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At least 19 records

Eddy Covariance Theory: A Review

Eddy covariance (EC), the gold standard for measuring ecosystem scale gas and heat exchanges, has transformed our understanding of the breathing of the biosphere, and thus global change biology. Despite numerous methodological improvements and insights gained from the technique, the community faces persistent challenges that have been present since the first EC measurements. Here, we review the theoretical developments underpinning EC. We present theoretical developments in four important areas that have relevance to EC measurements of the net ecosystem exchanges (NEE) of gases and heat from a single tower: (i) measuring the total vertical flux density, (ii) flux attenuation, (iii) coordinate rotations, and (iv) energy balance closure. Persistent problems with EC measurements, such as the inability to close the energy budget, led us to identify two priorities for revisiting the theory underlying: (i) sensible heat flux calculations, and (ii) constraining the mean vertical wind velocity. We present a framework for improved calculation of sensible heat flux derived from first principles of fluid mechanics and thermodynamics that considers coupled heat and mass transfer so that conservation of both is obeyed. These refinements are motivated by the need for unbiased measurements of energy and mass transfer between the land surface and atmosphere for ecosystem research and to validate satellite observations and land surface models.

ecosystem fluxes

3D modeling of n = 1 RMP driven heat fluxes on the SPARC tokamak PFCs using HEAT

3D heat flux calculations at the lower outer divertor plate of SPARC using the HEAT code show that 3D fields generated from error field correction coils can lead to enhanced peak heat fluxes up to 15 times larger compared to the axisymmetric case. Previously employed to simulate axisymmetric heat flux on 3D plasma facing components, the HEAT code can now predict 3D heat flux generated by non-axisymmetric plasmas. This is achieved via a new HEAT module which leverages the 3D field line tracing capabilities of MAFOT starting from an M3D-C1 (MHD resistive code) perturbed equilibria. The resulting heat flux is assigned using the magnetic footprint and the heat flux layer model, an extension of the 2D heat flux model also known as the Eich, to 3D non-axisymmetric plasmas. For SPARC, the new capabilities of HEAT are used to calculate the 3D heat loads resulting from n = 1 perturbation fields (with n indicating the toroidal periodicity) applied through a toroidal array of six picture frame coils with different amplitude. The comparison with the unperturbed case shows significant changes in shape and intensity of the heat flux profile. The results show that the application of n = 1 3D field leads to a localized enhancement of the heat flux peak, influenced by the wetted area impacted by the magnetic footprint, and the appearance of a secondary heat flux peak, whose intensity depends on amplitude of the applied 3D field and toroidal location.

3D heat flux

Divertor heat load estimates on NSTX and DIII-D using new and open-source 2D inversion analysis code

A thermography inversion algorithm has been developed in the open-source Python-based computer code, HYPERION, to calculate the heat flux incident on plasma-facing components (PFCs) in axisymmetric tokamaks. The chosen mesh size at the surface significantly affects the calculated transient heat flux results. The calculated transient heat flux will exceed the real value when the mesh size tends to zero but will underestimate the real value when the mesh size is large. A criterion for determining the appropriate mesh size for the transient heat flux calculation will be discussed. The numerical scheme for HYPERION uses a 2D fully implicit finite-difference approach, allowing temperature-dependent thermal properties of PFC materials. The inversion algorithm is benchmarked against established heat flux calculation codes, TACO and THEODOR, based on thermography data from NSTX and DIII-D respectively. The primary benefits of HYPERION compared to TACO and THEODOR are that it is open-source and it allows for the optimization of mesh thickness along the substrate. The algorithm also accounts for the thermal properties of thin surface layers that characteristically form on PFCs due to plasma-material interactions. The agreement between HYPERION and THEODOR is excellent, as the percent difference between the codes is ~5% on average in the case of the DIII-D data for moderate to high heat flux. Verification tests with TACO show slightly higher average percent differences of 8% and 12%. In using HYPERION to study filaments in heat flux, the initial results indicate that small ELMs filaments significantly broaden the divertor heat flux, and decrease divertor peak flux. Compared to the inter-ELM, the small ELM filaments decrease the divertor peak surface temperature. With intermittent divertor filaments, the divertor heat flux width is comparable with that found in L-mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Urban weather modeling using WRF: linking physical assumptions, code implementation, and observational needs

