lookup tables for predicting chf and film-boiling heat transfer

LOOKUP TABLES FOR PREDICTING CHF AND FILM-BOILING HEAT TRANSFER: PAST, PRESENT, AND FUTURE

THERMAL HYDRAULICS KEYWORDS: critical heat flux, film boiling, lookup table

D. C. GROENEVELD Atomic Energy of Canada Limited, Chalk River Laboratories Ontario K0J 1J0, Canada and University of Ottawa Department of Mechanical Engineering, Ottawa, Ontario K1N 6N5, Canada L. K. H. LEUNG, Y. GUO, and A. VASIC Atomic Energy of Canada Limited Chalk River Laboratories, Ontario K0J 1J0, Canada M. EL NAKLA, S. W. PENG, J. YANG, and S. C. CHENG* University of Ottawa, Department of Mechanical Engineering Ottawa, Ontario K1N 6N5, Canada

Received July 22, 2004 Accepted for Publication October 5, 2004

Lookup tables (LUTs) have been used widely for the prediction of critical heat flux (CHF) and film-boiling heat transfer for water-cooled tubes. LUTs are basically normalized data banks. They eliminate the need to choose between the many different CHF and film-boiling heat transfer prediction methods available. The LUTs have many advantages; e.g., (a) they are simple to use, (b) there is no iteration required, (c) they have a wide range of applications, (d) they may be applied to nonaqueous fluids using fluid-to-fluid modeling relationships, and (e) they are based on a very large database. Concerns associated with the use of LUTs in-

clude (a) there are fluctuations in the value of the CHF or film-boiling heat transfer coefficient (HTC) with pressure, mass flux, and quality, (b) there are large variations in the CHF or the film-boiling HTC between the adjacent table entries, and (c) there is a lack or scarcity of data at certain flow conditions. Work on the LUTs is continuing. This will resolve the aforementioned concerns and improve the LUT prediction capability. This work concentrates on better smoothing of the LUT entries, increasing the database, and improving models at conditions where data are sparse or absent.

I. INTRODUCTION

sequently used in reactor safety analysis codes. Physical models, however, depend on the mechanisms controlling the CHF and film-boiling heat transfer, which are flowregime dependent. Flow regimes change significantly during a typical reactor transient, and this necessitates the use of a combination of different models, equations, or correlations for CHF and film-boiling heat transfer in safety codes. Because of this, and because of the large proliferation of CHF and film-boiling heat transfer models, equations, and correlations, a new prediction methodology was required. Hence, lookup tables ~LUTs! for predicting either CHF or film-boiling heat transfer were subsequently derived.

Various thermal-hydraulic prediction methods for critical heat flux ~CHF! and convective film-boiling heat transfer have been proposed during the past 50 yr. 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 and film-boiling heat transfer were developed; many of these models were sub*E-mail: [email protected] NUCLEAR TECHNOLOGY

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LOOKUP TABLES FOR PREDICTING CHF AND FILM BOILING

The LUT is basically a normalized data bank. Compared to other available prediction methods, the LUT approach has the following advantages: ~a! it has greater accuracy, ~b! it has a wider range of application, ~c! it has correct asymptotic trend, ~d! it requires less computing time, and ~e! it can be updated if additional data become available. Although tabular techniques were initially developed for tubes and have been successfully used in subchannel codes, the greatest potential for their application is in predicting the consequences of postulated loss-of-coolant accidents. To apply the tables to transient heat transfer in bundles requires the use of adjustment factors to correct for geometry, flux shape, and possibly transient effects. Here, the advantages of the LUT technique ~wide range of application, greater accuracy, and greater efficiency in computing! are particularly important to the user. This paper describes the background, the derivation, and the application of the CHF and film-boiling LUTs. A description of the latest versions of these LUTs, as well as improvements to the derivation of the LUTs, is also presented.

II. CHF LUTs II.A. Background and History Since most empirical CHF correlations and models have a limited range of application, the need for a more generalized technique is obvious. As a basis of the generalized technique, the common local-conditions hypothesis was used; i.e., it was assumed that the CHF for a

water-cooled tube and a fixed tube diameter is a unique function of local pressure ~P !, mass flux ~G!, and thermodynamic quality ~ X !. An initial attempt to construct a standard table of CHF values for a given geometry was made by Doroshchuk et al.,3 using a limited database of 5000 data points. This table, and all subsequent tables, contains normalized CHF values for a vertical 8-mm water-cooled tube for various pressures, mass fluxes, and qualities. The CHF table development work has since been in progress at various institutions @e.g., Grenoble Nuclear Research Center; University of Ottawa; the Institute of Physics and Power Engineering ~IPPE! in Obninsk, Russia; and Atomic Energy of Canada Limited ~AECL!, Chalk River# using an ever-increasing database. The latest ~2003! CHF LUT version employed a database containing about 32 000 CHF points and provides CHF values for an 8-mm inner diameter ~i.d.!, watercooled tube, for 19 pressures, 20 mass fluxes, and 23 qualities, covering, respectively, ranges of 0.1 to 20 MPa, 0 to 8 Mg{m⫺2 {s⫺1 ~zero flow refers to pool-boiling conditions!, and ⫺50% to 100% ~negative qualities refer to subcooled conditions!. Linear interpolation between table values is used for determining CHF between table conditions. Extrapolation is usually not needed as the LUT covers a very wide range of conditions. Table I summarizes the various CHF LUTs, including the ranges of conditions, databases, and corresponding prediction accuracies. II.B. CHF Tube Database Table I shows that the earliest versions of the CHF LUTs used relatively small databases. The database has

TABLE I Evolution of CHF LUTs and Databases Number of Experimental Data Table Version

Number of Data Sets

Total

Used

;5 000

;5 000

9 786

9 786

Groeneveld et al.6 ~1986!

;15 000

14 401

13

Kirillov et al.60 ~1991!

;15 000

?

13

25 630

22 946

49

;31 795

25 927

76

Doroshchuk et al.3 ~1975! Groeneveld 59 ~1982!

Groeneveld et al.22 ~1996! University of Ottawa ~2003!

88

Table Accuracy

Comments

USSR data Not reported only 7 Not reported

Limited range of LUT conditions LUT range: 0.2 to 15 MPa, 0 to 7.5 Mg{m⫺2 {s⫺1 87% of data within 610% LUT range: 0.1 to 20 MPa, 0 to 7.5 Mg{m⫺2 {s⫺1 Not reported LUT range: P: 1 to 20 MPa, G: 0.5 to 7.5 Mg{m⫺2 {s⫺1 88% of data within 610%, LUT range: 0.1 to 20 MPa, rms error 7.82%, 0 to 8 Mg{m⫺2 {s⫺1 ; some smoothing of table smoothness index 0.098 87% of data within 610%, Additional smoothing, rms error 9.37%, improved subcooled smoothness index 0.097 region; in progress

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grown considerably and the range of conditions covered by the present database is shown below: Diameter Heated length Length0diameter ratio Pressure Mass flux Dryout quality Inlet subcooling

0.62 to 92.4 mm 0.011 to 20.0 m 4.6 to 2485 100 to 21 200 kPa 6 to 24 270 kg{m⫺2 {s⫺1 ⫺1.652 to 1.0 ⫺1211 to 2711 kJ{kg⫺1

The data obtained over a range of conditions such as mass flux, pressure and quality, and tube diameter are presented in Fig. 1. It can be seen that the data population


density for some flow conditions ~e.g., low flow and low qualities! remains relatively low. II.C. Screening of the Data Initially, all CHF data that had been published previously or obtained via data transfer agreements were all placed in a master CHF data bank. Subsequently, the following data were removed from the database: 1. duplicate data 2. data that do not agree with other data obtained at similar conditions 3. data that display significant scatter and do not follow a smooth trend. This suggests unstable flow conditions during the tests. 4. data that demonstrate some obvious inconsistencies, e.g., CHF qualities .1.0, reported local quality or outlet qualities that cannot be reproduced from a simple heat balance, and inlet temperatures below the triple point ~0.018C!. The remaining data are considered reliable but were not all used for the derivation of the CHF LUT. The additional screening criteria ~applied to remove data that were outside the range of general interest or obtained at conditions where additional length and diameter effects were present! were as follows: 1. tube diameter D: 3 ⬎ D . 25 mm 2. heated-length to tube-diameter ratio L h 0D a. for X in , 0 and X cr ⬎ 0 : L h 0D . 50 b. for X in , 0 and X cr ⬍ 0 : L h 0D . 25 c. for X in ⬎ 0: L h 0D . 100 3. pressure at CHF, P: 100 ⬍ P , 21 000 kPa 4. mass flux at CHF, G: 6 ⬍ G , 9000 kg{m⫺2 {s⫺1 5. quality range X cr : ⫺0.55 ⬍ X cr , 1. These screening criteria have evolved during the past 15 yr. For example, originally the L h 0D criteria were much stricter ~L h 0D . 80!, but as pointed out by Gotovsky and Kvetny,4 this would limit the range of qualities at CHF to higher values. Also, data with two-phase inlets were initially excluded, but this is not really necessary.5 As a result of the above screening criteria, about 26 000 CHF data points obtained from 76 data sets were selected for the latest version of the CHF LUT. II.D. Derivation of the Recent CHF LUT

