Sodium Heat Pipe Research Articles

Design of high-temperature sodium heat pipe with composite wick based on non-dominated sorting genetic algorithm (NSGA)

As small modular reactors continue to advance, heat pipe reactors (HPRs) are being developed by multiple organizations. Designing heat pipes with optimal heat transfer capability is crucial for the effective performance of HPRs. Based on NSGA-III genetic algorithm, this paper presented the design method of a high-temperature heat pipe featuring a composite wick. The study examined the influence of heat pipe structure parameters on performance parameters and heat transfer limits. Based on the analysis, we built multi-objective modeling of heat pipe and obtained the optimal structural parameters by NSGA-III. Verification confirmed that the heat pipe met the Mach number and effective capillary radius requirements. This study provided valuable insights for improving heat pipe manufacturing techniques and reactor miniaturization.

An emf-temperature reference function for Pt–20%Rh versus Pt thermocouples in the temperature range of 0 °C to 1100 °C

Abstract An electromotive force-temperature reference function for thermocouples made of platinum-20%rhodium versus platinum (Pt-20%Rh/Pt) was determined for the temperature range from 0 °C to 1100 °C. Three Pt-20%Rh/Pt thermocouples were constructed at the Physikalisch-Technische Bundesanstalt (PTB) and were compared with standard platinum resistance thermometers (SPRTs), an Au/Pt thermocouple and a Pt/Pd thermocouple, which were all calibrated at fixed points of the International Temperature Scale of 1990 (ITS-90). The comparison measurements were performed in stirred liquid baths in the range from 0 °C to 545 °C, in a sodium heat pipe from 560 °C to 980 °C, and in a five-zone furnace at temperatures between 1000 °C and 1100 °C. Furthermore, the Pt-20%Rh/Pt thermocouples were calibrated at fixed points of the ITS-90. The PTB reference function based on two of the three Pt-20%Rh/Pt thermocouples has an expanded measurement uncertainty of 0.25 K in the temperature range from 0 °C to 1100 °C.

Numerical modeling of alkali metal heat pipes

Heat pipe cooled reactors passively transfer heat from the core to the energy conversion system through alkali metal heat pipes. Further studies of the heat transfer characteristics of alkali metal heat pipes are needed to develop heat pipe cooled reactors. This work used a two-dimensional heat and mass transfer model of an alkali metal heat pipe. The flow field was validated against CFD predictions which showed that the model has less than 10 % errors in the velocity distribution and less than 5 % errors in the pressure distribution. A comparison of the predictions with experimental data in the literature indicated that the predicted wall temperature error was within 30 °C. This model was then used to analyze four factors that affect heat transfer in sodium heat pipes. The simulations show that higher heat fluxes shorten the startup time by approximately 70 % but significantly increase the operating temperature. The heat flux distribution significantly affects the evaporator temperature distribution. The heat transfer boundary condition on the condenser’s outer surface mainly affects the operating temperature and startup time. Increasing the heat pipe length-to-diameter ratio with a fixed heat flux increases the operating temperature with the increase proportional to the heat flux. This model provides accurate simulations of sodium heat pipes for various heat transfer boundary conditions. The simulations provide a reference for the selection of working conditions for heat pipe operation instability experiments.

Evaluation of start-up characteristics for heat pipe-cooled nuclear reactor coupled with recuperated open-air brayton cycle using hardware-in-the-loop

The heat pipe-cooled nuclear reactor (HPR) holds great importance for the low-carbon transition period and can be applied flexibly and stably in numerous scenarios. However, studies on the dynamic performance of the HPR coupled with the open-air Brayton cycle (OBC) are scarce, and achieving a balance between economy and accuracy has proven challenging. In this work, a hardware-in-the-loop (HIL) method is proposed and implemented for the coupled HPR-OBC prototype by combining the benefits of experimental measurements and numerical simulations. A sodium heat pipe test rig is heated in the real world, while neutronics and OBC dynamics are synchronously solved using Simulink models. A transient HIL test lasting for 12000 s is conducted to explore the start-up process of HPR-OBC. The coupled system successfully reaches steady-state by regulating reactivity and shaft speed. The results indicate a strong coupling effect between the shaft speed, the heat transfer rate of the heat pipes, and the air flow state in the OBC. The turbomachine operates within reasonable regions and no surge or choke phenomena occur. The final reached OBC efficiency is 20 %, and the generated electricity power output is 0.16 MWe.

