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Design and research on the measurement platform of the effective thermal conductivity for Li4SiO4 and Li2TiO3 pebble bed
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Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed Yuanjie Li ∗ , Wanli Yang, Cheng Jin, Pinghui Zhao, Hongli Chen University of Science and Technology of China, Hefei, Anhui 230026, China
a r t i c l e
i n f o
Article history: Received 3 October 2014 Received in revised form 7 February 2015 Accepted 25 February 2015 Available online xxx Keywords: Thermal probe Thermal conductivity measurement Li4 SiO4 pebble bed Li2 TiO3 pebble bed
a b s t r a c t China is carrying out the conceptual design of Chinese Fusion Engineering Testing Reactor (CFETR), and the Helium Cooled Pebble Bed (HCPB) blanket concept is one of the main choices for tritium production. Li4 SiO4 and Li2 TiO3 are the candidate breeder materials for the HCPB blanket concept. In the HCPB blanket, breeding pebbles with the diameter range of 0.6–1.2 mm are placed between two plates and the bed shall be cooled. Accordingly, effective thermal conductivity of pebble beds needs to be determined for the heat transfer calculation. Measurements of the heat transfer parameters of Li4 SiO4 and Li2 TiO3 pebble beds are being performed at the University of Science and Technology of China (USTC). Two measurement methods are being used. One is the steady state method with the use of thermocouples to measure the temperature distribution of the pebble bed. Another is transient thermal probe method using the temperature variation of the thermal probe and Monte Carlo inversion method to calculate the heat transfer parameters of the pebble bed. This paper will report on the progress of these measurement platforms. © 2015 Elsevier B.V. All rights reserved.
1. Introduction China is carrying out the conceptual design of Chinese Fusion Engineering Testing Reactor (CFETR), the fusion power was designed as 50–200 MW and its duty cycle time was designed 30–50%, and tritium self-sufficiency by breeding blanket. The sketch design was shown in Fig. 1 [1]. It is the essential step to validate fusion electrical energy between ITER and DEMO power stations by implementing generator in its power train, which intends to put fusion power on the grid and attenuates requirements for its cooling system, and the Helium Cooled Pebble Bed (HCPB) blanket concept is one of the main choices for tritium production. Li4 SiO4 and Li2 TiO3 are the candidate breeder materials for the HCPB blanket concept. The mechanical and thermal properties, especially the relationship between pebble bed’s thermal conductivity and temperature as well as compressive strain, are considered key issues to be investigated for a proper blanket design and assessment of the heat transfer processes. The pebble bed thermal conductivity depends on many parameters such as temperature, strain, pebble size, packing factor of the bed and the velocity of the gas, and the pebble bed thermal conductivity also depends on the pebble size even the packing fraction of
∗ Corresponding author. Tel.: +86 13739268960. E-mail address: [email protected] (Y. Li).
the bed remain same for pebbles of different sizes as reported by Mandala et al. [2]. The Li4 SiO4 ceramic pebbles have already been fabricated by wet method, and diameter, morphology, sphericity, grain size and crush load of the pebble had been gained in CAEP (China Academy of Engineering Physics) [3]. The effective thermal conductivity of this kind of Li4 SiO4 pebble bed should be known. In the last few years, many platforms have been set to measure the pebble bed thermal conductivity in different conditions. The measurement method of the thermal conductivity used in those rigs could be mainly divided into steady state method and non-steady state method. KIT measured the thermal parameters of Li4 SiO4 pebble beds using steady-state method in which a heat source in contact with the bed is used to generate a temperature gradient measured by thermocouples (TC) [4,5]. And then the hot wire technique is used to measure the thermal conductivity of compressed ceramic breeder pebble beds. Thermal conductivity of pebble bed with diameter ranging from 1.7 mm to 2.0 mm and a packing factor of 61% had been studied through steady-state method with the average temperature from 50 to 500 ◦ C in UCLA [6]. The experimental data of two correlations have been developed to estimate the effective thermal conductivity of packed lithiumtitanate pebble bed for different particle Reynolds number and at different temperatures through the steady-state method in India [7]. Besides, University of Pisa’s preliminary tests had been performed on lithium orthosilicate and lithium metatitanate pebble beds based on a steady state method with heat flux through a
http://dx.doi.org/10.1016/j.fusengdes.2015.02.061 0920-3796/© 2015 Elsevier B.V. All rights reserved.
