Atomic Energy of Canada Limited

ON THE PROCESS OF REWETTING

A HOT SURFACE BY A FALLING LIQUID FILM

by

T.S. THOMPSON

Chalk River Nuclear Laboratories

Chalk River, Ontario

June 1973

AECL-4516

ON THE PROCESS OF REWETTING A HOT SURFACE

BY A FALLING LIQUID FILM

byT.S. Thompson

ABSTRACT

A two-dimensional transient heat conduction model for therewetting of a hot surface by a falling liquid film is usedto predict the effects of wall thickness, thermal conductivity,volumetric heat capacity, and power generation on therewetting rate.

The model predicts that only a certain wall thickness takespart in the rewetting process, which is one of conductingheat from the dry to the wet region and removal of this heatin a narrow high-heat-flux zone. The critical thicknessbeyond which the rewetting rate is independent of wall thick-ness depends on wall thermal conductivity, dry-region surfacetemperature, and environmental pressure. For practicalpurposes the critical thickness for materials with a thermalconductivity of about 10 Btu/h.ft°F, such as stainless steelor Zircaloy, can be considered to be 0.020 in. for rewettingin a steam environment in the pressure range of 100-1000 psiawhen the dry-region surface temperature is 3OO-5OO°F abovethe appropriate saturation value.

The rewetting rate is predicted to increase with increasingthermal conductivity, but the increase is small if the wallthickness is greater than the critical wall thicknesses forthe thermal conductivities considered. The rewetting rate isinversely proportional to volumetric heat capacity.

For a given dry-region surface temperature, the rewetting rateis nearly independent of the individual values of heat fluxand dry-region heat-transfer coefficient. Furthermore if thewall thickness is greater than the critical thickness, therewetting rate is predicted to be the same for direct orindirect heating.

Experimental results reported in the literature are inter-preted in terms of the model, extrapolation is made to reactorspray-emergency-cooling conditions, and the requirements forfuture experiments are stated.

Chalk River Nuclear LaboratoriesChalk River, Ontario

June 1973

AECL-4516

Méthode de remouillage d'une surface chaudepar un film liquide en chute

par

T. S. Thompson

Résumé

On emploie un modèle bidimensionnel de conductionde chaleur transitoire pour le remouillage d'une surfacechaude par un film liquide en chute, afin de prédire leseffets de l'épaisseur des parois, de la conductivitéthermique, de la capacité thermique volumétrique et de laproduction énergétique sur le taux de remouillage.

Le modèle prédit que seule une certaine épaisseurde parois prend part au processus de remouillage quiconsiste a transporter la chaleur de la région sèche à larégion humide et à enlever cette chaleur dans une ?:oneétroite a haut flux thermique. L'épaisseur critiqueau-delà de laquelle le taux de remouillage est indépendantde l'épaisseur de la paroi dépend de la conductivitéthermique de la paroi, de la température de surface dela région sèche et de la pression environnementale. Pourtoutes fins pratiques, l'épaisseur critique pour lesmatériaux avant une conductivité thermique d'environ10 Btu/h.ft F, comme l'acier inoxydable ou le Zircaloy,peut être considérée comme étant de 0.020 in. pour leremouillage dans un environnement de vapeur pour une gammede pressions de 100 à 1000 psia, lorsque la températurede la surface de la région sèche est de 300 à 500°F supéri-eure à la valeur de saturation appropriée.

Le taux de remouillage est sensé s'accroîtresi la conductivité thermique est croissante mais l'aug-mentation est faible si l'épaisseur de la paroi estplus grande que les épaisseurs de paroi critiques pourles conductivités thermiques considérées. Le taux deremouillage est inversement proportionnel à la capacitéthermique volumétrique.

Pour une température donnée de surface de régionsèche, le taux de remouillage est presque indépendantdes valeurs individuelles du flux thermique et ducoefficient de transfert thermique de la région sèche.De plus, si l'épaisseur de la paroi est plus grande quel'épaisseur critique, le taux de remouillage est senséêtre le même pour le chauffage direct ou indirect.

Les résultats expérimentaux notés dans lalittérature sont interprétés en fonction du modèle;une extrapolation est faite pour les conditions derefioidi-SEement de secours par pulvérisation du réacteur;enfin, les besoins des expériences futures sont indiqués.

