Science and Technology of Nuclear Installations

Volume 2013 (2013), Article ID 868163, 10 pages

http://dx.doi.org/10.1155/2013/868163

Research Article

Application of the Critical Heat Flux Look-Up Table to Large Diameter Tubes

M. El Nakla,¹ M. Habib,¹ W. Ahmed,¹ A. Al-Sarkhi,¹ R. Ben Mansour,¹ and M. Y. Al-Awwad²

¹Mechanical Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

²Consulting Services Department, Saudi Aramco Oil Company, Dhahran 31261, Saudi Arabia

Received 13 August 2013; Accepted 10 September 2013

Academic Editor: Atef Mohany

Copyright © 2013 M. El Nakla et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

The critical heat flux look-up table was applied to a large diameter tube, namely 67 mm inside diameter tube, to predict the occurrence of the phenomenon for both vertical and horizontal uniformly heated tubes. Water was considered as coolant. For the vertical tube, a diameter correction factor was directly applied to the 1995 critical heat flux look-up table. To predict the occurrence of critical heat flux in horizontal tube, an extra correction factor to account for flow stratification was applied. Both derived tables were used to predict the effect of high heat flux and tube blockage on critical heat flux occurrence in boiler tubes. Moreover, the horizontal tube look-up table was used to predict the safety limits of the operation of boiler for 50% allowable heat flux.

1. Introduction

Critical heat flux (CHF) is a phenomenon corresponding to the point where a continuous liquid contact cannot be maintained at the heated surface. Strictly speaking, this particular term refers to the heat flux corresponding to the occurrence of the phenomenon. Other terms often used are burnout, dryout, boiling crisis, and departure from nucleate boiling (DNB).

CHF results in sudden drop in heat transfer rate between the heated surface and the coolant. Beyond CHF, a small increase in heat flux leads to large increase in surface temperature for a heat-flux-controlled surface (e.g., electric heaters), and a small increase in surface temperature leads to decrease in heat flux for a temperature-controlled surface (e.g., steam condensers). This could lead to overheating damaging of the surface, corrosion in the CHF region, and reduction in the operating efficiency.

Various prediction methods for CHF have been proposed during the past 60 years. The earliest prediction methods were primarily empirical [1, 2]. These crude empirical correlations lacked any physical basis and had a limited range of application. Subsequently, a large number of phenomenological equations or physical models for CHF were developed; many of these models were subsequently used in the safety analysis of nuclear reactors, boilers, and steam generators. Physical models, however, depend on the mechanisms controlling the CHF, which are flow-regime dependent. Flow regimes change significantly during a typical transient, and this necessitates the use of a combination of different models, equations, or correlations for CHF in safety analysis codes. Since most empirical CHF correlations and models have a limited range of application, the need for a more generalized technique is obvious. Hence, look-up tables (LUTs) for predicting CHF were subsequently derived. As a basis of the generalized technique, the common local-conditions hypothesis was used; that is, it was assumed that the CHF for a water-cooled tube with a fixed tube diameter is a unique function of local pressure (), mass flux (), and thermodynamic quality ().

The CHF-LUT is basically a normalized water CHF data bank for vertical tubes with 8 mm in tube diameter. Compared to other available prediction methods, the LUT approach has the following advantages: (i) greater accuracy, (ii) wider range of application, (iii) correct asymptotic trend, (iv) requires less computing time, and (v) can be updated if additional data become available. The greatest potential for the CHF-LUT approach is its application in predicting the consequences of pipe breakage in reactors and boilers.

The following sections describe the background, the derivation, and the application of the CHF-LUT to predict CHF occurrence in vertical and horizontal large-diameter tubes. The CHF-LUTs specifically for 67 mm diameter tubes were generated in this work covering wide range of flow conditions of pressure, mass flux, and thermodynamic quality.

