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At least 1,315 records · Page 73

Global energy spectrum of the general oceanic circulation

Abstract Advent of satellite altimetry brought into focus the pervasiveness of mesoscale eddies $${{{{{{{\bf{{{{{{{{\mathcal{O}}}}}}}}}}}}}}}}({100})$$ O ( 100 ) km in size, which are the ocean’s analogue of weather systems and are often regarded as the spectral peak of kinetic energy (KE). Yet, understanding of the ocean’s spatial scales has been derived mostly from Fourier analysis in small "representative” regions that cannot capture the vast dynamic range at planetary scales. Here, we use a coarse-graining method to analyze scales much larger than what had been possible before. Spectra spanning over three decades of length-scales reveal the Antarctic Circumpolar Current as the spectral peak of the global extra-tropical circulation, at ≈ 10 4 km, and a previously unobserved power-law scaling over scales larger than 10 3 km. A smaller spectral peak exists at ≈ 300 km associated with mesoscales, which, due to their wider spread in wavenumber space, account for more than 50% of resolved surface KE globally. Seasonal cycles of length-scales exhibit a characteristic lag-time of ≈ 40 days per octave of length-scales such that in both hemispheres, KE at 10 2 km peaks in spring while KE at 10 3 km peaks in late summer. These results provide a new window for understanding the multiscale oceanic circulation within Earth’s climate system, including the largest planetary scales.

54 ENVIRONMENTAL SCIENCES↗

A hardware-in-the-loop (HIL) testbed for cyber-physical energy systems in smart commercial buildings

In recent years, there has been a growing trend toward the development of smart buildings that rely on cyber-physical systems (CPS) to optimize occupant comfort, safety, and energy efficiency. To ensure the reliable and efficient operation of CPS with designed control strategies, it is important to evaluate their performance under various scenarios before deploying them in the real world. This is where a Hardware-in-the-loop (HIL) testbed designed for studying sensor and control-related studies in smart buildings can be highly valuable. With the growing threat of cyber-attacks and physical faults targeting smart buildings, it is essential to ensure the security of building operations. A HIL testbed can emulate cyber-attack and physical fault scenarios, allowing researchers to develop and test threat detection and mitigation algorithms. This enables researchers to identify potential issues and optimize the algorithms in a safe and controlled environment before they are deployed in real-world settings, reducing the risk of failures that can negatively impact occupant comfort, safety, and energy efficiency. Therefore, this paper developed a HIL testbed designed for cyber-physical energy systems (e.g. buildings automation system (BAS)) in smart commercial buildings. The HIL testbed is comprised of a real-time building and Heating, Ventilation, and Air-Conditioning (HVAC) emulator using Modelica-based dynamic models, a set of BAS controllers, and a BAS computer server. The data generation capability of the HIL testbed is demonstrated by tracking normal and faulty operating data in the BAS, as well as monitoring detailed network traffic in the local BAS network. Here, this study further demonstrates the HIL testbed’s capability by conducting case studies on real-time physical fault and cyber-attack experiments using a Department of Energy (DOE) prototype commercial building. It is anticipated that the fully functional HIL testbed will be utilized for a variety of sensor and control-related studies, including but not limited to testing, developing, validating of different HVAC control strategies, fault detection & diagnosis, energy monitoring and analysis, cyber security study, etc.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Dynamic Rupture Simulations of the Mw7.2 1992 Landers,California, Earthquake

