ANALYSIS OF MIXING PROCESSES IN VVER-440 ROD BUNDLE
WITH RANS METHOD
Sándor Tóth, Dr. Attila Aszódi
Budapest University of Technology and Economics
Institute of Nuclear Techniques
Muegyetem rkp. 9, 1111 Budapest, Hungary
toth@reak.bme.hu, aszodi@reak.bme.hu
ABSTRACT
Detailed knowledge of the flow and the heat transfer is very important in the case of fuel
rod bundles of nuclear reactors from the design and safe operation point of view.
Investigations of the thermal hydraulic processes in VVER-440 fuel assemblies are in
progress at the Institute of Nuclear Techniques, Budapest University of Technology and
Economics using the code ANSYS CFX 11.0 [1]. In the present work, one single subchannel
was investigated in order to reach the necessary resolution of the optimal mesh at first.
Models of a subchannel (triangular array, P/D=1.35) were built and comprehensive mesh
sensitivity study was performed. The mesh study showed that relatively high mesh density
was needed to reach the grid independent solution. Suitable mesh was chosen and turbulence
model study was accomplished using the k-epsilon, SST, SSG Reynolds Stress and
BSL Reynolds Stress models. Results of the predictions were compared to measurement
published by Trupp and Azad [2]. The best results were obtained with use of BSL Reynolds
Stress model. Distributions of the Reynolds Stresses and the turbulent kinetic energy were in
good agreement with Trupp and Azad’s measurement. Based on the experience of the study
two further models of a 250 mm long rod bundle section were developed that contained six
rods. One of these models involved a spacer grid to investigate its effects on the flow. Using
these models calculations were carried out in order to investigate the mixing effects. In both
cases the development of secondary flows were observed but convective mixing occurred
between adjoining subchannels only in the case of the model with spacer grid.
1. INTRODUCTION
Detailed knowledge of the flow field and the heat transfer in NPP’s fuel assemblies is very
important for safe operation. Investigations of the power upgrade possibilities of generation
two reactors and research of the generation three and four reactors require additional
improvement of our knowledge in this field. Experiments and computational fluid dynamics
codes can help to accomplish these important tasks.
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Numerical investigations of the fuel assembly of the VVER-440 reactor (Russian
pressurized water reactor) are under way at the Institute of Nuclear Techniques using the
ANSYS CFX code. This code applies the finite volume method for solving the Navier-Stokes
equations. Previously a fuel assembly head model [3] and a full-length 60-degree-segment
model of the active part of the fuel bundle were developed [4]. Using the assembly head
model the coolant mixing in the fuel assembly head was analyzed. Applying the fuel bundle
model average coolant temperature, average heat transfer coefficient, average cladding
temperate along the fuel bundle, outlet temperature and velocity of subchannels were
investigated. Rod bundle calculations were carried out applying different turbulent models (komega, SST and SSG Reynolds Stress). The investigated quantities of the k-omega and the
SST calculations were in good agreement but the SSG results were different from these in
many aspects. Since measurement data were not available, it was not possible to tell which
turbulence model gave a better prediction of the phenomenon. Outlet quantities of the
subchannels were compared with the results of COBRA subchannel code calculations. Some
differences were found between the CFX and COBRA results. The differences probably were
caused by the deficiencies of the COBRA model (inaccurate flow resistance and turbulent
mixing coefficients, etc.) and by the fact that our CFD model gave a more accurate prediction.
But it must be mentioned that there were some uncertainties in our CFD model as well: for
example suitability of the applied mesh and turbulence models. In this work our aim is to
study the effects of the mesh resolution and the turbulence model selection in the case of rod
bundle simulations. Moreover, investigation of the mixing processes in a VVER-440 fuel
bundle section is object of the study as well.
