fundamentals – burner – applicationsdownload.e-bookshelf.de/download/0000/6662/31/l-g... ·...

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Handbook ofBurner Technologyfor IndustrialFurnacesFundamentalsBurnerApplications

938_Cover_18mm Rücken 30-06-09:938_Cover_23mm Rutcken go 30.06.2009 14:38 Uhr Seite 1

Handbook of Burner Technology for Industrial Furnaces

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 29.06.2009 9:48 Uhr Seite I

III

Joachim G. Wünning /Ambrogio Milani (Editor)

VERLAGVULKAN

Handbook ofBurner Technology

for Industrial Furnaces

FundamentalsBurner

Applications

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 29.06.2009 9:48 Uhr Seite III

IV

Bibliographic information published by Deutsche Nationalbibliothek

Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available on the Internet at

http:/dnb.ddb.de.

ISBN 978-3-8027-2950-8

© 2009 Vulkan-Verlag GmbHHuyssenallee 52-56, D-45128 Essen, Fed. Rep. of GermanyTel.: +49 (0)201 8 20 02-0, Internet: http://www.vulkan-verlag.de

Cover picture: WS Wärmeprozesstechnik GmbH

All rights reserved. No part of this book covered by the copyrights hereon may be translated,reproduced or copied in any form or by any means – graphic, electronic, or mechanical, includingphotocopying, taping, or information storage and retrieval systems – without written permission ofthe publisher.

The listing of utility names, trade names, descriptions of goods etc. without special marking ordesignation in this book does not allow the presumption that such names are considered free inthe sense of the trademark and trademark protection laws and can, consequently, be used by anyperson.

This book was prepared with much care and devotion. Nonetheless, authors and publishing company do not assume responsibility for the correctness of data, comments, suggestions andpossible printing errors.

Managing Editor: Dipl.-Ing. Stephan SchalmEmail: [email protected]

Producer: Norbert Nickel

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 01.07.2009 14:19 Uhr Seite IV

Foreword V

Foreword

The demands made on the energy-efficiency and pollutant emissions ofindustrial furnaces are rising continuously and have, following the recentincreases in energy prices and in view of the discussion concerning theclimate changes for which CO2 emissions are, at least in great part,responsible, attained a new high priority. In numerous companies, includ-ing many in the steel industry, and in enterprises operating heat-treatmentinstallations, the saving of energy is now a top-ranking consideration. Forthis reason, this work focuses unequivocally on the fields of energy-efficiency and emissions reduction.

This book is intended to assist in bridging the gap between theory andpractice and thus to be of use both to the committed practitioner and tothose in the fields of research and teaching.

The opening chapters of the Handbook of Burner Technology for Industrial Furnaces examine thefundamental theoretical principles of combustion theory, fluid mechanics and heat transfer, focus-ing only on those aspects of significance for burner systems. Subsequent chapters then deal inmore detail with this technology, discussing combustion concepts, pollutant generation andreduction, and the recovery of heat for use in preheating of combustion air, the minimum require-ment for enhancement of energy-efficiency. The "Industrial burners" chapter then examines, citing examples, the more important types of industrial burner and their integration into the fur-nace-system concept. This is followed by chapters on standardization and regulatory legislation,suggestions for further reading, relevant research institutions and an annex containing pertinentphysical data.

A large range of tasks will need to be solved in the coming decades to enable mankind to main-tain high production levels as resources become ever scarcer. The rational requirement for thelowest possible environmental impact from industrial combustion processes will constitute one ofthe most important of these challenges. Developments in the field of combustion technology arestriding forward extremely rapidly at present, and many of the technical solutions advanced in thisbook will, without doubt, have been augmented by further developments and innovations within afew years; the underlying principles will remain valid, however. It is therefore vital to remaininformed on new developments at all times, and the book thus closes with an attempt to highlightsome of the potential sources of further information.