An important part of the simulation technique implemented in the Recipe is the earthquake rupture characterization based on established empirical scaling relationships between source parameters and seismic moment. The scaling relationships used in the rupture characterization are derived from recorded data and are tested against dynamic and kinematic rupture models of crustal earthquakes. Currently, a revised three-stage source scaling relationship between the source rupture area and seismic moment of inland crustal earthquakes, initially proposed by Irikura and Miyake, is being used. Recent analysis of results obtained with the Recipe for the 2016 M7.1 Kumamoto earthquake performed by several researchers, including the PI, Arben Pitarka, indicate that in order to reproduce the near-fault long-period ground motions and the permanent displacements, observed during surface-rupturing earthquakes, the recipe needs modifications to the kinematic rupture parametrization in the shallow crustal weak zone. In particular, improvements are required in characterizing the slip rate function at shallow depths, above the sesimogenic zone. The main objective of this research project was the development of a dynamic rupture model for the Mw7.2 1992 Landers, California earthquake. The dynamic rupture model was used to derive kinematic rupture parameters, such as slip, slip-rate, rupture time distributions, and slip rate functions in the weak (0-4km) and seismogenic crustal zones. In addition to the knowledge gained from the dynamic rupture modeling of Chi-chi, Ridgecrest, Kumamoto and other crustal earthquakes, studied by the PI, the rupture characterization of the Landers earthquake can be helpful in updating the conventional recipe for broadband ground motion simulations of crustal earthquakes with shallow rupture. The project emphasizes the need for performing physics-based earthquake rupture modeling which ultimately will inform further improvements of rupture characterization. In particular, the modeling of rupture dynamics for recorded earthquakes, and numerical simulations for different rupture scenarios, provides physical constrains on slip evolution in time and space, used in adjustments of empirical source scaling relationships for large crustal earthquakes.

58 GEOSCIENCES↗

Quantitative analysis of cost savings and occupants’ preferences in grid-interactive smart home operation

Many utility companies in the United States have introduced time-of-use (TOU) rates for homeowners with the goal of regulating electricity consumption during peak hours. The electrical appliances in homes include various thermostatically controlled devices, such as air conditioners (AC) for thermal comfort, and nonthermostatically controlled devices such as clothes washers. As a result, homeowners face the complicated challenge of economically operating multiple electrical appliances in their homes while maintaining comfort and convenience. This is usually due to the lack of an explicit understanding of the correlation between cost saving and the users’ comfort. To understand the correlation, this article is designed to construct a framework by integrating three major components: a multi-objective optimization method accommodating multiple competing goals with different weights, a learning-based system modeling approach describing the dynamics and thermal coupling effects of appliances, and a novel comfort index method differentiating preferred and acceptable thermal comfort. Our proposed framework can allow the indoor air temperature to fall into the "preferred" range with a marginal cost increase. Furthermore, the simulation result shows that an additional 8 h for the preferred thermal comfort can be achieved with a cost increase of only 1.77%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Computational capacity in hydrodynamic real-time hybrid simulation applied to simulate the dynamic response of floating offshore wind turbines

Real-time hybrid simulation (RTHS) mitigates similitude distortions in model-scale tests of floating offshore wind turbines (FOWTs) by coupling physical experiments with numerical models in real time. The coupling requires faster-than-real-time numerical computations to satisfy temporal similitude with the physical experiment, presenting a bottleneck for using more complex numerical models in RTHS. This paper presents a hydrodynamic-RTHS (hydro-RTHS) framework for FOWTs that simulates the hydrodynamics physically and the aerodynamics numerically with sensor feedback from the physical testing. The framework adapts the three-loop hardware architecture to leverage greater computational resources and mitigate strict temporal requirements, enabling more computationally demanding numerical analyses in hydro-RTHS. The three-loop hardware architecture integrates multiple machines, each dedicated to either numerical analysis or RTHS controls, with a rate-transition algorithm to synchronize the tasks executed across the different machine processors. Virtual and physical tests verified and validated the hydro-RTHS framework, respectively. The ”virtual” tests, which approximates the physical domain numerically, verified the RTHS framework with respect to a numerical full-scale complete FOWT model simulated in the open-source software, OpenFAST. The virtual tests were able to maintain comparable control signals while enabling greater computational resources for the numerical calculations. Real-world physical tests demonstrated that the hydro-RTHS framework computes aerodynamic forces similar to the complete OpenFAST model, validating the hydro-RTHS framework using the three-loop hardware architecture. Findings show that the hydro-RTHS framework with the three-loop hardware architecture is computationally efficient, with reserve capacity to simulate more complex problems due to the customized software, hardware, and rate-transition algorithm.