Please cite this article in press as: Y. Li, et al., Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.02.061
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disturbance of the bed, the thermocouples were placed inside the rod (0.1 mm under the surface of the heater). The temperature distribution on the outer tube wall was measured by 28 thermocouples (0.8 mm diameter) combined into groups and spread among seven axial positions. They were also placed inside the wall (1 mm under the inner surface of the outer tube), and the thermal probe is positioned in the middle of the inner surface of the outer tube wall and the heating rod. The velocity of the purge gas was controlled by the gas valve, to study the pebble bed thermal conductivity changing with the velocity. When the velocity of the gas is rather low, the convection does not affect the effective thermal conductivity of the bed, and the bed can be considered under a stagnant condition [12,13]. The pebble bed length is 600 mm, and the heated length of the inner rod is 570 mm. 2.1.1. Steady state measurement method Through the steady state method, when the pebble bed reaches steady state, the temperature distribution will not change with the time. According to theoretical analysis, the 8:1 depth–diameter aspect ratio is enough to establish steady state differential equations to the cylinder. In this case, the temperature is more uniform when the pebble bed reaches the steady state. The above design meets the demand, and the effective thermal conductivity could be drawn as follows: Ke = Fig. 1. Schematic of the CFETR.
material (alumina) of known conductivity [8]. Experiments with non-steady state method were used to measure the effective thermal conductivity and stress–strain properties of Li2 TiO3 pebble beds simultaneously under different compressive loads and temperatures at JAERI2 [9–11]. Steady-state method and nonsteady-state method both have their own drawbacks. In order to study and obtain more reliable correlation data of thermal conductivity of the pebble bed of Li4 SiO4 and Li2 TiO3 , a platform with the two methods are being simultaneously used in one condition. 2. Experimental apparatus 2.1. Description of the experimental device A schematic of the experimental rig which was designed for the measurements of the heat transfer parameters using two methods is shown in Fig. 2. The experimental platforms are described as follows. It consists of a test section containing the pebble bed, the tubular furnace, the gas flowmeter, the pressure control system, the gas and electric power supply systems, thermal probe system, and the measurement and data processing equipment. The pebble bed is contained in the tubular furnace. The tubular furnace’s inner diameter is 30 mm, and the pebble bed’s outer diameter is 28 mm. The pebble bed was kept horizontal when the experiment began. During the experiment, helium was flowing through the bed in axial horizontal direction from one side to the other side through expanded metal, which was placed in contact with the pebble bed and kept in place by a piston pressed with a pressure of 3 bar. The axial expansion can be measured through displacement sensor of the bed during the experiment and thus to measure any change in the packing factor of the bed. The radial distribution of temperatures was measured, at least the most important ones, should be numbered. The middle axial position of the test section by means of 28 thermocouples (0.8 mm outer diameter) placed at various radii at four azimuthal angles in one bracket. The surface temperature of the inner rod was measured by 28 thermocouples (0.3 mm diameter) uniformly distributed along the rod axial length. To avoid any
Q ln(r2 /r1 ) 2l(T1 − T2 )
(1)
where T is the pebble bed temperature, Q is the heat flux at the outer surface of the heater rod (W/m2 ); l is the length of the heater rod (m); T(r) is the temperature at radial position r in the bed; r1 is one point of the pebble bed to the center of the heater rod (m); T1 is the temperature of r1 ; r2 is another point of the pebble bed to the center of the heater rod (m); T2 is the temperature of r2 ; Ke is the effective thermal conductivity of the bed (W/m K). 2.1.2. Thermal probe measurement method Thermal probe measurement method is one of the non-steady state methods, and it could be convenient to measure the conductivity. A thermal probe system was designed and fabricated for the measurement of the thermal conductivity of the pebble bed. The measurement method of the thermal probe is to heat the probe inserted in the sample, through the vibration relation between the temperature and the time to analyze thermal parameters. Since the length of the probe is far greater than the diameter, and the thermal conductivity is far greater than the sample’s thermal conductivity, the thermal probe heated in the sample can be described to be infinite uniform heating element of radius r0 in an infinite medium. So the physical model of the thermal probe heating the sample could be simplified as an unsteady heat conduction problem. Considering thermal contact resistance, analytical solution of differential equations describing wall temperature of the probe can be drawn as follows [14]: Tw − T0 =
2qω2 3
∞
1 − exp −(˛/r0 2 )u2 u3 (u, ω)
du
(2)
0 2
(u, ω) = [uJ0 (u) − (ω − hu2 )J1 (u)] + [uY0 (u) − (ω − hu2 )Y1 (u)]
2
(3) where T0 is initial temperature (K), Tw is the wall temperature of the thermal probe (K), r0 is the radius of probe (m), is the heating time, q is the heating power per unit length, is the thermal conductivity and ˛ is the thermal diffusivity, ω = 2c/w cw , is the density of the sample and C is the specific heat of the sample. w
Please cite this article in press as: Y. Li, et al., Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.02.061
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Fig. 2. Schematic of the experimental platform.
