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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Supercritical CO2 Heat Pumps and Power Cycles for Concentrating Solar Power: Preprint

Pumped Thermal Energy Storage (PTES) is a promising technology for electricity storage applications. Grid electricity drives a heat pump which moves energy from a cold space to a hot space, thereby creating hot and cold thermal storage. The temperature difference between the storage is later used to drive a heat engine and return electricity to the grid. In this article, supercritical carbon dioxide (sCO2) is chosen as the working fluid for PTES, and results are compared to ‘conventional’ systems that use an ideal gas. Molten salts are used for the hot storage which means that a CSP plant with thermal storage and an sCO2 power cycle could potentially be hybridized with PTES by the addition of a heat pump. This article describes some of the benefits of this combined system which can provide renewable power generation and energy management services. Two methods by which an sCO2 heat pump can be combined with an sCO2 power cycle for CSP are described and techno-economic results are presented. Results indicate that these systems can achieve reasonable technical performance, but that costs are currently high.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2022

Compatibility Of Steels At 450°-650°C In Supercritical CO2 With O2 And H2O Additions

Direct-fired supercritical CO2 (sCO2) power cycles are being commercialized to revolutionize fossil energy as a low-emission power source. However, the cycle will increase O2 and H2O in the sCO2 and the implications of these additions have not been fully studied, particularly for lower cost steels that are needed in the lower temperature segments of the plant. Representative 9 and 12%Cr ferritic-martensitic (FM) steels and conventional and advanced austenitic steels were evaluated at 450-650°C to determine the maximum use temperatures in sCO2 with 1%O2 and 0.1%H2O at 300 bar. Compared to research grade (low impurity) sCO2 in indirect-fired cycles, the mass gains and scale thickness were not significantly changed for FM steels: both formed thick duplex Fe-rich scales. For stainless steels, higher mass gains were observed in all cases with increased Fe-rich oxide nodule formation. After 1000h at 650°C, the measured bulk C content was high for all of the steels with the addition of impurities suggesting a lower maximum operating temperature for steels. The post-exposure impact of the environment on room temperature tensile properties also will be discussed.

Pint, Bruce↗
DOE OSTI2022

Adaptive Mesh Refinement Large Eddy Simulation of the Supercritical Carbon Dioxide Round Turbulent Jet

Supercritical carbon dioxide (sCO2) is of interest to a range of engineering problems, including carbon capture, utilization, and storage (CCUS) as well as advanced cycles for power generation. Non-ideal variations in physical properties of sCO2 impact the physics of these systems. In this study, we simulate turbulent sCO2 jets to gain a better understanding of these physics.We use a second order finite volume method with adaptive mesh refinement as implemented in the first-principles simulation code PeleC to perform a Large Eddy Simulation (LES) of three turbulent jets of sCO2. Additionally, we use the Soave-Redlich-Kwong equation of state to close the system and examine the impact of a cubic equation of state on the turbulent flow physics. We look at velocity and Reynolds stress profiles at different downstream locations for three cases in which the temperature of the jet andthat of the ambient fluid differ in order to capture the effects of widely varying thermal properties in the pseudocritical region. These results are then contrasted with established theory for ideal gas jets.

adaptive mesh refinement↗
DOE OSTI2024

Integrated Thermal Energy Storage and Brayton Cycle Equipment Demonstration (Integrated TESTBED) Project Design Basis

The Integrated Thermal Energy Storage and Brayton cycle Equipment Demonstration (Integrated TESTBED) project seeks to retire commercial-scale risks associated with the design, integration,and operation of a supercritical carbon dioxide (sCO2) power cycle and concentrating solar power (CSP) thermal energy storage (TES) system. This requires an understanding of commercial-scale collector system transient impacts on the TES system, the dynamics of heat exchange from theTES to the power cycle, and the control and operation of the power cycle to accommodate various dispatch strategies. In order to retire these risks, Heliogen has proposed to construct a 5 MWe CSP demonstration facility based on directly heated particle and sCO2 technology. The receivers, primary heat exchanger, and power cycle will be deployed at a full commercial scale based on Heliogen’s modular plant architecture to ensure actual system integration risks are validated during design, construction, and operation. This work summarizes the design basis for the Integrated TESTBED project demonstration facility including a design target for capacity factor to support test operations, hours of storage, particle silo arrangement, centrifugal article receivers, a diffusion bonded particle-sCO2 heat exchanger, and a 5 MWe (net) integrally geared sCO2 recompression Brayton cycle.

