Heat Transfer Processes During Intermediate and Large ...

NUREG/IA-0002

IntemationalAgreement Report

Heat Transfer Processes DuringIntermediate and Large BreakLoss-of-Coolant Accidents (LOCAs)

Prepared by1. Vojtek

Reactor Safety CorporationGesellschaft fuer ReaktorsicherheitPorschungsgefaende, 8046 Garching,The Federal Republic of Germany

Office of Nuclear Regulatory ResearchU.S. Nuclear Regulatory CommissionWashington, D.C. 20555

September 1986

Prepared as part ofThe Agreement on Research Participation and Technical Exchange

* under the International Thermal- Hydraulic Code Assessmentand Application Program (ICAP)

Published byU.S. Nuclear Regulatory Commission

NOTICE

This report was prepared under an international cooperativeagreement for the exchange of technical information. Neitherthe United States Government nor any agency thereof, or any oftheir employees, makes any warranty, expressed or implied, orassumes any legal liability or responsibility for any third party'suse, or the results of such use, of any information, apparatus pro-duct or process disclosed in this report, or represents that its useby such third party would not infringe privately owned rights.

Available from

Superintendent of DocumentsU.S. Government Printing Office

P.O. Box 37082Washington, D.C. 20013-7082

and

National Technical Information ServiceSpringfield, VA 22161

NUREG/IA-0002

InternationalAgreement Report

Heat Transfer Processes DuringIntermediate and.-Large BreakLoss-of-Coolant Accidents (LOCAs)

Prepared by1. Voitek

Reactor Safety CorporationGesellschaft fuer ReaktorsicherheitPorschungsgelaende, 8046 Garching,The Federal Republic of Germany

Office of Nuclear Regulatory ResearchU.S. Nuclear Regulatory CommissionWashington, D.C. 20555

September 1986

Prepared as pert ofThe Agrement on Research Participation and Technical Exchangeunder the International Thermal-Hydraulic Coda Assessmentend Application Program 4ICAP)

Published byU.S. Nuclear Regulatory Commission

Translated by: Fischer Translation Service1928 Catoctin TerraceSilver Spring, MD 20906

NOTICE

This report documents work performed under the sponsorship of the Kraftwerk

Union in the Federal Republic of Germany. The information in this report has

been provided to the USNRC under the terms of an information exchange

agreement between the United States and the Federal Republic of Germany

(Technical Exchange and Cooperation Arrangement Between the United States

Nuclear Regulatory Commission and the Bundesminister Fuer Forschung und

Technologie of the Federal Republic of Germany in the field of reactor safety

research and development, April 30, 1981). The Kraftwerk Union has consented

to the publication of this report as a USNRC document in order that it may

receive the widest possible circulation among the reactor safety community.

Neither the United States Government nor the Kraftwerk Union or any agency

thereof, or any of their employees, makes any warranty, expressed or implied,

or assumes any legal liability of responsibility for any third party's use, or

the results of such use, of any information, apparatus, product or process

disclos'e-d inf this report, or represents that its use by such third party would

not infringe privately owned rights.

SUMMARY

Within the framework of this research project there were examined the

heat transfer ranges, as they occur during the high pressure phase of

a LOCA with intermediate and large breaks. Special attention was given

to the phenomena important for the prediction of the highest clad tube

temperatures of the maximum and minimum critical heat flux and to the

steam-droplets cooling. The experimental results of the 25-rod bundle

tests, conducted at the KWU facility in Karistein, were used as a data-

base for the verification of the assembled models and correlations.

The values of the heat flux and of the heat transfer coefficients, ob-

tained from these measurements, were used for the comparison with the

calculated results and allowed the evaluation of the used correlations

and models. The local values of the important thermal and fluid dynamic

parameters, required for this comparison, were calculated with the aid

of the computer code BRUDI-VA. -In particular, the following correlations

were evaluated on hand of these experimental results:

Maximum critical heat flux:

- W-3 correlation

- B-W-2 correlation

- Macbeth correlation- Zuber-Griffith correlation

- Biasi correlation

- CISE correlation

- Slifer-GE correlation

- Smalin correlation

- Tong correlation

- Thorgenson correlation

- Monde-Katto correlation

Minimum heat flux:

- Berenson modification of the Zuber correlation

i

Minimum temperature difference in case of rewetting:

- Berenson correlatio'n

- Henry correlation

- Ilceje correlation

Correlations for the calculations of the heat transfer coefficients in the

sphere of steam-droplets cooling:

- modified Dougall-Rohsenow correlation

- Groeneveld-5.7 correlation

- Condie-Bengston-IV correlation

- Groeneveld-Delorme correlation

- Chen-Ozkaynak-Sunderam correlation

The verification of the correlations for the calculations of the maximumcritical heat flux made apparent the limitation of the spheres of applica-tion of the individual correlations and showed, that none of these correla-

tions can be recommended for the entire range of the test parameters for

a safe prediction of the DNB moment and location. The verification of

the correlations for the calculation of the heat transfer coefficients

after the exceeding of the maximum critical heat flux showed, that these

correlations also lead only in certain ranges of the test parameters to

a good consistency between the measurement and the calculated results.

The use of the chosen correlations for the calculation of the minimum

temperature difference between wall and coolant and the minimum critical

heat flux showed, that none of these correlations, at least in the para-

meter combinations that resulted from the 25-rod bundle tests, can be used

for the prediction of the rewetting phenomenon.

On hand of the results of the verification of the correlations for the

calculation of the heat transfer coefficients in the case of steam-dropletscooling there was developed a new "two components correlation." Theapplication of this correlation within the entire range of the test

parameters of the 25-rod bundle measurements (pressure 2 to 12 MPa,

mass flow density 300 to 1400 kg/m'.s, steam quality 0.3 to 1, and wall

temperature 300 to 700'C) led to a very good consistency between measure-

ment and calculated results.

ii

ABSTRACT

The general purpose of this project was the- investigation of the heat trans-fer regimes during the high pressure portion of blowdown. The main at-tention has been focussed on the evaluation of those phenomena which aremost important in reactor safety, such as maximum and minimum criticalheat flux and forced convection film boiling heat transfer. The experimen-tal results of the 2S-rad bundle blowdown heat transfer tests, which wereperformed at the KWU heat transfer test facility in Karistein, were usedas a database for the verification of different correlations which are usedor were developed for the analysis of reactor safety problems. The compu-ter code BRUDI-VA was used for the calculation of local values of Impor-tant thermohydraulic parameters in the bundle.

In particular the following correlations have been evaluated in this study:

Maximum critical heat flux:

-W-3 correlation

-B-W-2 correlation

-Macbeth correlation

-Zuber-GriffIth correlation-Biasi correlation-CISE correlation

- Slifer-GE correlation- Smolin correlation

- ng correlation- Thorgerson correlation

- Monde-Katto correlation

Minimum critical heat flux and minimum film boiling temperature:

- Berenson modification of the Zuber correlation- Berenson correlation- Henry correlation- lioeje correlation

Heat transfer coefficients in flow film boiling:

- modified Dougal l-Rohsenow correlation- Groeneveld-5.7 correlation

iii

- Candie-Bengston-lV correlation- Groeneveld-Delorme correlation- Chen -Ozkayna k-Sundaram correlation.

The evaluation of correlations for the prediction of critical heat flux, film

boiling heat transfer coefficients and minimum film boiling temperatureshowed that none of the correlations should be used over the entire range

of test parameters investigated.

Using results of this investigations a new equilibrium correlation for the cal-culat!on of forced film boiling heat transfer coefficients has been developed.

This correlation is shown to agree well. with the experimental data over thefollowing range of testparameter: Mass flow rate 300 to 1400 kg/M 2 .s, pres-

sure 2 to 12 MPa and quality 0.3 to 1.0.

iv

TABLE OF CONTENTS

1. Introduction~

2.

2.1

2.2

Foundations and definitions

Forced convection with water as a coolant

Subcooled nucleate boiling

2.3 Nucleate boiling

2.4 Transfer from nucleate boiling ti

steam-dropl ets flow

2.4.1 Transfer from nucleate boiling ti

2.4.2 Transfer from nucleate boiling ti

2.5 Fil~m boiling

2.6 Steam-droplets cooling

2.7 Transfer fromfilm boiling, resp.

to nucleate boiling

2.8 *Forced steam convection

ofilm boiling, resp.

1

2

3

4

4

4

4

5

5

6

6

6

0 film boiling

steam-droplet cool ing

steam-dropl ets cool ing

3.

3.1

3.2

3.3

3.3.1

3.3.2

Experimental i nvestogations

The test device

Instrumentation

Test program

DNB tests

Post DNB tests

7

7

8

9

9

11

4. Calculation of the heat transfer coefficients from the

test data and the evaluation of the results

4.1 Calculation of the heat transfer coefficients from-

the test data

4.2 Compilation of the important parameters from the test

5. Calculation of the local thermal and fluid dynamic

parameters

5.1 The computer code BRUDI-VA

5.1.1 Basic equations of the homogenous point of equilibrium

model

5.1.2 Calculation of the two-phase pressure loss

12

12

12

14

14

14

15

V

5.1.3 Heat conduction model 1

5.1.4 Heat transfer model 16

5.2 Calculation of the chosen tests and determination of the

local thermal and fluid dynamic parameters at the DNB,

dry-out and RND moment 16

6. Compilation and comparison of the correlations for the

calculation of the heat transfer coefficients in the

region of the forced convection with one-phase coolant 18

6.1 Forced water convection 18

6.2 Forced steam convection 19

6.3 Comparison of the correlations 20

7. Compilation and comparison of the correlations for the

calculation of the heat transfer coefficients (HTC) of

the subcooled and saturated nucleate boiling 21

7.1 Calculation of the necessary temperature difference

for bubbles formation with subcooled fluid 217.2 Calculation of the heat transfer coefficients in the

region of the subcooled nucleate boiling 21

7.3 Calculation of the heat transfer coefficients in the

region of nucleate boiling 22

7.4 Comparison of the correlations 23

8. Transfer from nucleate boiling to film boiling, resp.

stea~m-droplets cooling - (maximum critical heat flux) 25

8.1 Vessel film boiling 25

8.2 Heat transfer crisis with forced convection, high heat

flux and low steam-cOntent - (DNB) 27

8.2.1 Semi-empirical models 27

8.2.2 Empirical models 31

8.3 Heat transfer crisis with forced convection, low to

intermediate heat flux, and intermediate to high steam

content (dry-out) 33

8.3.1 Analytical models 33

8.3.2 Semi-empirical and empirical correlations 36

8.4 Verification of the correlations for the calculation

of the maximum cri tical heat flux (KHB) based on the

experimental results 38

vi

862-.1 Selection of the correlations 388.4.2 Evaluation of the correlations for the calculation

of the maximum critical-heat flux 44

9. Heat transfer at boiling abd steam-droplets cooling 45

9.1 Film boiling 459.1.1 Film boiling with wettable wall 459.1.2 Film boiling with not wettable wall 46.9.1.3 Vessel film boiling 469.2 Steam-droplets cooling 499.2.1 Equilibrium models and correlations 509.2.2 Non-equilibrium models 529.3 Comparison of each of the correlations based on the

recalculation of selected 25-rid bundle tests 569.3.1 Recalculation of the test ONBi 579.3.2 Recalculation of the test DNB3 -59

9.3.3 Recalculation of the test DNB9 619.3.4 Recalculation of the test PDNB11 639.4 Evaluation of the correlations for the calculation

of the heat transfer coefficients in the steam-dropletscooling region 64

10. Transfer from steam-droplets cooling or film boilingto nucleate boiling (RNB-rewetting) 65

10.1 Compilation of the experimental data from the 25-rodbundle investigation 65

10.2 Correlations for the calculation of the minimum criticalheat flux and of the minimum temperature difference withrewetti ng 66

10.3 Investigation of the correlations based on the resultsof the 25-rod bundle tests 68

10.4 Evaluation of the correlations 70

11. Development of a new correlation for the calculation ofthe heat transfer coefficients in the steam-dropletscooling region 71

11.1 Heat transfer between wall and steam phase 72

vii

11.1.1 Comparison of various slippage and drift equations 73

11.2 Heat transfer between wall and droplets -76

11.2.1 Determination of the surface inherent to the heit"

transfer between wall and droplets 76

11.2.2 Determination of the droplet diameter 76

11.2.3 Determination of the number of droplets 78

11 .3 Heat transfer between steam and droplets 79

11.4 Calculation of the individual components of the heat

flux density between wall and steam-droplets flow 80

11.5 Formulation in agreement with the similarity theory

of the new model for the calculation of the heat transfer

coefficients with steam-droplets cooling 85

12. Conclusions 92-

13. Bibliography 93

Attachments 1-11 99

Distribution 141

viii

INDEX OF FIGURES

Figure 1: Heat transfer and flow configurations with- intermediate

heat flux 2

Figure 2: Heat transfer and flow configurations with high heat

flux 3

Figure 3: Schematic representation of the measuring section 7

Figure 4: Heating conductor geometry and power distribution 7

Figure 5: Position of the thermocouple elements in the bundle 8

Figure 6: Typical processes of the test parameters of the DNBtests 10

Figure 7: Typical processes of the test parameters of the

post-DNB tests 11

Figure 8.: Correlation of the temperature difference with

rewetting and of the electric power 13

Figure 9: Pressure difference along the measuring section

Test DNB-2 15

Figure 10: Pressure difference along the measuring section

Test DNB-9 15

Figure 11:

FigureFigureFigure

12:

13:14:

Figure 15:

Figure 16:

Figure 17:

Figure 18:

Figure 19:

Figure 20:

Comparison between the measured and the calculated

wall temperatures - Test DNB-9

Reynolds number multiplier F according to Chen

Suppression factor S according to Chen

Boiling curve according to Nukiyama for container

boiling with 0.1 MPa

Model representation for the determination of the

critical heat flux according to TongModel of the annular flow with entrainment and

depositionH-arwell correlation for the determination of the

entrainment coefficient

Harwell correlation for the determination of the

deposi ti on coeffi ci entComparison of the critical heat flux correlations

Test DNB3Comparison of the critical heat flux correlations

Test DNB3

1724

24

26

29

33

34

35

40

41

ix

Figure 21:

Figure 22:

Figure 23:

Figure 24:

.Comparison of the critical heat flux correlations

Test DNB9

Comparison of the critical heat flux correlations

Test DNB9

Schematic representation~of film boiling in vesselboiling

Model of the vessel film boiling according to

42

43

46

Figure

Figure

Figure

Figure

Fi gure

Figure

Figure

Berenson

25: Comparison of

26: Comparison of

Test DNBI

27: Comparison of

28: Comparison of

Test DNB3

29: Comparison-of

30: Comparison o 'f

Test DNB931: Comparison of

Test PDNB11

the equilibrium correlations Test DNB1the non-equilibrium correlations

the equilibrium correlations Test DNB3

the non-equilibrium correlations-

the equilibrium correlations Test DNB9the non-equilibrium correlations

49

57

58

59

60

61

62

63

the equilibrium correlations

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

32: Measuring points Tw-Tsat = f(P)33: Measuring points Tw-Tsat = f(q)34: Correlation of G to TW-Tsat35: Correlation of X to TW-Tsat36: Comparisons of the correlations for the calculation

Of &Tmin37: Comparison of the minimum and actual heat flux

38: Model representation for the heat transfer in the

steam-droplets cooling phase

39: Comparison of several correlations for the calculation

of the heat transfer coefficient with forced steam

convecti on

40: Comparison of various slippage equations

41: Comparison of the steam velocities calculated with

and without drift42: Comparison of the wall temperatures and the heat

transfer coefficients calculated with and without

slippage

55

55

56

56

58

59

11

Figure

Figure

Figure

T4

'5

x

Figure 43: Comparison of the correlations for the calculation

of the droplet diameter 77

Figure 44: HTC between steam and droplets 79

Figure 45: Heat flux density of steam on droplets 79

Figure 46: Components of the heat flux in steam-droplets

cooling 82

Figure 47: Comparison of the droplets mass flow densities 83

Figure 48: Components of the heat flux density acc. t6 the

"two-component model" 84

Figure 49: Results from the recalculation of the test DNB1 with

the application of the new correlation for the

calculation of the heat transfer coefficients 88

Figure 50: Results of the recalculation of the test DNB3 with


calculation of the heat transfer coefficients 89Figure 51: Results from the recalculation of the test DNB9 with



Figure 52: Results from the recalculation of the test PDNBil

with application of the new correlation for the


xi

INDEX OF TABLES

Table 1: Variation of the test parameters of the DNB tests 10Table 2: Variation of the test parameters of the post DNB

tests 1Table 3: Values of the Macbeth correlation coefficients

for various pressure ranges 32

Table 4: Comparison of the critical heat flux correlations 39

Table 5: Values of the correlation coefficients for the

Groenevel d correlation 52

xii

EXPRESSIONS (Notations)

a maAB

CCp J/kg K

D M

F m2

F

g rn/sec 2

G kg/M3 sec

h J/kgAhm J/kg

6&he J/kgH m<J> M3 /Sac

K

K soKa

I mM kgm kgM kg/sec

NP Pa (bar)

p mP C Pa (bar)

C

q W/M2 (W(CrnZ)

R mR SPOhm *MM2/M

SS mS

t sec

T OC, K

characteristic lengthcorrelation constantcorrelation constantcorrelation constantcorrelation constantspecific heat capacitydiameter, equivalent diameterpressure loss factorarea [surface]Chen factoracceleration due to gravitymass flow densityspecific enthalpymodified evaporation heatevaporation heatheight

volume flowconstantStefan-Bol tzmann constant

absorption coefficient

lengthmassmassmass flownumberpressure

heated rangecritical pressureheat fluxheat flux densityradiusspecific resistanceChen suppression factorthicknessslip~slippage]timetemperature

xiii

W kg/sec mass floww rn/sec velocityX steam content

xtt Martinelli-Nelson parameterY Jiiropolskij parameter

a W/rn2K heat transfer coefficient8 M film thickness, droplets diameter9 emission numbern~ kg/rn-sec dynamic viscosity#5 m film thicknessA. W/rnK heat conductivityTp volumetric steam content

p kg/rn3 densityT N/rn2 tangential stressT sec timea N/rn surface stress

Characteristic factors

Gr Grashoff numberNu rHusselt number

Pr Prandtl number

Re Reynolds numberWe Weber number

Subscripts (and superscripts)

A outlet [discharge]a actual [real]6 Berensonbs nucleate boiling

d steam

E) deposition

ONE Departure from nucleate boilingD0 dry-out

xiv

E inlet (entrainment)* equilibrium

effectivef fluid [liquid]

H Henryhorn homogenous (without slippage)in inletmin injection

I IloejeK convectionI localLF liquid filmmic microscopicalMac macroscopicalmax maximummin minimumstat stationary value

T dropletsTOT in tototP two-phasew waillZP two-phase

xv

1. INTRODUCTION

In the safety analyses of light water reactors there are examined hypothetical

LOCA cases. Depending on the size and the position of the assumed breaks,

the important thermal and fluid dynamic parameters, such as pressure, mass

flow and enthalpy in the primary loop, undergo more or less quick changes

compared with the conditions under normal operation. The therefrom resulting

reduction of the core mass flow can lead to~a so-called exceeding of the

maximum critical heat flux (KHB) [CHF] at the fuel rods and to a high increase

of the clad tube temperatures. Thus, an accurate knowledge of the heat

transfer conditions under high pressure and mass flow transients is one

of the most important prerequisites for a correct prediction of the

process of the clad tube temperatures in the case of LOCA. Therein, of

decisive influence upon the process of the clad tube temperatures are the

moment of the exceeding of the maximum critical heat flux and the magnitude

of the heat transfer coefficients (WUK) in the subsequent phase of film

boiling and steam-droplets cooling. For the clarification of these problems,

intermittently controlled tests with a 25-rod bundle with PWR geometry were

conducted in the KWU facility, within the framework of the German emergency

cooling program. The task of this research project was the analytical

examination of the heat transfer conditions under considerable pressure and

mass flow transients and under high pressure.