Fig. 3. Schematic of the thermal probe.
is the density of thermal probe and Cw is the specific heat of thermal probe. h = 2R, where R is the contact resistance; J0 (u), J1 (u) represents first zero-order Bessel function and one-order Bessel function; Y0 (u), Y1 (u) a second-order Bessel function of zero-order and one-order, and u is integration variable. The thermal probe will be based on the exact solution of the formula (2). Using the Monte Carlo inversion method to gain the specific heat capacity and the thermal conductivity considering the contact resistance has been developed in USTC, and through this method, some kind of solid had been measured and a lot of good result had been obtained [15]. The designed thermal probe was shown in Fig. 3. The length of the thermal probe is 60 mm, and outer diameter is 0.9 mm, the inner diameter is 0.6 mm. 0.1 mm kang copper wire was used as heating wire. Because kang copper thermal resistance coefficient is small, the heating power can be ensured relatively constant. Ttype thermocouple was used to be measurement thermocouple, and the wire core diameter is 0.12 mm. Thermocouple welded to the heating wire was placed in the middle position of the thermal probe. In order to reduce the influence of convection of air and increase heat transfer between the internal heating element and the wall of the thermal probe. Vacuum grease is filled inside the probe for better thermal conductivity. 3. Simulation analysis Measuring thermal conductivity by the thermal probe method needs some fundamental hypothesis. The thermal probe must be infinitely thin, infinitely long and the sample to be tested must be infinite as well. However, the conditions cannot be obtained in practical matters. To validate the feasibility of the rig simultaneously using the thermal probe method and steady state method, numerical simulation needs to be applied to compare the conductivity difference between ideal conditions and practical conditions. And the interrelationship of the two method used in a rig is need to analyze. The surface temperature rise of transient thermal probe can be approximately expressed as: T (r0 , t)
q = ln 4K
= A ln t + B
4˛t r02 C
q q ln t + ln = 4k 4k
4˛ r02 C
(4)
Fig. 4. The monitoring temperature changing with time in a linear/logarithmic plot.
In which q refers to the line heat flux density, k refers to the effective thermal conductivity of pebble bed, ˛ refers to thermal diffusivity and r0 refers to radius of the thermal probe. C is a constant. In normal conditions, the thermal probe can be put in anywhere of the cylindrical pebble bed. Given a constant heat flux density on the surface of the heating wire, and a constant temperature on the outer surface of the cylinder, temperature on the surface of the thermocouple changing with time is monitored. The designed rig in Fig. 2 was numerically simulated. The radius of the cylinder is 22 mm, diameter of the thermal probe is 0.9 mm and the axial length of the cylinder is 600 mm. The heat flux density is assumed as 100,000 W/(m2 K) and the outer surface temperature is fixed on 1073 K. The thermal conductivity of the cylinder was assumed as 1 W/(m K). The monitoring point is in the middle of the thermal probe. Fig. 4 shows the monitoring temperature changing with time in a linear/logarithmic plot. Take the linear part and make the fitting curve T = Aln t + B and can get A = 22.94. k=
q = 1.089 4A
(5)
Comparing with the giving k, the deviation is 8.9% which is acceptable and validates the feasibility of the transient thermal probe method in such practical conditions. To sum up, measuring thermal conductivity of solid material in practical finite rig through the thermal probe method is acceptable as the error to ideal condition is below 10%. Besides, the position of the thermal probe makes little difference to the experimental results.