L'Energie Atomique du Canada, LimitéeLaboratoires Nucléaires de Chalk River

Chalk River, Ontario

Juin 1973 AECL-4516

i i

Contents

Page

ABSTRACT ±

1. INTRODUCTION 1

2. PHYSICAL MODEL 3

3. EFFECT OF WALL THICKNESS ON REWETTING RATE 6

4. EFFECT OF THERMAL CONDUCTIVITY ON REWETTING RATE 10

5. EFFECT OF VOLUMETRIC HEAT CAPACITY ON REWETTING RATE 10

6. EFFECT OF POWER GENERATION ON REWETTING RATE 11

7. DISCUSSION 13

8. CONCLUSIONS 17

NOMENCLATURE 18

REFERENCES 19

ACKNOWLEDGEMENTS 21

1. INTRODUCTION

IET REGION

. Violent Nucleate B a i l i n g

Fila Bat ling

If a falling liquid film is fed on to a hot vertical sur-

face whose temperature is above a certain value, heat is con-

ducted from the hot part of the surface to the region covered by

the advancing liquid film at such a rate that violent nucleate

boiling occurs at the leading edge of the film (Fig. 1). This

phenomenon, termed "sputtering" by Shires et al. [1], restricts

the rate of rewetting; and is related to a given surface temper-

ature above which the time to rewet the surface increases

linearly with increasing temperature. This phenomenon is

important in the emergency cooling of nuclear reactors employing

a spray emergency cooling system.•all Temperatun

Experiments carried out at

Harwell [2] in which a stainless

steel tube was mounted in a steam

environment showed that the tube

temperature at which sputtering

occurred increased with environ-

mental pressure and was approx-

imately 200 'F above the appro-

priate saturation value in the

pressure range 100-1000 psia.

It was found that the rewetting

rate was dependent on the temper-

ature of the hot surface and the ambient pressure, but inde-

pendent of the cooling water flow rate.

Elliott and Rose [3] carried out experiments on the

rewetting race of the inside surface of a heated vertical tube

for various conditions of tube temperature, coolant flow rate,

and environmental pressure. Stainless steel and Inconel 600

tubes were tested and no difference in rewetting rate was found.

The results were in agreement with the Harwell experiments 12]

in which the tube was externally cooled. Recently Elliott and

Rose [4] showed that the rewetting rate of a Zircaloy tube was

approximately twice that of stainless steel and Inconel.

FIG

DRY REGION

REIETTING OF * HOT SURFACEBY A FALLING LIQUID FILM

In an attempt to understand the effect of wall thickness

and physical properties en revetting, some researchers [5,6]

have proposed physical models of rewetting and solved the gov-

erning energy equations analytically. Because of mathematical

complexity, the models were not entirely satisfactory and the

solutions were only approximate. Nevertheless the predictions

indicated that the revetting rate was not very sensitive to

changes in clad thickness or thermal conductivity, and that the

product pev tends to remain constant.

Recently the author [7] proposed a physical model for the

rewetting of a hot surface. The model differs from others in

that the form of the wet-side heat-transfer coefficient was

assumed to represent nucleate boiling, i.e. a function of local

temperature (h(T) = RT3}. The cubic relation was assumed valid

up to the sputtering temperature, and thereafter the heat.-

transfer coefficient was

assumed to be zero. The

energy equations were

solved numerically and

the magnitude of the

heat-transfer coeffi-

cient in the vicinity of

the advancing liquid

front was evaluated by los

analyzing the Harwell

data [2]. The impor-

tant conclusions were

that the heat-transfer ,os

coefficient and heat flux

were of the order of

105Btu/h.ftz°F and

107Btu/h.ft2 respectively ,o4

at the solid-liquid-

vapour interface (Fig. 2)

due to large localized

p-o

HEAT FLUX- BTU/h f t 2

3

O

-o

HEflT TRANSFER COEFFICIENT- BTU/h f t ' ° F

radial and axial

12 24 36 48 60 72 81 96 108 120

DISTANCE FROM INTERFACE - i n . x 1 0 3

FIG 2 HEAT FLUX AND HEAT TRANSFER COEFFICIENT IN THE

VIC IN ITY OF THE INTERFACE.

temperature gradients. These values are much higher than

steady-state values, but are comparable to those found by other

researchers studying transient boiling. A two-dimensional con-

duction analysis was necessary as the assumption of perfect

radial conduction overestimated the wet-side heat-transfer

coefficient and heat flux.

