Chapitre 6
Résultats et discussions
CHAPITRE 6
Résultats et discussions
1. Validation du code de calcul FLUENT :
56
Pour atteindre notre but, nous avons choisi certaines
géométries des conduites agressées installées dans
les réseaux de distribution du gaz naturel par SONELGAZ pour les
traiter. Nous avons comparé nos résultats obtenus par la
simulation numérique à l'aide de logiciel Fluent avec ceux
obtenus par une équation mathématique utilisée dans la
SONELGAZ, pour estimer le débit du gaz échappé vers
l'atmosphère.
2. Résultats :
Après les résultats obtenus par la simulation
numérique, On peut proposer différents scénarios de fuite
pour bien réaliser le problème :
> Premier scénario : (perforation
limitée)
Le diamètre de la brèche est, par hypothèse,
inferieur ou égale à 15%Di On a choisi 3 diamètres de
fuite: 3%,5% et 10%.
> Deuxième scénario :
(perforation importante)
Le diamètre de la brèche est, par hypothèse,
inferieur ou égale à 50%Di On a choisi 3 diamètres de
fuite: 20%,30% et 50%.
> Troisième scénario : (rupture
totale de la canalisation)
Le diamètre de la brèche est égal au
diamètre de la conduite (100%Di).
CHAPITRE 6
Résultats et discussions
57
2.1.Les vecteurs et les contours :
(a)
(b)
(c)
Figure 6-1 : vecteurs et contours de
la vitesse et la pression pour le 1er scénario.
(a)
CHAPITRE 6
Résultats et discussions
58
CHAPITRE 6
Résultats et discussions
59
(b)
(c)
Figure 6-2 : vecteurs et contours de
la vitesse et la pression pour le 2eme scénario
(fuite de 20%).
(a)
(b)
(c)
Figure 6-3 : vecteurs et contours de
la vitesse et la pression pour le 2eme scénario
(fuite de 50%).
(a)
CHAPITRE 6
Résultats et discussions
60
(b)
(c)
Figure 6-4 : vecteurs et contours de
la vitesse et la pression pour le 3eme scénario.
CHAPITRE 6
Résultats et discussions
61
2.2.Les profils de vitesse :
P=4 bars
P=3 bars
P=2 bars
-0,015 -0,010 -0,005 0,000 0,005 0,010 0,015
500
400
Vitesse du gaz à la fuite (m/s)
300
200
100
0
Figure 6-5 : profil de vitesse à
l'entrée et à la sortie de conduite.
Distance x (m)
Figure 6-6 : profils des vitesses de
la fuite pour différentes pression.
CHAPITRE 6
Résultats et discussions
62
2.3. Les tableaux et les graphes:
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.122
|
0.1155898
|
0.006409897
|
400102.1
|
10.71745
|
295.3291
|
|
7%
|
0.122
|
0.109406
|
0.01259339
|
400036.6
|
10.14061
|
310.6568
|
|
10%
|
0.122
|
0.0652322
|
0.0567678
|
3.99991
|
7.32964
|
313.3336
|
|
20%
|
0.122
|
0.01911469
|
0.1028811
|
399705.4
|
1.433075
|
319.5633
|
|
30%
|
0.122
|
0.1116409
|
0.233638
|
399436.5
|
8.355036
|
353.1843
|
|
50%
|
0.122
|
0.5233942
|
0.6453875
|
395562.9
|
39.11772
|
342.3486
|
|
Tableau A.1 PE 63 Di = 50 mm, P = 4 bars, V =
15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.163
|
0.1565798
|
0.006418215
|
400154.5
|
14.51388
|
295.9759
|
|
7%
|
0.163
|
0.1504109
|
0.01258906
|
400111.8
|
13.93913
|
310.8432
|
|
10%
|
0.163
|
0.1062544
|
0.0567456
|
399988.2
|
10.35962
|
313.3145
|
|
20%
|
0.163
|
0.0561617
|
0.1028395
|
399548.9
|
4.208486
|
319.6298
|
|
30%
|
0.163
|
0.07110308
|
0.234084
|
399289.9
|
5.321377
|
353.0439
|
|
50%
|
0.163
|
0.4833245
|
0.64633
|
395905.4
|
36.12309
|
342.3827
|
|
PE 63 D = 50 mm P = 4 bars, V = 20 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.122
|
0.1164491
|
0.00555106
|
300105.3
|
10.79845
|