2. Predicting CHF in Vertical Tube

2.1. Analysis

Groeneveld et al. [3] combined the CHF data of both Atomic Energy of Canada Limited and the Institute of Physics and Power Engineering in the Russian Republic (a total of over 30 000 points) and updated the look-up table for tubes. The new table (1995 CHF-LUT) provides a better prediction accuracy (root-mean-squared error of 7.82% for dryout power prediction against 25,630 CHF experimental data points from 49 different experiments) than other look-up tables and correlations over the complete range of flow conditions. In addition, Groeneveld et al. [3] employed a multidimension smoothing procedure of Huang and Cheng [4], which has eliminated several irregularities in the parametric trends.

The 1995 tube CHF-LUT as well as the earlier versions of the LUT have been assessed extensively. The most recent assessment was made by Baek et al. [5] using their database. Their assessment confirms the error statistics reported by Groeneveld et al. [3] and the improved prediction capability compared with previous versions of the table. Earlier assessments by Smith [6] and the developers of the RELAP code indicated the suitability of the table look-up approach and resulted in its use in system codes such as CATHARE [7], THERMOHYDRAULIK [8], and RELAP [9]. Considering all of these reasons, the 1995 CHF-LUT was selected as the base of the current analysis for predicting CHF in vertical tubes.

The 1995 CHF-LUT was built for water upward flow in 8 mm diameter vertical tube. To use the table for other tube diameters, Groeneveld et al. [3] derived a diameter correction factor () such that for ,

and for ,

This correction factor can be multiplied by the CHF values of 1995 CHF-LUT to get the corresponding CHF for non-8 mm diameter tube as follows:

2.2. Discussion

The 1995 CHF-LUT along with (2) (for = 0.067 m) were used to derive a modified LUT suitable for the current application. Table 1 shows the derived LUT using (3) and the 1995 CHF-LUT. This table has flow-condition limits other than the original table to suit the current application. The ranges of flow parameters are limited to pressures of 100–7000 kPa, mass fluxes of 100–2000 kg·m⁻²·s⁻¹, and qualities of −0.15–0.8.

Table 1: CHF-LUT for vertical up-flow in 67 mm diameter tube.

(kPa)
  (kg·m⁻²·s⁻¹)
Quality, (—)

−0.15
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.70
0.80

Critical heat flux, CHF (kW·m⁻²)