2. SUBCHANNEL SIMULATIONS
Our aim was the detailed examination of the flow and the heat transfer processes in a 250
mm long part of a triangular rod bundle with a P/D ratio of 1.35. At first, a subchannel was
investigated to study the effect of the grid resolution and effect of the turbulence model
selection. Measurement data published by Trupp and Azad [2] are available for this case
therefore the verification of the models were possible based on comparison between
measurement and calculation. Trupp and Azad published their work in 1975 [2]. They
examined full-developed uniform-density turbulent air flow in triangular arrays of rod
bundles in wind tunnel experiments. Measurements were made for three P/D ratios over a
wide range of Reynolds-number. The test sections involved 19 rods. The rod diameter was
50.8 mm and the pitch was different according to the selected P/D ratio. Measurements were
accomplished for a one-sixth part of a subchannel that aligned at the center rod bundle. In the
case of P/D=1.35 detailed experimental data were published for nominal Reynolds numbers
24,000 and 60,000 (actual Reynolds numbers were 23,510 and 59,880). The latter value is
closer to the nominal Reynolds number in a VVER-440 fuel assembly (about 220,000)
therefore this second experiment was selected for our investigations.
Numerical model description
VVER-440 fuel rod bundles contain 126 fuel rods arranged in a triangular configuration.
The outer diameter of the fuel rods is 9.1 mm and the rod pitch is 12.3 mm so the P/D ratio is
about 1.35. There are three types of subchannels according to their cross sectional shape:
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subchannels that are enclosed by the shroud of the fuel assembly and fuel rods; subchannels
that are enclosed by the shroud corner and fuel rod and subchannels that are bordered by fuel
rods only. The latter type (6 mm long) was investigated (Figure 1) with rod diameter equal to
9.1 mm and the pitch was 12.3 mm (P/D= 1.35). In this manner, the geometrical similarity
was ensured between the experiment and calculation.
The geometry and meshes were created using the ANSYS ICEM software. The geometry
was resolved by six different meshes (Figure 2) to study the influence of the grid resolution.
Unstructured prismatic meshes were applied: the cross sectional resolution was different but
the height of the three axial layers was the same. The height of the layers is less important
because full-developed flow was computed applying RANS models with periodic boundary
condition in axial direction.
Periodic interface
Wall
No slip, smooth wall
Figure 1. Geometrical model and boundary conditions
M1
M2
M3
M4
M5
M6
Figure 2. Cross sectional grids
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The main characteristics of the different meshes can be seen in Table I. The finest mesh
was M1 and the coarsest was M6. In the case of the mesh M1 the number of inflation layers
around the rods was 15, for the mesh M2 it was 6 and in the case of the other meshes it was 3.
In the case of the meshes M1 and M2 the average dimensionless distances from the wall
(y+ave) were 1 and 4.8, consequently the boundary layer was practically resolved. For the other
meshes y+ave was about 20 namely the log-law region of the boundary layer was resolved
only. The boundary conditions of calculations can be seen in Figure 1. For the surface of the
rods no slip smooth wall boundary condition was defined. Symmetry boundary condition was
applied on the symmetry planes (marked by red). The flow was modeled as full-developed
turbulent flow therefore the upper and the lower planes of the subchannel model were defined
as a periodic interface pair. Axial momentum source was used in order to form a flow with a
Reynolds number of 59,880. In this way the similarity of the flow between the measurement
and computation was ensured. The fluid was water at 123 bar and 265 ºC.
Mesh
Number of Nodes
Number of Elements
y+ave
M1
18,136
19,911
1
M2
8,864
10,767
4.8
M3
6,084
7,599
20.1
M4
2,472
2,802
20.0
M5
1,152
1,185
19.9
M6
456
396
19.5
Table I. Main characteristics of the various meshes.
