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DOE OSTI2026

Holistic energy analysis method for thermal management architectures of data centers

Modern high-performance computing (HPC) data centers (DCs), particularly those supporting energy-intensive artificial intelligence (AI) workloads, face escalating thermal management challenges that degrade performance through thermal throttling and drive up cooling power consumption and operational costs. To address this challenge, many have developed a wide variety of thermal management solutions (single-phase, two-phase, direct, indirect, hybrid, and more) which attempt to cool HPC DCs effectively while attempting to minimize overall system power consumption. However, the analysis of these solutions and methods to effectively compare one with another is lacking. Overall power usage effectiveness (PUE) and total-power usage effectiveness (TUE) provide a metric to quantify power consumption but fail to identify components in the system which require further optimization. To address this, we propose a holistic analytical framework – the waterfall diagram (WFD) – which leverages a waterfall chart methodology, offering a comprehensive visualization of both the thermal management system loop and heat flow pathways from individual server components to the outdoor ambient. Use of the WFD enables graphical estimations of power efficiency and cooling performance across each component of a DC cooling system and complements Sankey-style energy flow visualizations by additionally resolving stage-wise temperature changes and incremental TUE contributions. The framework is used in conjunction with simulation-based approaches, to conduct a detailed pressure drop and flow distribution analysis aimed at identifying the optimal coolant distribution architecture for a single-phase direct-to-chip water-cooled DC, which serves as the baseline for subsequent WFD analysis. Among the evaluated architectures, the 3 U modular coolant distribution architecture is found to demonstrate the best performance, considering minimal pressure drop and uniform flow distribution. In addition, TUE is calculated for each cooling loop component based on its associated pressure drop and corresponding pumping power, which are integrated into the WFD. This correlation between TUE and local temperature offers immediate insight into the power efficiency and thermal performance contributions of individual components, facilitating further development and optimization. Examples of WFD applications are presented under varying thermal loads and ambient conditions, demonstrating reasonable cooling strategies. Notably, the 3 U modular architecture maintains a consistent chip case temperature of 85°C, achieving a TUE of 1.016 at ambient temperature of 47°C, and a TUE of 1.026 at ambient temperature of 52°C. The WFD methodology provides an efficient, holistic, and streamlined framework for DC thermal management architecture assessment and enables design optimization which is important for addressing the thermal-fluidic energy challenges of current and next-generation DCs.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2020

An empirical study of moving horizon closed-loop demand response scheduling

The potential of electricity-intensive chemical plants to engage in demand response (DR) initiatives in support of power grid operations has been the subject of many conceptual studies. In this work, using an industrially-relevant model of an air separation unit, we undertake an extensive simulation study of moving horizon (MH) rescheduling approaches, where we "close the scheduling loop" based on updated information regarding disturbances such as changes in electricity prices, ambient conditions and chemical product demand. Our study produces several unexpected findings regarding the non-periodic nature of rescheduling solutions, the impact of the accuracy of disturbance forecasts on the economics of DR scheduling, and on the interplay of simultaneously dealing with fluctuations on both the supply side (i.e., electricity prices) and the product demand side of the plant. Furthermore, we posit that the latter fluctuations pose significant limitations to the potential of a chemical plant to engage in DR.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Effect of multiple calcination cycles on CO 2 capture efficiency during carbonation of MgO in a mineral looping process

Magnesium oxide (MgO) is considered as a potential sorbent for direct air capture of carbon dioxide in a looping process. Previous research on mineral looping for carbon capture from flue gas using MgO has shown deactivation of the sorbent with repeated cycles but repeated cycling for carbonation at ambient conditions has not been yet investigated. Here, we tested three cycles of carbonation for MgO nano-scale powders with different starting surface area. We find that carbonation efficiency is higher at higher surface area. No decrease in carbonation efficiency was observed with cycling, instead we find that carbonation efficiency and surface area are stable or even increasing with cycling. Based on our experimental data, we hypothesize that the carbonation in presence of relative humidity leads to first hydration of MgO, leading to formation of brucite (Mg(OH) 2 ). This formation of Mg(OH) 2 is a volume-increasing reaction, which leads to fracturing of MgO particles and results in an increase in surface area. We observed formation of amorphous and crystalline hydrated carbonates. The crystalline phase observed was nesquehonite (MgCO 3 ⋅ 3H 2 O). Our results show that MgO does not show any deactivation with repeated cycling for carbon capture at ambient conditions and in the presence of humidity. These findings therefore indicate that MgO is a suitable candidate as sorbent material for direct air capture of carbon dioxide.