It is the purpose here to use the predictions of this

model to explain in detail the effects of wall thickness, thermal

conductivity, volumetric heat capacity, and power generation on

the rewetting rate. Experimental results reported in the lit-

erature are discussed in terms of the model, extrapolation is

made to the reactor situation, and requirements for future

spray-cooling experiments are presented.

2. PHYSICAL MODEL

The model has been described previously in detail [7].

The mechanisms governing the rate of rewetting of a hot surface

by a falling liquid film are the conduction of heat from the dry

co the wet region and the removal of this heat in a narrow high-

heat-flux zone. The two-dimensional energy balance in cylin-

drical coordinates for an elemental wall section is:

1 J_ r 3T + l f T _ pc 3T + q m Q _m (1)

r 9r 3r 3z2 k 3t k

This is simplified by utilizing the observation of a constant

interface velocity [1,2,8,9], and hence relating the z- and t-

variables by Z * z-vt so that a set of coordinates, T and Z,

moves with the interface.

, . _, 92T 32T , pc 3T £cv 3TSubstituting = — — and - K = £

3z2 3Z2 k 3t k 3Z

into eq. 1, we have

l 3Tr

3T + £ = 0

r 3r 3r 3Z2 k 3Z

Knowing the boundary conditions T(-°°,r), T(+°°,r),

(dT/dr)_ , and (dT/dr) and the physical properties of the wall:Ri Ro

it is possible to solve eq. 2 and compute the rewetting velocity.

Alternatively, if the rewetting velocity is known one of the

boundary conditions can be evaluated.

This approach is used in Ref. 7 to compute the boundary

condition (dT/dr)p which ic directly related to the heat-K-O

transfer coefficient. The wall temperature at the interface of

the wet and dry area is assumed to be equal to the sputtering

temperature, and it is assumed that the wall is wetted and

nucleate boiling occurs up to this temperature. At higher wall

temperatures, film boiling is assumed to occur and the heat-

transfer coefficient is several orders of magnitude smaller.

The sputtering temperature at various pressures as

reported by Bennett et al. [2] is used and their experimental

data for the rewetting of a stainless steel tube are analyzed by

solving eqn. 2 with

q = 0

p = 494 lbm/ft3

k = 9.68 Btu/ti.ft°F

6 = 0.064 in.

R Q = 0,25 in.

c = 0.12 Btu/lbm°F

and the following boundary conditions in terms of T = 9-6sat

U—,r) =0 ... (a)

T(+o°,r) = T2 ... Cb)

dT(Z)dr

Rx f

14

Cc)

RT^Z) T(Z) <. T ... (d)c

0 T(Z) > Tc (sputtering temperature)

Knowing Tz and v, the parameter R is computed. The results aregiven in Table 1.

TABLE 1

Results of the Analysis of the Data of Bennett et al. [2]

Run

5609

5613

5612

5607

5598

5596

5595

5594

5593

5592

5558

5602

5556

5584

A2

5616

A3

5582

5630

5631

5635

5629

5634

5623

5622

5621

Pressure

(psia)

1000

1000

1000

1000

500

500

500

500

500

500

300

300

300

300

300

300

300

300

200

200

200

200

ZOO

100

100

100

e2

(°F)

851

827

805

794

868

824

808

783

771

741

822

800

781

758

734

737

725

702

738

724

714

670

638

693

675

624

T2

(°F)

306

282

260

249

401

357

341

316

304

Ilk

405

383

364

341

322

320

308

285

352

343

333

289

257

365

337

296

V

(ft/h)

684

792

1008

1116

396

504

576

684

720

972

360

396

432

504

568

576

633

756

396

468

468

612

756

360

432

540

Tc

(°F)

193

193

193

193

208

208

208

208

208

208

193

193

193

193

193

193

193

193

175

175

175

175

175

170

170

170

R

(Btu/h.ft2oF-)

0.0144

0.0122

0.0110

0.0098

0.0119

0.0110

0.0108

0.0098

0.0088

0.0075

0.0174

0.0162

0.0158

0.0152

0.0142

0.0142

0.0136

0.0122

0.0225

0.0246

0.0226

0.0200

0.0160

0.0265

0,0256

0.0215

RT3

(Btu/h.ft2oF

xlO

1.

