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 ). 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.  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 . 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)  and at Efromov Institute , 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 : 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 : 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 . 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 . 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 . 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  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  R. 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