for
Aero-Engine Exhaust Emission
Prediction
PROEFSCHRIFT
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus Prof. dr. ir. J.T. Fokkema,
voorzitter van het College voor Promoties,
in het openbaar te verdedigen op dinsdag 30 september 2008 om
10.00 uur
door
Savad A. SHAKARIYANTS
Master of Science in Aircraft Engineering
Moscow State Aviation Institute, The Russian Federation
geboren te Ashgabat, The Soviet Union.
Prof. ir. J. P. van Buijtenen
Samenstelling promotiecommissie:
Rector Magnificus voorzitter
Prof. ir. J. P. van Buijtenen Delft University of Technology, promotor Prof. R. Singh Cranfield University
Prof. dr. -ing. H. Spliethoff Technical University of Munich Prof. dr. ir. T. H. van der Meer University of Twente
Prof. dr. ir. E. Torenbeek Delft University of Technology Prof. dr. ir. A. H. M. Verkooijen Delft University of Technology Ir. W. P. J. Visser Micro Turbine Technology MTT
This research was funded by the Ministerie van Verkeer en Waterstaat, Directoraat-Generaal Luchtvaart (Directorate General of Civil Aviation of the Netherlands). Contract number: 2.02.71.763.
Copyright c 2008 by S. A. Shakariyants
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior permission of the author.
Over the past century, air transport has been transforming into a vital part of modern society by providing indispensable worldwide connections, facilitating economic growth and promoting social development. Alongside these obvious benefits, aviation is responsible for engine exhaust emissions which pose specific environmental concerns on both global and local levels. The emission species include products of complete combustion, such as CO2and H2O, and primary
pollutants. The latter contain a range of nitrogen oxides jointly designated as NOx, CO, an aggregated variety of unburned hydrocarbons (UHC) and soot.
The global environmental impact of air transport does not exceed few per-centage points of all anthropogenic activities. Yet, the industry comes under close scrutiny from the society, as aviation emissions occur either predominantly or significantly in the upper troposphere and lower stratosphere. Therein, they directly affect the Earth’s ozone layer and are not being subject to natural re-moval. Besides, aviation is extra challenged on the environmental impact due to its rapid growth that usually outpaces the world economy overall.
Locally, communities around airports are increasing their concerns about the impact of air transport on air quality. Although airplanes are not the only source of local pollution, they are often responsible for significant contributions. To give the society a proper account of the environmental impact and be successful in emission mitigation, the industry needs effective evaluation meth-ods. One of such methods is emission modeling.
In the thesis, generic methods have been developed for aero-engine com-bustor performance, combustion chemistry, as well as airplane aerodynamics, airplane and engine performance. These methods specifically aim to support diverse emission prediction studies coupled with airplane and engine simula-tion. Models for the engine exhaust composition can be either selected from existing methods or composed from the algorithms for combustor performance and combustion chemistry produced in the thesis.
The best application of this work is analysis of exhaust emissions under varying operating conditions representative of current civil transport airplanes powered by turbofan engines — the main body of today’s air transport. Var-ious objectives can be pursued in such analysis: Emission footprints of both single airplane operating phases and complete missions can be investigated.
The analysis may lead to comparison and optimization of operating practices from the viewpoint of emission production. This all may help better quantify the environmental impact of existing air transport technology, as well as de-velop and evaluate operational emission mitigation measures. Practices which conflict with the minimization of environmental impact can be articulated.
The methods developed in the thesis represent a versatile selection of en-gineering models, which have been synthesized, integrated and extended with additional sub-models, algorithms and solution practices. Important common characteristics of the produced methods is their generic nature and the ability to function with very limited information on the simulated technology, as available from open data sources (e.g. public manufacturers’ reports, technology cata-logues, reference books, emission certification measurements, etc.). The same kind of information is used in the case studies in the thesis for both input, val-idation and, often, model tuning. On one hand, this clearly increases reliance on engineering judgment and generic knowledge in the modeling process. On the other hand, this makes the models more attractive outside the manufac-turers’ environment, such as to research and academic institutions, aviation authorities and non-governmental organizations. These are often confronted with independent aero-engine emission studies, yet lack access to proprietary technology information.
The thesis places major emphasis on the development and demonstration of the combustor, combustor chemistry, engine and airplane models per se. Their integration and application to emission studies are then exemplified for gaseous emissions. In particular, NOx, UHC and CO were predicted by both existing correlation methods and by detailed multi reactor (MR) modeling. The MR approach was also applied to soot modeling. Various phenomena of soot for-mation and oxidation could be captured. Realistic net results, however, could not be maintained over the entire range of investigated operating conditions due to causes suggested in the thesis.
The use of different pollutant models also illustrates various levels of de-tail in making predictions. To our opinion, the obvious advantage of opting for detailed emission modeling is when available correlations draw their origin from very limited statistical data. Detailed models are also valuable to verify correlation methods in the absence of measurement data.
The added value of detailed emission modeling is in substantiation of pre-dictions. They resolve physical and thermochemical phenomena in the engine combustor that control, or at least affect, formation of emission species. This also extends the boundaries of analysis into tracing emission formation along the space of the engine combustor and making relation to combustor perfor-mance. Such information can be exploited in combustor design for low emis-sions. Effects of engine in-service deterioration on exhaust emissions can also be added to the analysis. This is very valuable to assess the environmental performance of actual aviation fleet containing aging engines.
In de afgelopen eeuw is luchtvervoer een belangrijk element van de moderne samenleving geworden door het verschaffen van onmisbare wereldwijde ver-bindingen, het stimuleren van economische groei en het promoten van sociale ontwikkeling. Naast deze voor de hand liggende voordelen is de luchtvaart ve-rantwoordelijk voor de uitstoot van emissies die specifieke milieuproblematiek met zich meebrengen, zowel op globaal als lokaal niveau. De emissies bevatten producten van volledige verbranding, zoals CO2 en H2O, en primaire
vervuil-ers. Deze laatstgenoemden bevatten een aantal stikstofoxiden die gemeenschap-pelijk worden aangeduid als NOx, CO, een verzameling van onverbrande kool-waterstoffen (UHC) en roet.
De wereldwijde impact van luchtvervoer op het milieu bedraagt niet meer dan een paar procent punten van alle antropogene activiteiten. De lucht-vaartindustrie wordt echter nauwkeurig bekeken door de samenleving omdat de emissies voornamelijk in de bovenste lagen van de troposfeer en onderste lagen van de stratosfeer terechtkomen. Hier hebben de emissies directe invloed op de ozonlaag en worden zij niet op natuurlijke wijze verwijderd. Daarnaast staat de impact op het milieu, veroorzaakt door de luchtvaart, extra in de be-langstelling vanwege de snelle groei van de luchtvaart die meestal de groei van de wereldeconomie voorbijstreeft.
Op lokaal niveau is er toenemende verontrusting bij de omwonenden van vliegvelden met betrekking tot de bijdrage van de luchtvaart op de luchtk-waliteit. Ondanks dat vliegtuigen niet de enige bron van lokale vervuiling zijn, zijn ze vaak verantwoordelijk voor een significante bijdrage.
Om de samenleving een gepast beeld te geven van de milieueffecten en om succesvol te zijn in het reduceren van emissies heeft de industrie effectieve evaluatie methoden nodig. E´en van deze methoden is emissie modellering.
In dit proefschrift zijn algemene methoden ontwikkeld voor het bepalen van de prestaties van verbrandingskamers in vliegtuigmotoren, verbrandingschemie evenals vliegtuig-aerodynamica, vliegtuigprestaties, en motorprestaties. Deze methoden richten zich specifiek op het ondersteunen van verschillende studies om emissies te voorspellen, gekoppeld aan vliegtuig- en motorsimulaties.
Modellen voor het bepalen van de chemische samenstelling van de uitlaat-gassen kunnen worden geselecteerd uit bestaande methoden of kunnen worden
samengesteld uit de algoritmen voor prestaties van de verbrandingskamer en verbrandingschemie, welke zijn omschreven in dit proefschrift.