I am particularly grateful, in completing this work, to my two mentors from my period of study inAachen. The essays on combustion theory (Prof. G. Woelk) and heat transfer (Prof. U. Renz) treatthe essential principles of combustion systems in depth. A large range of individuals and compa-nies contributed text and illustrations for Chapter 8, and to them I also extend my most sincerethanks. I also wish to thank Dr. Beneke for the whole of Chapter 9, on Standardization. My grati-tude is also due to my co-editor, Dr. Milani, whose ever positive approach and untiring industri-ousness again and again contributed to making the drafting of this title less strenuous work, andmore a pleasure.

Renningen, 2009 Joachim G. Wünning

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 29.06.2009 9:48 Uhr Seite V

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VII

Authors

Dr. Franz BenekeFachverband Thermoprozesstechnik im VDMALyoner Straße 18 60528 Frankfurt am Main / GermanyKapitel 9

Dipl.-Ing. Jörg tom Feldepromeos GmbHAm Weichselgarten 2191058 Erlangen / GermanyKapitel 8.1.5

Dr. Ing. Ambrogio MilaniSal inf san Barnaba 1016 136 Genova / ItalyKapitel 2, 4

Prof. Dr.-Ing. Ulrich RenzMeischenfeld 7752076 Aachen / GermanyKapitel 3

Prof. Dr.-Ing. Günther WoelkEenbesweg 46291CA Vaals / NetherlandsKapitel 1

Dipl.-Ing. Gerrit WohlschlägerElster Kromschröder GmbHStrotheweg 149504 Lotte (Büren) / GermanyKapitel 8.1.1 – 8.1.2

Dr.-Ing. Joachim G. WünningWS Wärmeprozesstechnik GmbHDornierstr. 1471272 Renningen / GermanyKapitel 2, 4, 5, 6, 7, 8

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 29.06.2009 9:48 Uhr Seite VII

THE GAP IS CLOSED

“The new Bible for industry and academia.The work of this distinguished group of

authors is a tribute to theircommitment to the

thermoprocess industry.”Paul. L. Huber

Former President of IHEA

“...this book will be established as thestandard work in its field.”

Dr. Gutman HabigGeneral Secretary of CECOF

“A very high and competent state of the artdescription for all manufacturers and users of

thermoprocessing equipment.”Prof. Dr. Axel von Starck

Editor and Chairman of the Exhibitors Councilfor the trade fair Thermprocess in 2003

Edited by A. von Starck, A Mühlbauer, C. Kramer, publishedby Vulkan Verlag, Essen, Germany 2005. 16,5 x 23 cm, 842 pages,

662 figures, 91 tables, hardcover, € 160,00

Content (Main chapters):Fundamentals of heating processes; Thermoprocesses with gas

circulation; Thermoprocesses with heat from electric energy; Meltingand casting of metals; Heating and heat treatment; Components;

Safety; Standards, etc.

Or visit our website:

Name/company:

Street address/P.O.B.:

Postcode/Zip, Town/City:

Date: Signature:

copy/copies Handbook of Thermoprocessing Technologies2005, 820 pages, hardcover, ISBN 3-8027-2933-1, € 160,-

FAX +49(0)201/82002-34ORDERFORM

- 81 authors - 842 pages- 662 figures - 91 tables

Your contact person: Silvia SpiesPhone: +49 (0) 201 82002-14Telefax: +49 (0) 201 82002-34E-mail: [email protected] GmbHP.O. Box 10 39 62D-45039 Essen

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 29.06.2009 9:48 Uhr Seite VIII

Contents

Foreword ...................................................................................................................... V

Authors ........................................................................................................................ VII

1. Combustion .......................................................................................................... 1

1.1 Stoichiometry .......................................................................................................... 1

1.1.1 Reaction elements of technical fuels ...................................................................... 1

1.1.2 Characteristic values for the composition of gaseous fuels .................................. 2

1.1.2.1 Characteristic amount of atoms for gaseous fuels ................................................ 2

1.1.3 Combustion calculation .......................................................................................... 4

1.1.3.1 Calculation of the air requirements ........................................................................ 5

1.1.3.2 Calculation of the exhaust gas amount and exhaust gas composition ................ 7

1.2 Energy flux in the furnace ...................................................................................... 10

1.2.1 Characteristic furnace interfaces ............................................................................ 10

1.2.2 Characteristic energies and heat flux .................................................................... 11

1.2.3 Energy balance ...................................................................................................... 13

