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Modélisation numérique du comportement thermo-aéro-dynamique des garnitures d'étanchéité pour gaz réels hautes pressions

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HAL Id: tel-00135573

https://tel.archives-ouvertes.fr/tel-00135573v2

Submitted on 5 Jun 2007

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thermo-aéro-dynamique des garnitures d’étanchéité pour

gaz réels hautes pressions

Sébastien Thomas

To cite this version:

Sébastien Thomas. Modélisation numérique du comportement thermo-aéro-dynamique des garnitures d’étanchéité pour gaz réels hautes pressions. Autre. Université de Poitiers, 2006. Français. �tel-00135573v2�

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Table des matières

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Nomenclature

4 !% "" " 8 #>" -1 - ! 8 % A "" " A , # " ? ! 6># >I 88 ! J ! # : ! A "" #> J % ! # : ! 8 : 4 #>D 6 0 K 8 1 8θ1 8? " , # % " " 8 >#< / 1 /* 1 1 1 1 61 6 1 ρ 1 ρ θ1 ρθθ ! " " , ! "" 8 # 8 4 4 6 F "" 8 # 8 # 4 1 4* ! : " " " , # : 8 " " # 4# "" # # 8 # 8 # I #5 ! ! I 1 I I ! 4 # % 8 1 " " , # D># >I " " 8 " " : # "" " # 0 # 0 4 0# 0 "" # H ># 0 ! # 0 4 A ! 8 # 8

(13)

* 0 1 0* " " : 8 " " " , # #• ! # "" % H >" # 0 # ; # 0 # ! # # " # L 1 * " " 8 " " " , # "" # "" # " 4! % "" % 8 !1 " "" A ! A " 8 # 8 1 " , # "" 1 : "" ; ! : ! 1 " , # "" ! "" , " %M # " !% # ! 1θ1 ? ! " ; % " #1 1 # " # "" % " ? 8 " 6> H >I ℜ " # " ? 8 " 6># >I 1 :1 # ;1 41 81 1 J1 *1 J*1 : * ; ! 1 : ! 1 # ; 1 4; % 1 8 1 " 1 J " 1 ! 1 J 1 ; : ! " , # # 1 # ! " #

(14)

< 1 # ; " " 1 " , # 1 * 8 " 8 # , " " , # 1 : 8 " ! : ! 8 # " , # :1 81 8 1 8*1 8 " !8 "" " *:1 * 81 * 1 *" 1 *" * 8 " !8 "" * # " " # ! I # ! % 8 I # ! J % # ! ! 8 : 4 I>#*>D # ! ! 8 ! # ! A ! 8 # 8 I 1 # ! " A 8 " 1 " , # I → , "" 8 θ # " " , "" 8! ># θ # 8 , "" 8! # #< # # # #<># 1 θ1 ? "" 1 8! 1 : " , # #>" D4 8 #

(15)

C B # "" ! 8 B # "" ! % 8 N 88 ! # β ! " 8 " β 88 " I φ → : 4 γ ! 8 % A "" " " ! 8 % A , # " O # # "" ! µ " " ! 8 >" µ- " " ! A "" "" >" ν 88 "" Ω # ! ρ 0 "" , # % H >#< τ? : " # >#* τθ? : " # 8! >#* ϖ % ω "" >" Ψ " L Ψ "" , "% " ( ; ! : ; : !

(16)

+ * . P # " ! Q # ; / ** 0 $1 $-1 $ 1 $ 1 $ $ # F #4 ?1 ? ! 1 !" 1 !" ! " !" " , # 6># 1 " " !% , D " ># 7># 1 #<># 91 # " 88 " !% , Θ1 η1 δ1 ε #5 " !% ! ; % >#7># *1 #<># 1 #<># 1 >#7># * α1 γ #5 " !% ! # 5 9D 1 α,,,,,, ,1 ,1 ,1 ,1 ,1 8,1 , 1 , 1 , 1 , 1 8, 1 ,*1 ,*1 ,*1 ,*1 8,* 88 " ! "" " , " " ! -@ % % 1 @1 @1 K1 B 1B*1ξ, #5 " , " " !