14 SOLAR ENERGY↗
DOE OSTI2024

Testing of Materials and Coatings at up to 1150°C and 300 bar for use in Oxy-Combustion Turbine

Various materials that may be used in a supercritical carbon dioxide (sCO2) oxy-fuel turbine in the 150-300 MWe size range are being evaluated in various environments of interest. The inlet of the turbine must be capable of 1,150 °C at 300 bar and the exhaust temperature is expected to be within the 725-775 °C range. The design requirements are pushing the known limits of high temperature materials. Little is known about the oxidation of the metallic alloys considered for turbine nozzles and blades or about the resilience of thermal management solutions, such as thermal barrier coatings (TBC), required to accommodate these high temperatures. The combinations of high temperature resistant materials and coatings must be tested in sCO2 to evaluate their reliability in an oxy-fuel turbine environment. A total of 13 alloys were chosen to be tested. They included bare samples, with nano deposited MCrAlY bond coat only, or with the addition of a TBC. A unique test facility was developed to expose those materials in sCO2 at up to 300 bar and 1150 °C for up to 5,000 hours. This was accomplished by placing an induction heater inside an autoclave to achieve those high temperature locally while the pressurized vessel is cooled externally. The specimens are weighed before and after exposure to determine the oxidation rate. The integrity, morphology, and composition of some of the coatings and thermally grown oxide will be investigated by scanning electron microscopy (SEM). This paper presents the up-to-date results of the testing coated and uncoated superalloys in sCO2 at up to 1150 °C and up to 300 bar performed at Southwest Research Institute.

Bocher, Florent↗
DOE OSTI2023

Simulation of Methane Oxycombustion in Supercritical Carbon Dioxide

The Allam-Fetvedt Cycle (AFC) offers the potential for electricity generation with minimal or even negative carbon emissions by using oxycombustion in supercritical carbon dioxide (sCO2). Because of the extreme high temperatures and pressures encountered in these systems, simulation of oxycombustion requires use of a complex equation of state such as the modified Soave-Redlich-Kwong (SRK) equation, coupled with equally complex correlations for transport properties. The current work simulates a model combustor using both an ideal gas equation of state and the SRK equation of state. The model combustor features a jet of CH4 mixing with and reacting with O2 in the sCO2 ambient. Two jet configurations are considered: one of pure CH4, and one of CH4 mixed with sCO2. Comparison of results shows that key output properties such as combustor temperature and flow distribution are impacted by the choice of equations of state. Inspection of simulation results shows that mixing and reaction rates, as well as the uniformity of the flow, are impacted by the choice of equation of state. These results show that even though use of a complex equation of state greatly increases the computational costs of these simulations, it is critical to accurately capturing the physics of these systems.

computational fluid dynamics↗
DOE OSTI2023

Compatibility of Wrought Superalloys with Supercritical CO2

Supercritical CO2 (sCO2) power cycles, particularly direct-fired cycles, have the possibility of revolutionizing clean fossil energy with peak temperatures above 700 °C and wrought precipitation strengthened alloys like Haynes 282™ for structural components. At temperatures <650 °C, it would be desirable to use less expensive alloys, however, steels are known to be susceptible to carburization. Laboratory 300 bar sCO2 autoclave results were collected on a range of alloys including less expensive Ni-based alloys like 825 compared to advanced austenitic steels like alloy 709 at 600 °C. Both alloys 825 and 709 formed thin, protective Cr-rich oxides after 1,000 h. Alloy 825 also was exposed for 1,000 h in sCO2 at 800 °C and compared to a range of Ni-based alloys. Comparing alloys 625, 825, and 282, the mass gain increased with increasing alloy Ti content under these conditions. High Al superalloys did not perform significantly better under these conditions at 800 °C.