1.2.4 Efficiency factors .................................................................................................... 13

1.2.4.1 Combustion efficiency ............................................................................................ 14

1.2.4.2 Furnace efficiency .................................................................................................. 16

1.2.4.3 Heating efficiency .................................................................................................. 16

1.2.5 Saving of fuel with preheating of the air ................................................................ 16

2. Fluid Dynamics .................................................................................................... 19

2.1 The ideal gas .......................................................................................................... 19

2.2 Equation of continuity ............................................................................................ 21

2.3 Equation of Bernoulli .............................................................................................. 22

2.4 Turbulent free jet .................................................................................................... 25

2.5 Pressure losses in pipings ...................................................................................... 26

3. Heat Transfer ...................................................................................................... 28

3.1 Mechanisms of heat transfer .................................................................................. 28

3.2 Heat radiation ........................................................................................................ 30

3.2.1 Electromagnetic spectrum ...................................................................................... 30

3.2.2 Stefan-Boltzmann’s law .......................................................................................... 31

3.2.3 Planck’s distribution law ........................................................................................ 31

3.2.4 Reflection, absorption, transmission ...................................................................... 32

3.2.5 Kirchhoff’s law ........................................................................................................ 33

IX

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 29.06.2009 9:48 Uhr Seite IX

3.2.6 Radiation from a diffuse surface and direction-dependent radiation .................... 34

3.2.7 Radiation transfer .................................................................................................. 34

3.2.7.1 Radiation flux .......................................................................................................... 34

3.2.7.2 Radiation transfer between two bodies .................................................................. 34

3.2.8 Gaseous radiation .................................................................................................. 39

3.3 Heat conduction .................................................................................................... 39

3.3.1 Differential equations of the temperature field ...................................................... 39

3.3.2 Steady state, one-dimensional heat conduction .................................................... 40

3.3.2.1 Plane walls with given surface temperatures ........................................................ 40

3.3.2.2 Plane walls with convective heat transfer .............................................................. 41

3.3.3 Unsteady state heat conduction without heat sources .......................................... 41

3.3.3.1 Bodies with high values of thermal conductivity .................................................... 41

3.4 Convection .............................................................................................................. 43

3.4.1 Application of the dimensional analysis for heat transfer ...................................... 44

3.4.2 Cylinders in a flow parallel and perpendicular to their longitudinal axis ................ 45

4. Burner Technology .............................................................................................. 49

4.1 Combustion techniques .......................................................................................... 49

4.1.1 Wood fire ................................................................................................................ 50

4.1.2 Ope grate fire .......................................................................................................... 50

4.1.3 Simple furnace ........................................................................................................ 50

4.1.4 Firing with burners .................................................................................................. 51

4.1.5 Flame formation ...................................................................................................... 51

4.1.6 Flame velocity ........................................................................................................ 53

4.1.7 Subdivision of flames ............................................................................................ 54

4.2 Classification of burners and flames ...................................................................... 55

4.2.1 Air supply ................................................................................................................ 55

4.2.2 Fuel and fuel preparation ........................................................................................ 55

4.2.3 Way of stabilization ................................................................................................ 55

4.2.4 Flame colour .......................................................................................................... 56

4.2.5 Air or fuel staging .................................................................................................... 56

4.2.6 Flame shapes .......................................................................................................... 57

4.2.7 Flow velocity .......................................................................................................... 57

4.2.8 Direct and indirect heating .................................................................................... 58

4.2.9 Air preheating .......................................................................................................... 58

4.2.10 Stoichiometry .......................................................................................................... 59

4.2.11 Turndown ................................................................................................................ 60

4.3 Flameless oxidation ................................................................................................ 60

4.3.1 Principle .................................................................................................................. 61

4.3.2 Computations and experimental results ................................................................ 64

4.3.3 Field measurements .............................................................................................. 66

X Contents

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 29.06.2009 9:48 Uhr Seite X

4.3.4 Applications ............................................................................................................ 69

4.3.5 Essential features .................................................................................................... 70

5. Computer Simulation ........................................................................................ 71

5.1 Assembly of input data .......................................................................................... 71

5.1.1 Computational mesh .............................................................................................. 71

