Search NASA⌕ Search

SEARCH · Search NASA

Results for “Large eddy simulation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Characterizing the Turbulent Structure of the Convective Boundary Layer Using ARM/ASR Observations and LES Model Output

This project will ultimately combine observations from Raman lidar, Doppler lidar, AERI, eddy correlation measurements, and airborne and ground-based high spectral resolution lidar systems with many large eddy simulations (LES) of realistic boundary layer cases to study: The diurnal evolution of the boundary layer thermodynamic structure; The turbulent structure of the CBL and the entrainment zone; The ability of LES models to simulate the thermodynamic and turbulent structure of the CBL; How perturbations in the surface properties and CBL properties influence boundary layer clouds; The similarities and differences in the boundary layer and cloud interaction in the marine vs. continental boundary layer.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Wake Statistics of Different-Scale Wind Turbines under Turbulent Boundary Layer Inflow

Subscale wind turbines can be installed in the field for the development of wind technologies, for which the blade aerodynamics can be designed in a way similar to that of a full-scale wind turbine. However, it is not clear whether the wake of a subscale turbine, which is located closer to the ground and faces different incoming turbulence, is also similar to that of a full-scale wind turbine. In this work we investigate the wakes from a full-scale wind turbine of rotor diameter 80 m and a subscale wind turbine of rotor diameter of 27 m using large-eddy simulation with the turbine blades and nacelle modeled using actuator surface models. The blade aerodynamics of the two turbines are the same. In the simulations, the two turbines also face the same turbulent boundary inflows. The computed results show differences between the two turbines for both velocity deficits and turbine-added turbulence kinetic energy. Such differences are further analyzed by examining the mean kinetic energy equation.

17 WIND ENERGY↗
DOE OSTI2022

A detailed experimental and modeling comparison of molecular radiative heat loss in a spark-ignition engine

Radiative heat transfer has been chiefly considered negligible in internal combustion engines, except for Diesel engines where soot radiation was recognized as a significant radiative transfer source. Only more recently, detailed simulations have shown that molecular radiation can be substantial as well. In extension to this, molecular radiative heat transfer can reach detectable levels of about 5–10% of the total heat transfer in spark-ignited engines. The broadband radiative nature of the significant emitting molecules, carbon dioxide and water, makes it necessary to address whether radiative trapping plays a substantial role in either total heat loss or energy redistribution within the cylinder. An experimental setup that allows measurements of the infrared emissions at a 2-crank-angle-degree resolution was developed to determine the importance of radiative trapping by carbon dioxide and water. Measurements were conducted in the well-characterized and documented TCC-III engine at the University of Michigan. The engine operated on a stoichiometric propane/air mixture at a speed of 1,300 RPM. Large Eddy Simulations with added line-by-line photon Monte-Carlo simulations of the molecular radiation were an integral part of this study to plan and devise the measurements. Post-processing of the simulation data included an accurate representation of the experimental volume from where infrared signals are collected. Additionally, the experimental data were used for validation of the photon Monte-Carlo simulations. Joint analysis of experimental and simulated spectra allowed quantifying the significance of radiative trapping. Results show the significant role of radiative trapping when predicting radiative heat transfer in the TCC-III engine.

