2021, M. Panchal, Measurement of effective thermal conductivity of lithium metatitanate pebble beds by steady-state radi

1. Fusion Engineering and Design 172 (2021) 112854 Contents lists available at ScienceDirect Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes Measurement of effective thermal conductivity of lithium metatitanate pebble beds by steady-state radial heat flow method Maulik Panchala,*, Vrushabh Lambadea, Vimal Kanpariyab, Harsh Patela,c, Paritosh Chaudhuria,c aInstitute for Plasma Research, Bhat, Gandhinagar 382428, India bThe Maharaja Sayajirao University, Vadodara 90001, India cHomi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India A R T I C L E I N F O A B S T R A C T Keywords: Effective thermal conductivity Lithium metatitanate Steady-state method Tritium breeding blankets As a functional material of the tritium breeding blankets of the future fusion reactor, different candidates of the lithium-based ceramics have been considered to generate and release tritium. These tritium breeding materials in the form of packed pebble beds of nearly spherical-shaped particles have many advantages over the sintered pellets or blocks. For the design and analysis of the breeding blanket, the effective thermal conductivity (keff) of lithium-based ceramic pebble beds are required to be well characterized under the fusion-relevant conditions. In this study, an experimental setup has been fabricated and installed to estimate the keff of pebble beds as a function of bed temperature and filling gas pressure. The working principle of the experiment is based on the steady-state radial heat flow method. The various experiments have been performed on lithium metatitanate (Li2TiO3) pebbles having a diameter of 1 ± 0.15 mm to measure keff in the temperature range from 400 ◦C to 800 ◦C and in the environments of stagnant helium gas. The pressure of helium gas was adjusted from 0.105 MPa to 0.4 MPa (abs.) to account the effect of helium gas pressure. The increase in keff has been found with increasing the bed temperature and also increasing the helium gas pressure. The obtained results have been found com- parable with the literature results with minimum difference. 1. Introduction gas, deformation of pebble bed in case of compressed or deformed bed and packing fraction [5]. In the previous studies, various techniques have been employed by different researchers to estimate the keff of different lithium-based ceramic pebble beds. Those techniques can be broadly categorized by the steady-state methods [6–11] and the tran- sient techniques [12–21]. The steady-state methods can be further divided into the axial heat flow methods [6, 7] and the radial heat flow methods [8–11] based on the heat flow direction in the pebble beds. In the radial heat flow methods, the heater is placed along the axial di- rection or at the centerline therefore the heat flows in the radial direc- tion from the heater to the cylindrical-shaped pebble beds. In this method, it is required to minimize the axial heat flow by placing the thermal insulation material at the ends. In axial heat flow methods, the heat flows in the axial direction of the pebble beds. In this method, the key measurement issue is to minimize the lateral heat losses from the axial heat flow during experiments. The steady-state methods are generally very time-consuming compare to the transient methods but at the same time require a simple mathematical expression for data The tritium breeding blankets of the future fusion reactor have the following main functions: to generate and release tritium fuel, extract heat energy from the plasma, and offer radioactive shielding [1, 2]. Different candidates of lithium-based ceramic material have been considered as the promising tritium breeders to breed the tritium fuel [3]. These tritium breeder materials have been considered in the form of packed pebble beds due to many advantages over the sintered pellet or block forms [4]. The ceramic pebble beds have to sustain the severe type of thermal and mechanical loadings during the operation of the tritium breeding blanket. The knowledge of the effective thermal conductivity (keff) is required for the fair prediction of the temperature profile of pebble beds under different operating conditions. The pebble bed is consisting of pebbles (solid phase) and gas (fluid phase). The interstitial gap or void space between the solid pebbles occupies by the gas. Therefore, the keff of pebble bed is the function of various parameters mainly the thermal conductivity of consisting phases, pressure of filling * Corresponding author. E-mail address: maulikpanchal@ipr.res.in (M. Panchal). https://doi.org/10.1016/j.fusengdes.2021.112854 Received 23 June 2021; Received in revised form 23 August 2021; Accepted 28 August 2021 Available online 15 September 2021 0920-3796/© 2021 Elsevier B.V. All rights reserved.

