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DOE OSTI2015

Xyce Parallel Electronic Simulator Users Guide Version 6.4

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been de- signed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel com- puting platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. Trademarks The information herein is subject to change without notice. Copyright c 2002-2015 Sandia Corporation. All rights reserved. Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Portions of the Xyce TM code are: Copyright c 2002, The Regents of the University of California. Produced at the Lawrence Livermore National Laboratory. Written by Alan Hindmarsh, Allan Taylor, Radu Serban. UCRL-CODE-2002-59 All rights reserved. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. Xyce 's expression library is based on that inside Spice 3F5 developed by the EECS Department at the University of California. The EKV3 MOSFET model was developed by the EKV Team of the Electronics Laboratory-TUC of the Technical University of Crete. All other trademarks are property of their respective owners. Contacts Bug Reports (Sandia only) http://joseki.sandia.gov/bugzilla http://charleston.sandia.gov/bugzilla World Wide Web http://xyce.sandia.gov http://charleston.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Xyce Parallel Electronic Simulator Reference Guide Version 6.4

This document is a reference guide to the Xyce Parallel Electronic Simulator, and is a companion document to the Xyce Users' Guide [1] . The focus of this document is (to the extent possible) exhaustively list device parameters, solver options, parser options, and other usage details of Xyce . This document is not intended to be a tutorial. Users who are new to circuit simulation are better served by the Xyce Users' Guide [1] . Trademarks The information herein is subject to change without notice. Copyright c 2002-2015 Sandia Corporation. All rights reserved. Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Portions of the Xyce TM code are: Copyright c 2002, The Regents of the University of California. Produced at the Lawrence Livermore National Laboratory. Written by Alan Hindmarsh, Allan Taylor, Radu Serban. UCRL-CODE-2002-59 All rights reserved. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. Xyce 's expression library is based on that inside Spice 3F5 developed by the EECS Department at the University of California. The EKV3 MOSFET model was developed by the EKV Team of the Electronics Laboratory-TUC of the Technical University of Crete. All other trademarks are property of their respective owners. Contacts Bug Reports (Sandia only) http://joseki.sandia.gov/bugzilla http://charleston.sandia.gov/bugzilla World Wide Web http://xyce.sandia.gov http://charleston.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Xyce Parallel Electronic Simulator Reference Guide Version 6.6.

This document is a reference guide to the Xyce Parallel Electronic Simulator, and is a companion document to the Xyce Users' Guide [1] . The focus of this document is (to the extent possible) exhaustively list device parameters, solver options, parser options, and other usage details of Xyce . This document is not intended to be a tutorial. Users who are new to circuit simulation are better served by the Xyce Users' Guide [1] . The information herein is subject to change without notice. Copyright c 2002-2016 Sandia Corporation. All rights reserved. Acknowledgements The BSIM Group at the University of California, Berkeley developed the BSIM3, BSIM4, BSIM6, BSIM-CMG and BSIM-SOI models. The BSIM3 is Copyright c 1999, Regents of the University of California. The BSIM4 is Copyright c 2006, Regents of the University of California. The BSIM6 is Copyright c 2015, Regents of the University of California. The BSIM-CMG is Copyright c 2012 and 2016, Regents of the University of California. The BSIM-SOI is Copyright c 1990, Regents of the University of California. All rights reserved. The Mextram model has been developed by NXP Semiconductors until 2007, Delft University of Technology from 2007 to 2014, and Auburn University since April 2015. Copyrights c of Mextram are with Delft University of Technology, NXP Semiconductors and Auburn University. The MIT VS Model Research Group developed the MIT Virtual Source (MVS) model. Copyright c 2013 Massachusetts Institute of Technology (MIT). The EKV3 MOSFET model was developed by the EKV Team of the Electronics Laboratory-TUC of the Technical University of Crete. Trademarks Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. All other trademarks are property of their respective owners. Contacts World Wide Web http://xyce.sandia.gov https://info.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only) Bug Reports (Sandia only) http://joseki-vm.sandia.gov/bugzilla http://morannon.sandia.gov/bugzilla

47 OTHER INSTRUMENTATION↗

DOE OSTI2016

Xyce Parallel Electronic Simulator Users' Guide Version 6.6.