The turbulence was modeled with the k-epsilon, Shear Stress Transport (SST), BSL
Reynolds Stress and SSG Reynolds Stress models [1]. The k-epsilon and the SST models are
two equations eddy viscosity models. In the k-epsilon model transport equations for the
turbulence kinetic energy and turbulence dissipation are solved and the turbulent viscosity is
determined from these quantities. The SST model applies a blending function that activates
the Wilcox k-omega model (transport equations for the turbulence kinetic energy and specific
dissipation) near the wall and k-epsilon model in the outer region. The eddy viscosity is
calculated form the turbulent kinetic energy and the specific dissipation considering an upper
limit determined form the turbulence kinetic energy, the absolute value of the strain rate and a
blending function.
The SSG Reynolds Stress and BSL Reynolds Stress models are second-order closure
models in which transport equations for the individual Reynolds stresses are solved. The SSG
Reynolds Stress model is closed with an epsilon equation while in the case of the BSL
Reynolds Stress model there is a blending between epsilon and omega equations similarly to
the SST model. The k-epsilon and SSG Reynolds Stress models were applied with scalable
wall function [5], while the SST and the BSL Reynolds Stress models were used with
automatic wall treatment [1]. Scalable wall function uses the friction velocity calculated from
the logarithmic law of the wall and an alternative velocity scale in determination of the wall
shear-stress. Because of the limitation for the minimum non-dimensional wall distance in
logarithmic formulation (y+min=11.06, which is intersection between the logarithmic and the
linear near wall velocity profile), there is no lower limit for the first cell size and consistent
grid refinement is possible differently from standard wall function. Automatic wall treatment
by omega equation based models means a smooth shift between the wall function approach
and low-Reynolds formulation based on the near wall mesh spacing. This shifting permits use
of coarser mesh next to the wall in contrast to a low-Reynolds formulation.
High Resolution Scheme [1] was employed to discretize the convection terms. The
computations were performed in steady state mode. The calculations were run until the mass
flow through the periodic interfaces did not varied with the progress of the iteration and all
normalized equations residuals and imbalances were below the defined convergence criteria
(10-5 in RMS for residuals and 0.01% for imbalances).
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Mesh sensitivity study
In order to check the influence of the mesh resolution on the results, comprehensive mesh
sensitivity study was performed. In the case of each mesh calculations were carried out
applying the same boundary conditions as described in Section 2.1. For the mesh sensitivity
study the BSL Reynolds Stress turbulence model was chosen among the four mentioned
models because based on its properties (the level of description of turbulence, wall treatment)
this model was expected to give the best solution. The results of the calculations were
compared with one another and with measurement data along a line that lies on the upper
surface of the model using the presented coordinate system (red line in Figure 3).
Z
L
Y
Figure 3. Location of the line “L” used for comparison
Trupp and Azad published turbulence quantities (namely the dimensionless Reynolds
stresses and dimensionless turbulence kinetic energy) as a function of the dimensionless
distance from the wall along “L” line [2]. Dimensionless distance from the wall was defined
2
using the length of this line: y*  y / L . Normal Reynolds stresses ( u i ), shear Reynolds
stresses ( uv ), turbulence kinetic energy (k) and axial velocity (U) were transformed into
dimensionless form using the average friction velocity ( u ):
ui
2


ui
u
2

uv 
,
uv
,
2
u
k 
k
u
2
,

U 
U
u
The Reynolds stress components were measured using linearized constant temperature
anemometry. The accuracies were estimated to be within ±3% for normal stresses and ±5%
for uv shear stress. The friction velocity was calculated from the axial pressure gradient,
which was measured by static pressure probe. The calculated and measured dimensionless
turbulence stresses ( u 2

is the axial, v 2


is the radial, w2 is the peripheral normal stresses

and uv is the shear stress), dimensionless turbulence kinetic energy (k+) and dimensionless
axial velocity (U+) are shown in Figures 4, 5 and 6.
