the study of critical heat flux in upflow boiling vertical...

Research ArticleThe Study of Critical Heat Flux in Upflow Boiling VerticalRound Tube under High Pressure

Wei Liu 1 Jianqiang Shan 2 Shinian Peng 1 Guangming Jiang1 and Yu Liu1

1State Key Laboratory of Reactor System Design Technology Nuclear Power Institute of China Chengdu 610213 China2School of Nuclear Science and Technology Xirsquoan Jiaotong University Xirsquoan 710049 China

Correspondence should be addressed to Wei Liu liuwei0958126com

Received 20 February 2019 Revised 13 April 2019 Accepted 5 May 2019 Published 4 June 2019

Academic Editor Rafa Miro

Copyright copy 2019 Wei Liu et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The Critical Heat Flux (CHF) prediction under high pressure condition even close to the vicinity of the critical pressure of wateris an important issue Although there are many empirical CHF correlations most of them have covered the pressure under 15MPaIn this study based on the CHF experiment database of upflow boiling in vertical round tube from 15MPa to the vicinity of thecritical pressure of water the Katto Bowring Hall-Mudawar Alekseev correlations and Groeneveld LUT-2006 are comparativelystudied With an error analysis of the predicted CHF to the experiment database the prediction capability and the applicabilityof these correlations are evaluated and the parametric trends of CHF varying with pressure from 15MPa to critical pressure areproposed Simultaneously according to the characteristics of Departure from Nucleate Boiling (DNB) type CHF under highpressure condition the constitutive correlations ofWeisman amp Pei model are proposedThe prediction results of three entrainmentand deposition correlations of Kataoka Celata and Hewitt corresponding to the Dry-Out (DO) type CHF are analyzed Based onthe two improved models above a comprehensive CHF mechanistic model under high pressure condition combining the DNBand DO type CHF is established The verification based on the experiment database of upflow boiling in vertical round tube andthe parametric trends analysis of CHF varying with thermal-hydraulic and geometric parameters are carried out Findings of thisstudy have a positive effect on further development of CHF prediction method for universal CHF mechanism especially underhigh pressure region

1 Introduction

The accurate prediction of critical heat flux (CHF) in flowboiling is important in the design and safety analysis ofnuclear reactor The occurrence of CHF results in a sharpdegradation of the convective heat transfer between the fuelrod cladding and the reactor coolant which may result incladding failure

The supercritical water cooled reactor (SCWR) has highoperating pressure and temperature and during slidingpressure start-up procedure from subcritical pressure tosupercritical pressure the thermophysical properties andtransport properties of the coolant in the core would changegreatly [1] Thus the CHF prediction under high pressurecondition even close to the vicinity of the critical pressureof water is an important issue for SCWR

Although the CHF phenomenon has been extensivelyinvestigated over the last five decades knowledge of the phys-ical nature of CHF is still incomplete and the mechanisms ofboiling crisis are still not well understood

Methods for predicting CHF can be categorized as empir-ical correlations look-up tables and mechanistic modelsAccording to the statistics [2] the number of published CHFcorrelations for water-cooled round tubes has increased towell over 500 and there are also over 50CHFmodels availableBased on the difference of flow regime and heat transfercharacteristics on the occurrence of CHF the boiling crisiscan be generally divided into DNB (Departure fromNucleateBoiling) type and DO (Dry-Out) type [3]

Although there are many empirical CHF correlationsthere is no valid and accurate CHF correlation verified byexperiment database in the range from 15 MPa to the vicinity

HindawiScience and Technology of Nuclear InstallationsVolume 2019 Article ID 3695685 14 pageshttpsdoiorg10115520193695685

2 Science and Technology of Nuclear Installations

Table 1 CHF experiment database under high pressure region

Reference Time No of dataMcGill amp Sibbitt [17] 1951 9Epstein et al [18] 1956 90Ornatskii amp Kichigin [19] 1962 31Ornatskii [20] 1963 69Alekseev et al [21] 1964 508Bailey amp Lee [22] 1969 41Peskov et al [23] 1969 127Zenkevich et al [24] 1969 1298Zenkevich et al [25] 1971 152Zenkevich [26] 1974 192Belyakov et al [27] 1976 360Smolin et al [28] 1979 393Williams amp Beus [29] 1980 25Kirillov et al [30] 1984 506Groeneveld [31] 1985 8Yin et al [32] 1988 130Soderquist [33] 1994 412Mudawar amp Bowers [34] 1999 4Total 4355

of critical pressure in which the parametric trend of CHFvarying with pressure is also unknown

Furthermore different CHF mechanistic models usuallyare proposed for specific flow regime and one CHF modelis only effective in one flow regime resulting in a narrowprediction scope This cannot satisfy the prediction of CHFwhen different flow regimes appear successively in the samechannel

In this study based on the CHF experiment databaseof upflow boiling in vertical round tube from 15MPa to thevicinity of the critical pressure of water the prediction capa-bility and the applicability of Katto [4] Bowring [5] Hall-Mudawar [6] Alekseev [7] correlations and LUT-2006 [8]will be evaluated The parametric trend of CHF varying withpressure from 15MPa to the vicinity of critical pressurewill bediscussed Simultaneously combining the DNB and DO typeCHF mechanism a comprehensive CHF model under highpressure conditionwill be established Finally the verificationof the CHF mechanistic model based on the experimentdatabase and the parametric trends analysis of CHF varyingwith thermal-hydraulic and geometric parameters will becarried out

2 The Experiment Database

Based on the existing CHF database of upflow boiling verticalround tube the evaluation and screening of experimentdatabase are carried out As a result 18 different sets of CHFexperiment database were obtained from 1951 to 1999 in totalof 4355 data points are applied in this study The databasesources and distribution are shown in Table 1 among which2735 experiment data points belong to the DNB type CHFof subcooled bubbly flow and 1620 experiment data points

belong to the DO type CHF of saturated annular flow Table 2shows the experimental ranges of database

3 The Comparative Study of CHF Correlations

31 CHF Correlations Through the comparison and analysisof dozens of round tube CHF correlations this study hasselected the Katto [4] Bowring [5] Hall-Mudawar [6]Alekseev [7] correlations and LUT-2006 [8] which all coverthe high-pressure region for further analysis The parameterrange of each correlation is shown in Table 3

