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Experimental investigations on start-up and thermal performance of sodium heat pipe under swing conditions
International Journal of Heat and Mass Transfer 152 (2020) 119505
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Experimental investigations on start-up and thermal performance of sodium heat pipe under swing conditions Wanfeng Teng a, Xiaoyuan Wang a,b,∗, Yuezhao Zhu a,∗ a b
School of Mechanical and Power Engineering, Nanjing Tech University, 30 Puzhu South Road, Nanjing 211816, PR China Chair of Energy Process Engineering, Friedrich-Alexander-University Erlangen-Nuremberg, Fürther Str. 244f, Nuremberg 90429, Germany
a r t i c l e
i n f o
Article history: Received 30 October 2019 Revised 12 February 2020 Accepted 13 February 2020
Keywords: High-temperature heat pipe Swing Start-up Thermal performance
a b s t r a c t High-temperature heat pipes (HTHPs) have a potential of being used for passive heat dissipation of marine nuclear reactors in emergency. In order to understand the influence of wave action on the performance of HTHPs, a sodium heat pipe is fabricated and experimentally tested in this work. The effects of low-frequency swing on start-up and thermal performance of this heat pipe are examined and compared with the static state tests. The results show that swinging motion has a negligible influence on the whole start-up performance of the heat pipe, however, it would lead to the small-amplitude periodic temperature fluctuations especially at the evaporator. Temperature fluctuation frequency is nearly corresponding to the swing, and the temperature fluctuation amplitude is increased with the swing amplitude. The steady-state thermal performance is slightly decreased with increasing swing speed and decreasing swing amplitude in terms of thermal resistance under test conditions, but the influence seems negligible as well. © 2020 Elsevier Ltd. All rights reserved.
1. Introduction The heat pipe is a kind of heat transfer component with remarkably high thermal conductivity and isothermal performance [1]. A typical heat pipe consists of the sealed shell, the wick structure, and the working fluid. The working fluid is normally filled after the shell is evacuated. Heat transfer in a heat pipe is achieved passively by the phase change and the circulation of the working fluid. The temperature difference of heat transfer in a heat pipe is much small since the evaporation and condensation occur at almost consistent pressure. A heat pipe usually requires different working fluids for different applications theoretically as long as the working temperature is between the triple point and critical temperature of working fluid. However, considering the discrepancy in thermophysical parameters of various working fluids, we tend to select the working fluid according to its merit number regarding heat transfer ability, as well as flammability and toxicity [2]. High-temperature heat pipes (HTHPs) refer to the heat pipes used at working temperature above 400 °C, usually employing liquid metal as working fluid, such as lithium, sodium, potassium, etc. [3]. Due to the excellent heat transfer performance and reliability, HTHPs have been extensively used and investigated for heat ∗ Corresponding author at: School of Mechanical and Power Engineering, Nanjing Tech University, 30 Puzhu South Road, Nanjing 211816, PR China. E-mail addresses: [email protected] (X. Wang), [email protected] (Y. Zhu).
https://doi.org/10.1016/j.ijheatmasstransfer.2020.119505 0017-9310/© 2020 Elsevier Ltd. All rights reserved.
transfer and temperature control in high temperature applications, e.g., Stirling systems [4], solar thermochemical reactors [5], solar receiver [6], biomass gasifier [7], and solid oxide fuel cell [8]. Moreover, HTHPs also have a potential of being used for the passive heat removal of nuclear reactors in emergency thus bringing it to safe conditions without human intervention. Wang et al. [9] proposed a kind of passive residual heat removal system based on sodium heat pipes for molten salt reactor (MSR). The numerical investigations using finite element method was performed for transient heat transfer behaviors of HTHPs in the case of MSR accident. The simulation results indicated that HTHPs can startup quickly and remove decay heat from fuel salt rapidly. They also numerically and experimentally examined the feasibility of potassium heat pipes’ use for heat removal in nuclear reactor applications in terms of temperature response in the start-up and the heat transfer limits [10,11]. However, all the research works mentioned above were carried out provided that the heat pipes were kept at static state. In practical nuclear reactor applications, e.g., aerospace and navigation, the influence of motion state on heat transfer of heat pipes is inevitable. Oliveira et al. [12,13] have developed a passive cooling system combining the heat pipes and loop-thermosyphons for avionics in aircrafts. They investigated the effect of real flight conditions, including the roller coaster and G-load turn maneuvers, on thermal performance of the heat rejection system. However, the corresponding working fluid was water with a working temperature range 0–120 °C. For high
2
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505 Table 1 Parameters of sodium heat pipe.
