Proceedings of the 18 th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010,...
17
Proceedings of the 18 th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China Hannam University Fluid-elastic Instability of Normal Square Tube Bundles in Two-Phase Cross Flow 22/03/22 Woo Gun Sim Mi Yeon Park ABSTRACT Some knowledge on damping and fluid-elastic instability is necessary to avoid flow-induced vibration problems in shell and tube heat exchanger such as steam generator. Fluid-elastic instability is the most important vibration excitation mechanism for heat exchanger tube bundles subjected to the cross flow. Experiments have been performed to investigate fluid-elastic instability of normal square tube bundles, subjected to two-phase cross flow. The test section consists of cantilevered flexible cylinder(s) and rigid cylinders of normal square array. From a practical design point of view, fluid-elastic instability may be expressed simply in terms of dimensionless flow velocity and dimensionless mass-damping parameter. For dynamic instability of cylinder rows, added mass, damping and critical flow velocity are
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Transcript of Proceedings of the 18 th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010,...
An Approximate Damping Model for Two-Phase Cross-flow in Horizontal
Tube BundlesProceedings of the 18th International Conference on
Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
*
ABSTRACT
*
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
- Flow parameter of two-phase flow - Damping ratio
- An analytical two-phase damping model
Experimental Study
Fluid-elastic Instability
Conclusions
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
o Flow Mechanism of Two-phase Flow
Homogeneous Model-Only for Bubbly Flow
o Analytical Approach for Hydrodynamic Forces
Experimental Study, Reliable Prediction of Dynamic Response
*
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Hydrodynamic Forces
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Dimensionless critical flow velocity
90
Sheet2
Sheet3
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Fundamental Theory
Boundary conditions
Characteristic equation
Natural Frequency
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Hydrodynamic mass due to the liquid in the annulus
Total mass acting on the flexible inner cylinder
*
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Homogeneous void fraction
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Damping ratio
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Euler number for single phase flow
Two-phase friction multiplier
Two-phase damping ratio
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Experimental Study
test section
- Pressure perturbation, Acceleration
Critical flow velocity,
Fluid-elastic instability coefficient
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Gp=414 No3
Gp=459 No3
Gp=581 No3
Gp=414 No1
Gp=459 No1
Gp=581 No1
Gp=414 Ana(Sim;2007)
No1, 1 : 2.495 m^3/hr
air [L/min]
air [L/min]
No1, 1 : 6.422 m^3/hr
air [L/min]
air [L/min]
2007. 10. 17 two-phase total damping ratio data modify
No1, 1 : 2.495 m^3/hr
air [L/min]
air [L/min]
No1, 1 : 5.839 m^3/hr
air [L/min]
air [L/min]
2007. 10. 17 two-phase total damping ratio data modify
No1, 1 : 6.422 m^3/hr
air [L/min]
air [L/min]
No1 total data
No1, 1 : 5.839 m^3/hr , 0.091 m/s
air [L/min]
3
5.839
0.029
10.209
13.0187
12.4515
0.0035883092
0.112825764
0.06394
0.3612552115
0.6462552115
0.0000013421
971.0348
0.0141259568