Please cite this article in press as: Y. Li, et al., Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.02.061
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4. Conclusion This study mainly designs a platform with the two methods to measure the thermal conductivity at steady state as constant helium pressure of 3 bar simultaneously in a rig. It can be used to measure the thermal conductivity of the pebble bed of Li4 SiO4 and Li2 TiO3 . The designed thermal probe can be used to measure the thermal conductivity of the pebble bed. A relative reliable pebble bed thermal conductivity can be obtained through comparative analysis of the data gained from the two methods. Now, the platform is being built in USTC. In the next step, thermal conductivity changing with different temperatures, different gas velocity, different pressure, pebble size and different pebbles will be studied. Acknowledgments This work is financially supported by the National Magnetic Confinement Fusion Science Program (2014GB111005). References [1] Y. Wan, Mission of CFETR, in: ITER Training Forum & Second workshop on MFE Development Strategy, Hefei, 2012. [2] D. Mandala, D. Sathiyamoorthy, M. Vinjamur, Void fraction and effective thermal conductivity of binary particulate bed, Fusion Eng. Des. 88 (2013) 216–225. [3] G. Xiaoling, C. Xiaojun, P. Shuming, Fabrication and characterization of Li4 SiO4 ceramic pebbles by wet method, J. Nucl. Mater. 424 (2012) 210–215.
[4] M. Dalle Donne, A. Goraieb, G. Piazza, Sordon measurements of the effective thermal conductivity of a Li4 SiO4 pebble bed, Fusion Eng. Des. 49–50 (2000) 513–519. [5] J. Reimann, S. Hermsmeyer, Thermal conductivity of compressed ceramic breeder pebble beds, Fusion Eng. Des. 61–62 (2002) 345–351. [6] A. Abou-Sena, A. Ying, M. Abdou, Experimental measurements of the effective thermal conductivity of a lithium titanate (Li2 TiO3 ) pebbles-packed bed, Mater. Process. Technol. 181 (2007) 206–212. [7] D. Mandala, D. Sathiyamoorthy, M. injamur, Experimental measurement of effective thermal conductivity of packed lithium-titanate pebble bed, Fusion Eng. Des. 87 (2012) 67–76. [8] R. LoFrano, D. Aquaro, S. Pupeschi, M. Moscardini, Thermo-mechanical test rig for experimental evaluation of thermal conductivity of ceramic pebble beds, Fusion Eng. Des. 89 (2014) 1309–1313. [9] H. Tanigawa, T. Hatano, M. Enoeda, M. Akiba, Effective thermal conductivity of a compressed Li2 TiO3 pebble bed, Fusion Technol. 75–79 (2005) 801–805; J. Crank, The Mathematics of Diffusion, Clarendon Press, Oxford, 1975. [10] M. DalleGoraieb, G. Piazza, G. Sordon, Measurements of the effective thermal conductivity of a Li4 SiO4 pebble bed, Fusion Eng. Des. 49–50 (2000) 513–519. [11] A. Ying, J. Reimann, L. Boccaccini, M. Enoeda, et al., Status of ceramic breeder pebble bed thermo-mechanics R&D and impact on breeder material mechanical strength, Fusion Eng. Des. 7–8 (2012) 1130–1137. [12] T. Hatano, M. Enoeda, S. Suzuki, Y. Kosaku, M. Akiba, Effective thermal conductivity of a Li2 TiO3 pebble bed for a DEMO blanket, Fusion Sci. Technol. 44 (2003) 94. [13] M. Enoeda, K. Furuya, H. Takatsu, S. Kikuch, T. Hatano, Effective thermal conductivity measurement of the binary pebble beds by hot wire method for the breeding blanket, Fusion Technol. 34 (1998) 877. [14] H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd ed., Clarendon Press, Oxford, 1986, pp. 342–344. [15] C. Wenlong, Z. Hongze, Z. Rui, A new method of thermal probe for thermal conductivities measurement based on Monte Carlo inversion, J. Univ. Sci. Technol. China 34 (8) (2008) 414–418.