32 Comparative Analysis For analysis the error E meanerror ME mean absolute error MAE and root mean squareerror RMS are defined as follows

Error E

119864 = 119902CHFpre minus 119902CHFexp119902CHFexp(1)

Mean errorME

119872119864 = 1119873 sum 119902CHFpre minus 119902CHFexp119902CHFexptimes 100 (2)

Mean absolute errorMAE

119872119860119864 = 1119873 sum 100381610038161003816100381610038161003816100381610038161003816119902CHFpre minus 119902CHFexp119902CHFexp

100381610038161003816100381610038161003816100381610038161003816 times 100 (3)

Root mean square error RMS

119877119872119878 = radic 1119873 sum(119902CHFpre minus 119902CHFexp119902CHFexp)2 times 100 (4)

Science and Technology of Nuclear Installations 3

Table 2 Experimental ranges of database

Variable Δℎ119894119899(kJkg) G (kgm2s) P (MPa) D (m) L (m) 119909e

The DNB type CHFMaximum value 1811 7530 2120 0016 7 054Minimum value 36 256 1517 00055 00254 -241

The DO type CHFMaximum value 1549 6578 2010 0016 20 097Minimum value 36 156 1517 00055 079 002

Table 3 Parameter ranges of CHF correlations

Variable Katto Bowring Hall-Mudawar Alekseev LUT-2006P (MPa) 05sim20 02sim190 1sim20 981sim1962 01sim20G (kgm2s) 105sim8800 136sim18600 300sim30000 1000sim5000 0sim8000119909e - - -100sim-005 0sim04 05sim1D (m) 0001sim0038 0002sim0045 000025sim0015 0004sim0012 0002sim0016L (m) 001sim88 015sim37 03sim8 ⩾02 -

Table 4 Prediction error of each CHF correlation

CHF correlations ME MAE RMSP gt 15 MPa P gt 19 MPa P gt 15 MPa P gt 19 MPa P gt 15 MPa P gt 19 MPa

Katto 142 67 156 80 234 141Bowring -142 -166 158 185 204 232Hall-Mudawar -83 -61 94 73 128 98Alekseev 01 07 63 86 96 90LUT-2006 13 11 44 55 79 84

where 119902CHFpre is the predictive value of CHF while 119902CHFexpis the experimental value of CHF

321 Prediction Error Analysis In evaluation of the corre-lations and LUT-2006 accuracy the Heat Balance Method(HBM) has been used The prediction errors of KattoBowring Hall-Mudawar Alekseev correlations and LUT-2006 are shown in Table 4 It demonstrates that the predictionerrors of LUT-2006 and Alekseev correlation are relativelysmaller in the high pressure region above 15MPa while theprediction errors of Katto and Bowring correlation are largerAlthough the Hall-Mudawar correlation is only applicablefor subcooled boiling its prediction error is also not largewhich belongs to the middle level between the LUT-2006 andAlekseev and Katto and Bowring correlations

The prediction errors of Katto Alekseev correlation andLUT-2006 varying with pressure are shown in Figure 1

It indicates that in the range of 19MPa to 203MPa theKatto correlation overpredicts the experimental value butwhen the pressure is higher than 203MPa the predictivevalue and the experimental value become closer

Although the RMS errors of the predictive value and theexperimental value for Alekseev correlation and LUT-2006are smaller in the range of 203MPa to 213MPa these twocorrelations underpredict the experimental values

When the pressure is higher than 213MPa to the vicinityof critical pressure the prediction capabilities of the three

correlations could not be evaluated due to the lack of CHFexperiment database

322 Parametric Trend Analysis In the vicinity of criticalpressure the physical properties and heat transfer character-istics of water have greatly changed consequently the CHFhas become more sensitive to pressure For simplicity Fig-ure 2 shows the predictive value of different CHF correlationvarying with pressure when other parametersGℎ119894119899D andL are fixed constant

Combined with the error comparison analysis in Sec-tion 321 the parametric trend of CHF in high pressureregion can be summarized as follows (identified by the reddotted line on Figure 2) in the range of 19MPa to 203MPait is close to the prediction trend of LUT-2006 when thepressure is higher than 203MPa it should be closer to theprediction trend of Katto correlation and when approachingcritical pressure the CHF quickly goes down to zero

4 The Development of CHFMechanistic Model

41 DNB Type CHF Mechanistic Model Weisman amp Pei [9]developed a phenomenological model for CHF at low voidfractions or subcooled conditions The model is generallyapplicable in the bubbly flow regime where it is assumedthat a bubbly layer exists adjacent to the heater surface At


190 195 200 205 210 215

minus08

minus06

minus04

minus02

00

02

04

06

08

P (MPa) Katto Alekseev LUT-2006

E

Figure 1 Prediction error of Katto Alekseev and LUT-2006 varying with pressure

190 195 200 205 210 215 220 2250

100

200

300

400

500

600

700

800

900

1000

Katto Bowring Alekseev

Hall-Mudawar LUT-2006

qCH

Fpre

(kW

m2 )

P (MPa)

Figure 2 q119862119867119865 as a function of pressure ( G=2000 kgm2sℎ119894119899=450 kJkg D=0013m L=3m)

high heat fluxes the local vapour generation rate becomes sohigh that it prevents the liquid from reaching and cooling theheated surface leading to CHF as shown in Figure 3

Weisman amp Pei utilized a number of assumptions in thedevelopment of the model and obtained

11990210158401015840119863119873119861ℎ1198911198921198661015840 = (1199092 minus 1199091)(ℎ119891 minus ℎ119897119889ℎ119897 minus ℎ119897119889 ) (5)

The quantity Grsquo represents the total mass velocity into thebubbly layer due to turbulent interchange at the edge of thebubbly layer

1198661015840 = 120595119868119887119866 (6)

The parameter I119887 represents the turbulent intensity at thebubbly layercore interface

