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Printed circuit primary heat exchanger for power conversion in heat pipe microreactor applications

Here, in the present study, a model was developed for a recuperated air Brayton cycle for heat pipe microreactors, and the effect of the primary heat exchanger type assessed. An annular flow heat exchanger and a printed circuit heat exchanger (PCHE) were evaluated. A sub-sized diffusion bonded, PCHE test specimen was manufactured and tested with nitrogen as the working fluid to validate and improve the PCHE model. A comparison of the thermal cycle efficiency for the Brayton cycle coupled to a heat pipe microreactor using each of the two primary heat exchangers showed competitive performance for both options, with achievable cycle efficiencies of 34 % and 35 % for the annular and printed circuit heat exchangers, respectively. The impact of heat pipe length and additional reheating stages on cycle efficiency was studied. Increasing the heat pipe condenser length from 0.8 to 2.0 m resulted in an increase in cycle efficiency of 3.5 % and 3.2 % for the annular and printed circuit heat exchangers, respectively. The use of additional reheating stages showed a reduction in cycle efficiency since the heat pipe surface area limits the primary heat exchanger size and effectiveness. These results highlight the importance of the primary heat exchanger on the performance of a heat pipe microreactor. Overall, the cycle model, testing, and heat exchanger model showed the potential for the PCHE to improve the economics of a heat pipe microreactor relative to the annular flow heat exchanger, which also opens the possibility to use different heat transfer fluids such as supercritical CO 2 .

PCHE↗

Calculation of Friction Factors in Heat Pipes Using CFD in Support of the Sockeye Code

A heat pipe is two-phase heat transfer device which relies on surface tension and capillary pressure to provide a very efficient heat transfer mechanism. Currently, there is interest in designing micro nuclear power reactors using high temperature heat pipes to provide totally passive cooling. To support this, Sockeye is being developed as a heat pipe simulation capability. To support the development of Sockeye, individual phenomena must be tested. This work focuses on applying a CFD model to evaluate friction factors for use in Sockeye. A CFD model has been developed in Nek5000 which simulates each component fluid, i.e. sodium liquid and vapor, independently and captures the effects of the wick on friction factor. The model tests the effect of the wick permeability and the thickness of the wick occupied by each fluid component. The thickness of the wick occupied by each component can be directly related to the local vapor volume fraction from the Sockeye heat pipe model. Results from the CFD model indicate that friction factor in the liquid flow decreases with increasing wick permeability, while the friction factor in the vapor flow increases with increasing wick permeability. In the liquid, this is likely a direct result of the increased cross sectional area available for the flow. For the vapor, this is explained as the wick acting like a rough wall, while the increased area has only a negligible impact. Results for the tests of the thickness of the wick occupied by each fluid showed a thresholding behavior for both liquid and vapor. When the thickness of the wick occupied by each fluid was increased, it increased the effect of the wick, but only up to a certain point. Once a certain thickness was reached, the friction factors remained constant. When the fluid occupied only a very small fraction of the wick, friction factors returned to nominal values.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Multi-directional heat pipes

An apparatus includes a reactor core with one or more heat pipes passing through in an x-direction, one or more heat pipes passing through in a y-direction, and one or more heat pipes passing through in a z-direction. The one or more heat pipes passing through in the z-direction are pumped heat pipes.

Reid, Robert Stowers↗

Sockeye Heat Pipe Analysis Code Verification and Validation

Some of the most promising microreactor designs currently under development utilize heat pipe technology to transfer heat from the reactor core to the secondary side heat exchanger, due to the technology’s compactness, efficiency, passivity, and reliability. Sockeye is an engineering-scale heat pipe tool developed under the Nuclear Energy Advanced Modeling and Simulation Program to be used for the design and safety analysis of microreactors. Sockeye’s core capability lies in a 1D, two-phase, compressible flow model, used to simulate the working fluid inside the heat pipe. Sockeye is built on the Multiphysics Object-Oriented Simulation Environment framework, which allows for seamless multiphysics coupling with other Nuclear Energy Advanced Modeling and Simulation tools and can thus be used in a full-scale simulation of a microreactor assembly, which can include hundreds of heat pipes. This paper presents some initial verification and validation assessments performed for Sockeye. We demonstrate good agreement between Sockeye’s numerical results and steady-state analytic solutions for velocity and pressure drop, with differences attributable to the underlying assumptions made by the analytic solutions. We also show that Sockeye reproduces analytic predictions of key operational limits, such as the capillary limit and the sonic limit. Finally, we compare Sockeye results to experimental data for the SAFE-30 heat pipe module test.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Effects of Heat Pipe Failures in Microreactors

