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THERMAL–HYDRAULIC MODELING OF NANOFLUIDS AS THE
COOLANT IN VVER-1000 REACTOR CORE BY THE POROUS MEDIA
APPROACH
G. JAHANFARNIA, E. ZARIFI *, F. VEYSI**
Department of Nuclear Engineering, Science and Research Branch, Islamic Azad University,
Tehran, Iran,[email protected]
*Department of Nuclear Engineering, Science and Research Branch, Islamic Azad University,
Tehran, Iran,[email protected]
**Mechanical Engineering School, Razi University, Kermanshah, Iran,
ABSTRACT
The aim of this study was to perform a thermal–hydraulic analysis of nanofluids as coolant in
the Bushehr VVER-1000 reactor core using the porous media approach. Water-based
nanofluids containing various volume fractions of Al2O3 and TiO2 nanoparticles were analyzed.
The conservation equations were discretized by the finite volume method and solved by
numerical methods. To validate the approaches applied in this study, the results of the model
and COBRA-EN code were compared for pure water. The achieved results show that the
temperature of the coolant increases with the concentration of the nanoparticles.
Key words: (porous media, nanofluids, thermal–hydraulic, VVER-1000 reactor)
Introduction
Nanofluids are engineered colloidal dispersions of nanoparticles in base fluids such as water, oils or
refrigerants. The nanoparticles can be metals such as copper, silver, gold or metal oxides such as alumina,
zirconia, silica or various forms of carbon such as diamond, carbon nanotubes and graphite.
The studies regarding nanofluids applications have been conducted in: conductive heat transfer [1],
convective heat transfer [2] and boiling heat transfer [3]. The nanofluids thermal conductivity
enhancement suggests the possibility of using them in nuclear reactors [4]. The nuclear effects of
nanofluids have been studied in recent literatures [5] but their thermal–hydraulic behavior have not been
discussed in details for a whole reactor core. There are so few analyses of the nuclear power plants in the
literatures using nanofluids as a coolant.
In this paper, the thermal–hydraulic modeling of Bushehr VVER-1000 reactor core with nanofluids as a
coolant is investigated by the porous media approach. The porous media is a well known approach for
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analyzing the fuel assemblies of nuclear reactor core. This method is introduced to form the conservation
equations by means of porosity concept within the control volume. The axial and transverse momentum
equations are solved with high accuracy for single-phase coolant fluid, but this method is not applied to
calculate the fuel temperature gradients.
Porous media approach
In porous media approach, there are three principles distinguishing it from others [6]:
(1) All the parameters are in the form of the average volume.
(2) Despite the sub-channel method in which the equations are written separately for fuel and coolant, in
porous media approach, the conservation equations are just written for fluid.
(3) In this method fuel rods which are considered as a source of heat have physical and geometrical
effects on coolant flow.
In Figure 1, control volume of single-phase fluid is shown. The ratio of fluid volume fV to total volume
TV is defined as the volume porosityT
f
VV
V. In some body formulations, only volume porosity is
utilized [6]. Some formulations have introduced the additional concept of an area porosity or percentage
area for flow associated with surface enclosing the volume (T
f
AA
A).
Figure 1 Region consist of a single phase fluid with stationary solid.
Mass balance
Mass conservation equation of the fluid is noted below:
0).( vt
nf
nf (1)
Integration Eq. (1) over the control volume yields:
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0)()()(
)()()(
z
v
y
v
x
v
t
znf
xi
Azzynf
yi
Ayyxnf
xi
Axxnf
i
V (2)
Axial momentum balance
The dynamic equation of fluid motion with gravity as the only force body is as follows:
gPvvt
vnfnf
nf..
)( (3)
By an analogous procedure to that mass conservation equation, the z-component of the linear momentum
equation can be written as follows:
z
vv
y
vv
x
vvv
t
z
zi
z
zi
nf
zi
Azzy
yi
z
yi
nf
yi
Axyx
xi
z
xi
nf
xi
Axx
z
i
nf
i
V
)()()()(
)()()()()()()()()(
z
i
Vzz
zi
Azzyz
yi
Ayyxz
xi
Axx
zi
Azzznf
i
V Rzyxz
Pg
)()()()()()()()(
(4)
In Eq 4, zR is the surface force exerted on the fluid by the dispersed solid, which can be written as:
f
flowfric
zV
APR
Pak and Cho[7] correlations for the nanofluids viscosity used in conservation equation are as below:
For Al2O3 + water:
)9.53311.391( 2
fnf (5)
For TiO2 + water:
)2.10845.51( 2
fnf (6)
Transverse momentum balance
The balance equation of transverse momentum is written as [8]:
kkGkjc
k
kkkkkj
n
kkk ww
sl
XvkXPg
l
swUwUww
t
X)(
2
1)(
/
11
/
1
/ (7)
The first term on the right-hand side of Eq. 7 is the lateral pressure difference on the boundaries of the
momentum control volume (Figure 2), while the last term is the pressure drop in the lateral flow through
the gap. On the contrary, there is no term representing lateral flow of transverse momentum because the
cross flow velocity is assumed to vanish away from the gap, i.e., on the boundary of the control volume
for transverse momentum balance.