Nomenclature D E L Q R T
T t X x
diameter, mm error length, mm heat transfer rate, W thermal resistance, °C/W temperature, °C temperature difference, °C start-up time, min dependent variable independent variable
Greek letters α inclination angle, ° αm maximum inclination angle at swing condition, ° δ thickness, mm ω swing speed, rad/s Subscripts a adiabatic section c condenser e evaporator end ending of start-up o outer start starting of start-up t total
Parameters
Specifications
Outer diameter of heat pipe Do Thickness of heat pipe δ Length of heat pipe L Length of evaporator Le Length of condenser Lc Length of adiabatic section La Filling quantity Mesh number of wick Tube material Mesh material
38 mm 4 mm 800 mm 450 mm 200 mm 150 mm 100 g 20 mesh, 2 layers 310s 304
encountered for the use of residual heat removal in nuclear reactors in marine application due to wave action. A wick-type sodium heat pipe is fabricated and experimentally tested under swing condition. The effects of swing amplitude and speed on start-up and thermal performance of this heat pipe are investigated and discussed by comparing the start-up time and thermal resistance to static state tests. 2. Experimental set-up and procedures
Abbreviation MSR molten salt reactor HTHP high temperature heat pipe
temperature applications, no research work can be found in the published literature concerning thermal performance investigation of heat pipes under motion condition. This work aims to investigate the cases of heat transfer behaviors of HTHPs at swinging motion conditions, which may be
The wick-type sodium heat pipe tested in this work is 800 mm in total length and 38 mm in outer diameter with a thickness of 4 mm. It is fabricated by 310 s steel shell and filled with 100 g sodium. Sodium is employed here since it has a higher boiling point and thermal conductivity compared with other alkali metal, e.g., potassium, sodium-potassium alloy. It implies sodium heat pipe has a wider operation margin and also higher heat transfer capability [9]. The employed wick structure in the tested heat pipe is composed of two layers of steel wire mesh. Sodium was filled into the heat pipe with a similar filling system as described in literature [14]. Sodium is first operated in a glove box under the protect of inert gas and then charged into the heat pipe shell after it is evacuated to about 10−4 Pa using a high vacuum pump unit. In order to reach a high vacuum degree like this, the heat pipe shell should be degassed at high temperature (40 0–50 0 °C) prior to the
Fig. 1. (a) Schematic view of experimental set-up, (b) arrangement of thermocouples.
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505
3
Fig. 2. In-situ pictures of (a) experimental set-up and (b) heat pipe operating at steady-state.
filling procedure. The detailed parameters of the heat pipe design are given in Table 1. An experimental set-up was built for the heat transfer tests of the heat pipe, as shown in Fig. 1. Both the heat pipe and heating furnace are fixed at the test platform that can swing at an adjustable speed under the drive of electric motor rotor and gear. The evaporator, adiabatic section, and condenser of the heat pipe are set as 450 mm, 150 mm, and 200 mm, respectively. Heat input at the evaporator is supplied by an electric furnace with four silicon carbide rods evenly distributed inside, providing a maximum heat output of 50 0 0 W under the control of power regulated device. Silicon carbide rods are axially placed in a ceramic cylindrical furnace. The diameter of the furnace hearth is slightly larger than that of heat pipe outer diameter to ensure it can be inserted. The condenser is cooled directly by natural air with room temperature at near 20 °C. Nine K-type thermocouples (T1 –T9 ) are used to measure the outer-wall temperature distribution of the heat pipe, and the arrangement of thermocouples are also shown in Fig. 1. It shows that T1 –T4 and T7 –T9 are placed respectively at the evaporator and condenser, and T5 and T6 , at the adiabatic section, are circumferentially distributed at the same height due to the space limitation. The temperature variations are recorded by a data logger (Agilent-34972A) at the frequency of 0.2 Hz. The adiabatic section of heat pipe and furnace are wrapped by 100 mm-thickness thermal insulation (aluminum silicate) to reduce the heat loss to the ambient. The in-situ pictures of this set-up and the heat pipe operating at steady state are shown in Fig. 2. Inclination angle α of the heat pipe in tests is defined as the angle between its axis and vertical direction, as illustrated in Fig. 3. Tests under static state of this heat pipe were first carried out with α at 0°, 15°, 30°, and 45°, respectively, with the purpose for further comparison to the swing tests. Swing tests were performed under varying swing amplitude (15°−45°) and swing speed (0.06– 0.12 rad/s). Swing amplitude means the maximum inclination angle α m in swinging motion. The detailed conditions of swing tests are shown in Table 2. Further, the heat input at evaporator was controlled at 2500 W before the steady state was reached in all tests. Heat input of 2500 W was taken here since the heat pipe could not start-up totally with heat input below 20 0 0 W, and the evaporator wall temperature would exceed 10 0 0 °C before the steady state is reached if heat input is larger than 30 0 0 W.
Table 2 Condition parameters of swing state tests. Swing speed w (rad/s)
Swing amplitude α m
Cycle time (s)
0.06 0.060.090.12
15°30°45° 30°
17.434.952.3 34.923.317.4
Fig. 3. Schematic view of inclination angle α .
3. Data reduction and error analysis Thermal resistance is employed here to evaluate the steadystate heat transfer performance under different conditions. The total thermal resistance Rt and the resistance at evaporator and
4
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505
Fig. 4. (a) Temperature variations in start-up and (b) steady-state temperature distribution for the heat pipe tested at static state (α = 0°, ω = 0 rad/s).
condenser, Re and Rc , can be defined by Eqs. (1)–(3), respectively.
