Lecturenotes part i, Study notes of Turbomachinery

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KTH Course MJ

Part I: Turbomachinery for Incompressible Fluids

Damian M. Vogt

KTH Heat and Power Technology

 Damian Vogt, 2012 All rights reserved

www.exploreenergy.eu www.kth.se compedu.net

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About This Learning

Material

he present learning material that you hold in your hands is a new type of material that non only contains text but also recorded lecture units and links to online self-assessment tests. The scope of this material is to provide new dimensions in learning, going beyond traditional lecture notes and add a dimension in which virtually are brought into the classroom – anywhere and at any time. The written sections in this document are kept brief on purpose such as to allow for additional activities. It is therefore not primarily to be understood as a replacement for a textbook and instead presents a structured and enhanced presentation of lecture notes.

What is New with This Learning

Material?

The novelty of this learning material is that it goes beyond traditional “static” books and in addition includes animated sections. These animated sections are recorded lecture units that give the learner the possibility to learn by following

various short learning units giving a feeling of virtual classroom attendance. The learners will follow the lecturer’s writing on a whiteboard while hearing the corresponding spoken explanations.

In addition, a number of self-study problems are posed throughout the learning material such as to give the learners the possibility to apply their newly gained knowledge. These problems are of similar types of the ones made available in the classroom problem solving that are provided if the present learning material is part of a taught course.

Animations and tools are included to give the learner a different means of understanding and to provide the possibility for own experience.

Where available, remote laboratory exercises give the learners the possibility to acquire test data on real hardware and by this apply their knowledge on real cases.

Furthermore, links or references to articles are included such as to link the taught subject to available material and by this provide additional reading for interested learners.

Last, class-attending learners will have access to a discussion forum in which several of the aspect can be discussed with other learners as well as the instructor and course assistants.

T

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Most items are linked to animated and/or interactive content via the item symbol.

Recorded lecture units are included throughout the learning material and are highlighted as follows:

Lecture Unit This lecture unit covers the theory or practical application of a specific subject.

Animations or tools are included throughout the learning material and are highlighted as follows:

Animations or Tools This animation or tool gives you of a different viewpoint.

Self-study problems are included throughout the learning material and are highlighted as follows:

Self-Study Problem This self-study problem allows you to get hands- on experience.

Remote laboratory exercises are included where available and are highlighted as follows: Remote Laboratory Exercise This remote laboratory exercise gives you the possibility to acquire real test data interactively on a test facility on a specific subject.

Links or references to articles are included throughout the learning material and are highlighted as follows: Link or Reference This link or reference gives you further reading in open literature on a specific subject

Indications to the Checkpoints are included throughout the learning material and are highlighted as follows:

Checkpoint This indicates a checkpoint of the learning of the subject, which must be understood for ensuring the successful mastering of this subject.

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Contents

Preface I

About This Learning Material II

What is New with This Learning Material? II

A Note on Sustainability IV

Nomenclature VII

List of Figures IX

List of Complementary Material X

Lecture Units X Tools XI Animations XI Self-Study Problems XI Remote Laboratory Exercises XI Links and References XII Checkpoints XII

Coordinate System and Views 1

Turbomachines for Incompressible Fluids 4

Review of Basic Laws 4 Conservation of Mass 4

Conservation of Energy 5 Conservation of Momentum 6 Euler’s Turbine Equation 8 Leonhard Euler 9 Pumps 11 Pumping Systems 12 Classification of Pumps 16 Pump Elements 17 Pump Types 19 Pump Velocity Triangles 21 Design Parameters 27 Constructional Aspects of Pumps 28 Pump Characteristics 30 Pump Operating Point 32 Pump Power 34 Pump Efficiency 35 Affinity Laws 36 Serial and Parallel Operation of Pumps 40 Harmful Effects 41 Preliminary Design of Pumps 44

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VIII

3 Outlet stator (pump)

c Total in absolute frame of reference

f friction

n Normal

p Pressure

r Radial component

s Static

v Velocity

tot Total

w Total in relative frame of reference

x Axial component

θ Tangential component

IX

List of Figures

XI

Lecture Unit 40: Preliminary Design of a Pump 45 Lecture Unit 41: Euler’s Equation for Hydro Turbines 49 Lecture Unit 42: Deviation of Flow in Turbines and Pumps 50 Lecture Unit 43: Blade Shapes and Flow Passages in Turbines and Pumps 53 Lecture Unit 44: Flow Direction at Rotor Inlet 53 Lecture Unit 45: Types of Hydro Turbines 54

Tools

Tool 1: Preliminary Design of a Pump 45

Animations

Animation 1: Absolute and Relative Streamlines in a Pump Rotor 18 Animation 2: Absolute and Relative Streamlines in a Turbine Rotor 52

