Ceaitctal de Stat pcatra Bacrgia Naclcarâ INSTITUTUL DB RLACro&I NUCLEARI BNBK2KTKI

IRWE-129-J97*

Aug (Ut

L.LUCA, T.MAC0PH, V.IAC06, N.PJRl/U

INVESTIGATION OF APT.FICIA! ROUGHNESS INFLUENCE

ON HEAT TRANSFER IN TRANSIENTS

Nu.tle.ati KeactoK the\mai peK^oimancei impnovement ii poaible by cote heat tnanif^en. intensifying, which. is possible to achieve iţ antiţicial louahness on fauel ele­ment sun^ace is used.

This papen pntsents the txpetimentat neseaich made with a view tc establish Koucihness suifaaces paia-mete.».s in unsteady conditions.

Rough element* weie pioved to be bettek than smooth one*, as a standa/id.

TABLES OF CONTENTS

1. Introduction l

2. Experimental installation and

its instrumentation 3

3. Measurement methods and

experimental data 6

4. Experimental data processing 6

5. Conclusion 32

6. Nomenclature 33

7. References 35

1. INTRODUCTION

A permanent advance of nuclear power stations in the

world was possible owing to several factors of different nature,

but the determining element was the improvement of the thermal

performances of the nuclear reactor.

Continuous! increasing of power density, of the heat

flux, on the fuel rods, as well as of the coolant parameters

were established which determined the reducing of the specific

investment for the .reactor and the amelioration of thermal effi­

ciency of nuclear power station.

Very important in reactor development is the improve­

ment of the heat transfer mechanism into the core which can be

obtained mainly by the increasing of the heat transfer coeffi­

cient between the fuel rods and the coolant.

This leads both to the thermal power rising and the

power density of the core, and to the reducing of heat transfer

surface and of the thermal stresses from fuel elements, all of

them having good economical results.

One of the methods used for this, consists in the prac­

tice on the heat transfer surfaces of a special profiles to

create artificial roughness, which appears in two effects:

the increasing of the friction coefficient, and of the heat

transfer coefficient. The improvement of the heat transfer

coefficient is due to the reducing of the thermal resistance of

the boundary layer by reducing the thickness of its, produced

by increased superficial turbulance.

Experiments showed that at small Reynolds'5 numbers,

the flow pattern is not influenced by small roughness, owing

to the covering of roughness by the laminar boundary layer.

The use of artificial roughness is of high interest,

a fact which is proved by the great number of published works

on the subject in literature.

Among these, remarkable results are obtained by

NUNNER [1], DIPIREY [2], ISACENKO [3], KJELLSTROM [4].

- 2 -

Nunner did a great number tZ measurements using copper

pipes with a diameter* of 50 mm and a lenght of 9800 mm provided

with rings of different shapes, which were inserted at various

levels in the test section obtaining heat transfer coefficient

increases of 75-100%.

In contrast with him, Isicenko used pipes with artifi­

cial roughness having the shape of triangular thread, indicating

an increase of the heat flux about three times higher than with

nmooth pipes.

Oipprey investigated experimentally sand-grain-type

roughness fabricated by electrolytic vleposition of nickel and

obtained heat transfer coefficient increases up to 270%.

Among the complex researches one must mention the work

of Kjellstrom regarding the augmentation of heat transfer study

on 23 rough geometries varying in profiles as well as in the

distribution of turbulancî promotors.

All rough surfaces experimented by him were superior

to the smooth surfaces, the obtained increasing being up to 40%.

The advantages of rough surfaces were demonstrated by

many authors, but only few of them study the behaviour of them

in transients.

This study is an attempt to improving the present

knowledge regarding the performances of artificial roughned

surfaces in transient regimes, processing experimental data ob­

tained on the 10 kW thermic loop at the Atomic Physics Institute.

Two main types of transient regimes, of power and of

flow were studied during the researches.

- 3 -

2. EXPERIMENTAL INSTALLATION AND ITS INSTRUMENTATION

The experimental installation is represented by the

10 kW thermal loop at the Atomic Fhysics Institute and is

described in [5], with the specification that the instri^nenta-

tion of the test section is adequated to actual experiments

(Fig. 2.1.).

The experimenta? elements, three in number, are manu­

factured of stainless steel, with the outer diameter of 12 mm,

and the inside diameter of 10 mm. The cooling water flows

through the interior of the pipes.

For the achievement of artificial roughness, two of

the three elements were equipped with an inside thread having

the geometric characteristics in the table 2.1. The symbols

result in figure 2.2.

TABLE 2.1.