255.8969
|
|
7%
|
0.122
|
0.1110946
|
0.01090494
|
300053.5
|
10.29753
|
269.1118
|
|
10%
|
0.122
|
0.06476478
|
0.0545676
|
299999.4
|
7.58938
|
274.8886
|
|
20%
|
0.122
|
0.03291773
|
0.08907889
|
299715.8
|
2.467602
|
276.7738
|
|
30%
|
0.122
|
0.08084189
|
0.2027093
|
299122
|
6.049084
|
299.4366
|
|
50%
|
0.122
|
0.4372156
|
0.5591855
|
296542.6
|
32.67701
|
296.4637
|
|
PE 63 Di = 50 mm, P = 3 bars, V = 15 m/s
CHAPITRE 6
Résultats et discussions
63
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.122
|
0.1174692
|
0.004530802
|
200116.4
|
10.893
|
209.0356
|
|
7%
|
0.122
|
0.1130978
|
0.008901861
|
200075.4
|
10.48404
|
219.8592
|
|
10%
|
0.122
|
0.1090457
|
0.01295430
|
199999.6
|
7.39620
|
223.129
|
|
20%
|
0.122
|
0.04929366
|
0.07270484
|
199780.1
|
3.694233
|
226.0577
|
|
30%
|
0.122
|
0.04323401
|
0.1652362
|
199671.9
|
3.235783
|
249.8292
|
|
50%
|
0.122
|
0.3350539
|
0.4570496
|
197889.7
|
25.04178
|
242.101
|
|
PE 63 D = 50 mm, P = 2 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.265
|
0.2511065
|
0.01389311
|
400152.8
|
9.83883
|
242.1661
|
|
7%
|
0.265
|
0.2376234
|
0.02737565
|
400094.2
|
9.06145
|
261.019
|
|
10%
|
0.265
|
0.209017
|
0.05598177
|
399960.8
|
7.97553
|
323.1077
|
|
20%
|
0.265
|
0.03974404
|
0.225251
|
399636.8
|
1.51535
|
350.4083
|
|
30%
|
0.265
|
0.2383129
|
0.5033067
|
399481.6
|
9.059322
|
331.7545
|
|
50%
|
0.265
|
1.142889
|
1.407879
|
396792.5
|
43.5546
|
370.948
|
|
PE 90 Di = 73.6 mm, P = 4 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.354
|
0.340115
|
0.01388461
|
400283.1
|
13.04317
|
242.312
|
|
7%
|
0.354
|
0.3266353
|
0.02736396
|
400204.3
|
12.56547
|
261.211
|
|
10%
|
0.354
|
0.2980356
|
0.05596146
|
400020.7
|
11.37123
|
323.3162
|
|
20%
|
0.354
|
0.1288632
|
0.225131
|
399385.5
|
4.910503
|
350.4783
|
|
30%
|
0.354
|
0.1493394
|
0.5033384
|
399289.5
|
5.677223
|
331.8085
|
|
50%
|
0.354
|
1.054635
|
1.40853
|
396312.5
|
40.1911
|
370.8444
|
|
PE 90 Di = 73.6 mm, P = 4 bars, V = 20m/s
CHAPITRE 6
Résultats et discussions
64
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.265
|
0.252971
|
0.01202873
|
300161.1
|
9.91853
|
209.7814
|
|
7%
|
0.265
|
0.2412956
|
0.02370371
|
300109.8
|
9.1184
|
226.125
|
|
10%
|
0.265
|
0.2165237
|
0.04847481
|
299991.4
|
8.261889
|
279.8983
|
|
20%
|
0.265
|
0.06997179
|
0.1950234
|
299631
|
2.66731
|
303.4794
|
|
30%
|
0.265
|
0.1709283
|
0.4359256
|
299569.4
|
6.497867
|
287.3343
|
|
50%
|
0.265
|
0.9546076
|
1.219563
|
297236.7
|
36.37954
|
321.1992
|
|
PE 90 Di = 73.6 mm, P = 3bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.265
|
0.255183
|
0.009816866
|
200170.7
|
10.01308
|
171.3829
|
|
7%
|
0.265
|
0.2456516
|
0.01934797
|
200129
|
9.50457
|
184.7511
|
|
10%
|
0.265
|
0.2254299
|
0.03956866
|
200031.2
|
8.601635
|
228.6666
|
|
20%
|
0.265
|
0.1058201
|
0.1591754
|
199676
|
4.032686
|
247.8473
|
|
30%
|
0.265
|
0.09091344
|
0.3559163
|
199620.9
|
3.456252
|
234.6414
|
|
50%
|
0.265
|
0.7311103
|
0.9961194
|
198098.3
|
27.8625
|
262.2072
|
|
PE 90 Di = 73.6 mm, P = 2 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.490
|
0.4641553
|
0.02584065
|
400003.1
|
11.46137
|
315.6
|
|
7%
|
0.490
|
0.4356193
|
0.0543807
|
399854.8
|
10.46734
|
326.25
|
|
10%
|
0.490
|
0.3854698
|
0.1044128
|
399854.8
|
8.916496
|
336.5532
|
|
20%
|
0.490
|
0.07840993
|
0.4115877