Ambient weathering↗

DOE OSTI2024

Thermally anisotropic composites for thermal management in building environments

An improved system for thermal management is provided. The system includes thermally anisotropic composites coupled with a thermal loop to re-direct, reduce, and shape heat flows through a building envelope, having the potential to (1) significantly reduce envelope-generated heating and cooling loads and (2) provide grid services such as decreasing peak loads and shaping energy use. In one embodiment, the thermal management system includes an anisotropic composite that consists of alternating layers of thermal insulation and thermally conductive materials that are immediately adjacent to each other, including polyisocyanurate foam boards and aluminum sheets. The thermal management system also includes a thermal loop along the long edge or the entire the perimeter of the anisotropic composite, the thermal loop having dynamically controlled or floating temperature that is maintained at lower than an outdoor ambient temperature (for cooling). An interior wall structure is inwardly adjacent to the anisotropic composite.

Shrestha, Som S.↗

DOE OSTI2023

Activation and Conversion of Methane to Syngas over ZrO 2 /Cu(111) Catalysts near Room Temperature

Enzymatic systems achieve the catalytic conversion of methane at room temperature under mild conditions. Here, in this study, varying thermodynamic and kinetic parameters, we show that the reforming of methane by water (MWR, CH 4 + H 2 O → CO + 3H 2 ) and the water-gas shift reaction (WGS, CO + H 2 O → H 2 + CO 2 ), two essential processes to integrate fossil fuels toward a H2 energy loop, can be achieved on ZrO 2 /Cu(111) catalysts near room temperature. Measurements of ambient-pressure X-ray photoelectron spectroscopy and mass spectrometry, combined with density functional calculations and kinetic Monte Carlo simulations, were used to study the behavior of the inverse oxide/metal catalysts. The superior performance is associated with a unique zirconia-copper interface, where multifunctional sites involving zirconium, oxygen, and copper work coordinatively to dissociate methane and water at 300 K and move forward the MWR and WGS processes.

03 NATURAL GAS↗

DOE OSTI2024

Pushing the Envelope-Moving Dynamic Building Envelope Thermal Energy Storage Systems Mainstream: Preprint

Buildings contribute to nearly 40% of the U.S. national energy consumption and a significant portion of CO2 emissions. More importantly, disadvantaged communities are disproportionately affected by energy burden and thermal discomfort in their homes. This paper will discuss two novel DOE's BTO supported thermal energy storage (TES) integrated dynamic building envelope technologies, their ability to harvest ambient energy, and improve energy efficiency by reducing HVAC loads and peak electricity demand while enhancing energy and thermal resilience in buildings. The paper will also discuss the recent advancements that have made these systems more affordable and easier to integrate into new and existing buildings. The first solution is a thermally anisotropic building envelope (TABE) system that can redirect ambient thermal energy (heat or coolness) from diurnal outdoor conditions, solar irradiance, and night sky radiation from the envelope to a hydronic loop. The redirected thermal energy can be stored in a TABE-integrated thermal energy storage system and use the stored energy to offset HVAC energy use and peak demand. The second solution is an innovative plug-and-play thermal switch in the form of insertable plugs integrated with a phase change material (PCM). The plug can vary its thermal resistance based on the indoor and outdoor conditions, thus allowing preferential directional heat flow, and enhancing utilization of free ambient cooling and heating to charge/discharge the PCM, much like a solid-state economizer. While the fist solution can be actively controlled, the second solution is passive, requiring no external power, and work solely based on the ambient temperature.

anisotropic envelope↗

DOE OSTI2024

Pushing the Envelope—Moving Dynamic Building Envelope Thermal Energy Storage Systems Mainstream

Shrestha, Som↗

DOE OSTI2026

Solventless, Ambient-Pressure Production of Bio-Based Lactones Over Earth-Abundant, Mixed Metal Oxide Catalysts for Circular Polyesters