ELEMENT

SMOOTH ELEMENT

ROUGH ELEMENT 1

ROUGH ELEMENT 2

i ^ l O 3

[mm]

10 .10

1 0 . 1 0

1 0 . 1 5

d 2 . i o 3

[mm]

1 0 . 1 0

10 .60

1 0 . 6 0

p . 1 0 3

[mm]

-

4 . 6 7

6 . 0

k . 1 0 3

[mm]

-

0 . 2 5

0 .225

The ent i re t e s t s e c t i o n was insu la ted with asbes tos fabric (X= 0.128 w/m.gr) , there fore , the thermal l o s s in the environment are merely 0.3% of the power generated by the heating system.

To e f f e c t u a t e the experimental measurements, the e l e ­ment was equipped with an adequate instrumentation for the de­termination of the fol lowing parameters: supply vo l tage [V] , i n t e n s i t y [A] , s p e c i f i c weight flow of water [Kg /m 2 . s ] , p r e s ­sure drop [cm.H20l , i n l e t and o u t l e t water temperature [°CJ, JS W-J11 as three temperatures on the wal l o f the element (one in the middle and two at 30 mm from e x t r e m i t i e s ) .

TRANSDUCERS

T-Temperature P-Differential pressure A-Intensity U-Supply voltage

1-Test section 2-Flow measurement section 3-Slackening section 4-Power transformer 5-Power control system

Fig. 2 . 1 . Element tos t Instrumentation

irig. Geometric characteristics of the elements

Intensity was measured with a current reducer, having

a precision class of 0.5 and transformation ratio of 1000/5, .

which discharges to an 5.0 A ammeter. The error of measurement

was = ± 0.5%.

Since the j.ower delivered in the element is P = U • I,

and the absolute error in the determining of the power is:

For

AP = P -AU + p.AI = I ' i U + U--M u i

; = 10V and I = ?fOA, the fol lowing e r r o r r e s u l t s :

The flow r a t e and the p r e s s u r e drop i n the element was mea­

sured wi th t r a n s d u c e r of d i f f e r e n t i a l p r e s s u r e type CH5310

(Schlumberger) wi th a measuring range of (0 - 300) mbar, having

the e r r o r of C.2%.

The power u n i t s u p p l i e s the t r a n s d u c e r wi th a l t e r n a ­

t i n g cur re ; , t .5 22 V and 1.000 Hz.

The s i g n a l o b t a i n e d from t r a n s d u c e r s i s then decoded,

a m p l i f i c a t e d and conducted t o an i n d i c a t o r . The r e l a t i v e e r r o r

was e s t i m a t e d ±1%.

The t empera tu res were measured v i t h i r o n - c o n s t a n t a n

thermocouples , the d i s p l a y b e i n g made on an e l e c t r o n i c thermo­

meter type Comark 1641) , which i s ab le to measure In the range

of -b5 C T +700°C, with an e r r o r of 2%. The compensation of

.mbiant t empera tu res i s e l e c t r o n i c a l l y made, by a system i n c o r ­

pora ted in the e l e c t r o n i c thermometers .

Al l t he se parameters a re recorded with two o p t i c a l r e ­

co rde r s ( type OM-4501), with 8 c h a n n e l s , each one having s en -

uibl. U t y between 2 rtV/cm + I . Z V/cm. An OM 4510 type a m p l i f i e r

wi th -m Input impedance o£ 10 kil w,u> ut;eU for the preampl i Cica-

tt.on of the s i g n a l .

2 : :j*.itu;:^ar ^ i K o o a ,-,:Â^ SXPER: MENTAL D/MA

" t f e x p e r i m e n t a l •measurement w e r e p e r f o r m e d t o r 2

" • / p e s O t :.r.; ;-i . . . . " - .

'" -.he t i i"- : - , . t h e power o c r . e r a t e a ; r. t h e e l - ^ e n t v.r>;;

c h a n g e d , by s t e p , frc;? 0 up t o v a l u e s i n c l u d e d b e t w e e n 4 and

10 kW. D u r i n g of t h e p r o c e s s t h e q u a n t i t i e s s p e c i f i e d in t h e

p r e v i o u s p a r a g r a p h and n o t e d in t h e f o l l o w i n g way were r e c o r d e d :

- t h e i n t e n s i t y of t h e c u r r e n t , I .

- t n e s u p p l y v o l t a g e , U.

- t h e w a t e r t e r r p e r a t u r e a t t h e in l e t and t h e o u t l e t o f

t h e e lement . T and T,. .

- t he 'fis.li tc r r .perar .ure on t h e e x t e r n a • b . r f d c a . i n t u r e e

j o i n t s p r e v i o u s l y s p e c i f i c a t e a.-: •'.'_, T^, T

- t h e p r e s s u r e rlron on t h e e l e m e n t , i ? P .

- d i e p r e s s u r e d r o p i n t h e s e c t i o n j f flow n e a s u r e m e n t , <iPri.

F i g u r e s S.\, 3 . 2 , 3 . 3 , p r e s e n t a i l * he r e c o r d i n g s

p i o d u c e d d u r i n u t h e power t r a n s i e n t .