1

2. FOUNDATIONS AND DEFINITIONS

The heat transfer conditions and the thereto belonging configurations of flow,

as they occur in the case of LOCA with intermediate and large breaks in

the central respectively hot channel of a pressurized water reactor core

are schematically represented in Fig. 1 resp. Fig. 2. Hereafter, are

discussed and explained the heat transfer and flow conditions in each of

the regions.

Steam flow

P: Steamn-droplets coolingSteam-dropl ets flow

Annular flow with

steam-dropl ets flowC3 C Nlucleate boiling

biubbles flow C1

8 Subcooled nucleate boiling

Water flowForced convection

A (water)

Fig. 1: Heat transfer and flow configurations with intermediate heat flux

2

Steam flow

Steam

droplets flow

Inverseannular flow

* 4

0 .**.

* 0o *.~ .~

* . 6.

,*~ 0

o~.

4,/

~;~ AlI :/~,

G Forced convection(steam)

F Steam-droplets cooling

E Film boiling

0 Transfer (DNB)

Slug flow C 2

Bubbles flow C 1C Nucleate boiling

"-'4;,Subcooled nucleate boiling

Water flow A Forced convection(water)

Fig. 2: Heat transfer and flow configurations with high heat flux

2.1 Forced convection with water as coolant (Region A, Fig. 1, 2)

This type of heat transfer occurs in steady-state operating conditions and

in the first, subcooled phase of LOCA in the greatest part of the reactor

core. The thereto belonging configuration of flow is the single-phase,

fully developed, turbulent flow.

3

2.2 Subcooled nucleate boiling (region B, Fig. 1, 2)

The mean water temperature in this region lies only a little below the

saturation temperature. Bubbles are formed on the wall if the wall

temperature presents a certain increase above the saturation temperature.

Due to the actio n of the flux, the bubbles are broken off the wall and

condense in the subcooled region of the flow. Because of the movement of

the bubbles in the center of the flow there occurs the destruction of the

laminar boundary layer and in increased mass transfer in the layers in

the proximity of the wall takes place. This leads to a significant

improvement of the heat transfer between wall and coolant. Also, in this

case, the flow is fully turbulent, but partially with a destroyed boundary

1laye r.

2.3 Nucleate boiling (region C, Fig. 1, 2)

When the saturation tCemperature reaches over the entire flow cross-section,

the bubbles that are broken off the wall spread into the flow, do not con-

dense any longer and the average enthalpy lies now above the boundary

value of x = 0. Due to the velocity distribution, the constantly

originating bubbles on the wall are conveyed to the center of the flow,

they coalesce and displace the water into the less accelerated layers near

the wall. The heat transfer between wall and coolant is also very effective

in this region and amounts to only a few dc-grees Kelvin. The configura-

tions of flow inherent to this heat transfer can appear to be quite dif-

ferent and range from a bubble flow (region Cl), through a slug flow

(region C2, Fig. 2), to the annular flow with steam-droplets cooling

in the center (region 03, Fig.).

2.4 Transfer from nucleate boiling to film boiling, resp. steam-droplets

flow (the first heat transfer crisis)

2.4.1 Transfer from nucleate boilin2_to film boilinS (region D, Fig. 2)

The transfer from nucleate boiling to the film boiling is characterized by

a high heat flux density and a low steam content. When the steam production

4

at nuclear boiling reaches a determined limit because of the high heat

flux density, the water is displaced from the wall and the heat is trans-

fered to the water only through the conduction-in the thin steam layer.

The sudden reduction of the heat transfer coefficient (WUK) brings about

a steep increase of the wall temperature. This type of transfer from

nuclear boiling to film boiling is hence called "Departure from Nucleate

Boiling - DNB." Characteristic for this heat transfer crisis is the

change of configuration of flow of bubbles and slug flow to the inverse

annular flow (region D, Fig. 1, 2).

2.4.2 Transfer from nucleate boilin2 t ta-r~ t oln

(region D, Fig. 1)

As shown in Fig. 1, in this transfer there exist completely different con-

ditions in the flow channel as in the above described transfer from nucleate

boiling to film boiling. In this case, the heated wall is covered only

with a thin film of water from which are broken off individual droplets

because of the great velocity difference between steam nucleus and water

film. Thus, in the center there is created a steam-droplets flow, also

called mist flow; Due to the constant evaporating of the water film, it

becomes always thinner downward the flow until it fully evaporates at the

end of this region. After the drying of the water film, the heat transfer

coefficient (WUK) does suddenly decrease also in this case, and the walltemperature increases rapidly. This transfer from nucleate boiling to

the steam-droplets cooling is called "dry-out" in the literature and

also henceforth. The configuration of flow changes from an annular

flow to steam-droplets cooling.

2.5 Film boiling (region E, Fig. 2)

Film, boiling is a heat transfer process which can chiefly occur at boiling

in the pool with a heated wall. In the case of a formed flow, the pure

film boiling could be observed locally limited only with a high heat flux

density. During a transient process with quickly dropping pressure, this

heat transfer range is also limited in time.

5

2.6 Steam-droplets cooling (region F, Fig. 1, 2)

The heat transfer conditions and the magnitude of the heat transfer coef-

ficient (WUK) in this region are of decisive influence on the process of

the clad tube temperatures after an exceeding of the maximum critical

heat flux. The analytical examination of the heat transfer in a steam-

droplets flow (liquid deficient region) was one of the main t asks of this

research project and it is dealt with in details in Chapters 9 and 11.

2.7 Transfer from film boiling, resp. steam-droplets cooling, to

nucleate boiling (the second heat transfer crisis)

In the new intermittent examinations with reactor LOCA-like conditions,

there was not only observed the first heat tran 'sfer crisis (DNB, dry-out)

but also the second one, the transfer from steam-droplets cooling or filmboiling to nucleate boiling. This process -described as "Return to

Nucleate Boiling (RNB)" in the literature -is thoroughly investigated

in Chapter 10.

2.8 Forced steam convection (region G, Fig. 1, 2)

If even the last droplets evaporate in the center of the flow because of

the constant addition of heat and the pressure relief, the steam~is super-

heated with a constant addition of heat. The inherent configuration of

flow in this region is, in most of the cases, the fully developed turbulent

steam flux.

6

3. EXPERIMENTAL INVESTIGATIONS

The experimental investigation of the intermittent heat transfer conditionsduring reactor LOCA-like transients was conducted in the KWU facility withinthe framework of the research project RS-37C, sponsored by the BMFT (FederalMinister for Technology). The purpose of the controlled 25-rod bundletests was the experimental determination of the heat transfer coefficient(WUK) in the region of the film boiling and of the steam-droplets cooling,and the investigation of various parameters on the magnitude of the maximumcritical heat flux.

3.1 The -test device

Figure 3 shows a schematic representation of the testing device.

Safety disk val vesP~f (time) heat

25s-rod bundle3.8 m

water

G;=f (time)

steam

G~f (time

Fiq. 3: Schematic representationof the measuring section

Fig. 4: Heating conductor geometryand power distribution

7

..--- -'The most important element of the testing device is the measuring section

with the electrically heated 25-rod bundle. The axial power distribution

of the five-stage, direct-heated heating conductor is shown in Fig. 4.

The measuring section is designed for a maximum pressure of 16 MPa. The

inlet mass flow and the inlet enthalpy were controlled by means of the

valves in the main steam pipe and in the water pipe. At the outlet of

the measuring section are installed two quick-controllable valves and a

safety disk, with the aid of which the desired pressure distribution is

repoduced. The desired heating capacity, adjustable in time, of maximum

5 MW was generated in the thereto belonging direct current plant. A

detailed description of the testing device is contained in /1 and 2/.

3.2 Instrumentation

The following parameters were measured in each conducted test.

377(cm)

_________________327

00000'00000 225

00000'300-0004 IS

A 6 C 0 E u

Beginning of heatedlength

Fig. 5: Position of the thermocouple elements in the bundle

8

- absolute pressure at the measuring section inlet and outlet

- pressure diffe -rence between inlet and outlet

- coolant-temperature at the inlet and outlet

- water and steam mass flows in the inlet pipes

- electrical current and voltage

- 8 temperatures in the measuring section wall

- 80 heating conductor wall temperatures at several positions in the

rod (Fig. 5).

3.3 Test program

Due to reasons of technical testing nature, the tests were divided into two

testing groups, the so-called "DNB tests" and the so-called "post-DNB tests."

3.3.1 DNB tests

The main purpose of the DNB tests was that of furnishing information aboutthe influence of the various test parameters upon the DNB delay times and

upon the value of the heat transfer coefficient (WUK) immediately after

the occurrence of the DNB. The test runs, compiled in Table 1, were set

up in connection with the LOCAS between the reactor pressure vessel and

the steam generator. In view of the importance of the hot channel for'the

safe technical investigation, all of the DNB test runs were conducted

with a heating capacity similar to that of the hot channel. But since all

25 rods had to be equally heated in order to be able to reproduce also the

other thermal and fluid dynamic conditions that appear in the hot channel

of a pressurized water reactor, the following parameter variations had

to be carried out:.

a) Bundle inlet enthalpy and initial mass flow as in the reactor, theoutlet enthalpy higher (DNBI, DNB2, DNB3)

b) Bundle outlet enthalpy and initial mass flow as in the reactor,

the inlet enthalpy lower (DNB4, DNB5, DNB6)

c) Rod inlet and outlet enthalpy as in the reactor, the mass flow

higher (DNB7, DNB8, DNB9).

9

In the post-'DNB phase, the inlet mass flow was reduced for each of the

three types a), b) resp. c) to three different levels (G/G STAT = 0.45;G/GSA= 0.3; and G/GTA=0.) In order to investigate the influence

of the pressure drop after the beginfii ng of the blowdown upon the DNB delay

times, two test runs w ere condu cted with a lower pressure drop time of

0.7 (DNB1O) resp. 1.2 s (DNB11). The typical time behaviors of the pressure,

of the heating capacity and of the inlet mass flow are represented in

Fig. 5.

Table 1; Variation of the test parameters of the DNB tests

Test

ON B-iON 8-2ON 8-3ON 8-4ON B-5ON B-SON 8-7DNS-8ON 8-9ONS8-10ON B-11

Initial massflow density

kg/M2 -S

3300.3300.3300.3300.3300.3300.3828.3828.3828.3300.3300.

Mass flow densityin the post DNB

regionkg/M2.S

1419.957.660.

1450.990.660.

1378.937.689.660.600.

Inlet enthalov

kJ/kg

1284.1284.1284.1233.1233.1233.1284.1284.1284.1233.1233.

'~15000.

S.-

3300

~216504-

CA

(1

4.5 9. 13.5 18.time (s)

0 4.5 9 13.5 18

time (s)

Fig. 6: Typical processes of the test'parameters of the DNB tests

10

3.3.2 Post DNB tests

The purpose of these tests~wa§ the experimental determination of the heat

exchange coefficient in the region of the steam-droplets cooling with dif-ferent mass flows and pressure transients. The test runs, compiled in

Table 2, were set up in connection with the accident conditions with various

leak cross-sections (0.25F to 2F). The inlet mass flow of this test series,

maintain constant during a test run, was varied between the values G/GSTAT=0.4 and G/GTT 0.3 The blowdown time, determining the pressure

gradient during a test, amounted to 15, 25, 50 resp. 150 s. The bundle

inlet enthalpy remains constant during a test and was varied between 1.086-10'

and 1.55-10' kJ/kg. Figure 7 shows typical time processes of the twocontrolled test parameters.

Table 2: Variation of the test parameters of the post DNB tests

Test Inlet Mass Maximum Pressureenthalpy flow heat flux relief

density density periodkJlkg kg/M2S W/CM2 s

PD 1 1247. 1254. 162. 21.PD 3 1086. 248. 113. 23.7PD 5 1238. 858. 121. 29.PD 7 1086. 248. 113. 29.PD 8 1519. -157. 74. 35.PD 9 1519. 165. 78. 29.PD 10 1466. 91. 74. 32.5PO 11 1295. 319. 112. 51.PD 14 1461. 91. 74. 150.

0.

I

S2-

20 4time (s)

204time (s)

Fig. 7: Typical processes of the test parameters of the post DNB tests

11

4. CALCULATION OF THE HEAT TRANSFER COEFFICIENTS FROM THE TEST DATA

AND THE EVALUATION OF-THE RESULTS

4.1 Calculation of the heat transfer coefficients from the test data

The task of the KWU Co. in Erlangen was the determination of the heat trans-

fer coefficients from the measured time processes of the heating conductor

wall temperature, the heating capacity and the pressure at the outlet.

More detailed information about the inverse heat conduction program, used

for the calculation of the heat transfer coefficients, and several examples

of the results are contained in /3/.

4.2 Compilation of the important parameters obtained from the test

From the tracings of the test results there were taken the required parameters

and made possible for the direct access of a sorting program in the form of

data records. The following data records were established:

a) Test data of the DNB, resp. dry-out moment

For the rods-B2, D3, D4, D2, 03, and 04 the below data were established

from the tracings of the 11 DNB tests and the 21 post DNB tests:

- height of the measuring point

- DNB, resp. dry-out moment

- electrical power

- heat flux

- pressure

These values were established for the first and, as the case may be,

also for the second DNB, resp. dry-out, moment.

b) Test data for the RNB moment

For the rods B2, B3, B4, C3, C4,- 02, 03, and D4 the following values

were determined for the tests in which occurred RNB, and incorporated

into the RNB data records:

- height of the m easuring point

- RNB moment

- wall temperature

- saturation temperature

- pressure

12

- electrical power- heat flux immediately prior to RNB

- heat transfer coefficient -

The data from these data records can be interpolated and expressed at will in

respect to each other.

By using a special plotting program there can be represented the dependence

of any pairs of values from these data records in the form of printer plots.

As example, there is shown in Fig. 8 the correlation of the temperature

difference between wall and saturation temperature and the electric power.

These data records were subsequently expanded with the mathematically

ascertained values of the mass flow and the steam content at the DNB, dry-out

and RND moment.

This data collection contains at present 624 parameter combinations for DNB,

resp. dry-out, conditions and more than 400 parameter combinations for

the conditions with RNB.

The description of the individual programs and of the input data is contained

in /4/.DT =F(GE) FOR ALL TESTS (2.5 to 3.27 M)

---------- ------------------- I ----------- 4-------- ----------. 4

A co .. _3

2+0* -- -- - -- - -- - -- - -- - - . ---- -- - - -- --- -- -- -- --

2010..

Fi 8:.Creaino h eprtredfeec.ihrwt~n n

ofr the. eletrcpwe

13

5. CALCULATION OF THE LOCAL THERMAL AND FLUID DYNAMIC PARAMETERS-*

The local values of the thermal and fluid dynamic parameters required for

the evaluation, not measured in the experimental investigation, were cal-

culated in the supplementary analysis of the tests with the aid of the

computer code BRUDI-VA.

5.1 The computer code BRUDI-VA

The computer code is a substantially modified version of the blowdown code

BRUCH-D /5, 6/ and was developed for the evaluation of the 25-rod bundle

tests. This computer program is based on a so-called homogenous point of

equilibrium model.

5.1.1 Basic eguations of the homoqenou s point of equil ibrium model

Starting from the one-dimensional formulation of the conservation theorems

for mass and energy and-the equation of condition, the following differential

set of equations can be differentiated for the homogenous point of equilibrium

model

P [-M(h+ -) (G-h)A + (G-h)E + Q]/fM( + v) (2)

with e av andc~ & (

C (p/2 W2 .F), -n. (p/2 W3), -F and g-p-w-sin~b-F are disregarded)at z at'

Through the integration of the theorem of conservation of momentum between the

points i and i+1 of the flow path with constant time, the equation for G is

derived

14

i+1 da -G f . - [Pi- P1+1-g-p(H.~1-H.)-K'G- IGI (4)

(with ommission of 2_ (W2~ 4 -W2 .)2 i1 i

The still unknown values of K, resp. Q, are determined with the aid of cor-relations for the calculation of the two-phase pressure loss, respectively

with the aid of a heat conduction and heat transfer model.

5.1.2. Calculation of the two-pha se_2ressure loss

For the calculation of the pressure loss coefficient in the region of the

two-phase flow there was used the Martinelli model. The compariso~n between

the measured and the calculated pressure difference between measuring

section inlet and outlet (Figures 9 and 10) shows a good consistency between

measurement and calculation.

s:;!v- ce 7- Pressure diff. =.-j V = = 9 ,. . rNIE Pressure difference

S-as

Q)iUr_

CLe

W-

S_

a)

4-.

4-',

V)

a, -

5-US_

CL

Hieasurernent- Calculation

:.-~~ * C a.d11 8.-^3 2 2.g ~ ':

time '

Fig. 9: Pressure difference alongthe mjeasurinq 'section TestDNB-2

Fig. 10: Pressure difference alonq

the measuring section Test DPIB-9

15

5.1.3 Heat conduction model

The fuel rod model implemented in the-computer code BRUCH-D did not allow th'6

simulation of the heat production by means of electric current in the heat

conductor wall. Therefore, for the evaluation of the 25-rod bundle tests

there was developed a heat conductor model. The following hypotheses were

taken for the specifications of the model describing the intermittent heat

conduction:

- The axial heat conduction was neglected,

- The heat is conducted only on the external wall,

- The heat is produced only in the heat conductor wall and calculated with the

aid of the Lenz-Joule law from the current and the specific resistance,

- The temperature dependence of the values of p, Cp, y and Rp was-taken

into consideration.

- The wall thickness remains constant within a heat conductor segment.

The heat conductor model was technically designed for the program in such a

manner, that the number of the radial layers for each of the heat conductor

segments can chosen at will.

5.1.4 Heat transfer model

The examination of the heat transfer conditions in the high pressure phase

during LOCA was the task of this research project and it is dealt with in

details in the below chapters.

5.2 Calculation of the chosen tests and determination of the local thermal

and fluid dynamic parameters at the DNB, dry-out and RND moment

The purpose of the calculation of the chosen experiments was the determination

of the local values of the mass flow and of the steam content in the bundle

from the boundary conditions that had been measured-or had been determined

from the.-measurements. The followinq parameters were given as boundary

conditions for the individual computer runs:

16

- Geometry and pressure loss coefficients

- Inlet mass weight rate of flow

- Inlet enthalpy

- Pressure at the measuring section outlet- Heat flux

The calculated values of the mass flow and steam content at the DNB, resp.

dry-out, moment are contained in Attachment 1. In Attachment 2 are compiled

the important parameters at the RNB moment.

These computer runs were concomitantly used for the verification of the heat

conductor model and of the Martinell-Nelson model for the calculation of

the two-phase pressure loss.

The slight deviations between the measured and the calculated temperature

are caused by the necessary flattening of the heat flux curves (Fig. 11).

The consistency of the time slopes of the pressure difference along the

measuring section can be described as good (Fig. 9 and 10). A detailed

information about the calculation of the 25-rod bundle tests is contained

in /7/ and /8/.

SRUDI VA DNS 9 HB given

4-3

S-

.4-)

9-] -calculation

time (s)Y~

Fig. 11: Comparison between the measured and the

calculated wall temperatures - test DNB-9

17

6. COMPILATION AND COMPARISON OF THE CORRELATIONS FOR THE CALCULATION

OF THE HEAT TRANSFER COEFFICIENTS IN THE REGION OF THE FORCED CON-

VECTION WITH ONE-PHASE COOLANT

6 .1 Forced water convection

For the calculation of the heat transfer coefficients (WUK) with fully developed

turbulent flow there were chosen two correlations, well established on hand

of test results:

a) Dittus-Boelter correlation /9/

a =0.023Re0.8 Pr0.4

wih Re-G*D and Pr = Alfcr'ff

The physical characteristics are calculated with the mean temperature

between wall and coolant.

Region of validity: 5000 ;9 Re ;9 7l10

0.7 ;1 Pr 9 100

b) Sieder-Tate correlation /10/

002Re0.8 0.33 rif 0.14

a003*~*Rf *Prf if;) (6).

The reference temperature for the physical characteristics is the

water temperature n* is calculated with the wall temperature [sic].

