Journal of Applied Mathematics and Physics, 2013, 1, 74-81
Published Online November 2013 (
Open Access JAMP
Numerical Simulation of PRHR System B ased on CFD
Bin Jia, Jianping Jing, Xuedong Qiao, Chunming Zhang
Nuclear and Radiation Safety Center, Beijing, China
Received September 2013
In this paper numerical simulation of PRHR HX and IRWST is demonstrated using FLUENT, and different numbers of
C-type heat transfer tubes and coolant inlet temperatures effects for the residual heat removal capacity of PRHR HX,
IRWST thermal stratification and natural circulation have been researched. Its found that at a con stant flow area when
heat transfer tubesnumber increased outlet temperature of PRHR HX is lower, the whole water temperature of IRWST
is higher, thermal stratification and natural circulation are more oblivious. At a constant mass flow when inlet
temperature of PRHR HX increased, inlet flow velocity increases and outlet temperature is higher. But on the other
hand the cooling rate increases at the same time, the average temperature of IRWST is higher, the range of thermal
stratification expands and the velocity of natural circulation increases.
Keywords: PRHR HX; IRWST; Numerical Simulation; FLUENT ; C-Type Heat Transfer Tubes
1. Introduction
Introducing passive concept into safety systems is typical
character for the 3rd generation nuclear power plant.
Currently many reactors under construction or under de-
sign use lots of this advanced concept both domestically
and abroad.
AP1000 passive residual heat removal system [1]
(PRHRS) is one of the important passive safety systems,
it can take the advantage of the coolant density difference
between in-core and C-type heat transfer tubes of passive
residual heat removal heat exchanger (PRHR HX) as a
driving force to establish natural circulation , and transfer
heat to in-containment refueling water storage tank
(IRWST) through PRHR HX, then remove the residual
heat in the core under accident conditions and ensure the
safety of the reactor. As two key devices in the system
PRHR HX and IRWST directly affect whether the resi-
dual heat in the core can be removed under accident con-
ditions, so it’s necessary to research PRHR HX heat
transfer performance and IRWST internal thermal strati-
fication and natural circulation.
With advances in computer hardware technology and
rapid development in computational fluid dyn a mics (CF D) ,
it has become a very effective techniques that using nu-
merical simulation to carr y out fluid flow and heat trans-
fer research for various heat exchangers [2,3]. Therefore
in this paper numerical simulation for PRHR HX and
IRWST has been taken via Fluent software, and our fo-
cus is the effect for PRHR HX heat transfer performance
and IRWST internal thermal stratification and natural
circulation when the C-type heat transfer tubes’ number
or the coolant inlet temperature changes.
2. Research Subjects and Mathematical
2.1. Research Subjects
In this paper AP1000 is seen as an example designed by
Westinghouse, its PRHR HX is consisted of 689 bundle
arran ged C-type heat transfer tubes, inlet head and outlet
head. Heat exchanger is submerged in IRWST, and it can
remove residual heat from core by transferring it to
IRWST in operation. In Table 1 parameter [1,4,5] of
IRWST and PRHR HX are listed, Figure 1 is the P RHR
syste m diagram.
Firstly on the basis of AP1000 PRHR HX various
geometric, operating design parameters modeling and
calculation are carried out. Though PRHR HX is con-
sisted of lots of heat transfer tubes, but each tube’s heat
transfer process is relatively independent, heat transfer
mechanism is the same. To reduce the amount of com-
putation and research the effects of different number of
C-type heat transfer tubes for PRHRS operation, and on
the basis of total flow area unchanged and through
changing tube size, physical models of 8-tube and
16-tube heat exchangers submerged in cubic IRWST are
built respectively, as showed in Figure 2. Then on the
basis of calculation result of 16-tube model at design
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Table 1. Parameters for IRWST and PRHR HX of AP1000.
parameter number parameter number
Minimum water capacity(m3) 2092 Heat load(J/s) 5.89E+07
Actual water capacity(m3) 2132 Design flow(kg/h) 2.28E+05
Design pressure(Mpa) 0.034 (Measurin g) Inlet water temperature() 297.2
Design temperature() 65.6 Outlet water temperature() 92.8
IRWST initial temperature() 48.9 Design pressure(Mpa) 17.1 (Measuring)
Normal depthmm 8534.4 Heat exchanger inlet pressure(Mpa) 15.5
Nominal depthmm 8778.2 Design temperature() 343.3
Material Stainless steel Number of heat transfer tubes 689
Size of heat transfer tubes(mm) 19.05*1.65
Spacing of heat transfer tubes(mm) 38
Material 690Alloy
Figure 1. Schematic diagram of PRHR system.
operating condition, through changing coolant inlet tem-
perature to research the effects for heat exchanger per- formance and IRWST stratification phenomena and nat-
ural circulation and master the law for much more heat
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(a) (b)
(c) (d)
Figure 2. Diagram of system model, (a) and (b) for 8 tubes, (c) and (d) for 16 tubes.
transfer tubes modeling and calculation in future.
