Textbook of machiens hydraulic

A

CONTENTS

CHAPTER (I) BASIC THEORY

Historical Review . . . . . . . . . . . . . 2

1.1 General Introduction . . . . . . . . . . . . 4

1.2 Velocity Diagram . . . . . . . . . . . . . . 5

1.3 Momentum Transfer Principles . . . . . . . . 6

1.4 Energy Equation . . . . . . . . . . . . . . 9

1.5 Theories of Turbomachines . . . . . . . . . .

Euler Theory (Elementary)

Modern Theory

Necessity for flow unsteadiness

1.5.4 Approximate calculation of deviation

after Stodola

11

11

14

18

19

1.6 Some Practical Considerations (Actual

Machine Design) . . . . . . . . . . . . . .

Friction

Disk Friction

Leakage

Pre-rotation of the fluid

20

20

20

21

21

1.7 Coefficients and Efficiencies . . . . . . . . .

Circulatory Flow Coefficient

Manometric Efficiency

Mechanical Efficiency

Volumetric Efficiency

Hydraulic Efficiency (Turbine)

22

22

22

23

23

23

CHAPTER (II) DIMENSIONAL ANALYSIS AND

SIMILITUDE OF TURBOMACHINES

2.1 Introduction . . . . . . . . . . . . . . . . 24

2.2 Dimensional Analysis . . . . . . . . . . . . 24

2.3 Hydraulic Similarity . . . . . . . . . . . . . 25

2.4 Application of Dimensional Analysis on

B

Turbomachines . . . . . . . . . . . . . . .

2.4.1 Discussion

2.4.2 Performance Curves

26

27

28

2.5 Scale Effect . . . . . . . . . . . . . . . .

Reynolds Number effect

Scale effects in Hydraulic Machines

Scale effects in compressible machines

29

29

30

35

2.6 Affinity Laws . . . . . . . . . . . . . . . . 39

2.7 Specific Speed . . . . . . . . . . . . . . .

Pumps

Compressors and Blowers

Hydraulic Turbines

40

41

43

43

2.8 Pressure and Flow Coefficients . . . . . . . . 44

2.9 Specific Diameter . . . . . . . . . . . . . . 44

CHAPTER (III) CASCADE MECHANICS

"TWO-DIMENSIONAL APPROACH"

3.1 Introduction . . . . . . . . . . . . . . . . 47

3.2 Cascade Nomenclature . . . . . . . . . . . . 47

3.3 Analysis of Cascade Forces . . . . . . . . . . 49

3.4 Lift and Drag . . . . . . . . . . . . . . . . 51

3.5 Cascades in Motion . . . . . . . . . . . . . 54

3.6 Cascade Performance . . . . . . . . . . . .

General Approach

Fluid Deviation

Off-Design Performance

Turbine Cascade Performance

55

55

57

59

59

3.7 Mach Number Effect . . . . . . . . . . . . 60

3.8 Ideal Characteristics . . . . . . . . . . . .

Zero Lift Angle

Impulse Flow Angle

62

62

63

3.9 The Head-Capacity Curve of Straight Cascade . 64

3.10 Radial Cascade . . . . . . . . . . . . . . 65

3.11 Cascade Characteristics Analysis . . . . . . . 67

3.12 Singularity Method . . . . . . . . . . . .

Method of Solution for Single Airfoil

Conformal Transformation Method

67

69

71

C

CHAPTER (IV) INCOMPRESSIBLE FLOW

TURBOMACHINES ( PUMPS )