In ;:he s e c o n d t y p e , t h e f low of t h e pump was m o d i f i e d ,

in s iuep s t a r t i n g wi t,:t Lhe n o m i n a l v a l u e down 0 , oy s t o p p i n g t h e

c i r c u l a t i o n pump.

The v a l u e s r e c o r d e d a r e t h e same as in t h e f i r s t t y p e .

F i g u r e s 3 . 4 , 3 . 5 , 3 . 6 , p r e s e n t t h e r e c o r d i n g s p r o d u c e d d u r i n g

t h e f low t r a n s i e n t .

The c a l i b r a t i o n c u r v e s ( F i g . 3 .7 7 3.16) a r e used i n

t h e i n t e r p r e t a t i o n of t h e r e c o r d s , i n t h e a b s c i s s a t h e d e p a r ­

t u r e of t h e r a y s p o t f ro ; i 0 [nur,J, and i n o r d i n a t e t h e v a l u e

which c o r r e s p o n d s of t r • d e p a r t u r e i s r e p r e s e n t e d .

The v a l u e s of t i m e i n t e r v a l s h a v i n g a s o r i g i n e t h e

b e g i n n i n g o f t h e t r a n s i t o r y r e g i m e h a v e beer, r e g i s t e r e d on

f i g u r e s "*. i r I.e..

4 • EXPERIMENTAL DATA PROCESSING

' r. or-J'?,- '-.o c o n p a r e t h o D r o c c s . i ' ^ fjor r e s p o n d i n g to t h e

v.mootn e lement . wLt.n t h e s e of rough e l e m e n t s v a r l a r l o n s d i a g r a m s

of t e m p e r a t u r e ! inr.rear,e.<; r e p o r t e d t o t h e smooth e iemer '. have

b e e n p l o t e d .

ffcp,u,ij

1 1

! 1 ! ! I 1 i I i

1 ^ — i

i j •

[ i . *

h II

/

I

•

G

U=10,7V

l'=895A

.

bPj&n ka/m2.s

Af̂ =40 cm. U*D

*.

" l

— i i

Fig. 3.1. Variation of parameters In power transients,

In the case of smooth element

• 8 -

kteuj]

1 1

1 a

1

!

i . . . . j

t . t

/

/

f

^ * -y^

0<

U=*L7V

I=900A

&f=8lcm^

APK540KC

«P ,

»m2.s

i !

1

1 t V ^v

1

1

|0[T,,Tj

o[T4]i—§2£L

Fig. 3.2. Variation of parameters in power transients,

in the case of rough element 3

- 9 -

jOu^U.ij- APE=3Acm HaO.

0[T,T]

o[\m Fig. 3.2. Variation of parameters in power t r a n s i e n t s ,

iri the case of rduqh element 2

- 10 -

K)[AF» G(Aţ)=5620

O[T;,T5]

0&VJ 0,5 1 2 3 A Variation of parameters in flow transient,

in the case of smooth element

- 11 -

|cw'](

7,5V

680 A

1

1 l > — i l l . APP=159 c

I 3lofys4600 J<

i 1

_

nruHjb *| 1

|

Ik 7,67 V

i=655A

\ \

\ \

V \

^

i

1 1 1 I i

l 1

•• 1

i

1

o[y3jj Variation of parameter» in flow transients,

in .he case of rough element 1

- 12 -

o C ^ u j ] ^ 5 8 2

PCWJ 0,5 1 2 3 * Fig. 3.6. Variation of parameters in flow transients,

in the case of rough element '>.

- 13 -

[Kg ^T 7000

/nWJ6000

5000

400U

3000

2000

1000

0 l i 1 1 1 1 1 6 fi

0 2 4 6 8 10 12 *rT(e« [mm]

Fig. 3.7. Flow ca l ib ra t ion curve

1 1 I 1

[ A - 1 0 3 ] | 0 r

0,9

0,8

0,7

0,6

I • • • • « ' i » - w • • » • • • ii • • • " ' J^dm-mK m

A0 50 60 70 80 90 100 Fig. 3.8. Intensity calibration curve

[.Tim]

- 14 -

IJU

110

90

70

50

^r S .

j

-10 0 10 20 30 40 50 60 70 80 90 [mm]

Fig. 3.9, T7 Thermocouple calibration curve

f<3l30

110

90

70

50 ) -.

- )

-10 0 10 20 30 40 50 60 70 80 [mm]

Fig. J. 10. T5 Thermocv^ie calibration curve

- 15 -

[*C]130

120

110

100

90

80

70

60

50

s

10 D 1

f

0 2 .

