The Stirling generators are also ignored, the operation of generators is approximated by setting reasonable boundary conditions of the condenser section of heat pipes. Tech. Three-dimensional CFD model of the experimental system. Energ. Thermal Performance Analysis of Nanofluids in a Thermosyphon Heat Pipe Using CFD Modeling. Heat Pipe Failure Accident Analysis in Megawatt Heat Pipe Cooled Reactor. Heat Mass Transfer 57 (2), 642656. HPTAMheatpipe Transient Analysis Model: an Analysis of Water Heat Pipes.

FIGURE 10. Lumped Parameter Model of Sintered Heat Pipe: Transient Numerical Analysis and Validation. Pressure Drop in the Vapor Phase of Long Heat Pipes, in Proc. 142, 107412. doi:10.1016/j.anucene.2020.107412, Ma, Y., Chen, E., Yu, H., Zhong, R., Deng, J., Chai, X., et al. To simplify the modeling, the lift table and support structure are all ignored; only the reactor is established (Figure 11). (B) Mass flow rate with different heating power. Meanwhile, the nonstandard operation during the experiment will also lead to uncertainty of the results. Des. Backflow calculation using network model. (1986). It can be predicted that if heat pipe is not well insulated, a considerable part of the heat will be transferred to the environment through the adiabatic section, leading to the decrease in heat transfer efficiency of the heat pipe. Temperature on the contact surface between fuel and heat pipe is always consistent. J. Nucl. Busse, C. A. (2020). This is because that both the temperature drop caused by vapor flow and the temperature gradient caused by heat conduction will increase with the increase of power (Figures 8, 9). From that, it can be concluded that there is a slight difference between the two results, and proposed model is suitable for the analysis of heat pipe cooled reactor system. Using a high-temperature adhesive, all K-type armored thermocouples are fixed in the groove (Figure 5A). Calculation of the Thermodynamic and Transport Properties of Sodium, Potassium, Rubidium and Cesium Vapors to 3000K. (A) Proposed model. The iron-chrome wire heater can provide a maximum heating power of 4000W. To reduce heat leakage as much as possible, the evaporator and the adiabatic section are both wrapped by an insulating layer with aluminum silicate wool. Simulation of a Miniature Oscillating Heat Pipe in Bottom Heating Mode Using CFD with Unsteady Modeling. Figure 8A shows the variation of total temperature difference of heat pipe under the different heating power conditions. It is assumed that vapor in vapor space and liquified working medium in wick are homogeneous. 1), S1S12. Nucl. Ohse, R. W. (1985). Thermal-hydraulic Analysis of a New Conceptual Heat Pipe Cooled Small Nuclear Reactor System. Combined with the network method, the proposed model can preliminarily calculate the evaporation, condensation, and flow rate of working medium.

The complex two-phase flow and heat transfer also brings challenges to the numerical calculation of heat pipe. Inst. Not only is it required that this model can well describe the transient characteristics of heat pipe, but it should be simple enough to reduce the computational resource. Figure 13 shows the axial distribution of power density obtained by Monte Carlo code RMC. Benefiting from the reactivity feedback of fuel, fission power gradually decreases to slow the rate of temperature rise. Nucl. Faghri, A. It should be noted that the two-phase flow simulation using CFD method requires large amounts of computing resources. The experimental system for high-temperature heat pipe is established to verify the proposed model. For example, the vapor flow in vapor space was assumed to be one-dimensional, while heat conductance in solid region was treated as two-dimensional. Combined with the network method, the evaporation rate, the condensation rate, and the flow rate in the wick region can be preliminarily obtained. 49 (1), 7. doi:10.7538/yzk.2015.49.01.0089, Lin, Z., Wang, S., Shirakashi, R., and Winston Zhang, L. (2013). ASME J. Eng. Closed-form Analytical Solutions of High-Temperature Heat Pipe Startup and Frozen Startup Limitation. uv is vapor velocity, Ladia is the length of adiabatic section, and Lcond is the length of condenser. is the density, C is the heat capacity, is the thermal conductivity coefficient, is the porosity, the subscripts of equ means the equivalent value, f means the fluid value, and wc is the wick mesh value. Using recommended equations to calculate the heat transfer limitation, this model can realize the safety judgment of heat pipe. Heat Transfer 114 (Nov), 10281035. Theoretical Investigation of Heat Pipes Operating at Low Vapor Pressures. Int. On the one hand, to realize the coupling calculation of the heat pipe cooled reactor, the proposed heat pipe model does not directly calculate the working fluid circulation, but adopts a simplified method, which may cause uncertainty to a certain extent. Reay, D., McGlen, R., and Kew, P. (2013). 1 are the physical parameters of the corresponding metal. Poston, D. I. Parameter description of sodium heat pipe. doi:10.1080/00295450.2020.1725382. J.