4.1 Introduction . . . . . . . . . . . . . . . . . 78

4.2 Centrifugal Pumps (Radial) . . . . . . . . . .

4.2.1 General Considerations

a. Volute type pump

b. Diffuser type pump

4.2.2 Effect of Impeller Exit Angle β2

4.2.3 Efficiencies and Coefficients of Centrifugal Pumps

i. Efficiencies

ii. Coefficients

iii. Affinity Laws

iv. Specific Speed

4.2.4 Centrifugal Pump Actual Performance

4.2.4.1 Actual Head Capacity Curve

4.2.4.2 Brake Horsepower and Efficiency Curves

4.2.4.3 Analysis of Characteristic Curves

4.2.4.4 Influence of Physical

Properties on

Performance

i. Viscosity Effect

ii. Density

4.2.5 Some Design Features of Centrifugal Pumps

4.2.5.1 Leakage Calculation

4.2.5.2 Disk Friction

4.2.5.3 Diffuser Losses

4.2.5.4 Mechanical Seals

a. Single Seals

b. Tandem Seals

c. Double Seals

4.2.5.5 Bearing Losses

4.2.5.6 Axial Thrust

4.2.5.7 Impeller Design

a. Impeller Inlet Dimensions and

Angles

b. Impeller Exit Dimensions and

Angles

78

78

79

79

80

82

82

83

83

83

83

83

85

86

87

87

88

88

88

89

89

90

90

93

95

96

96

99

100

101

105

105

106

D

4.2.6 Centrifugal Pump Types

4.2.6.1 Fire Pump

4.2.6.2 Dredge Pumps

4.2.6.3 Slurry Pumps

4.2.6.4 Deep Well Pumps

4.2.6.5 Circulating Pumps

4.2.6.6 Boiler Feed Pumps

4.2.6.7 Pumping Liquid/Gas Mixtures

106

106

107

107

108

4.3 Axial Pumps (Propeller Pumps) . . . . . . . .

Degree of Reaction

Pressure and Flow Coefficients

Study of Flow Inside the Rotor (Radial

Equilibrium)

Performance of Axial Flow Propeller Pumps

109

110

110

112

113

p Selection and Applications . . . . . . .

Pumps in Parallel

Pumps in Series

Economic Considerations

Design of the Intake Chamber of Vertical Pumps

4.4.4.1 General

4.4.4.2 Open Intake Chambers

4.4.4.3 Covered Intake Chambers

4.4.4.4 Inlet Elbows

Pressure Surges (Water Hammer) in Piping

Systems

Pump Installation

Centrifugal Pump Trouble Shooting

116

117

117

118

118

118

119

122

123

124

126

134

CHAPTER (V) INCOMPRESSIBLE FLOW

TURBINES ( Hydraulic Turbines )

General Introduction . . . . . . . . . . . . 142

5.1 Impulse Turbines (Pelton Wheel) . . . . . . .

General Considerations

142

142

5.2 Reaction Turbines . . . . . . . . . . . . .

5.2.1 General

5.2.2 Francis Turbines (Radial and

Mixed)

5.2.2.1 General

149

149

150

150

152

E

5.2.2.2 Power,

Efficiency and

Coefficients

5.2.2.3 Head

Delivered by

Turbine and

Draft Tube

5.2.2.4 Types of

Draft Tube

5.2.2.5 Net Head

5.2.2.6 Cavitation in

Turbines

5.2.2.7 Power and

Speed

Regulation

5.2.2.8 Francis

Turbine

Performance

5.2.3 Axial Flow Reaction Turbines

a. Propeller Turbine

b. Kaplan Turbine

5.2.4 Some Design Characteristics for Hydraulic

Turbines

153

156

157

157

160

161

162

163

163

164

5.3 Some Turbines Installations . . . . . . . . .

a. Impulse Turbine

b. Francis Turbine

c. Axial Turbine

165

165

166

173

5.4 Fluid Coupling and Torque Converters . . . .

5.4.1 Fluid Coupling

5.4.2 Torque Converter

173

174

176

5.5 Pump-Turbine, Power Storage System . . . . 178

CHAPTER (VI) COMPRESSIBLE FLOW

TURBOMACHINES

( Thermodynamic Principles )