Fig. 1. Flow conditions of 2002 CHF database. NUCLEAR TECHNOLOGY

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The latest version of the CHF LUT is derived using a similar methodology as described by Groeneveld et al.6 for regions where experimental data are available. The 89

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table derivation is based on the local-condition hypothesis ~CHFD⫽8mm ⫽ f @P, G, X # ! for tubes having a sufficiently large heated length-to-diameter ratio. The following procedure is used in the development of the recent CHF LUTs:

3. The following methods are used to provide table CHF values for regions where no data are available:

1. The most recent version of the CHF LUT is used as the preliminary table to provide the gradient of CHF with respect to P, G, and X.

b. the Zuber 7 pool-boiling correlation with a voidfraction correction suggested by Griffith et al.8 for the stagnant-flow conditions, and the Ivey and Morris 9 modification for the subcooling effect ~the approach described by Groeneveld et al.6 for zero or near-zero flow!

2. Tube data having an inner diameter between 3 and 25 mm are used to update the CHF table using a simple correction factor for diameter ~see Table II!.

a. interpolation and extrapolation of CHF values obtained at adjacent conditions

TABLE II Summary of Correction Factors Applicable to the CHF LUT Factor

Form

K1 , subchannel or tube-diameter cross-section geometry factor

For 3 , Dhy , 25 mm: K1 ⫽ ~0.0080Dhy ! 102 For Dhy . 25 mm: K1 ⫽ 0.57

K2 , bundle geometry factor

冉冉

K2 ⫽ min 1,

Comments

冊冉冊冊

1 2d ⫺x 103 exp ⫹ 2 d 2

Includes the observed diameter effect on CHF. This effect is slightly quality dependent. This is a tentative expression; an empirically derived factor is preferred. K2 is also a weak function of P, G, and X.

K3 , midplane spacer factor for a 37-element bundle

K3 ⫽ 1 ⫹ A exp~⫺BL sp 0Dhy ! A ⫽ 1.5K 0.5 ~G01000! 0.2 B ⫽ 0.10

This factor has been validated over a limited range of spacers.

K4 , heated-length factor

For L0Dhy ⬎ 5: K4 ⫽ exp@~Dhy 0L!exp~2ah !# ah ⫽ Xrf 0@Xrf ⫹ ~1 ⫺ X !rg #

Inclusion of ah correctly predicts the diminishing length effect at subcooled conditions.

K5 , axial flux distribution factor

For X ⱕ 0: K5 ⫽ 1.0 For X ⬎ 0: K5 ⫽ qloc 0qBLA

The F-factor method may also be used within narrow ranges of conditions.

K6 , radial or circumferential flux distribution factor

For X ⬎ 0: K6 ⫽ q~z!avg 0q~z!max For X ⱕ 0: K6 ⫽ 1.0

Tentative recommendation only and to be used with well-balanced bundle. May be used for estimating the effect of flux tilts across elements.

K7 , flow-orientation factor

K7 ⫽ 1 ⫺ exp~⫺~T1 03! 0.5 !,

This equation was developed by Wong et al.61 based on a balance of turbulent and gravitational forces.

where T1 ⫽

冉冊 1⫺X 1⫺a

2

fL G 2 gDhy rf ~rf ⫺ rg !a 0.5

fL is the friction factor of the channel. K8 , vertical low-flow factor

90

G , ⫺400 kg{m⫺2 {s⫺1 or X ⬍⬍ 0: K8 ⫽ 1 ⫺400 , G , 0 kg{m⫺2 {s⫺1 : Use linear interpolation between table value for upward flow and value predicted from CHF ⫽ CHFG⫽0, X⫽0 ~1 ⫺ ah !C1 .

For ah ⬍ 0.8: C1 ⫽ 1.0 For ah ⬎ 0.8: 0.8 ⫹ 0.2rf 0rg ah ⫹ ~1 ⫺ ah !rf 0rg Minus sign refers to downward flow. G ⫽ 0, X ⫽ 0 refers to pool boiling. C1 ⫽

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c. the Hall and Mudawar 10 equation ~which replaces the previously used equation 11 ! for subcooled flow-boiling conditions. The CHF table obtained at this stage is not smooth and displays an irregular variation ~without any physical basis! in the three parametric directions: pressure, mass flux, and quality. These fluctuations are attributed to data scatter, systematic differences between different data sets, and possible effects of second-order parameters such as heated length, surface conditions, and flow instability. Sharp variations in CHF were also observed at some of the boundaries between the region where experimental data are available and the region where correlations and extrapolations were employed. Prior to finalizing the LUT, a smoothing procedure 12 was applied. The principle of the smoothing method is to fit three third-order polynomials to six table entries in each parametric direction. The three polynomials intersect each other at the table entry, where the CHF value is then adjusted. This resulted in a significant improvement in the smoothness of the LUT, as can be seen in Fig. 2. The process of updating the table with experimental data and subsequent smoothing was repeated a few times until the root-mean-square ~rms! error ~based on constant inlet conditions! reached a constant value. The final CHF LUT is shown in Table III. Three levels of shading have been applied to highlight regions of uncertainty. The unshaded entries represent areas that are derived directly from the experimental data, and hence, their uncertainty is least. The lightly shaded ~light gray!


regions represent calculated values based on the prediction from the selected prediction methods found to give reasonable predictions at neighboring conditions. The uncertainty in this region depends on the level of extrapolation from regions where data are available. It is expected to be smaller at conditions slightly beyond the range of data but becomes larger as the extrapolation is further beyond this range. The heavily shaded ~dark gray! regions represent predictions that are often impossible to obtain. They include conditions where critical flow may exist, and conditions where the bulk temperature is lower than zero and the liquid is in a solid phase ~Tbulk , 0!. These heavily shaded entries are included only to improve interpolation accuracy of the lightly shaded regions. Extrapolation into the heavily shaded regions should be avoided. II.E. Other Applications of the CHF LUT to Nonaqueous Fluids II.E.1. Nonaqueous Fluids The water-based CHF LUT may also be used to predict the CHF in nonaqueous fluids. Groeneveld et al.13,14 tested several fluid-to-fluid modeling relationships in conjunction with the CHF LUT and predicted the CHF in seven different fluids with good accuracy. Figure 3 shows an example of the excellent agreement between R-134a data 5 and the water-based 1995 CHF LUT after conversion to equivalent Freon conditions.

Fig. 2. A 3-D representation of CHF LUT for P ⫽13 MPa: ~a! 1996 LUT and ~b! 2003 LUT with extra smoothing ~note CHF scale for different shadings!. NUCLEAR TECHNOLOGY

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92 6 028 6 691 7 260 7 597 7 678 7 788 8 304 9 478 10 920 11 805 12 571 13 251 13 932 14 574 15 273 15 915 16 766 17 416 18 055 18 668

6 627 7 360 7 975 8 422 8 611 8 910 9 484 10 673 11 889 12 905 13 861 14 783 15 675 16 537 17 373 18 184 18 979 19 755 20 521 21 279

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

0 50 100 300 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000

⫺0.4

P G ~kPa! ~kg{m⫺2 {s⫺1 ! ⫺0.5 5 619 6 371 6 981 7 492 7 577 7 594 7 700 8 187 8 962 9 731 10 456 11 146 11 816 12 447 13 033 13 573 14 101 14 608 15 109 15 629

⫺0.3 4 685 5 523 6 252 7 295 7 464 7 466 7 468 7 552 7 788 8 149 8 659 9 203 9 746 10 239 10 745 11 285 11 770 12 172 12 524 12 866

4 058 4 991 5 685 7 089 7 327 7 329 7 349 7 424 7 544 7 728 8 005 8 342 8 754 9 182 9 599 10 064 10 479 10 857 11 194 11 463

3564 4436 5281 6901 7177 7192 7230 7281 7314 7370 7450 7591 7750 7859 8124 8595 8933 9325 9725 9958