119868119887 = 046211989606Reminus01 (119863119887119889 )06 [1 + 119886 (120588119897 minus 120588V)120588V ] (7)


dz

q

tube wall

bubblylayer

bulk flow

R-SS

Ｇ2

Ｇ2+Ｇ2

Ｒ2

Ｒ2+Ｒ2

Ｇ1

Ｇ4

Ｇ3

Ｇ1+Ｇ1

Ｒ1

Ｒ1+Ｒ1

Figure 3 Schematic diagram of Weisman amp Pei model

The parameters k (= 24) and a (which depends on themass velocity) were empirically determined by fitting a largenumber of uniform heat flux experiment data Therefore thevalidity of the Weisman amp Pei model is limited by the rangesof the databases fromwhich these empirical coefficients wereobtained

In this study based on the experiment database of upflowboiling in vertical round tube under high pressure conditionthe new parameter k=18 is obtained and parameter a is asso-ciated with the velocity change and pressure effect (through120588V120588119897)

The final expression is as follows

119886

=

123 minus 125119906 + 547 times (120588V120588119897 )23 119906 lt 12119898119904

minus015 times (3 minus 119906) + 547 times (120588V120588119897 )23 12119898119904 le 119906 lt 3119898119904

547 times (120588V120588119897 )23 times (1199063)03 119906 ge 3119898119904

(8)

42 DO Type CHF Mechanistic Model The majority of theavailable annular flow DO models are based on that ofWhalley et al [10] which is a three-field model representingtwo-phase interactions between vapour liquid film andentrained droplets as shown in Figure 4The difference fromeach model is in the constitutive correlations representingthe mechanisms of entrainment and deposition In fact itis these correlations that distinguish one phenomenologicalDO model from another since the basic conservation equa-tions are the same for any DO model in the annular flowregime

In this study three different entrainment and depositioncorrelations of Kataoka Celata andHewitt are compared andanalyzed

The droplet deposition rate is calculated from

119863 = 119896119862 (9)

where C is the concentration of droplets in the vapour coreand k is the deposition mass transfer coefficient

(1) Kataoka Correlation Kataoka et al [11] developed correla-tions for entrainment rate covering both entrance region and


tube wall

dryout

liquid film

liquid droplet

R

vapour bubble

vaporization rate

entrainment rate

deposition rate

single-phase liquid

Figure 4 Schematic diagram of DO model

equilibrium region from a simplemodel in collaborationwithdata

The deposition mass transfer coefficient k is determinedby Paleev amp Filippovich correlation [12]

119896119895119892 = 0022Reminus025119892 ( 119862120588119891)minus026 (120588119892120588119891)

026

(10)

The entrainment fraction is calculated by Ishiiamp Mishima [13]correlation which was developed based on the mechanisticmodel of shearing-off of roll wave crest by a streaming gas

(2) Celata Correlation In developing of Celata et alrsquos [14] DOtypeCHFmodel liquid film flow rate is obtained by a balanceof liquid entrainment and droplet deposition

The droplets deposition rate is calculated with the equa-tion given by Kataoka amp Ishii [15]

119889119863120583119897 = 022Re074119897 (120583V120583119897 )026 119864074 (11)

The droplets entrainment rate is calculated considering thecontribution of two different mechanisms of droplets forma-tion breakup of disturbance waves (119864119908) and boiling in theliquid film (119864119861) 119864 = 119864119908 + 119864119861 (12)

(3) Hewitt Correlation Hewitt et al [16] derived improvedmodels for deposition and entrainment in annular flowThe new models successfully predicted a wide range ofequilibrium and non-equilibrium data

The correlation for the deposition rate coefficient is asfollows

119896 = 018radic 120590120588V119889 119862120588V le 030083radic 120590120588V119889 ( 119862120588V)

minus065 119862120588V gt 03 (13)

The entrainment correlation is

119864119866V

= 575 times 10minus5 [(119866119871119865 minus 119866119871119865119862)2 1198891205881198971205901205882V ]

0316 119866119871119865 gt 1198661198711198651198620 119866119871119865 le 119866119871119865119862

(14)

where 119866119871119865119862 is the critical film mass velocity for the onset ofentrainment

43 The Comprehensive CHF Mechanistic Model Accordingto the two improved CHF mechanistic model types above


Start

Input data pGhsub DL

Calculate physical properties

Initial guess q

Calculate x and

Use DNB model

CHF = q

Use DO model

Print output

Stop

Use DNB model

YES

NO

For node I

I=I+1

Last node

I=I+1

GF0lt1

x gt 0

YES

YES

YES

YES

YES

YES

NO

NO

NO

NO

NO

NO

Last node

lt 06

lt 07

q lt q

q lt q

qq minus 1

lt 1lowast10minus4

|GF0| lt 1

Figure 5 Flow chart of detailed calculation

a comprehensive CHF mechanistic model under high pres-sure condition combining the DNB and DO type CHF isestablished The detailed calculation process of the presentmechanistic model is shown in Figure 5

The void fraction 120572ann is the transition point of bubbleflow and annular flow When 120572 lt 120572ann the flow regime isbubble flow and the CHF is calculated by the DNB modelWhen 120572 gt 120572ann the flow regime is annular flow and the CHFcalculation is divided into two situations (1) if 120572 lt 120572DNBthe DNB model is still used (2) if no DNB occurrence or120572 gt 120572DNB then the DO model is used to calculate the flowrate of liquid film

44 Results Analysis

441 Prediction Error Analysis In evaluation of the presentmechanistic model accuracy the Heat Balance Method(HBM) has been used Table 5 shows the prediction errorof the present mechanistic model for the whole experimentdatabase and the DNB type CHF respectively Table 6 showsthe prediction results of three different entrainment anddeposition correlations

It demonstrates that the present mechanistic model isapplicable for theCHFprediction of upflowboiling in verticalround tube under high pressure conditions and the RMS


Table 5 Prediction error of the present mechanistic model

Data points Maximum error Minimum error The fraction of error within 10 The fraction of error within 20 ME RMSThe whole experiment database

4355 442 -389 822 960 05 83The DNB type CHF

2735 445 -460 858 964 06 70

Table 6 Prediction results of three different entrainment and deposition correlations

Datapoints

Differentcorrelation

Maximumerror

Minimumerror

The fractionof error

within 10


within 20ME RMS

1620Kataoka 347 -389 721 945 04 99Celata 403 -613 362 490 279 401Hewitt 144 -861 29 158 406 450

qCH

Fpre

(kW

m2 )

0 4000 8000 12000 16000 20000 24000 28000 32000 360000

4000

8000

12000

16000

20000

24000

28000

32000

36000

-20

20

qCHFexp (kWm2 )

