conference heat transfer and the design and operation heat
TRANSCRIPT
These papers have been reproduced only in thelanguage as submitted by the authors.
C O N F E R E N C E
"HEAT TRANSFER AND THE DESIGN AND OPERATIONOF
HEAT EXCHANGERS"
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Hierdie referate word aangebiedpresies soos deur die skrywersvoorgele en die' borge onderskryf nienoodwendig die sienswyses daarinvervat nie.
S.75
Sponsored byThe South African Inititution of Chemical EngineersThe South African Institution of Mechanical Engineers
in collaboration withThe Council for Scientific find Industrial Research
18th & 19th April 1974
Univaraity of the WiiuaterBrandJohannesburg
Republic of South Africa
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CHAR 24
23.
HERMAN, L.D.
Evaporative cooling of circulating vater
BERGAMOX PRESS (LONDON) 1957
DUPONT, A
Tich. Rtp. CEHCEM-CCS 70/1039
(Conpagnit Eltctxomtaaniqu* I£ BOURGET, FRANCE)
BERMA.V, L.D. and ZAUER, A
T*ylMn*rt*tika, 1971 18 (B) 41-45
W0.IG, J.G.Brtiuui ttiir«i-Kr«fc,i968 20 (2) 49-56
COLB 1
THE DETERMINATION OF HEAT
TRANSFER COEFFICIENTS FOR SLURRIES
IN A SPIRAL HEAT EXCHANGER
P.P. CCB.SORN* Pr. Eng., Ph.D.(Natal)
D. I . "iXCQL t B.Sc.CEng)(Rand)
S Y N O P S I S
The spiral neat exchanger can &s used for tha oxchange of heat from
ono slurry to another. Tha rates of corrosion and aroslon measured
during ths excerlments conauoted on a slurry made •from typical Wltwaters-
rand gold- and urenlum-ssarlng ores are well within tht pirmlssible
limits for industrial applications.
A method Is given for ths determination of heat-transfer coefficients
for tha slurries investigatsd.
•* Atomic Energy Ecara - PellndaSa
t National Institute for Metallurgy - Johannasburg
COLB 2
I N T R O D U C T I O N
On moat South African gold and uranium mines the recovery of heat
from hot slurries (3D to 50°C) Is not considered to be economically
feasible. Rasearch worK conducted by the Atomic Energy Board ha3 shown
the desirability of leaching temperatures In excess of 60 C and of a more
dilute leach. The greater part of this resulting increased heat
requirement par tonne of ore treated can be recovered by the exchange of
heat between the hot slurry from the last pachuca and the cold Incoming
slurry to the first pachuca.
On certain of the South African mines slurries are water-cooled, prior
to filtration, in modified shell-and-tube heat exchangers, with the
slurry an the tube side. The maintenance of these heat exchangers is
considerable, and the tubes tend to become blocKed periodically.
Spiral heat exchangers (SHE) designed by Alfa-Laval have Been used
with success on bauxite slurries in the Bayer process, with the slurry
on only one side. On receipt of an offer from Alfa-laval to provide a
small unit of this design for basic tests on heat transfer in slurries,
an investigation was immediately commenced. Table 1 lists the details
of the SHE supplied by Alfa-Laval.
COLB 3
DESIGN OF THE HEAT EXCHANGER
The geometry of a heat exchanger must allow for an unrestricted flow
of pulp. The SHE satisfies this requirement in tiat the pulp flows along
one continuous channel, end not a series of channels as in the tube side of
a shell-and-tube heat exchanger. The channel of the SHE has no dead
spaces, and is uniform in cross-section throughout its entire length, unliKe
the shell of the shell-and-tube heat exchanger. The Lamella Heat Exchanger,
produced by Alfa Laval, shares certain of the properties of the SHE, notably
the uniformity of cross-section, out it also has a number of parallel flow
paths. The disadvantage of a multiplicity of paths is that some of these
may become blocked and impair the performance of the heat exchanger. The
velocity of flow in the remaining open channels will increase, resulting in
an increased pressure drop across the exchanger and an increase in pumping
costs. The SHE with its single channel (par side) tends to be self-
cleaning. Local build-up in the spiral will reduce the effective cross-
sectional area at that point, increase the pulp velocity, and thus tend to
erode away the build-up.
By virtue of its design, the SHE operates as a countercurrant sy3tem,
is much more efficient in heat transfer than the conventional shell-and-
tuea unit, and hence occuoles much less spacs for a given duty. This Is
of particular importance in an Industry handling large tonnages.
The major disadvantage of tne ShE is that any damage to ths spiral wall
cannot £>e repaired, ana 3 unit might have to be prematurely scracpss as a
result of careless operation.
The overall dimensions cf tr.e SHE used in this testworK are shown in
c;g-..-s 1. =igura 2 is a detailed lirrensiorec drawing of tne channel
An examination /
C01.B 4 COLB 5
- 3 -- 2 -
i 'j !i
An examination of Figure 2 shows -that, along the sections ab and hk of
the walls in tha 10 mm channel, the same fluid flows on both sides of the
wall. Similarly, in the 2SITRI channel, the same fluid flows on both sides
of the wall along the sections np and ed. Negligible heat transfer takes
place along these wetted wall sections, and the wetted wall perimeter along
which heat transfer effectively taKss place Is the wall section bcefh.
Each channel thus consists of two separate zones - an effective heat-
transfer zone and a negligible heat-transfer, or by-passing, zone.
As a direct consequence of the 10mm channel geometry different average
fluid velocities wern considered for the effective heat transfer zone and
the by-paislng zone. Thsse two velocities tend to the same value only at
very high flow velocities.
The materials of construction of the SHE should be sufficiently resilient
to withstand the combined effects of corrosion and erosion.
The stainless steel materials of construction of the SHE were subjected
to a aeries of prolonged corrosion and erosion tests with typical acidified
uranium pulps containing S to 8 g of HjSO^ per litre. Corrosion and
•roslon rates were determined from measurements of the channel wall
thickness by an ultrasonic technique.
An average erosion rate of 0,Q4nn per week was measured over a five-
week continuous test at a mean slurry velocity of 3,0 m/sec. At a
velocity of 1,06 m/s, the erosion rate was less than 0,01 mm per week over
a five-week period. In a subsequent corrosion ana erosion test of 860
hours at a slurry temperature of 30cC, negligible corrosion and erosion was
se-.zzxsz sz i slurry velocity of 1,1 m/s. Curing tie duration of tns
slurry tests reported here significant erosion was not apparent.
Table 2 /
Table 2 lists the particle size distributions for the solids In seven
samples of (lurry (51 to S7) taken at regular Intervals during the course
of tha tests. No significant change in the particle size distribution in
the ore was noted during the entire series of runs. No marked reduction
In the erosive properties of the slurry, based on the average particle size,
thus took place.
Design Equations for Spiral Heat Exchangers
The following empirical relationship of Sander has been found to
glvs acceptable correlations for the flow of Newtonian fluids in spiral
channels at Reynolds number greater than 1000.
Nu • C3.15 x lO*2 Re0'9 -6.65 x io"7(l/»)1<8) Pr°'25 tv/u^0'17 .... (11
The physical properties of the fluid are all evaluated at the mean Dulk
fluid temperature.
The value of the term 6,65 x lo"7(*/s)llB is 0.042 for the 25mm channel
and 0,22 for tha 10mm channel. In all the tests these values are lass than
1 per cent of the values of 3.15 x io"2 Re0'8. The Sander equation was thus
simplified by neglect of the S.65 x 10*7 U / s ) 1 ' 8 term and the writing of,
Nu - 3.15 x 10"2 ReD'S Pr 0' 2 5 tv/v/' 1 7 12)
The hydraulic diameter of the cnannel Is defined Dy tne -"cnnula
4 x cross-sectional areado " wetted psrinster
For rectangular channels with tne channel width, a » s . t*e channel
spacing, the formula for d& reduces to
"C 2ti*-i '*•-
:»i"g to tne /
- 4 -
Owing to the departure of tha channel geometry from rectangular shape
in the SHE used for this study, the hydraulic diameters were determined
from thg wetted wall perimeters and flow areas in the effective heat
transfer zones indicated in Figure 2.
25mm channel: GL. • 47,9mm, and•
10mm channel: d. • 19,7mmb
Two specific performance factors that suitably characterize heat-
exchanger operations are the number of heat transfer units, NTU, and the
specific pressure drop, j, defined by the following equations.
NTU • -U^" • »nd 13)
m
J • & • (4)
The total rate of heat transfer, 0. Is given by:Q • UAA0m (5)
PHVSICAL PROPERTIES OF THE SLURRY
Physical Gravity
The specific gravity of the slurry. S&, was derived from the formula
Ss " V tX * sq t1"x)1
If the value of the mean specific gravity of the solids, Sq, is taken
as 2,70, then the equation *or S reduces to
S • 1/ (1-0.630 X) (6)
Specific Heat
Table 3 gives the specific ^a^t af suertz, - -.=>- -*=> r»»e« ~ -- •--c-'5)
A.mean /
COLB 7
- 5 -
A maan value of c • 775J/Tkg K) was used avar tha temparatura
range 35 to SS°C (-2,2 per cant variation In c ovar this rang*).
The specific heat of the slurry, cs> was calculated as tha weighted
mean of the water and the ore comprising thB slurry according to the
aquation
c s • tl - X) c w • (X x cq)
If c , the mean specific heat of water is taken as 4187 J/fkg K) (sae
Table 4), then this equation for c raduces to
• C41B7 - 3412 X) J/tkg K) (7)
Thermal Conductivity
15)Table 3 gives tha thermal conductivities of quartz . a thermally
bi-axial crystal, parallel (K 1) and perpendicular tk ) to tha thermal
axis. A mean value, k , was calculated as the arithmetic mean of k . and
VThB thermal conductivity of the slurry, k , was calculated according
to Tareef's equation
2k • k • Alk - k 1w q w q
IB)
Table 5 shews the values of * as a function of both temperature and
slurry composition. The mean values of ks over the range 35 to 55 C are
also tabulated.
- 6 -
EXPERIMENTAL PROCEDURECOLB 9
The haat transfer te»ts ware conducts:! in three phases, a aeries of
runs on the heat transfer from water to water being conducted before and
aft*r the tests on the haat transfer from slurry to water.
The hot fluid (water or slurryl was pumped in closed circuit from a
rubber-lined tonk, which was fitted with an agitator and a stainless-steel
Itaam coil, through the 25 mm channel of the SHE ana back to the tank.
Tha cooling water was pumped in closed circuit from a cooling-water
pond (30 m ) through the 10™ channel of the SHE and a rotameter back to
the pond.
During the first series of water-to-watsr runs the SHE was mounted with
its cover plates in a horizontal position. The SHE was mounted in a vertical
plan* for the slurry-to-water and the sacond series of water-to-weter tests.
The flowrate of hot fluid was varied by
(&) throttling down on the pump discharge side during the water-to-water
tests, and
(b) changing pf the pump speed during the slurry-to-water tests.
Tha flowrate of cooling water was measured by a 0 tc 250 1/min rotanetsr.
The flowrate of hot water was measured direct. The measured values of hot-
water flowrate were always within 4 per cent of the values calculated from
the steady-state heat-balance equation. Slurry flowrates were calculated
from the steady-state heat-balance eouation.
Once the flowrates had been changed, 1 hour was allowed to elapse
before the recording of the stsady-state inlet and outlet temperatures and
pressjres /
- 7 -
pressures, which ware mad* at IS minute intervals for tha next 15 minutes.
Standard procedures wara adopted to ensure the accuracy of the pressure
snd temperature measurements.
EXPERIMENTAL RESULTS
First Series of Water Runs - 25mm Channel Side
The experimental data for this side or* listed in Table 6. The average
water velocity, uflv> was calculated on the basis pf a flow cross-sectional
area of 6.96 X 10" m . The physical properties of the water ware evaluated
at the mean bulk fluid temperature, 9.
Approximate film (net-transfer coefficients were calculated by neglect
of the wall-viscosity correction terra, tv/v ) 0 ' 1 7 , in the simplified
Sander equation. The mean wall temperature, 9 , was then calculated from
dthe equation
where r,_ and h,« are calculated by use or the values of U in each channel.
The wall-viscosity correction term was then applied in the determination
of the film heat-transfsr coefficient, h .
G ™ Channel Side
As a result of the geometry of the 10mm channel, a different procedure
for analysis was aoolied to tie results for this side.
Table 7 lists /
COLB 10
Table 7 lists the experimental data. The average water velocity,
u • was calculated on the basis of a flow cross-aectlanal area of
3,635 x 10 m . The approximate film heat transfer coefficient, h* ,
was calculated from the simplified Sander equation by use of the average
velocity u and the application of the wall-viscosity correction term.
Table S gives the data used for the correction of the approximate
film heat transfer coefficient, h* . Tha approximate clean overall heat
transfer resistance, R , was calculated from the equation
COLB 11- 9 -
Figure 4 shows a plot of u g f f against uflv> Also indicated in Figure 4
Is the velocity in the bypass zona, ufa, as a function of the average
velocity, uav> This bypass zone velocity was calculated from thy mass
balance equation
xuav * (Vf tob t 1 3 )
From the geometry of the channel, a », • 0,746 a and a • 0,2S4a
1/h2,
tlQl
where R the wall resistance, is 1,23 x 10*4m2 K/W.
Shown in f-igure 3 is a plot of 1/U - R against u , where U is the
experimentally determined overall heat transfer coefficient.
Second Series of Water Runs
Table 9 lists the values of u, "25" h 1 Q, uflu and u g f f for the second
series of water runs. The dirt factor, R ., was calculated from thed
equation
The overall dirt factor, R ., for water-to-water heat transfer is given
by the value of 1/U - Rc* at high average velocity values (i.e. as h* tanos
to h 1 0 ) .
The corrected values of the film heat transfer coefficient, h » , were
then calculated from the equation
1/h • 1/U - i/h_, - R - R (11)
where R • 1,05 x io"4 m2 K/WQ
'4 2The mean value of R ., was 0.75 x 10 tn K/W.
Slurry to Water Runs
The experimental data for the water side (10 mm channal] are listed
in Table 10.
On the slurry side (Table 11) the film heat-transfer coefficient, h2
was calculated from the equation
1/h.. . 1/h._ - R -R._ (11)
The water velocity, u ^ , in the effective heat transfer zone was then
derived from the formula:
(12)
R , the dirt factor for slurry-to-water heat transfer, was assumed
to be f.e same as the overall dirt factor for the second aeries of water
c"
Figure 4 /•«itr -.r,e filr. /
! • - -
COLB 14COLD 15
- 13 -
- 12 -
1.84p • Bu
where B we3 dependent on the composition of the slurry. ThB measurements
of pressure drop conducted at 45°C for various slurry compositions were
characterized in terms of the slurry density and viscosity relative to
water. The following equation was *ound to hold for slurries up to a mass
fraction of 0,6 and for fluid velocities In the range 0,4 to 1,8 m/s
at a temperature of 45°C.
Ap * B Pr ' v '* u ' kPa/m (16)
The effectiveness of this empirical corrslation is shown in Figure 6.
The factor B in thB equation has a value of 1,124 at 45QC, and is
temperature dependent because it contains the numerical value of the
density and viscosity of pure water at 45°C. B is also a function of
the hydraulic diameter oJ the heat exchanger channel. The values of 8
as a function of temperature are listed in Table 14 for channels with
hydraulic diameters in the rsnga 48 to 49mm.
CONCLUSIONS
The spiral heat exchanger is suitable for heat exchange between slurries
from typical Witwatersrand gold and uranium-bearing ores.
The corrosion and erosion rates encountered are sufficiently low to
permit the industrial application of the spiral heat exchanger, provleed
that slurry velocities are Kept Below 1,5 m/s. A further safety factor
would be incorporated if a design velocity in the region of 0,8 to 1,2 m/s
were adopted. For the prevention of local excessive erosion due to local
regions of "igh velocity within the heat-excsanger sDiral. prscauticrs nust
be taken to /
be taken to remove, from the slurry streams entering tha heat'exchanger,
particles that are large enough to become wedged across the spiral channel.
This can be achieved most effectively by the incorporation of coarse meshed
screens upstream of the pumps supplying the heat exchanger.
The heat-transfer coefficient between the slurry and the heat-transfer
surface can effectively be determined on the assumption that the pulp is
Newtonian in behaviour, with a relative viscosity compared with the viscosity
of water. A satisfactory relation between this relative viscosity and the
mass fraction of solids in the slurry was established for the system
investigated, but this relation will be unique for this system, ana the
relative viscosities for different systems may vary considerably.
Pressure-drop correlations for slurries of various densities wBre
satisfactorily obtained. However, thesa correlations also reiy on the
ability to determine the relative viscosity of the system under consideration.
The equation presented for the determination of the relative viscosity
of slurries of a Witwatersrand ore, a3 a function of the mass fraction of
solids, permits the use of
(a) the Sander Equation to determine the film heat transfer coefficient
and
tb) the empirical correlation to predict the pressure drop per unit lengtr
of heat transfer channel, for such a slurry flowing In a channel with
a spacing of 25m.
The evaluation of these two parameters makes passible the 3esign of a
heat excra-ger circuit for 3 typical plant installation. It is 2lsn
possi-le to optimise a circuit, and determine the relative economic
advantages of sifar recovering -eat or providing aflditio-si -<eat. _
The spiral /
COLB 16
The spiral heat exchanger can be constructed of exotic materials,
including titanium and Honel, and therefore high temperature, high pressure
leaching with aggressive reagents, accompanied by ths recovery of heat
may become feasible.
The possible uses of the spiral heat exchanger in the metallurgical
processing industry are extremely varied. The development of processes
that initially proved uneconomical and not technically feasible because
they were prohibited by heating and cooling problems at normal and
elevated pressures may be possible if spiral heat exchangers are Included
In the procaas circuit.
ACKNOWLEDGEMENTS
The authors wish to acknowledge the assistance and collaboration of
colleagues at ths National Institute for Metallurgy.
This paper Is published with the approval of the Director General
of tne National Institute for Metallurgy ami the Director of the
Extraction Metallurgy Division of the Atomic Energy Board.
-- 0O0 --
COLB 17
R E F E R E N C E S
1. HARGIS, A.M., BECKMANN, A.T., and LOIAC0N0. J.J., Applications
of spiral plate haat exchangers. Chem. Engng Prog. vol. 63,
no. 7. July 1967. pp. 62 - 67.