|
399606.8
|
1.818217
|
320.3371
|
|
30%
|
0.490
|
0.444124
|
0.9341094
|
399576.3
|
10.25816
|
353.1648
|
|
50%
|
0.490
|
2.114755
|
2.604738
|
396988.8
|
48.80903
|
386.0303
|
|
PE 125 Di = 100 mm, P = 4 bars, V = 15 m/s
CHAPITRE 6
Résultats et discussions
65
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.653
|
0.6271976
|
0.02580233
|
400044.1
|
15.4991
|
315.5721
|
|
7%
|
0.653
|
0.5985979
|
0.0544021
|
399988.1
|
14.19531
|
327.4231
|
|
10%
|
0.653
|
0.5491723
|
0.1038242
|
399910.9
|
12.70449
|
338.5402
|
|
20%
|
0.653
|
0.2416173
|
0.4113756
|
399356.6
|
5.595623
|
320.3779
|
|
30%
|
0.653
|
0.28106
|
0.9340584
|
399263.6
|
6.491906
|
353.1942
|
|
50%
|
0.653
|
1.95384
|
2.606875
|
396653.3
|
45.09528
|
385.9935
|
|
PE 125 Di = 100 mm, P = 4 bars, V = 20 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.490
|
0.4676461
|
0.02235222
|
300013.7
|
11.55193
|
273.2088
|
|
7%
|
0.490
|
0.4 31555
|
0.058445
|
299984.2
|
10.4720
|
293.1016
|
|
10%
|
0.490
|
0.400061
|
0.0899386
|
299925.7
|
9.256322
|
293.1016
|
|
20%
|
0.490
|
0.1336226
|
0.356363
|
299613.3
|
3.096739
|
277.4269
|
|
30%
|
0.490
|
0.3189278
|
0.8089139
|
299554.7
|
7.366544
|
305.8561
|
|
50%
|
0.490
|
1.766504
|
2.256496
|
297555.3
|
40.7715
|
334.264
|
|
PE 125 Di = 100 mm, P = 3 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.490
|
0.4717563
|
0.01824273
|
200025
|
11.65715
|
223.2201
|
|
7%
|
0.490
|
0.4503435
|
0.0396565
|
199988
|
9.637535
|
230.349
|
|
10%
|
0.490
|
0.4165387
|
0.07344767
|
199957
|
9.637535
|
239.6393
|
|
20%
|
0.490
|
0.1991569
|
0.290827
|
199663.2
|
4.612857
|
226.561
|
|
30%
|
0.490
|
0.1704971
|
0.6604848
|
199600.2
|
3.93823
|
249.7596
|
|
50%
|
0.490
|
1.353306
|
1.843325
|
198243.6
|
31.23512
|
272.9098
|
|
PE 125 Di = 100 mm, P = 2 bars, V = 15 m/s
CHAPITRE 6
Résultats et discussions
66
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
1.534
|
1.453475
|
0.08052
|
400019.8
|
10.24508
|
306.7689
|
|
7%
|
1.534
|
1.374736
|
0.1592582
|
399958
|
9.679874
|
337.8764
|
|
10%
|
1.534
|
1.209299
|
0.3246875
|
399851.6
|
9.520221
|
331.8445
|
|
20%
|
1.534
|
0.236773
|
1.297181
|
399565.8
|
1.871204
|
333.6403
|
|
30%
|
1.534
|
1.399398
|
2.93343
|
399506.6
|
11.00427
|
365.0653
|
|
50%
|
1.534
|
4.265803
|
8.193681
|
398660.4
|
59.4522
|
381.7649
|
|
PE 200 Di = 177 mm, P = 4 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
2.045
|
1.964518
|
0.080475
|
400055.6
|
13.84599
|
306.9794
|
|
7%
|
2.045
|
1.885244
|
0.1597029
|
399939.9
|
13.26669
|
338.227
|
|
10%
|
2.045
|
1.720497
|
0.324497
|
399827.4
|
13.55444
|
332.1011
|
|
20%
|
2.045
|
0.748437
|
1.296522
|
399287
|
5.878054
|
333.5584
|
|
30%
|
2.045
|
0.8883746
|
2.933404
|
399201.2
|
6.98598
|
365.0765
|
|
50%
|
2.045
|
6.155489
|
8.200326
|
398321.5
|
54.95032
|
381.7885
|
|
PE 200 Di = 177 mm, P = 4 bars, V = 20 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
1.534
|
1.46428
|
0.06971297
|
300021.1
|
10.31906
|
265.7745
|
|
7%
|
1.534
|
1.396101
|
0.1378862
|
299967.1
|
9.828638
|
292.7187
|
|
10%
|
1.534
|
1.252868
|
0.2811109
|
299880.3
|
9.869008
|
287.5069
|
|
20%
|
1.534
|
0.4108094
|
1.123128
|
299577.7
|
3.237315
|
288.8908
|
|
30%
|
1.534
|
1.006482
|
2.54045
|
299535.3
|
7.914713
|
316.1739
|
|
50%
|
1.534
|
5.565635
|
7.099744
|
299181.4
|
49.68501
|
330.6653
|
|