Please cite this article in press as: Y. Li, et al., Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.02.061
ARTICLE IN PRESS
FUSION-7811; No. of Pages 4
Fusion Engineering and Design xxx (2015) xxx–xxx
Contents lists available at ScienceDirect
Fusion Engineering and Design journal homepage: www.elsevier.com/locate/fusengdes
Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed Yuanjie Li ∗ , Wanli Yang, Cheng Jin, Pinghui Zhao, Hongli Chen University of Science and Technology of China, Hefei, Anhui 230026, China
a r t i c l e
i n f o
Article history: Received 3 October 2014 Received in revised form 7 February 2015 Accepted 25 February 2015 Available online xxx Keywords: Thermal probe Thermal conductivity measurement Li4 SiO4 pebble bed Li2 TiO3 pebble bed
a b s t r a c t China is carrying out the conceptual design of Chinese Fusion Engineering Testing Reactor (CFETR), and the Helium Cooled Pebble Bed (HCPB) blanket concept is one of the main choices for tritium production. Li4 SiO4 and Li2 TiO3 are the candidate breeder materials for the HCPB blanket concept. In the HCPB blanket, breeding pebbles with the diameter range of 0.6–1.2 mm are placed between two plates and the bed shall be cooled. Accordingly, effective thermal conductivity of pebble beds needs to be determined for the heat transfer calculation. Measurements of the heat transfer parameters of Li4 SiO4 and Li2 TiO3 pebble beds are being performed at the University of Science and Technology of China (USTC). Two measurement methods are being used. One is the steady state method with the use of thermocouples to measure the temperature distribution of the pebble bed. Another is transient thermal probe method using the temperature variation of the thermal probe and Monte Carlo inversion method to calculate the heat transfer parameters of the pebble bed. This paper will report on the progress of these measurement platforms. © 2015 Elsevier B.V. All rights reserved.
1. Introduction China is carrying out the conceptual design of Chinese Fusion Engineering Testing Reactor (CFETR), the fusion power was designed as 50–200 MW and its duty cycle time was designed 30–50%, and tritium self-sufficiency by breeding blanket. The sketch design was shown in Fig. 1 [1]. It is the essential step to validate fusion electrical energy between ITER and DEMO power stations by implementing generator in its power train, which intends to put fusion power on the grid and attenuates requirements for its cooling system, and the Helium Cooled Pebble Bed (HCPB) blanket concept is one of the main choices for tritium production. Li4 SiO4 and Li2 TiO3 are the candidate breeder materials for the HCPB blanket concept. The mechanical and thermal properties, especially the relationship between pebble bed’s thermal conductivity and temperature as well as compressive strain, are considered key issues to be investigated for a proper blanket design and assessment of the heat transfer processes. The pebble bed thermal conductivity depends on many parameters such as temperature, strain, pebble size, packing factor of the bed and the velocity of the gas, and the pebble bed thermal conductivity also depends on the pebble size even the packing fraction of
∗ Corresponding author. Tel.: +86 13739268960. E-mail address: [email protected] (Y. Li).
the bed remain same for pebbles of different sizes as reported by Mandala et al. [2]. The Li4 SiO4 ceramic pebbles have already been fabricated by wet method, and diameter, morphology, sphericity, grain size and crush load of the pebble had been gained in CAEP (China Academy of Engineering Physics) [3]. The effective thermal conductivity of this kind of Li4 SiO4 pebble bed should be known. In the last few years, many platforms have been set to measure the pebble bed thermal conductivity in different conditions. The measurement method of the thermal conductivity used in those rigs could be mainly divided into steady state method and non-steady state method. KIT measured the thermal parameters of Li4 SiO4 pebble beds using steady-state method in which a heat source in contact with the bed is used to generate a temperature gradient measured by thermocouples (TC) [4,5]. And then the hot wire technique is used to measure the thermal conductivity of compressed ceramic breeder pebble beds. Thermal conductivity of pebble bed with diameter ranging from 1.7 mm to 2.0 mm and a packing factor of 61% had been studied through steady-state method with the average temperature from 50 to 500 ◦ C in UCLA [6]. The experimental data of two correlations have been developed to estimate the effective thermal conductivity of packed lithiumtitanate pebble bed for different particle Reynolds number and at different temperatures through the steady-state method in India [7]. Besides, University of Pisa’s preliminary tests had been performed on lithium orthosilicate and lithium metatitanate pebble beds based on a steady state method with heat flux through a
http://dx.doi.org/10.1016/j.fusengdes.2015.02.061 0920-3796/© 2015 Elsevier B.V. All rights reserved.