2. MINTON, P.M., Designing spiral plate heat exchangers. Chsm.Engng,
Albany, vol. 77, May 4. 1970. pp. 103 - 112.
3. SKUBN1K. M., and PETERS. D.L. Heat transfer and pressure drop in
cooling eantu beer mash In a spiral heat exchanger.
Pretoria, C.S.I.R., special report Chem. 166. May 1S71.
4. Private communication, Alfa Laval, Heating of Bauxite Slurry in the
Bayer Process. Feb. 1970.
5. INTERNATIONAL CRITICAL TABLES.
6. ALFA LAVAL [Sweden!, Thermal HandnooK.
COLB IS
a
A
b
B
c
db
h
i
k
1
n
Nu
NTU
AP
Pr
Q
R
Re
ds
s •
S >
NOMENCLATURE
cross sectional area of channel (m )
heat transfer surface area (m )
channel width (mm)
constant
specific heat of fluid tJ/(kg K) .
hydraulic diamster af channel (mr)
film heat transfer cotfficient (W/(m2 K]
specific pressure drop (kPa)
thermol conductivity of fluid (W/trnK))
length of chantnl (m)
constant
Nuisett Numbsr • hdb/k
Number of heat transfer units
pressure drop per unit length (KPa/m)
total rate of Mat transfer (W/h)
resistance to heat transfer (mK/W)
Reynolds NumbBr - ^~U
Approximate value of the Resistance to hsat transfer in thBabsence of any fouling (m K/W)
heat transfer resistance due to
heat transfer (m2K/W)for water-to-watar
heat transfer resistance due to fouling for water-to-slurry
heat trans-fer tm2K/W)
channel spacing (mm)
Specific gravity
Velccitv of fluid tm/s)
overall heat transfer coefficient tW/tm2K)J
mass fraction af solids in a slurry
COLB 19
- 2 -
temperature correction factor
ten-psrature ( C)
mean wall temperature
temperature change (°C)
log mean temperature difference t°C)
viscosity tmPa s)
kinematic viscosity turn /s)
kinematic viscosity at th* tr.ean wall temperature [mmVsl
density (kg/m )
----—oDo-—---
COLB 21
COLS 20
SUBSCRIPTS
10 • 10 mm channel
25 • 25 mm channel
av • average (due to channel geometry)
aff • effective (due to channel geometry)
b " bypass [due to channel geometry)
in • inlet condition
pi • parallel to principle thermol axis
pr • perpendicular to principle thermol axis
q • quartz
r • relative to water
• • slurry
w * water
T A B L E 1
PHYSICAL PROPERTIES OF THE SHE
Channel spacing (mm)
Cross-sectional areas (X 10" rc )
(1) Total a n a
(ill Effective h«at transfer zone
Wetted wall perimeter in heattransfer Cm)
Surface area for heat transfer (ro )
Length of channels (m)
Maximum working pressure UPa)
Material of construction:
Thermal conductivity of SIS 2343
Distance studs
10 25
3.6352,710
0,550
6,5
11.6
500
2 mm SIS 2343316 SS)
6.9G06,590
0,550
(equivalent to
(W/(mK)) 16.3750 4,8-mm diameter studs perchannel4 rows of studs per channel
T A B L E 2
PARTICLE-SIZE DISTRIBUTION OF SOLIDS
SUPERSCRIPT
* > approximate value
Size rangemicrons
>147
<147>104
<1W >74
<74 >44
<44 >37
<37
M A S S P E R C E N T A G E S
S1
10,4
17,1
12,5
14,2
5,1
40,7
S2
9.6
16.9
12,6
15,5
3,0
42,4
S3
10,4
16.1
12,3
15,5
2,5
43.2
S«
10,1
16.2
12.3
15,4
3,0
43,0
SS
12,8
16,3
12,8
14,4
3,2
40,5
SS
14,0
15,6
11,8
15.1
2.1
41,4
S7
12,7
15,5
11.1
13,4
1.8
45,5
L E 2 /
COLB 22
T A B L E 3
PHYSICAL PROPERTIES OF QUARTZ
e
°c
0
50
100
J/(kg K)
695
7B3
854
K W/(m K)
k p l
13,41
10, BB
6,SO
V7,13
6,24
5,48
kq
10,27
S,46
7,14
T A B L E 4
PHYSICAL PROPERTIES OF WATER
©
°c
0
20
40
60
BO
100
p
xlO3Kg/m3
1,000
0,938
0,992
0.983
0,972
O.95B
V
mPa s
1,787
1,002
0,653
0,467
0,355
0,283
K
W/(m K)
0,564
0,596
0,628
0,652
0,563
0,669
c
J/(kg K)
4216
4183
4178
4183
4195
4216
T A B L E 5
THERMAL CONDUCTIVITY OF QUARTZITIC SLURRIES IN W/tn K)
X
•
2Q°C
4Q°C
60°C
80°C
35 - 55°C
0,00
0.00
0.59
0,63
0,651
0.66
0.64
0.25
0,108
0,78
0.61
0,84
0,85
0,82
0.35
0,166
0,88
0.92
0.95
0,95
0.93
0.45
0,234
1,03
1.07
1.10
1,10
1.08
0,55
0,314
1.23
1.27
1.30
1,30
1.28
0.65
0,408
1,51
1.56
1.59
1,59
1,57
COLB 23
T A B L E 6
FIRST SERIES OF HATER RUNS - VALUES OF THE EXPERIMENTAL
PARAMETERS FOR THE 25m CHANNEL
Runno.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
" a *
°C
1.345
0.882
0.894
0.686
0.694
0,698
0,543
0,515
1.345
1.337
0,858
0,850
0,858
0,882
0,878
i n
°C
48.8
51,2
53,6
54.7
52,9
50,8
49,5
61,4
48,3
57,1
52,6
54,7
53,8
42,5
47,1
°C
1,9
3,2
4,2
4,4
4.9
5,3
4,6
4,6
2,8
2.4
4,2
4.2
4.3
3.8
2,9
RexlO4
11,34
7.63a.oi
6,25
6.16
5.92
4,52
4,72
11,15
1?,84
7.57
7,78
7,73
6,50
7,14
Pr
3,65
3,55
3,40
3.34
3.46
3.63
3.72
2.98
3.74
3,13
3,46
3.32
3,38
4,28
3,82
Nu
476
343
352
287
286
280
227
224
471
sa338
342
341
315
331
h*10
W/tm2 K)
6380
4610
4760
3895
3855
3745
3035
3090
6285
6925
4560
4635
4620
4130
4395
TABLE 7 /
COLB 24
T A B L E 7
FIRST SERIES OF WATER RUNS --- VALUES OF THE EXPERIMENTAL
PARAMETERS FOR THE 10mm CHANNEL
Runno,
1
2
3
4
S
6
7
8
S
10
11
12
13
14
IS
LJav
ffl/3
0.287
0,287
0,655
0.300
0.542
1,047
0.550
0,261
0.787
3.344
0.84B
Q.841
1.131
0.536
0.303
"a"
26,2
24.3
34.2
26,3
30,8
33.8
32,6
36,6
32,2
32,6
35,9
37,9
38,9
21,4
22,9
°C
-15,6
-18,Q
-10,5
-18,7
-11.6
-6,7
-8.3
-16,3
-8,6
-16,8
-8.0
-8,0
-6,0
-11,4
-15,8
Rexio"3
7,64
7,51
19.69
6,26
IS, 20
29,73
15.50
8.49
22.00
10,52
25,39
25,14
35.17
12.38
7.SS
Pr
4,95
5,06
3,34
4,78
4,68
«,62
4,66
3,94
4,70
4,24
4,34
4.15
4,1?
5,64
5,35
Nu
82,1
61.8
126
65,6
105
177
106
63.3
141
77,1
154
156
197
94.5
62.7
h*ioW/[m2 K.)
1350
1940
1045
2070
3320
5615
3340
2045
4445
2460
4915
4630
632C
2523
1S55
COLB 25
T A B L E 8
DATA USED IN THE CORRECTION PROCEDURE EOR M*10
no.
1
2
3
4
5
-
7
6
9
10
11
12
13
14
15
«./tm2 K)
932
802
1367
832
1093
1477
1029
739
1570
989
1512
1483
1634
1093
814
R*
" 3 2 C
xlOm K/W
0,792
0,856
0,582
0.864
0.S84
0,568
0.7S2
0.93S
0.507
0.674
0.546
0.552
0.498
0.708
0,662
hio
W/(m2 K)
1220
1250
3405
1395
2340
5465
2415
1245
4000
1565
4665
4330
5965
2250
1295
m/s
0.287
0.287
0,656
0,300
0,542
1,047
0,550
0,261
0,767
0,344
0,848
C.64C
1.131
2.536
0,303
Vf
0,160
0,165
0.533
0,183
0,352
1.017
0,367
0,141
0.630
0.195
0,735
0.762
1.051
0,367
G,:S:
l/U-Rc
xiom2 K/U
0.410
Q.391
0.150
0.338
0.231
C.109
0.220
C.418
0.130
0,337
0.115
0.122
C.114
C.2O7
0.3S7
TAgLE
COLB 26 T A B L E 10COLB 27
RUNS - EXPERIMENTAL DATA ON THE WATER SIDE
T A B L E 9
EXPERIMENTAL RESULTS OP THE SECONO SERIES OF
WATER RUNS
Runno.
16
17
l f l
IS
ZO
Z l
22
23
24
U
W/(m2 K)
1756
1419
1198
601
1196
1064
740
733
1243
h25
w/(m2 K)
6586
3750
3850
3910
2430
2510
2S75
1040
6635
h l o
W/tm2 K)
4520
4460
2580
1320
4315
2755
1275
4350
2250
m/s
0,955
0.963
0.6SE
0,394
0,955
0,660
0.330
0,940
0,5BB
m/s
0,903
0,912
0,518
0,252
0.903
0,522
0,205
0,888
0,440
io"3m2K/w
0,074
0,091
0,065
0,112
0,069
0,055
0.071
0,051
0,087
TABLE 10 /
Runno.
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
uavm/s
0,660
1.040
0,257
0,649
1,052
0,269
0,649
1,028
0,547
0,993
0,341
1.049
0,255
1,049
0,683
1,051
0,289
0,642
1,029
1,009
0,714
0.336
0,360
0,742
1,123
0,241
0,688
1,022
1,033
0,683
0,337
0,256
0,362
1,0651
m/s
0,539
1,008
0,161
0,514
1.022
0,164
0.514
0,994
0,383
0,953
0,211
1,019
0,161
1,019
0.556
1,022
0,169
0,503
0,994
0,972
0,594
0,208
0,222
0,633
1,103
0,153
0,567
0,986
1,000
0,558
0,208
0,161
0,786
1,336
28,2
31,3
26,2
30.5
33.4
26.4
30.8
33,7
30.5
32,8
23,3
32,6
26,3
34,0
21.4
24,9
22,9
26,6
29,8
27.3
29,8
32,1
28,2
32,3
35,9
16,5
21,9
26,6
25,3
28,8
31,1
13,5
23.8
26,3
°C
-8,8
-5,5
20.7
-9,7
-6,1
-21.4
-9,4
-6,1
-11,6
-7,0
-16,6
-6,9
-23,4
-6,4
-7,7
-4.9
-18.1
-9.5
-6,8
-6,0
-8,2
-14,5
-13,0
-9,7
-6,3
-26,1
-10,6
- 6,9
- 6,7
-10,1
-17,2
-16,8
- 5,2
- 4 , 0
exio"3
13,95
26,88
4,49
14,07
28,66
4,65
14,13
27,99
10,70
26.60
5.35
28,35
4,65
28,92
12,31
23,69
4,61
12,69
26,02
24.02
15,79
6,18
6,33
18,04
32,453,71
13,09
24,20
23,80
14,83
6,21
3,70
17,81
24,49
Pr
5,08
4,91
4,63
4,75
4,64
4,58
4,73
4,61
4,65
4,65
5,21
4,68
4,49
4,57
6,08
5,77
5,17
5.23
5,01
5,38
4,93
4,35
4,57
4,57
4,385,47
5,80
5,41
5,60
4,92
4,33
5,85
5,91
5,64
Nu •
100
166
40,2
98,9
172
41.3
99,3
169
79,5
163
47.5
172
41,2
174
94,6
157
42,0
93,4
163
156
109
54,9
52,5
120
188
36,5
98,9
158
157
104
50,9
36,4
i 125
! 1 5 9
~i — —
•
h*10
W/tm2 K)
3140
5225
1275
3120
5450
1305
3130
5360
2520
5170
1485
5440
1310
5505
2910
4845
1315
2920
5125
4855
3430
1430
1665
3790
5990
1135
3055
4900
4685
3275
1620
1120
3860
494G
COLB 28COLB 29
TABLE ID (continued) TASL, 10 [continued)
Runno.
5960
. 61626364656667
Vm/s
1,0440,6350,3421,0050,6790.3370,2490,6581.010
m/s
1,0140,4940,2110,9690.5530,2110,1560,5220,975
in°C
23.225,527,325,727,929,324,929,232,7
°c
- 5,1- 6,3-16,7- 5,6- 7.2-12.5-23.7- 9,5- 5,8
RexlO*3
22,6811,775,83
22,9914,005,804,38
13,9226,80
Pr
6,005,604,725,635,214,734,604,914,73
Nu
15388,949,4
152
100
49,339,699,9165
W/(m Kl
471027601560471531351555125531355200
Runno*
59606162636465
66
67
ua«m/s
0,8000,8210,8000,9501,0090.9651,2021,2711,273
>°c37.638.753.739.642,048,457.447.346,4
&e°c4.13.04,43453.02.73.13.12.9
uW/tm* K)
12571103892
13931301922808
12721474
h25•}
W/tfrT Kl
260028953555326039854095414037303480
X
0,540,540,540,550.550,550,570,570,57
r
6,445,754,876,154,784,807,928,679,70
T A B L E 11 /
TABLE 12 /
SLURRY-TO-WATER RUNS -
T A B L E 11
EXPERIMENTAL OATA ON THE SLURRY SIDE
Run
no.
25
262728
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47484950
51
52
53
54
55
56
57
58
uavm/s
0,976
0,962
0,777
0,815
0,808
1,523
1,540
1,581
1,758
1,835
1,818
1,745
1,500
1,547
1,319
1,291
0,817
0,839
0,808
0,998
0,995
0,970
1,281
1.330
1,269
1,272
1,258
1,249
0,984
0,981
0,936
0,787
0,770
0,755
9 in°C
45,1
44,7
55,4
49,3
48,5
55,2
47,1
46,4
49,3
46,7
47,1
46,9
57,5
47,6
36,2
36,5
49,8
45,746,9
41,6
46,1
54,0
54,6
50,2
50,4
52,1
42,0
42,4
41,8
48,4
57,4"
43,1
36,3
37,6
40
°C
3,3
3,3
3,8
4,3
4,4
2,1
2,2
2,22,0
2,11,82,42.3
2.52,3
2.3
3,7
4,2
5,0
3,5
3,4
2.9
2.93,1
3,2
2,9
3,4
3,3
4,2
4,2
3,7
3,2
3,4
3,3
1289
1495
813
1275
1526
902
1420
1754
1322
1795
999
1789
871
1754
1288
1512
832
1184
1470
1497
1335
930
1032
1503
1708
785
1335
1559
1474
1325
911
746
1278
1297
h25
W/(m2 K]
3865
3590
4080
3775
3660
6880
5385
5410
6220
6055
7910
5975
5415
5265
4275
3905
4110
3305
3490
3800
3865
5645
5905
4930
4545
5125
4490
4185
3645
3985
3545
4010
3080
2700
X
0,23
0,23
0,23
0,23
0,23
0,23
0,23
0,23
0,25
0,25
0,38
0,38
0,35
0,35
0,35
0,35
0,35
0,35
0.35
0,35
0,35
0,35
0,37
0,37
0,37
0,43
0,43
0,43
0,46
0,46
0,46
0,43
0,43
0.43
" r
1.73
1.911,32
1,48
1,52
1,39
1.92
1,88
1,93
2,06
2,29
3,88
3,68
3,53
3,31
3,80
2,23
3,37
2,76
2,98
3,20
1,40
2,55
3.45
3,76
3,66
3,81
4,30
4,14
3.92
5,33
2,41
3,32
4,24
T A B L E 12
MEAN RELATIVE VISCOSITIES
0 .
a.o.a.0 ,
a.
X
23
25
36
43
46
55
1
2
3
3
4
6
"r
. 64
, 0 0
,08
.62
.46
.55
T A B L E 13
DATA ON PRESSURE DROP
11 {za e continued -n ~ext sags
X
0.00
0,24
0,44
m/s
1.5?
0.83
0.43
1,79
1,55
0,96
Q.3O
1.26
0,97
0,77
1.25
~,9?
C.31
m3/ti
39.420.810.8
45,038.824, a
20.0
31.S20.219.3
31.321.4
kPa/m
2,490.838
0,243
3,942.911.350.922
2.54
1,430,995
2 , 9 1
1.7-
!.» j
COLB 31
CULb ii.
WLB
FIGURE 1
PLAN VIEW
(with coverplate removed)
SPIRALBODY"
GASKET-
CWEA PLATE- 3 "
300 720Tnm trim
\~±
FRONT ELEVATION
FIGURE 2
300mm
37mm
25mm
10
V
4mmSTUOS
V
25mm
U-> 1 1 —
I tJQrom
EFFECTIVE VELOCITY Uef f.BY-PASS VELOCITY u b
S'l
p/ui) ran A1I0013A 3GV4J3AV
O'l S'O o'oO'O
k
Ie'o
anoo
COLB 36 COLB 37
FIGURE 5
0.* 0J6 0.70,5
t i - X lX: MASS FRACTION OF SOLIDS
04 0,9 uo
FIGURE 6
0.02
0.2 0,5 1,0 2,0 3,0
AVERAGE VELOCITY uQy [m /s l
KROG 22
12. Van der Walt, J. and Krfiger, D.G., K^at Transfer During Filn Conden-
sation of Saturated and Superheated Freon 12, International Symposium
on two-phase Systems, Technion City, Haifa Israel, Aug. 29 - Sep. 2,
1971.
LQUW 1
13. S i e g e r s , L. and Seban, R.A. , Laninar F i l m Condensat ion of Steam Con-
t a i n i n g Small Concen t ra t i ons o f A i r , I n t . J . Heat l-'ass T r a n s f e r , V o l .