2859 3928 4851 6766 7110 7124 7153 7192 7202 7206 7179 7143 7141 6988 6794 6647 6351 6654 7272 7773

⫺0.2 ⫺0.15 ⫺0.1 ⫺0.05 2175 3323 4268 6620 7048 7022 7013 7012 6979 6966 6910 6778 6500 5900 5800 5530 5228 4850 5409 6039

0 1910 2944 3386 6215 6818 6705 6604 6401 6100 5900 5800 5752 5537 5107 4822 4654 4460 4232 4227 4447

0.05 1438 2469 2799 5289 5771 5694 5532 5196 5028 4920 4849 4757 4627 4361 4239 4096 3913 3734 3683 3684

0.1 1030 2071 2651 4760 5094 5042 4989 4720 4668 4647 4628 4584 4477 4211 4085 3966 3804 3547 3525 3536

0.15

X

Section of the CHF LUT

TABLE III

717 1752 2531 4456 4660 4634 4422 4404 4397 4391 4385 4380 4304 3924 3729 3625 3484 3336 3287 3341

0.2 519 1559 2415 4120 4233 3953 3952 3952 3924 3898 3865 3794 3715 3338 3112 3050 2973 2867 2851 3061

0.25 389 1414 2292 3432 3856 3264 3236 3143 2999 2880 2765 2723 2689 2581 2523 2519 2497 2461 2478 2571

0.3 312 1307 2184 2600 2754 2670 2429 2259 2081 1955 1797 1891 1953 1978 2017 2063 2115 2178 2246 2306

0.35 286 1230 2041 2151 2284 2035 1557 1373 1281 1234 1252 1484 1498 1579 1703 1767 1852 1945 2006 2062

0.4

270 1157 1891 1924 1979 1741 1145 980 925 908 1059 1292 1327 1363 1469 1555 1633 1707 1774 1834

0.45

256 1076 1703 1708 1659 1516 930 713 690 701 1000 1021 1034 1126 1235 1325 1406 1480 1548 1612

0.5

0.7

0.8

0.9 1 198 188 181 175 0 876 806 804 700 0 1312 1291 1250 732 0 1343 1289 1215 660 0 1035 825 767 589 0 958 592 452 338 0 637 411 370 266 0 541 343 137 86 0 512 306 84 25 0 510 349 95 30 0 595 356 108 36 0 605 375 134 51 0 643 401 159 65 0 726 438 188 83 0 816 484 227 104 0 902 546 275 129 0 983 616 326 155 0 1057 681 375 180 0 1126 744 423 204 0 1190 802 470 227 0

0.6

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Fig. 3. Comparison of R-134a CHF data and the 1995 CHF LUT.

where

II.E.2. Bundles The tube CHF LUT has been widely applied to fuel bundle geometries.15–18 Generally one of the following three methods is used: 1. subchannel-based approach 2. cross-sectional average bundle-based approach 3. enthalpy imbalance approach. These methods are described by Groeneveld et al.19 Ideally a subchannel code should be used to predict the CHF of a new fuel bundle design. Several subchannel codes are currently in existence, but they have been validated only for a limited number of fuel bundle types and narrow ranges of flow conditions. In addition, their constitutive relations have been tuned to agree with the experimental database. With time this limitation is expected to be resolved as more appropriate constitutive relations are being derived and the robustness of the codes is continuously improved. In the subchannel or bundle-average approach, the CHF needs to be modified to account for bundle-specific or subchannel-specific effects. The following methodology is recommended to evaluate the bundle CHF: CHFbundle ⫽ CHFtable ⫻ K1 ⫻ K2 ⫻ K3 ⫻ K4 ⫻ K5 ⫻ K6 ⫻ K7 ⫻ K8 , NUCLEAR TECHNOLOGY

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~1!

CHFbundle ⫽ cross-sectional average value of the CHF CHFtable ⫽ CHF value for a tube as found in the tube CHF LUT for the same cross-sectional average values of pressure and mass flux K1 through K8 ⫽ correction factors to account for specific bundle effects. A similar approach may be used for predicting the subchannel CHF ~Ref. 20!. Note that the form of Eq. ~1! implies that all correction factors are independent. Many factors are somewhat interdependent, but these interdependencies are assumed to be second-order effects unless indicated otherwise throughout this paper. Table II lists the approximate relationships for the correction factors. II.F. CHF LUT Assessment II.F.1. Tubes The 1995 CHF tube LUT as well as the earlier versions of the LUT have been assessed extensively. The most recent assessment was made by Baek et al.21 using their database. Their assessment confirms the error statistics reported by Groeneveld et al.22 and the improved 93

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prediction capability compared with the 1986 AECL-UO LUT ~Ref. 6!. Earlier assessments by Smith 23 and the developers of the RELAP code indicated the suitability of the table lookup approach and have resulted in its use in systems codes such as CATHARE ~Ref. 24!, THERMOHYDRAULIK ~Ref. 25!, and RELAP ~Ref. 26!. Assessments were also made 27,28 in which the 1985 version of the CHF LUT ~AECL-UO table! was compared to other leading CHF correlations, and the impact of the differences in CHF predictions on nuclear plant transients of interest was assessed. II.F.2. Bundles An independent assessment was made of the CHF LUT as a predictive tool for bundle CHF in conjunction with the subchannel code COBRA-IV-1 ~Ref. 15!. The LUT was compared with six leading CHF prediction methods.15,29–32 It was concluded that, in the absence of a database, the LUT has the greatest potential as a general predictor for CHF in new rod bundle designs. The CHF LUT has also been used and assessed in conjunction with the ASSERT subchannel code 33 and the ANTEO subchannel code.34

III. FILM-BOILING LUT

1. The database has been approximately tripled. 2. The range of thermodynamic quality has been expanded to ⫺0.2 through 2.0. The previous upper limit in thermodynamic quality was 1.2. A wider range was needed as nonequilibrium effects at low flow can extend well beyond the point where the thermodynamic quality equals unity. 3. The wall heat flux has been replaced by the surface temperature as an independent parameter. This change was needed because ~a! in safety analysis the surface temperature, rather than the heat flux, is the independent parameter, and ~b! the surface temperature uniquely defines the heat transfer mode. 4. The new LUT is based only on fully developed film-boiling data @film boiling is considered “fully developed” when Tfb is unaffected by the upstream CHF location ~for the same value of P, G, X, and q, see also Groeneveld et al.41 !#. 5. Table entries, at flow conditions where no data are available, are based on the best of five selected filmboiling prediction methods. The resulting table is referred to as the 2001 filmboiling LUT. It predicts the 23 500 fully developed filmboiling data with an average error of 2.5% and an rms error of 10.5% ~Ref. 41!. Pertinent details of all the filmboiling LUTs are given in Table IV.

III.A. Background and History During the past 50 yr, a large number of heat transfer prediction methods ~more than 80! for the inverted annular film boiling ~IAFB! and the dispersed flow film boiling ~DFFB! regimes have been proposed.35,36 These film-boiling prediction methods generally are empirical or semiempirical ~e.g., models that are fine-tuned by empirical interfacial relationships! and are applicable only over limited ranges of flow conditions. Most of them do not provide reasonable predictions when extrapolated outside the range of their respective database, as exemplified by high errors and incorrect asymptotic trends. To improve the prediction accuracy, a preliminary filmboiling LUT was originally proposed.37 This LUT ~referred to as PDO-LW-96! was subsequently improved significantly.38,39 A similar version was subsequently proposed by Kirillov et al.40 The original film-boiling LUT ~Ref. 38! was a desirable alternative to the many filmboiling models, equations, and correlations for the IAFB and DFFB regimes. It was based on 14 687 data and predicted the surface temperature ~in degrees Celsius! with an average error of 1.2% and an rms error of 6.73%. Error statistics were not provided for the film-boiling LUT proposed by Kirillov et al.40 Subsequently, the following major revisions were made to the PDO-LW-96 LUT: 94

III.B. Film-Boiling Database Earlier film-boiling LUTs ~Refs. 38 and 39! had access to ;20 000 film-boiling data, of which 14 687 were used for the development of the PDO-LW-96 LUT. Since then thousands of additional data have become available. The current film-boiling data bank compiled at the University of Ottawa is the largest known film-boiling database available anywhere and is described in detail by Vasic et al.42 It currently contains more than 77 000 data points obtained in water-cooled vertical tubes. These data have been scrutinized carefully prior to adding them to the University of Ottawa film-boiling database.42 Corrections were applied to some data to correct for the impact of the variation of the test section tube resistivity with temperature for resistance-heated test sections ~this is especially important for stainless steel tubes where the temperature coefficient of resistance is significant!. Many of the data in the expanded data bank are considered questionable and were not used for the development of the new LUT. Reasons for rejecting data or qualifying them as “secondary data” are as follows: 1. The data display significant scatter and do not follow a smooth trend. This suggests unstable flow conditions during the tests. NUCLEAR TECHNOLOGY

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TABLE IV Evolution of Film-Boiling LUTs and Databases Number of Experimental Data Table Version

Total

Groeneveld and Leung 37 ~1989!