Te − Tc Te−c = Q Q
(1)
Te − Ta Te−a Re = = Q Q
(2)
Ta − Tc Ta−c = Q Q
(3)
Rt =
Rc =
where, Q is the heat input, namely 2500 W, T denotes the average temperature at outer wall, and the subscripts e, a, and c represent evaporator, adiabatic section, and condenser, respectively. Heat loss during tests is really hard to be evaluated accurately. However, according to the work performed by Saha [15], the use of nominal heat input (without deducting the heat loss), or known as apparent heat input, in parametric analysis for thermal resistance of heat pipes is reasonable as its qualitative trends are similar to actual thermal resistance. Error analysis takes the method introduced in literature [16].
E (X ) =
∂X dx ∂ xi i
The error of thermal resistances can be calculated based on the following step.
2 (4)
where, X and x denote the dependent variable and independent variable, respectively.
E (R ) =
2 2 d 2 T T 2 d 2 Q ∂R ∂R d ( T ) + dQ = + 2 ∂ (T ) ∂Q Q Q4 (5)
E (R ) = R
d 2 T Q2
2 2 + TQ d4 Q
T Q
=
d 2 T d2 Q + 2 2 T Q
(6)
where d(T) and dQ represent the absolute error of T and Q, respectively. d(T) is the sum of the temperature measurement errors of two corresponding sections. For the thermocouples employed here, the measurement error is ±1.5 °C when the temperature below 375 °C and ±(0.4% × T) °C when it is larger than 375 °C. And the reading error of temperature data logger for K-type thermocouples is ±1 °C. The error of power input is ±(0.4% × reading+0.1% × maximum measuring range+2)W, and so dQ is about ±18.3 W since the heating power is set as 2500 W for all cases.
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505
5
Fig. 5. Effect of inclination angle on (a) start-up and (b) steady-state thermal resistance at static state (ω = 0 rad/s).
4. Results and discussion 4.1. Static state tests Static state tests of this heat pipe were carried out with inclination angles α at 0°, 15°, 30°, and 45° respectively, for the verification of its quality and further comparison with swing tests. Fig. 4 shows the wall temperature variation in start-up and the steady-state temperature distribution of static state test with α =0°. From the temperature variations in Fig. 4(a), a typical flat-front start-up of sodium heat pipe from frozen state can be observed. The wall temperature at adiabatic section (T5 –T6 ) and condenser (T7 -T9 ) rises in sequence along with the bottom-up transition of inner vapor flow state from molecular to continuum [17]. In addition, the steady state temperature profile in Fig. 4(b) shows that the condenser has a reasonable isothermal characteristic, without the so-called “cold finger” phenomenon [18], by which it means there’s no non-condensable gas in this sodium heat pipe and it has good quality. For the evaporator, the temperature at T2 and T3 are slightly higher than that at T1 and T4 , which can be attributed to the uneven heat generation characteristic of silicon
carbon rod heating element that the middle part is of higher temperature. The average temperature difference between evaporator and condenser Te-c is employed here to make the comparison for start-up performance of static state tests at various inclination angles, as shown in Fig. 5(a). A comparison and analysis between Fig. 5(a) and Fig. 4(a) reveals that the starting of Te-c to decline is at about 17 min and is corresponding to the starting of temperature increase at condenser top, namely the measuring point T9 , and the level out of Te-c at nearly 30 min corresponds to the reaching of isothermal state at condenser. These two time points are labeled as tstart and tend respectively to denote the start and end of start-up of this heat pipe. It can been seen from Fig. 5(a) that tstart or tend are quite close for different test conditions and the time-varying curves are almost overlapped. Fig. 5(b) shows the steady-state total thermal resistance Rt , and thermal resistance at evaporator Re and condenser Rc with error bars for various inclination angles. Clearly, the values of Rt , Re and Rc are almost the same for different cases, among which Rt is near 0.11 °C/W, Re is about 0.08 °C/W, and Rc near 0.03 °C/W. Anyway, the experimental results imply an insignificant effect of inclination angle on start-up
6
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505
Fig. 6. Effects of (a) swing speed ω and (b) swing amplitude α m on start-up.