100
100
2967
2351
1677
1110
661
648
640
631
618
610
591
548
426
314

100
500
2999
2454
2148
1826
1163
1076
1073
1069
983
921
834
677
429
318

100
1000
3071
2637
2354
2010
1441
1303
1300
1260
1156
943
930
817
485
244

100
1500
3096
2698
2403
2055
1512
1383
1371
1306
1188
1058
1058
910
478
198

100
2000
3097
2701
2404
2061
1535
1418
1394
1330
1171
1093
1035
836
384
104

1000
100
3240
3010
2765
2433
1930
1595
1511
1443
1306
1163
971
748
736
713

1000
500
4176
4091
4053
4017
3886
3289
2904
2656
2198
1302
946
590
470
437

1000
1000
4178
4099
4061
4003
3822
3246
2874
2641
1860
1160
864
546
337
258

1000
1500
4189
4121
4077
3997
3764
3153
2844
2521
1845
887
530
363
234
211

1000
2000
4232
4150
4099
3997
3649
2962
2690
2510
1792
783
406
308
196
78

2000
100
3301
3132
2944
2658
2140
1796
1703
1629
1487
1330
1160
998
920
809

2000
500
4241
4195
4200
4181
4079
3640
3276
2941
2469
1618
1420
1077
760
595

2000
1000
4243
4201
4173
4142
4032
3574
3206
2922
2127
1457
1178
822
523
365

2000
1500
4254
4215
4168
4118
3948
3475
3126
2698
2003
1211
758
489
296
248

2000
2000
4293
4232
4174
4078
3740
3198
2860
2540
1889
1041
548
327
204
133

3000
100
3361
3254
3123
2882
2349
1996
1896
1816
1668
1496
1349
1249
1104
905

3000
500
4306
4298
4347
4344
4273
3990
3648
3226
2740
1933
1895
1565
1049
752

3000
1000
4309
4302
4285
4282
4243
3902
3539
3203
2394
1755
1492
1097
708
473

3000
1500
4319
4309
4258
4239
4133
3797
3409
2875
2161
1534
985
616
357
284

3000
2000
4355
4313
4248
4160
3832
3435
3030
2569
1986
1299
690
347
213
188

4000
100
3315
3215
3097
2885
2362
2027
1933
1853
1706
1547
1380
1280
1164
953

4000
500
4114
4093
4115
4093
3959
3629
3333
3089
2678
2100
1946
1649
1226
880

4000
1000
4134
4097
4064
4021
3862
3565
3277
3014
2384
1860
1626
1137
762
531

4000
1500
4162
4109
4041
3955
3713
3414
3101
2728
2113
1617
1101
648
439
398

4000
2000
4212
4136
4003
3821
3416
3079
2770
2420
1907
1378
725
364
292
279

5000
100
3268
3177
3071
2887
2374
2057
1971
1890
1745
1598
1411
1311
1224
1001

5000
500
3923
3887
3883
3841
3645
3268
3019
2951
2615
2266
1997
1733
1402
1008

5000
1000
3958
3893
3844
3759
3481
3227
3015
2825
2375
1965
1759
1178
817
589

5000
1500
4004
3910
3823
3671
3294
3031
2792
2582
2065
1700
1216
681
520
512

5000
2000
4069
3958
3758
3483
2999
2724
2511
2271
1827
1457
759
381
371
371

6000
100
3173
3097
3006
2835
2325
2012
1925
1845
1691
1553
1386
1045
939
861

6000
500
3694
3627
3600
3569
3407
3061
2853
2749
2470
2173
1977
1638
1353
933

6000
1000
3706
3566
3485
3425
3211
3040
2768
2525
2159
1948
1689
1120
716
458

6000
1500
3753
3609
3503
3299
2929
2681
2466
2259
1886
1618
1179
587
447
407

6000
2000
3874
3739
3515
3153
2688
2409
2209
2013
1664
1358
625
303
295
250

7000
100
3052
2990
2910
2746
2255
1939
1846
1763
1607
1479
1312
975
864
843

7000
500
3470
3393
3386
3356
3243
2926
2669
2460
2223
1977
1799
1480
1261
905

7000
1000
3497
3305
3194
3138
3031
2890
2549
2218
1908
1728
1618
1011
639
419

7000
1500
3564
3355
3194
2933
2664
2452
2208
1987
1689
1438
985
459
278
156

7000
2000
3694
3501
3240
2823
2437
2157
1942
1780
1557
1153
481
246
184
112

Figure 1 shows pressure effect on the predicted CHF value at low, low-to-moderate and moderate, mass fluxes. At low mass flux (Figure 1(a)), there is no apparent effect of pressure on CHF. At low-to-moderate and moderate mass fluxes (Figures 1(b) and 1(c)), however, evident pressure effect was observed. For the low-to-moderate quality region (<~0.35), which is the region of interest, CHF increases with decreasing pressure. This is similar to what is reported in the literature (e.g., [10]).

(a)

(b)

(c)

Figure 1: Effect of pressure on CHF for vertical up-flow of water in 67 mm diameter tube as predicted by CHF-LUT.

The effect of mass flux on CHF is shown in Figure 2. Similar to pressure effect, CHF increases with increasing mass flux then starts decreasing. The decrease in this region in CHF is due to the vapor generation rate and the interaction between vapor and liquid at the interface (see also [10]).

Figure 2: Effect of mass flux on CHF for vertical up-flow of water in 67 mm diameter tube as predicted by CHF-LUT.

As an example of the application of the LUT approach on predicting the safe operation of boilers, consider the results shown in Table 2. For the base case, which represents the normal operating conditions of an actual boiler, CHF is unlikely to occur because it is 32 times higher than the operating heat flux. When the operating heat flux is increased by four times, the exit quality increased which results in reduction in CHF value. Even with that increase in operating heat flux, the CHF value is still much higher (6 times) than the operating heat flux. The final case is with 90% blockage of the tube which will result in reduction in mass flux and increase in quality. Table 2 shows that even with this amount of blockage it is still unlikely for CHF to occur.