17 WIND ENERGY↗

Effect of disease progression on the podocyte cell cycle in Alport Syndrome

Progression of glomerulosclerosis is associated with loss of podocytes with subsequent glomerular tuft instability. It is thought that a diminished number of podocytes may be able to preserve tuft stability through cell hypertrophy associated with cell cycle reentry. At the same time, reentry into the cell cycle risks podocyte detachment if podocytes cross the G1/S checkpoint and undergo abortive cytokinesis. In order to study cell cycle dynamics during chronic kidney disease (CKD) development, we used a FUCCI model (fluorescence ubiquitination-based cell cycle indicator) of mice with X-linked Alport Syndrome. This model exhibits progressive CKD and expresses fluorescent reporters of cell cycle stage exclusively in podocytes. With the development of CKD, an increasing fraction of podocytes in vivo were found to be in G1 or later cell cycle stages. Podocytes in G1 and G2 were hypertrophic. Heterozygous female mice, with milder manifestations of CKD, showed G1 fraction numbers intermediate between wild-type and male Alport mice. Proteomic analysis of podocytes in different cell cycle phases showed differences in cytoskeleton reorganization and metabolic processes between G0 and G1 in disease. Additionally, in vitro experiments confirmed that damaged podocytes reentered the cell cycle comparable to podocytes in vivo. Importantly, we confirmed the upregulation of PDlim2, a highly expressed protein in podocytes in G1, in a patient with Alport Syndrome, confirming our proteomics data in the human setting. Thus, our data showed that in the Alport model of progressive CKD, podocyte cell cycle distribution is altered, suggesting that cell cycle manipulation approaches may have a role in the treatment of various progressive glomerular diseases characterized by podocytopenia.

59 BASIC BIOLOGICAL SCIENCES↗

Tensor factorization for elucidating mechanisms of piezoresponse relaxation via dynamic Piezoresponse Force Spectroscopy

Spatially resolved time and voltage-dependent polarization dynamics in PbTiO 3 thin films is explored using dynamic piezoresponse force microscopy (D-PFM) in conjunction with interferometric displacement sensing. This approach gives rise to 4D data sets containing information on bias-dependent relaxation dynamics at each spatial location without long-range electrostatic artifacts. To interpret these data sets in the absence of defined physical models, we employ a non-negative tensor factorization method which clearly presents the data as a product of simple behaviors allowing for direct physics interpretation. Correspondingly, we perform phase-field modeling finding the existence of ‘hard’ and ‘soft’ domain wall edges. This approach can be extended to other multidimensional spectroscopies for which even exploratory data analysis leads to unsatisfactory results due to many components in the decomposition.

36 MATERIALS SCIENCE↗

Efficient prediction of attosecond two-colour pulses from an X-ray free-electron laser with machine learning

Abstract X-ray free-electron lasers are sources of coherent, high-intensity X-rays with numerous applications in ultra-fast measurements and dynamic structural imaging. Due to the stochastic nature of the self-amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two-coloured X-ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networks and decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high-repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X-ray spectroscopy using XFELs, such as in time-resolved X-ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Data-driven recovery of hidden physics in reduced order modeling of fluid flows

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.

42 ENGINEERING↗

Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

We introduce a safe extremum-seeking (Safe ES) algorithm which achieves the minimization of an unknown objective function while ensuring that an unknown, yet measured, control barrier function (CBF) remains above an arbitrarily small negative value for all time. In other words, “practical safety” is maintained during the entire period of convergence to the constrained extremum. Our design is based on quadratic program (QP) CBF style filters for safety, which is applied in an average and estimated sense. Using nonsmooth analysis tools, we guarantee semiglobal practical asymptotic (SPA) stability of the global constrained optimum, practical convergence to the safe set if starting in a condition violating the CBF, and practical safety for all time—semiglobally—if starting in safe set. The safety result of the paper is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients which guarantee that such a small violation is not exceeded. The paper outlines a set of sufficient conditions on the barrier and objective functions, and by way of a Lyapunov argument, we demonstrate that nonconvex constrained optimization problems can be solved. We present these results in the setting of a static map and a dynamical system. A simulation example illustrates the results.