0.

0.

0.

1.

0.

0.

0.

0.

0.

1.

1.

1,

1,

1.

1,

0,

0

1

1

1

1

0

1

1

1

~5)

04

88

79

70

07

99

97

88

79

,67

.25

.16

.14

.09

.02

.02

.98

.88

.21

.32

.21

.07

.86

.30

.26

.06

RT1*

(Btu/h.ft2

xlO

2.

1.

1.

1.

2.

2.

2.

1.

1.

I.

2.

2.

2.

2.

1.

1,

1.

1

2

2

2

1

1

2

2

1

~ 7)

00

69

53

36

23

06

02

83

65

40

41

,25

,19

.11

.97

.97

.89

.69

.11

.31

.12

.88

.50

.21

.14

.80

3. EFFECT OF WALL THICKNESS ON RESETTING RATE

If we look at a typical predicted wall temperature profile

for Bennett's data (Fig.

made. The thermal per-

turbation due to the

advancing interface

requires a finite time

to propagate through

the wall and only a

portion of the wall

thickness appears to

contribute heat to the

high-heat-flux zone in

the interface region.

This poses an inter-

esting question; is

there a critical wall

thickness beyond which

rewetting rate is

independent of wall

thickness3? Assuming

all else remains con-

stant, the model pre-

dicts that such a

thickness exists. It

3), an interesting observation can be

aoo -

300

200T,

100

DEPTH

- i n / l O " 3

61.0 a

32.0

. • • • £ *£&••*•«<•••

ox

o

V 2

_ O0

- I I I I I I

AERE - R5146 RUN 5564T2 =341 "F« = 504 f t / hR = 0.0152Tc = 193 °F

f = 300 psiaE = 0.0b4 i n .P = 494 i bm / f t 3

c = 0.12 Btu/lbm °FRo = 0.25 i n .K = 9 68 Blu/h I I °F

- I I I I-120 -10B -% - g i 72 -fco -43 -3fe -24 -12 0 12 24 3b 48

DISTANCE FROM IHTEFFRCE - in X 103

.71.5 ,35 .8

TIME - ms

FIG. 3 PREDICTED iALL TFJIPERATURE PROFILE

-35 .8

decreases with increasing velocity of the rewetting front, and

hence is a function of downstream temperature T2 (Fig. 4) and

environmental pressure (Fig. 5). The reason for this becomes

apparent when the isotherms predicted by the model for three

different downstream temperatures are compared (Figs. 6, 7, 8).

If we use as a reference the isotherm 1°F less than the down-

stream temperature T2, the portion of the wall in the dry region

(hatched) from which heat must be conducted to the wet region at

any instant in time decreases with increasing v.

• * T j » 28S (B . 0.0122)

* T , • 341 (R » 0.0152)

X T, = 405 (R - 0.0174)

CONDITIONS

P • 300 psiik • 9.68 Btu/h.ft 'Fp - 494 l t » / F t 'c - 0.12 Btn/lba'F

R_ - 0.25 in.

0.0064 0.0192 0.032 0.0448 0.0576Hall Thickness - i n .

FIG. 4 PREDICTED EFFECT OF MALI. THICKNESSON REVETTING RATE- Tg as parameter -

- K L

300

200

Locus of Critical Thickness

p

p

p

* 500

- 300

- 100

psia

psia

psia

R

RT

= 0.0108. - 20B*F

• 0.0152- 193'F

* 0.0256- 170"F

k = 9.68 Bto/h.ffFp • 494 lba/ft1

c • 0.12 Btu/lb»°FR * 0.25 in.

