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Ying2011-SubcooledBoilingHeatTransferModeling.pdf
Fusion Engineering and Design 86 (2011) 667–670
Contents lists available at ScienceDirect
Fusion Engineering and Design
journal homepage: www.elsevier.com/locate/fusengdes
A subcooled boiling heat transfer predictive model for ITER EHF FW designs
A. Ying a,∗ , T. Waku b , D.L. Youchison c , R. Hunt a , H.G. Zhang a , M.A. Ulrickson c
a
b
c
Mechanical and Aerospace Engineering Dept., UCLA, Los Angeles, CA 90095, USA
Software Cradle Co. Ltd., Osaka 532-0011, Japan
Sandia National Laboratories, Albuquerque, NM 87185-1129, USA
a r t i c l e
i n f o
Article history:
Available online 12 February 2011
Keywords:
ITER FW design
Subcooled boiling heat transfer
CHF
Numerical simulation
CFD
a b s t r a c t
Recent experimental data from the ITER critical heat flux (CHF) mock-ups was used to benchmark a 3D CFD
code concerning subcooled boiling heat transfer for high heat flux removal. The predicted temperatures
show good agreement with experimental measurements for a range of operating parameters and of
cooling configurations. Specifically, it applies to a hypervapotron channel exposed to a 5 MW/m2 surface
heat load and cooled by velocity of 2 m/s. Such flow geometry and operating condition seem necessary for
ITER-enhanced heat flux first wall modules if an adequate design margin in CHF is needed. A detailed CFD
and heat transfer analysis performed on a prototyped CAD model provided a higher confidence on the
design and is deemed a desirable feature for continued design exploration and optimization processes.
This is particularly crucial in regard to flow distribution among the FW fingers.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
Under a limited regime of an inductive operation, the thermal
heat load deposited onto the first wall (FW) panel reaches a peak as
high as 5 MW/m2 [1,2], caused by conduction and convection loads
carried from charged particles. The heat load profile associated with
the peak depends on plasma geometric parameters and SOL data,
and has been computed (i.e. FW panel 8 for limiter-type contact
during flat top diverted plasma [3]). An auspicious circumstance
is transmitting the single phase flow to a higher heat transfer rate
of a subcooled boiling flow in these high thermal load regions. As
such, the calculated temperature at the CuCrZr wall/water interface clearly indicated the occurrence of subcooled boiling when
such a heat flux profile (from Ref. [3] Fig. 12) was imposed onto
the CATIA model of FW panel 8 (BLKT 08 FW#2U8JN5) as illustrated in Fig. 1. In order to achieve controlled boiling over a wide
range of operation conditions as is expected in FWs, detailed flow
and heat transfer analysis is essential. The challenges a designer
faces include: (1) a manifold design capable of diverting adequate
flow into the impacted high heat flux region, and (2) knowing what
velocity is needed to avoid the boiling crisis (departure from nucleate boiling) and having an enough design margin with respect to a
CHF.
A typical FW panel consists of a number of fingers; each finger
is cooled by the coolant channel instituted in the CuCrZr sink. The
coolant supplied to each finger is generally attained by distributing a sum amount of the mass flow rate to a number of parallel
flow paths through a manifold. The best way to ensure proper
design of the flow distributing manifold is to design by analysis.
In particular, to perform the analysis directly on the prototype CAD
model.
The superior ability to analyze thermo fluid/CFD accurately on a
large scale with complex geometry triggered further evaluation of
the SC/Tetra® CFD code for enhanced heat flux FW module design
analysis [4]. SC/Tetra is based on finite volume method, supports
hexahedral, prismatic, pyramidal and tetrahedral elements for its
computational mesh, and provides powerful functions for various
exploitations. The objectives are: (1) to validate the subcooled boiling models in the SC/Tetra with the experimental data recently
acquired at Sandia National Laboratories (SNL) [5] and at Efromov Institute [6], and (2) to identify regimes where heat transfer
associated with flow boiling occurring in the FW cooling channels can be predicted with acceptable accuracy. This is deemed
a desirable feature for the design exploration and optimization
processes.
2. Regime of validity using SC/Tetra CFD code boiling
models
∗ Corresponding author at: Mechanical and Aerospace Engineering Department,
Room 44-136, Engineering IV, UCLA, Los Angeles, CA 90095, USA. Tel.: +1 310 206
8815; fax: +1 310 825 2599.
E-mail address: [email protected] (A. Ying).
