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Modélisation dynamique des décharges se propageant
sur des surfaces isolantes polluées avec des dépôts
discontinus sous différentes formes de tension
Siméon Diampeni Kimbakala
To cite this version:
Siméon Diampeni Kimbakala. Modélisation dynamique des décharges se propageant sur des surfaces
isolantes polluées avec des dépôts discontinus sous différentes formes de tension. Energie électrique.
Ecole Centrale de Lyon, 2007. Français. �tel-00220521�
HAL Id: tel-00220521
https://tel.archives-ouvertes.fr/tel-00220521
Submitted on 28 Jan 2008
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3
Chapitre II
MODELISATION DYNAMIQUE DE L’ARC
ELECTRIQUE SUR DES COUCHES
DISCONTINUES
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@ 4 ""
!5!
+= I
5
6
6
x 10
4
" 4
. "
"
"
+= J)
#5
4! !
4A 4A
" 4
4
! ""
!
"
" 4 4A
" 5%5
N O ,
4! !
C"
" 4 4A
!5 " !
[email protected] "@
6
4
!
" 5
4
5
S 5 "!
"
"" !
8 U
" 4
S
4A
" 4
!
64 ." 4
4A #
; [email protected]
5!""! 4
"
"
"
@
" 5
@
!5
%
4! !
5
"
!5
+= ' C +=
C "
4
" 4
# 55 @ 4 ""
# !
"
5!?
S
. "
!
'3 3 F=
5
4
8!#
"
!
I( (I F=
!
.
6
4! 5
[email protected] C
"" !
!
5
I r2
"!
4A
!
!
""
5%5
5& ) N I. (O
4
Tension appliquée
Chute de tension
Tension à la tête de l'arc
5
Tension (V)
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
8 4
! "
""
!
4
5
Temps (ms)
Q!#
+= '
5 !?
" !
!8 5 D 4
5
""
!
4! !
Ir2
"
4A #
!
55 *
; [email protected] ` I(. (I F=
'
0
0.35
0.3
Courant (A)
0.25
0.2
0.15
0.1
0.05
0
Q!#
+=
""
0
" !
5
1
5
5 !?
4
0.5
1.5
""
!8 5 D 4
2
2.5
Temps (ms)
3
3.5
4
4.5
4
"
4A #
8 4
! "
4! !
Ir2
!
55 *
!
; [email protected] ` I(. (I F=
2
x 10
4
Tension appliquée
Chute de tension
Tension à la tête de l'arc
1.8
1.6
Tension (V)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Q!#
+=
5 !?
0
" !
!8 5 D 4
0.5
5
1
""
4! !
1.5
2
!
I r2
2.5
3
Temps (ms)
"
3.5
4
4A #
!
. 55 *
4.5
5
8 4
! "
""
!
4
5
; [email protected] ` '3. 3 F=
' I
0
1.5
Courant (A)
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
Q!#
""
4
+=
" !
5 !?
5
5
""
!8 5 D 4
4
4! !
I
"
4A #
r2
!
.
8 4
! "
55 *
!
; [email protected] ` '3. 3 F=
1200
Vitesse de la décharge (m/s)
1000
800
600
400
200
0
78
0
0.5
1
1.5
2
2.5
3
3.5
4
4! !
4
4.5
Temps (ms)
Q!#
+= I =!
"" !
!
"
. 55 *
!
4A #
4
5
I r2.
!
; [email protected] ` I(. (I F=
' J
0
800
700
Vitesse de la décharge (m/s)
600
500
400
300
200
100
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
Q!#
+= J =!
!
"
"" !
9)
9*
. 55 *
B *
9)
9)
/ *
9)
9)
/)
/
7
B *
* P
.
4! !
" " 4
g'
"
*
g
" "
!4
!
$8!#
"
D
"
4
4
<
4! !
! 8 ! $8!#
6
)
8" 4
! @
+= ''
σ.
" "
@
8 !."
8 !
# "
@
" 4
!
"
!
!
! !
T" 4
?8 ! " .
4
"
8 !
"!
!?
"" @
@
4
#5
4
8 U
5 @
" !
8!
8 !
#
" #
" #?
5
+= ' ) *
$ & )
!5
5 ! 4
!
4R
! !
5 @
6
4 ""
5 @
!4
!
σ'
4! !
6
"
! 5
4;4"
!
)
8 4 4 5
4! !
" $g' q g )
T4 4
4! 4
4
6!?5
C += '
+
"
# "
5!?