Pint, Bruce↗
DOE OSTI2025

Computational Modeling of a 3D Printed Recuperator and Subsequent Experimental Loop for Supercritical Carbon Dioxide Cycles

Oak Ridge National Laboratory (ORNL), in collaboration with mechanical-thermal energy storage (mTES) provider EarthEn, a US Department of Energy (DOE) Lab-Embedded Entrepreneurship Program (LEEP) recipient at ORNL’s Innovation Crossroads 2023, is utilizing a state-of-the-art patented 3D printing technique to design an additively manufactured (AM) supercritical CO2 (sCO2) recuperator (REC) for EarthEn’s charge/discharge cycle. The AM REC will be printed at ORNL’s Manufacturing Demonstration Facility using Inconel Alloy 718 and tested on a closed-loop, ∼100 kW scale experimental facility that is under construction. The testing will compare the printed design against a commercial-off-the-shelf Printed Circuit Heat Exchanger (PCHE) REC. The design of the sCO2 facility is guided by a Modelica-based system model which is primarily dependent on the open-source TRANSFORM library developed at ORNL and uses the open-source CoolProp library for thermophysical properties of sCO2 via the External Media library. It is envisioned that an iterative process will be followed between the physical loop and the system model wherein the initial experimental data will be used to tune the model, which in turn will be used to guide future loop operation. Simultaneously, the AM REC is being designed using computer-aided design models, and it is also being analyzed for hydraulic and thermomechanical response using commercial computational fluid dynamics software, Simcenter STAR-CCM+, on highperformance computing resources.1

See, Nate [ORNL] (ORCID:0000000178581202)↗
DOE OSTI2022

Convective Heat Transfer Potential of Particles/Airflow Through Single Cell Thick Additively Manufactured Octet-Shaped Lattice Frame Material

Abstract Particle-to-Supercritical Carbon Dioxide (sCO2) heat exchangers are one of the most critical components of the next-generation Concentrating Solar Power (CSP) plants. There have been several efforts to enhance the overall heat exchanger performance which essentially comprises of thermal resistances offered by sCO2 channel, wall (separating sCO2 with particles) thickness, particle-wall contact resistance and particle-side effective heat transfer coefficient. This study is focused towards reducing the particle side thermal resistance by incorporating single unit cell thick reticulated Octet lattice frame structures on the falling particle side to enhance the effective thermal conductivity of the particle channel and to enhance convective heat transfer between the falling particles and the solid phase of the falling particle channel (endwalls and fibers). Steady-state experiments were conducted to measure the effective thermal conductivity of lattice frame material for two cases: a) when void space was occupied by air, b) when void space was occupied with particles. Further, convective heat transfer experiments have been conducted with both air (steady-state) and particles (quasi steady-state) as “working fluid” for panels sandwiching the Octet array. Three different lattice porosities ranging from 0.75 to 0.9 have been tested for a wide range of air flow rates and a fixed particle flow rate (highest potential).

Aider, Youssef↗
DOE OSTI2023

Binder Jet Additive Manufacturing Process and Material Characterization for High Temperature Heat Exchangers Used in Concentrated Solar Power Applications

The U.S. Department of Energy’s (DOE) Sunshot 2030 initiative has a goal of reducing the cost of concentrating solar power (CSP) to 5 cents per kWh for baseload power plants. One of the potential pathways to this goal includes a reduction in the cost of the supercritical CO2 (sCO2) power block to 0.9 cents per kWh. Recuperators—high and low temperatures, used in the sCO2 power cycle, contribute to >50% of the cost of the power cycle. This work studies the feasibility towards a ≥10% cost reduction for High Temperature Recuperators (HTR) used in the sCO2 power cycle. One way to address the cost reduction is by leveraging low-cost additive manufacturing, specifically, Binder Jet Additive Manufacturing (BJAM) to 3D print HTRs at scale. This study focuses on the development of a BJAM process towards 3D printing HTR cores using Stainless Steel alloy 316L (SS316L). To evaluate the suitability of the BJ process towards the HTR, high level specifications of the application are translated to materials capability requirements. Subsequently, at-temperature materials testing is conducted on as-printed and sintered additively manufactured coupons. Data from the coupons are compared against cast and wrought SS316L data obtained from the literature. Results show that the tensile properties from the BJ process compare well against cast properties. Furthermore, a baseline analysis of creep testing data is established for the BJ process, and insights are drawn from the results towards future improvements of the process.