Transitioning to a circular plastics economy will require use of renewable feedstocks, energy-efficient processes, and closed-loop recyclable polymers, such as polyesters. A key challenge lies in sustainably sourcing monomers used to make recyclable polyesters. This work presents a catalytic platform utilizing earth-abundant Cu(x)Ca(1-x)O mixed metal oxides for the oxidative dehydrocyclization of bio-based diols to lactones, which are advantaged for energy-efficient ring-opening polymerization. Operating below 200 degrees C, at ambient pressure, and without solvent, the process uses air as the sole oxidant, achieving high yields of lactones across a broad substrate scope of C4-8 diols in the liquid phase. The oxidative dehydrocyclization reaction is thermodynamically downhill due to water formation and energy-efficient compared to incumbent, non-redox pathways utilized in fossil carbon-based industrial processes for lactone production. Mechanistic studies reveal facile redox cycling of Cu2+-O(Ca2+)-Cu2+ interfacial sites unique to the developed catalyst. Techno-economic analysis and life cycle assessment estimate 40% lower energy demand and 15% lower GHG intensity per mass of butyrolactone produced compared to the fossil carbon-based route. Liquid-phase oxidative dehydrocyclization offers a promising approach for scalable lactone production from renewable, bio-based diols to enable circular polyesters.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Packaging a 650V/400A GaN Half-bridge Power Module with Ultra-low Parasitics for Electric Vehicle Drive Applications

This paper proposes a compact and efficient half-bridge power module with three 650 V / 150 A GaN dies in parallel. The power module incorporates a main power printed circuit board (PCB), an interface PCB, and a flex PCB to achieve low parasitics in both power loop and gate-side connection, resolving the issue of high parasitics typically encountered with wire bonding in high-current applications. Additionally, the interface PCB decouples the design constraints between the power loop and the gate loops. The proposed design is optimized with a vertical loop configuration to reduce power loop inductance through magnetic flux cancellation. Finite element analysis indicates that the power loop inductance is 0.58 nH at 100 MHz, while the maximum die junction temperature reaches 131 °C under an ambient temperature of 65 °C and a load current of 385 A. The proposed multi-piece PCB structure reduces the inductance of the drive circuit to minimize EMI and to mitigate false triggering. At the same time, it reduces impedance mismatches across different driver circuits, thereby achieving dynamic current sharing in multi-chip parallel configurations. Under simulation conditions of 400 V / 385 A, the current imbalance among chips was limited to 5 A. A 400 V / 385 A double-pulse test was conducted to experimentally validate the performance of the proposed power module.

30 DIRECT ENERGY CONVERSION↗

DOE OSTI2023

Laboratory demonstration of the prediction of wind-blown turbulence by adaptive optics at 8 kHz with use of LQG control

The low-latency adaptive optical mirror system (LLAMAS) is designed to push the limits on achievable latencies and frame rates. It has 21 subapertures across its pupil. Here, a reformulated version of the linear quadratic Gaussian (LQG) method predictive Fourier control is implemented in LLAMAS; for all modes, it takes just 30 µs to compute. In the testbed, a turbulator mixes hot and ambient air to produce wind-blown turbulence. Wind prediction clearly improves correction when compared to an integral controller. Closed-loop telemetry shows that wind-predictive LQG removes the characteristic “butterfly” and reduces temporal error power by up to a factor of three for mid-spatial frequency modes. Strehl changes seen in focal plane images are consistent with telemetry and the system error budget.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Inhibition of Reaction Layer Formation on MgO(100) by Doping with Trace Amounts of Iron

Despite extensive research on MgO’s reactivity in the presence of CO 2 under various conditions, little is known about whether impurities incorporated into the solid, such as iron, enhance or impede hydroxylation and carbonation reactions. The purity of the MgO required for the successful implementation of MgO looping as a direct air capture technology affects the deployment costs. With this motivation, we tested how incorporated iron impacts MgO (100) reactivity and passivation layer formation under ambient conditions by using atomic force microscopy, electron microscopy, and synchrotron-based X-ray scattering. Based on electron microprobe analysis, our MgO samples were 0.5 wt % iron, and Mössbauer spectroscopy results indicated that 70% of the iron is present as Fe(II). We find that even these low levels of iron dopants impeded both the hydroxylation at various relative humidities (10%, 33%, 75%, and >95%) and carbonation in CO 2 (33%, 75%, and >95%) on the (100) surface. Crystalline reaction products were formed. Reaction layers on the sample were easily removed by exposing the sample to deionized water for 2 min. Overall, our findings demonstrate that the presence of iron dopants slows the reaction rate of MgO, indicating that MgO without incorporated iron is preferable for mineral looping applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