0.0347598072
0.0357995263
0.0147598072
6
0.058
10.5575
13.6392
12.3443
0.008145036
0.1248227927
0.06394
0.3725283289
0.6575283289
0.0000013791
942.0696
0.0137133604
0.0471694323
0.0509474892
0.0271694323
9
0.085
10.9703
13.7305
12
0.02305545
0.1150083333
0.06394
0.4108007813
0.6958007813
0.0000014155
915.102
0.0129346315
0.0381337019
0.0448698928
0.0181337019
12
0.109
10.6922
13.8551
12.5063
0.0404259984
0.1264522681
0.06394
0.3556041083
0.6406041083
0.0000014495
891.1308
0.0135611801
0.048951088
0.05445544
0.028951088
15
0.134
10.8525
14.1076
12.8101
0.0564853864
0.1270520917
0.06394
0.3255797041
0.6105797041
0.0000014866
866.1608
0.0138384635
0.0492736282
0.0537513083
0.0292736282
17
0.149
10.1867
13.5167
12.9575
0.0534394259
0.1284970095
0.06394
0.311767233
0.596767233
0.0000015099
851.1788
0.0139421564
0.050614853
0.0549152302
0.030614853
21
0.178
10.5604
13.8921
12.4648
0.0725369967
0.1336443425
0.06394
0.3598768325
0.6448768325
0.0000015569
822.2136
0.0129033023
0.0568010402
0.0689412361
0.0368010402
28
0.223
11.112
14.3959
13.2298
0.0940589568
0.1241099639
0.06394
0.2874543323
0.5724543323
0.000001636
777.2676
0.0136724687
0.0464974951
0.0529944632
0.0264974951
35
0.265
10.4338
14.0766
13.125
0.1201291
0.1387733333
0.06394
0.2966326531
0.5816326531
0.0000017174
735.318
0.0130953316
0.0617380017
0.0755712854
0.0417380017
42
0.301
11.0752
14.563
13.8988
0.119816504
0.1254712637
0.06394
0.2336719872
0.5186719872
0.0000017939
699.3612
0.0138715693
0.0476596944
0.0546982169
0.0276596944
50
0.339
10.928
14.8449
13.2808
0.119569293
0.1474647612
0.06394
0.2830661758
0.5680661758
0.0000018824
661.4068
0.0125523111
0.0709724501
0.0943301947
0.0509724501
60
0.381
11.5303
14.4878
12.8125
0.1665274
0.1154146341
0.06394
0.3253509816
0.6103509816
0.000001991
619.4572
0.0114567332
0.0400179009
0.0610173447
0.0200179009
No1, 1 : 6.422 m^3/hr , 0.106 m/s
air [L/min]
3
6.422
0.027
10.8038
13.1352
12.809
0.005765594
0.0910063237
0.06394
0.3256845783
0.6106845783
0.0000013396
973.0324
0.0147553308
0.0123109929
0.0119567566
-0.0076890071
6
0.053
11.3481
13.7385
12.3185
0.0148423603
0.0970248001
0.06394
0.3752854821
0.6602854821
0.0000013726
947.0636
0.0137102844
0.0193745157
0.0209032645
-0.0006254843
9
0.078
11.4112
13.8464
12.6577
0.032932509
0.0961944113
0.06394
0.3403711002
0.6253711002
0.0000014059
922.0936
0.0140715037
0.0181829076
0.0190834456
-0.0018170924
12
0.101
11.0648
13.6007
12.1856
0.0486922971
0.1040531447
0.06394
0.3897665854
0.6747665854
0.000001438
899.1212
0.0131075366
0.0270056081
0.0313631697
0.0070056081
15
0.123
10.3609
13.9317
13.469
0.0471455322
0.1325562403
0.06394
0.2673021048
0.5523021048
0.00000147
877.1476
0.0150245017
0.0535917386
0.0522194776
0.0335917386
18
0.144
10.8225
14.0866
12.3239
0.0757170358
0.1324296692
0.06394
0.3747069704
0.6597069704
0.000001502
856.1728
0.0129742702
0.055515399
0.0661963082
0.035515399
21
0.164
11.4262
13.9352
12.1875
0.07029494
0.1029333333
0.06394
0.389556213
0.674556213
0.0000015338
836.1968
0.0125929522
0.0264003811
0.0329572146
0.0064003811
24
0.183
10.6087
14.1161
11.0929
0.0835643417
0.158092113
0.06394
0.529248952
0.814248952
0.0000015653
817.2196
0.0107960288
0.0833560841
0.12852464
0.0633560841
27
0.201
10.755
14.1955
12.0393
0.0830250612
0.1428862143
0.06394
0.4062655775
0.6912655775
0.0000015963
799.2412
0.0120559099
0.0668903044
0.0895284155
0.0468903044
30
0.219
10.7354
14.5535
13.8022
0.0899969362
0.1383149063
0.06394
0.2409576444
0.5259576444
0.0000016286
781.2628
0.0146112682
0.0597636381
0.0622617482