?
I r2.
+*
L +
#
#
+=
4! !
; [email protected] ` '3. 3 F=
! "
5!?
!
#5
5
* +
! ?
"! "
$'& )
4
+ ,.
4
!
4
7
+
A
!
7
4 4 .
4
4A #
" 4!?
5
! 4 ""
# !
. ""
'
0
"
?#
"" 4
<
"
8 !
5 5
" ""
"
"
#
6 "[email protected]
"
" "
14
#
x 10
4A #
! "
" !
!
#
"
4
# !
"
4A #
! # C
4 "!
"
!
$8!#
+= ' ) D
4 55 4
4 !
4 . 4
4A # D 4 @ !
4
@
4
Tension appliquée
Chute de tension
Tension à la tête de l'arc
12
Tension (V)
10
8
6
4
2
0
0
0.5
1
1.5
2
Temps (ms)
2.5
3
3.5
2.5
3
3.5
$ )
0.7
0.6
Courant (A)
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
Temps (ms)
$ )
Q!#
+=
! "
g ` ' r2
u " !
5
""
8 5 4;"!
[email protected]
"
!
4
"
5
#
!
8
$ )
4
` '3 45.
!
$ )
"
"" !
4A #
"
55. g' ` I r2
; [email protected] ` 'I J' F=
' 3
0
6
x 10
5
Tension appliquée
Chute de tension
Tension à la tête de l'arc
5
Tension (V)
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
3
3.5
4
4.5
5
Temps (ms)
$ )
0.2
0.18
0.16
Courant (A)
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0
0.5
1
1.5
2
2.5
Temps (ms)
$ )
Q!#
+= 3 u " !
! "
g ` .' r2
8 5 4;"!
!
5
""
[email protected]
"
4
"
#
5
!
8
$ )
4
` '3 45.
!
; [email protected] ` I
$ )
"
"" !
4A #
"
55. g' ` I r2
.(' F=
' (
0
18
x 10
4
Tension appliquée
Chute de tension
Tension à la tête de l'arc
16
14
Tension (V)
12
10
8
6
4
2
0
0
1
2
3
Temps (ms)
4
5
6
4
5
6
$ )
1.6
1.4
Courant (A)
1.2
1
0.8
0.6
0.4
0.2
0
0
1
2
3
Temps (ms)
$ )
Q!#
+= ( u " !
! "
g ` ' r2
8 5 4;"!
!
4
5
""
"
[email protected]
"
5
#
!
8
$ )
4
` '3 45.
!
$ )
"
"" !
4A #
"
. 55. g' ` I r2
; [email protected] ` 'J(. 3 F=
''
0
6
x 10
5
Tension appliquée
Chute de tension
Tension à la tête de l'arc
5
Tension (V)
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
3
3.5
4
4.5
5
Temps (ms)
$ )
0.14
0.12
Courant (A)
0.1
0.08
0.06
0.04
0.02
0
0
0.5
1
1.5
2
2.5
Temps (ms)
$ )
Q!#
+= '
! "
g ` .' r2
u " !
8 5 4;"!
!
5
[email protected]
4
""
"
"
#
5
!
8
$ )
` '3 45.
4
!
$ )
"
"" !
4A #
"
. 55. g' ` I r2
; [email protected] ` I 3 F=
'''
0
1400
Vitesse de la décharge (m/s)
1200
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
3
3.5
Temps (ms)
$ )
2500
Vitesse de la décharge (m/s)
2000
1500
1000
500
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
$ )
Q!#
+= '' u " !
4;"!
[email protected]
!
4
"
4
5
#
5
8
5
""
` '3 45.
; [email protected]
; [email protected] ` I
"
!
!
!
"
"" !
4A #
! "
8 5
55 $ ) g' ` I r2
g ` ' r2
` 'I J' F= D $ ) D g' ` I r2
g ` .' r2
!
.(' F=
''
0
1600
Vitesse de la décharge (m/s)
1400
1200
1000
800
600
400
200
0
0
1
2
3
4
5
6
Temps (ms)
$ )
2500
Vitesse de la décharge (m/s)
2000
1500
1000
500
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
$ )
Q!#
+= '
u " !
4;"!
[email protected]
"
!
4
4
5
#
5
8
5
""
"
` '3 45.
; [email protected]
!
!
!
"
"" !
4A #
! "
8 5
. 55 $ ) g' ` I r2
g ` ' r2
` 'J(. 3 F= D $ ) g' ` I r2
g ` .' r2
!