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been de- signed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel com- puting platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. The information herein is subject to change without notice. Copyright c 2002-2016 Sandia Corporation. All rights reserved. Acknowledgements The BSIM Group at the University of California, Berkeley developed the BSIM3, BSIM4, BSIM6, BSIM-CMG and BSIM-SOI models. The BSIM3 is Copyright c 1999, Regents of the University of California. The BSIM4 is Copyright c 2006, Regents of the University of California. The BSIM6 is Copyright c 2015, Regents of the University of California. The BSIM-CMG is Copyright c 2012 and 2016, Regents of the University of California. The BSIM-SOI is Copyright c 1990, Regents of the University of California. All rights reserved. The Mextram model has been developed by NXP Semiconductors until 2007, Delft University of Technology from 2007 to 2014, and Auburn University since April 2015. Copyrights c of Mextram are with Delft University of Technology, NXP Semiconductors and Auburn University. The MIT VS Model Research Group developed the MIT Virtual Source (MVS) model. Copyright c 2013 Massachusetts Institute of Technology (MIT). The EKV3 MOSFET model was developed by the EKV Team of the Electronics Laboratory-TUC of the Technical University of Crete. Trademarks Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. All other trademarks are property of their respective owners. Contacts World Wide Web http://xyce.sandia.gov https://info.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only) Bug Reports (Sandia only) http://joseki-vm.sandia.gov/bugzilla http://morannon.sandia.gov/bugzilla

47 OTHER INSTRUMENTATION↗

DOE OSTI2017

Xyce Parallel Electronic Simulator Reference Guide Version 6.7.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Xyce Parallel Electronic Simulator Users' Guide Version 6.7.

This manual describes the use of the Xyce Parallel Electronic Simulator. Xyce has been designed as a SPICE-compatible, high-performance analog circuit simulator, and has been written to support the simulation needs of the Sandia National Laboratories electrical designers. This development has focused on improving capability over the current state-of-the-art in the following areas: Capability to solve extremely large circuit problems by supporting large-scale parallel com- puting platforms (up to thousands of processors). This includes support for most popular parallel and serial computers. A differential-algebraic-equation (DAE) formulation, which better isolates the device model package from solver algorithms. This allows one to develop new types of analysis without requiring the implementation of analysis-specific device models. Device models that are specifically tailored to meet Sandia's needs, including some radiation- aware devices (for Sandia users only). Object-oriented code design and implementation using modern coding practices. Xyce is a parallel code in the most general sense of the phrase -- a message passing parallel implementation -- which allows it to run efficiently a wide range of computing platforms. These include serial, shared-memory and distributed-memory parallel platforms. Attention has been paid to the specific nature of circuit-simulation problems to ensure that optimal parallel efficiency is achieved as the number of processors grows. The information herein is subject to change without notice. Copyright c 2002-2017 Sandia Corporation. All rights reserved. Trademarks Xyce TM Electronic Simulator and Xyce TM are trademarks of Sandia Corporation. Orcad, Orcad Capture, PSpice and Probe are registered trademarks of Cadence Design Systems, Inc. Microsoft, Windows and Windows 7 are registered trademarks of Microsoft Corporation. Medici, DaVinci and Taurus are registered trademarks of Synopsys Corporation. Amtec and TecPlot are trademarks of Amtec Engineering, Inc. All other trademarks are property of their respective owners. Contacts World Wide Web http://xyce.sandia.gov https://info.sandia.gov/xyce (Sandia only) Email xyce@sandia.gov (outside Sandia) xyce-sandia@sandia.gov (Sandia only) Bug Reports (Sandia only) http://joseki-vm.sandia.gov/bugzilla http://morannon.sandia.gov/bugzilla