0.0397636381
33
0.236
11.0002
13.8092
12.2389
0.0988278136
0.1147570452
0.06394
0.383902211
0.668902211
0.0000016603
764.2832
0.0120510298
0.0387660154
0.0525037278
0.0187660154
No1, 1 : 8.186 m^3/hr , 0.135 m/s
air [L/min]
No3 total data
No3, 3 : 2.495 m^3/hr , 0.041 m/s
air [L/min]
3
2.495
0.067
8.5941
10.6105
9.688
0.001873
0.1040668869
0.06136
0.3700914443
0.6550914443
0.000001391
933.0804
0.015455
0.0273
0.0296077913
0.0033
6
0.126
8.617
10.5192
9.688
0.00820419
0.0981729975
0.06136
0.3700914443
0.6550914443
0.0000014745
874.1512
0.014907
0.0219
0.0254039771
-0.0021
9
0.178
7.7785
10.744
9.219
0.018085
0.1608363163
0.06136
0.4384400665
0.7234400665
0.0000015569
822.2136
0.013374
0.0861
0.1172360397
0.0621
12
0.224
7.8161
10.5267
8.906
0.0275425332
0.1521783068
0.06136
0.4901840106
0.7751840106
0.0000016378
776.2688
0.012297
0.0785
0.1213416587
0.0545
15
0.265
8.6112
11.5066
9.3669
0.002967
0.1545548687
0.06136
0.4157747097
0.7007747097
0.0000017174
735.318
0.012866
0.0803
0.1184694379
0.0563
18
0.302
8.0397
10.8167
10
0.034039591
0.13885
0.06136
0.3298514304
0.6148514304
0.0000017961
698.3624
0.013784
0.0637
0.0867956996
0.0397
21
0.336
8.5555
11.0487
9.375
0.0495415134
0.1329706667
0.06136
0.4145642941
0.6995642941
0.0000018751
664.4032
0.012163
0.0594
0.0968638015
0.0354
24
0.366
7.8526
10.7583
10
0.04966698
0.145285
0.06136
0.3298514304
0.6148514304
0.0000019508
634.4392
0.013051
0.0709
0.1062916181
0.0469
27
0.394
8.2251
11.4302
9.062
0.0528271867
0.1768428603
0.06136
0.4637245475
0.7487245475
0.0000020272
606.4728
0.010971
0.1045
0.1996678049
0.0805
30
0.419
8.3313
11.9952
9.6875
0.0570502359
0.1891045161
0.06136
0.3701590684
0.6551590684
0.0000021007
581.5028
0.011836
0.1159
0.2020890626
0.0919
33
0.442
8.2371
11.3697
9.5932
0.0541737358
0.1632719009
0.06136
0.3831026435
0.6681026435
0.0000021731
558.5304
0.011394
0.0905
0.1675568273
0.0665
No3, 3 : 5.839 m^3/hr , 0.091 m/s
air [L/min]
3
5.839
0.029
9.4869
10.9278
10.0932
0.0053709134
0.0713797408
0.06136
0.3185488541
0.6035488541
0.0000013421
971.0350
0.016800
-0.0068
0.0262120324
-0.0308
6
0.058
8.6588
10.2594
9.53125
0.008803468
0.0839659016
0.06136
0.3918157643
0.6768157643
0.0000013791
942.0696
0.015162
0.0074
0.0243541973
-0.0166
9
0.085
8.2767
10.2931
9.375
0.01875655
0.1075413333
0.06136
0.4145642941
0.6995642941
0.0000014155
915.102
0.014555
0.0316
0.1018594596
0.0076
12
0.109
8.477
11.4461
9.3688
0.0286065156
0.1584567928
0.06136
0.4154905032
0.7004905032
0.0000014495
891.1308
0.014329
0.0828
0.095516423
0.0588
15
0.134
8.318
10.6903
9.5191
0.0398735421
0.1246073683
0.06136
0.3935446167
0.6785446167
0.0000014866
866.1608
0.014445
0.0488
0.0973829642
0.0248
17
0.149
8.2778
10.9448
9.6235
0.0391884996
0.1385670494
0.06136
0.3789021673
0.6639021673
0.0000015099
851.1788
0.014542
0.0627
0.0768939476
0.0387
21
0.178
8.5752
11.7642
8.90625
0.04554998
0.1790315789
0.06136
0.4901404921
0.7751404921
0.0000015569
822.2136
0.012700
0.1050
0.0867284048
0.0810
28
0.223
8.9349
13.4875
9.6875
0.05511512
0.2349729032
0.06136
0.3701590684
0.6551590684
0.000001636
777.2676
0.013961
0.1597
0.0924474703
0.1357
35
0.265
7.6279
10.6298
9.5312
0.06639893
0.1574775474
0.06136
0.3918228654
0.6768228654
0.0000017174
735.318
0.013206
0.0829
0.1488665502
0.0589
42
0.301
8.2065
11.782
10
0.07535615
0.178775
0.06136
0.3298514304
0.6148514304
0.0000017939
699.3612
0.013795
0.1036
0.1576944891
0.0796
50
0.339
8.1387
11.4293
9.6898
0.0863031956
0.1697971062
0.06136
0.3698480843
0.6548480843
0.0000018824
661.4068
0.012748
0.0957