De beste toepassing van dit werk is een analyse van emissies onder vari¨erende operationele omstandigheden, welke representatief zijn voor de huidige civiele vliegtuigen voortgestuwd door turbofan motoren, het hoofdbestanddeel van het huidige luchtvervoer. Verschillende doelen kunnen worden nagestreefd in een dergelijke analyse: Emissieprofielen van zowel enkelvoudige vluchtfasen als complete missies kunnen worden onderzocht. De analyse kan leiden tot een vergelijking en optimalisatie van vlieghandelingen vanuit het oogpunt van emissie uitstoot. Dit alles kan ertoe bijdragen het milieueffect van bestaande luchtvervoertechnologie te kwantificeren. Dit geldt ook voor het ontwikkelen en evalueren van operationele emissiereductiemaatregelen. Toepassingen die conflicteren met het minimaliseren van milieueffecten kunnen duidelijk worden gearticuleerd.
De methoden die zijn ontwikkeld in het proefschrift vertegenwoordigen een veelzijdige selectie van engineeringmodellen, die verbonden zijn tot een nieuw geheel, ge¨ıntegreerd en uitgebreid met extra sub-modellen, algoritmen en oplossingsmethoden. Belangrijke gemeenschappelijke eigenschappen van de voortgebrachte methoden zijn hun algemene aard en de mogelijkheid om te functioneren met beperkte informatie over de te simuleren technologie, zoals beschikbaar uit openbare informatie bronnen (b.v. openbare rapporten van pro-ducenten, technologiecatalogussen, standaardwerken, emissie certificatie metin-gen, etc.). Dezelfde soort informatie wordt gebruikt in de casestudies van het proefschrift voor zowel input, validatie, als vaak ook voor de afstemming van modellen. Enerzijds neemt hiermee de afhankelijkheid van kritisch engineer-ing vermogen en algemene kennis voor het modelleren toe. Anderzijds maakt dit de modellen aantrekkelijker voor niet-producenten zoals academische in-stituten, luchtvaart autoriteiten en niet-overheidsorganisaties. Deze worden vaak geconfronteerd met onafhankelijke vliegtuigmotor emissie studies maar ontberen toegang tot beschermde technologische informatie.
Het proefschrift benadrukt de ontwikkeling en de validatie van de mod-ellen voor de verbrandingskamer, de verbrandingschemie en de prestaties van motor en vliegtuig. Hun integratie en toepassing op emissie studies worden dan verklaard voor gasachtige emissies. Vooral NOX, UHC en CO zijn voor-speld door beide bestaande correlatiemethoden en door uitvoerige multi-reactor (MR) modelleringen. De MR aanpak is ook toegepast voor roet en verschil-lende mechanismen van roetvorming en oxidatie. Realistische netto resultaten konden echter niet worden verkregen over het gehele operationele bereik van de bestudeerde condities. Dit vanwege oorzaken die worden aangeduid in het proefschrift.
Het gebruik van verschillende emissie modellen illustreert ook de verschil-lende niveaus van detail in het maken van voorspellingen. Volgens de auteur manifesteert het evidente voordeel van de keuze voor gedetailleerde emissie modellering zich vooral wanneer de beschikbare correlaties hun oorsprong
vin-om correlatiemethoden te veriެeren bij afwezigheid van meetgegevens.
De toegevoegde waarde van gedetailleerde emissie modellen zit in de on-derbouwing van voorspellingen door het oplossen van de vergelijkingen voor de fysische en thermo-chemische verschijnselen in de verbrandingskamer die de formatie van emissies bepalen, of op zijn minst be¨ınvloeden. Dit breidt ook de analysegrenzen uit naar het traceren van emissievorming in de verbrand-ingskamer en de relatie tot verbrandverbrand-ingskamer prestaties. Zulke informatie kan worden aangewend in het ontwerpen van een verbrandingskamer met lage emissies. Effecten op uitlaatgas emissies door de verslechtering van de motor tijdens het gebruik kunnen ook in de analyse mee worden genomen. Dit is erg waardevol om de milieueffecten van de daadwerkelijke luchtvaartvloot met motoren in verschillende levensduur stadia in te schatten.
Summary i
Samenvatting iii
1 Introduction 1
1.1 Air Traffic versus Environment . . . 2
1.2 Emission Mitigation Measures. . . 4
1.3 The Research Scope and Objective . . . 6
1.3.1 Emission Modeling . . . 6
1.3.2 Research Objective. . . 8
1.4 Thesis Layout . . . 9
Bibliography . . . 10
2 Whole-Airplane Aerodynamics Model 13 2.1 Airplane Lift Prediction . . . 14
2.1.1 Total Wing-Fuselage Lift . . . 14
2.1.2 Total Horizontal Tail-Fuselage Lift . . . 18
2.1.3 Wing and Tail Lift-Curve Slopes . . . 20
2.1.4 Maximum Lift Coefficient . . . 20
2.2 Airplane Drag Prediction . . . 21
2.2.1 Profile Drag. . . 22
2.2.2 Vortex-Induced Drag. . . 25
2.2.3 Interference Drag . . . 25
2.3 Airplane Aerodynamics at Takeoff-Landing . . . 26
2.3.1 Airplane Lift at Takeoff-Landing . . . 26
2.3.2 Airplane Drag at Takeoff-Landing . . . 33
2.4 Case Studies . . . 37
2.4.1 Aerodynamic Modeling of a Boeing Airliner . . . 37
2.4.2 Aerodynamic Modeling of an Airbus Airliner . . . 48
2.5 Conclusions and Recommendations . . . 51
Nomenclature . . . 56
Bibliography . . . 58 vii
Appendix A: Supplementary Algorithms . . . 60
Appendix B: Selected Geometry Definitions . . . 64
3 Airplane Performance Model 67 3.1 Airplane Model . . . 68
3.2 Engine Performance Lookup. . . 70
3.3 Airplane Mission . . . 71
3.3.1 Takeoff . . . 72
3.3.2 Initial Climb and Accelerate. . . 73
3.3.3 En Route Climb and Accelerate. . . 74
3.3.4 Cruise and Step Climb(s) . . . 74
3.3.5 Descent and Decelerate . . . 74
3.3.6 Approach and Landing. . . 76
3.3.7 Taxiing . . . 77
3.4 Modeling Procedure . . . 78
3.5 Case Studies . . . 82
3.5.1 Performance Modeling of a Boeing Airliner . . . 82
3.5.2 Performance Modeling of Airbus Airliners . . . 91
3.6 Conclusions and Recommendations . . . 97
Nomenclature . . . 104
Bibliography . . . 106
Appendix A: General Definitions . . . 107
Appendix B: Control Programs . . . 111
4 Aero-Engine Performance Model 115 4.1 Turbofan Performance Model . . . 115
4.1.1 Cycle Reference Point . . . 117
4.1.2 Off Design Performance . . . 118
4.1.3 Verifying and Finalizing The Model . . . 122
4.1.4 Installation Losses . . . 127
4.1.5 Thrust Ratings . . . 127
4.2 Implementing The Model . . . 132
4.3 Case Studies . . . 136
4.3.1 Performance Modeling of a PW Turbofan . . . 136
4.3.2 Performance Modeling of a CFMI Turbofan . . . 140
4.3.3 Performance Modeling of a GE Turbofan . . . 146
4.4 Conclusions and Recommendations . . . 151
Nomenclature . . . 155
Bibliography . . . 156
5.1 Aero-Engine Combustors. . . 159
5.2 Generic Aero-Engine Combustor Definition . . . 161
5.2.1 Flow Model . . . 164 5.2.2 Diffuser . . . 165 5.2.3 Flow Division . . . 167 5.2.4 Snout . . . 168 5.2.5 Swirler. . . 168 5.2.6 Fuel Injector . . . 170
5.2.7 Casing and Liner Alignment. . . 175
5.2.8 Liner. . . 177
5.2.9 Liner Air Admission Holes. . . 181
5.2.10 Liner-Wall Cooling Skirt. . . 183
5.2.11 Casing and Annuli . . . 185
5.3 Case Study: Definition of a GE Combustor . . . 186
5.4 Conclusions and Recommendations . . . 190
Nomenclature . . . 194
Bibliography . . . 197
6 Models for Combustion Chemistry 201 6.1 Kerosene Combustion . . . 202
6.1.1 Flame Structures . . . 202
6.1.2 Surrogates. . . 203
6.1.3 Kinetic Models . . . 204
6.1.4 Combustion Models for Gas Turbines . . . 205
6.1.5 Equilibrium vs. Kinetics for Emission Modeling. . . 206
6.2 Equilibrium Combustion . . . 211
6.2.1 Adiabatic Flame Temperature . . . 212
6.2.2 Thermodynamic Properties . . . 213
6.2.3 Equilibrium Constants . . . 213
6.3 Simplified Flame Front Modeling . . . 214
6.4 Pollutant Formation Mechanisms . . . 218
6.4.1 Nitrogen Oxides . . . 218
6.4.2 Unburned Hydrocarbons and CO . . . 236
6.4.3 Soot . . . 238
6.5 Case Studies . . . 246
6.5.1 Equilibrium Combustion of Hydrocarbons in Air . . . . 246
6.5.2 Generic Pollutants Modeling . . . 249
6.6 Conclusions and Recommendations . . . 260
Nomenclature . . . 263
7 Integration and Application 275
7.1 Types of Emission Models . . . 275
7.2 Emission Analysis by Correlation Methods. . . 277
7.2.1 Flight Emission Studies with the Boeing Method . . . . 278