Table 2: Effect of high heat flux and tube blockage on CHF occurrence for a 67 mm vertical boiler tube.

Parameter
Base case
High heat flux case
90% tube blockage

Heat flux (KW·m⁻²)
100
400
100

Pressure (kPa)
6,000
6,000
6,000

Vertical heated length (m)
10
10
10

Inlet quality to vertical tube (—)
0
0
0

Mass flux (kg·m⁻²·s⁻¹)
1,000
1,000
100

Tube exit quality (—)
0.038
0.152
0.380

Critical heat flux (kW·m⁻²)
3,262
2,760
1,580

3. Predicting CHF in Horizontal Tube

3.1. General Considerations

CHF prediction for a horizontal flow differs from that of vertical flow. For horizontal flow, flow stratification effect appears as a result of gravitational forces. For instance, in annular flow regime of vertical upward flow, the liquid film is said to be uniformly distributed (has the same thickness) on the tube wall. In the same flow regime of horizontal flow, the liquid film has greater flow thickness at the bottom of the tube while it is thinner on the upper part (Figure 3). This will dramatically decrease the heat flux value at which CHF occurs specially at low mass fluxes and large tube diameters ( kg·m⁻²·s⁻¹,  mm) [3]. At high mass fluxes and smaller tube diameters, CHF is predicted for horizontal tubes in the same manner as in vertical tubes.

Figure 3: Flow patterns during evaporation in horizontal tube with uniform heat flux [10].

To improve the value of CHF for horizontal flow, Collier and Thome [10] suggested the use of flow enhancers such as twisted tape tube inserts and replacing the tubes by microfinned tubes (see Figure 4). For twisted tapes, heat transfer augmentation ratios are typically in the range from 1.2 to 1.5 while the two-phase pressure drop ratios are often as high as 2.0 because the tape divides the flow area into two smaller areas with smaller hydraulic diameters. By using the microfinned tube, heat transfer enhancements can be as high as three to four times for horizontal flow with low mass fluxes. Two-phase pressure drop ratios range from 1.0 at low mass fluxes up to a maximum of 1.5 at high mass fluxes.

(a)

(b)

Figure 4: Suggested boiling enhancement geometries: (a) tape tube insert; (b) microfinned tube.

3.2. Analysis

Due to the reliability of the LUT approach, it is widely used to predict CHF of horizontal flow, CHFhor, in many industries including nuclear power generation for which accuracy of prediction is crucial. To use the CHF-LUT to predict CHF occurrence in horizontal tube, the LUT values are adjusted to account for flow stratification. Groeneveld [11] suggested that the CHF for vertical flow, CHFver, be multiplied by a stratification factor such that

To determine the stratification factor, the exact flow regime must be known. Figure 5 shows the flow-regime map for horizontal flow (modified from Taitel and Dukler [12] by [13]). The modification included the extension of curve into the annular flow regime (Lockhart-Martinelli’s parameter, ), resulting in subdivision of the annular regime into homogeneous annular and stratified annular.

Figure 5: Modified, generalized, flow-regime map for horizontal flow [13].

For stratified-flow regimes, the liquid waves will not be sufficiently large to cool the upper part of the tube which leads to a CHF value and of zero. If the flow regime falls in the homogeneous annular region (above the line ), the effect of orientation on the phase distribution is insignificant. The CHF for horizontal flow may be assumed equal to that for vertical flow and . For flow conditions between curves A and D, the stratification factor varies from zero to unity. As a quick estimate, a linear interpolation was used to evaluate [14]. However, Wong [13] showed that a large portion of the horizontal CHF data was underpredicted using direct interpolation. A more accurate prediction method for was developed by Wong [13]. A dimensionless parameter, , representing the ratio of turbulence to gravity force was derived as follows:

where is liquid Reynolds number, is gravitational acceleration, is void fraction, and is density. The subscripts and denote saturated liquid and vapor, respectively.