97 MATHEMATICS AND COMPUTING↗

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

FORCE Development Status Update: Vertical Integration and Benchmarking of System Dynamics

Recent efforts to establish effective models for grid energy analysis, especially given the increase in variable renewable energy (VRE) sources and the economic challenges faced by traditional nuclear energy, have generated new technological considerations. One effort to improve the economic viability of nuclear power involves investigating integrated energy systems (IES) which include secondary energy systems that introduce flexibility and secondary market possibilities to existing and perceived future nuclear energy generation technologies. To analyze the technical and economic potential of IES, the Framework for Optimization of Resources and Economics (FORCE) tool suite was developed through a collaboration among national laboratories. Within the FORCE tool suite, the Holistic Energy Resource Optimization Network (HERON) provides algorithms for analyzing the long-term viability of potential IES technologies, while HYBRID provides algorithms and models to achieve high-resolution analysis of coupling physics over a short time period. Continued maturing of the FORCE tool suite requires further interconnections between the various tools in the suite in order to ensure consistent analysis. Analyses performed by applying HYBRID to transient process modeling should be easily harvestable as inputs to HERON analyses. The first item in this status update is a demonstration of an automated data pipeline for loading data from HYBRID into HERON analyses. Application of HYBRID results to HERON, as part of using the FORCE tool suite, relies on robust modeling assumptions for the various models included in HYBRID. The second result of this status update is the benchmarking and validation of cost and operational data, with a particular focus on natural gas energy generators. These generators are benchmarked with a focus on contrasting them with proposed thermal energy storage (TES) technologies.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

A unifying modeling abstraction for infinite-dimensional optimization

Infinite-dimensional optimization (InfiniteOpt) problems involve modeling components (variables, objectives, and constraints) that are functions defined over infinite-dimensional domains. Examples include continuous-time dynamic optimization (time is an infinite domain and components are functions of time), PDE optimization problems (space and time are infinite domains and components are functions of space-time), as well as stochastic and semi-infinite optimization (random space is an infinite domain and components are a function of such random space). InfiniteOpt problems also arise from combinations of these problem classes (e.g., stochastic PDE optimization). Given the infinite-dimensional nature of objectives and constraints, one often needs to define appropriate quantities (measures) to properly pose the problem. Moreover, InfiniteOpt problems often need to be transformed into a finite dimensional representation so that they can be solved numerically. Here in this work, we present a unifying abstraction that facilitates the modeling, analysis, and solution of InfiniteOpt problems. The proposed abstraction enables a general treatment of infinite-dimensional domains and provides a measure-centric paradigm to handle associated variables, objectives, and constraints. This abstraction allows us to transfer techniques across disciplines and with this identify new, interesting, and useful modeling paradigms (e.g., event constraints and risk measures defined over time domains). Our abstraction serves as the backbone of an intuitive Julia-based modeling package that we call InfiniteOpt.jl. We demonstrate the developments using diverse case studies arising in engineering.

42 ENGINEERING↗

Dynamic Reconfiguration of Switchgrass Proteomes in Response to Rust ( Puccinia novopanici ) Infection

Switchgrass (Panicum virgatum L.) can be infected by the rust pathogen (Puccinia novopanici) and results in lowering biomass yields and quality. Label-free quantitative proteomics was conducted on leaf extracts harvested from non-infected and infected plants from a susceptible cultivar (Summer) at 7, 11, and 18 days after inoculation (DAI) to follow the progression of disease and evaluate any plant compensatory mechanisms to infection. Some pustules were evident at 7 DAI, and their numbers increased with time. However, fungal DNA loads did not appreciably change over the course of this experiment in the infected plants. In total, 3830 proteins were identified at 1% false discovery rate, with 3632 mapped to the switchgrass proteome and 198 proteins mapped to different Puccinia proteomes. Across all comparisons, 1825 differentially accumulated switchgrass proteins were identified and subjected to a STRING analysis using Arabidopsis (A. thaliana L.) orthologs to deduce switchgrass cellular pathways impacted by rust infection. Proteins associated with plastid functions and primary metabolism were diminished in infected Summer plants at all harvest dates, whereas proteins associated with immunity, chaperone functions, and phenylpropanoid biosynthesis were significantly enriched. At 18 DAI, 1105 and 151 proteins were significantly enriched or diminished, respectively. Many of the enriched proteins were associated with mitigation of cellular stress and defense.