6.1 Equation of state . . . . . . . . . . . . . . 189

6.2 Specific Heat . . . . . . . . . . . . . . . 190

6.3 Enthalpy . . . . . . . . . . . . . . . . . 190

F

6.4 Entropy . . . . . . . . . . . . . . . . . 191

6.5 Work . . . . . . . . . . . . . . . . . .

6.5.1 For a constant volume process

6.5.2 For a constant pressure process

6.5.3 For a constant temperature

process

6.5.4 For an adiabatic process

6.5.5 For polytropic process

191

192

192

193

193

193

6.6 First Law of Thermodynamics . . . . . . . . 194

6.7 Second Law of Thermodynamics . . . . . . . 194

6.8 Compression of Gases . . . . . . . . . . .

6.8.1 Adiabatic Compression

6.8.2 Isothermal Compression

6.8.3 Polytropic Compression

195

195

196

197

6.9 Plane Compressible Flow . . . . . . . . . . 198

6.10 Gothert's Rule . . . . . . . . . . . . . . 199

6.11 Prandtl-Glauert Rule . . . . . . . . . . . 201

CHAPTER (VII) FANS, BLOWERS, and

TURBO-COMPRESSORS

7.1 General . . . . . . . . . . . . . . . . .

7.1.1 Fans

7.1.2 Blowers

7.1.3 Turbo-compressors

202

202

203

203

7.2 Head and Power . . . . . . . . . . . . . . 204

7.3 Coefficients and Specific Speed . . . . . . .

7.3.1 Pressure Coefficient φ'

7.3.2 Slip Factor

7.3.3 Standard Air

205

205

205

206

7.4 Performance Characteristics . . . . . . . . 206

7.5 Mach Number Consideration . . . . . . . . 211

7.6 Pre-Whirl . . . . . . . . . . . . . . . . 211

7.7 Surging . . . . . . . . . . . . . . . . . 212

7.8 Radial Type Impeller Design . . . . . . . . 212

G

CHAPTER (VIII) VOLUMETRIC MACHINES

8.1 Reciprocating Pumps . . . . . . . . . . . .

8.1.1 Piston Pumps

8.1.2 Instantaneous Rate of Flow

8.1.3 Diaphragm Pumps

8.1.4 Reciprocating Pump Trouble

Shooting

218

218

219

222

224

8.2 Rotary Pumps . . . . . . . . . . . . . . .

8.2.1 Rotating Cylinder Pump

8.2.2 Gear Wheel Pump

8.2.3 Rotary Pump Trouble Shooting

225

225

226

227

8.3 Performance of Positive Pumps . . . . . . . 228

8.4 Inertia Pressure in Delivery and Suction Pipes . 229

APPENDIX “I” Pressure Recovery Devices

1 General . . . . . . . . . . . . . . . . . .

1.1 Calculation of Loss Coefficient

231

233

2 Diffuser Types . . . . . . . . . . . . . . . .

2.1 Vaneless Diffuser

2.2 Vaned Diffuser

2.3 Volute Type Diffuser

2.3.1 Parallel Walls

2.3.2 Tapering Side Walls

2.3.3 Rectangular Cross Section

236

237

239

241

241

242

244

References “Appendix I” . . . . . . . . . . . 245

APPENDIX “II” Theory of Cavitation in Centrifugal

Pumps

1 Introduction . . . . . . . . . . . . . . . . 246

2 Inception of Cavitation . . . . . . . . . . . . 248

3 Signs of Cavitation . . . . . . . . . . . . . 250

H

3.1 Noise and Vibration

3.2 Drop in Head-Capacity and Efficiency

Curves

3.3 Impeller Vane Pitting and Erosion

250

250

253

4 Mechanisms of Damage . . . . . . . . . . . 253

5 Thermodynamic Effects on Pump Cavitation . . 257

6 Net Positive Suction Head . . . . . . . . . . 260

7 Net Positive Suction Head Test . . . . . . . . 262

8 Thoma’s Cavitation Constant . . . . . . . . 263

9 Suction Specific Speed . . . . . . . . . . . . 264

10 Some Discussions Concerning the NPSH . . . 266

11 Cavitation Noise in Centrifugal Pumps . . . . 268

12 Cavitation Detection by Digital Acoustic

Emission Analysis . . . . . . . . . . . . . 286

13 How to Prevent Cavitation . . . . . . . . . 288

References “Appendix II” . . . . . . . . . 290

APPENDIX “III” Solved Examples and Problems

Chapter I . . . . . . . . . . . . . . . . . 292

Solved Examples

Problems

294

301

Chapter II . . . . . . . . . . . . . . . . . 303

Solved Examples

Problems

305

311

Chapter III . . . . . . . . . . . . . . . . 312

Solved Examples

Problems

314

319

Chapter IV . . . . . . . . . . . . . . . . 320

