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Quasi-elastic nuclear scattering at high energies

The quasi-elastic scattering of two nuclei is considered in the high-energy optical model. Energy loss and momentum transfer spectra for projectile ions are evaluated in terms of an inelastic multiple-scattering series corresponding to multiple knockout of target nucleons. The leading-order correction to the coherent projectile approximation is evaluated. Calculations are compared with experiments.

Cucinotta, Francis A.

Commercial Building Prototypes Based on ANSI/ASHRAE/IES Standard 90.1-2019 Appendix G PRM: Technical Support Document

The two paths for documenting compliance with ANSI/ASHRAE/IES Standard 90.1 are the prescriptive path and the performance path. Beyond code programs and rating systems (for example, USGBC-LEED ) are primarily known to use a third path – the Appendix G Performance Rating Method. An update in the 2016 edition of Standard 90.1 approved the Appendix G Performance Rating System for code compliance, extending its application and allowing for greater consistency of modeling rules for code and beyond code building energy modeling. The Appendix G PRM provides rules for the development of whole building energy models of baseline and proposed models for calculating the “performance cost index target” value using the simulated energy results of the baseline and proposed models and the building performance factors published in Table 4.2.1.1 of the Standard. This report documents (1) the methodology used for development of the baseline and proposed energy models of the Pacific Northwest National Laboratory and U.S. Department of Energy commercial building prototypes using the Appendix G Performance Rating Method; and (2) the building performance factors that were calculated using those models.

97 MATHEMATICS AND COMPUTING

Economic modeling and energy policy planning

A structural economic model is presented for estimating the demand functions for natural gas and crude oil in industry and in steam electric power generation. Extensions of the model to other commodities are indicated.

Thompson, R. G.

On Kinetics Modeling of Vibrational Energy Transfer

Two models of vibrational energy exchange are compared at equilibrium to the elementary vibrational exchange reaction for a binary mixture. The first model, non-linear in the species vibrational energies, was derived by Schwartz, Slawsky, and Herzfeld (SSH) by considering the detailed kinetics of vibrational energy levels. This model recovers the result demanded at equilibrium by the elementary reaction. The second model is more recent, and is gaining use in certain areas of computational fluid dynamics. This model, linear in the species vibrational energies, is shown not to recover the required equilibrium result. Further, this more recent model is inconsistent with its suggested rate constants in that those rate constants were inferred from measurements by using the SSH model to reduce the data. The non-linear versus linear nature of these two models can lead to significant differences in vibrational energy coupling. Use of the contemporary model may lead to significant misconceptions, especially when integrated in computer codes considering multiple energy coupling mechanisms.

Gilmore, John O.

Stagnation point nonequilibrium radiative heating and the influence of energy exchange models

A nonequilibrium radiative heating prediction method has been used to evaluate several energy exchange models used in nonequilibrium computational fluid dynamics methods. The radiative heating measurements from the FIRE II flight experiment supply an experimental benchmark against which different formulations for these exchange models can be judged. The models which predict the lowest radiative heating are found to give the best agreement with the flight data. Examination of the spectral distribution of radiation indicates that despite close agreement of the total radiation, many of the models examined predict excessive molecular radiation. It is suggested that a study of the nonequilibrium chemical kinetics may lead to a correction for this problem.

Hartung, Lin C.

Stagnation Point Nonequilibrium Radiative Heating and the Influence of Energy Exchange Models

A nonequilibrium radiative heating prediction method has been used to evaluate several energy exchange models used in nonequilibrium computational fluid dynamics methods. The radiative heating measurements from the FIRE II flight experiment supply an experimental benchmark against which different formulations for these exchange models can be judged. The models which predict the lowest radiative heating are found to give the best agreement with the flight data. Examination of the spectral distribution of radiation indicates that despite close agreement of the total radiation, many of the models examined predict excessive molecular radiation. It is suggested that a study of the nonequilibrium chemical kinetics may lead to a correction for this problem.

Hartung, Lin C.

Validating Simulated Models of Energy Consumption by a Battery Electric Motorcoach: A real-world deployment in a harsh climate.