(17)

7 / * -1 1 *1 <1 C 88 " ! 8 % A "" " " !1 I 1 I*1 I<1 IC / Ψ 1α 1β 1 B #5 " ! 4 # %

(18)

=

Introduction

# ! , ! " ! "" # " 8 # " " # "" " & . " R "" " " " 1 , "" " ! A : # " # 1 8 ! ! ,! > ! 4! ! ; # % " " " A " J 8"> # % !, # " #! % " ! 4! ! 4 , 8 # "> 2 ( 3 4 1 5 6 78 J 8 #! % " "" ! 4! ! # 4 " # " 45 > " #! "# " " "!" "% " " " " "" % "1 " % " J " ; 4 "1 , , > 8 " , A 8 " 8 "" ! 4! !> 8 1 4 4 A ! 8 " 8 "" "" 8 # " " " 8 " !, 8 # " " 5 "> * # " ?> / ! 4! !

(19)

E 2 ( 9 4 ' 6' ,% 78 " " ! 4! ! " " ! " : " " " 2 " 1 ! 1 " S 1 ! " > 8 # 8 1 8 1 "! " > ! "" 8 # " 5" 8 1 % % " # #5 "> $8 " " # A 1 "" 8 # # 1 # " " 8 " " 8 :! " " > " 8 " " " % " 8 :! " " R " " 1 8 > " ! 1 " " " ! ! ! !# 8 > " # , # "" " " : > ! 4! ! 4 % " " 1 ! ! 4! ! " 1 " "" ! " J " ! " #5 & <.> 2 ( : 4 % ) * 2

;

%

% % # 2 * Parcours du gaz -% " 2

(20)

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

%

2 * 2 )

%

: 8 4 : 4

(21)

# # ? " " > " " "1 " : ! # " A 8 " " "" 1 " " # " " !% "> "1 " 88 " 4 # % " " 8 # 8 " "> , 4 " 8 " # ! 1 " # 5 ! 1 " " 8 " "" "> 8 1 # 5 #! % " !, ! ! #! % " ! "! > # 4 " ! 4 % " #! "# " 8 !" ?> 8 T 4 " % ! " 88! " ; " #! "# " !, !" 8 # " ! ; # % > "1 # ! " 8 # ? : " ! ! > " ! " " ;" # # ; # % " " " ! # ! ! "> 8 1 % % " , : " " !8 # " " " " " 8" " " A ? " !" !"> " " 8" # 5 " " !8 "> 4 !" ;" 4! #! % 8 # 8 > " 5# " % " ! # A 4 "" " !" !" ! !"> , ! # % " 88 " 4 # % " " 88 " , ) ! !" # 5 > " # " # 5 " ! # !8 "> 4 " " ! # # ?> $ 4 "" 1 # 5 ? ! ) " " ! # 5 " ? 8 > ! 5 " "! 1 " , " " 88! " ! " % " ? &, " " !1 ! 4 # % 1 ! 8 % . 8 "" U # ! " " " # > # 5 4! % " !, ! 4 > " 88! " !% " " " : # " "" ! " " !" ! "> " 8 " "1 " : !8 # " &! " % 4 # % . " " " "8 4 ? " " " , "1 " > 8 " # 5 ! 1 "! " " # , > "1 " " # ! " : 4; 45" " "" % " " ! !"> " % " 4 > 4 !" : > $ " 1 ! #! % " # ! 8 ! # 8 " 88! " " 8 # " #5 " ! #! % "> 4 # " % % " !" " V " !8 # " 4 # ! " % " " 8 " " " " # > # 1 " " " " , " " , " !" ! ">

(22)