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

A Cost-Performance Analysis of a Sodium Heat Engine for Distributed Concentrating Solar Power

We present that a sodium thermal electrochemical converter (Na-TEC) generates electricity directly from heat through isothermal expansion of sodium ions across a beta"-alumina solid-electrolyte. This heat engine has been considered for use with conventional concentrating solar power (CSP) systems before. However, unlike previous single-stage devices, the improved design uses two stages with an interstage reheat, allowing more economical and efficient conversion up to 29% at a hot side temperature of 850 °C. Herein, a cost-performance analysis for this improved design assesses opportunities for distributed-CSP in the context of micro-combined heat and power systems. A high-level techno-economic analysis (TEA) is presented that explores four scenarios where a Na-TEC is used as the heat engine for a distributed-CSP system. Overnight capital cost and levelized cost of electricity (LCOE) are estimated for a system lifetime of 30 years, revealing that overnight capital costs in a range from $3.57 to $17.71 per W e are feasible, which equate to LCOEs from 6.9 to 17.2 cents kWh e -1 . This analysis makes a significant contribution by concurrently quantifying the efficiency and unit costs for a range of multistage configurations, and demonstrating that a Na-TEC may be a promising alternative to Stirling engines for distributed-CSP systems at residential scale of 1–5 kW e .

14 SOLAR ENERGY↗

DOE OSTI2018

Thermal modeling and efficiency of a dual-stage sodium heat engine

In this paper, a thermal design of an axisymmetric dual-stage sodium thermal electrochemical converter (Na-TEC) is presented, where a reduced-order finite-element model is used in conjunction with a Na-TEC thermodynamic model to determine the total parasitic heat loss of this dual-stage design. A number of simplifications are applied in the reduced-order model to decrease the computational time while maintaining acceptable accuracy. These include the use of effective thermal conductivities to account for complex corrugated geometries and apparent surface emissivities to accommodate the effect of radiation shields. Furthermore, a simplified analytical model is developed to account for conduction bypass through the Na-TEC liquid-return path. An iterative procedure between the finite-element and thermodynamic models is described in detail, and the thermal performance of the design proposed herein is analyzed. According to this analysis, a maximum efficiency of 29% and a maximum power output of 125 W can be achieved.

14 SOLAR ENERGY↗

DOE OSTI2017

A dual-stage sodium thermal electrochemical converter (Na-TEC)

We report that the sodium thermal electrochemical converter (Na-TEC) is a heat engine that generates electricity through the isothermal expansion of sodium ions. The Na-TEC is a closed system that can theoretically achieve conversion efficiencies above 45% when operating between thermal reservoirs at 1150 K and 550 K. However, thermal designs have confined previous single-stage devices to thermal efficiencies below 20%. To mitigate some of these limitations, we consider dividing the isothermal expansion into two stages; one at the evaporator temperature (1150 K) and another at an intermediate temperature (650 K–1050 K). This dual-stage Na-TEC takes advantage of regeneration and reheating, and could be amenable to better thermal management. Herein, we demonstrate how the dual-stage device can improve the efficiency by up to 8% points over the best performing single-stage device. We also establish an application regime map for the single- and dual-stage Na-TEC in terms of the power density and the total thermal parasitic loss. Generally, a single-stage Na-TEC should be used for applications requiring high power densities, whereas a dual-stage Na-TEC should be used for applications requiring high efficiency.