PE 200 Di = 177 mm, P = 3 bars, V = 15 m/s
CHAPITRE 6
Résultats et discussions
67
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
1.534
|
1.4771
|
0.05689531
|
200034
|
10.41274
|
217.1364
|
|
7%
|
1.534
|
1.421465
|
0.112529
|
199986.6
|
10.01118
|
239.1527
|
|
10%
|
1.534
|
1.30458
|
0.2294151
|
199910
|
10.27829
|
234.9093
|
|
20%
|
1.534
|
0.6173331
|
0.9166232
|
199614.5
|
4.851403
|
235.8937
|
|
30%
|
1.534
|
1.399395
|
2.074213
|
199569.1
|
4.247723
|
258.1606
|
|
50%
|
1.534
|
4.265803
|
5.799736
|
199178.8
|
38.08158
|
269.9655
|
|
PE 200 Di = 177 mm, P = 2 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
2.391
|
2.264394
|
0.1266074
|
399997.9
|
12.99858
|
326.9218
|
|
7%
|
2.391
|
2.141115
|
0.2498834
|
399946.1
|
12.28637
|
351.7559
|
|
10%
|
2.391
|
1.885043
|
0.5059589
|
399848.1
|
10.78795
|
327.9315
|
|
20%
|
2.391
|
0.3479779
|
2.042766
|
399522.8
|
1.969338
|
371.7065
|
|
30%
|
2.391
|
2.177372
|
4.56847
|
399563.6
|
12.46917
|
343.3654
|
|
50%
|
2.391
|
10.3878
|
12.77921
|
398931.4
|
59.48454
|
380.5328
|
|
PE 250 Di = 221 mm, P = 4 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
3.188
|
3.061455
|
0.1265456
|
400016.9
|
17.5745
|
327.201
|
|
7%
|
3.188
|
2.938254
|
0.2497498
|
399948.5
|
16.86691
|
352.0639
|
|
10%
|
3.188
|
2.682439
|
0.5055544
|
399811.4
|
15.36916
|
328.2776
|
|
20%
|
3.188
|
1.145494
|
2.042463
|
99280.7
|
.538694
|
373.6047
|
|
30%
|
3.188
|
.380715
|
4.568798
|
99235.5
|
7.907147
|
343.3425
|
|
50%
|
3.188
|
9.606046
|
12.79441
|
98812.1
|
55.00829
|
380.6571
|
|
PE 250 Di = 221 mm, P = 4 bars, V = 20 m/s
CHAPITRE 6
Résultats et discussions
68
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
2.391
|
2.281379
|
0.1096199
|
300005.7
|
13.09768
|
283.2535
|
|
7%
|
2.391
|
2.174644
|
0.2163525
|
299960.7
|
12.48256
|
304.7713
|
|
10%
|
2.391
|
1.952997
|
0.4379914
|
299873.2
|
11.18335
|
284.1454
|
|
20%
|
2.391
|
0.6213042
|
1.769674
|
299572
|
3.549835
|
323.6298
|
|
30%
|
2.391
|
1.566114
|
3.956867
|
299598.3
|
8.96892
|
297.4197
|
|
50%
|
2.391
|
8.679427
|
11.07087
|
299036.2
|
49.70212
|
329.5963
|
|
PE 250 Di = 221 mm, P = 3 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
2.391
|
2.301534
|
0.0894656
|
200014.9
|
13.21509
|
231.432
|
|
7%
|
2.391
|
2.214428
|
0.1765679
|
199978.4
|
12.71532
|
249.0544
|
|
10%
|
2.391
|
2.033593
|
0.3574049
|
199906.2
|
11.66142
|
232.2228
|
|
20%
|
2.391
|
0.9467853
|
1.444135
|
199605.2
|
5.389893
|
264.2969
|
|
30%
|
2.391
|
0.8390659
|
3.230107
|
199341.8
|
4.805682
|
240.4397
|
|
50%
|
2.391
|
6.657432
|
9.048403
|
199387.9
|
38.12362
|
269.1956
|
|
PE 250 Di = 221 mm, P = 2 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
1.638
|
1 .551
|
0.0865
|
400011.9
|
11.45575
|
308.6645
|
|
7%
|
1.638
|
1.467728
|
0.1702734
|
399950.7
|
10.82814
|
337.8439
|
|
10%
|
1.638
|
1.292888
|
0.3450958
|
399857.9
|
9.536435
|
310.9709
|
|
20%
|
1.638
|
0.253143
|
1.384797
|
399564.5
|
1.915819
|
333.8473
|
|
30%
|
1.638
|
1.493127
|
3.131186
|
399506.7
|
10.99728
|
348.3919
|
|
50%
|
1.638
|
7.07305
|
8.711164
|
398580.9
|
57.11683
|
358.012
|
|
AC 150 Di = 182.9 mm, P = 4 bars, V = 15
m/s
CHAPITRE 6
Résultats et discussions
69
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
2.184
|
2.097534
|
0.08646359
|
400041.8
|
15.4865
|
308.9003
|
|
7%
|
2.184
|
2.01383
|
0.1701684
|
399967.8