Microreactors provide new opportunities for nuclear reactor applications given their long-lived fuel source, compact size, portability, reliability as it relates to safety and their self-regulating nature. To take advantage of these opportunities there are technological challenges that need to be overcome. One advancing technology often used in conjunction with microreactor designs are heat pipes, which are used for heat removal from the reactor core to the power conversion system. Heat pipes are a substitute for the traditional system in which the same fluid used as coolant in the reactor is then used as the working fluid in the power conversion system. This document describes how heat pipes operate, what happens when a heat pipe fails, and what codes can be used to simulate the results. Our analyses show that a single/double heat pipe failure results in a temperature increase of 15-50°C respectively in surrounding heat pipes. Heat pipe microreactors could be easily designed such that this increase is within the maximum parameters allowable for safety and does not result in cascading heat pipe failure. Thus, such failures do not lead to severe degradation of the reactor.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Heat Pipe Cooled Microreactors

Microreactor technologies are required to provide reliable carbon-free power generation in remote applications. The heat pipe cooled microreactor concept in particular offers notable advantages due to the passive operation of heat pipes enabling increased reliability and simplicity in a more compact form factor. There is a significant need for experimental work to aid and expedite the deployment of heat pipe microreactors due to their unique technological characteristics. Thus, there has been increased interest in heat pipe experiments by numerous institutions in order to support these efforts. The present work is a comprehensive review of heat pipe experiments, describing instrumentation, methods, phenomena of interest, and recent developments. In addition, legacy work on the operation of high-temperature heat pipes under irradiation is reviewed and discussed. Furthermore, the verification and validation efforts for the flagship heat pipe simulation code Sockeye are reviewed and requirements for future experiments are outlined. Lastly, future directions are proposed for heat pipe experimentation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The Monolithic Heat Pipe Microreactor Reference Plant Model

This work introduces a reference plant model for a generic monolithic heat-pipe-cooled microreactor. The model will serve as a springboard to develop future evaluation models in the licensing process of similar microreactor designs at the U.S. Nuclear Regulatory Commission. This model has been developed with the Comprehensive Reactor Analysis Bundle and its specifications are based on open literature publications for the eVinci TM design. BlueCRAB is the U.S. Nu- clear Regulatory Commission non-light-water reactor analysis system based on the Multiphysics Object-Oriented Simulation Environment framework, which can couple the Griffin, BISON, and Sockeye applications to resolve the various physics that are essential for the safety analysis of this type of reactor system. The core specifications includes tristructural isotropic fuel, graphite monolith, graphite reflectors, and drums composed of graphite and B 4 C. No moderator or burnable poison pins are used in the design. The fuel enrichment is reduced to control excess reactivity in the core. This core design is not optimized and only serves for testing purposes, since the primary objective of this work is to exercise the multiphysics coupling for this type of reactor system. A three dimensional (3D) core heterogeneous Griffin discrete ordinates (SN) transport model allows the precise calculation of the flux distribution and pin powers. Griffin transfers the power density distribution and obtains a temperature distribution to and from BISON. The BISON model com- putes the 3D core temperature distribution and is coupled to 876 Sockeye subapplications running a heat pipe model. This 3D conduction model is coupled to the various heat pipes via heat flux boundary conditions. The model includes a small gap between the heat pipe and the monolith. Convective heat transfer boundaries with either ambient temperature or condenser temperature as heat sinks are imposed at the model boundaries. The 2D Sockeye heat pipe model uses a vapor- only methodology, which provides the needed resolution for transient calculations and allows the determination of various heat pipe limits. This approach is superior to the superconductor model traditionally used in steady-state calculations. BlueCRAB computes steady-state power and temperature distributions that serve as the initial condition for a loss-of-heat-sink transient simulation. The steady-state results show significant peaking due to the position of the control drum, but this is a characteristic of the particular design used, which is not optimized at this stage. The transient results show the reactor power slowly stabilizing towards a 3% power level after the partial loss of secondary heat removal. Several recriticalities are observed due to cooling through the secondary system but the reactor is self-stabilizing and behaves as expected.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

CODE-TO-CODE BENCHMARK STUDY FOR THERMAL STRESS MODELING AND PRELIMINARY ANALYSIS OF THE HIGH-TEMPERATURE SINGLE HEAT PIPE EXPERIMENT