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1.2
1.0
v2+
u2 +
1.4
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Experiment
M1
M2
M3
M4
M5
M6
0.0
0.2
0.8
Experiment
M1
M2
M3
M4
M5
M6
0.6
0.4
0.2
0.0
0.4
y*
0.6
0.8
0.0
1.0
0.2
0.4
0.6
0.8
1.0
y*


Figure 4. Distribution of u 2 and v 2 normal stresses
1.6
1.4
1.2
Experiment
M1
M2
M3
M4
M5
M6
0.8
0.6
0.4
0.2
0.0
0.0
0.2
uv+
w2+
1.0
0.4
0.6
0.8
-1.0
-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
1.0
Experiment
M1
M2
M3
M4
M5
M6
0.0
0.2
0.4
y*
0.6
0.8
1.0
y*


Figure 5. Distribution of w2 normal and uv shear stresses
1.4
3.5
Experiment
M1
M2
M3
M4
M5
M6
k+
2.5
2.0
1.5
1.2
1.0
M1
M2
M3
M4
M5
M6
0.8
U+
3.0
0.6
1.0
0.4
0.5
0.2
0.0
0.0
0.0
0.2
0.4
0.6
0.8
0.0
1.0
y*
0.2
0.4
0.6
0.8
1.0
y*
Figure 6. Distribution of the dimensionless turbulence kinetic energy
and dimensionless axial velocity
Calculated results are marked by continuous lines and the measurement data are indicated
by points. For this case measurement data concerning the axial velocity were not published
therefore only our calculated results are presented.
Based on the dimensionless turbulence quantities it can be stated that the accuracy of the
calculation results are strongly affected by the resolution of the mesh. The largest difference
between the measured and calculated values can be observed in the case of the coarsest mesh
(M6). Using finer grids (M5, M4, M3) discretization errors decrease and for this reason the
discrepancies between measured and calculated values decrease, too. The results are
converging towards the exact solution of the system of partial differential equations. Owing to
this differences between calculation results decrease with increasing mesh density.
Calculations performed with M1, M2 and M3 meshes show the same except the near wall
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region and agree well with the measured values. The differences close to the wall are caused
by the resolution of the boundary layer. In the case of the meshes M1 and M2 the boundary
layer was practically resolved therefore simulation of the near wall processes is possible. For
mesh M3 the near wall region was not resolved fine enough therefore the effect of the wall
was modeled using wall function. In the case of the dimensionless axial velocity (Figure 6)
the dependence from mesh density is smaller. The difference of the dimensionless axial
velocity distributions at the wall is caused by the near wall resolution of the grid as it was
mentioned previously.
M1
M2
M3
M4
M5
M6
Figure 7. Cross sectional velocity vectors on the upper surface
In Figure 7 cross flow can be seen at the top surface of the model. Formation of secondary
flows was expected based on Trupp-Azad measurements [2] and LES simulations by Mayer
and Házi [6]. Meshes M5 and M6 are not even suitable to predict quantitatively the secondary
flows because of the small cross sectional grid density. Using mesh M4 secondary flows
appear but based on the flow field and the previous comparisons, the mesh resolution is
unsatisfactory to calculate the flow accurately. In the case of other meshes the resolution is
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suitable to calculate the flows. Six symmetric primary flow cells were formed in a subchannel
in accordance with the measurement. It has to be mentioned that the flow close to the wall is
erroneous for mesh M2. This problem can be caused by the first cell size at the wall. Whereas
the first cell size of the meshes M1 and M3 were adequate applying automatic wall treatment.
Based on the presented investigations, meshes M1 and M3 are acceptable to calculate the
flow field accurately in this subchannel. Use of a mesh with very fine near wall resolution like
mesh M1 can be difficult in the case of more intricate and larger geometry (for example a rod
bundle with spacer grid) because of the mesh generation problems and high number of cells.
For this reason and since the examination of the processes in the viscous sublayer was not an
objective of the study mesh M3 was chosen for further calculations. Since the BSL Reynolds
Stress turbulence model is the most sensitive to mesh resolution among the four models thus
mesh M3 is most likely adequate for the three other models.
Turbulence model study
In subchannel and fuel assembly investigations it is very important to choose an adequate
turbulence model. In this study, calculations were carried out using k-epsilon, Shear Stress
Transport (SST), SSG Reynolds Stress and BSL Reynolds Stress turbulence models. The kepsilon and the SST models belong to the two equations eddy viscosity models thus the
Reynolds stresses can be calculated from the Boussinesq approximation [7]:
 U i U j
2
ui u j  k ij  T 

 x
3
xi
j





where  ij is the Kronecker delta,  T is the turbulent viscosity and U i / x j are the mean
velocity gradients. The SSG Reynolds Stress and BSL Reynolds Stress models are secondorder closure models in which transport equations for the individual Reynolds stresses and
turbulence dissipation or specific dissipation are solved.
The dimensionless turbulence quantities are shown in Figures 9, 10 and 11 calculated with
several turbulence models and measured by Trupp and Azad [2]. The shear stress

uv computed with several turbulence models agrees well. The only exception is the near wall
region. The congruence between the calculated and measured shear stresses is good. In the
case of the normal stresses there is a difference between the results. The eddy viscosity
models predict isotropic normal stresses therefore the v 2



and w2 stresses are overestimated
and the u 2 stress is underestimated compared to measurement data. Reynolds Stress models
are able to predict the anisotropic normal stresses, which are responsible for secondary
motions. Based on the comparison with measured data, the BSL Reynolds Stress model gives
a better prediction for normal stresses than the SSG Reynolds Stress model and the eddy
viscosity models give worse estimation than the SSG model. The results calculated by BSL
Reynolds Stress model are in relatively good agreement with the measurement.
The difference of the turbulence kinetic energy is smaller than the difference of the
individual normal Reynolds stresses calculated with several turbulence models (Figure 10).
However the BSL Reynolds Stress model predicts this quantity more accurately than the
other.
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1.4
1.2
1.0
v2+
u2+
1.6
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
0.8
Experiment
BSL Reynolds Stress
SSG Reynolds Stress
SST
k-epsilon
Experiment
BSL Reynolds Stress
SSG Reynolds Stress
SST
k-epsilon
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
y*
0.6
0.8
1.0
0.6
0.8
1.0
y*


Figure 8. Distribution of u 2 and v 2 normal stresses
1.6
-1.2
1.4
-1.0
1.0
0.8
uv+
w2+
1.2
Experiment
BSL Reynolds Stress
SSG Reynolds Stress
SST
k-epsilon
0.6
0.4
0.2
-0.8
-0.6
Experiment
BSL Reynolds Stress
SSG Reynolds Stress
SST
k-epsilon
-0.4
-0.2
0.0
0.0
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
0.4
y*
y*


Figure 9. Distribution of w2 normal and uv shear stresses
1.2
4.0
3.5
2.0
1.5
1.0
0.9
U+
2.5
k+
1.1
Experiment
BSL Reynolds Stress
SSG Reynolds Stress
SST
k-epsilon
3.0
BSL Reynolds Stress
SSG Reynolds Stress
SST
k-epsilon
0.8
0.7
1.0
0.5
0.6
0.0
0.5
0.0
0.2
0.4
y*
0.6
0.8
1.0
0.0
0.2
0.4
0.6
0.8
y*
Figure 10. Distribution of the dimensionless turbulence kinetic energy
and dimensionless axial velocity
Figure 11. Cross sectional velocity vectors calculated with BSL Reynolds Stress
and SSG Reynolds Stress models
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1.0
The dimensionless axial velocity profiles differ slightly (Figure 10). Since the turbulence
quantities calculated with BSL Reynolds Stress model show the best agreement with
measurement data therefore the velocity profile calculated with this model can be the best
prediction.