7.2.2 Additional Means of Analysis . . . 283
7.3 Emission Analysis with a Multi Reactor Model . . . 285
7.3.1 Description of Multi Reactor Model . . . 289
7.3.2 Emission Simulation Results . . . 292
7.4 Conclusions and Recommendations . . . 298
Nomenclature . . . 300
Bibliography . . . 301
Appendix A: Comments on The Application of Pollutant Models . . 304
8 General Conclusions 307
Acknowledgements 311
Curriculum Vitae 313
Introduction
Today’s air transport is almost solely powered by gas turbine engines fueled by kerosenes. The exhaust of an aero-gas turbine contains species pertaining to hydrocarbon combustion in air. 90% to 95% of the exhaust is composed of oxygen and nitrogen, as a result of high rates of excess air in the engine combustor. The term ”exhaust emissions” (or simply ”emissions”) is reserved for CO2, H2O, a range of nitrogen oxides jointly designated as NOx, CO, an
aggregated variety of unburned hydrocarbons (UHC) and soot particles (also known as smoke). The former two are the products of complete combustion. Due to a highly efficient combustion process in airplane engines under typical operating conditions, CO2and H2O attain nearly equilibrium values. Together
with oxygen and nitrogen, they make up to 99% and higher of the engine exhaust.
CO and unburned hydrocarbons are products of incomplete combustion. The former arises when either oxidation of the fuel carbon does not complete to CO2 or when CO2 dissociates under high-temperature conditions. UHC
include some unburnt fuel and products of its thermal conversion into other hydrocarbons.
NOx in the aero-engine exhaust is mainly the product of oxidation of at-mospheric nitrogen strongly dependent on high temperature and oxygen avail-ability. If the fuel contains chemically bound nitrogen, then some of it will likely form the so-called fuel NOx. Aviation fuels, though, contain only trace amounts of bound nitrogen, and fuel NOx will not be considered in this thesis. Eventually, soot (smoke) represents carbonaceous particulates that form in the areas of the engine combustion chamber where the local oxygen is not sufficient for complete combustion.
In the aero-engine community, gaseous emissions are often reported in the form of the so-called emission indexes (EI) defined as
EIi= mass of produced emission i in g
mass of consumed fuel in kg . (1.1) 1
A broadly accepted measure of soot is smoke number: a dimensionless term ”based upon the staining of a filter by the reference mass of exhaust gas sample, and rated on a scale from 0 to 100” [1,2].
An impression of actual exhaust smoke numbers and EI’s of NOx, CO and UHC for both modern and earlier aero-engines by the world’s manufacturers can be gained from the Engine Emissions Databank of the International Civil Aviation Organization (ICAO) [3]. Formation mechanisms of these species strongly depend on performance profiles of the engine combustor, which are, in turn, dependant on operating conditions, engine performance and combustor design. As a result, exhaust concentrations of NOx, CO, UHC and soot differ between different engines and vary with operating conditions. For a review of formation mechanisms, the reader is referred to the general literature on combustion, as well as dedicated treatises, such as by Lefebvre [4,5] and Mellor, ed. [6].
NOx, CO, UHC and soot, to a different extent, adversely impact both human health and the atmosphere. Due to this, they are commonly termed as pollutants. The pollutants together with CO2and H2O perturb the
Earth-atmosphere energy balance, thereby contributing to climate change. A review of these effects per species can be found in [7] and in references quoted therein. NOx, CO, UHC and soot are also referred to as ”principal pollutants”. This is because the list of all undesirable chemicals in the exhaust can be extended to species containing sulfur and metals. They can be present in the fuel as contaminants. In particular, aviation fuels may contain maximum up to 0.3% of sulfur. The true level lies in the range of 0.04 - 0.06% [7] and projected to drop to 0.02% [8]. Nearly all fuel sulfur oxidizes in the combustion chamber. Metals in the exhaust are mainly linked to contaminants that are picked up in fuel manifolds and storage systems and can be present in a part-per-billion range.
The only efficient way of controlling the exhaust of metals and sulfur oxides is by tightening requirements to fuel treatment and supply. Due to this, they are often excluded from studies on engine emissions — especially those focused on modeling methods. Neither sulfur nor metals are considered in this thesis.
1.1
Air Traffic versus Environment
If the engine-powered flight was born in 1903, the history of civil aviation started its count rather in the mid-1930s, when air travel began transforming into a safer and even comfortable experience. Today’s air transport was tech-nically shaped some 30 years later, in the 1960s, with the entry of turbofan engines into service. By that time, the world air traffic had already reached al-most 200 billion revenue passenger kilometers (RPKs), compared to 920 million in 1935 ([9], cited ICAO statistics).
eco-decades (1960-2000), the output of air transport has increased by a factor of 28, growing at nearly 9% a year [9]. This makes 2.4 times the average world GDP growth rate. The global air traffic approached 4.24 trillion RPKs and 200 billion revenue ton kilometers (RTKs) of cargo by the end of 2006 [10]. At the same time, the world’s fleet amassed 16250 passenger and 1980 cargo airplanes [10].
Over the history, the robust growth dynamics of air transport has been only interrupted for short terms. This was ether in line with global economic cycles, as a result of geopolitical instabilities, health, security or fuel supply threats. A recession from growth into contraction happened only twice: in 2001 and 2002. In a perspective, air transport is posed to continue its expansion. According to the latest available Boeing’s forecast, the world’s passenger traffic is expected to increase by some 4.5% per annum until 2026, cargo traffic may grow at an annual rate of 6.1% [10]. This outpaces the world economy overall, which is expected to grow at some 3.1% yearly over the same period. To support the growth, 28600 new airplanes are forecast to be delivered, bringing the total world’s fleet to 36420 airplanes. These outlooks are comparable with other industrial sources [11, 12]. They are also in a general long-term agreement with earlier forecasts [13,14,15,16, 17, 18].
The outlined progress of air transport provides a worldwide transportation network that delivers indispensable connections. This has been transforming aviation into a vital part of modern society. The industry has assumed an important role in facilitating economic and social developments worldwide, and this role is supposed to be retained and extended in the future.
Alongside the benefits generated by air transport, aero-engine exhaust emis-sions pose specific environmental concerns on both global and local levels: They contribute to the anthropogenic emission of greenhouse gases and particulates, as well as directly affect the local air quality around airports.
Global inventories of aviation CO2, H2O and gaseous pollutants for the
past years, as well as future forecasts, can be found in [8, 19, 20, 7, 21] and in references quoted therein. Inventories of both gaseous and smoke emissions can be found in [22]. Cumulatively, the global environmental impact of air transport does not exceed few percentage points of all anthropogenic activities: 3.5% in 1992, according to [7]. Yet, the industry comes under close scrutiny from environmental groups, policymakers and society in general, as aviation emissions occur either predominantly or significantly in the upper troposphere and lower stratosphere. Therein, produced emissions directly jeopardize the Earth’s ozone layer and are not being subject to natural removal processes.