Please cite this article in press as: Y. Li, et al., Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.02.061
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disturbance of the bed, the thermocouples were placed inside the rod (0.1 mm under the surface of the heater). The temperature distribution on the outer tube wall was measured by 28 thermocouples (0.8 mm diameter) combined into groups and spread among seven axial positions. They were also placed inside the wall (1 mm under the inner surface of the outer tube), and the thermal probe is positioned in the middle of the inner surface of the outer tube wall and the heating rod. The velocity of the purge gas was controlled by the gas valve, to study the pebble bed thermal conductivity changing with the velocity. When the velocity of the gas is rather low, the convection does not affect the effective thermal conductivity of the bed, and the bed can be considered under a stagnant condition [12,13]. The pebble bed length is 600 mm, and the heated length of the inner rod is 570 mm. 2.1.1. Steady state measurement method Through the steady state method, when the pebble bed reaches steady state, the temperature distribution will not change with the time. According to theoretical analysis, the 8:1 depth–diameter aspect ratio is enough to establish steady state differential equations to the cylinder. In this case, the temperature is more uniform when the pebble bed reaches the steady state. The above design meets the demand, and the effective thermal conductivity could be drawn as follows: Ke = Fig. 1. Schematic of the CFETR.
material (alumina) of known conductivity [8]. Experiments with non-steady state method were used to measure the effective thermal conductivity and stress–strain properties of Li2 TiO3 pebble beds simultaneously under different compressive loads and temperatures at JAERI2 [9–11]. Steady-state method and nonsteady-state method both have their own drawbacks. In order to study and obtain more reliable correlation data of thermal conductivity of the pebble bed of Li4 SiO4 and Li2 TiO3 , a platform with the two methods are being simultaneously used in one condition. 2. Experimental apparatus 2.1. Description of the experimental device A schematic of the experimental rig which was designed for the measurements of the heat transfer parameters using two methods is shown in Fig. 2. The experimental platforms are described as follows. It consists of a test section containing the pebble bed, the tubular furnace, the gas flowmeter, the pressure control system, the gas and electric power supply systems, thermal probe system, and the measurement and data processing equipment. The pebble bed is contained in the tubular furnace. The tubular furnace’s inner diameter is 30 mm, and the pebble bed’s outer diameter is 28 mm. The pebble bed was kept horizontal when the experiment began. During the experiment, helium was flowing through the bed in axial horizontal direction from one side to the other side through expanded metal, which was placed in contact with the pebble bed and kept in place by a piston pressed with a pressure of 3 bar. The axial expansion can be measured through displacement sensor of the bed during the experiment and thus to measure any change in the packing factor of the bed. The radial distribution of temperatures was measured, at least the most important ones, should be numbered. The middle axial position of the test section by means of 28 thermocouples (0.8 mm outer diameter) placed at various radii at four azimuthal angles in one bracket. The surface temperature of the inner rod was measured by 28 thermocouples (0.3 mm diameter) uniformly distributed along the rod axial length. To avoid any
Q ln(r2 /r1 ) 2l(T1 − T2 )
(1)
where T is the pebble bed temperature, Q is the heat flux at the outer surface of the heater rod (W/m2 ); l is the length of the heater rod (m); T(r) is the temperature at radial position r in the bed; r1 is one point of the pebble bed to the center of the heater rod (m); T1 is the temperature of r1 ; r2 is another point of the pebble bed to the center of the heater rod (m); T2 is the temperature of r2 ; Ke is the effective thermal conductivity of the bed (W/m K). 2.1.2. Thermal probe measurement method Thermal probe measurement method is one of the non-steady state methods, and it could be convenient to measure the conductivity. A thermal probe system was designed and fabricated for the measurement of the thermal conductivity of the pebble bed. The measurement method of the thermal probe is to heat the probe inserted in the sample, through the vibration relation between the temperature and the time to analyze thermal parameters. Since the length of the probe is far greater than the diameter, and the thermal conductivity is far greater than the sample’s thermal conductivity, the thermal probe heated in the sample can be described to be infinite uniform heating element of radius r0 in an infinite medium. So the physical model of the thermal probe heating the sample could be simplified as an unsteady heat conduction problem. Considering thermal contact resistance, analytical solution of differential equations describing wall temperature of the probe can be drawn as follows [14]: Tw − T0 =
2qω2 3
∞
1 − exp −(˛/r0 2 )u2 u3 (u, ω)
du
(2)
0 2
(u, ω) = [uJ0 (u) − (ω − hu2 )J1 (u)] + [uY0 (u) − (ω − hu2 )Y1 (u)]
2
(3) where T0 is initial temperature (K), Tw is the wall temperature of the thermal probe (K), r0 is the radius of probe (m), is the heating time, q is the heating power per unit length, is the thermal conductivity and ˛ is the thermal diffusivity, ω = 2c/w cw , is the density of the sample and C is the specific heat of the sample. w
Please cite this article in press as: Y. Li, et al., Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.02.061
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Fig. 2. Schematic of the experimental platform.