Figure 6 Predicted CHF as a function of measured CHF

of the DNB model is the lowest For the DO type CHFprediction the results of the Kataoka correlation are the best

The comparison of predicted CHF and measured CHF isshown in Figure 6

Figure 7 shows the prediction results of the presentmechanistic model Katto correlation and LUT-2006 Itindicates that the present mechanistic model is more accuratethan the other two predictions especially when pressure ishigher than 19MPa

442 Continuity of the Developed Model The significantcharacteristic of the present mechanistic model is that for acertain flow regime it can automatically judge and select theparticular model to calculate the CHF value

Figures 8 and 9 show the continuous variation of DNBand DO type CHF predicted by the present mechanisticmodel with mass velocity and inlet subcooled enthalpyrespectively It indicates that the DO type CHF occurs atlow mass velocity and low inlet subcooled enthalpy With

the increase of mass velocity and inlet subcooled enthalpythe DNB type CHF occurs In this study the DNB and DOtype CHF can be smoothly joined together with the presentmechanistic model

443 Parametric Trend Analysis The parametric trends ofthe CHF vary according to the thermal-hydraulics conditionsdetermined by the combination of the various ranges of pres-sure mass velocity inlet subcooled enthalpy and geometricparameters

The CHF predicted by the present mechanistic model asa function of independent variables pressure mass velocityinlet subcooled enthalpy tube diameter and tube length areshown in Figures 10ndash14 respectively It indicates that thepredicted CHF decreases with the increase of pressureWhenapproaching the critical pressure CHF rapidly drops to zeroThepredictedCHF almost linearly increaseswith the increaseof mass velocity and inlet subcooled enthalpy As for thegeometric parameters the predicted CHF increases with the


0

5

10

15

20

25

=19MPa=15MPa

RMS

()

Katto LUT-2006 The present model

Figure 7 RMS histograms of each method

0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800

P=20MPaΔh in =650kJkgL=2mD=0008m

Dry-Out DNB

G (kgm2 s)

qCH

Fpre

(kW

m2 )

Figure 8 Continuous variation of CHF with mass velocity

increase of tube diameter and decreases with the increaseof tube length While beyond the threshold of D or L theinfluence of the D and L is small

5 Conclusion

In this study based on the CHF experiment database ofupflow boiling in vertical round tube from 15MPa to thevicinity of the critical pressure of water five CHF cor-relations under high pressure conditions are selected andthe prediction results have been comparatively analyzed

Simultaneously a comprehensive CHF mechanistic modelunder high pressure condition combined the DNB and DOtypeCHFhas been establishedThe verification of the presentmechanistic model based on the experiment database andthe parametric trends analysis of CHF varying with thermal-hydraulic and geometric parameters have been carried outThe conclusions can be briefly summarized as follows

(1) In the high pressure range of 15MPa to the vicinity ofcritical pressure the Alekseev correlation and LUT-2006 are recommended for their smaller predictionerror to predict CHF in round tube


50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500

P=19MPaG=4500kgm2 sL=2mD=0008m

Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )

Figure 9 Continuous variation of CHF with inlet subcooled enthalpy

15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600

=150kJkg=300kJkg=600kJkg

P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ

Figure 10 CHF as a function of pressure (G=1000kgm2s)

(2) The parametric trend of CHF varying with pressurein the range from 15 MPa to the vicinity of criti-cal pressure is obtained In the transition point of203MPa the CHF parametric trend varies from theLUT-2006 curve to the Katto correlation curve andwhen approaching critical pressure the CHF quicklygoes down to zero

(3) The present mechanistic model is applicable for theCHF prediction of upflow boiling in vertical roundtube under high pressure conditions and the fraction

of error within plusmn20 is 960 of total data points Forthe DO type CHF prediction the prediction resultsof Kataoka correlation are more accurate than Celataand Hewitt methods and the whole RMS is 99

(4) For a specific flow regime the present mechanisticmodel can automatically judge and select the partic-ular model to calculate the CHF value which cansmoothly join the DNB and DO type CHF

(5) The parametric trends of predicted CHF varyingwith thermal-hydraulic and geometric parameters are


0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000

P=17MPaP=19MPaP=21MPa

G (kgm2 s)

qCH

Fpre

(kW

m2 )

Figure 11 CHF as a function of mass velocity (Δℎin=500kJkg)

minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000

G=1000kgm2sG=6000kgm2sG=8000kgm2s

qCH

Fpre

(kW

m2 )

Δh in (kJkg)

Figure 12 CHF as a function of inlet subcooled enthalpy (P=22MPa)

quite similar to those for the conventional modelswhich are consistent with the physical mechanismand experimental phenomena

Nomenclature

119886 Empirical coefficient119862 Concentration of droplets (kgm3)119889 Hydraulic diameter (m)

119863 Tube diameter (m)droplet deposition rate(kgm2s)119863119887 Vapour bubble diameter (m)119864 Entrainment rate (kgm2s)119864119908 Wave droplet entrainment rate (kgm2s)119864119861 Boiling droplet entrainment rate (kgm2s)119866 Mass velocity (kgm2s)ℎ Enthalpy (kJkg)ℎ119891119892 Latent heat of vaporization (kJkg)


0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ

Figure 13 CHF as a function of tube diameter (P=17MPa G=1000kgm2s L=1m)

00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )

Figure 14 CHF as a function of tube length (P=21MPa Δℎin=100kJkg D=0008m)

ℎ119897119889 Enthalpy of liquid at the point of bubbledetachment (kJkg)119895 Volumetric flux of superficial velocity(ms)119896 Deposition mass transfer coefficient (ms)119871 Tube length (m)119875 Pressure (MPa)119902 Heat flux (kWm2)

Re Reynolds number

119906 Velocity (ms)119909 Steam quality

Greek Symbols

120572 Void fraction120588 Density (kgm3)120590 Surface tension (Nm)120583 Dynamic viscosity (kgsm)


Subscripts

119886119899119899 Annular119890 Equilibrium119891 Fluid119892 Gas119901119903119890 Predictive value119890119909119901 Experimental value119894119899 Inlet conditions119904119906119887 Subcooled conditionsV Vapour119897 Liquid119871119865 Liquid film119871119865119862 Critical liquid film mass velocity