Besides, aviation is extra challenged on the environmental impact due to its rapid growth. Even though any emission forecasts are subject to large uncertainties, various scenarios considered by IPCC [7] suggest that the global aviation impact may rise up to 7% of all anthropogenic activities by 2050. Separate forecasts for the global emission of exhaust species can be found in
[21, 20,22]. Despite variations on individual figures, the forecasts agree that all exhaust emissions are posed to increase in absolute terms.
On the local level, communities situated around airports are increasing their concerns about the impact of air transport on air quality. Although airplanes are not the only source of local pollution, they are often responsible for either significant of primary contributions, as can be deduced from various records. For example, air traffic NOx accounts 60% of all anthropogenic NOx at the Zurich Airport [23] and close to 70% at the Seattle-Tacoma International Airport [24]. It is reported that about 50% of UHC emissions are also associated with airplane operation at both airports.
1.2
Emission Mitigation Measures
Over the years, climate change and local pollution have been growing into a powerful force which is increasing its influence on shaping the air transport industry. These issues may significantly constrain air transportation. The more conflict between growth and environmental impact the society will see, the more the industry will be subjected to operational restrictions, prohibitive regulation and opposition to the infrastructure expansion. ”Role” scenarios to that are lavishly provided by the evolution of airplane noise limits enacted so far on local and state levels. Herein, Europe is particularly vocal with its bans on the operation of noisy airplanes, as well as the curfew hours and ”Quota Count” systems establishing absolute allowable noise levels in airports.
Switzerland and Sweden have already pioneered penalizing measures to pol-luting airplanes in 1997-1998 by introducing landing fee surcharges. Particu-larly, landing surcharges in the Zurich airport vary from 0% to 40% based on landing take-off emissions of NOx and UHC. The Swedish regulations also apply for NOx and UHC exhaust with surcharges between 0% and 30%.
In 2007, a new level of regulatory exposure for the air transport industry was set in Europe: The European Parliament and EU ministers voted on aviation’s inclusion into the EU greenhouse gas Emissions Trading Scheme. The measure aims at coming into force in 2012. One of its major provisions gives airlines CO2 allowances of 90% of their average annual emissions during 2004-06.
Emissions trading implies that participating entities will have to either pur-chase emission allowances or invest into emission reduction technology in order to meet their environmental obligations. Besides the European initiative, har-monized recommendations on including airplane flights into emission trading schemes worldwide are expected from ICAO, which is considering such recom-mendations since the early 2000s.
To reduce the environmental impact of air transport, or minimize it versus the expanding traffic, the industry’s stakeholders are continuously delivering emission mitigation measures. These are focused on reducing pollutant con-centrations in the exhaust, decreasing fuel consumption, curbing the growth of
grouped into three types, namely
• Technical measures related to both engine and airframe design. These generally target reductions in fuel consumption and optimization of com-bustor design aiming at lower pollutant concentrations in the post-com-bustion products.
• Operational mitigation measures, which are based on existing airplane and engine technologies and usually involve optimization of flight mis-sion, fleet utilization and airspace management, flight routing, special operating procedures, etc.
• Regulatory and policy measures as ways of accelerating the introduction of emission reduction technologies. Related policies are either enacted or recommended on national, regional and international levels by govern-mental bodies, aviation/aerospace councils and organizations. Interna-tionally, the leading role traditionally belongs to ICAO, which produces standards recommended for compulsory aero-engine emission certifica-tion [1]. Until the late 1990s, ICAO’s environmental work was primarily focused on the local air quality around airports. Since then, the policy scope has been extending to include airplane altitude operation.
• Market-based measures, which are meant to cap exhaust emissions at a certain agreed level and provide incentives for the introduction of emis-sion reduction technologies and improvement of operational efficiency. These measures mainly involve emissions trading, environmental levies and voluntary programs.
As a result of the industry’s efforts so far, the growth rate of fuel con-sumption by air transport has been historically lower than the growth in traffic demand. The emission of pollutants has been also offset by reductions in their production per revenue passenger kilometer. These trends are expected to be maintained in the future, as exemplified in Fig. 1.1 based on the results of Baughcum et al. [21]1.
Fuel economy translates into CO2and H2O reductions, yet it does not
neces-sarily help achieving the optimum band of internal engine cycle and combustor parameters from the view point of pollutant formation. To reduce the emission of pollutants, design of the engine combustion chamber has been subjected to continuous improvement. Progress in combustor technology led to higher than 99.9% combustion completeness in modern turbofan engines, therefore remark-ably suppressing the exhaust of CO and UHC. Reductions in the levels of CO
1
The analysis of Baughcum et al. [21] is based on the traffic growth rate of 3.4% per year predicted by Boeing in 1996 [25]. This is, one hand, lower compared to today’s expectations [10]. On the other hand, the traffic forecast does not take into account the contraction experienced in 2001 and 2002.
1975 1981 1987 1993 1999 2005 2011 2017 0 1 2 3 4 5 6 7 8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Fuel burn N or m al iz ed R P K s an d fu el b ur n, -Year RPKs M as s of p ol lu ta nt p er R P K , g /R P K NOx CO UHC
Figure 1.1: Trends in annual world’s scheduled passenger traffic, fuel burn and primary gaseous pollutants (based on [21] and [25]).
and UHC generally outpace the rise of total fuel burn by the world’s air fleet (Fig. 1.2).
Constant efforts are also applied to reduce NOx emissions. At the same time, the worldwide boom in air travel has been creating a market need for larger airplanes and higher-thrust engines to propel them. Together with the struggle for efficiency, this resulted into tripling of the engine pressure ratio. The turbine entry temperatures also rose significantly compared to the 1960s. These developments slowed down the pace of NOx reduction compared to the other pollutants and contributed to a faster growth of air traffic NOx inventories versus fuel burn (Fig. 1.2).
We do not have quantitative trends for smoke emissions. It is, however, known, that major smoke reduction efforts were taken in the late 1960s and 1970s and resulted into literally transparent exhaust plumes from civil turbo-fans.
1.3
The Research Scope and Objective
1.3.1
Emission Modeling
To give the society a proper account of the environmental impact and be suc-cessful in emission mitigation, the industry needs effective evaluation tools. One of such tools is emission modeling, which helps assess the composition of
1975 1981 1987 1993 1999 2005 2011 2017 0 2 4 6 8 10 12 14 NOx CO UHC E ffe ct iv e em is si on in de x, g /k Year
Figure 1.2: Trends in effective emission indexes for world’s scheduled pas-senger traffic: annual masses of produced pollutants per annual fuel burn for the entire fleet (based on [21] and [25]).
post-combustion products in both newly developed and existing engines. In the former case, modeling directly contributes to the emergence of ”cleaner” technologies and constitutes part of technical mitigation measures. It is usually carried out either by the manufacturers themselves or in collaborative efforts with third parties. The models can feature a great level of detail and can be ex-tensively tuned to the readily available experimental data. Substantial efforts are also directed towards the development of pre-test prediction capabilities.
Emission modeling of existing engines serves various purposes. For instance, it is part of the compilation of emission inventories on both global and local scales. This increases public awareness of the aviation environmental impact and promotes either accelerated implementation or enforcement of various mit-igation measures. As part of operational emission mitmit-igation measures, model-ing helps asses and compare emission footprints of different airplane operatmodel-ing phases and entire missions. The results can suggest how to modify and optimize operational practices from the viewpoint of environmental performance, as well as articulate practices which conflict with the minimization of environmental impact.
Exhaust emissions of exiting engines are often modeled independently of the manufacturers by aviation authorities, academia, research institutes and non-governmental organizations. A primary requirement to the models is usu-ally the ability to properly capture the sensitivity of emission production to operating conditions. For the sake of absolute predictions, tuning is applied at operating conditions for which measurements are available. These are typically limited to engine emission certification results, which are open to the general public [3].
Various information required for the development and validation of models outside the manufacturers’ environment is severely limited. This constitutes a very specific challenge. For instance, the proprietary nature of engine
com-bustion chamber data often precludes development of emission models which take into account combustor performance and detailed chemistry. This partic-ularly leaves formation mechanisms of exhaust pollutants unresolved. Besides, practical emission studies do not only require modeling of the engine exhaust composition, but also simulation of the engine and airplane operation. The implementation of these tasks is often hampered by a lack of information.
