Model Of 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 efficient two-stage heating strategy for embedded heat pipe system considering power and energy requirements from battery

The battery thermal management system (BTMS) embedded heat pipe system cannot only quickly heat the battery, but also improve its temperature consistency. In order to accurate predict the electro-thermal performance of the battery pack with such a BTMS, an electro-thermal model integrating heat pipe model is established for the pack. This model extends the traditional RC model to a dual-RC model at the cell level for predicting the cell anode potential, which clearly senses the status of lithium plating during the heating process. At the pack level, a distributed electro-thermal model combined with a thermal resistance network-based heat pipe model is proposed for the precise determination of the overall pack temperature. To further enhance the accurate monitoring of lithium plating status and control of the heating process for each cell within the pack, the control criterion is based on the terminal voltage rather than the state of charge (SOC). Additionally, an absolute SOC is defined to unify the SOC calculation across different low-temperature scenarios. With the assistance of the model frameworks above, a two-stage heating strategy is proposed for the BTMS, including the power requirement stage to ensure the heating rate and energy requirement for more available depth of discharge (DoD). In the stage of power requirement, air parameters are determined as Vair = 9 m/s and Tair = 60 °C, and the corresponding temperature rising rates are 1.05 °C/min under discharge and 1.08 °C/min under charge condition, respectively. Additionally, in order to ensure the high heating rate and 98 % available DoD, the second stage heats the pack with the air parameters of Vair = 5 m/s and Tair = 60 °C, with the temperature rising rates of 1.02°C/min under discharge and 1.74°C/min under charge condition. Unlike the air parameters used in the first phase, those in second phase also considers the energy conservation of the BTMS and temperature homogeneity inside the pack. The energy consumptions of BTMS are 0.323 kW·h for the discharging and 0.133 kW·h for the charging. Moreover, the tested temperature difference among cells in the whole heating process is no more than 1.3 °C.

Experimental study of heat pipe start-up characteristics and development of an enhanced model considering gas diffusion effects

Heat pipe-based cooling reactors, offering passive heat transfer and modularity, are becoming the preferred type for micro-reactors. Alkali metals such as sodium, potassium and lithium are usually used as the working medium of the heat pipe, which is in a frozen state at normal atmospheric temperature. After heating the heat pipe, the working medium will melt and enter the gas chamber, and its flow state will undergo a transition from discontinuous flow to continuous flow. The start-up of the heat pipe affects the heat export and neutron physical characteristics of the heat pipe cooling reactor. Building a model of heat pipe can predict the start-up of heat pipe effectively, which can be helpful to study the start-up and safety analysis of heat pipe cooling reactor. In this paper, a heat pipe flat-front model considering the gas diffusion effect is established, and the gas temperature distribution characteristics in the non-continuous flow region are obtained through the start-up experiment of heat pipe. The calculated results of the flat-front model considering gas diffusion effect and the vertical flat-front model are compared with the experiment. The results show that the model in this paper can better describe the start-up of heat pipe. At the same time, the evaporation and condensation coefficient model based on temperature change is used to deal with the evaporation and condensation mass flow at the phase change interface of the heat pipe, which can better describe the temperature difference at the interface of the heat pipe.

A steady-state distributed parameter ultrathin heat pipe model considering the unsaturated wick

Ultrathin heat pipes have become mainstream to address the heat dissipation issues of small electronic devices. Numerous numerical studies based on the saturated wick assumption have been proposed to analyze their heat transfer performance. In order to achieve a more accurate assessment, this study presents a three-dimensional model that quantitatively reflects the relationship between capillary pressure and medium volume, along with a corresponding correlation. Based on this, a steady-state distributed parameter ultrathin heat pipe model considering the retreating of medium volume in the wick and the unsaturation vapor-liquid interface was developed, whose accuracy was verified by the experimental data. The results demonstrated that the capillary pressure increased with the decrease of medium volume and contact angle. The evolution of the overall meniscus with medium volume was categorized into two stages, where capillary pressure dependent on the main and micro meniscus at different stage. The medium volume distribution, corresponding to capillary pressure, will automatically adjust to match the overall medium pressure drop. Comparative analysis against experimental data, the proposed model reduced the maximum temperature difference error by 8.43 % compared to the saturated wick assumption at a heat load of 6 W, revealing that the unsaturated liquid wick model exhibited higher accuracy.

