Research Journal
J
of Appllied Sciences, Engineering annd Technologyy 5(1): 332-3388, 2013
ISSN: 2040-7459; e-ISSN
N: 2040-7467
© Maxwelll Scientific Orrganization, 2013
Submitted:: June 28, 2012
2
Accepted: July 19, 20012
Publisheed: January 01, 2013
Effect of
o Heat up Rate
R
on Theermal Stratiification in Horizontal
H
P
Pipe
Athar Rasool,
R
Sun Zhongning
Z
annd Wang Jianjjun
College of Nuclear
N
Sciennce and Technnology, Harbiin Engineering University, Harbin,
Heilongjiaang 150001, China
C
Abstract: The study is performed to analyze the efffects of heat up
u rate on thermal stratificaation phenomennon in
pressurizerr surge line. Th
he horizontal section
s
of presssurizer surge line
l
is consideered for this stuudy since significant
thermal strratification is usually
u
observeed in horizontall sections of thhe pressurizer surge
s
line. The tendency of thhermal
stratificatioon reduces witth increasing flow
f
rates baseed on which four
f
cases of heat
h
up rates with
w increasingg flow
velocities are analyzed. The selected flow
f
velocitiess of 0.01, 0.05, 0.1 and 0.2 m/sec for the study are calcculated
from the operating rangee of dimensionlless Froude nuumber 0.02-0.22 of pressurizedd water reactorr type nuclear power
plants. Thee horizontal pip
pe model innerr diameter is 3005 mm with thickness of 33.55 mm and lenggth of four diam
meters.
The Richaardson number for the four cases
c
is greateer than unity and
a thermal strratification is likely to occuur. The
transient analysis
a
is performed using commercially available sofftware ANSYS
S CFX. The trransient tempeerature
distributionn along the horizontal
h
pipee wall with different
d
heat up
u rates is reepresented in this
t
study. Thhermal
stratificatioon reduces with
h increase in heat
h up rate or flow
f
velocity.
Keywordss: Pressurizer surge
s
line, reactor heat up ratee, RNG K-Eturrbulence modeel, thermel strattification
INTRO
ODUCTION
Pressuurized Water Reactor (PWR
R) type Nucleear
Power Plannt (NPP) has been widely useed as commerccial
power souurce. Pressurizer is a key coomponent of the
t
primary looop of a PWR. It
I controls and compensates the
t
pressure annd volume surges in the prrimary loop. The
T
pressurizerr is connected with the hot leeg of the primaary
loop throuugh pressurizerr surge line making
m
it a viital
part. Any damage
d
to the pressurizer
p
surrge line influennce
the integriity of primary
y loop and hennce hampers the
t
operation of NPP. A scchematic diaggram of PWR is
depicted inn Fig. 1.
Thermal stratification
n: Thermal stratification in
pressurizerr surge line is well
w known phhenomena. Whhen
during in-ssurge or out-su
urge hot fluid from hot leg or
pressurizerr flows in the pressurizer suurge line alreaady
occupied with
w the cold fluid,
f
distinct layers
l
of fluidd is
formed duue to density
y difference. Such flow is
categorizedd as thermally
y stratified flow
w and the relatted
phenomenoon is known as
a thermal strattification (IAE
EA,
2003).
Fig. 1: Schematic diaagram of Pressuurized Water Reactor
R
(PWR)
thermall stratification is usually observed in horiizontal
sectionn of the presssurizer surge line, since vertical
v
portionn is near to the pressurizer and
a there is enough
e
mixingg in the sections with varying
v
slopess and
curvatuures.
h a complex geometry it ruuns
Pressurizeer surge line: has
down from
m the pressurizeer till the hot leg
l vertically and
a
horizontallly with varyin
ng slopes andd curvatures. A
generic pressurizer surgee line layout is depicted in
Fig. 2. Greebner and Hofleer (1995) indiccated that the
PWR operating coonditions: Thhe PWR typee NPP
operatees at high preessure and tem
mperature (15.55 MPa
Correspond
ding Author: Athar
A
Rasool, College of Nucleear Science and Technology, Haarbin Engineerinng University, Harbin,
H
Heilongjiang
H
1500001, China
332
Res. J. Appl.