13, pp . 1941-1946 (1970)PROFILE DISTORTION IN LIQUID METAL HEAT TRANSFER
14.
l o .
Siegers, L. and Seban, R.A., Nusselts Condensation of n-Butyl Alcohol,
In t . J . Heat Mass Transfer, Vol. 12, op. 237-239 (1969)
M i l l s , A.F. an3 Se&an, R.A., The Condensation Coeff icient of toatsr,
Int . j . Heat Mass Transfer, Vol. 10, pp. 1815-1827 (1967)
van der iValt, J. and KrSger, O.G., Thin f i l m Flow Sown a .-sr
To fee published. See Appendix A reference (17).
3'jrf 3C=
R.A. LOW
Lecturer• Department of
Bio-engineering,
University of Cape Town.
17. Van der Walt, J . , Heat Transfer During Laminar F i ln Condensation of
Saturated and Superheated Freon-12, Ph.D. thesis . University of St= l ler -
bosch. South A f r i ca , February 1972.
H.O. BOHR
Associate Professor, Department of
Chemical Engineering,
University of Cape Town.
LOUW 2
ABSTRACT
Turbulent velocity and temperature profiles for
mercury flowing vertically upwards in a round pipe under
conditions of constant wall heat flux were measured.
Readings were taken at Reynolds Numbers of 33 000 and
54 000 at various values of heat flux.
Non-isothermal velocity profiles were all found to
differ markedly from the normally accepted isothermal
velocity profile, even at low heat fluxes.
To ensure that the measured distortion was not due
to entrance length effects, velocity and temperature pro-
files were measured for thermal calming lengths of 17, 36,
61 and 84 diameters. Profiles were found to be fully de-
veloped after 61 diameters.
Correlations are presented whereby the amount of
distortion of the non-isothermal velocity profile from the
isothermal profile may be estimated and the value of the
Nusselt Number under given conditions may be predicted.
LOUW 3
NOMENCLATURE
A = axial temperature gradient, dT/dz
a,b,---f = coefficients in equ.(3)
C = specific heat at constant pressure
D = inside diameter of tube
g — acceleration due to gravity
h » heat transfer coefficient
k = thermal conductivity
L/D = length-to-diaaeter ratio
Nu = Nusselt number, hD/k.
Nu i = Nusselt number based on isothermal velocity
profile
Pe =* Peclet number, Pe = Re x Pr
Pr = Prandtl number, C_pA
q w = heat flux through the pipe wall
R = tube radius
Ra = Rayleigh number, ISgADVvMPr
Re « Reynolds number, u D/y
r = radial distance from tube centre
T =• fluid temperature
T = = temperature at tube centre
T = mean cup temperature
T w = wall temperature
u = axial fluid velocity
u = average fluid velocity
LOUU 4
NOMENCLATURE (contd.)
2
sn
U
V
P.
•
• radial distance from tube wall
« axial distance
» coefficient of volume expansion
» dimansionless radius, r/R
• viscosity
» kinematic viscosity, u/p
» density
- (* -T)/(T -T )
Note.* All physical properties are evaluated at the mean,
cup temperature, T m.
LOUW S
INTRODUCTION
The influence of free convection on the velocity
and temperature distribution in the case of turbulent
forced convection has generally been regarded as insig-
nificant by the majority of investigators in the field
of heat and momentum transfer. A numerical study by
Ojalvo and Grosh (1,) in 1962 suggested, however, that
free convection effects could influence velocity and
temperature profiles to a marked extent, and an experi-i
mental investigation of the temperature distribution in
liquid metals (2) produced evidence of distortion of
temperature profiles.
More recently the problem was comprehensively in-
vestigated by Horsten (3,) who confirmed experimentally
that, for mercury flowing upwards in a heated pipe, both
velocity and temperature profiles distort significantly
with increasing heat flux, due to the influence of super-
imposed buoyancy forces on the flow field. Although the
magnitude of the distortion demonstrated was somewhat un-
expected, some of Horsten's results were subsequently
duplicated in an independent set of experiments by Professor
Sesonske's research group at Purdue University (£).
In evaluating the validity of these results, however,
a question that arises is whether the measured profiles
were fully developed, or whether the observed effects were
due to incomplete profile establishment. A program was
LOUH 6
accordingly undertaken to Investigate the rate at which
profiles develop, by measuring velocity and temperature
distributions for various thermal calming lengths and a
variety of heat fluxes (5,).
Results show that, based on an isothermal velocity
distribution, profiles distort rapidly from the start of
heating, but after a heated length of about 60 diameters,
the normalised velocity and temperature profiles arc both
fully developed. It is thus clear that the observed dis-
tortion is not merely an entrance effect, but is a funda-
mental characteristic of flow under heated conditions.
Distortion of the velocity and temperature profiles
also causes the Nusselt number to change and a correlation
of the variation for the case of liquid metals is presented.
EXPERIMENTAL EQUIPMENT
The test loop used in this investigation is shown
schematically in Fig.l. All the sections were constructed
from type 316 seamless stainless steel tubing. Mercury
flowed vertically upwards through the test section which
was 5,67 m long, with an I.D. of SO mm and an O.D. of
52 mm. A 300 mm centrifugal pump was mounted at the top
of the loop so as to minimize static pressure on the gland-
ing. The pump -was driven by a 2,3 kw motor through a
70-300 rpm variable speed drive. A mercury manometer,
connected to an orifice meter mounted in the top portion
LOUW 7
of the loop indicated the flow rate.
The test section was evenly wound with 25 mm wide
by 0,8 mm thick chromel heating tape, which was electric-
ally insulated from the pipe by asbestos paper and woven
fibreglass ribbon. Heat input to the system was by means
of a 16 kW variable transformer and the rate of input was
measured with a calibrated conventional domestic kWh meter.
Thermal insulation was achieved by asbestos rope and pre-
formed fibreglass pipe lagging. Heat loss, as determined
by thermocouples embedded in the lagging, was less than 2%.
Mixing cups, whose design ensured complete mixing of
the mercury, were welded onto each end of the test section.
During all runs, test section inlet and outlet temperatures
were regularly measured by means of iron-constantan thermo-
couples placed in the two mixing cups. These thermocouples
allowed the mean fluid velocity to be determined by means
of a heat balance and in general the velocity obtained in
this manner was in good agreement with the velocity obtained
by integration of the velocity profile and the velocity
calculated from the orifice meter readings.
The mercury leaving the test section was cooled by
water jackets on the vertical and bottom horizontal return
pipes.
To enable simultaneous measurement of velocity and
temperature profiles, a probe as shown in Fig.2 was constructed
LOUW 8
to sarve as a combined pltot-static tube and lron-constantan
thermocouple. The Impact tube was goose-necked and was
made from 25-gauge stainless steel hypodermic tubing, allow-
ing measurements to be taken from the centre of the pipe to
a radial position within 2% from the wall. Two grooves were
made down the side of the static tube to accommodate the
thermocouple wires. The thermocouple bead had an O.D. of
0,57 mm and to minimize flow interference around the probe
tip was placed 6 mm downstream from the tip. The probe
was carried on a nozzle and inserted into the pipe through
a hole drilled 790 Mil from the outlet end of the test
section.
Static and impact pressures were transmitted from the
probe, by means of nylon pressure tubing, to two reservoirs
filled half with mercury and half with water. Water lines
then transmitted the pressures from the reservoirs to the
ports of a differential pressure transducer. The transduced
pressure signals were electronically filtered to remove
high frequency components and recorded on a 250 mm pen re-
corder. The probe thermocouple signal was offset by a
reference voltage and then recorded directly onto a pen
recorder.
In order that the shape of the velocity and temperature
profiles might be measured at various distances from the
start of heating, power cable connections were provided on
the heating tape at 16,8 35,6 60,6 and 83,6 diameters up-
stream of the probe tip. Thus, to obtain a thermal calming
LOUU 9
length of 16,8 diameters, for example, the power cable
was connected to the first position upstream of the probe.
Since the total length of the test section to the probe
tip was constant, this meant that the hydrodynamic calming
length in all tests was constant at 96,4 diameters. Down-
stream of the probe were 5 diameters of heated and a further
12 diameters of unheated pipe.
Further details of the experimental equipment may be
found in reference (5).
LOUH 10
RESULTS
Test runs were carried out at Reynolds numbers of
approximately 33 OOO and 54 000 for a variety of heat
fluxes. The effect of thermal calming length on the rate
of profile development was investigated at the lower Rey-
nolds number. Operating conditions for these tests are
summarised in Table 1.
Developing Velocity and Temperature Profiles
Pig.3 illustrates the developments the velocity
profile for a Reynolds number of approximately 3,3 x 10*,
at three different rates of heat input. The Rayleigh
number represents the heat input, while the L/D values
shown are the thermal calming lengths between the start
of heating and the probe tip. (L/D = 0 corresponds to
the isothermal velocity profile).
It is seen that distortion from the initial isother-
mal velocity profile already exists at an L/D ratio as
low as 16,8. At a given heat flux, distortion of the
velocity profile increases until the normalised profile
attains a constant shape. For all the cases considered
the differences observed between velocity profiles measured
at an L/D of 6G,6 and 83,6 are small and within the bounds
of experimental error, and it may be concluded that both
the velocity and temperature profiles are fully developed
for a thermal calming length greater than 60 diameters.
LOUW 11
The results show that at high heat fluxes the veloc-
ity profiles develop more rapidly. At a Rayleigh number
of 1,39 x 10 !, for example, velocity profiles were all
very similar at L/D ratios of 83,6 60,6 and 35,6.
Developing temperature profiles corresponding to the
first set of velocity profiles in Fig.3 are given in Fig.4.
For the two higher rates of heat input hardly any difference
between the developing temperature profiles could be detected,
and it therefore appears that the temperature profile ap-
proaches its final shape more quickly than the velocity
profile.
From the data available, it is not possible to deter-
mine the exact entry length required for fully developed
flow to be attained. It is quite clear, however, that a
fully developed condition may be assumed for the temperature
and velocity profiles measured in this equipment at a
thermal calming length of 83,6 diameters. This conclusion
at the same tine confirms the validity of the results ob-
tained by Horsten (3J in the same apparatus.
LOUM 12
Velocity and Temperature Profile Trends
Fully developed profiles (i.e. for L/D = 83,6) are
shown in Fig.5 for two Reynolds numbers and increasing
Rayleigh number.
The velocity profiles clearly illustrate that at
a given Reynolds number the degree of distortion increases
with heat input. Horsten 13) has pointed out that at high
heat fluxes a condition of saturation is reached beyond
which an increase in the heat flux does not cause any
further distortion of the velocity profile.
The effect of heat flux on the normalised velocity
profiles may be more easily interpreted through the repre-
sentation given in Fig.6 where the variation in the dimen-
sionless velocity profile is plotted against Ra/Re for a
number of radial positions. The combination Ra/Re was
found by trial to be a parameter which permits the heat
flux distortion for different Reynolds numbers to be ade-
quately correlated on one diagram. Fig.6 includes data
reported by Horsten (3) and Hochrelter (.6) . From this
figure it is seen that beyond the relatively small value
of Ra/Re = 0,2, significant distortion of the velocity
profile takes place. This is clearly illustrated by a
rapid drop in-the lowest curve in the figure, representing
the centreline velocity. Beyond a value of Ra/Re of about
3,5, on the other hand, only very small changes in velocity
are noticed, which confirms the observation made by Korsten
LOUW 13
that a saturation condition is reached.
It should be noted that the correlation of Fig.6
is not Intended to be exact, since there should be a
small Reynolds number effect on the curves shown. At
Ra/Re = 0,0 (i.e. isothermal conditions), for example,
u/um distributions are well established and known to
vary with Reynolds number, nevertheless Fig,6 will ade-
quately permit the reconstruction of a distorted velocity
profile for any heat flux in the range of Reynolds numbers
covered here.
Fully developed temperature profiles are also given
in Fig.5. In the range of Reynolds numbers and heat
fluxes used in this Investigation it is clear that the
temperature profile tends to move in the direction of a
flatter shape with increasing heat flux. Horsten (3J
has observed that at very low heat fluxes the dimension-
less temperature values as plotted first decrease and
then increase as heat flux is increased, and that the
temperature profile reaches saturation in a similar
fashion to the velocity profile.
At this stage no correlation of the tenperature
profile is apparent.
LOUW 14
Nusselt numbers
Nusselt numbers may be evaluated from the relation-
ship
Since T m, the mean mixed cup temperature, which is defined
as
Tndn (2)
is dependent on both the velocity and temperature dis-
tribution, it is clear that the Nusselt number would be
affected by any distortion of these distributions.
Many of the Nusselt numbers calculated to date have
been erroneously computed on the assumption that an
isothermal velocity distribution exists under non-iso-
thermal conditions. Values determined on this basis
would be too low, since the mean cup temperature based
on an isothermal velocity distribution would be lower
than that based on the actual non-isothermal velocity
distribution. To illustrate the effect of the velocity
profile on the Nusselt number, Nusselt numbers were
computed using both the measured isothermal and non-
isothermal v&locity profiles in conjunction with the
corresponding temperature profile, and the difference
between the two values is illustrated graphically in
Fig.7 as a fraction of the "isothermal" value. It
LOUW IS
is clear that even for very low heat inputs there is a
rapid change in the Nusselt number. Thus if accurate
values of the Nusselt number are required it would be
unwise to assume an isothermal velocity distribution
for Ra/Re values greater than 0,2.
In order to account for the effect of heat input
on Nusselt number, available data were correlated using
an equation of the form
Nu = a + b Pe c + d(Ra/Re) + e(Ra/Re)2 + f(Ra/Re)!. (3)
This equation retains the form of the Lyon (2) equation
for Ra = 0,0 and describes the free convection effect by
a third order polynomial in Ra/Re. Equation (3) was
fitted to data obtained for L/D = 83,6 as well as to the
data recorded by Horsten using the same equipment. A
plot of the resulting correlation is shown as (Nu-O,O26
Pe3'"4) vs. Ra/Re is in Fig.3. The data of r.any other
investigators have been excluded from this figure, since
these data were either computed under conditions of non-
fully developed flow or on overall measurements rather
than using actual velocity and temperature profiles.
The effact of free convection is perhaps best illus-
trated in Fig.9 where the Nusselt number is plotted vs.
Peclet Nurcber with Ra/Re as a parameter, and compared
with the Lyon equation. Initially there is a drop in
LOUN 16
the Nusselt number aa Ra/Re is increased from zero,
while for values of Ra/Re greater than 1,0 Nusselt number
increases with heat flux.
CONCLUSIONS
It has been shown that, for mercury flowing upwards
in a round pipe/ velocity and temperature profiles are
distorted by heat input, even at very low flux. This
distortion is not an entrance effect/ since it has been
shown that profiles are fully developed after a calming
length of 60 diameters. The shape of the velocity pro-
file may be reasonably well estimated by the use of Fig.6
over the range of operating conditions considered here.
The observed distortion has a significant effect on
the Nusselt number> which initially decreases and then
increases as heat flux increases. A correlation that
permits estimation of the Nusselt number for vertical
upflow has been presented.
Connor (6) has demonstrated similar distortion of
the velocity and temperature profiles in air at a Reynolds
number of 5 000, and it thus appears that distortion due
to heat input would occur in most liquids and gases. For
mercury, distortion becomes noticeable for values of Ra/Re
above 0,2. Horsten (3,) has shown that the distortion may
be mainly ascribed to a variation in the driving force
caused by radial density differences, rather than to
LOUW 17
changes in viscosity with temperature. It is clear that
these superimposed buoyancy forces are significant even
in turbulent flow, and must be taken into account in any
study of combined heat and momentum transfer.
ACKNOWLEDGEMENT
The authors gratefully acknowledge financial assis-
tance received from the S.A. Atomic Energy Board and
C.S.I.R.
LOUW 18
REFERENCES
LOUW 19
1. Ojalvo, M.S. and Grosh, R.J. "Combined free and forced
turbulent convection in a vertical tube", Argonne National
Laboratory Report ANL - 6528 (1962).
2. Buhr, H.O., Carr A.D., and Balzhiser, R.E., "Temperature
profiles in liquid metals and the affect of superimposed
free convection in turbulent flow," International Journal
of Heat and Mass Transfer ('.968) pp.641-654.
3. Horsten, E.A. "Combined free and forced convection in
turbulent flow of mercury", Ph.D. Thesis, University of
Cape Town (1971).
4. Jacoby, J.K., "Free convection distortion and eddy dlffu»i-
vity effects in turbulent mercury heat transfer", M.S. Thesis,
Purdue University, (1972).
5. Louw, R.A., "Velocity and temperature distributions for
mercury in turbulent flow", M.se. Thesis, University of
Cape Town (1971).
6. Eochreiter, L.E., "Turbulent structure of isothermal and
non-isothermal liquid metal pipe flow", Ph.D. Thesis,
Purdue University (1971).
7. Lyon, R.N., "Liquid metal heat transfer coefficients",
Chemical Engineering Progress (1951) pp.75-79.
8. Connor, M.A. "Velocity, temperature and turbulence measure-
ments in air under combined free and forced convection
conditions", Ph.D. Thesis, University of Cape Town (1971).
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and Ra = 2,5 x 1O4.
1. Run NO.14: L/D > 16,8
2. Run No.13: L/D = 35,6
3. Run No.12: L/D > 60,6
4. Run No.11: L/D = 83,6
Fig.2 Details of the velocity/temperature probe.
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with heat flux.
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STEV
A WORLD SURVEY OF OPERATING EXPERIENCE WITHWATER-COOLED NUCLEAR REACTOR STEAM GENERATORS
Peter D. Stevcns-Gullle 1.5c.(Cape),M.A.Sc.(Waterloo) P.Enj.Heaber SAlML
ACoclc Energy of Canada LI talcedChalk River Nuclear Laboratories
ABSTRACT
In Kerch 1971 the iOOth nuclear power reactor In the world commenced
operacloo. By the end of 1972. 100(3 reactor years of operating experience
had been accumulated. When South Africa builds nuclear power •tattoos,
leasons learnt fro* this operating experience can lea** to substantial
savings in capital And operating coste. This paper surveys world wide
operating experience of water-cooled nuclear reactor steam generators to
the end of 1972.