Dry-out limit enhancement strategy in sodium heat pipes: Overfilling effect and modified capillary limit model

Despite the significant impact of the filling ratio on dry-out of heat pipe, current operating limit models do not adequately address this factor. This study proposes an advanced capillary limit model that incorporates the effect of the filling ratio. An experimental study was conducted to compare the operating limits of sodium heat pipes with filling ratios of 107 % and 246 %. The results showed that the existing capillary model is difficult to predict the operating limits based on filling ratios, leading to significant deviations between theoretical predictions and actual outcomes. Specifically, a heat pipe filled to 107 % experienced dry-out at a point 31.1 % lower than expected, while a heat pipe filled to 246 % reached dry-out at 20.2 % higher than expected. Notably, the overfilled heat pipe maintained a steady state even at 10.5 % above the expected dry out point. The key point of the proposed model, based on optical imaging and temperature data at dry-out, is that the excess liquid in vapor region travels and forms a liquid plug at the end of the condenser, which shortens the length required for capillary transport. Based on this insight, the Chi model was modified to predict the operating limit of overfilled heat pipes more accurately within a 5 % margin of error. The study highlights the critical role of filling ratio in heat pipe design, noting that overfilling can shorten the effective capillary length through liquid plug formation, thereby increasing the dry-out limit. However, these pools also limit the reach of sodium vapor and potentially reduce the effective area of the condenser.

Startup characteristics of the large length–diameter ratio high-temperature heat pipe

Large length–diameter ratio high-temperature sodium heat pipes (HTSHPs) are uniquely structured heat-transfer devices with significant application potential in high-temperature solar thermal power and small-scale nuclear systems. This study tested HTSHPs' startup characteristics examining various parameters. Results indicate that the transition temperature for flow transition is 564 K, and the continuous flow transition temperature is 722 K. Heat pipes at 15 % fill ratio are adaptable across various inclination angles, whereas those at 25 % and 35 % fill ratios show optimal startup at smaller angles (15°, 30°), with decreasing startup time as angle increases, notably significant at 45°.The start-up time refers to the duration from the initiation of heating to the point when all the normal operational temperature points of the HTSHP reach the continuous flow transition temperature during the condensation section. During the experiments, heat pipes with a large length–diameter ratio exhibit heat transfer instability, temperature oscillation and local overheating. Reducing the fill ratio and inclination angle effectively reduces the probability of temperature oscillation and local overheating. This study proposes a novel method for optimizing temperature oscillations in heat pipe design, offering pioneering insights and experimental data crucial for specialized high-temperature heat pipe research.

Numerical simulation analysis of high-temperature bent sodium heat pipes

Abstract High-temperature bent heat pipes are safety-level heat transfer components used in heat pipe cooled reactor, and their applications are becoming increasingly widespread. In this study, a comprehensive three-dimensional numerical model was established to evaluate the effects of different bending angles and radii on the performance of high-temperature heat pipes. The model solved for the temperature, pressure, and velocity fields in the wall, wick, and evaporator, considers the compressibility effect of the vapor. The study investigated parameters such as vapor pressure, vapor velocity, radial secondary flow field, wall temperature, wick temperature, and equivalent thermal resistance of powder sintered core sodium heat pipes with bending angles of 45°, 90°, 135°, 180°, and a bending radius under 90°. The results showed that when sodium vapor enters the bent pipe, the vapor flow deviates towards the outer side, resulting in higher vapor pressure at the outer side than the vapor pressure at the inner side, and the generation of radial secondary vortex. This leads to higher temperature in the evaporator and adiabatic sections of the bent heat pipe, while lower temperature in the condenser. Fractal patterns are observed in the outer and inner wall temperature curve in the adiabatic section, with lower temperatures on the inner side and higher temperatures on the outer side. The bent heat pipe exhibits higher equivalent thermal resistance than that of a straight heat pipe, and the equivalent thermal resistance increases with increasing bending angle, and the equivalent thermal resistance decreases with increasing bending radius.

