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Chapter 7
Introduction to Fluid Machinery
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Classification of Fluid Machines– Positive diplacement machines (static type)– Turbomachines (dynamic type)
• Turbines: extract energy to the flow :the fluid does work on them
• Pumps: add energy to the flow = do work to the fluid
• Pumps• Fans• Blowers• Compressor
3
Positive diplacement machinesforce a fluid into or out of a
chamber by changing the volume of the chamber.
Typical positive displacement pumps:(a) tire pump,(b) human heart, (c) gear pump,(d) Peristaltic pump.
From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley(d)
4
Turbomachines• Machines for Doing Work on a Fluid
– Pumps– Fans– Blowers– Compressors
• Machines for Extracting Work (Power) from a Fluid– Hydraulic Turbines – Gas Turbines – Wind-Power Machines
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Machines for Doing Work on a Fluid
Centrifugal Blower Centrifugal Pump
left ventricular assist devices
Fan
http://www.youtube.com/watch?v=V3aPHmZ97yM
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Figure 12.7 (p. 694)(a) Open impeller, (b) enclosed or shrouded impeller. (Courtesy of Ingersoll-Dresser Pump Company).
From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley
7
Machines for Extracting Work
Very simple impulse turbine Impulse turbine
Propeller turbine:Kaplan type
Windmill
8
Turbomachinery AnalysisBlade speed U = ω rr : radial distance from the axis of the fan. ω:angular velocity
Relative velocity W(that seen by a person riding on the fan blade)
Absolute fluid velocity V = W + U(that seen by a person sitting stationary at the
table on which the fan rests)
Fan = pump = do work
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Turbomachinery Analysis• Blade speed U = ω rr : radial distance from the axis of the fan. ω:angular velocity
Relative velocity W
Absolute fluid velocity V = W + U
Windmill = turbine = extracting work Here we are looking for U
Home work: coloring
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Pump or Turbine?• the tangential component of the force of
the blade on the fluid is ►in the direction of the blade motion : PUMPS► in the opposite direction of the blade motion : TURBINE
V=U+WPUMP
W
U
TURBINE
W
U
V=U+W
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Angular momentum principle
Sum of external torques
Net rate of flow of moment-of-momentumThrough the surfae control
Shaft torque :Torque that the shaft applies to the rotor
Torque of the gravity force
Torque of surface forces
Time rate of change of the moment-of-momentum in the volume
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Euler turbomachine equation• Volume controle enclosing the
rotor• Steady flow• Force due to the surface force
may be ignored• Gravity may be ignored
CV
shaft dAVVrT
Notes:
: flow rate m = ρQ = ρVS
Vt > 0 if Vt and U are in the same dircetion
m
13
Pump or Turbine?• if the shaft torque and the rotation of the rotor are in the same direction:
► the energy is transferred from the shaft to the rotor and from the rotor to the fluid
►the machine is a pump
• if the torque exerted by the shaft on the rotor is opposite to the direction of rotation:
►the energy transfer is from the fluid to the rotor►the machine is a turbine.
So if we choose Vt > 0 if Vt and U are in the same directionTshaft > 0 for PUMPSTshaft < 0 for TURBINE
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Pump or Turbine?
VV
Vr
V
Vt
Vn
r
PUMP TURBINE
ω
VVt Vn
r
ω
15
Mechanical Power orShaft Power
shaftm TW
0mW
Using U = r ω and
0mWPUMP TURBINE
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Theoretical Head:
Note: Mechanical Power and Theoretical Head come from angular-moment equation for a control volume then it if for:-Steady flow-Uniform flow at each section
Hydraulic head is a specific measurement of total energy per unit weight
It is usually measured as a water surface elevation :
msm
sm
sm
2
1
H
http://www.youtube.com/watch?v=473XQrJjDZE&list=TLoxakqLv6wIM
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– Negligible torque due to surface forces (viscous and pressure).