|
14.8655
|
338.1199
|
|
10%
|
2.184
|
1.88934
|
0.3610314
|
399882.3
|
13.39503
|
341.1250
|
|
20%
|
2.184
|
0.7998115
|
1.384129
|
399282.7
|
6.011661
|
333.7926
|
|
30%
|
2.184
|
0.9472739
|
3.131243
|
399185.3
|
6.97711
|
348.3945
|
|
50%
|
2.184
|
6.541337
|
8.725496
|
398819.1
|
52.82365
|
358.1168
|
|
AC 150 Di = 182.9 mm, P = 4 bars, V = 20
m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
1.638
|
1.563096
|
0.07490101
|
300013.2
|
11.53871
|
267.4232
|
|
7%
|
1.638
|
1.490561
|
0.1474246
|
299962.5
|
10.99717
|
292.7231
|
|
10%
|
1.638
|
1.339192
|
0.298787
|
299884.2
|
9.8829
|
269.3874
|
|
20%
|
1.638
|
0.4389511
|
1.198985
|
299576.8
|
3.320665
|
289.0827
|
|
30%
|
1.638
|
1.073889
|
2.711925
|
299557.8
|
7.909607
|
301.7319
|
|
50%
|
1.638
|
5.909091
|
7.547177
|
299045.4
|
47.71771
|
310.0346
|
|
AC 150 Di = 182.9 mm, P = 3 bars, V = 15
m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
1.638
|
1.576876
|
0.06112809
|
200024.3
|
11.64443
|
218.5014
|
|
7%
|
1.638
|
1.517699
|
0.1203084
|
199984.8
|
11.20463
|
239.1739
|
|
10%
|
1.638
|
1.394145
|
0.243847
|
199915
|
10.29157
|
220.0702
|
|
20%
|
1.638
|
0.6593918
|
0.9785649
|
199618.4
|
4.95316
|
236.0772
|
|
30%
|
1.638
|
0.5759711
|
2.214017
|
199552
|
4.242386
|
246.3668
|
|
50%
|
1.638
|
4.527675
|
6.165773
|
199074.8
|
36.56265
|
253.1432
|
|
AC 150 Di = 182.9 mm, P = 2 bars, V = 15
m/s
CHAPITRE 6
Résultats et discussions
70
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
3.32
|
3.143499
|
0.1764995
|
399990.5
|
13.24934
|
339.2915
|
|
7%
|
3.32
|
2.977534
|
0.3424579
|
399939.7
|
12.52945
|
309.2568
|
|
10%
|
3.32
|
2.614853
|
0.7051145
|
399841.8
|
10.98205
|
339.1997
|
|
20%
|
3.32
|
0.4877199
|
2.831992
|
399548.8
|
2.027164
|
359.634
|
|
30%
|
3.32
|
3.046438
|
6.366931
|
399479.4
|
12.80826
|
356.2566
|
|
50%
|
3.32
|
14.41358
|
17.73483
|
398736.2
|
60.15195
|
345.0054
|
|
AC 250 Di = 260.4 mm, P = 4 bars, V = 15
m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
.426
|
4.249582
|
0.1764174
|
400003.3
|
17.9106
|
339.7419
|
|
7%
|
.426
|
4.083716
|
0.3422844
|
399935.4
|
17.19663
|
309.4522
|
|
10%
|
.426
|
3.721426
|
0.7045718
|
399800.6
|
15.65394
|
339.6198
|
|
20%
|
.426
|
1.596176
|
2.829741
|
99282.3
|
6.65131
|
360.2558
|
|
30%
|
.426
|
1.945034
|
6.371065
|
99210.1
|
8.177862
|
356.2645
|
|
50%
|
4.426
|
13.31671
|
17.74286
|
398129.3
|
56.19277
|
345.1315
|
|
AC 250 Di = 260.4 mm, P = 4 bars, V = 20
m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
3.32
|
3.167181
|
0.1528164
|
299997.9
|
13.35033
|
294.0494
|
|
7%
|
3.32
|
3.023495
|
0.2964996
|
299953.4
|
12.72848
|
267.9034
|
|
10%
|
3.32
|
2.709594
|
0.6103947
|
299867.3
|
11.39052
|
293.9449
|
|
20%
|
3.32
|
0.8679014
|
2.45195
|
299572.9
|
3.609034
|
311.9653
|
|
30%
|
3.32
|
2.195364
|
5.515445
|
299542.3
|
9.230513
|
308.5789
|
|
50%
|
3.32
|
12.05028
|
15.37035
|
299221.5
|
50.46854
|
298.7821
|
|
AC 250 Di = 260.4 mm, P = 3 bars, V = 15
m/s
CHAPITRE 6
Résultats et discussions
71
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
3.32
|
3.195269
|
0.1247296
|
200006.6
|
13.46981
|
240.3322
|
|
7%
|
3.32
|
3.078
|
0.2419955
|
199970.1
|
12.96446
|
218.8717
|
|
10%
|
3.32
|
2.821885
|
0.4981136
|
199898.1
|
11.87537
|
240.2596
|
|
20%
|
3.32
|
1.318802
|
2.000944
|
199615.2
|
5.458784
|
254.8595
|
|