Self-Study Problems

Self-Study Problem 1: Fluid Forces on a Blade Row 7 Self-Study Problem 2: Euler’s Turbine Equation 10 Self-Study Problem 3: Different Forms of Energy 11 Self-Study Problem 4: Pumping System 14 Self-Study Problem 5: Deviation of Flow in Blade Rows 19 Self-Study Problem 6: Velocity Triangles 23 Self-Study Problem 7: Design Parameters 28 Self-Study Problem 8: Pump Off-Design Operation 32 Self-Study Problem 9: Pump Operating Point 34 Self-Study Problem 10: Affinity Laws 39 Self-Study Problem 11: Preliminary Design of a Pump 45 Self-Study Problem 12: Turbine System 48 Self-Study Problem 13: Flow Deviation in a Turbine 49 Self-Study Problem 14: Deviation of Flow in a Turbine Blade Row 52

Remote Laboratory Exercises

Remote Laboratory Exercise 1: Off-Design Operation of Pumps 38 Remote Laboratory Exercise 2: Serial and Parallel Operation of Pumps 41

XII

• Hydro Turbines
  • Turbine Systems
  • Application of Euler Turbine Equation to Turbines
  • Turbine Elements
  • Turbine Types
• Summary of Equations
• Index
• References
• turbomachinery coordinate system Figure 1. Schematic turbomachine showing the
• Figure 2. Axial view of a schematic turbomachine
• Figure 3. Side view (cut) of a schematic turbomachine
• turbomachine (no change in swirl) Figure 4. Unwrapped view of the stream surface in a
• turbomachine (change in swirl) Figure 5. Unwrapped view of the stream surface in a
• Figure 6. Example of a pumping system
• Figure 7. Typical system characteristic
• Figure 8. Example Pump system
• Figure 9. Pump classification
• Figure 10. Pump stage denotations (axial)
• Figure 11. Pump stage denotations (centrifugal)
• Figure 12. Examples of schematic pump rotor blade row
• Figure 13. Examples of profiled pump rotor blade row
• Figure 14. Pump types and their specific speeds
• Figure 15. General concept of absolute and relative velocity
• Figure 16. Impeller velocity triangles
• Figure 17. Concept of relative eddy (adapted from [1])
• Figure 18. Effect of slip on velocity triangle at impeller exit
• blade metal angle Figure 19. Dependence of the pump characteristics from
  • Figure 20. Pump operating point
  • Figure 21. Pump head and efficiency
  • Figure 22. Effect of speed regulation
  • Figure 23. Effect of impeller trim (diameter change)
  • Figure 24. Cavitation phenomenon
  • Figure 25. Pump and system NPSHs
  • Figure 26. Example of a turbine system
  • Figure 27. Hydro turbine stage denotations (axial)
  • Figure 28. Hydro turbine stage denotations (centripetal)
  • Figure 29. Example of schematic turbine rotor blade row
  • Figure 30. Examples of profiled turbine rotor blade row
  • Figure 31. Pump types and their specific speeds
• Lecture Unit 1: Conservation of Mass Lecture Units
• Lecture Unit 2: Conservation of Energy
• Lecture Unit 3: Conservation of Momentum
• Lecture Unit 4: Introduction to Euler’s Turbine Equation
• Lecture Unit 5: Analysis of Euler’s Turbine Equation (1/2)
• Lecture Unit 6: Analysis of Euler’s Turbine Equation (2/2)
• Lecture Unit 7: Pumping System
• Lecture Unit 8: Analysis of Pumping Systems
• Lecture Unit 9: Total Head of a Pumping System
• System Lecture Unit 10: Different Forms of Energy in a Pumping
• Lecture Unit 11: Concept of Frame of Reference
• Components Lecture Unit 12: Flow Deviations in Turbomachine
• Lecture Unit 13: Pump Velocity Triangles
• Velocities Lecture Unit 14: Influence of Flow Channel Shape on
• Lecture Unit 15: Influence of Blade Shape on Velocities
• Lecture Unit 16: Flow at Various Spanwise Positions
  • Lecture Unit 17: Different Shapes of Pump Flow Channels
  • Blade Rows Lecture Unit 18: Change of Total Head in Stator and Rotor
  • Coefficient Lecture Unit 19: Dependence of Head Coefficient from Flow
  • Lecture Unit 20: Main Components of Axial Pumps
  • Lecture Unit 21: Main Components of Radial Pumps
  • Lecture Unit 22: Separation Phenomena in Pump
  • Lecture Unit 23: Tip Leakage Loss
  • Lecture Unit 24: Minimizing Leakage Losses
  • Lecture Unit 25: Pictures of Pumps
  • Lecture Unit 26: Pump Operating Characteristics
  • Lecture Unit 27: Pump Operating Point
  • Lecture Unit 28: Pump Power
  • Lecture Unit 29: Pump Efficiency
  • Lecture Unit 30: Pump Operation at Off-Design
  • Lecture Unit 31: Pump Operation at Variable Speed
  • Lecture Unit 32: Pump Affinity Laws
  • Lecture Unit 33: Pump Operation at Varying Speed
  • Lecture Unit 34: Pump Operation after Diameter Change
  • Lecture Unit 35: Reason for Cavitation
  • Lecture Unit 36: Analysis of Cavitation Phenomenon
  • Cavitation Lecture Unit 37: Implosion of Vapor Bubbles during
  • Lecture Unit 38: Measures against Cavitation
  • Lecture Unit 39: NPSHr and NPSHa
• Reference 1: Pump Manufacturer (ITT Flygt) Links and References
• Reference 2: Pump Manufacturer (SULZER)
• Reference 3: Pump Design in Industry
• Reference 4: Hydro Turbine Manufacturer (VOITH)
• Checkpoint 1: Euler equation Checkpoints
• Checkpoint 2: Classification of Pumps
  • Checkpoint 3: Absolute and Relative Flow Paths
  • Checkpoint 4: Pump Velocity Triangles
  • Checkpoint 5: Slip
  • Checkpoint 6: Design parameters
  • Checkpoint 7: Pump Operating Characteristics
  • Checkpoint 8: Pump Operating Point
  • Checkpoint 9: Pump Power
  • Checkpoint 10: Pump Efficiency
  • Checkpoint 11: Affinity Law
  • Checkpoint 12: Preliminary Design of a Pump
  • Checkpoint 13: Types of Hydro Turbines