14 SOLAR ENERGY↗
DOE OSTI2022

Measurement of Convective Heat Transfer Coefficients with Supercritical CO2 in Novel Additively Manufactured Helically Patterned Pin Fin Tubes Using the Wilson Plot Technique

This paper describes the measurement of convective heat transfer coefficients and friction factors for sCO2 flowing in pin-fin patterned pipes in the Heat Exchange and Experimental Testing (HEET) facility at the US DoE’s National Energy Technology Laboratory (NETL) in Morgantown, WV. The measurement procedures in the HEET rig were validated by conducting benchmark tests with smooth stainless-steel tube and comparing the results with published correlations for Nusselt number (Nu) and friction factor. Over typical Reynolds number range in sCO2, the measured Nu and friction factors were within 7% of classical correlations for smooth tube flow.The candidate pin fin patterned pipes were additively manufactured (AM) at the Oak Ridge National Laboratory. The pins were circular or elliptical in cross-section. Pin length to diameter aspect ratios were 1.33 and 2, while the pin diameter to tube diameter ratio was 0.188 and 0.125. Tests were performed for ReD varying from 6.9×104 to 2.2×105 and at conditions equivalent to the low pressure outlet (8.69 MPa, 361 K) of the low temperature recuperator (LTR) in an indirect sCO2 power cycle. The Wilson plot technique was utilized to measure the bulk heat transfer coefficients.For the better performing design (tube A, pin length to tube diameter ratio: 1.33, pin diameter to tube diameter ratio: 0.188), the local heat transfer coefficient increased by 112% relative to the Dittus-Boelter correlation at the LTR low pressure outlet. This corresponded to a 282% increase in the product of the heat transfer coefficient and the surface area. Large pressure drops across the test articles were observed.

Searle, Matthew↗
DOE OSTI2024

High-Temperature Oxidation Behavior of Wrought and Additive Manufactured Ni-based Alloys in Direct-Fired Supercritical CO2 Power Cycle Environments

Materials selection is a key concern for corrosion resistance in elevated temperature and pressure direct-fired supercritical CO2 (sCO2) power cycles. Herein, the wrought product form of alloy H282, as well as several additional nickel-based commercial alloys (230, 263, 617, 625, 740H), were exposed to direct-fired supercritical CO2 conditions (95CO2 – 4H2O – 1O2) at 750 °C and 20 MPa for over 2,000 h. Additionally, additive manufactured (AM) 282 produced by laser powder bed fusion (LPBF) were also included in the exposures. This paper focuses primarily on the differences observed in the degradation behavior of the wrought and additively manufactured materials. AM samples in the as-printed state were found to form less protective oxide scales resulting in higher oxidation rates compared to wrought samples. However, applying a 600 grit surface finish to the AM samples modified the oxidation behavior to closely resemble that of the wrought material. The AM samples formed Mo-rich carbides in the alloy beneath the oxide following sCO2 exposure, implying potentially higher levels of carbon uptake relative to the wrought material. Conversely, the AM samples seemed to be less affected by water-assisted oxide volatilization compared to the wrought material. The results are discussed in terms of the potential compatibility issues that may arise when using Ni-based alloys in the hot portions of direct-fired sCO2 power cycles, particularly in the case of thin-walled components.

Carney, Casey↗
DOE OSTI2024

Heat Transfer Experiments of Ribbed, Serpentine Cooling Passages with Supercritical CO2

The results of heat transfer experiments with supercritical CO2 (sCO2) to capture the performance of ribbed, serpentine cooling passages for Reynolds numbers in the range of 100,000 - 400,000 are presented. The oxy-combustion turbine operating in an Allam-Fetvedt cycle has a turbine inlet temperature exceeding 1100°C, necessitating internally cooled turbine blades due to material creep strength limits. Reynolds numbers for sCO2, with its combination of high fluid density and low viscosity, can be up to an order of magnitude higher than comparable internal cooling conditions for an air-breathing engine where the majority of experimental data exists. To improve the prediction of cooling performance through turbulated passages, a test rig was designed and constructed with interchangeable insert capability for operation in sCO2 with heat transfer from a heater outlet flow stream to a lower temperature recuperator outlet flow stream. The inserts included serpentine passage geometry with five passes, one of the inserts including chevron ribs and the other a plain wall. The multi-pass serpentine geometry allowed for the evaluation of the effects 180 deg. tip turns have on the return passage flow characteristics, as they can depart significantly from fully-developed flow characteristics. The test procedure included the use of a modified Wilson plot method, with hot flow stream conditions kept effectively constant so that monitored changes in the overall thermal resistance could be attributed to manipulations in cooling flow stream conditions. Conditions during testing consisted of test section pressures of approximately 180 bar, cooling flow stream temperature of 175°C and hot flow stream temperature of 410°C. Test points at discrete cool flow Reynolds numbers up to 400,000 demonstrated an expected trend of decreased fluid thermal resistance with increasing Reynolds number, while at comparable Reynolds number there was an exhibited lower thermal resistance and higher passage pressure drop for the ribbed insert compared to the plain-walled insert. Processing of test data included establishment of Nusselt number enhancement ratios, so that for different internal cooling passage dimensions in the actual turbine blade at comparable Reynolds number the ratio could be applied to predict cooling performance.