_L j _ _L0.0064 0.0192 0.032 0.0448 0.0576

Wall Thickness - in.FIG. 5 PREDICTED EFFECT OF M L l THICKNESS

ON RESETTING RATE- Pressure as parameter -

K' ?'«

F'G 6 ISOTHERMS IN THE VICINITY

GF RElETTlMS FRONT

HUN 5558 »ERE - S5I46P 3QO p s nT, 405'FTc 193-F

fl • 0174P - 494 itM-Illc -- 0 12 Blu I M *F. - 9 68 Btu n r. >fg = 0 X* :n*r 0 25 -n

MG r ISOTHEMS IN IHE

R 0 0p 494 I an I t 1

c 0 I I Blu Inn *fk S Gl Btu h t i *F

i ; 0 Q6* in

V 0 35 '«

CRT SIDE

(SOTHEimS >N THE K1C.NITI

OF REITT' hG H O t fRUN » S 2

P ^

VR -P -c ;h :fi =

•ERE

300 fl>'

,,

aJ3-F

0121494 IOT

a90a

U BtBfl B1064 i25 in

R514Ej

I t 'u 1 at ' Fi i h i i 'fn

1000

^ 900

t eoo

g 700

£ 600

500

C0NDITI0H5P = 300 psiaTj= 341 "FR = 0.015?p = 494 Ibm/ft1

e = 0.12 Btu/lbmT

.5- in

.0031

4.64 9.68 19.36

5 10 15 20

THERMAL CONDUCTIVITY - Btu/h f t V

FIE. 9 EFFECT OF THERMAL COIOUCTIVITY ON REIETTINB RATE

- i a l l thickness as a parameter -

1000

900

BOO

700

600

500 U

t- 400

300

200

100

LOCUS OF CRITICAL THICKNESS

* — k = 19.36 Btu/h f t *Fg-k = 9.68

CONDI TIONSP = 300 psiaT,= 341 -FR = 0.0152p = 494 Ibm/ftJc = 0.12 Btu/lbm -F

.0128 .0256 .0344 .0312 .064

FIG.

.0192 .032 .0448 .0576

MALL THICXNESS - i n .

ID EFFECT OF ULL THICKNESS ON SEIETTING RATE- thermal conductivity as parsaetar -

10

4. EFFECT OF THERMAL CONDUCTIVITY ON REWETTING RATE

The effect of thermal conductivity is rather complex.

Intuitively one would think that increasing the thermal conduc-

tivity would increase the axial flow of heat from the dry to the

wet region, with a resultant increase in rewetting velocity.

This is true, but the increase is not ar great as expected

(Fig. 9), especially if the wall thickness is greater than the

critical wall thicknesses corresponding to the values of thermal

conductivity considered. The reason for this is that increasing

conductivity also increases the critical thickness (Fig. 10)

with a corresponding increase in amount of heat that must be

conducted from the dry to the wet region. This is further

illustrated by comparing the predicted isotherms of the hypothet-

ical case of k = 19.36 Btu/h.ft°F (Fig. 11) to the predictions

with k = 9.68 Btu/h.ft°F (Fig. 7).

5. EFFECT OF VOLUMETRIC HEAT

CAPACITY ON REWETTING RATE

To understand the effect

of volumetric heat capacity, pc,

we look, to approximate solution

of eq. 2 as presented in [7].

The method of solution

was to use the method of finite

differences, and to write separate energy equations for surface

and interior nodes. In this way the nonlinear heat-transfer

coefficient appeared directly in the surface-node energy equa-

tion, and the equation could easily be linearized. The equation

for a surface node in the wet region was:

HG >t ISOTHERMS - HYPOTHETIC*!. USE HUH

azJL IIAr 3r

+ pcv 3T _ 2RT"(Z)

k dZ kAr

(3)

which tends to - k dT(Z)dr (Z)

R

as Ar -* o, i.e. it is an approximation to boundary condition (_d)

11

Examining eq. 3 we see that, unlike k, pc appears only in

combination with v. This is true also of the energy equation of

an internal node, i.e. eq. 2. The conclusion is that the

rewetting velocity is inversely proportional to the volumetric

heat capacity.

6. EFFECT OF POWER GENERATION ON REWETTING RATE

If we consider eq. 2

1 3 3T , 32T L pcv 3T 1r — + + * + - = 0 ... (2)

r 3r 3r 3Z2 k 3Z k

but with boundary conditions: (uniform heat generation in the

wall)

(R-R 2) (R -r2) q R

2R RT3 (-«•=>,R ) 4k 2k X r

(e)

(R2-R2) (R2-r2) . RO X O * *> A Oq + q - Rf k —

2R h,, 4k 2k x rO D

(f)

(g)

RT"(Z);T(Z) <. Tc ... (h)

hDT(Z);T(Z) > Tc

For the same downstream surface temperature

(R2 R2s

= q2 Ro hD h

the rewetting velocity is nearly independent of the individual

values of q and h . Predicted rewetting rates for a 0.020 in.