Fig. 3. Schematic of the thermal probe.
is the density of thermal probe and Cw is the specific heat of thermal probe. h = 2R, where R is the contact resistance; J0 (u), J1 (u) represents first zero-order Bessel function and one-order Bessel function; Y0 (u), Y1 (u) a second-order Bessel function of zero-order and one-order, and u is integration variable. The thermal probe will be based on the exact solution of the formula (2). Using the Monte Carlo inversion method to gain the specific heat capacity and the thermal conductivity considering the contact resistance has been developed in USTC, and through this method, some kind of solid had been measured and a lot of good result had been obtained [15]. The designed thermal probe was shown in Fig. 3. The length of the thermal probe is 60 mm, and outer diameter is 0.9 mm, the inner diameter is 0.6 mm. 0.1 mm kang copper wire was used as heating wire. Because kang copper thermal resistance coefficient is small, the heating power can be ensured relatively constant. Ttype thermocouple was used to be measurement thermocouple, and the wire core diameter is 0.12 mm. Thermocouple welded to the heating wire was placed in the middle position of the thermal probe. In order to reduce the influence of convection of air and increase heat transfer between the internal heating element and the wall of the thermal probe. Vacuum grease is filled inside the probe for better thermal conductivity. 3. Simulation analysis Measuring thermal conductivity by the thermal probe method needs some fundamental hypothesis. The thermal probe must be infinitely thin, infinitely long and the sample to be tested must be infinite as well. However, the conditions cannot be obtained in practical matters. To validate the feasibility of the rig simultaneously using the thermal probe method and steady state method, numerical simulation needs to be applied to compare the conductivity difference between ideal conditions and practical conditions. And the interrelationship of the two method used in a rig is need to analyze. The surface temperature rise of transient thermal probe can be approximately expressed as: T (r0 , t)
q = ln 4K
= A ln t + B
4˛t r02 C
q q ln t + ln = 4k 4k
4˛ r02 C
(4)
Fig. 4. The monitoring temperature changing with time in a linear/logarithmic plot.
In which q refers to the line heat flux density, k refers to the effective thermal conductivity of pebble bed, ˛ refers to thermal diffusivity and r0 refers to radius of the thermal probe. C is a constant. In normal conditions, the thermal probe can be put in anywhere of the cylindrical pebble bed. Given a constant heat flux density on the surface of the heating wire, and a constant temperature on the outer surface of the cylinder, temperature on the surface of the thermocouple changing with time is monitored. The designed rig in Fig. 2 was numerically simulated. The radius of the cylinder is 22 mm, diameter of the thermal probe is 0.9 mm and the axial length of the cylinder is 600 mm. The heat flux density is assumed as 100,000 W/(m2 K) and the outer surface temperature is fixed on 1073 K. The thermal conductivity of the cylinder was assumed as 1 W/(m K). The monitoring point is in the middle of the thermal probe. Fig. 4 shows the monitoring temperature changing with time in a linear/logarithmic plot. Take the linear part and make the fitting curve T = Aln t + B and can get A = 22.94. k=
q = 1.089 4A
(5)
Comparing with the giving k, the deviation is 8.9% which is acceptable and validates the feasibility of the transient thermal probe method in such practical conditions. To sum up, measuring thermal conductivity of solid material in practical finite rig through the thermal probe method is acceptable as the error to ideal condition is below 10%. Besides, the position of the thermal probe makes little difference to the experimental results.
