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At least 631 records · Page 35

Mahakala: A Python-based Modular Ray-tracing and Radiative Transfer Algorithm for Curved Spacetimes

We introduce Mahakala, a Python-based, modular, radiative ray-tracing code for curved spacetimes. We employ Google's JAX framework for accelerated automatic differentiation, which can efficiently compute Christoffel symbols directly from the metric, allowing the user to easily and quickly simulate photon trajectories through non-Kerr spacetimes. JAX also enables Mahakala to run in parallel on both CPUs and GPUs. Mahakala natively uses the Cartesian Kerr–Schild coordinate system, which avoids numerical issues caused by the pole in spherical coordinate systems. We demonstrate Mahakala's capabilities by simulating 1.3 mm wavelength images (the wavelength of Event Horizon Telescope observations) of general relativistic magnetohydrodynamic simulations of low-accretion rate supermassive black holes. The modular nature of Mahakala allows us to quantitatively explore how different regions of the flow influence different image features. We show that most of the emission seen in 1.3 mm images originates close to the black hole and peaks near the photon orbit. We also quantify the relative contribution of the disk, forward jet, and counterjet to 1.3 mm images.

79 ASTRONOMY AND ASTROPHYSICS↗

Jamming Detection for Low-Resolution SC-FDE Systems: A Machine Learning Approach

Jammers interfere with communication between base stations (BSs) and legitimate users, leading to degradation of wireless system performance. Our study focuses on jamming detection for wideband single-carrier frequency domain equalization (SC-FDE) systems with low-resolution analog-to digital converters (ADCs). In such systems, jamming detection is challenging because traditional analytical approaches cannot be directly applied due to the delay dispersion in wideband channels and the non-linearity induced by low-resolution ADCs. We propose a machine learning (ML)-based jamming detection method that directly uses the quantized receive signals. Significantly, our ML-based detector can be integrated into existing standard frameworks, such as unique word (UW)-based SC-FDE systems, as it uses existing pilots without requiring additional pilots for jamming detection. Through numerical simulations, we show that two or more bits provide satisfactory performance compared to unquantized scenarios. Additionally, we demonstrate that using more and well-separated pilot symbols improves performance.

99 GENERAL AND MISCELLANEOUS↗

Large Eddy Simulation of Gasoline Sprays in a Lagrangian–Eulerian Framework Using the High-Order Spectral Element Method

Predicting the spray evolution using simulations requires accurate modeling of the turbulent gas-phase flow field. Here, in this study, the high-order spectral-element method (SEM), implemented in the code Nek5000, was used to provide highly resolved solutions to the turbulent flow field. Spray modeling capabilities were implemented into the Nek5000 code. The spray is modeled in a Lagrangian–Eulerian (LE) framework, where the liquid is represented by discrete parcels of droplets. The method for coupling liquid and gas in the context of SEM is described, which allows for very fine meshes to be used without affecting the stability of the solution. Large-eddy simulations (LES) of the eight-hole ECN Spray G gasoline injector were conducted. Numerical results are compared against experimental data for liquid penetration, droplet size and gas velocity. The morphology of the multiplume spray is compared against experimental data. The effect of different spray injection inputs is analyzed. It was found that using a plume direction of 33 deg and an injection cone angle of 30 deg produced the best results overall. This work shows the applicability of SEM for spray modeling applications, where use of a high-order flow solver can help us understand the multiplume spray aerodynamics and how it leads to plume collapse under certain conditions. Results also highlight the need for tuning spray input parameters in the LE framework, even when high-fidelity gas flow solutions are possible.

33 ADVANCED PROPULSION SYSTEMS↗

A conservative, interface-resolved, compressible framework for the modeling and simulation of liquid/gas phase change

This paper presents a method for simulating evaporation in a compressible, interface-resolved framework appropriate for modeling problems of engineering interest. In order to achieve robustness and broad applicability, the method has been designed to discretely enforce consistent mass and thermal energy transport at the phase interface, to globally conserve mass, momentum, and energy, and to be capable of modeling compressible and incompressible systems. Verification is performed via the Sod-shock test, one-dimensional heat conduction, evaporation from a planar interface, and evaporation of three-dimensional droplets. Convergence with increasing mesh resolution is demonstrated in all tested configurations, and conservation is maintained near machine precision for a translating droplet. Conservation and accurate phase change rates are preserved at the low numerical resolutions commonly encountered in engineering calculations. Following verification, the method is validated by comparison to an empirical correlation for evaporating droplets in high temperature crossflow, and the presentation concludes with the simulation of an iso-octane spray at conditions representative of gasoline direct injection. In conclusion, successful verification, validation, and demonstrated practical utility suggest the method to be an accurate, efficient, and robust approach for the study of phase change in engineering systems.