Analysis of geyser boiling in liquid metal heat pipe: Impact on startup and shutdown, fuel temperature, and heat removal performance

Liquid metal heat pipes are efficient heat transfer devices with diverse applications in various industries, including nuclear power plants. The use of liquid metal heat pipes in Heat Pipe-Cooled Nuclear Reactors (HPNRs) has been proposed for high-temperature heat utilization during electricity generation. This study experimentally investigates the impact of geyser boiling on the temperature of the fuel and its effect on heat removal performance using a sodium heat pipe. The investigation includes the influence of both increasing and decreasing power levels. The study reveals significant differences between operating the heat pipe in vertical and horizontal orientations. The thermal resistance and efficiency of the heat pipe are analyzed under different operating conditions. The results show that geyser boiling has a more pronounced impact in unsteady states compared to steady states, leading to non-periodic behavior and fluctuations in temperature and heat removal. The study emphasizes the importance of considering the changing liquid pool in liquid metal heat pipes to prevent or mitigate geyser boiling effects. Modifications to the optimal filling ratios of heat pipes are suggested to enhance stability and efficiency, making liquid metal heat pipes more feasible for HPNR applications.

Numerical study on the characteristics of sodium heat pipes for space application at operation limits

Sodium heat pipes are important thermal conductive components in space nuclear power sources. They efficiently transfer heat within the range of 500–1000 °C by utilizing the latent heat of phase change. However, their maximum heat transfer capacity is limited by various factors. In this study, numerical simulations were conducted to investigate the operating conditions of sodium heat pipes when encountering different heat transfer limits, with a focus on analyzing the vapor–liquid distribution and axial temperature distribution in evaporator section. It is revealed that as reaching the heat transfer limits, sodium heat pipes exhibit wall temperature fluctuations in evaporator section. When encountering the viscous limit, liquid aggregation occurs within the wick, causing discontinuous flow. As reaching the sonic limit, a vapor blockage zone forms at the outlet of evaporator section, disrupting the flow circulation within heat pipe. For the entrainment limit, the liquid inside wick is carried away by vapor flow, reducing the amount of liquid involved in phase change cycle. As in the capillary limit, inadequate liquid reflux leads to thinner liquid layer, weakening the flow circulation. During the transition from the viscous limit to the sonic limit, no significant phenomena of phase distribution occur in the evaporator section. As the sonic limit and the entrainment limit act together, both vapor blockage and liquid entrainment occur, accompanied by liquid accumulation. The phenomena when the entrainment limit and the capillary limit act together differ from those occurring individually. The simulation results provide references for a deeper understanding of heat transfer limit mechanism and other operating characteristics.

A special-shaped sodium heat pipe with a “bridge-type” artery for coupling free-piston Stirling generator and fission reactor

The nuclear-powered free-piston Stirling generator (FPSG) by using heat pipes as heat transfer devices has significant potential for future applications in the deep space exploration. Due to the compact size of the FPSG, it is very difficult to directly insert the cylindrical heat pipe into the heat head to transfer heat, which has been a challenge for application in such a system. Here, a special-shaped heat pipe is designed to match the heat head. In this design, the surface of the heat head was used as the condensing surface and a “bridge-type” composite artery was used to transfer the liquid sodium from the condensing surface to the evaporating surface, which could greatly simplify the structure and improve the capillary limit. A simplified model for arterial wick was proposed to predict the artery geometrical parameters and capillary limit and the performance of the startup and steady state were experimentally investigated. It successfully transmitted about 4 kW of heat with a tilt angle of −35°, verifying the feasibility of the new structure. The effect of different cooling conditions and inclinations were also investigated. To ensure that the heat pipe was fully activated, it was necessary to meet the minimum input power under different cooling conditions.

Experimental and numerical simulation study of sodium heat pipe with large aspect ratio

As a core cooling device of reactor, a high temperature sodium heat pipe is designed in this paper which has a large aspect ratio of 126. The effects of heating mode and evaporation section length on its start-up are studied experimentally. The results show that the axial temperature uniformity of the heat pipe is better under variable power heating mode. As the evaporation cross-section length increases, thermal resistance decreases by 50%. Compared with heat pipes with low aspect ratio, heat pipes with large aspect ratio are more difficult to start up. Furthermore, numerical simulation is conducted on the designed sodium heat pipe to acquire the velocity and pressure distribution during steady-state operation.