The Weather Research and Forecasting (WRF) model includes urban schemes that simulate the influence of urban surfaces on the atmosphere using parameterizations for flux, and radiative exchanges. Three core schemes – the Bulk urban parameterization, Single-Layer Urban Canopy Model (SLUCM), and Multi-Layer Urban Canopy Model (MLUCM) – represent increasing levels of complexity. Although the parameterizations within these urban schemes are described in the literature, their specific implementation remains poorly documented, thus slowing down model development efforts. This manuscript provides a roadmap to the three urban schemes in WRF version 4.5.2, presenting equations using the same symbols as in the model code, along with references to code lines, and including graphics and explanations that connect the code to its physical foundations. Our thorough review of the urban parameterizations implemented in WRF version 4.5.2 highlighted a handful of parameters that may introduce discontinuities in simulations: (i) in the SLUCM, a 1 mm h −1 rain rate threshold is employed to switch between two minimum moisture availability parameterizations, thus impacting latent heat flux calculations; (ii) in the SLUCM a threshold is used to partition shortwave radiation into direct and diffuse components; (iii) in all three urban schemes, the bulk Richardson number is employed to select the similarity function, which influences the vertical distribution of heat and momentum. We also identified a highly simplified treatment of the radiative balance on roof surfaces. The implications of these simplifications can be assessed through targeted observations across relevant conditions, including varying precipitation rates, cloud cover, and transitions between stability regimes. Furthermore, the widespread application of the Monin-Obukhov similarity theory in these urban schemes warrants model evaluation under highly stable and unstable conditions and in heterogeneous urban settings with variable land cover and building heights on scales finer than model resolution. To address these challenges, we offer guidance on observational strategies, emphasizing the need for multi-parametric measurements to capture potential compensating biases and multi-height measurements that align with the levels where quantities are diagnostic and prognosed in the model (i.e., the lowest atmospheric level of the WRF model). Finally, our inspection of the code revealed implementation bugs that have now been corrected in WRF versions 4.6.0 and 4.6.1. Sensitivity tests over the Atlanta urban area show that these corrections affect surface temperatures, underscoring the importance of performing rigorous documentation and verification of the implementation of parameterizations in model code.

54 ENVIRONMENTAL SCIENCES

First Wall Design of a Tokamak Pilot Plant Using a Monte Carlo Model for 3-D Heat Flux Deposition

We present a method for calculating the heat fluxes deposited on nonaxisymmetric tokamak first wall components, allowing for a first-of-its-kind model for power handling in the tokamak far scrape-off layer (SOL). The DIV3D Monte Carlo model features strict global power conservation and can calculate the finite cross-field plasma transport into magnetically-shadowed regions, which is significant when dealing with meter-scale shadows introduced by components such as poloidal limiters or antennas. As a case study, we apply the DIV3D model to inform the distribution of first wall poloidal limiters in an ARC-class reactor device. We demonstrate that discrete protection limiters can efficiently reduce peak heat fluxes on recessed breeder wall components in the presence of significant far-SOL plasma fluxes. By varying the toroidal periodicity and radial standoff depth of the limiters, we demonstrate one of the tradeoffs that must be considered in first wall design: more limiters provide greater protection, but at the cost of reduced breeding performance. We also present the impact that radial misalignments between limiters would have on first wall power loading.

Monte Carlo methods

Meteorological Variables and Energy Fluxes at the Pumphouse Site, Crested Butte, CO 2017-2019

This data contains output from the pumphouse eddy covariance tower that includes shortwave radiation, longwave radiation, net radiation, air temperature, relative humidity, as well as sensible, latent, and ground heat fluxes. Also included is calculated evapotranspiration from the latent heat flux and the latent heat of vaporization. All data are on a daily timestep and displayed in Mountain Time. The data has been processed, and Quality Assurance / Quality Control (QA/QC) was done, but any daily gaps in the data have not been filled in. This research was funded by the Department of Energy and performed as part of the Watershed Function Scientific Focus Area. This research aimed to constrain evapotranspiration in a high-elevation catchment.The dataset includes one comma-separated values (CSV) data file (EddyCovariance_MeteorlogicalVariables_CrestedButtePumphouse.csv). Additionally, three metadata CSV files are included: (1) location metadata file (locations.csv), which contains location metadata and coordinates; (2) a file-level metadata (flmd.csv) file that lists each file contained in the dataset with associated metadata; and (3) a data dictionary (dd.csv) file that contains column/row headers used throughout the files along with a definition, units, and data type.This work was supported by the Watershed Function Science Focus Area at Lawrence Berkeley National Laboratory funded by the US Department of Energy, Office of Science, Biological and Environmental Research under Contract No. DE-AC02-05CH11231.