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.

High-Fidelity Multiphysics Modeling of a Heat Pipe Microreactor Using BlueCrab

Researchers who are actively developing nuclear microreactors are planning to employ innovative designs and features using traditional commercial modeling tools that may be inadequate for their design and licensing activities. The codes developed under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program provide flexibility in terms of geometry modeling and multiphysics coupling and are particularly well suited for modeling novel microreactor concepts. To test the maturity of these codes, this paper introduces a conceptual heat pipe microreactor (HP-MR) designed to gather various technologies of interest to microreactor developers such as control drums, heat pipes, and hydride moderators. The objective of this effort is to demonstrate NEAMS tools capability to perform high-fidelity multiphysics simulations, using coupled neutronics (via the Griffin code), heat conduction (via the BISON code), heat pipe modeling (via the Sockeye code), and hydrogen redistribution in hydride metal moderator (via the SWIFT code). Codes are coupled in-memory through the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, which permits flexible multiphysics data transfer schemes. The analysis confirmed two key aspects of the HP-MR concept: (1) its ability to follow the power load requested from the heat pipe and (2) its ability to avoid heat pipe cascading failure unless designed with high power close to operating failure limits of its heat pipes. The developed computational model was distributed publicly on the Virtual Test Bed for training purposes to accelerate adoption by industry and to provide a high-fidelity multiphysics solution for benchmarking against other tools. Additional multiphysics analyses including other transients and coupled physics were identified as necessary future work, together with a focus on validating multiphysics behavior against experiments.

Rotating heat pipe model based on lumped parameter method

On the basis of many theoretical studies about rotating heat pipes, a simplified mathematical model is established based on the lumped parameter method, ignoring the temperature difference inside each section of the heat pipe is ignored, and comparing the calculated results with the experimental data. It is identified that this model has a good applicability at high speeds and low liquid filling rates, and effectively reduces the amount of calculation, which is of practical significance to the engineering application of rotating heat pipes.

Heat transfer performance of high-temperature heat pipe startup in small heat pipe reactors

High-temperature heat pipe is an important heat transfer component in small heat pipe reactors (SHPR). Research on the transient heat transfer characteristics during heat pipe startup is crucial for safety analysis of SHPR. This manuscript investigates the startup performance of a lithium heat pipe from the frozen state with various influencing factors, including heating power, inclination angle, and convection heat transfer coefficient. The objective of this work is to speed up the heat pipe startup process in a safe and economic manner based on its heat transfer characteristics. In order to illustrate the startup characteristics and further to reduce the startup time, this manuscript constructs a CFD heat pipe model via the multi-physics simulation software, COMSOL. The phase change process of heat pipe startup is described by the Phase Change Material method, with the fluid velocity and pressure fields of wick established using the Brinkman equation. Results show that the heat pipe thermal resistance decreases with increasing heating power, positive inclination angle, or convection heat transfer coefficient. On the other hand, the heat pipe startup time reduces with increasing heating power, increasing positive inclination angle, or decreasing convection heat transfer coefficient. Moreover, numerical analysis indicates that heat pipe temperature rises faster in the evaporation section than in the condensation section at the beginning of startup. Temperature rise process in the condensation section occupies the majority of the entire heat pipe startup process. Therefore, to speed up the startup process, this work proposes a novel extra heating method applying to the condensation section at early startup. Compared with the conventional startup, the proposed method is able to shorten the startup time by 10.5 % and 15.8 % with an extra heating power of 10 % Full Power (FP) and 20 %FP respectively.

Modeling and performance analysis of separate heat pipe containing non-condensable gas for pool-type low-temperature heating reactor

The application of separate heat pipe technology in the Passive Residual Heat Removal System (PRHRS) of Swimming Pool-type Low-Temperature Heating Reactor (SPLTHR) can efficiently transfer heat without concerns of working medium leakage and installation difficulties. Since the reactor pool is at atmospheric pressure, the separate heat pipe is required to operate at sub-atmospheric pressure. In this paper, a one-dimensional program code to evaluate the heat transfer performance of a separate heat pipe loop containing non-condensable gas (NCG) is established. On this basis, the effects of some parameters on the system performance are investigated. The results show that the NCG occupies part of the condenser space, weakening the heat transfer performance of the system significantly. Within the calculated range, the presence of NCG can lead a maximum 79% decrease in system's heat transfer rate. For the system's external conditions, the heat transfer rate exhibits greater sensitivity to the water temperature of the pool as compared to the air temperature. Moreover, an increase in the air velocity tends to diminish the strengthening effect in system heat transfer capacity gradually. The obtained analytical results can provide reference for practical engineering application.

