International Journal of Application or Innovation in Engineering & Management (IJAIEM)
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Volume 2, Issue 11, November 2013
ISSN 2319 - 4847
Investigation of effects of helical wire-wrapped
spacers on thermo hydraulic properties of a
fluid flow along to heated fuel bundle
Mansour Talebi1, Reza Abdolahi1 and Afshin Ahmadi Nadooshan2
1
2
Nuclear Science & Technology Research Institute, Isfahan, Iran
Department of Mechanical Engineering, Shahrekord University, Shahrekord, Iran
Abstract
The fluid flow and heat transfer along to heated fuel bundle with helical wire-wrapped spacers in hexagonal channel is
investigated by 3D numerical simulation. Hexagonal channel's walls are isolated and heat fluxes are applied on fuel rods
surfaces. Finite volume method and SIMPLE algorithm is used to solve governing equations. A parametric study is undertaken
and the effects of the Rayleigh number, inlet temperature and heat fluxes on the fluid flow and heat transfer inside the channel
are investigated. Results show that using of helical wire-wrapped spacers is resulted to pressure drop increasing. In construct,
these spacers uniform fluid velocity and temperature in the channel. Furthermore, heat transfer coefficient and average Nusselt
Number increase with Reynolds number and heat flux increscent.
Keywords: Wire-Wrapped, Spacer, Fuel Bundle, Numerical Simulation
1. INTRODUCTION
One of the most important issues of nuclear reactors is core cooling, better heat transfer, and improving system efficiency.
Increasing heat transfer from fuel bundle to coolant is a key parameter in nuclear power enhancement. Of course fuel
element should not be overheated. In case of overheating, fuel rod and cladding would be molten and a huge portion of
radioactive materials would be released in coolant fluid. A way for enhancing heat transfer from fuel is increasing
convective heat transfer coefficient which is available by installing fins in fluid flow path which increases flow
turbulence. The most common method is using turbulent fin (spacers). This tool causes more pressure drop which is a
negative effect in reactor thermohydraulic performance. Hence, in design of fins, optimization calculations should be
conducted. Helical wire-wrapped forces fluid to rotate around fuel rods and in turn increases heat transfer. It is a new
technology of spacers. Effects of helical wire-wrapped on rector cooling system, performance of fluid flow, and heat
transfer of fuel rods should be investigated by higher accuracy to enhance efficiency of reactor.
Nijsing and Eifler [1] presented a numerical method to predict thermohydraulic properties of single-phase and steady
flow around fuel rods of a fast reactor with a molten salt coolant. Results show that in case of fuel bundle with net spacers
which distance between wall and fuel center is equal or greater than distance between two adjacent rods, it is possible that
temperature of fuel rods vary significantly (70˚C or more). It is also observed that increasing turbulence of subchannel
two times of natural condition has a very small effect on temperature variation. Rotating flow in subchannels which is due
to helical wire-wrapped causes temperature to decrease. Experimental study of friction factor and heat transfer in laminar
and turbulent flow over a 61-pin fuel bundle with helical wire-wrapped in a water loop was conducted by Armikar and
Fenech [2]. Results show that pressure profile (pressure around fuel rod) has a significant drop trough helical wirewrapped. In addition helical wire-wrapped causes more heat and momentum transfer in laminar flow rather than
turbulent flow. Calculated friction factor in laminar flow is very close to friction factor of smooth pipes and is in
agreement with semi-empirical results of Novendstem [3].
Fenech [4] studied local heat transfer on 61-pin fuel element with helical wire-wrapped experimentally. In this study,
eight fuel rods with heater were located in a hexagonal channel to obtain more accurate bulk temperature under channels.
He also obtained a more accurate relationship for Nusslt number in comparison to the previous investigation [3]. In this
relationship effects of all near rods (which produce heat simultaneously) on heattransfer coefficient are considered.
Shimizu et al [5] presented a numerical method in order to calculate temperature distribution of a single-phase and steady
flow in a fast rector with molten salt coolant and helical wire-wrapped.
Results indicate that pressure drop for fuel rods without helical wire-wrapped in Reynolds numbers smaller than 1200 is
in good agreement with experimental results [6-8]. 3D results of cross flow distribution around 7-pin fuel bundle with
helical wire-wrapped show that most of rotational cross flow is observed in empty distance of hexagonal channel wall and
when helical wire-wrapped be located in 180˚ position from empty distance and along rod surface. These results are in
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Volume 2, Issue 11, November 2013
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agreement with experimental results for same geometry and condition [9]. using a CFD code, Gajapathy et al [10]
investigated fluid flow and temperature filed in helical wire-wrapped 7-pin fuel bundle. Molten Sodium was used as
coolant. Results show that calculated friction factor is in good agreement with experimental results in both cases with and
without helical wire-wrapped. Results also indicate that pressure drop due to helical wire-wrapped is greater for turbulent
flow rather than laminar flow. In addition, velocity and temperature distribution obtained from numerical results show
that helical wire-wrapped makes a rotating flow around fuel rods which increases fluid mixing and flattens temperature
profile. Such a rotational flow decreases molten sodium temperature difference between subchannel's inlet and outlet from
86 ˚C without spacer to 21˚C with spacer. Thermohydraulic investigation of steady and transient flow in reactor core with
helical wire-wrapped is done by Diller et al [11]. In this study, two type of fuel (oxide and hybrid fuels) are used and
reactor power is calculated as a function of fuel rod diameter and spacer pitch to diameter ratio. Results show that
difference in fuel type has no effect on thermohydraulic performance. The reactor highest power is obtained for spacer
pitch to diameter ratio equal to 1.42 which is 25% higher than reactor with net spacers. According to this study the most
important advantage of helical wire-wrapped is decrease in pressure drop and increase in critical heat flux.
Natesan et al [12] using a 3D CFD simulation of turbulent flow to investigate the pressure drop and heat transfer of a 19pin fuel bundle with helical wire-wrapped in a fast reactor with molten salt coolant. In this simulation three types of
turbulence models (k-e, k- , Reynolds stresses) were used. Comparison of results of these three models with experimental
relationship indicates that calculated friction factor with these models are close to each other and differ from Novendstern
experimental relationship about 6%. Morover, the obtained Nusselt numbers from these three models are in agreement
with each other and differ from Fenech experimental relationship about 1%. Also, results show that friction factor is a
function of helical wire-wrapped pitch. By decreasing pitch from 300mm to 100 mm, friction factor becomes 1.6 times
greater. Nusselt number and heat transfer coefficient are not sensitive to pitch variation. Any decrease in pitch would
increase cross flow velocity and turbulent intensity which causes more thermal mixing of coolant and in turn temperature
distribution in fuel assembly cross section would be more uniform.
Rolfo et al [13] conducted heat transfer and fluid flow 3D simulation for 7, 19, 61, and 271 pin fuel bundle with helical
wire-wrapped in fast reactor with molten salt coolant. In this simulation constant temperature and heat flux boundary
conditions were applied. Results illustrate a strong rotational secondary flow in edge subchannels where the combination
of effects of helical wire-wrapped and outer boundaries causes flow to swerve. Calculated friction factor in "secondary
moment limit" model was more than the obtained friction factor from "eddy viscosity model".
Results also included local friction factor. In addition, It was observed that heat transfer in fluid was not sensitive to the
selected turbulence model. In case of constant heat flux boundary condition in contrast to constant temperature boundary
condition, increasing number of fuel rods would decrease Nusselt number and would make temperature field less uniform
Most numerical studies and simulations in the field of helical wire-wrapped is conducted for fast reactors with molten
sodium coolant. In addition, experimental investigations have not presented a relationship for effects of geometrical
properties on thermohydraulic parameters.
Current study aims to answer these unknowns. In this article, flow of water around fuel bundle with helical wire-wrapped
in pressurized water reactor is simulated and thermohydraulic properties of coolant such as temperature, velocity,
pressure and etc. are calculated.
2. PHYSICAL MODEL AND GOVERNING EQUATIONS
Geometry properties of fuel rods and spacers are selected according to nuclear reactor standards. Simulation includes of
7-pin fuel rods with helical wire-wrapped located in a hexagonal channel. Boundary conditions are inlet velocity (from
0.852 m/s to 8.52 m/s), outlet pressure, isolated hexagonal walls and fuel rod's surface heat flux (from 200 kW to 1800
kW). Figure 1 illustrates the geometry and dimensions of the control volume under consideration (all length units are
mm).
Figure 1: Geometry model of fuel rods helical wire-wrapped
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Simulation and resolving of governing equations (momentum and energy equations) are conducted using numerical
calculation software which uses finite volume method. It also couples momentum and heat transfer equations.
Boundary conditions in this simulation include velocity and pressure for inlet and outlet boundaries, respectively.
Hexagonal channel's walls are isolated and heat fluxes are applied on fuel rods surfaces. Since calculations need high
computer memory, length of model was taken equal to pitch of helical wire-wrapped. Reynolds number is in range of 104
to 105 and k-ε turbulence model is used. Finite volume method and SIMPLE algorithm is used to resolve governing
equations. Governing equations and turbulence model equations are:
Continuity:

u j  0
x j
 
(1)
Momentum:
p

u j u i   ij  
x j
x i


(2)
where shear stress tensor and strain rate tensor are:
 ij  2s ij 
2 u k

 ij
3 x k
(3) 1  u i u j
s ij  

2  x j x i




(4)
Energy:

x j

  u j c p T  K T

x j


0


(5)
Turbulence kinetic energy:

 


u j k     t

x j 
k

 k

 x j



     2   t ui  k  ui
 x

3  xi
 i

 

 x j
2





  C 1    2  t ui  k  ui   C 2  
 x

k  3  xi
k
 i

(6)
Dissipation energy rate:

x j


 u j      t





t  C  
k2

(7)
(8)
The constants used in Equation (8) are presented in Table 1.
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Table 1: Constant values used in turbulence equation
C 1
C 2

C
0.09
1.44
1.92
1.3
4 VALIDATION OF RESULTS
To validate the present results, they are compared to the results of [3] and [10]. For this purpose, friction factor is
calculated and compared to numerical results of Gajapathy et al [10] and experimental results of Novendstern [3]. Figure
3 illustrates this comparison. Friction factor is calculated according to:
 P  d h 

f  2

2 
 V  l 
(9)
Figure 2 indicates that obtained results of current model are in good agreement with numerical and experimental data. As
is understood from this figure, current study results are so close to Novendstern experimental results and Gajapathy et al.
[3] simulation except for first Reynolds. It should be mentioned that Gajapathy et al. [3] also compared their results to
experimental results of Novendstern [10]. According to Figure 2 the difference between Gajapathy et al. [3] and
Novendstern [10] results is more than the difference between current work and Novendstern results. In addition trend of
friction factor variation against Reynolds number is entirely similar to both experimental and numerical results.
Figure 2: Comparison of friction factor between current work and other studies
5 RESULTS
In order to investigate effects of helical wires on fluid flow performance and heat transfer around fuel rods, results are
compared with a system without helical wire wrapped.
5.1 Fluid flow performance in reactor core Body paragraphs
Figures 3 and 4 illustrate velocity contours in different heights for both cases (with and without helical wire wrapped) in
Re=89618. According to Figure 3 fluid velocity in regions of channel where helical wires are near wall is more than other
regions. This region is shown by red color in Figure 3. Position of maximum velocity point along the channel varies with
rotation of helical wire which indicates rotation of fluid along the channel. Rotation of fluid along channel from front
view is clockwise. On the other hand, in the system without helical wire wrapped, maximum velocity position remains
constant along the channel (see Figure 4).
In other word, coolant in this case without any kind of rotation and mixing flow through channel. It should be mentioned
that maximum velocity is more when helical wire is used. Comparison of pressure drop values and friction factors
between both cases (with and without helical wires) is illustrated in Table 2.
Calculations indicates that hydraulic diameter for channel with helical wire is 4 mm and for channel without helical wire
is 4.9 mm. According to the results, pressure drop in channel with helical wires is about two time greater than pressure
drop in channel without helical wires. Also it is understood that by increasing fluid inlet velocity pressure drop would
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increase. Friction factors values are nearly constant. According to friction factor relationship, this parameter is a function
of hydraulic diameter and inlet velocity. Variation of these two parameter causes reduction in friction. Figure 5 illustrates
velocity values along hexagonal channel with helical wire-wrapped for two positions near channel central rod (black line)
and near channel wall (red line).
Z=0L
Z=0.6L
Z=0.2L
Z=0.8L
Z=0.4L
Z=L
Figure 3: Velocity distribution around heating rods with helical wire-wrapped
Z=0L
Z=0.6L
Z=0.2L
Z=0.8L
2
Z=0.4L
Z=L
Figure 4: Velocity distribution around heating rods without helical wire-wrapped
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Table 2: Comparison of pressure drop and friction factor in channels with and without helical wire-wrapped
Re
wire
Without wire
0.01018
0.00623
0.00556
0.00536
Without
wire
0.01143
0.00678
0.00577
0.00552
602
8737
18550
23926
329
4972
9371
1201
0.00518
0.00529
30633
15260
wire
10308
50053
77463
89618
10308
5
∆P(pa)
F
According to Fig. 5, a velocity variation along the channel for both lines is approximately uniform, and velocity near
channel wall is greater than channels central rod velocity. This is because of fluid flow rotation which is due to helical
wire-wrapped. Points where their velocity values are zero are locations of helical wire-wrapped. Velocity values along
hexagonal channel without helical wire-wrapped are reported for two positions near channel central rod (black line) and
near channel wall (red line). According to Fig. 5, velocity variations along the channel for both line is non-uniform and
velocity near channel wall is smaller than channels central rod velocity
Figure 5: Velocity distribution in heating rod channels with helical wire-wrapped (Re=89618)