Marshall, Michael↗
DOE OSTI2023

Modular Design of High Temperature and Pressure Heat Exchangers Using 3D Printing

Functionally graded material (FGM), leveraged by latest additive manufacturing (AM) technologies, can add significant values to high temperature applications such as the HTR in supercritical sCO2 Brayton cycles. The project was focused on fabricating FGMs with complex geometries such as flow channels using DED and L-PBF technologies to support the modular design concept in achieving high-performance and low-cost high temperature recuperators for the sCO2 Brayton cycle. Samples printed from the base materials including both SS 316 and Inconel 625 have mostly met the material standards. L-PBF samples have achieved the fine feature sizes with good geometrical accuracy. In addition, DED has demonstrated its printability on LPBF part with both direct transition and using 50/50 mixed powders. Despite various challenging, the project helped advance the current state-of-the-art of DED technology in terms of printing fine geometries.

14 SOLAR ENERGY↗
DOE OSTI2022

Creep and Fatigue Characterization of High Strength Alloy Thin Sections in Advanced CO2 Heat Exchangers

The objective of this work was to characterize and model elevated temperature creep and fatigue behavior for thin sheet and foil forms of gamma-prime strengthened alloys in wrought form and as-processed folded and brazed constructions. This work was motivated by the demanding temperature and pressure service conditions of the GEN3 Concentrated Solar Power (CSP) and supercritical CO2 (sCO2) power cycle working fluid. More specifically, the possibility of leveraging the superior creep strength of gamma-prime alloys in folded-fin and brazed-plate heat exchanger constructions. Gamma-prime alloys represent a step-change in raw-material strength over solid-solution strengthened alloys. And the folded-fin and brazed-plate heat exchanger architecture is lightweight and leverages cost-effective material stock forms. The investigation contained two parallel paths. (1) The first is referred to as a fundamental investigation where Oak Ridge National Laboratory conducts uniaxial creep testing on thin sheet and foil in wrought form. This effort aimed to serve as a benchmark against a relatively sparse existing database and a baseline comparison for path number 2. (2) The second path is referred to as the practical investigation where Brayton Energy manufactures plate-fin heat exchangers and performs pressurized creep and fatigue testing. This effort aimed to de-risk heat exchanger manufacturing process for service under sCO2 CSP conditions. A total of 14 uniaxial creep tests were completed using Haynes 282 thin sheet and foil. A variety of heat treatments were specified to coincide with path number 2. Baseline metallography of test samples and creep strength performance are contained. Benchmarks relatively to existing thick-form Haynes 282 are made, as well as to other thin-form Nickel-based superalloys. Description of a wrought-form modeling approach for thin gamma-prime alloys is also discussed. A total of 11 pressurized creep and fatigue tests were completed successfully with Haynes 282 heat exchanger prototypes. Manufacturing processing details, testing details, testing results, and failure analysis are discussed. Additionally, creep modeling techniques to predict failure are discussed, and modeling to support technological-to-market. In conclusion, Haynes 282 foils were demonstrated to yield rupture two-to-three orders of magnitude higher than Haynes 230 foils under similar conditions. And the manufactured heat exchanger prototypes demonstrated strength similar to the wrought constituents. Both of which contribute to elevated performance potential or cost savings in practice. Discussion is included.