and heat transfer performance of this sodium heat pipe operating at static state. 4.2. Swing state tests Fig. 6 presents the comparison of start-up among the tests of static state and swinging motion in terms of time-varying Te-c , among which Fig. 6(a) focuses on the effect of swing speed (0– 0.12 rad/s) with α m fixed at 30° and Fig. 6(b) is about the influence of swing amplitude (0–45°) with ω = 0.06 rad/s. The selection of control variables, α m = 30° and ω = 0.06 rad/s, considers the actual rolling period of a ship in voyage. It is shown in Fig. 6 that the whole variation trend of Te-c and both tstart and tend of these test cases are approximately consistent with that of static state test (ω = 0 rad/s). It follows that the swinging motion has little influence on the whole start-up performance of this sodium heat pipe at test conditions. However, the phenomenon of small-amplitude periodic fluctuation of Te-c is observed under swing conditions after the heat pipe complete start-up (after tend ), which is not found for the static state tests. Basically, the observed fluctuation frequency of Te-c is the same as that of swing frequency. In addition, the fluctuation amplitude of Te-c is increased with increasing swing amplitude under test conditions, as shown in Fig. 6(b),
and yet the effect of swing speed on fluctuation amplitude is relatively small under test conditions based on Fig. 6(a). The influence of swing condition on steady-state thermal performance of the sodium heat pipe is shown in Fig. 7 in terms of thermal resistance. Fig. 7(a) reveals that the whole thermal resistance Rt exhibits a slight increasing trend with increasing swing speed, meaning a decrease of heat transfer performance. However, the increase of swing amplitude would marginally enhance the heat transfer performance, according to the Rt variation with varying α m as plotted in Fig. 7(b). Moreover, from the variations of Re and Rc , it seems that the swing has a more significant influence on the heat transfer at evaporator. For further understanding, the steady-state temperature variations at different measuring points are plotted in Fig. 8 for the case with α m = 30° and ω = 0.06 rad/s. It can be seen that the fluctuation of temperature mainly takes place at the evaporator, and the temperature variations at the adiabatic section and condenser are relatively smooth. And thus, it can be deduced that swing primarily affects the inner heat and mass transfer at the evaporator of the heat pipe in this work. This deduction is reasonable due to the fact that the rotation axis is set at adiabatic section, and the length of below part of this heat pipe is almost double of the upper part, resulting in a larger centrifugal force influence at evaporator during swing.
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505
Fig. 7. Effects of (a) swing speed ω and (b) swing amplitude α m on steady-state thermal resistance.
Fig. 8. Steady-state temperature variation of T1 –T9 at swing condition (α m = 30°, ω = 0.06 rad/s).
7
8
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505
5. Conclusions
References
The start-up and steady-state thermal performance of a sodium heat pipe under swing conditions are experimentally tested and compared with static state tests in this work. The results show that the effect of swinging motion on the whole start-up performance of this heat pipe is small concerning the start-up time. However, swing would lead to the phenomenon of small-amplitude periodic temperature fluctuation especially at the evaporator. The fluctuation frequency of temperature is corresponding to the swing, and the increase of swing amplitude would cause the increase in temperature fluctuation amplitude of heat pipe. The steady-state thermal performance is slightly decreased with increasing swing speed and decreasing swing amplitude in terms of thermal resistance under test conditions, but the influence seems negligible.
[1] X. Wang, Y. Zhu, Y. Wang, Development of pressure-based phase change model for cfd modelling of heat pipes, Int. J. Heat Mass Transf. 145 (2019) 118763. [2] D.A. Reay, P.A. Kew, R.J. McGlen, Chapter 2 - Heat transfer and fluid flow theory, in: D.A. Reay, P.A. Kew, R.J. McGlen (Eds.), Heat Pipes, 6th ed., Butterworth-Heinemann, Oxford, 2014, pp. 15–64. [3] A. Faghri, M. Buchko, Y. Cao, A study of high-temperature heat pipes with multiple heat sources and sinks. Part II. Analysis of continuum transient and steady-state experimental data with numerical predictions, J. Heat and Trans. 113 (1991) 1010–1016. [4] W.G. Anderson, C. Tarau, Variable conductance heat pipes for radioisotope stirling systems, AIP Conf. Proc. 969 (2008) 679–688. [5] X. Wang, T. Ma, Y. Zhu, H. Chen, J. Zeng, Experimental investigation on startup and thermal performance of a high temperature special-shaped heat pipe coupling the flat plate heat pipe and cylindrical heat pipes, Exp. Therm. Fluid Sci. 77 (2016) 1–9. [6] L. Yang, X. Ling, H. Peng, L. Duan, X. Chen, Starting characteristics of a novel high temperature flat heat pipe receiver in solar power tower plant based of“Flat-front”Startup model, Energy 183 (2019) 936–945. [7] J.M. Leimert, M. Neubert, P. Treiber, M. Dillig, J. Karl, Combining the heatpipe reformer technology with hydrogen-intensified methanation for production of synthetic natural gas, Appl. Energy 217 (2018) 37–46. [8] M. Dillig, J. Leimert, J. Karl, Planar high temperature heat pipes for SOFC/SOEC stack applications, Fuel Cells 14 (2014) 479–488. [9] C. Wang, D. Zhang, S. Qiu, W. Tian, Y. Wu, G. Su, Study on the characteristics of the sodium heat pipe in passive residual heat removal system of molten salt reactor, Nucl. Eng. Des. 265 (2013) 691–700. [10] C. Wang, J. Chen, S. Qiu, W. Tian, D. Zhang, G.H. Su, Performance