– Steady flow– Inlet and exit flow tangent to blades.– Uniform flow at inlet and exit.– Zero inlet tangential velocity = purely radial– Incompressible flow
Example: Idealized Centrifugal Pump
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• Governing equation:
CV
shaft dAVVrT Euler turbomachine equation : from momentum
Continuity
CSCV
AdVVdt
0Steady
R1
R2
VW
U = R2ω
Given: Q , WFind: b2, Tshaft, Wm
ω
b2
Idealized Centrifugal Pump…
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Idealized Centrifugal Pump…
222 2 rW
Qb
Then from continuity: 02 2222
11 brWrV
r1
r2
W
U = r2ω
Given: Q , WFind: b2, Tshaft, Wm
ω
b2
or the mass flow rate:
then
222 2 brWQm
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Idealized Centrifugal Pump…
r1
r2
W
U = r2ω
Given: Q , WFind: b2, Tshaft, Wm
ω
b2
mrTshaft 22U = r2ω = Vt2
V=U+W
W = Vn2
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Idealized Centrifugal Pump…(case: W normal)
shaftm TW
r1
r2
W
U = r2ω
Given: Q , WFind: b2, Tshaft, Wm
ω
b2
U = r2ω = Vt2
V=U+W
W = Vt2222 mRWm
1 0tV
22 2 2 2 2 2 2 2 2
2
cos cos cotsin
nt n
VV U W U U V
Vt2
case: W with a angle β2
b2
2nV2tV
2V
nVt2
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2222 nVbrQ so, 22
2 2 brQVn
H become :
2
2 2 22 2 2 22 2 2 2
cotcot 2nt
QU UU U VU V r bH
g g g
222
22 cot
2
brgQ
gUH
Ideal head developed by a pump with Q flow rate
2 2shaft tW U VHmg g
http://www.youtube.com/watch?v=IiE8skW8btE
b2
2nV2tV
2V
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Torque: Power:
2 2 1 11 ( )shaft
t t
WH U V U V
mg g
Theoretical head :
SUMMARY
b2
tt
tt
t tt
t
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Performance characteristicsFor design a pump or a turbine we must know:-Head-Torque-Power requirement-Efficiency
Note: The idealized analyses presented previously is useful to predict approximate the performances : It is a stat point for design….
But to determined the real performance we must perform measurement of
-Head or pressures-Speed -Input torque-PowerFor different flow rate
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Head as function of flow rateEffect of losses on the pump head-flowrate curve.
From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley
1. Recirculation in the impeler (At low flow rate)
2. Fiction loss (increase with the flow rate)
3. Leakage (increase with the flow rate)
4. « shock loss » mismatch between relative velocity direction and the tangent to impeller blade at the inlet (largest at low and hight flow rate, decrease around the optimum operating condition )
PUMP
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Performance characteristics
Pump head:
Hydraulic Power:
Pump Efficiency:
Note: in term of horse power550
hWePowerWatterHors
For machine doing work on a fluid: Hp is rate of the mechanical energy input to the fluid
For machine doing work on a fluid
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Typical performance characteristics for a centrifugal pump of a given size operating at a constant impeller speed.
From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley
PUMP
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• To vary pump capacity, we could change the impeller size:
Performance curves for a two-stage centrifugal pump operating at 3500 rpm. Data given for three different impeller diameters.
From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley
Bhp: brake horse power
NPSH: Net positive suction head
Best efficiency point
PUMP
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NPSH: Net positive suction head
• On the suction side of a pump: low pressures ►possibility of cavitations( liquid pressure to small ► bubbles ; liquid boil)
►loss in efficiency or pump damage
NPSH = total Head on the suction side (inlet) – liquid vapor pressure
To avoid cavitations NPSH have to be maintained or exceeded.
gPv
gVs
gPsNPSH
2
2
PUMP
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NPSH: Net positive suction head
• NPSH could be determined experimentally• Calculate with known parameters:
Lsss hzg
Vg
Pzg
Vg
P22
2
1
211
Energy equation:
Lssatm hg
Vg
Pzg
P2
2
1 atms PPzV 100;1
Lh Head loss between free surface and pump intlet
Latmss hzg
Pg
Vg
P1
2
2 So,
Then :
gPvhz
gP
gPv
gVs
gPsNPSH L
atm
1
2
2def
PUMP
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Dimensional Analysis
Flow Coefficient:
Head Coefficient:
Performance may be defined by curves head/flow rate for different values of speed, different flow properties etc…But, This would be difficult to represent all the data on a single chart!
Power Coefficient:
Torque Coefficient:DEMO
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Typical performance data for a centrifugal pump: (a) characteristic curves for a 12-in. centrifugal pump operating at 1000 rpm, (b) dimensionless characteristic curves. (Data from Ref. 8, used by permission.)