Steea generators mrm critical components, vulnerable to Internal leak
due to zheir large, thin heat transfer surfaces. Many flew plants have
•teas generators with over 1 hectare of *V2 am hecv transfer surface, compri-
sing over 75% of the total primary system pressure retaining bouudary.
Of the 41 reactors with steam generators In operation prior Co January
1st, 1973, 19 had experienced in-eervlce steam generator tube failures:
Various types of corrosion were responsible for over half of theje
failures4 Other causes include tubesheet cladding failure, mechanical
damage by debris and tube fretting by flow Induced vibration.
Hew technology alaed at improving steam generator reliability Is
discussed In the fields of design, manufacturing and operation.
In March 1971 che lOOeli nuclear power reaccor in the world coaaenced
operation. Figure 1 taken froa an International Atomic Energy Agency
directory'1' shows Che predicted nuaber of reectors Installed In the 28
year period, 1954 to 1979. The number is lncr«»«lnt rapidly. An exponen-
tial curve fitted to theae data hat a doubling tin* of only 3.7 ytara.
The area under thi« curve la cht product of reactor* and yearaa 1.*.
opericlnf experience. To the beginning of 1973 thti amounted to aboot
1000 reaccor ycara. A property of an exponential curve ia that the area
under it la a doubling period la equal to that area under the curve back to
alnus infinity. Thlt aeana that la the next 4 years new operating experience
will exceed that aceuaulated alnee the firat power- reactor entered operation.
Theae statistic* show that already there exlata a formidable aaount of
operating experience, Lessons le»rnt froa it can lead to substantial
taproveaenta ia existing power plant* and large tavlnga in capital aad
operating cotta In new plantt.
Inherent in the exponential growth of power reactor* la the aeatage
that we auat take step* to organize operating experience If ve are not to
be overwhelaed by It in the next few doubling perloda.
Thla paper aurvey* the world vide operating experience with water
cooled nuclear reactor ateaa generator! to the end of 1972. When South
Africa decides to install power reactorst an exaaination of operating
experience can be useful In * selection of the type and supplier of nuclear
tyttea*.
STEAM OEHERATORS
Stcaa generators are a special class of heat exchangers coaaon only
to nuclear reactors, they fora the boundary between the hot, pressurized
wster of the reactor's primary circuit and the secondary circuit where
steaa is raised to drive the turbine. Figure 2 shows a typical steaa
STEV2
- 2 -
generator. Hater from the reactor core enters the wacet box and passes
through a large number of saall thin tubes where it gives up Its heat and
raises sceaa on she outside of the cubes, the wet steaa passes Into a drum
either Integral or separate froa the boiling section where cyclone separa-
tors laprove the steaa quality to over 99X.
Steaa generator size has Increased rapidly and will aoon be curtailed
by transportation tad arectlon limitations. The largest in operation are
over 23 a high and 4 a in dlaaeter and can generate about 1200 HU(ch) of
ateaa in over 1S000 tubes. A large reactor aay have over 1 hectare of heat
tranafer area coaprialng 75!! of the total primary system pressure retaining
boundary.
Sceia generators era critical coaponants in wacer-cooled nuclear
reactors at they sra vulnerable co internal leaka, which result In radio-
active contaatnatlon spreading froa primary to secondary coolant systeas.
Aa an exaaple, a hole as sasll as 0.5 aa dlaaeter can leak over 50 t/h at
4.a HN/a* (700 ptl) preaaure differential and cause a reactor shutdown for
repair.
Kepalre are aade by plugging both ends of the defective tubes with
either seal welded aetal plugs or'explosive plugs. KadldClon fields Inside
the ateaa generators Bay be so high that workers are restricted to a few
alnutes exposure. Thus, on occasions soae hundreds of workers sre required
for repairs which would cake only a short time in a conventional heat
exchanger.
The econoaic penalty for shutting down a power reactor is also large*
Zt ia at least R350 sad aaybe MB high am R650 per hour per 100 HW(e),
These two factors, repair cloe and loss of revenue, are Che main incentives
to improve eceam generator reliability'
SURVEY OF STEAM CESERATOB FAUURES
Of the large number of reactors in operation at the end of 1972* about
60 were non-experimental. Of these, 41 were water-cooled reaccors with
STEV 3
- 3 -
steam generators. Figure 3 is a world map showing the location of these
41 reactors and their operating experience to the end of 1972. The map la
from World Bank data and shows country 5lie in proportion to population
size. The bars show the total reactor-years per country. Yeara of opera-
tion in this figure and subsequent tables is the time during which the
resctor generates electricity. Shutdown time is excludsd.
Although Che number of reactors in Esst Germany and the U.S.S.R. la
known, no details of their opsratlon are divulged. the U.S.A. haa a clear
lead in operating experience, with West Germany and Canada in aecond and
third place.
Failure statistics la the following survey ate updated from a previous
report by the author'2). The reader is referred to this report for detailed
Information. Steam generators can fall in many waya. la practice, however,
tube leaks and tubeaheet cladding defect! have been the major failure modea.
Steam leneratora are classified by cube material in the following
discuaalon.
Stainless Steel Tubed Stesm Csnerstors
Although carbon ateels were, and still are, widely used for fossil
fired boilers, austenitic stainless steels were selected for the early
nuclear steam generators to avoid the problem of pitting corrosion,
especially at low temperatures. Table 1 aummarlzes operating experience
of all the atalnleaa ateel tubed steam generatore in the world. Defective
tubes identified in the table are either thole that have leaked or chose
that were damaged by corrosion, {retting or other failure mecbanlams.
Defective tubes are usually identified in situ by eddy current inspection.
The mean tine between steam generator failure. (MT5P) is shown aa an Index
of performance. It la calculated by dividing the product of atean generator
yeara by total tube defecta.
Widespread caustic stress corrosion cracking caused total tube failure
of the four steam generators at Tarapur, India which reaulted in a 6 month
STEV 4
delay In construction. Strees corrosion cracking also caused massive tube
failures at the N-reactor in the U.S.A. where a steam generator had to be
retubud prior to aervlce. It also caused failure in Indian ?olnt-l,
Shlpplngport-1 and probably Yankee Rowe, ell in the U.S.A., and poaalbly
KWL In Heat Germany. Most failures occurred in secondary aide crevlcea
especially where tubes ere rolled into tubeeheete. In theee regions
chloride lone may concentrate and in the presence of dissolved oxygen
attack stslnless steel under cens'ile stress.
Good chemical control of the secondary circuit is essential to avoid
caustic stress corrosion. However, many plants have operated tor extended
periods with out-of-ap«cificatioc chemical control, particularly during
initial startup when economic and political preaauraa predominate.
Table 1 ahowa that S of 11 reactors have had failures. The mean time
between stein generator failures la about 1 year or less: an unacceptable
rat* for equipment designed for 20 or more yeara of operation.
Monel-aOO Tubed Steam Ceaeracors
When the uafavoureble experience with stainless ateel became known,
steam generetor deeignera turned to other materials. In Che U.S.A.
Inconel-600* waa aelected, while la Canada, Moo«l-400« (70wtZMl, 30wtZCu)
waa chosen for CANDU (Canada Deuterium tlraolum) reactors. Monel-400 Is
generally free froa atress corroaion cracking in normal environments and
has general corroeion resistance comparable to Znconel-600 while being
considerably cheaper. However, Monel-400 has less reelstence to oxygen In
wacer Chan Znconel-600 and muse be protected from water chemistry excur-
alon.<3'.
Tab It 2 Hats all the Hone I tubed ateaa generatora In the world, With
the exception of Garigliano, an Italian boiling water reactor, all are CANDC
reactors. Failures In Garigllano are attributed to corrosion; no detail*
are available. Of the remainder only Douglas Point la Canada has had a
'International Hlckel Corporation trade naaet
STEV 5
- 5 -
tube leak* It occurred under e baffle piece end resulted froft fretting
wear Induced by vibration. With the exception of Garlglldno the record
ef Hone 1-400 tubed (tea* generators la exemplary.
It should be aentloned that stress corrosion cracking of Monel-400
feed vaccr heaters ha* occurred In a nuaber of foss i l (Ired power stations
In the U.S.A. tesldual stressaa Induced by tube bending and not relieved
adequately by stress relief are chought to be the cau»e of failure.
lnconel-600 Tubed Steea Ceneratota
Inconel-600 containing approximately 72 wet HI, IS wtl Cr and 8 utZ
F* was aalectsd for steali generator tubee in the U.S.A. aalnly as a result
of extensive operating experience with nucleer subaarlne*. It is reelstanc
to caustic stress corrosion sad has low corrosion rates even In oxygenated
water. The change froa stainless steel to Inconel-oOO anticipated the use
of aes water or brackish vatec cooling ia the turblae condenser. Even eamll
condenser tube leeks allow the Ingress of cooling water and hence chloride
Ions into the secondary circuit which cause etress corrosion cracking in
stainless steel eteaa generator tubea.
tarty experience with Inconel-600 was good; to the end of 1969 only
2 failures had occurred, one of vhlch was due to fretting induced by
vlbretlon. However, Inconel-600 ia susceptible to intetgranular attack by
caustic euch as sodlun or potassium hydroxide, which can be concentrated
in crevice regions of eteaa generators. Many hundreds of tubes have failed
by this aechenlsa since 1971.
Table 3 shows all the Incone]-600 tubed steaa generators In operation.
The large*t nuaber of failures occurred in Beznau-1 In Switzerland. They
occurred in two batches. The first was caused by lntergranular cracking
1Q tht tupcatitct circvictss uti d viiat due to pool? ch£Q*>caX ccottiroX o' the
secondary circuit. The second batch also failed by intergranular cracking
Just above the tubesheet when the chenlstry was changed by adding phosphate
to buffer the existing excess alkalinity. The plant had continued condenser
STEV 6
leakage during the period o£ these failures which contributed to the free
caustic In the secondary circuit'",
Intergrsnular cracking on the outside of tubes was also reeponsible
for failure* In H.I. »oblneon-2 tad Heddaa Neck in the U.S.A., and IHO
(Obrigheia) In West Ceraany. It aaj also be the cauae of failure in
Shlpplngport-2 la the U.S.A. and Hlhaaa-1 in Japes. The reeeon for
failures in San Onofre-1 in the U.S.A. are not kaown; however, one steaa
generetor wae dropped «50 as during Installation which could hav* de'foraed
tubes. The single tube failure la M D , Canada, was caused by frsttlng
wear with no evidence ot corrosion.
Oveeell Tube Failure Stetlatlcs
Table * summarizes the failure statistics by tube aaterlel. Epidemic
failures, I.e., (rots failure early la Che life of the reactor, are excluded
as they would distort the average* unduly; they are identified In Tables 1(3.
The data base is large. To the tad of 1972, 41 reactors with over
300,000 tubes had accuaulated over 90 years 'on line1. The acan tlae between
•teas generator failure for each tube aatcrlal la leas than 1 year. Although
Che MT8F 1* only an index of perfaraance, a* la praccic* cube defect* are
located in batches by eddy current lnepeetlon, it doe* ehov that eteaa
generator reliability is marginal and chat failures sre frequent.
CAMDt) reactore had over 401 of all nuclear steaa generators in operi-
tlon In the world at the beginning of 1973. Due to the theraodynemics of
their design and the use of heavy water coolant they also have acre tubes
per steaa generator than other design*. Thus CANDV designers are well aware
of the consequencee of tube leaka end have well-tested repair equipment on
hand. However, to date only 2 tube defects have occurred in 132,930 tubes
in operation.
Other Tube Materials
lncoloy-800* (70/30 cupro nickel) la a relatively new alloy designed
*Internetlonai Nlchel Corporation trade name
STEV 7
- 7 -
to •void the problems of caustic lntergranular cracking and chloride
•tress corrosion. It has been used In the KKS (Stade) reactor In West
Cernany and In other steaa generators not yet In operation. Carbon
steel can also be a satisfactory Material If pitting attack can be pre-
vented. Two reactors In the U.S.S.R., Novovoronezh-1 and -2 are reputed
to have carbon steel tubed sctaa generators. No operating detail* arc
avallable however. Other reactor* with unknown tube sattrials are
Siberian and Hovovoroneih-3 la the U.S.S.R. and AKW-1 in East Ceraany.
Tube sheets of nuclear steaa generators are usually clad with a
Material compatible with the tubes for reliable seal welding. Failure of
the cladding resulting In tube leaks was a special case which occurred
In 27 steaa generator* manufactured In one plant of Wcstlnghousc Electric
Cotpt In the U.S.A. The largest failure occurred la toe tt.B. &oblnson-2
reactor in the tf.S.A. DeZaainatloa of the cladding in two stcaa genera*
tore caused 376 tube failures aud occurred a# a result of variation* in
the explosive bond between the cladding and the tube sheet forging.
Repairs took 255 aen 67 days.
t a ii.\it**_C a u s e *
Table 5 auaaarlzes the cause of failure. Various types of corrosion
were responsible for 561 of all failures. Tubeehect eleddin* failure
caused 20Z of all failures, while vibration was responsible for 8t. Other
reasons such as aechanical damage due to debris accounted for 16X.
OUTLOOK FOR THE FUTURE
In principle, ateaa generators are simple Iceas of equlpvent in
comparison with others In nuclear eyateas. The preceding discussion has
shown, however, that staple or no, ateaa generator f-l*ure* are frequent
and costly. Thus nuclear designers and manufacturers are becoalng
Increasingly aware .that new technology is required to tap rove reliability.
STEV 8
- a -
In Canada, although the operating record has been cxeaplary, new
technology Is being Introduced in the following areas:
TherasZ-hydrauZlc conpueer codes are to be used co predict conditions
in 5 dimensional space of simulated sceaa generator*. The/ will not only
aid the designer in establishing option* heat transfer area for all opera-
ting conditions but will enable physical properties such as steaa quality
and velocity to be predicted at say point such as a baffle or tube support.
Hue to their saaller outside diameter, tubes in CAHDU steaa genera-
tors arc flexible and cat be susceptible to vibration. Analyses and
laboratory tests are made of new designs to determine their sensitivity
to flow induced vibration. The ala of this work is to proYlrfe ateaa
generator designer* with computer code* which can d*t*ct Tlbratloo-proae
geom£ tc conftjurations(5).
The choice of tube aaterlals is an Important input Co designers aud
Involves ongoing aetallurgicaj. developaenc both in the laboratory ani in
test reactors. Sections of full six* steaa generators are also tcated
under adverse chemical conditions.
Manufacture
New developments In explosive welding are being used to Join cubes to
tubesheets In a single operation^). Explosive welding has the promise ot
elininating secondary side crevices, being quick and cheap, but above all,
being reliable.
Nondestructive testing methods such as ultrasonic flaw detection are
used in tube manufacturing plants. Recently, che new Nuclear and Ioservlce
Inspection sections of the ASME Pressure Vessel Code have given impetus
to the use of ultrasonic testing la all aspects of steaa generator fabri-
cation, including tubesheet cladding and pressure retaining tfelda.
STEV 9
~ 9 -
Ope rat Ion
The Importance of precise and complete chemical control of both
primary and aecondary circuits has been mentioned. These exacting demands
may toon result In the use of automatic control In the reactor by on-line
tBMlyats and chemical addition.
Tube failure can be anticipated by eddy current testing on a periodic
basis. The statistical probability of detecting defective tubes by
• amp ling is vary snail, thus 1002 tube Inspection is required If the
failure rates are high. Defective tubes can then be sealed by a well
trained repair creu using explosive plugs.
CONCLUSIONS
1. Operating experience with nuclear power reactors is increasing
rapidly. This survey shows that steam generator failures, usually frea,
tube defects, were frequent and costly. Of the 41 power reactors in
operation ID 1972, 19 had experienced failures.
2. Various types of corrosion were the most frequent cause of
failure. Others Include Manufacturing faults* tube vibration and damage
due to debris.
3* The choice of tube material is Important to steam generator
reliability. Both stainless steel and Inconel-600 tubed steam generators
have experienced many failures. As a class Konel-400 tubed CANDU steao
generators have demonstrated the highest reliability. They account for
40X of all nuclear steati generators in operation at the beginning of 1973.
4. New technology Is being introduced into all aspects of steam
generator design* manufacture and operation to Improve rellabillty.
ACKNOWLEDGEMENT
The author thanks the many reactor operators all over the world who
made this survey possible.
ST£V 10
REFERENCES
1 .
Member S t . i t * * . V i e n n a , 1 9 7 2 ,
2- Steve _S_t*aa G nerator Tube Failures:^ Tube Failures: A WorldSurvey of ffater-CpoX'gd Nuclear Power Reactors to the End of 1971.Atomic Energy of Canada Limited. Report AECL-4449. Apr. 1971.
kf* Surf^.J •E - *-,Taylo_r_._ _C. F. Material Selection and CorrosionControl Methods for CAMDU Nucleaj_ Power React
Atomic Energyj_ r Reactors.of Canada Llnlted. Report AECL-4057, April 1972.
tiL.P . &g.Plcone_,_ L.P. Secondary tfaCfer Trea_toent ofGenerators. _ n t of ?tJR
International Witer Conference of EngineersSociety of Western Pennsylvania, Pittsburgh Pennsylvania, October1573-1972.
Goria«nr n . j . . P i . c t e n , . , S v
t i p e r l a t n u l StadttJ «nj Flow Ind . . . .„ , , . , . „ j ^ gC«ner«tor Oejlao. P»rt3 1 to 3. Proc-edlt>ts InttrnitlonalSyopofllua on Vibration Problesis la Industry. Kesulck, EaglAnd.M»y 197).
6• l tJ^QP,l Be . • Current Canadian Use of ExpI»s 1 ve Weldln% for
Repair and Manufacture of Nuclear Steas Genera to rs. AteoicEnergy of Canada Llalted. Report AECI.-4427, February 1973.
TABLE 1: Stainless Steel Tubed Steam Generator (SG) Defects to 1/1/73
Reactor
Indian Polnt-1Yankee (Rove)Dresden-1KHL
Shtppingport-1Tsrapur-1
Tarapur-2
A r d e n n e s
KRB
HZPR
Type
LUC- ( 2 )
PUR
BUR
BVft
FUR
RUB
BW»
PWR
bUR
r«»n
Bo. Tube
> 9341
44> Zl<*>
> 17
Gross
Grass
0
0
0
No.Tubes/
3224
7204
10000
603413200
•<-32O0
663057B74226
Ho.SG's/
4
4
2
42
2
4
3
2
OperatingTime
(years)
6 . 7
a. a3 . 0
4.7Prior CoservicePrior Coservice
2 . 9
4 . 6
4 . 2
MTBF/SG
(years)
' 1 )
0 . 3
0 . 8
<0.3<1.1
(1)
( 1 )
--
-
Defect causes ,Remarks
t b d d to °s e c
cause not availablecorrosion
S C C
s e c
damaged by debris
HOTESi
(1) Excluded fro. totals,(2) LWGR, llght-vater cooled, graphite moicrsteij reactor.