Figure 2. Axial view of a schematic turbomachine

The side view is defined by viewing a cut through the machine in an axial-radial plane. The cross-section that one would see is referred to as the meridional cross-section. The direction of the mean radius is referred to as the meridional direction. For constant mean radii, this is then the same as the axial direction. An example of a turbomachine side view is included in Figure 3.

Figure 3. Side view (cut) of a schematic turbomachine

In order to address the flow in detail inside a turbomachine, an unwrapped view of a stream surface is used. For a 1D analysis, this would be the stream surface on the reference radius. This view is the defined by the meridional (or axial) direction and the unwrapped circumferential coordinate ( r ⋅ θ) as included in Figure 4 and Figure 5.

Hub^ Casing

Radial direction

Circumferential direction Casing

Hub

Flow enters

Axial direction

Flow exits

Radial direction (^) Meridional direction

Figure 4. Unwrapped view of the stream surface in a turbomachine (no change in swirl)

Figure 5. Unwrapped view of the stream surface in a turbomachine (change in swirl)

Meridional direction

Unwrapped circumferential direction (

Streamlines

Streamlines

Meridional direction

Unwrapped circumferential direction (

)^ Streamlines

Streamlines

• A smaller cross section means that the velocity will be greater
• A larger cross section means that the velocity will be smaller

Lecture Unit 1: Conservation of Mass This lecture unit covers the conservation of mass.

Conservation of Energy

The first law of thermodynamics applied to closed process, i.e. system taken through a complete cycle

∫ (^ dQ^ −^ dW )=^0 Eq. 5

Change in internal energy during change in state from one point to another in the cycle

dE = dQ − dW Eq. 6

For a steady flow process the conservation of energy per unit time is regarded, i.e. conservation of power

dE ^ = m ⋅( dh 0 + gdz )= Q − W  Eq. 7

Where dh 0 denotes the change in total enthalpy and the term

gdz change in specific potential energy. As we now deal with liquid flows the latter term cannot be neglected. Furthermore a change in static enthalpy in liquids is rather pressure than temperature dependent as is the case for gases leading to

ρ dh =^ dp Eq. 8

The change in internal energy can therefore be rewritten as

de = dp + dv + gdz 2

2 ρ

Eq. 9

, which contains the same contributions as the total head introduced further above apart from the fact that the friction head is not addressed specifically. This can be expressed by

de = Htot ⋅ g Eq. 10



, where

3 1 3 1 32 12 2 z z g

v v g H p p tot + − = − + − ρ

Eq. 11

The energy balance in a hydraulic turbomachine therefore writes as

W ^ = − m ⋅ Htot ⋅ g Eq. 12

Note:

• For H (^) tot > 0 , which for example is the case if the pump gives an increase in pressure, velocity or head, the work is negative  work absorbing machine (pump)
• In contrary, if the pressure, velocity or head over the machine decreases then (^) H (^) tot < 0 indicating the the work is positive  work producing machine (turbine)

Lecture Unit 2: Conservation of Energy This lecture unit covers the conservation of energy.

Conservation of Momentum Note that in a steady flow process the momentum is entirely due to a change in flow velocity as the mass flow rate is constant, as well as a pressure contribution. This is expressed in a general form by

F = m ^ ( c 1 − c 2 ) + p 1 A 1 − p 2 A 2 Eq. 13

For a rotodynamic turbomachine, it is the conservation of moment of momentum (i.e. the momentum in circumferential direction) that is of interest. Given the rotational symmetry, the pressure forces cancel out yielding

M (^) z = r ⋅ F θ = m ^ ( r 1 c θ 1 − r 2 c θ 2 ) Eq. 14

Note:

• From the perspective of the fluid the forces are acting as pressure forces ( (^) F = p ⋅ A ).