Thermal Modeling of an eVinci™-like heat pipe microreactor using OpenFOAM

The simulation of heat pipe microreactors is an active area of research. In this paper, a thermal analysis of a heat pipe microreactor motivated by the eVinci™ design is performed. Thorough discussion on the modeling of heat pipes without a dedicated heat pipe modeling code, such as Sockeye, is also provided. The performance of two heat pipe modeling techniques is compared, one a more accurate approach which explicitly tracks heat pipe temperatures, and the other an approximation which simplifies the thermal hydraulic model development. One-way coupling is used where the Serpent neutronics code is used to generate a power distribution which is applied in an OpenFOAM model to calculate a temperature distribution. After a detailed convergence analysis, the core temperature distribution resulting from a core with control drums facing outward, or fully withdrawn, is compared with one having the control drums facing inward, or fully inserted. Finally, a parametric analysis was performed where the thermal resistances associated with the heat pipe model were varied and core temperatures were tracked. It was observed that the relationship between average and maximum core temperatures had a highly linear relationship to the thermal resistances used in the heat pipe model.

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.

Simulation of, Optimization of, and Experimentation with Small Heat Pipes Produced Using Selective Laser Melting Technology

With the development of microsatellite technology, the heat generated by onboard components is increasing, leading to a growing demand for improved thermal dissipation in small satellites. Metal powder additive manufacturing technology offers the possibility of customizing and miniaturizing heat pipes to meet the specific requirements of small satellites. This article introduces a small-scale heat pipe designed using selective laser melting (SLM) technology. The heat pipe’s material, structure, and internal working fluid were determined based on mission requirements. Subsequently, the SolidWorks 2021 software was used for heat pipe modeling, and the ANSYS 2021R2 finite element analysis software was employed to simulate the heat transfer performance of the designed heat pipe, confirming its feasibility. The heat pipe’s structure was optimized using multi-objective regression analysis, considering various structural parameters, such as the channel diameter, vapor chamber height, and narrow gap width. The simulation results demonstrate that the optimized heat pipe achieved a 10.5% reduction in thermal resistance and an 11.6% increase in equivalent thermal conductivity compared to the original heat pipe. Furthermore, compared to conventional metal heat-conducting rods, the optimized heat pipe showed a 38.5% decrease in thermal resistance and a 62.19% increase in equivalent thermal conductivity. The heat pipe was then fabricated using a 3D printer (EOS M280), and a vacuum experimental system was established to investigate its heat transfer characteristics. The experimental results show that the heat pipe operated most efficiently at a heating power of 20 W, reached its maximum heat transfer capacity at 22 W, and had an optimal fill ratio of 30%. These results highlight the excellent performance of the heat pipe and the promising application prospects for SLM technology in the field of small satellites.

Development of Analysis Tools for Heat Pipes Used in Small Modular Reactors: Sodium Property Correlations

Abstract Advanced small modular reactors strive to improve reactor safety through increased utilization of passive heat transport and safety systems. An innovative means of meeting this design goal is to use alkali metal heat pipes to cool the reactor under both normal and abnormal operating conditions. A heat pipe model has been added to the ARIANT thermalhydraulic code to enable reactor modeling and support the design and licensing of new reactors. Saturation fluid properties are a fundamental input to this model. Consequently, this article provides a comprehensive comparative overview of the best available sodium saturation property correlations developed over the past century. The results show most of the sodium property correlations needed to model a heat pipe are relatively well-defined and recommendations for their use can be provided.