PVR, pressurised llght-uac«r Botteratsd and cooled reactor.BUR, bolUag llght-«at*r aoderated and cooled reactor.PHKR, pressurlied heavy-Hater aoderated and cooled reactor.
(3) Stress corrosion cracking.(4) Additional 109 tubea plugged tor prevantatlve maintenance.
TABLE 2: Monel-400 Tubed Steam Generator (SG) Defect* to 1/1/73
Reactor
GarlgllanoDouglos Pt.Plckering-1Plckerlng-2Plckerlng-3KANUPP
BAPP-1
Type
BUR
PHHR
PI1MR
PIIUR
PIIUR
PHWR
PIIHR
N o . T u b e
1 0 8
1
0
0
0
0
0
Ko.Tubes/
35 7015600312003120031200SI 30
1S600
No. SG's/
2
8
12
12
12t*
Operat IIIRTime
(years)
6 . 0
J .2
l . t t
0 . 8
0 . 3
0 . 4
1.0.0
HTBT/SG
(years)
0 . 1
25. 6-
-
-
-
De fec t causes.Keaarks
corrosionfrett ing wear
a** M
<u a
OS
ht al *%
w a ua •• N
• 1*» oO WM U
i • a* 0 at
3 •SS) H u
1 0 ft1 X
• I
M 1
aa .t*»
•>o
a;
i•H
e ji
3 * " s
* a —
2 = o =
2.2
•A
64
0PU
R
1
c
| S
V ia it,
B C
c a.
^ 3« *«a a
g ? :A
a
1
t
' 9 a i
J • a
o o o J • «
S S | 5 S § S
•4 a i. a M
A 1 •* "o k
i
i
I .1
X
aa i-tto i
u a o o « o , - i »
1 •
*
s s ;
N
1 ha
n a.
-= u
1
3.1
3
i a
) *:
: *- •
« i
s 1
a ae u
•> i
PU
R
«c
u
oua
I
t ^
• i i
0.5
0.1 0.0
1
a: M M3 3 3
a *J« c
• C OV a a.
« a u« B j |n m ;
STEV 14
TABLE 4: World Steaa Ccncrator (SC) Delicti to 1/1/73
TubeMaterial
S. St . . l ( 1 >Monel~400lncon«l-600(1)
Ho.
204109273
Mo.
43,60"136,500174,558
Me.SC'a
236057
OperatingTime
(yean)
43.011.543.5
HTBF/SC
(reare)
0 . 7
0 .6
0 . 4
NOTE;
(1) Exclude* "epldeolc" failure*, noted In Tablet 1 and 3.
STEV 15
STEV 16
TABLE 5: Cjuiti „< Sta.o Generator F«lur.
Cause
Corrosion
Tubesheec claddingfailure
Vibration
Other treasons
Reactors inOperationAffectedd)
14
5
2
4
X
56
20
S
16
NOTE!
cause of failure*
400
LLJ
h 30°
iUJ
Ig IOO
INSTALLATION ' OFPOWER REACTORS
EXPONENTIAL CURVEFIT, DOUBLING TIME3,7 YEARS
54 58 62 66 70YEARS
74 78
Figure 1 : Installation of Power Reactors 1954-78
WATER-COOLED REACTOR STEAM GENERATOR EXPERIENCE
(REACTOR-YEARS OF OPERATION AT 1/1/73)
Figure 3 : World Hap Showing Location of Reactors with Steam Generators
JAW 1
A LATENT-HEAT-BASEO CORRELATION OF SATURATED
POOL BOILING HEAT TRANSFER
H.H. jawurek
Physical Metallurgy Disivion, Atomic Energy Board,
Pretoria
JAW 2
ABSTRACT
A breakdown is given of the energy flows associated with an area
of bubole influence! The primary surface-to-liquid heat transfer
processes, although the ideal basis of correlation, are shown to be
amenable to analysis only if severely simplifying assumptions are maae.
Examination of thB 'bulk convection1 correlations Illustrates this
difficulty. An alternative approach is suggested. Its Basis is the
experimental finding that the energy initially transferred from
surface to liquid is redistributed in the fluid phases so as to
manifest itself almost entirely in vapour detachment ('latent heat
transport1). Tha resulting modBl is analysed without recourse to
mechanistic assumptions. Coupled with a method of surface characterisation
(similar to that of Mikic and Rohsenow) this leads to a new and
realistic heat transfer correlation. Comparisons with experimental
data ara presented. These Indicate that the correlation allows the
prediction of boiling curves q/A versus AT . at any pressure, provided
that at least one-ltoiUng cun/e for the same surface, or preferably
the same surface-liquid combination, is available as a reference.
JAW 3
NOMENCLATURE
a
A
9
Gr
h
Ja
kL
Mu
P
Pcrit
Pr
constant
heat transfer area, m
fraction of total area supporting natural convection
heat capacity of liquid, kJ/kg K
equivalent spherical bubble diameter at departure, m
bubble departure frequency, s~
mean volumetric vapour flow rate per bubble source,m/s
correction function, equations 24 and 25
gravitational acceleration, m/s
Grasnof number • L p SgAT /vc
hBat transfer coefficient, W/m K
Jakob number • pLC iT3 a t /Pv^
thermal conduct- v.ty of liquid, W/m K
constants
constants
characteristic length, m
constant describing nudeation properties of surface or
surface-liquid combination
-2
q/A
number of active nucleation sites per unit heater area, m
number of nucleation sites of mouth radius r per unitmax
heater area, ro~
number of bubble sources (including coalescence effects)
per unit neater area, m~
Musselt number - hL/«L
pressure, kN/m
critical pressure, kN/n
Pranatl number - C u. A
rate of hEac transfer, W
mean rats of Meat trarsfer for one area of bubble influence,
M, (suDscriDts defines in text)
heat flux, U/r-
JAW 4
(q/A)LH
NB
min
'sat
w(mean)
sat
mean heat flux in area of Dubble influence, W/m*
critical or peak nucleate boiling heat flux, W/ffl
heat flux, referred to total heater area, due to latent
heat transport, W/m
heat flux, refarrsd to total heater area, due to nucleate
boiling, (-Nq1), W/m2
natural convection heat flux, W/m
total heat flux, W/m2
- (q/A)T - [q/A)NC. ^
mouth radius of potentially active nucleation cavity, m
mouth radius of largest potentially active cavity, m
mouth radius of smallest active cavity, m
mouth radius of largest active cavity, m
time, a
saturation temperature of liquid, K
mean heater wall temperature, K
wall superheat, [-\{mean) - T^,), K
volume of bubble at departure, m
distance from heater wall into liquid, m
GREEK SYMBOLS
a
•B
X
A
u
thermal diffusivity ), m2/s
coefficient of cubic expansion, K
latent heat of vaporization, kJ/kg
function defined by equation 31
dynamic viscosity Ns/m
liquid and vapour density, kg/m
surface tension, J/m
Function defined be equation £9
JAW 5
1. INTRODUCTION
This paper deals with the correlation and prediction of heat transfer
rates during saturated nucleate pool boiling. 'di h such boiling several
classes of bubble behaviour may be distinguished [i]. The simplest of
these, occurring at low heat flux, is characterised by isolated bubbles, .
that is, by Bubbles so distributed on the heating surface that each is
essentially unaffected by its neighbour. The present analysis is
initially restricted to this case.
Each isolated bubble has associated with it an •ares of bubble
influence', that is, a portion of the heating surface, ths heat transfar
from which is influenced by the action of the bubble. The heating surface
outside the 'areas of bubble influence' is undisturbBd by bubbles and
supports natural convection.
Under such conditions the requirements of a heat transfer correlation
are:
(1) to predict the heat transfer within an area of bubble influence,
(2) to sum this over all areas of bubble influence, and
(3) to predict the heat transfer from the ismaining nonboiling area.
1.1 Breakdown of Heat Flow in Area of Bubble Influence
An area of bubble influence supports a complex pattern of tra^fer
processes at the heating surface, and subsequent redistributions of energy
in the Fluid pnases. Ths Oraakdov.n of these neat flows for oath
saturated and subcc jleo boiling is summarised in Figure 1 and equation 1
below. Each q is a ";ean rate of heat transfer (for one area of
influence), identifying a particular heat transfer process, a relatea group
Gf processes or a convenient fraction of these. The heat flows are
interrelated as foiio.vs:
qj (-negl.)
JAW 6
(la)
i 1 . ^ i"ML + °3WE + qBC
Y.A.i i i
\.H,vis + "CONOENS * "ac
(•)
(f)
Tha symbols have the following significance:
q* (T»TOTAL) ia ths total heat transferred per unit time in the area
of bubble influence; it may be resolved into a and q .
q~ (V«rt/APOufl) is the heat transferred from the heating surface directly
to the vapour within the bubble; it is considered neglibly small
compared with q^ .
q. (L»LIQUID) is the collective term for the heat transferred by
various mechanisms from the heating surface into the liquid; it is
essentially equal to qT and may be resolved into the three components
next listed,
qj^ (LW»LIQUID,WAITING PERIOD) is the heat transfer to the liquid during
the waiting period (thermal boundary layer recovery period).
(l.'L='.'ICr'CL'-YC?] i3 ths isat ;rar.jfs'rr;3 tc f.s liquia ricrcia/sr nr.-zHMLcausing micrclayer vaporisation.
qLWA
"LH
qCQNDEN
aLH vis
JAW 7
(LA-LIQUID ANNULUS) is the heat transfer into the liquid annulus
surrounding tha attached bubble.
[LWA-LIBUID, WAITING PERIOD AND ANNULUS) is a convenient collective
term for the sum of q ^ and q^; it manifests itself in the
next two modes.
(BWE-BU6BLE WALL EVAPORATION) is the heat transferred from the
bubble surroundings to the walls of attached bubbles (microlayer
excluded), there resulting in vapour evolution,
(BOBIBBLE CONVECTION) is the porCion of q* not involved in
evaporation into attached bubbles; it is transferred to tha
liquid bulk By convection induced by bubble movement.
(OMATENT HEAT) is tna collective term for the heat flows
associated with vapour evolution (latent heat transfer) at all
surfaces of the attached bubble,
(CONDENS-CONOENSATION) is that portion of o£H which, in subcooled
Boiling, recondenses from the attached bubble,
(LH.vis-LATENT HEAT, visible) is the remaining portitn of o£H
which visibly detaches from tha surface as vapour, •
Clearly the chain of equation 1 could be continued by considering
the further redistribution of heat occurring after bubble departure. In
saturated boiling, for example, qi_ is redistributed between evaporation
into rising bubbles and evaporation at the liquid surface at the top of
the pool. These events, however, occur well away from the heating surface
and are no longer associable with a particular area of bubble influence.
*The presentation of this brsakdawi asrivss in part from the work of
judd and Merte [2]{ the quantities Mere identified are, nowever, different.
JAW 8
1.2 Ideal Treatment of Area of Influence Heat Transfer
Ideally the correlation of heat transfer in tha area of bubble
influence should be based an the primary transfer process at the
heating surface, that is on q w, q , and q .. These processes are
complex and have bean insufficiantly investigated.
For example, the mechanism of qT. would appear to be intermittent
convection arising from the woke flow of the departed bubble [3,a]. The
radial velocity varies throughout the noiting period, while simultaneously
the surface temperature of tha heater (recovering from microlayer
evaporation) varies both with time and position [5,6]. The convection
velocities governing q. . are more complex^ presumably they are the
resultants of the wake flow of the previous bubble and the outward flow
induCBd by the growth of the attached bubble. Concerning q , thare
is as yet no agreement on initial micro-layer thickness or on the flow
pattern within it fo,?].
Attempts at the mechanistically detailed correlation of each of these
processes would at present appear to be unprofitable.
1.3 Bulk Convection Correlations
The successful boiling correlations of Han and Griffith [6] and
WLKic and Rohsenow [9] offar remarkable examples of a simplified treatment
of the area-of-influence heat transfer. In both cases all q. processes
were approximated by cyclic transient conduction into the liquid. The
initial and boundary conditions for each cycle were given Dy the following
physical model:
At the instant of departure from the heating surface, a bubble of
negligible latent heat content totally strips away the. layer of superheated
liquid over the entire area of duOble influence. At the same tine (t*G),
liquid from main bulk, at temperature T ^_t rushes to the heater surface
x=0) which i= invariable at T,,•.V(mean)
j the superheat layer is reformed
JAW 9
by pure conduction and, a t the departure of the nsxt bubble, i s again
stripped away, the superheat being dissipated in the bulk of the l iquid.
(This in termi t ten t bubble-induced pumping of superheated l iqu ia in to the
bulk i s referred to as 'bulk convect ion ' ) . Each t ransient conduction
cycle in to tha l iquid (x>0) i s thus subject t o :
Initial conditions:
(2a)
T - Tsat
at x>0, t-Q
Boundary conditions:
T " Vmean) o t * * • « *
x-a>, tX)T =. Tsat at
With these conditions and with the liquid considered infinite in the
x direction, thB solution of the one-aimensional conduction aquation is
q/A - kL 4Tsafc/(rat).0,5
(3)
The two bulk convection models differ in the detailed application of
aquation 3. The simpler model (that of ffi.Kic and flohsenow) illustrates
the general principles and is analysed below.
According to this modal, transient conduction as given by equation 3
extends over the entire area of bubble Influence, that i s , the bubble
contact area is negligible. The transients repeat at the frequency
of bubble departure, f. Thus the rean heat flux in tie area of influence
is
iD-S ;A',
JAW 10
Each area acts independently and has an assumed magnitude of rtD .
The heat flux (referred to total heater area) due to nucleate boiling
(natural convection excluded), that is, due to all areas of influence, is
thus
NB
Substitution into equation 5 of largely empirical expressions for N,
f and Oj led to the f inal correlation equation. Agreement with
experimental data was good.
The area-of-influencB energy flows and transfer mechnisms implied
by this model (of. equation 1) may be summarised as;
inhere
(6)
and
(LBB-LIQUID, BUBBLE BASE) is the hypothetical mean heat
transfer into the liquid over the area actually occupied
by the bubble base,
Subscript '" con1 indicates purs conduction into the semi-inifinite
l iquid.
The scheme given by equation 6 and the associated boundary conditions
of equation 2 dif fer severely from real i ty. When applied together, however,
they are mutually corrective.
Surface microthermometry studies (e.g, [6]) show that, ever a
substantial portion of the area of influence, the heater temperature is
not T / , , as 3ta"ao tiy equation la snti 2c, but is considerably ic.ver.*• in BHri j
Schlieren and liquid microthermometry studies fe.g. [4,10]) indicate that
JAW U
the temperature of liquid rushing to the surface after bubble departure
is not Tsa1;, as stated by equation 2b, but is higher. The model thus
overestimates considerably tha AT driving force available for the assumed
conduction. Through neglect of the bubble base area (see term a ,
equation 6) the model furthermore overestimates the area available for
such conduction. Clearly these overestimates correct for the omission
of the microlayer term, qj^, and of the convective effects in q*
and q^.
Similar arguments apply, with minor modifications, to the more
elaborate model of Han and Griffith. The success of the bulk convection
correlations must thus be attributed, at least partially, to the
cancelation of unrealistic approximation errors. The most disturbing
of these, viz. the neglect of microlayer evaporation, was forced upon
the model by adherence to the widely accepted notion of negligible latent
heat transport.
1.A Latent Heat Transport in the Area of Bubble Influence
The concept of negligible latent Meat transport (q*H « o T ) has been
popular to the extent that it is stated or implied in all major published
boiling correlations. It appears to derive from sarly bubble observations
during subcooled boiling [11,12] (see Fig. 1c) in which not qLH , but
q, was measured and found to be negligible. Neglect of cue term
LH,V1S
qj; , loose semantics and aroitrary extrapolation nave led to tne
application of tne concept to both suocoolsd and saturated boiling.
Evidence now available shows, however, that tne concept is of duBiaus
validity in subcooled boiling and is invalid in saturated eoilina.
In the case of subcooling, re-estinatas of the terr- o.CQfligE s
*.13,14] s-ggesi strongly, i f "Ct innclusively, that % _, {» a, _rji- *
,.) is of i-ougnly -ne sane nagnituae as q^.
JAW 12
In the sa tura ted case, with qLH • qLH v i s (SBB Fig. 1b), l a t e n t
heat t ranspor t i s d i r ec t ly measurable from bubble cine records . Such
measurements have gradually become ava i l ab le and a re summarised in
Table 1.
TABLE 1
LATENT HEAT TRANSPORT IN SATURATED SOILING
Source
Rallis et alFigs. 5»,12* in [15]
Pall is 6 JawurekFig. 7 in [16]
Novsfcovifi et alFig. 5* in L18J
Van StralenFig. 1* in [17]
Judd & MsrteFig. 10 in [19]
1951
1964
1366
1967
1972
Liquid
waterethanol
water
ethanol
water
Freon 113
tester
thinwire
thinwire
mercurypool**
thinwire
coatedglassplate
PressureklM/nT
83
83
101
101
57
Gravity
1 9
1 9
1 S
1 3
10 g100 g
•4/4epprax)
1,0
0,85
1,0
1,0
0,80,250,08
* Discussion of these figures i s covered oy the discussion of Figure 7in [16]
* * Surface supported a apecail type of nucleate bailing with N independentof iT _
The overall conclusion from Table 1 may be stated as follows:
JAM 13
In saturated boiling at terrestrial gravity, latent heat transoort
accounts for at least 80 per cent of the total area of influence
heat transfer, that is
4 (7)
The validity of this conclusion is now assuned to extend to all
conventional pure liquids (excluding liquid metals), to all heating
surfaces and to all pressures supporting normal nucleate boiling.
The first two extensions are well supported by thB data in Table 1.
The extension to high pressure is a working hypothesis.
Since latent heat transport a is dependent on bubble departure
volume and frequency, and since empirical expressions for these parameters
are available in the literature, equation 7 forms a practical basis for
the development of a heat transfer correlation.
