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Original Article
COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF THE
CANADIAN DEUTERIUM URANIUM MODERATOR TESTS AT
THE STERN LABORATORIES INC.
HYOUNG TAE KIM
a,*
and SE-MYONG CHANG
b
a
Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon, 305-353, South Korea
b
Kunsan National University, 558 Daehak-ro, Gunsan-shi, Jeonbuk, 573-701, South Korea
article info
Article history:
Received 28 April 2014
Received in revised form
16 November 2014
Accepted 10 December 2014
Available online 22 January 2015
Keywords:
Calandria
Canadian Deuterium Uranium
CFX
Computational Fluid Dynamics
Moderator Subcooling
Pressure Drop
Stern Laboratory
abstract
A numerical calculation with the commercial computational fluid dynamics code CFX-14.0
was conducted for a test facility simulating the Canadian deuterium uranium moderator
thermalehydraulics. Two kinds of moderator thermalehydraulic tests at Stern Labora-
tories Inc. were performed in the full geometric configuration of the Canadian deuterium
uranium moderator circulating vessel, which is called a calandria tank, housing a matrix of
horizontal rod bundles simulating calandria tubes. The first of these tests is the pressure
drop measurement of a cross flow in the horizontal rod bundles. The other is the local
temperature measurement on the cross section of the horizontal cylinder vessel simu-
lating the calandria system. In the present study, the full geometric details of the calandria
tank are incorporated in the grid generation of the computational domain to which the
boundary conditions for each experiment are applied. The numerical solutions are
reviewed and compared with the available test data.
Copyright ©2015, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society.
1. Introduction
The Canadian deuterium uranium (CANDU) reactor has a
square array of horizontal fuel channels surrounded by a heavy
water moderator contained in a horizontal, cylindrical vessel
called a calandria. Each fuel channel consists of two concentric
tubes, a pressure tube inside a calandria tube, and a gap that
contains CO
2
insulating gas. Because a CANDU reactor has a
high-pressure primary cooling system and an independently
cooled moderator system, the moderator in the calandria will
act as a supplementary heat sink during a loss of coolant ac-
cident (LOCA) if the primary cooling and emergency coolant
injection systems fail to remove the decay heat from the fuel.
The CANDU industry has widely accepted that the fuel
channel integrity can be ensured if the available moderator
subcooling at the onset of a large LOCA is greater than the
subcooling requirements. The premise of this approach is
based on a series of contact boiling experiments [1], which
*Corresponding author.
E-mail address: kht@kaeri.re.kr (H.T. Kim).
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://
creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any me-
dium, provided the original work is properly cited.
Available online at www.sciencedirect.com
ScienceDirect
journal homepage: http://www.journals.elsevier.com/nuclear-
engineering-and-technology/
Nucl Eng Technol 47 (2015) 284e292
http://dx.doi.org/10.1016/j.net.2014.12.012
1738-5733/Copyright ©2015, Published by Elsevier Korea LLC on behalf of Korean Nuclear Society.
derived the subcooling requirements [2] to preclude a
sustained calandria tube dryout by the minimum available
moderator subcooling and the pressure tube/calandria tube
contact temperature. The local temperature of the
moderator is a key parameter in determining the available
subcooling. However, to predict the moderator temperature
distribution, numerous experimental and numerical studies
have been performed, because only the inlet/outlet
temperature can be measured in a real CANDU reactor.
Huget et al. [3] experimentally investigated the moderator
circulation and temperature distribution of a CANDU
moderator using a two-dimensional (2D) moderator circulation
facility at Stern Laboratories Inc. (SLI) at Hamilton in Canada.
The cross-section of this facility was a ¼-scale of a real
calandria vessel, while the geometry and flow conditions were
uniform in the axial direction. They also predicted the velocity
and temperature distribution using the MODTURC_CLAS code
[4] to validate it against the experimental results and for each
test. The Chalk River Laboratory in Canada built the moderator
temperature facility (MTF) for 3D moderator flow
measurements and conducted an experimental study [5].
The Korea Atomic Energy Research Institute has been
performing the experimental research on moderator circula-
tion as one of the national R&D programs since 2012. This
research program includes the construction of the Moderator
Circulation Test facility [6], production of the validation data
for self-reliant computational fluid dynamics (CFD) tools,
and development of an optical measurement system using
the particle image velocimetry [7] and laser-induced
fluorescence [8] techniques.
Hadaller et al. [9] developed a frictional pressure drop
model for the tube bundle region of the calandria vessel and
implemented it into the MODTURC_CLAS code because the
MODTURC_CLAS adopts a porosity-based approach. Yoon
et al. [10] applied this pressure drop model into the
commercial CFD code, CFX-4, and conducted a 3D
calculation for the experiments at SLI.