0 30 40 50 60 ' 70 80 Ijtwij-

Fig. 3.11. T2 Thermocouple calibration curve

-10 0 10 20 30 40 50 60 70 80L

Fig. 3.12. Tj Thermocouple calibration curve

- 16 -

170

150

130

110

90

7D 10 0 10 30 50 70 90

[mm]

Fig. 3.13. T.Thermocouple calibration curve

[v] 12

10

8

60 £ 0

/

1C

/

)0

/

120 [mm]

Fig. 3.14. Voltage calibration curve

- 17 -

[ K j . K ţ K ^ V-

11 V

V

09

ryt 0 5 5 & 3

I 65

is

K î

70

- - -

75 PC]

F i g . 3 .15 . k , k , k. v a r i a t i o n ve rs n P t

water t empera tu re

us

Lc cm.Hx0 320 280

240 200

160

120

80

40

0

! i i I I '•

0 4 8 12 16 20 24 28 32 [mm]

Fig . 3.1C. App c a l i b r a t i o n curve

- 18 -

These reported increases equate the thermohydrau1ics

conditions of measurements so that they should be equal to those

of the smooth element.

The reported temperature increases are equated starting

with the quantity of heat trans itted by elements to the fluid

through boundary layer:

% - V ^ V V N ( 4 - ^

QR = V s « W * (4-2)

From [ 6] i t r e s u l t s that

Nu - c -Fe?Pr 0 * 4 3 ' (Pr f /Pr ) 0 , 2 5 and oR = k^c-Re* (4.3)

where c and a are constants , with d i f ferent values for each

type of roughness, and k, i s a factor of p ropor t iona l i ty .

Knowing t h a t Re = G«d/n and, replacing in equation

( . 2 ) , we obta in :

QR = k j . c ( G R . d/n) a . S-(T - T f ) R (4.4)

A similar equation can be written for the rough element

with the changed values of the heat quantity and of the flow:

QN = kl*C'(GN,d/n)a'S'(VTf)R ( 4 < 5 )

N where (T -T,)_ represents the temperature drop in the boundary p I K

layer of the rough element, if the flow and the heat quantity

are those corresponding to the smooth element.

Deviding the equations (4.4) and (4.5), part by part

and considering that the heat quantities are proportionally with

the dissipated power in the experimental element, it results:

v pN - (VGN)a' <vTfV (vTf}S (4-6)

from where

ATRP . ( T T f ) N . <T - T f ) R . P H / P R . ( G R / < V a (4 .7)

- 13 -

The temperature drop in the laminar boundary layer i s determined with T. thermocouple a t 30 mm in front of the end of the experimental e lement.

The water temperature i s t h i s c a l c u l a t e d knowing the values at the i n l e t and o u t l e t , and cons ider ing a l i n e a r v a r i a ­t i o n determined by the heat f lux :

Tf - T 1 + 45/48 < V V ( 4 # 8 )

Calculat ing X by [ 6] and q P

A = 24 .3 + 0.013-T 4 (4 ,9)

q • P/2'3.14»0»L (4.10)

The temperature drop in wa l l and i m p l i c i t l y the. tempe-

the inner s

couple r e s u l t s from: rature at the inner surface of the wal l i n front of T. thermo'

AT4 - 4 .775/10 4 . q/X (4.11)

Tp = T4 - A?4 (4.1?.)

Having all these data, the temperature drop in film can

be calculated:

A T = T _TC (4 13)

r p 5

The determination of the s p e c i f i c weight flow i s made

by the pressure drop (measured in the s e c t i o n of the upstream

element t e s t ) and of c o r r e l a t i o n s :

ApD 1 5 - 2.358 + 15.476 N-3.156* IO2. N2 (4.14)

G15 » 2 7 7 . 3 2 . ( 4 p D f l 5 ) ° ' 5 7 2 (4.15)

GT - 6 1 5 . X . k (4.16)

- 20 -

TABLE 4 . 1 .

ELEMENT

PN «= 9576

Gj, - 4350

P R 1 * 9 2 7 0

GR 1» 4540

P p 2 - 9831

G R 2 - 390n

TIME / [SEC] •PARAM.

T 5

T l

A T a

<

*î A T « P

"N

T 5

T l

A T a

A TC

a

*5°

a R l

T 5

* 1

A T a

" S n

RELATION

MEASURED

MEASURED

T 5 - T x

45/48-AT

ATf + T.

<

MEASURED

MEASURED

T - T

4 5 / 4 8«A T

AT^ + T I

c * a

MEASURED

MEASURED

** " Ti

4 5 / 4 8 ' A T a

AT* • T 2

C 2) AT.»P"«G»