The stratification factor for water was suggested as

Wong [13] showed that comparing against horizontal CHF data, prediction using (6) is superior to the method of direct interpolation. values were found to decrease with increasing tube diameter. The tube diameter correction factor is approximated by [13] as

Therefore, using the table look-up technique, the CHF in a horizontal tube is calculated with

3.3. Discussion

At the same flow conditions for a horizontal tube and vertical tube, it is more likely for CHF to occur in the horizontal tube first. The main reasons which led to this argument are:

(i)flow stratification may cause partial dryout at low mass fluxes and high qualities;(ii)the presence of the partial dryout causes a reduction in the CHF value;(iii)in addition, corrosion potential is higher due to the change in flow direction and due to partial/complete dryout.

So, more detailed examination is performed on the horizontal flow configuration.

The vertical CHF-LUT was used with (6) and (7) to build a LUT for CHF in horizontal flow. The resulting LUT is shown in Table 3 for the same conditions of the vertical tube table. It is clear in the table that the CHF values are much less for the horizontal flow than those of the vertical flow for the same pressures, mass fluxes, and qualities.

Table 3: CHF-LUT for horizontal flow in 67 mm diameter tube.

  (kPa)
  (kg·m⁻²·s⁻¹)
Quality, (—)

−0.15
−0.10
−0.05
0.00
0.05
0.10
0.15
0.20
0.30
0.40
0.50
0.60
0.70
0.80

Critical heat flux, CHF (kW·m⁻²)