0920-3796/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.fusengdes.2011.01.033
The onset of nucleate boiling (ONB) point marks the transition
from the single-phase region to a partially developed boiling (PDB)
region. A correlation suitable for estimating the heat flux at the ONB
668
A. Ying et al. / Fusion Engineering and Design 86 (2011) 667–670
300
Solid symbols: RF-CHF flat channel data
Open symbols: Simualtion
2 m/s
280
Thermocouple temperature (ºC)
4 MW/m
Fig. 1. Temperature characteristics at CuCrZr/water interface against the onset of
nucleate boiling temperature of 238.6 ◦ C (water pressure: 3 MPa). Arrows indicate
water flow direction.
Table 1
Values of ONB and FDB heat fluxes (MW/m2 ) at different velocities (water pressure:
2 MPa, water temperature at 130 ◦ C, Tsat = 212.2 ◦ C).
Velocity
Tw,ONB
qONB
Tw,FDB
qFDB
1 m/s
2 m/s
4 m/s
215.7 ◦ C
216.9 ◦ C
218.4 ◦ C
0.8
1.4
2.5
227.0 ◦ C
230.3 ◦ C
234.1 ◦ C
1.25
2.26
4.03
point qONB is given by the following equation [7]:
kl hfg v
8Tsat
(Tw,onB − Tsat )2
(1)
where kl is the liquid thermal conductivity, hfg is the latent heat of
vaporization, v is the vapor density, is the liquid surface tension,
Tw,ONB is the wall temperature at ONB, and Tsat is the saturation
temperature. After the ONB, many nucleation sites are activated,
and the bubbles either adhere on the hot surface or disappear in the
bulk fluid as it moves downstream. The heat transfer is enhanced in
PDB region until it reaches a fully developed boiling (FDB) region.
The heat flux at FDB is given by Bowring model [8]:
qFDB = 1.4qE
2 MW/m 2
220
200
1 MW/m 2
0.15
0.2
0.25
Downstream distance (m)
Fig. 2. Comparison of the calculated and experimental temperature values (pressure: 2 MPa, inlet temperatures vary but fall between 125 ± 5 ◦ C).
inlet velocities with respect to their corresponding experimental inlet temperatures and operating pressures of 2 MPa. In the
SC/Tetra solver, flow and heat transfer computations are carried
out using RNG k–ε turbulence model with wall function and log
law describing the near-wall behaviors. Sensitivity tests on average Y+ (between 30 and less than 100) were performed to ensure
that computed heat transfer results were not affected by the mesh
and the prism layer thickness setting. Relatively good comparisons
were obtained for heat fluxes of 3 MW/m2 or lower under the experimental operating conditions. There was about an 8% difference in
temperature value (normalized to the amount of surface temperature increase) found at a higher heat flux of 4 MW/m2 ; however,
the last high temperature reading could not be predicted with the
existing boiling model capability. The CFD code must incorporate
two phase flow modeling capabilities to simulate RF CHF testing at
300
(2)
where qE is the heat flux at the intersection point of the extension
of the single-phase heat transfer curve and the FDB curve based on
Rohsenow model [9]. In SC/Tetra, the heat transfer in the PDB region
is interpolated between the forced convection and FDB curves as
given by Bergles and Rohsenow [10]. Strictly speaking, the nucleate boiling heat transfer model adopted in the present version of
SC/Tetra (v. 8) is limited to the region prior to the flow boiling
becoming fully developed. Subsequently, this limits the heat flux
to 2.26 MW/m2 at 2 m/s water velocity in a flat rectangular channel
as noticed in Table 1.
The CHF testing performed at Efromov Institute included flow
in both rectangular flat and hypervapotron (HV) channels where
water velocities ranged from 1 to 4 m/s, and surface heat fluxes
up to 10 MW/m2 imparted to the heated surface [6]. A noticeable
feature on the RF-CHF mockup is its relatively short downstream
flow path (∼8 cm) followed by a 90◦ downward bend return line
(see Fig. 4). This could potentially cause vapor stagnant and vapor
blanket blockage from secondary slow recirculation flow. Thus,
the axial conduction at downstream was reduced as more vapors
were generated and probably accumulated, which increased the
last thermocouple reading as shown in 4 MW/m2 results (see experimental results in Figs. 2 and 3).
Figs. 2 and 3 show the comparison of the predicted temperatures
of SC/Tetra boiling model and measured values under different
240
3 MW/m 2
180
Solid symbols: RF-CHF flat channel data
Open symbols: Simualtion
4m per s
280
4 MW/m
Thermocouple temperature (ºC)
qONB =
260
2
2
260
3 MW/m
2
240
220
2 MW/m
2
200
180
1 MW/m 2
160
0.15
0.2
0.25
Downstream distance (m)
Fig. 3. Comparison of the calculated and experimental temperature values (pressure: 2 MPa, inlet temperatures vary but fall between 125 ± 5 ◦ C).