97 MATHEMATICS AND COMPUTING↗

Capturing the fractocohesive length scale in elastomers through a statistical mechanics-based gradient enhanced damage model

Here, this study aims to examine modeling flaw sensitivity in elastomers. The direct incorporation of polymer chain statistical mechanics considerations into a continuum stretch-based gradient-enhanced damage formulation, in turn, allows a representation of diffuse chain damage and fracture events that align with known micromechanical mechanisms. Through a series of numerical experiments, we simulate crack propagation and extract the fracture energy as an output of the model, while keeping track of the micromechanical signatures of diffuse chain damage that accommodate fracture propagation and eventually influence flaw sensitivity. Finally, by combining the fracture toughness and the work to rupture, we identify a fractocohesive length of the material, corresponding to the full width of the damage process zone. As the damage-to-fracture cascade in the proposed GED model is influenced by the introduction of a length scale associated with network imperfection and long-range load transfer, the emerging relationship of the two length scales is discussed, providing a potential link between microscopic damage mechanisms and the observed macroscopic fracture response.

36 MATERIALS SCIENCE↗

Verification and Validation of Spectral Element Code for Supercritical CO2 Flow in Vertical Heated Tubes

The investigation of heat transfer in supercritical CO2 (sCO2) has garnered considerable attention in recent decades, given sCO2's potential as a promising working fluid for advanced power conversion cycles. Despite previous research efforts, there are still gaps in our understanding of sCO2 heat transfer, particularly in conditions associated with heat transfer deterioration. To delve into sCO2 heat transfer more comprehensively, we propose employing the high-fidelity computational fluid dynamics code NekRS to simulate sCO2 flow using the large eddy simulation technique. Through graphics processing unit acceleration, NekRS achieves a higher computational speed than traditional CPU-based systems. However, before using NekRS in practical applications involving sCO2, it is imperative to perform verification and validation. Here, this paper presents our efforts to verify and validate the NekRS code's capability for simulating sCO2 using heated vertical tubes, where heat transfer deterioration usually happens. To accommodate the unique properties of sCO2, we have modified the NekRS code by integrating third-party property modules, such as REFPROP and PROPATH. Our simulations are compared with experimental and numerical data from the literature, instilling confidence in leveraging NekRS for future engineering applications. Our simulations also reveal that the accuracy of the property module significantly impacts the results, with REFPROP outperforming PROPATH for sCO2 properties. Additionally, we observed that, depending on the flow direction, buoyancy can either enhance or suppress turbulence in sCO2 flow. In upward flow, under certain conditions, the suppressed turbulence leads to heat transfer deterioration, resulting in elevated wall temperatures.

NekRS↗

EchemAMR (electro-chemical microsctructure scale models with adaptive meshing) [SWR-23-111]

A 3D microstructure resolving electrochemical transport and interfacial chemistry solver. Electrode microstructure plays an important role in determining the performance of an electrochemical system, e.g. lithium ion battery. EchemAMR is a microstructure scale model that solves the governing equations for ion transport, electrical current continuity, interfacial chemistry and structural mechanics. Complex microstructure geometries from imaging can be directly imported into EchemAMR. A volume fraction based description of the geometry on Cartesian grid with an immersed interface formulation enables simplified meshing and large-scale simulations with millions of degrees of freedom. EchemAMR has been tested against systems with analytic solutions for numerical convergence and highly resolved lithium ion battery microstructures. EchemAMR demonstrates excellent mass conversation and efficient scaling on heterogenous High-Performance Computing (HPC) with central and graphics processing units.