MODEL DEVELOPMENT AND VERIFICATION OF A 1,350°C AIR RECEIVER TEST SYSTEM

Open-loop volumetric receivers work with air at atmospheric pressure and are suitable for single-cycle or multicycle power plants. A novel additively manufactured (AM) silicon carbide (SiC), ceramic matrix composite (CMC) volumetric receiver was developed that consisted of a lattice structure, which absorbs solar radiation and converts it into heat energy. Heat energy from the porous receiver was transferred to heated ambient air. The receiver acted as a convective heat exchanger, transferring heat to the fluid through convection. Engineering was facilitated to develop a high-temperature air receiver test bed at Sandia national Laboratories (SNL) capable of demonstrating a 50kWth open-loop volumetric SiC air receiver module developed by General Electric Aerospace Research (GE Aerospace). This paper presents the development of the high temperature AM SiC-CMC air receiver, the test bed, and the first testing operations of this device, which was experimentally demonstrated to achieve 1,350°C for over 3.5 hours of operation, based on input flux levels of 67–91 W/cm2 0.5-2.5 kg/s flow rates. From the test campaign results, based on the measured convective heat transfer to the airflow and bounded radiative-loss assumptions, the solar-thermal efficiency of HOTSSTAR test module was estimated to be approximately as high as 74% for representative test conditions.

14 SOLAR ENERGY↗

DOE OSTI2024

Three phase spectral interferometry for recording high dynamic range optical waveforms with <1 ps resolution over >2 ns records applied to closed-loop pulse shaping

Herein we demonstrate, to our knowledge, a novel spectral interferometry technique that simultaneously captures three spectral interferograms of a signal waveform with a reference pulse. The measured performance is robust to nonidealities and ambient drifts by implementing a precisely calibrated 3 × 3 polarization maintaining (PM) splitter that provides three phase shift differences nominally spaced 120° apart. The system can achieve long record length by implementing three, high resolution, virtually imaged phase array (VIPA) spectrometers. Here, we experimentally implement this technique and demonstrate the measurement of waveforms with >2ns of record while maintaining <1ps resolution.

42 ENGINEERING↗

DOE OSTI2020

Role of the Terrestrial Biosphere in Atmospheric Chemistry and Climate

The terrestrial biosphere–atmosphere interface provides a key chemical, biological, and physical lower boundary for the atmosphere. The presence of vegetation itself modifies the physical boundary, or the biogeophysical aspects of the system, by controlling important climate drivers such as soil moisture, light environment, and temperature. The leaf surface area of the terrestrial biosphere provides additional surface area for emissions, and it can be up to 55% of the total Earth’s surface area during the boreal summer. Vegetation also influences the biogeochemical aspects of the system by emitting a broad suite of reactive trace gases such as biogenic volatile organic compound (BVOC) emissions and climate-relevant primary biological aerosol particles (PBAP). Many of these emissions are a function of meteorological and climatological conditions at the surface, including temperature, light environment, soil moisture, and winds. Once emitted, they can be processed in the troposphere through a suite of chemical reactions. BVOC can contribute to the formation of ozone and secondary organic aerosols (SOA), and PBAP can rupture to form smaller particles with climatic relevance. These emissions and subsequent aerosol products can influence atmospheric processes that affect the surface climate, such as the attenuation of radiation, the formation of greenhouse gases such as ozone that can feedback to surface air temperature, and the alteration of clouds and subsequent precipitation. These atmospheric changes can then feedback to the land surface and emissions themselves, creating positive or negative feedback loops that can dampen or amplify the emission response. For the dominant BVOC isoprene, the feedback response to temperature can be positive or negative depending on ambient temperatures that drive isoprene emissions. The feedback response to soil moisture and precipitation can be positive, negative, or uncoupled depending on the moisture content of the soil and the total atmospheric aerosol loading. For light, the isoprene response can be positive or negative depending on the role of diffuse light. Overall, these feedbacks highlight the dynamical response of the biosphere to changing atmospheric conditions across a range of time scales, from minutes for trace gases and aerosols, to months for phenological changes, to years for land cover and land use change. Here, the dynamic aspect of this system requires us to understand, simulate, and predict the complex feedbacks between the biosphere and atmosphere and understand their role in the simulation and understanding of climate and global change. From the observational perspective, these feedbacks are challenging to identify in observations, and predictive modeling tools provide a crucial link for understanding how these feedbacks will change under warming climate scenarios.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

