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At least 217 records · Page 12

Data-driven variational multiscale reduced order models

We propose a new data-driven reduced order model (ROM) framework that centers around the hierarchical structure of the variational multiscale (VMS) methodology and utilizes data to increase the ROM accuracy at a modest computational cost. The VMS methodology is a natural fit for the hierarchical structure of the ROM basis: In the first step, we use the ROM projection to separate the scales into three categories: (i) resolved large scales, (ii) resolved small scales, and (iii) unresolved scales. In the second step, we explicitly identify the VMS–ROM closure terms, i.e., the terms representing the interactions among the three types of scales. In the third step, we use available data to model the VMS–ROM closure terms. Thus, instead of phenomenological models used in VMS for standard numerical discretizations (e.g., eddy viscosity models), we utilize available data to construct new structural VMS–ROM closure models. Specifically, we build ROM operators (vectors, matrices, and tensors) that are closest to the true ROM closure terms evaluated with the available data. We test the new data-driven VMS–ROM in the numerical simulation of four test cases: (i) the 1D Burgers equation with viscosity coefficient v = 10 -3 ; (ii) a 2D flow past a circular cylinder at Reynolds numbers, Re = 100, Re = 500, and Re= 1000; (iii) the quasi-geostrophic equations at Reynolds number Re = 450 and Rossby number Ro = 0.0036; and (iv) a 2D flow over a backward facing step at Reynolds number Re = 1000. The numerical results show that the data-driven VMS–ROM is significantly more accurate than standard ROMs.

42 ENGINEERING↗

Total Water Level Prediction at Continental Scale: Coastal Ocean

We demonstrate recent progress made in the simulation of total water level (TWL) at continental scale, using the coastal ocean of US East Coast/Gulf of Mexico coast as an example. A key difference between the continental-scale and small-scale modeling is that the former requires a more accurate vertical datum. Using a geoid-based datum (xGEOID20b), a satellite altimetry product, and a state-of-the-art 3D unstructured-grid model, we significantly improve the accuracy for TWL both near- and off-shore. The average root-mean-square error at all NOAA stations is 14 cm. The non-tidal signals are found to be sensitive to the representation of a large-scale current system near the boundary and extending the domain extent to accommodate this system improves these signals.

Cui, Linlin↗

Disentangling multiple gas kinematic drivers in the Perseus galaxy cluster

Galaxy clusters, the Universe’s largest halo structures, are filled with an X-ray-emitting gas with a temperature between 10 million and 100 million degrees. Their evolution is shaped by energetic processes such as feedback from supermassive black holes (SMBHs) and mergers with other cosmic structures. The imprints of these processes on gas kinematics remain largely unknown, restricting our understanding of energy conversion within clusters4. High-resolution spectral mapping with the X-Ray Imaging and Spectroscopy Mission (XRISM) observatory offers a way forward. Here we present XRISM kinematic measurements of the Perseus cluster, radially covering the extent of its cool core. We find direct evidence for at least two dominant drivers of gas motions operating on distinct physical scales: a small-scale driver in the inner approximately 60 kpc, probably associated with the SMBH feedback; and a large-scale driver in the outer core, powered by mergers. This finding suggests that, during the active phase, SMBH feedback drives gas motions, which, if fully dissipated into heat, could have a substantial role in offsetting radiative cooling losses in the Perseus core. Furthermore, our study underscores the necessity of kinematic mapping observations of extended sources to robustly characterize the velocity fields and their role in the evolution of massive halos. It further offers a kinematic diagnostic for SMBH feedback models.

Astronomy and AstroPhysics↗

Light in the dark forest. Part I. An efficient optimal estimator for 3D Lyman-alpha forest power spectrum

The highly anisotropic nature of the Lyman-alpha (Lyα) forest data introduces a complex survey window function that complicates the measurement of the three-dimensional power spectrum ( P 3D ). In this paper, we present the first fully optimal estimator for P 3D , which exactly deconvolves the survey window function and marginalizes contaminated modes that distort the power spectrum. Our approach adapts optimal estimator techniques developed for the 2D cosmic microwave background data to the 3D case. To achieve computational feasibility, we employ the conjugate gradient method and implement the P 3 M formalism to handle large-scale and small-scale operations separately and efficiently. We validate our estimator using Monte Carlo mocks and Gaussian simulations, demonstrating its accuracy and computational efficiency. We confirm that mode marginalization eliminates distortions arising from quasar continuum errors and delivers robust power spectrum estimation, though it also inflates errors at large scales. This first implementation works in the flat-sky case; we discuss the remaining steps needed to generalize it to the curved-sky case. This formalism offers a foundation for the Lyα forest P 3D measurements and a new path toward cosmological constraints from the Lyα forest data.