2. DERIVATION OF NEW CORRELATION
An expression is developed below, relating latent heat transport,
summed over all areas of bubble influence, to AT . , T^ . , physical
properties and heater surface characteristics. The refraining area
of influence heat transfer (20 per cent or less.of the total) and the
nonbailing natural—convection heat transfer are then aea~t with in a
sirnui taneaus approximation,
2.1 Expression for Latent Heat Transport
For saturated isolated buCble boiling *e have
2 XfV_
or summing ovtr all nijci.sjtj.on .sites j^t^at: 13.-areas of
influence) per unit are;2,
JAW 14
LH
where fv, is the mean volumetric vapour flow rate per nucleation site,d
Expressions for N and are now needed.
Nucleation site concentration N
Nucleation generally proceeds from vapour entrapped in microscopic
surface cavities [20,21,22]. The mouth radius of potentially active
cavities, that is,cavities capable of entrapping vapour [23], will, for
a certain surface-liquid combination, have some frequency distribution,
for example, as in Figure 2. Under given conditions a range of these
cavities will be active, as shown.
An approximate nucleation criterion (a slight modification of that
of Griffith and Wallis [22]) may be stated as follows:
(10)
This equation suffers from several defects (see detailed discussion
[24]); tests with normal boiling surfaces, however, indicate [22,25]
that r* is at least proportional to the terms on the right-hand side,min
Equation 10 gives the mouth radius of the smallest cavity that will
be active for a saturated liquid at a particular pressure and wall
superheat. Thus, as AT is raised from zero, the largest potentiallysac
active cavity on the surface is the first to Become active (r » r ).fftaX fflQX
Further increase in LT *. causes activation of progressively smallersat
cavities, while all*larger cavities remain active. Thus N, the total
number of active cavities per unit area, i s given by the integral with
resoect tc r^.n or Figure 2, or in other words N versus r_. i s the
cumulative cavity size distribution (see also [16,25]).
JAW 15
This cumulative distribution is now approximated by the simple
power function
and NQ is the concentration of
is the mouth radius of the largest potentially active cavity
^ Figures 3 and a illustrate normal
and lognormal distributions and the success over their lower range of the
power function approximation.
An equation of the form
N - const./(r*.nf (12)
was apparently first proposed by Brown on empirical grounds (see [9]),
and found to hold quite well.
Combining equations 10 and 11, we obtain
(13)
Essentially the same relation was obtained Dy Mikic and Rohsenow [3]
from equation 10 and Brown's aquation 12.
Detailed tests L24] against experimental data indicate tnat
equation 13 i s valid not cnly For a particular surfsce—Iiauia comoinaticn
but, at slightly increased risk, Per a surface irrespective cf liquid.
A proportionality constant in equation 10 might, howe----r, be necessary
for numerical correctness. This constant should be carried thrcjgn
to equation 13 which can then be writtsr in final for"" as
JAW 16
K^ and m, which are generally unkwon, now characterise nudestion from
a surface-liquid combination or, at slightly increased r isk, from a surface
irrespective of l iquid.
Mean volumetric vapour flow rate per nucleation site, Tsj
A large number of expressions have been proposed, mostly on semi-
empirical grounds, for the product of bubble frequency and bubble departure
volume (or diameter). Extensive reviews are given by Ivey [26] and
Cole [27].
ThB following correlation, developed by Cole [27], appears to have
the widest validity:
3/a
Ky is a dimensionless constant (» 1,25 x 1O~a), and the last bracketed
term is the Jakob number.
Figure 5, reproduced from Cole [27], compares equation 15 with
experimental values. (For convenience of plotting the cube roots of
dimensicnless groups are shown). The scatter probably arises largely
from the neglect in equation 15 of bubble contact angle, nucleation site
concentration, active cavity size and bubble growth rate, a l l of which
are known to affect bubble departure size and/or frequency. Mevertheless,
equation 15 correlates with some success the data for a wide range of
liquids at pressures ranging from low subatmospheric to sligntly acove
atmospheric. The limited high-pressure bubble departure data that are
available are not sufficiently completely reported to permit testing
of the equation.
Inherent in equation 15 is the following equation for bubble departure
diameter [27]:
JAW 1?
Dd " "D
Cole has tested equation IS against the low-pressure data of the
investigations shown in Figure 5 and, with K_ * 4 x 10 , has ootained
excellent agreement. Indirect arguments have been advanced [24] which
indicate that the validity of equation 16 might well extena to hign
pressure. This, in turn, lends some confidence to the extension of
equation 15 to high pressure.
At constant pressure, equation 15 predicts an increase of Tv *Lth
increasing AT ; this is Consistent with the measurements of Rallissac
and Jawurek [15] and the confirmatory evidence of Preckshot and Denny [31].
Division of equation 15 hy equation 16 squared, however, leads to
fD. » const.1/4
(17)
which, at constant pressure, is consistent with the well-known approximation
TO- const. (18)
Equation !5, together with equation 16, thus offers an attractively
rounded-off description of bubble departure.
Final expression for latent neat transport
Substitution of equations 54 and 15 into ecjuation 5 Isads to the
following ;xpr9ssion for latent neat transport:
' 2
(13)
JAW 18
which may be rearranged to give
>V KL'LH "sat (20)
Here the constant K (having dimensions of length^""2') and thB exponent
m characterise a particular surface-liquid combination or perhaps even a
particular surface independent of liquid.
2.2 Expression for Total Heat Flux
The total heat flux in isolated bubble boiling is given by the
relation
(q/A)T - (q/A)NB + (q/Aj^ ( A ^ ) (21)
where (q/A)NB • N qT , that is, the flux referred to total area due to
nucleate boiling, (q/ A) N C is the flux due to natural convection when it
alone is operative, and the last term is the area fraction available for
such undisturbed natural convection.
Summing equation 7 over all nucleation sites we have
(q/A)LH 2 0,8 (q/A)NB (22)
123)
where F^ is a Correction function', the value of which i s given By
1 s F s 1,25
JAW 19
Equation 21 now becomes
(q/A)T (25)
whsre (q/A)LH i s given by equation 20 and (<J/A)NC i s obtainable fro
standard correlations of the form
Nu * const. (Gr.Pr)a (26)
whore the constant and exponent depend on system geometry and the range
of the product Sr.Pr.
The area fraction A /AT can b B related to buoblB departure
diameter and nudeaticn site concentration using equations 14 and 16
(see [24]); the resulting expression is, however, too complex for
practical use. As an alternative a simple approximation is given below.
A^_/A is unity at incipience of boiling, and decreases towards
zero as the surface becomes progressively covered by areas of bubble
influence. Simultaneously, however, the ratio (q/A)NC/(q/A)T decreases
rapidly so that the precise value of A /A becomes unimportant in
equation 25. For example, at atmospheric pressure, total area of influence
coverage, corresoonding roughly to the onset of lateral bubble coalescence,
occurs at B - 20 per cent of ( o / A ) c r i t t1]" 3t tnat =ta39 (see fi-9- s)i
(q/A) is some 10 - 25 per cent of (q/A)T . It would thus seem
reasonable to replacs the fraction \r''^j ^n equation 25 0y unity ana,
in partial compensation, to drop the correction function F .
Total nsat flux is then -jiven ainoiy by
(q/A)T(27)
JAW 20
Mechanistically this means the bubble-induced convection is ignored in
the areas of bubble influence and is replaced by undisturbed natural
convection. This approximation, i.e. equation 27, has been tested at or
near atmospheric pressure [15, 16, 17, 13] and found to hold within + 30
per cent.
Combination of equations 27 and 20 gives our final correlation:
(q/A)T
where
ga/a 7374
(2B)
(29)
and (q/A) N C is obtained from standard correlations.
3. APPLICATION OF CORRELATION
Boiling heat fluxes can be predicted by equations 28 and 29,
provided that at least one boiling run (q/A)_ versus AT is
available for the surface-liquid combination under study. (q/A) ,
as obtained experimentally or by calculation, is subtracted from (q/A)T
and the difference, K'J&T,.^ . i s Plotted against A T ^ on log-log
paper. The beat straight line is fitted to the lower (isolated bubble]
portion of the data and the slope (ra+2) is established. With m Known,
K is obtained from equations 28 and 29. Thus ali terms in equations
2B and 29 are known and (q/A)T can be calculated at any cither pressure
for the same surface-liquid combination. At slightly increased risk
the prediction can be extended to other liquids bciliig on the ^ame
surface.
JAW 21
4. TESTING OF COflHELATIO-M
The correlation scheme outlined above is now tested against the
experimental results of Addons {see [32]) for water boiling at high pressures,
and against those of Booilla and Perry [33] for ethanol at lo* pressures.
Both sets of data are presented as sets of boiling curves (q/A) versusa T
s a t • Po*" testing data in this form, equation 28 i s rewritten as
(30)
where
A - (31)
and f i s given by equation 29. Thus for one surfaca-liquid combination a
log-log plot of (q/A)T_NC versus A-ATsat should accommodate data at
a l l pressures on a single straight l ine of slope (m+3).
Test against high-pressure water data of Addoms
Figure 6, taken from Figure 14.14 in McAdams [32], shows the data of
Addoms for water bailing from a 0,51 mm diameter p la t ing wire. The
natural convection fluxes (three sapola curves are shown) were calculated
from equation 26; details are given in [24],
Figure 7 shows (q/A)T .lr. versus AT_ . The run at 17 OCC k\/n
(P=0,77 P ...) is excluded because sane physical properties cecane
unreliable am equation 15 for f\7 probably no longer nolds (see ' Z&1).
f.tikic and Poh^eno/j [9], in correlating Aado^s1 ctata, similarly amit tnis
run. The ^ean slope of the lav.ac Halves of the curves in Pigure 7 is
taken as 4, Th s f=2 and equations 23, 30 ana 31 give
where
JAW 22
(33)
The data points inserted into Figure 7 are now processed by
equations 32 and 33, with physical properties evaluated at T .
Figure 8 shows the correlation to be satisfactory. Since m=2, the
constant K is dimensionless.
Figure 8 further shows that our correlation scheme continues to hole)
at high heat fluxes beyond the end of the isolated bubble region, and thus
beyond the limit of validity of our model. This can be explained as
follows! In the presence of lateral bubble coalescence, equation 9 must
be modified to read
(34)
where f and V. now refer to bubbles arising from one or more nudeation sites
and N1 is the concentration of such bubble sources. Now fV_, increasesd
more rapidly with AT . for coalescence bubbles than for isolated bubblessat
(see Fig. 11b in [16]), and N' ( with increasing coalescence) increases
more slowly than N. The two effects at least partially cancel each other,
and thus our correlation scheme remains approximately valid.
As the critical heat flux is approached, massive vapour patches
form on the heating surface [i]j Dur model breaks down altogether and
the correlation equations cease to hold.
Test against low-pressure ethanol data of Sonjlla ana Perry
Figure 9 shows (q/A)T versus AT for Sonilla and Perry's
data [33] on ethanol boiling an a horizontal chrome surface. The v/ali.
(q/A)T were taKen From Bonilla ana Perry'i "igure 10, ana fq/d). as
obtained, via equation 25, by esciTatf^ ^utlinec in [24]. .Mth the
mean slope of the straight lines interpreted as 6, m.4. Thus from
equations 29, 30 and 31 the correlation is
where
[f(XPv)3
0"'*
(3S)
(36)
Figure 10 shows the data points correlated by equations 35 and 36.
Over the lower half of the flux range the correlation is again acceotable.
The whole procedure was repeated with the slope in Figure 9 interpreted
as 7, instead of 5, i .e . m»5. No significant spread in the correlated
points resulted. These tests and the test against Addoms1 data with m»2
show that our correlation scheme i s not fortuitously successful for certain
values of m, but appears to have general val idi ty.
5. CONCLUDING COMMENTS
1. Idea l l y , the cor re la t ion of nucleate bo i l i ng heat t ransfer should
be based on the primary sur face- to- l iqu id heat transfer processes in tne
area of bubble inf luence. These processes are complex and incompletely
understood. Thus t h e i r models have generally become arenabls to
analysis only when s impl i f ied to the point where they no longer relate -a
r e a l i t y . The bulk convection corre la t ions, despite the i r numerical
success, i l lustrate this d i f f icul ty.
2. An alternative approach is outlined in this paper. I ts nasis is
the experimental finding that a l l area-of-influence "631: transfer prczssses
may be largely approxinatsa by latent ^eat transport. 7is rasul-ing model
l/-j-io ..ithc^t r="^j ~ f jrtnar "•ecri
JAW 24
3. A new correlation of haot transfar during saturated pool boiling
has resulted. The correlation allows the prediction of bailing curves
q/A versus ATsat at any pressure, provided at least one boiling curve
for the same surfacB, or preferably for the same surface-liquid combination,
is available as a reference. This feature and the underlying methoe of
surface characterisation are essentially identical to those in Mikic and
Rohsenow's correlation [9].
4. Although derived in terms of isolated bubbles ( i .e. low heat f lux] ,
the correlation remains approximately valid throughout the linear range
of log-log boiling curves. I ts validity is restricted to terrestrial
gravity and probably to ane-compunent, conventional (e.g. non-metallic)
liquids.
ACKNOWLEDGEMENTS
Initial ideas on this paper were developed some years ago during
discussion with Professor C.J. Rallis, School of Mechanical Engineering,
University of the Witwatersrand, The work wus executed in tne Physical
Metallurgy Division of the Atomic Energy Board. The author is deeply
grateful to these institutions, their Heads and staff, and in particular to
Professor Rallis for his continued interest and neipful criticism.
JAW a
1. R.F. GAERTNER, Photographic study of nucleate pool boiling on ahorizontal surface. General Electric Co. Research Lab. Rep->rt63-RL-3357 C. 3>;henectady, N.Y. (1963)
2. R.L. JUDO and H. MERTE, Influence of acceleration on subcoolednucleate pool boiling. Paper BB.7, 4th Int. Heat Transfer Conf.,Versailles (1970).
3. M. BE"HAR and R. SEM^RIA, Sur la mise en evidence oar strioscopiede certain mecanismes d'Schanges thermiquas dans le dSgazage et1*Ebullition de l'eau, Comptns Rcnrfus Acad. Sc. Paris 257,2801-1803 (1963). ~
4. N. ISSHIKI and H. TAMAKI, Photographic study of boiling heattransfer mechanism, Bui. Japan Soc. Mech. Engrs 5, 505-513 (1963).
5. F.D. MOORE and R.B. VESLER, The measurement of rapid surfacetemperature fluctuations during nucleate bailing of water,Amer. Inst. Chem. Enqrs J. 7, 620-624 (1961).
6. M.G. COOPER and A.J.P. LLOYD, Transient local heat flux innucleate boiling, Proc. 3rd Int. Heat Transfer Conf. 3, 193-203,Chicago (1966).
7. H.H. JAWUREK, Simultaneous determination of microlayergeometry and bubble growth in nucleate boiling. Int. J. HeatMass Transfer 12. 843-848 (1969)
8. C.Y. HAN and P. GRIFFITH, The mechanism of heat transfer in nucleatepool boiling, Int. J. Heat Mass Transfer a. 887-914 (1965).
9. B.B. MIKIC and W.W. ROhSENOW, A new correlation of pool boilingdata including effect of heating surface characteristics,J.Heat Transfer C91, 245-250 (1369)
10. R. SEMERIA and J.C. FLAMAND, utilisation d'un micro-thermocouplepour l'fitude de 1'fibullition locale de l'eau en convection librc.Report T.T. no. 81, Centra a'Etude Nucleaires, Grencole (1967).
11. F.C. 3UNTHER ana F. KREITH, =!-iotographic study of bubble formationin heat transfer to subcoaled racer, °roc. Heat Trai-afer and fluidUtecn. Institute, 113-133, ASUE (1949~J7
12. '.V.!. RQhSEMOIS and J.A. CLARK, A study of the ir.ecnar.ism of boilingheat transfer, Trans, tear. Soc. '.teen. £nqrs 73, 5K-a20 (1951).
13. S.G. BACKOFF, A note en latent neat transport in Nucleate botiinj,Amer. Inst. Chem. Zngrr. ;. 3, 63-65 [1962).
14. 7.1", ROBI*. ana 'i.H. S.'JYDER, Bubnls dyndmicr3 in sjOcuclea nuciedtGboiling based on the nass trar.fer ^Ecnanism, Int. .'. H^^t '.'ar.-:Tran-:f^r 13, 305-316 f'.37O;.
C.J. BALLIS, ^.V. GPEE\L"!D a:ia A. KCK, Stagnant pool nucioatsb^ili''": '':"-'" ~Z'.~iszi~*L .-.Lrps ..r-lv jtjrat^d and •I'AZZQI':^
conditions, 3.Afr. ••••-c-. '.r.-.ir 1:, '^1-iSo (1961).
JAW 26
16. C.J. RALLIS and H.H. JAWJREK, Latent heat transport i n saturatednucleate ha i l i ng , I n t . J . Heat Mass Transfer 7, 1051-106B (1964).
17. S.J.D. van STRALEN, The mechanism of nucleate bo i l i ng i n pure l i qu idsand binary mixtures, Part 3i I n t . J . Heat Mass Transfer JO, 1463-1484(1967).
18. M.M. NQVAKOVTC, L.L. JOVANOVlfi, M.S. STEFMIOVlfi and N.C. NINIC,Nucleating from a mercury surface, Proc. 3rd I n t . Heat Transfer Cpnf.3, 213-218, Chicago (1956).
19. R.L. JUOD and H. MEHTE, Evaluation of nucleate bo i l i ng heat f l uxpredict ions at varying levels of subcooling and accelerat ion, I n t .J . Heat Mass Transfer 15, 1075-1096 (1972).
20. S.G. BANKOFF, Ebul l i t ion from sol id surfaces in the absence of apre-exist ing gaseous phase, Trans. Amer. Soc. Mech. Engrs 73,735-740 (1957).
21. H.B. CLARK, P.S. STRENGE and J.W. WESTWATER, Active s i tes fornucleate ba i l i ng , Chem. Engng Progr. Symp. Sar. 55, Mo29, 103-110(1959).
22. P. GRIFFITH an* J.D. WALLIS, The ra le af surface conditions i nnucleatB bo i l i ng , Chem. Engng Progr. 3ymp. Ser. 56, No 30, 4S-65(1950). ~~
23. S.G. BANKDFF, Entrapment of gas i n the spreading of a l i qu id overa rough surface, J. Amer. I ns t . Chem. Engrs 4. 24-26 (1958).