2. M. Panchal et al. Fusion Engineering and Design 172 (2021) 112854 Fig. 1. (a) Steady-state radial heat flow method (b) radial temperature distribution and (c) Temperature gradient. analysis. Apart from this, some of the researchers [22, 23] have also measured the pebble bed effective thermal conductivity numerically. In the present study, an experimental setup working on the principle of the steady-state radial heat flow method has been fabricated and installed. The objectives of the present work were to measure the keff of Li2TiO3 pebble beds as a function of bed temperature (up to 800 ◦C) and in the presence of helium gas environments. The effects of helium gas pressure (0.105 - 0.4 MPa (abs.)) on keff of Li2TiO3 pebble beds were investigated using the experimental setup based on the steady-state radial heat flow methods, which have not been studied earlier as per the author’s knowledge. At high temperatures, the radial heat flow method has the advantage that it inherently reduces the need for guard heaters or additional thermal insulation to restrict unwanted heat flow which can cause serious errors in the measurements compare to the axial heat flow methods. Especially at high temperatures, this feature is also important because the thermal insulation that may be needed in axial heat flow methods may become as thermally conductive as the specimen or pebble beds being examined. Typically, in the radial heat flow apparatus, a cylindrical heater is located along the axis of a cylindrical- shaped pebble bed. The sufficiently enough length to diameter ratio of the pebble bed could avoid significant errors due to the end effects. At the middle of the cylindrical-shaped pebble bed, the heat flows radially outward from the heater and creates an angularly uniform temperature distribution in the pebble bed. In Section 2, the theory of the steady-state radial heat flow, the experimental setup and steady-state temperature distribution are discussed. In Section 3, the obtained results of keff of Li2TiO3 pebble beds are presented and compared. In Section 4, the conclusion and future work have been discussed. 2. Experiment 2.1. Steady-state radial heat flow method Fig. 1(a) shows a simple representation of the steady-state radial heat flow method to measure the effective thermal conductivity of pebble beds. In this method, a temperature gradient is generated using a heat source which is located at the axis of the cylindrical-shaped test spec- imen or pebble bed. After reaching the steady-state condition, the heat flow through the heat source and the temperatures at the known loca- tion in the radial direction are monitored. At the steady-state condition, by neglecting the axial heat conduction and the natural convection heat transfer, the heat flow Q can be expressed by the below-mentioned equation, Tr− Tw ( Simplifying the above equation, the temperature Tr at radius r can be given by, (qR1 (1) Q = ( )) ( ) R2 r 1 1 1 2πkLln + 2πR2L hw (r )) ( ) Tw+qR1 (2) Tr= − ln + keff R2 hwR2 2

3. M. Panchal et al. Fusion Engineering and Design 172 (2021) 112854 Fig. 2. Schematic of the experimental setup and Location of radial thermocouples. after a 10 mm radius the magnitude of the temperature gradient is significantly reduced. Therefore, the errors in the measurements generated due to the uncertainty in the location of temperature monitor points can be significantly reduced if the temperatures are measured after a 10 mm radius in the pebble bed from the center. ( ) is the heat flux (W/m2), R1 is the radius of the Q Where q heater wire (m), keff the effective thermal conductivity of the pebble bed (W/m ◦C), R2 is the radius of the pebble bed (m), Tw is the temperature of the outer surface of the pebble bed (◦C), hw is the interface heat transfer coefficient (W/m2 ◦C) between the pebble bed and the con- taining structure, L is the length of the pebble bed (m). After achieving the steady-state condition, Tw and hw remains constant and the tem- perature distribution Tr has a linear relationship with the ln = 2πR1L 2.2. Experimental setup ( ( ) ) Fig. 2 shows the schematic diagram of the installed experimental setup that mainly comprised of a cylinder with welded ConFlat flanges at both ends, top & bottom ConFlat flanges with the provision of ther- mocouples & gas inlet/outlet ports, heater wire, 1 mm sheath diameter K-type ungrounded thermocouples, supporting discs, thermal insulation blocks, Li2TiO3 pebbles, conductor wire, inline barrel connectors, KF (QF) flanges, gaskets, clamps, band heaters, data acquisition system, PC, temperature controllers, vacuum pump, vacuum valves, helium gas supply, controlled DC power supply, pressure gage, etc. After assembling r . Using R2 qR1 keff the least-square regression fitting technique, the slope m = straight line can be obtained. From the known values of heat flux q, heater wire radius R1 and the slope m; the effective thermal conductivity keff of the pebble bed can be calculated. In Fig. 1(b), an example plot of the radial temperature distribution is shown. Fig. 1(c) shows the tem- perature gradient as a function of the pebble bed radius. It shows that of the Fig. 3. Experimental setup. 3