Zircaloy-2 sheath are presented in the following table.

12

TABLE 2

Effect of Power Generation on Rewetting Rate

Case

1

2

3

4

q

x 10"7

Btu/h.ft3

12.532

6.266

3.133

0

hD

Btu/h.

387

193

96

0

ftz°F

.0

.5

.8

x 10"5

Btu/h.ft

2.0

1.0

0.5

0

T2(+°°,Ro)

2 op

518

518

518

518

V

ft/h

528

533

537

545

The reason for this becomes obvious when the magnitude of

the heat flux in the interface zone is compared to the equilib-

rium flux. In the interface region the flux is of the order of

106-107 Btu/h.ft2, whereas the equilibrium flux is only of the

order of 105 Btu/h.ft: The important parameter is the down-

DIRECT HEATING

stream surface temperature T(+°°,R ) not the individual values

of q and h .

It is interesting to

look at another type of

power generation. Consider

an infinite-thermal-capacity

constant-temperature core

providing the same downstream

heat flux to coolant as

Case 2 in the direct-heating

problem just discussed, and

with the same downstream

surface temperature T(+°°,R ).o

Beyond a certain wall thick-

ness, tne rewetting rate is

the same for the two types of

heating, Fig. 12. This once

again demonstrates the impor-

tance of the downstream sur-

face temperature rather than

900

800

700

too

500

400

300

200

100

<O-/3c CORE/INDIRECT HEATING

REF.

.0128 | .0256 .0384 .0512 .064

SHEATH MATERIAL = Z i r - 2

* = 105 Btu/h f t 2

T!+<D,o) = 516 °F

R = 0.0215

Tc = 193 °c

P = 300pst0

.0064 .0192 .032 .0448 .0976WALL THICKNESS - i n

F I G . 12 EFFECT OF M I L THICKNESS ON RESETTING RATE I I T H

POIER GENERATION

13

temperature profile in the wall. Upstream of the interface how-

ever the temperature profile is considerably different for the

two types of heating and for a thin-walled tube the heat flux to

coolant is very large with indirect heating by an infinite-

thermal-capacity core, large enough in fact to decrease rewetting

rate. The increase in rewetting rate with decreasing wall thick-

ness for the direct-heating case is similar to the non-generating

case (section 3) as expected.

7. DISCUSSION

With a clear understanding of the effect of wall thick-

ness, thermal conductivity, volumetric heat capacity, and the

type of heating on the rewetting rate; it is possible (i) to

better interpret existing experimental data, (ii) to extrapolate

these data to reactor conditions, and (iii) to better specify

future experiments on spray emergency cooling.

The model predicts that only a certain thickness of the

wall takes part in the rewetting process. This "thickness

effect" depends on one physical property of the wall only,

thermal conductivity; hence stainless steel should simulate

Zircaloy in this respect. However the volumetric heat capacity

of Zircaloy is less than one-half that of stainless steel, and

the model predicts that the rewetting rate is inversely propor-

tional to volumetric heat capacity. This means that experiments

in which stainless steel is the sheath material will be pessi-

mistic by a factor of two. This was observed experimentally by

Elliott and Rose [3,4]. The thermal diffusivities of Inconel 600

and stainless steel are nearly the same and hence the model

predicts similar rewetting rates for the two materials, in

agreement with experiment [3].

The critical thickness increases with increasing down-

stream temperature and with decreasing pressure. However for

practical purposes, the critical thickness for materials such as

Zircaloy, stainless steel, or Inconel with a thermal conductivity

of about 10 Btu/h.ft°F can be considered to be 0.020 in. for

14

rewetting in a steam environment in the pressure range of

100-1000 psia when the rod temperature is 300-500°F above the

appropriate saturation value. Since the critical thickness is

small with respect to the rod radius, the model predicts the

rewetting rate to be independent of rod curvature. This explains

the agreement between the Harwell experiment [2] in which a

0.5 in. OD by 0.064 in. thick tube was cooled externally and the

experiments of Elliott and Rose [3] in which a 0.625 in. 0D by

0.050 in. thick tube was cooled internally.