Therefore, the basis of coupling calculation on this type of reactor system is to have a suitable model for high-temperature heat pipe simulation. 33) is not completely equal to the real value. In addition, Zuo ignored the energy transport caused by the backflow of working medium in wick. is the emissivity of material, and is the Stefan-Boltzmann coefficient. In this section, the proposed model will be used for numerical simulation of KRUSTY reactor. Busse, C. A. Detailed Transient Model of a Liquid-Metal Heat Pipe. Heat generated in the reactor core is absorbed by high-temperature heat pipes. Am. In this paper, the proposed model simplified the heat transport into multi-region heat conduction. Nucl. Therefore, for heat conduction calculation of vapor space, the key is to solve the equivalent thermal conductivity of this subregion. 19 Articles, Proc. 50 (1), 12801290. Reid, R. S. (2002). To ensure the accuracy of temperature data, the groove with 1mm depth is processed in wall. The three-dimensional CFD model of the experimental system is shown in Figure 6, which includes the sodium heat pipe, the electric heater, and the insulating layer. ElGenk, M. S., and Tournier, J. M. (2004). When heating power is 1600W, it takes about 13min to enter the quasi-steady state; when heating power is 3000W, it takes only about 7min. doi:10.2298/tsci100331023a, Asmaie, L., Haghshenasfard, M., Mehrabani-Zeinabad, A., and Nasr Esfahany, M. (2013). Heat Transfer 115 (1), 247254. Los Alamos, NM (United States): Los Alamos National Lab, McClure, P. R., Poston, D. I., Clement, S. D., Restrepo, L., Miller, R., and Negrete, M. (2020). (B) Network model. AIP Conf. doi:10.1016/j.ijheatmasstransfer.2012.09.007, Liu, X., Zhang, R., Liang, Y., Tang, S., Wang, C., Tian, W., et al. Ann. Thermionic Conversion Specialist Conference, This article is part of the Research Topic, https://doi.org/10.3389/fenrg.2022.819033. From Figures 1214, it can be concluded that only the three-dimensional modeling of heat pipes and the coupling calculation between heat pipe and the reactor core can obtain the accurate results of heat transfer. (1993). Annamalai, S., and Ramalingam, V. (2011). Tech. (1967). Combined with the recommended heat transfer limitation model (Busse, 1973; Levy, 1968; Deverall et al., 1970; Tien and Chung, 1979), the fast calculation of heat pipe performance and the evaluation of heat pipe safety are realized. When the heating power is low enough, more power leads to the larger temperature difference. Using the feedback coefficient, this important phenomenon can be preliminarily simulated (Guo et al., 2022). Because of the large aspect ratio of this reactor, the power density presents the distribution of a large value in the middle and a small value on both sides. We use cookies to help provide and enhance our service and tailor content and ads. If the calculated value is less than the heating power, the heat transfer limitation will be deemed to occur, and it is assumed that the heat pipe will be damaged. FIGURE 15. The equation that needs to be solved is the differential equation of heat conduction (Eq. The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. At T = 0.0s, the cooling power of the condenser of heat pipe is set as 2.54kW to represent the decrease of engine power, and the initial fission power is set as 2.67kW. 149, 107755. doi:10.1016/j.anucene.2020.107755, Mcclure, P. R. (2015). Even if the power is high enough, generated vapor can quickly transport heat to the condenser, meaning the heat pipe shows excellent isothermal property and efficient heat transfer capability. This is because heat pipes absorb less power, leading to the increase of Na inventory in the reactor (Poston, 2017). 17 (6), 643646. Industry. The electric heater is simplified as the thin layer with a thickness of 2mm, and the heating source is set in this layer as equivalent to an electrical heating. FIGURE 16. For example, for wick with a mesh type, the density, specific heat capacity, and thermal conductivity can be approximately described by Eqs 57 (Chi, 1976). Phys. KRUSTY Reactor Design. It is then used for the simulation on KRUSTY reactor to discuss the applicability of this model and the characteristics of this type of reactor system. Proc. 28 (8), 428. doi:10.1021/ed028p428. To verify the proposed model, a heating system for high-temperature heat pipe is built (Figure 4). *Correspondence: Zeguang Li, lizeguang@mail.tsinghua.edu.cn, Experimental and Analytical Investigations on Nuclear Reactor Safety, Severe Accident Phenomena and Severe Accident Mitigation of Nuclear Power Plants, View all Core thermal-hydraulic Evaluation of a Heat Pipe Cooled Nuclear Reactor. Moreover, for the numerical analysis of heat pipe cooled reactor, more attention should be paid to the heat absorption capability, the temperature variation and distribution, and the operating safety of heat pipe. In these figures, the curve represents the calculated results using this model, and the scatter points represent the results measured by the experiment. 90, 547552. doi:10.1063/1.1358010, Poston, D. I., Gibson, M. A., Godfroy, T., and McClure, P. R. (2020). Heat Pipe Theory and Practice [M]. The difference between the two values is the heat leakage through shield. It can be a powerful tool for the design and simulation of heat pipe cooled reactor systems. Combined with the thermal resistance, the evaporation and condensation at vapor-liquid interface can be obtained: where qv is the vapor mass flow rate at vapor-liquid interface, Tw is the temperature in wall subregion, Tv is the temperature in vapor space, R is the thermal resistance, and hv is the vapor enthalpy. Figure 12 shows the fuel temperature distribution using the proposed model and network model. Comparing with the experimental results, the applicability of the proposed model on heat pipe cooled reactor is verified. Compared with the results using network model, the peak temperature of fuel increases from 1,087.6k to 1,090.8k, and the total temperature difference increases from 14.4k to 21.2k. For KRUSTY reactor, the operation is sensitive to fuel temperature, so the slight variation of temperature may cause an obvious change in fission power. Wall is usually a cylindrical closed shell made of metal. Network model was proposed by Zuo and Faghri (1998); the schematic diagram of this model is shown in Figure 2. Proc. FIGURE 3. The thermophysical parameters required to solve Eq. In the early stage of this accident, the reactor will be briefly supercritical, resulting in the increase in reactor power. Heat Transfer Capacity Analysis of Heat Pipe for Space Reactor[J]. Design of Megawatt Power Level Heat Pipe Reactors. Nucl. FIGURE 5. doi:10.1016/j.applthermaleng.2012.07.022, Fink, J. K., and Leibowitz, L. (1995). The Heatpipe-Operated Mars Exploration Reactor (HOMER). Washington, DC: Hemispere Publishing Corporation. doi:10.1016/j.pnucene.2015.10.002, Yue, C., Zhang, Q., Zhai, Z., and Ling, L. (2018). Figure 7A shows the surface temperature distribution with different heating powers, and Figure 7B shows the temperature variation of heat pipe with time. Am. No use, distribution or reproduction is permitted which does not comply with these terms. 246 (1), 10231037. Minsk, Belarus: CIS. The proposed model can calculate the variation of absorbed power of heat pipes. The applicability of this model will be discussed. ScienceDirect is a registered trademark of Elsevier B.V. Click here to go back to the article page. Then, the temperature is recorded with the increase of heating power. Zuo ignored the temperature drop caused by the vapor flow and considered that the temperature drop of the heat pipe was mainly caused by the heat conduction in wall and wick. Prog. 1), S56S67.