*

Chapitre I

Bibliographie

A. Introduction

J 8 # " ? " "" "! " 8 " 8 # ? : % ! 8 # !, ## # > " # # "1 " ! "" A ! 8 # 8 1 , ) ! " 88 " 4; ; # % " 4; " % "> " 1 # ! " 4! % 8 # 8 " !" ! " % " " " ; % " #! % "> "1 "; 45" # # ; # % " " " !, ! > # 1 " # 5 " "!" " " " " " !" !">

B. Création d’un film de gaz

" " ! "1 5 # " " " "1 # " 8 # " % !" " 4 " ; " ; 4 " " 8 " W G=EX % " " ! "> " ""5 " A 88 4; ; # % " " " W/$9 G=GX> " " ! " GE-1 " " A ? # " J " A 4 > ";" 5# 8 " J " % " " Y 1 " # 8 # " # > "1 " ## # " ! W / GE=X> $8 : 5# " 8 # " , " " 4 " " ) ( !# " ";" 5# "1 " ! " " " ! ""! " A !, " " # " > " # # "1 W GG*X " " ! ""!" A " " ! " ; , 8 " ! & ( . # 8 # " " : " " 1 4 " )1 " # "" " , "

(23)

** " " 88! 1 A " ! # , " ?> ; # 8 ! 1 #)# " "" " ! ,! "1 ""5 " ! ; # % 1 % " "" " 8 # " ";" 5# "> 2 (>3 4 ? * . ( @( 3AA9B 4 8 6 4 " W F GG*X ! ! # ! 4! ! 8 " " : " " & (*.> " " !8 "" " #5 " ! #! # > " # "" % " ! " 88 " ## 4; ; # % 8 " # " " 8 "> 2 (>9 4 ? * # @ 3AA9B " " 4 ? W GG X % 8 ! ! A ? , " " " # 8 # " " : " " & (<.> " " ! ! " " : ; " 2 A 8 A 8 "> " # % ! ""5 " #)# " ! " % " % ! 8 " " " " > $ $ 9 9 $ $ 9 9

(24)

*< 2 (>: 4 .* 0 @0(-3AA3B 8 1 # " " #5 " ! #! % " " " " "" W GGCX> : " " , " # " 8 " " "1 " % ; 8 "1 " 88 # #> 88 1 % ; # 1 ! 4 # 1 " % ! > 8 , # # "> 1 " J " #! " 8 # " ! 4! !> " # # "1 H 9 " W GG=X !8 " #5 " % 8 " " 8 # " # " ! A ?> 1 " ! ! 88! " ; " # & (C. 8 # J " "!" & (+.> " # " % " 8 # " # " ! A ? , ) !8 " 8 ! #! ";" 5# # 1 # J " 1 " # ! : :1 88 #! !> 2 (>< 4 ' ** 4 * 68= * 5 6 8= .68 @2 $3AACB & . & . $ $ $ $ $ $

(25)

*C 2 (>D 4 ' E @2 $3AACB $ " 1 "H; Z W GGEX # ! % "" ";" 5# , ! " % # ' Y 8 # 8 ! " " A ## "" " & (7.> # ! " ! !# " 8 " # " ! # ! #! # ;" " !8 # "> 1 ! : ! # # " !, # " " !" !8 # " 8 " ; ";" 5# > 2 (>F 4 ? G H @ 3AAIB " ! ## 1 D WD GGGX "! 4; # "! " ! 4 " & (=. " # J " 8 , # " " " )" ( !# "> 88 1 # " 88 " 4; " % 4; ; # % 1 " " 88 1 " 8 " , "" " > " 8 " " 8 " % > $ $ 9 9 $ $ 9 9

(26)

*+ "" % # 1 " : " # ! " #1 # "1 S A " , " J "1 " " 88 "" 8 # # > 2 (>C 4 ? J @J $3AAAB4 68= ) E 6 8 " ! " " ! 4! ! A ?1 " # ! "" # ; 1 " " " " " 5 # 88 " 4; ; # % 1 " % " " ";#! % " # 8 # " " : " " > # J " " 1 1 " " " " ## " "" "" ? ! " !, 5# " " 4 " " )" !# > 8 1 " % " " 88! " ! "1 " "" " # " " J : " , # 8 "1 ! ! # # " * 0 >