A
Sci. Engg. Technol., 5(11): 332-338, 20013
expansion (β), tem
mperature diffference (ΔT)) and
charactteristic length (D) and inverrsely proportioonal to
the squuare of flow velocity (v). The expressioon for
Richarddson number (R
Ri) is given below:
Ri
Fig. 2: Layoout of pressurizeer surge line
and 345°C
C). Shah and Co
onley (1989) discussed
d
that the
t
temperaturre difference between
b
the hoot leg fluid of the
t
primary loop and the preessurizer fluid can
c be as high as
180ºC duriing heat up. Th
he magnitude of the maximuum
temperaturre difference depends on the pressure at
which a stteam bubble forms
fo
in the prressurizer duriing
heat up annd the pressuree at which thee reactor coolaant
pumps aree started. Prior to start of thee reactor coolaant
pumps, thee temperature of the coolant in the hot legg is
typically 54ºC and the teemperature of the
t coolant in the
t
pressurizerr can be as hig
gh as the saturaation temperatuure
218ºC, whhich correspon
nds to the minnimum pressuure,
typically 2.24
2
MPa at wh
hich the reactoor coolant pum
mps
can be opeerated. Grebneer and Hofler (1995)
(
discusssed
that the tem
mperature diffeerence betweenn the hot leg fluuid
of the prim
mary loop and the pressurizeer fluid can be as
high as 1500°C during heaat up phase.
Shah and Conley (1989)
(
mentioned potential of
thermal strratification is greatest
g
during heat up and coool
down phasses of reactor operation
o
becauuse the differennce
between thhe pressurizerr and hot leg temperatures is
largest theen. Similarly, (Kang
(
and Jo, 2010) discusssed
that the significant thermal stratiffication in the
t
pressurizerr surge line occcurs in the 2 modes
m
of reactor
operation starting
s
up phaase (heat up) att the reactor coold
shut downn condition and cooling-dow
wn at the norm
mal
operation condition.
c
Thiss makes both reactor
r
operatiion
modes boounding cases in terms of temperatuure
gradients caused
c
in the wall
w of the surge line.
Non-dimensional param
meters: The surge
s
lines weere
w
the assum
mption that the coolant surgges
designed with
would sweeep the whole cross section of the surge liine
piping buut the actual flow pattern appears to be
stratified (Shah and Conley,
C
1989). The therm
mal
stratificatioon can be deefined with thhe help of noondimensionaal parameters like Richarddson or Frouude
numbers.
Richardsoon number: Iss a non-dimenssional parametter,
which is directly
d
proporrtional to Gravvity (g), therm
mal
gβΔTD/v
(1)
Whhen 2 fluids at different temperatures flow
throughh a space, the convection
c
typpe can be deterrmined
based on the magniitude of the Richardson
R
nuumber.
Shah and
a
Conley (11989) mentionned the presennce of
stratifieed flow for Ricchardson numbber greater thann unity
and Kaang and Jo (2010) mentionned for Richaardson
numberr above 10 thee natural conveection dominattes the
flow field
f
and a strongly strattified flow caan be
maintaiined until eiither the tem
mperature diffe
ference
decreasses or the floow velocity inncreases enouugh to
lower the
t value of Richardson
R
nuumber below 0.1 or
less.
Froudee number: Is
I a non-dimeensional paraameter,
which is directly prooportional to fllow velocity (vv) and
inverseely proportional to the tem
mperature diffe
ference
(ΔT). Taupin
T
et al. (1989) and Ensel
E
et al. (1995)
(
perform
med test for thhermal stratificcation in presssurizer
surge line
l
and reveaaled that tempperature profilee in a
stratifieed cross sectioon is mainly correlated
c
to Froude
F
numberr, depending on the flow
w velocity annd the
temperature differencce between hott leg and pressuurizer.
The exppression of Frooude number (F
Fr)is given bellow:
Fr
⁄
with
2
(2)
where, ρ is the fluuid density at hot leg (HL
L) and
pressurrizer (PZR) tem
mperature. Abbove critical Froude
F
numberr for high flow
w velocities strratification vannishes.