; [email protected] ` I 3 F= $ )
''
0
200
180
Longueur de la décharge (cm)
160
140
120
100
80
60
40
20
0
0
0.5
1
1.5
2
2.5
3
3.5
Temps (ms)
$ )
200
180
Longueur de la décharge (cm)
160
140
120
100
80
60
40
20
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
$ )
Q!#
+= '
#
45.
!
"" !
` 'I J' F= D $ ) g' ` I r2
"
4A #
! "
55 $ ) g' ` I r2
g ` .' r2
!
8 5 4;"!
g ` ' r2
4
!
5
[email protected]
"
4
; [email protected] ` I
#
5
8
` '3
; [email protected]
.(' F= $ )
''
0
9)
9)
/)
9
* P
7
4R
.
+
4
4
" " 4
"! "
4
D" @
4A #
"
"
8!#
+=
! "
"
#
'
@
;
'() D !"
5%5
[email protected]
4 ""
"
!
"
@
4A #
!5
"
4
! "
!
[email protected] C
. 5
[email protected] 5
"
d
4
B
g
!
g 5
5!?
D ""
J. I 45
!5
. 4 @!
4A #
. 5
+=
!
!5 "
"
!
$8!#
5 6!5 "
A
4! !
!5
@ "
g &g' "
"
+= ' C ' )
! 4 ""
4 g'
!5
4
" @ "
;
" " 4
;
4
5
"
"
4
!
!5
!
6
4
6!?5
"
5
4R
@ "
@
" 4A #
4
!
"
4
" !
;
g'.
""
"
5 .4 @!4
+= '3
"
#
?4A $8!#
@
$8!#
#5
4 !
"
5
!
" !
!4
!
4 55 4
"
" "
" 4
4
.
!5
"
" 4A #
4 <
@
4! !
. I 45 "
5
5
@!
g'
5
4
! # " 5
4A #
8 ! $ 8)
" 4
!
"" !
4! !
4?
4! !
$ & )
8
8 5 4;"!
4
"
"! "
' !""
" 4
! @
#
)
4
"
"
4A #
5!?
"
@!
!
4A #
+
@ " 4
8 4
#5
4
4
L +
g' d g
"
! .
@
!
5
4
."
" "
! @
#
!
$'& )
4! ! g
"
* +
8!#
A
4
"
*
)
!
"
3'
C
6!?5 4 . " 4A #
C I. 5 $8!#
"
5
+=
)
g &g' I 8 !
#
''I
0
x 10
12
4
Tension appliquée
Chute de tension
Tension à la tête de l'arc
10
Tension (V)
8
6
4
2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
2.5
3
3.5
4
Temps (ms)
$ )
1.4
1.2
Courant (A)
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
Temps (ms)
$ )
Q!#
+= '
! "
g ` I r2
u " !
5
8 5 4;"!
!
[email protected]
4
""
"
5
"
#
!
8
$ )
` '3 45.
; [email protected] ` '
4
!
$ )
"
"" !
4A #
"
55. g' ` ' r2
. ( F=
''J
0
3.5
x 10
5
Tension appliquée
Chute de tension
Tension à la tête de l'arc
3
Tension (V)
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
3
3.5
4
4.5
5
Temps (ms)
$ )
4
3.5
Courant (A)
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
Temps (ms)
$ )
Q!#
+= 'I u " !
! "
8 5 4;"!
g ` I r2
!
5
[email protected]
4
""
"
5
"
#
!
8
$ )
` '3 45.
; [email protected] `
4
!
$ )
"
"" !
4A #
"
. 55. g' ` .' r2
J. 3 F=
''
0
x 10
12
4
Tension appliquée
Chute de tension
Tension à la tête de l'arc
10
Tension (V)
8
6
4
2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
2.5
3
3.5
4
Temps (ms)
$ )
16
14
12
Courant (A)
10
8
6
4
2
0
0.5
0
1
1.5
2
Temps (ms)
$ )
Q!#
+= 'J u " !
8 5 4;"!
r2
!
[email protected]
4
5
"
#
5
""
"
8
!
` '3 45.
4
!
"
"" !
4A #
"
. 55. g' ` ' r2
! "
g `I
; [email protected] ` '' .IJ F=
''3
0
x 10
3.5
5
Tension appliquée
Chute de tension
Tension à la tête de l'arc
3
Tension (V)
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
Temps (ms)
2.5
3
3.5
4
2.5
3
3.5
4
$ )
80
70
Courant (A)
60
50
40
30
20
10
0
0
0.5
1
1.5
2
Temps (ms)
$ )
Q!#
+= '
8 5 4;"!
r2
!
u " !