C. Modélisation du film de gaz

" 4 " 4! % ! 4! !1 " ! : "" !" 2 # 5 " 4 ; % " " " !" #! % > " 1 " " : ; " 4 " " ! "!> /! ! # ? " " ! ! ## 8 1 " ! " ! , 2 # [ℜ 1 , "" 1 # , # # 1 # ! ℜ " " ? 8 > !% ; " " " , " "" " 8 # 8 " !" " " " % # ! , " " ! " " "> !% " ! 1 ! " " W GGCX 2 ∂ ∂ F < *µ ∂ * ∂ \∂θ∂ F < * µ ∂ * ∂θ [ 7 F θ*∂θ 7 θ*

&

4 \ 4*

.

∂θ * ? \ * F ∂ ∂ K 3 & . & .

(27)

*7

: "" "" " " " # 8 1 " 5 # " ! # " # " " >

1. Quelques approches analytiques

" # # "1 " ! "" % % " ! " ; % " " " J " " " J " "" ? 4 "> " # 5 " ; % " ! ! # ! ! !, !" 8 ! " ! " A ? 8 " "> " # 5 " ! " " " J , D # WD G7CX % ! ! A ?> "! # ! : " 2 ! 1 ! & (E.> " ! 1 4 # "" " 8 " "" , # " " " 4 " " " # " 4 # ! "" > ! "" " "" ! " > 1 8 "" " " "! ! > " # 1 # 5 " : ";#! % > $ " 1 ! # 8 T ; % "" 1 % ! % # ; > 1 # 5 " , % " 8 " , " # # "" ! Λ [7µ ω # : 4 * > " # " " # " !" # " 88 " ! ; # % " A "" !8! % " ! ! # "" # " 4! % > Λ ] -1 " Λ " " ! ! R " Λ ^ --" " ! ,!> 88 1 " # , 1 8 "" " " ! 1 " 4; 45" " # 5 " ! "> 2 (>I 4 5 68= 6 8= * .) ΛΛΛΛ 68 @J (03AF<B & . & . & . Λ ! ,! Λ 8

(28)

*= 0 "H; W0$ G7+X ! " # 5 4! % ! 8 # " " " " # # ! A ?> " # " " # 1 " " " ! "> " " " " " % " 88 " 1 M" A " , " "% " "" "" " "1 " " ! "> " 4! ! & / 2 _ / , 4 ;.> $ " 1 "" " : # % # 8 ; > # 5 8 " " ) % ! " " V " " " # " " " # " # "" ! ! ,!"> ; ";" 5# "" ! ! # ! "! 0 J # W0 G77X> ! ! # " " " " " " ## " (G> "1 4 # "" " " "! , ! # " " " > 2 (>A 4 ' E @ $(3AFFB J " " # " ! " A 1 D # WD G7EX " # 5 " # " # "" ! ! ,!"> ! , ! " " ! 8 " " " ## " 4 " "1 # " ## ; 8 # " " ` & ( -.> $ " 1 !, " ; % " # > # % % ! ! ! 4 % " A O " 8 " , " 1 # " % , " " O ! ,!"> 4 # ""

(29)

*E 2 (>3L 4 % * 68 * + 6 8 @J (03AFIB # 5 "! 0 "H; W0$ G7+X ! ! #! ! " " / " W GE=X ! " ! ; # % " ! " A ? ! " & ( .> " " 1 8 "1 # ! : " "> " # " % #! "# ! ! , " "% " , "" " " ! ,! "1 M" A " , " O ! ,! "> 1 # 5 "" # " # !, % 8 # " " " #5 8 " ! W GG*X> 2 (>33 4 / ? @/ 3AICB a b 4 4* : & . & .

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