XYZ mentioned
m
that the pressurizeed water reactoor type
nuclearr power plant operates in thhe range of Froude
F
numberr 0.01 to 0.2. The damagee to the presssurizer
surge line due to thermal strattification has been
reporteed since 1988 (NRC, 1988a, b, c). IAEA (2003)
(
mentionned that high temperature
t
diffference in exiistence
of therrmal stratificaation can conssiderably affect the
integritty of the presssurizer surge liine. Initially thhermal
stratificcation effects have not beenn considered in the
design of NPP. Hoowever, the new design off NPP
incorpoorates the effects of thermal stratifiication
phenom
menon to thhe pressurizerr surge linee and
subsequuently is part of
o safety analyssis report. Therrefore,
it is necessary
n
to analyze
a
and evvaluate the thhermal
stratificcation phenom
menon in presssurizer surge line
l
of
PWR. Kang and Joo (2008) highhlighted that many
researchers and scienntists have ussed various meethods
and teechniques to annalyze this pheenomenon. How
wever
333 Res. J. Appl.
A
Sci. Engg. Technol., 5(11): 332-338, 20013
Table 1: Propperties of pipe material and fluid
Values
Parameters
Pipe Materiial
ASME SA--312
Pipe inner diameter
d
(ID)
305 mm
Pipe thickneess (t)
33.5 mm
Density
m3
8000 Kg/m
16.3 W/m-K
K
Thermal connductivity
Specific heaat capacity
500 J/kg-K
Thermal exppansivity
17e-6 /K
Fluid (waterr)
IAPWS IF997
Fluid Initiall Temperature
51.7 C
Fluid Inlet Velocity
V
0.05 m/sec
Fluid Inlet Velocity
V
0.05 m/sec
Reynolds nuumber
0.283x105 - 1.05x105
The trransient tempperature distrribution alongg the
horizonntal pipe wall for
f the reactor starting up (heeat up)
phase at
a reactor coldd shutdown coondition is anaalyzed
and reppresented.
EL DESCRIPT
TION
MODE
Geomeetric configu
uration and properties: The
dimenssions of horizoontalpipe are selected
s
on thee basis
of surgge line dimenssions. Generallly pressurizer surge
line is 250 to 350 mm
m diameter stainless steeel pipe
(Shah and Conley, 1989). The geeometrical datta and
propertties of pipe material andd fluid are givven in
Table 1.
1 IAPWS IF977, built in ANS
SYS CFX, is utilized
u
for fluid properties inn calculations (A
ANSYS, 2010a).
Thhe horizontal pipe
p
geometry configuration along
with loocation of monnitoring points (top to bottom
m inner
and outter surface) andd planes (at disstance 1D to 3D) are
depicteed in fig. 3.
Fig. 3: Horrizontal pipe laayout and location of monitoriing
poiints and planes
with the breakthrough
b
in
i computer technologies
t
a
and
advert of parallel
p
processing it has beeen made possibble
to simulatee such complex
x phenomena.
The sttudy is perform
med to evaluaate the effects on
thermal stratification
s
in horizontaal sections of
pressurizerr surge line wiith increasing heat
h
up rate. For
F
the same 4 cases based on increasing fllow velocities are
a
consideredd. The horizon
ntal pipe moddel is simulatted
using com
mmercially avaailable software ANSYS CF
FX.
Table 2: Frouude number for fou
ur cases
C)
Temperature (°C
Dia.
----------------------------------D (m)
TC
TH
Case 1
218
0.35
51.7
Case 2
0.35
51.7
218
Case 3
0.35
51.7
218
Case 4
0.35
51.7
218
Probleem Statement:: In the presennt problem, 4 cases
with diifferent flow veelocities basedd on general rannge of
Froudee number for PWR
P
type NPP given in Taable 2,
are connsidered. The flow is strattified based on
o the
Richarddson number range
r
for 4 casses given in Taable 3,
thus, thhe buoyancy force
f
will stronngly affect thee flow
field. Initially cold fluid
f
at a specified temperatture of
51.7ºC occupies thee horizontal pipe
p
maintainning a
steady state conditionn. Then at a certain time hot fluid
at a specified temperrature of 218ºC
C begin to flow
w into
the horrizontal pipe, a typical out surrge case. The pipe
p is
horizonntal with one inlet
i
and outleet. The fluid fllow in
the horrizontal pipe reemains turbuleent for the fourr cases
as the Reynolds num
mber range iss large as shoown in
Table 1.