2.2. Mathematical Models
Since there is a big temperature difference between water
in heat exchanger C-type tubes and water in IRWST,
turbulence phenomenon will happen in the heat exc ha nge r .
Because of that, to close the Reynolds-averaged N - S eq-
uations, a turbulence model is necessary and k - ε equation
is used, the corresponding equations are as follows [6,7].
Continuity equation:
( )
+∇ =
Momentum equation:
uuu f
ρ ρσ
+ ∇=+∇
Energy equation:
( )
cu Tpu
λρ φ
+ ∇+∇
= ∇∇+−∇+
k - ε equation:
j kj
ρεµ σ
=−+ +
tx kk
ρεξ ξ
In the formula: Sm is the source term, u is the flow
velocity, λ is the thermal conductivity, qr is the heat
transfer. For the k-ε equation, k and ε are turbulent kinet-
ic energy and turbulent dissipation rate, Pt is the turbu-
lent kinetic energy production term, μt is the turbulent
viscosity coefficient, model constants are: Cξ1 = 1.44, Cξ2
= 1.92, σk = 1.0, σε = 1.3, Cμ = 0.09.
As the temperature of the coolant through the heat ex-
changer will be drastically reduced, while the refueling
water tank will be heated, water temperature changing
will directly cause changing in density, thereby affecting
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the entire natural circulation and heat transfer process. So
water density varied with temperature udf relation [8] is
introduced into material properties table in FLUENT
program. Since the density of water reaches the maxi-
mum at 3.98˚C atmospheric pressure, density and tem-
perature parabolic relation are selected:
In the formula: ρ0 is the maximum value of water den-
sity, T0 is the water temperature at the same time, γ is the
thermal expansion coefficient. Although PRHR HX de-
sign pressur e is 16.9 Mpa, design temperature is 297.2˚C,
and the IRWST runs at atmospheric pressure, the design
temperature is 48.9˚C. However after verification, it’s
found that thermal expansion coefficients at two condi-
tions are very close, with little effect on the calculation,
the final γ is selected as 3.1e6.
3. Simulation Results
3.1. Effect of Different C-T ype Heat Transfer
Tubes Number
At design parameters 8-tube and 16-tube heat exchanger
models outlet temperature is demonstrated in Table 2,
tube number is according to system model Figure 2 from
left to right and from top to bottom in order. It can be
seen from both sets of data that because of long stroke
for outer tubes, their cooling effect is better than inner
ones’. Though comparing it’s found that whether the
characteristic tube or the average value the outlet tem-
perature of 16-tube model is obviously lower than 8-tube.
The reason is that on the basis of certain flow area in-
creasing tube number means heat transfer area increases.
Further heat transfer will be enhanced and performance
of the hea t exchanger will be impro ve d .
The internal thermal stratification diagram of IRWST
is showed in Figure 3, respectively longitudina l direc tion
slitting figure along the width of the tank and transverse
direction slitting figure along the height of the tank, Fig-
ures 3(a) and (c) are for 8-tube model, Figures 3(b) and
d are for 16-tube model. By contrast, the thermal strati-
fication phenomenon of 16-tube model is more obvious,
the temperature of high temperature area is higher and
the range is larger, from Figure 3(d) it can be seen that
thermal stratification has basically spread throughout the
tank section.
3.2. Effect of Different Coolant Inlet
On the basis of 16-tube model effect of different coolant
inlet temperature has been researched. Coolant outlet
temperature changing through changing inlet temperature
is demonstrated in Table 3. It’s found that when inlet
temperature increases the outlet temperature also in-
creases. The reason is that when the whole flow is con-
stant, increasing inlet temperature means increasing heat
input, but the water loaded in IRWST is unchanged, so
the outlet temperature will become higher.
Although with the inlet temperature increasing the
outlet temperature has a clear upward trend, but PRHR
HX cooling rate is increased too, the cooling rate equa-
tion is as follows.
inlet outlet
Tinlet and Toutlet are coolant inlet and outlet temperature
respectively. By calculation, when the inlet temperature
is 275˚C, 297.2˚C and 325˚C, the cooling rate is 24.9 9%,
25.87% and 26.87%. The reason is that when whole flow
is constant, coolant volume will expand with higher
temperature, and meanwhile the flow area is also con-
stant the flow velocity of the coolant will improve. Thus
the heat transfer coefficient [9] between the coolant and
heat transfer tube wall will be increased and the heat
transfer performance of PRHR HX will be enhanced.