Region of validity: 2300 ;S Re 9 106

0.6 9 Pr -%70

For the calculation of the heat transfer coefficients (WUK) with laminar

flow there was used the Sieder-Tate correlation

18

- Sieder-Tate correlation for laminar flow /10/

a =1.86 - (R - 0r-) .(-.14D (R * P (7)

The physical characteristics are calculated with the coolant temperature.

For n*is used the wall temperature.

*Region of validity: Re ;S 2300Pr %1

6.2 Forced steam convection

For the calculation of the heat transfer coefficients with turbulent flow

there were chosen the following correlations:

- Dittus-Boelter equation /9/

0.03 d *Re0.8 0.40O 3 .~Rd Pr d (8)

with Re d =G*D and Ord = %dCPd

The physical characteristics are calculated with the mean temperature

between wall and coolant.

Region of Validity: SOCO :i Re ;1 7-10~0.7 9 Pr ;S 100

- McEligot correlation /11/

a =0. 021 - d 0.8 0.4 T d 0.5*- D Re4d .Prd f- (....)

W(9)

The physical characteristics are

between wall and steam.

calculated with the mean temperature

19

Region of validity:140 R 4.*O1450 S Re S 4.5-10 4

The heat transfer coefficients in the region of the laminar steam flow were

calculated with the aid of the Hausen correlation.

-Hausen correlation for laminar steam flow/12/

a =~.s . d Td 0.23 10

Xd is calculated with the mean temperature between wall and steam.

Region of validity: Re 1 2300

6.3 Comparison of the correlations

The values of the heat transfer coefficients, as calculated with these cor-

relations for typical parameter combinations in loss-of-coolant accidents,

are shown in Attachment 3 and compared with each other. An examination of

these correlations within a wider parameter scope is contained in /13/..

20

7. COMPILATION AND COMPARISON OF THE CORRELATIONS FOR THE CALCULATION

OF THE HEAT TRANSFER COEFFICIENTS (WUK) OF THE SUBCOOLED AND

SATURATED NUCLEATE BOILING

7.1 Calculation of the necessary temperature difference for bubbles

formation with subcooled fluid

For the calcu lation of the temperature difference between the wall and

saturation temperatures, necessary for the formation of bubbles, there

were chosen two empirical equations.

- Jens-Lottes equation /14/

A~s= 7.9 -(q.10-4) 0 25 - eA (11)

A =- 66.205.106

Region of validity: P :9 14 MPa'q S 11 .10 6 WV/M

G 9 10000 kg/m2-s

- Thom equation /15/

AT bs = 2.2.5 .(q.10-4)1- -e A(12)

A= p8. 687 .106

Region of validity: 5 MWa 5 P :5 14 MWa

q 5 6-1 W/m2

1000 1 G 5 3800 kg/mZ.s

7.2 Calculation of the heat transfer coefficients in the region of the

subcooled nucleate boiling

For the calculation of the heat flux there was used the modified Chen cor-

relation.

21

- Modified Chen correlation /16/

q rMc(T -VT)f+ aMc . T -Tsa) (13)

'If 0.3 0.4with a Mac =0.023 * _D Reg f Pr f (14)

and amic. 0.00122-C- )aTO 24 '.P 0.3,S (15)

wheei A X0.79 0.45 0.49

0.5 0.29 0.24.02B =a - ah e

and s = eff 0. 99 co seCatr73and S C -~~~- ) - suppression faco (seCatr73

This correlation was verified by Butterworth based on experiments with water

and butyl alcohol and it led to a good consistency between the calculated and

the measured values. However, the exact region of validity was not given

in /16/.

7.3 Calculation of the heat transfer coefficients (WUK) in the region of

nucleate boing

For the calculation of the heat transfer coefficients (WUK) during nucleate

boiling there were used the Chen and Schrock-Grossmann correlations.

a) Chen correlation /17/

a =a Mi . C a (16)

Af 0.8 0.4mac =0.023 - :1 Ref Pr~ o F (17)

with F = Re~ 0.

%c=0.00122 LT 0.2 T *AP 0.SS (18)

22

A X0.79 0.45 0.49Af Cpf -Pf

0.5 0.29 0.24. 0.24

The curves of F and S are shown in Fig. 12 resp. Fig. 13.

Region of validity: o < x < 0.7

70 < G < 8000 kg/M2 .s40. < q < 2.40 W/CM2

b) Schrock-Grossmann correlation /18/

a2.5 * 1 0.752. C-I) . CItt0

= 0.023 f .[D-G 0.8 0.4

1 -- X- 50 -9 P 0 S 'i, 0.x 1x x ' 'I , (Ifd

(19)

(20)

(21)

Region of validity: x > 0. 02

7.4 Comparison of the correlations

The values of ATBS and of the heat transfer coefficients for some typicalparameter combinations are contained in Attachment 4.

23

C1

43

LL.

4XIt~

Fig. 12: Reynold's numiber multiplier F according to Chen

00~0

~1N

4JI-

II

104 106Re=ReLX '

Fig. 13: Suppression factor S according to Chen

24

8. TRANSFER FROM NUCLEATE BOILING TO FILM BOILING, RESP. STEAM-DROPLETS

COOLING - (MAXIIMUM CRITICAL HEAT FLUX)

The two fundamental physical appearances of the first heat transfer crisis

were already dealt with in Chapter 2. Here, there shall be examined the

individual physical models and correlations for the calculation of the

critical heat flux.

8.1 Vessel film boiling

The phenomenon of the critical heat flux easily examined during boiling in

heated vessels. A closed process of the dependence between heat flux and

temperature difference (Twall -Tsat) was first represented by Nukiyama /19/

in the manner of a so-called boiling-curve (Fig. 14). Due to the r~ise

of the heat transfer coefficients in the region of the nucleate boiling

the slope of the boiling-curve becomes gradually steeper up to point B.

When the heat flux reaches the value of point B, there is formed a steam

film between the wall and the fluid, the heat elimination from the wall is

limited now by the low heat conductivity of the steam, and the temperature

difference increases suddenly (B-C jump of the boiling-c~irve).

The hypothesis of the fuild dynamic origin of the heat transfer crisis

was first formulated by Kutateladze /20/. From the separated impulse

and continuity equations for water and steam there were established thefollowing dimensionless groups, describing the conditions during the first

heat transfer crisis:

W 2 A__ Wf*T Wdt Pf'f 2 Wd 2Pd a

With the assumption, that with free convection the first five groups can be

disregarded, there was deduced the following equation in agreement with

the Rayleigh theory of stability for the maximum steam volume flow from

the heated surface:

- a~g~f~p~)0.2S

(id~max pd -Ah K-( , Pd 2 (22)

25

610I-,

2

s-i

5~. 10

I-te~

a,=

.10

102

1~0,

Temperature di fference: (Tw -Tsat ) K 3

Fig 14: Boiling-curve according to Nuki~yama for containerboiling with 0.1 MPa

26

The value of K was analytically determined by Zuber

K = 4n

so that the equation for the maximum critical heat flux reads:

qmx=0.1567 Ahe'Pd2 [a.g.(Pf-Pd)l],2 (23)

Similar equations were established at a later date by other authors, as

for example by Zuber /21/ and Chang, Snyder /22/.

8.2 Heat transfer crisis with forced convection, high heat flux and

low steam content - (DNB)

8.2.1 Semi:e2irical miodel

Essentially, two different models were devel~oped-for the description of the

physical processes during the'transfer between nucleate boiling and film

boiling. For the first and more simple model one starts with the premise,

that the isolating steam layer is located directly between the wall and

-the fluid. Based on the result of an experimental investigation, Kutateladze

and Leontev /23/ developed an equation for thecalculation of the separation

of the boundary layer in fluid flow with lateral injection of air into the

flow channel.

P..jV.in.=2*1f * wff (24)

Tong /24/ modified this equation for the conditions under DNB

Pg * Vb= i-C a t= .P wf (25)

He further used the correlation of Maines /25/ for a calculation of ft with

low steam content

-0.6f---= Re -(25)tp

27

established, based on test results, the correlation constant C as function

of steam content:

C 1.76 -7.43x +12.22 -x2 (27)

Tong equation for the calculation of the critical heat fl ux (KHB):

q ~ ~ ~ ~ ~ ~~! (17 -74x122x).J ij W. 0.4. 0.4tia =(.7-.4x122X2 he. D f Pf (28)

Starting from the Reynolds analogy, Thorgerson et al /26/ developed another

equation for the calculation of the critical heat flux (KHB):

Pf~lf*CPf

therefrom results:

f- AT 2f *C~f (29)

and for the,DNB con ditions:

q = fDNBmx 2 1f Wf*Cpf (TwT sa) (30)

For the calculation of f there was used the equation (31):

f DNB =7.413 -Re OS (31)

Monde, Katto /27/ and Katto, Ishii /28/ started from the dimensional analysis

for the development of their own correlations and they established for the

volume-related steam velocity the following dimensionless groups:

q____ ma Pf 2_f r (f 9(PfPd)I (32)

PdA e d 'Id Pf~w2*' Pf~wI' ~

It was assumed that the influence of viscosity and buoyancy can be disregarded

during the first-heat-transfer--crlisis-in-the-f-lowed-through-channel.,-so-thatthe equation (32) reads:

28

_____ f__ Pf a

Pd-ahe-W =F (;(33)

Through the adaption of the individual exponents and of the correlationconstant to each of the used test results, there were established thefollowing correlations:

Monde-Katto correlation /27/

ma ` .O0745 - w - A

Katto-Ishii correlation /28/

q 0.014 - w- P .Ah (p 0.867 C /

~max d e ' Pd )W-P(P nhe2. a

(34)

(35)

These correlations were chosen from the plethora of similar equations'andused for the calculation of the critical heat flux (KHB). The figures inAttachment 5.show the comparison of the processes of qmxfor some typic~lparameter combinations.

W.- Z

f,bIy

Fig. 15: Model representation for the determination of the critical heat flux

.accordi ng to Tong

29

The second model -developed by Tong starts from the premise that the isolatingsteam 1ayer~is not located directly between wall and fluid but rather, as

shown in Fig. 15, that there is a thin layer of water between wall and the

bubbles. The presence of this layer of water was observed during the

photographic examination with freon of the flow conditions at DNB /29/.

The energy equation for the layer of water between the wall and the

bubbles was established by Tong as follows /30/:

j (Pf-Wf-P-h) + afb* -qp 0 (36)

with s =thickness of layer of waterlf ,bl = heat transfer coefficient (WUK) .between layer of water and bubbles

p = heated range

Under the assumption that pf-wf- remains constant along the flow path,

the equation (36) can be simplified as follows:

dz (h -h~ ) + C~h lh ) . Cpf-q (7M~~ ~ ~ ff~stbtf~a

wi th c = rf~bfPf Wf S.Cpf (38)

Z)ince the individual parameters in the equation (38) are partially unknown,

an empirical equation was established for C, based on measured results

C=O0. 44. A. inch- 1 (9

with A = (1'X DNB) .9and B 7 (G-10' ) 17

The practical application of this model is however very difficult because of

the very narrow region of validity for C and because of the complicated

conversion to conditions with variable heat flux.

30

8.2.2 Emeiricalcorrelations

In a manner similar to the one for the preceding case, a series of empirical

-correlations was published for the calculation of the maximum critical heatflow (KHB). Already in the year 1964, in the treatise of Milioti /31/

there were compiled 59 correlations for the calculation of the critical

heat flux, which were developed in connection with the reactor safety

analysis. The deviations of the values of the-maximum critical heat flux,

calculated with each of the-correlations, were denoted in this treatise as

very large. Instead of this group of correlations there were chosen three

equations, most used in the reactor safety analysis:

a) W-3 correlation /32/

=ma 3.15459 - 10

-[(2.022 - 0.0004302 * P) - (0.1722 -0.0000984

*P) * exp[(18.177 - 0.004129 -P) xJ])

*[(0.1484 - 1.596 - x + 0.1729 * x lxi )* (40)

*G*10 + 1.0371 - [1.157 - 0.869 -x]

*(0.2664 + 0.8357 -exp (-3.151 * 0)]

*(0.82s8 + 0.000794 - hi - hd

Region of validity 7 1 P :5 16 MPa

1360 1 G '1 6800 kg/m 2.s

-0.15 ;S x $ 0.15S-103 : 0 ; 175-1-3

0.25 $ L 1 3.6 m

Observation: This equation is applicable only in the case of homogenouspower distribution.

b) B-W-2 correlation /33/

=mx - 12.71.[3.0S45G.Gio-]A (41)

-{3.702-1.10 7 -(059137-G-10 I - 0.15208.x.,ah *'G}

.31

-3A = 0.71186 +'0.20729-10 -(P-2000)

8 = 0.834 + 0.68479-10- 3.(P-2000)

Region of validity: 14 9 P ý 16 MPa1020 S G !5 5430 kg/mZ-s

c) N-acbeth correlation /16/

=16 A+C*D*(G*10- ).O.25.(hz-h)1+C-1

(42)q ax

with A = yo* Dy (G-10-6) Y2

B = y3* DY'4 (G-10-6)Y

The values of y0, Y1, Y2-Y. yv4, and Y5for various pressures arein Table 3.

contained

Table 3: Values

ranges

of the Macbeth-correlation coefficients for various pressure

P~~essi~tt M.S No. of7 7 ' I 7P'Sia I I~ I IIPoinus

is 11 -0-211 0-3:4 0-0010 -1-4 -1-03 13-8 882-40 (norn) 177T -05353 _-0260 0-0166 :-14 -03M727530 (nomn) 1S57 0-i366 -0-329 00127 -14 0-07377 5.7 170

1000 1-06 -0-487 -0-179 0_003S -14 -0-SSS 7-4 .031570 (nozm) 07r0 -0-527 0-024 0.0323 -1.4 -0096 3-4 1332000 0-627 -0-268 0-192 0-0093 -1.4 -0-343 9-0 362Z"00 (no m) 0-011:4 -1-45 01439 0-0097 -1-4 -0S529 4-T 37

Observation: The parameters in the equations (40), (41) and (42) are tobe given in British units.

The values of the critical heat fluxes, calculated with these three cor-

relations, for the same paramater combinations as in Chapter 8.2.1., areshown in Attachment 5.

32

8.3 Hjeat-transfer crisis with forced convection, low to intermediate

heat flux, and intermediate to high steam content (dry-out)

8.3.1 Analytical models

The known model designs for the calculation of the dry-out of the water film

in.dependence of the supplied energy-, total mass flow and system pressure

do mostly originate from a mass balance for the film flowing along the wall.

The change of the liquid mass flowing in the film has to be attributed to

the evaporation, to the breaking-off of droplets (entrainment) and to the

originating renewed deposition of the droplets caused by the turbulent

radial velocity component (Fig., 16).

The mass balance equation for the water film with an annular flow *in'the

flowed-through-pipe was first established by Leslie and Kirby /34/ as

follows:

B = LF nD(G-G~ (43)

e

liquid film tdropletsG E/

Gjo

Fig. 16: Model of the annular flow with entrainment and deposition

33

he mass balance for the separated-fluid:-

BWE = nD(G -G )_ 4t0 8Caz E 0 I-,Y (44)

with C as droplet concentration in the steam flow.

The deposition of droplets in the liquid film was described with the 'aid

of a mass transfer coefficient K

G D =K *C

andG E K CE

(45)

(46)

Under the assumption that C E is a function of T*6/a and that K is a func~tion

of a, the correlations shown in Figures 17 resp. 18 were established for

these two unknown quantities. For the determination of the local pressure

loss (necessary for the calculation of T) there was used the equation (47).

46 = (dP/dz) LF 10-5

(7dp/dZ)(47)

Ica

10IC

It

I

0

-TA -At 07 Wta011~

0.1

C.C 0.1 0.2 0.3 . . . . . .

Fig. 17: Harwell correlation for the' determination of

coefficient.the entrainment

34

* - I.IWUIu .1"itnil~

z 0* ~ a0FREON 12

000(2.4

0.0c0 .14

0.O01 0.01 0.1CEPOSITIO?4 COEFFICI.ENT, k (rnsi

Fig. 18: Harwell correlation for the determination of the deposition

coefficient

For BWR conditions, Belda /35/ developed a model for the calculation of

the film thickness in dependence of time. For the determination of the

film thockness in the case of a BWR LOCA one started from the conservation

ths~orems for mass and energy, whereby the mass flows, given by film and

droplets, were described by simple statements. T he obtained differential

equation for the film thickness in dependence of time was solved numerically

and the dry-out moment was determined with film thickness = zero.

An equation for the calculation of the dry-out moment was developed by

Mayinger and Belda /36/:

tDO (aCPr/3P ) -(3P/8t) B n( )(8

A a -L*h - 60 ~ 2-.- 2:.. BI1-) Dtln~o8P e I 8t 4-1-pffi vz"IEo

f' e f f- D

35

wherein 6 0 is the film thickness in the stati onary initial state and the

constant C was determined by the adaption t .o the test results.

C = 0.15 for-freon 12 and C = 0.6 for water.

8.3.2 Semi: m2irical and empirical correlations

a) Hsu-Beckner correlation /37/

Hsu and Beckner developed a correlation for the calculation of the

maximum critical heat flux (KHB) in transient processes. This cor-

relation is, according to the assertions by the authors, valid for

a wide sphere of the determining parameters and can be used for both

types of the first heat transfer crisis DNB and dry-out.

q a-wd=1.33 -(O.96-tp)0* (49)

wherein q - is the heat flux with steam content x = 0, calculated

with the aid of the W-3 correlation, and xq,, d represents the heatflux density between wall and steam, calculated with the aid of the

Dittus-Boelter correlation for heat transfer coefficient.

b) Zuber-Griffin correlation /38/

This correlati on represents a modified form of the Kutateladze-Zuber

correlation for the calculation of the critical heat flux (KHB)

during nucleate boiling and it was developed for the range of the

low mass flows.

c) Slifer-GE correlation /39/

This correlation has a. very simple form and it was divided into tworegions of validity through the modification of the correlation

coefficient.

.36

qmx= 3.155-10 6 (0.8-x) for G 680 kg/M 2 .S

and (51)

qmx= 3.155.106 (0.84-x)fdr G 9 680 kg/M 2 -S

d) Smolin correlation /40/

Also this correlation has a simple form and according to the assertions

of the authors a relatively wide region of validity.

S 0.2 1.2.8qmx= 6.S-10 * EG *(1_X), *(1 .3-4.2S-10 -P) (52)

Reqion of validity: 380 9 G Z 4930 kg/M2-S

2.94 :5 P 9 13.7 MPa

e) Biasi correlation /41/

4

q2.7S510 1.4-A X) (S3)mx (1000)n .G0-167 GO- 167

for low steam contents (x < 0.3) and

4

q 1.51.10 8 1-)(4max (1OOD)n G*" 1)(4

for higher steamd contents and UG < 300 kg/in2 s

wherein n = 0.4 for 0 Z; 0.01 mn = 0. 6 for D < 0. 01- m

A =0.7249 + 0.99 * P -exp (-0.32P)

B = -1.159 + 1.49 -P - exp (-0.19P) + 8. 99-P1+lOPZ

f) CISE correlation /42/

1 .2S8-Ah(8)F (5S)

37

A =( -1)und B =(f-P )/(G-10Pr r

wherein p = P and PC = 22.1 MPa - critical pressure --.r PC

In Attachment 5 are shown the values of qmxfor chosen parameter combinations,calculated with the equations (49), (50), (51), (52), (53), and (55).