Sitaraman, Hariswaran↗

Wake-Resolving Acoustic Tomography: Advances through Numerical Covariance Methods

Acoustic tomography offers path-integrated measurements of atmospheric velocity and temperature fluctuations with high spatial resolution. Classical implementations of time-dependent stochastic inversion rely on homogeneous, isotropic covariance models that are poorly suited to the anisotropic structure of wind turbine wakes. By directly estimating heterogeneous covariances from large-eddy simulations (LESs) into the time-dependent stochastic inversion operator, we relax implicit assumptions in the analytical models used historically. Retrievals using these LES-informed models improve agreement with true fields in variance, turbulent kinetic energy, and spectral content compared to analytical and precursor-based covariance models. The results indicate that LES-informed covariance models can enhance the accuracy of acoustic tomography retrievals in complex, anisotropic flows such as wind turbine wakes in some cases and highlight instances where analytical models still offer competitive performance, despite their simplifying assumptions.

17 WIND ENERGY↗

Numerical simulation of falling film sensible heat transfer over round horizontal tubes

Numerical simulations are performed to explore the heat transfer characteristics of falling films over horizontal round tubes with uniform heat flux imposed for a range of Reynolds numbers spanning the droplet, jet, and sheet regimes. Simulations results agree well with available experimental measurements. The study analyzes the local as well as average heat transfer behavior under the different flow modes. The numerical results show that the local Nusselt number (Nu) distribution depends on the flow features in each mode and varies substantially in all directions for the respective mode. In the droplet mode, the Nu value varies significantly as the droplet impinges and the remnant liquid-bridge retracts (peak instantaneous Nu near 6), followed by wave propagation over the tube surface with peak Nu around 0.25. For the jet modes, the local maximum in the heat transfer occurs off-center to the impingement location with magnitudes of peak Nu = 3.1 for the inline jet mode and Nu = 2.7 for the staggered jet mode, while on the rest of the tube surface, it has an inverse relation with the liquid film thickness. Substantial variations in the heat transfer value are also recorded in the middle of the two impinging jets with Nu = 0.95 in the inline jet mode where the neighboring jets do not interact, and Nu = 0.60 in the crest region of the staggered jet mode where the neighboring jets interact with each other. In the sheet mode, the Nu was seen to depend on the thickness of the liquid waves traversing over the tube surface. Lower Nu values were recorded beneath the crest location of the liquid waves, which increases (1.4–11.6% depending on circumferential location) abruptly in magnitude at the advancing fronts of the waves. The temperature distribution in the liquid film in each of the modes was examined to evaluate the mechanism of heat transfer process. This study also compares the local heat transfer coefficient distribution with the analytical heat transfer models derived to predict heat transfer performance over horizontal tube surfaces.

42 ENGINEERING↗

Frame invariant neural network closures for Kraichnan turbulence

Numerical simulations of geophysical and atmospheric flows have to rely on parameterizations of subgrid scale processes due to their limited spatial resolution. Despite substantial progress in developing parameterization (or closure) models for subgrid scale (SGS) processes using physical insights and mathematical approximations, they remain imperfect and can lead to inaccurate predictions. In recent years, machine learning has been successful in extracting complex patterns from high-resolution spatio-temporal data, leading to improved parameterization models, and ultimately better coarse grid prediction. However, the inability to satisfy known physics and poor generalization hinders the application of these models for real-world problems. In this work, we put forth a frame invariant closure approach to improve the accuracy and generalizability of deep learning-based subgrid scale closure models by embedding physical symmetries directly into the structure of the neural network. Specifically, we utilized specialized layers within the convolutional neural network in such a way that desired constraints are theoretically guaranteed without the need for any regularization terms. We demonstrate our framework for a two-dimensional decaying turbulence test case mostly characterized by the forward enstrophy cascade. We show that our frame invariant SGS model (i) accurately predicts the subgrid scale source term, (ii) respects the physical symmetries such as translation, Galilean, and rotation invariance, and (iii) is numerically stable when implemented in coarse-grid simulation with generalization to different initial conditions and Reynolds number. This work opens up a possibility of connecting physics-based theories and data-driven modeling paradigms, and thus represents a promising step towards the development of physically consistent data-driven turbulence closure models.