In the present study, the full geometric details of the cal-
andria system are incorporated in the CFX-14.0 [11] model and
this CFD analysis model for moderator thermalehydraulics is
validated against the available test results at SLI.
2. Numerical basis
The simulation with CFX-14.0 is based on the finite volume
method (FVM) modified with the shape function used in finite
element methods to make the construction of a node-
centered computation possible. This is different from FLUENT
using a classical cell-centered FVM scheme. Therefore, the
numerical method is strong for complex geometries or
skewed grids [11].
2.1. Governing equations and boundary conditions
The governing equations consist of conservative laws on
mass, momentum, and energy. They are written as follows in
tensor form [11]:
vr
vtþv
vxjrUj¼0 (1)
v
vtðrUiÞþv
vxjrUiUj¼di;j
vp
vxjþvti;j
vxjþSMi (2)
v
vtðrhtotÞvp
vtþv
vxjrUjhtot¼v
vxjlvT
vxjþv
vxjUjti;jþUiSMi þSE
(3)
where r,Uj,p,ti;j,Tare density, velocity vector, pressure, shear
stress, temperature, etc.; the coefficient lis thermal conduc-
tivity. The shear stress tensor in Eq. (2) by the NaviereStokes
equation and total enthalpy, htot in Eq. (3) by energy equation
are defined as:
ti:j¼mvUi
vxjþvUj
vxi2
3di;j
vUi
vxj(4)
htot ¼hþ1
2U2
j(5)
where the coefficient mis viscosity, and h¼eþp=r;eis the
internal energy per unit mass.
In addition, equation of state should be considered to relate
total enthalpy to temperature and pressure. The local time
derivative term in Eq. (1), the continuity equation, can be
deleted under the assumption of incompressible flow, and
then the source term in Eq. (2),SM;iis expressed as the
Boussinesq approximation. The source term in Eq. (3),SEis a
volumetric heat source in the computational domain, which
is set at zero in this research.
The boundary condition at the solid surface is a “no-slip”
condition while the heat flux is given on calandria tubes or
adiabatic on the inner surface of the tank, for example. The
inlet condition specifies the mean mass flow rate, and the
pressure is set to ambient at the outlet.
2.2. Turbulence model and numerical technique
In the high Reynolds number flow, a turbulence model is
required for RANS (Reynolds averaged NaviereStokes)
formulation. There has been much research dealing with
various turbulence models and their implementation, which
presents no absolute solution so far [12]. The kemodel with
scalable wall functions is applied for this research [13]. The
incident turbulence intensity is assumed to be 5%, and
turbulence length scale is set to the diameter of a tube.
Eqs. (1e3) are solved numerically with boundary conditions
and the turbulence model. The direct integration of conser-
vative equations with the edge-centered FVM is different from
conventional incompressible schemes such as SIMPLE [14].In
the convergence, the relative tolerance of time iterative error
is set to 105for the steady solution. For the unsteady time
iteration in Section 3.2, the time marching technique is
applied to all the equations. The accuracy on both time and
space is second order overall, which is also denoted in
NUREG-2052 [15].
The yþvalue is defined as Dy, the normal length of the first
grid neighboring the wall as:
yþ¼Dyffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r
m
Dut
Dyy¼yw
s(7)
Nucl Eng Technol 47 (2015) 284e292 285
where utis the tangentially transformed velocity component
along the wall [16]. To get the proper result of computation
without wall functions, the dimensionless wall distance
should be guaranteed yþ<1 as in the whole computational
domain.
However, the required number of grids can be reduced with
the use of wall functions [14]:
yþ¼maxr
mDyC1=4
mffiffiffi
k
p;11:06(8)
where kis the turbulence kinetic energy, and Cmis a coeffi-
cient. Therefore, the grids in the range of yþ<11:06 are
neglected due to being unnecessary, and yþ<300 is sufficient
for the capture of the outer layer in a low Reynolds number
flow for engineering computation.
3. CFX simulation of the SLI test
Two kinds of moderator thermalehydraulics tests at SLI were
performed. One of these tests is the pressure drop measure-
ment of a cross flow in the horizontal rod bundles. The other is
the local temperature measurement on the cross section of
the horizontal cylinder vessel simulating the calandria tank.
The CFX-14.0 (version 14.0) is used for the present calcula-
tions. Fig. 1 shows the configuration of the test facility at SLI.
Fig. 1 eConfiguration of Stern Laboratories Inc. test facility.