8.4 Verification of the correlations for the calculation of the maximumcritical heat flux (KHB) based on the experimental results

8.4.1 Selection of the correlations

For the verification based on the results from the 25-rod bundle tests therewere chosen the-following correlations:

- Tong equation-(28)- Thorgerson equation (30)

- Monde-Katto equation (34)

- W-3 equation (40)

- B-W-2 equation (41)

- Macbeth equation (42)

- Silfer-GE equation (51)

- Smolin equation (52)

- Zuber-Griff in equation (50)

- Biasi equation (53)

- CISE equation (55)

The chosen tests from the DNB and post-DNB test groups were recalculated with

the computer code BRUDI-VA, whereby the maximum critical heat flux (KHB)

was determined with the aid of each of the correlations in parallel with

the calculation. If, in accordance with the correspondincq correlation, the

value of the critical heat flux was below the value cf the local heat flux,

there was effected the transfer from nucleate bubbling to the correlation

for the calculation of the heat transfer coefficients ih the post-DNB resp.

post-dry-out region's. The moments of this transfer, as determined in the

-recalculation of several tests with each of the correlations, are compiled

in Table 4 and compared with the test results.

38

critical he~t flux (KHB) correlationsTable 4: Comparison of the

TE DNS time delay (s)TEST Height

Cen)teasur. Mod. W-3 Sli- Smo- B-W-2 Mlac- Biasi Tons Thor-Zuber fer lin bet~h gerson

135 No DNIB 2.6 - - - - - - --

190 No DNB 0.7 0.65 - - 0.7 1.2 - 0.92 0.4DNB-l 2.59 0.7 0.6 0.45 - - 0.52 0.8 0.9 0.75 0.4

327 0.4 0.5 0.2 1.1 1.1 0*.4 '0.6 0.6 0.8 0.4377 0.7 0.5 0.1 1.15 1.15 0.3 0.68 0.6 - 0.4

135 No DN'B 0.8 0.7 1.5 1.5 0.7 1.0 1.4 - 0.38190 No DNB 0.65 0.5 1.2 1.2 0.65 0.84 1.0 0.64 0.38

DNB-3 259 0.45 0.5 0.35 1.0 1.0 0.4 0.7 0.7 0.57 0.3327 0.2 0.4 0.15 0.85 0.85 0.2.5 0.55 0.46 0.63 0.3377 0.5 0.4 0.1 0.8 0.8 0.2 0.62 0.5 - 0.3

135 No D*NB 2.3 - - - - - - --

190 'No DNB 0.8 0.65 - - 0.8 1.4 - o .6DNB-7 259 0.7 0.65 0.5 - - 0.7 0.9 0.9 0.8 0.5

327 0.5' 0.55 0.35 1.5 - 0.4 0.65 0.65 0.8 0.4377 0.7 0.6 0.4 1.45 1.45 0.4 0.75 0.65 - 0.4

135 No DNB 1.1 0.65 - - - - - - -

190 No DNB 0.8 0.6 - - 0.82 0.93 1.2 0.85 0.8DNB-8 259 0.6 0.65 0.45 1.2 1.2 0.6 0.85 0.85 0.7 0.5

327 0.5 0.55 0.4 0.95 0.'95 0.45 0.75 0.7 0.75. 0.4377 0.6 0.6 0.4 1.0 1.0 0.4 0.8 0.6 - 0.4

135 No DNB 0.9 0.85 - - - - - - -

190 No DNB 0.75 0.65 1.3 1.3 0.75 0.9 1.2 0.8 0.8DNB-9 259 0.7 0.65 0.5 1.1 1.1 0.6 0.8 0.85 0.7 0.5

327 0.5 0.55 0.4 1.0 1.0 0.5 0.75 0.7 0.78 0.4377 0.6 0.6 0.45 1.0 1.0 0.5 0.8 0.65 - 0.4

135 No DNB 2.0 - - - - - - - -

190 No DNB 1.5 1.6 3.2 3.2 1.7 1.9 1.8 1.5 1.5DNB-11 259 1.2 1.2.5 1.25 1.45 1.45 1.35 1.5 1.5 1.4 1.3

327 0.9 1.2 1.2 1.75 1.75 1.3 1.45 1.5 1.5 1.2377 1.0 1.2 1.2 1.7 1.7 1.3 1.5 1.4 - 1.2

39

The Figures 19 to 22 show the processes of the critical heat flux, calculated

-with the chosen correlations, in the initial stage of two different DNB-tests.

By way of comparison, in these figures are also plotted the processes of. the

heat flux as determined from measurement.

ONE2 3 KHO CWNPARIS-ON ONE 3 KHE COM~PARISON

Zr

r_U-

U

[P

TINIE (S) TE HEIC-HT 190 CM

ONE 9 KHE COMiPARISON0N9 3 KHE CEi'PARIS01i

U

rn

0.0

00*N

S'W-

HZ EXE9.ZU

CD,

*j . . .

(S I 7'm HEIGHT,1259CM0 O0G 3 .4 3 0 1 .20

TI HE (S E HEIGHT 259CM1

Fig. 19: Comparison of the critical heat flux (KHB) correlations - Test DNB3

40

ONE DN2 9 K~---COM1PAR ISON

ON 9K!HGSr-K-= ThZPM==

LX KH3"VC

E,

TI1V1E (S I TE HEIGHT 927 CMI

ONE 13 KHE CO3MPARISONiONE

Th1E 7SE: H~IEIGHT3 77CM


41

ONE 9 KHE CO1f'PAR I SONI OjNE S)<V COIMPAR ISJO.N

(-)

7 " '71 ........

TIME (ScI TE HEIGHT190 C-M

-NrE 9 KH9 COINPARISON~%*- \-

- -a ENT,!

ONE 9 KHE2- C01,iPAIRIS3!No %*- SL !.=9

C Iý-~~SU- 7 l-'TCG

A.10--= MCrCEýE- E(FR!MNT

~to 15r

!s)~ 1c T HE-IGHT"~OrM


42

4

DNJE 9 <P.9 C0i11PARISON DN8- 9 KHE2 COMPARI SON

0

bm.O o.ýdo -o.rTII-,iE 1S) TE:HEIGHT 227CM TIES! TEHEIGHT S27 rC'M

0N96- 9 KH9 C011PARISON 0N9 9- KH9 COMPARISON

U

*-*.j9 .2T IIME (S I TE HLEI GHT 277C'A


43

r.

8.4.2 Evaluation of the correlations for the calculation of the maximum

critical heat flux

The results of the verification of the chosen correlations for the calculation

of the maximum critical heat flux, compiled in this Chapter, show that none

of the used correlations can calculate with sufficient accuracy for this

phenomenon the critical heat flux in the abovementioned sphere of the test

parameters of the 25-rod bundle tests. The graphic comparison of theprocesses of the critical heat flux under the same conditions in the measuringsection", calculated with these correlations, shows how the values of thecritical heat flux can differ. From the tabular comparison of the DNB delay

times, calculated with each of the correlations, it'results, that most of

the equations calculated the moment of DNB too late and also an exceeding

of the critical heat flux at axial positions in the bundle, whereas in theexperiment the critical heat flux was not exceeded. As only realistic

and, in the sense of the reactor safety analysis, conservative correlation

proved to be, and this only after leaving the given region of validity, the

W-3 equation. For the prediction of the dry-out moment with intermediate

heat flux, based on this examination, there can be recommended the cor-

relations by Slifer, Smolin and Biasi.

44

9. HEAT TRANSFER AT FILM BOILING AND STEAM-DROPLETS COOLING

This region of the heat transfer was, not only because of the importance

in the reactor loss of coolant accident analysis, the center of many

ex perimental and theoretical investigations. In this chapter is ex-

plained the phenomenology of each of the partial regions of the two-

phase heat transfer after the exceeding of the maximum critical heat

flux and some correlations are presented for the calculation of the heat

transfer coefficients in this region. Subsequently, these correlations

are used for the verification of selected tests of the research project

RS 37C and the results will be comparied with the test results.

9.1 Film boiling

As already mention in Chapter 2, in the case of film boiling it deals with

a form of heat transfer which occurs in the high pressure phase of a LOCA

with a rapid depressurization only very limited in function of time and

place.

The transfer of the inverse annular flow, the flow form typical for this

heat transfer mechanism, to the steam-droplets flow is additionally

accelerated in a PWR bundle, in contrast to the flowed-through pipe, due

to the effect of spacers and of the transverse exchange.

9.1.1 Film boili nq with wettable wall

The accurate calculation of the heat eliminated from the wall in this area

is very difficult because of the unstable thermal and fluid dynamic processes.

The thin steam film, enveloping the wall, can be pierced by the waves at

the core water flow. The liquid reaches the still wettable wall and it is

again forced away from the wall by the very high evaporation. The wall

temperature has however dropped because of the very effective nucleate

boiling. This process can repeat itself several times.

Since the heat flux density in the case of an inverse annular flow has to

be generally very high, the wall temperature increases very sharply

45

(up-to 300 K per second) after the formation of the insulating steam film

and the wetting temperature is rapidly exceeded. Therefore, the area of

film boiling with wettable wall is only of subordinate importance for

the calculation of the clad tube temperature processes and for the cal-

culation of the heat transfer coefficients (WUK) there can be used byapproximation the correlations described under 9.1.3.

9.1.2 Film boil ins with not wettable wall

In case the wall temperature lies above the temperature of application, the

liquid does always remain separated from the wall by A steam film (Leiden-

frost phenomenon). The heat removal from the wall can be determined in this

case with the aid of the correlations for the calculation of the heattransfer coefficients (WUK) with forced steam convection (equations (8), (9)

Chapter 6.2) or with the correlations for the calculation of the heat

transfer coefficients (WUK) with vessel film boiling.

9.1.3 Vessel film boilin

The conditions dur~ing film boiling in the heated vessel are schematically

represented in Figure 23.

Fig. 23: Schematic representation of film boiling in vessel boiling

46

One of the first models of the film boiling mechanism with free convection

was established by 8Vtberr /43/. The heat that was conveyed to the water

phase was calculated in this model as the sum of the heat fluxes which

are conveyed to the water through the steam film because of conduction andradiation, less the heat required for the additional evaporation.

According to his conception, the heat flux was then determined at thewall through the free convection in the water phase, so that for the

Nusselt number there can be used the following equation:

Nu f K * GIP (56)

(n =1/3 for horizontal plate)

All values in the equation were calculated with the mean temperature between

saturation temperature (water surface) and the mean water temperature. For

the calculation of the heat flux density there was derived the following

equation:

q = (TsatT) K-(T -T )4.'3(f.2.~fp)nfI' (57)stfsat f ((~p..f Cp)q]'

The correlation constant was determined through the adpation to experimen-

tal data:

K = 0.0015

2rornIey /44/ postulated, in a manner similar to Awberry, that the heat

from the wall is conveyed to the liquid through heat conduction and heat

radiation. The heat conduction share was adequately treated pursuant to

the film condensation theory of Nusselt, so that heat transfer coefficient

(WUK) was defined as relation between the heat conductivity and the steam

film thickness.3 (K {%*d (T W- sat) /[p*p/p).g.-_jiC] }1 /4 (58)

with Ah-1 = Ah (i04p(WT )Ih(9e e sa4c(T~ t )Aie'(9

thus, the correction for the heat transfer coefficient with laminar film

boiling reads:

K[Xdgp-h][j(T-st-]II (0

47

The mean value of the correlation constant was given by Bromley as K =0.62.

In cylinder geometry, is replaced with D.

The heat transfer coefficient for the calculation of the radiation share

was calculated according to Bromley from the following equation:

at= {K52 /[(1/C).(1/Ka)-11j[TW4Ta 4 )/CTWTa) (61

Hsu and Westwater /45/ did take into consideration the influence of the

turbulence in the upper region of the steam film and developed for the con-

-vective heat transfer coefficient the equation:

Cr = .02-Re 4 Wd[j2[,-pd (f-d(2

wi th Re=d

wherein Wd is the steam mass flow at the end of the film boiling region.

Berenson /46/ used for the determination of the characteristic geometric

parameter (:resp. D in equation (60)) the Taylor-Helmholz instability

theory and established for the calculation of the convective heat transfer

coefficient the following equation:

e~ (63)sa

with a = {a/[g(pf-pd])1 12 (64)

and the correlation constant K =0.425.

The physical model, based on.which is the reasoning of Berenson, is

schematically represented in Fig. 24.

The values of the heat transfer coefficients, as they were calculated withthe correlations of Bromley and Berenson, are shown in Attachment 6.

48

Fig. 24: Model of the vessel film boiling according to Berenson

9.2 Steam-droplets cooling

During the last few years, there were developed many more or less empiricalcorrelations for the calculation of the heat transfer coefficients in the

region of the steam-droplets cooling. Generally, these correlations can

be divided into two groups:

- semi-empirical (pheomenological) models

- empirical correlations.

The empirical correlations are valid mostly only in a determined region of

the parameters, without differentiating if in this region it deals with

different physical processes. On the other hand, in the development of

of the phenomenological models it was endeavored to take into consideration

the mechanism of the physical processes. The resolution of the overall

49

process into individual steps, led however in the majority of the casesto the need for the determination of parameters, which cannot be unobjectionably

determined through measuring techniques and, thus, have to be finallyestabl ished empirically.

In connection with the development of the so-called progressive computer

programs hereafter will be subdivided the existing models into so-calledequilibrium models, which are established on the assumprion of the thermo-dynamic equilibrium, and the so-called nonequilibrium models, in which the.

thermodynamic non-equilibrium was taken into consideration.

9.2.1 Equilibrium models and correlations

Into this category fall most of the empirical correlations. They are based

on the statement derived from the similarity principle for the on-phaseforced convection.

Nu =K - Ren , Prm (5

In order to take into account the varied nature of the two-phase flow,

there was expanded either only the Reynolds number or the entire right side

of the equation (65).

Dougall-Rohsenow and, simultaneously, Miropolskij introduced the Reynoldsnumber modified for the two-phase flow.

Rep Re (66)

wherein the steam volume share q was defined as follows:

ý1=X/(x+$*(1-x)*p d/pt] (67)

If the same velocity Is postulated for water and steam, one obtains for the

RezP :

Rez c x4.(1-X).Pd/pfI 68

50

22M11lland Rohse now /47/ inserted then this Reynolds number into the Dittus-Boelter equation-(8) for forced convection and obtained:

Nud = 0.023 Rez 0.8 - Prd 0.4 (69)

wherein all the values of the steam were calculated with the saturation

temperature. The influence of the certainly higher temperature in the boundary

layer upon the magnitude of the Prandtl number was later on consideredthrough the expansion of the right side of this equation with the correction

term (Tf/T W)05$, so that the modified Dougall-Rohsenow equation reads:

Nud = 0.023 - Re 0 8 * Pr0 '(0

d ~ ZP rdo (Tf/Tw) 0-5(0

The wall and water temperature has to be inserted in this equation in degree

Kel1vi n.

Uiro221il /48/ expanded besides the Reynolds number the right side of

the equation (65) with the so-called two-phase multiplier Y

Y =1-0.1 (P f/pd)-1O4* 0 -. )4 (71)

so that his equation assumes the following form:

Nu = 0.023 - ReO-8 Pr 0-S * Y (72)ZP d

The values for the Husselt and the Yenolds numbers were relative to the

saturation temperature, and that of the Prandtl number to the wall tem-

perature.

Groeneveld /49/ presented in this treatise the general form of his equation

for the calculation of the heat transfer coefficients (WUK) in the region

of the steam-droplets cooling:

Nu K Ra Pb. c.qZP d (73)e

The correlation constant and the exponents were determined with the aid of

venious experimental data and they are contained in Table 5.

The values of the Nusselt and Reynolds numbers and of the two-phase multiplier

are calculated with the saturation temperature, that of the Prandtl number

with the wall temperature.

51

Table 5: Valu-es of the correlation coefficients for the Groeneveld correlation

Gcaeorry ab C d e No. nr R.M.s. Equationpoints error(7.) no.

Tubes 1.85 X 10-4 1.00 1.57 -1.12 0.131 438 10.1 181.09 x 10-1 0.989 1.41 -1.15 0 438 11.5 19

Annuli -1.30 x 10-2 0.664 1.68 -1.12 0.133 266 6.1 205.20 x 10-2 0.688 1.26 -1.06 0 266 6.9 21

Tubes and 7.75 x 10' 0.902 1.47 -1.54 0.112 704 11.6 22annuli 3.271x 10-3 0.901 1.32 -1.50 0 704 12.4 23

A surmmary of the empirical correlations for the calculation of the heattransfer coefficients after the exceeding of the maximum critical heatflux was established by Groeneveld /50/ and it contains 24 differentequations.

Conde andBen9ston /51/ used the regression analysis for the evaluation ofthe experimental data contained in the NRC data bank and they determined

the following equation for the calculation of the heat transfer coefficients

(WUK):

0.05345 - (,a . Pr b ReC)/(D)d .*x,)] (74)

with Re = D. und a = 0.4593; b =2.2598;

C= (0.6249 + 0.2043 -In (x+1)l; d = 0.8059 and e =2.0514.

Reqion of validity 0.42 :9 P' 22.15 MPa

40.1 ;9 b ý 3939 kg/m2-s

X <

The values of the heat transfer coefficients for typical parameter combinations,

calculated with the equations (69), (70), (72), (73), and (74), are shown in

Attachment 6 and compared with each other.

9.2.2 Non:tguilibrium -models

The fact, that the steam and water phase in the region of the steam-droplets

cooling can be in thermodynamic non-equilibrium, was determined already in

52

196-1 during the experimental investigation by Parker and Grosh /52/. The

resence of water droplets was observed during this investigation although

the equilibrium steam contents lay far above the value of x = 1. One of the

first so-called "Two-step'"'-hbat transfer models for the steam-droplets

cooling was developed by Laverty and Rohsenow /53/. The first step in

this model - the heat transfer from the wall to steam - serves mainly

for the superheating of the steam, which is then cooled in the second

step through the evaporation of the droplets. This viewpoint of the heat

transfer between wall and the steam-droplets cooling was used as the basis

for most~of the subsequently developed models.

Forslund and Rohsenow /54/ expanded the "two-step" heat transfer model and

attempted to determine quantitatively the heat transfer between wall and

the droplets near the wall. The heat transfer coefficient between wall

and droplets was determined with the aid of the Baumeister correlation

/55/

UWT 1 (X~p-pf -g.Ah-)/B] (75)

with B * (TW.T U) . V(rd~/61 1/3

and Ah he * (1+0. 35Cd(Tw-T )/I,3 (76)e eC~ sat)&e]

The number of droplets in the proximity of the wall was calculated with the

following equation:

N =~ / (777)

wherein NT is the droplets density per volume unit and was calculated as

follows:

im =G - 1-x a]/t(P,*W,*rr*&3 )/6] (78)

The local droplets diameter 6 TI still unknown in the equations (75) and (78),

was calculated with -the aid of the energy balance for one droplet and the

initial droplets diameter, determined from some measurements.

The equation for the calculation of the heat flux density between all and

droplet reads:

53

q = Cr * (n-8 2/4-) - N * (TW-TwT wT T Tw sat - (79)

Hynek, Rohsenow and Ber9!es /56/ determined the values of the correlation

constant for various liquids

Nitrogen K 1 * K2 =0.2

Water K1 I * 2 1.

Methane K1I * K2 =2.

Propane K 1 * K2 =1. 2.

In lieu of the non-equilibrium models in this treatise were examined the

correlation systems of Groeneveld-Delorme and Chen-Ozkaynak-Sundaram.

a) Groeneveld-Delorme model /57/

The Groeneveld-Delorme method is based on the following important

assumptions:

- The wall temperature is higher than the Leyden frost temperature

- The heat removal from the wall through the flow can be disregarded

- The velocity difference between steam and water phase can bedisregarded

- The entire heat removal from the wall can be calculated with the

aid of a correlation for the calculation of the heat transfer coef-ficient (WUK) with forced convection of steam with the applicationof the steam velocity.

