increases pressure

• If fluid is too close to vapor pressure at pump• If fluid is too close to vapor pressure at pump inlet, it could flash upon entering pump

• Pumps are designed to handle liquids and do not behave well with vapor


NPSHNPSH

• NPSHA = Pinlet – P *NPSHR

• NPSHA= NPSH “available”

NPSHR

• NPSHR = NPSH “required”i f i li d b f

v&

– information supplied by pump manufacturer


NPSHNPSH

• Common situation

• Apply MEB

1202

2WezgvP

sf −→Δ=−+Δ+Δ

+Δρ

2

02

2

212

fL

DfLvghPP

=+−−

ρ

ρ

*2*

2

2

2

12

PfLvghPPPNPSH

DfLvghPP

+==

−+=

ρρ

ρρ


** 12 PD

ghPPPNPSH A −−+=−= ρ

NPSHNPSH

52

2

1 *32 PD

vfLghPNPSH A πρρ −−+=

&

2

form of

vbaNPSH A −= &NPSH

1

32*

fLb

PghPavbaNPSH A

ρρ −+=

NPSHA

5232

DfLb

πρ

=v&

this is for turbulent flowf l i fl t i ht li


for laminar flow – straight linewith negative slope

NPSHNPSH

2

1

2

32*

fLPghPavbaNPSH A

ρ −+=−= &• How to increase NPSHA

• base case is line (1)increase a line (2)

5232

DfLb

πρ

=– increase a – line (2)

• increase h• increase P1• decrease P*

– decrease T

– decrease b – line (3) NPSHA

• decrease L• increase D

– suction line usually larger D1

32


v&

NPSHNPSHNPSHA > NPSHRpump operates appropriately

R

NPSHA < NPSHRpump will cavitateinappropriate pump operationbut it will operate

NPSHbut it will operate

v&

A

v&


OutlineOutline


• NPSH• NPSH



– compressors


Pump and System CurvesPump and System Curves

• Pump curve (centrifugal pump shown)• Pump curve (centrifugal pump shown)

• Supplied by manufacturer

• Can be measured in lab

• centrifugal is sometimes called “constant head” pump

ΔP in pressure unitsor head developedor head developed

Copyright J. A. Shaeiwitz and R. Turton - 2012 16v&


• System curvepump supplies pressure increase

)()( 323121 Δ−+Δ−+Δ=Δ −−− PPPP fr

to increase fluid pressure and to overcome all of these pressure losses

0)(h)0or0becould()0usually(n destinatio tosource

in-out

31

Δ<>Δ+>Δ=Δ

=Δ

−

PzgPP ρ

0)(valveacrossdroppressurefrictional

0)( pipesin drop pressure frictional0)(pumpacrosschange pressure

32

21

<=Δ

<=Δ>=Δ −

P

PP

fr

0)( valveacrossdroppressure frictional32 <=Δ −P



• To plot system curve – look at source to destination and frictional loss

31

31

)0or0becould()0usually(n destinatio tosourcein-out

)(

zgPP

PPP frsys

<>Δ+>Δ=Δ=Δ

Δ−+Δ=Δ −

ρ

52

2

31

2

31

31

so

322

)obecou d()usu y(des oosou ce

DvfLP

DfLvPP

g

sys&

+Δ=+Δ=Δ −−

−

πρρ

ρ

ΔPsys

( )2 form empirical

so

vbaP

PPP

sys

valvesyspump

&+=Δ

Δ−+Δ=Δ

v&

ΔPsys


v&this is for turbulent flowfor laminar flow – straight line


• Often expressed as head

sysvfLhfLvhh +=+= −−

32252

2

31

2

31&

sys DggD −−

so

523131 π

valvesyspump hhh += hsys


v&


ΔP

ΔPpump < ΔPsysimpossible operation

sys

ΔP

a = ΔPsource dest + ρgΔz if know this point2

{-ΔPvalve

ΔPpump

a ΔPsource-dest + ρgΔzwithcan find a and b

2vbaPsys &+=Δ

operatingv& v&

pumpa}-ΔPfr

ΔPpump > ΔPsysexcess pressure dissipated across partially closed valveas open and close valve, flowrate changes

operating v&


as open and close valve, flowrate changesintersection point is fully open valve

OutlineOutline


• NPSH• NPSH



– compressors


Pumps in Series and ParallelPumps in Series and Parallel

• Series– Pump curve

two pumps

Pump curve

– 2X head at same flowrate

ΔPpump

one pump

v&



• ParallelP

two pumps

– Pump curve

– 2X flowrate at same head

ΔPpumpone pump

same head

v&



• Which configuration

two pumpsseries

configuration maximizes flowrate?

ΔPpumpflowrate?– No general result

one pumptwo pumps parallel

result


v&

OutlineOutline


• NPSH• NPSH



– compressors


Centrifugal – variable speedCentrifugal variable speed

ΔPΔPpump

rpm 5

rpm 3

rpm 2

rpm 4

v& rpm 1

rpm increases with numbermore expensive pump


p p pcost of “wasting” pressure across valve may be less than cost of pump

Positive Displacementfl l /flow regulation/pump curve

ΔP in pressure unitssometimes called “constant volume” pump

por head developed

v&


OutlineOutline


• NPSH• NPSH



– compressors


CompressorsCompressors

locus of maxima = surge line

can also draw systemPout /Pin

rpm 5

can also draw systemcurves on this graph –must change form of left-hand side to ratio

rpm 3

rpm 2

rpm 4

v& rpm 1

rpm 2

usually worth using speed control here because of compression costs


usually worth using speed control here because of compression costs

OutlineOutline


• NPSH• NPSH



– compressors