Lyman alpha forest↗

Relaxation of the turbulent magnetosheath

In turbulence, non-linear terms drive energy transfer from large-scale eddies into small scales through the so-called energy cascade. Turbulence often relaxes toward states that minimize energy; typically these states are considered globally. However, turbulence can also relax toward local quasi-equilibrium states, creating patches or cells where the magnitude of non-linearity is reduced and the energy cascade is impaired. We show, using data from the Magnetospheric Multiscale (MMS) mission, and for the first time, compelling observational evidence that this ‘cellularization’ of turbulence can occur due to local relaxation in a strongly turbulent natural environment such as the Earth’s magnetosheath.

79 ASTRONOMY AND ASTROPHYSICS↗

Federated Architecture for Secure and Transactive Distributed Energy Resource Management Solutions (FAST-DERMS)

This document provides system-level specifications for a federated architecture for secure and transactive distributed energy resource management solutions (FAST-DERMS), presents a solution, and describes operational concepts for the proposed solution. FAST-DERMS enables the provision of reliable, resilient, and secure transmission and distribution (T&D) grid services through the scalable aggregation and near-real-time management of utility-scale and small-scale distributed energy resources (DERs). We first present the principles and objectives of FAST-DERMS. Then, after discussing important system concepts, we present the specifications for FAST-DERMS and a solution that employs a distributed and federated control methodology in which the DERs connected to a single point of common coupling with the rest of the system, such as individual substations, are optimized coordinately to provide system-level grid services. FAST-DERMS aims to aggregate and coordinate the operations of DERs to support T&D grid operations. The key optimization and control component of this FAST-DERMS reference implementation is a flexible resource scheduler (FRS) that aggregates the DERs within a substation service area. These FRSs operate at the substation level and perform constrained economic dispatch of DERs, either directly or through a transactive market or aggregator, as shown in Figure ES-1. An FRS Coordinator at the distribution system operator (DSO) level aggregates distribution substations operated by FRSs and interfaces with the transmission system operator (TSO) to provide transmission services. FAST-DERMS also allows for the integration of the FRS Coordinator with an existing distribution utility management system that could be employed by the DSO to enhance distribution grid operations.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Grid Architecture Guidance Specification for FAST-DERMS (V.1.0)

This document provides grid architecture guidance to support the Grid Modernization Laboratory Consortium (GMLC) Federated Architecture for Secure and Transactive Distributed Energy Resource Management Solution (FAST-DERMS) project. The FAST-DERMS project seeks to develop an architecture and reference implementation solution that enables the provision of reliable, resilient, and secure transmission and distribution (T&D) grid services through the scalable aggregation and near-real-time management of utility-scale and small-scale distributed energy resources (DERs).

24 POWER TRANSMISSION AND DISTRIBUTION↗

FEED Study of Carbon Capture Inc. DAC and CarbonCure Utilization Using United States Steel's Gary Works Waste Plant