[email protected]
4
5
"
#
5
""
"
8
!
` '3 45.
4
!
"
"" !
4A #
"
. 55. g' ` .' r2
! "
g `I
; [email protected] ` I . ( F=
''(
0
1400
Vitesse de la décharge (m/s)
1200
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Temps (ms)
$ )
2000
1800
Vitesse de la décharge (m/s)
1600
1400
1200
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
$ )
Q!#
+= '3 u " !
4
5
""
8!#
!
+= '
!
4A #
$ )
+= 'I
4
6
$ )
'
0
1400
Vitesse de la décharge (m/s)
1200
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Temps (ms)
$ )
2500
Vitesse de la décharge (m/s)
2000
1500
1000
500
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Temps (ms)
$ )
Q!#
+= '( u " !
4
5
""
8!#
!
+= 'J
!
4A #
$ )
+= '
4
6
$ )
' '
0
2.5
x 10
-7
Charge (C)
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Temps (ms)
$ )
9
x 10
-7
8
7
Charge (C)
6
5
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
$ )
Q!#
+=
4;"!
[email protected]
u " !
"
#
5
8
""
` '3 45.
" 4A # "
!
"" !
4
5
! "
. 55 $ ) g' ` ' r2
g ` I r2 D
8 5
$ )
g' ` .' r2 . g ` I r2
'
0
-3
5
x 10
4.5
Rayon de la décharge (mm)
4
3.5
3
7
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
Temps (ms)
$ )
9
x 10
-3
8
Rayon de la décharge (mm)
7
6
5
4
3
2
1
0
0.5
0
1
1.5
2.5
2
3
3.5
4A # "
4
4.5
4
5
Temps (ms)
$ )
Q!#
+= ' u " !
8 5 4;"!
r2 D
[email protected]
"
5
#
""
8
;
` '3 45.
"
!
"" !
5
! "
. 55 $ ) g' ` ' r2
g `I
$ ) g' ` .' r2 . g ` I r2
'
0
9)
9)
9*
+
: +*
B
4
!4! 4
@
! "
!88
8 U
"
?
4 ""
9)
9)
9)
/ *
O
6
"
A
!
"
B
!
.
4
4A
4
T"
C
#5
#5
!
!
5 6!5 "
6
4A #
# .
! .
"
8!#
! ."
@ "
4
"
!88
'I 45
.
"
"
I 45
"
! !?5
"
!
!
!
5%5
! !
"
4
!
" .
4
4
5
"
5
4
C 'J
! [email protected]
"
4 !4
"
" #
" 4
8!#
!88
"
" C
C4 <
4
4
" "
@ "
4A # 4 55 4
"
!5
)
"?#? 5
!?
"
8&
4
#5
"
4 5 "? 5
4
@ "
" !
@ 4 ""
"
$ !
4 !4
4A
6 "
# "
" 4
"
"!
"!
@
" "
!
#
! ' r2. "
C I
4
#5
#5
!
" 4
8!#
5
4! ! .
+=
"
88 4
8!#
!
" #
5 @
5 ! "
6 4
5!? 4
!
!!
5 4
!4 " !
8 5
4
+*
*
8!#
4
"!
8 ! "
5%5 4
r2
55
!
!
" " 4
+
" 4
4! !
"
@
6!?5
6 %5
4A #
"
4! !
. ' 45
"
"
4
!
4! !
4
*.
!
!
4
""
" " 4
4
"
7
@
!
"! "
!
" 4
5!?
" 5%5 ! "
4 5
8 4
*
!
C
# !
4 !4 D
"
?
G
5&
'
0
1.4
1.2
Courant (A)
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Temps (ms)
Q!#
+=
;
"
'I 45.
!
!
4A #
"" !
4
5
2
x 10
"! "
. 55 D " #
4;"!
44
[email protected]
!
"
#
8
!
` '3 45
I. '
'I 45. "
'( . I F=
-7
1.8
1.6
Charge (C)
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Temps (ms)
Q!#
+=
A # "
; 'I 45.
!
4
!
4
5
"" !
5
"! "
. 55 D " #
4;"!
44
!
[email protected]
"
!
#
8
` '3 45
I. '
'I 45.