0.1386876087
0.0717
60
0.381
8.1313
12.5271
9.375
0.08794881
0.2344426667
0.06136
0.4145642941
0.6995642941
0.000001991
619.4572
0.011685
0.1614
0.282061054
0.1374
No3, 3 : 6.422 m^3/hr , 0.106 m/s
air [L/min]
3
6.422
0.027
9.5491
11.1316
10.1355
0.0073288333
0.0780671896
0.06136
0.3223222113
0.6153222113
0.0000013396
973.0320
0.016463
0.0002
0.0002393659
-0.0238
6
0.053
9.1661
11.2373
10.3962
0.01365337
0.0996133203
0.06136
0.2918489257
0.5848489257
0.0000013726
947.0636
0.016849
0.0214
0.0204547928
-0.0026
9
0.078
8.4265
10.8717
9.9591
0.0267158146
0.122762097
0.06136
0.344312977
0.637312977
0.0000014059
922.0936
0.015567
0.0458
0.049024215
0.0218
12
0.101
7.757
10.9735
10.0177
0.0309729771
0.1605408427
0.06136
0.3368786741
0.6298786741
0.000001438
899.1212
0.015487
0.0837
0.0907328814
0.0597
15
0.123
8.6519
11.5449
9.3669
0.0354413693
0.1544267581
0.06136
0.4274455788
0.7204455788
0.00000147
877.1476
0.013812
0.0793
0.1007364083
0.0553
18
0.144
8.6258
11.8423
10.1694
0.0453790207
0.1581460066
0.06136
0.3182266589
0.6112266589
0.000001502
856.1728
0.015416
0.0814
0.0898956009
0.0574
21
0.164
8.5745
11.2337
9.661
0.0502396458
0.1376255046
0.06136
0.3842496416
0.6772496416
0.0000015338
836.1968
0.014088
0.0622
0.0779301698
0.0382
24
0.183
8.3058
10.459
9.5304
0.0580492381
0.1129648283
0.06136
0.402938224
0.695938224
0.0000015653
817.2196
0.013628
0.0380
0.0500479738
0.0140
27
0.201
8.5744
11.6689
9.8445
0.0543339255
0.1571689776
0.06136
0.3592372849
0.6522372849
0.0000015963
799.2412
0.014130
0.0817
0.1031498376
0.0577
30
0.219
9.0726
12.4425
9.9935
0.0593430534
0.168604593
0.06136
0.3399329634
0.6329329634
0.0000016286
781.2628
0.014269
0.0930
0.1165627424
0.0690
33
0.236
8.0639
11.4904
9.3966
0.0536700443
0.1823265862
0.06136
0.4228985259
0.7158985259
0.0000016603
764.2832
0.012851
0.1081
0.1567176805
0.0841
No3, 3 : 8.186 m^3/hr , 0.135 m/s
air [L/min]
Gp=414 No3
Gp=459 No3
Gp=581 No3
Gp=414 No1
Gp=459 No1
Gp=581 No1
Gp=414 Ana(Sim;2007)
interpolation curve
0 20
interpolation curve
Interpolation curve
Interpolation curve
Interpolation curve
Interpolation curve
Interpolation curve
Interpolation curve
interpolation 0,89,60
Interpolation 2.03, 89.7, 95
Interpolation
0510152025
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
ACCELERATION,m/s
2
Interpolation, 2.03, 93, 60
Interpolation 2.03, 45, 72
Interpolation 2, 34.9, 72
Interpolation 2, 44.9, 60
Interpolation 2, 49.9, 72
Interpolation 0, 125, 72
Interpolation
Interpolation 2, 50.81, 60
Interpolation 1.58, 125, 60
Interpolation 1.58, 98, 72
Interpolation 1.85, 49, 60
interpolation 1.85, 90.8, 72
interpolation 0, 109.6, 70
interpolation
0.000.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.00
0.00
0.02
0.04
0.06
0.08
0.10
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Fluid-elastic Instability
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
*
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Conclusions
An experimental program has been performed with normal square array of cylinders subjected to air/water flow, to investigate fluid-elastic instability of tube bundles.
The pitch over diameter ratio was 1.3 and the diameter of cylinder is 20 mm.
The dynamic instability of cylinder(s) is evaluated with added mass, damping and the threshold flow velocity.
The two-phase damping was calculated, considering viscous damping, structure damping and the total damping, measured at two-phase flow.
The measured two-phase damping ratios are compared to the semi-analytical results proposed by Sim (2007).