Three-dimensional CFD simulation of geyser boiling in high-temperature sodium heat pipe

A deep understanding of the characteristics and mechanism of geyser boiling and capillary pumping is necessary to optimize a high-temperature sodium heat pipe. In this work, the Volume of Fluid (VOF) two-phase model and the capillary force model in the mesh wick were used to model the complex phase change and fluid flow in the heat pipe. Computational Fluid Dynamics (CFD) simulations successfully predicted the process of bubble nucleation, growth, aggregation, and detachment from the wall in the liquid pool of the evaporation section of the heat pipe in horizontal and tilted states, as well as the reflux phenomenon of capillary suction within the wick. The accuracy and stability of the capillary force model within the wick were verified. In addition, the causes of geyser boiling in heat pipes were analyzed by extracting the oscillation distribution of heat pipe wall temperature. The results show that adding the capillary force model within the wick structure can reasonably simulate the liquid backflow phenomenon at the condensation; Under the horizontal and inclined operating conditions of the heat pipe, the phenomenon of local dry-out will occur, resulting in a sharp increase in local temperature. The speed of bubble detachment and the timely reflux of liquid sodium (condensate) replenishment in the wick play a vital role in the geyser temperature oscillation of the tube wall. The numerical simulation method and the results of this study are anticipated to provide a good reference for the investigation of geyser boiling in high-temperature heat pipes.

Investigation of key parameters for the operation of a sodium heat pipe with visualization using X-ray radiography

Alkali metal heat pipes are considered as a promising primary cooling system of special-purpose nuclear reactors. For the deployment, it is important to understand the heat pipe’s behaviors under different operation conditions. In this paper, the startup characteristics and operation performance of three sodium heat pipes with 67%, 102% and 172% sodium filling ratios, respectively, were investigated, and the two-phase sodium flow was visualized using high-speed, high-resolution x-ray radiography. The boiling flow regimes in the evaporator region were categorized into stagnant sodium liquid pool, geyser boiling and developed boiling. The effect of key parameters, such as the boundary conditions of the evaporator and condenser, the sodium filling ratio, and the inclination angle were investigated. It was found that the heater power and condenser cooling conditions have a great influence on the operation temperature within the achievable range of heat transfer rate. The filling ratio and inclination angle affect the boiling phenomena and the heat pipe operational range. The experiments can provide valuable data for heat pipe model validation as well as the design of the special-purpose nuclear reactor and other high-temperature heat pipe systems.

Molecular dynamics simulation of homogeneous nucleation of melting in superheated sodium crystal

The melting process and nucleation behaviour of sodium (Na) crystals are crucial for the frozen start-up of high-temperature sodium heat pipes and the working performance of molten sodium batteries. Equilibrium melting and the homogeneous nucleation of melting in superheated Na crystal are studied by molecular dynamics simulation. The thermodynamic properties and nucleation of Na crystal during the heating process are investigated by the characterization of the density, radial distribution function (RDF), self-diffusion coefficient (D), nucleation rate (Ihom), etc. Firstly, the equilibrium melting of Na crystal is simulated and verified by the single-phase method. Results show that Na's equilibrium melting temperature, densities, and RDF simulated match well with experimental values, demonstrating that the EAM/FS potential is suitable for studying the melting processes of Na crystal. Secondly, the calculated D of liquid Na increases approximately linearly with rising temperature within 440 K∼540 K and fits with experimental data well. The activation energy for the diffusion of Na obtained by linear fitting is 1.6406·10-20 J, which agrees well with the observed values. Finally, the homogeneous nucleation of melting in superheated Na crystal is analyzed. It is found that the Ihom of melting in superheated Na crystal rises exponentially with increasing temperature, which is consistent with the prediction in literature. The kinetic stability limit of superheated Na crystal is 468.3 K, and the relation between the Ihom of melting in superheated Na crystal and temperature is given. The physical properties and nucleation theory of Na crystal simulated during the melting can provide theoretical support for sodium's heat and mass transfer-related applications, such as sodium heat pipes and sodium batteries.