1 The turbulennt flow behavioor is considered with
the RN
NG K-E turbulence model. (K
K-E, RNG K--E and
SST). For
F buoyancy calculations thhe density diffe
ference
is evaluuated directly using full buuoyancy model. The
referennce pressure is equal
e
to 2.24088 Mpa.
Density (kg/m3)
D
---------------------------------ρC
ρH
9
988.3
8442.78
9
988.3
8442.78
9
988.3
8442.78
9
988.3
8442.78
Table 3: Richhardson number fo
or four cases
Temperaturre (°C)
Dia.
----------------------------------------D (m)
TC
TH
Case 1
0.35
51.7
218
Case 2
0.35
51.7
218
Case 3
0.35
51.7
218
Case 4
0.35
51.7
218
Acc.
(m/s2) g
9.81
9.81
9.81
9.81
334 Acc.
(m
m/s2) g
9.881
9.881
9.881
9.881
Expansion
Coefficient
(1/K) β for ΔT
Δ avg
9.63×10-4
9.63×10-4
9.63×10-4
9.63×10-4
Velociity
(m/s) v
0.01
0.05
0.10
0.20
Velocityy
(m/s) v
0.01
0.05
0.10
0.20
Froude
numberr (Fr)
0.014
0072
0.145
0.29
Richardson
number (R
Ri)
4696
187
47
11
Res. J. Appl.
A
Sci. Engg. Technol., 5(11): 332-338, 20013
Boundaryy Conditions: The solution domain consiists
of horizonttal pipe, which
h can be further subdivided innto
two sub domains,
d
fluid and solid dom
mains. The fluuid
domain coonsists of flow
w field inside horizontal pippe.
The solid domain
d
consistts of the regionn bounded by the
t
inner and outer
o
wall surfa
faces of horizonntal pipe. To taake
into accouunt the Fluid
d Structure Innteraction (FS
SI)
Conjugate Heat Transfer (CHT) analysiis is incorporatted
into the CF
FD analysis. In
n solid domainn, where theree is
no flow and
a
conductio
on is the onlyy mode of heeat
transfer, thhe conservation
n of energy eqq. is simplified as
the unsteaady heat con
nduction eq. The Unsteaady
Reynolds Averaged Navies
N
Stokess equations for
f
conservatioon of mass, mo
omentum, enerrgy and turbuleent
quantities used in this study can bee expressed inn a
Cartesian coordinate sysstem as in refe
ference (ANSY
YS,
2010a; Whhite, 1991)
CFD analyysis:
Model Meesh: To simullate the flow as accurately as
possible both flow and fluid solid intterface boundaary
hed using ANS
SYS ICEM. The
T
regions aree finely mesh
grid densitty along the pip
pe length is less fine comparred
with radiaal or circumferrential directioons as shown in
fig. 4.The fluid and sollid domain is discredited innto
e
in fluuid
43,065 hexxahedral elements (30,537 elements
domain annd 12,528 eleements in soliid domain). The
T
hexahedrall elements typee grid scheme is used due to its
more realiistic results. The overall mesh
m
quality is
greater thaan 0.65 on thee scale from 0 to 1 based on
ANSYS IC
CEM mesh quality criteria (A
ANSYS, 2010b).
The aspecct ratio, edge length ratio, element volum
me
ratio and mesh expansio
on factor lies well within the
t
YS,
specified criteria based on ANSYS CFX (ANSY
T
2010a). Thhe same mesh is used for all simulations. The
first node distance is approximated
a
on the basis of
boundary layer thicknesss for pipe (δ = 0.0324 D Re
R 0.875
) and the
t boundary layer is resolveed using over 10
nodes. Thee overall grid expansion ratiio of 1.2 is ussed
Rasool et al. (2012). Th
he same meshh is used for all
cases.