Figure 11 shows the cross sectional velocity distribution on the upper surface calculated
with Reynolds Stress models. The k-epsilon and the SST models could not predict the
secondary flows whereas the Reynolds Stress models were able to calculate them. The
average cross sectional velocity is 0.16% of the bulk velocity (1.34 mm/s) calculated with
BLS Reynolds Stress and 0.06% of the bulk velocity (0.52 mm/s) using SSG Reynolds Stress
model. Based on the Trupp and Azad measurements, this velocity is less than 0.5% of the
bulk velocity.
The above-described study pointed out that the BSL Reynolds Stress model is suitable for
the prediction of the secondary motions and capable to estimate the turbulence quantities in
the investigated subchannel accurately therefore it is appropriate for subchannel and rod
bundle simulations at this P/D ratio. For that reason, this model was chosen for the further
examinations.
3. ROD BUNDLE CALCULATIONS
Two models were built to examine the mixing processes in a VVER-440 rod bundle
section: a rod bundle model without (model “A”) and a rod bundle with spacer grid (model
“B”). The calculations were performed for the operational flow conditions of the VVER-440
reactor. The Reynolds number is about 220,000 in this case which is higher than the Reynolds
number was taken into account in the subchannel simulations (60,000). Since the flow is fully
turbulent in both cases therefore the results of the turbulence model study are acceptable for
the higher Reynolds number flow as well.
Numerical model description
The geometrical models of rod bundles can be seen in Figure 12. The 250 mm long models
contain six fuel rods with an outer diameter of 9.1 mm and the rod pitch is 12.3 mm likewise
as in our subchannel model. The difference between them is that the model “B” involves a flat
spacer grid of which the wall thickness is 0.5 mm (in some places 0.25 mm) and its height is
10 mm.
The model “A” was meshed with unstructured prism elements with the same density as the
mesh density of the model M3 farther from the rod walls. Because of the higher Reynolds
number of the modeled flow, the grid density at the rod walls had to be increased. That is why
the cell size of the prism mesh was decreased and four inflation layers were used (y+ave=34.4)
instead of three on the walls. The axial height of the prism mesh layers is about 2 mm. The
number of elements is 4,015,104.
In the case of the model “B” prism mesh was used with a cross sectional resolution similar
to resolution used in mesh M3 farther from the rod walls. The number of inflation layers is
four on the wall of the rods and the spacer grid (y+ave= 32.7). The height of the axial layers
was decreased near the spacer grid to calculate its effect accurately. Farther from the spacer
grid the height of the axial layers is 2 mm similarly to model “A”. The number of elements is
6,168,028.
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Outlet
pout=123 bar
Outer wall
of the rods
Symmetry
Wall
q’’=840 kW/m2
Inlet
vin=3.18 m/s
Tin=265 °C
iturb=10%
t/
Spacer grid
model “B”
model “A”
Figure 12/1. Geometrical models and boundary conditions
model “A”
model “B”
Figure 12/2. Grids of the fuel bundle models on the outlet surface
Calculations were accomplished for both geometry applying the same boundary conditions
(Figure 12). Inlet boundary condition was used at the lower surface of the models. The
velocity of the incoming uniform flow was set to 3.18 m/s and the inlet temperature was 265
°C. 10% turbulence intensity and 100 viscosity ratio (eddy viscosity/dynamic viscosity) were
defined as turbulence boundary conditions. Outlet condition of 0 Pa average static pressure
was applied at the top end of the models (reference pressure was 123 bar). No slip smooth
wall boundary condition with constant heat flux (840 kW/m2) was used for modeling the rod’s
surface. The six border surfaces of the models were defined as symmetry planes. In the case
of the model “B” the wall of the spacer grid was modeled as no slip smooth adiabatic wall.