'( . I F=
' I
0
1800
1600
Vitesse de la décharge (m/s)
1400
1200
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
3
3.5
[email protected]
"
4
4.5
Temps (ms)
Q!#
+=
;
=!
'I 45.
!
"
!
4A #
"" !
4
5
5
x 10
! "
. 55 D " #
4;"!
44
!
#
8
!
` '3 45
I. '
'I 45. "
'( . I F=
7
4.5
Résistance de la décharge ( /m)
4
3.5
3
2.5
2
1.5
1
0.5
0
0.5
0
1.5
1
2
2.5
3.5
3
4
4.5
Temps (ms)
Q!#
4;"!
44
+= I
[email protected]
!
u " !
"
#
!
"
8
!
4
` '3 45
I. '
"
;
4A # "
'I 45.
4
!
5
"" !
"! "
. 55 D " #
'I 45
' J
0
.O
4
! ? 4
@
4
55
"
4
4! !
I r2
4
4
4
6 %5
. ' r2
"
8 ! 4!
@
! @ "
4
#
! [email protected]
4
!
4
18
x 10
4
"
"
@
!5
"
!
4! !
?4A
?
[email protected]
""
$ 8& )
5 @
@
" 4
4
8!#
"
4
"
4S
C !
4
4
4
4! !
+= J
5 "!
!5
@ "@
4
$ )
6
tension appliquée
chute de tension
tension à la tête de l'arc
16
14
Tension (V)
12
10
8
6
4
2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
3
3.5
4
4.5
Temps (ms)
0.07
0.06
Courant (A)
0.05
0.04
0.03
0.02
0.01
0
0
0.5
1
1.5
2
2.5
Temps (ms)
'
0
-3
1.2
x 10
Rayon de la décharge (mm)
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
3
3.5
4
4.5
Temps (ms)
3500
Vitesse de la décharge (m/s)
3000
2500
2000
1500
1000
500
0
0
0.5
1
1.5
2
2.5
Temps (ms)
' 3
0
4.5
x 10
9
Résistance de la décharge ( /m)
4
3.5
3
2.5
2
1.5
1
0.5
0
0.5
0
1
1.5
2
2.5
3
3.5
4
4.5
3
3.5
4
4.5
Temps (ms)
200
180
Longueur de la décharge (cm)
160
140
120
100
80
60
40
20
0
0
0.5
1
1.5
2
2.5
Temps (ms)
Q!#
+= J
5 "
4A # .
!
4
45
;
'I 45.
'I 45. "
!
"
4
4
4
"
4
#
!
! [email protected]
"
4A #
"" !
5
!
. 4
.
;
"! "
. 55 D " #
"
4;"!
44
!
4A # . !
[email protected]
"
!
#
"
8
` '3
I. '
'. ( 0 =
' (
0
O
"
#
#
" 5%5 4
"
4
6 %5 .
4A 4
!
" @
!
"
+=
!4 "!? 5
4
#
"
4
5 @ @ "
"
" #
#!
"
16
x 10
"
8 U
"
?
4.
4
4
!# !8!4 !
"
4A # . "
!
!!
.
$! "
!
' r2
"
!
4
4A #
4
"
"
$
44
.' 55
!!
4! !
#
4! !
""
." 4
!
4
" "
""
4
!
"
#
I r2
"
"
"
# "
"
+= 3
)
""
8 !
4
4A # "
4! !
# !
! [email protected]
"
4! !
!4 " 5
) "
4A #
4
Tension appliquée
Chute de tension
Tension à la tête de l'arc
14
12
10
Tension (V)
4
"
5 !
!
"
4
.
!
. 55
"
4A #
8!#
8&
4A
""
"
" @!
" "
4
8!#
8
6
4
2
0
0
0.5
1
1.5
2
2.5
Temps (ms)
$ )
'
0
0.9
0.8
0.7
Courant (A)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
Temps (ms)
$ )
Q!#
"! "
+=
u " !
4;"!
. 55
"
[email protected]
"
""
!
#
8
.' 55 D " #
2.5
x 10
$ )
4
` '3 45
44
$ )
;
!
"
'I 45.
!
4A # "
!
4
" 4
I. '
5
4A
?
""
'I 45
7
Résistance de la décharge ( /m)
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
Temps (ms)
$ )
' '
0
1600
1400
Vitesse de la décharge (m/s)
1200
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
Temps (ms)
$ )
Q!#
+= 3
4
4
u " !
5
4A
?
"! "
""
. 55
"
!
4
4;"!