Microreactors are very small nuclear reactors with typical thermal-energy output of up to 20 MWth. The microreactor concept is gaining more and more attention for safe, robust, and reliable supply of electricity for remote locations and to meet industrial process heat needs. Heat-pipe-cooled microreactor is one of the microreactors being investigated at Idaho National Laboratory. In the heat-pipe-cooled microreactor, heat pipes remove heat from the reactor core as a passive heat-transfer device, so the fluid circulation is not required for cooling, which can substantially simplify the overall reactor design. However, given the extremely high temperatures in the core region and potentially large temperature gradients across the structure materials, thermal stresses need to be well-analyzed to ensure structural integrity during normal operations and accident scenarios for the heat-pipe-cooled microreactor designs. This paper discusses finite element method-based thermal-stress analysis for the high-temperature single heat-pipe test article in the Single Primary Heat Extraction and Removal Emulator (SPHERE) facility at Idaho National Laboratory, using two commercial software packages, Abaqus and STAR-CCM+. A code-to-code benchmark study was performed to crosscheck the model setup and capability of each code and to gain insights into the potential thermal stress concerns from the current experimental setup. It is observed the significant thermal stresses happen at the locations where the largest temperature gradients appeared between heat pipe and electric heater. The temperature fields have good agreements between Abaqus and STAR-CCM+, while the induced thermal stresses show modest deviations probably due to differences of meshing engines used in these two codes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Study of the heat pipe vapor flow using the MOOSE application Sockeye and the CFD code Nek5000

Heat pipes are efficient heat transfer devices used in various applications, including nuclear microreactors. Heat pipe-cooled microreactors offer advantages in size and cost, which can significantly accelerate their deployment and adoption. Developing accurate models of heat pipes is crucial for a heat pipe-cooled microreactor design and operation. In this work a verification and validation of the heat pipe application Sockeye is presented. Results are compared against RANS simulations, performed with the code Nek5000, and the SPHERE experiment, conducted at INL.

42 ENGINEERING↗

Method to fill heat pipe arrays

A fill tool system that fills, seals, and inspects a heat pipe array, which includes one or more heat pipes with heat pipe working fluid.

Reid, Robert S.↗

HePHAESTUS: Heat Pipe Heterogeneous Approximation of Energy and Navier-Stokes Equations, Transience, and Non-Uniform Surface Heating [Slides]

A heat pipe is a liquid/vapor filled metal pipe capable of transporting large amounts of heat through evaporation of a liquid at one end and condensation of vapor at the other end creating a closed fluid loop. Heat pipes are widely used in the cooling of electronics and in space applications. Heat pipes are typically composed of a pipe wall, a wick material, a working fluid, and a central vapor channel. Heat is transferred into the working fluid at the “evaporator” end, through an adiabatic section, and heat is removed at the opposite end at the “condenser.” If no wick is used, gravitational acceleration can circulate the fluid due to the buoyancy of the vapor in the central core and a falling film of liquid at the pipe wall forming a “thermosyphon."

42 ENGINEERING↗

AN INITIAL LOOK AT THE HEAT PIPE RESILIENCY TO REACTOR OPERATION

Several special purpose reactor designs are aiming to utilize heat pipes due to its inherently passive features allowing safe heat removal to the power conversion systems. There is insufficient data on heat pipe survivability in reactor environments, although heat-pipe failures are predicted to have low failure rates. In this paper, we perform a coupled neutronics and thermo-mechanics analyses for a 45 kWth HALEU fueled, hydride moderated homogenous design to evaluate the transient effects during both startup and a heatpipe-failure scenario. The heatpipe-failure study includes both a single failure case and a failure-propagation (cascading) case. While the model only evaluates a homogenous core, the approach could be applied to more complex models for any heat pipe cooled small reactor.

99 GENERAL AND MISCELLANEOUS↗

Recent Developments and Findings of Heat Pipe Experiments for Microreactor Applications

Microreactor technologies are required to provide reliable carbon-free power generation in remote applications. The heat pipe–cooled microreactor concept, in particular, offers notable advantages due to the passive operation of heat pipes, enabling increased reliability and simplicity in a more compact form factor. There is a significant need for experimental work to aid and expedite the deployment of heat pipe microreactors due to their unique technological characteristics. Thus, there has been increased interest in heat pipe experiments by numerous institutions in order to support these efforts. Finally, the present work is a comprehensive review of recent heat pipe experiments from six major institutions, describing their designs, instruments, methods, and results. In addition, this paper also presents a background on heat pipe experiments along with discussions on instrumentation, accident scenarios, wick enhancement, and proposed future directions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Modeling Heat Pipes with Non-Condensable Gases

The report showcases advancements in modeling heat pipes, considering both scenarios with and without non-condensable gases. To achieve this, two distinct modeling approaches are juxtaposed. Firstly, the effective conduction model, implemented in the MOOSE-based code Sockeye, is employed. Secondly, a first-of-a-kind two-phase Euler-Euler Computational Fluid Dynamics (CFD) model is developed using the STAR-CCM+ code. Both models undergo validation against experimental data, acknowledging the inherent uncertainties associated with each modeling assumption. Interestingly, the non-tuned CFD model surpasses the performance of the calibrated conduction model for heat pipes operating under both conditions: with and without non-condensable gases. It's worth noting, however, that the CFD models entail significantly longer runtimes compared to the conduction models. Nevertheless, the insights garnered from the CFD model shed invaluable light on the intricate operational dynamics of heat pipes. Future work involves broadening the validation scope of these models and continuing their development to enhance their utility as robust tools for heat pipe design and operational support.