However the two-phase damping data is scattered, average values of the data versus void fraction agree well with the analytical results.
Two-phase damping is very dependent on void fraction
*
00.10.20.30.40.5
Gp=175 kg/(m^2*s) No3Gp=414 No3Gp=459 No3Gp=581 No3Gp=414 No1Gp=459 No1Gp=581 No1Gp=414 Ana(Sim;2007)
0
20
40
60
80
100
0
10
20
30
40
50
60
70
80
90
100
Hannam University
*
ABSTRACT
*
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
- Flow parameter of two-phase flow - Damping ratio
- An analytical two-phase damping model
Experimental Study
Fluid-elastic Instability
Conclusions
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
o Flow Mechanism of Two-phase Flow
Homogeneous Model-Only for Bubbly Flow
o Analytical Approach for Hydrodynamic Forces
Experimental Study, Reliable Prediction of Dynamic Response
*
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Hydrodynamic Forces
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Dimensionless critical flow velocity
90
Sheet2
Sheet3
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Fundamental Theory
Boundary conditions
Characteristic equation
Natural Frequency
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Hydrodynamic mass due to the liquid in the annulus
Total mass acting on the flexible inner cylinder
*
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Homogeneous void fraction
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Damping ratio
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Euler number for single phase flow
Two-phase friction multiplier
Two-phase damping ratio
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Experimental Study
test section
- Pressure perturbation, Acceleration
Critical flow velocity,
Fluid-elastic instability coefficient
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Gp=414 No3
Gp=459 No3
Gp=581 No3
Gp=414 No1
Gp=459 No1
Gp=581 No1
Gp=414 Ana(Sim;2007)
No1, 1 : 2.495 m^3/hr
air [L/min]
air [L/min]
No1, 1 : 6.422 m^3/hr
air [L/min]
air [L/min]
2007. 10. 17 two-phase total damping ratio data modify
No1, 1 : 2.495 m^3/hr
air [L/min]
air [L/min]
No1, 1 : 5.839 m^3/hr
air [L/min]
air [L/min]
2007. 10. 17 two-phase total damping ratio data modify
No1, 1 : 6.422 m^3/hr
air [L/min]
air [L/min]
No1 total data
No1, 1 : 5.839 m^3/hr , 0.091 m/s
air [L/min]
3
5.839
0.029
10.209
13.0187
12.4515
0.0035883092
0.112825764
0.06394
0.3612552115
0.6462552115
0.0000013421
971.0348
0.0141259568
0.0347598072
0.0357995263
0.0147598072
6
0.058
10.5575
13.6392
12.3443
0.008145036
0.1248227927
0.06394
0.3725283289
0.6575283289
0.0000013791
942.0696
0.0137133604
0.0471694323
0.0509474892
0.0271694323
9
0.085
10.9703
13.7305
12
0.02305545
0.1150083333
0.06394
0.4108007813
0.6958007813
0.0000014155
915.102
0.0129346315
0.0381337019
0.0448698928
0.0181337019
12
0.109
10.6922
13.8551
12.5063
0.0404259984
0.1264522681
0.06394
0.3556041083
0.6406041083
0.0000014495
891.1308
0.0135611801
0.048951088
0.05445544
0.028951088
15
0.134
10.8525
14.1076
12.8101
0.0564853864
0.1270520917
0.06394
0.3255797041
0.6105797041
0.0000014866
866.1608
0.0138384635
0.0492736282
0.0537513083
0.0292736282
17
0.149
10.1867
13.5167
12.9575
0.0534394259
0.1284970095
0.06394
0.311767233
0.596767233
0.0000015099
851.1788
0.0139421564
0.050614853
0.0549152302
0.030614853
21
0.178
10.5604
13.8921
12.4648
0.0725369967
0.1336443425
0.06394
0.3598768325