42 ENGINEERING↗

The inviscid incompressible limit of Kelvin–Helmholtz instability for plasmas

The Kelvin–Helmholtz Instability (KHI) is an interface instability that develops between two fluids or plasmas flowing with a common shear layer. KHI occurs in astrophysical jets, solar atmosphere, solar flows, cometary tails, planetary magnetospheres. Two applications of interest, encompassing both space and fusion applications, drive this study: KHI formation at the outer flanks of the Earth’s magnetosphere and KHI growth from non-uniform laser heating in magnetized direct-drive implosion experiments. Here, we study 2D KHI with or without a magnetic field parallel to the flow. We use both the GAMERA code, which solves the compressible Euler equations, and the STRATOSPEC code, which solves the Navier-Stokes equations under the Boussinesq approximation, coupled with the magnetic field dynamics. GAMERA is a global three-dimensional MHD code with high-order reconstruction in arbitrary nonorthogonal curvilinear coordinates, which is developed for a large range of astrophysical applications. STRATOSPEC is a three-dimensional pseudo-spectral code with an accuracy of infinite order (no numerical diffusion). Magnetized KHI is a canonical case for benchmarking hydrocode simulations with extended MHD options. An objective is to assess whether or not, and under which conditions, the incompressibility hypothesis allows to describe a dynamic compressible system. For comparing both codes, we reach the inviscid incompressible regime, by decreasing the Mach number in GAMERA, and viscosity and diffusion in STRATOSPEC. Here, we specifically investigate both single-mode and multi-mode initial perturbations, either with or without magnetic field parallel to the flow. The method relies on comparisons of the density fields, 1D profiles of physical quantities averaged along the flow direction, and scale-by-scale spectral densities. We also address the triggering, formation and damping of filamentary structures under varying Mach number or Atwood number, with or without a parallel magnetic field. Comparisons show very satisfactory results between the two codes. The vortices dynamics is well reproduced, along with the breaking or damping of small-scale structures. We end with the extraction of growth rates of magnetized KHI from the compressible regime to the incompressible limit in the linear regime assessing the effects of compressibility under increasing magnetic field. The observed differences between the two codes are explained either from diffusion or non-Boussinesq effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Understanding the structural mechanics of ligated DNA crystals via molecular dynamics simulation

DNA self-assembly is a highly programmable method to construct arbitrary architectures based on sequence complementarity. Among various constructs, DNA crystals are macroscopic crystalline materials formed by assembling motifs via sticky end association. Due to their high structural integrity and size ranging from tens to hundreds of micrometers, DNA crystals offer unique opportunities to study the structural properties and deformation behaviors of DNA assemblies. For example, enzymatic ligation of sticky ends can selectively seal nicks resulting in more robust structures with enhanced mechanical properties. However, the research efforts have been mostly on experiments involving different motif designs, structural optimization, or new synthesis methods, while their mechanics are not yet fully understood. The complex properties of DNA crystals are difficult to study via experiments alone, and numerical simulation can complement and aid the experiments. The coarse-grained molecular dynamics (MD) simulation is a powerful tool that can probe the mechanics of DNA assemblies. Here, we investigate DNA crystals made of four different motif lengths with various ligation patterns (full ligation, major directions, connectors, and in-plane) using oxDNA, an open-source, coarse-grained MD platform. We found that several distinct deformation stages emerge in response to mechanical loading and that the number and the location of ligated nucleotides can significantly modulate structural behaviors. These findings should be useful for predicting crystal properties and thus improving the design.

DNA crystal↗

Final DOE-ASR Report for the Project “Using LASSO to bridge the gap between model and observations and to learn about atmospheric convection”