Please cite this article in press as: Y. Li, et al., Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.02.061
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4. Conclusion This study mainly designs a platform with the two methods to measure the thermal conductivity at steady state as constant helium pressure of 3 bar simultaneously in a rig. It can be used to measure the thermal conductivity of the pebble bed of Li4 SiO4 and Li2 TiO3 . The designed thermal probe can be used to measure the thermal conductivity of the pebble bed. A relative reliable pebble bed thermal conductivity can be obtained through comparative analysis of the data gained from the two methods. Now, the platform is being built in USTC. In the next step, thermal conductivity changing with different temperatures, different gas velocity, different pressure, pebble size and different pebbles will be studied. Acknowledgments This work is financially supported by the National Magnetic Confinement Fusion Science Program (2014GB111005). References [1] Y. Wan, Mission of CFETR, in: ITER Training Forum & Second workshop on MFE Development Strategy, Hefei, 2012. [2] D. Mandala, D. Sathiyamoorthy, M. Vinjamur, Void fraction and effective thermal conductivity of binary particulate bed, Fusion Eng. Des. 88 (2013) 216–225. [3] G. Xiaoling, C. Xiaojun, P. Shuming, Fabrication and characterization of Li4 SiO4 ceramic pebbles by wet method, J. Nucl. Mater. 424 (2012) 210–215.
[4] M. Dalle Donne, A. Goraieb, G. Piazza, Sordon measurements of the effective thermal conductivity of a Li4 SiO4 pebble bed, Fusion Eng. Des. 49–50 (2000) 513–519. [5] J. Reimann, S. Hermsmeyer, Thermal conductivity of compressed ceramic breeder pebble beds, Fusion Eng. Des. 61–62 (2002) 345–351. [6] A. Abou-Sena, A. Ying, M. Abdou, Experimental measurements of the effective thermal conductivity of a lithium titanate (Li2 TiO3 ) pebbles-packed bed, Mater. Process. Technol. 181 (2007) 206–212. [7] D. Mandala, D. Sathiyamoorthy, M. injamur, Experimental measurement of effective thermal conductivity of packed lithium-titanate pebble bed, Fusion Eng. Des. 87 (2012) 67–76. [8] R. LoFrano, D. Aquaro, S. Pupeschi, M. Moscardini, Thermo-mechanical test rig for experimental evaluation of thermal conductivity of ceramic pebble beds, Fusion Eng. Des. 89 (2014) 1309–1313. [9] H. Tanigawa, T. Hatano, M. Enoeda, M. Akiba, Effective thermal conductivity of a compressed Li2 TiO3 pebble bed, Fusion Technol. 75–79 (2005) 801–805; J. Crank, The Mathematics of Diffusion, Clarendon Press, Oxford, 1975. [10] M. DalleGoraieb, G. Piazza, G. Sordon, Measurements of the effective thermal conductivity of a Li4 SiO4 pebble bed, Fusion Eng. Des. 49–50 (2000) 513–519. [11] A. Ying, J. Reimann, L. Boccaccini, M. Enoeda, et al., Status of ceramic breeder pebble bed thermo-mechanics R&D and impact on breeder material mechanical strength, Fusion Eng. Des. 7–8 (2012) 1130–1137. [12] T. Hatano, M. Enoeda, S. Suzuki, Y. Kosaku, M. Akiba, Effective thermal conductivity of a Li2 TiO3 pebble bed for a DEMO blanket, Fusion Sci. Technol. 44 (2003) 94. [13] M. Enoeda, K. Furuya, H. Takatsu, S. Kikuch, T. Hatano, Effective thermal conductivity measurement of the binary pebble beds by hot wire method for the breeding blanket, Fusion Technol. 34 (1998) 877. [14] H.S. Carslaw, J.C. Jaeger, Conduction of Heat in Solids, 2nd ed., Clarendon Press, Oxford, 1986, pp. 342–344. [15] C. Wenlong, Z. Hongze, Z. Rui, A new method of thermal probe for thermal conductivities measurement based on Monte Carlo inversion, J. Univ. Sci. Technol. China 34 (8) (2008) 414–418.
Please cite this article in press as: Y. Li, et al., Design and research on the measurement platform of the effective thermal conductivity for Li4 SiO4 and Li2 TiO3 pebble bed, Fusion Eng. Des. (2015), http://dx.doi.org/10.1016/j.fusengdes.2015.02.061