Solved Examples

Problems

324

333

Chapter V . . . . . . . . . . . . . . . . 336

Solved Examples

Problems

338

347

Chapter VII . . . . . . . . . . . . . . . . 349

Solved Examples

Problems

350

353

Chapter VIII . . . . . . . . . . . . . . . 354

I

Solved Examples

Problems

356

359

APPENDIX “IV” Tables and Charts

Tables and Charts . . . . . . . . . . . . . . . 360

General References . . . . . . . . . . . . . 366

1

Types and shapes of turbomachines (adopted from Sayers)

2

CHAPTER (I)

BASIC THEORY

HISTORICAL REVIEW

Turbomachines by definition are those class of machines in which

occurs a continuous energy transfer between a rigid body (Rotor) and a

deformable media (fluid). A large number of machinery is characterized

by this energy transfer process.

Historically, the first turbomachines can be traced back to hero of

Alexandria who lived since 2000 years ago, (Fig. A.1). The machine was

simply consists of a closed spherical vessel. The steam leaves the vessel

through two pipes facing tangentially at the vessel's periphery. The vessel

is then driven by the reaction of the steam jets.

The Romans introduced paddle-type water wheels, pure "impulse"

wheels in around 70 BC for grinding grain, it seems that they were the

true initiators, because Chinese writings set the first use of water wheels

there at several decades later (26). In the succeeding centuries, water

wheels of impulse type and windmills have been used.

In the 17th century Giovanni de Branca has suggested the idea of

impulse steam turbine, (Fig. A.2).

3

Fig. A.1 Hero’s rotating sphere

of 120 B.C.

Fig. A.2 Giovanni de Branca's

turbine of 1629

Through the eighteenth century, the mankind has acquired a

suitable knowledge in hydrodynamics and thermodynamics to permit a

real movement toward modern turbomachinery. In this time, the Swiss

mathematician Leonard Euler (1707-1783), has published his application

of Newton's law to turbomachinery which is known now as Euler's

equation, since that time the development of turbomachinery has not

ceased.

Now, the utilization of turbomachines is in all engineering applications. It

is difficult to find any engineering construction without having a

turbomachine element. The wide application of turbomachines has

justified its important space in engineering curriculum.

1.1 General Introduction:

Every common turbomachine contains a rotor upon which blades

are mounted, only the detailed physical arrangements differ. Fluid flows

through the rotor from an entrance to an exit submit a change in

momentum during the process because of the torque exerted on or by

rotor blades.

4

Fig. A.3 Modern turbomachinery rotor

Throughout this text, the emphasize has put on the practical aspects

of the machines without going deep inside the mathematical formulation.

Some important applications are treated separately as; cavitation

5

phenomena, pressure recovery devices and maintenance of

turbomachines.

The turbomachines can be classified by the energy transfer

principle, Figure 1.1:

1. Turbines, energy transfers from the fluid to the rotor.

2. Pumps, energy transfers from the wheel to the

fluid.

The rotors also can be classified by the direction of flow in the wheel:

- Radial Wheel,

- Axial Wheel,

- Mixed Wheel.

Fig. 1.1 Flow direction in turbines and pumps

Hydraulic Turbomachinery Classification

Energy Conversion

Principle Impulse Reaction

Energy transfer direction + ve + ve - ve + ve - ve

Flow Direction Radial Radial Axial Axial

Turbomachine Pelton

Wheel

Francis

Turbine

Centrifugal

Pump

Kaplan

Turbine

Propeller

Pump

+ ve means energy transfer from fluid to wheel.

- ve means energy transfer from wheel to fluid.

1.2 Velocity Diagram: