jet impingement technique with a sectorial extended surface (SES) concept for the modular heliumcooled divertor has been studied within the framework of the post ITER tokamak, at the Institute for plasma research (IPR), INDIA. Experimental and numerical studies have been conducted to predict the thermal-hydraulic performance of a finger-type divertor design with proposed SES. Critical thermal hydraulic parameters, effective heat transfer coefficient and pressure loss have been measured in the experiment for the reference divertor as well as for a divertor with SES. The experimental mock-ups are made to full scale respecting Reynolds and Prandtl number similarities. Air is used as the simulant to represent helium, which is used as the coolant in prototype. A novel heat concentrator has been developed to simulate the high heat flux, by electrical heating.

1. Research paper
An experimental and numerical study of flow and heat transfer
in helium cooled divertor finger mock-up with sectorial
extended surface
Sandeep Rimza a, *
, Samir Khirwadkar a
, Karuppanna Velusamy b
a
Divertor and First Wall Technology Development Division, Institute for Plasma Research (IPR), Bhat, 382428 Gandhinagar, Gujarat, India
b
Mechanics and Hydraulics Division, Reactor Design Group (RDG), Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam 603102, India
h i g h l i g h t s
Sectorial extended surface is proposed to cool modular diverter finger mock up.
We study its thermal-hydraulic characteristics by experimental and computational simulations.
A novel heat concentrator has been developed to achieve high heat flux.
Experimental correlations for pressure loss and Nusselt number are proposed.
Effectiveness of extended surface has been demonstrated.
a r t i c l e i n f o
Article history:
Received 14 November 2014
Accepted 24 February 2015
Available online 5 March 2015
Keywords:
SES
Fusion reactor
Divertor
Tile
Thimble
Heat transfer enhancement
a b s t r a c t
A jet impingement technique with a sectorial extended surface (SES) concept for the modular helium-
cooled divertor has been studied within the framework of the post ITER tokamak, at the Institute for
plasma research (IPR), INDIA. Experimental and numerical studies have been conducted to predict the
thermal hydraulic performance of a finger type divertor design with proposed SES. Critical thermal
hydraulic parameters, effective heat transfer coefficient and pressure loss have been measured in the
experiment for the reference divertor as well as for a divertor with SES. The experimental mock-ups are
made to full scale respecting Reynolds and Prandtl number similarities. Air is used as the simulant to
represent helium, which is used as the coolant in prototype. A novel heat concentrator has been
developed to simulate the high heat flux, by electrical heating. The benchmark experimental data have
been used to validate the three dimensional conjugate heat transfer models. The computational result for
heat transfer coefficients and pressure loss are in satisfactory agreement with the experimental results.
Based on detailed parametric studies, correlations have been proposed for Nusselt number and pressure
loss coefficient as a function of Reynolds number which can be used for design applications. The pro-
posed SES divertor is seen to significantly augment the thermal performance of the finger type divertor at
the penalty of a minimum pressure drop at the prototypical condition. The results of the present study
provide added confidence in the numerical model used to design the divertor and its applicability to
other high heat flux gas cooled components.
© 2015 Elsevier Ltd. All rights reserved.
1. Introduction
It is generally accepted that fusion power is one of the promising
sources of sustainable energy in the future. Towards development
of fusion reactor technology, India is seriously pursuing research
and development activities at the Institute of plasma Research. The
study was launched with the aim of developing an attractive power
plant concept for the future fusion reactor called DEMO [1]. Design
of DEMO poses interesting and challenging thermal hydraulics is-
sues, arising out of very high heat flux. Divertor is one of the vital
components of fusion reactor and employed to ‘Divert’ the hot
plasma. It faces a direct thermal attack of plasma and is subjected to
heat flux of the order of 10 MW/m2
. The complete divertor target
* Corresponding author.
E-mail addresses: sandeepr@ipr.res.in (S. Rimza), sameer@ipr.res.in
(S. Khirwadkar), kvelu@igcar.gov.in (K. Velusamy).
Contents lists available at ScienceDirect
Applied Thermal Engineering
journal homepage: www.elsevier.com/locate/apthermeng
http://dx.doi.org/10.1016/j.applthermaleng.2015.02.066
1359-4311/© 2015 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 82 (2015) 390e402

2. plate is divided into a number of small volumes known as cassettes.
The plasma-facing surface of each cassette is made up of numerous
small cooling “finger mock up” to reduce the thermal stress as
depicted in Fig. 1.
Many experimental and numerical studies have been reported
in the open literature to investigate the heat transfer enhancement
and fluid flow characteristics of extended surface. The focus of
these studies has been to achieve a high surface area to volume
ratio, a large convective heat transfer coefficient, and a minimum
volume of coolant inventory. Heat transfer characteristics of jet
impingement have been numerically investigated with sectorial
extended surfaces by Rimza et al. [2], in the divertor finger mock up.
Their result shows that, the addition of SES enhances heat removal
potential with minimum pumping power. Gayton et al. [3] inves-
tigated the heat transfer and friction characteristics in a plate type
divertor, and predicted that the thermal performance of the
divertor significantly increases with the use of metallic foam.
Thermal performance and flow instabilities in multi-channel heli-
um-cooled porous metal divertor modules were analyzed by You-
chison et al. [4] and it was shown that the design can survive a
maximum heat flux of ~29.5 MW/m2
. Various heat transfer
enhancement techniques (swirl tape, roughening, porous media,
etc.) and the design issues associated with pumping power of the
cooled divertor have been studied by Baxi and Wong [5] and Baxi
[6]. Ihli and Ili
c [7] studied various cooling concepts for future
fusion power plants and found that the V-rib based surface
roughness is very efficient in heat removal.
Yuan et al. [8] investigated the potential of a plate pin fin heat
sink for electronics cooling. The predicted result shows that pin
height and air velocity have significant influences on the thermal
hydraulic performances. Numerical simulation of flow and heat
transfer of fin structure in air-cooled heat exchanger has been
investigated by Li et al. [9]. It was found that the air-side heat flux
and heat transfer coefficient increase sharply for the wavy fin
arrangement. Shafeie et al. [10] numerically investigated the effect
of micro channel and pin fin on the thermal performance of heat
sinks. It was observed that, heat removal capability of the finned
heat sinks is lower than that of the micro-channel for an identical
pumping power. A fan-shaped pin fin in a rectangular channel was
analyzed by Moon et al. [11] and their studies revealed that, fan-
shaped pin fin showed an improved Nusselt number (Nu)
compared to a circular pin fin, at Reynolds number (Re) less than
100,000. On the other hand, the pressure drop in the channel with
the fan-shaped pin fin was marginally less small than that with the
circular pin fin. The heat transfer enhancement characteristics of
wavy fin-and-flat tube heat exchangers have been analyzed by
Dong et al. [12]. They found that wavy fin with large waviness
amplitude can provide a high heat transfer coefficient. A numerical
study on the heat transfer enhancement with interrupted annular
groove fin was performed by Lin et al. [13]. Their results reveal that,
interrupted annular groove has a dual effect on fluid flow, guiding
and detached eddy inhibition to reduce the size of the wake region.
Experimental studies on staggered and in-line pin fin arrays
installed in an internal cooling channel were performed by Van
Fossen [14] and Sparrow et al. [15]. It was found that the heat
transfer coefficient and pressure drop for the in-line array are lower
than those for the staggered array. A novel heat transfer enhance-
ment technique was evaluated by Collins et al. [16]. In their studies,
they showed that the use of wire-coil significantly increases the
heat transfer at reasonably low flow rates, and hence pumping
power. The flow and heat transfer performance in a channel with
dimples has been studied by Moon et al. [17], Mahmood and Ligrani
[18], and Mahmood et al. [19]. In their studies revealed that by
providing dimple on the surface can enhance the Nusselt number
compared to a smooth surface by a factor of 1.8e2.8.
From the above literature survey, it is clear that heat transfer
enhancement is an active area of current research. In the context of
DEMO, it is desirable to explore efficient cooling technology for
helium cooled divertor, which can withstand a high heat load
(~10 MW/m2
) for divertor. Towards this a new sectorial extended
surface was proposed and studied for the divertor in an earlier
investigation [2]. However, no experimental data have been
Fig. 1. Schematic of (a) He cooled divertor finger mock-up and (b) 3-D and close up views of SES (all dimensions in mm).
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402 391

3. reported till date to validate the findings. The main objective of the
present work is to conduct, an experimental and numerical inves-
tigation to validate the thermal hydraulic performance of a design
that has close geometric and dynamic similarities of a finger mock-
up reported in Ref. [2]. The thermal performance has been evalu-
ated by comparing the heat transfer coefficient and pressure drop
across the test section.
2. Description of the physical model
The proposed helium cooled divertor finger mock up has been
depicted in Fig. 1. An earlier computational study by the authors [2]
indicated that this design is capable of handling heat flux 10 MW/
m2
, while maintaining the design temperature limit for the tung-
sten [20]. In the divertor design plasma facing component uses
tungsten as the “Tile” (width 17.8 mm) which is brazed to a
“Thimble” (Ø15 1 mm) made up of tungsten alloy (WL-10). A
concentric steel jet cartridge (Ø11.2 1 mm) carrying the nozzle
(2 mm) is positioned within the thimble. Coolant enters through
the nozzle and flows radially outwards through the space between
the cartridge and the thimble.
Helium is used as the coolant due to its attractive chemical and
neutronic properties and safe operation. However, low thermo
physical characteristics of helium require high pressure and large
pumping power. To enhance the rate of heat transfer, the sectorial
extended surface (made of WL-10) has been added to the finger
mock up with supporting plate. The SES is angularly constructed at
every 30 sector, resulting in thirty six extended surfaces as
depicted in Fig. 1. Each radial row consists of twelve SES evenly
spaced at 30 spacing. Alternating rows of SES have been offset by
30 to promote circumferential flow in between the extended
surfaces. By a proper design of the extended surface, all the surfaces
are made to participate in the heat transfer process.
3. Experimental studies
3.1. Experimental condition
It is known that geometric and dynamic similarities are very
essential to carry out model experiments, and enable one to scale
up the results from model to prototype. In the present investigation
test geometries were manufactured to closely resemble the pro-
totype for testing in an air loop. The test condition studied has
Reynolds (Re) and Prandtl (Pr) numbers similar to the prototypical
operating condition of the divertor as presented in Table 1. Jet
diameter is selected as the characteristic length scale, due to the
impingement heat transfer. The Reynolds number based on the jet
diameter (2 mm) is defined as:
Re ¼ mD
mAjet
(1)
From Table 1, it is observed that the effect of Pr number on
thermal performance of divertor is less affected due to negligible
difference in Pr numbers for air and helium. The Re number of
the jet is 1.1 105
and for the present investigation, it is varied over
a wide range 6.9 104
e2.6 105
with an incident flux of
~0.75 MW/m2
.
3.2. Experimental test module
Thermal conductivity of brass is similar to tungsten alloy at high
temperature. Hence, experiment has been performed in a brass
alloy test module with uniform incident heat flux, as depicted in
Fig. 2. The test module consists of jet cartridge, outer brass shell
assembly and heat concentrator. The experimental investigation
has been carried out in test module with two design configurations,
with and without arrays of sectorial extended surface.
3.2.1. Heat concentrator
A copper heater block is used to achieve a uniform incident
heat flux, and the block is tapered at the neck region to focus and
increase the incident flux at the test module. A high density
950 W cartridge heater (OD 15 mm 80 mm long) is tightly
fitted to the copper heater block to heat the test module as
shown in Fig. 2. A high thermal conductivity paste has been used
between the mating surfaces to minimize the thermal resistance.
A variable transformer has been connected to an ammeter and
voltmeter to control the power output through the cartridge
heater for a uniform heat flux on top of the test module. The neck
region (OD 13 mm) of the concentrator is slip fitted in the test
module.
3.2.2. Jet cartridge and outer shell assembly
The inner cartridge (ID 9.2 mm 53 mm long) has been con-
structed in brass that simulates the steel cartridge in the prototype
as shown in Fig. 1. The gap between the brass cartridge and outer
assembly is maintained at 2 mm for the case without SES config-
uration. The configuration with SES has been manufactured as
depicted in Fig. 3.
An outer brass shell surrounding the inner cartridge that closely
duplicates the W-alloy structure, in the first set of configuration
tile, thimble and supporting plate unit has been manufactured as a
single entity (Fig. 3). The test module is instrumented by way of
four 0.6 mm diameter, K-type thermocouples (TCs). All the ther-
mocouples used in the present experimental work, have been
subjected to three points (50 C, 100 C and 170 C) calibration
within ±1 C accuracy. The thermocouples are insulated with
Kapton to have a negligible heat loss. The TCs are positioned within
brass alloy, 0.5 mm from the cooled surface and offset by 90 to the
each other at a radial distance of 2.5, 4.5, 6.5 and 8.5 mm respec-
tively as depicted in Fig. 3. To ensure correct positions of the
thermocouples in the test module, thermocouple wires were
graduated with a length which was used as a reference for insertion
length. A high thermal conductivity paste has been used to fix the
thermocouples in the test section and to minimize the thermal
contact resistance. The output from these TCs are used to compute
the average heat transfer coefficient over the cooled surface for a
given incident heat flux. Photographs of jet cartridge with different
configurations are shown in Fig. 4.
3.3. Experimental flow loop and procedure
The experimental test module was investigated in an open air
flow loop as shown in Fig. 5. Cartridge heater (Kerone, 120 V and
950 Watts) was placed in the copper heater block to heat the test
Table 1
Comparison of thermal hydraulic parameters for the actual He-cooled divertor and experiment studies using air loop.
Coolant Inlet temperature (
C) Inlet pressure (bar) Dynamic viscosity (kg/m-s) Heat flux (MW/m2
) Gas flow rate (g/s) Rep Prp
He 600 100 4.16 105
10 7.3 1.1 105
0.70
Air ~27 6.86 1.80 105
~0.75 3.1 1.1 105
0.68
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402
392

4. Fig. 2. Experimental test module assembly without SES (all dimensions in mm).
Fig. 3. Close up views of experimental test module with thermocouples locations (a) without SES and (b) with SES.
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402 393

5. module and a variable transformer was connected to control the
power output through the cartridge heater for the uniform heat
flux on top of the test module. Air from a compressed air line at
gauge pressures of 6.86 bars was used as the coolant. Pressure
regulators (Marsh, 0.1%) are used to control the outlet pressure of
the compressor. The compressed air was passed through a Rota-
meter (Omega, ±2% of FS) before the test module and was finally
discharged to an atmosphere.
Fig. 4. Photographs of (a) Test section (b) close up view of heat concentrator, (c) jet cartridge and (d) with and without SES configuration.
Fig. 5. Schematic of the experimental facility.
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402
394

6. The mass flow rate (m) through the test section, measured by
the flow meter, was controlled by a 1/400 high pressure needle valve
(Parker Autoclave, SW4071). Pressure transmitter (Marsh, ±1%) and
Thermocouples (Omega, ±1 C) were used to measure the test
section inlet/outlet pressures and temperature. The whole test
section assembly was insulated with a thick glass wool layer. The
flow is considered to have “steady state”, when the temperatures
measured by the TCs did not change more than 1 C over 10 min
interval. Each experiment took approximately 30 minutes to reach
steady state. The air inlet temperature was ~27 C. The mass flow
rate of air was varied from 2 g/s to 7.5 g/s for Reynolds number
6.9 104
to 2.6 105
. Energy balance validation shows a deviation
of less than ~3.5% for the experiments over the whole Reynolds
number range.
4. Numerical approach
4.1. Computational model, meshing and boundary condition
Three dimensional and steady sate conjugate numerical simu-
lations were performed, to predict flow and heat transfer charac-
teristics in the finger mock up with and without sectorial extended
surface. In order to validate the numerical results the heat transport
in the solid wall and in the fluid and the boundary conditions were
made identical to the experiments. A schematic of the test module
used for the numerical simulation with boundary conditions is
depicted in Fig. 6.
Due to the presence of symmetry, one half of the test section
(180 sector) is modeled in the present simulation. Temperature
dependent material properties were adopted for all solid domains,
namely jet cartridge, outer shell assembly, SES, cartridge heater and
heat concentrator. For all the simulations, the ideal gas assumption
was used for the working fluid air. In the numerical model, exper-
imental value of inlet temperature, mass flow rate (m) and power
inputs to the heater as volumetric heat generation were specified as
a boundary condition. At the exit, the pressure outlet boundary
condition was specified. A natural convection boundary condition
was imposed over all the other exterior surface of the model which
was insulated with glass wool insulation and it was estimated
through standard natural convection correlations [21]. Thermo-
couples are mounted on the outer surface of insulation to measure
the surface temperature and to account for the convection heat loss
from test module.
4.2. Governing equations
The keε turbulence model was used, due to high Reynolds
number and complicated geometrical model. This model accurately
predicts the complex turbulent flows with rotation, boundary
layers under strong adverse pressure gradients, separation, and
recirculation [22,23]. This model has been successfully used to
simulate the flow and heat transfer in channel with pin fins [24,25].
The steady state forms of continuity, momentum and energy
equations for gas flow were solved in the present numerical
simulation. A second order discretization scheme is used to reduce
the numerical errors, and the SIMPLE algorithm was used to resolve
the pressureevelocity coupling in the computation [26]. The re-
sidual for declaring convergence was 104
for continuity and mo-
mentum equations. The same was 107
for the energy equation. The
whole numerical simulation was carried out using commercial
computational fluid dynamics (CFD) software ANSYS Fluent [22].
5. Empirical correlation for thermal performance
5.1. Extraction of heat flux and surface temperatures
The heat flux is the ratio of net heating power (Qnet), to the area
of the cooled surface, Ac ¼ 13 103
m2
. The net heating power is
the balance of total electric power supplied to the heater and the
Fig. 6. Schematic symmetry sector of 180 computational model of the air loop mock-
up.
Fig. 7. Computational grid near the extended surface (a) expanded view of medium grid and (b) surface mesh.
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402 395

7. minor heat loss (estimated as 2e3.5% of total heating power)
through the test module by natural convection. Fig. 3 is the sche-
matic view of the cooled surface showing the locations and the
areas used to determine the area weighted mean temperature us-
ing various TC readings. The average temperature of the cooled
surface in the experiments was estimated from the TCs entrenched
just below the cooled surface. The TC readings were first extrapo-
lated to the cooled surface assuming conduction through 0.5 mm
thickness of the brass shell using the calculated heat flux. These
extrapolated temperatures were used to find the area weighted
main plate temperature ðTcÞ from,
Tc ¼2p
Z
c
TðrÞrdr=Ac ¼ 0:01TC1*
þ0:10TC2*
þ0:33TC
3*
þ0:55TC4*
(2)
where, ‘*’ represents extrapolated readings of TCs at the cooled
surface.
5.2. Extraction of heat transfer coefficient
The effective heat transfer coefficient (heff) for the case without
SES is determined based on the average heat flux incident on the
cooled surface (Ac) and the temperature difference between the
cooled surface wall and the bulk fluid as defined by,
heff ¼
Qnet
Tc Tb
Ac
(3)
Computation of the effective wall heat transfer coefficient for
the test section with SES requires accounting the fin efficiency (h),
because the surface temperature of the SES is spatially nonuniform.
Therefore,
heff Ac ¼ hact
Ap þ Aeh
(4)
where, ‘hact’ actual heat transfer coefficient and for the bare test
section, hact ¼ heff. To determine efficiency, an adiabatic boundary
condition has been assumed at the tip of the extended surface. This is
justified due to the presence of a small air between the extended
surface and the jet cartridge and the fact that air is a relatively poor
thermal conductor. Accordingly, the fin efficiency (h) is given by [21].
h ¼ tanh nl=nl; (5)
where, n ¼
ffiffiffiffiffiffiffiffiffi
hact P
KeAce
q
and ‘l’ is the length of SES.
Effectiveness (z) of the extended surface is defined as the ratio of
heat transfer rate by SES to that without extended surface and is
written as:
z ¼ Ae h=Ac (6)
The pumping power (Wair) is determined from,
Wair ¼ m Dpair=rair (7)
Fig. 8. Results of grid sensitivity analysis.
Fig. 9. Comparisons of measured and predicted thermocouple temperatures (a) TCs
1e2 and (b) TCs 3e4 at various Reynolds number.
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402
396

8. where the symbols have their usual meanings and are described in
the nomenclature.
5.3. Error analysis
The uncertainty in the experimental data has been determined
by the standard error analysis method described by Bevington and
Robinson [27]. The measurement error in net heating power (Qnet)
and temperature are ±2.5% and ±0.4 C respectively, and the air
property is ±1.1%. Based on this data, the measurement error in
derived quantities heff, Dp, h, Wair and z are respectively ±4.95%,
±5.6%, ±1.2%, ±6.1% and ±1.29%. The values are very small
compared to the mean values of the corresponding quantities in
the respective graphs. Hence, the error bar is not visible in the
graphs.
6. Results and discussion
6.1. Grid sensitivity analysis
Identification of an optimum mesh size beyond which, the
computed simulation is independent of the mesh size is the first
step in computational simulation. The number of radial grid di-
visions on the periphery of the extended surface and in the nozzle
is a useful constraint to determine the mesh for an accurate pre-
diction of the cooled surface wall temperature. Towards this, an
effort is made to investigate the sensitivity of the results to various
computational grids, where the computational domain is exam-
ined for three grid systems, that is coarse (13 105
), medium
(15 105
) and fine (18 105
) grids. Fig. 7 shows a detailed view
for the medium grid around the extended surface and SES grid
domain.
The grid sensitivity analysis was performed for Reynolds
number of 6.9 104
. The predicted results of mean surface tem-
perature and pressure drop in the finger mock up are presented in
Fig. 8 for various grid counts. It is clear that the surface
temperature and pressure drop of test section do not change
significantly between the medium grid and fine grid. The
maximum relative deviation of the two variables is within 4.5%.
However, it is found that the computational time required for each
iteration in the case of fine mesh is large compared to that of the
medium grid. Therefore, the medium grid has been chosen for
further investigations. The yþ
value is also an important criterion
in the numerical simulation for the accuracy of predictions for wall
shear stress and heat transfer near the solid/fluid interface region.
To capture the heat transfer performance close to the wall,
meshing with denser grids was adopted by using a boundary layer
mesh as depicted in Fig. 7. In the present study, yþ
values were
maintained around ~1 [22]. The measured value of wall
Fig. 10. Comparison of predicted temperature (C) distribution over the cooled surface at Re ¼ 1.3 105
.
Fig. 11. Comparisons of the measured and predicted pressure drop against Re.
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402 397

9. temperature for Re ¼ 6.9 104
is 154 C. The corresponding value
predicted in the medium grid is 151 C and it compares satisfac-
torily with the experimental data.
6.2. Comparative studies of the thermocouple temperatures
The thermocouple temperatures in the test section with and
without SES have been measured in the Reynolds number range of
6.9 104
e2.6 105
. The comparison between computed ther-
mocouple temperatures against the experimental data for different
Reynolds number is depicted in Fig. 9. From Fig. 9, it is seen that the
local surface temperatures of the test module decrease with an
increase in Reynolds number as expected, but the reduction is more
in case with SES. The wall temperature exhibits a radial non-
uniformity to the extent of 4e6 C. This is expected since coolant
temperature increases along the flow direction. The temperature
values at thermocouples location obtained from the simulation are
in satisfactory agreement with the experimental results with
maximum deviation less than 5 C. Predicted wall temperatures are
consistently less than the measured data.
6.2.1. Discussion on temperature drop by SES
The temperature distributions in the target plate with/without
SES, as predicted by the mathematical model are depicted in Fig. 10
for Re ¼ 1.3 105
. It is seen that for identical heat flux, addition of
SES in the design reduces the plate temperature appreciably. It is
due to the improvement in the effective heat transfer coefficient by
SES, as a result of increase in surface area and turbulence. Further,
Fig. 12. Comparison of velocity (m/s) distribution on xey plane at a distance of 0.5 mm from the cooled surface at Re ¼ 1.3 105
. (a) without SES (b) with SES and (c) vector plot
with SES.
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402
398

10. the surface temperature of the test section at the center (TC-1)
drops down rapidly while it increases in the radial direction. The
rapid decrease in temperature at the center is due to the direct
impingement of a high velocity jet, which leads to high heat
dissipation, that is clearly evident in Fig. 10. Similar trends are
observed in the experiments also. These results suggest that the
heat transfer efficiency is improved with the provision of SES.
6.3. Comparative studies on pressure drop by SES
Pressure drops in the test section were measured for a heat load
~0.75 MW/m2
at various Reynolds numbers. Fig. 11 compares the
measured pressure drop against numerically predicted pressure
drop, with and without SES in the test section. The predicted and
measured results exhibit identical trends. The pressure drop in the
test module with the presence of SES arrays is higher than that
without the SES module, as the fluid has to cross a series of barriers
provided by the SES. It can be observed that the numerical results of
the both the test modules are in satisfactory agreement with the
experimental results at the low Reynolds number (~1.5 105
).
Maximum deviation observed between the measured and predicted
results for both configurations is ~18% for the high Reynolds number.
6.3.1. Correlation for loss coefficient
An engineering parameter of practical interest is the pressure
loss coefficient. It is essential to know its dependence on the Rey-
nolds Number. The functional relationship for loss coefficient can
be written as:
KL ¼ fnðReÞ
The loss coefficient (KL), based on the coolant property and
measured pressure drop (DP) across the test module is determined
from,
KL ¼
DP
rairV2
air
.
2
(8)
where, Vair stands for the mean velocity of the jet. The data cor-
responding to all experimental tests for both the configurations
have been used for determination of KL. Based on this, the following
relationships have been developed:
KL ¼ 2:6271 Re0:1708
Without SES
ð Þ (9)
and
KL ¼ 3:8251 Re0:1379
With SES
ð Þ (10)
The R2
values for these equations are 0.996 and 0.992,
respectively.
6.3.2. Discussion on pressure drop by SES
In order to develop further understanding into the effect of SES
on the pressure drop mechanism, a comparison of the contour and
vector plots of the streamwise velocity distribution on xey plane of
both the configurations is depicted in Fig. 12. It can be seen, from
Fig. 12(b) and (c), that a high velocity jet flow and symmetric
vortices are generated in the vicinity of the extended surface as
compared to the case without SES. Due to the formation of vortex
and high velocity, turbulence level increases, leading to the asso-
ciated increase in heat transfer coefficient. However, the eddies and
flow acceleration caused by blockage, increase the pressure loss in
SES.
6.4. Comparative analysis of heat transfer by SES
For the experimental test section shown in Fig. 2, thermal per-
formance has been analyzed to find the efficacy of SES. A compar-
ison of experimental data that predicted by three-dimensional
conjugate analysis is presented in Fig. 13. Effective heat transfer
coefficient of the test section with SES is significantly larger than
the case without SES for the entire Re range. As expected, the
effective heat transfer coefficient is large with SES, as it offers a
relatively large surface area. Also, due to a proper layout of the SES,
all the walls of the extended surface are forced to participate in the
heat exchange process.
It can be seen from Fig. 13, that the predicted values of heff are in
good agreement with the experimental values for the entire range
of Reynolds number. The maximum deviation between the
measured and predicted results at the prototypical condition for
both configurations is less than 6.5%. The numerical simulation is
reasonably accurate in predicting the heat transfer enhancement
potential of the test section with SES. This serves as a validation for
the computational model which is the most important consider-
ation in the mock up design for the divertor [2].
6.4.1. Correlation for Nusselt number
The intensity of heat exchange between the cooled surface wall
and flowing fluid is characterized by the Nusselt number (Nu). The
Nusselt number over the cooled surface is determined from heff, jet
diameter and thermal conductivity of air evaluated at the bulk fluid
temperature. From the above description and data presented in
Fig. 13, it is found that the Nusselt number has also strong rela-
tionship with Re. The average Nu can be correlated as,
Nu ¼ C Ren
The values of coefficient ‘C’ and exponent ‘n’ have been deter-
mined from the experimental data and curve fitted as a function of
Re, from which the following correlation for the Nusselt number are
proposed.
Nu ¼ 0:1488 Re0:711
Without SES
ð Þ (11)
and
Nu ¼ 2:2762 Re0:578
With SES
ð Þ (12)
Fig. 13. Comparison of the measured and predicted effective heat transfer coefficients.
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402 399

11. The values of R2
for above equations are 0.995 and 0.983,
respectively. These are valid for Re number range of 6.9 104
to
2.6 105
, and Pr ~ 0.7.
6.4.2. Discussion on heat transfer by SES
From Fig. 10, it is seen that in the present design, the SES
offers a relatively large surface area to the volume ratio. Further
with an appropriate arrangement of the SES, satisfactory coolant
velocity can be achieved on the entire surface. Also, since the
extended surfaces are short, efficiency and effectiveness are ex-
pected to be very high (Section 6.5). Thus, the addition of SES
greatly enhances the heat transfer performance of the present
design.
6.5. Comparative analysis of thermal hydraulic performance
The performance of the extended surface is determined by both
the efficiency (h) and effectiveness (z). Effectiveness of extended
surface gives the quantity of additional heat dissipated by the
extended surface. The effectiveness of extended surface should be
large to keep the extra cost of adding the extended surface as low as
possible. On the other hand, by determining the efficiency of an
extended surface, one can assess the heat transferring capacity of
the extended surface.
Fig. 14(a) and (b) shows the variations of h and z illustrating the
performance of SES as a function of Re. As expected, when the Re
increases in the SES, both h and z decrease due to the increase in
heat transfer coefficient. At the prototypical operating condition,
the values of h and z for air are ~89% and 2.98, respectively. This
result suggests that extended surface could potentially enhance
thermal performance when compared with its bare counterpart.
The values of efficiency and effectiveness predicted from the three
dimensional conjugate computations are also presented in Fig.14. It
is found that, satisfactory agreements between the experimental
and numerical results exist with maximum deviations of 0.9% for h
and 1.2% for z.
Fig. 14. Comparison of measured and predicted data, (a) efficiency of SES and (b)
effectiveness of SES.
Fig. 15. (a) Dependence of pumping power on Reynolds number and (b) pumping
power as a function of the heff.
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402
400

12. Fig. 15(a) depicts the variation in pumping power required for
air flow through the test section as a function of Re at a constant
heat flux. It is seen that, the pumping power (Wair) constantly in-
creases with Re in both cases of with and without SES. However,
Wair required for the case with extended surface is significantly
higher at the same Re, due to increase in the pressure drop by the
SES.
Fig. 15(b) compares the variation in the effective heat transfer
coefficient (heff) with pumping power with/without extended
surface. From the figure, it can be observed that heff continuously
increases with Wair. But at identical pumping power, the test
section with extended surface offers a higher heff as compared to
that without SES. When the experimental data are extrapolated
to the prototypical operating condition, the pumping power for
the extended surface test section is found 25% greater and heff
increases more than the double, compared to the bare test
section.
7. Summary and conclusions
An experimental and computational approach has been pro-
posed for the evaluation of thermal hydraulics performance of a
finger type divertor. Experiments have been performed on a full
scale divertor respecting geometric and dynamic similarities. Both
a bare divertor and divertor with sectorial extended surface have
been tested in air (which represents helium in the prototype) for a
wide range of Reynolds number. The geometric parameter of the
divertor with extended surface resembles that of future fusion
power plant DEMO.
The experimental data on pressure drop, heat transfer coeffi-
cient, SES effectiveness and efficiency have been used as a
benchmark for validation of conjugate 3-D numerical model
including keε turbulence model. A novel heat concentrator has
been developed for achieving a high heat flux similar to that of
plasma heating by electrical heating. Both the finger mock-ups
have been numerically simulated towards validation of the nu-
merical model. It is seen that the effective heat transfer coefficient
increases more than double with the addition of SES at the cost of
~25% higher pumping power. The efficiency and effectiveness of
the SES are found to be ~89% and ~2.98, respectively at the pro-
totypical Reynolds number. The numerical results of effective heat
transfer coefficient compare satisfactory with the experimental
data within 6.5% at the prototype Reynolds number. Suitable
correlations have been derived for Nusselt number and pressure
loss coefficient in the finger mock-up as a function of Reynolds
number. Details of velocity and temperature distributions have
been brought out to understand the improvement in heat transfer
rate in the case of divertor with SES.
Acknowledgements
Useful discussion with Dr. Kamalakanta Satpathy and Dr. Deepak
Sangwan regarding numerical simulations of the experimental
mock-up is gratefully acknowledged. The authors thank Mr. Gattu
Ramesh Babu, Mr. Vinay Menon, Mr. Rajmannar Swamy, Mr. Tushar
Patel, Mr. Prakash K. Mokaria, and Mr. Nikunj Patel for their help in
performing the experiment at Vidhata Lab, Gandhinagar (India).
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Nomenclatures
Ac: area of cooled inner surface wall, m2
Ajet: area of jet nozzle, m2
Ap: area of the bare plate between the SES, m2
Ae: surface area of the SES, m2
Ace: cross section area of the SES, m2
D: jet diameter, m
heff: effective heat transfer coefficient, W/(m2
K)
hact: actual heat transfer coefficient, W/(m2
K)
KL: loss coefficient
Ke: thermal conductivity of the SES, W/(m K)
k: turbulent kinetic energy, m2
/s2
l: length of the SES, m
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402 401

13. m: mass flow rate, kg/s
Nu: Nusselt number
p: pressure, Pa
P: perimeter of the SES, m
Pr: Prandtl number
Qnet: net heating power, W
r: radial coordinate, m
Re: Reynolds number
SES: sectorial extended surface
T: temperature, K
Tb: bulk temperature of the fluid, (Ti þ To)/2, K
Tc: area weighted temperature, K
TC: thermocouple temperature, K
Ti: inlet temperature of fluid, K
To: outlet temperature of fluid, K
V: jet velocity, m/s
Wair: pumping power for air, W
Greek symbols
ε: rate of dissipation, m2
/s3
D: difference
h: efficiency of SES
m: viscosity of air, N-s/m2
r: density of fluid, kg/m3
z: effectiveness of the SES
S. Rimza et al. / Applied Thermal Engineering 82 (2015) 390e402
402

14. Research Paper
Computational fluid dynamic studies on plasma facing heat sink
concept for fusion tokamak application
Sandeep Rimza a,
*, Samir Khirwadkar a
, Karupanna Velusamy b
a Divertor and Firstwall Technology Development Division, Institute for Plasma Research (IPR), Bhat – 382428, Gandhinagar, Gujarat, India
b Mechanics and Hydraulics Division, Reactor Design Group (RDG), Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam – 603102, Tamilnadu,
India
H I G H L I G H T S
• A modular divertor heat sink concept is proposed for fusion tokamak application.
• Effects of important parameters on the heat transfer characteristics are critically discussed.
• The use of multiple nozzles of various shapes is investigated by 3-dimensional CFD studies.
• Thermo-mechanical analysis is performed toward ensuring acceptability of the design from structural integrity consideration.
A R T I C L E I N F O
Article history:
Received 21 October 2015
Accepted 28 February 2016
Available online 7 March 2016
Keywords:
Divertor
Fusion reactor
Thimble
Pumping power
Stresses
Heat transfer
A B S T R A C T
Development of an efficient divertor heat sink concept capable of extracting intense heat flux while main-
taining temperatures and thermo-mechanical stress levels within allowable limits is a challenging task
to meet in the scenario of the future fusion power plant known as DEMO. Typically, divertor is expected
to extract a steady state heat flux up to 10 MW/m2
. In the present study, an efficient divertor concept
based on helium gas cooling has been proposed for the fusion grade tokamak. The effects of critical thermal
hydraulic parameters and geometrical parameters on the heat transfer characteristics of the divertor module
are studied as a function of Reynolds number (Re). This includes critical parameters, viz., thimble diam-
eter (DT), nozzle diameter (DN), the ratio of nozzle-to-wall space and nozzle diameter (H/DN) and nozzle
shape. Elliptical nozzles at specific orientation are found to give the best performance, whereas trian-
gular nozzles are found to give the worst performance for identical Reynolds numbers. Similarly, a minimum
thimble temperature and pressure drop in the circuit is achieved at H/DN ~1.66. The proposed design is
found to have a margin of 10%, i.e., capable of handling 11 MW/m2
against target heat flux values of 10 MW/
m2
. The stress values arising out of temperature gradient and pressures are found to be within acceptable
limits, demonstrating the reliability of the proposed concept.
© 2016 Elsevier Ltd. All rights reserved.
1. Introduction
Helium cooled divertor design is considered as one of the po-
tential options for future fusion reactors known as DEMO [1]. This
is mainly due to its inert nature, compatibility with plasma and
ability to operate at higher pressures and temperatures. Addition-
ally, helium has favorable neutronic properties, which are preferred
from safety aspects. However, due to its poor density and thermal
conductivity, high pressures have to be adopted to achieve an ef-
ficient cooling desired for extracting high heat flux from the divertor
system in a DEMO reactor. Toward this, a new modular divertor
concept has been investigated in the present paper.
A number of helium-cooled divertor designs have already been
reported in the literature. Diegele et al. [2] investigated the modular
He-cooled divertor design for power plant application. From their
studies, they found that modular concept has the potential of re-
moving very high heat flux at a reasonable pumping power. Visca
et al. [3] and Pizzuto et al. [4] devised a thermal shield concept for
the DEMO divertor application, and found that their design can
handle a heat flux of ~10 MW/m2
. Rimza et al. [5–7] have per-
formed numerical and experimental studies on divertor finger mock-
up with an improved heat transfer technique. They showed that the
capability of divertor to handle heat flux increase largely by the use
of the sectorial extended surfaces. Ihli et al. [8] and Končar et al.
[9] analyzed an advanced helium cooled divertor concept, and the
effect of nozzle diameter on the thermal performance, respective-
ly. The results suggested that equal sized nozzle decreases the peak
thimble temperature. An experimental investigation to study the
effect of nozzle inlet chamfering on heat transfer distribution over
* Corresponding author. Tel.: +918141511655; fax: +917923962277.
E-mail address: sandeepr@ipr.res.in (S. Rimza).
http://dx.doi.org/10.1016/j.applthermaleng.2016.02.132
1359-4311/© 2016 Elsevier Ltd. All rights reserved.
Applied Thermal Engineering 100 (2016) 1274–1291
Contents lists available at ScienceDirect
Applied Thermal Engineering
journal homepage: www.elsevier.com/locate/apthermeng

15. flat plate was performed by Attalla and Salem [10]. They showed
that the Nusselt numbers have the highest value for the square
edge inlet nozzle. Whelan and Robinson [11] investigated the
effects of nozzle geometry in liquid jet array impingement. They
found that chamfering and contouring the nozzle inlets result in a
significant decrease in the pressure drop across the nozzle plate.
Linares et al. [12] studied the suitability of supercritical CO2 Brayton
power cycles for low-temperature divertor fusion reactors cooled
by helium.
Gayton et al. [13] devised a plate-type divertor concept to ac-
commodate a surface heat load of ~10 MW/m2
. They found that the
divertor with metallic foam significantly enhances heat transfer. Ihli
et al. [14] investigated a helium-cooled tube divertor concept for
a compact stellarator and tokamak configuration to accommodate
a heat flux value of ~10 MW/m2
. Norajitra et al. [15,16] reported the
experimental verification of modular design and status of divertor
development for the DEMO reactor.
From the above brief review, it is observed that the helium cooled
divertor design has the capability to handle the high heat flux at a
reasonable pumping power. This paper describes a detailed design
study of a new modular divertor concept for the future tokamak
to sustain the steady state heat flux up to ~10 MW/m2
. The perfor-
mance of heat transfer and fluid flow in divertor heat sink is
investigated by numerical simulation. Additionally, the effect of crit-
ical parameters like thimble diameter (DT), nozzle diameter (DN), the
ratio of nozzle-to-wall space with nozzle diameters (H/DN) and
various nozzle shapes on the heat transfer and pressure loss mech-
anism are also studied. The numerical simulations are carried out
using the CFD software ANSYS Fluent 14.0 [17].
2. Description of divertor heat sink concept
A schematic diagram of the proposed divertor module for fusion
reactor application is shown in Fig. 1. A divertor is a toroidally sym-
metric structure divided into a number of cassettes, for easier
handling and maintenance. A modular design has been developed
to reduce the thermal stresses, which allows a higher heat flux han-
dling capability. The plasma-facing components are exposed to
energetic plasma particles that lead to physical and chemical sput-
tering of the target surface and heat deposition. Tungsten (W) is
40mm
Outlet manifold
Inlet manifold
HeIn
Heat Flux
Thermal
shield (W)
Heout
Thimble (WL-10)
Jet cartridge
Nozzle
Heout
Fig. 1. Schematic diagram of divertor heat sink and detailed view (All dimensions in mm).
1275
S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

16. considered as the most promising divertor material, because it has
excellent thermo-physical properties such as high melting point, low
sputtering yield, high thermal conductivity, low-activation, etc.
[18,19].
As illustrated in Fig. 1, the plasma-facing surface of divertor is
made up of tungsten material with a sacrificial layer (~4 mm thick)
as the thermal shield. The thermal shield is not cooled directly, to
avoid the probability of crack formation. Thermal shield is brazed
on top of the thimble made of high ductility tungsten alloy (WL-
10). A high melting temperature filler material Pd-Ni 40 (1511 K)
has been considered as the brazing filler between the mating sur-
faces [20–23]. A steel jet cartridge carrying the multiple nozzles is
placed concentrically inside the thimble for efficient heat transfer.
The coolant fluid (He) enters through the inlet manifolds to the car-
tridge, and accelerates through the multiple nozzles (DN = 0.7 mm).
The helium jet impinges upon and cools the heated surface, then
flows down along the space (H = 1 mm) between the inner car-
tridge to the outlet manifold as shown in Fig. 1.
2.1. General design constraint
The total allowable heat flux limit for the helium cooled divertor
heat sink is determined by the maximum temperature of the thimble,
the pumping power of the helium coolant gas and the thermo-
mechanical stresses. The main design constraint is maximum thimble
temperature, which is limited by Ductile-to-Brittle Transition Tem-
perature (DBTT ~600 °C) and re-crystallization temperature
(~1300 °C) of the W-alloy [24]. Peak thimble temperature must be
lower than the filler material melting temperature (1511 K) to
enhance the life of the divertor and its safe operation. Next limit
is the necessary power to pump the helium gas through the divertor
structure, which is targeted to be less than 10% of the total inci-
dent power to be removed from the structure. The third limit is
thermo-mechanical stresses, which should be lower than the al-
lowable stress limit of respective materials at the corresponding
temperature attained during heat transfer.
3. Theoretical formulation and numerical model
3.1. Governing equations and numerical method
The heat transfer performance of the divertor heat sink struc-
ture has been analyzed numerically using the CFD code ANSYS Fluent
14.0 [17]. Heat transfer equations through solid and fluid are solved
simultaneously. The fluid inside the divertor heat sink structure is
modeled as an ideal gas under steady flow. The governing equa-
tions for the flow and heat transfer in the fluid domain can be
expressed as follows [25]:
• Continuity equation:
∂( )
∂
=
ρu
x
i
i
0 (1)
• Momentum equation:
u
u
x
P
x x
u
x
j
i
j i j
eff
i
j
∂( )
∂
= −
∂
∂
+
∂
∂
∂
∂
⎛
⎝
⎜
⎞
⎠
⎟
ρ
μ (2)
• Energy equation:
∂( )
∂
=
∂
∂
∂
∂
⎛
⎝
⎜
⎞
⎠
⎟
ρC u T
x x
K
T
x
p i
i i
eff
i
(3)
In the solid, heat conduction equation for steady state temper-
ature field is given by:
∂
∂
∂
∂
⎛
⎝
⎜
⎞
⎠
⎟ =
x
K
T
x
i
s
i
0 (4)
where all the symbols have been described in nomenclatures.
Realizable k − ε turbulence model [26,27] has been adopted to
account for turbulent heat transfer and fluid flow. The second
order upwind scheme is used to combine the convection and
diffusion transfer. The SIMPLEC algorithm is used to resolve cou-
pling between pressure and velocity in the computations. The
convergence criteria for the momentum and continuity equations
are set to a value below 10−4
, whereas for energy equation it is set
to below 10−7
.
3.2. CFD mesh and boundary condition
Fig. 2 shows an isometric view of the CFD mesh for the divertor
heat sink model. In order to reduce the computational effort, only
half of the section has been modeled. The commercial software
GAMBIT has been used to create a structured grid for the
y
x
z
Symmetry (x-y plane)
Fig. 2. CFD mesh for divertor heat sink model.
1276 S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

17. computational model. For accurate resolution of heat transfer phe-
nomenon near the fluid–solid interface, the boundary layer mesh
has been adopted as depicted in Fig. 2. Temperature dependent ma-
terial properties have been considered for the solid domains [24].
Helium (He) is specified as an ideal gas. A constant heat flux of
10 MW/m2
is prescribed on the top surface wall, while the remain-
ing walls are assumed adiabatic. No-slip conditions are applied at
all the walls for flow calculations. Uniform mass flow rate, temper-
ature and pressure (600 °C and 10 MPa) are assigned at the inlet
manifold. Viscous dissipation is neglected, since the Eckert number
(Ec) is very small (0.018).
3.3. Grid independence analysis
In order to get a grid independent solution, careful grid inde-
pendence check has been carried out with several grid systems. The
number of grid cells considered ranges from 2.75 × 105
to 7.42 × 105
,
as shown in Table 1. The maximum thimble temperature has been
selected as the target parameter for grid optimization, as it is an
important design constraint. The exercise revealed that the com-
puted results based on 6.5 × 105
cells are insensitive to further grid
refinement, and the same is employed for all the results pre-
sented herein.
3.4. Parameter definitions
The Reynolds number (Re) based on the hydraulic diameter is
defined as:
Re mD A
h N
= ( )
μ (5)
where m, μ, Dh and AN are helium mass flow rate, viscosity, hydrau-
lic diameter and area of nozzle, respectively.
The pressure drop (ΔP) from the inlet to the outlet of the flow
domain, which reflects the hydraulic performance of the divertor
heat sink, is determined by,
ΔP P P
in out
= − (6)
The pumping power, which is required to pump the helium
through the divertor heat sink structure, is calculated as:
W m P
= ( )
ρ Δ (7)
To compare the thermal-hydraulic performance associated with
geometric variation in modular divertor, pumping power ratio is
defined as:
P W Q
p T
= (8)
In the above equations, Pin and Pout are pressure at the inlet and
outlet of the flow passage, ρHe is the density of helium at the bulk
temperature [(Tin + Tout)/2]. Additionally, QT is the total incident power,
and W is the power required to pump the helium through the
divertor heat sink.
Heat transfer coefficients is calculate by [17]:
h
q
T T
w f
=
′′
( )
(9)
where, q″, Tw, and Tf are heat flux from the wall, wall surface tem-
perature and local fluid temperature, respectively.
Table 1
Comparison of the maximum thimble temperature for different grid pattern at Re
=1.58 × 104.
Grid Number
of cells
Predicted maximum
thimble temperature (K)
Percentage difference
in temperature
Very coarse 275,000 1,520
Coarse 384,240 1,503 −1.118%
Intermediate 508,638 1,496 −0.465%
Fine 650,000 1,493 −0.200%
Very fine 742,800 1,493 0.000%
Fig. 3. Comparison of present result of maximum thimble temperature and pressure drop against reported results.
1277
S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

18. 4. Results and discussion
4.1. Validation of numerical model
To test the validity and enhance the level of confidence in the
numerical solutions, the numerical model has been validated against
the reported results of Widak et al. [28]. For the validation exer-
cise, same geometric structure as reported in the literature has been
adopted. In the reported literature, helium-cooled concept based
on jet impingement has been adopted. The coolant has an inlet tem-
perature and pressure of about 907 K and 10 MPa, respectively. The
thermal hydraulic performance of concept was analyzed by varying
the mass flow rate in the range of 6.8–9 g/s. The comparison between
the present simulation and reported results is depicted in Fig. 3. It
presents the maximum temperature of thimble and pressure loss
as a function of mass flow rate. As expected, the pressure loss
(a)
H/DN = 1.43
(b)
Design constraint
1511 (K)
Fig. 4. Comparison of (a) thermal shield and (b) thimble maximum temperature at various Re number.
1278 S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

19. increases as the square of the flow rate. On the other hand, tem-
perature monotonically decreases with increase in the flow rate. A
good agreement is noticed between the present simulation and the
reported results. The maximum deviation between present simu-
lation and reported results are less than ~4%.
4.2. Thermal-hydraulic performance analysis
Following satisfactory validation, three-dimensional simula-
tions are performed to investigate the heat transfer and fluid flow
characteristics in divertor heat sink. The objective of this study is
to find the optimum cooling approach for divertor heat sink. It is
aimed to obtain a larger thimble diameter (DT) to have lower pres-
sure drops as well as lower manufacturing and operating costs. It
is known that a smaller thimble diameter leads to more thimble
modules and the associated increase in the cost of manufacturing.
Five inlet mass flow rates (m) of 10, 13, 15, 20 and 25 g/s, corre-
sponding to the Re numbers of 1.2 × 104
, 1.5 × 104
, 1.8 × 104
, 2.4 × 104
and 3.0 × 104
, respectively are adopted to analyze the thermal hy-
draulic performance of divertor heat sink as shown in Figs. 4 and
5. Numerical studies are carried out at a constant heat flux of
10 MW/m2
.
Fig. 4(a) and (b) presents a comparison of maximum tempera-
ture on the surface of thermal shield and thimble under a wide range
of Re number. It can be observed that when the thimble diameter
increases, both the thermal shield and the thimble experience an
increment in temperature at the same Re number. A possible ex-
planation of the above phenomenon is that when thimble diameter
grows, the total heat load to the structure increases. Therefore, higher
mass flow rates are needed to maintain the thimble temperature
limit. Thimble temperatures are well below the filler temperature
constraint (1511 K) at Re numbers of 1.58 × 104
, 2.2 × 104
and 2.7 × 104
with the corresponding thimble diameters 16, 20 and 25 mm, re-
spectively as seen in Fig. 4(b).
A comparison of pumping power ratio as function of Re number
at various thimble diameter is shown in Fig. 5. It is clear that with
the increase in Re number, the pumping power ratio increases as
the square of Re. However, increasing the thimble diameter reduces
the pumping power ratio. One notable fact is that the pressure drop
decreases significantly in a larger diameter tube. This is due to an
increase in diameter of the inlet manifold section and surface area
of divertor heat sink; hence the velocity of fluid decreases.
It may be noticed that the pumping power ratio is well within
the design limit at Re number 1.58 × 104
for 16 mm diameter of the
tube. About 60% and 140% higher pumping power ratio is re-
quired for 20 and 25 mm diameter tubes to maintain the desired
thimble temperature constraint. The results show that the perfor-
mance of divertor heat sink reduces with increase in thimble
diameter, and better thermal-hydraulic performance can be achieved
from the small diameter tube. Therefore, thimble with 16 mm di-
ameter has been selected for further studies.
To develop further understanding on the effect of thimble
diameter on the heat transfer performance in the divertor heat
sink, a comparison of temperature distribution at prototypical
Re = 1.58 × 104
is depicted in Fig. 6. It can be seen that the tempera-
tures of thermal shield and the thimble are higher for larger tube,
and they decrease significantly with reduction in thimble diame-
ter. This is due to the reduction in conductive resistance as the
diameter of thimble reduces. However, this would need more
thimbles for divertor heat sink with the associated cost implication.
4.3. Parametric studies
As already mentioned in Fig. 4(b), the thimble temperature is
seen to be close to the temperature limit of filler material at a
prototypical Re number. Therefore, an effort is made to reduce the
thimble temperature as much as possible below the brazing
filler-melting limit for enhanced life of divertor and safe opera-
tion. The Re number corresponding to the prototypical condition
based on the mass flow rate of 13 g/s for the DEMO is 1.58 × 104
.
Therefore, parametric studies have been performed at this Reyn-
olds number.
Design constraint
Fig. 5. Comparison of pumping power ratio as function of Re number at various thimble diameter.
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20. 4.3.1. The effect of nozzle diameter (DN) on thermal-hydraulic
performance (circular nozzle)
A comparison of the performance of divertor heat sink as a func-
tion of nozzle diameter (DN) is depicted in Fig. 7(a) and (b) for circular
nozzle. The investigation has been carried out for five different nozzle
diameters, viz., 0.7, 0.65, 0.6, 0.55 and 0.5 mm, while the nozzle-
to-wall distance (H = 1 mm) and the number of nozzle holes are kept
constant. Fig. 7(a) shows that a change in diameter of the nozzle
holes has a strong influence on the maximum thermal shield and
thimble temperatures. Temperature of divertor heat sink is de-
creases with the reduction in nozzle diameter, because for the
identical Re, the velocity of impinging jets increases significantly,
leading to the associated increase in heat transfer coefficient.
Fig. 7(b) shows the pressure drop (ΔP) and pumping power (Pp)
ratio as a function of nozzle diameter. It is seen that ΔP and Pp
extensively increase as the jet diameter decreases. Thus, while
fluid velocity increases largely, it increases the heat transfer coef-
ficient. On the other hand, it causes a strong increase in pressure
loss due to the direct relation between pressure loss and flow
velocity of the working fluid. It can be observed that while thimble
temperature continuously decreases, pressure drop and the pumping
power ratio also increase largely below the 0.6 mm nozzle diam-
eter. The above discussions reveal that 0.6 mm nozzle diameter
reduces the thimble temperature substantially at the acceptable
pumping power limit. Therefore, this diameter has been consid-
ered for further studies.
Temperature
[K]
Max. temp. = 1943 K
Max. thimble
temp. = 1563k
[DT = 20 mm, H/DN = 1.43]
[DT = 16mm, H/DN = 1.43]
Max. temp. = 1843 K
Max. thimble
temp. = 1493 K
Max. temp. = 2093 K
Max. thimble
temp. = 1683 K
[DT= 25mm, H/DN = 1.43]
Fig. 6. Comparison of temperature distribution for various thimble diameters at Re = 1.58 × 104
.
1280 S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

21. Fig. 8 illustrates the comparison of velocity and temperature dis-
tributions predicted by CFD analysis for a heat flux value of 10 MW/
m2
. It can be clearly seen that the velocity is high at the center of
the nozzle and it continuously increases as nozzle diameter de-
creases. The nozzle with 0.5 mm diameter has the smallest cross
section of jets and consequently the highest nozzle velocity.
Furthermore, it is clear that the temperature of the thimble is also
reduced by an increase in the velocity of fluid. The high velocity of
jet causes higher turbulence in divertor heat sink, leading to an in-
crease in heat transfer coefficient at the cost of higher-pressure drop.
The contours of the local heat transfer coefficient (HTC) for differ-
ent nozzle diameters are shown in Fig. 9. The heat transfer coefficient
Fig. 7. Effect of circular nozzle diameter on (a) maximum thermal shield and thimble temperature and (b) pumping power ratio and pressure drop.
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S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

22. at the jet impingement locations is very high, since the local heat
transfer coefficient is strongly influenced by jet velocity. A typical
value of heat transfer coefficient is about 104
W/m2
K.
4.3.2. The effect of nozzle to wall space (H) on thermal-hydraulic
performance
Fig. 10(a) presents the variation of thermal shield and thimble
temperatures as a function of H/DN, where H is the nozzle to wall
space. Here, the nozzle diameter (DN = 0.6 mm) and the number of
nozzle holes are kept constant, while the nozzle to wall space is
varied from 0.7 to 1.2. The corresponding H/DN ratios vary from
1.33 to 1.83. It can be observed that the divertor heat sink temper-
ature increases mildly as the nozzle to wall space increases. This
is due to the reduction in momentum of jet velocity at the im-
pingement location. As the space between nozzle to wall increases,
the effective heat transfer coefficient decreases. Furthermore, no
significant difference is found in results with a reduction in nozzle
to wall space.
Fig. 10(b) illustrates the effect of H/DN ratio on pressure drop and
pumping power ratio. The pumping power ratio decreases as H in-
creases, due to the reduced velocity magnitude in the system. The
results demonstrate that jet to wall space does not significantly affect
the thermal hydraulic performance of divertor heat sink. Therefore,
nozzle to wall space H = 1 mm with H/DN = 1.66 is considered to be
optimal.
From the thermal-hydraulic parametric studies, it is evident that
divertor heat sink concept has potential to accommodate the design
heat flux (~10 MW/m2
) at an acceptable pumping power limit. The
optimized dimension of the thimble (Dt), nozzle diameter (DN) and
H/DN are 16 mm, 0.6 mm and 1.66 mm, respectively. To respect thimble
temperature and pumping power limit, 13 g/s mass flow rate
(Re = 1.58 × 104
) is adequate for the present divertor heat sink concept.
DN = 0.7mm
DN = 0.6mm
DN = 0.5mm
Velocity
[m/s]
Max. thimble temp. 1454 K
Max. Vel. at nozzle
227 m/s
Hein
Heout
Max. thimble temp. 1493 K
Max. Vel. at nozzle
165 m/s
Max. thimble temp. 1423 K
Max. Vel. at nozzle
313.5 m/s
Fig. 8. Comparison of velocity and thimble temperature distributions in divertor heat sink for different nozzle diameters at Re = 1.58 × 104.
1282 S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

23. 4.4. The influence of nozzle shapes on thermal-hydraulic
performance
It is necessary to assess the influence of different nozzle shapes
on heat transfer characteristics that have been determined for the
proposed divertor heat sink concept. For all the nozzle geom-
etries, simulations have been performed for h = 1 mm with mass
flow rate in the range of 10–14 g/s. These mass flow rates corre-
spond to Re of 1.2 × 104
− 1.7 × 104
for circular jet. Five different
nozzles, viz., circular, elliptical, rectangular, square and triangular
shapes of approximately equal cross-sectional area, are chosen for
the present simulations. Details of the jet exit geometries are given
in Table 2. Schematic of different nozzle shapes studied for divertor
heat sink is depicted in Fig. 11.
A comparison of thermal shield and thimble temperature for the
various nozzle shapes is shown in Fig. 12(a) and (b). It can ob-
served at any Re that the thermal shield and thimble temperatures
are the minimum for the elliptical nozzle (Case-B) as compared to
all the other shapes. The maximum deviation in temperature among
the various cases is ~30 °C. Fig. 13 is a comparison of the turbu-
lent kinetic energy (TKE) at Re = 1.58 × 104
for elliptical (Case-B) and
circular (Case-A) nozzles. It can be observed that TKE is higher for
the case of elliptical nozzle contributing to increased mixing and
the associated enhancement in HTC.
It can be noticed in Fig. 12 that the square nozzle (Case-F) also
offers a temperature similar to that of circular nozzle (Case-A) for
the same Re number. All the other nozzle shapes and vertical ori-
entation of nozzles (Cases-C and E) are counterproductive toward
the thermal performance of divertor heat sink. The tile and thimble
temperatures achieved for elliptical nozzle are respectively ~12 °C
and ~18 °C less than the reference circular nozzle at same Re.
Fig. 14(a) and (b) illustrate the dependence of pressure drop and
pumping power ratio on Re number for the various nozzle shapes.
It is clear that both pressure drop and pumping power ratio are the
highest for triangular nozzles. Similarly, the elliptical nozzle also
demands marginally higher pumping power compared to the cir-
cular nozzle (Case-A).
4.5. Design analysis of divertor heat sink concept at various heat flux
values
Thermal-hydraulic performance of divertor heat sink concept has
been investigated at higher thermal loads to estimate the toler-
ance of the design. Toward this, numerical studies have been
performed at various heat flux values, viz., 8, 10, 11, and 12 MW/
m2
over a wide range of Re number 1.2 × 104
–3.0 × 104
for the
optimized case (Case-B). The temperature distribution on the surface
of thermal shield and thimble at various heat loads are depicted
DN = 0.7 mm
DN = 0.5 mm
DN = 0.6 mm
Heat transfer coeff.
(W/m2 K)
Fig. 9. Comparison of local heat transfer coefficient contour for various circular nozzle diameters.
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24. in Fig. 15(a) and (b), respectively. The peak temperature increases
linearly with increase in heat flux at a fixed Re number. This is ex-
pected because for identical heat transfer coefficient and fluid
temperature, the peak structural temperature is directly propor-
tional to heat flux. Further, for a fixed heat flux the peak temperature
decreases gradually with Re number, as the heat transfer
coefficient increases with the Re numbers. The predicted heat trans-
fer coefficient for the multi-jet elliptical nozzle is compared with
the circular nozzle correlation proposed by Martin [29] in Fig. 16,
for H/DN = 1.66. It is clear that the heat transfer coefficient of ellip-
tical nozzle is ~14% higher than that of the circular nozzle. This
comparison indirectly validates the present CFD simulations.
Fig. 10. (a) Comparison of maximum thermal shield and thimble temperatures and (b) pumping power ratio at various H/DN ratios for circular nozzle.
1284 S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