The BREKTRIA 500 – A Breakthrough in Technology and Power Density for an Advanced 500kW Utility-Scale String Inverter (Final Technical Report)

The primary goal of this development project, planned to be 36 months in duration, was to create a 500kW utility-scale string inverter, demonstrating an advanced hybrid architecture that would achieve unprecedented high power density, and bring the inverter to the stage of production readiness. Specific key objectives for the 500kW utility-scale string inverter were: Create a 500kW 3-phase 600Vac inverter that was similar in overall size to the existing 250kW string inverters in the market, thereby demonstrating dramatically increased power density; Achieve a cost of goods, including all manufacturing-related costs and overheads, at or below 2.5¢/Wac ($12,500); Demonstrate full-power operation at a 45-50C ambient temperature with no power de-rating; Accommodate a PV array DC input of up to 1MWdc, aka a DC/AC Ratio of 2.0; Demonstrate peak efficiency greater than 99% at any operating dc voltage, and a CEC weighted average efficiency greater than or equal to 98.5%. The motivation for this project was to leapfrog the competition by creating the world’s most powerful string inverter, utilizing an innovative topology and achieving a step change increase in power density. Achieving the goals of the project would have enabled Yaskawa Solectria Solar to demonstrate its technology leadership, manufacture the utility-scale string inverter in the company’s facilities in Illinois, and bring to the market a highly-differentiated and compelling product to help the company grow its share in the large and growing utility market segment. During the course of this project, BREK Electronics’ hybrid architecture inverter was taken from an early-stage 125kW prototype, to a more mature and successfully demonstrated power stage at twice the power. Two 250kW power stages were planned to build the 500kW inverter. Significant progress was made in the inverter controls, achieving a clean AC sinewave and closed-loop operation into the grid, and improved efficiency by control of the high-speed switching. Further, the updated 250kW power stage was on track to achieve full power operation at an ambient temperature of 50C. At the time of the project’s closure in September 2022, global semiconductor supply remained limited, with shortages creating dramatic swings in both availability and price. Given this situation, our ability to predict cost-of-goods two years out with any accuracy or confidence was limited. As a result, the probability of attaining the target cost of 2.5¢/Wac for the 500kW inverter remained uncertain at the closure of the project. This project successfully demonstrated the potential for the advanced hybrid architecture inverter that emerged from a decade of university research on Si IGBTs and SiC mosfets, leading to this unique inverter topology. The team has taken the first steps toward an evolutionary advancement in inverter technology that remains to be fully realized.

14 SOLAR ENERGY↗

DOE OSTI2025

Kelvin probe force microscopy under ambient conditions

Kelvin probe force microscopy (KPFM) is a technique derived from atomic force microscopy that provides maps of surface potential or work function differences across material systems, with nanometre-scale resolution. KPFM is a useful tool for investigating electrical phenomena such as dipole orientation, interfacial charge transfer, charge accumulation, band bending and doping levels. This Primer aims to provide an overview of typical ambient-condition KPFM measurements, covering their underlying principles, experimental implementations and wide-ranging applications. Key KPFM variants, including amplitude and frequency modulation, heterodyne detection schemes and innovative open loop and pulsed force techniques, are discussed, with practical guidance on optimizing signal acquisition and reducing errors. Specialized approaches, such as time-resolved KPFM and multimodal KPFM, are discussed for their ability to capture dynamic charge processes and chemical information, respectively. Here, we highlight recent advances in KPFM applications, spanning metal alloys, soft matter, ferroelectrics, photovoltaics and 2D materials, showcasing its versatility across research domains. By addressing current limitations and identifying future opportunities, this Primer underscores the transformative potential of KPFM in advancing the understanding of nanoscale electrical phenomena.