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The temperature dependency of the water properties was taken into account using IAPWSIF97 water data, which is implemented in the code. BSL Reynolds Stress turbulence model
was used with automatic wall treatment for the calculations based on the turbulence model
study carried out for subchannel. The computations were performed in steady state mode
applying High Resolution advection scheme. The calculations were run until all equation’s
residuals and imbalances reached the defined convergence criteria (10-5 in RMS for residuals
and 0.01% for imbalances).
Results of the rod bundle calculations
Calculations were accomplished applying the before mentioned models and boundary
conditions. Distributions of the axial velocity component at the outlet plane can be seen in
Figure 13.
model “A”
model “B”
Figure 13. Axial velocity distribution on the outlet plane
The axial velocity has local maximums at the center of the subchannels and its magnitude
is lower in the gaps between rods. Boundary layer is developed near the walls. There are some
differences between the results calculated with the two models. In the case of the model “A”
the axial velocity distribution is the same in all subchannels while calculated with the model
“B” there is a difference between subchannels that are induced by the spacer grid. In the case
of model “B” the axial velocity is slightly higher and more peaked in subchannels that involve
the hexagonal part of the spacer grid.
The cross sectional velocity distribution is shown in Figure 14 for model “A”. Secondary
flows are visible in all subchannels whose distribution is the same. Nature of the secondary
motions agrees with the observed flow by subchannel simulations. Namely secondary flows
in a subchannel consist of six primary flow cells, which are symmetric in pairs. Since the
primary flow cells are symmetric therefore the secondary flows do not cause convective
mixing between the adjoining subchannels. The magnitude of these flows is about 0.21% of
the bulk velocity.
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Figure 14. Cross sectional flow at the outlet (model “A”)
Figure 15. Cross sectional flow at the outlet (model “A”
with periodic boundary condition)
An other calculation was performed applying periodic boundary condition in the axial
direction for the same mass flow in order to model a full developed flow. Figure 15 shows the
secondary motions on the top surface of the model. The character of the flow agrees with the
previous case. The magnitude of the cross flows is about 0.14% of the bulk velocity, which
agrees relatively well with the calculated value in subchannel simulation in which Reynoldsnumber was much lower. Mention must be made that the velocity of cross flows calculated
with periodic boundary condition is lower than the velocity calculated with use of inlet
boundary condition thus the flow is not fully developed in the second case.
Figure 16 shows the cross sectional flow field for model “B”. Secondary flows occur
similarly to the preceding cases but their nature differs. The cross sectional flow is not the
same in all subchannels and not symmetrical. This difference is caused by the different
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geometry of the subchannels namely by the spacer grid. The magnitude of the secondary
flows is higher in subchannels that contain the hexagonal part of the spacer grid. Further
effect of the asymmetric geometry is that the cross flows cross the wall of subchannels and
can cause convective mixing between adjoining subchannels (Figure 16) in contrast to the
previous case (model “A”). The magnitude of the convective flow between subchannels is
about 5-8 mm/s at the outlet. Convective mixing can be more significant and efficient in the
case of such spacer grid that has mixing flags and not so even as the investigated one. In order
to calculate the flow and heat transfer processes in a fuel assembly accurately it is important
to take into account the spacer grid satisfactorily because it can cause considerable convective
mixing between the adjoining subchannels.
Figure 16. Cross sectional flow at the outlet (model “B”)
model “A”
model “B”
Figure 17. Temperature distribution on the outlet plane
The outlet temperature distributions can be seen in Figure 17. The temperature in the
center of the subchannels is lower than in the gap regions, which can be explained with the
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distance form the rods and the axial velocity distribution. Thermal boundary layer develops
next to the rods in which the temperature is higher. It is visible that in the case of the model
“A” the temperature distribution is the same in all subchannels, the outlet average temperature
of each subchannel is 272.3 °C. Apparently the situation is the same for model “B”, but the
outlet average temperature of subchannels that involve the hexagonal part of the spacer grid is
272.1 °C. This value for other channels is slightly higher, namely 272.5 °C. This difference is
caused by the little bit higher mass flow of the subchannels that involve the hexagonal part of
the spacer grid.
