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
- 26 -
Fig. 4.3. Variation of reported temperature drops in water
and in laminar boundary layer (film)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
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