5.1.2 Stationary and non-stationary calculations ............................................................ 73

5.1.3 Material properties .................................................................................................. 73

5.1.4 Boundary conditions .............................................................................................. 74

5.1.5 Computing models ................................................................................................ 75

5.2 Solution of equations .............................................................................................. 77

5.3 Presentation of the results ...................................................................................... 78

6. Reduction of Pollutants ........................................................................................ 81

6.1 NOx reduction by flame cooling .............................................................................. 83

6.2 Lean premixed combustion .................................................................................... 84

6.3 Flame staging ........................................................................................................ 84

6.4 Recirculation of combustion products .................................................................. 85

6.5 Oxygen combustion ................................................................................................ 86

6.6 Limits of air-preheating .......................................................................................... 86

6.7 Reduction of fuel NOx ............................................................................................ 86

6.8 NOx – removal ........................................................................................................ 87

6.9 NOx Units ................................................................................................................ 87

6.10 NOx measurements ................................................................................................ 87

7. Heat Exchangers ................................................................................................ 90

7.1 Basic design .......................................................................................................... 91

7.2 Characteristics ........................................................................................................ 94

7.3 Determination of the efficiency .............................................................................. 97

7.3.1 Determination of the idle value .............................................................................. 97

7.3.2 Measurement of the air preheating temperature .................................................... 101

7.3.3 Measurement of the flue gas temperature ............................................................ 101

8. Industrial Burners .............................................................................................. 103

8.1 Cold air burners ...................................................................................................... 103

8.1.1 Premix burners ...................................................................................................... 103

8.1.2 Nozzle mix burners ................................................................................................ 103

8.1.3 Fan burners ............................................................................................................ 108

Contents XI

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 02.07.2009 10:41 Uhr Seite XI

8.1.4 Surface burners ...................................................................................................... 108

8.1.5 Porous burners ...................................................................................................... 109

8.1.6 Flat flame burners .................................................................................................. 110

8.1.7 Burners for low calorific and special fuel gases .................................................... 111

8.1.8 Multi-fuel burners .................................................................................................... 111

8.1.9 Burners for oxygen-enriched air ............................................................................ 113

8.2 Hot air burners ........................................................................................................ 114

8.2.1 Proportionally controlled hot air burners with central recuperator ........................ 117

8.2.2 Pulse-fired hot air burners with central recuperator .............................................. 118

8.2.3 Hot air burners with central regenerator ................................................................ 124

8.2.4 Steady controlled hot air burner with zone recuperator or regenerator ................ 124

8.3 Recuperative burners ............................................................................................ 126

8.3.1 Recuperative burners with eductor ........................................................................ 129

8.3.2 Recuperative burner with flue gas valve ................................................................ 132

8.4 Regenerative burners ............................................................................................ 132

8.4.1 Regenerative burners pair ...................................................................................... 133

8.4.2 Regenerative burner .............................................................................................. 136

8.5 Radiant tubes .......................................................................................................... 137

XII Contents

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00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 02.07.2009 10:41 Uhr Seite XII

8.5.1 Types of radiant tubes ............................................................................................ 137

8.5.2 Heat recovery with radiant tubes .......................................................................... 140

8.5.3 Temperature uniformity .......................................................................................... 143

8.5.4 Control of radiant tubes .......................................................................................... 144

8.5.5 Arrangement of radiant tubes ................................................................................ 145

9. Standardization for Industrial Burners .......................................................... 148

9.1 Introduction and principle ...................................................................................... 148

9.2 Standards organizations and designations of standards ...................................... 148

9.3 Standards and their domain .................................................................................. 149

9.4 Fundamentals about European standardization work ............................................ 150

9.4.1 New approach ........................................................................................................ 150

9.4.2 Connection between directives and standardization ............................................ 151

9.4.3 Application of European harmonized standards .................................................... 152

9.5 Machinery Directive (MD) ........................................................................................ 152

9.5.1 EU declaration of conformity for machinery .......................................................... 153

9.5.2 Declaration by the manufacturer ............................................................................ 154

9.5.3 CE-Marking ............................................................................................................ 154