14 SOLAR ENERGY↗
DOE OSTI2024

Reduced LCoE CSP Through Utilizing Process Gas Lubricated Bearings in Oil-Free Drivetrains

The GE Research team proposed to advance the TRL level of process lubricated gas bearings from TRL3 based on the DE-EE0007109 program to TRL5 addressing a critical risk item that radial gas bearings can provide satisfactory rotordynamic performance in supporting a representative rotor for sCO2 Power Cycles. The ability to apply process lubricated gas bearings can provide cost savings with reduction of the associated lube oil systems and an efficiency benefit worth 2% efficiency for the turbomachinery configuration first presented in DE-EE005804. The process lubricated gas bearings are enablers for advanced hermetically sealed configurations that have the potential for significant advancement in sCO2 Power Cycles for CSP applications including the 2% efficiency increase referred to above in addition to OPEX savings with no need to refill the CO2 valued at 60k USD/yr and cost reductions of 50 USD/kWe all leading to a potential 0.95¢/kWh reduction positively impacting CSP goals.

14 SOLAR ENERGY↗
DOE OSTI2024

Analysis and Optimization of the Recompression Cycle with High Temperature Recuperator Bypass for Concentrating Solar Power Applications

This work analyzes the sCO2 recompression with high temperature recuperator (HTR) bypass power cycle for use in concentrating solar power (CSP) systems. CSP operation differs from other thermal power plants in that CSP must balance between maximizing the heat transfer fluid (HTF) temperature difference and maximizing the cycle thermal efficiency, which typically are inversely related. Large HTF temperature differences reduce the size and cost of thermal energy storage (TES), improve the solar receiver efficiency, and require lower mass flow rates that reduce pumping power required to elevate the HTF to the receiver. The recompression cycle with HTR bypass potentially offers improved thermal efficiency with larger HTF temperature differences as compared to the recompression cycle, and it has fewer turbomachinery components than the partial cooling cycle. The recompression with HTR bypass cycle adds a second lower temperature primary heat exchanger which transfers heat from the HTF to the fraction of sCO2 flow that bypasses the HTR. We developed a model to compare the recompression with HTR bypass cycle to the recompression and partial cooling cycles. A sweep of design parameters including bypass fraction, recompression fraction, recuperator conductance, and pressure ratio is used to form a pareto-optimal front with the cycle thermal efficiency and HTF temperature difference as objectives. An optimization routine has also been developed to find optimal design point parameters for a target HTF temperature difference. The performance of the recompression with HTR bypass cycle is compared with recompression and partial cooling cycles.

concentrating solar power↗
DOE OSTI2023

Performance Analyses of Supercritical Carbon Dioxide-Based Parabolic Trough Collectors with Double-Glazed Receivers

Supercritical carbon dioxide is becoming a hot research topic as a potential heat transfer fluid in parabolic trough concentrators since it enables operating the solar system at high temperatures for a higher quality of energy. However, the corresponding inflated thermal losses necessitate alternative receiver designs. This work examines four double-glazed receivers, with each annular space being evacuated or non-evacuated, in terms of the absorber tube's diameter (53-80 mm) and the diameter ratios of the two glass shells (1.2-2.0). An analytical model is developed and validated for this purpose, and the four designs are further examined using ground-level solar and meteorological measurements. The results demonstrate higher performance in the case of fully evacuating the receiver and using the smallest possible diameters of the three concentric cylinders, where the energy and exergy efficiencies reach 65.3 and 40.3%, respectively. Yet, evacuating only the inner annular space is sufficient to achieve virtually the same performance level. This energy efficiency decreases to 62% in case of increasing the tube diameter to 80 mm. As the operating temperature increases from 423 to 850 K, the specific thermal losses increase by 3.98-4.34 folds, depending on the receiver design. Double glazing the receivers is favorable only at high operating temperatures of sCO2, where the reduction in thermal losses overcomes the drop in optical efficiency. For an inlet sCO2 temperature of 850 K, thermal losses are reduced by 33.64 and 53.92%, compared to evacuated and non-evacuated single-glazed receivers, respectively. Throughout the year, the fully evacuated and fully non-evacuated double-glazed receivers have energy efficiencies of 54.96 and 52.39%, exergy efficiencies of 33.64 and 32.06%, and thermal losses of 348.8 and 402.5 W/m, respectively.

analytical model↗