As a result, aero-engine emission analysis often begins with an over-simpli-fied treatment of the airplane and engine. It aims at a generalized description of either single operating phases or complete mission. This usually involves assumptions on the airplane lift and drag relation, dependence of the engine performance on ambient conditions, as well as assumptions on the airplane and engine performance variations which enable a simple description of flight phases by arithmetic relations. The obtained results are then used to correlate exhaust emissions. Even though, correlation models per se may serve as viable emission simulation methods, such analyses become doubtful overall. In addition to that, there might be practical cases for which no valid correlations are available at all. In other cases, existing correlations can be either based on limited statistics or have no proven applicability record. Therein, modeling has to be, at least, cross-checked with alternative methods. Eventually, most of the correlation methods do not allow tracing emission formation along the space of the engine combustor and making relation to combustor design and performance.
This all requires progress in the development of simulation methods for exhaust emissions, airplane and engine. Moreover, methods relying on neither proprietary technology information nor measurements are needed.
1.3.2
Research Objective
The objective of this research work is to develop methods to support diverse studies on aero-engine emission prediction under a limited amount of informa-tion available outside the manufacturers’ environment. These methods cover simulation of combustion chemistry and pollutants formation, combustor and engine performance, as well as airplane performance and aerodynamics. They are envisaged as generic models, which can be applied to exiting civil aviation technology. They employ either generic input or data that can be readily found in open sources, such as public manufacturers’ reports and product information, certification figures, catalogues, reference books, etc. The methods primarily target civil transport airplanes with turbofan engines, which form the core of air transport. The list of considered emission species includes the products of complete combustion (CO2and H2O) and primary pollutants (NOx, CO, UHC
and smoke).
The approach selected in the work makes extensive use of existing engineer-ing methods known to the academia and industry. These methods are selected, synthesized, integrated and extended with additional sub-models, algorithms and solution practices — as described in detail in the thesis. The methods are
The thesis concludes with briefly exemplifying integration of the models for coupled airplane, engine and emission simulation studies. Various levels of detail are demonstrated in the prediction of exhaust composition by ap-plying both existing correlations and detailed models developed in the thesis. Herein, the former cases demonstrate an added value of the developed airplane and engine models to combined exhaust emission and flight mission analysis. The latter provide insights into emissions production in the engine combustion chamber.
1.4
Thesis Layout
Modeling methods for airplane aerodynamics, airplane, engine and combustor performance and combustion chemistry are developed and tested in separate chapters: Chapters2to6, as sketched in Fig. 1.3to the reader’s convenience. Each chapter ends with specific conclusions and recommendations on the sub-ject it concerns and provides an outlook on how can the presented material support aero-engine emission studies.
Several possibilities for the integration of the developed methods and their application to practical aero-engine emission studies are presented in Chapter
7. This chapter concludes with discussing both strong points and limitations that these methods bring to emission analysis.
Considering the diverse nature of the subjects covered in the thesis, Chap-ters2to7are designed as independent and self-contained texts with their own nomenclature and bibliographic references.
General conclusions are given in the final chapter of the thesis. It very concisely refers to the accomplishment of the research objective, added value of the work and application potential. Specific conclusions on individual research topics are not duplicated in the final chapter.
airp lane perfo rman ce ai rp la n e ae ro d yn am ics
Ch
ap
ter
5
C
h
ap
te
r
6
C
ha
pt
er
3
C
h
ap
te
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2
Chapter 4
7
C
hapter
engineperformance com bus tor pe rfo rm an ce com bu st io n ch em is tr yin
teg
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n & appl
ica
tio
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Cha
pter 8
: General Conc
lus
ion
s
Chap
ter 1: Introduction
Figure 1.3: Thesis layout.
Bibliography
[1] International Civil Aviation Organization. Aircraft Engine Emissions. In Environmental Protection, Annex 16 to the Convention on International Civil Aviation, volume II of International Standards and Recommended Practices. ICAO, 1993.
[2] Society of Automotive Engineers. Aircraft Gas Turbine Engine Exhaust Smoke Measurement. In SAE Publications, number ARP 1179. 1974. [3] UK Civil Aviation Authority. Aircraft engine emissions
individ-http://www.caa.co.uk/. cited in 2006.
[4] A. H. Lefebvre. Gas Turbine Combustion. Hemisphere Publising Corpo-ration, 1983.
[5] A. H. Lefebvre. Gas Turbine Combustion. Taylor&Francis, 1999.
[6] A. M. Mellor, editor. Design of Moderen Turbine Combustors. Academic Press, 1990.
[7] P. J. E. Lister, D. H. Griggs, D. J. Dokken, and M. (eds.) McFarland. Aviation and the global atmosphere. Technical report, IPCC, 1999. [8] S. L. Baughcum, T. G. Tritz, S. C. Henderson, and D. C. Pickett.
Sched-uled civil aircraft emission inventories for 1992: Database development and analysis. Technical Report CR-4700, NASA, 1996.
[9] G. Thomas and C. F. Smith. Flightpaths. Aerospace Technical Publications International Pty Ltd, 2003.
[10] Boeing Commercial Airplanes. Current Market Outlook 2007, 2007. [11] Airbus. Global Market Forecast 2006-2025, 2006.
[12] Rolls-Royce. Market Outlook 2007, 2007.
[13] Boeing Commercial Airplanes. Current Market Outlook 2001, 2001. [14] Boeing Commercial Airplanes. Current Market Outlook 2004, 2004. [15] Boeing Commercial Airplanes. Current Market Outlook 2005, 2005. [16] Boeing Commercial Airplanes. Current Market Outlook 2006, 2006. [17] Airbus. Global Market Forecast 2004-2023, 2004.
[18] Rolls-Royce. The Outlook 2005, 2005.
[19] S. L. Baughcum, S. C. Henderson, and T. G. Tritz. Scheduled civil air-craft emission inventories for 1976 and 1984: Database development and analysis. Technical Report CR-4722, NASA, 1996.
[20] R. M. Gardner, K. Adams, T. Cook, and et al. The ANCAT/EC global inventory of NOx emissions from aircraft. Atmospheric Environment, 31:1751–1766, 1997.
[21] S. L. Baughcum, D. J. Sutkus, and S. C. Henderson. Year 2015 aircraft emission scenario for scheduled air traffic. Technical Report CR-1998-207638, NASA, 1998.
[22] C. J. Eyers, P. Norman, M. Middel, P. aand Phlor, S. Michot, K. Atkinson, and R. A. Christou. AERO2k global aviation emission inventories for 2002 and 2025. Technical Report QINETIQ/04/01113, QinetiQ, 2004.
[23] J. Whitelegg and H. Cambridge. Aviation and sustainability. Technical report, Stockholm Environment Institute, 2004.
[24] D. L. Daggett. Ultra efficient engine technology systems integration and environmental assessment. Technical Report CR-2002-211754, NASA, 2002.
Whole-Airplane
Aerodynamics Model
Within the scope of this thesis, airplane aerodynamics modeling covers the prediction of lift (L) and drag (D). These are the two aerodynamic forces accounted for in the solution of airplane equations of motion in the performance studies of Chapter3.
Airplane lift and drag are commonly expressed in a non-dimensional form as lift and drag coefficients, defined as
CL = 2L (ρV2) ∞Sw (2.1) and CD= 2D (ρV2) ∞Sw , (2.2)
where Sw is the planform area of the gross isolated wing.
This chapter presents a synthesis of different methods and algorithms avail-able to the academia and industry, which are compiled into procedures to predict the lift and drag coefficients. The approach is based on the calculation of CL and CD in the airplane en route (clean) configuration. During airplane
takeoff-landing operation, special methods are applied to estimate arising pos-itive and negative increments in the aerodynamic coefficients.
Plausibility of the lift and drag estimates is tested in case studies for Boeing and Airbus airliners presented in this chapter. The results are assessed quan-titatively and compared with available validation data. The chapter completes with conclusions and recommendations for improvement.
It should be mentioned that the basic aerodynamic concepts underlying the methodology are consistent with those adopted in the aviation community and, therefore, not elucidated in this chapter. Airplane components and their
geometric parameters are treated in accordance with the definitions accepted in the Western literature, e.g. as given in references [1,2, 3].