Used

Number of Data Sets

4 384

8

rms error in Tw : 5.5%

Limited LUT range: 7 to 12 MPa, 1 to 6 Mg{m⫺2 {s⫺1 q-based LUT

Table Accuracy

Comments

PDO-LW-96, Leung et al.39 ~1997! IAEA ~Ref. 58! ~2001!, App. IV

21 525

14 687

16

rms error in Tw : 6.7% rms error in h: 16.9%

q-based LUT, smoothed

PDO-LW-99, Vasic et al.42 ~2000!

21 182

15 116

18

rms error in Tw : 6.1%

q-based LUT, smoothed

71 120

21 116

25

rms error in h: 10.6% Changed from q-based to Smoothness index: 0.12 T-based LUT, smoothed

71 120

20 014

25

rms error in h: 13.1% T-based LUT with Smoothness index: 0.09 additional smoothing and data screening

41,50

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~2002!

El Nakla et al.62 ~2003!

2. At locations near the inlet, outlet, or hot patch, the temperature distribution suddenly changes. This is usually because of significant axial conduction due to the presence of a nearby heat source or heat sink, e.g., a. copper power terminals ~clamped to the test section! with large power cables

7. Only the maximum film-boiling temperatures measured along the tube surface were reported. For example, Bailey and Lee 44 tabulated only the maximum wall temperatures, while all other temperatures were presented in graphical form. 8. The data were reconstructed from graphs.

b. a high contact resistance ~poor electrical contact! of the power terminals, which can result in additional local heat generation

9. The data were obtained in the developing filmboiling region and are strongly dependent on the location where CHF occurred.

c. a high-temperature hot patch.

10. The flow conditions were outside the range of the LUT.

3. The data demonstrate some obvious inconsistencies, i.e., dryout qualities .1.0, or reported local quality or outlet qualities that cannot be reproduced from a simple heat balance.

11. The quality at dryout X do is unknown and was evaluated from the CHF LUT ~Ref. 22! for a given D, P, G, and q. This permitted the inclusion of three additional data sets into the database as “secondary data.”

4. Significant liquid-wall interaction takes place because the temperature of the wall is below the minimum film-boiling temperature, e.g., Tw ⫺ Tsat , 50 and0or Tw ⬍ Tmfb ; such data are representative of the transition boiling regime and should be treated as such.

More details of the data-qualifying procedures may be found in Groeneveld et al.41 Figure 4 shows schematically the conditions where qualified, fully developed film-boiling data are available.

5. Data obtained at roughly similar conditions do not result in similar film-boiling temperatures.

III.C. Film-Boiling LUT Derivation

6. The experimenter provided inadequate documentation, e.g., a. no error analysis b. no correction to the heat flux due to heat loss c. dryout quality or quench front location were not reported ~e.g., Bishop et al.43 !. NUCLEAR TECHNOLOGY

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The film-boiling LUTs were developed following a similar method used in the development of the CHF LUT. Prior to deriving their LUTs, Leung et al.38 and Groeneveld et al.41 first created a “skeleton” table of heat transfer coefficients ~HTCs! at discrete values of pressure, mass flux, thermodynamic quality, and heat flux, based on predictions from leading models and correlations. Leung et al. used the Hammouda model 45 for the IAFB 95

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was used in previous LUT versions! by the wall temperature since wall temperature is generally used as an independent parameter in safety analysis. The skeleton tables were subsequently “updated” after normalizing the experimental HTCs h D to a diameter of 8 mm using the correction h D⫽8mm ⫽ h D ~80D! 0.2 . ~Note that this correction is based on the well-known single-phase heat transfer relation Nu @ Re 0.8.! Finally, the table was smoothed using various spline functions in a method similar as was done for the CHF LUT. A section of the 2003 filmboiling LUT is shown in Table V and a three-dimensional ~3-D! representation is shown in Fig. 5. The 2003 LUT contains 29 744 table values for the HTC and has been described by Groeneveld et al.50 A comparison of the prediction accuracy of the 2001 LUT ~Ref. 41! ~which is quite similar to the 2003 LUT! with that of six leading film-boiling prediction methods by Guo et al.51 showed the 2001 LUT to be far superior. III.D. Applications of Film-Boiling LUT

Fig. 4. Flow conditions of 2003 film-boiling database.

region at low void fractions ~a , 0.5!, the GroeneveldDelorme 46 correlation for DFFB region at high void fractions ~a . 0.8!, and a linear interpolation between the two for 0.5 , a , 0.8. Groeneveld et al.41 created a hybrid skeleton table based on the best of five filmboiling models ~Groeneveld-Delorme,46 Shah-Siddiqui,47 Chen-Chen,48 Hammouda,45 and Köhler-Hein 49 ! for each of 64 subregions in P, G, and X. They also replaced the fourth independent parameter q ~the wall heat flux q that 96

The film-boiling LUT is based on fully developed film-boiling data obtained in vertical round tubes ~normalized to an 8-mm-i.d. tube! cooled by light water at steady-state conditions. The results may be applied to other fluids provided appropriate correction factors and scaling laws are applied.14 Extrapolation to other tube diameters requires the diameter correction factor h D ⫽ h D⫽8mm ~D08! 0.2 referred to in Sec. III.C. Applying the film-boiling LUT to bundle geometries ideally requires subchannel codes. They are designed to capture the enthalpy and flow imbalance effects ~although subchannel codes are not yet validated for filmboiling applications!. The effect of flow obstructions can have a significant effect on film-boiling heat transfer by improving the wall-vapor heat transfer and by desuperheating the vapor through more effective interfacial heat transfer. Groeneveld and Yousef,52 Groeneveld et al.,53 and Peng et al.54 have suggested methods to account for this. Other effects such as tight gap spacings, presence of cold walls, and bundle orientation can also affect the bundle HTC. Although the present LUT was based only on fully developed film-boiling measurements, it can be applied to predict film-boiling heat transfer in the developing region. Guo et al.51 have developed a correction factor to the LUT that successfully predicts the heat transfer in this region. Their correction factor depends on mass flux, local quality, quality at CHF, and fluid properties. The LUT should not be extrapolated to temperatures less than the minimum film-boiling temperatures ~TMFB !. For the wall temperature range TCHF ⬍ TTB ⬍ TMFB , which corresponds to transition boiling ~TTB !, the following approach recommended by Groeneveld and Snoek 35 should be followed: CHF m qTB ⫽ , ~2! qMFB qMFB

冉冊

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TABLE V Section of the Film-Boiling LUT ~Tw ⫺ Tsat ! ~K! P G ~kPa! ~kg{m⫺2 {s⫺1 !

X

5

50

100

200

300

400

500

600

750

900

1050

1200

1.008 0.823 0.762 0.795 0.781 0.873 1.020 1.488 1.938 2.353 2.617 4.604 5.590 6.153 6.466 6.657

1.082 0.895 0.824 0.837 0.822 0.896 1.036 1.478 1.907 2.324 2.637 4.660 5.823 6.408 6.679 6.880

5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

⫺0.20 ⫺0.10 ⫺0.05 0.00 0.05 0.10 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

0.622 0.489 0.439 0.559 0.642 0.781 1.111 1.545 1.825 2.250 2.556 3.790 4.423 4.694 4.889 5.084

0.620 0.552 0.533 0.618 0.693 0.797 1.071 1.581 2.046 2.432 2.669 3.814 4.451 4.741 4.956 5.152

0.618 0.622 0.637 0.684 0.750 0.815 1.027 1.621 2.292 2.634 2.795 3.841 4.482 4.793 5.030 5.228

0.632 0.652 0.642 0.710 0.769 0.825 1.023 1.476 2.174 2.604 2.758 3.880 4.575 4.916 5.180 5.406

0.651 0.690 0.659 0.720 0.788 0.836 1.005 1.421 2.182 2.619 2.781 3.956 4.695 5.058 5.339 5.608

0.689 0.709 0.677 0.726 0.793 0.836 0.998 1.385 2.144 2.603 2.816 4.051 4.822 5.208 5.512 5.821

0.735 0.693 0.665 0.719 0.784 0.834 1.008 1.411 2.053 2.488 2.712 4.195 4.990 5.374 5.687 6.049