30%
|
3.32
|
1.181991
|
4.502316
|
199556.5
|
4.969511
|
251.0336
|
|
50%
|
3.32
|
9.23626
|
12.5564
|
198912.5
|
38.74894
|
243.984
|
|
AC 250 Di = 260.4 mm, P = 2 bars, V = 15
m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
4.858
|
4.601211
|
0.2567871
|
399982.4
|
13.50503
|
322.9294
|
|
7%
|
4.858
|
4.353309
|
0.5046869
|
399933.1
|
12.76119
|
327.4004
|
|
10%
|
4.858
|
3.831568
|
1.026399
|
399842.3
|
11.21522
|
322.5926
|
|
20%
|
4.858
|
0.728692
|
4.129037
|
399551.6
|
2.109864
|
336.5209
|
|
30%
|
4.858
|
4.460923
|
9.320305
|
399537.8
|
13.0671
|
347.2106
|
|
50%
|
4.858
|
21.10399
|
25.96276
|
398878.6
|
61.81758
|
357.7593
|
|
AC 300 Di = 315 mm, P = 4 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
6.477
|
6.220356
|
0.2566422
|
400000
|
18.25917
|
323.206
|
|
7%
|
6.477
|
5.97261
|
0.5043917
|
399923.1
|
17.52105
|
327.7183
|
|
10%
|
6.477
|
5.451316
|
1.025666
|
399794.2
|
15.96595
|
323.0491
|
|
20%
|
6.477
|
2.351275
|
4.125449
|
399286.2
|
6.821879
|
336.6228
|
|
30%
|
6.477
|
2.846019
|
9.323364
|
399207.3
|
8.33683
|
347.0953
|
|
50%
|
6.477
|
19.51224
|
25.9895
|
398751.2
|
57.15487
|
357.6926
|
|
AC 300 Di = 315 mm, P = 4 bars, V= 20 m/s
CHAPITRE 6
Résultats et discussions
72
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
4.858
|
4.635672
|
0.2223249
|
299989.6
|
13.60825
|
279.792
|
|
7%
|
4.858
|
4.421044
|
0.4369548
|
299946.5
|
12.96562
|
283.6873
|
|
10%
|
4.858
|
3.969375
|
0.8886143
|
299865.2
|
11.62287
|
279.5852
|
|
20%
|
4.858
|
1.283138
|
3.574703
|
299570.1
|
3.710322
|
291.4725
|
|
30%
|
4.858
|
3.211061
|
8.068868
|
299646.9
|
9.406189
|
299.2795
|
|
50%
|
4.858
|
17.64445
|
22.50261
|
299125.2
|
51.68395
|
309.7784
|
|
AC 300 Di = 315 mm, P = 3 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
4.858
|
4.676557
|
0.1814414
|
199998.2
|
13.73042
|
228.6194
|
|
7%
|
4.858
|
4.501405
|
0.3565914
|
199962.9
|
13.20858
|
231.8182
|
|
10%
|
4.858
|
4.132915
|
0.7250782
|
199893.8
|
12.10842
|
228.5275
|
|
20%
|
4.858
|
1.941059
|
2.916799
|
199610.4
|
5.721022
|
238.2119
|
|
30%
|
4.858
|
1.727639
|
6.58593
|
199531.7
|
5.060787
|
244.7823
|
|
50%
|
4.858
|
13.53598
|
18.39422
|
199342.1
|
39.64973
|
252.9212
|
|
AC 300 Di = 315 mm, P = 2 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
5.646
|
5.34884
|
0.29714
|
399979
|
12.3854
|
307.233
|
|
7%
|
5.646
|
5.06767
|
0.57828
|
399932
|
11.73101
|
291.3977
|
|
10%
|
5.646
|
4.46997
|
1.17608
|
399842.8
|
10.8496
|
284.6852
|
|
20%
|
5.646
|
0.808613
|
4.83708
|
399527.2
|
1.641057
|
391.3561
|
|
30%
|
5.646
|
5.159687
|
10.80492
|
399478
|
11.2692
|
361.444
|
|
50%
|
5.646
|
24.59445
|
30.2417
|
399331.5
|
63.072
|
383.8413
|
|
AC 350 Di = 339.6 mm, P = 4 bars, V = 15
m/s
CHAPITRE 6
Résultats et discussions
73
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
7.528
|
7.231077
|
0.2969187
|
399983.7
|
16.74576
|
307.4649
|
|
7%
|
7.528
|
6.950097
|
0.5778875
|
399920
|
16.09131
|
291.5723
|
|
10%
|
7.528
|
6.352558
|
1.175492
|
399795.6
|
15.41939
|
284.869
|
|
20%
|
7.528
|
2.693285
|
4.834529
|
399230.3
|
5.370292
|
391.4555
|
|
30%
|
7.528
|
3.279782
|
10.80761
|
99168.8
|
7.16355
|
361.4198
|
|
50%
|
7.528
|
22.76968
|
30.29789
|
399103.7
|
58.39238
|
383.8371
|
|
AC 350 Di = 339.6 mm, P = 4 bars, V = 20
m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