[email protected]
4A # $ )
"
4 " "
""
#
8
"
!
` '3 45
.' 55 D " #
"
;
44
4 $ ) "
'I 45.
!
!
"
!
I. '
'I 45
9)
9)
9)
9*
.
4
" 44
4 ' r2 "
!
"
+
*
4 "" @ ! C "
"
@ "
" 5%5 "
6
#
6 %5
! " !
" 4
4! !
" 5%5 4
" " #
" 5 !
4! ! C
"
"
!
r2
8 !
'
0
10
9
8
7
Courant (A)
6
5
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
Q!#
+= (
;
'I 45.
4
"
4A #
!
"! "
"" !
" D" #
44
!
4;"!
. 55
!
[email protected]
"
I. '
"
#
8
6 %5
'I 45. "
` '3 45
.' 55
!
"
4
5
'3 .IJ F=
4.5
x 10
-7
4
3.5
Charge (C)
3
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4;"!
[email protected]
"
4.5
5
Temps (ms)
Q!#
;
4
+=
'I 45.
" D" #
A # "
!
44
!
4
5
"" !
. 55
!
"! "
"
I. '
6 %5
'I 45.
#
8
` '3 45
.' 55
!
4
"
5
'3 .IJ F=
'
0
1800
1600
Vitesse de la décharge (m/s)
1400
1200
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
Q!#
;
4
+= ' =!
'I 45.
"
4A #
!
! "
"" !
" D" #
44
4;"!
. 55
!
"
!
[email protected]
"
#
6 %5
I. '
'I 45. "
8
` '3 45
.' 55
!
"
4
5
'3 .IJ F=
3
x 10
7
Résistance de la décharge ( /m)
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Temps (ms)
Q!#
4;"!
6 %5
+=
[email protected]
" !
"
"
#
8
.' 55
"
!
4
"
4A # "
4
5
` '3 45.
;
'I 45.
!
"" !
. 55
"
!
I. '
'I 45
4
" D" #
44
!
"! "
'
0
9)
9)
=*
*
!5 " !
5
!
5 ?"
4
"
7
"
!
+=
@
+= 3 5
4
4! !
" 4
4
4! !
'
! ! !
# !
I5
#
' r2
"
4
#
5
"
"
!
5 !
!
4A
+*
! 4! "
5
4
4
! [email protected]
8 ! " 5
""
""
'
!88
4
.' r2 "
@ "
4 5 ?"
!
!5 " !
!5!
4
@!
r2
8!#
! [email protected]
"
"" !
3.I 45
"" . " 4
D" 4
5
. I5
@
"
8
!
."
#5
!
4
4A #
4
"
5 D "" 4
5
"
"" !
!
@
?
"
5
4! !
.' r2
! 4 <
"!
4! !
5
" !
" 4 4A
4! !
5
!
# !
4
"
"" !
5
+++ '(
"
D4
+*.
,
+++ '(.
5%5 4
"
8 !
" 4
"
*
8 ! "
" 8!#
4A
4
" 4
+:
" 8!#
!
8
#
[email protected]
" 4
@
+*K
4! !
+= I
"" !
"
[email protected]
+*
" 4 5
4A
55
+
.
" 4
"
4 ""
r2
!
B
4A #
+= J. +=
!
4
. +=
" 4! !
!
B
+
# " C ' r2 "
!5
"! "
R" @
+
8!#
4
*
" ! 8"
!""
9)
9)
=)
/
7
!
$8!#
!4
! !
5
+= I
"
" !
"
4
!
"
@!
C"
#
4
#
"
4A
4
!
!5
# !
4 !
"
+= 3) +"
" 5
4!?
<
@
"
!8 ! C
6
"
4
4
!4
4A C
!
' I
0
4
x 10
4
Tension appliquée
Chute de tension
Tension à la tête de l’arc
3.5
3
Tension (V)
2.5
2
1.5
1
0.5
0
0
1
2
3
4
5
6
4
5
6
Temps (ms)
$ )
0.05
0.045
0.04
Courant (A)
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0
1
2
3
Temps (ms)
$ )
Q!#
"! "
""
+=
u " !
"
4 5
C'
r2
!
$ )
8 ! " 5
. 55
!
4
"
""
C ' r2
!
4
4A # $ ) "
.' 55
5
4
!
5
8
5
J. J F=
' J
0
1.2
x 10
-3
Rayon de la décharge (mm)
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
4
5
6
Temps (ms)
$ )
1.4
x 10
-8
1.2
Charge (C)
1
0.8
0.6
0.4
0.2
0
0
1
2
3
Temps (ms)
$ )
Q!#
+=
u " !