O . l

6 5 . 8

6 4 . 3

1 .57

1 . 5 0

6 5 . 8

1 .50

6 2 . 0

6 0 . 5

1 .50

1 ,42

P i . 9

1 .54

5 6 . 7

54 .8

1 .91

1.80

6 6 . 6

1 .60

0 . 2 5

6 8 . 4

6 4 . 0

4 . 4 4

4 . 2 1

6 8 . 2

4 . 2 1

6 5 . 0

6 0 . 2

4 . 8 0

4 . 5 1

6 4 . 7

4 . 9 1

7 0 . 4

6 4 . 2

6 . 2 1

5 . 8 4

7 0 . 0

5 . 2 0

0 . 5

6 9 . 6

6 3 . 3

6 . 1 1

5 . 8 1

6 9 . 1

5 . 8 1

6 6 . 1

6 0 . 2

5 , 9 0

5.i>5

6 5 . 7

6 . 0 4

7 1 . 4

6 4 . 0

7 .40

7 .00

7 1 . 0

6 . 2 2

1 .0

7 0 . 5

6 3 . 6

6 . 7 0

6 . 3 7

7 0 . 1

6 . 3 7

6 6 . 8

6 0 . 7

6 . 1 0

5 . 7 3

6 6 . 4

6 . 4 0

7 2 . 2

6 4 . 5

7 . 7 0

7 . 2 8

7 1 . 7

6 . 4 8

2 . 0

7 1 . 3

6 4 . 4

6 . 3 0

6 . 5 6

7 0 . 9

6 . 5 6

6 7 . 6

6 1 . 2

6 . 4 0

6 . 1 0

6 7 . 3

6 . 6 6

7 2 . 8

6 5 . 0

7 . 8 2

7 . 4 0

7 2 . 4

6 . 6 6

3 . 0

7 2 . 0

6 5 . 0

7 . 0 1

6 . 6 6

7 1 . 6

6 . 6 6

6 8 . 1

6 1 . 7

6 . 4 0

6 . 1 0

6 7 . 8

6 . 6 6

7 3 . 3

6 5 . 5

7 . 8 2

7 . 4 0

7 2 . 9

6 . 6 6

' P%G' - V PR l ' « W V a R 1 » -R1- 0.577

2> P--G- - P H / P W ' ^ / G ^ ; 8 R 2 . 0 # 5 5

- 2 1 -

TABLE 4 . 2 .

IZLSXMEI"

riME / | [SSCr [RELATION

PARAM.I

Y-0 . 1 ! 0 . 2 ! 0 . 5 1 .0 ! 2 . 0 3.0

"1 7 ! 5 1 . ( - T - 2 7 . 3 3 9 . 5 I 4 3 . 5 4S.Î | 5 0 . 7 5 1 . G

5 : i l

» P N = * 5 7 6 ! A . T ^ 2 7 . 3 , 3? . 5 I 4 " , . t I 4 6 . 9 ! £ 0 . 7

I Q —4 2?0 ! . .FO i 4 . 2 1 i 5 . i i i 6 . 3 7 C . 5 t f 6 . 66

fiT' S.S j ' S . - 7 , 4B.4 5 5 . 3 5 " \ 2

5 1 . 0

5 6 . 6

ni

Si-*'

.". .0 :3 . 2 3.- . 2

= 92 7? ! ,'iTV'-' i .:,T., I " -

._.L

AT:

! , T *

< . T C . P ' .

. ' 8 .0

40 .5 I 4 2 . : " . 7 I

AT , 1 " . rJ ! 1 . 5 4 : 4 . • 1 a i i

'V-- . . o-, !' -

,04

AT ,; i '*f.T

4 2 . o ! 4 4 . : | 4 4 . 8 I

C . 4 0 ! 6 . 6 6

4 4 . 1 ' 43 . 0

-l-

6 . 6 6

5 1 . 4

i'. y

i „~- -957d

2 2 . < ; o . 5 4 5 . 1

AT1;11 AT f P", 3" J 1 9 . 3

aT K.:>

20. . "

,= î " . G" ; 1 . 6 0 1 5 . 2 0

34.8 3 7 . J ' ? ° . ~ 3<>.?

1 1

6 .22 6 - <i 8 6 . 6 c

p., A T ^ A ^ ! 2 0 . 9 V. 41 .0 13 .5 4 5 . :

6 . 6 6

4 5 . 8

22 -

TABLE 4 . 3 .

ELEMENT

SMOOTH

ROUGH 1

ROUGH 2

TIME S [SEC]

^^PARAM.

T 5

T l

A T a

<

*? A T 1 *

Hi

T 5

T l

AT a

<

T 5

A T * a R l

T 5

T l

* T a

**î T?

AT1* aR2

RELATION

MEASURED

MEASURED

T 5 - T l

45/48*AT •St

« « • T l

<

MEASURED

MEASURED

T 5 - T l

4 5 / 4 8 ' 0 T a a

< • T i

ATC»P'.G'

MEASURED

MEASURED

T , - T ,

4 5 / 4 8 . A T ,

ATj 4 T l

AT°.P"»G"