Data Availability

The CHF data in upflow boiling vertical round tube underhigh pressure supporting this manuscript 3695685 are frompreviously reported studies and datasets which have beencited at relevant places within the text as references Theprocessed data are available from the published journal articleor reports

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

The authors would like to express their appreciation toNuclear Power Institute of China for their financial support

References

[1] J Shan J Pan andY Jiang ldquoThermal considerationofCANDU-SCWR sliding pressure startup through subchannel analysisrdquoNuclear Engineering and Design vol 240 no 5 pp 1005ndash10122010

[2] D C Groeneveld ldquoThe critical heat flux story [C] The 15thInternational Topical Meeting on Nuclear Reactor ThermalHydraulicsrdquo Pisa Italy 2013

[3] L S Tong ldquoHeat transfer in water-cooled nuclear reactorsrdquoNuclear Engineering and Design vol 6 no 4 pp 301ndash324 1967

[4] Y Katto and H Ohno ldquoAn improved version of the generalizedcorrelation of critical heat flux for the forced convective boilingin uniformly heated vertical tubesrdquo International Journal ofHeatand Mass Transfer vol 27 no 9 pp 1641ndash1648 1984

[5] R W Bowring A Simple but Accurate Round Tube Uni-form Heat Flux Dryout Correlation over Pressure Range 07-17MNm2(100-2500psia) AEEW-R-789 UK Atomic EnergyAuthority Winfrith England UK 1972

[6] D D Hall and I Mudawar ldquoCritical heat flux for water flow intubes-II Subcooled CHF correlationsrdquo International Journal ofHeat and Mass Transfer vol 43 no 14 pp 2605ndash2640 2000

[7] GVAlekseev andBA Zenkevich ldquoBurn-out heat fluxes underforced water flowrdquo in Proceedings of the Third United NationsInternational Conference on the Peaceful Uses of Atomic EnergyMay 1964

[8] D C Groeneveld J Q Shan A Z Vasic et al ldquoThe 2006 CHFlook-up tablerdquo Nuclear Engineering and Design vol 237 no 15-17 pp 1909ndash1922 2007

[9] JWeisman and B S Pei ldquoPrediction of critical heat flux in flowboiling at low qualitiesrdquo International Journal of Heat and MassTransfer vol 26 no 10 pp 1463ndash1477 1983

[10] P B Whalley P Hutchinson and G F Hewitt ldquoThe calculationof critical heat flux in forced convection boilingrdquo in Proceedingsof the 5th International Heat Transfer Conference Tokyo Japan1974

[11] I Kataoka M Ishii and A Nakayama ldquoEntrainment anddesposition rates of droplets in annular two-phase flowrdquo Inter-national Journal of Heat and Mass Transfer vol 43 no 9 pp1573ndash1589 2000

[12] I I Paleev and B S Filippovich ldquoPhenomena of liquid transferin two-phase dispersed annular flowrdquo International Journal ofHeat and Mass Transfer vol 9 no 10 pp 1089ndash1093 1966

[13] M Ishii and K Mishima ldquoDroplet entrainment correlation inannular two-phase flowrdquo International Journal of Heat andMassTransfer vol 32 no 10 pp 1835ndash1846 1989

[14] G P Celata K Mishima and G Zummo ldquoCritical heat fluxprediction for saturated flow boiling of water in vertical tubesrdquoInternational Journal of Heat and Mass Transfer vol 44 no 22pp 4323ndash4331 2001

[15] I Kataoka and M Ishii ldquoEntrainment and deposition ratesof droplets in annular two phase flowrdquo in Proceedings of theASMEJSMEThermal Engineering Joint Conference Y Mori andW J Yang Eds vol 1 1983

[16] G F Hewitt and A H Govan ldquoPhenomenological modellingof non-equilibrium flows with phase changerdquo InternationalJournal of Heat and Mass Transfer vol 33 no 2 pp 229ndash2421990

[17] H McGill and W L Sibbitt Heat Transfer and Pressure Dropof Water Flowing in a Small Tube ANL-4603 (Part I) ArgonneNational Laboratory Argonne Ill USA 1951

[18] H M Epstein J W Chastain and S L Fawcett ldquoHeat transferand burnout to water at high subcirtical pressuresrdquo Report NoBMI-1116 Battelle Memorial Institute Columbus Ohio USA1956

[19] A P Ornatskii and A M Kichigin ldquoCritical heat loads in high-pressure boiling of underheatedwater in small diameter tubesrdquoTeploenergetika vol 9 no 6 pp 44ndash47 1962

[20] A POrnatskii ldquoCritical heat loads and heat transfer for a forcedflow of water in tubes in the region of superhigh pressures (175-220 atm)rdquo Teploenergetika vol 10 no 3 pp 66ndash69 1963

[21] G V Alekseev B A Zenkevich O L Peskov et al ldquoBurn-out heat fluxes under forced water flowrdquo in Proceeding of theInternational Conference on the Peaceful Uses of Atomic EnergyInternational Atomic Energy Agency pp 295ndash304 ViennaAustria 1964

[22] N A Bailey and D H Lee ldquoAn experimental and analyticalstudy of boiling water at 2000 to 2600 psirdquo Part I Dryout andPost-Dryout Heat Transfer AEEW-R659 1969

[23] O L Peskov V I Subbotin B A Zenkevich et al ldquoThe criticalheat flux for the flow of steam-watermixtures through pipesrdquo inProblems of Heat Transfer and Hydraulics of Two-Phase Mediapp 48ndash62 Pergamon Press Oxford UK 1969

[24] B A ZenkevichO L PeskovN Petrishchevaet alAnAnalysisand Correlation of the Experimental Data on Burnout in theCase of Forced Flow of Boiling Water in Pipes Physics-EnergyInstitute Atomizdat Moscow Russia 1969


[25] B A Zenkevich O L Peskov and N D Sergeev Burnout withforced flow of water in uniformly heated long tubes IPPE-254Institute of physics and power engineering Obninsk Russia1971

[26] B A Zenkevich ldquoAnalysis and generalization of experimentaldata on heat transfer crisis associated with forced convection ofcooling water in tubesrdquo AECL-Tr-Misc-304 1974