4. CONCLUSIONS
Flow and heat transfer processes in a subchannel and in triangular array of rod bundles
were investigated using the code ANSYS CFX 11.0. Subchannel models were developed and
comprehensive mesh sensitivity study was performed at first. The sensitivity study showed
that the suitable mesh resolution is very important to predict the turbulence quantities in a
subchannel well and relatively high mesh density is needed to calculate the secondary flow
adequately. Using an “optimal” mesh a turbulence model study was performed applying kepsilon, SST, SSG Reynolds Stress and BSL Reynolds Stress models. The investigations
pointed out that the SSG Reynolds Stress and BSL Reynolds Stress models are able to predict
the anisotropic normal Reynolds stresses and the secondary flows in contrast to the k-epsilon
and the SST models. Results calculated with the BSL Reynolds Stress model agree the most
with measurement data published by Trupp and Azad. Based on these studies, the BSL
Reynolds Stress model was selected for the further investigations.
Using a suitable mesh resolution and turbulence model two 250 mm long rod bundle
section models were built that contain six rods. One of the models involves a spacer grid as
well. Calculations were carried out for both models applying the same boundary conditions in
order to investigate the mixing processes. In the case of the calculation without spacer grid the
investigation showed that the secondary flows are symmetric to the subchannel walls and they
do not cause convective mixing between the adjoining subchannels. In the other case the
secondary flows cross the walls of the subchannels in consequence of the effect of the spacer
grid and can cause convective mixing between subchannels. In this case the outlet
temperature of subchannels was different in spite of the symmetrical boundary conditions.
The reason for that is the different mass flow of channels influenced by the spacer grid.
In the future, our aim is to improve our full length fuel bundle model applying the acquired
experiences and validate it using measurement data performed by Kurchatov Institute on a full
scale test facility for VVER-440 fuel assembly. Applying the validated model the verification
and the improvement of COBRA model (for example increase of the accuracy of the flow
resistant and turbulent mixing coefficients, etc.) will become possible. Besides, we intend to
validate our VVER-440 fuel assembly head model and investigate the reasons of deviation
between the average outlet temperature of fuel assembly and temperature measured with
incore thermocouples.
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REFERENCES
1. ANSYS Inc, ANSYS CFX-Solver Modeling Guide, ANSYS CFX-Solver Theory
Guide, 2007.
2. A. C. Trupp and R. S. Azad, The Structure of Turbulent Flow in Triangular Array Rod
Bundles, Nuclear Engineering and Design, 32, 1975, pp. 47-84.
3. A. Aszódi and G. Légrádi, Detailed CFD Analysis of Coolant Mixing in VVER-440 Fuel
Assemblies With the Code CFX 5.5, Proceeding of Technical Meeting on Use of CFD
Codes for Safety Assessment of Reactor Systems, Italy, 2002.
4. S. Tóth and A. Aszódi, Calculations of Coolant Flow in a VVER-440 Fuel Bundle with the
Code ANSYS CFX 10.0, Workshop on Modeling and Measurements of Two-Phase Flows
and Heat Transfer in Nuclear Fuel Assemblies, Sweden, 2006.
5. H. Grotjans and F. R. Menter, Wall Functions for General Application CFD Codes, Fourth
European Computational Fluid Dynamics Conference, Greece, 1998.
6. G. Mayer, J. Páles and G. Házi, Large Eddy Simulation of Subchannels Using the Lattice
Boltzmann Method, Annals of Nuclear Energy, 34, 2007, pp. 140-149.
7. S. B. Pope, Turbulent Flows, Cambridge University Press, New York & USA, 2000.
8. W. K. In and T. H. Chun, Assessment of the RANS Turbulence Models for a Turbulent
Flow and Heat Transfer in a Rod Bundle, Nuclear Technology, 150, 2005, pp. 231-250.
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