Sci. Combining Eq. During the operation of heat pipe, liquified working medium in wick will return from condenser to the evaporator. The heating experiments with different heating powers is tested. All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. The Clausius-Clapeyron equation is chosen to describe the relationship between temperature and pressure (Brown, 1951): Changing Eq. Therm. Ten thermocouples are arranged along the axial direction; the layout position for each thermocouple is shown in Figure 5B. It includes the U-Mo fuel, the BeO reflector, the control rod, the shielding layer, the Na heat pipes, the vacuum vessel, the lift table, and the Stirling generators. 65, 102114. 18 (4), 483502. (2013) proposed a simplified method to consider the evaporation, condensation, and backflow (Figure 3). Before the 1990s, computing power was limited, so the complex physical phenomena that existed in heat pipe could not be simulated in detail. The results obtained using the uniform temperature assumption will deviate from the reality. J. (1992). support team Forms of it include channels, screen, and concentric annulus (Reay et al., 2013). The Clausius-Clapeyron Equation. 1), S13S30. According to the comparison with the experimental results, the accuracy of the model is verified. KRUSTY Experiment: Reactivity Insertion Accident Analysis. Moreover, it is assumed that the fluid circulation is always constant, so backflow in wick can be obtained based on the mass conservation: ql is the liquid mass flow rate in wick subregion, hl is the liquid enthalpy, and V is the subregion volume. In this section, the steady state of KRUSTY reactor system is investigated. doi:10.1007/s00231-013-1110-6, Brown, O. L. I. CFD modeling and calculation have gradually become the main method for heat pipe analysis. (2017). For reactor systems with a solid attribute, heat conductance is the only way for heat transfer. Heat Mass. During the steady state calculation, it can be found that the proposed model can obtain a more realistic fuel temperature distribution. Los Alamos, NM (United States): Los Alamos National Lab, Poston, D. I. Wicks with a porous structure can generate an effective pressure head at the vapor-liquid interface, maintaining the stable circulation of working medium (Reay et al., 2013). About ScienceDirectShopping cartContact and supportTerms and conditionsPrivacy policy. It includes the iron-chrome wire heater, the holding device, the angle controlling derive, and the temperature data collection. Heat Pipes: Theory, Design and Applications. Sonic Limitations and Startup Problems of Heat Pipes. Energy Res. FIGURE 6. Educ. Based on the temperature field calculated at the latest time, the value of each temperature node can be obtained. The heat transport of vapor flow is simplified as high efficiency heat conductance. where Nu is the Nusselt number, Gr is Grashof number, Pr is the Prandtl number. Am. The physical processes such as heat conduction, evaporation, condensation, and vapor flow in the heat pipe can be modeled and calculated. doi:10.1063/1.41777. The network system for heat pipe operation. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. 135, 106948. doi:10.1016/j.anucene.2019.106948, Yuan, Y., Shan, J., Zhang, B., Gou, J., Zhang, B., Lu, T., et al. Temperature distribution of contact surface between fuel and heat pipe. For heat pipe, it includes the wall, the wick, and the vapor space. Wick is composed of a porous structure and liquified working medium. (2022). Costello, F. A., Montague, A. F., and Merrigan, M. A. Energ.