Presented algorithms are generally suitable for conventional civil transport airplanes which form the main body of air transport. Specifically, they can be best applied to the configurations featuring:
• A fuselage with a near-circular cross section, with no excessive sweep-up in its tail geometry. The local fuselage width-to-wing-span ratio and width-to-horizontal-tail-span ratio should be below 0.2.
• A swept wing and horizontal tail with t/c > 0.09, Λ0.25< 35◦ and AR >
4/ cos Λ0.25. For the wing specifically, the thickness-to-chord ratio should
preferably be not less than 0.12 and not more than 0.21. The horizontal tail should preferably be fuselage-mounted, however modeling procedures can be extended to fin-mounted tails.
• Turbofan engines installed on under-wing pylons. Yet, modeling algo-rithms can be also extended to fuselage-mounted engines.
2.1
Airplane Lift Prediction
We assume that airplane lift is the sum of the lift forces produced by the wing-fuselage and horizontal tail-wing-fuselage combinations in the untrimmed (stick-fixed) condition. Quantitatively, the forces are expressed via the lift of the gross isolated wing and horizontal tail, both affected by aerodynamic inter-ference. The effects of wing twist are not explicitly accounted for. Instead, airfoil section properties are considered at the location of the mean aerody-namic chord.
The lift coefficient is sought according to the following expression for a given angle of attack, Mach number, Reynolds number and airplane configuration:
CL= (CL)w/f + (CL)ht/fkdecSht
Sw
+ ∆T OL(CL)w. (2.3)
Equation2.3takes into account that the tail lift is produced in an air stream decelerated by the upstream airplane components. In the absence of a better information, this effect is accounted for by a deceleration factor kdec, which
would usually lie between 0.85 and 0.95 [1,4].
2.1.1
Total Wing-Fuselage Lift
We shall first find a conceptual expression for the total lift produced by the wing-fuselage combination in the en route configuration: Assume that the whole system is positioned in the flow at an angle of attack α (relative to the fuselage datum line), and the wing is characterized by a zero-lift angle αL0,
(alo w) iw (aL0 w) aw air flow a
wing zero-liftline
Figure 2.1: Definition of the wing-fuselage-tail combination.
as shown in Fig. 2.1. The total lift force would then be composed of, firstly, the lift acting on the net wing due to the angles α and αL0, as well as the
lift acting on the fuselage: Lw,α, Lw,αL0 and Lf,α. Secondly, the aerodynamic interference between these components generally results into positive lift incre-ments on the net wing and the fuselage due to the angles α and αL0: ∆αLw,
∆αL0Lw, ∆αLf and ∆αL0Lf.
Expressing the stated above via non-dimensional coefficients and area ratios, we obtain a conceptual expression for the the total lift coefficient:
(CL)w/f = [(CL)w,α+ ∆α(CL)w+ (CL)w,αL0+ ∆αL0(CL)w] Snet S w + [(CL)f,α+ ∆α(CL)f+ ∆αL0(CL)f] π b2 f 4Sw . (2.4)
Relating various lift contributions in Eq. 2.4 to the net-wing lift, the ex-pression for (CL)w/f can be re-written in terms of the lift of the wing and the
fuselage, when both are taken alone:
(CL)w/f =(CLα)w[(kα+ ∆αk)α + (kαL0+ ∆αL0k)αL0] Snet S w + (CLα)fαπ b2f 4Sw, (2.5) where kα= Lw,α+ ∆αLw Lw,α , kαL0 = Lw,αL0+ ∆αL0Lw Lw,αL0 , ∆αk = ∆αLf Lw,α , ∆αL0k = ∆αL0Lf Lw,αL0 . (2.6)
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 In te rf er en ce F ac tor , -bf/bw, -k k k k kI k L0 L0k kL0 L0k kII
Figure 2.2: Lift interference factors, [5,1].
The factors in Eq. 2.6therefore stand for the effects of interference on lift within the wing-fuselage combination. They were first derived by Pitts et al. [5] on the basis of the slender-body theory, as replicated in Fig. 2.2. In addition to these effects, (CL)w/f will be affected by the wing vertical displacement
relative to the fuselage center line. The latter will be further accounted for by ∆z(CL)w/f.
Recurring to Eq. 2.5, it should be mentioned that any estimate of (CLα)f
would be subject to a significant uncertainty. Besides, making a distinction between the gross and net wing in establishing (CLα)w would be not justified
within the framework of our approach. This brings us back to the idea of expressing (CL)w/f via lift properties of the gross isolated wing and results
into:
(CL)w/f = (CLα)w{(KI)wα + (KII)w[iw− (αlo)w]} + ∆z(CL)w/f. (2.7)
The contributing components to the total wing-fuselage lift are illustrated in Fig. 2.3, where the isolated-wing lift is expressed via
(CL)w= (CLα)w[α + iw− (αlo)w]. (2.8)
In Eq. 2.7, the factor (KI)w should incorporate: a) the sum of kα and
∆αk; b) a consideration that the lift on the wing center section is usually larger
cl wing-fuselage interference isolated fuselage
tota
l lift ofthewing-fuselage combinatio
n
Figure 2.3: Lift breakdown for the the wing-fuselage combination.
fuselage contribution to lift. Point b) should also be considered in the factor (KII)w, alongside with the sum of kαL0 and ∆αL0k. Relevant expressions for both of these factors were found in the work of Torenbeek [1], as recapitulated below: (KI)w= kI Snet S w + 1 (CLα)w πb2 f 2Sw (2.9) and (KII)w= kII Snet S w ; (2.10) where (kI)w= 1 + 2.15bf bw (2.11) and (kII)w= 1 + 0.7bf bw . (2.12)
Equations2.9to2.12are applicable for bf/bw< 0.2, where bf is the
repre-sentative fuselage width at the wing-body intersection.
A close look at coefficients (kI)w and (kII)w shows that they are in a
close agreement — both conceptually and numerically — with (kα+ ∆αk)
and (kαL0+ ∆αL0k) respectively. This is confirmed in Fig. 2.2.
Eventually, the lift delta ∆z(CL)w/f due to vertical wing displacement in
Eq. 2.7can be estimated as suggested by Hoerner [6]:
∆z(CL)w/f = −0.1bf(cr/S)w : high wing 0 : mid wing 0.1bf(cr/S)w : low wing. (2.13)
a)
b)
Figure 2.4: Typical transport passenger (a) and rear-loading cargo (b) airplanes. a) Schematic of the Airbus A330. b) Schematic of the CASA/IPTN CN235 (enlarged 2.5 times with respect to (a)).
2.1.2
Total Horizontal Tail-Fuselage Lift
The production of lift on the horizontal tail-fuselage combination can be con-ceptually treated in the same way as applied to the total wing-fuselage lift in Section2.1.1. A special attention though should be paid to interference effects: Let’s consider the tail-body interference first. Generally speaking, the flow pattern around this combination is complicated by the usually cambered aft-fuselage sections. For transport passenger airplanes however, the rear-body camber is not as pronounced as for the case of, specifically, swept-up tails of cargo airplanes with aft-loading arrangements (Fig. 2.4). Therefore, we limit ourselves to quantifying the interference lift as due to the angle of attack and zero-lift angle. The modeling methods are then similar to those described in Section2.1.1. As for the lift due to vertical displacement — no account is made in that respect.
Secondly, the tail-body combination functions in the downwash field behind the airplane wing. This causes a subsequent change in the angle of attack, as
αht/f = α − ǫ. (2.14)
The downwash angle (ǫ) depends on the design of the wing, its zero-lift angle and its interference with the fuselage, the angle of attack of the wing-fuselage combination, Mach number, influence of the propulsion system and other parameters. It is however common to express ǫ via its derivative with
cl tail-fuselage isolated tail interference to tal
tail lift with uselagef pres
ent
Figure 2.5: Tail lift in the presence of the fuselage. respect to the wing angle of attack [4,1]. Therefore,
αht/f = α − αw
dǫ dαw
. (2.15)
An approximate method for evaluating dαdǫ
w was found in reference [1]: dǫ dαw = 1.75 (CLα)w πARw 2λwblxw 0.25 1 + 2ly bw , (2.16)
where the tail moment arms lx and ly are related to the airplane geometry as
shown in Fig. 2.34in Appendix B.