0.6448768325
0.0000015569
822.2136
0.0129033023
0.0568010402
0.0689412361
0.0368010402
28
0.223
11.112
14.3959
13.2298
0.0940589568
0.1241099639
0.06394
0.2874543323
0.5724543323
0.000001636
777.2676
0.0136724687
0.0464974951
0.0529944632
0.0264974951
35
0.265
10.4338
14.0766
13.125
0.1201291
0.1387733333
0.06394
0.2966326531
0.5816326531
0.0000017174
735.318
0.0130953316
0.0617380017
0.0755712854
0.0417380017
42
0.301
11.0752
14.563
13.8988
0.119816504
0.1254712637
0.06394
0.2336719872
0.5186719872
0.0000017939
699.3612
0.0138715693
0.0476596944
0.0546982169
0.0276596944
50
0.339
10.928
14.8449
13.2808
0.119569293
0.1474647612
0.06394
0.2830661758
0.5680661758
0.0000018824
661.4068
0.0125523111
0.0709724501
0.0943301947
0.0509724501
60
0.381
11.5303
14.4878
12.8125
0.1665274
0.1154146341
0.06394
0.3253509816
0.6103509816
0.000001991
619.4572
0.0114567332
0.0400179009
0.0610173447
0.0200179009
No1, 1 : 6.422 m^3/hr , 0.106 m/s
air [L/min]
3
6.422
0.027
10.8038
13.1352
12.809
0.005765594
0.0910063237
0.06394
0.3256845783
0.6106845783
0.0000013396
973.0324
0.0147553308
0.0123109929
0.0119567566
-0.0076890071
6
0.053
11.3481
13.7385
12.3185
0.0148423603
0.0970248001
0.06394
0.3752854821
0.6602854821
0.0000013726
947.0636
0.0137102844
0.0193745157
0.0209032645
-0.0006254843
9
0.078
11.4112
13.8464
12.6577
0.032932509
0.0961944113
0.06394
0.3403711002
0.6253711002
0.0000014059
922.0936
0.0140715037
0.0181829076
0.0190834456
-0.0018170924
12
0.101
11.0648
13.6007
12.1856
0.0486922971
0.1040531447
0.06394
0.3897665854
0.6747665854
0.000001438
899.1212
0.0131075366
0.0270056081
0.0313631697
0.0070056081
15
0.123
10.3609
13.9317
13.469
0.0471455322
0.1325562403
0.06394
0.2673021048
0.5523021048
0.00000147
877.1476
0.0150245017
0.0535917386
0.0522194776
0.0335917386
18
0.144
10.8225
14.0866
12.3239
0.0757170358
0.1324296692
0.06394
0.3747069704
0.6597069704
0.000001502
856.1728
0.0129742702
0.055515399
0.0661963082
0.035515399
21
0.164
11.4262
13.9352
12.1875
0.07029494
0.1029333333
0.06394
0.389556213
0.674556213
0.0000015338
836.1968
0.0125929522
0.0264003811
0.0329572146
0.0064003811
24
0.183
10.6087
14.1161
11.0929
0.0835643417
0.158092113
0.06394
0.529248952
0.814248952
0.0000015653
817.2196
0.0107960288
0.0833560841
0.12852464
0.0633560841
27
0.201
10.755
14.1955
12.0393
0.0830250612
0.1428862143
0.06394
0.4062655775
0.6912655775
0.0000015963
799.2412
0.0120559099
0.0668903044
0.0895284155
0.0468903044
30
0.219
10.7354
14.5535
13.8022
0.0899969362
0.1383149063
0.06394
0.2409576444
0.5259576444
0.0000016286
781.2628
0.0146112682
0.0597636381
0.0622617482
0.0397636381
33
0.236
11.0002
13.8092
12.2389
0.0988278136
0.1147570452
0.06394
0.383902211
0.668902211
0.0000016603
764.2832
0.0120510298
0.0387660154
0.0525037278
0.0187660154
No1, 1 : 8.186 m^3/hr , 0.135 m/s
air [L/min]
No3 total data
No3, 3 : 2.495 m^3/hr , 0.041 m/s
air [L/min]
3
2.495
0.067
8.5941
10.6105
9.688
0.001873
0.1040668869
0.06136
0.3700914443
0.6550914443
0.000001391
933.0804
0.015455
0.0273
0.0296077913
0.0033
6
0.126
8.617
10.5192
9.688
0.00820419
0.0981729975
0.06136
0.3700914443
0.6550914443
0.0000014745
874.1512
0.014907
0.0219
0.0254039771
-0.0021
9
0.178
7.7785
10.744
9.219
0.018085
0.1608363163
0.06136
0.4384400665
0.7234400665
0.0000015569
822.2136
0.013374
0.0861
0.1172360397
0.0621
12
0.224
7.8161
10.5267
8.906
0.0275425332
0.1521783068
0.06136