Key features and highly effective prediction of complete startup from frozen state for high-temperature heat pipe in heat pipe reactor

High-temperature heat pipe is an efficient phase change heat transfer device, widely applied in the space nuclear reactors, the China Fusion Engineering Test Reactor, solar collectors, and the thermal protection of hypersonic vehicles. In order to understand the startup characteristics of the heat pipe and to predict its transient behavior with high accuracy, this paper first experimentally investigated the startup performance of a sodium heat pipe from the frozen state under different heating powers from 534 W to 1897 W. Then, a new compressible flow model for startup from the frozen state was developed and verified, solved the independence problems of mesh number and time-step used in the numerical treatments of most traditional heat pipe codes. Finally, based on the assessed model and experimental data, the startup procedure and the influences of heating power on the working temperature, kick-in time, and temperature difference were analyzed respectively. The comparisons indicated that the new model is extremely informative and effective, and the results provided knowledge for understanding the safe and optimum working regime of a high-temperature heat pipe using in heat pipe reactor.

Experimental investigation of thermal behavior of overfilled sodium heat pipe

Operating limitations model of heat pipes are difficult to evaluate the effect of the charging amount of working fluid, which is one of the crucial factors in heat pipe performance of startup and maximum heat transfer. To reduce the knowledge gap on the effect of filling amount, the purpose of this paper is an investigation of the thermal behavior of excess liquid. Overfilled sodium heat pipe having about 260% filling ratio was fabricated and tested with the change of boundary and initial condition. Sodium heat pipe showed good isothermal characteristics that the temperature difference between evaporator and condenser reduced as the development of continuum flow until reaching operating limit condition. The characteristics of an overfilled heat pipe appear at power increased after the continuum flow fully developed to the condenser that sudden temperature rise about 100 °C in the overall heat pipe except the end region of the condenser where a continuous temperature about 50 °C drop occurs. Excess liquid moves toward the condenser end and forms the liquid pool and lessening the active condenser length which reduces the maximum heat transfer of heat pipe and induced the operating limitation. The results showed that this phenomenon only occurs at high heat flux conditions as sufficient vapor flow is required to allow excess liquid to propagate to the condenser and determined the operating limitation of overfilled sodium heat pipe that continuous temperature rises as the liquid propagates to the end of the condenser rather than the abrupt rising such as dry out. However, the operating limitations occur sudden dry-out of the evaporator similar to the conventional results of liquid metal heat pipe when the liquid propagation did not occur. Compared to the entertainment limit model, there was a significant difference in the dry-out point of the experimental results with excessive liquid propagation. It was confirmed that the horizontal operation of overfilled heat pipe was in good agreement with the prediction of capillary limit model within 22.6% of the maximum error.

Experimental study of non-condensable gas effects on sonic limit of sodium heat pipe

Due to unexpected gas leakage and long-term operation, the non-condensable gas (NCG) inevitably exists in high-temperature alkali metal heat pipe. Previous studies have mainly focused on its influences on startup and steady state operation characteristics of heat pipes. However, few of them conducted experiments to study the effects of NCG on sonic limit, which usually occurs during heat pipe startup or during steady state operation when the heat transfer coefficient at condenser section is high. In present work, experimental and analytical studies are conducted to the explore the effects of NCG on sonic limit of sodium heat pipes. With the heating power ranging from 500 to 1400 W, the sonic limit of 1 m-long sodium heat pipes with artery wick and axial groove wick are obtained based on oil-cooling system, which can widely adjust the cooling capacity at condenser section. The amount of NCG in heat pipe is estimated by Heat Pipe Transient Analysis Code (HPTRAN) and verified by experimental data. It is found that the existence of NCG in heat pipe leads to the decrease of maximum heat transfer rate under sonic limit. The mechanism of NCG effects on sonic limit is discussed based on phenomenological analysis. By introducing the added back pressure, a modified model to predict sonic limit considering NCG effect is proposed and the comparison with experimental data shows good agreements.