4. M. Panchal et al. Fusion Engineering and Design 172 (2021) 112854 Fig. 4. First steady-state: Axial temperature distribution at different radius. all the components, the leak test and heater wire electrical continuity were checked. The diameter of the heater wire was 0.7 mm. The top and bottom support discs were used to keep the thin heater wire in straight condition and concentric to the cylinder. The radial thermocouples were supported by the middle and bottom supporting discs. All the supporting discs were made of macor, a machinable ceramic material that has low thermal conductivity (around 1.4 W/m ◦C) and electrically insulating property. To measure the pebble bed temperature in the radial direction, a total of eight thermocouples were arranged in two sets (four thermocouples in a set) and inserted from the bottom side of the cylin- der. The arrangement of the radial thermocouples has been also shown in Fig. 2. To measure the pebble bed temperature in the axial direction, a total of five thermocouples were inserted at the same azimuth angle from the lateral side of the cylinder through the individual welded pipes. The length and diameter of the pebble bed were kept 160 mm and 45 mm, respectively which has a requirement of close to 500 gs of Li2TiO3 pebbles to attain the packing fraction of at least 63%. A total of three resistive band heaters controlled via the PID temperature controllers Fig. 5. First steady-state: Radial temperature distribution. 4

5. M. Panchal et al. Fusion Engineering and Design 172 (2021) 112854 Fig. 6. First and second steady-state: Selected thermocouples for data analysis. were installed on the cylinder to execute the experiments at elevated desired temperatures. The additional thermocouples were also attached to the surface of the cylinder to control the temperature of each heater zone during experiments. The first steady-state in the pebble bed was attained by running all the three band heaters wrapped outside the cylinder. To produce heat energy from the heater wire it was supplied with a direct current with help of a controlled power supply. The second steady-state was attained by energizing the heater wire and also the band heaters, simultaneously. The vacuum pump was used to remove any undesirable gasses produced from the pebbles during heating and then the pebble bed was filled with helium gas at the desired pressure to begin the experiments. In Fig. 3, all the components of the experimental setup have been presented in detail. The role of the middle supporting disk was to hold the two sets of radial thermocouples at 10 mm, 13 mm, 16 mm and 19 mm radius from the center of the cylinder. The thickness of it was 2 mm and surrounded by pebbles from both sides. A total of eight thermo- couples were used to measure the temperature distribution in the radial direction of pebble beds. At the same radius, two thermocouples were positioned as shown in the figures. The axial thermocouples were able to move in or out from the cylinder using the thermocouple feedthroughs. During experiments, when the heater wire along with the external heaters was energized, the axial thermocouples were taken away from the pebble bed to maintain homogeneous conditions. 