For the calculation of the heat transfer density between wall and steam

there was used the Hadaller correlation /58/:

q (=- ad I -0.O.08348.ReO .774..PrO.6112 (80)

The actual steam content xa was determined from the energy balance:

Xa =Xe ' he/(hd-hf) (1

54

For the determination of the steamntehnperature and, thus, also of the

"actual" steam enthalpy there was established an empirical equation:

(h da-hd )/&h e= exp [-tan 0] (82)

with the rather complicated function:

* *Pb * eC d i=2a Pr Re am (pD-Cpd/Xd*.h el I fi(e1=0

(83)

with Re ham G -D- /l *'hamanu *'ham =Xe/l:Xe+( Pd/Pt) (1Xe)]

The values of the correlation constant and of the exponents were given

as follows:

a =0.13864; b =0.2031;

f 1.3072;

c= 0. 20006;

f 1 = 1. 0833;

d =0. 09232;

f 0. 8455

Region of validity 0. 71 ý6 P130 9 G

-0. 12 9 xe0. 005 9 D

S 21.47 MPa;S 5100 kg/M2 .S;S 1.69 0. 02 m

b) Chen-Ozkaynak-Sundaram model /59/

Chen at al developed for this model a new equation, based on the Reynolds

analogy, for the calculation of the convective heat transfer between

wall and steam:

Starting with the statement for the Stanton number:

St = f/2 (84)

the following equation was developed for the steam convection in the

steam-droplets cooling region:

St= a wd/(p *w*CP)d (85)

55

After the introduction of Gd = G*Xa and the expansion of the's~tatement

also for Pr f1 (Colburn modification of the Reynolds analogy) theequation for the convective share of the heat flux read s:

Qw,d = d CPd -Prd /3 (T -Td) -f/2 (86)

For the calculation of f there was ued the approximate correlation ofBeattie /60/:

f = 0. 037 * R eO -17 (87)

with the following definition of'the Reynolds number:

Re = (Dpd.<j>)!nqd; <j> = (Gd/pd) + CGf/pf)

For the calculation of the relation xa /xe there was developed a cor-relation with the use of several experimental results:

Xa 1 - S(P) - o(88)

with S(P) 0.26/[l-i5-(P/P )0 * 6 3 ] (89)

and 7.D (Td-TSat) / (TW-Td) (90)

The heat transfer through radiation was also disregarded in this

model.

Region of validity P 9 19.S MPa16.6 ;5 G 9 3011 kg/M 2 .S

0.5 ý Xe ý 1.728

9.3 Comparison of each of the correlations based on the recalculation of

selected 25-rod bundle tests

For the investigation of the equilibrium and non-equilibrium correlations

the tests DNB1, DNB3 and DNB9 were selected from the "DNB test sre" and

the test PDNBil was selected from the "Post DNB test series."

56

9.3.1 Recalculation of the test DNB1

The curves of the important test parameters, of the local values of the

mass flow calculated with the computer code BRUD I-VA, and of the steam

contents, and a complete set of the calculated results in comparison with

the test are compiled in Attachment 7.

ONG I CORR. COMPARISON 0N9 I CORR. COU!PARISON

IN

LU

2-,

LU

a-

.0N8

LD

(Dol-

0,-.

_i 0

I. CORR. COf IPARISO'N 0N9 CORR, C0O11PARISON'7l I

V

2

2

0-00"

00.

0 M. CUJGCJ.=- Rq-'SEj.W

*- CRI-EýZELD 3.7

---Exerirnent

THIjE S TE C3 327 G-10.00 2.00, '..n SJ

TUiE S- TEE C-m 327 CM-,'

Fig. 25: Comparison of the equilibrium correlations - Test DNB1

The values of the wall temperatures and of the heat transfer coefficients,as they were calculated with the equilibrium correlations at two differentaxial positions in the bundle, are compared in Fig. 25 to each other and

with the values determined from the test.

The comparison of the values of the wall temperature, calculated with the

non-equilibrium correlations,of the heat flux, of the steam temperature, and

of the actual steam content is shown in Fig. 26.

0N9 :CORR. CO[IPARISN.hH

wU

CDw

0~EwH

-J-J

14.c1-~~1-4

0:

-I

I,

9,1

tZN 3z<R1'1A

Experiment

ON9 if CORR. CO!"PARISON

U Zx;eriment

04-

T IME E- CSm 32.7 CM3.13 2.23 d.13.3 a

TIME S T C3 =27 CM

0j

0n

-I/ -

Ri I

~-li ' * I-~,, -~--

-i C C.'-SN ~IC'P~

j*flTh

3.30 2.30 433

TIME S TE 02 227 CM

911U

Lo.I

Cn 7

4.- oj :..

TIMiE S 7-C-2 227 CN"11

Fig. 26: Comparison of the non-equilibrium correlations - Test DNB1

58

9.3.2 Recalculation of Test DNB3

The curves of the important test parameters, of the local values of the mass

flow, calculated with the computer code BRUDI-VA, and of the steam content,

and a complete set of the calculated results in comparison with the test

are compiled in Attachment 8.

DN19 3 CORR. COMPARIOSUN D N t23 CORR. COMPARISON

01-

C-

p.

N

D

.00O 6.'30 .05 T C3 259 CMTIMlE. TIME -9 TE C-3 259 CM

DN9 3 CORR. CO1',1PARISO14

0-1

C-_.,0

5-

*1~11

Clo.J

I,-~ *1

070~*101

o .~

rI[IE

I= ;3 *HSE CcCNý31E 'S O IV*i- GNZr-L. S .7

-- Ex--eri~ent

D0N9230

NOI

CORR. COMIPARISON

S C'773 B277 Cm T I ME E r C3 ':277 r"


59

The values of the wall temperatures and of the heat transfer coefficients,as they were calculated with the equilibrium correlations at two differentaxial positions in the bundle, are compared in Fig. 27 to each other andwith the values determined from the test.

The comparison of the values of the wall temperature, calculated with thenon-equlibrium correlations, of the heat flux, of the steam temperature, andof the actual steam content is shown in Fig. 28.

No

DN9 3 CORR. COIIPARISUN 0N93 CORR. COfIPARI SON'

F xperiment

aI.

C-

-j-j

2:

2:N.2- = - . = - - S

0-- Experienert

0'ý 10I

0*

a

a-

wH

wHU)

-J

HC-,

;.J3 S.0 6.00 9.03

Ti1 i-E s TE C 3 27 CM,

. - - - - - . . I

T IiME* ~SJ

S E.C 3 B27 CM

zcH0

0

LU

U)

T I HE SZ6,00 . 9.00

TE C3: 3217 C> TI PIE S !E c3n 327' C-II

.Fig. 28: Comparison of the non-equilibrium correlations - Test DNB3

60

9.3.3 Recalculation of the Test DNB9

The curves of the impcrtant test parameters, of the local values of, the

mass flow, calcdlated with the computer code BRUDI-VA, and of the steam

content, and a complete set of the calculated results in comparison-with


ONE 9 CORR, C0i'iPARISOIN ON.E 9 CORR. COIMPARISON

C-.,0

0~

-j-J

0

0~

I--J-J

J!6

D

TIME S TE C3 259 CM TIME S .T E rC'3 2 59 C M

1-9 9 CORR. COMAPARISONDONE 9 CORR, COM1PARISON'1 0-M. 0CJG72L L~'c CzNO!E ~ESr-UCN ;V~1+ CRC2/EL.Dý S.7

1-- Experiment2:

0

TIMETE C3 .2 C

TIME T!:0 32 CM=7


61

The values of the wall temperatures and of the heat transfer coefficients,as they were calculated with the equilibrium correlations at two differentaxial positions in the bundle, are compared in Fig. 29 to each other and

with, the values determined from the test.

The comparison of the values of the wall temperature, calculated with the

non-equilibrium correlations, of the heat flux, of the steam temperature, andof the actual steam content is shown in Fig. 30.

DN299

t-

CORRI COIPARI SOiN DN2 g CORR. C01"'PARISON1

E

U

TIME STE Cm 327 CM1 T IME TE_ C-7 327 C:"'

C,,

C-,

I-

u-II-0U

u-iI-U,

-J

I-U

TIME S CE 3 :327 TIME 55 *EC3m 327

Fig. 30: Comparison of the non-equilibrium correlations - Test DNB9

62

9.3.4 Recalculation of the Test PDNBl1

The curves of the important test parameters, of the local values of the

mass flow, calculated with the computer code BRUDI-VA, and of the steam

content, and a complete set of of the'calculated results in comparison with


PONE 1 t CJ~RR CO1"PARISON'

U c:>n!S: SEr-\STrM IIV+ G~rMZY'ELD S.7

E- xperiment

5-

,PDNE 1! CORR. COMPARISON

.1!

TINE 5 TE C3 259ý CM

PONG 1 1 CORR. COi1PARISOIN

TIM*E S TE C3 25591 Cii

P-DN9 CORR, C01";PARISON

0

0~

I--J-J

p.

-.J 3n.0~ 6-.'n 3 J .

TIME S~ 77 C3B 327 Cii T I la *S T C. 52. C

Fig. 31:Comparison of the equilibrium correlations - Test PONBII

63

The values of the wall temperatures and of the heat transfer coefficients,

as they were calculated with the equilibrium correlations at two different

axial positions in the bundle, are compared in Fig. 31 to each other and

with the values determined from the test.

9.4 Evaluation of the correlations for the calculation of the heat transfer

coefficients in the steam-droplets cooling region

The recalculation of the selcted tests with the utilization of the verious'

correlations for the calculation of the heat tran'sfe"r --coefficients in the

region after the exceeding of the critical heat flux showed, that none of

the selected correlations can be recommended for the entire scope of the

test parameters. In the recalculation of the tests with intermediate tohigh steam content (0.5 < X < 0.9) and with intermediate mass flow density

(1300 to 1800 kg/m 2-s) there could be obtained a good agreement between

calculated and test results if the modified correlation of Dougall-Rohsenow

was used for the calculation of the heat transfer coefficients. In the

recalculation of the tests with a lower mass flow density (G < 1000 kg/m2-s)

the curves of the measured wall temperatures were better reproduced with

aid of the Condie-Bengston equation and partially also with that of Groene-

veld. The application of the newer non-equilibrium correlations showed

to be rather complicated and did not lead to a better agreement between

the calculated and the test ~results.

- - 64---- ----

10. TRANSFER FROM STEAM-DROPLETS COOLING OR FILM BOILING TO NUCLEATE

BOILING (RNB-REWETTING)

10.1 Compilation of the experimental data from the 25-rod bundle investigation

As already mentioned in Chapter 4.2, the following parameters were compiled

for the specific R14B moment in the RNB data set.

- RNB moment

- Wall temperature

- Saturation temperature

- Pressure

- Electric power

- Heat flux immediately prior to RNB- Heat transfer coefficient

In the recalculation of the test there were determined the pertinent values

of the mass flow and of the steam content and they were inserted into-.the

data set.. The Figures 32 to 35 show.the dependence of the temperature

difference of pressure, heat flux, mass flow, and steam content.

C0,

3.5.0 7.0

Pressure (M.Pa)

9.0 11 . 20. so. 80.

Heat flux110. 140

(W/crn -cn)

Fiq. 32: m~easuring pointsTW-T sa = f(p)

Fig. 33: measuring pointsT WT sa (q)

65

C-

E-4-

0.0 2.0 4.0 6.0 8.0 0.1 0.2 0.3 0.4Mass flow (kg/s) Steam contenXt

Fig. 34: Correlation of G to TwT sat Fig. 35: Correlation of X to T -T sat

10.2 Correlations for the calculation of the minimum critical heat flux and

of the minimum temperature difference with rewetting

The transfer from steam-droplets cooling or film boiling back to the nucleate

boiling in the high pressure phase of a LOCA was thoroughly investigated

only after both nuclear LOFT tests (L2-2 and L2-3) had been conducted. Forthe calculation of the minimum critical heat flux or of the minimum- temperature

difference with rewetting, in these investigations were mostly used the

correlations of Berenson, Henry and Iloeje.

Berenson /61/ used his correlation for the determination of the heat transfer

coefficient in the proximity of the minimum of the Nukiyama boiling curve

(Fig. 14).

with a = {O/[g(pf~pd 111/2

The Zuber correlation for the calculation of the maximum critical heat flux

was modified by Berenson and adapted to the conditions with rewetting.

66

q =iný0.09.P (92)lga(fPd/P-d 2 / (92)

The equation for the calculation of the minimum temperature difference withrewetting was obtained by dividing the equations (87) and (86):

Clg-(f-d)11/2.n/( -d 11,3 (93)

The minimum temperature difference resulting from this equation was used asthe basis for the development of further empirical correlations.

U22er~v /82/ investigated, among others, the influence of the relative values

upon'the magnitude of the monimum temperature difference and he established

the following equation:

0 6C(T _T )/(T -T )J=0.42 -(A]*min,H min,B min,B f

(94)

wherein A = [*/Af.pf-Cpf/4A." P*'CP ]*[Ah e/4Tmin,]

and T min,8 =6T min, 8 + Tsat

Iloeje et al /63/ developed an empirical correlation, in which the influence

of mass flow and steam content is taken into consideration and he determinedthe correlation coefficients based on own tests.

A~TmnI = 0.2 9*ATiB(1-0.295-X2 4S)(1+(G.10-4) (95)

The tests with an internally flowed-through tube were conducted within the

following range of the test parameters:

68 ;5 G ;5 340 kg/mz*s

0.3 9 1

P = S. 9 MPa

D =0.0124 - internally flowed-through

67

10.3 Investigation of the correlations based on the results of the 25-rodbundle tests

During the recalculation of the tests DNB3 and DNB9, the values of theminimum temperature difference and of the minimum critical heat flux werecalculated with the aid of the correlations (93), (84), (95), and (92).

DN9 3 TEST DM8 3 TLES T

Z,1 OTo test

SOTM!N !LCL.C

Id:

zz

-JLU0

0.00 3.00TIME S HEIGHT 2-59CM TIME S HEIGHT 327CM

DM8 9 TEST

~0.(~0

0*Zo-(0

I--IU0~~~

TIME S HEIGHT -327CM

Fig. 36: Comparisons of the correlations for the calculation of ATmin

68

In Fig. 36 are compared the values of the ATmi n with the temperature~dif-

ference between wall and saturation temperature, determined from the test.

Fig. 37 shows the comparison of the local heat flux with the values of

qmnwhich were calculated with the Berenson correlation (92).

ON9ES TESTr ONE 3 TrEST

z0

ONE 9 TE~ST

CD

0

N aC C.1 IN =- J-NS4

ONE 9 TEST

o aCCHW/ci1CM

c~ 1 I1N

Oen

o 1.'

TIME S HEIGHT 2590CM TIME S8 .1)O

HEIGHT,1 27 1.

Fig. 37: Comparison of the minimum and actual heat flux

69

10.4-- Evaluation of the correlations

From the comparison of the minimum temperature difference, calculated withthe aid of correlations, with the test results it follows that all threecorrelations rendered too high values of ATmi n* The Berenson correlation

for the calculation of the minimum critical heat flux (KHB) [CHF) is mass

flow and steam content independent and, thus, inadequte for the applicationto the conditions in a flowed- throuqh coolant channel.

Further, it has to be established that precisely for the parameters thatare typical for the high pressure phase of a LOCA there exist only a fewpublished test results. The experimental results, determined within theframework of the 25-rod bundle tests, are thus very valuable and they canbe used for the verification of the correlations and models.

70

11. DEVELOPMENT OF A NEW CORRELATION FOR THE CALCULATION OF THE HEAT

TRANSFER COEFFICIENTS IN THE STEAM-DROPLETS COOLING REGIME

The comparison of the calculated and test results in Chapter 9 showed, that

none of the used correlations for the heat transfer coefficients in the

steam-droplets cooling phase can be recommended without limitations to be

applied to all of the test parameters. The individual correlations, that

were developed and verified based in the majc~rity of the cases on deadbeat

investigations, covering only a certain phase of the important parameters,

did show significant deviations from the test results ascertained from

the 25-rod bundle tests. Also the use of later models, in which the

thermodynamic non-equilibrium between the two phases was taken into con-

sideration and which separated the heat transfer mechanism into individual

steps, did not lead to an approximation of the calculated time behaviors

of the wall temperature to the test results. Therefore, each of the

heat transfer processes during steam-droplets cooling was throroughly

investigated.

Figure 308 shows the heat transfer meachanism in the steam-droplets cooling

phase.

.X1Qd SUPERHEATING

qwdI (1-Ff)

q TOT - T, EVAPORATIO'N

IqWtT*F;

Fig. 38: Model representation for the heat transfer in the steam-droplets

c-ooling phase

71

According to this consideration, the entire heat flux density is made up

of two componrents:

= ~d (1-Ff) + q w,T P Ff (96)

wherein cy~ - is the amount of heat per surface unit of the heated wall,

eliminated by the steam phase (convection and radiation)

and qw, - is the amount of heat per surface unit of the heated wall,

eliminated by the water phase (convection, conduction,

radiation).

11.1 Heat transfer between wall and steam phase

For the cakculation of the heat transfer coefficients between wall and the

steam phase there were used not only the correlations given in Chapter 6(equations 8 and 9) but also the Hadaller correlation (equation 80) and

the Chen equation (equation 80)'derived from the Reynolds-Colburn analogy.

DM8 3 CORR. CUMPARES"OiN DM8 CORR. COMPARISON'

-14F11 :-i 1 C MCMGO

0--- Zxperizent

-40 -r

-JE-

-j Ex~eriment -. 0

.Q .0 .0 .00.00 3 .0 0 6.00 9.-00TIME S TE C3 259 CM TIME S TE C-3 2-59 CM

Fig. 39: Comparison of several correlations for the calculation of the

heat transfer coefficients with forced steam convection

72

The processes of the wall temperatures and of the heat transfer coefficients,

calculated with these correlations, as they were determined in the recal-

culation of the DNB3 test, are shown in Figure 39 and they are compared

with the experimentally established values of the entire heat flux density.

For the calculations of the Reynolds number in the correlations, there was

firstly taken the homogenous steam velocity and the density of the steam.

The heat flux density was calculated in this case with the entire temperature

difference between the wall and the saturation temperatures. As shown by.

the results, the heat eliminated from the wall by the pure steam convection

is too-low. If it is postulated that between the droplets present in the

steam flux and the wall there does not take place a direct heat transfer,

and the heat is eliminated from the wall solely by the steam convection,

the steam velocity has to be considerably higher as the one calculated

with the homogenous statement. In other words, there has to exist a con-

siderable slippage between steam and droplet.

Therefore, the known equations for the calculation of the slippage and the

drift correlations were set up and used for the determination of the'steam

velocity.

1.1.1 Comearison of various slip2age and drift eguations

For the calculation of the slippage there were used the following correlations:

a) Ahmad correlation /64/:

SA= (/d0.20 G* )-0.016 (7

b) Groeneveld modification of the Ahmad equation /65/:

Soo = 0.5 . (S A-1) + 1 (98)

c) Hemn correlation /66/:

SH ~ * .7.5 (99

73

The values of the slippage, calculated with these correl~ations, and the

therefrom resulting courses-o? the steam velocity are compared to each

other in Fig. 40.

DN9 3 CORR, COMTPARISON

Cz,

Fig.

~~ C-

b-o sb 6.0 90

TIME S H I HT 22 7r_ w40 oprsno vrossipg

0.00 3.00 6.00 9.00TIME S HEIGHT 227CM

equations

For the calculation of the drift there was used the Ishii correlation /67/:

U jý(1-qi) - .12- ag.P Pd/ d]02 (100)

(101)and U d =C 00) + U

The course of the steam velocity, calculated with this correlation, is com-

pared in Fig. 41 with the mean steam velocity with homogenous flux.

74

0.00 3.00 6.00 9.00TI ME S HEIGHT 927 CM

Fig. 41: Comparison of the steam velocities calculated with and withoutdrift

In Figure 42 are shown the calculated courses of the wall temperature and

of the heat transfer coefficients. For the calculation of the Reynolds

number there was used in this case the steam velocity calculated with the

Groeneveld correlation. As shown by the comparison of the results, the

influence of the velocity calculated with slippage is not significant upon

the course of the wall temperature. Therefore, there was maintained the

assumption of homogeneity, as it was also recommended by many authors for

this sphere of the steam-droplets coolong.

a

<0

u0~

Lu

V

Fig. 42: Comparison of the wall temperatures and the heat transfer coefficientscalculated with and without slippage

75

11.2 Heat tranfer between wall and droplets

For the determination of the heat transfer between the heated wall and the

individual droplets there was first taken the following assumption:

- The wall temperature lies above the Leyden frost temperature.