[27] I I Belyakov V P Lavrentrsquoev S N Smirnov and V VSokolov ldquoInvestigation of post-dryout in vertical tubesrdquo TsKTI-0535010-9119 Tsentralrsquonyii Kotlo-Turbinnyii Institut (CentralBoiler-Turbine Institute) Leningrad Russia 1976

[28] V N Smolin S V Shpansky V I Esikov and T K SedovaldquoExperimental data and prediction of crisis in boiling waterin tubes (for uniform and nonuniform heat flux)rdquo roblemsof Atomic Science and Engineering-Physics and Engineering ofNuclear Reactors vol 5 no 9 pp 3ndash154 1979

[29] C Williams and S Beus ldquoCritical heat flux experiments in acircular tube with heavy water and light water (AWBA Devel-opment Program)rdquo WAPD-TM-1462 Westinghouse ElectricCorp Pittsburgh PA USA 1980

[30] P L Kirillov O L Peskov and N P Serdunrsquo ldquoControl experi-ment on critical heat transfer during water flow in pipesrdquo SovietAtomic Energy vol 57 no 6 pp 858ndash860 1984

[31] D C Groeneveld ldquoThe onset of dry sheath condition - A newdefinition of dryoutrdquo Nuclear Engineering and Design vol 92no 2 pp 135ndash140 1986

[32] S T Yin T J Liu Y D Huang and R M Tain ldquoMeasurementsof critical heat flux in forced flow at pressures up to the vicinityof the critical point of waterrdquo in Proceedings of the 25th NationalHeat Transfer Conference vol 2 pp 501ndash506 Houston USA1988

[33] B Soderquist SwedishCHFData Received via Personal Commu-nication with Groeneveld DC Department of Nuclear ReactorEngineering Stockholm March 1994

[34] I Mudawar and M B Bowers ldquoUltra-high critical heat flux(CHF) for subcooled water flow boiling-I CHF data and para-metric effects for small diameter tubesrdquo International Journal ofHeat and Mass Transfer vol 42 no 8 pp 1405ndash1428 1999

Hindawiwwwhindawicom Volume 2018

Nuclear InstallationsScience and Technology of

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Power ElectronicsHindawiwwwhindawicom Volume 2018

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CombustionJournal of


Journal of


Renewable Energy

Acoustics and VibrationAdvances in


EnergyJournal of


Hindawiwwwhindawicom

Journal ofEngineeringVolume 2018


International Journal ofInternational Journal ofPhotoenergy


Solar EnergyJournal of


Shock and Vibration


Advances in Condensed Matter Physics


RotatingMachinery



High Energy PhysicsAdvances in


Active and Passive Electronic Components

Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

Volume 2018

Submit your manuscripts atwwwhindawicom


Table 1 CHF experiment database under high pressure region

Reference Time No of dataMcGill amp Sibbitt [17] 1951 9Epstein et al [18] 1956 90Ornatskii amp Kichigin [19] 1962 31Ornatskii [20] 1963 69Alekseev et al [21] 1964 508Bailey amp Lee [22] 1969 41Peskov et al [23] 1969 127Zenkevich et al [24] 1969 1298Zenkevich et al [25] 1971 152Zenkevich [26] 1974 192Belyakov et al [27] 1976 360Smolin et al [28] 1979 393Williams amp Beus [29] 1980 25Kirillov et al [30] 1984 506Groeneveld [31] 1985 8Yin et al [32] 1988 130Soderquist [33] 1994 412Mudawar amp Bowers [34] 1999 4Total 4355

of critical pressure in which the parametric trend of CHFvarying with pressure is also unknown

Furthermore different CHF mechanistic models usuallyare proposed for specific flow regime and one CHF modelis only effective in one flow regime resulting in a narrowprediction scope This cannot satisfy the prediction of CHFwhen different flow regimes appear successively in the samechannel

In this study based on the CHF experiment databaseof upflow boiling in vertical round tube from 15MPa to thevicinity of the critical pressure of water the prediction capa-bility and the applicability of Katto [4] Bowring [5] Hall-Mudawar [6] Alekseev [7] correlations and LUT-2006 [8]will be evaluated The parametric trend of CHF varying withpressure from 15MPa to the vicinity of critical pressurewill bediscussed Simultaneously combining the DNB and DO typeCHF mechanism a comprehensive CHF model under highpressure conditionwill be established Finally the verificationof the CHF mechanistic model based on the experimentdatabase and the parametric trends analysis of CHF varyingwith thermal-hydraulic and geometric parameters will becarried out

2 The Experiment Database

Based on the existing CHF database of upflow boiling verticalround tube the evaluation and screening of experimentdatabase are carried out As a result 18 different sets of CHFexperiment database were obtained from 1951 to 1999 in totalof 4355 data points are applied in this study The databasesources and distribution are shown in Table 1 among which2735 experiment data points belong to the DNB type CHFof subcooled bubbly flow and 1620 experiment data points

belong to the DO type CHF of saturated annular flow Table 2shows the experimental ranges of database

3 The Comparative Study of CHF Correlations

31 CHF Correlations Through the comparison and analysisof dozens of round tube CHF correlations this study hasselected the Katto [4] Bowring [5] Hall-Mudawar [6]Alekseev [7] correlations and LUT-2006 [8] which all coverthe high-pressure region for further analysis The parameterrange of each correlation is shown in Table 3

32 Comparative Analysis For analysis the error E meanerror ME mean absolute error MAE and root mean squareerror RMS are defined as follows

Error E

119864 = 119902CHFpre minus 119902CHFexp119902CHFexp(1)

Mean errorME

119872119864 = 1119873 sum 119902CHFpre minus 119902CHFexp119902CHFexptimes 100 (2)

Mean absolute errorMAE

119872119860119864 = 1119873 sum 100381610038161003816100381610038161003816100381610038161003816119902CHFpre minus 119902CHFexp119902CHFexp

100381610038161003816100381610038161003816100381610038161003816 times 100 (3)

Root mean square error RMS

119877119872119878 = radic 1119873 sum(119902CHFpre minus 119902CHFexp119902CHFexp)2 times 100 (4)























190 195 200 205 210 215

minus08

minus06

minus04

minus02

00

02

04

06

08


E


190 195 200 205 210 215 220 2250

100

200

300

400

500

600

700

800

900

1000



qCH

Fpre

(kW

m2 )

