Combustion Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation

J. Warnatz · U. Maas · R.W. Dibble Combustion

J. Warnatz · U. Maas · R.W. Dibble

Combustion Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation

4th Edition With 227 Figures and 22 Tables

Prof. Dr. Dr. h.c. Jürgen Warnatz

Prof. Dr. Ulrich Maas

Universität Heidelberg Interdisziplinäres Zentrum für Wissenschaftliches Rechnen Im Neuenheimer Feld 368 D-69120 Heidelberg, Germany

Universität Karlsruhe (TH) Institut für Technische Thermodynamik Kaiserstr. 12 D-76128 Karlsruhe, Germany

Prof. Dr. Robert W. Dibble University of California Dept. of Mechanical Engineering Etcheverry Hall 94720 Berkeley, CA, USA

Library of Congress Control Number: 2006927345

ISBN-10 3-540-25992-9 4th ed. Springer Berlin Heidelberg New York ISBN-13 978-3-540-25992-3 4th ed. Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under German Copyright Law. Springer is a part of Springer Science+Business Media springer.com © Springer-Verlag Berlin Heidelberg 1996, 1999, 2001, and 2006 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Digital data supplied by data Final processing: PTP-Berlin Protago-TEX-Production GmbH, Berlin (www.ptp-berlin.com) Cover-Design: medionet AG, Berlin Printed on acid-free paper 62/3141/Yu – 5 4 3 2 1 0

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0 GRL GRk GRh GR:

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lgJ@;F@g@JF-e ;F@g@JF?1Cqe@E1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L:3

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22 LLRL LLRk LLRh LLR: LLR:RL LLR:Rk LLR:Rh LLR:R: LLR9

1E*".3":@C:"?F+!@+1/ ?/(+/"?/1, RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lc9 lF/E1FgCe>1FJE1Fe@FeggJeF;@F1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lc9 p@/g@JFege Fg1^E1/@g1e1EN1^gl^1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lc3

Jo?1EN1^gl^1ep@/g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LcG

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;F@g@JFe@Fe@1`1CeF;@F1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lb: >1e  eJF,1Ng RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lb9 >1e  eJF,1Ng RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lbb p1^,@`1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR Lb3

2B LkRL LkRLRL LkRLRk LkRLRh LkRLR: LkRk LkRkRL LkRkRk LkRkRh LkRkR: LkRh

)"?D+":*@1,";*8C@+1/;?%1:?):""*+."/;+1/-?"@+/(?-1E?RRRR LbG >1eJF`1^ng@JFeUlg@JF` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LbG n1^CCe``eJF`1^ng@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL3s N1,@1`e``eJF`1^ng@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL3L JE1FglEeJF`1^ng@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL3L F1^;qeJF`1^ng@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRReL3k >1eEN@^@,Ce o` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3h 1ogJF\`e oeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3h Jl^@1^\`e oeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3: @,B\`e oeF/e>1^ECe@88l`@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3: C,lCg@JFeJ8eg>1e^F`NJ^geJ188@,@1Fg`e8^JEeJC1,lC^e^E1g1^`eRRRRRRRR L39 p1^,@`1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L39

2A LhRL LhRk LhRh LhR: LhR9 LhRc LhRb LhR3 LhRG LhRLs LhRLL

C:C-"/@?"@+/(?-1E; RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3b JE1elF/E1FgCe>1FJE1F RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3b @^1,gelE1^@,Ce@ElCg@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR L3G JF,1Ng`e8J^el^&lC1F,1eJ/1C@F;-e@E1?eF/en^1?
n1^;@F; RRRRRRRRRR LGk 1qFJC/`?
n1^;1/en@1^?gJB1`eO
PeUlg@JF` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LG: l^&lC1F,1eJ/1C` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR LGc 1Fe1,g@JFeg1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kss JF,1Ng`e8J^el^&lC1F,1eJ/1C@F;-e^J&&@C@gqe1F`@gqelF,g@JF`eRRRRRRRRRRRRR ksk //q?^1B?NeJ/1C`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR ksc l^&lC1Fge,C1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR ksb