Considering the stated above and that the tail airfoil sections are typically symmetrical, the following relation expresses the total lift coefficient (CL)ht/f
via the lift of the gross isolated horizontal tail: (CL)ht/f = (CLα)ht
(KI)htαht/f + (KII)htiht
. (2.17)
Lift production on the tail-body combination is graphically illustrated in Fig. 2.5, where the isolated-tail lift (in the downwash of the wing) is expressed via
(CL)ht= (CLα)ht(αht/f+ iht). (2.18)
Equation 2.17is written for zero elevator and trim tab deflection and re-quires an input of the initial incidence iht relative to the fuselage datum line
(Fig. 2.1). The latter can be assigned different values for different flight phases. The lift interference factors (KI)htand (KII)htare found in the same
fash-ion as for the wing-body combinatfash-ion — expect for making no more account for the fuselage lift, as it has been already considered in (CL)w/f:
(KI)ht= kI Snet S ht (2.19)
and (KII)ht= kIISnet S ht ; (2.20)
where (kI)ht and (kII)ht are functions of the tail span and (representative)
aft-fuselage width. The functions are of the the same form as given by Eq.
2.11and2.12and illustrated in Fig. 2.2.
2.1.3
Wing and Tail Lift-Curve Slopes
The Jones formula for high and low aspect ratio lifting surfaces is used to find the wing and horizontal tail lift-curve slopes:
(CLα)i= (clα)i ARi E′ iARi+ (clα)i/π : i = w, ht; (2.21) where E′
is the Jones edge velocity factor equal to the ratio of the surface planform semiperimeter to the span. For a swept, tapered wing or horizontal tail in a compressible flow, E′
is given by: E′ i= 1 2 q 1 − M2 i + tan2(Λle)i+ q 1 − M2 i + tan2(Λte)i + 2λi ARi(1 + λi) : i = w, ht. (2.22)
The wing Mach number in Eq. 2.22is taken as the free-stream Mach num-ber, while Mht=√kdecM∞.
2.1.4
Maximum (Wing) Lift Coefficient and Stalling
Angles of Attack
It is practical to limit the estimate of the maximum attainable lift coefficient and stall angles of attack to the wing, as the major source of airplane lift.
As stated by Abbot and von Doenhoff [7]: ”The maximum lift coefficient of the wing may be estimated from the assumption that this coefficient is reached when the local section lift coefficient at any position along the span is equal to the local clmax for the corresponding section.” The statement establishes a
relation between the maximum wing and airfoil lift coefficients. For a plausible estimate, this relation should also consider the effects of wing twist, sweep and taper. If the former is not explicitly accounted for, as is the case in our approach, it is a common practice to consider the airfoil clmax for the section
located at the mean aerodynamic chord. As for the effects of sweep and taper, the following expression was found in reference [1] for moderately tapered wings with t/c > 0.12:
clmax. This also corresponds well with the envelope of clmaxvalues attainable
with NACA standard airfoils, which was composed by Abbot and von Doenhoff [7]: For 4- and 5-digit airfoils, the maximum section lift coefficient of 1.8 was attained for the thickness/chord ratios between 12 and 14 percent at Re = 9 · 106. At Re = 3 · 106, (c
lmax)w ≈ 1.6 was obtained for the same classes
of airfoils at the t/c ratio between 10 and 12 percent. In the case of 6-digit airfoils, clmax was recorded between 1.7 and 1.5 for the range of Reynolds
numbers between 9 · 106and 3 · 106 respectively.
The angle of attack at which CLmax is attained is called the critical angle
attack, i.e αcr = CLmax− CL0 CLα w + ∆αcr, (2.24)
where ∆αcraccounts for the non-linearity of the lift curve-slope near the critical
α. It is usually assumed [8, 1, 4, 9] that ∆αcr lies between between 2 to 3
degrees.
The angle of attack at which the lift-curve slope starts deviating from linear is common to roughly locate in the vicinity of αcr. This angle is referred to as
the angle of attack at stall initiation, e.g.
αsi= 0.85 CLmax− CL0
CLα
w
, (2.25)
where the factor of 0.85 is recommended in reference [8].
2.2
Airplane Drag Prediction
Any sub-division or breakdown of airplane drag is somewhat arbitrary and relies on certain bookkeeping assumptions as much as it does on the physics of fluids. Various authors use different drag ”build-up” schemes [1, 3, 10, 4,
9, 11, 12], while airplane manufacturers traditionally employ their propriety breakdown definitions. We treat airplane drag as being composed of the profile drag of the major components and vortex-induced drag. A limited correction for aerodynamic interference is made by adding a hypothetical interference drag. Correction is also made for the so-called miscellaneous drag to account for such contributing factors as airframe protuberances, gaps, inlet/outlet ports, unaccounted interference, etc. With respect to lift production, the drag is sub-divided into lift-independent and lift-induced components, as shown in Fig.
2.6.
Based on the presented scheme and making account for the airplane con-figuration (en route, takeoff, landing), the coefficient of total drag is calculated according to the following expression:
TOTAL DRAG
LIFT-INDUCED LIFT-INDEPENDENT
CDpr0
'
intCDpr0'
compCDpr0'
LCDpr0 CDvi'
f(C
Dpr)
wINCREMENT at TOL
'
s(C
Dpr)
w'
f(C
Dvi)
w'
gr(C
D)
w'
ucCD0Figure 2.6: Airplane drag breakdown.
or
CD =kmisc[CDpr0+ ∆compCDpr0+ ∆intCDpr0]
+ ∆LCDpr0+ CDvi+ ∆T OLCD;
(2.27) where the miscellaneous-drag factor kmisc can be assigned a value between
1.0 and 1.10. The drag associated with airplane takeoff-landing operation, ∆T OLCD in the equations above comprises both additional lift-independent
and lift-dependent drag.
2.2.1
Profile Drag
Profile drag (expressed via CDpr) is the drag due to the boundary layer and
regions of separated flow around the major airplane components. First, it results from the action of tangential forces exerted by the flow and pressure drag associated with components’ frontal areas. The former makes up the least part of CDpr, which would be dominant at small angles of attack. As α
compressibility effects at high Mach numbers.
In the light of the stated above, the following expression is accepted for profile-drag coefficient prediction for the en route airplane configuration (which can be also recognized as part of Eq. 2.27):
CDpr= CDpr0+ ∆LCDpr0+ ∆compCDpr0. (2.28)
Minimum Profile Drag
The minimum profile drag of each airplane component is estimated by compar-ing it to the friction drag of an equivalent (adiabatic) flat plate with the same wetted area, length and a similar boundary layer. The difference between the actual and flat-plate drag is then accounted for by the so-called shape factors, φ. The total CDpr0 of all major airplane components is therefore found as
CDpr0= X i=w,vt,p,f,n (CF)i(1+φi) (Swet)i Sw +(CF)ht(1+φht)kdec (Swet)ht Sw , (2.29)
where (Swet)i are found according to the methods given in Section Component
Wetted Areas in Appendix B.
To account for the surface irregularities and roughness, the boundary layer is assumed to be fully turbulent. The friction coefficient in Eq. 2.29according to Prandtl-Schlichting is then given by
(CF)i= 0.455
(log Rei)2.58
: i = w, ht, vt, p, f, n; (2.30) where the Reynolds number is based on the component chord/lenght. The bulk flow velocity around components is taken as the free-stream velocity, except for Vht=√kdecV∞.
The flat-plate analogy is a customary practice in preliminary airplane de-sign and aerodynamics modeling for performance studies. As a result, shape factors φi are widely available in the open literature [1, 3, 4, 9, 11] based on
experimental findings. We adopted the values recommended for civil transport airplanes by Torenbeek [1] and Barinov [11], as recapitulated in Eq. 2.65 to
2.69in Appendix A.