9.5.4 New Machinery Directive dated 26 Feb 2009 ........................................................ 155

9.6 Additional EU - Directives ...................................................................................... 157

9.6.1 Pressure Equipment Directive (PED) ...................................................................... 157

9.6.2 Gas Appliance Directive (GAD) .............................................................................. 157

9.7 Operation of plants and accident prevention regulations ...................................... 158

9.8 Standardizations structure for the machine directive ............................................ 158

9.9 Important standards for Type A and Type B standards for industrial burners ...... 160

9.9.1 Important Type A standards for thermoprocessing equipments and industrial

burners .................................................................................................................... 160

9.9.1.1 EN ISO 14121-1 ...................................................................................................... 160

9.9.1.2 EN 60204 - 1 .......................................................................................................... 160

9.9.1.3 EN ISO 12100 - 1 .................................................................................................. 160

9.9.1.4 EN ISO 12100 - 2 .................................................................................................. 161

9.9.2 Important Type A standards for thermoprocessing equipment and industrial

burners .................................................................................................................... 161

9.9.2.1 EN ISO 13850 ........................................................................................................ 161

9.9.2.2 EN ISO 13732 - 1 .................................................................................................. 162

9.9.2.3 EN 953 .................................................................................................................... 162

9.9.2.4 EN 61496 - 1 .......................................................................................................... 163

9.10 Important Type C standards for industrial burner .................................................. 163

9.10.1 EN 746 - 1 .............................................................................................................. 163

9.10.2 EN 746 - 2 .............................................................................................................. 164

9.11 Standards for components of industrial burners .................................................. 165

Contents XIII

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9.11.1 EN 161 .................................................................................................................... 165

9.11.2 EN 225 - 1 .............................................................................................................. 165

9.11.3 EN 225 - 2 .............................................................................................................. 165

9.11.4 EN 230 .................................................................................................................... 165

9.11.5 EN 264 .................................................................................................................... 166

9.11.6 EN 298 .................................................................................................................... 166

9.11.7 EN 1643 .................................................................................................................. 167

9.11.8 EN 1854 .................................................................................................................. 167

9.11.9 EN 12067 - 1 .......................................................................................................... 167

9.11.10 EN 12067 - 2 .......................................................................................................... 168

9.12 Standard for package burner ................................................................................ 168

9.12.1 EN 267 .................................................................................................................... 168

9.12.2 EN 676 .................................................................................................................... 168

9.13 Standards for thermoprocessing equipment .......................................................... 169

9.13.1 EN 746 - 3 .............................................................................................................. 169

9.13.2 EN 746 - 4 .............................................................................................................. 170

9.13.3 EN 746 - 5 .............................................................................................................. 170

9.13.4 prEN 746 - 6 .......................................................................................................... 171

9.13.5 prEN 746 - 7 .......................................................................................................... 172

9.13.6 EN 746 - 8 .............................................................................................................. 173

9.13.7 EN 1547 .................................................................................................................. 173

9.13.8 EN 1539 .................................................................................................................. 174

9.14 Principles for the design of a standard .................................................................. 175

9.14.1 How does one read a standard .............................................................................. 175

9.14.2 Structure of a type C standard according to the machinery directive .................. 176

Appendix ............................................................................................................................ 178

Heat table .............................................................................................................. 178

Heat processing keywords .................................................................................... 193

Further technical information .................................................................................. 196

Index ................................................................................................................................ 199

Index of Advertisers .......................................................................................................... 203

XIV Contents

00_Brennert_2950_S_I-XVI:001_VorspannSeite_I_XXXII 29.06.2009 9:48 Uhr Seite XIV

All you ever wanted to knowon Refractory Materials

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REFRACTORY MATERIALSDesign, Properties, Testing

Gerald Routschka, Hartmut Wuthnow (Editors)

The book aims to provide in a compact format

basic knowledge and practically oriented information

on specific properties of refractory materials, on their

testing and inspection, and on interpretation of test results.

Tables and illustrations are used to clarify fundamental concepts

on a comparative basis.

This pocket-format manual provides an overview of the diverse range

of modern refractories and their application-relevant properties. Its main

feature is a series of practice-derived articles by well-known authors in the

field on the various material groups and their characteristic property data.