- The realtive velocity between droplets and wall can be disregarded.

*(The evaporation time of the droplets lies in the order of 10-6 to

- The heat transfer by radiation between wall and droplets can be dis-

regarded /66/.

Under these assumptions, for the calculation of the heat transfer coefficient

-between wall and droplets there can be used either the correlation for vessel

film boiling (equations 60 and 63) or the correlation developed by Baumeister

(equation 75).

11.2.1 Determination of the surface inherent to the heat transfer between* wall and d roplets

For the determination of the surface (area) inherent to the wall-droplets heat

transfer there has to be determined the size of the droplet and the number

of droplets involved in this process.

11.2.2 Determination of the dropl et diameter

The mean droplet diameter was determined in most of the treatises in this

sphere from their own experimental investigations /54, 66 and 68/. Since

these investigations were normally conducted with low pressure, the values

of the droplet diameter determined in these treatises are inadequate for

the application in the high pressure region of the steam-droplets cooling.

For the determination of the size of droplets in this pressure range, among

others, two frequently used empirical correlations were developed:

a) Cumo correlation /69/

6T= 123.1 - (1-pr )0.32 [rjf/(G~x)] 12

76

wherein Pr = P/Pc wheei P =and PC 22.1 MPa critical pressure

b) Determination of the average-droplet diameter from the critical Weber

number

We kr 2konst, We =[pr * (Wd wf)2 6 T]1 a~

therefrom results for the critical droplet diameter

45T, kr = We kr o/[Pd(wd wf)2J (103)

The average droplet diameter can be then determined by means of various

9T= f6T r

statements.

(104)

This method for the determination of the droplet diameter

preclude the knowledge of the phase velocities and of the

the critical Weber number and is not used in this investig

the uncertainties for the determination of the phase veloc

11.1). The values of the droplet diameter, calculated wit

slippage according to the Groeneveld equation (equation 98

in Figure 43.

' D N9 31 [i~EWm cORii D N9 9 NLEW

does, however,

magnitude of

~ation due to

:ity (Chapter

:h We = 1 and

)are shown

CORR.

1 0-,J

0.. -

C 0 7RC-.1a T- MCC. "--c.10 T=

TI MET IME

Fig. 43: Comparison of the correlations for the calculation of the droplet

diameter

77

The values of the droplet diameter, determined with the.4C~u-mo correlation

in the recalculation of the DNB3 and DNB9 tests, are shown in Fig. 43.

The average value of the droplet diameter of 6 v is, however, too low

in comparison with the experimentally deternined values of 100 to 200 v.

The correlation constant in the Cumo equation was therefore adapted to

the experimental values, so that the modified correlation reads:

6T= 3.0 - 103 [.~/G (1- r(105)

This correlation will be henceforth used for the calculation of the droplet

diameter in the steam-droplets cooling.

11.2.3 Determination of the number of droplets

For the determination of the number of droplets involved in the heat transfer

between wall and droplets it is precluded that with the droplets in question

it deals with the droplets present in the boundary layer.

The boundary layer thickness is calculated with the Prandtl equation /70/:

6GS z34.2 /(0.5. Re)0.8?s (106)

The number of droplets per volume unit of the coolant can be calculated as

follows:

NT = 6 * (1-tb) / [nt.63. (107)

Therefrom results the number of droplets in the boundary layer per surface

unit of the wall:

NT,w = T - GS(18

Forslund and Rohsenow /54/ determined the number of droplets per surface

unit of the wall from the equation:

NTwz K -NT 2 /3 (10OS)

78

This equation was used for the calculation of the droplets mass flow

densi ty.

11.3 Heat transfer between steam and dtroplets

For the calculation of the heat transfer coefficients between steam anddroplets there are generally used the equations for the determination ofthe heat transfer coefficients for flow-encircled sphere.

Forslund and Rohse now /54/ used the equation

NU = 2 + f [Re, Pr] (110)

with f(Re,Pr) = 0.55 * [((wd-Wf ). 6T/rld Pd) 1 O * Prd 1' 3 (111)

The values of the heat transfer coefficients, calculated with this equation,are shown in Figure 44. The .veloci~tydAifference required for correlation(111) was determined with the aid of the Groeneveld equation (equation 98)

for slippage. The pertinent values of the heat flux density, which werecalculated with a temperature difference between steam and water phase of10 K, are shown in Figure 45 and they are compared with the wall-coolant

heat flux density determined from the test.

ONE 9 HTC1 AN~D 0 STEAFI--D RDOPLETS

rz1 ý'_IQ

in

< LL

TIME IS) HEIGHT 3927 CM TIME -(S) HEIGHT _2127 CNIFig. 411:HTG between steam and Fig. 45: Heat flux density of

droplets steam on droplets

79

11.4 Calculation of the individual components of the heat flux dtensitybetween wall and steam-droplets flow

The entire heat flux density between wall and coolant is according to the

equation (96):

qO = w'd*(- dl-Pf CT -T) +tw,T Ft.-(Tw-Tsa) (112) N

During the recalculation of the post-DNB tests with low mass flow rate, thecorrelations for the calculation of the heat transfer coefficients withforced steam convection were compared to each other and with the testresults /7/. From the comparison it results, that the best agreementbetween the measured and the calculated processes of the wall temperature

could be obtained with the aid of the McEligot correlation.

The value of the correlation constant in this equation was determined through

the adpation to the test results. The modified McEligot equation reads:T .

aCd 0.022 Re - Tr. .(d (1.3D' d 71ý9w

and is used for the calculation of the convective heat transfer between

wall and steam.

For the calculation of the heat transfer coefficients between wall anddroplets are sued the baumeister and Berenson equations (equations 75 and

63). If one postu;ates a spherical shape of the droplets, the equation for

Ff reads:

F= NT n-6 2/4] .(114)

The heat per surface unit, which can be eliminated t 'hrough steam convection

(with the assumption, that the steam outside of the boundary layer is not

superheated) can be calculated with the following equation:

A 0 0..5st -Q =0.022- :1 sat-r (ý )-T T )(w, d 0 d' d E--- s(T at ) 15

80

with F f from equation (114).

The heat transfer between wall and droplets results from the following

equation:

QW,T Cr BAUM *(TW-T sat~ Ff (115)

or

The entire heat flux dens~ity is then calculated as follows:

qTT 2 w,d + w,T(17

The individual components, as they were determined during the recalculation of

the tests DNB1, DNB3 and DNB9, are shown in Fig. 46 and they are compared

with the heat flux density calculated from the test. From this comparison

it results, that the heat flux density calculated from this model is much

too low in comparison with the test. But since the steam convection pai-t

was already calculated with the entire temperature difference, the steam-

droplets share~to be necessarily too low.

The results in Chapter 11.3 showed, that the heat transfer between superheated

steam and the water droplets is very effective. Therefrom, henceforth one

starts with the consideration that all droplets present in the boundary

layer do immediately evaporate because of the therein reigning great

temperature difference. The droplets mass flow density can be defined in

the steam-droplets flow as follows:

GT =N T-1"P6 (fc -/S.f *pf (118)

With the aid of equation (109) there is effected the correlation of the

droplets mas s flow density per surface unit of the heated wall as follows:

G N23.[.36w,T NTZ [T~.6 Wf *Pf(19

81

DM8 3 T ES T CDN9 3 TF E S T

C 03 A'or~S~

UN --- Experi~ent

X

o1L

7 I

Q~O.

0-U 0

('.4.

-jLI.

1-w00.

a C W O 1rr 0 -!C O T0 cwr =_a9tv I T~iAOTOT Er-F!SOZN

Zxnerirmner

£ I I I'

0.00 a3.0TIMES

I6 .00 9.00

HEIGHT 2591CM0.00 t3.00

TIME S HEIGHT9.00327C-M

DM9 9 T ES T

0~

U

X~

0_

TIME S HEIGHT

7

Fig. 46: Components of the heat flux in steam-droplets cooling

82

Another possibility for the determination of the droplets mass f-lix- density

results from the consideration for the calculation of the number of droplets

in the boundary layer according to equation (108). The mean mass flow density

can be calculated by using the mean droplets velocity in the boundary

layer as follows:

w,T T N GS *WfGS *n. 3/]-* (120)

The comparison with the droplets mass flow densities per cm2 of the wall,

calculated with the eqiations (119) and (120), is shown in Fig. 47.

ul

NjEW' CORR.

C.--A!T-R FSLUkC-71 Boundary layer

m'c 0N9 9LU(j)1

IN

U' 1

C:)C

N~EW CORR.

773 Boundary layer

5.Q 04OTIME S HEIGHT 227CM TIME Z HEIGHT 327CM1

Fig. 47: Comparison of the droplets mass flow densities

The heat per surface unit necessary for the evaporation of the droplets can

be calculated from the following equation:

Qw, T = Ah e * G T (121)

The entire heat flux density does then rsult from the sum of the two

components:

=TO ý w (1-F f + Qw(122)

83

DN9 3 T E S*T CON9 3 T ES T

7-0U

-J

U_

DN299 T E S T D0N 99 T ES T

CL

0

LL

0

40 C~a Mc S.1 _S04 Ow new corr....new corr.

-- Ex:_erizent

XV

C-

XN.

-J

o 'new corr.+ GWT new corr.

LxPeriment

Al I

. ý b i !I I

T IME4.1)0

S

........................................................................a

HEIGHT12.0012 5--C M

0.00 I .1 0 0

TIME SE6. 00HEIGHT

12.00O=27CM

Fig. 48: Components of the hat flux density acc. to the "two-component

model"

84

In Figure 48 are shown the components of the heat flux density, calculated

with this model, and compared with the test results. As shwon by these

results, the agreement of the entire heat flux densities can be considered

good.

11.5 Formulation in agreement with the similarity theory of the new model

for the calculation of the heat transfer coefficients with steam-

droplets cooling

The equation (97) can be expressed as follows:

=TO ý w,d -(1-Pf) *(TW-Td)+C w a Ff -(T ;T a (123)

Ad T 0.5with aw~d =0.022 *A Re 0 .8

*PrO.4 d

0 d d ý

Hereafter it is postulated that also a wT can be expressed in a similar

manner:

a.02. Ad pO.4T, d .R4 (124)

The Reynolds number is formed with the mass flow density of the droplets in

the steam-droplets flow.

Re7 [ND. w.*~S * DI/n, (12S

and with the exponent from the equation (119) there can be established the

following equation for awT:

,T T d.2 . (126)

The heat flux desnity share through the heat transfer between wall anddroplets per surface unit of the heated wall is then:

0 w,T Ow,T ' v (T sat)

85

After the inserting of the equations (123) and (126) into the equation (122),

one obtaines the expression for the entire heat flux density.

-(0.022 -~Re0 -8 Pr0 .4 T~ sa. 0

qTOT ~ ~ d d ýý ).(- T- a]

+[ Id 23 04 T st0.5+(.022 D * Re2'T Pr 0 4 ,ý )*Ff,(wTsd

W (127)

with Re T from equation (125).

The equation (127) can be written as follows:

= 0.022 A d [Re--1 )+R23j ]Pr. Tst0.5

TWTsat)(128)

and for the entire heat transfer coefficient results:

(ITOT = 0.022- Ld [[e3-1F j[e/CfjPr4.Tst0.5

In order to eliminate the difficulties that result in the practical applica-

tion of this correlation for the determination of the surface distri~butionfor the steam and droplets components (droplets diameter, number of droplets,and shape of droplets), it was attempted to determine the abovementioned

distribution with the aid of the steam content. The ratio between the

variables F f and x was taken into consideration through the introduction of

a corrective factor, which was defined as the proportion of volume and mass

steam content. The exponent of this corrective factor was determined

through the adaption to the test values.

K A )0-21(10

The correlation for the calculation of the heat transfer coefficients in

the steam-droplets cooling phase can then be written as follows:

aTT 0.022 [ (Re0-8-x)+(Re2/3.(1-X)]1.

* ~ŽO.1 Pr 0 4' sat. (131)X d TW

86

The physical characteristics in this equation were generally calculated

with the mean temperature between wall and coolant. The physical charac-

teristics of the Reynolds number are relative to the saturation temperature.

This equation for the calculation of the heat transfer coefficients was

used for the recalculation of the tests DNB1, DNB3, DNB9, and PONBil in

the phase after the exceeding of the critical heat flux (KHB). The

results of these computer runs are shown in the Figures 49 to 52 and the

calculated time behaviors of the wall temperature, of the heat transfer

coefficients, and of the heat flux are compared with the test results.

From this comparison it results, that the agreement between the calculated

and the test results in the sphere of the test parameters can be described

as very good. The comparison of the calculated time behaviors of the

wall temperature and of the heat transfer coefficients, calculated with

the aid of the new correlation and other equilibrium correlations, is shown

in Attachment 11 and compared with the test result.

87

SN 2 1. NEW CORRELATION

* 0

wL

F-

1-i

V.'

- I*0.

-I

- I1

ol

t...

~ a~7:1* !-Z~-E 3~7~i

ExperimerLt*................I

,jn1 2 . DTIME

,4.0

S.1ts- 1 , '' * I5.J 0

TIME S

ri

I NEW CORRELATION

HOEHE: HEIGHT

U-

U-

TIME :-

Fig. 49: Results from the recalculation of the test DNB1 with the application

of the new correlation for the calculation of the heat transfer coefficients

88

WE 3 1'Ei4 COIRRELATIOIN

'27:%I

C.120

cLo

I.j

wU

_3

=-00;TIME TIME S

UN

(cn IN..- .

Wx<

3 N~EW CORRELATION

HOEHE: HEIGHT

TIME

Fig. 50: Results of the recalculation of the test DNB3 with the application


89

DNE99 N51!i CORRELATION

0

I.-

F-

4, - IZE 2Hr. Ir, nEf*`7!'

o--- Exmeriment

.F.

C31

I.Z

-- Experiment

1

0.110 1.00TIME S

! 2. 0 .0 02. .00TIME S

CDN9 9T-

I0-Z

NN2W1 CORRELATION

HOEHE: HEIGHT

TIME --

Fig. 51: Results from the recalculation of the test DNB9 with the application

of the new correlation for the calculation of the heat transfer coefficient

90

PCM9 1 1 NEWi CORRELATIO14

C-,

0

w

I-

wa-

wI--J-J

01frD

rol

1352''*

-- Experiment

-I

TIME SZ T IME

6 .'J~.5

S. 1

U.1

!ii NEW CORRELM\TON

HOEHE: HEIGHT

-- Experimenlt

* S

9/YZ

T IME

Fig. 52: Results from the recalculation of the test PDNB11 with application


91

12. CONCLUSIONS

The 25-rod bundle tests, conducted within the-framework-of--the--research project

RS 37C, furnished a valuable experimental data-base for the verification of

the compiled models and correlations for the calculation of the critical heat

flux and of the heat transfer coefficients in the steam-droplets cooling

regime.

The verification of the various correlations for the calculation of the maximum

critical heat flux illustrated the limitation of the spheres of applicationof the individual correlations and showed, that none of the equations used inthe wide sphere 'of the important thermal and fluid dynamic test parameters

can be recommended fo r an accurate prediction of the DNB moment and point.

A similar result was shown in the verification of the correlations for the

calculation of the heat tra-sfer-coefficients after the exceeding of themaximum critical heat flux. Even the use of new models, which took into con-

sideration the thermodynamic non-equilibrium between the steam and water

phases, did not lead to the expected approximation of the calculated an~dmeasured time behaviors of the wall temperatures. It was further established,

that the herein verified correlations for the calculation of the minimum

temperature dofference between wall and coolant, and of the minimum critical

heat flux for the conditions with rewetting in the high pressure phase of

a pressure drop process cannot be used for a prediction of the rewetting

phenomenon at least in the sphere of the parameter combinations, cropped

up in the 25-rod bundle tests.

The application of the "two components correlation," developed for the cal-

culation of the heat transfer coefficients in the steam-droplets cooling

regime, led to a very good agreement between the test and calculated results

during the recalculation of the representative DNB and post-DNB tests.(Test parameter range: pressure 3 to 12 MPa, steam content 0.3 to 1 andmass flow rate 300 to 1400 kg/in2 sec).

To prove the general validity of this correlation there is necessary the

examination with the aid of further experimental investigations, which is

planned within the framework of the evaluation of various experiments.

92

13. BIBLIOGRAPHY

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/ 2/ Agemar, Brand, EmmerlingPWR Main Tests with a 25-rod bundlePart 1: Experimental Implementation and Documentation ofthe Test ResultsKWU-RE23/012/77

/ 3/ Emmerl ingPWR Main Tests with a 25-rod bundlePart 2: Calculation of the Heat Transfer CoefficientsKWU -RE23/029/77

/4/ HD-Heat Transfer in 25-rod bundle testsTest EvaluationPSP Ingenieur-Planung No. 8204

I5/ H. Karwat, K. WolfertBRUCH-D- A Digital Program for PWR Blowdown InvestigationsNucl. Eng. Des. 11, 1970, p. 241-254

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/ 7/ I. VoitekPWR-25-rod bundle testsVerification of the conducted DNB and post-DNB TestsMRR-I, December 1976

/ 8/ I. VojtekEvaluation of the 25-rod bundle Tests with the Computer CodeBRUDI -VAGRS-A-208, September 1978

/ 9/ F.W. Dittus, L.M.K. BoelterHeat Transfer in Automobile Radiators of the Tubular TypeUni. of Cal. Publications in Engineering, Vol. 2, No. 13, pp'443-461October 1980

/10/ E.N. Sieder, G.E. TateHeat Transfer and Pressure Drop of Liquids in TubesIndustrial and Engineering Chemistry, Vol 28, No. 12, pp 1429-1435

93

/11/ D.M. McEligot, L.W. Ormand, M.C. PerkinsInternal Low Reynolds Number Turbulent and Transitional Gas Flowwith Heat TransferJ. of Heat Transfer, Trans ASME, May 1966

/12/ H. HausenRepresentation of the Heat Transfer in Tubes through GeneralizedExponential equationsVDI-Zeitschrift, 1943

/13/ K.J. Liesch, G. Raemhild, K. HofmannFor the Determination of the Heat Transfer and the Critical Heat. Fluxin View of Special Conditions in the Coolant Channels of a PWR withlarge LOCAsMRR 150, 1975

114/ W.H. Jens, P.A. LottesAnalysis of Heat Transfer, Burnout, Pressure Drop and DensityData for High Pressure WaterUSAEC Rep. ANL-4627, 1951

/15/ I.R.S.-Thom et alBoiling in Subccoled Water During Flow Up Heated Tubes or AnnuliProc. Instr. Mech. Engrs. 1965-1966, Vol . 180, 3C, 1966

/16/ J.G. CollierConvective Boiling and CondensationMcGraw-Hill Book Company, 1972

/17/ J.C. ChenCorrelation for Boiling Heat Transfer to Saturated Fluids inConvestive Flow1-EC Process Design and Development, Vol. 5, No. 3, July 1966

/18/ V.E. Schrock, L.M. GrossmannForced Convection Boiling in TubesNucl. Sci. and Eng. 12, pp 474-481, 1962

/19/ S. NukiyamaMaximum and Minimum Values of Heat Transmitted from Metal toBoiling Water under Atmospheric PressureJ. Soc. Mech. Engrs., Japan 37, 53-54 and 367-374, 1934

/20/ S.S. KutateladzeFundamentals of Heat TransferEdward Arnold (Publishers) Ltd., 1963

/21/ ,N. ZuberHydrodynamic Aspects of Boiling Heat TransferOh. D. Thesis, University of California, Los Angeles, 1959

/22/ Y.P. Chang, N.W. SnyderHeat Transfer in Saturated BoilingChem. Progr. Symp. Ser. 56, No. 30, 1960

94

/23/ 5.5. Kutateladze, A.I. LeontevSome Applications of Asymptotic Theory of the Turbulent BoundaryLayerProc. 3rd Int. Heat Transfer Conference, 1960

/24/ L.S. TongBoiling Heat Transfer and Two-Phase FlowJohn Wiley, Inc., 1966

/25/ D. MainesSlip Ratios and Friction Factors in the Bubble Flow Regime inVertical TubesInstitut for Atomenergi, Kjeller, Norway, 1966