Lift Correction to Profile Drag
The flat-plate analogy allows getting a reasonable estimate of profile drag under the conditions zero or small lift. This is however not satisfied for the airplane lift-producing components in flight and requires a correction. For the sake of our study, lift correction is made to the wing and horizontal-tail profile drag
using relations recommended by Torenbeek [1] and applied under the conditions of lift production by the isolated components:
∆LCDpr0=0.75(∆lcdstall)w CL− CLi CLmax− CLi 2 w + 0.33 cos2(Λ 0.25)ht (CL)2ht πARht kdec Sht Sw . (2.31)
The lift correction to wing profile drag (first term in Eq. 2.31) is related to the lift increment relative to the design lift coefficient CLi and based on
the section (two-dimensional) profile drag increment at the stalling angle of attack, ∆lcdstall. The latter is considered at the mean aerodynamic chord and estimated by Eq. 2.71–2.72 in Appendix A, as derived in reference [1] from experimental data on NACA 4- and 5-digit airfoils.
Drag Rise due to Compressibility
Compressibility effects on drag are generally negligible at low Mach numbers. A steady creep in drag is experienced as the free stream attains a M∞ above
0.7. This phenomenon is fairly independent of the angle attack and quantified in our study as a rise in minimum profile drag, which initiates at M′
cr.
As M∞increases further, regions of supersonic flow start appearing in the
low-pressure regions, usually on the top of lift-generating surfaces. These re-gions terminate in shock waves which thicken the boundary layer, provoke its separation and increase airplane drag. The occurrence of this phenomenon de-pends on the angle of attack and can be related to lift production. Its incipience is marked by M′′
cr in this study.
We find the Mach numbers M′
cr and M ′′
cr for the airplane wing only. The
account of drag rise due to compressibility is therefore limited to the wing, which is a common practice for civil airplanes. The suitable algorithms for M′
cr and M ′′
cr were found in Eger [9], as summarized in Eq. 2.73 and 2.74
in Appendix A. These relations were derived for civil transport airplanes and, generally, produce realistic results. However, tuning is often required based upon engineering judgement or validation drag data.
Based on the Mach number M′
cr, the minimum profile drag rise due to
compressibility is found for the condition M∞> M ′ cr, as ∆compCDpr0= 2πARw(t/c)2wcos(Λ0.35)w 2 + ARw(t/c)1/3w cos5/3(Λ0.35)w × M∞− M ′ cr MCDmax− M ′ cr 3 × 4 − 3 M∞− M ′ cr MCDmax− M ′ cr , (2.32)
drag. It is given by Eq. 2.75in Appendix A.
The lift-dependent part of drag rise due to compressibility is implicitly accounted for in the vortex-induced drag, as will be given in Section2.2.2.
2.2.2
Vortex-Induced Drag
Vortex-induced drag accounts for a pressure drag associated with the kinetic energy required to generate trailing vortexes shed by a lifting surface. In our treatment, induced drag is related to the gross isolated wing and horizontal tail, as accounted for by the first and second terms in the following equation:
CDvi= (1 + δ)(1 + δcomp) (CL)2w πARw + 1.02 (CL)2ht πARhtkdec Sht Sw. (2.33)
Factors (1 + δ) and 1.02 consider the effects of sweep, aspect and taper ratios on the lift distribution in a non-compressible flow along the wing and tail span respectively. The value 1.02 is suggested by Torenbeek [1] for the horizontal tail. While for the wing, it is customary to evaluate the vortex-drag factor by empirically established correlations, such as those compiled in [1,4,9,11]. We adopted the method of Eger [9], which relies on the following expression:
δ = kδ AR cos Λ0.25 w 3.1 − 14λw+ 20λ2w− 8λ3w , (2.34)
where kδ is the increment factor for wing vortex-induced drag, which lies
be-tween 0.01 and 0.02.
Factor δcomp in Eq. 2.33additionally accounts for the effects of
compress-ibility on the wing lift distribution, i.e. vortex drag rise due to compresscompress-ibility. It is found that [9]: δcomp= ( 10ARw(t/c)(1/3)(M∞− M ′′ cr)3 : M∞> M ′′ cr 0 : M∞≤ M ′′ cr; (2.35) where M′′
cr is given in Eq. 2.74in Appendix A.
2.2.3
Interference Drag
We limit our account of interference effects on drag to the increase of the minimum profile drag of the airplane wing and horizontal tail due to viscous interference with the fuselage. This is primarily caused by thickening of the boundary layers and an increase in the local flow velocity near the component junctions. Kolesnikov [4] related these effects to the planform areas of the wing-and tail center boxes in a way summed up in the following expression:
∆intCDpr0= 1
Sw{[kDpr0CF(S − Snet)]w
+[kDpr0CF(S − Snet)]htkdec} ,
where (kDpr0)i are interference factors equal 0.2 for the horizontal tail and one
of the following values for the wing, depending on its vertical displacement [4]:
(kDpr0)w= 0.1 : high wing 0.2 : mid wing 0.75 : low wing . (2.37)
2.3
Airplane Aerodynamics at Takeoff-Landing
The algorithms presented below are a compilation of generalized methods for modeling airplane lift and drag in a low speed flight under the conditions of de-ployed high-lift devices in or out of the proximity of ground. The consideration of ground effects on aerodynamics is restricted to the airplane wing. Besides, the effect of undercarriage extraction is taken into account as an increase in the minimum profile drag.
A single-slotted Fowler flap is considered as a general type of the trailing-edge high-lift device commonly selected for civil transport airplanes. We remind that the Fowler flap travels aft on tracks over about its entire chord, when deflected downward to its maximum angle. For the best applicability of the selected models, the flap chord ratio should lie between 0.1 and 0.4, which covers customary design solutions.
The wing leading edge is supposed to be equipped with full-span slats. These are highly cambered airfoils which deflect forth-downward of the leading edge.
Overall, the high-lift system is assumed to be fully optimized — ”the com-bination of the main airfoil plus trailing-edge flap, plus slat is designed in such a way that at high cl all parts of the system are simultaneously in a condition
of separation” [1].
2.3.1
Airplane Lift at Takeoff-Landing
The prediction of airplane lift during takeoff-landing is based on the condition that the lift in en route configuration is known. The modeling procedures then focus no quantifying the lift-induced increments depicted in Fig. 2.7.
Thus, trailing-edge flaps increase the section camber and improve the flow at the trailing edge, yet promote leading-edge stall. This translates into a positive increment in the maximum lift coefficient and lift at zero angle of attack. The deployment of trailing-edge flaps also changes the slope of the lift curve, mainly due to a change in the wing area resulting from the section chord extension.
Leading-edge slats postpone leading edge stall, thereby increasing the crit-ical angle of attack and the maximum achievable lift coefficient. At the same time, their deployment have little effect on the wing area and the section cam-ber as a whole. Therefore, the effect of slats on the slope of the wing-lift curve
(C )La w a CL L a (C )La wf Dgr(C )L w (CLmax w) Df(CLmax w) Ds(CLmax w) acr DTOLCL Df(C )L0 w CL0 (C )La wfa en-route configuration
Figure 2.7: Build-up of airplane lift.
is often neglected.
Eventually, the flow field changes with an increasing proximity to the ground. This particularly affects aerodynamic characteristics of the airplane wing. As the free stream approaches the wing, it decelerates and deflects downwards at the same time. The former leads to a reduction in the wing lift, while the latter translates into an increase in the angle of attack and, subsequently, lift. Depending on which of the two opposing effects prevails, the lift increment due to ground effect can be either positive or negative.
Summing up the contributing components shown in Fig. 2.7and neglecting the secondary effects of flap-fuselage and flap-horizontal tail interference, the equation for airplane lift (Eq. 2.3) can be re-written as
CL = CL0+ ∆f(CL0)w+ (CLα)wfα + ∆gr(CL)w, (2.38)
where CL0 is the whole-airplane lift at zero angle of attack for the en-route
configuration, given by the sum of Eq. 2.7and2.17(with α = 0). Increment in Lift at Zero Angle of Attack due to Flaps
Based on the lifting surface theory, a theoretical value of the lift increment due to flaps at α = 0◦
would be a product of the lift-curve slope and the rate of change of zero-lift angle with flap deflection times the deflection angle itself. In practice, however, this increment cannot be realized. The discrepancy will be growing with the flap deflection angle and will depend on the flap type. This is