25. It can be seen that the maximum temperature of divertor heat
sink is well within the design limits for heat loads of ≤10 MW/m2
at Re = 1.58 × 104
. On the other hand, when the heat flux is 11 MW/
m2
the peak temperature on thimble would still be under the
required temperature limit indicating a margin of 10% in the design.
For heat flux values exceeding 11 MW/m2
, the Re number has to be
increased with the associated penalty in pumping power.
5. Solid mechanical analysis
Structural analysis is performed to determine the state of stresses
in divertor heat sink assembly as a result of high pressure (10 MPa)
and large temperature gradient. The predicted results of pressure and
temperature distributions by the computational fluid dynamics anal-
ysis are used to carry out the thermo-mechanical analysis through
the finite element based program ANSYS Workbench 14.0 [24].
Table 2
Detailed dimension of the nozzle exit geometries.
Name Geometry Hydraulic Diameter (mm)
Case-A 0.6
Case-B ~0.6 (major axis = 0.80 mm, minor axis = 0.48 mm)
Case-C 0.6 (major axis = 0.48 mm, minor axis = 0.80 mm)
Case-D ~0.6 (height = 0.48 mm, width = 0.70 mm)
Case-E ~0.6 (height = 0.70 mm, width = 0.48 mm)
Case-F 0.6 (side = 0.60 mm)
Case-G 0.6 (triangle height = 0.9 mm)
Case – E Case – F Case – G
Case - A
s = 4 mm
p = 4.9 mm
Steel Cartridge
Case – B Case – C Case – D
Fig. 11. Schematic of different nozzle shapes studied for divertor heat sink.
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26. Fig. 12. Influence of nozzle shape on the maximum temperatures (a) thermal shield and (b) thimble.
1286 S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

27. 5.1. Calculation model, mesh and boundary condition
In the solid mechanical study a computational model identical
to that used as in thermal hydraulic analysis has been adopted. The
x–y plane is defined as the symmetry plane. The finite element mesh
for the computational model is generated by the internal ANSYS
Workbench mesh-tool. It consists of a uniform hexahedral mesh with
~2.5 × 104
elements. Temperature dependent material properties have
been considered for tungsten and tungsten lanthanum oxide. The
property values are taken from ITER Material Handbook [24]. The
nodal temperature and pressure data are imported from CFD results
(Case-A) for the solid mechanical analysis, and suspension is defined
at the lower end of the thimble as frictionless.
5.2. Solid mechanical analysis results
Fig. 17(a) represents the imported temperature distribution at
the thimble surface from the CFD calculation. It can be seen that
the peak temperature at the thimble are very close to the CFD
results, and the maximum deviation in imported temperature
is found to be less than ~1 °C. Fig. 17(b) depicts the predicted von
Misses stress distribution in the divertor heat sink design. It is
seen that the maximum resulting stress in the thimble is ~365 MPa
occurring in the sharp corner on its inner side at a temperature of
~726 °C, which is well below the allowable limit of~462 MPa [24].
The computed stress of ~145 MPa at the thermal shield–thimble
interface at a maximum temperature of ~1182 °C is still within
the allowable value 310 MPa. For the tungsten tile the maximum
stress is ~145 MPa. It occurs at the top surface at an existing
temperature of ~1543 °C. This is also well below the allowable
limit of 246 MPa.
6. Conclusions
A divertor module concept with multi-jet helium cooling system
has been proposed for use in a divertor system of fusion reactor.
Three-dimensional thermal hydraulic investigations have been
carried out to understand the performance of the cooling system
as a function of various critical parameters, which includes
thimble diameter, nozzle diameter, nozzle-to-wall space, nozzle
shape, etc. Among various nozzle shapes studied, for identical Re,
elliptical nozzles are found to give the best performance whereas
triangular nozzles are found to give the worst performance. Simi-
larly, a minimum thimble temperature and pressure drop in the
circuit is achieved at H/DN ~1.66. The proposed design is found to
have a power-handling margin of 10% over target heat flux value
of 10 MW/m2
. The stresses induced in the divertor module due to
thermal gradients and pressure loads are important factors that
limit the life of the divertor. Therefore, structural analysis of the
divertor module has also been carried out, and the stress values
arising out of temperature gradient and pressures are found to be
within acceptable limits, demonstrating the reliability of the pro-
posed concept.
Nomenclatures
AN Area of the nozzle [m2
]
DN Diameter of nozzle [m]
DT Thimble diameter [m]
H Nozzle to wall space [m]
Keff Effective molecular thermal conductivity of fluid
[Keff = Kl + Kt] (W/m − K)
Kl Laminar thermal conductivity of fluid [W/m − K]
Kt Turbulent thermal conductivity of fluid (W/m − K)
Ks Thermal heat conductivity of solids (W/m − K)
k Turbulent kinetic energy [m2
/s2
]
m Mass flow rate [kg/s]
μeff Effective viscosity of the fluid [μeff = μl + μt] [N·s/m2
]
μl Laminar viscosity of the fluid [N·s/m2
]
μt Turbulent viscosity of the fluid [N·s/m2
]
P Pressure [Pa]
p Axial pitch [m]
s Circumferential pitch [m]
QT Total incident power [W]
q” Heat flux from the wall [W/ m2
]
Tw Temperature of wall surface [K]
Tf Local fluid temperature [K]
uj Velocity components in three spatial directions [m/s]
W Pumping power [W]
Greek symbol
ε Rate of dissipation [m2
/s3
]
μ Dynamic viscosity [N·s/m2
]
ρ Helium density [kg/m3
]
TKE
[m2
/s2
]
Case-A Case-B
Fig. 13. Comparison of turbulence kinetic energy distributions for reference Case-A and optimized Case-B at Re = 1.58 × 104
.
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28. Fig. 14. Influence of nozzle shape on (a) pressure drop and (b) pumping power ratio.
1288 S. Rimza et al./Applied Thermal Engineering 100 (2016) 1274–1291

29. Fig. 15. Comparison between (a) maximum thermal shield and (b) thimble temperature at different heat loads for optimized case (Case-B).
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32. Fusion Engineering and Design 100 (2015) 581–595
Contents lists available at ScienceDirect
Fusion Engineering and Design
journal homepage: www.elsevier.com/locate/fusengdes
Optimal design of divertor heat sink with different geometric
configurations of sectorial extended surfaces
Sandeep Rimzaa,∗
, Kamalakanta Satpathya
, Samir Khirwadkara
, Karupanna Velusamyb
a
Divertor and First Wall Technology Development Division, Institute for Plasma Research (IPR), Bhat – 382428, Gandhinagar, Gujarat, India
b
Mechanics and Hydraulics Division, Indira Gandhi Centre for Atomic Research (IGCAR), Kalpakkam 603102, India
h i g h l i g h t s
• Effect of design variables in enhancing heat removal potential with pumping power assessed.
• The optimization objective is to minimize the thimble temperature.
• Investigation of optimum design parameters for various Reynolds number.
• Practicability of the optimum designs is verified through structural analysis.
• Benchmark validation of divertor finger mock-up against in-house experiment and good agreement is achieved.
a r t i c l e i n f o
Article history:
Received 17 April 2015
Received in revised form 22 July 2015
Accepted 20 August 2015
Available online 5 September 2015
Keywords:
SES
Relative pitch
Relative thickness
Jet diameter
Nuclear fusion
Divertor
a b s t r a c t
Cooling of fusion reactor divertor by helium is widely accepted due to its chemical and neutronic inert-
ness and superior safety aspect. However, its poor thermo physical characteristics need high pressure
to remove large heat flux encountered in fusion power plant (DEMO). In the perspective of DEMO, it
is desirable to explore efficient cooling technology for divertor that can handle high heat flux. Toward
this, a novel sectorial extended surface (SES) was proposed by the authors Rimza et al. (2014) [2]. The
present work focuses on design optimization of divertor finger mock-up with SES to enhance the thermal
hydraulic performance. The maximum thimble temperature is considered as the vital design constraint.
Various non-dimensional design variables, viz., relative pitch, thickness, jet diameter, the ratio of height
of SES to jet diameter and circumferential position of the SES are considered for the present optimiza-
tion study. The effects of design variables on thermal performance of the divertor are evaluated in the
Reynolds number (Re) range of 7.5 × 104
–1.2 × 105
. The analysis reveals that, the heat transfer perfor-
mance of divertor finger mock-up with SES is improved for two optimum designs having relative pitch
and thickness of 0.30 and 0.56, respectively. Also, it is observed that finger mock-up heat sink with SES
performs better, when the ratio of SES height to jet diameter, reduces to 0.75 at the cost of marginally
higher pumping power. The effects of jet diameter and circumferential position of SES are found to be
counterproductive toward the heat transfer performance. To understand the stress distribution in the
optimized geometries, a combined computational fluid dynamics (CFD) and structural analysis has been
carried out. It is found that deviation in peak stresses among various optimized geometries is not sig-
nificant. The CFD model has been benchmarked against in-house experiments and good agreement is
achieved.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
Nuclear fusion is a promising energy option for the future, which
is characterized by almost unlimited fuel supplies and best safety
∗ Corresponding author.
E-mail addresses: sandeepr@ipr.res.in (S. Rimza), satpathy@ipr.res.in
(K. Satpathy), sameer@ipr.res.in (S. Khirwadkar), kvelu@igcar.gov.in (K. Velusamy).
characteristics. In a design of future fusion power plant [1], divertor
must handle a high heat flux (∼10 MW/m2). Thermal management
of such high heat flux gives rise to numerous engineering issues,
which affect the thermal hydraulic performance and lifetime of
the divertor components. Therefore, the complete divertor target
plate is divided into a number of small volumes known as cassettes
and each cassette is made up of several small cooling finger mock-
ups to reduce the possible thermal stress as depicted in Fig. 1. The
most important design criterion is to keep thimble temperature
http://dx.doi.org/10.1016/j.fusengdes.2015.08.008
0920-3796/© 2015 Elsevier B.V. All rights reserved.