analysis of heat pipe radiator unit for space nuclear power reactor, Ann. Nucl. Energy 103 (2017) 74–84. [11] C. Wang, L. Zhang, X. Liu, S. Tang, S. Qiu, G.H. Su, Experimental study on startup performance of high temperature potassium heat pipe at different inclination angles and input powers for nuclear reactor application, Ann. Nucl. Energy 136 (2020) 107051. [12] J.L.G. Oliveira, C. Tecchio, K.V. Paiva, M.B.H. Mantelli, R. Gandolfi, L.G.S. Ribeiro, In-flight testing of loop thermosyphons for aircraft cooling, Appl. Therm. Eng. 98 (2016) 144–156. [13] C. Tecchio, K.V. Paiva, J.L.G. Oliveira, M.B.H. Mantelli, R. Gandolfi, L.G.S. Ribeiro, Passive cooling concept for onboard heat sources in aircrafts, Exp. Therm. Fluid Sci. 82 (2017) 402–413. [14] Y. Ji, M. Wu, Y. Feng, C. Yu, L. Chu, C. Chang, Y. Li, X. Xiao, H. Ma, An experimental investigation on the heat transfer performance of a liquid metal high-temperature oscillating heat pipe, Int. J. Heat Mass Transf. 149 (2020) 119198. [15] N. Saha, P.K. Das, P.K. Sharma, Influence of process variables on the hydrodynamics and performance of a single loop pulsating heat pipe, Int. J. Heat Mass Transf. 74 (2014) 238–250. [16] L. Michalski, K. Eckersdorf, J. Kucharski, J. McGhee, Temperature Measurement, 2nd edition, John Wiley & Sons, Ltd, 2001. [17] X. Wang, T. Ma, Y. Zhu, H. Chen, J. Zeng, Experimental investigation on startup and thermal performance of a high temperature special-shaped heat pipe coupling the flat plate heat pipe and cylindrical heat pipes, Exp. Therm. Fluid Sci. 77 (2016) 1–9. [18] J.M. Leimert, M. Dillig, J. Karl, Hydrogen inactivation of liquid metal heat pipes, Int. J. Heat Mass Transf. 92 (2016) 920–928.
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. CRediT authorship contribution statement Wanfeng Teng: Conceptualization, Writing - original draft. Xiaoyuan Wang: Investigation, Formal analysis, Methodology, Writing - review & editing. Yuezhao Zhu: Funding acquisition, Project administration, Conceptualization, Methodology, Writing review & editing. Acknowledgment The authors acknowledge the financial support received from “National Key R&D Program of China” [Grant no. 2018YFB1502903], ‘‘National Natural Science Foundation of China” [Grant no. 51906101], and “Top-notch Academic Programs Project of Jiangsu Higher Education Institutions, TAPP” [Grant no. PPZY2015A022]. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatmasstransfer. 2020.119505.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt
Experimental investigations on start-up and thermal performance of sodium heat pipe under swing conditions Wanfeng Teng a, Xiaoyuan Wang a,b,∗, Yuezhao Zhu a,∗ a b
School of Mechanical and Power Engineering, Nanjing Tech University, 30 Puzhu South Road, Nanjing 211816, PR China Chair of Energy Process Engineering, Friedrich-Alexander-University Erlangen-Nuremberg, Fürther Str. 244f, Nuremberg 90429, Germany
a r t i c l e
i n f o
Article history: Received 30 October 2019 Revised 12 February 2020 Accepted 13 February 2020
Keywords: High-temperature heat pipe Swing Start-up Thermal performance
a b s t r a c t High-temperature heat pipes (HTHPs) have a potential of being used for passive heat dissipation of marine nuclear reactors in emergency. In order to understand the influence of wave action on the performance of HTHPs, a sodium heat pipe is fabricated and experimentally tested in this work. The effects of low-frequency swing on start-up and thermal performance of this heat pipe are examined and compared with the static state tests. The results show that swinging motion has a negligible influence on the whole start-up performance of the heat pipe, however, it would lead to the small-amplitude periodic temperature fluctuations especially at the evaporator. Temperature fluctuation frequency is nearly corresponding to the swing, and the temperature fluctuation amplitude is increased with the swing amplitude. The steady-state thermal performance is slightly decreased with increasing swing speed and decreasing swing amplitude in terms of thermal resistance under test conditions, but the influence seems negligible as well. © 2020 Elsevier Ltd. All rights reserved.
1. Introduction The heat pipe is a kind of heat transfer component with remarkably high thermal conductivity and isothermal performance [1]. A typical heat pipe consists of the sealed shell, the wick structure, and the working fluid. The working fluid is normally filled after the shell is evacuated. Heat transfer in a heat pipe is achieved passively by the phase change and the circulation of the working fluid. The temperature difference of heat transfer in a heat pipe is much small since the evaporation and condensation occur at almost consistent pressure. A heat pipe usually requires different working fluids for different applications theoretically as long as the working temperature is between the triple point and critical temperature of working fluid. However, considering the discrepancy in thermophysical parameters of various working fluids, we tend to select the working fluid according to its merit number regarding heat transfer ability, as well as flammability and toxicity [2]. High-temperature heat pipes (HTHPs) refer to the heat pipes used at working temperature above 400 °C, usually employing liquid metal as working fluid, such as lithium, sodium, potassium, etc. [3]. Due to the excellent heat transfer performance and reliability, HTHPs have been extensively used and investigated for heat ∗ Corresponding author at: School of Mechanical and Power Engineering, Nanjing Tech University, 30 Puzhu South Road, Nanjing 211816, PR China. E-mail addresses: [email protected] (X. Wang), [email protected] (Y. Zhu).