14 SOLAR ENERGY↗

DOE OSTI2020

Sodium Ion Expansion Power Block for Distributed CSP

The Sodium Ion Expansion Power Block for Distributed CSP was a three-plus-one-year effort under the Concentrating Solar Power: Advanced Projects Offering Low LCOE Opportunities (CSP: APOLLO) funding program within the U.S. Department of Energy Solar Energy Technologies Office. The primary objective of this project is to develop a dual-stage modular sodium thermal electrochemical converter (Na-TEC) heat engine power block, which can be potentially integrated with either a small-scale dish solar or large-scale heliostats and parabolic trough CSP. Na-TEC is a heat engine that generates electricity through the isothermal expansion of sodium ions. The Na-TEC is a closed system that can theoretically achieve conversion efficiencies above 45% when operating between thermal reservoirs at 1150 K and 550 K. However, thermal designs have confined previous single-stage devices to thermal efficiencies below 20%. To mitigate some of these limitations, we consider dividing the isothermal expansion into two stages; one at the evaporator temperature (1150 K) and another at an intermediate temperature (650 K –1050 K). This dual-stage Na-TEC takes advantage of regeneration and reheating, and could be amenable to better thermal management. In light of this, we first designed and developed a thermo-electrochemical model, and thermodynamically demonstrated how the dual-stage device can improve the efficiency by up to 8% points over the best performing single-stage device. We also established an application regime map for the single- and dual-stage Na-TEC in terms of the power density and the total thermal parasitic loss. Moreover, a thermal design of an axisymmetric dual-stage Na-TEC is developed to guide the scale-up and fabrication of sub-components of prototype module. A reduced-order finite-element model is used in conjunction with a Na-TEC thermodynamic model that was developed to determine the total parasitic heat loss of this dual-stage design. A number of simplifications are applied in the reduced-order model to decrease the computational time while maintaining acceptable accuracy. According to this analysis, a maximum efficiency of 29% and a maximum power output of 125 W can be achieved. Ultimately, we were able to demonstrate thermal efficiency improvements of the Na-TEC heat engine from 19% up to 40.3%, in a dual-stage (non-optimized) prototype module that we designed, fabricated, and tested with high temperature stage at 923 K. Furthermore, a cost-performance analysis for this improved dual-stage design was carried out for distributed-CSP systems. A high-level techno-economic analysis (TEA) explores four scenarios where a Na-TEC is used as the heat engine for a distributed-CSP system. Overnight capital cost and levelized cost of electricity (LCOE) are estimated for a system lifetime of 30 years, revealing that overnight capital costs in a range from $3.57 to $17.71 per We are feasible, which equate to LCOEs from 6.9 to 17.2 cents/kWh e -1 . This analysis makes a significant contribution by concurrently quantifying the efficiency and unit costs for a range of multistage configurations, and demonstrating that a Na-TEC may be a promising alternative to Stirling engines for distributed-CSP systems at residential scale of 1–5 kW e .

14 SOLAR ENERGY↗

DOE OSTI2016

Thermodynamics of a Dual Stage Sodium Thermo-Electro-Chemical Converter

The need for reliable and distributable energy is evident, but one prominent obstacle is the lack of an efficient direct heat-to-electricity converter. The sodium thermo-electro-chemical converter (Na-TECC) is a highly efficient thermally regenerative electrochemical system (TRES) that can fill this void. This electrochemical technology uses an ion-selective solid-electrolyte called beta-alumina that is highly conductive to sodium cations. The Na-TECC generates electric power by allowing high pressure sodium cations to expand isothermally through the solid-electrolyte. Theoretically, a device interacting with thermal reservoirs at 1150 K and 550 K should operate above 45% efficiency, but actual devices have not surpassed efficiencies of 20%. The maximum potential voltage in these previous devices was substantially reduced by the kinetic limitations of the charge transfer in the cathode (referred to as the overpotential) and by Joule heating losses due to the solid-electrolyte resistance, electrode resistance, and current collector resistance. To overcome this discrepancy, a dual stage conversion process is being proposed. Rather than using one isothermal expansion step, the dual cycle will employ two separate electrolytes to allow two separate expansion steps: one at the high temperature, and another at an intermediate temperature. This new cycle is thermodynamically favorable as it allows for regeneration from the isobaric cooling of the first expansion step, and reheat to complete the expansion in the second step. This allows the engine to reach a lower condenser temperature than its single stage counterpart for a given heat input, resulting in an increased overall efficiency. The temperature drop across each electrolyte in the dual stage device (e.g., ~ 400 K) is smaller than the temperature drop across a comparable single stage device (e.g., ~ 800 K). This makes the device amenable to better thermal management and allows for less heat loss. Also, the intermediate stage will mitigate the thermal shock across the very thin (< 1 mm) solid electrolyte, reduce crack propagation, limit the percolation of the molten dendrites, and ultimately increase the lifetime of the device. A dual stage concept for the Na-TECC has never been demonstrated in literature, so it is necessary to properly re-define the thermodynamic parameters such as heat loss, maximum power, and optimal current density. Certain drawbacks from a dual stage concept will also be addressed, such as the need for larger electrochemical area and the increased pressure losses. It will be demonstrated that the dual stage device must have lower thermal losses than a single stage device if it is to have a higher efficiency. The improved operation of the Na-TECC can have a transformational effect on small combined heat and power (CHP) systems at the 1-5 kW range.