8 ! " 5
55
!
""
!
;
" 4A #
C 'r2
.' 55
!
5
J. J F=
4
"
4
5
8
5
"! "
""
4 5
C'
r2
.
'
0
1000
900
Vitesse de la décharge (m/s)
800
700
600
500
400
300
200
100
0
0
1
2
3
4
5
6
4
5
6
Temps (ms)
$ )
9
8
Longueur de la décharge (cm)
7
6
5
4
3
2
1
0
0
1
2
3
Temps (ms)
$ )
Q!#
"! "
""
+= I u " !
"
4 5
C'
r2
!
" "
8 ! " 5
. 55
!
#
""
"
C 'r2
!
4
4A #
.' 55
5
"
4
!
5
8
5
J. J F=
' 3
0
10
x 10
4
Tension appliqué
Chute de tension
Tension à la tête de l’arc
9
8
7
Tension (V)
6
5
4
3
2
1
0
0
0.5
1
1.5
2
2.5
3
3.5
2
2.5
3
3.5
Temps (ms)
$ )
0.01
0.009
0.008
0.007
Courant (A)
0.006
0.005
0.004
0.003
0.002
0.001
0
0
0.5
1
1.5
Temps (ms)
$ )
Q!#
"! "
""
+= J u " !
"
4 5
C'
r2
!
$ )
8 ! " 5
. 55
!
4
"
""
C .'r2
!
4
4A # $ ) "
4
.' 55
!
5
'' .I' F=
5
8
5
' (
0
6
x 10
-4
Rayon de la décharge (mm)
5
4
3
2
1
0
0.5
0
1
1.5
2
2.5
3
3.5
2.5
3
3.5
Temps (ms)
$ )
2
x 10
-8
1.8
1.6
1.4
Charge (C)
1.2
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
Temps (ms)
$ )
Q!#
+=
u " !
8 ! " 5
. 55
!
""
;
" 4A #
C .'r2
!
4
.' 55
5
"
4
!
5
8
"! "
5
""
4 5
C'
r2
'' .I' F=
'
0
1400
1200
Vitesse de la décharge (m/s)
1000
800
600
400
200
0
0
0.5
1
1.5
2
2.5
3
3.5
2.5
3
3.5
Temps (ms)
$ )
9
8
Longueur de la décharge (cm)
7
6
5
4
3
2
1
0
0
0.5
1
1.5
2
Temps (ms)
$ )
Q!#
"! "
""
+= 3 u " !
"
4 5
C'
r2
!
" "
8 ! " 5
. 55
!
#
""
"
C .'r2
!
4
4A #
"
4
.' 55
!
5
'' .I' F=
5
8
5
' '
0
9)
9)
=)
9 7
+
7
"
"
**
" ! 8"
4A # .
+
4
"
"!
!
!
4
!88
"" !
!
"
5!
""
"
4
"
4
"
4A
4.
4
@
4
!
C
4A
C'
" "
!
55. "
"
;
!
4
5
!
!
" @
!
4
!
4
! [email protected]
5 5
! "
4
55
5%5
C4
!
"
4!
5
4A
""
!
5
$8!#
4
I 5&
4 4A
!
7
" @
"
r2
4
"
!
# !
!
"
4
!
!4
8! "
!
!
!5 " !
"
!8
' 55
""
5 @
8! "
+=
"
@ 4
"
#
) 7
!?
' 55
!
! "
.
! "
" 5%5 ! "
8 4
"! "
4
6 %5
4
?4A $ .
4
@ !"
4
@
8 ! " 4
44 !
4A
4
" " #
55
" "
"
#
;
4
[email protected] "
'3 45
4
!!
6
+= ')
4
G!5
5!
! "
! "
. "
!
# !
+=
5
5 U#
"
"[email protected]
" 4 "
)
4A #
6! 4!
5 !
0 %5
8 !.
$8!#
[email protected]
' 45
. 0=
@!
4
!
" #
$8!#
6 6
4
"
5
` '3 45
8
" #
"[email protected]
55
4 ! "
;
8 !
""
I r2
8 !
*
8 !
. !"
4! !
#
""
5
"
!
4
!5
[email protected]
4 5
!
;
"
" 8 ! @ !"
4;"!
'r2) 7
6 "[email protected]
"
!
!!
!
C
'I 45
$ 8& ). "
!