Inst. However, there are limitations to using these models. The reason for this phenomenon is the uneven power distribution in space. The main parameters of this heat pipe are listed in Table. FIGURE 8. (1951). Oxford, United Kingdom: Butterworth-Heinemann. During this accident, with the decrease of engine power, heat transport power of heat pipes also reduces, leading to the increase of fuel temperature. Meanwhile, to ensure the safety of heat transport, there are a large number of high-temperature heat pipes in the reactor core. Differing from the traditional Pressurized Water Reactor (PWR), heat pipe cooled reactor adopts the high-temperature heat pipes to transport fission heat generated in the reactor core. doi:10.1080/00295450.2020.1722544, McClure, P. R., Poston, D. I., Gibson, M. A., Mason, L. S., and Robinson, R. C. (2020). Using the network method, the flow of working medium is approximately accounted for. Considering the high temperature of the condenser section, not only the natural convection, but the radiation heat transfer also exist. Nucl. This study was funded by the National Key Research and Development Project of China, No. Zuo divided the heat pipe into several subregions, and the lumped temperature was used to represent the real temperature of specific subregions. Three boundary conditions (Eqs 24) can be selected for heat transfer: where Q is the heating source, A is the surface area, h is the convective coefficient, T(i) is the surface temperature of wall, and T is the environment temperature. Due to these characteristics, high-temperature heat pipe is widely used for the design of heat pipe cooled reactor systems. During the transient calculation, each limiting power will be calculated using Eqs 2932. Or contact our For vapor space, the density and specific heat capacity of vapor are the physical parameters of alkali metal (Fink and Leibowitz, 1995; Ohse, 1985; Lee et al., 1969).