14 SOLAR ENERGY↗

DOE OSTI2017

Dual Stage Sodium Thermo-Electro-Chemical Converter (Na-TEC)

The need for reliable and distributable energy is evident, but one prominent obstacle is the lack of an efficient direct heat-to-electricity converter. The sodium thermo-electro-chemical converter (Na-TECC) is a highly efficient thermally regenerative electrochemical system (TRES) that can fill this void. This device uses an ion-selective solid-electrolyte called beta”-alumina that is highly conductive to sodium cations. The Na-TECC generates electric power by allowing high pressure sodium cations to expand isothermally through the solid-electrolyte. Theoretically, a device interacting with thermal reservoirs at 1150 K and 550 K should operate above 45% efficiency, but actual devices have not surpassed efficiencies of 20%. The maximum potential voltage in these previous devices was substantially reduced by the kinetic limitations of the charge transfer in the cathode, by pressure losses through the porous electrodes, and by Joule heating losses caused by the solid-electrolyte, electrode, and current collector resistances. To overcome these low efficiencies, a dual stage conversion process is being proposed. Rather than using one isothermal expansion step, the dual cycle will employ a second electrolyte to allow two separate expansion steps: one at the high temperature, and another at an intermediate temperature. This new cycle is thermodynamically favorable as it allows for regeneration from the isobaric cooling of the first expansion step, and reheat to complete the expansion in the second step. This allows the engine to reach a lower condenser temperature than its single stage counterpart for a given heat input, resulting in an increased overall efficiency. The temperature drop across each electrolyte in the dual stage device (e.g., ~ 400 K) is smaller than the temperature drop across a comparable single stage device (e.g., ~ 600 K). This makes the device amenable to better thermal management and allows for less heat loss. Also, the intermediate stage will mitigate the thermal shock across the very thin (< 1 mm) solid electrolyte, reduce crack propagation, limit the percolation of the molten dendrites, and ultimately increase the lifetime of the device. A dual stage concept for the Na-TECC has never been demonstrated in literature, so it is necessary to properly re-define the thermodynamic parameters such as heat loss, maximum power, and optimal current density. Certain drawbacks from a dual stage concept will also be addressed, such as the need for larger electrochemical area and the increased pressure losses. It will be demonstrated that the dual stage device must have lower thermal losses than a single stage device if it is to have a higher efficiency. The improved operation of the Na-TECC can have a transformational effect on small combined heat and power (CHP) systems at the 1-5 kW range.