A. Ying et al. / Fusion Engineering and Design 86 (2011) 667–670
Fig. 4. RF-3-HV CHF mockup computational model. Calculated temperatures shown
are for 5 MW/m2 with a water velocity of 2 m/s (RF-3-HV thermocouple readings
were between 250 and 260 ◦ C, inlet temperature: 116 ◦ C, pressure: 2 MPa, run #7).
275
symbol: simualted results
270
CHF-RF-3, HV
(Data range)
area where a vapor film can form, the fin structures in a HV channel help dissipate the surface heat flux into a larger area and result
in a lower heat load at the wall/water interface. Subsequently, this
enlarges the applicability of the SC/Tetra’s boiling model capability. Predicted results in the HV configuration show a mostly flat
temperature profile across the 4 thermocouples’ readings as that
of experimental observations (Fig. 4). These thermocouples were
located at 1.5 mm below the top surface and at 12 mm into the copper heat sink from the side. Additional comparisons for a range of
operating parameters with other test runs show good agreement
between the calculated and experimental results as presented in
Fig. 5.
The CHF testing at SNL so far is on a flat rectangular cooling channel with a flow gap of 5 mm. The surface heat is applied over a 10 cm
heating length starting at 15 cm downstream; however, unlike the
outlet design in the RF CHF mockup, the flow leaves the channel
straight without making a 90◦ turn (as shown in Fig. 6). Fig. 7 shows
the comparison of the temperature history of the SC/Tetra predicted
values and the experimental measured values under a square wavelike heat input of 2.16 MW/m2 (run #200,637). There was a good
agreement between the predicted and experiment data of the thermocouple at the end of heating region. A much slower ramp-up
characteristic found in the experiment was caused by the contact
resistance as well as the indirect contact between the thermocouple
junction and the stainless steel wall.
3. CHF discussion for flat rectangular cooling channels
4m/s 7 MW/m 2
Examination of several existing correlations and models for CHF
in subcooled flow boiling show overestimations of the CHF by ∼60%
for all velocity ranges when compared to the RF CHF mock-up test
265
Temperature (C)
669
260
2m/s 5 MW/m 2
260
2.16 MW/m
Run 200637
255
1m/s 4 MW/m 2
2 MPa
velocity 2 m/s
inlet Temp. 119.2C
240
TC1
TC3
TC5
TC1
TC3
TC5
245
1m/s 3 MW/m
240
0.15
2
0.2
0.25
Downstream heating distance (m)
Fig. 5. Comparison between simulated and experimental temperature profiles for
various runs of RF-3-HV (all runs were at 2 MPa. Inlet temperatures varied between
110 and 118 ◦ C).
Temperature (C)
220
200
240
220
200
180
180
Solid symbol: experiment
Open symbol: simualtion
160
TC1= thermocopule one
Pyrometer for surface heat
250
260
160
140
Pyrometer
higher heat fluxes in order to capture vapor phase flow characteristics at the 90◦ bend region.
The good agreement between the calculated and experimental
temperature data went up to 5 MW/m2 for the HV channel at 2 m/s
velocity. In addition to increasing turbulence and segmenting the
140
120
80
90
100
110
120
130
140
Elapsed tiem (s)
Fig. 7. Comparison of predicted and experimental temperature histories under a
surface heat load of 2.16 MW/m2 .
Fig. 6. US flat, rectangular channel CHF mockup computational model (calculated temperatures shown are for run #200,638 with a heating input of 2.14 MW/m2 . Water
velocity: 2 m/s, inlet temperature: 119.7 ◦ C).
670
A. Ying et al. / Fusion Engineering and Design 86 (2011) 667–670
Table 2
Comparison of RF CHF data for flat channel with Kureta and Alimoto’s correlation.
Note that the flow gap in the RF’s experiments was 2 mm wider than the range
covered in the correlation (3 mm).