0.4901840106
0.7751840106
0.0000016378
776.2688
0.012297
0.0785
0.1213416587
0.0545
15
0.265
8.6112
11.5066
9.3669
0.002967
0.1545548687
0.06136
0.4157747097
0.7007747097
0.0000017174
735.318
0.012866
0.0803
0.1184694379
0.0563
18
0.302
8.0397
10.8167
10
0.034039591
0.13885
0.06136
0.3298514304
0.6148514304
0.0000017961
698.3624
0.013784
0.0637
0.0867956996
0.0397
21
0.336
8.5555
11.0487
9.375
0.0495415134
0.1329706667
0.06136
0.4145642941
0.6995642941
0.0000018751
664.4032
0.012163
0.0594
0.0968638015
0.0354
24
0.366
7.8526
10.7583
10
0.04966698
0.145285
0.06136
0.3298514304
0.6148514304
0.0000019508
634.4392
0.013051
0.0709
0.1062916181
0.0469
27
0.394
8.2251
11.4302
9.062
0.0528271867
0.1768428603
0.06136
0.4637245475
0.7487245475
0.0000020272
606.4728
0.010971
0.1045
0.1996678049
0.0805
30
0.419
8.3313
11.9952
9.6875
0.0570502359
0.1891045161
0.06136
0.3701590684
0.6551590684
0.0000021007
581.5028
0.011836
0.1159
0.2020890626
0.0919
33
0.442
8.2371
11.3697
9.5932
0.0541737358
0.1632719009
0.06136
0.3831026435
0.6681026435
0.0000021731
558.5304
0.011394
0.0905
0.1675568273
0.0665
No3, 3 : 5.839 m^3/hr , 0.091 m/s
air [L/min]
3
5.839
0.029
9.4869
10.9278
10.0932
0.0053709134
0.0713797408
0.06136
0.3185488541
0.6035488541
0.0000013421
971.0350
0.016800
-0.0068
0.0262120324
-0.0308
6
0.058
8.6588
10.2594
9.53125
0.008803468
0.0839659016
0.06136
0.3918157643
0.6768157643
0.0000013791
942.0696
0.015162
0.0074
0.0243541973
-0.0166
9
0.085
8.2767
10.2931
9.375
0.01875655
0.1075413333
0.06136
0.4145642941
0.6995642941
0.0000014155
915.102
0.014555
0.0316
0.1018594596
0.0076
12
0.109
8.477
11.4461
9.3688
0.0286065156
0.1584567928
0.06136
0.4154905032
0.7004905032
0.0000014495
891.1308
0.014329
0.0828
0.095516423
0.0588
15
0.134
8.318
10.6903
9.5191
0.0398735421
0.1246073683
0.06136
0.3935446167
0.6785446167
0.0000014866
866.1608
0.014445
0.0488
0.0973829642
0.0248
17
0.149
8.2778
10.9448
9.6235
0.0391884996
0.1385670494
0.06136
0.3789021673
0.6639021673
0.0000015099
851.1788
0.014542
0.0627
0.0768939476
0.0387
21
0.178
8.5752
11.7642
8.90625
0.04554998
0.1790315789
0.06136
0.4901404921
0.7751404921
0.0000015569
822.2136
0.012700
0.1050
0.0867284048
0.0810
28
0.223
8.9349
13.4875
9.6875
0.05511512
0.2349729032
0.06136
0.3701590684
0.6551590684
0.000001636
777.2676
0.013961
0.1597
0.0924474703
0.1357
35
0.265
7.6279
10.6298
9.5312
0.06639893
0.1574775474
0.06136
0.3918228654
0.6768228654
0.0000017174
735.318
0.013206
0.0829
0.1488665502
0.0589
42
0.301
8.2065
11.782
10
0.07535615
0.178775
0.06136
0.3298514304
0.6148514304
0.0000017939
699.3612
0.013795
0.1036
0.1576944891
0.0796
50
0.339
8.1387
11.4293
9.6898
0.0863031956
0.1697971062
0.06136
0.3698480843
0.6548480843
0.0000018824
661.4068
0.012748
0.0957
0.1386876087
0.0717
60
0.381
8.1313
12.5271
9.375
0.08794881
0.2344426667
0.06136
0.4145642941
0.6995642941
0.000001991
619.4572
0.011685
0.1614
0.282061054
0.1374
No3, 3 : 6.422 m^3/hr , 0.106 m/s
air [L/min]
3
6.422
0.027
9.5491
11.1316
10.1355
0.0073288333
0.0780671896
0.06136
0.3223222113
0.6153222113
0.0000013396
973.0320
0.016463
0.0002
0.0002393659
-0.0238
6
0.053
9.1661
11.2373
10.3962
0.01365337
0.0996133203
0.06136
0.2918489257
0.5848489257
0.0000013726
947.0636
0.016849
0.0214
0.0204547928
-0.0026
9
0.078
8.4265
10.8717
9.9591
0.0267158146
0.122762097
0.06136
0.344312977
0.637312977
0.0000014059
922.0936
0.015567
0.0458