24. H.H. JAWUREK, A latent-hcat-based correlat ion of saturated poolbo i l i ng heat transfer. (Detailed version of present paper).S. Afr. Atomic Energy Board Report PEL 233, Pretoria (1974). ISBN0 B69S0 473 2.
25. C.J. RALLIS and H.H. JAWUREK, The mechanism of nucleate bo i l i ng .Paper A/CONF. 5B/P/600, 3rd U.N. I n t . Conf. Peaceful Uses AtomicEnergy, Geneva |/i964j.
26. H.J. IVFY, Relationships between bubble frequency, departure diameterand r ise ve loc i ty in nucleate bo i l i ng , I n t . J . Heat Mass Transfer 10,1023-1040(1967).
27. R. COLE, Bubble frequencies and departure volume at subatmosphericpressures, Amer. Ins t . Chem. Engrs J . 13, 770-783 (1967).
28. R.L. NICKELSON and G.W. PRECKSHOT, Observations on bo i l i ng carbontetrachlaride from surfaces, J. Chem. Engnq Data 5, 310-315 (1950).
2S. P.W. McFADOEN and P. GRASSMANN, The re la t ion between bubble frequencyand diameter Curing nucleate pool bo i l i ng , I n t . J . Heat Mass Transfer 5,163-1.73(1962).
30. H.S. PERKINS and J.',V. WESTWATER, Measurements of bubbles formed i nbo i l ing methanol, Amer. Inst . Chem. Engrs j . 2, 471-475 ("956).
31. G.W. PRF.CKSHOT and V.E. DENMY, Exploration of surface and cavitypraasrties on tns nucleate bo i l ing c f carbon ts t rach lcr ide, Canad.J. CheT;. Encng 45. 241-S45 (1357).
JAW 27
32. W.H. McADAMS, Heat Transmission, 3rd ed. p 382,McGraw H i l l , New York (1954;.
33. C.F. BONILLA and C.W. PERRY, Heat transmission to bo i l ing binaryl i q u i d mixtures, Trans, ftner. Ins t . Cnem. Engrs 37, 585-705 (1941).
JAW 28
JAW 29
- AREA OF INFLUENCE
1 "V'BC I
BOILING
(a) GENERAL CASE,
SATURATED AND SUBCOOLEO
*BC
Ib) BUBaE DEPARTURE,SATURATED BOILING
Ic) BUBBLE DEPARTURE,
SUBCOOLED BOILING
NO. OFPOTENTIALLYACTIVECAVITIESOF MOUTHRADIUSr to (r+dr)
MOUTH. RAOIUS OF POTENTIALLYACTIVE CAVITIES, r -'
. ATsat
FIGURE 2Hypothetical size distribution of nucleation cavities.
FIGURE 1Breakdown of heat flow in area of bubble influence.
JAW 30
I3
Is
NORMAL OISTR. OP
MEAN * 3VARIANCE s i
121,5
lrmin>S
to
'min
ARBITRARY UNITS
FIGURE 3Normal distribution of 'min approximated by power function.
JAW 31
I(D
/UX5N0RMAL OtSTR. OF f
MEAN »O.96"j PQOVARIANCE *0,12J « * *
11,35
6 10
min
ARBITRARY UNITS
FIGURE 4Lognormal distribution of r r o jn approximated by power function.
JAW 32
COLE [27j I° ACETONEO CARBON TET.a METHANOL
* METHANOL
a METHANOL• METHANOL• METHANOL• N-PENTANE« N-PENTANE* WATER• WATER« WATER« WATER
NKKELSON S. PRECKSHDT C281
• CARSON TET. 152• CARBON TET. 101 kN/m*x CARBON TET 50,7 kN/m2
McFAOOeN t GRASSMANN C29I+ NITROGEN 101 kN/m 2
PERKINS I WESTWATER [30]
• METHANOL 101 kN/m 2
RALLIS & JAWUREK [16J
• V/ATER 83,4 k N / m 2
FIGURE 5Cole's correlation for bubble departure, |27|.
JAW J3
FIGURE 6Water boiling at high pressures, data of Addoms |32|.
JAW 34
CM
E
FIGURE 7Total flux minus natural convection flux for data of Addoms 1321.
JAW J5
106
10 L
103 ID4
P. kN/m2e 101,4Q 2641A 5309
+* iffi H« 13690
A ATs a t i (W/m2)V*
FIGURE 8New correlation applied to data of Addoms 1321.
JAW 36JAW 37
CM
E
FIGURE 9Total flux minus natural convection flux for low-pressure ethanol
data of Bonilla and Perry {33 j .
FIGURE 10New correlation applied to data of Bonilla and Perry [331
SF
Dune 1
APPLICATIOH CF EXPERIMENTAL ESAT TRANSFER DATA
TO BOILIHG WATER REACTOR (BWR/6)
LOSS-OP-COOLANT ACCIDENT ANALYSIS
John D. Duncan and Jamas E. Leonard
General Electric Company
Nuclear Energy Division
175 Curtner Avenue
San Jose't California
Dune 2
DISCLAIMER (^.RESPONSIBILITY
This report was prepared as an account of research and development
work performed by General Electric.Company. It is being made
available by General Electric Company without consideration in the
interest of promoting the spread of technical knowledge. Neither
General Electric Company, nor the individual authors:
A. Make any warranty or representation, expressed
or implied, with respect to the accuracy, com-
pleteness, or usefulness of the information
contained ia this report, or that the use of any
information disclosed in this report may not
infringe privately owned rights; or
Assume any responsibility for liability or damage
which stay result from tha use of any information
disclosed in this report.
Dune 3
BtfR Background
In this era of greater ecological emphasis, dwindling fossil
fuel supply and increased power demand, it becomes necessary to us*
to the fullest extent possible all technological advances available
to us. Nuclear fuel; replacing coal, oil, and gaa; provides the most
economical, the most reliable, and the most stabilised power source
of the era.
The beginning of the General Electric product line was the
VallecMoa BWR in 1957. This 1000 psi reactor powered • 5 Mtfe
generator and provided power to the Pacific Oas 4 glectrie Co. grid.
A major extrapolation from that first test facility is the Dresden 1
plant, located near Morris? Illinois. Construction on this 180 Mtfe
plant began in 1959, with commercial power production achieved in
1961.
Since that time, General Electric has been innovative in the
timely and controlled manner in which equipment design improvements,
backed up by a' prototypical development program, have been introduced
into the marketplace. This strategy of methodical design evolution
permits operational feedback from the field prior to the introduction
of further design improvements. A Summary of General Electric SWR
evolution i3 presented in Table 1.
Dune 4
TABLE 1
Evolution of the general Electric BWH
Product Line
Humber
Year of
IntroductionCharacteristic Plants
BWR/l 1955 Dresden 1, Big Rock Point, KRBHumboldt Bay
Initial commercial EWR'aFirst internal steam separation
BWR/2 1963 Oyster CreelcPlants purchased solely oneconomicsLarge direct cycle
Bvm/5 1965 Dresden 2First jet pump applicationImproved ECOS: spray & flood
1966 Browns PerryIncreased power density
BWR/5 1969 ZimaerImproved SCCS systemsValve flow control
BWH/6 1972 BWH/68 by 8 fuel bundleImproved jet puapa and steamseparatorsAdded fuel bundles, increasedoutputReduced fuel duty (l3.4kW/ft)Improved ECCS performanceImproved lieensability
Dune 5
BWR/6
The nuclear system discussed in this paper is typical of the
improved General Electric 1972 product line boiling water reactor, BWR/6
This system incorporates significant advancements over previous designs.
These advantages illustrate the aethod of product improvement Just
discussed! a eomoination of development program payoff and field
eiporieoce.
The BWH/6 product line is capable of producing 2Oj6 more power
froa current standard 3iae BWR pressure vessels without increasing the
size of the reactor building and supporting subsystems. Power output
capabilities range from 682 HWe to 1436 XVe gross.
Summary Description of BWR
Tho direct cycle boiling water reactor nuclear system (Figure l)
is a steam generating system consisting of a nuclear core and an inter-
nal structure assembled within a pressure vessel, auxiliary systems to
accommodate the operational and safeguard requirements of the nuclear
reactor, and necessary controls and instrumentation. V»ter is circu-
lated through the reactor core, producing steam which 13 separated from
reeirculation water, dried in the top of the vassal, and directed to the
steam turbine-generator. The turbine employs a conventional regenera-
tive cycle with condenser deaeration and condensate deisineralization.
With a compatible balance of plant equipment, startup and operation
of the reactor are npt dependent upon outside sources of power.
Dune 6
The reactor core, the source of nuclear heat, consists of fuel
assemblies and control blades contained within the reactor vassal
(Figure 2) and cooled by the recirculation water system. A 1220-MWe
BWH/6 core consists of 732 fuel assemblies and 177 control rods, forming
a. core array 16 feet in diameter and 14 feet high. The power level is
maintained or adjusted by positioning control rods vertically in the
core. Sach independent control rod drive penetrates the core from the
bottom to accurately position its associated control rod. During a
scram the drive is capable of exerting a force approximately ten times
that of gravity to insert the control rod. Bottom entry allows optimum
power shaping in the core, ease of refueling and convenient drive main-
tenance .
Recirculation water is forced through the core and steam
separators by jet pumps located in the peripheral area around the core,
inside the reactor vessel (Figure 3). Motive power for the jet pumps is
provided by two centrifugal pumps which circulate water from the vessel
with increased pressure through the jet pumpa.
The boiling water reactor is controlled as a nearly constant
pressure system. During normal operations, the steam admitted to the
turbine is controlled by the turbine initial pressure regulator which
maintains essentially constant pressure at the turbine inlet, thus
controlling reactor vessel pressure.
The integration of the turbine pressure regulator and control
system with the reactor water recirculation flow control system permits
the quantity of steam being produced to respond automatically to the
deoand3 of the turbine. This automatic load control permits changes in
turbine-generator 3peed cf load d.emand to change reactor power and steam
flow.
Dune 7
The Lo33-of-Coolant Accident
For light water-cooled nuclear plants lilce the BtfR, the term
Io33-of-coolant accident (LGCA) refers to a postulated pipe rupture in
the primary coolant loop. In reality such an accident is extremely un-
likely, probabilities of approximately 1 in 10,000 per reactor year are
calculated for current BWRs. Thus, the postulated accident is used as
a very conservative basis for the design and evaluation of certain plant
safety features.
Immediately aftsr a 1OCA is postulated to have occurred the void
for&ation in the coolant inventory and control blade insertion halts the
fission reaction and associated energy release. After the reactor has
been shut down, the energy released by the radioactive decay of fission
products built up in the fuel during normal operation and the energy
stored in the high temperature fuel remain to be dissipated. Although
the relative magnitude of these terms is small compared to the rated out-
put of the plant, their absolute magnitude is large enough to require
active cooling during the period following the L00A to prevent core
damage from over-heating. The emergency core cooling systems (SCCS)
supply the required active cooling action.
In the BWR there are two primary emergency core cooling systems:
l) core spray and 2) low pressure coolant injection (LPCI). The core
spray system consists of a header and nozzle arrangement positioned
above the core which provides cooling by spraying water over the top of
the core. The LPCI system pumps large amounts of water back into the
reactor vessel resulting in a re-subaergence of the core. Beta of these
systems include sufficient redundancy to assure their availability.
Dune 8
ABSTRACT
Emergency core cooling systems are required to mitigate the con-
sequences of the postulated loss-of-coolant accident in light water
reactors. The emergency core cooling systems of the current General
Elsctric BWH design (HWH/6) limit the post-accident fuel cladding tem-
perature to approximately 1500°F when the analysis is performed in accor-
dance with the conservative USAEC Interim Acceptance Criteria. The
design of the emergency core cooling systems is supported by an extensive
data base vhich has been developed by General Electric over the last
several years • This paper describes the application of a recently-
obtained set of experimental data. A series of emergency sore cooling
tests of a simulated BVR/6 fuel bundle were conducted in November and
December, 1972' The General Electric core heatup model was used to pre-
dict the thermal response of the test bundle to simulated loss-of-coolant
transients. Predictions of maximum cladding temperature ia BWE/6 acci-
dent simulations ranged from 30°F below to 100°P above the recorded
tsst-bundle pemperatures, thus providing excellent confirmation of the
emergency core cooling systom(design and of the models used to calculate
the results of the postulated accident in the BWR.
Dune 9
MTRODPCTIOH
The postulated de3ign basis loss-of-eoolant accident (LOCA)
in a light water reactor results in a loss of the normal core cooling
flew as well as a loss of the fluid inventory in the reactor pressure
vessel.
During the initial "blowdown" phase of the LOCA, the BUS core is
cooled entirely by natural phenomena (nucleate boiling, film boiling,
convection to steaa> and radiation) requiring no coolant injection from
external sources until the initial 3tored energy of the fuel is essen-
tially removed. This fact, plus the relatively low-power density of the
BWR core, limits the cladding teoperaturs rise during the blowdown to a
low value. This temperature rise in current designs is typically 600°
to 800°P as predicted by the conservative USAEC Interim Acceptance
Criteria (IAC) evaluation models. Emergency core cooling systems are
provided to limit the subsequent cladding heatup so that fuel damage can
be minimized. In the case cf the current boiling water reactor design
(Btfit/6). the size, diversity, and redundancy of the emergency core cool-
ing systems are sufficient to "overwhelm" the accident. Realistic cal-
culations indicate that the design basis accident would result in fuel
rod claddiag temperature increases of less than 300 F above the normal
operating temperatures. Calculations using the conservative IAC oodels
indicate that the maximum -cladding temperature will be limited to appro-
xiirately 1500 7 well below the fuel cladding perforation threshold.
Dune 10
The present paper provides a brief sumasry of the experimental
effort conducted by General Electric over the past several years in
support of the emergency core cooling system design. The application
of nest transfer data from a recent experimental program, directed
specifically a BWTt/6, is discussed in detail. This program consisted of
a aeries of emergency core cooling tests of a simulated BWH/6 fuel bundle
conducted in November and December, 1972.
The General Electric core hestup model was modified to match the
test geometry and the test conditions, and the model was used to predict
the thermal response of the test bundle. Predictions of maximum bundle
temperature in BWR/6 accident simulations ranged from 30°F below to
100°F above the recorded test aaxioum bundle temperatures. Therefore,
the modified core heatup model ia considered appropriate for use in BViB/6
loss-of-coolant calculations! It is concluded that this series of tests
provides sufficient justification for the conservative nature of reactor
safety analysis report calculations with the codified model using the
Atomic Energy Commission Interim Acceptance Criteria assumptions.
Therefore, no further confirmatory testing ia required to demonstrate the
adequacy of the model for application to 8 x 8 fuel geometry.
Dune 11
THE BWR/6 LOSS-OF-COOLANT ACCTDEH?
The calculated response of the BWR/6 fuel rod cladding is shown
graphically in Figure 4. These calculations were performed in accor-
dance with the Atomic Energy Commission's Interim Acceptance Criteria (l).
Briefly summarized, the postulated accident proceeds as follows:
1. A double ended break of one of the recirculation lines
is assumed. Coincident with the break, all normal
auxiliary power is assumed to be lost.
2. The reactor is shut down by sudden voiding of the
moderator and a mechanical scram, and the reactor
blowdown begins.
3. Decreasing core flow results as the rtcircul&tion
pump in the unbroken loop coasts down. Nucleate
boiling is maintained for 7 to 10 seconds (flow stag-
nation i3 assumed when the jet puisps uncover) and no
cladding heatup occurs.
4. Shortly after the break flow turns to Jteao, tha in-
ventory in the lower plenum flashes violently due to
the sudden increase in depresaurisation rate and flow
through the core is established again. Pi1B boiling
(2) is assumed during this tine, and the cladding is
heated primarily by the fuel initial stored energy
to approximately 1COC F.
5. Core flow ceases again a 35 to 40 seconds after the
LOCA, and the cladding is then heated primarily by
decaying fission products following the reactor shut-
down.
6. Sated core spray is achieved when the fuel rod cladding
is at about 1150°? and core spray heat transfer begins.
Dune 12
7, Accumulated emergency core cooling system (ECCS;
water (core spray and low-pressure coolant injection)
fills the lower plenum of the reactor vessel and be-
gins to flood the fuel bundles. The fuel bundle
heatup at till elevations ia assumed to continue
unaffected by flooding heat transfer until that
elevation ia covered by flooding water.
8. At about 100 seconds after the accident, the hottest
plane has been re-covered, and film boiling results
in rapid cooling of the fuel rods, the hottest of
which had reached approximately 1500°P.
It should bs emphasised that the above summary of the postulated
accident is the reault of several very conservative assumptions, a few
of which will be noted her*. The results of the Deficient Cooling Heat
Transfer Program (3) indicates that nucleate boiling continues for seve-
ral seconds after flow stagnation. If the BWE/6 calculations were made
consistent with these longer periods of nucleate boiling, a larger frac-
tion of the energy originally stored in the fuel would be removed early
in the accident and the resulting peak cladding temperature would be
significantly reduced. The Deficient Cooling Program observations are
consistent with data currently being taken at General Electric under the
OB/ABC sponsored Slowdown Beat Transfer Test Program (4). The results
of both programs indicate that the early phases of the accident are
modeled very conservatively. As a final example of the conservatisms
inherent in the calculation shown on Figure 1, it is noted that that
calculation is performed vith a decay heat generation equivalent to the
proposed American Huclear Society Standard, plus a 20$ allowance for un-
certainty (l). A recent Seneral Electric survey and analysis of the
applicable data (5) indicates a significant amount of conservatism in
this value of decay heat generation which is required in the USASC
approved evaluation model.
Dune 13
GENERAL ELECTRIC EMERGENCY CORE
COOLI11S EXPERIMENTAL SOPPORT
The core heatup model and the experiments which support it have
been developed aver the past several years. Literally hundreds of expe-
riments and calculations have been performed in support of this model
development. Only the most recent experiments and thoa* which have
significance during the emergency cooling phase of the postulated LOCA
will be briefly summarized here.. The reader is referred to the references
and appendices of Reference 6 and to the references cited here for back-
ground regarding other phases of the accident and for aore details re-
garding the experimental support of the model as applied to the period
of emergency cooling system operation.