O.G

6 6 . 7

6 4 . 0

2 . 7 0

2.5'J

6 6 . 5

2 . 5 4

6 4 . 5

6 1 . 0

3 . 5 0

3 . 3 0

6 4 . 4

3 . 3 0

6 9 . 3

6 5 . 0

4 . 3 0

4 . 1 2

6 9 . 1

4 . 5 0

C . l

6 7 . 2

6 4 . 0

2 . 7 0

2 . 5 4

6 6 . 5

2 . 5 4

6 4 . 7

6 1 . 0

3 . 7 0

3 . 5 7

6 4 . 5

3 . 5 7

6 ° . 3

6 5 . 0

4 . 3 0

4 . 1 2

6 9 . 1

4 . 5 0

0 . 2 5

6 7 . 2

6 4 . 0

3 . 2 0

3 . 0 4

6 7 . 0

3 . 0 4

6 4 . 9

6 1 . 0

3 . 9 0

3 . 7 5

6 4 . 9

3 . 7 5

7 1 . 3

6 5 . 0

6 . 3 0

6 . 1 2

7 1 . 1

6.C8

0 . 5

7 1 . 0

6 4 . 0

7 .00

6 . 5 8

7 0 . 5

6 . 5 8

6 8 . 5

6 1 . 0

7 . 5 0

7 . 1 0

6 8 . 1

7 .00

7 4 . 8

6 5 . 0

9 . 8 0

9 . 2 2

7 4 . 2

1 0 . 0

1 .0

9 2 . 2

6 4 . 0

2 8 . 2

2 6 . 5

9 0 . 5

2 6 . 5

9 2 . 8

6 1 . 0

3 1 . 8

2 9 . 8

9 0 . 8

2 9 . 2

9 8 . 3

6 5 . 0

3 3 . 3

3 1 . 3

9 6 . 3

3 4 . 1

2 . 0

111

6 4 . 0

4 7 . 2

4 4 . 3

108

4 4 . 3

112

6 1 . 0

5 1 . 3

4 8 . 3

109

4 7 . 8

116

6 5 . 0

5 1 . 4

4 8 . 4

113

5 2 . 7

- 23 -

TABLE 4 . 4

ELEKENT

SMOOTH

ROUGH 1

ROUGH 2

TIME / [SEC]

/^PARAM

ATf

A T ^

V »

<

ATf

AT*P

A T f

<

ATf

A T f

AT1* â

* » »

RELATION

T p - T f

ATf

<

A T ^ + A T ^

T p " T 5

A T f ' P ' ' G '

A T C . P ' . G '

&?+&?

T - Tc P 5

AT f«P • G

AT C .P" . G" a

ATf + A T f

0 . 0

2 7 . 5

2 7 . 5

2 . 5 4

2 9 . 0

2 5 . 6

2 5 . 0

3 .30

2 8 . 3

14 .1

15 .4

4 .50

19 .9

0 . 1

2 7 . 6

2 7 . 6

2 . 5 4

3 0 . 1

2 5 . 6

2 5 . 0

3 . 5 0

2 6 . 5

1 7 . 3

1 8 . 9

4 . 5 0

2 3 . 4

0 . 2 5

4 1 . 8

4 1 . 8

3 .04

4 4 . 8

4 0 . 8

3 9 . 2

3 .70

4 2 . 9

3 0 . 5

3 3 . 4

6 . 6 8

4 0 . 1

0 . 5

7 2 . 9

7 2 . 9

6 . 5 8

7 9 . 5

6 9 . 1

6 7 . 7

7 .00

7 4 . 7

5 5 . 1

6 0 . 3

1 0 . 0

7 0 . 3

1 .0

6 8 . 7

6 8 . 7

2 6 . 5

-.5.2

6 4 . 1

6 3 . 4

2 9 . 2

9 2 . 6

5 2 . 6

5 7 . 4

3 4 . 1

9 1 . 5

2 . 0

5 9 . 2

5 9 . 2

4 4 . 3

103 .6

5 4 . 1

5 3 . 0

4 7 . 8

1 0 0 . 8

4 3 . 3

4 7 . 2

5 2 . 8

9 9 . 9

- 24 -

O 0,5 1 2 \rrc) 3 t Fig. 4.1. Variation of reported temperature drops in water

and in laminar boundary layor (film) for power transients

- 25 -

Fig. 4.2. Variation of reported temperature drops of wall

for power transients

- 26 -

Fig. 4.3. Variation of reported temperature drops in water

and in laminar boundary layer (film)for

flow transient

- 27 -

iq. 4.4. Variation of reported temperature drops of wall

for flow transient

Li.-.ru\ •: 7 5 *

1 ';

a

• : • - ' ) .

th

•oc - " - ! en-; , W i : :q ' v ' j : t;.0:!

i . 1 7 ,

. . . : h i ( : 5 4 • , - . :. c e n t >\\ : • •./ I-;,- »'.-;..•. i . ...". • ' . :_<- . p : \ ; " < ~ s -

'j ^rvj r - ' t ' . ; " ? . . " ' t i l e . t _>; • .*:•.-.•.: *. :..-.:'.p-..: '.; *. . . J . i '•-...• - ^ .>•-•_•:,

":!"•.•;• i ' i - t . ..••'. ;.si o u ' - - i . i . . i . '..-uiii ; • - u r i a . ! y ; ,i _ ;; a n ^ r i i t

>;!•..•..r:^;.-j-f. . f *••• T - U .7c.: r ".••.'••:. " U . T , •.• t. .••.-• p- ••'' i • i r i s i e r .. .