33. 582 S. Rimza et al. / Fusion Engineering and Design 100 (2015) 581–595
Nomenclature
A area of the jet (m2)
D diameter of jet (m)
h height of extended surface (m)
J pumping power ratio
Keff effective molecular thermal conductivity of fluid
[Keff = Kl + Kt] (W/m K)
Kl laminar thermal conductivity of fluid (W/m K)
Kt turbulent thermal conductivity of fluid (W/m K)
K thermal conductivity of solid (W/m K)
k turbulent kinetic energy (m2/s2)
ṁ mass flow rate (kg/s)
eff effective molecular viscosity of the fluid
[eff = l + t] (N s/m2)
l laminar viscosity of the fluid (N s/m2)
t turbulent viscosity of the fluid (N s/m2)
p pitch of extended surface (m)
P pressure (Pa)
QT total incident power (Watt)
q heat flux (MW/m2)
SES sectorial extended surface
t thickness of extended surface (m)
T temperature (K)
uj velocity components in three spatial directions
(m/s)
W pumping power (Watt)
Greek symbol
ε rate of dissipation (m2/s3)
differences
ı relative
dynamic viscosity (N s/m2)
density of fluid (kg/m3)
above ductile brittle transition temperature (∼600 ◦C) and below
the brazing filler temperature (1050 ◦C). Also, it is required to main-
tain the pumping power of the coolant to be below ∼10% of incident
power.
Over the past few decades, the study of fluid flow and heat
transfer in cooling channel with extended surface has become one
of the active research areas. The extended surfaces enhance the
cooling effect by increasing the total surface area, and occasion-
ally generating secondary flows. In the past, various investigations
have been performed on the effects of geometrical parameters on
the flow friction and heat transfer in the cooling channel. Toward
this, heat transfer characteristics of divertor cooling finger mock-
up have been investigated with sectorial extended surfaces (SES) by
Rimza et al. [2]. They revealed that, addition of SES greatly increases
performance of the finger mock-up as compared to a smooth chan-
nel. A variety of heat transfer enhancement techniques have been
evaluated by Baxi [3] and Baxi and Wong [4] to improve the heat
transfer performance of the divertor. From their studies, they found
that helium cooled divertor design for fusion machines is feasible,
at a reasonable pumping power. The mass flow rate and pumping
power required can be minimized by a combination of enhance-
ment techniques and use of high pressure gas. Hageman et al. [5]
investigated a plate-type divertor with fins, and found that the
heat transfer performance of divertor increases to a great extent
by the addition of fins. Critical heat flux experiments for diver-
tor application have been performed by Ezato et al. [6–8]. They
discovered that, capability of divertor to handle high heat flux
increases significantly, by the use of screw tube and saw toothed fin.
Sharafat et al. [9] performed a numerical analysis to optimize the
design of metallic heat exchanger tube for minimum pressure drop
through the porous media and for uniformity of surface tempera-
tures. Youchison et al. [10] reviewed the convective heat transfer
through helium cooled porous metal divertor modules. They found
that, the porous metal helium divertor exceeded its design specifi-
cations, and survived at the maximum heat flux of ∼29 MW/m2. An
optimization study was performed by Rader et al. [11], to assess the
thermal performance of the modular divertor with fin. Their results
revealed that the performance of the divertor enhances with vari-
ation in geometric configuration. Optimization of T-tube divertor
design concept of modular helium cooled units was investigated
by Bruke et al. [12]. Based on their studies, the design was modi-
fied by changing the dimensions of the slot-jet, inner cartridge and
tungsten armor to accommodate higher heat fluxes. Experimen-
tal and numerical investigations on plate type divertor with the
use of metallic foam have been conducted by Gayton et al. [13].
Fig. 1. (a) Schematic of divertor finger mock-up, (b) plan and (c) 3-D view of SES (all dimensions in mm).

34. S. Rimza et al. / Fusion Engineering and Design 100 (2015) 581–595 583
Fig. 2. (a) 30◦
sector of computational model of finger mock-up with boundary conditions and (b) close-up view of meshed SES.
Table 1
Comparison of the maximum thimble temperature for different grid size at Re = 1.1 × 105
.
Grid Number of control volume Predicted maximum thimble temperature (◦
C) Percentage difference in temperature
Very coarse 183,647 1057.7 −
Coarse 262,358 1052.2 −0.529%
Fine 375,840 1049.8 −0.280%
Very fine 428,567 1049.7 −0.006%
Their results indicated that the heat transfer performance of the
divertor significantly increases with metallic foam as compared to
a smooth channel. Ihli and Ilić [14] analyzed the various helium
cooling methods for nuclear fusion devices. It was found that, a
V-rib-based surface roughness for the first wall and the multi-
ple jet impingement cooling technique are useful for heat transfer
enhancement.
Optimization of the fan-shaped pin fin was performed by Moon
and Kim [15] to maximize the heat transfer. They discovered that
the fan-shaped pin fin increases heat transfer by over 20% com-
pared with a circular pin–fin. Metzger et al. [16,17], Fossen [18]
and Chyu et al. [19,20] discovered that the ratio of fin height
to diameter, orientation of the fin, and fin cross-sectional shape
are critical parameters that affect the thermal hydraulic perfor-
mance of the heat sink. An experimental and numerical study
in channels with various dimple depths was performed by Rao
et al. [21,22]. Their study revealed that, dimples enhance the
convective heat transfer in the channel and shallower dimples
show relatively lower friction factors (17.6%) as compared to pin
fin channel. The heat transfer performance due to the orienta-
tion effect in square pin fin heat sinks has been experimentally
investigated by Huang et al. [23]. They reported that the addi-
tion of surface is comparatively more effective for the downward
arrangement. Erek et al. [24] studied the effect of geometrical
parameters on the thermal hydraulic performance of tube heat
exchangers. The results suggested that the distance between the
fins has a substantial effect on heat transfer and pressure drop
features.
The literature review presented above shows that the ther-
mal performance of heat sink can be enhanced by the use of
extended surface, and the variation in geometric parameters can
augment the thermal-hydraulic performance to a great extent.
However, studies that compare the effect of the various geomet-
ric parameters on the thermal performance of divertor are very
limited. Therefore, in the present study the effect of geometric vari-
ation on the thermal performance is evaluated, and an optimal
design of SES is found through numerical simulations. In addi-
tion, details of flow structure at various Reynolds number and
Fig. 3. Comparison of numerical pressure drop against in-house experimental
results.

35. 584 S. Rimza et al. / Fusion Engineering and Design 100 (2015) 581–595
influence of SES geometric parameters on heat transfer and pres-
sure loss characteristics in the mock-up have been studied. The
principal aim of the optimization study is to reduce the thimble
temperature as much as possible below the brazing filler temper-
ature (1050 ◦C) to enhance the life of divertor finger mock-ups
design with SES, and simultaneously limit the pressure drop to
a reasonable value to save pumping power. The heat transfer
and flow characteristics in divertor finger mock-up are compared
with experimental data toward validation of the computational
model.
2. Problem description
2.1. Design of finger mock-up with SES
The design of the diverter finger mock-up with SES as depicted
in Fig. 1, consists of high heat flux plasma facing component known
as “tile” (width 17.8 mm) made up of tungsten (W). The pressure
absorbing part is known as a “thimble” (Ø15 mm × 1 mm) fabri-
cated in tungsten alloy (WL-10) which is brazed to the tile. To
enhance the thermal performance, SES made up of tungsten alloys
Fig. 4. Non-dimensional velocity contours and the pathline in x–y plane at a distance of 1 mm from the target surface at different mass flow rates.
Fig. 5. Comparison of turbulent kinetic energy distribution and pathlines in y–z plane (a) without SES and (b) with SES at Re = 1.10 × 105
.

36. S. Rimza et al. / Fusion Engineering and Design 100 (2015) 581–595 585
Fig. 6. Non-dimensional temperature contours for reference case ‘B’ at various mass flow rates.
have been brazed to thimble inside the finger mock-up. A concen-
tric steel cartridge (Ø11.2 mm × 1 mm) having a jet diameter 2 mm
is used to cool the divertor finger mock-up. Helium flows radially
outward after passing through an array of SES.
2.2. Numerical approach and mathematical formulation
The computational fluid dynamic software (CFD) code ANSYS
Fluent 14.0 [25], is used for the heat transfer and fluid dynamics
simulation of the finger mock-up with SES. The pressure–velocity
coupling between the Navier–Stokes and continuity equations is
resolved using the SIMPLE algorithm [26]. The realizable k–ε tur-
bulence model is adopted to describe the fluid behavior in divertor
finger mock-up. This model has been successfully used to simulate
the flow and heat transfer in channels with pin fins [2,27–29]. The
convective and diffusive fluxes are combined using the second
order upwind scheme. To declare convergence, the errors in the
discretized momentum and continuity equations are set to a value
Fig. 7. Schematic of variation in heat transfer coefficient along radial position at target surface for divertor without SES (case ‘A’).