14 SOLAR ENERGY↗

DOE OSTI2017

Thermal Modeling of a Dual-Stage Sodium Thermal-Electrochemical Converter (Na-TEC)

The sodium thermal electrochemical converter (Na-TEC) is a heat engine that generates electricity through the isothermal expansion of sodium ions through a beta”-alumina solid-electrolyte. The Na-TEC is a closed system that can theoretically achieve conversion efficiencies above 45% when operating between thermal reservoirs at 1150 K and 550 K. However, thermal designs have confined previous single-stage devices to thermal efficiencies below 20%. To mitigate some of these limitations, we consider dividing the isothermal expansion into two stages; one at the evaporator temperature (1150 K) and another at an intermediate temperature (550 K – 950 K). This dual-stage Na-TEC takes advantage of regeneration and reheating, and could be amenable to better thermal management through a reduction of parasitic losses. These losses are comprised of (i) the heat input that does not participate in power production but simply bypasses the thermo-electrochemical process and is transferred to the condenser, and (ii) heat that is lost from the device directly to the surroundings due to poor insulation. Heat loss to the surroundings occurs from a lower average hot-side temperature given that a fraction of the power conversion occurs at an intermediate stage. Also, the condenser now directly interacts with the lower temperature of the intermediate stage, thereby reducing radiation loss. A simplified geometry is developed for this device to help guide its design from a heat transfer perspective. All thermal contact and boundary conditions are discussed, including the evaporation and condensation of sodium vapor, thermal leakage through the housing, and the thermal contact between the beta”-alumina and the housing. A ray tracing method assuming gray, diffuse surfaces is used to account for the internal radiation heat transfer within the device. Liquid sodium flows in a capillary wick between the condenser and the evaporator with Pe << 1, so only conduction heat transfer is considered within this liquid return path. For simplicity, natural convection between the sodium vapor and the device housing is neglected. A numerical linear resistance model (<5% error when compared to a finite element model) is used to determine the expected conversion temperatures of each stage for a range of candidate materials. Furthermore, a numerical model (<2% error) is developed to find the factor of increase in the thermal resistance for several designs of corrugated features for the device housing. By using an iterative scheme, efficiency vs. power curves are created for a number of material and size combinations. Finally, the fundamental tradeoff between the power and efficiency is explored in conjunction with the total system size.

14 SOLAR ENERGY↗

DOE OSTI2017

Sodium Pumping via Condensation within a Non-Wetting Porous Structure

The sodium thermal electrochemical converter (Na-TEC) is a heat engine that generates electricity via the isothermal expansion of sodium ions through a beta”-alumina solid-electrolyte. The transfer of liquid sodium from a low-pressure condenser to a high-pressure evaporator is necessary to complete the thermodynamic cycle for this conversion process. A unique sodium capillary pump for the Na-TEC is proposed, whereby low-pressure sodium vapor is condensed within a non-wetting (i.e. contact angle > 90o) stainless steel porous structure. Due to the curvature of the non-wetting liquid-vapor interface, the liquid adjacent to the interface is at a higher pressure than the vapor. This is in contrast to traditional wicks, where the liquid adjacent to the interface has a lower pressure. Thus, the curvature created at this non-wetting condensation interface supplies a directed force upon the liquid sodium that effectively “pushes” it towards a high pressure region, whereas a traditional capillary wick “pulls” the liquid. Porous structures made of stainless steel 316 are commercially available, and this material is non-wetting to sodium at the relevant temperature range of the Na-TEC condenser (500K – 673K). An experimental set-up is used to measure several interfacial and transport properties of the condensed sodium within this porous structure. These properties include the temperature dependent Laplace pressure generated at the phase change interface and the permeability of the porous structure. Liquid sodium is in contact with the porous structure and is progressively pressurized with argon gas until the sodium “breaks through” and the liquid begins to flow. This break-through pressure is determined when electrical contact is established between the flowing liquid metal and a set of electrodes cemented along the flow path. The velocity of the flowing sodium can also be measured with these electrodes, and the permeability is then determined by fitting velocity data to the classical Darcy law. These interfacial properties are then applied to a conjugate heat transfer model, which treats the coupled momentum and thermal transport processes within the non-wetting porous structure as sodium vapor is condensed. Due to the low mass flowrates in the Na-TEC (< 0.1 mg/s), higher order friction terms are neglected and the classical Darcy’s law is used for non-isothermal, compressible sodium vapor flow. At lower temperatures, the sodium vapor density becomes sufficiently small and there is a transition from classic Poiseuille flow (Kn < 0.1) to Knudsen flow (Kn > 10). Furthermore, transport due to binary diffusion is considered for situations where there is a substantial presence of non-condensable argon inside the sodium vapor plenum. Initial modeling results showing expected mass flowrates, temperature profiles, and liquid-vapor interface locations are presented for various physical conditions. Finally, the main design features of an experimental set-up used to demonstrate this capillary pumping is described in detail, including the method used to measure the low sodium mass flowrates. Initial experimental results demonstrating sodium pumping for a range of temperatures (800K – 1100K) will be presented and compared against the model predictions. A pump curve used to gauge the performance of this pumping mechanism is also created.