^;1?//qe@ElCg@JFeO PeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR ksG p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kLL



&C1eJ8eJFg1Fg`

2' L:RL L:Rk L:Rh L:R: L:R9

C:C-"/@?1/3:".+F"!?-.";eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kLh JFN^1E@p1/eCE1`eo@g>eUl@C@&^@lEe>1E@`g^qeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kL: @F@g1?g1e>1E@`g^qe@FeJFN^1E@p1/eCE1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkLb CE1epg@F,g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kkL ?@ElCg@JF`eJ8el^&lC1FgeJF?^1E@p1/eCE1`e`@F;eeJFg1? ^CJe1g>J/ RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekk: p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkkc

2& L9RL L9Rk L9RkRL L9RkRk L9Rh L9R: L9R9 L9Rc

C:C-"/@?:".+F"!?-.";eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkkb C``@8@,g@JFeJ8el^&lC1Fge^1E@p1/eCE1` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kkb CE1C1geJ/1C`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khs CE1C1geJ/1CC@F;e`@F;ee1,g@JFe^J;^1``e^@&C1eRRRRRRRRRRRRRRRRRRRRRRR khL CE1C1geJ/1CC@F;e`@F;ee 1n1C?1ge1g>J/ RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khk l^&lC1FgeCE1e1CJ,@gqeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkhh CE1epg@F,g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkh9 g>1^eJ/1C`eJ8el^&lC1Fge^1E@p1/eJE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khb p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkh3

2> LcRL LcRLRL LcRLRk LcRk LcRkRL LcRkRk LcRkRh LcRkR: LcRkR9 LcRh LcRhRL LcRhRk LcRhRh LcRhR: LcR:

1.C;@+1/?1%? +8C+!?/!?1-+!?C"-;eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khG ^JNC1geJE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR khG JE&l`g@JFeJ8e@F;C1e^JNC1g`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:s JE&l`g@JFeJ8e^JNC1ge^JlN`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:: N^qeJE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:c J^Eg@JFeJ8eN^q`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:c N^qeJE&l`g@JFeJ/1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:b gg@`g@,Ce1`,^@Ng@JFeJ8eN^q`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k:G J/1C@F;eJ8el^&lC1FgeN^qeJE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRk9k CE1C1g?qN1eJ/1C`e8J^eN^qeJE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9h JCeJE&l`g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k99 q^JCq`@`eJ8eeJCeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k99 l^F@F;eJ8eJCg@C1eJENJlF/`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9c l^F@F;eJ8eg>1eJB1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9c JCe`@8@,g@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9b p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRk93

2= LbRL LbRk LbRh LbR: LbR9 LbRc LbRb LbR3

1:.@+1/?1%?+@:+?F+!";eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9G >1^ECeeO1C/Jn@,>eP RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR k9G ^JENgeeO1F@EJ^1ePeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kck e1F1^g1/en@e@g^Jl`ep@/1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kc9 JFn1^`@JFeJ8el1Ce@g^J;1Fe@FgJe RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kc9 e1/l,g@JFe&qeJE&l`g@JFeJ/@8@,g@JF` RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kcb gCqg@,eJE&l`g@JF RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkbL e1/l,g@JFe&qeJ`g?JE&l`g@JFe^J,1``1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR kbk p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekb9

&C1eJ8eJFg1Fg`



2# L3RL L3RLRL L3RLRk L3Rk L3Rh L3R: L3R9

1:.@+1/?1%?G!:1:1/;?/!?11@ RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekbb F&l^Fge q/^J,^&JF`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekbb CE1epg@F,g@JFel1egJeg^@FeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekb3 CE1epg@F,g@JFegeCC`eF/e@FeN`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekb3 J^Eg@JFeJ8eJCq,q,C@,e
^JEg@,e q/^J,^&JF`eO
P RRRRRRRRRRRRRRRRRRRRRRRRRRek3s >1e>1FJE1FJCJ;qeJ8eJJgeJ^Eg@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRk3h J/1CC@F;eF/e@ElCg@JFeJ8eJJgeJ^Eg@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRek3b p1^,@`1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkGc

20 LGRL LGRLRL LGRLRk LGRLRh LGRkR LGRkRL LGRkRk LGRkRh LGRh LGR:R LGR:RL LGR:Rk LGR:Rh LGR9 LGR9RL LGR9Rk LGRc LGRcRL LGRcRk LGRcRh LGRcR: LGRb

%%"@;?1%?1.C;@+1/?:1";;";?1/?@)"?
@.1;3)":"eRRRRRRRRRRRRRRRRRRRRRRRRRRRRekGb >1eg^l,gl^1eJ8eg>1e
gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRekGb ^1``l^1e@Feg>1e
gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRkGb 1EN1^gl^1eF/eC``@8@,g@JFeJ8eJEN^gE1Fg`e@Feg>1e
gEJ`N>1^1eRRRRRRRekGG JENJ`@g@JFeJ8eg>1e
gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehss >1e
gEJ`N>1^1e`ee>JgJ,>1E@,Ceq`g1EeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehss

E&1^g?11^e oeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRhss g1^F?JCCE1^eUlg@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsL J^Eg@JFeJ8e>JgJ,>1E@,Ce q1^`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsk

F,JE@F;elFe/@[email protected]>JgJ,>1E@,Ce^@E^qe^J,1``1`eRRRRRRRRRRRRRRRRRRRRRRehsh >q`@,Ce^J,1``1`e@Feg>1e
gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehs9 JF`1^ng@JFeJ8eg>1e``eJ8eN1,@1`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehs9 JF`1^ng@JFeJ8eF1^;qeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsc JClg@JFeJ8eg>1eJF`1^ng@JFeUlg@JF`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsb >1E@`g^qeJ8eg>1eFNJCClg1/e
gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsb l^1epq;1Fe
gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehsb pq;1F?@g^J;1F? q/^J;1F?^&JFe
gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehs3 >1E@`g^qeJ8eg>1eJCClg1/e
gEJ`N>1^1eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehLs >JgJ,>1E@,CeEJ;eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehLs lN1^`JF@,e^F`NJ^g`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehL: ^11F? Jl`1e881,geRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehL9
,@/e^@FeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehLc >1eJC1eJ8eJE&l`g@JFeJl^,1`e@Fe
gEJ`N>1^@,eJCClg@JFeRRRRRRRRRRRRRRRRRRRRRehLb

BI ksRL ksRkRL ksRkRk ksRkRh ksRkR: ksRh ksRhRL ksRhRk ksRhRh ksRhR: ksRhR9 ksRhRc


33"/!+F?2? @)".@+;eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehLG JE1e18@F@g@JF`eF/e o`e8J^e1,gJ^`eF/e1F`J^`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehLG J^ElCg@JFeJ8eg>1e^J&C1EeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehks 1F1^Ce1E^B`eJFeJClg@JFe
C;J^@g>E`e8J^eeq`g1E`eRRRRRRRRRRRRRRRRRRRRRRehkL lC1^e1g>J/eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehkk pg^NJCg@JFe1g>J/eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehk: lE1^@,CeJClg@JFeJ8e^g@Ce@881^1Fg@CeUlg@JFeq`g1E`eRRRRRRRRRRRRRRRRRRRRehk9 Ng@Ce@`,^1g@rg@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehkc

F@g@CeCl1`.eJlF/^qeJF/@g@JF`.egg@JF^qeJClg@JFeRRRRRRRRRRRRRRRRRRRRRRRRRRehk3 pNC@,@geJClg@JFe1g>J/`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehkG

ENC@,@geJClg@JFe1g>J/`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehhs 1E@?@ENC@,@geJClg@JFeJ8e^g@Ce@881^1Fg@CeUlg@JF`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRehhs

ENC@,@geJClg@JFeJ8e^g@Ce@881^1Fg@CeUlg@JF`eRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRehhL



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B2 kLRL kLRk


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BB

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BA

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