0.783 0.724 0.674 0.719 0.774 0.821 1.012 1.465 2.042 2.456 2.667 4.296 5.116 5.526 5.852 6.202

0.868 0.732 0.694 0.742 0.759 0.817 1.024 1.512 1.994 2.401 2.617 4.518 5.349 5.787 6.119 6.438

0.953 0.772 0.713 0.753 0.759 0.855 1.023 1.500 1.971 2.377 2.619 4.546 5.497 6.006 6.321 6.572

5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000 5000

1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500 1500

⫺0.20 ⫺0.10 ⫺0.05 0.00 0.05 0.10 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00

0.837 0.774 0.748 0.896 0.978 1.274 1.720 2.481 3.211 3.961 4.459 6.081 6.712 7.052 7.357 7.669

0.827 0.747 0.735 0.849 0.970 1.201 1.658 2.557 3.273 3.926 4.320 6.042 6.745 7.115 7.431 7.751

0.816 0.717 0.720 0.797 0.961 1.120 1.589 2.641 3.342 3.887 4.166 5.999 6.782 7.185 7.513 7.842

0.840 0.699 0.735 0.818 0.991 1.116 1.527 2.525 3.242 3.859 4.157 5.904 6.852 7.332 7.715 8.044

0.856 0.649 0.652 0.798 0.998 1.108 1.459 2.461 3.157 3.718 4.118 5.714 6.903 7.490 7.947 8.265

0.892 0.675 0.703 0.781 0.981 1.116 1.455 2.365 3.067 3.694 4.115 6.022 7.121 7.666 8.109 8.523

0.938 0.675 0.650 0.758 0.916 1.112 1.496 2.379 3.030 3.593 4.068 6.312 7.341 7.864 8.306 8.825

0.995 0.775 0.692 0.734 0.922 1.101 1.534 2.386 3.032 3.608 4.021 6.568 7.524 8.070 8.530 9.083

1.057 0.858 0.783 0.811 0.925 1.104 1.549 2.376 3.037 3.642 4.028 6.862 7.797 8.406 8.886 9.411

1.128 1.151 1.103 0.937 0.998 1.073 0.868 0.945 1.008 0.917 0.982 0.984 0.975 1.052 1.076 1.117 1.137 1.146 1.549 1.548 1.541 2.358 2.337 2.311 3.016 3.000 2.984 3.653 3.664 3.669 4.052 4.097 4.157 7.008 7.110 7.269 8.075 8.331 8.705 8.793 9.183 9.541 9.269 9.657 9.983 9.708 10.036 10.392

where ln m⫽

冉冉

TMFB ⫺ Tsat TTB ⫺ Tsat

TMFB ⫺ Tsat ln TCHF ⫺ Tsat

冊冊

data are scarce because of better submodels. In addition, enhancements to the algorithms used for deriving LUTs will also affect the LUT values. .

This will ensure the correct asymptotic trends within the transition boiling region. IV. LUT IMPROVEMENTS IV.A. General LUTs are continuously changing because of additions to the database and improvements in the areas where NUCLEAR TECHNOLOGY

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IV.B. Expanded Database Improving LUTs because of an expanding database for water-cooled tubes is an ongoing process as new data are continuously added to the data pool. In addition, the data screening procedures have changed, as indicated in Secs. II.B and III.B. One area where progress has been made is the use of nonaqueous fluid data. Approximately 15 CHF data sets and 8 film-boiling data sets have been compiled in a nonaqueous data bank, and these will be used to supplement the water data bank at conditions where water data are scarce or nonexistent. 97

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Fig. 5. A 3-D representation of film-boiling LUT for G ⫽ 3000 kg{m⫺2 {s⫺1, X ⫽ 0.1: ~a! 2001 LUT and ~b! present LUT.

Data sets can contain outliers, which may be due to experimental difficulties or data transcribing errors. To identify additional outliers ~beyond the measures suggested in Secs. II.B and III.B!, the number of data not satisfying the relationship 1 CHFexp ⬍ ⬍n n CHFLUT

IV.D. Finer Table Subdivision

were determined, where n was changed gradually from infinity to 1.18. Table VI shows the impact of varying n on the number of data used, and the prediction errors. Note a removal of 2% of the data ~outliers! resulted in the remaining experimental data falling within the error bounds of ⫹30% and ⫺23% and a reduction in rms error from 9.37 to 6.59%. A similar approach was applied to the ratio HTCexp 0HTCLUT . IV.C. Improved Submodels Although there are currently about 800 CHF prediction methods and 80 film-boiling prediction methods available, predictions at low-flow and subcooled conditions

TABLE VI Effect of Removing Outliers on Accuracy of 2003 CHF LUT Data Removed ~%! 0 1 2 5

98

continue to be a significant challenge as few data are available at these conditions, especially for film boiling. The development and assessment of new models applicable to these conditions will be a continuing activity for many years.

n

Number of Data Used

Average Error ~%!

rms ~%!

⫹` 1.45 1.30 1.18

25 927 25 658 25 409 24 624

0.35 0.23 0.00 ⫺0.23

9.37 7.37 6.59 5.53

The 1995 CHF LUT ~Ref. 22! provided CHF table entries for the following values of the independent parameters: 1. 19 pressures: 100, 300, 500, 1000, 3000, 5000, 6000, 7000, 8000, 9000, 10 000, 11 000, 12 000, 13 000, 14 000, 15 000, 16 000, 17 000, and 20 000 kPa 2. 20 mass fluxes: 0, 50, 100, 300, 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500, 7000, 7500, and 8000 kg{m⫺2 {s⫺1 3. 23 thermodynamic qualities: ⫺0.5, ⫺0.4, ⫺0.3, ⫺0.2, ⫺0.15, ⫺0.1, ⫺0.05, 0.0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. Similarly, the 2001 film-boiling LUT ~Ref. 41! is based on the following values of the independent parameters: 1. 13 pressures: 100, 200, 500, 1000, 2000, 5000, 7000, 9000, 10 000, 11 000, 13 000, 17 000, and 20 000 kPa 2. 13 mass fluxes: 0, 50, 100, 200, 500, 1000, 1500, 2000, 3000, 4000, 5000, 6000, and 7000 kg{m⫺2 {s⫺1 NUCLEAR TECHNOLOGY

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3. 16 thermodynamic qualities: ⫺0.2, ⫺0.1, ⫺0.05, 0.0, 0.05, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, and 2.0 4. 11 wall superheats: 50, 100, 200, 300, 400, 500, 600, 750, 900, 1050, and 1200 K. Linear interpolation is used when determining LUT values for CHF or h FB , and this is a source of error. The magnitude of this error depends on the variations in adjacent table entries for h FB or CHF, which can be quite significant ~i.e., .50%!. To minimize this error, a finer subdivision in P, G, and X and wall superheat can be used. This used to be a problem for handbook applications since the table could then become extremely large; this concern has disappeared by using electronic versions of the LUT. However, greater subdivision affects the smoothness of the table. Work is in progress to determine the optimum table subdivision. IV.E. Improved Smoothness The CHF and film-boiling LUTs have been used in reactor safety codes such as RELAP, CATHARE, ASSERT, and CATHENA. One potential concern is the smoothness of the LUT: Irregular trends of the HTC or CHF versus flow, quality, pressure, and wall superheat ~in the case of the film-boiling LUT! can lead to convergence problems. The following factors contribute to irregular trends:


of table entries used in the derivation of the polynomial fit for each parameter direction; and ~c! the weighting coefficient, which is related to the accuracy and reliability of the original data. Huang and Cheng concluded that polynomials of the third degree fitting six table entries in each parametric direction provide a reasonably optimum improvement, and this was recently confirmed independently. In addition, a separate program was employed that searched for unexpected maxima or minima in the h FB or CHF versus X, P, G, or wall superheat diagrams and by replacing these maxima0minima by the average of the original table entry and the average of the original two adjacent table entry values, i.e., CHFi, new ⫽ @CHFi ⫹ 0.5~CHFi⫺1 ⫹ CHFi⫹1 !#02 . This resulted in a smoother LUT but with a slightly increased rms error. This approach can be used before or after Huang and Cheng’s smoothing approach. Applying this to the 2003 CHF LUT resulted in an increase in rms error from 9.37 to 9.61% but a decrease in the smoothness index from 0.135 to 0.111. Another parameter, which affects the smoothness as well as the prediction accuracy, is the weight of the underlying experimental data. A high weight to the experimental data results in an improved prediction accuracy but less smooth table. Factors affecting the weight of the experimental data include the following: 1. the number of data contributing to each table entry

1. discontinuities within the skeleton table. The skeleton table was based on the predictions of five submodels, and discontinuities occurred at the boundaries between these models.