54 ENVIRONMENTAL SCIENCES

Simulation of Divertor Performance in ST40 Under Dynamic Double-Null Plasmas

A power fraction model was implemented for the simultaneous prediction of 3-D surface temperature evolution at all four divertor targets in near-double-null (DN) tokamak configurations, which is especially important for compact high-field devices that may not have the ability to dissipate large amounts of power on the high-field side. Evaluating the power-sharing between the four divertor strike points in a disconnected DN configuration is important for understanding the overall power balance, as well as for optimizing the power exhaust performance and prolonging the survivability of the plasma facing components (PFCs). This power-sharing is typically evaluated in terms of the separation between the primary and secondary separatrices at the outboard midplane, $\textit {dR}_{\text {sep}}$. The Heat flux Engineering Analysis Toolkit (HEAT) is coupled with Brunner’s power fraction model to simulate the deposited heat flux and resultant temperature change on 3-D divertor targets in a dynamic DN (DDN) pulse operation in ST40, a high-field spherical tokamak. The simulation results showed that with DDN operation, the operation time has significantly increased compared with single-null geometry configurations.

ST40

Predictive turbulence-driven flux model of scrape-off layer widths across confinement regimes in tokamaks

Reliable scrape-off layer (SOL) profile decay lengths predictions are needed to design and operate future tokamaks. The present manuscript describes a new model based on turbulent transport that is able to predict SOL widths for both L-mode and H-mode plasmas. The model is based upon the sheared-spectral filament paradigm (Peret et al (WEST Team) 2022 Phys. Plasmas 29 072306), however, incorporating the effects of thermal transport in order to calculate the parallel heat fluxes. The effects of magnetic shear and ExB shear on the cross-field transport are crucial to explain the shorter SOL decay lengths found in H-mode. The model is validated against a database of thousands of DIII-D L-mode and H-mode SOL profiles. We also calculate SOL decay length predictions in terms of plasma and engineer control parameters, which are in agreement with the multi-machine empirical H-mode scaling (Eich et al (ASDEX Upgrade Team and JET EFDA Contributors) 2013 Nucl. Fusion 53 093031), however, with an additional device geometry dependence. ITER SOL width predictions by the model are 3 times higher than the empirical scaling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Direct Observations of Surface Fluxes and Air‐Sea Exchange Coefficients in Low Winds Using a Small Uncrewed Aircraft System

In the marine boundary layer, the exchange of momentum, heat, and moisture occurs between the atmosphere and ocean. Since it is too dangerous for a crewed aircraft to fly close to the ocean surface to directly obtain these measurements, a sUAS (small Uncrewed Aircraft System) is one of the only viable options. On 24 March 2023 a Black Swift Technologies S0 sUAS was deployed from the NOAA P-3 on a calm clear day off the west coast of Florida. For 23 min at the end of the mission, the sUAS flew 8 straight line legs with an average length of 2.15 km, at roughly 10 m above the ocean surface, with wind speeds between 3.0 and 4.5 m s −1 . For the first time over the open ocean using a sUAS, the 4-Hz wind and thermodynamic data was used to calculate surface momentum flux, sensible heat flux, and latent flux using both direct covariance methods and the bulk aerodynamic formulas. Since all the flux quantities can be found using both direct and indirect methods, we are able to calculate the exchange coefficients of momentum flux (C D ), latent heat flux (C E ), and sensible heat flux (C H ) with results that are generally in good agreement with previous studies over the same wind speed range. This study demonstrates the ability of sUAS to measure air-sea interactions. Future intention is to use sUAS to obtain similar measurements in high wind events such as hurricanes which could better help understand hurricane intensification and improve model physics.

Deloach, Christopher J. [Embry-Riddle Aeronautical

Surface freshening contributes to weak Atlantic Meridional Overturning Circulation (AMOC) in non-eddying ocean simulations

To complete this study, researchers developed a suite of water mass diagnostics to be compatible with E3SM simulation data. These diagnostics were applied to two ocean-sea ice simulations run using E3SM Version 2.0 on non-eddy-resolving and eddy-resolving ocean meshes. The atmospheric component was forced using reanalysis data spanning 1948–2009. The simulations were analyzed over a 5-year period coinciding with surface freshening and AMOC decline in the non-eddying simulation. SWMF was calculated from the surface heat, salt, and freshwater fluxes, and transport across boundaries was calculated from the mesh edge velocities. Both SWMF and cross-boundary transport were binned by density, temperature, and salinity to produce diagnostics in density coordinates and in temperature–salinity coordinates.