Molecular dynamics simulation of the evaporation of thin liquid sodium film on the conical nanostructure surface

Deeply understanding the evaporation of the nanoscale thin liquid film on the nanostructure substrates is significant for further constructing the novel wick structure with nanostructure surfaces, which would be used in the optimal design of the sodium heat pipe. For this purpose, this paper investigates the evaporation of thin liquid film on conical nanostructured surfaces by the molecular dynamics method. A cuboid evaporation system is constructed. It consists of the bottom solid substrate and thin liquid sodium film. A flat solid wall is set as the reference. By changing the nanoscale cone's number and height, five conical nanostructure surfaces are built. The number of gas atoms and the total energy of fluid atoms are observed respectively. The evaporation rate and the average heat flux (q) of six cases are compared. The conical nanostructure suppresses evaporation. With the roughness of the conical nanostructures, the evaporation rate decrement maximum can reach 83% and the q decrement maximum can reach 58%. Based on the thermal resistances in the solid-liquid contact region, the D (Self-diffusion coefficient), and the peak values of RDF (Radial distribution function), the mechanisms of the conical nanostructure surfaces are analyzed. The suppressing effects of the conical nanostructure surfaces are achieved by weakening the heat conduction in the solid-liquid contact region and mitigating the collision heat transfer of liquid atoms.

Experimental investigation of heat transfer limitations in concentric annular sodium heat pipes and thermosyphon

This paper presents experimental investigations on the heat transfer performance of concentric annular heat pipe (CAHP) and thermosyphon (CATP) using sodium as a working fluid for microreactor applications. CAHP characterized by wicks on the inner and outer walls offers the potential to enhance capillary force and enable more compact microreactor designs. The research aims to understand the implications of structural differences between CAHP, CATP and conventional heat pipe (CHP) and identify favorable conditions for their use in microreactors. The thermal behavior and heat transfer limits of CAHP and CATP were examined under various boundary conditions. The experimental results revealed that CAHP exhibited capillary limits approximately 71.2% higher than cylindrical heat pipes under horizontal conditions. However, the Chi model used for predicting capillary limits showed a difference about 19.7% in horizontal operation and exceeded 44.6% in vertical operation, highlighting the need for considering the effect of non-uniform capillary forces in CAHP. The presence of additional inner wick in CAHP provided large evaporation areas, which facilitated rapid vapor generation and enabled the development of a continuum flow faster than in CHP, by approximately 70 °C. However, in vertical operation, CATP necessitates higher heat fluxes and exhibits notable temperature disparities between the evaporator and condenser regions compared to CAHP. This difference can be explained depend on the vapor generation mechanisms: heat pipes utilize additional wick area to facilitate evaporation, while thermosyphon depend on boiling that the advantages related to the annular flow path in CATP are not clear. Furthermore, the presence of an adiabatic section yields contrasting effects: while it promotes the formation of larger menisci in heat pipes, its presence is unfavorable in thermosyphons as it can elevate boiling temperatures that delayed operations. The findings underscore the advantages of CAHP over CHP, particularly in microreactor applications, provide insights into design optimizations for compact microreactors, and showed gaps in operating prediction models and experimental results.

Experimental study on transient heat transfer performance of high temperature heat pipe under temperature feedback heating mode for micro nuclear reactor applications

The use of heat pipe-cooled micro nuclear-powered reactors (HPNRs) is crucial for shaping a low-carbon energy structure in the future. However, there is still a lack of experimental investigations on the transient heat transfer performance of high-temperature heat pipes (HTHPs) under the application of HPNRs. To address this issue, a hardware-in-the-loop (HIL) test platform has been developed to dynamically adjust the heating power of the heat pipe in real-time considering the temperature feedback (TF) effect. A horizontal test rig composed of a hex block, a sodium heat pipe, and six electric heaters has been built in the laboratory, and its thermal effectiveness has been evaluated at 60%. Subsequently, a transient HIL test under the TF heating mode has been conducted. The results show that the frozen start-up of the HTHP can be divided into five stages based on the power exponential growth rate and the state of the sodium vapor. During the transient start-up process, the worst axial heat transfer of the HP occurs when the front of the continuum vapor arrives at the adiabatic section, where the maximum thermal resistance is 500 K/W. Heat pipes with a high filling ratio can avoid integral overheating of the evaporator when occurring viscosity limit at the start-up period. Different time scales of neutron growth and thermal inertia cause alternating oscillation of power and temperature. This work provides valuable insights into the transient heat transfer behavior of the HTHP under the running process of the HPNR system.