2. the number of different data sets used for deriving each table entry

2. discontinuities at the boundaries between regions with and without data, where a jump can occur because of differences between experimental data and the submodels

The method of deriving an average experimentallybased table entry value was described in detail by Groeneveld et al.6 The smoothing process subsequently replaced this table entry by a value generated based on the smoothing program. The weight factor assigned to the table entry ~prior to it being modified by the smoothing program! could be made linearly proportional to the number of underlying data points. This would result in an optimum improvement to the smoothness of the CHF table with only a minimum increase in rms error. Originally the absolute value of the CHF and h FB were used in the LUT derivation and the smoothing process. This, however, resulted in giving a higher weight to the high values of CHF and h FB . To provide a more equal weight, the ln~CHF! and ln~h FB ! were subsequently used in the derivation and smoothing process. This resulted in a reduction in both the rms error and the smoothness index.

3. disagreement between data sets obtained at adjacent conditions. This is particularly important at conditions where data are relatively scarce and for data sets that contain questionable data. These discontinuities become obvious when plotting the HTC or CHF against the independent variables. The smoothing approach developed by Huang and Cheng 12 was initially applied, but this did not mitigate the effect of these discontinuities sufficiently. Improvements to the smoothing approach are currently being made at the University of Ottawa to reduce these irregularities. To quantify the smoothness, an expression for the smoothness index was derived ~see Sec. IV.E.1!. The net effect of a smoother table is usually a slight deterioration in prediction accuracy. In the smoothing approach of Huang and Cheng,12 three factors affect the smoothness: ~a! the degree of the polynomial for each parameter direction; ~b! the number NUCLEAR TECHNOLOGY

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3. the quality of the data set.

IV.E.1. Definitions of the Smoothness Index Peng 55 has suggested that the local smoothness of the CHF ~or qcr ! LUTs can be simply presented by the 99

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average of the absolute value of the relative slope differences at each direction at a local grid point: vqcr ~Pi , Gj , X m ! ⫽

1 3

冋冨冉 ⫹ ⫹

冊冉冊冨冊冉冊冨冨冉冊冉冊冨册冨冉 1 ]qcr qS cr ]i

⫹

1 ]qcr qS cr ]i

⫺

1 ]qcr qS cr ]j

1 ]qcr qS cr ]m

⫹

⫹

⫺

⫺

1 ]qcr qS cr ]j

⫺

⫺

1 ]qcr qS cr ]m

⫺

, Pi , Gj , X m

~3! where ⫹ ⫽ forward slope ⫺ ⫽ backward slope qcr ⫽ CHF qS cr ⫽ average qcr at the corresponding interval. The smoothness for the whole LUT, referred to here as the smoothness index, can then be defined as the overall average of the local smoothness at all internal grid points: I⫺1 J⫺1 M⫺1

( ( ( vq

Vqcr ⫽

cr

~Pi , Gj , X m !

i⫽2 j⫽2 m⫽2

~I ⫺ 2!~J ⫺ 2!~M ⫺ 2!

.

~4!

We can also define the LUT smoothness as a function of P, G, or X, respectively. The definition for average smoothness as a function of P is

1. void fraction, which is used in predicting pressure drop, heat transfer, or flow regimes, and for which a large number of models and equations have been proposed, e.g., Collier and Thome 56 and Hetsroni.57 The void fraction is a unique function of the local pressure, mass flux, quality, and, in a heated system, heat flux. 2 2. the two-phase friction multiplier Ffo , used for calculating two-phase friction pressure drop. A large num2 ber of prediction methods for Ffo have been proposed, including several graphical-based predictions ~e.g., Col2 lier and Thome 56 !. The Ffo is a unique function of flow quality, pressure, flow, and possibly heat flux or wall superheat if the flow channel is heated. The effects of cross-section geometry, surface roughness, and equivalent diameter are considered less important parameters and can be included by using a correction factor similar to those in Table II.

3. heat transfer surface or boiling surface, used for identifying the correct heat transfer mode and HTC. The boiling surface is basically a 3-D boiling curve, as shown in Fig. 6, where the effect of thermodynamic quality is also shown. A boiling surface LUT can be viewed as a digitized boiling surface, and this could eliminate the need for heat transfer correlations or property subroutine. The postdryout table lookup method described is probably the most complex part of such a digitized heat transfer surface. The digitized boiling surface will thus provide a simple table lookup method for finding Tw ⫽ f ~q '', X, P, G ! or for finding q '' ⫽ f ~TW , X, P, G !. Effects of heat transfer configurations, flow direction, etc., can be accounted for by the use of correction factors similar to those in Table II.

VI. FINAL REMARKS

J⫺1 M⫺1

~5!

1. The LUT technique, although unsophisticated, has been extremely successful in predicting the CHF and film-boiling HTC during convective conditions.

The average smoothness of the CHF LUT as a function of G and X is defined in a similar manner. The smoothness for the film-boiling LUT can be defined similarly.

2. By applying fluid-to-fluid modeling to the LUT parameters, the CHF and film-boiling LUTs have been applied successfully to fluids other than water.

( ( vq

Vqcr ~Pi ! ⫽

cr

~Pi , Gj , X m !

j⫽2 m⫽2

~J ⫺ 2!~M ⫺ 2!

.

V. OTHER APPLICATIONS OF THE LUT APPROACH The LUT approach can be applied to any field of study where the dependent parameter is known to be a unique but highly complex function of several independent parameters. Provided a large empirical database is available, an LUT approach can be used as an alternative to a mathematical equation or model. Three examples where the LUT appears to have promise as an alternative to a mathematical model or equation are 100

3. LUTs are never cast in stone but will experience constant changes as the database is increased and analytical models ~for areas where data are scarce or unavailable, or more data become available! are improved. As LUTs can be very large, and are subject to change, they will be made available on the Internet at ^http:00www. magma.ca0;thermal&. 4. The LUT technique is expected to be a promising general method for predicting the void fraction, the twophase friction multiplier, and the convective boiling surface. NUCLEAR TECHNOLOGY

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Fig. 6. A 3-D representation of the boiling surface.

NOMENCLATURE

r

⫽ fluid density ~kg{m⫺3 !

Cp

⫽ heat capacity at constant pressure ~J{kg⫺1 {K⫺1 !

s

⫽ Stephan-Boltzmann constant ~W{m⫺1 {K⫺4 !

D

⫽ tube inside diameter ~m!

2 Ffo

⫽ two-phase friction multiplier

G

⫺2 {s⫺1 !

v

⫽ local smoothness

V

⫽ smoothing index

⫽ mass flux ~kg{m

~J{kg⫺1 !

H

⫽ enthalpy

Hfg

⫽ heat of evaporation ⫽ Hg ⫺ Hf ~J{kg⫺1 !

h

⫽ HTC ~W{m⫺2 {K⫺1 ! ~W{m⫺2 {K⫺1 !

Dimensionless Groups Pr

⫽ Prandtl number ⫽ Cp{m{k⫺1

Re

⫽ Reynolds number ⫽ G{D{m⫺1

hN

⫽ average HTC

J

⫽ axial temperature distribution index

k

⫽ thermal conductivity ~W{m⫺1 {K⫺1 !

Subscripts

P

⫽ pressure ~Pa ⫽ N{m⫺2, bar ⫽ 10 5 N{m⫺2 !

avg

⫽ average

q

⫽ surface heat flux ~kW{m⫺2 !

bulk

⫽ at bulk-fluid conditions

T

⫽ absolute temperature ~K!

DT

⫽ temperature difference ⫽ Tw ⫺ T ~K!

X

⫽ thermodynamic quality ⫽ ~H ⫺ Hf !0Hfg

DFFB ⫽ at dispersed flow film boiling

Greek a

⫽ void fraction

«

⫽ emissivity

m

⫽ dynamic viscosity ~N{s{m

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⫺2

⫽

kg{m⫺1 {s⫺1 !

OCT. 2005

do

⫽ dryout

e

⫽ equilibrium conditions

exp

⫽ experimental

f

⫽ saturated liquid

g

⫽ saturated vapor

h

⫽ HTC

hom

⫽ homogeneous 101

Groeneveld et al.