The moat significant parts of the model during the emergency
cooling phase of the accident are:
1. Spray heat transfer coefficients
2. Channel wetting during spray operation
3. Reflooding time and heat transfer coefficient.
Other parts of the model suck as decay power and metal-water reaction
are also significant, but are not discussed here. The present experi-
ments were not designed to investigate these parameters because the
geometry change from 7 x 7 to 8 i 8 cannot be expected to change them.
Stiray Heat Transfer Coefficients - Early MCA calculations
used empirical SFray heat transfer coefficients developed by Janssen (7)
wnich were uniform for all rods in the bundle. In the subsequent BWR
Full Length Ei.erger.cy Cooling Seat Transfer (PLSCHT) Prcgr-s^ (3) these
Dune 14
coefficients were improved to reflect differences in the heat transfer
characteristics for individual rods within the bundle.
The BWR FLECHT wer« for the moat part transient simulations of
the emergency cooling phase of the BWR MCA. Most of these tests were
conducted with stainless-stael clad heater rod assemblies modeled after
the BWR 7 x 7 fuel bundle (9i 10, 11, and 12). A smaller number of
transient tests which correctly simulated the Zircaloy fuel rod cladding
material was conducted to check the models developed from the atainleas-
steel tests and to investigate the metallurgical properties of the Zir-
caloy cladding at high temperatures (ll, 13, and 14)4 One of the signi-
ficant roaults of the P1ECHT tests was the development of the spray
cooling models currently in use for 7 x 7 fuel assemblies. Individual
spray cooling convective heat transfer coefficients were calculated for
several rods in the 7 x 7 , full length stainless-steel clad h*attr
bundle (9). Those calculations were later refined (15) and resulted in
the General Electric spray cooling heat transfer correlation presented in
Appendix A, Supplement 1, of Reference 6. The General Electric best
estimate of core spray heat transfer coefficients for 7 x 7 fuel is
repeated in Table 2.
The higher heat transfer coefficients on the outside of the
bundle have been attributed to the fact that these rods are adjacent to
the unheated channel where the density of cooling water can be expected
to be higher than in the center of the array. There haa been some con-
troversy over the best value of heater rod emissivlty to be used in the
reduction of test data to determine the convective heat transfer
Dune 15
coefficients. The General Electric best estimate coefficients were
determined with emissivity equal to 0.6 to 0.7 where the least scatter
in the data was observed (15). The USAEC has directed (l) that a value
of emissivity of 0.9 be used for determining heat transfor coefficients
from the PLECHT data for application to reactor calculations. According-
ly, the values of the convective heat transfer coefficient shown in
Table 2 with emissivity - 0.9 are used for 7 x 7 calculations performed
in accordance with the AEC Interim Acceptance Criteria.
A set of spray cooling heat transfer coefficients was developed
in a similar test program to be described in following paragraphs for use
in calculating the response of 5 x 8 fuel during the 10CA.
Channel Wetting During Scrav Operation - Radiation heat transfer
within the fuel bundle during the emergency cooling phase of the accident
plays a significant role in determining the ultimate thermal response of
the fuel rods. Energy is redistributed among the rods and is ultimately
transferred to the cooler channel. Test channels have been observed to
wet (i.e. to be cooled to saturation temperature) a short time after core
spray initiation. The higher the channel temperature at spray initiation,
the longer it takes to wet (9). After channel wetting occurs, the water
fila on the channel serves as the final heat sink for radiation heat
transfer from the rods. The wetting of the channel appears to be in the
nature of an advancing film proceeding downward from the top of the
channel. The speed of the film's advance is a function of the ehannei
tecperaturs. The staialess-steel and Zircaioy test channel we'ting data
fros -.he FLECK? program were correlated (15; in a manner suggested by
Yaaar.ouchi '16). The channel wetting correlation is presented in
Dune 16
Appendix D of Reference 6.
Reflooding - The calculation of the thermal response of the BWR
fuel bundle when reflooding occurs has changed little during the past
several years. The tiae of reflooding ia calculated using the long tern
tnerBal hydraulics «odel (Appendix B of Reference 6). Convective heat
transfer resulting froa bottoa flooding is conservatively ignored at any
elevation until the plane has been recovered. At that tiae a film
boiling heat transfer coefficient of 25 Btu/h-ft2F is applied to the
fuel rod surfaces.
Dune 17
TABLE 2
Core Spray Convective Heat Transfer Coefficients
Hod Croup
1
2
3
4
For 7 x 7
Location in Bundle
Corner
Next to Channel
One Row froa Channel
Kine Central Rods
Fuel
HTC
f..(Btu/h-ft2P)
.• 0.6 - 0.7
3.03-51.51.5
£i02.0
3.2
1.51.7
(CS Best Estimate) (ASC)
Dune 18
BWR/6 EMERCE8CY CORE COOLIMG TESTS.
A series of 50 transient emergency core cooling testa was con-
ducted in November and December, 1972, with a full scale, stainless-steel
clad mockup of a BWR/6 fuel bundle. Electric heaters were used to simu-
late fuel rods. A constant power was used to heat the teat bundle to
temperatures equal to or exceeding the temperatures calculated to exist
at the time of spray cooling initiation in the BWR/6 loss-of-eoolant
accident. Spray cooling was then introduced at the top of the test
bundle and the electrical power was decayed with time to simulate the
post-accident shutdown decay power. At a later time the test bundle was
flooded from the bottom to simulate the reflooding portion of the acci-
dent. Thermocouples imbedded in the cladding were used to record the
transient thermal response of the test bundle. These transient simula-
tions of the emergency cooling phase of the BWR/6 loss-of-coolant acci-
dent were conducted over a wide range of bundle power, coolant flow rate,
and cladding temperature at the start of emergency cooling.
Using the conservative Interim Acceptance Criteria assumptions,
the maximum BWR/6 fuel cladding temperatures are calculated to be leas
than 1600 P. With realistic assumptions the maximum calculated tempera-
ture is approxiisately 700°P. Test tenperatures higher than 1600°F were
obtained by starting bottom flooding at times significantly later than
those appropriate for the BWR/6 accident. Therefore, the test conditions
conservatively bounded the BWR/6 loss-of-coolant accident.
Dune 19
APPLICATION OP THE EXPERIMENTAL DATA
The General Electric heatup model w*s modified for uae with 8 x 8
geometry and was used to calculate the thermal response of the teat bundle
cladding. Two major pieces of test information war* input to th» computer
program — (l) the cladding temperatures at apr*y Initiation, and (2)
the local power decay of each rod during the transient. The use of the
computer program for the prediction of test data wai somewhat different
from it3 use for reactor calculations. These differences result from
the physical differences between the test bundle and the reactor. The
differences are discussed in the following paragraphs.
The relatively fine noding of the fuel rod us*d in safety analysis
calculations (four fuel nodes enclosed by an inside cladding node which
does not oxidise and an outside cladding node which is oxidized by the
cladding-steam reaction) was not required for this study. This fine
noding is required to track the energy redistribution phase of the acci-
dent when significant temperature gradients exist across the fuel rod.
It is aleo of value in calculating the extent of Zirconium atean reaction
during the course of the accident. 7he energy redistribution phase of
the accident was not simulated in the present tests. Further,the energy
released as a result of the stainless-steel steam reaction is not signi-
ficant at the temperatures considered in the present tests. Therefore,
a single slaidi.".? nods with the heat capacity of the entire neater crsss
39ciaon «as used for the calculations disc-jsssd here. Since an insig-
nificant amount of ciaddisg stean chemical reaction occurred in the tests.
Dune 20
none vas assumed to occur in the calculations. The electrical heat gene-
rated in the heater rod coil was assumed to be uniformly distributed
in the single cladding node modelling each heater rod. The heat input
to the computer program for each heater rod was a somewhat conservative
(low) estimate * ot the haating which actually occurred in the test.
This procedure is significantly different from that employed in the
reactor calculation. The local power used in reactor calculations accom-
plished in accordance with the Interim Acceptance Criteria is estimated
to be approximately 20 to 30$ higher than the most likely value (5).
In the reactor calculation the individual fuel rod cladding tem-
peratures result from the transient solution of the earlier phases of the
accident. The calculations in the present case were started at spray
initiation and the actual test data were used to specify the heater rod
temperatures. la the cases where heater rods were not instrumented,
initial cladding temperatures were estimated from the observed tempera-
tures of similarly powered rods in similar positions in the heater bundle.
The calculation of radiation heat transfer from surface to surface
in the test bundle was accomplished in a manner identical to that used is
•When calculating test temperatures, it is conservative to under-estimate the heat input because this biases the calculation toward lowertemperatures. Ttoeae lover temperatures are then compared with the testdata* In reactor calculations! it is conservative to overestimate theheat input.
Dune 21
reactor calculations. Different grey body factors were used to account
for the differences in surface emissivities between the stainless-steel
heater rod cladding and the Zircaloy fuel cladding. Steady state radia-
tion only teats, in which the test channel was coolid on the outside,
were used to estimate the appropriate heater rod emis3ivity. Radiation
grey body factors consistent with the accurate prediction of bundle
temperature distributions in these steady state radiation only tests,
were used for the transient calculations presented in this section.
Dune 22
COMPARISON OF CALCULATED
AWD OBSERVED TEMPERATURES.
In the BWR/6 reactor loss-of-coolant accident, the hottest plane
is reflooded shortly after rated core spray flow is achieved. Therefore,
it is appropriate to consider the test transients which included bottom
flooding to deteraine the acceptability of the present methods in calcu-
lating the response of BWH/6 fuel.
The best single check on the adequacy of the modified core
heatup model for design safety analysis of the BWR/6 LOCA is a compa-
rison between the maximum calculated cladding temperature and the
maximum temperature observed in tests in which bottom flooding occurred.
Such a comparison is illustrated in Figure 5. The horizontal line on
this figure represents an e.iact prediction of the maximum bundle tempe-
rature. Host of the points fall below that line (one by 125°F), indi-
cating conservative predictions. The four points above the line repre-
sent predictions which are at worst 30cF below the observed maximum
bundle temperature. These results indicate that the aodified sodel ray
be used with confidence for predicting the thermal response of the
BWR/6 fuel under loss-of -coolant/emergency coolir.g situations.
Figure 6 compares the observed peak bundle temperature and the
calculated values for spray only transients. As on Figure 5, the
horizontal line represents an exact prediction of the naxixua bundle
temperature. The predictions are generally within 50°? of the data and
all are within 30°F. Most of tne data fall3 below the exact Dredicticr.
Dune 23
line, indicating conservative predictions of maximum bundle temperature.
One point, representing a 2.0 gpm spray transient with 300kW peak power
(bundle power when top spray is initiated), falls almost exactly on the
line. This indicates that th« modified model is adequate even at spray
rates significantly leas than the design mininun of 5.25 gpo. It can
therefore, be concluded that the modified model is suitable for predic-
ting 8 x 8 assembly maximum temperatures in a postulated LOCA even when
no bottom flooding occurs.
Dune 24
CONCLUSIONS
As a result of the teat data and analysis presented in this
paper and in the topical report (17) documenting this test program, the
following conclusions were reached:
Test Conditions Bounded the BWR/6 MCA - An extensive series of
tests investigating emergency core cooling effectiveness in the BWH/6
fuel geometry have been completed. The test program included a study of
effect of delayed bottom flooding. Maximum BWH/6 cladding temperatures
are less than 1600°F when calculated using Atomic Energy Commission's
Interim Acceptance Criteria assumptions. Maximum temperatures of appro-
ximately 7OG°F are calculated using realistic assumptions. The teat
series was conducted at temperatures exceeding 1600°F by delaying the
onset of bottom flooding. Therefore, the test conditions conservatively
bounded the BWR/6 LOCA.
ECCS la Effective In the 3 x 8 Geometry - The teat data indicate
that top spray and bottom flooding modes of ECCS are effective means of
controlling the LOCA transient in the 8 x S BWH/6 fuel geometry.
OE Core Heatup Model With S z 8 .Modifications la Appropriate -
The results of tests which simulated the emergency cooling phase of the
BWH/6 LOCA transient were predicted using the General Electric core heat-
up model as modified for the 8 x 8 geometry. Predicted maximum test
bundle temperatures generally exceeded those observed. The maximum
underprediction was 30°F. Therefcre, the modified nodel is appropria-.a
for calculating- the results of the postulated accident in the BWR/6,
Dune 25
and Reactor Safety Analysis Report calculations using the modified model
and Interim Acceptance Criteria assusptions are justified. This aeries
of tests provides support for these calculations, and further confirma-
tory testing is not required.
The results of transients which simulated the accident with no
bottom flooding were also predicted. These transients simulated the
LOCA in a non-jet pump EWE. Predicted bundle maximum temperatures foro
these conditions were within 90 P of the observed values and were usually
above them. Therefore, the modified model is suitable for this type of
plant where no bottom flooding occurs.
Dune 26
REFERENCES
1. USAEC, "Criteria for Emergency Core Cooling Systems for Light-Water Power Reactors", Federal Register, 36, June 29, 1971.
2. B.C. Broeneveld, "An Investigation of. Heat Transfer in the LiquidDeficient Regime", (AECL-3281).
3. E.E. Polomik, "Deficient Cooling", July, 1972, (GEAP 10221-12).
4. G.W. Burnette, et. al.. "Blowdown Heat Transfer Program Task C-lInformal Report, Preliminary Systea Design Description of Two-LoopTest Apparatus", March, 1972, (GEAP 13276).
5. G.J, Scatena and G.L. Upham, "Power Generation in a BWH FollowingNormal Shutdown of Loss-Of-Coolant Accident Condition", March, 1973,(NEDO 10625).
6. B.C. Slifer, "Loss-Of-Coolant Accident and Emergency Core CoolingModels for General Electric Boiling Water Reactors", April, 1971,(HEDO 10329).
7. E. Janssen, et. ai., "Core Spray Test Program, Browns FerryNuclear Power Station Design and Analysis Report", Appendix S,1965,
8. J.D. Duncan and J.E. Leonard. "Emergency Cooling in BWR's UnderSimulated Loss-Of-yoolant Conditions", June, 1971, (GBAP 13197).
9. J.D. Duncan and J.E. Leonard, "Heat Transfer in a Simulated BWRFuel Bundle Cooled by Spray Under Loss-Of-Coolant Conditions",(GEAP 13086).
10. J.D. Duncan and J.E. Leonard, "BWR Standby Cooling Heat TransferUnder Simulated Loss-Of-Coolant Conditions Between 15 and 300 psia".May, 1971, (GEAP 13190)
11. J.D. Duncan and R.O. Bock, "The Performance of Molybdenum Fila-mer.ts in BWR Emergency Cooling Heat Transfer Tests", November,1969. (GEAP 13086).
12. J.D, Duncan and J.E. Leonard, "Response of a Simulated 3'«R FuelBundle Cooled by Flooding Under Loss-of-Coolsnt Conditions",December, 1969, (ttEAP 10117).
13. J.D. Duncan and J.E. Leonard, "Thermal Response =nd Cladding Per-formance of an Internally Pressurized, Zircaloy-Clad, SimulatedBWR Fuel BWidle Cooled by Spray Under Loss-Of-Coolant Conditions",April, 1971, (5EAF 1J122,
Dune 27
14. J.D. Duncan and J.3. Leonard, "Thermal Response and CladdingPerformance of Zircsloy-Clad Simulated Fuel Bundles Under HighTemperature Lo9s-0f-Coolant Conditions", May, 1971, (GSAP 11174).
15. A.E. Rogers and J.S. Leonard, "An Analytical Model of the Tran-sient Core Spray Cooling Process"; Distributed at the December,1971, A,I, ChE Meeting Symposium on Heat Transfer in Water CooledNuclear Reactor Systems.
16. A. Yamanouchi, "Effect of Core Spray Cooling in Transient StateAfter Loss-Of-Coolant Accident", Journal of Nuclear Science andTechnology, 5. 11. pp. 547-558, November, 1968.
17. J.D. Duncan and J.S. Leonard, "Core Spray and Bottom FloodingEffectiveness in the BWR/6", September, 1973, (KEDO 10993).
mSTUKJEPMUTMAMKHEATER
HEATERS
Figure 1 . Direct Cycle feictor System.
Dune 70Dune 31
STEAM DRYERSMAIN STEAM FLOW
TO TURBINE
MAIN FEED FLOWFROM TURBINE
I- —::—-<
LOWER PUNUH
• Figure 3. Steam and Red rail ati on Water Flow Paths.l O Qi O O i: c BE
l i :M:
155
Ifi8
Idol 3UniVU3dW3X dN
ENGE 1
gg .too
if
UNDER PREDICTIONS
EST CONDITIONSaf SPRAV*ATE-3.0|fi>ii9 (LOOOING RATE - I S l o t O i g i« FLOODING WATER AT IOTTOM
OF HEATED LENGTH 46 10 SIS *• PEAK POWER - 100 kW
OVER PREDICTIONS
OBSERVED MAXIMUM•UNDLE TEMPERATURE
MAXIMUM TEMPERATUREIN COMBINED SPRAY
AND FLOODING TRANSIENTS
Figurt 5 Compatiton ofPndicndtnd Obsanmt Bundla Faak Cladding Umptrtiurta in
Combinad Spray and Flooding Transoms
UNDER PREDICTIONS
OVER PREDICTIONS
3gp«> SPRAY 300 KM
• • • *
TEST CONDITIONS• SPRAY RATE4 NO FLOODING# PEAK POWER
3.0 tun
» 0 k W
OBSERVED MAXIMUMBUNDL £ TEMPERATURE
MAXIMUM TEMPERATUREIN3gpmS»KAY
ONI Y TRANSIENTS
Figura 6 Comparison of Pndicted and Ob&rv* 1 Bundle Peak Cladding Temperaturas in
Spray Only Transients
TITLE
AUTHORS
CONFERENCE OS HEAT TRANSFER AND THE DESIGN ANDOPERATION OF HEAT EXCHANGERS
DEVELOPMENT OP A CONTINUOUS PROCESS FOR CONCEN-TRATION OF ALUMINIUM SULPHATE SOLUTIONS IN ACLIMBING FILM EVAPORATOR
BNGELBRECHT, A.D. *nd HUNTER, J.B.Technical Dtpurtmenc, AE&CI Limited, Johannesburg.
APRIL 1974
SOUTH AFRICAN INSTITUTION OF CHEMICAL ENGINEERS