100
100
63
50
35
26
41
52
61
67
76
83
88
87
72
56

100
500
650
532
465
399
369
405
447
478
478
467
441
358
227
168

100
1000
1347
1157
1107
960
729
678
687
666
611
499
491
432
256
129

100
1500
1596
1426
1270
1086
799
731
725
691
628
560
559
481
253
105

100
2000
1637
1428
1271
1090
811
749
737
703
619
578
547
442
203
55

1000
100
68
64
58
51
72
78
85
90
92
89
77
61
59
55

1000
500
508
497
370
586
748
739
731
727
680
440
341
225
188
183

1000
1000
795
778
1039
1272
1372
1266
1197
1160
871
568
437
281
178
136

1000
1500
1152
1128
1517
1673
1687
1483
1390
1279
975
469
280
192
124
111

1000
2000
1566
1533
1625
1809
1828
1566
1422
1327
947
414
215
163
103
41

2000
100
70
66
62
56
69
73
80
85
89
86
79
68
62
51

2000
500
583
576
404
526
654
693
689
675
645
462
432
346
255
209

2000
1000
897
895
957
1178
1270
1230
1181
1135
898
650
550
397
260
186

2000
1500
1217
1187
1340
1522
1582
1486
1401
1246
982
640
400
259
156
131

2000
2000
1641
1611
1648
1705
1700
1584
1512
1342
999
550
290
173
108
70

3000
100
71
69
66
63
72
76
83
88
92
90
85
79
69
53

3000
500
622
620
426
515
632
697
707
682
660
510
534
465
326
244

3000
1000
908
900
937
1109
1227
1234
1200
1151
943
737
659
505
337
232

3000
1500
1275
1260
1341
1473
1536
1504
1426
1251
1010
771
502
318
186
149

3000
2000
1708
1689
1695
1727
1700
1637
1534
1323
1050
687
365
183
112
99

4000
100
70
68
65
64
68
71
78
83
87
86
80
75
67
52

4000
500
623
619
412
456
538
578
591
596
591
508
504
450
349
261

4000
1000
868
841
845
939
1016
1028
1014
996
872
732
677
496
346
250

4000
1500
1266
1246
1247
1289
1272
1244
1204
1114
939
770
541
326
225
207

4000
2000
1694
1664
1613
1575
1477
1410
1340
1213
1008
729
383
192
154
148

5000
100
69
67
65
66
64
66
73
77
81
81
75
71
65
50

5000
500
622
614
396
400
451
470
485
517
524
499
472
431
364
271

5000
1000
828
784
758
783
826
841
844
851
802
721
688
486
353
266

5000
1500
1255
1228
1156
1116
1032
1009
1001
985
870
766
575
334
262
265

5000
2000
1678
1636
1530
1425
1264
1196
1159
1107
966
770
401
201
196
196

6000
100
76
74
72
67
61
63
68
72
75
75
70
54
47
41

6000
500
517
503
378
366
410
422
437
457
469
454
444
388
334
239

6000
1000
796
737
705
711
725
753
738
722
694
683
634
445
299
200

6000
1500
1206
1166
1093
1023
928
885
858
827
763
704
542
281
222
208

6000
2000
1691
1587
1471
1315
1145
1057
1008
964
863
718
330
160
156
132

7000
100
81
79
77
67
58
58
62
65
68
68
63
48
42
38

7000
500
422
405
365
339
379
387
389
387
398
391
382
332
295
220

7000
1000
771
701
663
650
649
678
644
600
582
577
581
385
257
177

7000
1500
1174
1116
1026
927
853
802
745
696
656
604
439
215
135
79

7000
2000
1702
1525
1394
1200
1049
945
877
837
792
610
254
130
97
59

Figure 6 shows the effect of pressure on CHF for different mass fluxes. In all cases, the CHF value decreases with increasing pressure. In Figure 6(a) one can expect that flow stratification is high which results in low values of CHF for the whole range of qualities. At higher mass fluxes (Figures 6(b) and 6(c)), the pressure effect is weakened at quality of about 0.4 followed by sudden drop in CHF values. This drop in CHF results from the high quality which leads to stronger effect of flow stratification.

(a)

(b)

(c)

Figure 6: Effect of pressure on CHF for horizontal flow of water in 67 mm diameter tube as predicted by CHF-LUT.

The effect of mass flux on CHF is shown in Figure 7. For qualities less than 0.4 the CHF value increases with increasing mass flux. At higher qualities, the sudden drop in CHF leads to a reverse effect of mass flux.

Figure 7: Effect of mass flux on CHF for horizontal flow of water in 67 mm diameter tube as predicted by CHF-LUT.

Similar to the vertical flow analysis, some cases of boiler operation conditions are investigated and the results are shown in Table 4. The results show that for the base case (normal operation conditions) the CHF value is seven times higher than the operating heat flux. So for this case, any failure of the boiler tube may result due to other causes than dryout (e.g., corrosion). Although at this CHF value, it is still safe to operate the boiler, the safety margin is much less than that of a vertical flow.

Table 4: Effect of high heat flux and tube blockage on CHF occurrence.

Parameter
Base case
High heat flux case
80% tube blockage
90% tube blockage

Heat flux (kW·m⁻²)
100
400
100
100

Pressure (kPa)
6,000
6,000
6,000
6,000

Heated length (m)
15
15
15
15

Inlet quality to vertical tube (—)
0
0
0
0

Mass flux (kg·m⁻²·s⁻¹)
1,000
1,000
200
100

Tube exit quality (—)
0.057
0.228
0.285
0.570

Critical heat flux (kW·m⁻²)
729
714
173
58.8

The second case of Table 4 is for high heat flux. In this case, the CHF value is not much higher than the operating heat flux, and CHF could happen for this case. Also for the case of 80% tube blockage, CHF is very close to the operating heat flux. At 90% tube blockage the whole flow is affected by flow stratification, and the CHF is lower than the operating heat flux. This is likely to lead to complete dryout of the boiler tubes causing either failure of the tubes or accelerating the corrosion.

To determine the safety limits of the boiler, an allowable heat flux was taken to be 50% of the corresponding CHF. Figure 8 shows the safety operational limits at different pressure. As the CHF is expected to occur downstream of the flow, corresponding exit qualities are show on the same figure. The boiler will operate safely as long as the operation conditions are to the left of the heat flux line and the mass flux is above the intersection of the exit quality line and the heat flux line. For example, at a pressure of 6000 kPa and a heat flux of 300 kW·m⁻², the mass flux should not be below 800 kg·m⁻²·s⁻¹ and the quality should be to the left of the 300 kW·m⁻² curve.

(a)

(b)

Figure 8: Safety limits of the operation of boiler for 50% allowable heat flux.