IAFB ⫽ at inverted annular flow film boiling l

⫽ liquid

ln

⫽ natural logarithm

max

⫽ maximum

mfb

⫽ minimum film boiling

model ⫽ predicted by model pred ⫽ predicted rad

⫽ radiation

sat

⫽ saturation

7. N. ZUBER, “Hydrodynamic Aspects of Boiling Heat Transfer,” AECU-4439, Atomic Energy Commission ~1959!. 8. P. GRIFFITH, J. F. PEARSON, and R. J. LEPKOWSKI, “Critical Heat Flux During a Loss-of-Coolant Accident,” Nucl. Safety, 18, 3, 298 ~1977!. 9. H. J. IVEY and D. J. MORRIS, “On the Relevance of the Vapour-Liquid-Exchange Mechanism for Subcooled Boiling Heat Transfer at High Pressures,” AEEW-R-137, United Kingdom Atomic Energy Authority Research Group ~1962!.

table ⫽ LUT value v

⫽ evaluated at vapor conditions

vf

⫽ vapor-film temperature

w

⫽ wall conditions ACKNOWLEDGMENTS

The development of the present CHF and film-boiling LUTs has been accomplished over a period of more than 25 yr. The following organizations have contributed to the development of the present and previous versions of these tables: AECL, National Sciences and Engineering Research Council of Canada, CANDU Owners Group, Inc.; Commissariat à l’Energie Atomique; IPPE; University of Ottawa; International Atomic Energy Agency ~IAEA! ~Ref. 58!; Atlantic Nuclear Services Limited; and Electric Power Research Institute.

REFERENCES 1. W. H. McADAMS, W. E. KENNEL, C. S. MINDEN, R. CARL, P. M. PICORNELL, and J. E. DEW, “Heat Transfer at High Rates to Water with Surface Boiling,” Ind. Eng. Chem., 41, 9, 1945 ~1949!. 2. D. C. GROENEVELD, “An Investigation of Heat Transfer in the Liquid Deficient Regime,” AECL-3281, Atomic Energy of Canada Limited ~1969!. 3. V. E. DOROSHCHUK, L. L. LEVITAN, and F. P. LANTZMAN, “Investigation into Burnout in Uniformly Heated Tubes,” 75-WA0HT-22, American Society of Mechanical Engineers ~1975!. 4. M. A. GOTOVSKY and M. A. KVETNY, “Some Problems of Look-Up Tables Method Usage for CHF Determination,” Proc. 8th Int. Conf. Nuclear Engineering (ICONE-8), Baltimore, Maryland, April 2– 6, 2000. 5. I. L. PIORO, D. C. GROENEVELD, S. C. CHENG, S. DOERFFER, A. Z. VASIC, and Y. V. ANTOSHKO, “Comparison of CHF Measurements in R-134a Cooled Tubes and the Water CHF Look-Up Table,” Int. J. Heat Mass Transfer, 44, 73 ~2001!. 102

6. D. C. GROENEVELD, S. C. CHENG, and T. DOAN, “1986 AECL-UO Critical Heat Flux Look-Up Table,” Heat Transfer Eng., 7, 46 ~1986!.

10. D. D. HALL and I. MUDAWAR, “Critical Heat-Flux ~CHF! for Water-Flow in Tubes—II—Subcooled CHF Correlations,” Int. J. Heat Mass Transfer, 43, 2605 ~2000!. 11. Y. KATTO, “A Prediction Model of Subcooled Water Flow Boiling CHF for Pressure in the Range 0.1–20 MPa,” Int. J. Heat Mass Transfer, 35, 5, 1115 ~1992!. 12. X. C. HUANG and S. C. CHENG, “Simple Method for Smoothing Multidimensional Experimental Data with Application to the CHF and Postdryout Look-Up Tables,” Numerical Heat Transfer, Part B, 26, 425 ~1994!. 13. D. C. GROENEVELD, L. K. H. LEUNG, B. P. KIAMEH, and S. C. CHENG, “A Universal Method for Predicting Critical Heat Flux for Aqueous and Non-Aqueous Fluids in Forced Convective Boiling,” Proc. HTFS Research Symp., Edinburgh, United Kingdom, September 1986. 14. D. C. GROENEVELD, S. S. DOERFFER, R. M. TAIN, N. HAMMOUDA, and S. C. CHENG, “Fluid-To-Fluid Modelling of the Critical Heat Flux and Post-Dryout Heat Transfer,” Proc. 4th World Congress Experimental Heat Transfer, Fluid Mechanics and Thermodynamics, Brussels, Belgium, June 2– 6, 1997. 15. T. H. CHUN, D. H. HWANG, W. P. BAEK, and S. H. CHANG, “Assessment of the CHF Look-Up Table Method for Bundle CHF Predictions with a Subchannel Code,” Proc. 4th Int. Seminar on Subchannel Analysis, Tokyo, Japan, September 25–26, 1997. 16. V. P. BOBKOV, P. L. KIRILLOV, I. P. SMOGALEV, and V. N. VINOGRADOV, “Look-Up Table Developing Methods for Critical Heat Flux in Rod Bundles,” Proc. 8th Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-8), Kyoto, Japan, September 30–October 4, 1997. 17. M. LEE, “A Critical Heat Flux Approach for Square Bundles Using the 1995 Groeneveld CHF Table and Bundle Data of Heat Transfer Research Facility,” Nucl. Eng. Des., 197, 357 ~2000!. 18. T. H. HWANG, Y. J. YOO, and S. K. JI, “Assessment of the CHF Look-Up Table Method for SMART Core Conditions,” Proc. 2001 Spring Mtg. Korean Nuclear Society, Cheju, Korea, May 24–25, 2001. NUCLEAR TECHNOLOGY

VOL. 152

OCT. 2005

Groeneveld et al.

19. D. C. GROENEVELD, L. K. H. LEUNG, N. AKSAN, A. BADULESCU, J. CLEVELAND, W. P. BAEK, M. K. CHUNG, F. D’AURIA, X. CHENG, P. L. KIRILLOV, and J. MACEK, “A General Method of Predicting Critical Heat Flux in Advanced Water-Cooled Reactors,” Proc. 9th Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-9), San Francisco, California, October 3–8, 1999, American Nuclear Society ~1999! ~CD-ROM!. 20. D. C. GROENEVELD, K. JOOBER, S. DOERFFER, W. WONG, L. K. H. LEUNG, and S. C. CHENG, “The Effect of Fuel Subchannel Geometry on CHF,” Proc. 5th Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-5), Salt Lake City, Utah, Vol. 2, p. 683, September 21–24, 1992, American Nuclear Society ~1992!. 21. W. P. BAEK, H. C. KIM, and S. H. CHANG, “An Independent Assessment of Groeneveld et al.’s 1995 CHF Look-Up Table,” Nucl. Eng. Des., 178, 331 ~1997!. 22. D. C. GROENEVELD, L. K. H. LEUNG, P. L. KIRILLOV, V. P. BOBKOV, I. P. SMOGALEV, V. N. VINOGRADOV, X. C. HUANG, and E. ROYER, “The 1995 Look-Up Table for Critical Heat Flux in Tubes,” Nucl. Eng. Des., 163, 1 ~1996!. 23. R. A. SMITH, “Boiling Inside Tubes: Critical Heat Flux for Upward Flow in Uniformly Heated Tubes,” ESDU Data Item 86032, Engineering Science Data Unit International Ltd., London ~1986!. 24. B. BESTION, “The Physical Closure Laws in the CATHARE Code,” Nucl. Eng. Des., 124, 229 ~1990!. 25. G. ULRYCH, “CHF Table Applications in KWV PWR Design,” Proc. Int. Workshop CHF Fundamentals—CHF Table Improvements, Braunschweig, Germany, March 3–5, 1993. 26. W. L. WEAVER, R. A. RIEMKE, R. J. WAGNER, and G. W. JOHNSON, “The RELAP50MOD3 Code for PWR Safety Analysis,” Proc. 4th Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-4), Karlsruhe, Germany, October 10– 13, 1989. 27. S. N. AKSAN, F. D’AURIA, and V. FALUOMI, “A Comparison and Assessment of Some CHF Prediction Models Used in Thermalhydraulic Systems Codes,” IAEA-RC-574, International Atomic Energy Agency ~Sep. 5–8, 1995!. 28. V. FALUOMI and S. N. AKSAN, “Analysis and Assessment of Some Selected CHF Models as Used in Relap50Mod3 Code,” Proc. 5th Int. Conf. Nuclear Engineering (ICONE-5), Nice, France, May 26–30, 1997. 29. L. BIASI, G. C. CLERICI, S. GARRIBA, R. SALA, and A. TOZZI, “Studies on Burnout, Part 3,” Energ. Nucl., 14, 530 ~1967!. 30. Y. KATTO and H. OHNO, “An Improved Version of the Generalized Correlation of Critical Heat Flux for the Forced Convective Boiling in Vertical Uniformly Heated Tubes,” Int. J. Heat Mass Transfer, 27, 9, 1641 ~1984!. NUCLEAR TECHNOLOGY