Interestingly then, it becomes clear that it is more

important to accurately simulate sheath volumetric heat capacity

than thickness, thermal conductivity, or outside diameter in

emergency-cooling experiments. Further if a relatively thick

wall is used,the type of heating employed (direct or indirect)

will have little effect on rewetting rate.

A wall thickness of 0.020 in. is typical of the fuel

cladding used in many reactors. This means that during rewet-

ting of a moderately hot cladding surface by a falling liquid

film there is little interaction between cladding and core. The

rewetting rate will be almost entirely dependent on the cladding

surface temperature approximately one wall thickness downstream

of the advancing rewetting front, and it should be of sufficient

magnitude to be the dominant heat removal mechanism in the

accident situation.

However if the sheath temperature exceeds 1000°F, the

core interacts with the sheath, the heat removal requirement is

higher, and the rewetting velocity is correspondingly lower. In

this case heat removal by water sputtered from one rod to another,

convective heat transfer to wet steam; and radiation heat transfer

to water vapour, water droplets, and channel walls will become

very important in determining the sheath temperature transient.

Implicit in this argument is the importance of the clad-

ding heatup rate and the delay time between the accident situa-

tion and coolant injection in determining the maximum cladding

temperature reached.

15

It is important to note that the rewetting rate increases

with pressure for a given downstream temperature 02. The reason

for this is the increasing values or 0 and 8 . For a given

downstream temperature difference T2, the r'jwetting rate increases

between 100-500 psia and then decreases between 500-1000 psia.

The reason is that Tc reaches a maximum at 500 psia, and the

rewetting rate is inversely proportional to T2-Tc. The heat

flux in the vicinity of the interface is nearly independent of

pressure (Fig. 13), and decreases with decreasing T2 (Fig. 14);

hence it is not related to the observed pressure effect.

The model is consistent with the existing experimental

evidence [2,3,4] that the rewetting rate of a falling liquid film

is independent of cooling water flow rate when the environment is

steam and the pressure greater than atmospheric. However a flow

dependence does exist for rewetting in an air environment at

atmospheric pressure [1,11,12,13], The reason for this discrep-

ancy is not understood, but it is probably related to the relative

magnitude of steam specific volume at low and high pressures.

Duffey and Porthouse [6] have shown that at atmospheric pressure

the heat flux on the wet side is a function of mass flow. Hence

the model in its present form is not applicable for ambient

pressures less than 50 psia.

Although the various arguments presented in this report

have been discussed in terms of rewetting during spray emergency

cooling, the basic phenomenon is considered to be the same for

rewetting during emergency cooling by flooding 16,10] or

following post-dryout operation.

16

10'

10s

?

- *x1

g

-_

1 1

X

0

+

S XX« X

i 1 1

* - 500 ps

P = 300 ps

P - 100 ps

» 1

1 1

fR =ia I T -*•' c

j"R =

' a 1 T =

• • { ? ;

T,k»

c

"o

1

0.01081208°F J « = 576 f t /h

0.0152\193oF J V = 504 f t /h

!£?} »•« «/„

CONDITIONS

= 341 - 337-F

= 9.68 Btu/h f t °F= 494 Ibm/f t3

= 0 . 1 2 Btu/16m= 0.25 i n .

5 x

s s1 1

12 24 36 46 60 72 84 96 108 120

DISTANCE FROM INTERFACE - i n X l O 3

F I G . 13 HEAT FLUX IN THE V I C I N I T r OF THE INTERFACE

- PRESSURE as PARAMETER -

~ 10' -

106

A T; = 405°F (R = 0.0174) V = 360ft/h

O T, = 341°F (R = 0.0152) V = 504ft/h

• T, = 285°F (R - 0.0U2) V = 75bft/h

CONDITIONS

P = 300 psiak = 9.68 Btu/h ft °FP = 494 Ibm/ft3

c = 0.12 Btu/lbm °FRo = 0.25 in.

I I I I I J I \ L12 24 36 48 60 72 84 96 108 120

D1ST MICE FROM INTERFACE inXIO3

FIG 14 HEAT FLUX Hi THE VICINITY OF THE INTERFACE

- T, as PARAMETER -

17

8. CONCLUSIONS

The process of rewetting a hot surface by a falling liquid

film is one of axial conduction of heat in a thin surface layer

from the dry to the wet region, and the removal of this heat in

a narrow high-heat-flux zone.