2.3. Temperature distribution in pebble bed After attaining the first steady-state condition in the pebble bed using the three-band heaters, the temperature distribution in the axial direc- tion or Z-direction of the pebble bed has been measured at different five locations. Fig. 4 shows the different plots of temperature distribution at the center of the pebble bed (r = 0), at 5 mm radius, at 10 mm radius and 15 mm radius at five different set temperature values of band heaters. The purpose of these temperature measurements was to examine the temperature distribution in the axial direction. Similarly, the tempera- ture distribution in the radial direction of the pebble bed was measured by two sets of the thermocouple. Both the sets were equipped with four thermocouples in each set, here named as A-B-C-D and 1–2–3–4. Fig. 5 shows the temperature plot for set-I (A-B-C-D) and set-II (1–2–3–4) at the middle of the cylinder (z = 0). The purpose of these temperature measurements was to collect data for the calculation of the effective thermal conductivity of pebble beds. From Fig. 4, it can be observed that the temperature is not uniform at each Z location; it decreases from the center to the wall of the pebble bed container. This indicates that there is a significant heat loss due to the thermocouple pipes welded on the cylinder which is the reason for the reduced temperature measured by thermocouples (C, D, 1& 2) as observed in Fig. 5 because they are located near the thermocouple pipes. It is noted that the temperature measured by a radial thermocouple (4) was higher due to the wall effects [23] as it is located very near to the container wall. By considering all these factors the measurements of thermocouples (C, D, 1, 2& 4) were Fig. 7. Effect of helium gas pressure on keff of Li2TiO3 pebble beds and its percentage increase. 5

6. M. Panchal et al. Fusion Engineering and Design 172 (2021) 112854 Fig. 8. Repeatability of keff of Li2TiO3 pebble beds and comparison. not considered for the data analysis. Fig. 6 shows the first and second steady-state temperature plots of the selected radial thermocouples (A-B-3) that were used for the data analysis. Table 2 Helium at 0.4 MPa. T, ◦C 394 496 600 703 808 keff, W/mK 1.202 1.211 1.256 1.318 1.355 Standard deviation, W/mK 0.026 0.022 0.030 0.022 0.009 Uncertainty,% 6.7 8.0 9.5 11.3 13.0 3. Results and discussion Fig. 7 shows the influence of stagnant helium gas pressure on the keff of Li2TiO3 pebble beds as a function of bed temperature and also the percentage increase in keff. The keff has been found to increase with pebble bed temperature. At 0.105 MPa helium gas pressure, the keff at 400 ◦C was increased by 15% at 800 ◦C. As the temperature of the pebble bed increases, due to the thermal expansion of each pebble in the pebble bed the pebble-pebble contact increases. As the contacts evolved, more heat conduction occurs which may increase the overall effective thermal conductivity of the pebble bed with an increase in temperature. In addition to that, the thermal conductivity of helium gas and lithium metatitanate [24] is also increasing within the studied range of tem- perature. Therefore, the unified effect of both as discussed above may raise the effective thermal conductivity of pebble beds with an increase in temperature. The values of keff have been also increasing with the helium gas pressure in the studied range (0.105 to 0.4 MPa). It has been observed that the keff at 0.105 MPa is increased by 5%, 4.3% and 2.7% at 0.4 MPa, 0.3 MPa and 0.2 MPa, respectively. Similar effect of helium gas pressure on the effective thermal conductivity of pebble beds (due to smoluchowski effect) has also been reported by experiments in the previous studies [10, 13, 17, 20]. The thermal conductivity of the un- confined gas is not dependent on its pressure (above atmospheric pres- sure). The mean free path of the gas is inversely proportional to its pressure at a given temperature. The decrease in gas pressure increases the mean free path of gas molecules. When the mean free path reaches the order of gap size (confining dimension) the heat transfer occurs mainly by the interaction of the gas molecule with the walls (of pebbles) that results in the pressure-dependent gas thermal conductivity. Fig. 8 shows the repeatability check of the obtained experimental results and comparison with the results of previous works. A total of three experimental runs (Exp #1, Exp #2 and Exp #3) were performed at different temperature and helium gas pressures. The same Li2TiO3 pebbles were refilled during starting of each new run. The obtained result of keff for an experimental run was an average value of five measurements obtained at particular gas pressure and temperature. The error bar in the repeatability plot has also been mentioned which rep- resents the standard deviation associated with the measurements. It shows good repeatability in the measurements as the average values fall under the range of error bars. The obtained results of keff of Li2TiO3 pebble beds have been compared with various experimental literature works [12–19]. The details of the experimental parameters like pebble size, packing