P (MPa)






1198661015840 = 120595119868119887119866 (6)


119868119887 = 046211989606Reminus01 (119863119887119889 )06 [1 + 119886 (120588119897 minus 120588V)120588V ] (7)


dz

q

tube wall

bubblylayer

bulk flow

R-SS

Ｇ2

Ｇ2+Ｇ2

Ｒ2

Ｒ2+Ｒ2

Ｇ1

Ｇ4

Ｇ3

Ｇ1+Ｇ1

Ｒ1

Ｒ1+Ｒ1





119886

=

123 minus 125119906 + 547 times (120588V120588119897 )23 119906 lt 12119898119904


547 times (120588V120588119897 )23 times (1199063)03 119906 ge 3119898119904

(8)




119863 = 119896119862 (9)




tube wall

dryout

liquid film

liquid droplet

R

vapour bubble

vaporization rate

entrainment rate

deposition rate

single-phase liquid




119896119895119892 = 0022Reminus025119892 ( 119862120588119891)minus026 (120588119892120588119891)

026

(10)




119889119863120583119897 = 022Re074119897 (120583V120583119897 )026 119864074 (11)





minus065 119862120588V gt 03 (13)


119864119866V


0316 119866119871119865 gt 1198661198711198651198620 119866119871119865 le 119866119871119865119862

(14)




Start



Initial guess q

Calculate x and

Use DNB model

CHF = q

Use DO model

Print output

Stop

Use DNB model

YES

NO

For node I

I=I+1

Last node

I=I+1

GF0lt1

x gt 0

YES

YES

YES

YES

YES

YES

NO

NO

NO

NO

NO

NO

Last node

lt 06

lt 07

q lt q

q lt q

qq minus 1

lt 1lowast10minus4

|GF0| lt 1




44 Results Analysis






4355 442 -389 822 960 05 83The DNB type CHF

2735 445 -460 858 964 06 70


Datapoints


Maximumerror

Minimumerror


within 10


within 20ME RMS


qCH

Fpre

(kW

m2 )

0 4000 8000 12000 16000 20000 24000 28000 32000 360000

4000

8000

12000

16000

20000

24000

28000

32000

36000

-20

20

qCHFexp (kWm2 )











0

5

10

15

20

25

=19MPa=15MPa

RMS

()



0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800


Dry-Out DNB

G (kgm2 s)

qCH

Fpre

(kW

m2 )



5 Conclusion





50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500


Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )


15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600


P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ








0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018
























190 195 200 205 210 215

minus08

minus06

minus04

minus02

00

02

04

06

08


E


190 195 200 205 210 215 220 2250

100

200

300

400

500

600

700

800

900

1000



qCH

Fpre

(kW

m2 )

P (MPa)






1198661015840 = 120595119868119887119866 (6)


119868119887 = 046211989606Reminus01 (119863119887119889 )06 [1 + 119886 (120588119897 minus 120588V)120588V ] (7)


dz

q

tube wall

bubblylayer

bulk flow

R-SS

Ｇ2

Ｇ2+Ｇ2

Ｒ2

Ｒ2+Ｒ2

Ｇ1

Ｇ4

Ｇ3

Ｇ1+Ｇ1

Ｒ1

Ｒ1+Ｒ1





119886

=

123 minus 125119906 + 547 times (120588V120588119897 )23 119906 lt 12119898119904


547 times (120588V120588119897 )23 times (1199063)03 119906 ge 3119898119904

(8)




119863 = 119896119862 (9)




tube wall

dryout

liquid film

liquid droplet

R

vapour bubble

vaporization rate

entrainment rate

deposition rate

single-phase liquid




119896119895119892 = 0022Reminus025119892 ( 119862120588119891)minus026 (120588119892120588119891)

026

(10)




119889119863120583119897 = 022Re074119897 (120583V120583119897 )026 119864074 (11)





minus065 119862120588V gt 03 (13)


119864119866V


0316 119866119871119865 gt 1198661198711198651198620 119866119871119865 le 119866119871119865119862

(14)




Start



Initial guess q

Calculate x and

Use DNB model

CHF = q

Use DO model

Print output

Stop

Use DNB model

YES

NO

For node I

I=I+1

Last node

I=I+1

GF0lt1

x gt 0

YES

YES

YES

YES

YES

YES

NO

NO

NO

NO

NO

NO

Last node

lt 06

lt 07

q lt q

q lt q

qq minus 1

lt 1lowast10minus4

|GF0| lt 1




44 Results Analysis






4355 442 -389 822 960 05 83The DNB type CHF

2735 445 -460 858 964 06 70


Datapoints


Maximumerror

Minimumerror


within 10


within 20ME RMS


qCH

Fpre

(kW

m2 )

0 4000 8000 12000 16000 20000 24000 28000 32000 360000

4000

8000

12000

16000

20000

24000

28000

32000

36000

-20

20

qCHFexp (kWm2 )











0

5

10

15

20

25

=19MPa=15MPa

RMS

()



0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800


Dry-Out DNB

G (kgm2 s)

qCH

Fpre

(kW

m2 )



5 Conclusion





50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500


Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )


15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600


P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ








0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



dz

q

tube wall

bubblylayer

bulk flow

R-SS

Ｇ2

Ｇ2+Ｇ2

Ｒ2

Ｒ2+Ｒ2

Ｇ1

Ｇ4

Ｇ3

Ｇ1+Ｇ1

Ｒ1

Ｒ1+Ｒ1





119886

=

123 minus 125119906 + 547 times (120588V120588119897 )23 119906 lt 12119898119904


547 times (120588V120588119897 )23 times (1199063)03 119906 ge 3119898119904

(8)




119863 = 119896119862 (9)




tube wall

dryout

liquid film

liquid droplet

R

vapour bubble

vaporization rate

entrainment rate

deposition rate

single-phase liquid




119896119895119892 = 0022Reminus025119892 ( 119862120588119891)minus026 (120588119892120588119891)

026

(10)




119889119863120583119897 = 022Re074119897 (120583V120583119897 )026 119864074 (11)





minus065 119862120588V gt 03 (13)


119864119866V


0316 119866119871119865 gt 1198661198711198651198620 119866119871119865 le 119866119871119865119862

(14)