14 SOLAR ENERGY↗

DOE OSTI2018

Interfacial and Transport Property Measurements of Liquid Sodium within a Porous Structure

The sodium thermal electrochemical converter (Na-TEC) is a heat engine that generates electricity via the isothermal expansion of sodium ions through a beta”-alumina solid-electrolyte. The transfer of liquid sodium from a low-pressure condenser to a high-pressure evaporator is necessary to complete the thermodynamic cycle for this conversion process. A unique sodium capillary pump for the Na-TEC is proposed, whereby low-pressure sodium vapor is condensed within a non-wetting (i.e. contact angle > π/2) porous sample. The curvature created at this non-wetting condensation interface supplies a directed force upon the liquid sodium that effectively “pushes” it towards a high pressure region, rather than a traditional capillary wick that “pulls” the liquid. Porous structures made of stainless steel 316 are commercially available, and this material is non-wetting to sodium at the relevant temperature range of the Na-TEC condenser (500K – 673K). An experimental set-up is used to measure several interfacial and transport properties of the condensed sodium within this porous structure. These properties include the temperature dependent Laplace pressure generated at the phase change interface and the permeability of the porous structure. For the former, liquid sodium is in contact with the porous structure and is progressively pressurized with argon gas in increments of ~ 5 kPa until the sodium “breaks through” and the liquid begins to flow. This breakthrough pressure is determined when electrical contact is established between the flowing liquid metal and a set of electrodes cemented into the flow path. The velocity of the flowing sodium can also be measured with these electrodes, and the permeability is then determined by fitting velocity data to the classical Darcy law. Statistically significant results of these measurements, taken at multiple sodium temperatures, are presented. Furthermore, contact angle measurements of sessile sodium drops on stainless steel 316 are demonstrated. This contact angle information is used to define an effective pore radius for the porous structure, which is then validated with microscopy. All the physical parameters described herein are used as inputs in a condensation model to predict the mass flowrate of condensing sodium under a given pressure gradient across the porous structure. This condensation model is used to design the capillary pump for the Na-TEC.