Fig. 2 eTest section for pressure-drop test.
Fig. 3 eMesh configuration for pressure-drop test. (A) Rod
channel; (B) 3D configuration.
Nucl Eng Technol 47 (2015) 284e292286
3.1. Pressure-drop test
For the pressure-drop test, the rectangular channel sur-
rounding the square array of rod bundles is inserted into the
main test facility, as shown in Fig. 1. This test section part is
separately shown in Fig 2. The computational domain is a
0.286-m wide, 2-m long rectangular channel, with a
thickness of 0.2 m. The tube bank of a 0.0714 m
2
pitch, in
which the tube diameter is 0.033 m, is staggered or in-lined,
and the perforated plate installed in the wake region near
the outlet suppresses the instability of unsteady flow.
Fig. 3 shows the mesh generation procedure for the
pressure drop test. The mesh generation tool used in the
present work is the ANSYS ICEM CFD [17]. To capture the
local flow in the boundary layer around the rod bundles, fine
mesh layers are generated as a hexagonal surface mesh, and
Table 1 eComparison of measurement and calculation results.
Stern T.P. 326
(Case 1)
Stern T.P. 299
(Case 2)
Stern T.P. 306
(Case 3)
Mass flow (kg/s) 3.089 3.904 5.734
Temperature (C) 39.5 63.6 79.8
Density (kg/m
3
) 992.25 981.0 971.6
Dynamic viscosity (Pa
.
s) 6.53 10
4
4.44 10
4
3.55 10
4
Inlet velocity (m/s) 0.054 0.070 0.103
Tube Reynolds No. 2,746 5,237 9,392
DP (Pa)] Measurement 28.2 41.3 78.7
CFX-14.0 23.6 37.6 77.5
Difference (%) 16.3 9.0 1.5
T.P. (Test Procedure).
Fig. 4 ePressure and velocity distribution for pressure-drop test (Case 3).
Fig. 5 eTest vessel for a thermalehydraulic test at Stern
Laboratories Inc.
Nucl Eng Technol 47 (2015) 284e292 287
this 2D mesh in the region of the tube pitch is extruded to
obtain the 3D mesh. At the wall, the yþvalue in Eq. (8) is
checked to yþ<30. Half of the test section is modeled by
applying the symmetric boundary condition on the center
plane to enhance the computational efficiency with a
reduced number of mesh elements. A series of convergence
tests for the grid has been done to make sure that the
number of grids should be sufficient for the precise solution.
Finally, the total number of hexagonal elements is estimated
as 424,320.
The test conditions and comparisons of the experimental
and predicted pressure drops are summarized in Table 1. The
full geometric CFX model gives closer pressure drop values to
the measured values between the first and third pressure taps
as the Reynolds number becomes higher. For example, the
relative error between the measured and predicted values is
1.5% when the Reynolds number is 9,392 (Case 3). The
calculation results for the pressure and temperature
distribution of Case 3 are shown in Fig. 4. The longitude
pressure gradient is shown to be more dominant than the
pressure gradient around the rod bundle. The local flow
around the rod bundle including the wake flow is well
captured and the flow is stable.
However, for the low Reynolds number 2,746 (Case 1), the
error from the measurement is estimated to be 16.3%, which is
due to the fact that the flow regime at such a Reynolds number
is still unstable, so the turbulence model is thought not to work
properly. According to other literature [12,15], the low Reynolds
number kemodel or kuSST model should be used for these
kinds of computations while the kemodel with scalable wall
functions is applied overall in this study. Therefore, the result
of low Reynolds numbers should be considered as an incon-
sistency from the flow instability, which can be regarded as the
limitation of the turbulence model.
3.2. Thermalehydraulic test
The moderator test vessel shown in Fig. 5 is a cylinder with a
diameter of 2 m and a length of 0.2 m. The vessel does not
have a scaled geometry from the actual CANDU reactors and
is rather close to a thin axial slice of a CANDU-6 reactor. The
working fluid is light water (H
2
O). In the core region, there is
a matrix of 440 heating pipes, which have an outer diameter
of 0.033 m with a lattice pitch of 0.071 m. The two inlet
nozzle slots are located at the horizontal centerline and
span the full thickness (0.2 m) of the test vessel. For the
present simulation, the width of the nozzle slot is 6 mm and
the total inlet flow rate is 2.4 kg/s, corresponding to an inlet
velocity of 1 m/s, and the inlet temperature is 55 C. The
heater power is 100 kW.