4. Procedures of Determining Safety Limits Using the LUT Approach

The LUT can easily be used to determine the safety limits of boiler operations by applying the following steps.

(1)Determine the operating pressure ().(2)Estimate the mass flux () in each boiler tube and determine the minimum value. If not possible, determine the average mass flux as

(3)Calculate the thermodynamic equilibrium quality (). The CHF occurrence is expected at higher qualities which means downstream of the flow. The quality at any location along the boiling length can be obtained using the heat balance equation such that

where is the inlet quality, is the heat flux, and is the latent heat of vaporization.(4)Use the tube diameter modified CHF-LUT to evaluate . Interpolation between the values for nongrid points might be necessary.(5)Compare the operating heat flux to the calculated CHF value (considering uncertainty).

 If , then the boiler is operated safely and CHF is unlikely to occur. If , then the boiler operation exceeds safety limits and accidents may occur.

The CHF-LUT can easily be programmed into a computer code for quick interpolation and other calculations.

5. Other Considerations

The CHF-LUTs for this work are developed for steady-state water flow in uniformly heated tubes with inside diameter of 67 mm. During normal operation of reactors, boilers, and steam generators, the heat flux is nonuniform. Also the flow fluctuates in pressure and mass flux. For such cases, the CHF-LUTs still can be used with some considerations.

Most CHF measurements have been obtained in uniformly heated tubes because of relative ease in construction of the test section and known location of dryout (downstream end of heated length). Hence, the large majority of CHF prediction methods were derived based only on the data of uniformly heated channels. A change in axial-flux distribution (AFD) from uniform to nonuniform can have an effect on the location of dryout and magnitude of CHF or dryout power since:

(i)the location of dryout may shift from the downstream end to well upstream from the downstream end (the shift in initial-dryout location depends primarily on the shape of AFD and flow conditions), and(ii)the location of dryout and magnitude of CHF is affected by upstream history of the flow (flow memory effect).

Yang et al. [15] performed experimental study on the effect of AFD on CHF. They concluded that the AFD effect on CHF power is relatively small. The CHF power increases slightly as a result of AFD change from uniform to nonuniform in addition to the shifting in CHF location at low inlet qualities. This slight increase in CHF, especially at low inlet temperature, makes it more conservative to apply the CHF-LUT.

El Nakla [16] showed that the steady-state CHF prediction techniques can be used to predict flow oscillation and flow transients CHF with great accuracy. The method used in such cases is applying the instantaneous local conditions of the flow. For instance, if the flow is oscillating, then it is only needed to determine the flow conditions (, , and ) at a specific instant, and by using these values along the CHF-LUT, the safety limits can be determined as in steady-state cases.

Corrosion of tubes might play a major role in boiler tube failure especially after a sudden turn and in horizontal flow where flow stratification could result in dryout or partial dryout in the tube. Collier and Thome [10] provided that the corrosion in such flow configurations is very quick, and they also summarized some of the previous work on the topic.

6. Conclusions

Two look-up tables were developed to predict critical heat flux in vertical and horizontal boilers tubes. The tables are applicable for 67 mm diameter tubes with water as coolant. These tables cover wide range of flow conditions ( = 100–7000 kPa, = 100–2000 kg·m⁻²·s⁻¹, and = −0.15–0.80) so that they can be used during normal operation as well as during accident scenarios and flow oscillation.

The derived CHF-LUTs show correct asymptotic trends compared to those reported in the literature. The prediction accuracy for the vertical LUT is expected to be better than that of the horizontal one. This is due to the less imposed correction on the vertical flow table and the general practice in applying the table for vertical flow. The results of the analysis showed that the vertical flow will unlikely experience any dryout while the chances are much higher for dryout in the horizontal part.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The authors would like to acknowledge the support provided by King Abdulaziz City for Science and Technology (KACST) through the Science & Technology Unit at King Fahd University of Petroleum & Minerals (KFUPM) and for funding this work through Project no. 10-ENE1371-04 as part of the National Science, Technology and Innovation Plan. The help offered by Saudi Aramco Oil Company is also highly acknowledged.

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