Turbine Thermal Appraisal: A Spreadsheet Approach

Copyright © 2016 by Ernesto Novillo.

Library of Congress Control Number:   2016902305

ISBN:      Hardcover      978-1-5144-5992-8

                  Softcover      978-1-5144-5991-1

                  eBook            978-1-5144-7043-5

All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner.

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Rev. date: 03/04/2016

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CONTENTS

Objective and Philosophy of this Book

Symbols, Nomenclature and Units

PART I. NOZZLE OPERATION

Chapter 1. Phenomena Inside a Nozzle

1.1. Presentation of nozzle and diffuser technology

1.1.1. Today's technology

1.2. The basic physical laws in a nozzle

1.2.1. The principle of conservation of energy

1.2.2. The ideal gas equation of state

1.2.3. The principle of flow mass continuity

1.2.4. Isentropic relations

1.2.5. Enthalpy and internal energy formulas

1.3. Energy conversion in nozzle flow

1.4. Flow velocity behavior in nozzles

1.5. Flow critical properties

1.6. Discharge jet shape

1.7. Specific mass flow

1.8. Turbulence in nozzles

1.9. Shock waves in CD nozzles

1.10. Flow choking

1.11. Example of a critical ratio calculation

Chapter 2. Available energy and efficiency of nozzles

2.1. Available energy for V1 = 0

2.2. Energy efficiency of a nozzle

2.3. Friction losses and enthalpy discharge

2.5. Total available energy and discharge enthalpy for V1≠ 0

2.6. Steam expansion in a nozzle

Chapter 3. Velocity and mass flow in nozzles

3.1. Flow velocity calculation with enthalpy drop

3.2. Saint Venant - Wantzel equation for ideal gases

3.3. Speed of sound and critical ratios

3.4. Example of critical properties calculation

3.5. Throat and outlet velocities

3.6. Example of velocity curves calculation

3.7. Mass flow in a choked flow

3.8. Example of a critical velocity and mass flow calculation

3.8.1. Case a) p2 = 4 kg / cm2

3.8.2. Case b) p2 = 14 kg/cm2 a

Chapter 4. Flow perturbations: Friction, Turbulence and Shock Waves

4.1. Friction in nozzles

4.1.1. The Moody diagram

4.1.2. Velocity coefficient formula

4.2. Example of nozzle efficiency sensitivity versus relative roughness

4.2. Example of nozzle efficiency calculation

4.4. Example of turbulence assessment in conical nozzle

4.5. Normal shock waves in CD nozzles

4.6. Shock wave identification

4.7. Example of shock wave calculation

4.8. Example of a turbine power affected by a normal shock wave

Chapter 5. Geometric design and performance curves

5.1. Cross section area calculation

5.1.1. Formula of area versus pressure ratio rpx for ideal gas

5.1.2. Example of nozzle profile and cross sections area calculation

5.1.3. Formula of area versus Mx

5.1.4. Formula of inlet area for CD conical nozzles

5.2. Flow shape and optimum design condition

5.3. Expansion ratio definitions and types of expansion

5.3.2. Overexpansion. Xg> Xf

5.3.3. Underexpansion. Xg< Xf

5.3.4. Notes to expansion types

5.4. Velocity coefficient. US Naval Institute

5.5. Velocity coefficient. C. P. Steinmetz curve

5.6. Geometric design procedure

5.7. Example of a CD nozzle design

5.7.1. Technical specifications

5.7.2. Expansion ratios

5.7.3. Nozzle performance curves

5.8. Summary of most important nozzle aspects

PART II. NOZZLE PROJECTS

Chapter 6. Gas Nozzle Project

6.1. Project plan

6.2. Input data and physical constants

6.3. Critical properties and nozzle type identification

6.4. Thermodynamics properties

6.5. Energy properties

6.6. Flow properties

6.7. Geometric design

6.8. Expansion ratios

6.9. Performance table and curves

Chapter 7. Steam nozzle project

7.1. Project technical specifications

7.2. Case 2. Critical properties and nozzle type identification

7.3. Case 2. Thermodynamic properties

7.4. Case 2. Energy properties

7.5. Case 2. Geometric design of conical nozzle

7.6. Case 2. Flow properties

7.7. Case 2. Expansion ratios and efficiency validation

7.8. Case 2. Performance curves

7.9. Efficiency assessment under operating conditions other than design specifications

7.9.1. Case 1. Efficiency assessment for p2 = 1.2 kg/cm2 a

7.9.2. Case 5. Efficiency assessment for p2 = 5.0 kg/cm²

7.10. Cases 1 to 7. Nozzle operation sensitivity to discharge pressure

7.10.1. Power sensitivity to discharge pressure

7.10.2. Flow cross section areas sensitivity to discharge pressure

7.10.3. Velocity coefficient and efficiency sensitivity to discharge pressure

7.11. Example of normal shock waves calculation

Chapter 8. Derivation of formulas

8.1. Alternative formula for the available energy of gases

8.2. Conversion efficiency formula

8.3. Saint Venant - Wantzel equation

8.4. Critical ratios formulas

8.5. Mass flow versus nozzle pressure ratio

8.6. Thermodynamic properties versus Mach number

8.7. Cross section area versus pressure ratio rpx

8.8. Cross section area versus Mach number

Bibliography

List of Figures

List of Uploaded Files

This book must be read along with the spreadsheet files uploaded in:

https://www.facebook.com/groups/turbinia

Spreadsheet files are free to download and have no property copyright

Dedicated to Marité... my life support

and to my son Ernie, the meritorious editor of this book

and to my daughter Monica, the artist who designed the cover

OBJECTIVE AND PHILOSOPHY OF THIS BOOK

This is a book of practical Thermotechnics for turbines, aimed at technicians and engineers who have responsibilities in turbine facilities, or participate in engineering projects where turbines are a component of a larger complex. This book is also aimed at professionals who are responsible for turbine procurement, either in its complete form or for acquisition of spare parts.

The different topics have been developed on the basis of Thermodynamics and Fluid Mechanics and conceived as the application of these sciences to nozzle engineering. Therefore, no theoretical discussions are included in the book, just the technical application of formulas and methods, some of them developed by the author. The theoretical basis can be consulted in the excellent and extensive bibliography about Thermodynamics and Fluid Mechanics. Some specialized information and recommended texts are under the Bibliography title at the end of the book.

Part I (Chapters 1 to 5) describes the process that takes place in the nozzle. Useful formulas of practical interest are presented to implement the nozzle design and performance assessment. These formulas are used in Part II, which is only dedicated to the project of both a gas nozzle (Chapter 6) and a steam nozzle (Chapter 7). The steam nozzle project culminates with the impact assessment of operating conditions other than design conditions, which are mainly due to the generation of turbulence and shock waves.

In both Parts I and II mathematical derivations have been avoided to focus only on final practical formulas and how to use them to design or assess nozzle behavior. No calculus operations have been included in this book, only algebraic expressions.

However, most important formulas discussed in the text are derived in Chapter 8. This chapter isn't essential for the purpose of the book. It's only useful to those professionals interested in seeing the mathematical fundaments of formulas set forth in the text.

An important part of this book's philosophy is to explain easy-to-use mathematical tools to evaluate actual operational turbines, or generate behavior models of a turbine operation for benchmarking purposes. These mathematical tools are specifically developed in spreadsheets to solve practical problems. These tools can be downloaded free from https://www.facebook.com/groups/turbinia. It's recommended to download all spreadsheet files, for these encompass almost 40% of the book.

To facilitate the application of spreadsheets, the use of charts and graphs has been avoided in the calculation procedures. Instead, all calculations have been designed for their implementation in spreadsheets. Conceptual explanations have been reinforced by means of behavior curves, which are substantial only for a better understanding of the topic under study. However, it's strongly recommended to use the Mollier chart in the design and assessment of steam nozzles, due to its clear graphical representation of steam transformations.

All spreadsheet calculations are based on theoretical formulas, valid for practical applications, and other empirical formulas, to avoid the use of tables or graphs.

The use of spreadsheet as a mathematical tool for design or assessment evaluations must be considered a theoretical and acceptable approach, according to formulas of Thermodynamic and Mechanic of Fluids. However, turbulence is a complex to simulate phenomenon and results of algebraic formulas barely assess the turbulence impact on nozzle performance. Fortunately, significant advances in Computational Fluid Dynamics (CFD), which calculate trajectories of hundreds of thousands of fluid particles, is a highly recommended technology, mainly to optimize the nozzle design. Different software packages applicable to turbomachinery are available in the market and some of them are open source.

Formulas have a single system of units, which is the SI. All formulas have consistent units, hence, they don't require transformations of any kind, except pressures and nozzle dimensions, which use centimeters instead of meters.

I'd like to mention the merit of numerous people in teaching me the theory and practice of turbine technologies and their supporting science. To all of them I am very grateful for the teachings I received in the ships of the Argentine Navy, the National University of Cordoba in Argentina, and in different countries where I worked on projects for the installation, maintenance and commissioning of turbines, mainly for naval propulsion and power generation. I cannot list the names of all these people who helped me so much over more than 40 years of professional activity, but I would like to manifest my remembrance and tribute to all of them.

Ernesto Novillo

Electrical and Mechanical Engineer

P.Eng, Canada

P.Energy Mgr, USA

Canada, 3rd of December, 2015

SYMBOLS, NOMENCLATURE AND UNITS

• Latin letters

aV: Velocity constant,|m/s|/ 70474.png

aG: Mass flow constant, 70491.png

A1: Inlet section area of the nozzle, m². Also expressed in cm²

A2: Outlet section area of the nozzle, m². Also expressed in cm²

Aft: Flow area at the throat, m². Also expressed in cm²

Af(x): Section area of the flow at a distance x of the inlet, m²

An(x): Section area of the nozzle at a distance x of the inlet, m²

At: Throat area of the nozzle, m². Also expressed in cm²

C: Convergent nozzle

CD: Convergent divergent nozzle

cp: Specific heat at constant pressure, kJ/|kg.°K|

cv: Specific heat at