Velocity
RF dataa
Correlationa
2 MPa
100 ◦ C
3 MPa
100 ◦ C
3.73
5.37
7.72
3.88
5.61
8.09
Critical heat flux (MW/m2 )
1 m/s
2 m/s
4 m/s
a
4
5
7
3.3
4.8
6.95
At 2 MPa with 125 ◦ C inlet temperature.
results in the flat rectangular coolant channel. The discrepancy can
be attributed to many factors including heating conditions, channel
geometries, shapes, etc. This revealed the significant importance of
the operating conditions and specific geometries when using CHF
correlations. The calculated CHF value reached agreement when
the operating conditions between the RF experiments and the
experiments used to derive the correlation became similar. These
calculations were based on the correlation presented by Kureta and
Akimoto [11] for the subcooled boiling CHF in one-side heated narrow rectangular channels. As shown in Table 2, the calculated CHFs
for 2 and 4 m/s cases almost reproduced experimental CHF values,
although the calculated CHF for 1 m/s is 17.5% lower than the experimental CHF data. This suggests that a coolant velocity of more than
2 m/s is needed for the enhanced heat flux module to overcome the
CHF if the FW is cooled using a flat rectangular channel. Because of
the correlation’s accuracy in predicting the CHF for the ITER-like flat
channel, one may explore CHF values at different operating spaces
and evaluate their corresponding impacts on the design. For example, the CHF values increase by 11% for the 2 m/s flow as the inlet
temperature decreases from 125 ◦ C to 100 ◦ C. It increases further by
enlarging water pressure from 2 MPa to 3 MPa. This is due to further
subcooling. The calculated CHF value in 2 m/s gives a design margin
of 1.17 if water is operated at 3 MPa with an inlet temperature of
100 ◦ C. By reducing the heated length, as the peak heat flux predicted for the EHF module spans ∼5 cm, the CHF margin increases
by about 3.3% (with a shorter heated length of 5 cm).
4. Implication to FW panel designs and summary
The above discussion showed a cooling velocity of ∼4 m/s is
needed to avoid CHF with an ample design margin of 1.4 if fingers were cooled using flat rectangular cooling channels. Current
analysis indicates that this can be difficult. The calculated veloc-
ity ranged from 1 to 1.7 m/s among the fourteen fingers (per half
FW panel) that were connected in parallel for a mass flow rate of
10 kg/s. Worst of all, the flow was not properly directed toward the
needed high heat load region. If the finger is cooled using a HV cooling channel, this 10 kg/s mass flow rate can give a desired velocity
of 2 m/s for the 5 MW/m2 surface heat removals if, in addition, the
fourteen fingers were grouped into seven parallel flow paths (per
half FW panel).
The analysis presented in the paper showed that the heat transfer associated with the aforementioned subcooled boiling model is
adequate to analyze the anticipated heat loads of ITER enhanced
heat flux modules using HV cooling channels. The benchmark
also showed that the subcooled nucleate boiling model can be
applied to flat cooling channels with velocity as low as 1 m/s
for a surface heat flux up to 1.2 MW/m2 . This range of operation is applicable to the thermal heat load of ITER normal heat
flux modules. This provides further confidence in using a CFD
code (in this case SC/Tetra) for ITER FW/shield blanket design and
optimization.
Acknowledgments
This work was funded by the US ITER Project Office, Oak
Ridge National Laboratory, which is managed and operated by UTBattelle, LLC for the United States Department of Energy under
contract number DE-AC05-00OR22725.
The views and opinions expressed herein do not necessarily
reflect those of the ITER Organization.
References
[1] R. Mitteau, Heat flux profile along a single finger, ITER internal document (UID:
2LU7FK).
[2] R. Mitteau, P. Stangeby, C. Lowry, M. Merola, and the ITER Blanket Section, Heat
loads and shape design of the ITER first wall, Fusion Eng. Des. 85 (10–12) (2010)
2049–2053.
[3] H. Labidi, Heat flux analyses on FW panel 8 for limiter-Type contact during flat
top diverted plasma, ITER internal document, ITER D 2ZZV3G.
[4] SC/Tetra Version 8 Solver Reference, Software Cradle Co., Ltd., Sep. 2009.
[5] US CHF Test Results, Sandia National Laboratory, May, 2010 (Private communication).
[6] RF CHF MoM Final.doc, Efromov Institute, presented at ITER Blanket CDR
meeting, ITER (UID: 2YGHM8).
[7] J.G. Collier, J.R. Thome, Convective Boiling and Condensation, 3rd ed., Oxford
University Press, 1994.
[8] W.M. Rohsenow, Trans. ASME 74 (1952) 969.
[9] W.R. Bowring, OECD Halden Reactor Project Report No. HPR-10, 1962.
[10] A.E. Bergles, W.M. Rohsenow, Trans. ASME J. Heat Transfer 86 (1984) 365–372.
[11] M. Kureta, H. Akimoto, Int. J. Heat Mass Transfer 45 (2002) 4107–4115.
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