Optimized core design and shield analysis of a medium temperature heat pipe cooled reactor

Medium Temperature heat pipe cooled Reactor (MTR) is a new reactor concept proposed by Li et al. in (2022). Low enriched uranium zirconium hydride fuel and mercury heat pipe are introduced in MTR. The unique advantages of MTR have been verified (Li et al., 2022) and it is considered as a potential candidate for energy supply in decentralized markets. In this work, an optimized MTR core design is proposed with detailed neutronic analysis and evaluation on mercury heat pipe, reflector and control rod arrangement, further increasing the economic efficiency and mobility of MTR. Heat transfer limit of the improved heat pipe model is further increased, contributing to a great reduction on core volume. Reflector material and thickness are analyzed in detail for mass minimization. Core physics characteristics are analyzed for four control rod arrangement schemes. The control mechanism is further simplified with only 9 control rods involved in the normal regulation of the core. Core lifetime is far more than 10 years. High inherent safety of the core is ensured. Besides, preliminary design of the shielding system is also carried out. A shieling layer of 60 cm LiH and 20 cm Pb can reduce the total dose to less than 40 % of the design limits. The total mass of the optimized core is greatly reduced and its specific power is increased by 60 % compared with that of the previous design.

Experimental analysis of temperature and vapor core pressure for an annular heat pipe

The main contribution of this study is the effects of the operating conditions on the internal vapor pressure and temperature in an annular screen wick heat pipe, using distilled water as the working fluid. High-resolution pressure transducers, optical fiber distributed temperature sensors, and K-type thermocouples were employed to measure the internal and external temperatures as well as the local static pressures at different axial positions of the heat pipe. Temporal and frequency analysis using a one-dimensional continuous wavelet transform was performed on the differential pressure data to characterize flow behavior and infer the flow regime occurring within the heat pipe. The heat pipe was tested in multiple orientations with respect to the horizon (θ=0°, 45°, and 90°), heat loads (25, 50, and 75 W), and condenser coolant temperatures (Tw,in= 10 °C, 20 °C, and 30 °C). To estimate the vapor-phase flow friction factor for multiple Reynolds numbers, the Lockhart–Martinelli correlation was employed. This study provides critical experimental data and analyses for complex two-phase flow behavior in an annular wick heat pipe geometry. The thermal resistance and effective thermal conductivity were estimated as a function of the heat pipe orientation and power input. The experimental investigation revealed that power input and orientation influence both the internal vapor core and external surface temperatures, as well as the local pressure response. The outcomes from this study provide a valuable database that supports the advancement of heat pipe design, modeling, and validation.

State-space model construction and dynamic analysis for a space thermionic nuclear reactor

The space nuclear reactor (SNR) is an important energy pattern for spacecrafts due to its high power density, long life and stabilization. A linear dynamic model is necessary to analyze the dynamics and design the appropriate control system analytically. A simplified nonlinear model based on conservation equations including point reactor kinetics model, thermal-hydraulic model, coolant model and heat pipe and radiator model was constructed. The state-space linear model was derived using perturbation theory. To verify the linear model, comprehensive comparisons were made in both time domain and frequency domain. The dynamic characteristics with respect to reactor power and reactivity were obtained in frequency and time domains. It is concluded that the reactor is an unstable system with a large time delay and strong nonlinearity at different power levels. This study provides solid foundation for future control system design.

Capillary limit of a sodium screen-wick heat pipe

High-temperature alkali-metal heat pipes are passive heat transfer devices, where the capillary pressure created by the menisci in the wick pumps the condensed fluid back to the evaporator. Thus, the heat pipe heat transfer capacity is limited by the maximum capillary pressure at high heat fluxes. This work presents a two-dimensional heat and mass transfer model for alkali metal heat pipes. In addition to the traditional wall heat conduction model, the model also incorporates gas–liquid flow heat transfer and capillary structure models, enabling the model to simulate both steady-state operation and transient capillary limit processes. The predictions of the model agreed well with experimental data. The predicted critical heat flux temperature has an error of less than 20℃ and a relative error of 6%. The predicted transient sequences are consistent with the measurements. The model shows that capillary limit is affected by inclination angle, heat flux, and wick structure. For inclinations, the critical heat flux at the capillary limit is linearly related to the inclination angle with the predicted temperature rising 2–10℃/s during the early stage of the capillary limit critical heat flux condition. The evaporator temperature oscillates before the capillary limit with positive inclinations. For heat fluxes, increasing the heat flux by 17% increases the temperature increase rate 10 fold with a longer dryout length. The evaporator exhibits hysteresis after the capillary limit due to partial dryout of evaporator. For wick structures, reducing the mesh screen pitch from 80 μm to 15 μm reduces the critical heat flux to 10% of the CHF at 80 μm. This model can accurately predict the heat pipe temperature variations at the capillary limit and can explain the physical mechanisms for the dryout oscillations and recovery hysteresis at the capillary limit. Thus, the measurements and model provide analytical guidelines for designing heat pipe cooling systems.