Power Coefficient
Head Coefficient
Flow Coefficient
From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley
34
Similarity RulesTo achieve dynamic similarity requires geometric and
kinetic similarity:
Head
Power
Flow
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Similarity Rules
For the same pump (same dimension) working a different speed:
21
22
1
2
hh
1
2
1
2
Head
Power
Flow
31
32
1
2
36
Specific Speed
Specific Speed:(dimensionless)
Specific Speed(Customary Units US):
By combining of Flow and Head coefficient, and eliminating the machine size :
4/3
2/1
SN
ScuS NN 46.43
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Specific Speed
Holding specific speed constant describes all operating conditions of geometrically similar machines with similar condition:
Variation in specific speed with type of pump. (adapted from Ref. 10, used with permission.)From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley
38
Applications to Fluid SystemsSystem equation
• Application of equation enegy to a control volume consisting af a pump-pipe system:
Due to the frictionAt the
inlet of the system
At the outlet of the system
Head due to the pump only
flp HHzg
Vg
pzg
Vg
p
1
21
11
2
22
22
22
α : Correction factor=2 for laminar flow close to 1 for hight reynolds number.Cf chap 8 of the text book
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flp HzzH 12
For pipes flows the losses 2KQH fl
212 KQzzH p
flp HHzg
Vg
pzg
Vg
p
1
21
11
2
22
22
22
Applications to Fluid SystemsSystem equation : typical fluid system
Flow loss
40http://www.pipeflow.co.uk
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Applications to Fluid SystemsSystem curve : typical fluid system
Utilization of the system curve and the pump performance curve to obtain the operating point for the system.
System curve :system equation & pump performance
Intersection represent the operating point
If you change the system equation -Change pipe friction (fouling)-Change the watter elevation►You will change the operating point
Idealy: opreating point close the best efficiency
http://www.youtube.com/watch?annotation_id=annotation_261560&feature=iv&src_vid=IiE8skW8btE&v=pWSyrxFJmt4
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– Pump Wear
Applications to Fluid Systems
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-Pumps in Series
Applications to Fluid Systems
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Applications to Fluid Systems
– Pumps in Parallel
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Centrifugal blood pumpExtracorporeal blood pump for cardiac surgery
• Specific requierements: Avoid hemolysis
http://www.medtronic.com/cardsurgery/arrested_heart/centrifugal_pump.html
46
Positive diplacement pumpsforce a fluid into or out of a
chamber by changing the volume of the chamber.
Typical positive displacement pumps:(a) tire pump,(b) human heart, (c) gear pump,(d) Peristaltic pump.
From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley(d)
47
Positive-Displacement Pumps• Fluid with higth viscosity can not be moved with standard
centrifugal pump : viscosity above 850 cP (loss efficiency)
• PD is better! it can work with viscosity changing in a same batch from 1 over 100,000 cP!
• The majority of problems, both centrifugal and PD start at the suction, There must be a minimum amount of absolute pressure avaible to suplly fluid pum suction. PD pumps generally requiere less absolute pressure than centrifugal pumps.
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PD : EfficencyVolumetric efficency = actual volumetric delivery / pump displacement
As pressure is raised or pumps speed reduced
Overall efficency = power delivred to the fluid / power input to the pump
Tends to rise as pump speed increase
49
Peristaltic pump
50
Syringe-pump
Modern medical infusion pump
Blood pumps
Exemples
CHAP. 7- Fluid Machinery…
http://www.youtube.com/watch?v=YqvTKrRJIl8
Jarvik 7 CardioWest TAH• The CardioWest TAH replaces each ventricle with a separate
diaphragm-type pump– Each pump is divided into two chambers by a flexible diaphragm with
blood on one side and air on the other• As air is forced into the device, the diaphragm deforms into the blood
chamber causing blood ejection (systole)• As air is evacuated from the device, the diaphragm deforms into the air
chamber causing blood the enter the device (diastole)– This device is driven pneumatically by an external console attached
to the device by two drivelines that go through the skin– The maximum stroke volume in this device is 70 mL with a flow rate
of 6 to 8 L/min under normal conditions
• This device is currently being used in patients under 67 years old who suffer from biventricular failure and are candidates for transplantation
Nikkiso
• The Nikkiso HPM-15 (Nikkiso Co., Ltd., Tokyo, Japan) is an extracorporeal centrifugal blood pump currently in use in Japan for CPB
– This pump has an impeller with 6 blades
• Extensive simulations of flow and hemolysis have been performed on this device
• According to their website, Nikkiso is presently developing an implantable centrifugal pump
Nikkiso HPM-15 (from Takiura et al., 1998).
HeartQuest VAD
• This device makes use of MagLev technology to magnetically suspend the pump impeller
• Currently, this device has a wearable external battery and controller– Future versions will
make use of TET technology
Upper housing
Outflow cannula
Lower housingImpeller
Figure 5-14. HeartQuest VAD (from Song et al., 2004).
Impella Recover• The Impella Recover (Impella
CardioSystems GmbH, Aachen, Germany) is a catheter-based pump offering short term uni- or biventricular support
– This device is the smallest mechanical circulatory support device in the world
– The Impella Recover can be inserted via the femoral artery or directly into the left ventricle and provides circulatory support for up to 7 days
– A portable console is use to drive and control the pump, thus allowing for easy patient transport
– This device is in use in Europe
Impella Recover Pump (from www.impella.com/bilder/produkte/pumpe_a.jpg).
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