Atmospheric convection spans a wide range of spatial and temporal scales and involves complex interactions with the surrounding dynamic and thermodynamic environment, particularly over tropical continental regions. These processes remain a major source of uncertainty in weather and climate models, including persistent biases in the diurnal cycle of convective precipitation that directly affect estimates of climate sensitivity. Addressing these challenges requires the combined use of high-resolution observations and cloud-resolving modeling frameworks. In this context, the DOE Atmospheric Radiation Measurement (ARM) program’s Large-Eddy Simulation ARM Symbiotic Simulation and Observation (LASSO) activity provides a powerful platform that pairs comprehensive observations with numerical simulations to enable process-level understanding of atmospheric convection. Within this context, this Research and Development Partnership Pilot (RDPP) project was designed to initiate and expand DOE ARM/ASR research capacity at minority-serving institutions, while advancing scientific understanding of convective processes over the Amazon rainforest. Consistent with the RDPP mission, the project emphasized partnership development, training, and workforce capacity building alongside exploratory research activities. On the scientific side, the project produced two peer-reviewed journal articles, and one manuscript currently under review (see list in section 3.1). Together, these studies combine long-term ARM observations and cloud-resolving and convection-permitting modeling to investigate the environmental controls on the shallow-to-deep convective transition during the Amazon wet season. The results demonstrate the central role of early-day moisture preconditioning and large-scale dynamical forcing in regulating isolated deep convection, provide mechanistic insight into convective evolution, and establish physically informed modeling frameworks for future sensitivity experiments. These scientific outcomes are described in sections 2.1 to 2.3 and were disseminated in 8 conference presentations (see section 3.2) and 5 invited talks (see section 3.3), reflecting broad engagement with our community. Equally important, the project achieved its RDPP capacity-building objectives (see section 2.4). A sustained research partnership was established among the University of Maryland, Baltimore County (UMBC), Morgan State University (MSU), and Howard University (HU), and extended to include collaboration with Pacific Northwest National Laboratory (PNNL). The project organized multiple multi-day training events focused on ARM data, LASSO simulations, and quantitative analysis methods, directly engaging students, postdoctoral researchers, and faculty across institutions. These activities broadened participation in ASR research and led to independent adoption of LASSO workflows by students beyond the immediate project team. Finally, the project successfully positioned the participating institutions to pursue future DOE research. Preliminary scientific results, coupled with strengthened partnerships and technical capacity, enabled the submission of follow-on proposals to DOE ASR funding opportunities. In this way, the project fulfilled the RDPP goal of seeding durable research capacity and laying the foundation for larger-scale, sustained engagement with DOE ARM and ASR programs.

54 ENVIRONMENTAL SCIENCES↗

Infrasonic directivity of monopole, dipole and bipole ground-surface reflected sources

Infrasound (acoustic waves below 20 Hz) can be used to detect, locate and quantify activity in the atmosphere such as volcanic eruptions and anthropogenic explosions. Attempts to quantify volcanic eruption parameters such as exit velocity, plume height and mass flow rate using infrasound data depend strongly on assumptions of the acoustic source type. Infrasonic sources may produce omnidirectional or directional wavefields, while propagation effects, such as interaction with topography, can induce further wavefield directivity that is measured by field instrumentation. Limited sampling of these wavefields can hinder our ability to infer the underlying source, and thus our understanding of the eruption characteristics. Equivalent sources are often used to represent acoustic source mechanisms and resultant wavefields. In this study, we review equivalent acoustic sources as they pertain to infrasonic scale and wavelengths commonly encountered in very local (⁠<5 km range) geophysical field deployments. We highlight the equivalent infrasonic bipole source that can be induced by ground-reflection of an elevated monopole; we are not aware of any prior infrasound studies that use the bipole source concept. We use analytical and numerical methods to explore source directivity of monopole, dipole and bipole ground-reflected sources at infrasonic frequencies as well as the additional directivity complications introduced by interactions with topography. We illustrate that for typical volcano-infrasound wavelengths, increasing height above the ground as well as increasing source frequency leads to increased wavefield directivity. Numerical modelling using a simple omnidirectional monopole source embedded in topography further illustrates that both horizontal and vertical infrasound directionality can be induced by topography at the distance scales appropriate for local volcano infrasound monitoring. Information summarized in this analytical and numerical exploration of infrasound directivity may be used to help guide future volcano-infrasound field deployments intended to estimate source parameters or quantify wavefield directivity. Analytic solutions for simple whole-space or half-space atmospheres provide useful formulations for planning or initially analysing geophysical field-scale experimental data; however, especially at very local distances from the source (⁠<5 km), 3-D simulations are necessary to account for complex topography commonly encountered in volcano-infrasound applications.