Figure 6: Velocity distribution in heating rod channels without helical wire-wrapped (Re=89618)
5.2 Heat transfer performance of coolant in reactor core
Temperature contours for cases with and without helical wire-wrapped are shown in Fig. 7 and 8, respectively. According
to fig. 7, because of fuel rod's heat flux, temperature is maximized in center of channel with helical wire-wrapped. Also,
temperature of points near hexagonal wall of channel with helical wire-wrapped is greater than channel without helical
wire-wrapped near wall temperature. Temperature is maximized in center of channel without helical wire-wrapped, too.
Temperature of points near hexagonal wall of channel without helical wire-wrapped is near inlet fluid temperature. In
other word existence of helical wire-wrapped causes more coolant mixing along channel and hence the temperature
counter would be more uniform in channel cross section. Temperature of points where helical wires join rods is
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maximum. These pointes are “hot spot”. Simulation shows that by decreasing Reynolds number (decreasing inlet
velocity) number and hot spot and the maximum temperature of them decrease.
Z=0L
Z=0.6L
Z=0.2L
Z=0.8L
Z=0.4L
Z=1L
Figure 7: Temperature distribution over heating rods with helical wire-wrapped (Re=89618)
Z=0L
Z=0.6L
Z=0.2L
Z=0.85L
Z=0.4L
Z=1L
Figure 8: Temperature distribution over heating rods without helical wire-wrapped (Re=89618)
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In Fig.9, red zone in contact region of helical wires and rods is representative of hot points.
Figure 9: Contour of Temperature for total fuel bundle
Figure 10 illustrates fluid temperature variation along channel for different heat fluxes. According to Fig.10, any increase
in heat flux causes to increase in temperature.
Figure 10: Temperature distribution for different fluxes
Table 3 illustrates temperature variation along channel for water and molten Sodium with Re=89618. According to this
table for same heat fluxes, temperature variation along the channel for water is less than molten Sodium. Temperature
rise rate for water is about 1% and for molten Sodium is about 4%.
Table 3: Comparison of temperature variation in channel with helical wire-wrapped for water and molten sodium
Sodium
Water
0
673.2
565.6
0.25
679.2
565.0
Z/L
0.5
685.4
566.9
0.75
691.3
570.4
1.0
697.5
573.5
Variation of averaged heat transfer coefficient and Nusslt number on central fuel rod with helical wire-wrapped in
hexagonal channel and for different Reynolds numbers is shown in Fig.11.
Results indicate that by increasing Reynolds number, averaged heat transfer coefficient and averaged Nusslt number
increase. Rate of increase in these two parameters decreases with increase in Reynolds number.
Nusselt number and heat transfer coefficient variations against inlet temperature are plotted in Fig.12 for different
Reynolds numbers (for channel with helical wire-rapped). According to thes Fig, increase in inlet temperature causes
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Nusselt number and heat transfer coefficient to increase. But increase in Reynolds number causes Nusselt number and
heat transfer coefficient to decrease. Shown in Fig. 13 is the variation of ratio of Nusselt number of rods with helical
wires to the Nusselt number of rods without helical wires against Reynolds number. According to this Fig, with increase
of Reynolds number, the Nasselt ration increases.
Figure 11: Averaged heat transfer coefficient and averaged Nusslt number against for Reynolds numbers
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Figure 12: Averaged Nusslt number and averaged heat transfer coefficient variation against inlet temperature for
different Reynolds numbers
Figure 13: Ratio of Nusslt number of rods with helical wires to Nusslt number of rods without helical wires against
different Reynolds number
6 CONCLUSION
Tree dimensional numerical simulation of fluid flow over fuel bundle with and without helical wire-wrapped in a
hexagonal channel is performed. The results indicate that helical wire-wrapped causes coolant rotation along the channel
which leads to more mixing and more uniform temperature distribution. Utilization of helical wire-wrapped leads to
creation of hot points in contact regions. Number and temperature of these hot points increase by increasing flow rate. For
same heat fluxes, temperature variation of water is less than that of molten sodium. Helical wire-wrapped causes rotation
of coolant along the channel which this leads to more fluid mixing and more uniform velocity distribution in channel
cross section. Helical wire-wrapped approximately doubles pressure drop and uniforms fluid velocity along the channel.
Averaged heat transfer coefficient and averaged Nusslt number increase by increasing Reynolds number and heat flux.
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AUTHOR
Mansour Talebi received the B.S., M.S. and PhD degrees in Mechanical Engineering from Isfahan University of
technology in 1992, 1994 and 2003, respectively.
.
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