Direct Air Capture (DAC) has been proposed as a means of reducing atmospheric concentrations of CO2. While DAC has been evaluated through lab-scale, bench-scale, and small-scale pilot units, large-scale deployment has not been achieved. Feasibility studies are one tool to understand the potential design, operation, performance, and impact of commercial-scale DAC. This paper presents the results of a feasibility study for a passive DAC system deployed at >100,000 tpy scale in three different regions across the U.S. and awarded to Carbon Collect by the U.S. Department of Energy National Energy Technology Laboratory (DOE NETL). The MechanicalTree™technology has been designed and engineered by Carbon Collect based on the concept initially developed at Arizona State University Center for Negative Carbon Emissions. It uses a tower of stacked, sorbentcontaining disks supported by a lifting mechanism, exposed to the air to capture CO2 during the adsorption phase. The disks are then lowered into a regeneration chamber for vacuum and steam regeneration to produce CO2 product during the desorption step. The modular tree design allows large installations with repeatable, mass-manufactured units connected to common utilities such as steam supply, vacuum, and CO2 processing for compression and geologic storage. The passive DAC system eliminates the equipment and energy of forced air fans by using natural air circulation to contact the sorbent with the CO2 in the air. Because of this, the performance is dependent on the wind speed in addition to the temperature and relative humidity. Performance and flow rate fluctuations were incorporated into equipment and facility design with considerations for turndown to 10% of maximum rated flow to allow operation in all seasons. The feasibility study was undertaken to evaluate the technology in different regions and climates. Three locations were selected for this study representing different climates: Alabama (hot and humid), California (hot and arid), and Wyoming (continental). For each region, the adsorption/desorption cycle was optimized including tuning the heat integration and cycle timings. The performance of individual trees was then scaled to the full facility with the same design of more than 20,000 trees common between all regions. The installations had expected average CO2 capture rates of between 330,000 and 485,000 tonnes of CO2 per year depending on the climate. The initial engineering design for the facility at each location was performed with cost and performance estimates for the trees, carbon purification and compression, and the balance of plant. To supply thermal and electrical energy for the facility, carbon-free or low-carbon power must be considered. Options for low-carbon, continuous thermal and electrical energy were considered. The best-performing option from those considered was identified to be an electrically-heated molten salt energy storage system, powered by an on-site photovoltaic field. During molten salt thermal discharge, steam is produced from heat exchange with the molten salt and used to generate power in a steam turbine as well as steam for regenerating the DAC carbon trees. The thermal and electrical supply and analysis is presented in the context of low-carbon power for carbon removal. Modelling and economics of transportation and geologic storage of the CO2 is considered and presented for each location. The results of the feasibility study are incorporated into the presented techno-economic and life-cycle assessments. This work is intended to provide an understanding of the performance, cost, and impact of capturing CO2 at the commercial scale and the impact of climate and regional siting on the considered passive DAC system.

42 ENGINEERING↗

Massive neutrinos and degeneracies in Lyman-alpha forest simulations

Using a suite of hydrodynamical simulations with cold dark matter, baryons, and neutrinos, we present a detailed study of the effect of massive neutrinos on the 1-D and 3-D flux power spectra of the Lyman-α (Lyα) forest. The presence of massive neutrinos in cosmology induces a scale- and time-dependent suppression of structure formation that is strongest on small scales. Measuring this suppression is a key method for inferring neutrino masses from cosmological data, and is one of the main goals of ongoing and future surveys like eBOSS, DES, LSST, Euclid or DESI . The clustering in the Lyα forest traces the quasi-linear power at late times and on small scales. In combination with observations of the cosmic microwave background, the forest therefore provides some of the tightest constraints on the sum of the neutrino masses. However there is a well-known degeneracy between Σmν and the amplitude of perturbations in the linear matter power spectrum. We study the corresponding degeneracy in the 1-D flux power spectrum of the Lyα forest, and for the first time also study this degeneracy in the 3-D flux power spectrum. We show that the non-linear effects of massive neutrinos on the Lyα forest, beyond the effect of linear power amplitude suppression, are negligible, and this degeneracy persists in the Lyα forest observables to a high precision. Here, we discuss the implications of this degeneracy for choosing parametrisations of the Lyα forest for cosmological analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

Scale interactions and anisotropy in Rayleigh–Taylor turbulence

We study energy scale transfer in Rayleigh–Taylor (RT) flows by coarse graining in physical space without Fourier transforms, allowing scale analysis along the vertical direction. Two processes are responsible for kinetic energy flux across scales: baropycnal work Λ, due to large-scale pressure gradients acting on small scales of density and velocity; and deformation work Π, due to multiscale velocity. Our coarse-graining analysis shows how these fluxes exhibit self-similar evolution that is quadratic-in-time, similar to the RT mixing layer. We find that Λ is a conduit for potential energy, transferring energy non-locally from the largest scales to smaller scales in the inertial range where Π takes over. In three dimensions, Π continues a persistent cascade to smaller scales, whereas in two dimensions Π rechannels the energy back to larger scales despite the lack of vorticity conservation in two-dimensional (2-D) variable density flows. This gives rise to a positive feedback loop in 2-D RT (absent in three dimensions) in which mixing layer growth and the associated potential energy release are enhanced relative to 3-D RT, explaining the oft-observed larger α values in 2-D simulations. Despite higher bulk kinetic energy levels in two dimensions, small inertial scales are weaker than in three dimensions. Moreover, the net upscale cascade in two dimensions tends to isotropize the large-scale flow, in stark contrast to three dimensions. Furthermore, our findings indicate the absence of net upscale energy transfer in three-dimensional RT as is often claimed; growth of large-scale bubbles and spikes is not due to ‘mergers’ but solely due to baropycnal work Λ.