TS AND DISCU
USSION
RESULT
Thhe transient progressionss of tempeerature
differennce between thhe top and bottom inner waall and
outer wall
w surfaces of
o horizontal piipe at a distannce 2D
for diff
fferent heat upp rates are deppicted in Fig. 5& 6,
respecttively.
Thhe top to bottom
m inner wall surfaces
s
tempeerature
differennce is large in the beginning and quickly reeduces
and later on progresssively stabilizees almost to unniform
temperature differencce for each casee.
Thhe top to bottom
m outer wall surfaces
s
tempeerature
differennce increases initially and progresssively
decreasses with the elaapsed time.
Inner wall
w surfaces:: The large tem
mperature diffe
ference
initiallyy between the inner wall suurfaces of horiizontal
pipe is due to the flow
w of hot fluid (218°C) in horiizontal
pipe alrready occupiedd with cold fluiid (51.7ºC). Thhe hot
0.01 m/s
0.05 m/s
0.1 m/s
m
0.2 m/s
m
1800
1600
1400
Temperature ( C)
Fig. 4: Horizontal pipe grid scheme and gridd density
Probleem setup: The governinng equationss are
discreddited using the finite volume approach. Thee CFD
calculaations are perfo
formed for totaal time of 10000 sec
with tim
me step size of 0.1. The turbbulent flow behhavior
is simuulated using RNG
R
K-E turbuulence model. Flow
near wall is treated using
u
scalable wall functionss, 1 of
the built in user optioons in ANSYS
S CFX. Heat trransfer
in fluidd and solid dom
mains is simullated using tottal and
thermall energy optioons respectiveely in ANSYS
SCFX,
consideering both connduction and convection inn fluid
domainn and conduuction in soolid domain. The
conservvative interface flux option is selected foor heat
transferr between fluid and solid. High resoolution
advectiion scheme and 2nd ordeer backward Euler
transiennt scheme is used. The convergence criteriion for
all majjor parameterss is determined at each tim
me step
when RMS
R
residual is
i less than 100-3. The converrgence
condition is met afterr 3 or 4 iteratioons at each timee step,
except for the initial time
t
steps whiich requires upp to 10
or moree iterations.
o
1200
1000
800
600
400
200
0
0
200
400
6000
Time (sec))
800
1000
Fig. 5: Transient progrressions of tempperature differennce for
d
different
heat upp rates betweenn top and bottom
m inner
w surfaces of cross section at a distance 2D
wall
335 Res. J. Appl. Sci. Eng. Technol., 5(1): 332-338, 2013
100
0.01 m/s
0.05 m/s
0.1 m/s
0.2 m/s
fluid having lesser density settles in the upper region of
the horizontal pipe thus elevating the top inner wall
surface temperature and resulting in large top to bottom
temperature difference. The primary mode of heat
transfer between fluid molecules is convection which is
much quicker thus sharply reduces the top to bottom
inner wall surfaces temperature difference. The hot
fluid inflow is constant which keeps on increasing the
bulk fluid temperature and thus progressively
increasing the bottom inner wall surface temperature
which in result reduces the top to bottom inner wall
surfaces temperature difference.
90
Temperature (°C)
80
70
60
50
40
30
20
10
0
0
200
400
600
Time (sec)
800
Outer wall surfaces: The less quick progression of top
to bottom outer wall surfaces temperature difference
than top to bottom inner wall surfaces temperature
difference is due to the mode of heat transfer. The heat
transfer between the inner wall surfaces to the outer
wall surfaces is only through conduction whereas
convection takes place
1000
Fig. 6: Transient progressions of temperature difference for
different heat up rates between top and bottom outer
wall surfaces of cross section at a distance 2D
(a)
250
TIS
TOS
BIS
BOS
(b)
250
TOS
BOS
200
Temperature (°C)
Temperature (°C)
200
150
100
50
150
100
50
0
0
0
200
400
600
Time (sec)
800
1000
0
200
250
400
600
Time (sec)
800
1000
(d)
250
(c)
200
Temperature (°C)
200
Temperature (°C)
TIS
BIS
150
100
50
TIS
TOS
BIS
BOS
150
100
50
0
0
0
200
400
600
Time (sec)
800
TIS
TOS
0
1000
200
400
600
Time (sec)
800
1000
Fig. 7: Transient progressions of Top Inner Surface (TIS), Top Outer Surface (TOS), Bottom Inner Surface (BIS) and Bottom
Outer Surface (BOS) temperatures for different heat up rates, (a) 0.01 m/s, (b) 0.05 m/s, (c) 0.1 m/s, (d) 0.2 m/s along