https://doi.org/10.1016/j.ijheatmasstransfer.2020.119505 0017-9310/© 2020 Elsevier Ltd. All rights reserved.
transfer and temperature control in high temperature applications, e.g., Stirling systems [4], solar thermochemical reactors [5], solar receiver [6], biomass gasifier [7], and solid oxide fuel cell [8]. Moreover, HTHPs also have a potential of being used for the passive heat removal of nuclear reactors in emergency thus bringing it to safe conditions without human intervention. Wang et al. [9] proposed a kind of passive residual heat removal system based on sodium heat pipes for molten salt reactor (MSR). The numerical investigations using finite element method was performed for transient heat transfer behaviors of HTHPs in the case of MSR accident. The simulation results indicated that HTHPs can startup quickly and remove decay heat from fuel salt rapidly. They also numerically and experimentally examined the feasibility of potassium heat pipes’ use for heat removal in nuclear reactor applications in terms of temperature response in the start-up and the heat transfer limits [10,11]. However, all the research works mentioned above were carried out provided that the heat pipes were kept at static state. In practical nuclear reactor applications, e.g., aerospace and navigation, the influence of motion state on heat transfer of heat pipes is inevitable. Oliveira et al. [12,13] have developed a passive cooling system combining the heat pipes and loop-thermosyphons for avionics in aircrafts. They investigated the effect of real flight conditions, including the roller coaster and G-load turn maneuvers, on thermal performance of the heat rejection system. However, the corresponding working fluid was water with a working temperature range 0–120 °C. For high
2
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505 Table 1 Parameters of sodium heat pipe.
Nomenclature D E L Q R T
T t X x
diameter, mm error length, mm heat transfer rate, W thermal resistance, °C/W temperature, °C temperature difference, °C start-up time, min dependent variable independent variable
Greek letters α inclination angle, ° αm maximum inclination angle at swing condition, ° δ thickness, mm ω swing speed, rad/s Subscripts a adiabatic section c condenser e evaporator end ending of start-up o outer start starting of start-up t total
Parameters
Specifications
Outer diameter of heat pipe Do Thickness of heat pipe δ Length of heat pipe L Length of evaporator Le Length of condenser Lc Length of adiabatic section La Filling quantity Mesh number of wick Tube material Mesh material
38 mm 4 mm 800 mm 450 mm 200 mm 150 mm 100 g 20 mesh, 2 layers 310s 304
encountered for the use of residual heat removal in nuclear reactors in marine application due to wave action. A wick-type sodium heat pipe is fabricated and experimentally tested under swing condition. The effects of swing amplitude and speed on start-up and thermal performance of this heat pipe are investigated and discussed by comparing the start-up time and thermal resistance to static state tests. 2. Experimental set-up and procedures
Abbreviation MSR molten salt reactor HTHP high temperature heat pipe
temperature applications, no research work can be found in the published literature concerning thermal performance investigation of heat pipes under motion condition. This work aims to investigate the cases of heat transfer behaviors of HTHPs at swinging motion conditions, which may be
The wick-type sodium heat pipe tested in this work is 800 mm in total length and 38 mm in outer diameter with a thickness of 4 mm. It is fabricated by 310 s steel shell and filled with 100 g sodium. Sodium is employed here since it has a higher boiling point and thermal conductivity compared with other alkali metal, e.g., potassium, sodium-potassium alloy. It implies sodium heat pipe has a wider operation margin and also higher heat transfer capability [9]. The employed wick structure in the tested heat pipe is composed of two layers of steel wire mesh. Sodium was filled into the heat pipe with a similar filling system as described in literature [14]. Sodium is first operated in a glove box under the protect of inert gas and then charged into the heat pipe shell after it is evacuated to about 10−4 Pa using a high vacuum pump unit. In order to reach a high vacuum degree like this, the heat pipe shell should be degassed at high temperature (40 0–50 0 °C) prior to the
Fig. 1. (a) Schematic view of experimental set-up, (b) arrangement of thermocouples.
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505
3
Fig. 2. In-situ pictures of (a) experimental set-up and (b) heat pipe operating at steady-state.