Many efforts have been made to simulate energy consumption of battery electric buses (BEBs) to optimize their deployment into existing fleets. The models produced, however, are rarely validated against real-world consumption data, limiting their generalizability and widespread application to fleets around the US. Furthermore, a major concern specific to BEBs is the effects of harsh climates on their performance. We build upon the state-of-the-art energy consumption modeling techniques developed for BEBs and apply them to a unique geographic context and a unique electrified vehicle. This geography, climate, and vehicle further the existing understanding of the factors affecting medium- and heavy-duty electric vehicles (MHDEVs) by allowing for new relationships to be tested and by assessing the generalizability of known relationships to new contexts. We find that temperature is less predictive of energy consumption for the battery electric motorcoach (BEM) in the case study environment than it is for BEBs in other studies. A mitigating factor that we presume to be working on the relationship between temperature and energy consumption is the fact that the BEM route does not stop between origin and destination to exchange passengers, and in turn, conditioned cabin air. Our model also incorporates wind speed and direction relative to travel, which is a novel contribution of our methodology. Results from our study are helpful for transit service planners, fleet operators, and logistics firms for improving their ability to predict performance of potential deployments of MHDEVs into existing operations.

32 - ENERGY CONSERVATION, CONSUMPTION, AND UTILIZA

Multiphysics Meshfree Degradation Modeling of Energy Storage Materials with Kernel Enrichment

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and ultimately diminishing performance and service life. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based meshfree model construction by the reproducing kernel particle method (RKPM) is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. The first kernel enrichment discussed will be the interface modified reproducing kernel (IM-RK) [1, 2], constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The IM-RK is especially useful for areas in which a known discontinuity-type is expected a priori. The second kernel enrichment to be discussed is a neural network-enhanced reproducing kernel (NN-RK) [3, 4], which is introduced to effectively model non-obvious damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RK is additionally used to inform how crack opening and closure in turn affect the electro-chemo-mechanical responses in the material microstructure. Reference: [1] Wang, Y., Baek, J., Tang, Y. et al. "Support vector machine guided reproducing kernel particle method for image-based modeling of microstructures," Comput Mech 73, 907-942 (2024). https://doi.org/10.1007/s00466-023-02394-9. [2] Susuki, K., Allen, J. & Chen, J. S.. "Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method," Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-02016-9. [3] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, 4422-4454 (2022). https://doi.org/10.1002/nme.7040.

25 ENERGY STORAGE

Prototype-Wise Sensitivity Analysis of Urban Building Energy Simulation Surrogate Modeling Accuracy

Urban Building Energy Modeling (UBEM) is an important reference for urban energy-related policymaking. Because of the significant impact of urban microclimates on the energy simulation, UBEM requires simulations of many microclimate-prototype pairs. Surrogate modeling is commonly used to reduce the cost of simulation computations. In UBEM surrogate modeling, it is important to determine the percentage of microclimates related to a prototype used for generating surrogate model training data. This study analyzes the prototype-wise variations and sensitivities of surrogate model estimation accuracy to the microclimate sampling ratios. The results of the study can help determine the number of simulations used for generating surrogate modeling data, avoid redundant simulations, and reduce the computational cost for UBEM surrogate modeling and its time.

Pan, Xiyu

Climate sensitivity with a seasonal cycle energy balance model

The sensitivity of climate which may have a local maximum as the ice cap passes through a midlatitude region where the atmosphere's transport efficiency varies strongly with latitude is examined. This behavior, found in a two level primitive equations climate model forced with annual mean insolation, was reproduced in an energy balance model (EBM) by making the diffusion coefficient a function of latitude. The two level seasonally varying EBM was applied and the global mean surface temperature vs. solar constant for this model are shown and two regions of enhanced sensitivity appear. The snowcover distributions around the year for three cases are shown.

Suarez, M. J.