1 • •; ! ;•:-, 't. ..- , ' 4 ~j i •. ' .• i. '.'• • .'. r'.>5 . "--"> • •* .^or.G^r.q t -

t . 'H :• .r.. i r > o r :J* . ' ' .he vc ...•'• • ;•_;.-;•. t.iir •.'.'"• I •'••.- • .h«- d i a -

>..;)"•• i . ; r i •-,'(;r-;;.. ' ,• 4 -• f.'Oi. p o v o ' r r . ; r - : i ^ - n t AI--' -\ . '.), i . 4 f o t -

i i v ' '--:.r..-. . •<: - . • ..• :. r a c e d .

How , •;" - . . ' i . i ' . / s e t.i.e '.rariL-1< •: *. ;,r-:.c<-:..; .-, Iav;>jd i n

'..h\' L.- i r -.t-'ton-.: '.. .: *J-e re- o >i"-i m,".- - cj-.-:: ET - '..' y -v . - • . . L i f e r e n t i a i

•i»-.vr-:/\M r r. 4 . 10 I

w i t h t V : 5 o i : , ! : n . n

Thti s t e a d y •i.a-'*> r e g i m e . e ^ ( (

•'' f .'.;..-h *-h<i ;"•"..' :. :.'•*• i.'-.i. '. i . ' i n s i s n t :

- • / a ••"'-.:

(4 . 20 ?

j . / b i s ey trib l i s t c d

M . ? I

i.'! !. t.J. ! (• !.J

M e , \ : " , 0 !• /'

• \ . ; / . )

- 29 -

from where i t results that T i s the necessary time for the achievement of the steady-state value i f the i n i t i a l slope re­mains constant.

Between T and t. the following relation i s established:

tfc = (2 -r 3)T (4.23)

The value 0.964 K i s achieved for t = 3T.

J* v •

k 2*5%=fc

0,623 k

jtfpj i0^000e

>

<

-

e

Transient regime. *» Steady-state t regime.

Fig. 4.5. The variation of the output value e , in the case of the step modification of the input value i

In a l l cases the time constant was lover than 1 second, in th is way after 3 seconds the transient process i s practically finished and the value at 3 seconds can be considered as maximum values of the steady-state regime.

Now i s possible to determine the steady-state regime value and the time constant for the increasings of water tem­perature between in l e t and outlet AT , in film AT. and in the wall AT [ 7 ] .

P All these values, for all elements are centralized in

the table 4.5.

It has been found that the experimental values confirm

the previsions, the time constant of the process for the smooth

element being higher than for the rough elements.

TABLE 4 . 5 .

TEMPERATURE

INCREASINGS

AT a

A T f

i T ?

i

ELEMENT

SMOOTH

ROUGti 1

ROUGH 2

SMOOTH

ROUGH 1

P.GUGH 2

SMOOTH

ROUGH 1

?.OUGH 2

m

en

0 . 5 6

6 . 6 6

6 . 6 6

5 1 . 1

4 4 . 8

3 9 . 2

5 7 . 7

5 1 . 5

1 5 . 3

i

3 . i l

0 . 3 5

0 . 3 0

0 . 1 8

0 .16

0 . 1 4

0 . 2 2

0 . 2 0

0 . 1 8

4 k ' 1 0 p

6 .35

6 . 9 5

6 . 9 5 j

5 3 . 3 |

4 6 . " j |

4 1 . 1

i

1 6 0 . 3

5 3 . 9

47 .9

- 31 -

For the determination of the Jc p r o p o r t i o n a l i t y , ST

we s t a r t from the r e l a t i o n :

e g - i / b (4.24)

from where

k - 1/b =» e e / i (4.25) p &

In our case i * 9576 W and this is the steady-state

value of the dissipate power by smooth element (in the last

column of table 4.5 the k values are written). P

In the case of flow transient, the process is more complex, owing to:

- after the shut-down of the pump, owing to inertia the

fluid velocity does not slow down abruptly, in this

way the winimum value is achieved after 0.2 seconds.

- after 0.4 seconds from the shut-down of the pump, the

cooling agent temperature increases and the effect of

natural convection appears.

The variation of temperatures, between inlet and out­

let, in the film, and in the wall (Fig. 4.1, 4.2, 4.3, 4.4)

during transitory regime, nekes evident the three fields sepa­

rated by the time values 0.2 and 0.4.