$ 5)
)
'
"! "
# !
4
+
4
4
5%5
4 5
!
C
[email protected]
4! !
#5
4!?
"
#5
5& @
9)
= .*
4
!
+=
+=
"
"
4 "
@ 4 " ! 4!
!
""
# !
5
"
4
"
5
. 55 $8!#
B !8!
" !
45
"
!
@!
+= (
# !
4;"!
4
55
4
."
!!
I5
8!#
"
! "
""
'55
@
"
"" !
" 5 ?"
5
!
"
4A
" 4 4A
8
!
"
!
!5 " !
8 4
6
0 +
"
4
4 8 ! 4A
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4
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0.04
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1.5
2
2.5
3
3.5
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4.5
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0.035
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Courant (A)
0.025
0.02
0.015
0.01
0.005
0
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0.2
0.4
0.6
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1000
900
Vitesse de la décharge (m/s)
800
700
600
500
400
300
200
100
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
1.2
1.4
1.6
1.8
Temps (ms)
$ )
900
800
Vitesse de la décharge (m/s)
700
600
500
400
300
200
100
0
0
0.2
0.4
0.6
0.8
1
Temps (ms)
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Tension (V)
1.5
1
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Tension appliquée
Chute de tension
Tension à la tête de l'arc
0
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4
6
8
10
12
Temps (ms)
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1.4
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1.2
Courant (A)
1
0.8
0.6
0.4
0.2
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8
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25
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3000
Vitesse de la décharge (m/s)
2500
2000
1500
1000
500
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4
6
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10
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Rayon de la décharge (mm)
1.4
1.2
1
0.8
0.6
0.4
0.2
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10
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70
60
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40
30
20
0
5
10
15
20
25
30
35
40
45
35
40
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2.6
2.5
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Temps de contournement (ms)
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1.9
1.8
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5
10
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70
60
50
40
30
20
10
0
0
5
10
15
20
25
30
35
40
45
50
Conductivité surfacique (µS)
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0.4
0.2
0
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0.2
0.4
0.6
0.8
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1.4
1.6
1.8
2
Temps (ms)
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Courant (A)
5
4
3
2
1
0
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1
1.5
2
2.5
3
Temps (ms)
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2.5
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Résistance de l'arc ( /m)
2
1.5
1
0.5
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
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Résistance de l'arc ( /m)
2.5
2
1.5
78
1
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1
1.5
2
2.5
3
Temps (ms)
$ )
'II
1200
Vitesse de la décharge (m/s)
1000
800
600
400
200
0
0
0.2
0.4
0.6
0.8
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1.4
1.6
1.8
2
Temps (ms)
$ )
800
700
Vitesse de la décharge (m/s)
600
500
400
300
200
100
0
0
0.5
1
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Chute de tension
Tension à la tête de l’arc
1
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40
60
Temps (µs)
80
100
120
80
100
120
80
100
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0.05
0.04
0.035
0.03
0.025
0.02
0.015
0
20
40
60
Temps (µs)
$ )
9
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Longueur de la décharge (cm)
Courant (A)
0.045
7
6
5
4
3
2
1
0
0
20
40
60
Temps (µs)
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800
Vitesse de la décharge (m/s)
700
600
500
400
300
200
100
0
0
20
40
60
80
100
120
Temps (µs)
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Tension de contournement (kV)
21.8
21.6
21.4
21.2
21
20.8
20.6
20.4
0
10
20
30
40
50
60
70
Conductivité surfacique (µS)
80
90
100
$ )
22
Tension de contournement (kV)
Q!#
21.8
21.6
21.4
21.2
21
20.8
20.6
20.4
735
740
745
750
755
760
765
Vitesse de la décharge (m/s)
$ )
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22
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Tension de contournement (kV)
21.6
21.4
21.2
21
20.8
20.6
20.4
112
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112.5
113
113.5
114
Temps de contournement (µs)
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Tension appliquée
Chute de tension
Tension à la tête de l’arc
10000
8000
6000
4000
2000
0
0
20
40
60
Temps (µs)
80
100
80
100
80
100
120
$ )
18
16
14
Courant (A)
12
10
8
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20
40
60
120
Temps (µs)
$ )
9
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Longueur de la décharge (cm)
Tension (V)
14000
7
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5
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1
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20
40
60
120
Temps (µs)
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800
700
Vitesse de la décharge (m/s)
600
500
400
300
200
100
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20
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80
100
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770
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0.012
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800
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700
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80
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