42 ENGINEERING↗

Test Article and Test Plan for Heat-Pipe Gap-Conductance Testing

The SPHERE Facility at INL is established to test phenomena related to heat pipes in nuclear applications. The current capability of the SPHERE testbed is operation of liquid alkali-metal-cooled heat pipes in a variety of atmospheres. The controlled atmosphere can be used to prevent oxidation of system parts and also to affect the thermal conductivity of gases for any interfacial gaps within the heat-pipe assembly. Currently available modes are vacuum, air, nitrogen, helium, and argon. Controlled mixtures of helium and argon are available to vary the thermal conductivity of the gas. The primary test article will be based on the existing 7-hole block design used for shakedown testing of the SPHERE Facility. The SPHERE test stand will be used with test articles to establish the conductivity between fuel elements as well as between the heat pipe and other layers of the fuel-rod assembly. Existing and new test blocks will be used and modified with additional instrumentation to establish the thermal conductivity between the gap of the block wall and the heat pipes.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Design optimization of gap distance for the capillary limitation of a heat pipe with annular-type wick structure

In this study, an experimental investigation was conducted on the rising height and contact angle of fluid in an annular wick-type heat pipe. The annular wick-type heat pipe was characterized by a small gap between the wick structure and tube wall, which compensated for the pressure drop along the porous media and created additional capillary force. To describe and model the advantage of this gap, the rising of a wetting liquid in the gap between a vertical solid plate and a mesh (with a small angle between them) was experimentally measured and analyzed. An additional experiment was performed to investigate the effect of curvature on the capillary rise using tubes and meshes of varying radii. Resultantly, we confirmed that the linear combination of the contact angles of the solid plate and mesh could be applied to calculate the rising height from the Laplace–Young equation. Furthermore, the effect of curvature on the rising height of the liquid was negligible. These results were extended to the investigation of finding the optimal gap distance for the annular wick-type heat pipe by referring to previous studies. We observed that a gap distance of 1.27 mm provided the largest permeability (K) over the effective pore radius (r eff ) value for a heat pipe with ethanol, which in turn resulted in the highest capillary limitation. For a sodium heat pipe, a gap distance of 0.84 mm resulted in the highest capillary limitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Experimental study on the startup of the annular wick type heat pipe using fiber optical temperature measurement technique

This study used optical fiber-distributed temperature sensors to measure the internal and external temperature distributions of a water-cooled heat pipe. The sensor technology used in this study is fiber optical distributed temperature sensing, a distributed sensing technique based on the naturally occurring Rayleigh backscatter in optical fibers. This measurement technique provides maximum spatial resolution for static and semi-static applications. Using this sensor, the temperature distribution of the heat pipe's internal, external, vapor core, and the wick was measured with a spatial resolution of 0.65 mm, a sampling frequency of 40 Hz, and a temperature resolution of 0.1 °C. Through the measured temperature distribution database, the starting phenomenon, the effective length trend, and the limitation onset were observed. From the results, it is found that a high-temperature peak appears at the evaporator if a high initial power (75 W) is imposed on the heat pipe, even after the heat pipe approaches the normal operating status. The peak is not observed in a slower startup (30 W initial power then slowly increased to 75 W). It is also found that the temperature distributions and effective condenser length of the heat pipe highly depend on the cooling conditions. There are variations in the temperature according to the radial direction of the horizontal heat pipe due to gravity. In conclusion, lead and lag of the temperature evolution were observed at the onset of the operating limitations.

42 ENGINEERING↗

Investigations of Advanced Measurement Methods for High-Temperature Heat-Pipe Experiments

Various types of microreactor designs are under consideration, and among those, the heat-pipe cooled reactor designs are currently being actively investigated at Idaho National Laboratory (INL). In order to support non-nuclear testing and demonstration of technology under the Department of Energy (DOE) Microreactor Program (MRP), Single Primary Heat Extraction and Removal Emulator (SPHERE) was designed and constructed to perform high-temperature heat pipe (HP) experiments at INL. Based on the SPHERE experimental setup, this summary paper conducts the preliminary investigations among the available literature and summarizes some potential advanced measurement techniques for operando high-temperature heat pipe which can be implemented to support MRP. The primary objective for the extensive literature research is to investigate the possibilities and feasibilities for designing and construct an advanced experimental test facility with the aim of producing high-fidelity high-resolution heat pipe data during its operations.

42 ENGINEERING↗