The content has deliberately been kept concise and instructive, abstracting

and more detailed works are referenced.

Ex. Pocket Manual Refractory MaterialsDesign-Properties-Testing

Editor:Gerald Routschka und Hartmut Wuthnow

3. edition 2008, 625 pages, plastic,(EUR) 60,00

ISBN 978-3-8027-3158-7

Date of Publication:30.05.2008

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1. Combustion 17

(1.57)

If a heating process is performed both with and without preheating of the air, then the chosenoperating method influences only the combustion efficiency. The furnace heat flux must remainthe same for both methods as the same heating process is to be accomplished in the furnace.

For a constant furnace heat flux, therefore, an increase in the combustion efficiency necessarilypermits a reduced delivered energy and thus lower fuel volume flow.

This fact enables a "fuel saving factor" or more simply a "fuel saving" to be defined as follows:

(1.58)

Fig. 1.10: Saving of fuel with pre-heatingof the air

Delivery temperature of the fuel = 20°CDelivery temperature of the air = 20°CWater vapour content of the air = 1.39 %Air factor λ = 1.1

whereby PA,O refers to operation without pre-heating and PA,V to operation with pre-heating. If thevariables are inserted into equation 1.58 in accordance with the definition equation for the com-bustion efficiency (Equation 1.53), and if it is observed that the heating energy PB without pre-heating is equal to the delivered energy PA, then the following is obtained:

(1.59)

The fuel saving factor is illustrated in Fig. 1.10.

A recuperator, even if it could be operated without losses, is unable to recover the whole enthalpyout of the exhaust gas of a furnace. This is due to the fact that the capacity flux of the exhaustgas is almost always greater than that of the air and because even an ideal recuperator can onlypush the pre-heating temperature of the air to at most the exhaust gas temperature. Consequently,even the best recuperator is unable to compensate all exhaust losses.

01_Brenner_Kap_01_2950:001_VorspannSeite_I_XXXII 29.06.2009 9:53 Uhr Seite 17

2. Fluid Dynamics 19

2. Fluid Dynamics

Joachim G. Wünning and Ambrogio Milani

Fluid dynamics is a very interesting but complex technical domain. The shape of many productsderives from fluid flow requirements. Good examples are airplanes, race cars or sailboats. Fluiddynamic design requires a good knowledge of the basic principles but also much experience andeven creativity. Suitable fluid dynamic shapes often feature even aesthetic shapes.

Technical fluid dynamics is in many respects quite relevant for burner technology. Examples are:

• Determination of pressure drop in gas pipes

• Flow rate measurements

• Prediction of mixing pattern

• Jet expansion from burner nozzles

In this book no comprehensive introduction of the fluid dynamic techniques is provided. Never-theless, some physical laws are mentioned here because of their relevance to burner design.

2.1 The ideal gasThe assumption that real gases behave like ideal gases is accurate enough for most technicaldesign and calibration of burner systems. According to Avogadro’s law, an ideal gas that containsa certain number of molecules at a known pressure and temperature occupies a well defined vol-ume. In the first chapter (Combustion Fundamentals) the number of oxygen molecules required forthe complete combustion of a known number of fuel molecules was determined (stoichiometry).As a consequence of the above statement, this molecular ratio is directly proportional to a volumeratio. This circumstance is also the reason why for burner technology (with the exception of gasturbines) the use of normal cubic metres as quantity of gas flow rates is preferred. A gas flow rateis therefore defined by the number of normal cubic meters per hour, that is the volume flow at apressure 1013 hPa and a temperature of 0°C.

The density of ideal gases at constant temperature is proportional to the pressure

(2.1)

with

ρ density [kg/m3]

ρ pressure [absolute pressure - Pa)

Furthermore, at constant pressure the density is inversely proportional to the absolute tempera-ture measured in Kelvin K.

(2.2)

with T absolute temperature [K]


20 2. Fluid Dynamics

The absolute temperature is referred to the absolute zero at –273°C and measured in Kelvin.