59 BASIC BIOLOGICAL SCIENCES↗

Autonomous Intelligent Charging/Discharging of Electric Vehicles using Distributed Multi-Agent ADMM Framework for Grid Ancillary Services

The increasing popularity of Electric Vehicles (EVs) in the distribution grid along with technological advancement in EV electronics such as vehicle to grid (V2G) technique has enabled them to participate in grid ancillary services. To achieve this, the EVs need to establish a contract with third-party aggregators and connect to a charging unit, either residential or commercial. At any time they are connected, the EVs can decide to take part in the ancillary services program offered to them by the aggregators. If agreed, the aggregators will use the EVs as a power source capable of charging/discharging power according to the input signal, and in return, they will be compensated. This inter-temporal nature of charging/discharging is also transforming the traditional optimal power flow (OPF) problem into a dynamic OPF problem. This chapter aims at developing a multi-layer time-dependent optimization algorithm to utilize EV potential and provide ancillary services while maximizing its utilization function. Specifically, in the upper layer, an autonomous distributed ADMM algorithm is developed to optimize the cost for charging/discharging EVs while using them to regulate the voltage at each bus in the distribution grid. The distributed ADMM algorithm is also expanded to the lower layer where the individual EVs active and reactive power is controlled for voltage regulation while maintaining the desired state of the charge of the vehicle at the end of the charging period. The effectiveness and performance improvement of the proposed multi-layer algorithm is illustrated through analytical analysis and simulation results.

Rahman, Towfiq↗

Application of Atmospheric Gases and Particulate Matter to the Assessment of Urban Heat Island

Background: Urban heat island (UHI), where built areas are warmer compared to non-urban regions, increases human related diseases and mortality. A key challenge in UHI analysis is the designation of sites as urban or suburban/rural; however, the growing complexity of green spaces in urban areas and the predominance of the transportation sector in nonurban areas creates a dilemma for distinct delineation. Objectives: This study aims to utilize the variability of atmospheric components such as particulate matter (PM), inorganic gases, and volatile organic compounds (VOCs) as direct tracers of the degree of urbanization for ground-based measurements to fully comprehend UHI in convoluted regions with indistinct delineation of urban and nonurban environments. Methods: Atmospheric gases and aerosols were used as direct tracers of urbanization for UHI analysis. Inorganic gases and particulate matter were monitored in two sites in a southeastern US city with varying degrees of urbanization. VOCs were analyzed using a proton transfer reaction time-of-flight mass spectrometer. Results: The more-urbanized site exhibited warmer night conditions and elevated total oxidant levels, leading to the formation of nanometer-sized particles. Machine learning analysis revealed similar atmospheric pollutant profiles for both sites, suggesting comparable sources and variability. Biogenic VOCs were enhanced at the less-urbanized site; however, levels of anthropogenic aromatic VOCs were comparable for both sites. A comprehensive mass spectra analysis revealed distinct molecular backbones per site that further affirmed the applicability of VOCs as indicators of urbanization. Conclusion: This study concludes that VOCs provide more direct and accurate information than typical inorganic gases and PM parameters for characterizing the degree of urbanization. Further exploration of VOCs can enhance our understanding of UHI dynamics and its interaction with vegetation in urban green spaces.

Air quality sensor↗

Optimization of metal-supported solid oxide electrolysis cells with infiltrated catalysts

We report metal-supported solid oxide electrolysis cells (MS-SOECs) are being developed for steam-to-hydrogen electrolysis, especially for utilization of dynamic or intermittent electrical power from renewable sources. Various aspects of the electrocatalyst processing and composition, and metal support structure were explored. Catalyst materials, infiltration temperature and infiltration cycles were optimized for high performance and durability. Numerous catalyst materials were screened for both oxygen and steam electrodes. The oxygen catalyst had moderate impact on both initial cell performance and durability. Reducing Ni content in the steam electrode had little effect on durability, but reduced initial performance. Ex-situ XRD analysis and cell assessment of catalyst infiltration temperature revealed that the optimal range is 750–850 °C. The best cell performance and durability was achieved with LSCF-SDC oxygen electrocatalyst and SDC-Ni (60:40 vol%) steam electrocatalyst infiltrated 11 times at 800 °C and operated at 700 °C. At low steam content, a significant mass transport limitation on the steam side results in limiting current behavior. Thinner and more porous metal supports were implemented, and found to improve steam mass transport at low steam content, relevant for SOECs operating under high H 2 recycle rate or high steam utilization.

08 HYDROGEN↗