14 SOLAR ENERGY↗

DOE OSTI2018

Sodium Pumping via Condensation within a Non-Wetting Porous Structure

In a sodium thermal electrochemical converter (Na-TEC), the transfer of liquid sodium from a low-pressure condenser to a high-pressure evaporator is necessary to complete the thermodynamic cycle. This pumping can be typically achieved via capillary action. A unique capillary pump is explored in this work, whereby low-pressure sodium vapor is condensed within a non-wetting (i.e. contact angle > π/2) stainless steel porous structure. Due to the curvature of the non-wetting liquid-vapor interface, the liquid adjacent to the interface is at a higher pressure than the vapor. This is in contrast to traditional wicks, where the liquid adjacent to the interface has a lower pressure. Conjugate heat transfer techniques are required to model the coupled momentum and thermal transport processes within this porous structure. Due to the low mass flowrates in the Na-TEC (< 0.1 mg/s), higher order friction terms are neglected and the classical Darcy’s law is applied for the non-isothermal, compressible vapor flow. At lower temperatures, the sodium vapor density becomes sufficiently small and there is a transition from classic Poiseuille flow (Kn < 0.1) to Knudsen flow (Kn > 10). The permeability of the porous structure is modeled using the Blaze-Kozeny expression, with an additional factor that accounts for this change in Kn. Initial modeling results showing expected mass flowrates, temperature profiles, and liquid-vapor interface locations are presented. The design of an experiment to validate the results from this modeling effort is also described. The main design features of the experimental set-up are presented, and the method used to measure the low sodium mass flowrates is discussed. Initial experimental results demonstrating sodium pumping for a range of temperatures (850K – 1150K) will be presented and compared against the model predictions. A number of challenges affecting the successful completion of this experiment will also be discussed. Primarily, the sodium vapor must be superheated to prevent condensation anywhere except within the porous structure. Other challenges include the requirement to keep the condensation interface above ~ 675K to prevent transition to a wetting regime, and the control of the transient heating rate so that vapor flows slower than the quasi steady-state mass flowrate, which would otherwise lead to a flooding condition that prevents pumping. Specific strategies used to address these challenges are presented, and the experimental procedures used to gather data are discussed.

14 SOLAR ENERGY↗

DOE OSTI2019

Sodium Pumping via Condensation within a Non-Wetting Porous Structure

The transfer of liquid sodium from a low-pressure condenser to a high-pressure evaporator is required to complete the thermodynamic cycle of a sodium thermal electrochemical converter (Na-TEC). A unique capillary pump is explored in this work, whereby low-pressure sodium vapor is condensed within a non-wetting (i.e. contact angle > pi/2) stainless steel porous structure. Due to the curvature of the non-wetting liquid-vapor interface, the liquid adjacent to the interface is at a higher pressure than the vapor. This is in contrast to traditional wicks, where the liquid adjacent to the interface has a lower pressure. Conjugate heat transfer techniques are used to model the coupled momentum and thermal transport processes within this non-wetting porous structure. Due to the low mass flowrates in the Na-TEC (< 0.1 mg/s), higher order friction terms are neglected and the classical Darcy’s law is used for the non-isothermal, compressible vapor flow. At lower temperatures, the sodium vapor density becomes sufficiently small and there is a transition from classic Poiseuille flow (Kn < 0.1) to Knudsen flow (Kn > 10). Furthermore, transport due to binary diffusion is also considered for situations where there is a substantial presence of non-condensable argon in the sodium vapor plenum. Initial modeling results showing expected mass flowrates, temperature profiles, and liquid-vapor interface locations are presented for various physical conditions. The main design features of an experimental set-up used to demonstrate this capillary pumping is also described in detail, including the method used to measure the low sodium mass flowrates. Initial experimental results demonstrating sodium pumping for a range of temperatures (800K – 1100K) will be presented and compared against the model predictions. Finally, several of the challenges with this experiment will be discussed, and specific strategies used to address these are presented.

14 SOLAR ENERGY↗

DOE OSTI2019

A Dual-Stage Sodium Thermal Electrochemical Converter (Na-TEC)

The sodium thermal electrochemical converter (Na-TEC) is a heat engine that generates electricity via the isothermal expansion of sodium ions through a solid-electrolyte. The Na-TEC can ideally achieve conversion efficiencies above 45%, but thermal management limitations have constrained previous single-stage devices to thermal efficiencies below 20%. To mitigate some of these limitations, the isothermal expansion can be divided into two stages; one at the evaporator temperature (1150K) and another at an intermediate temperature (550K – 1050K). This dual-stage Na-TEC takes advantage of regeneration and reheating, and is amenable to improved thermal management through reduced parasitic losses. The dual-stage device can improve the efficiency by ~8% points over the best performing single-stage device. Generally, a single-stage Na-TEC should be used for applications requiring high power densities, whereas a dual-stage Na-TEC should be used for applications requiring high efficiency.

14 SOLAR ENERGY↗