/26/ F.G. Thorgerson, D.M. Knoebel, J.H. GibbonsA Model to Predict Convective Subcooled CriticalTrans ASME Series C, 96, 1976

/27/ M. Monde, Y. KattoBurnout in a High Heat Flux Boiling System withInt. J. H. M. Transfer 21, 1978

/28/ Y. Katto, K. IshiiBurnout in a High Heat Flux Boiling System withof Liquid through a Plane Jet6th Int. Heat Transfer Conference, 1978

/29/ L.S. Tong et alInfluence of Axially Non-Uniform Heat Flux on DNI8th National Heat Transfer Conference, Los Angel

Heat Flux

an impinging Jet

a Forced Supply

Bes, 1965

/30/ L.S. TongBoiling Heat Transfer and Two-Phase FlowJohn Wiley, Inc., 1966

/31/ S. MiliotiA Survey of BurnoufECorF61Thtions as applied to Water Cooled NuclearReactorsM. Engng. thesis, Pennsylvania State University, 1964

/32/ L.S. TongPrediction of Departure from Nucleate Boiling for one Axially Non-uniform Heat Flux DistributionJour. of Nucl. Energy, Vol. 21, pp 241-243, p967

/33/ R.H. Wilson, L.J. Stanek, J.S. GellerstedtCritical Heat Flux in a Non-uniformly Heated Rod Bundle9th Winter Annual Meeting, Los Angeles, Cal., November 16-20, 1969

/34/ D.C. Leslie, KiroyApplication of Flow Modell to Predicting Burnout under TransientCondi tionsAEEW R542, 1967

95

K

/35/ W. BeldaDryou-t. delay with LOCA in Nuclear ReactorsDisse'rtation TU Hannover, 1975

/36/ F. Mayinger, W. BeldaSome Deliberations and Measurements Concerning Burnaout-DelayDuring BlowdownEuropean Two-Phase Flow Group Mtg., Harwell, 1974

/37/ Y.Y. Hsu, W.D. BecknerCorrelation for the Onset of Transient CHFUnpubl ished report

/38/ P. Griffith, J.F. Pearson, R.J. LepkowskiCritical Heat Flux during Loss-of-Coolant Acc dentNuclear Safety 18, 298, 1977

/39/ B.C. SliferLoss-of-Coolant Accident and Emergency Core Cooling Models for'General Electric Boiling Water ReactorsNEDO-10329, 1971

/40/ V.N. Smolin et alTeploenergetica No. 4, p. 54-58, 1967

/41/ L. Biasi et alStudies on Burnout, Part 3Energia Nucleare, Vol 14, No. 9, September 1967

/42/ Bertoletti et alHeat Transfer Crisis with Steam-Water MixturesEnergia Nucleare, Vol 12, 1965

/43/ J.H. AwberryJ. Iron and Steel Inst. 144, 1941

/44/ A. Bromley, R. NormanHeat Transfer in Forced Convection Film BoilingInd. and Eng. Chemistry, Vol 45, December 1953

/45/ Y.Y. Hsu, J.W. WestwaterAl ChE Hournal , Vol . 15, 1958

/46/ P.J. BerensonFilm Boiling Heat Transfer from a Horizontal SurfaceJ. of Heat Transfer, Vol 83, August 1961

/47/ R.S. Dougall, W.M. RohsenowFilmboiling on the Inside of Vertical Tubes with Upward Flow of theFluid at Low Qualities'II-T 9079-26, September 1963

96

/48/ .Z.L. Miropolskij-W t rM x u ei S ea-Heat Transfer in Film Boiling of Steam-WtrMxuei ta

Generating Tubes

Teptoenergetica Vol. 10, No. 5, pp 49-53, 1963

/49/ D.C. GroeneveldAn Investigation of Heat Transfer in the Liquid Deficient RegimeAECL-3281, December 1969

/50/ D.C. GroeneveldPost Dryout Heat TransferPhysical Mechanisms and Survey of Prediction MethodsNuclear Engineering and Design 32, 1975

/51/ K.G. Condie, 'S.J. Bengston, S.L. RichlienPost-CHF Heat Transfer Data, Analysis, Comparison and CorrelationUnpubl1i shed Report

/52/ J.D. Parker, R.j. GroshHeat Transfer to a Mist FlowANL-6291, 1962

/53/ W.F. Laverty, W.M. RohsenowFim Boiling of Saturated Liquid Nitrogen Flowing in a Vertical TubeJ. of Heat Transfer, Vol 89, pp 90-98, 1967

/54/ R.P. Forslund, W.M. RohsenowDispersed Flow Film BoilingASME Paper No. 68-HT-44, J. of Heat Transfer, 1968

/55[ K.J. Baumeister, T.D. Hamill, G.J. SchoessowA Generalized Correlation of Vaporization Times of Drops in FilmBoiling on a Flat PlateU.S.-AICHE, 3rd International Heat Transfer Conference, August 1966

/56/ S.J. Hynek, W.M. Rohsenow, A.B. BerglesForced Convection Dispersed Flow BoilingMIT Report No. DSR 70586-63, 1969

/57/ D.C. Groeneveld, G.G.J. DelormePrediction of Thermal'Non-Equilibrium in the Post-Dryout RegimeNuclear Engineering and Design 36, pp 17-26, 1976

/58/ G. Hadaller, S. BanarjeeHeat Transfer to Superheated Steam in Round TubesAECL unpublished Report, 1969

/59/ J.C. Chen, F.T. Ozkaynak, B.K. SundaramVapor Heat Transfer in Post-CHF Region including the Effect ofThermodynamic Non-Equil ibriumNuclear Engineering and Design 51, pp. 143-155, 1979

97

/60/ D.H.R. BeattleFriction Factors and Regime Transition in High Pressure Steam-WaterFlowsAus. Atomic Energy Coin. Sutherland 2232, NSW, Australia

/61/ P.J. BerensonTrans. ASME J. Heat Transfer, 83, 351, 1961

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/63/ O.C. Iloeje, D.N. Plummer, W.M. Rohsenow, P. GriffithAn Investigation of the Collapse and Surface Rewet in Film Boilingin Forced Vertical FlowTrans. of the ASME, J. of Heat Transfer, May 1975

/64/ S.Y. AhinadAxial Distribution of Bulk Temperature and Void Fraction in aHeated Channel with Inlet SubcoolingASME J. of Heat Transfer, 92, pp. 595-509, 1970

/65/ D.C. GroeneveldThe Thermal Bahaviour of a Heated Surface at and beyond DryoutPh.D. Thesis University of Western Ontario, 1972

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/68/ A. GhazanfariExperimental Investigation of the Heat Transfer in a Droplet Flowafter Exceeding of the Rewetting TemperatureDissertation, Techn. Universitaet, Bochum, 1977

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/70/ W. BohlTechnical Fluid DynamicsVogel Verlag, 1971

98

ATTACHMENT 1

Compilation of the important parameters at DNB moment (extract)

99

MR. HOUEII STABlim)

70:401"3

GH ICLImIct'.*cm)

150S 2.59151.5 2.5A9Iscs 2.5915c5 3.1815c5 3.li315c5 3.1815.6b 2.5:!151'6 2.51.1ISC6 2.5'!IMC 2.5915f6 2.5915C6 2.591506 3.10151.6 3.181546 3.1815-.7 2.5.i15!..? 2.5.)15t*7 2.5,j15 G7 2.591507 1.59W5( i.53)15C7 3.18154.7 3.11315C7 3.18.15. 0 2.531509 2.5,1509 2.5.i15-:9 2.5915C.9 2.59is :9 2.591509 3.181509 3.18C15-19 3.181510 2.591510 2.591513 3.101513 3.181510 3.181513 2.501513 2.5:15 13 Z.5971513 2.591514 2.5i1514 2.501514 2.5915 1§ 2.5915-14 2.591514 3.181514 3.181514 3.181515 51!15 :51515 2.591515 2.591515 3.181515 3.18

11-3 .11516 2.59151if 3.1815 16 3.18a

84 3.5 1603.02 0.5 134'.83 0.~5 136.

3z .5 1Z..03 0.5 12j..04 a.1. 122.04 1 ., 136.02 1.0^ 134.00V 1.0 13:..03 1.: 139.94 -3.5 142z.02 0.5 137.03 ).5 122.C4 o'.5 124.82 0.5 121.82 0.W 168.03 3.5 164t.04I 0.5 173.84 J.5 17'.02 j.! 167.P3 0.5 169.04 0.5 149.03 0.5 15;;.92 J.5 152.04 0.5 169.03 0.3 lol.82 3.c lbs.U2 0.5 163).53 32.5 162.84 3.5s 166.92 0.5 144.03 .3.5 146.04 .i.5 14n~.04 0.5 166.83 .).a 166.02 0.5 147.CV 3.5 11411.04 3.5 1,49.04 U.5 169.03 .3.5 162.02 0.5 16',.e3 L5 79.C4 1.5 121.03 0.5 16-3.02 1 .0 MIg.83 1 . . 13'j.8' 1.0 133.e2 .1.5 14-,.03 13.5 141.04 03.5 1141.04 I .t 133.03 1.5 12Z .02 1.3 128.84 1 .4) 13,2.02 1 .31 114.CV 1.2 114.-04 0 --114.

e - ., 17,~r.3 *3.5 154.04. 0.5 154.

144.136.L36.120.123.L22 .136.13q.13.1.139.142.137.122.124.

142.14d.1#46.144.143.123.126.126.153.1403.148.140.141.144.125.125.125.016 .

145.125.125.L26.

144.141.14Z.121.140.131.131.133.125.125.

133.-

IN0.13:

114.

148.126.120.

( OAR)I

107.

W13.N~2.

t.'3.1,;3.

118.112.

115.1-.9.

115.

117.

115.116.112.

112.112.I12.114.110.

115.119.114.

112.115.119.

111.

114.11:.112.116.

11G.

116.114.

10pNe CapeCKE151

0.163771 7.e124Co0.163771 7.F124i.303.163771 7.8124CO0.117633 10.41.34C0

13.117633 W1L.63420

0.t?1152 8 .2716700.131152 8.271670

0.131152 8.2716700.131152 8 .2716 7'20.131152 8.2716700.11.3813 WU.436CO0.1'.3613 10 .4346r000.1-.3813 1*.43146 0Q&.9.4169 8 .7252*.,0 .-94189 8 .728200C..'14189 8s.7'i2-2.:0C.':94189 13.72112';30..294100 8.1282:0O.0.S4189 8.7282:0.IIP.855 12 .6262CO0.128B855 12.t626230.109855 12.f252000.124239 8.21934"50a.121Z89 8.3932!00.12i289 8.j932!00.1242a9 8.33932500.124#289 8.3932100.124289 8.3932500.13ES72 8 .919903.138072 B.SC39100.132872 8.9.'39900.162266 7.3269CO0.162266 7.3269r0-3.14C996 9.Z621200.14.'996 9.C62130-3 I4C996 9 t.621200.18C299 6.4443100.18C299 &.4443500 IBCZ') 6.4443500. 118 -2 2)9 6.444350

11.144118 6.!438200.044118 6.!438200.144118 6.1%3P-100.144118 6..43820)*3.118276 7L.L45800.119276 7.C:45eO0.11827-6 7 .CI34580

100

ATTACHMENT 2

Compilation of the important parameters at RNB moment (extract)

101

15e7 3. L6 C415C7 !.6b C315C7 3 . G 041507 3.613 0215C7 3.77 C31507 3.77 04

M5i7 3.77 F131509 2 .0 0,j 41509 2.5.) C41519 Z.b' C3159 2. 5:. r215C9 2.59 C31509 2.5n) 0I15 ;9 .1.59 P31509 2.59 P4

15.9 3. Il 021M9 3.1A 031ISO 3 .. IL 0

1509 3.27 0215L9 3.27 F.31509 3.:7 E4ISLO 3.6a C'.15.19 3.Cm C41509 3 .6e 031509 3.68 a 21509 3.77 C3111V 3.77d F3150'? 3.77 e41510 2.59 C31510 2.59 P4Isla 2.50 e3I1!10 3.11: C4.1510 3.1 Il e02151.3 3.1if! 031510 3.10 0*1510 3.27 C31!510 3.27 P3151-3 3.27 021513 3.Z7 8415 IJ 3.77 C31513 3.77 e4

1513 3.77 021510 3.77 031s515 3.68 C4.1515 3.613 821515 3.bfi C3

1515 3.77 021!515 3.77 V031515 3.77 1 4

S.4.54.55.5

6 .-j

2.5

3.:

6-

6.56. :6.f6.5

7.57.'7.:

C.53.54 .:ý

3.C

5.:

ft .1)3.5~3.53.53.5

6.54..,4.0.

3.54.j6 .41

5.55.37. 17.;

64.54.

56.45.4!.

Lis.

9A..al..94.

021.7: .67.7'.*74.

65..60.

51.61.56.74.6L.67.93p.

913.9s.

a7.9'.72.67.62.'35.63.721.67.-

6'..67.64.

46.46.46.44.42.45.45.

115.

12j .be.944.a1.71.66.64 .61.65.5L.54.51.52.69.68.69.06.-58.41.6.3.

84.87.9..85.C2.82.1:5.03.64.67.G8.V7.6j.59.62.59.61.ezl.58.

f6. 17'.66. 170.: 41r~. 200.e6j. 16C. 4!C:. 290.

f:2. 17-.*62. 17C: 45C. M0.62. 17'.. 45,:. 280.

SIC. 2Vfl. 21:. 'a. 0.73. 24".. 530. 250.59. 13.. 144C4 310.62. 28f6. 27~. C. 2064. 28.. 56t0C. 2P,).e1. 29.. 57C. 280.03. 14 1.1:5. 230. I510.. 2bo.621. 23: S1C. 28u).62. 240. 52C. 280.59. 2: 52...0

t6. 23.. 500. 270.!6. Z3;. 51C:. .170.72. 16:73. 16.. 'o. 5.72. 16c. 4!C. 250.71. 16z:. #!':. 290.6b. 17..66. 18.-.. 4&C. 200).66. 17.1. 45C. 200.74. 27.10. 26'o 55C. 210.75; 27,.. 560 290.69. &2:.

71. 21L. 500C. 250).71. ZI . 510:*. 25o.

61. 210:.99. 23.. SIC:. 2120.65. 24 :. 53C. 250.61. 22. . Sec. 20.67. 16..:7.2. 16'. 4 ! C. 2-9.72. 16'. 45C. 2CM.69. t6,:. 4!1.. 290.

ift. L8 Z 45C. Z70.5e. 19C. 460. 2170.!*1 l 40.~ 46z. t054. 10.. 460. .70.!4 . 19:. . 46C. 270.1.5. Lac.. 45C. Z70.

(7.33q910 3O;C7 o'0.33511`2 2.99q971C0.339192 3.919770L..339192 3 099771 i0.339192 3.q94017I0ý.33 c192 3.99977470.339192 30'991V'C.243641.4bl'i0.Z24,691, 4.63R25'C.24!601 4.63!29:.C.124691 4.53!2e'0.24?691 4.631;2!f0-243691 4.63i"25'0.243691 4 .6 3; 15

o.2P4R25 '.Z94ffC

0 .F91125 4.2946!f0'.UA582 4.2044!tC0.2!q82! 4 .204'e'J

0ý.2eO!825 4 .214 I i00.2e;RZ5 4.294560.7.204934 6 .:2n 9-ofCC.29993! 6 02", 7rC.2q193! 6.22091C0i.290935 6 .120801'-1.2?1931 b.i:7091:0.29~q35 6 .0299le'o.29;0315 6.C2cc1C

%.;55 !.136q5o

O.2P!5Fe. 5 .1359xf::....891A 6 .54377 Vý.2.67914 6.543771:0).267914 6.`54171C0.267914 6.5*37tf0.267914 6.54!770.CG.26191t 6.54377'0.267914 6 .143 7100.267`114 6.14377C0.2!12".5 7.75I0l.26227! 7 .97RCE60C.262275) 7.07!C!i!I.'6227F 7.97Vq C V

v .3 It I-IJ4 .28!74 !0.3410e4k 4 e!74!f:C.349354 4."7''0"u.3'50!4 4.8!7'5'(..3496,4 4.SP74!f0 .3 4 1)F4 4 .8F74!#10.34.C084 4.11874!C

*N,

102

.R. ?COiIE STAU01.

M5U 2.59 0315CS 2.5'; 04is CS 2.517 0215CS 2.59 p 3ISO5 3.1.1 C415cs 3.1L e 821505 3 .IH. C31503 3.11- 0415.5 3.27 C31505 3.27 C2isCS 3.Z.7 a I151.5 3.Z7 8315015 3.68 C4151. 3.60 IPZ15 0 3.L0 C31505 3.633 0415 1:5 3.77 C 31505 3.77 P.31005 3.77 02?1515 3.77 E-41506 2.5.) C'.1506 2.51 C415C6 2.53 r215C6 2 .5: 031506 2 .Sr9 C31506 2.59 831506 2.39 041506 2.59 CZ1506 3.18 C.415S6 3.1 C315C6 3.10 0415C6 3.16 021506 3.27 C3ISO6 3.27 031IS. 3.27 021506 3.17 P415F.6 3.68 C'v15C6 3.65 C315C6 3 .61J 0'15cb 3 rift F21506 3.77 0315C6 3.77 03lI'S 6 3.77 04t1507 2-C-5 Cq1507V 2 .5 -1 r2.1507 2.50 V03

1507 2.5 04#15027 2.59 C315 07 2.59 04IS'.? 2.59 C21307 2.59 P 3195:7 3.1.1- C4.1507 3 .12! C41!;;7 34.1 C31SC7 3.1-1 a.,1!5;7 3.27 C31!1)7 3.27 !'1507 3.217 0215"? 3.Z7 F3

111.U1 I (1 Ul .C L(S) ill/c".C.10

f 'III(CAR I ( X

T1I-Nh 72.ASSER XPI.0(W) M'

(CC/i)

3 .7

3.5

3.53.515.

3.52 . ;6.0

3.54..

.20

3.56.1

2.5'S.!

6.06..J6.5

6.063.3

0.37.5

4 .,J4 .. )4.4

4 .55.05 .f54.55.54.S .5

9.5a.57.::

7.57.57.5

.9.5

9.

71.2.166.

U72.

97.023.

a.366,t..

79 .73.

75.

79.6.1.65.

63.

121.122.

96.364.

179.7-j.69..66.7j.75.7*.62.64.5'..63.62.

35.574.6 .0.

idB.I06.

on.07.Ea.7j.0l.72.6?.74.al.79.e-3.67.69.7^-.68.

112.123.

69.77.71.79.67.64.66.66.

6o3.67.57.66.67.

61.59.64.

ki.69.44.46.54.

51d.'7.'.6.

44.13.

7'.. 26.. 5C 2O74. 27C. 5~. 2391. 19.. 49C. 31.'0 .If4. 27.. 56C. 250 .t9. 221:.7?. zz * i. 29-1.69. 22. 51.. ISO.71. z21. SCC. 290.t4. 4"3.. 3*5. 25..5, 28J63. 23.. SIC. 280.62. 23':. SIC. 260.74 . 16%.

7 2. 12.. 420,. 3.C0.

ez. 162L. 42C:. - 29.

019 . 16.:. 4Z ZO71. 16 . 4!t. 2130.6A. 16.. 45Z. 29o.3

e9~. 25:I. i. 20

S4. 17. 4F0. 310.74. 254. 54Z. 290.

e. 2:. S7C. 280.!9. 29.. 57'.. zeo.U2. 27.. 55C. 280.62. 241ZV . 23.: 51C. 280.6:1 23C. 51C. 20o.62. 2331. SIC. 280.t5. -4..53. ;3:. SCC. 270.56. 241. 51C. Z'70.58. 22C. SCC. 280.7.,. 16 :.7%~ 16!- 45C. 250.7-C. 16C. 4!C. 290.7:4 . 18:. 47C.. 290.64. 17:.