Mechanical energy flow models of rods and beams

It has been proposed that the flow of mechanical energy through a structural/acoustic system may be modeled in a manner similar to that of flow of thermal energy/in a heat conduction problem. If this hypothesis is true, it would result in relatively efficient numerical models of structure-borne energy in large built-up structures. Fewer parameters are required to approximate the energy solution than are required to model the characteristic wave behavior of structural vibration by using traditional displacement formulations. The energy flow hypothesis is tested in this investigation for both longitudinal vibration in rods and transverse flexural vibrations of beams. The rod is shown to behave approximately according to the thermal energy flow analogy. However, the beam solutions behave significantly differently than predicted by the thermal analogy unless locally-space-averaged energy and power are considered. Several techniques for coupling dissimilar rods and beams are also discussed. Illustrations of the solution accuracy of the methods are included.

Wohlever, J. C.

Atmospheric flow over two-dimensional bluff surface obstructions

The phenomenon of atmospheric flow over a two-dimensional surface obstruction, such as a building (modeled as a rectangular block, a fence or a forward-facing step), is analyzed by three methods: (1) an inviscid free streamline approach, (2) a turbulent boundary layer approach using an eddy viscosity turbulence model and a horizontal pressure gradient determined by the inviscid model, and (3) an approach using the full Navier-Stokes equations with three turbulence models; i.e., an eddy viscosity model, a turbulence kinetic-energy model and a two-equation model with an additional transport equation for the turbulence length scale. A comparison of the performance of the different turbulence models is given, indicating that only the two-equation model adequately accounts for the convective character of turbulence. Turbulence flow property predictions obtained from the turbulence kinetic-energy model with prescribed length scale are only insignificantly better than those obtained from the eddy viscosity model. A parametric study includes the effects of the variation of the characteristics parameters of the assumed logarithmic approach velocity profile. For the case of the forward-facing step, it is shown that in the downstream flow region an increase of the surface roughness gives rise to higher turbulence levels in the shear layer originating from the step corner.

Bitte, J.

Thermodynamic modeling of CsF with LiF-NaF-KF for molten fluoride-fueled reactors

Gibbs energy models were developed to describe the thermochemical behavior of CsF in molten FLiNaK (46.5LiF-11.5NaF-42KF mol%), a proposed molten salt reactor (MSR) fuel solvent and coolant, as cesium is of concern due to its high radiotoxicity and volatility. Initially, it was necessary to obtain a more accurate Gibbs energy function for CsF which required fitting parameters to reported vapor pressures over condensed phase CsF. The pseudo-binary systems CsF-LiF, CsF-NaF and CsF-KF were then evaluated utilizing phase equilibria and enthalpy of mixing (Δ mix H) values, together with original differential scanning calorimetry (DSC) measurements performed for the CsF-LiF and CsF-KF systems. The CsF-LiF-NaF, CsF-LiF-KF and CsF-NaF-KF pseudo-ternary system representations were obtained by interpolation of the constituent pseudo-binary systems, with DSC measurements performed for the CsF-LiF-NaF system to corroborate the calculated liquidus temperature. Ultimately, the pseudo-ternary systems were interpolated to obtain Gibbs energy models for the pseudo-quaternary CsF-LiF-NaF-KF system, supported by DSC measurements at low CsF compositions (1–10 mol%), yielding computed equilibria and cesium-containing vapor pressures that compare favorably with reported values. In conclusion, the Molten Salt Thermal Properties Database – Thermochemical (MSTDB-TC) was subsequently expanded to include these Gibbs energy models allowing description of the thermochemical behavior of the CsF-LiF-NaF-KF system.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Theoretical quasar emission-line ratios. VII - Energy-balance models for finite hydrogen slabs

The present energy balance calculations for finite, isobaric, hydrogen-slab quasar emission line clouds incorporate probabilistic radiative transfer (RT) in all lines and bound-free continua of a five-level continuum model hydrogen atom. Attention is given to the line ratios, line formation regions, level populations and model applicability results obtained. H lines and a variety of other considerations suggest the possibility of emission line cloud densities in excess of 10 to the 10th/cu cm. Lyman-beta/Lyman-alpha line ratios that are in agreement with observed values are obtained by the models. The observed Lyman/Balmer ratios can be achieved with clouds whose column depths are about 10 to the 22nd/sq cm.

Hubbard, E. N.