Multiphysics simulations of Self-Regulating performance of an optimized molten metal fuel microreactor design

Advanced microreactors are expected to play an indispensable role in reliable energy solutions for civilian/military applications in off-grid regions and space applications such as power supplies for Lunar and Mars bases. An innovative fast neutron spectrum heat pipe microreactor (HP-MR) concept was recently proposed with two unique features: molten U-Mn fuel and heat pipes as the heat removal mechanism. The microreactor was designed to be self-regulated, solely relying on reactivity feedbacks from fuel temperature. The reactor design has been further optimized to provide sufficient engineering safety margin and effective heat removal. In this study, the self-regulating performance of the optimized molten metal fuel microreactor was investigated by multiphysics simulations (neutronics, heat-transfer and heat pipe modeling) based on the MOOSE MultiApps system. The responses of the reactor to a series of transient scenarios were simulated to demonstrate the exceptional and inherent safety features of the novel microreactor concept.

Effect of filling ratio, number of loops, and transverse distance on the performance of pulsating heat pipe in a microchannel heat sink

In this study, three-dimensional modeling of a pulsating heat pipe is carried out, and the effect of physical and geometrical parameters such as filling ratio (FR), transverse distance (Z), and the number of loops (N) on its performance is investigated. In this study, it is assumed that the heat pipe is embedded in the microchannel heat sink, and its boundary condition is the thermal condition in the microchannel heat sink. The volume of fluid (VOF) multiphase flow model is used in the current numerical analysis. For the PHP, four different filling ratios (FR = 40, 50, 60, 70%), four transverse distances (Z = 2, 5, 8, 18 mm), and four numbers of loops (N = 1, 2, 3, 4) are considered, and the results will be compared with each other. It is shown that PHP with FR = 60% has the best performance. Also, comparing different values of transverse distance, Z = 18 mm has the lowest thermal resistance. The results show that by embedding a 4-loop PHP, the thermal resistance of MCHS decrease from 0.0268 to 0.0221 K/W, which indicates a 21.27% increase in the thermal performance of the microchannel heat sink compared to the basic design (without PHP).

Multi-physics coupled simulation on steady-state and transients of heat pipe cooled reactor system

With superior inherent safety and low maintenance demand, heat pipe cooled micro-reactor is a potential solution for decentralized remote electricity supply, as well as space power technology. Multi-physics coupled analysis is important to evaluate the inherent safety feature of micro-reactor. However, in the existing multi-physics coupling simulations, lumped parameter core heat transfer model and low-fidelity heat pipe model cannot accurately predict steady-state and transient safety margin of the reactor. In order to improve the simulation accuracy, a standalone two-dimensional transient high-temperature heat pipe analysis code was developed and validated. The heat pipe analysis code was coupled with the three-dimensional thermal conduction calculation of reactor core, as well as the point reactor kinetics, the alkali metal thermal-to-electric converter model and the heat pipe radiator model, to realize fully coupled analysis of reactor system. With the power distribution in the reactor core, the steady state, startup transient and single heat pipe failure accident were simulated based on the multi-physics coupling. The steady-state simulation results show that the heat flux of heat pipes shows significant non-uniformity in both circumferential and axial directions. The peak heat flux (120 kW/m2), with the twice value of averaged one (60 kW/m2), occurs on the heat pipes near the reactor edge rather than in the center. During reactor startup, the reactivity-insertion rate of 1.67e-3 $/s increases the transient peak heat flux to 260 kW/m2. The isothermal feature of heat pipes results in inverse heat transfer, i.e. from heat pipes to reactor structure, which improves the axial and radial reactor heat transfer and flattens the reactor temperature distribution. In the central heat pipe failure accident, more severe local temperature rise was observed in the core structure than that in the fuel pins. The peak heat flux location is shifted to the heat pipes adjacent to the failed heat pipe. Benefitted from the developed high-fidelity multi-physics coupling approach, the realistic transient phenomena in heat pipe cooled micro-reactor could be revealed.