5.646
|
5.388708
|
0.2572562
|
299984.1
|
12.47188
|
266.1868
|
|
7%
|
5.646
|
5.145359
|
0.5006502
|
299945.3
|
11.91977
|
252.4386
|
|
10%
|
5.646
|
4.627767
|
1.018263
|
299866.3
|
11.25381
|
246.6212
|
|
20%
|
5.646
|
1.456889
|
4.188279
|
299521.4
|
2.892501
|
338.0942
|
|
30%
|
5.646
|
3.712728
|
9.359003
|
299523.7
|
8.109154
|
313.0399
|
|
50%
|
5.646
|
20.57915
|
26.22592
|
299358.5
|
52.77557
|
332.1892
|
|
AC 350 Di = 339.6 mm, P = 3 bars, V = 15
m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
5.646
|
5.436059
|
0.2099221
|
199993.6
|
12.58729
|
217.482
|
|
7%
|
5.646
|
5.237468
|
0.4085556
|
199962.6
|
12.14765
|
206.2265
|
|
10%
|
5.646
|
4.814999
|
0.8310395
|
199895.6
|
11.73144
|
201.4782
|
|
20%
|
5.646
|
2.22586
|
3.419715
|
199568.4
|
4.38085
|
276.7581
|
|
30%
|
5.646
|
1.995888
|
7.641966
|
199537.3
|
4.359476
|
255.5975
|
|
50%
|
5.646
|
15.80215
|
21.44851
|
199225.4
|
40.52487
|
271.101
|
|
AC 350 Di = 339.6 mm, P = 2 bars, V = 15
m/s
CHAPITRE 6
Résultats et discussions
74
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.02
|
0.01930409
|
0.0006958855
|
200569.6
|
9.022092
|
140.2884
|
|
7%
|
0.02
|
0.0186319
|
0.001368041
|
200532.2
|
8.719384
|
126.0242
|
|
10%
|
0.02
|
0.01711064
|
0.002889384
|
200373.8
|
8.01185
|
202.3276
|
|
20%
|
0.02
|
0.008437281
|
0.01156188
|
199849.9
|
3.948246
|
215.2935
|
|
30%
|
0.02
|
0.006333834
|
0.02633359
|
199765.5
|
2.958752
|
236.8527
|
|
50%
|
0.02
|
0.05312596
|
0.0731268
|
197127.7
|
24.81665
|
248.8896
|
|
CU 20-22 D; = 20 mm, P = 2 bars, V = 15 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.026
|
0.02530442
|
0.0006954088
|
200936.7
|
11.82601
|
140.6084
|
|
7%
|
0.026
|
0.02463375
|
0.001366194
|
200895.5
|
11.52654
|
126.1831
|
|
10%
|
0.026
|
0.02311129
|
0.00288851
|
200675.7
|
10.82058
|
202.6016
|
|
20%
|
0.026
|
0.01444609
|
0.01155353
|
199832.6
|
6.759177
|
215.4553
|
|
30%
|
0.026
|
0.0003142867
|
0.02631437
|
199659.4
|
0.1468839
|
236.9761
|
|
50%
|
0.026
|
0.04727702
|
0.07327805
|
197527.1
|
22.08452
|
249.0942
|
|
CU 20-22 D; = 20 mm, P = 2 bars, V = 20 m/s
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.02
|
0.01950819
|
0.0004917001
|
100588.2
|
9.117467
|
99.55608
|
|
7%
|
0.02
|
0.01903432
|
0.0009656065
|
100559.1
|
8.907615
|
89.28838
|
|
10%
|
0.02
|
0.01795716
|
0.002042626
|
100436.4
|
8.408098
|
143.3804
|
|
20%
|
0.02
|
0.01183137
|
0.008168538
|
99976.7
|
5.536016
|
152.4482
|
|
30%
|
0.02
|
0.00139803
|
0.01860196
|
99808.06
|
0.6539955
|
167.6062
|
|
50%
|
0.02
|
0.03183668
|
0.05183678
|
98780.18
|
14.87187
|
176.1512
|
|
CU 20-22 D; = 20 mm, P =1 bars, V = 15 m/s
CHAPITRE 6
Résultats et discussions
75
|
|
Df en
%deDi
|
Q1
(kg/s)
|
Q2 (kg/s)
|
Qf (kg/s)
|
P1 (Pa)
|
V2 (m/s)
|
Vf (m/s)
|
|
5%
|
0.02
|
0.01965264
|
0.0003472852
|
50603.8
|
9.184971
|
70.87627
|
|
7%
|
0.02
|
0.01931889
|
0.0006810535
|
50585.09
|
9.040709
|
63.43159
|
|
10%
|
0.02
|
0.01855548
|
0.001444363
|
50491.82
|
8.688157
|
101.8578
|
|
20%
|
0.02
|
0.01423012
|
0.005769786
|
50147.43
|
6.658114
|
108.199
|
|
30%
|
0.02
|
0.006875825
|
0.01312409
|
49847.96
|
3.215104
|
118.6681
|
|
50%
|
0.02
|
0.01673624
|
0.03673603
|
49491.21
|
7.818035
|
124.76
|
|
CU 20-22 Di = 20 mm, P = 0.5 bars, V = 15
m/s
Tableaux VI-1 : variation des
paramètres de gaz en fonction de diamètre de fuite.