Start



Initial guess q

Calculate x and

Use DNB model

CHF = q

Use DO model

Print output

Stop

Use DNB model

YES

NO

For node I

I=I+1

Last node

I=I+1

GF0lt1

x gt 0

YES

YES

YES

YES

YES

YES

NO

NO

NO

NO

NO

NO

Last node

lt 06

lt 07

q lt q

q lt q

qq minus 1

lt 1lowast10minus4

|GF0| lt 1




44 Results Analysis






4355 442 -389 822 960 05 83The DNB type CHF

2735 445 -460 858 964 06 70


Datapoints


Maximumerror

Minimumerror


within 10


within 20ME RMS


qCH

Fpre

(kW

m2 )

0 4000 8000 12000 16000 20000 24000 28000 32000 360000

4000

8000

12000

16000

20000

24000

28000

32000

36000

-20

20

qCHFexp (kWm2 )











0

5

10

15

20

25

=19MPa=15MPa

RMS

()



0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800


Dry-Out DNB

G (kgm2 s)

qCH

Fpre

(kW

m2 )



5 Conclusion





50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500


Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )


15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600


P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ








0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



tube wall

dryout

liquid film

liquid droplet

R

vapour bubble

vaporization rate

entrainment rate

deposition rate

single-phase liquid




119896119895119892 = 0022Reminus025119892 ( 119862120588119891)minus026 (120588119892120588119891)

026

(10)




119889119863120583119897 = 022Re074119897 (120583V120583119897 )026 119864074 (11)





minus065 119862120588V gt 03 (13)


119864119866V


0316 119866119871119865 gt 1198661198711198651198620 119866119871119865 le 119866119871119865119862

(14)




Start



Initial guess q

Calculate x and

Use DNB model

CHF = q

Use DO model

Print output

Stop

Use DNB model

YES

NO

For node I

I=I+1

Last node

I=I+1

GF0lt1

x gt 0

YES

YES

YES

YES

YES

YES

NO

NO

NO

NO

NO

NO

Last node

lt 06

lt 07

q lt q

q lt q

qq minus 1

lt 1lowast10minus4

|GF0| lt 1




44 Results Analysis






4355 442 -389 822 960 05 83The DNB type CHF

2735 445 -460 858 964 06 70


Datapoints


Maximumerror

Minimumerror


within 10


within 20ME RMS


qCH

Fpre

(kW

m2 )

0 4000 8000 12000 16000 20000 24000 28000 32000 360000

4000

8000

12000

16000

20000

24000

28000

32000

36000

-20

20

qCHFexp (kWm2 )











0

5

10

15

20

25

=19MPa=15MPa

RMS

()



0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800


Dry-Out DNB

G (kgm2 s)

qCH

Fpre

(kW

m2 )



5 Conclusion





50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500


Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )


15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600


P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ








0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



Start



Initial guess q

Calculate x and

Use DNB model

CHF = q

Use DO model

Print output

Stop

Use DNB model

YES

NO

For node I

I=I+1

Last node

I=I+1

GF0lt1

x gt 0

YES

YES

YES

YES

YES

YES

NO

NO

NO

NO

NO

NO

Last node

lt 06

lt 07

q lt q

q lt q

qq minus 1

lt 1lowast10minus4

|GF0| lt 1




44 Results Analysis






4355 442 -389 822 960 05 83The DNB type CHF

2735 445 -460 858 964 06 70


Datapoints


Maximumerror

Minimumerror


within 10


within 20ME RMS


qCH

Fpre

(kW

m2 )

0 4000 8000 12000 16000 20000 24000 28000 32000 360000

4000

8000

12000

16000

20000

24000

28000

32000

36000

-20

20

qCHFexp (kWm2 )











0

5

10

15

20

25

=19MPa=15MPa

RMS

()



0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800


Dry-Out DNB

G (kgm2 s)

qCH

Fpre

(kW

m2 )



5 Conclusion





50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500


Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )


15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600


P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ








0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018





4355 442 -389 822 960 05 83The DNB type CHF

2735 445 -460 858 964 06 70


Datapoints


Maximumerror

Minimumerror


within 10


within 20ME RMS


qCH

Fpre

(kW

m2 )

0 4000 8000 12000 16000 20000 24000 28000 32000 360000

4000

8000

12000

16000

20000

24000

28000

32000

36000

-20

20

qCHFexp (kWm2 )











0

5

10

15

20

25

=19MPa=15MPa

RMS

()



0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800


Dry-Out DNB

G (kgm2 s)

qCH

Fpre

(kW

m2 )



5 Conclusion





50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500


Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )


15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600


P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ








0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



0

5

10

15

20

25

=19MPa=15MPa

RMS

()



0 500 1000 1500 2000 2500 30000

200

400

600

800

1000

1200

1400

1600

1800


Dry-Out DNB

G (kgm2 s)

qCH

Fpre

(kW

m2 )



5 Conclusion





50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500


Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )


15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600


P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ








0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



50 100 150 200 250 300 350 4001000

1250

1500

1750

2000

2250

2500


Dry-OutDNB

Δh in (kJkg)

qCH

Fpre

(kW

m2 )


15 16 17 18 19 20 21 22 230

200

400

600

800

1000

1200

1400

1600


P (MPa)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ








0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



0 1000 2000 3000 4000 5000 6000 7000 80000

1000

2000

3000

4000

5000

6000


G (kgm2 s)

qCH

Fpre

(kW

m2 )


minus100 0 100 200 300 400 500 6000

1000

2000

3000

4000

5000

6000


qCH

Fpre

(kW

m2 )

Δh in (kJkg)



Nomenclature




0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



0004 0006 0008 0010 0012 0014 0016 0018 0020600

800

1000

1200

1400

1600

1800

2000

2200

2400


D (m)

qCH

Fpre

(kW

m2 )

ΔℎＣＨ

ΔℎＣＨ

ΔℎＣＨ


00 05 10 15 20 250

500

1000

1500

2000

2500

3000


L (m)

qCH

Fpre

(kW

m2 )



Re Reynolds number


Greek Symbols



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018



Subscripts


Data Availability




Acknowledgments


References
















































Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018

























Advances in



Journal of


Renewable Energy



EnergyJournal of









Shock and Vibration




RotatingMachinery








Volume 2018


the study of critical heat flux in upflow boiling vertical...

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