An optimization model for energy generation and distribution in a dynamic facility

An analytical model is described using linear programming for the optimum generation and distribution of energy demands among competing energy resources and different economic criteria. The model, which will be used as a general engineering tool in the analysis of the Deep Space Network ground facility, considers several essential decisions for better design and operation. The decisions sought for the particular energy application include: the optimum time to build an assembly of elements, inclusion of a storage medium of some type, and the size or capacity of the elements that will minimize the total life-cycle cost over a given number of years. The model, which is structured in multiple time divisions, employ the decomposition principle for large-size matrices, the branch-and-bound method in mixed-integer programming, and the revised simplex technique for efficient and economic computer use.

Lansing, F. L.

A study of aircraft cruise

The long range aircraft cruise problem is analyzed using a model intermediate in complexity between energy model and point mass model. It is shown that this formulation imbeds the classical steady state cruise as the central member along with several other oscillatory extremals. The oscillatory cruise trajectories are shown to exist if the Hessian of the function QD/VT with respect to altitude and airspeed is positive definite. An expression for predicting the frequency of oscillation is developed. Qualitative effects of increasing the vehicle thrust and improving the L/D are discussed. Numerical results for two fighter aircraft and a transport aircraft are given. While oscillatory cruise mode exists for the two fighter aircraft, steady state cruise at full throttle is found to be optimal for the transport aircraft. A second variation analysis to bring out the reason for fuel savings is developed. It is shown that whenever the Hessian of the function QD/VT is positive definite, the second variation will be zero along the classical steady state cruise arc, indicating that a neighboring extremal is competitive. Comparisons with the previous point mass and energy modeled results are given.

Menon, P. K. A.

An Energy Balance Model to Predict Chemical Partitioning in a Photosynthetic Microbial Mat

Studies of biosignature formation in photosynthetic microbial mat communities offer potentially useful insights with regards to both solar and extrasolar astrobiology. Biosignature formation in such systems results from the chemical transformation of photosynthetically fixed carbon by accessory microorganisms. This fixed carbon represents a source not only of reducing power, but also energy, to these organisms, so that chemical and energy budgets should be coupled. We tested this hypothesis by applying an energy balance model to predict the fate of photosynthetic productivity under dark, anoxic conditions. Fermentation of photosynthetically fixed carbon is taken to be the only source of energy available to cyanobacteria in the absence of light and oxygen, and nitrogen fixation is the principal energy demand. The alternate fate for fixed carbon is to build cyanobacterial biomass with Redfield C:N ratio. The model predicts that, under completely nitrogen-limited conditions, growth is optimized when 78% of fixed carbon stores are directed into fermentative energy generation, with the remainder allocated to growth. These predictions were compared to measurements made on microbial mats that are known to be both nitrogen-limited and populated by actively nitrogen-fixing cyanobacteria. In these mats, under dark, anoxic conditions, 82% of fixed carbon stores were diverted into fermentation. The close agreement between these independent approaches suggests that energy balance models may provide a quantitative means of predicting chemical partitioning within such systems - an important step towards understanding how biological productivity is ultimately partitioned into biosignature compounds.

Hoehler, Tori M.

Climate warming due to increasing atmospheric CO2 - Simulations with a multilayer coupled atmosphere-ocean seasonal energy balance model

The transient response of the climate to increasing CO2 is studied using a modified version of the multilayer energy balance model of Peng et al. (1982). The main characteristics of the model are described. Latitudinal and seasonal distributions of planetary albedo, latitude-time distributions of zonal mean temperatures, and latitudinal distributions of evaporation, water vapor transport, and snow cover generated from the model and derived from actual observations are analyzed and compared. It is observed that in response to an atmospheric doubling of CO2, the model reaches within 1/e of the equilibrium response of global mean surface temperature in 9-35 years for the probable range of vertical heat diffusivity in the ocean. For CO2 increases projected by the National Research Council (1983), the model's transient response in annually and globally averaged surface temperatures is 60-75 percent of the corresponding equilibrium response, and the disequilibrium increases with increasing heat diffusivity of the ocean.

Li, Peng