Chapter 7. Introduction to Fluid Machinery

Transcription

1 Chapter 7 Introduction to Fluid Machinery 1

2 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 machines force 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. (d) From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley 3

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 4

5 Machines for Doing Work on a Fluid Centrifugal Blower Centrifugal Pump left ventricular assist devices Fan 5

6 Figure 1.7 (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 6

7 Machines for Extracting Work Very simple impulse turbine Impulse turbine Propeller turbine: Kaplan type Windmill 7

8 Turbomachinery Analysis Blade speed U = ω r r : 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 8

9 Turbomachinery Analysis Blade speed U = ω r r : radial distance from the axis of the fan. ω:angular velocity Relative velocity W Absolute fluid velocity V = W + U Home work: coloring Windmill = turbine = extracting work Here we are looking for U 9

10 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 W W V=U+W PUMP U V=U+W U TURBINE 10

11 Angular momentum principle Sum of external torques Time rate of change of the moment-ofmomentum in the volume Net rate of flow of moment-ofmomentum Through the surfae control Torque of surface forces Torque of the gravity force Shaft torque : Torque that the shaft applies to the rotor 11

12 Euler turbomachine equation Volume controle enclosing the rotor Steady flow Force due to the surface force may be ignored Gravity may be ignored T shaft CV r VV da Notes: m : flow rate m = ρq = ρvs Vt > 0 if Vt and U are in the same dircetion 1

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 direction Tshaft > 0 for PUMPS Tshaft < 0 for TURBINE 13

14 Pump or Turbine? V V Vn V Vt V Vn r Vt r ω r V ω PUMP TURBINE 14

15 Mechanical Power or Shaft Power W m T shaft Using U = r ω and W m 0 PUMP W m 0 TURBINE 15

16 Theoretical Head: Hydraulic head is a specific measurement of total energy per unit weight H It is usually measured as a water surface elevation : 1 m s m m m s s 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 16

17 Example: Idealized Centrifugal Pump 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 17

18 Idealized Centrifugal Pump W V R R 1 U = R ω ω Given: Q, W Find: b, T shaft, Wm Governing equation: Euler turbomachine equation : from momentum Continuity Steady T t shaft CV dv r V CV CS b Vd A 0 V da 18

19 Idealized Centrifugal Pump W r r 1 U = r ω ω Given: Q, W Find: b, T shaft, Wm Then from continuity: V r W r b 0 b 1 1 or the mass flow rate: then m Q W b Q W r r b 19

20 Idealized Centrifugal Pump W r r 1 U = r ω ω Given: Q, W Find: b, T shaft, Wm b V=U+W T shaft r m W = V n U = r ω = V t 0

21 r Idealized Centrifugal Pump r 1 W (case: W normal) U = r ω ω Given: Q, W Find: b, T shaft, W m b W m W m T shaft R m W = V t V=U+W U = r ω = V t 1

22 case: W with a angle β V n V V t Vt Vt n Vt1 0 b V V U W cos U cos U V cot n t n sin

23 H W shaft mg UV g t V n V V t Q rb Vn so, V n Q r b H H become : Q U UV g g g cot U UU V ncot t rb H U Q cot g g r b b Ideal head developed by a pump with Q flow rate 3

24 SUMMARY Torque: Power: t t t t t t t t Theoretical head : W shaft 1 H ( UVt UV 1 t1 ) mg g b 4

25 Performance characteristics For 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 -Power For different flow rate 5

26 PUMP Head as function of flow rate Effect of losses on the pump head-flowrate curve. 1. Recirculation in the impeler (At low flow rate). Fiction loss (increase with the flow rate) 3. Leakage (increase with the flow rate) From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley 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 ) 6

27 Performance characteristics For machine doing work on a fluid Pump head: For machine doing work on a fluid: Hp is rate of the mechanical energy input to the fluid Hydraulic Power: Pump Efficiency: Note: in term of horse power WatterHorsePower W h 550 7

28 PUMP 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 8

29 PUMP To vary pump capacity, we could change the impeller size: Best efficiency point Bhp: brake horse power NPSH: Net positive suction head 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 9

30 PUMP 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 NPSH Ps g Vs g Pv g To avoid cavitations NPSH have to be maintained or exceeded. 30

31 PUMP NPSH: Net positive suction head NPSH could be determined experimentally Calculate with known parameters: hl Energy equation: P1 V1 g g z 1 Ps Vs g g z s Head loss between free surface and pump intlet h L V 1 z 0 P1 0 ; s P atm P g atm z 1 Ps g Vs g h L So, Ps g Vs P g g atm z 1 h L Then : NPSH def Ps g Vs g Pv g P g atm z 1 h L Pv g 31

32 Dimensional Analysis 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! Flow Coefficient: Head Coefficient: Power Coefficient: Torque Coefficient: DEMO 3

33 Head Coefficient Power Coefficient Flow Coefficient Typical performance data for a centrifugal pump: (a) characteristic curves for a 1-in. centrifugal pump operating at 1000 rpm, (b) dimensionless characteristic curves. (Data from Ref. 8, used by permission.) From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley 33

34 Similarity Rules To achieve dynamic similarity requires geometric and kinetic similarity: Flow Head Power 34

35 Similarity Rules For the same pump (same dimension) working a different speed: Flow Q Q 1 1 Head h h 1 1 Power

36 Specific Speed By combining of Flow and Head coefficient, and eliminating the machine size : N S 1/ 3/ 4 Specific Speed: (dimensionless) Specific Speed (Customary Units US): N N S cu S 36

37 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 37

38 Applications to Fluid Systems System equation Application of equation enegy to a control volume consisting af a pump-pipe system: p g V p V z z g g g H p H fl At the outlet of the system At the inlet of the system Head due to the pump only Due to the friction α : Correction factor = for laminar flow close to 1 for hight reynolds number. Cf chap 8 of the text book 38

39 39 p H fl z z H 1 For pipes flows the losses H fl KQ 1 KQ z z H p H p H fl z g V g p z g V g p Applications to Fluid Systems System equation : typical fluid system Flow loss

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41 Applications to Fluid Systems System curve : typical fluid 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 Utilization of the system curve and the pump performance curve to obtain the operating point for the system. 0&feature=iv&src_vid=IiE8skW8btE&v=pWSyrxFJmt4 41

42 Applications to Fluid Systems Pump Wear 4

43 Applications to Fluid Systems -Pumps in Series 43

44 Applications to Fluid Systems Pumps in Parallel 44

45 Centrifugal blood pump Extracorporeal blood pump for cardiac surgery Specific requierements: Avoid hemolysis 45

46 Positive diplacement pumps force 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. (d) From fundamentals of fluid mechanichs Monson (5th edition) Young Okiishi Wiley 46

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. 47

48 PD : Efficency Volumetric 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 48

49 Peristaltic pump 49

50 Syringe-pump Modern medical infusion pump 50

51 CHAP. 7- Fluid Machinery Blood pumps Exemples

52 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

53 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).

54 HeartQuest VAD Outflow cannula This device makes use of MagLev technology to magnetically suspend the pump impeller Upper housing Currently, this device has a wearable external battery and controller Future versions will make use of TET technology Lower housing Impeller Figure HeartQuest VAD (from Song et al., 004).

55 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