42 ENGINEERING↗

Powering Arctic Observations with Marine Energy

Energy derivation from renewable marine sources is a rapidly expanding field of research with large and small-scale applications. Large-scale applications such as tidal turbines supplying grid scale power are under development in several locations around the world but small-scale applications such as powering ocean observations with renewable energy have not received the same attention. Ocean observations such as temperature measurements are becoming increasingly valuable, especially in the Arctic where the effects of climate change are most dramatic. The marine environment of the Arctic poses unique opportunities and challenges for powering observations with renewable energy, and the technology to power sensors operating in the Arctic with marine renewable energy does not exist yet. This report discusses the power usage and requirements of instruments currently being used in the Arctic and how marine renewable energy could be used to power these instruments. Wave motion, tidal currents, and thermal gradients all are explored as having potential to be used for energy extraction and the powering of sensors at sea. These resources are investigated for Arctic locations and recommendations are made for future studies of specific use cases.

16 TIDAL AND WAVE POWER↗

Unraveling Interdiffusion Phenomena and the Role of Nanoscale Diffusion Barriers in the Copper–Gold System

Diffusion is one of the most fundamental concepts in materials science, playing a pivotal role in materials synthesis, forming, and degradation. Of particular importance is solid state interdiffusion of metals which defines the usable parameter space for material combinations in the form of alloys. This parameter space can be explored on the macroscopic scale by using diffusion couples. However, this method reaches its limit when going to low temperatures, small scales, and when testing ultrathin diffusion barriers. Therefore, this work transfers the principle of the diffusion couples to small scales by using core–shell nanowires and in situ heating. This allows us to delve into the interdiffusion dynamics of copper and gold, revealing the interplay between diffusion and the disorder–order phase transition. Our in situ TEM experiments in combination with chemical mapping reveal the interdiffusion coefficients of Cu and Au at low temperatures and highlight the impact of ordering processes on the diffusion behavior. The formation of ordered domains within the solid-solution is examined using high-resolution imaging and nanodiffraction including strain mapping. In addition, we examine the effectiveness of ultrathin Al 2 O 3 barrier layers to control interdiffusion of the diffusion couple. Our findings indicate that a 5 nm thick layer serves as an efficient diffusion barrier. Furthermore, this research provides valuable insights into the interdiffusion behavior of Cu and Au on the nanoscale, offering potential applications in the development of miniaturized integrated circuits and nanodevices.

alloys↗

Cross-scale covariance for material property prediction

A simulation can stand its ground against an experiment only if its prediction uncertainty is known. The unknown accuracy of interatomic potentials (IPs) is a major source of prediction uncertainty, severely limiting the use of large-scale classical atomistic simulations in a wide range of scientific and engineering applications. Here we explore covariance between predictions of metal plasticity, from 178 large-scale (~10 8 atoms) molecular dynamics (MD) simulations, and a variety of indicator properties computed at small-scales (≤10 2 atoms). All simulations use the same 178 IPs. In a manner similar to statistical studies in public health, we analyze correlations of strength with indicators, identify the best predictor properties, and build a cross-scale “strength-on-predictors” regression model. This model is then used to estimate regression error over the statistical pool of IPs. Small-scale predictors found to be highly covariant with strength are computed using expensive quantum-accurate calculations and used to predict flow strength, within the statistical error bounds established in our study.