Infrasound↗

Development and Validation of a Two-Phase Thermal-Hydraulic CFD Code NEK-2P

A project is underway to develop, verify and validate an advanced two-phase flow modeling capability for the highly-scalable, high-performance Computational Fluid Dynamics (CFD) code NEK5000. The goal of this work is to verify and validate the two-phase version of the NEK5000 code, named NEK-2P, to simulate the two-phase flow and heat transfer phenomena that occur in a Boiling Water Reactor (BWR) fuel bundle under various operating conditions. The NEK-2P two-phase flow models follow the approach used for the Extended Boiling Framework (EBF) previously developed at Argonne but include more fundamental physical models of boiling phenomena and advanced numerical algorithms for improved computational accuracy, robustness, and computational speed. The development of the NEK-2P two-phase solver and the implementation of the Extended Boiling Framework two-phase models were initially supported by Argonne National Laboratory (Argonne) through a Laboratory Directed Research and Development (LDRD) project during FY2014-2016. The development and validation of the two-phase models through analyses of selected two-phase boiling flow experiments was supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY2017-2020. This report focuses on verification and validation of the water-steam boiling model NEK-2P Two-Phase, CFD code. The NEK-2P was validated with Nuclear Power Engineering Corporation (NUPEC) Pressurized Water Reactor (PWR) Sub-channel and Bundle Test (PSBT) void distribution benchmark. Three different simulations were performed and analyzed for various operating conditions such as wall-heat flux and sub-cooled inlet temperatures. Reasonably good agreement with measured data was obtained in predicting the measured void distributions. Simulations were performed for Virginia Tech. (VT) 3x3 rod bundle geometry with and without spacers. The preliminary results were presented for Simplified Spacer Grid (SSG). In addition, the implementation of interface reconstruction model was tested with one of the Becker benchmark Critical Heat Flux (CHF) experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Adjoint DSMC for nonlinear Boltzmann equation constrained optimization

Applications for kinetic equations such as optimal design and inverse problems often involve finding unknown parameters through gradient-based optimization algorithms. Based on the adjoint-state method, we derive two different frameworks for approximating the gradient of an objective functional constrained by the nonlinear Boltzmann equation. While the forward problem can be solved by the DSMC method, it is difficult to efficiently solve the high-dimensional continuous adjoint equation obtained by the “optimize-then-discretize” approach. This challenge motivates us to propose an adjoint DSMC method following the “discretize-then-optimize” approach for Boltzmann-constrained optimization. We also analyze the properties of the two frameworks and their connections. Here, several numerical examples are presented to demonstrate their accuracy and efficiency.

97 MATHEMATICS AND COMPUTING↗

TRUST-EABM End-of-Year Report: Release FY20

The Delivery Environments (DE) program work package Testbeds to Reduce Uncertainties in Simulations and Tests (TRUST) is designed to quantify and reduce the uncertainty associated with experimental testing and numerical simulation of large engineering assemblies to support the efficient and responsive development of future systems. Because engineering assemblies contain a large number of uncertainty sources, well-characterized testbeds must be designed to isolate individual uncertainty sources. Once quantified, uncertainty sources can be compared to direct research and development funding towards the largest sources driving behavior of interest. Quantified uncertainty may also be propagated through engineering simulations to determine quantitative confidence in simulation predictions and for comparison against uncertainty in the experimental measurements.

97 MATHEMATICS AND COMPUTING↗

Investigating Performance of Geothermal Reservoirs With Bi-Directional Heat Transfer for Seasonal Thermal Storage Using Thermal-Hydraulic Reservoir Simulations

This paper presents initial simulation results of deep subsurface seasonal thermal storage of waste heat from a natural gas-fired power plant during the summer months for providing heating during winter months at the Cornell University main campus in Ithaca, New York. An injection temperature profile is calculated with the MEnU tool and numerical reservoir simulations are conducted with the simulator FALCON. Both a porous medium and large single fracture geothermal reservoir are considered at about 3 km depth with initial reservoir temperature of 75 degrees C. Simulations indicate that a much smaller reservoir - which is technically easier and less risky to develop - is sufficient when operating the reservoir for seasonal thermal storage instead of for continuous heat production. For example, storing 13 GWh of heat seasonally in a 100 m thick porous medium based on the Galway formation requires about 65 m of well spacing to limit the yearly variation in production temperature to 10 degrees C. Operating this reservoir for continuous heat production would require a well spacing of 365 m to limit the thermal decline to 10 degrees C after 10 years. Neglecting wellbore heat losses and assuming uniform and homogeneous properties, a round-trip thermal efficiency of 100% can be obtained if the yearly averaged injection temperature matches the initial reservoir temperature.

district heating↗