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Figure 2 Control volume for mass, energy and axial momentum balance finite-volume equation (lateral view)
Energy balance
Energy conservation equation is given by:
Dt
DPqqvh
t
hnfnf
nfnf /////.).()(
(8)
Therefore the local volume average of Eq. 11 is:
y
vh
x
vhh
t
y
yi
nf
yi
nf
yi
Ayyx
xixi
nf
xi
Axx
nf
i
nf
i
V
)()()(
)()()()()()(
y
y
TK
x
x
TK
Dt
DP
z
vh nf
yi
Ayynf
xi
Axx
i
V
z
zi
nf
zi
nf
zi
Azz
)()()(
)()(
)()()(
)(
)(//////
)(
ii
rb
i
V
nf
zi
Azz
qqz
z
TK
(9)
Results and discussion
According to neutronic album of Bushehr VVER-1000 reactor (AEOI, 2010), the reactor power is
continuously varying from cold zero to nominal power. In this study, power distributions in the 100th day
(nominal power) are considered for calculations. The arrangement of fuel assemblies in the reactor core
are shown in Figure 3 (FSAR of BNPP- 1, 2003). The achieved results are compared with COBRA-EN
code for validation. There are only thermal properties of liquid water in the library of the COBRA-EN
code and there is no possibility to insert nanofluid properties, therefore the results of the modelling are
compared with COBRA-EN code only for the pure water. The comparisons show good agreement
without significant deviations (Figure 4).
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Figure 3 The meshing and channels arrangement used in porous body approach
The same boundary conditions such as heat flux, outlet pressure, inlet temperature and mass flow rate are
considered both for nanofluids and pure water. In Figure 5 and Figure 6, velocity and temperature
distributions in the hottest channel for two nanofluids and pure water in various volume percentages are
presented and compared with each other, respectively. The axial variation of above mentioned parameters
is needed for coupling the written thermohydraulic code with a neutronic code.
Figure 4 Axial temperature distribution in hot fuel assembly
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The results interpret the variation of enthalpy with density and specific heat capacity changes. As seen in
Figure 5, by considering equal coolant mass flow rate and inlet temperature, the coolant exit temperature
increases with increment of nanoparticles concentration due to preserve constant heat flux value. Based
on continuity equation, for equal mass flow rate in various nanoparticles concentration, the coolant
velocity decreases with increasing the nanofluid density in the reactor core (Figure 6).
Figure 5 Axial coolant temperature in hot fuel assembly
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Figure 6 Axial velocity in hot fuel assembly.
Conclusion
Porous media approach is used to analyze the reactor core, because less number of the meshes and shorter
program execution time are needed. The results show that in low volume percentages, there is no
significant difference between nanofluids and pure water parameters values, but the deviations are
remarkable for concentrations more than 0.1%. As a conclusion, it can be showed that there is not
remarkable difference in thermohydraulic behavior of Al2O3 and TiO2 nanofluids as a reactor coolant.
Due to increment of nanoparticles concentration, fluid temperature increases as a result of variation of
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specific heat capacity and heat transfer coefficient. It can be seen that for 10 volume percentage of
nanoparticles the coolant temperature difference with pure water is about 20°C. Thus, to preserve equal
design temperature difference, lower coolant flow rate is necessary for cooling the reactor core.
Consequently, the reactor core can be more compact and the capital cost of the power plant will be
reduced.
References
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[3] I.C. Bang, S.H. Chang, Boiling heat transfer performance and phenomena of Al2O3/water
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[5] K. Hadad, A. Hajizadeh, K. Jafarpour, B.D. Ganapo, Neutronic study of nanofluids application to
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[6] G. Ricciardi, S. Bellizzi, B. Collard, B. Cochelin, Modelling pressurized water reactor cores in
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submicron metallic oxide particle. Exp. Heat Transf. 11, 151–170
[8] D. Basile, M. Beghi, R. Chierici, E. Salina, E. Brega, COBRA-EN, an Updated Version of the
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