54 ENVIRONMENTAL SCIENCES

1D model of SOL with self consistent calculation of non-coronalradiation and applications to shallow field line angles

A 1D model of the scrape off layer (SOL) is created with a physics based calculation of the impurity radiation and the inclusion of the perpendicular heat flux q ⊥ compared to previous 1D models. The calculation of the impurity radiation includes the addition of a model using parallel and perpendicular motion to calculate the impurity confinement time τ and the inclusion of charge exchange between neutral hydrogen and impurity ions. Reasonable agreement is found between the model and the 2D fluid code SOLPS-ITER. Additionally, an improvement is shown over the constant τ used in previous works The model is used to examine the effects of shallow field line angles at ITER levels of parallel heat flux (q || ). A large increase in radiation results in an increase in the upstream parallel heat flux which can still be in detachment at shallow field line angles for both q ⊥ and the calculated τ for traditional impurities (argon and nitrogen) as well as boron. The physics behind this increase in radiation at shallow field line angles is shown to be a decrease in τ and a change in the temperature profile with the inclusion of q ⊥ .

ITER

Impact of error fields and error field correction on heat fluxes in SPARC

Using a single toroidal array of coils to reduce the m,n = 2,1 resonant error field (EF) produced by the misalignment of the axisymmetric coils in SPARC can result in the enhancement of the local divertor heat fluxes. Managing high divertor heat fluxes (q ∥ $\simeq$ 10 GW m -2 ) poses a challenge for compact tokamak devices such as SPARC. The presence of non-axisymmetric magnetic field perturbations adds complexity to the problem by generating intricate 3D edge magnetic topologies that alter the heat flux distributions on the target plates. The aim of this work is to investigate the impact of the EF correction (EFC) on the heat fluxes at the divertor plates in SPARC. The MHD code M3DC1 has been used to simulate the 3D magnetic perturbations generated by the shift and tilt of several axisymmetric coils within specified tolerances, as well as from the array of EFC coils located at the midplane. Using a heuristic model that extends the concept of an axisymmetric heat flux layer to 3D plasmas, the resultant heat flux distributions is derived from magnetic footprints calculated with the MAFOT code. The results show that the EFC could either decrease or further enhance the local heat flux when used to correct the m,n = 2,1 resonant EF to enhance the core plasma performance.

3D fields

Software Verification of VARPOW

The VARPOW program is a post-processing utility program for DIF3D, specifically DIF3DVARIANT, and it was developed to provide interface files for the thermal analysis program DASSH. The basic methodology of VARPOW is to take the neutron and gamma flux (moments) calculated by DIF3D (or GAMSOR) and combine them with the heating (coefficient) cross sections to calculate the spatial power distributions using the DIF3DVARIANT spatial basis. VARPOW can use the output from GAMSOR (both steady state neutron and gamma flux calculations) or standard DIF3D/REBUS calculations (neutron flux only). The correct approach for defining the power distribution is to use GAMSOR as its purpose was to properly compute the gamma heating throughout the modeled domain. The power desnities calculated by VARPOW are broken into fuel, cladding and coolant terms for which isotope-wise categorization is needed. VARPOW has built in options the user can select for the isotope categorization or VARPOW can import a file that details the isotope categorization. VARPOW can export the solution in the polynomial basis of DIF3D-VARIANT or the monomial basis of DIF3D-VARIANT. Recently the clad neutron damage calculation capability was introduced into VARPOW, and it now allows a pathway to get distributions of clad DPA. The purpose of this work is to verify the power distribution, fast neutron flux and clad DPA results calculated by VARPOW from both the GAMSOR and DIF3D input options and verify that the input and output options are consistent with the manual. Hand calculation and independent numerical calculation are used for this verification work.

Zhong, Zhaopeng [Argonne National Laboratory (ANL)

Software Verification of VARPOW

The VARPOW program is a post-processing utility program for DIF3D, specifically DIF3DVARIANT, and it was developed to provide interface files for the thermal analysis program DASSH. The basic methodology of VARPOW is to take the neutron and gamma flux (moments) calculated by DIF3D (or GAMSOR) and combine them with the heating (coefficient) cross sections to calculate the spatial power distributions using the DIF3DVARIANT spatial basis. VARPOW can use the output from GAMSOR (both steady state neutron and gamma flux calculations) or standard DIF3D/REBUS calculations (neutron flux only). The correct approach for defining the power distribution is to use GAMSOR as its purpose was to properly compute the gamma heating throughout the modeled domain. The power desnities calculated by VARPOW are broken into fuel, cladding and coolant terms for which isotope-wise categorization is needed. VARPOW has built in options the user can select for the isotope categorization or VARPOW can import a file that details the isotope categorization. VARPOW can export the solution in the polynomial basis of DIF3D-VARIANT or the monomial basis of DIF3D-VARIANT. The purpose of this work is to verify the power distribution results calculated by VARPOW from both the GAMSOR and DIF3D input options and verify that the input and output options are consistent with the manual. Hand calculation and independent numerical calculation are used for this verification work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Reactor Containment Passive Safety Analysis: Steam Condensation in Presence of Non-condensable Gas Scaled Experiment and Modeling