0.049024215
0.0218
12
0.101
7.757
10.9735
10.0177
0.0309729771
0.1605408427
0.06136
0.3368786741
0.6298786741
0.000001438
899.1212
0.015487
0.0837
0.0907328814
0.0597
15
0.123
8.6519
11.5449
9.3669
0.0354413693
0.1544267581
0.06136
0.4274455788
0.7204455788
0.00000147
877.1476
0.013812
0.0793
0.1007364083
0.0553
18
0.144
8.6258
11.8423
10.1694
0.0453790207
0.1581460066
0.06136
0.3182266589
0.6112266589
0.000001502
856.1728
0.015416
0.0814
0.0898956009
0.0574
21
0.164
8.5745
11.2337
9.661
0.0502396458
0.1376255046
0.06136
0.3842496416
0.6772496416
0.0000015338
836.1968
0.014088
0.0622
0.0779301698
0.0382
24
0.183
8.3058
10.459
9.5304
0.0580492381
0.1129648283
0.06136
0.402938224
0.695938224
0.0000015653
817.2196
0.013628
0.0380
0.0500479738
0.0140
27
0.201
8.5744
11.6689
9.8445
0.0543339255
0.1571689776
0.06136
0.3592372849
0.6522372849
0.0000015963
799.2412
0.014130
0.0817
0.1031498376
0.0577
30
0.219
9.0726
12.4425
9.9935
0.0593430534
0.168604593
0.06136
0.3399329634
0.6329329634
0.0000016286
781.2628
0.014269
0.0930
0.1165627424
0.0690
33
0.236
8.0639
11.4904
9.3966
0.0536700443
0.1823265862
0.06136
0.4228985259
0.7158985259
0.0000016603
764.2832
0.012851
0.1081
0.1567176805
0.0841
No3, 3 : 8.186 m^3/hr , 0.135 m/s
air [L/min]
Gp=414 No3
Gp=459 No3
Gp=581 No3
Gp=414 No1
Gp=459 No1
Gp=581 No1
Gp=414 Ana(Sim;2007)
interpolation curve
0 20
interpolation curve
Interpolation curve
Interpolation curve
Interpolation curve
Interpolation curve
Interpolation curve
Interpolation curve
interpolation 0,89,60
Interpolation 2.03, 89.7, 95
Interpolation
0510152025
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
ACCELERATION,m/s
2
Interpolation, 2.03, 93, 60
Interpolation 2.03, 45, 72
Interpolation 2, 34.9, 72
Interpolation 2, 44.9, 60
Interpolation 2, 49.9, 72
Interpolation 0, 125, 72
Interpolation
Interpolation 2, 50.81, 60
Interpolation 1.58, 125, 60
Interpolation 1.58, 98, 72
Interpolation 1.85, 49, 60
interpolation 1.85, 90.8, 72
interpolation 0, 109.6, 70
interpolation
0.000.050.100.150.200.250.300.350.400.450.500.550.600.650.700.750.800.850.900.951.00
0.00
0.02
0.04
0.06
0.08
0.10
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Fluid-elastic Instability
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
*
Proceedings of the 18th International Conference on Nuclear Engineering ICONE18 May 17- 21, 2010, Xi’an, China
Hannam University
Conclusions
An experimental program has been performed with normal square array of cylinders subjected to air/water flow, to investigate fluid-elastic instability of tube bundles.
The pitch over diameter ratio was 1.3 and the diameter of cylinder is 20 mm.
The dynamic instability of cylinder(s) is evaluated with added mass, damping and the threshold flow velocity.
The two-phase damping was calculated, considering viscous damping, structure damping and the total damping, measured at two-phase flow.
The measured two-phase damping ratios are compared to the semi-analytical results proposed by Sim (2007).
However the two-phase damping data is scattered, average values of the data versus void fraction agree well with the analytical results.
Two-phase damping is very dependent on void fraction
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Gp=175 kg/(m^2*s) No3Gp=414 No3Gp=459 No3Gp=581 No3Gp=414 No1Gp=459 No1Gp=581 No1Gp=414 Ana(Sim;2007)
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