36 MATERIALS SCIENCE↗

Data for Filling the Cellulosic Bio-economy Gap by Utilizing a Wedge Approach Combined with Stakeholder Collaboration

The price gap between the market and breakeven prices of cellulosic biomass for farmers represents a significant barrier to the development of a low-carbon cellulosic bioeconomy. Using a bottom-up, agent-based modeling tool that replicates the behaviors and interactions of key stakeholders, this study analyzes the emergence of a cellulosic bioeconomy at the local scale through a wedge approach that examines an integrated portfolio of multiple policy options, including subsidies for small-scale bioproducts and environmental credits. The role of collaboration among multiple stakeholders, such as biomass producers (farmers), bio-refinery industry, government, and society, is assessed for filling the price gap. Using the Sangamon River Basin as a case study site, we evaluate the effectiveness of the wedge approach by comparing simulation results from multiple scenarios, each incorporating different combinations of bioeconomy wedges, with and without stakeholder collaboration. Results underscore that active collaboration among stakeholders acts as a catalyst enlarging the effectiveness of bioeconomy wedges. Including the carbon credits and environmental value in the policy portfolio is found to bridge the price gap through collective contributions from diverse stakeholders, where the cellulosic biofuel and bioproduct industry plays a pivotal role. Although this study is conducted at the local watershed scale, the methodology and findings offer valuable insights for market development in other watersheds and the potential scaling of local markets to regional and national levels.

Economics↗

Full forward model of galaxy clustering statistics with AbacusSummit light cones

ABSTRACT Novel summary statistics beyond the standard 2-point correlation function (2PCF) are necessary to capture the full astrophysical and cosmological information from the small-scale (r < 30h−1Mpc) galaxy clustering. However, the analysis of beyond-2PCF statistics on small scales is challenging because we lack the appropriate treatment of observational systematics for arbitrary summary statistics of the galaxy field. In this paper, we develop a full forward modelling pipeline for a wide range of summary statistics using the large high-fidelity AbacusSummit light cones that account for many systematic effects as well as remain flexible and computationally efficient to enable posterior sampling. We apply our forward model approach to a fully realistic mock galaxy catalog and demonstrate that we can recover unbiased constraints on the underlying galaxy–halo connection model using two separate summary statistics: the standard 2PCF and the novel k-th nearest neighbour (kNN) statistics, which are sensitive to correlation functions of all orders. We will demonstrate its strong constraining power on extended galaxy–halo connection models and cosmology in follow up papers. We expect this to become a powerful approach when applying to upcoming surveys such as DESI where we can leverage a multitude of summary statistics across a wide redshift range to maximally extract information from the non-linear scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DEVELOPMENT AND DEMONSTRATION TESTBED FOR THE REMOTE OPERATIONS AND MONITORING OF MICROREACTORS

The nuclear industry is rapidly developing many advanced-reactor concepts for near-term deployment in both traditional and non-traditional nuclear-powered applications. One such category of advanced reactor is the microreactor, a class of reactor with less than 20MWth power output, intended for applications where the economics or logistics of traditional power sources are difficult. This includes applications such as remote communities, mining sites, defense installations, or humanitarian and disaster-relief missions. One key enabling feature for the successful deployment of microreactors is a remote operations capability. Remote operations provide monitoring and control capabilities which can significantly reduce staffing costs by eliminating the need for licensed operators at each reactor facility and improve the economic viability for microreactor deployment. A remote concept of operations is not currently an established capability in the nuclear industry. In addition, no demonstration microreactor is expected to complete construction or go critical until at least 2026. This leaves two major capability gaps: the successful demonstration of a remote concept of operations for microreactors and a test bed suitable for said demonstration. Both gaps must be addressed in order to advance the remote concepts of nuclear operation and, more broadly, microreactors themselves from paper to reality. This paper aims to fill these gaps and describes a test bed that would support development and deployment of a remote concept of nuclear operations, initial experimental results from that test bed, and the application of the test bed and experimental results for a digital-twin-based remote concept of operations underdevelopment at Idaho National Laboratory (INL). The platform chosen as a remote concept of nuclear operations test bed is the Single Primary Heat Extraction and Removal Emulator, known as SPHERE, located at INL. SPHERE is a small-scale non-nuclear test bed that emulates thermal behavior of a microreactor. The small-scale and non-nuclear nature of SHPERE limit safety concerns associated with remote operations while still providing the physical response representative of a microreactor. A network connection was added to SPHERE that enables remote-monitoring capability. This allows for real-time data streaming to networked workstations, data historians, and human-machine interfaces (HMIs). These are all critical components in a remote concept of operations, thus providing a robust development and demonstration platform. An initial experiment was performed using the SPHERE remote operations testbed. This included running a comprehensively instrumented SPHERE through a series of steady-state and transient operating scenarios in both normal and abnormal operating conditions, all while streaming live test data to a remote HMI and data warehouse. This initial experiment served three purposes: (1) characterizing the response of SPHERE, (2) demonstrating the remote connection to SPHERE, and (3) providing a baseline data set for development of a digital-twin-based remote concept of operations that is under development at INL.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DEVELOPMENT AND DEMONSTRATION TESTBED FOR THE REMOTE OPERATIONS AND MONITORING OF MICROREACTORS