This study presents steam condensation scaled experiments and semi-empirical models in presence of nitrogen (N)—a noncondensable gas (NCG), simulating air in the reactor containment—to support water-cooled small modular reactors (SMRs) passive containment cooling system (PCCS) design and analysis. Previous experimental studies on PCCS are focused on fixed and smaller tube (mostly 2-in.) geometries and specific test condition variations, bringing challenges with geometric scaling and mismatching with SMR prototypic design. To address these challenges, this study presents steam condensation test dataset obtained from three scaled test sections of 1-, 2-, and 4-in.-diameter steam condensers with an annular/jacket cooling of 2-, 3-, and 6 in.-diameter tubes, respectively. Test data were collected for steam ranges from 58 to 63 kg/hr., and NCG flow of 4.4 to 13.3 kg/hr. Annular cooling water flow was varied to obtain required testing conditions of saturated steam inlet and fully condensed outlet. Axial temperature test data of bulk cooling water, steam and condensate were collected by thermocouples for three test sections and various steam-NCG mixing/testing conditions. A standard data reduction method was adopted—utilizing iterative and nodalized mass and heat transfer calculation—to estimate axial local heat fluxes, heat transfer coefficients (HTCs), condensation rates, film thickness, and Nusselt number. Based on the obtained dataset semi-empirical model results—a ratio of experimental and Nusselt’s theoretical HTC are presented. Such results and findings are supportive of developing scaled-up testing facility, to enable model validations and accelerate next generation of reactors development and deployment

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

Presentation: Reactor Containment Passive Safety Analysis: Steam Condensation in Presence of Non-condensable Gas Scaled Experiment and Modeling

This study presents steam condensation scaled experiments and semi-empirical models in presence of nitrogen--a noncondensable gas (NCG), simulating air in the reactor containment--to support water-cooled small modular reactors (SMRs) passive containment cooling system (PCCS) design and analysis. Previous experimental studies on PCCS are focused on fixed and smaller tube (mostly 2-in.) geometries and specific test condition variations, bringing challenges with geometric scaling and mismatching with SMR prototypic design. To address these challenges, this study presents steam condensation test dataset obtained from three scaled test sections of 1-, 2-, and 4-in.-diameter steam condensers with an annular/jacket cooling of 2-, 3-, and 6 in.-diameter tubes, respectively. Test data were collected for steam ranges from 58 to 63 kg/hr., and NCG flow of 4.4 to 13.3 kg/hr. Annular cooling water flow was varied to obtain required testing conditions of saturated steam inlet and fully condensed outlet. Axial temperature test data of bulk cooling water, steam and condensate were collected by thermocouples for three test sections and various steam-NCG mixing/testing conditions. A standard data reduction method was adopted--utilizing iterative and nodalized mass and heat transfer calculation to estimate axial local heat fluxes, heat transfer coefficients (HTCs), condensation rates, film thickness, and Nusselt number. Based on the obtained dataset semi-empirical model results--a ratio of experimental and Nusselt's theoretical HTC are presented. Such results and findings are supportive of developing scaled-up testing facility, to enable model validations and accelerate next generation of reactors development and deployment.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS

An Optothermal Raman Model Accounting for Convection, Radiation, and Substrate Effects for Evaluation of the Thermal Conductivity of Two‐Dimensional Coatings

Thermal conductivity of two‐dimensional (2D) materials is important to characterize as this will govern thermal transport physics in the various thermal and energy applications benefitting from the unique properties of these materials. Here, analytical and numerical techniques are presented to determine the thermal conductivity and interfacial conductance of a 2D material coating using confocal micro‐Raman spectroscopy as a noncontact diagnostic. While several methods have been proposed for calculating the values of thermal conductivity, interfacial conductance, and spatial temperature profile, these models often do not consider effects of radiation, convection, and substrate resistance on the temperature and heat flux profiles. We present a model to calculate the thermal conductivity and interfacial conductance which accounts for convection, radiation, and substrate effects to characterize a variety of 2D material coatings, which is demonstrated using large area graphene transferred onto copper and nickel substrates. Convection and radiation effects are found to have a negligible effect on the temperature profile of supported coatings, while the substrate effects have a considerable effect and therefore impact the quantification of thermal conductivity and interfacial conductance in addition to limiting the spatial resolution of the technique. These findings will allow for more accurate and reproducible extraction of the thermal conductivity of graphene and other 2D material coatings when employing noncontact optothermal Raman spectroscopy methods.

2D coatings