filling procedure. The detailed parameters of the heat pipe design are given in Table 1. An experimental set-up was built for the heat transfer tests of the heat pipe, as shown in Fig. 1. Both the heat pipe and heating furnace are fixed at the test platform that can swing at an adjustable speed under the drive of electric motor rotor and gear. The evaporator, adiabatic section, and condenser of the heat pipe are set as 450 mm, 150 mm, and 200 mm, respectively. Heat input at the evaporator is supplied by an electric furnace with four silicon carbide rods evenly distributed inside, providing a maximum heat output of 50 0 0 W under the control of power regulated device. Silicon carbide rods are axially placed in a ceramic cylindrical furnace. The diameter of the furnace hearth is slightly larger than that of heat pipe outer diameter to ensure it can be inserted. The condenser is cooled directly by natural air with room temperature at near 20 °C. Nine K-type thermocouples (T1 –T9 ) are used to measure the outer-wall temperature distribution of the heat pipe, and the arrangement of thermocouples are also shown in Fig. 1. It shows that T1 –T4 and T7 –T9 are placed respectively at the evaporator and condenser, and T5 and T6 , at the adiabatic section, are circumferentially distributed at the same height due to the space limitation. The temperature variations are recorded by a data logger (Agilent-34972A) at the frequency of 0.2 Hz. The adiabatic section of heat pipe and furnace are wrapped by 100 mm-thickness thermal insulation (aluminum silicate) to reduce the heat loss to the ambient. The in-situ pictures of this set-up and the heat pipe operating at steady state are shown in Fig. 2. Inclination angle α of the heat pipe in tests is defined as the angle between its axis and vertical direction, as illustrated in Fig. 3. Tests under static state of this heat pipe were first carried out with α at 0°, 15°, 30°, and 45°, respectively, with the purpose for further comparison to the swing tests. Swing tests were performed under varying swing amplitude (15°−45°) and swing speed (0.06– 0.12 rad/s). Swing amplitude means the maximum inclination angle α m in swinging motion. The detailed conditions of swing tests are shown in Table 2. Further, the heat input at evaporator was controlled at 2500 W before the steady state was reached in all tests. Heat input of 2500 W was taken here since the heat pipe could not start-up totally with heat input below 20 0 0 W, and the evaporator wall temperature would exceed 10 0 0 °C before the steady state is reached if heat input is larger than 30 0 0 W.
Table 2 Condition parameters of swing state tests. Swing speed w (rad/s)
Swing amplitude α m
Cycle time (s)
0.06 0.060.090.12
15°30°45° 30°
17.434.952.3 34.923.317.4
Fig. 3. Schematic view of inclination angle α .
3. Data reduction and error analysis Thermal resistance is employed here to evaluate the steadystate heat transfer performance under different conditions. The total thermal resistance Rt and the resistance at evaporator and
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Fig. 4. (a) Temperature variations in start-up and (b) steady-state temperature distribution for the heat pipe tested at static state (α = 0°, ω = 0 rad/s).
condenser, Re and Rc , can be defined by Eqs. (1)–(3), respectively.
Te − Tc Te−c = Q Q
(1)
Te − Ta Te−a Re = = Q Q
(2)
Ta − Tc Ta−c = Q Q
(3)
Rt =
Rc =
where, Q is the heat input, namely 2500 W, T denotes the average temperature at outer wall, and the subscripts e, a, and c represent evaporator, adiabatic section, and condenser, respectively. Heat loss during tests is really hard to be evaluated accurately. However, according to the work performed by Saha [15], the use of nominal heat input (without deducting the heat loss), or known as apparent heat input, in parametric analysis for thermal resistance of heat pipes is reasonable as its qualitative trends are similar to actual thermal resistance. Error analysis takes the method introduced in literature [16].
E (X ) =
∂X dx ∂ xi i
The error of thermal resistances can be calculated based on the following step.
2 (4)
where, X and x denote the dependent variable and independent variable, respectively.
E (R ) =
2 2 d 2 T T 2 d 2 Q ∂R ∂R d ( T ) + dQ = + 2 ∂ (T ) ∂Q Q Q4 (5)
E (R ) = R
d 2 T Q2
2 2 + TQ d4 Q
T Q
=
d 2 T d2 Q + 2 2 T Q
(6)
where d(T) and dQ represent the absolute error of T and Q, respectively. d(T) is the sum of the temperature measurement errors of two corresponding sections. For the thermocouples employed here, the measurement error is ±1.5 °C when the temperature below 375 °C and ±(0.4% × T) °C when it is larger than 375 °C. And the reading error of temperature data logger for K-type thermocouples is ±1 °C. The error of power input is ±(0.4% × reading+0.1% × maximum measuring range+2)W, and so dQ is about ±18.3 W since the heating power is set as 2500 W for all cases.
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Fig. 5. Effect of inclination angle on (a) start-up and (b) steady-state thermal resistance at static state (ω = 0 rad/s).
4. Results and discussion 4.1. Static state tests Static state tests of this heat pipe were carried out with inclination angles α at 0°, 15°, 30°, and 45° respectively, for the verification of its quality and further comparison with swing tests. Fig. 4 shows the wall temperature variation in start-up and the steady-state temperature distribution of static state test with α =0°. From the temperature variations in Fig. 4(a), a typical flat-front start-up of sodium heat pipe from frozen state can be observed. The wall temperature at adiabatic section (T5 –T6 ) and condenser (T7 -T9 ) rises in sequence along with the bottom-up transition of inner vapor flow state from molecular to continuum [17]. In addition, the steady state temperature profile in Fig. 4(b) shows that the condenser has a reasonable isothermal characteristic, without the so-called “cold finger” phenomenon [18], by which it means there’s no non-condensable gas in this sodium heat pipe and it has good quality. For the evaporator, the temperature at T2 and T3 are slightly higher than that at T1 and T4 , which can be attributed to the uneven heat generation characteristic of silicon
carbon rod heating element that the middle part is of higher temperature. The average temperature difference between evaporator and condenser Te-c is employed here to make the comparison for start-up performance of static state tests at various inclination angles, as shown in Fig. 5(a). A comparison and analysis between Fig. 5(a) and Fig. 4(a) reveals that the starting of Te-c to decline is at about 17 min and is corresponding to the starting of temperature increase at condenser top, namely the measuring point T9 , and the level out of Te-c at nearly 30 min corresponds to the reaching of isothermal state at condenser. These two time points are labeled as tstart and tend respectively to denote the start and end of start-up of this heat pipe. It can been seen from Fig. 5(a) that tstart or tend are quite close for different test conditions and the time-varying curves are almost overlapped. Fig. 5(b) shows the steady-state total thermal resistance Rt , and thermal resistance at evaporator Re and condenser Rc with error bars for various inclination angles. Clearly, the values of Rt , Re and Rc are almost the same for different cases, among which Rt is near 0.11 °C/W, Re is about 0.08 °C/W, and Rc near 0.03 °C/W. Anyway, the experimental results imply an insignificant effect of inclination angle on start-up
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Fig. 6. Effects of (a) swing speed ω and (b) swing amplitude α m on start-up.