The nuclear industry is rapidly developing many advanced-reactor concepts for near-term deployment in both traditional and non-traditional nuclear-powered applications. One such category of advanced reactor is the microreactor, a class of reactor with less than 20MWth power output, intended for applications where the economics or logistics of traditional power sources are difficult. This includes applications such as remote communities, mining sites, defense installations, or humanitarian and disaster-relief missions. One key enabling feature for the successful deployment of microreactors is a remote operations capability. Remote operations provide monitoring and control capabilities which can significantly reduce staffing costs by eliminating the need for licensed operators at each reactor facility and improve the economic viability for microreactor deployment. A remote concept of operations is not currently an established capability in the nuclear industry. In addition, no demonstration microreactor is expected to complete construction or go critical until at least 2026. This leaves two major capability gaps: the successful demonstration of a remote concept of operations for microreactors and a test bed suitable for said demonstration. Both gaps must be addressed in order to advance the remote concepts of nuclear operation and, more broadly, microreactors themselves from paper to reality. This paper aims to fill these gaps and describes a test bed that would support development and deployment of a remote concept of nuclear operations, initial experimental results from that test bed, and the application of the test bed and experimental results for a digital-twin-based remote concept of operations underdevelopment at Idaho National Laboratory (INL). The platform chosen as a remote concept of nuclear operations test bed is the Single Primary Heat Extraction and Removal Emulator, known as SPHERE, located at INL. SPHERE is a small-scale non-nuclear test bed that emulates thermal behavior of a microreactor. The small-scale and non-nuclear nature of SHPERE limit safety concerns associated with remote operations while still providing the physical response representative of a microreactor. A network connection was added to SPHERE that enables remote-monitoring capability. This allows for real-time data streaming to networked workstations, data historians, and human-machine interfaces (HMIs). These are all critical components in a remote concept of operations, thus providing a robust development and demonstration platform. An initial experiment was performed using the SPHERE remote operations testbed. This included running a comprehensively instrumented SPHERE through a series of steady-state and transient operating scenarios in both normal and abnormal operating conditions, all while streaming live test data to a remote HMI and data warehouse. This initial experiment served three purposes: (1) characterizing the response of SPHERE, (2) demonstrating the remote connection to SPHERE, and (3) providing a baseline data set for development of a digital-twin-based remote concept of operations that is under development at INL.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Finite-rate entrainment effects on nitrogen oxide (NO x ) emissions in staged combustors

Axially staged combustors offer the potential for achieving low NO x emissions from gas turbines at the elevated temperatures required to achieve at least 65% combined cycle efficiencies. While there is evidence that premixing between the main burner products and secondary stream reduces NO x , it is important to characterize the specific requirements needed to achieve low emissions at gas turbine conditions. This study examines the sensitivity of NO x to finite-rate, large-scale entrainment of the main and secondary streams under the simplifying assumption of infinitely-fast small-scale mixing. Essentially, this allows us to isolate the effects of limited large-scale entrainment rates by using a homogeneous/uniform condition for the entrained and reacting gases. We use a reduced-order reactor network model to examine a generic staged-combustor whose inputs are physical time scales that embody the finite-rate entrainment characteristics. With simulations conducted over a large parameter space at typical operating conditions (25 atm, 650 K air), the results show that, even when small-scale mixing is infinitely fast and the reaction zone is uniform, entrainment significantly affects NO x emissions due to its influence on the equivalence ratio — and thus the temperature and time — at which the entrained mixture ignites. Fuel-air staging is shown to be vital to NO x reduction in most practical cases where entrainment times exceed roughly 1 ms and the secondary stream finishes entraining before the main burner products. A constrained NO x minimization indicates that using the leanest possible main burner and re-routing as much air as possible to the secondary stage is key to low NO x with finite-rate entrainment; for example, less than 10 ppm NO x can be achieved if the secondary stage contains 20% of the total mass flow.

03 NATURAL GAS↗