cross section at a distance 2D
336 Res. J. Appl.
A
Sci. Engg. Technol., 5(11): 332-338, 20013
Fig. 7: Traansient temperatture distributionns along the cross
secction at a distance 2D at elapsed time of 100 sec
Fig. 8: Trransient temperatture distributionns along the crosss
sectioon at a distance 2D
2 at elapsed tim
me of 200 sec
between fluid
f
moleculees and is mucch quicker thhan
conductionn. The bulk
k fluid tempperature slow
wly
progresses towards un
niformity whhich results in
comparativvely large top to bottom outter wall surfacces
temperaturre difference. The top to boottom outer wall
w
surfaces teemperature diffference signifiicantly decreasses
towards thhe end of simu
ulation period as the bulk fluuid
temperaturres reaches hom
mogeneity.
Figuree. 7 depicts thaat with the inccrease in heat up
rate the innner wall surfaaces temperatuures approach to
homogeneiity and simillarly the outeer wall surfacces
temperaturre exhibits thee same trend.. Thus with the
t
increase inn heat up ratte top to botttom temperatuure
difference reduces.
Fig. 9: Transient tempperature distribuutions along thee cross
section at a disttance 2D at elappsed time of 400 sec
Fig. 10:: Transient tempperature distribuutions along thee cross
section at a disttance 2D at elappsed time of 10000 sec
Thhe transient temperature disttributions alonng the
cross section
s
at a distance
d
2D at elapsed time of
o 100,
200, 4000 and 1000 sec
s for differeent heat up rattes are
depicteed in Fig. 8, 9, 10 and 11, reespectively. It can
c be
observeed that with thee increase of heat
h up rate the top to
bottom
m temperature difference
d
reduuces. The maxximum
top to bottom
b
temperrature differencce is observed at low
flow veelocity of 0.011 m/sec for whhich the Richaardson
numberr is very high as shown in Table
T
3, whereaas it is
minimuum at flow veelocity of 0.2 m/sec
m
for which the
local Richardson
R
num
mber is close too unity.
337 Res. J. Appl. Sci. Eng. Technol., 5(1): 332-338, 2013
CONCLUSION
A simple horizontal pipe is considered to study the
effects of heat up rate on thermal stratification of
pressurizer surge line of PWR. The turbulent behavior
of fluid flow is analyzed with RNG K-E turbulence
model. The temperature distribution along the cross
section is highly dependent on flow velocity and with
increase of heat up rate top to bottom temperature
difference reduces quickly with elapsed time. The
maximum top to bottom inner and outer wall surfaces
temperature difference is obtained for flow velocity of
0.01 m/sec and minimum top to bottom inner and outer
wall surfaces temperature difference is obtained for
flow velocity of 0.2 m/sec. Hence at low flow velocities
the flow is highly stratified and the tendency of
stratification reduces with increase in heat up rate. The
results obtained verify the dependency of stratified
flows on Richardson number.
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including stratification effects. J. Nucl. Eng.
Design, 153: 197-203.
Grebner, H. and A. Hofler, 1995. Investigation of
stratification effects on the surge line of
pressurized water reactor. Comput. Struct., 56-2:
425-437.
IAEA, 2003.Assessment and management of ageing of
major nuclear power plants components.
Kang, D.G. and J.C. Jo, 2008. CFD analysis of
thermally stratified and heat transfer in a PWR
surge line. Proceedings of Pressure Vessel and
Piping Division Conference, July 27-31, Chicago,
Illinois, USA.
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