and heat transfer performance of this sodium heat pipe operating at static state. 4.2. Swing state tests Fig. 6 presents the comparison of start-up among the tests of static state and swinging motion in terms of time-varying Te-c , among which Fig. 6(a) focuses on the effect of swing speed (0– 0.12 rad/s) with α m fixed at 30° and Fig. 6(b) is about the influence of swing amplitude (0–45°) with ω = 0.06 rad/s. The selection of control variables, α m = 30° and ω = 0.06 rad/s, considers the actual rolling period of a ship in voyage. It is shown in Fig. 6 that the whole variation trend of Te-c and both tstart and tend of these test cases are approximately consistent with that of static state test (ω = 0 rad/s). It follows that the swinging motion has little influence on the whole start-up performance of this sodium heat pipe at test conditions. However, the phenomenon of small-amplitude periodic fluctuation of Te-c is observed under swing conditions after the heat pipe complete start-up (after tend ), which is not found for the static state tests. Basically, the observed fluctuation frequency of Te-c is the same as that of swing frequency. In addition, the fluctuation amplitude of Te-c is increased with increasing swing amplitude under test conditions, as shown in Fig. 6(b),
and yet the effect of swing speed on fluctuation amplitude is relatively small under test conditions based on Fig. 6(a). The influence of swing condition on steady-state thermal performance of the sodium heat pipe is shown in Fig. 7 in terms of thermal resistance. Fig. 7(a) reveals that the whole thermal resistance Rt exhibits a slight increasing trend with increasing swing speed, meaning a decrease of heat transfer performance. However, the increase of swing amplitude would marginally enhance the heat transfer performance, according to the Rt variation with varying α m as plotted in Fig. 7(b). Moreover, from the variations of Re and Rc , it seems that the swing has a more significant influence on the heat transfer at evaporator. For further understanding, the steady-state temperature variations at different measuring points are plotted in Fig. 8 for the case with α m = 30° and ω = 0.06 rad/s. It can be seen that the fluctuation of temperature mainly takes place at the evaporator, and the temperature variations at the adiabatic section and condenser are relatively smooth. And thus, it can be deduced that swing primarily affects the inner heat and mass transfer at the evaporator of the heat pipe in this work. This deduction is reasonable due to the fact that the rotation axis is set at adiabatic section, and the length of below part of this heat pipe is almost double of the upper part, resulting in a larger centrifugal force influence at evaporator during swing.
W. Teng, X. Wang and Y. Zhu / International Journal of Heat and Mass Transfer 152 (2020) 119505
Fig. 7. Effects of (a) swing speed ω and (b) swing amplitude α m on steady-state thermal resistance.
Fig. 8. Steady-state temperature variation of T1 –T9 at swing condition (α m = 30°, ω = 0.06 rad/s).
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5. Conclusions
References
The start-up and steady-state thermal performance of a sodium heat pipe under swing conditions are experimentally tested and compared with static state tests in this work. The results show that the effect of swinging motion on the whole start-up performance of this heat pipe is small concerning the start-up time. However, swing would lead to the phenomenon of small-amplitude periodic temperature fluctuation especially at the evaporator. The fluctuation frequency of temperature is corresponding to the swing, and the increase of swing amplitude would cause the increase in temperature fluctuation amplitude of heat pipe. The steady-state thermal performance is slightly decreased with increasing swing speed and decreasing swing amplitude in terms of thermal resistance under test conditions, but the influence seems negligible.
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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. CRediT authorship contribution statement Wanfeng Teng: Conceptualization, Writing - original draft. Xiaoyuan Wang: Investigation, Formal analysis, Methodology, Writing - review & editing. Yuezhao Zhu: Funding acquisition, Project administration, Conceptualization, Methodology, Writing review & editing. Acknowledgment The authors acknowledge the financial support received from “National Key R&D Program of China” [Grant no. 2018YFB1502903], ‘‘National Natural Science Foundation of China” [Grant no. 51906101], and “Top-notch Academic Programs Project of Jiangsu Higher Education Institutions, TAPP” [Grant no. PPZY2015A022]. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatmasstransfer. 2020.119505.