Sci. Heat pipes using alkali metal can realize efficient heat transport in special environments with high temperature (Faghri, 2014). The backflow of working medium is treated as a heating source in a differential equation of heat conduction. Due to the high thermal conductivity of material and the compactness of this reactor, the total temperature difference of the reactor is small enough, and the peak temperature locates at the inner surface of the fuel.

Heat Transfer 114 (4), 10281035. Experimental Investigation and CFD Analysis of a Air Cooled Condenser Heat Pipe. Tech. Energ. 206 (Suppl. Numer. Alkali metal has the characteristics of having a high boiling point and large latent heat of vaporization. Tech. FIGURE 9. Proc. Front. Nucl. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). From Figure 8B, it can also be found that although there is an insulating layer wrapped outside the adiabatic section, the high-temperature vapor will still be partially condensed in this section, resulting in the reduction of vapor flow rate in vapor space. Adding the heat transfer limitation, it can realize the judgment of heat pipe safety. The backflow in wick subregion was ignored. Energ.

National Institute of Space Research (INPE), Brazil. Appl. Eng. (2020). Using this model, the numerical simulation on KRUSTY reactor is executed. (1998). doi:10.1080/10407789008944804, Cao, Y., and Faghri, A. From Figure 7B, it can also be seen that with the continuous increase of heating power, operating temperature of heat pipe will be higher, resulting in the faster response of heat pipe. Tech. AV Luikov Heat and Mass Transfer Institute, Byelorussian Academy of Sciences. Tech. Calculated results using proposed model. Transient Two-Dimensional Compressible Analysis for High-Temperature Heat Pipes with Pulsed Heat Input. unpublished data. During this period, several typical models for heat pipe were put forward successively, including the self-diffusion model (Cao and Faghri, 1993a), the plat-front model (Cao and Faghri, 1993b), the network model (Zuo and Faghri, 1998), and the improved network model (Ferrandi et al., 2013). Eng. Phys. Kilowatt Reactor Using Stirling TechnologY (KRUSTY) Component-Critical Experiments. Inst. Sci. doi:10.1016/j.applthermaleng.2018.01.011, Zuo, Z. J., and Faghri, A. The comparison between simulated results using the proposed model and experimental results shows in Figure 15. 86, 1830. It is the prototype reactor to evaluate the performance of Kilopower reactor system (Poston et al., 2020; Sanchez et al., 2020; McClure et al., 2020b) The composition of KRUSTY reactor is shown in Figure 10. At about T = 300.0s, fuel reaches the peak temperature of about 1,080.3K. At about T = 2,200.0s, the reactor reaches the new steady state. (2014).

Combined with the network method, the evaporation, condensation, and backflow can be obtained (Ferrandi et al., 2013). Copyright 2020 Elsevier B.V. or its licensors or contributors. Proc.

This type of reactor system has the advantages of having a compact structure and high safety. TABLE 1. Particularly for the thermocouples in the evaporator, to reduce the effect of heating on temperature measurement, when winding the iron-chrome wire, all the measuring points are bypassed. In the transient calculation, the load-following accident is chosen. Energ. Moreover, for reactor systems with higher power density and more complex heat pipe arrangement, it can be expected that the temperature non-uniform effect of the contact surface will have a more significant impact on the operation of the reactor. Phenomena such as vapor flow and vapor-liquid interface shape variation are not important for the safety analysis of heat pipe cooled reactor. doi:10.1016/j.net.2019.06.021, Yan, B. H., Wang, C., and Li, L. G. (2020). Heat Pipes: Review, Opportunities and Challenges. (B) T = 2,200.0s. J.