Beyond a certain sheath thickness; which depends on

thermal conductivity, downstrtam temperature, and ambient pres-

sure, neither the wall thickness nor type of heating affects the

rewetting rate. The rewetting rate is inversely proportional to

volumetric heat capacity.

This information is useful for the extrapolation of

existing data to reactor conditions, and for specifying future

experiments on emergency cooling. Of particular significance is

the deduction that the rewetting process is governed almost

entirely by clad thermal diffusivity for surface temperatures

less than 1000°F. At higher temperatures, the core of the fuel

element contributes to the rewetting process.

18

NOMENCLATURE

Symbols

c specific heat Btu/lbm°F

h heat transfer coefficient Btu/h.ft2oF

k thermal conductivity Btu/h.ft°F

q volumetric generation rate Btu/h.ft

r radial coordinate ft

Ar radial node size ft

R parameter of wet-side heat transfer

coefficient Btu/h . f t 2oFlf

R. inside radius ft

R outside radius fto

t time h

T temperature difference 6-9 °F

v rewetting velocity ft/h

z axial coordinate ft

Z Z = z-vt, axial coordinate moving with interface ft

p density lbm/ft3

<i> heat flux Btu/h.ft2

6 wall thickness in.

9 temperature °F

+°° far downstream of interface ft

-00 far upstream of interface ft

Subscripts

2 far downstream

c sputtering

D dry side

19

REFERENCES

1. G.L. Shires et al., Film cooling of vertical fuel rods,

AEEW-R343, 1964.

2. A.W. Bennett et al., The wetting of hot surfaces by water

in a steam environment at high pressure, AERE-R5146, 1966.

3. D.F. Elliott and P.W. Rose, 1970, Unpublished work.

4. D.F. Elliott and P.W. Rose, 1971, Unpublished work.

5. E.V. Gilby (ed.), United Kingdom contribution - Heat

Transfer Newsletter No. 3, CREST-NL-3, April 1968.

6. R.B. Duffey and D.T.C. Porthouse, The rewetting of hot

surfaces by falling films and bottom flooding, CEGB

RD/B/N2530, January 1973.

7. T.S. Thompson, An analysis of the wet-side heat transfer

coefficient during rewetting of a hot dry patch,

Nucl. Eng. and Design, _22̂ , 1972.

8. R. Semeria and B. Martinet, Calefaction spots on a heating

wall; temperature distribution and resorption, Symposium

on Boiling Heat Transfer in Steam Generating Units and

Heat Exchangers, Manchester, 1965.

9. H. Fujie et al., Studies for safety analysis of loss of

coolant accidents in light-water power reactors,

NSJ-Tr-Hz, 1968.

10. T.S. Thompson, Simulated bottom-flooding emergency

cooling of a closed-spaced rod bundle, European Two-Phase

Flow Meeting, Casaccia, Rome, June 1972.

11. A. Yamanouchi, Effect of core spray cooling in transient

state after loss of coolant accident, J. Nuc. Sci. Tech.,

5_, 11, p 547, November 1968.

12. K. Yoshioka and S. Hasegawa, A correlation in displacement

velocity of liquid film boundary formed on a heated

vertical surface in emergency cooling, J. Nuc. Sci. Tech.,

1, p 418, August 1970.

20

13. R.B. Duffey and D.T.C. Porthouse, Experiments on the

cooling of high temperature surfaces by water jets and

drops, CREST Specialist Meeting on Emergency Core

Cooling for Light Water Reactors, Munich, October, 1972,

21

ACKNOWLEDGEMENTS

The computational work presented in Sections 3, 4, and 6

of this report was carried out while the author was attached to

Centro Informazioni Studi Esperienze (CISE), Milan, and the

assistance of the computer staff is greatly appreciated. The

helpful discussion with members of Divisione Process and in

particular Ing. R. Martini is gratefully acknowledged.

Addi t ional copies of this documentmay be obtained from

Scientific Document Distr ibution OfficeAtomic Energy of Canada Limited

Chalk River, Ontario, CanadaKOJ 1J0

Price - 50$ per copy

1219-73