VOL. 152

OCT. 2005


31. J. WEISMAN and S. H. YING, “A Theoretical Based Critical Heat Flux Prediction for Rod Bundles,” Nucl. Eng. Des., 85, 239 ~1985!. 32. W. LIN, C. H. LEE, and B. S. PEI, “An Improved Theoretical Critical Heat Flux Model for Low Quality Flow,” Nucl. Technol., 88, 294 ~1989!. 33. M. B. CARVER, J. C. KITELEY, R. Q. N. ZHOU, and S. V. JUNOP, “Validation of ASSERT Subchannel Code for Standard and Non-Standard Geometries,” Proc. 2nd Int. Seminar Subchannel Analysis, ARD-TD-454P, Electric Power Research Institute ~1993!. 34. S. CEVOLANI, “Description and Validation of ANTEO, an Optimized PC Code for the Thermalhydraulic Analysis of Fuel Element Bundles,” Proc. 2nd Regional Mtg. Nuclear Energy in Central Europe, Portoroz, Slovenia, September 11– 14, 1995. 35. D. C. GROENEVELD and C. W. SNOEK, “A Comprehensive Examination Heat Transfer Correlations Suitable for Reactor Safety Analysis,” Multiphase Science and Technology, Chap. 3, p. 181, G. F. HEWITT et al., Eds., Begell House, New York ~1986!. 36. D. C. GROENEVELD, “A Review of Inverted Annular Film Boiling,” Post Dryout Heat Transfer, Chap. 5, p. 327, G. F. HEWITT et al., Eds., Hemisphere Publishing Corporation, CRC Press, New York ~1992!. 37. D. C. GROENEVELD and L. K. H. LEUNG, “Tabular Approach to Predicting Critical Heat Flux and Post-Dryout Heat Transfer,” Proc. 4th Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-4), Karlsruhe, Germany, October 10–13, 1989. 38. L. K. H. LEUNG, N. HAMMOUDA, and D. C. GROENEVELD, “Development of a Look-Up Table for Film-Boiling Heat Transfer Covering Wide Range of Flow Conditions,” Proc. 5th Int. Conf. Simulation Methods in Nuclear Engineering, Montreal, Canada, September 8–11, 1996. 39. L. K. H. LEUNG, N. HAMMOUDA, and D. C. GROENEVELD, “A Look-Up Table for Film-Boiling Heat Transfer Coefficients in Tubes with Vertical Upward Flow,” Proc. 8th Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-8), Kyoto, Japan, September 30–October 4, 1997. 40. P. L. KIRILLOV, I. P. SMOGALEV, A. A. IVACSHKEVITCH, V. N. VINOGRADOV, M. O. SUDNITSINA, and T. V. MITROFANOVA, “The Look-Up Table for Heat Transfer Coefficient in Post-Dryout Region for Water Flowing in Tubes ~the 1996-Version!,” Preprint FEI-2525, Institute of Physics and Power Engineering, Obninsk, Russia ~1996!. 41. D. C. GROENEVELD, L. K. H. LEUNG, A. VASIC, Y. GUO, M. EL NAKLA, and S. C. CHENG, “An Improvement in Predicting Post-CHF Temperatures,” Proc. 22nd Canadian Nuclear Society Nuclear Simulation Symp., Ottawa, Canada, November 3–5, 2002. 42. A. Z. VASIC, S. C. CHENG, O. RENON, Y. J. GUO, and YU. ANTOSHKO, “Compilation and Assessment of 103

Groeneveld et al.


Post-Dryout Heat-Transfer Data Sets,” UO-MCG-TH-2000008, University of Ottawa ~Nov. 2000!.

1), Saratoga Springs, New York, October 5–8, 1980, U.S. Nuclear Regulatory Commission ~1980!.

43. A. A. BISHOP, R. O. SANDBERG, and L. S. TONG, “Forced Convection Heat Transfer at High Pressure After the Critical Heat Flux,” ASME-65-HT-31, American Society of Mechanical Engineers ~1965!.

53. D. C. GROENEVELD, L. K. H. LEUNG, J. ZHANG, S. C. CHENG, and A. VASIC, “Effect of Appendages on Film Boiling Heat Transfer,” Proc. 9th Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-9), San Francisco, California, October 3–8, 1999, American Nuclear Society ~1999! ~CD-ROM!.

44. N. A. BAILEY and D. H. LEE, “An Experimental and Analytical Study of Boiling Water at 2000 to 2600 psi, Part I: Dryout and Post-Dryout Heat Transfer,” AEEW-R 659, United Kingdom Atomic Energy Authority Research Group ~1969!. 45. N. HAMMOUDA, “Subcooled Film Boiling in NonAqueous Fluids,” PhD Thesis, University of Ottawa, Canada ~1995!. 46. D. C. GROENEVELD and G. G. J. DELORME, “ Prediction of Thermal Non-Equilibrium in the Post-Dryout Regime,” Nucl. Eng. Des., 36, 17 ~1976!. 47. M. M. SHAH and M. A. SIDDIQUI, “A General Correlation for Heat Transfer During Dispersed-Flow Film Boiling in Tubes,” Heat Transfer Eng., 21, 18 ~2000!. 48. Y. Z. CHEN and H. Y. CHEN, “A Tabular Method for Prediction of the Heat Transfer During Saturated Film Boiling of Water in a Vertical Tube,” Proc. 11th Int. Heat Transfer Conf., Seoul, Korea, August 23–28, 1998. 49. W. KÖHLER and D. HEIN, “Influence of the Wetting State of a Heated Surface on Heat Transfer and Pressure Loss in an Evaporator Tube,” NUREG0IA-0003, U.S. Nuclear Regulatory Commission ~1986!. 50. D. C. GROENEVELD, L. K. H. LEUNG, A. Z. VASIC, Y. J. GUO, and S. C. CHENG, “A Look-Up Table for FullyDeveloped Film Boiling Heat Transfer,” Nucl. Eng. Des., 225, 83 ~2003!. 51. Y. J. GUO, D. C. GROENEVELD, L. K. H. LEUNG, A. Z. VASIC, M. EL NAKLA, and S. C. CHENG, “ Prediction of Film Boiling Heat Transfer over a Wide Range of Conditions,” Proc. 10th Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-10), Seoul, Korea, October 5–9, 2003. 52. D. C. GROENEVELD and W. W. YOUSEF, “Spacing Devices for Nuclear Fuel Bundles: A Survey of Their Effect on CHF, Post-CHF Heat Transfer and Pressure Drop,” Proc. 1st Int. Topl. Mtg. Nuclear Reactor Thermal Hydraulics (NURETH-

104

54. S. W. PENG, R. REVELLIN, D. C. GROENEVELD, A. VASIC, D. SHANG, and S. C. CHENG, “Effects of Flow Obstacles on Film Boiling Heat Transfer,” Nucl. Eng. Des., 222, 89 ~2002!. 55. S. W. PENG, “On the Smoothness of CHF0PDO Look-Up Tables,” Internal Report, University of Ottawa, Canada ~2002! ~unpublished!. 56. J. G. COLLIER and J. THOME, Convective Boiling and Condensation, 3rd ed., McGraw-Hill, London ~1994!. 57. G. HETSRONI, Handbook of Multiphase Systems, Hemisphere0McGraw-Hill, New York ~1992!. 58. “Thermalhydraulic Relationships for Advanced WaterCooled Reactors,” IAEA-TECDOC-1203, International Atomic Energy Agency ~2001!. 59. D. C. GROENEVELD, “A General CHF Prediction Method for Water Suitable for Reactor Accident Analysis,” DRE0STT0 SETRE082-2-0DGR, Centre d’Etudes Nucléaires de Grenoble, Commissariat à l’Energie Atomique ~1982!. 60. P. L. KIRILLOV, V. P. BOBKOV, E. A. BOLTENKO, V. N. VINOGRADOV, I. B. KATAN, and I. P. SMOGALEV, “Look-Up Tables of Critical Heat Fluxes,” At. Energ., 71, 1, 18 ~1991!. 61. Y. L. WONG, D. C. GROENEVELD, and S. C. CHENG, “CHF Predictions in Horizontal Tubes,” Int. J. Multiphase Flow, 16, 123 ~1990!. 62. M. A. EL NAKLA, S. C. CHENG, and D. C. GROENEVELD, “Improvements to the Film Boiling Look-Up Table,” UO-MCG-TH-2003-001, University of Ottawa ~2003!.

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