Zahmatkeshsaredorahi, Amirhossein [Lehigh Univ., B↗

DOE OSTI2025

Comparative analysis of thermal management systems in electric vehicles at extreme weather conditions: Case study on Nissan Leaf 2019 Plus, Chevrolet Bolt 2020 and Tesla Model 3 2020

With the surge in electric vehicle (EV) adoption and the need for extended driving ranges, optimizing energy efficiency, particularly through thermal management, is critical, especially in extreme weather. Managing the substantial energy needed for cabin climate control and battery temperature regulation can increase energy demands by over 50 %, severely limiting range. This study conducts a comparative analysis of thermal management systems (TMS) in three popular EV vehicles, 2020 Chevrolet Bolt, 2019 Nissan Leaf Plus, and 2020 Tesla Model 3, evaluating their distinct TMS configurations and performance under varied weather conditions. Using both numerical simulations and experimental data collected on a controlled test bench at Argonne National Laboratory, we assess how TMS architecture and operational modes influence energy consumption and range. A comprehensive TMS model was developed, integrating cabin and battery thermal sub-models in the Autonomie software platform, to simulate temperature fluctuations and range impacts. Cabin climate was modeled using a mono-zonal approach, while battery cell temperature distribution was estimated through a 2D nodal structure. Each vehicle's distinct TMS setup was evaluated: the Chevrolet Bolt and Tesla Model 3 use a dual evaporator vapor compression cycle with a PTC heater for the cabin and a coolant loop for battery thermal management; the Nissan Leaf Plus employs a heat pump with a PTC heater for the cabin and air-cooling for the battery. Tests conducted at ambient temperatures of 35°C, 22°C, -7°C, and -18°C reveal significant differences in energy use and range reduction across both configurations and conditions. At 35°C, the Tesla Model 3, Chevrolet Bolt, and Nissan Leaf Plus have a range reduction of 8%, 9%, and 13%, respectively, due to air conditioning. In winter, heating technology is paramount; at -7°C, the Nissan Leaf's heat pump configuration achieves a lower range reduction (19.3%) compared to the Tesla and Chevrolet Bolt PTC heaters, which reduce range by 28.3% and 31%, respectively. Further, this study provides valuable insights for automotive engineers, EV technology researchers, and thermal management system designers aiming to enhance electric vehicle performance by understanding how different weather conditions and TMS architectures impact energy consumption and driving range.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2023

A Propane Hydronic Heat Pump with Energy Storage

Propane is an environment-friendly refrigerant, having a 20-year GWP (global warming potential) of 0.072 and a 100-year GWP of 0.02, as compared to R-410A having a GWP > 2000. It has superior thermodynamic cycle performance and heat transfer characteristics. However, propane is classified as a A3 refrigerant, which is highly flammable, and not allowed to be used indoor if the system charge is higher than 150 grams. It is a challenge to use propane in residential applications requiring a rated capacity larger than 10 k Watts. A hydronic heat pump, i.e., containing propane in an outdoor unit and distributing the cooling and heating capacity through a hydronic coil to the indoor space addresses the flammability issue, while maintaining a high efficiency. We developed a hydronic heat pump with propane, it uses a two-stage compressor, a brazed plate indoor heat exchanger, and a microchannel outdoor heat exchanger. It achieves a rated cooling capacity larger than 10 k Watts, and a cooling SEER (cooling seasonal energy efficiency rating) > 16.0 (cooling seasonal COP > 4.7) and a heating HSPF (heating seasonal performance factor) > 9.5 (heating seasonal COP > 2.78), while requiring a system charge < 1200 grams. Additionally, the hydronic heat pump was evaluated in a laboratory water heating loop to heat a 50-gallon water tank in a full condensing mode. Experiments of heating the tank water from 58F(14.4°C) to 150F(65.6°C) were conducted under ambient temperatures from 17F(-8.3°C) to 75F(23.9°C), at the compressor high and low stages.

Shen, Bo↗