|
|
Df en
%deDi
|
Qf (kg/s) par
simulation
numérique
|
Qf (kg/s) par
équation
mathématique
|
|
5%
|
0.2567871
|
0.13128
|
|
7%
|
0.5046869
|
0.25731
|
|
10%
|
1.026399
|
0.52513
|
|
20%
|
4.129037
|
2.10052
|
|
30%
|
9.320305
|
4.72617
|
|
50%
|
25.96276
|
13.12825
|
|
AC 300 Di = 315 mm, P = 4 bars, V = 15 m/s
|
|
Df en
%deDi
|
Qf (kg/s) par
simulation
numérique
|
Qf (kg/s) par
équation
mathématique
|
|
5%
|
0.006409897
|
0.00331
|
|
7%
|
0.01259339
|
0.00648
|
|
10%
|
0.0567678
|
0.01323
|
|
20%
|
0.1028811
|
0.05292
|
|
30%
|
0.233638
|
0.11908
|
|
50%
|
0.6453875
|
0.33077
|
|
PE 63 Di = 50 mm, P = 4 bars, V = 15 m/s
Tableaux 6-2: comparaisons entre la
solution numérique et la solution analytique.
|
CHAPITRE 6
|
Résultats et discussions
|
débit de la fuite (kg/s)
-0,01
0,08
0,07
0,06
0,05
0,04
0,03
0,02
0,01
0,00
Qf (p=2 bar.v=15m/s) Qf (p=2bar.v=20m/s) Qf (p=1 bar.v=15m/s)
Qf (p=0.5 bar.v=15m/s)
5% 7% 10% 20% 30% 50%
76
diamètre de la fuite (% de Di)
Réseau CU 20-22 (20)
5% 7% 10% 20% 30% 50%
débit de la fuite (kg/s)
0,7
0,6
0,5
0,4
0,3
0,2
0,1
0,0
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3 bar.v=15m/s)
Qf (p=2 bar.v=15m/s)
diamètre de la fuite (% de Di)
Réseau PE 63 (50)
|
CHAPITRE 6
|
Résultats et discussions
|
débit de la fuite (kg/s)
0,8
0,6
0,4
0,2
0,0
1,6
1,4
1,2
1,0
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3 bar.v=15m/s)
Qf (p=2 bar.v=15m/s)
5% 7% 10% 20% 30% 50%
Dfdiamètre de la fuite (% de Di) Réseau PE
90 (73.6)
débit de la fuite (kg/s)
3,0
2,5
2,0
0,5
0,0
1,5
1,0
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3 bar.v=15m/s)
Qf (p=2 bar.v=15m/s)
77
5% 7% 10% 20% 30% 50%
diamètre de la fuite (% de Di)
Réseau PE 125 (100)
|
CHAPITRE 6
|
Résultats et discussions
|
8
6
4
2
débit de la fuite (kg/s)
0
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3bar.v=15m/s) Qf
(p=2 bar.v=15m/s)
5% 7% 10% 20% 30% 50%
78
diamètre de la fuite (% de Di)
Réseau PE 200 (177)
10
8
débit de la fuite (kg/s)
6
4
2
0
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3 bar.v=15m/s)
Qf (p=2 bar.v=15m/s)
5% 7% 10% 20% 30% 50%
diamètre de la fuite (% de Di)
Réseau AC 150 (182.9)
CHAPITRE 6
14
|
débit de la fuite (kg/s)
|
12 10 8 6 4 2 0
|
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3 bar.v=15m/s)
Qf (p=2 bar.v=15m/s)
-2
5% 7% 10% 20% 30% 50%
79
diamètre de la fuite (% de Di)
Réseau PE 250 (221)
5% 7% 10% 20% 30% 50%
débit de la fuite (kg/s)
20
18
16
14
12
10
-2
4
8
6
2
0
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3 bar.v=15m/s)
Qf (p=2 bar.v=15m/s)
diamètre de la fuite (% de Di)
Réseau AC 250 (260.4)
|
CHAPITRE 6
|
Résultats et discussions
|
débit de la fuite (kg/s)
35
30
25
20
15
10
5
0
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3 bar.v=15m/s)
Qf (p=2bar.v=15m/s)
5% 7% 10% 20% 30% 50%
80
diamètre de la fuite (% de Di)
Réseau AC 300 (315)
5% 7% 10% 20% 30% 50%
débit de la fuite (kg/s)
30
25
20
15
10
5
0
Qf (p=4 bar.v=15m/s) Qf (p=4 bar.v=20m/s) Qf (p=3bar.v=15m/s) Qf
(p=2 bar.v=15m/s)
diamètre de la fuite (% de Di)
Réseau AC 350 (339.6)
Figures 6-7 : variation du
débit de fuite en fonction de diamètre de l'orifice
pour
différentes pressions et vitesses.
CHAPITRE 6
Résultats et discussions
35
30
solution numérique solution mathématique
25
20
15
10
5
0
-0,02 0,00 0,02 0,04 0,06 0,08 0,10 0,12 0,14 0,16 0,18
Débit de fuite Qf (kg/s)
Diamètre de fuite Df (m)
Figure 6-8 : comparaison des solutions
numérique et mathématique du débit de fuite en fonction de
diamètre de l'orifice.
0,18
Qf=f(P)
Débit de fuite Qf (kg/s)
0,17
0,16
0,15
0,14
0,13
81
0,12
2,0 2,5 3,0 3,5 4,0
Pression effectif du gaz P (bars)
Figure 6-9 : l'influence de la
variation de pression sur le débit de fuite.
CHAPITRE 6
Résultats et discussions
| 