Fig. 6 shows the mesh generation procedure for the
thermalehydraulic test simulation. Two kinds of surface
meshes for the regions of the channels of the rod bundle
and for the outer region of the channel are generated and
extruded together to obtain all the 3D mesh elements of the
test vessel. The meshes of the nozzle slot part are extracted
from the existing mesh elements of the outer channel region
with the corresponding location and size. Because the flow
is assumed to be a 2D dominant flow, only three layers of
the 3D elements with a 0.02 m depth (1/10 of the actual
depth) are modeled by applying the symmetric boundary
conditions at both end planes of the test vessel in the axial
direction. The total number of mesh elements used for this
simulation is 672,912. The yþvalue in Eq. (8) is checked, and
yþ<30 for this problem. Since the momentum of inlet water
is transported to the upper stagnation point of the tank, the
deficiency of the number of grids at the nozzle is not a
serious problem in the global domain of computation (see
iteration No. 1,000 in Fig. 7).
Fig. 6 eMesh generation for thermalehydraulic test at Stern Laboratories Inc. (A) Rod region; (B) near tank wall; (C)
combination of 2D mesh; and (D) extrusion of 2D mesh.
Nucl Eng Technol 47 (2015) 284e292288
This problem is not converged to the steady state, and the
flow field is transient. The experimental observations have
revealed that the thermal conditions inside the tank never
reach a steady state, as evident by the measured temperature
fluctuations. The full 3D simulation of Sarchami et al. [18] can
be compared with this result for the surface heating case in
the cross section.
The predicted results for velocity vectors and a tempera-
ture distribution for each iteration step are shown in Figs. 7
and 8, respectively. Initially (at iteration number, 0), the flow
stops; the water temperature is set to 55 C. The uniform
surface heat flux is provided on the tube walls and the con-
stant velocity condition is applied on the inlet surface of the
nozzle. As the iteration proceeds in Fig. 8, the peak
Fig. 7 eVariation of two-dimensional velocity vectors for each iteration step.
Nucl Eng Technol 47 (2015) 284e292 289
temperature becomes higher than the outlet temperature
(~65 C), and finally after about 4,000 iterations, it shows an
asymmetric temperature distribution governed by the
combination of momentum force (arising from the inlet jet)
and buoyancy force (arising from the local heat generation),
which also agrees with the 3D simulation [18]. The inlet
nozzle flows go through the upper edge of the vessel,
impinging on each other, and form downward moving flows
(Fig. 7). Since the impingement point is tilted to the left side
of the vessel and the jet from the right side travels a longer
Fig. 8 eVariation of two-dimensional temperature distribution for each iteration step.
Nucl Eng Technol 47 (2015) 284e292290
distance to the impingement point (for this simulation), a
large recirculation loop is formed at the right side of the
nozzle and a small one at the left side. The large
recirculation loop pushes down the peak temperature from
the top of the vessel.
Some small disturbances in the flow or temperature make
the system unstable and the magnitude of the disturbances is
amplified. A mixing flow then occurs to restore the asym-
metric flow distribution. The iteration number of 8,800 is one
of the iteration steps at which a relatively stable temperature
distribution is obtained.
Temperature predictions at the vertical centerline are
compared with the test data as shown in Fig. 9. The CFX-14
prediction (at the iteration number of 8,800) using the full
geometric model captures the temperature variation along
the elevation of the measurement points, where the peak
temperature is found well below the top of the vessel, and
the temperature gradient at the upper side is higher than
that at the lower side of the vessel.
4. Conclusion
The present CFD model with a full geometric configuration of
the calandria system, a new approach different from the
previously used porosity based approach, is used to simulate
the pressure-drop measurement and the temperature distri-
bution measurement around the horizontal rods performed at
the SLI test facility.
The present CFD prediction without the empirical corre-
lation based on the pressure drop test is in good agreement
with the test results. The prediction becomes more accurate,
as the flow conditions become more turbulent with a higher
Reynolds number.
However, the temperature fluctuation is observed during
iteration steps for a steady-state simulation of the thermal-
ehydraulic test. This result shows that the flow and temper-
ature distribution inside the moderator tank may not be stable
in the actual test, which should be confirmed by additional
test results. The effect of the full geometric model, capturing
the small disturbances in the flow or temperature and the
porous media model approximating the local flow behavior on
the prediction of the moderator circulation behavior, should
be investigated using test results which will be produced in
the Moderator Circulation Test facility.
Conflicts of interest
All contributing authors declare no conflicts of interest.
Acknowledgments
This work was supported by the National Research Founda-
tion of Korea (NRF) grant funded by the Korea government
(Ministry of Science, ICT, and Future Planning; No. NRF-
2012M2A8A4025964).
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