Figures 4(a)-(c) and (d)-(f) are the internal thermal
stratification diagrams of IRWST when temperature is
275˚C, 297.2˚C and 325˚C and respectively longitudinal
direction slitting figure along the width of the tank and
transverse direction s litting figure along the heigh t of the
tank. When the coolant inlet temperature increases the
water temperature of IRWST is also changing, the range
of thermal stratification is expanding gradually, it means
that the utilization of IRWST is improving. So once
again it confirms that with inlet temperature rising
Table 2. Outlet temperature of 8 and 16 tubes models at designed inlet temperature.
Unit (˚C) Tube 1 Tube 2 Tube 3 Tube 4 T ube 5 Tube 6 Tube 7 Tube 8 Average
Outlet temperature(8) 224.06 232.02 236.22 231.95 240.75 244 240.78 249.81 237.45
Outlet temperature(16)
Tube 1 Tube 2 Tube 3 Tube 4 T ube 5 Tube 6 Tube 7 Tube 8
201.68 201.67 209.72 213.39 213.52 209.76 219.29 224.03
Tube 9 Tube10 Tube 11 T ube 12 Tube 13 Tube 14 Tube 15 Tube 16
224.07 219.39 227.69 230.24 230.17 227.51 236.44 236.57
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(a) (b)
(c) (d)
Figure 3. IRWST thermal stratification, (a) and (c) for 8 tubes, (b) and (d) for 16 tubes.
Table 3. Outlet temperature of 16 tubes model at different inlet temperature.
Unit (˚C) Tube 2 Tu be 4 Tube 6 Tube 8 Tube10 Tube12 Tube14 Tube16 Average
Outlet temperature(275˚C) 189.65 200.07 197.03 209.39 205.44 215.17 212.86 220.75 206.27
Outlet temperature(297.2˚C) 201.67 213.39 209.76 224.03 219.39 230.24 227.51 236.57 220.32
Outlet temperature(325˚C) 216.49 229.98 225.56 242.04 236.64 248.89 245.7 256.22 237.68
PRHRS performance is improved.
At the above three conditions velocity vector of natu-
ral circulation phenomena in IRWST is showed in Fig-
ure 5. Figures 5(a)-(c) are respectively correspo nding to
the inlet temperature 275˚C, 297.2˚C and 325 ˚C.
When the water in IRWST is heated by PRHR HX, not
only thermal stratification is built but also density strati-
fication. Near the heat transfer tubes the temperature is
higher and density decreases natural convection pheno-
mena will occur. Meanwhile at the area that far away
from the tubes but near the inner wall of IRWST the wa-
ter temperature is relatively lower and density is rela-
tively higher, then the natural circulation phenomena will
be generated within the whole tank. As showed in Figure
5, with the increasing of coolant inlet temperature heat
transfer inside IRWST is improved and velocity of natu-
ral circulation is increasing gradually, thus the heat
transfer coefficient [9] between the coolant and heat
transfer tube wall will be increased and the heat transfer
performance of PRHR HX will be enhanced further.
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(a) (b)
(c) (d)
(e) (f)
Figure 4. IRWST thermal stratification, from left to right inlet temperature is increasing.
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(a) (b)
Figure 5. Natural circulation velocity vector of IRWST at different inlet temperature.
4. Conclusions
In this paper PRHRS is simulated with different number
of C-type heat transfer tubes and different coolant inlet
temperature via FLUENT software, the main conclusions
are as follows:
1) Keep the total flow area of PRHR HX constant in-
creasing the number of C-type heat exchanger tubes can
increase the heat transfer area, thus heat transfer will be
improved and the performance of PRHR HX will be en-
2) Keep the number of C-type heat transfer tubes and
overall flow constant increa sing coolan t inlet temperatur e
the coolant will expand and flow velocity will increase
too. The range of thermal stratification in IRWST will
become larger and the velocity o f natural circulation will
3) With the increase in the coolant inlet temperature,
outlet temperature will also increase, but the cooling rate
of the system to the coolant rises. It means the heat
transfer performance of PRHR HX is improved to some
extent, it can guar antee the PRHRS still be s afe and reli-
able operation when the parameters are deviated from the
design conditions.
5. Acknowledgements
This work was financially supported by Major Projects
CAP1400 safety re view technolog y and independ ent ve-
rification testing(No.2011ZX06002010) and “CAP1400
safety review key technologies research” (No.2013
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