fraction, pebble material, gas pressure, etc. are also shown in the plot. The observed deviation in percentage while comparing the obtained results with previous work has been mentioned in table 1. The measured values of keff of Li2TiO3 pebble beds with standard deviation and the average uncertainty have been mentioned in table 2-5. As discussed in Section 2.1, keff of the pebble bed can be obtained using the following equation, keff=qR1 m Where q is the heat flux released by a unit length of heater wire. The above equation can be expressed as, VI 2πmL keff= Where V is the voltage drop across the heater wire, I is a current supplied Table 1 Percentage deviation of obtained keff results with literature. T, ◦C 394 496 601 704 809 Ref. [12] H. Patel 2021 3.3 2.0 2.5 3.4 2.6 Ref. [13] M. Panchal 2020 12.4 8.8 6.5 6.0 1.1 Ref. [14] Y. H. Park 2019 −9.2 −8.9 −6.3 −2.7 −0.5 Ref. [15] M. Panchal 2018 3.0 – 1.4 3.5 7.9 Ref. [16] C. Kang 2017 −1.7 2.9 5.3 18.7 4.8 Ref. [17] S. Pupeschi 2017 1.8 −6.0 −2.2 – – Ref. [18] T. Hatano 2003 11.9 12.1 6.3 7.7 – Ref. [19] M. Enoeda 2001 12.0 6.2 5.6 15.7 – 6

7. M. Panchal et al. Fusion Engineering and Design 172 (2021) 112854 Lambade: Investigation, Data curation, Software, Visualization, Writing – review & editing. Vimal Kanpariya: Conceptualization, Software, Visualization, Methodology. Harsh Patel: Formal analysis, Writing – review & editing. Paritosh Chaudhuri: Supervision. Table 3 Helium at 0.3 MPa. T, ◦C 394 496 600 703 808 keff, W/mK 1.185 1.204 1.247 1.313 1.348 Standard deviation, W/mK 0.024 0.020 0.011 0.026 0.026 Uncertainty,% 6.7 8.0 9.4 11.2 13.2 Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Table 4 Helium at 0.2 MPa. T, ◦C 394 496 600 703 808 Acknowledgments keff, W/mK 1.169 1.192 1.220 1.291 1.329 Standard deviation, W/mK 0.022 0.019 0.010 0.029 0.020 Uncertainty,% 6.6 7.8 9.3 11.1 12.7 Thankful to Mr. Abhishek Saraswat, Mr. Shrikant Verma, Mr. San- deep Gupta, Mr. Chirag Sedani, Mr. Aroh Shrivastava and IPR workshop for their help. References Table 5 Helium at 0.105 MPa. T, ◦C 394 496 601 704 809 [1] L.M. Giancarli, M.Y. Ahn, I. Bonnett, C. Boyer, P. Chaudhuri, W. Davis, G. Dell’Orco, M. Iseli, R. Michling, J.C. Neviere, R. Pascal, Y. Poitevin, I. Ricapito, I. Schneiderova, L. Sexton, H. Tanigawa, Y.Le Tonqueze, J.G. van der Laan, X. Wang, R Yoshino, ITER TBM Program and associated system engineering, Fusion Eng. Des. 136 (August 2017) (2018) 815–821, https://doi.org/10.1016/j. fusengdes.2018.04.014. [2] P. Chaudhuri, S. Ranjithkumar, D. Sharma, C. Danani, E.R. Kumar, Thermal- hydraulics of LLCB TBM under different ITER operational conditions, Fusion Eng. 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According to the equation of standard uncertainty propagation, uncertainty in the measurement of keff can be expressed as [25], (∂k The values of the uncertainty for each temperature and pressure set values are tabulated in tables 2, 3, 4 & 5. As seen from these tables the value of the uncertainty increases significantly with temperature rise. The maximum uncertainty in the measurement was found to be ~13% at 800 ◦C. )2 (∂k )2 (∂k )2 (∂k )2 σk2= ∂IσI ∂VσV ∂mσm ∂LσL + + + 4. Conclusions and future work The steady-state radial heat flow method-based experimental setup has been fabricated and installed to measure the effective thermal conductivity of lithium metatitanate pebble beds. The effective thermal conductivity has been measured as a function of bed temperature (400 - 800 ◦C) and helium gas environment (0.105 - 0.4 MPa (abs.)). The effective thermal conductivity of lithium metatitanate pebble beds at 400 ◦C has been increased by 15% at 800 ◦C. The helium gas pressure influenced the effective thermal conductivity of lithium metatitanate pebble beds. It has been observed that the effective thermal conductivity at 0.105 MPa helium gas pressure is increased by 5%, 4.3% and 2.7% at 0.4 MPa, 0.3 MPa and 0.2 MPa, respectively. The obtained data of effective thermal conductivity of lithium metatitanate pebble beds have been also in good agreement with the previous experimental results. As future work, a similar experiment will be performed without the welded pipes for the axial thermocouples on the cylinder, with the flowing he- lium gas and using the thermocouples of less than 1 mm diameter. CRediT authorship contribution statement Maulik Panchal: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing – original draft, Writing – review & editing. Vrushabh 7

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