Firstly, the pressure drops in the evaporator, adiabatic section, and condenser are calculated (Busse, 1967; Reid, 2002; Li et al., 2015). doi:10.1115/1.2911873. When the heat transfer limitations occur, the heat transfer capacity of heat pipe will significantly reduce. However, the proposed model can consider the nonuniformity of temperature on contact surface. (B) Temperature sensing point arrangement along the axial direction. It can be used as a mobile nuclear power system or space nuclear system for portable and efficient energy supply (Yan et al., 2020). Schematic diagram of heating system. Vasiliev, L. L., and Kanonchik, L. E. (1993). AIP Conf. Received: 20 November 2021; Accepted: 06 January 2022;Published: 27 January 2022. FIGURE 2. (1991).

The Stirling cycle is adopted to generate 1kW electric power. Then, this model is applied on the numerical calculation of Kilowatt Reactor Using Stirling TechnologY (KRUSTY) reactor. 2020YFB1901700, Science Challenge Project (TZ2018001), Project 11775126/11775127 by National Natural Science Foundation of China, and Tsinghua University Initiative Scientific Research Program. (2020). 1): where is the density, C is the specific heat capacity, T is the temperature, is the thermal conductivity coefficient, and H is the volumetric heating source. Basic constitution of a heat pipe cooled reactor (Mcclure, 2015). doi:10.1016/0017-9310(73)90260-3, Cao, Y., and Faghri, A. (A) Temperature difference with different heating power. who will be happy to help. doi:10.1063/1.1449720, Sanchez, R., Grove, T., Hayes, D., Goda, J., McKenzie, G., Hutchinson, J., et al. These models were applied for the simulation of heat pipe cooled reactor (Yuan et al., 2016; Liu et al., 2020; Ma et al., 2020; Wang et al., 2020). Transfer 49 (5), 667678. doi:10.1115/1.3604687, Li, H., Jiang, X., Chen, L., Ning, Y., Pan, H., and Tengyue, M. (2015).

This model does not directly calculate the vapor flow in the vapor space, however, the evaporation, the condensation, and vapor flow rate can be obtained using the simplified method mentioned in Section 2.2.2. Phys. Department of Engineering Physics, Tsinghua University, Beijing, China. Figure 1 shows the basic constitution of a heat pipe cooled reactor (Mcclure, 2015). Ann. For heat pipe models using the analysis on heat pipe cooled reactors, it is hoped that it can describe the transient behavior of heat pipes well, and it should be simple enough to reduce the computational resources as much as possible. Nucl. The model proposed in this paper ignores the two-phase flow and capillary phenomenon in heat pipe, as it simplifies the heat transport caused by vapor flow into high-efficiency heat conductance. Eng. This model does not directly calculate the two-phase flow of working medium in heat pipe, and the difference is acceptable. During the load-following analysis (section 4.3), it is set as the fixed temperature gradient. Thermodynamic and Transport Properties of Sodium Liquid and Vapor. Oxford: Blackwell. Chi, S. W. (1976). Heat Pipe Transient Response Approximation. AIP Conf. FIGURE 11. Creative Commons Attribution License (CC BY). Deverall, J. E., Kemme, J. E., and Florschuetz, L. W. (1970). Generally, there is no heat source in wall, and the heat transfer between heat pipe and environment can be described using suitable boundary conditions. Thermionic Conversion Specialist Conference, United States, November 1-2, 1967, 391398. Using commercial codes such as FLUENT and CFX, the modeling difficulty can be greatly simplified, and built-in advanced numerical algorithms can ensure the stability of numerical calculation as much as possible. doi:10.1016/s0017-9310(97)00220-2, Keywords: heat pipe cooled reactor, high-temperature heat pipe, STCM, heating system, KRUSTY reactor, Citation: Guo Y, Su Z, Li Z and Wang K (2022) The Super Thermal Conductivity Model for High-Temperature Heat Pipe Applied to Heat Pipe Cooled Reactor.