For most materials the density can be read from diagrams and tables, but the density of gases canbe derived from the law of the ideal gas. Only at high pressures and very low temperatures doesthe behavior of real gases deviate noticeably from the ideal gas.

(2.3)

with

molar mass m [kg/kmol]

general gas constant R = 8413 Joule/(kmol K)

The pressure is approximated with the normal atmospheric pressure of 1.013 bar in many appli-cations. Only at great altitudes is this pressure considerably less than the normal pressure. Thepressure decrease with different altitude depends on composition and temperature distribution ofthe air column and therefore an international acknowledged standard atmosphere has beendefined. Using this standard, the pressure can be computed with the following formula

(2.4)

with the height above sea level “h” is expressed in meters. If more accurate values are required,the pressure must be measured on the field, as it is well known that the air pressure can oscillateby several hundreds Pa depending on weather conditions. For instance, if combustion equipmenthas to be installed in Mexico at 3000 m above sea level, the air pressure is approximately 700 hPainstead of 1013 hPa.

The molar mass is the mass of a defined number of molecules of a substance and for most gasescan be simply determined as follows:

hydrogen mH = 1 kg/kmol

carbon mC = 12 kg/kmol

nitrogen mN = 14 kg/kmol

oxygen mO = 16 kg/kmol

The molecular mass of multiatomic molecules is calculated from the number of atoms in the mol-ecule. For instance the molar mass of :

molecular hydrogen mH2 = 2 kg/kmol

molecular oxygen mO2 = 32 kg/kmol

molecular nitrogen mN2 = 28 kg/kmol

molecular water vapour mH2O = 18 kg/kmol

For gas mixtures the following is valid:

with m = molar mass of mixture [kg/kmol]

fraction of component i: xi [1]


2. Fluid Dynamics 21

molar mass of the component i: mi [kg/kmol]

The fraction of a component in an ideal gas corresponds to the volume fraction.

For standard air, consisting of 21% oxygen and 79% nitrogen, one obtains:

fraction of oxygen: xO2 = 0.21

fraction of nitrogen: xN2 = 0.79

mair = 0.21 · 32 kg/kmol + 0.79 · 28 kg/kmol

mair ~ 29 kg/kmol

For air at a pressure of 1013 mbar and 25°C one obtains:

(2.5)

The molar mass of combustion products can be determined in a similar way. The molar mass offlue gases from natural gas is about

mflue ~ 28 kg/kmol

2.2 Equation of continuityThe continuity equation states that the mass flow rate in a stationary flow without mass additionor subtraction between two control sections 1 and 2 must remain constant.

The equation is

(2.6)

or

w1 A1 ρ1 = w2 A2 ρ2 (2.7)

with :

mass flow rate M.

[kg/s]

average flow velocity: w [m/s]

flow cross-section: A [m2]

density: ρ [kg/m3]

Example:

As an example for the continuity balance consider a tube piece where a gas flows with the veloc-ity of 10 m/s. Then the diameter is reduced as shown in Fig 2.1 from D1 = 100 mm to D2 = 50 mm.The density can be considered constant in the flow restriction, then:

w2 = w1 ( A1 / A2)

or

w2 = w1 ( D1 / D2)2

and the flow velocity in the restricted area is 40 m/s.


22 2. Fluid Dynamics

Fig. 2.1: Equation of continuity

2.3 Equation of BernoulliThe conservation of mechanical energy along the streamline of a frictionless flow is expressed bythe Bernoulli equation:

½ w2 + ρ g h + pst = constant

with:

density: ρ [kg/m3]

flow velocity:: w [m/s]

acceleration of gravity: g = 9.81 m/s2

height: h [m]

static pressure: pst [Pa]

The Bernoulli equation is also referred to as pressure equation because it states that the sum ofstatic, dynamic and hydrostatic pressure remains constant. This sum is also referred to as totalpressure.

The statement of the Bernoulli equation can be better explained with a simple example. Waterflows out of a large reservoir filled up to a height of 1 m (Fig 2.2). If the room pressure is taken asreference pressure, then:

density of water ρwater = 1000 kg/m3

acceleration of gravity: g = 9.81 m/s2

height of the water level above discharge opening: h = 1 m

Fig. 2.2: Bernoulli's equation


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