112. 18C. -6C. Z-00.113. 17 Z'. 4!C. 280.04., 27:.t6. 24C. SFC. 2M.6'.. 27*.. 55C. 2N0.ti. !a.. SEC. NO0.52. '6-:

iZ.. 26C. 53C. 270.!6. 261'. 53C. 270.

!4. 27.. 54C:. 270.

56. 23.. 300. 270.56. Z2k. 49c. 220.

53. 21.. 4 e C. 2 V.)!5. Z4.:. 510. 270.44. 22:. 46*.. 260.

C, .2&*66*9 6 .1P7F!!L. .22'69q 6 .)P7P4-

v .226655 6 .?87P850.2286q9 6.46P7700.262861 6 .46'P77C-.242861 6IA'fi'771 C

02442861 6.46'71'.242P161 6.46671C

0.242861 6 .46:77l".242861 6 .406??.)'

4.373R14 5.39?1100 .37Z2814 5.302132P0.373814 5Sjq5I2'C.372814 i.3q912'0.3718114 .3.2814,P0.373M14 1.39PI200.37?914 it.198l2':2.3 7 ?114 5 .3v'9F12F0.2!t465 4.Ve7e7cC.236461! 4 .3P.7eopC.23*465 '.3q727P0.23646'S Sq37P V!C .27"465 4.Se 7PC..236465 4 .187F 7C0.226465 4.RP7P7'*C.2?1465 i .197Pl.7'0.301111 4 .312re:!

0.3f.101 1 4.312C6!:

w .3010311 4.312CIC0.3l01012 4.31206':0 .301011I 4.112idt0Z.ZOA8S1 6 .4 130!0.2q6851 6.41';CZC( Zieed4t 6 .4 [email protected] 6.41IC2':0.296951 6 .4 I"O't I.2:2685 1 6 .401902e

C.29C8S51 6.419CICC.2613Ce 3 .21111117.2.2613"8 3.24312'O.2613CS 3.24!11:O.V2 13195 .4U.Z-6130f- .4220'.ZA13'ýi 3.24212'0 .2 13 ̂ ! 3 .24312':0.2e13Z8 3.243121C.3224341 o.ý!Ce;'C .32434.3 3.P~20.324343 3-1Ffe2p0.3243'63 3:6C.324343 3.':Feti-.'2434' 3 f:A'I- z r

n.374,343 ?3O"1Z

103

ATTACHMENT 3

Comparison of the correlations for the calculation of the heat transfer

coefficients with forced convection

104

FORCED CONVECTIlON' - WATER

ro

!0.00 20.00 p0.00 40.00MASS FLOW DENSITY KG!M-*fr*S

CORR. COMPARISON

MASS FLOW DENSITY

105

CORR, COPI1PARI SON~

0

22

MASS FLOWi DENSITY KG/M-4M*S

CORR. COM'PARISON

A0 C!TTLs E5L-TM F3- 71, =-=a SEC-1- IATE I TW-TF-30 K

MASS FLOW DENSITY ~-"-M~

106

FORCED CONVECTION - STEAM1

2.00 4.00 6.00 S.00MASS FLOW DENSITY KG/M*r1*S

FORCED CONVECTION - "STEANI

.00 2.00 4 s

MASS FLOW DENSITY KGP/-v1-1 *&S

107

FOR~CED CON~VECT ION - STEEN1i

07

400 .01O soo.'33MASS FLOW DEN'SITY KG/M.*M-*S

FORCED CONIVECTION - STEAM

MASS FLOW DENSITY K/~~

108

ATTACHMENT 4

Comparison of the correlations for the calculation of the heat transfer

coefficients and of the temperature difference in nucleate boiling

109

CORR. CatPARISO.'-

mL~ -XS orr-s OT X13

.HEAT FLUX

-~ CORR. COI-IPARI SJN

HEAT FLUXW.MM

CO~RR. "U'CLEATE BOILINiG

MASS FLOW DENSITY KG/M-,M.*S

MASS FLOW DENSITY K CS/M-M !* S

ill

ATTACHMENT 5

Comparison of the correlations for the calculation of the maximum criticalheat flux

112

CORR. COHIPARISON

r -D

r-

CORR. CONiPARI SON

6

V CSE+j MIO.CE^~ rS11. I

MtLJ!-3 t )G C'WF~ -310 C

0.00 0.20 0.20 .0.'=I0.STEAM CONTENT

0.00 0.!o 0.20 0 .30ZSTEAM CONTENT

CORR. CON1PARISONCORR. COHIPARISON0

Lfl

(?p

-,Q

-;- i

i4f

ITM)n

aU

CE SL!7-:.S'-fL.! N -~ z

CCI. V.. SE

cFc<-!C

a I I aI I I I

O .~ 0 0.10 0.20 0.3STEAM CONTENT

0 .00STEAM CONTENT

Inside legends: Druck = pressure.Wand = wall

113

CO-R8l. CONAPRISOIN CORR, CONPAR ISOUN0

STEAM CONTENT STEAM CONTENT

C...0 CORR. COMPARISON4

1ora

*1

N,

CI.

GR! =! TNH

C! STCNG

9c.ur<- ! 43 O1 e-.FUU 1 ~3'1 C

a

=-S*iL -!F*!43i ERR

I I . I I . . . . . . . . I I ~*~l.* .~***I

.- STEAM CONTEN4T

Inside legends: Druck pressureWand =wall

I I I 1 1

STEAM CONTENT

114

CORR. COMPARISON I'.0 CORR. COfi-PARISON

0 0.20 0.30STEAM CONTENT

,.00 0.0 .! 3.20u 1 a.:STEAM CONTENT

0 CORR. COMiPARISdN

STEAM CONTENT

Inside legends: Druck =pressureW.'and =wall

f'.0

~0i- -

-- 2

CORR. COM'PARI SON'

c

TON7ý~ -31 C

~4.

STEAM CONTENT

115

ATTACHMENT 6

Comparison of the correlations

for the calculation of the heat transfer

coefficients in the steam-droplets

cooling regime

a

1.16

CORR. COi'~PARI'%SJN CORR, COiMPARI SON11

U,.

Cc~D!E--=j-sNGST IVMI-=~Ls1 I j

r.,

r.1

C

FLU10-200 ,C

I**. ~ ~. - r

b.00' 0.2 0.S 0 .75 I.0 0.O 0.25 0.50 0.~STEAM CONTENT

I ~

STEAM CONTENT

CORR. COITARI SON

x. I

tr InnIla-o GL~~HS~CW

~ ri

A Z~J' ~-~NC5~N IV~

*rý--NO =10iCc=50 cGm-q * a ~ ~

EN~V~fl 3.' Cý-.Eo

a I S

12.ýJ 0 .25 0 .10 0.75

STEAM CONTENT

.. 1. T I.1.) 0..5 . ..5 I ..0

STEAM CONTENT1 .01--

117

CORR. CO1'PARIS-ili CORR. CNjIPARI SON0

N-

tT,

W

o c-L-ME.co -N !-7,c5z, IV

.11 R=U.SE! DP-!30

c-~~-A LC.-4ST !V 7FL\Dl-=!oo c

G2!I I

G.25 .0.0 0.7STEAM CONTENT

I.30 0.00 0.25 0.~0 0.75

STEAM CONTENT

.0-LI,-

ro

V0

Ln

2'.rzLc

o~ CzG~-\:Cw0 M. .cc t--L- Rl:C4~ C*~\E'/~..IV

Aii= RD!--G~N77-J!05o` C

00

A*1

C:N : E-=-lNG57TZV IV

4

FUJ!-~OC~l~~RJD=~C

I

STEAM CONTENT0.00 0.5 .0 .1.

i

STEAM CONTENT

118

0 CORR, COM"PARISON CORR. COM.-PARISONi

to.U,-4.-

~Lm4,

*

'I,

(.40

UrZEINSIV8 f) S. 7A C !E-ENGSTU-4 IV

MIP.PO.SKIJ

P. 6 -0 rAf7FLUIQ-_ý00 C71.Pf'J =700 C

to.U,.4..

4,

4

;ii0

0-I.A

DCL*L-=ýlcECWmzi .flLi' 6:-rJA~

CCNO! E-EN'riSTC IV

Fl- 6 0 EARTFLL'IO-500 C7WP?\U =7^,0 C-1 00M~G/mo.m's

STEAM CONTEN~T0.130 0.25s 0.50 0.7S5

STEAM CONTENT

CORR. COMPARISON,,----CORR. COM~'PARISON

to.

to.

AI.

-j0D

r NE~P~ ~ =

~ G=I5-v-. /M

C

A

LL~~L~S~.4CW~ _ =- El. 1=

7 *r-Nl, C'-

-..... I

0.00 0.25 030 0 ~75 a0. 0 0.;2 030c 0 .73

STEAM CONTENT .qTFAM CnNTENT

119

0 CORR. COMPARISON CORR, COM1PARISON

X0.tr.I

I.,I

M

I44'

r- c?:zEvfL) 5.7 7F*UJ!O-3^j C-A Ca !E"-ýNC STCLN 1V T.v.Ft',- C

GIZNW LL-M5.7- P-!C c I=_M.7F%2j!0-2Q C*ratND .0 c

: .- I .I I I . , . I

0.00 0.25 o.Eso 0* .1

I .30STEAM CONTENT

CORR. COPIiPARISON

0.40

*%

STEAM CONTENT

CORR. CO.'IPARIS0N

=01EIEý: .7 K1O-"~ ~ !V P~FT~rf =!,I

* I

0 .3- 3 .;_STEAM CON~TENT

I .33 G.10 0.ý 0.co 0.75STEAM CONTENT

120

ATTACHMENT 7

Test parameters and results from the recalculation -Test DNBI

121

Test parameters and local values of the mass flow and steam content

I- C ~.. ~

w1 w~1 UEtihT.i.T inlet

00

< 0

TIME ~ ~ C (S(IMDS

- (L.'n-~I.o 4CL ~7C~

"77Cý

0.0 2.00 i C 0R01 inlet0 .0 .0 80IE (ITM S

TIME(STIM CS) H-EIGHT B27 CM

H bundleT i nlet

1z

CL

01-

TIME T3 P IM) EIH 2211 CM

a,122

Comparison of the equilibrium correlations

LD

LD

11.

1W

0.00 2.00 4.130 6.00TIME S TE C3 25=9 CM

b.00' 2.00 4.'00 -6.00TIME 0- TE C3 259 CM1

* MCC. rCaJG--L. FRCHSM'4,.J* CCND!F St.:ýSTON IV* UCENEYSLO 5.7

Experiment

<0

kv0.00 -2.00 14.00 6 .00TIME 5 TE C3 327 CM TIME *-S5 TE C3 327 CM

2J

- 'I

oC2-NEl!E SEýS70- IV

-- Exneriment~L.

a

0'0N

-s

0 .00r i ME

2.-00 .4 , 6.0II* 3 iI - 2.~TIME. q- T7-3 377 '

123

Comparison of the non-equilibrium. correlations

LU

to

rUz-.

N.2

~1~

C-,

0

LUI

t

.0.30 . 2.00 -. 0 '63TIME % E C3 25-9 (-l1: TIME 5 TE. C3 2591 0`

u

.7.

TIME S TE C3 27COM

L;

u

U

T IME S,:. ý 8..

TIMIAE.. j.J ~

- .. - S I

124

ATTACHMENT 8

Test parameters and results from the recalculation -Test DNB3-

125


0

Cn

CtR

0

C . I E:N-rR!TT inlet

1:

0 .13( TI14

IS)

£ I

TIME

. I I - . -6.0-3

I S )

V

0z I

H EINTRITT

inlet

LU

0lTI MIE S I

h el, S

CE- ý-CF--E ?-2 01L-1

0

TIME IS) HEIGHT 2327 C-M

CD CUt*A

3:

U-

bundle inlet

aU != - *'N I?-

!a; NI h ih

LUU

zo0ULUý-,Zjcn %

Cbundle inlet

X BTr

X ;-rX C I I

TIME So%

TIME

a

126

Co-mparison of the equilibrium corrclations

---] Experimnent

. 1

v

-J-J o .00

TI ME S6.00 9.00TE C.= 259 CM TIME S TE C3 259 C-

.4

-:1

cN,1

_j

=... =CLjC.-L ROI,5C--WC C'JDE E=-N'ZsT3MN 1V

+. I 57-

-- Exneriment

v

.I

I.

~~=1TIME S 7E C3 B27 CM

0.02 2-00 6 .00 9.00TIME S* T#E- C 3 3 227, C

C, Exmeriment

4 :-

0L i.

.i*.*. \~L~1 g

a

-0 'A

-J

~*1

Exzeriment

=2-I

< -

TIME

I. .I..

C * .j

=7 I...' T IME S - .- .-.

-7 -11

127

Comparison of the non-equilibrium correlations

0 1

ý: 8

A&~1

+ CLrLZ 1

^AK

merimernt

11

I

-- xzerizent

0

-J-J

*................I

TIME S TE C33255.0 L` T IME

* *I..3~133.5

I

TE C%"3 25-'.:,'

-jUiU

L)

~ --- Experim~ent

UoJ

O.>3 .;')3 8:30 9.^0TIME S TE C3 327 C.`1

0.00 3:30 6.020 9.00TIME S 7=E t-3 327 0-1

c !T

LU--

TIE 1 ý

Uoc%*

U .?'

u S,-~ - -- - -- C

-- 'x~erimret~

a

TIME* .4 .4

.I-. -- 0 '

128

ATTACHMENT 9

Test parameters and results from the recalculati~on - test DNB9-

129

Test parameters ana local values oi- tne mass flow and steam content

0.

0

t;j

in-C,,

ROPLS

00

C9on

W w :L'VMrrrinlet

It

C,, 0.

0.01:T IME

Is J2.00TIME

I ,.

8.00IS]

j2.60

0

00-

0-0

CH EIMMITn77inlet

Ci

UN

i t

0L>C0

0L.

0.00 .4.00 E.00 !2.00TIME ISI

).00 A*Q 80 20TIME IS) HEIGHT327 CM

(J) C0.1-o

3i:CO

4

bundle inletW ~EUCCE-TtRTU ?--CEýE 19 ^1.1!T heighlU Ew i 2=3 ZýMW FCE~- -5 CM1

FC-UZ- ýý7 C-j

0U-

wL(H

1'.- J.

* I I

2.')~ .4.%I I-

IS!2. 0- 0

T IME TIME130

Comparison of the equilibrium correlations

(D00

L)

mc m. 00ý-- S~iENS.C~Cr.3S GC:CS70N !V

+c~rfiN2V-/..:D 5.7

a.

S.-

I-- Experim-ent

-i I I I . I I ~ *IIIg~III II t

TIMES

2.')0 !2.00TE C3 259 CM TIME S TE C3 259 CM1

D

TIME S -TE CS327 CM TIME S TýE CS 3=27 CM

U.00 a.

11.% a: 1-.:; f: 2 nTIME 37 > - Z C3 377 CsA

131

Comparison of the non-equilibrium correlations

-Juu

1

U

2-

0

00.~,...

+c:-F-N

-- Ex~eriment

0.T

.00 4.00 9.00 !2.00IME S TE C3 25-0 C`MTIME C TE C33 2259 CM1

UJ

0--

U

2

TIME %5 TE C3 B27 CM

ILiU

U

U

2

0

4.C .3 :2. -.1'T IME C377l TIME S 3 770

132

ATTACHMENT 10

Test parameters and results from the recalculation -Test PDNB11-

133


3: W E! kr!-r-r

_J inlet

ci'

CL'

0.00 3.00 6.00 9.00 0.00 3.00 6.00 9.00TIME (SI T IME (SI

4 - -I

inlet + O. a hCEL B27 C.-I

_j 01-

0.00 S.00 a.010 93.10 W 0.00 3.10 6.00 9.0.0TIMcE- (S) TIME (SIHEIGHT 3271 CM

~\ I bundle inlet o -

a WJ L-CcLý. !9 c-i* helght :E

+ < X Lya7I N9 'M

TIM X3 TIMvE C1L~j_ 134

Comparison of the equilibrium correlaticns

.. i 1~. Gv 5.71~~ 1 E-- Eeriment '

a.-

0.00 3.00 6.00 9.00 0.Oc... .. **.. * . . III . . I

~.0O 6.00 9.00E S TE C3 25101CtlTIME S TC3259 C1 TIM

G ýO! S2:..iJ ~ l IV~

L) 1 - Experiment

-I7-- xme - - - - --.t

CI

-J1.. . .. . . . .........

V

\1,~0

0N ,~

0

0

X,4MC ZLLCSOT

II X ~..... ..

TIME6.rý C;. ^ ".IJ

T IME

. . . . . . . . . .

j - s.

135

ATTACHMENT 11

Comparison of the new correlations with the equili~brium correlations and

with the measured values

-V

136

Test ONBi

.1- i

U

i0 .

QoCR.

<-

0l

wr

-J

Lu

0

a70

LU

14

C

*1* C*:ENEvC-.. .~1 N~LPi- newcExperiment

orr.

:orr.

b0.00 2.00O 4.00T IME ( SI TE *r C Z 259 CM

IN

TIME (S) TE C3 927 CM

E~:~ .N newcorr.t.xcerlCfl

TIME 'M C 7~ TIME

137

4 . 1

-. -, 7

Test DNB3

I

C-:

-IR

<

0 MOO. Ozu'i-R P-1EEI'JJ13 CCND!E ~~rN~

-r CCENE-/V-1 SA~ Nc.E aF:L~a new

-- Experimentco rr

v

IN2

V

I I R ! I - A - A 1 4 ! - ;E . i

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NRIC FORM 335 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUMBER (A ssigned by TIDC, add VoL No., deany)12-84)NRCM 1102, BBIGAHCDT HE3201, 3202 BBIGAHCDT HE

SEE INSTRUCTIONS ON THE REVERSE. -- NUREG/IA-00022. TITLE AND SUBTITLE 3. LEAVE BLANK

Heat Transfer Processes'ýDuring Intermediate and Large ________________

Break LOCAs. 4. DATE REPORT COMPLETED .-

MONTH -YEAR

5. AUTHOR(S)1 March 19826. DATE REPORT ISSUED

MONTH 18YEAR

I. Vo~itek September I 967. PERFORMING ORGANIZATION NAME AND MAILING ADDRESS (Includ Z~p Code) B. FROJECTITASKIWORK UNIT NUMBER

Reactor Safety Corporation B. FIN OR GRANT NUMBER

Gesellschaft Fuer ReaktorsicherheitForschungsgelaende, 8046 GarchingWest Germany

10. SPONSORING ORGANIZATION NAME AND MAILING ADDRESS (Include Z,0 Code) I1Is. TYPE OF REPORT

Division of Reactor- System SafetyOffice of Nuclear Regulatory Research Technical ReportU.S. Nuclear Regulatory Commission b. PERIOD COVERED (mnclusive dares)

Washington, D.C. 20555

12. SUPPLEMENTARY NOTES

33. ABSTRACT (200 words or less)

The general purpose of this project was the investigation of the heat transfer regimesduring the high pressure portion of blowdown. The main attention has been focussed onthe evaluation of those phenomena which are most important in reactor safety, such asmaximum and minimum critical heat flux and forced convecti',n film boiling heat transfer.The experimental results of the 25-rod bundle blowdown heat transfer tests, which 'wereperformed at the KWU heat transfer test facility in Karlstein, were used as a databasefor the verification of different correlations which are used or were developed for theanalysis of-.reactor safety problems. The computer code BRUDI-VA was used for thecalculation of local values of important thermohydraulic parameters in the bundle.

15.AVAILABiLITY14. DOCUMENT ANALYSIS - a. KEYWORDS/DESCRIPTDRS

Critical Heat Flux (CHF)rewetMinimum film boiling temperatureFilm Boiling

b. IDENTIFIERIS/OPEN.ENDED TERMS

STATEMENT

Unl imi ted

1B. SECURITY CLASSIFICATION

('This pa#e)

Unclassified~17. NUMBER OF PAGES

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4

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4

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Heat Transfer Processes During Intermediate and Large ...

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