In the fields between 0 f 0.2 seconds and 0.4 T 2

seconds, temperatures are different which demonstrates the

influence of artificial roughness.

In the field of 0.2 f 0.4 seconds temperatures are

nearly the same indicating a small Influence of the roughness.

Although they are lower than in the case of the power

transients, the temperature differences between the smooth and

the rough element, demonstrate the superiority of the artificial

roughness element even in the case of the flow transient.

- 32 -

5. CONSLOSIONS

The theoretical and experimental analysis concerning

artificial roughness in transitory regime leads to the following

conclusions, which can be extended to the fuel rods of the

nuclear power plant:

- during transitory regimes, the rough element has superior

performances conducting to lower temperatures in the ma­

terial of the experimental elements (or in fuel rods).

Temperature reducings are proportional to the value of

the convection coefficient.

- the tine constant of the transitory process is lower

at the rough elements than at the smooth elements appro­

ximately (1.1 T 1.4) times, and it is inversely propor­

tional to heat transfer coefficient.

- K proportionality factor has lower values at the rough

element being inversely proportional to convection factor.

Thus, for temperature drops in the film, K (rough)

is about (1.1 r 1.3) times less than the smooth one, and for the

wall temperatures it is about (1.1 7 1.2) times.

Consequently, the employment of artificial roughness

is completely justified to improve heat transfer and to improve

the performances of fuel rods in the transitory regimes, confe-

ring them functional parameters (temperatures, mechanical

stress in material, etc) lower than smooth elements.

- 33 -

NOMENCLATURE

- d.. - pipe diameter/ m

- u_ - pipe diameter, without roughness, m

- p - rugosity step, m

- k - rugosity height, m

- Q - heat quantity, J

- a - heat transfer coefficient, W/m °C 2

- S - heat t rans fer surface , m

- T - temperature, C

- Re - Reynolds nuafc«r 2

- G - specific weight flow, Kg/m s 2

- n - dynamic viscosity, N s/m

- P - power,W

- c - specific heat,* J/Kg °C

- X - wall conductivity, W/m °C

T .2 q - thermic flux, W/m Ap_ - pressure drop on the tronsom for flow

measurements, bars &p„ - element pressure drop, bars N - spot detlection, mm

k - correction factor for the density variation p

with the temperature

k - correction factor for the viscosity

variation with the temperature

i - inlet quantity

e - outlet quantity

a,b - constants

k - proportionality factor

T t - time constant, representing the required

time to reach 6231 k P

tt - transitory regime period, or required time period that the outlet value shouid be equal to ( 2 - 5 ) % from steady-state value ec

- 34 -

INDEX

- R - rough - N - smooth - p - wall - f - fluid - 15 - a t c a l i b r a t i on

temperature, 15 C - T - a t work tempe­

r a t u r e , T - S - s t eady-s t a t e regime

R E F E R E N C E S

/ l / . NUNNER, W., "Waermenebergang und druckabfall in rauhren rohren", Forscht t f t Ver. 455, Ser ies B, 22, 1956

/ 2 / . DIPPREY, D., SABERSKY, R., "Heat and momentum t rans fe r in smooth and rough tubes at various Prand t l " , J .P .L . Techni­cal Rep. , 32-269, 1962

/ 3 / . ISACENKO, B . , OSIPOVA, V., "Heat t r ans fe r " , Mir Publisher Moskow, 1969

/ 4 / . KJELLSTROM, B. , LARSSON A., "Improvement of reactor fuel element heat t ransfe r by surface roughness", AE-271, 1967

/ 5 / . LUCA, L . , MIHAILA, A., DOBRESCU,C, PANA, M., "Fluxuri termice c r i t i c e la f ierberea subrăc i tă în canale v e r t i c a l e " , Energet ica, XIX, 7, 1971

/ 6 / . LECA, A., "Transferul că ldur i i în reac toare le nucleare, cu r e f e r i r e la fo los i rea r u g o z i t ă ţ i i a r t i f i c i a l e la reac­toa re l e nucleare r ă c i t e cu apă", Teză de doc tora t , I . P . Bucureşt i , 1972

/!/. KOPELOVICI, A., "Sisteme de reglare automată - metode de calcul i n g i n e r e ş t i " , Editura tehnică , 1963

/ 8 / . LUCA, L., "Cercetări de f luxuri termice c r i t i c e în canale de r ă c i r e v e r t i c a l e ş i o r i z o n t a l e " , Referat de doc to ra t , I . P . Bucureşt i , 1975

/ 9 / . HANGANUT, M. , "Automatica", Editura d idac t i că , Bucureşt i , 1971

C t M l t t t v l 4m S t a t » « « t r « • « • r « l « 31 « § • ! • • rS

ENERGETICI

Pi teş t i _ • . » . « r 7 S . . 1 N 1 0 - t«i«* 1 SSTt