42 ENGINEERING↗
DOE OSTI2022

Generalized Lapse Rate Formulas for Use in Entraining CAPE Calculations

Abstract Common assumptions in temperature lapse rate formulas for lifted air parcels include neglecting mixing, hydrostatic balance, the removal of all condensate once it forms (pseudoadiabatic), and/or the retention of all condensate within the parcel (adiabatic). These formulas are commonly derived from the conservation of entropy, which leads to errors when nonequilibrium mixed-phase condensate is present. To evaluate these assumptions, a new general lapse rate formula is derived from an expression for energy conservation, rather than entropy conservation. This new formula incorporates mixing of the parcel with its surroundings, relaxes the hydrostatic assumption, allows for nonequilibrium mixed-phase condensate, and can be formulated for pseudoadiabatic or adiabatic ascent. The new formula is shown to exactly conserve entropy for reversible ascent. Predictions by the new formula are compared to that of older and less general formulas. The errors in previous formulas arise from the assumption of hydrostatic balance, which results in considerable warm biases due to the neglect of the energy sink from buoyancy. Predictions of ascent with entrainment using the new formula are then compared to parcel properties along trajectories in large eddy simulations. Simulated parcel properties are better predicted by the formula using a diluted analogy to adiabatic ascent, wherein condensate is diluted at the same rate as other parcel properties, than by the diluted analogy to pseudoadiabatic ascent, wherein all condensate is removed. These results suggest that CAPE should be computed with adiabatic, rather than pseudoadiabatic, parcel ascent.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Development and validation of the cavitation-induced erosion risk assessment tool

This work presents the development of a cavitation-induced erosion risk assessment (CIERA) tool that links multiphase flow simulation predictions with the progress towards material erosion. To develop a robust erosion modeling tool, the cavitation and erosion predictions for pressurized diesel fuel flow within a channel geometry were validated over a range of Reynolds and cavitation number conditions in two different aluminum channel geometries, one featuring a rounded inlet corner and the other with a sharp inlet corner. The multiphase flow development within the channel was modeled using a compressible mixture model, where phase change was represented with the homogeneous relaxation model and the turbulent flow evolution was modeled using a dynamic structure approach for Large Eddy Simulations. To improve representation of the incubation period before material rupture over existing approaches, a physics-based metric was derived based on the cumulative energy absorbed by the solid material from repeated hydrodynamic impacts. When the average peak pressure was related to the incubation period, the incubation period and its sensitivity to changes in flow conditions were found to be overpredicted. In contrast, predictions from CIERA provided a more accurate means to qualitatively and quantitatively predict the influence of flow conditions on the incubation period before material erosion. When the predicted stored energy was related to the solid material properties to estimate the incubation period, multiphase flow simulations demonstrated accurate representation of the sensitivity of erosion severity to changes in flow conditions. The use of CIERA led to quantitative agreement of the predicted incubation period within 5% of the experimentally measured incubation period.

42 ENGINEERING↗
DOE OSTI2024

Application of passive vortex generators to enhance vertical mixing in an open raceway pond

A novel use of vortex generators in a raceway pond is described here, with the flow field quantitatively simulated using computational fluid dynamics using the large eddy simulation turbulence model. Persistence lengths of the swirling motion generated by the vortex generators indicate that significant vertical mixing can be achieved by placing vortex generators in the straight section opposite the paddle wheel, downstream of the first hairpin bend. Relatively simple vortex generators are capable of creating stronger swirling motions that persist for a longer distance than those created by the paddle wheel. For optimal performance, vortex generators are positioned side by side but in opposite directions, and their diameters should be equal to or slightly less than the desired liquid depth. The optimal length of a 0.18 m diameter vortex generator in a 0.2 m deep pond was determined to be 0.3 m. As a result, it has been demonstrated that a longer persistence length is achieved by inducing a swirling motion with its rotational axis parallel to the primary flow direction.

09 BIOMASS FUELS↗
DOE OSTI2021

Comparing Growth Rates of Simulated Moist and Dry Convective Thermals

The spreading rates of convective thermals are linked to their net entrainment, and previous literature has suggested differences in spreading rates between moist and dry thermals. Here, growth rates of idealized numerically simulated axisymmetric dry and moist convective thermals are directly compared. In an environment with dry-neutral stratification, the increase of thermal radius with height dR / dz is a larger by a factor of 1.7 for dry thermals relative to moist thermals. The fractional change in thermal volume ε is also greater for dry thermals within a distance of ~4 radii from the initial thermal height. Values of dR / dz are nearly constant with height for both moist and dry thermals consistent with classical theory based on dimensional analysis. The simulations are also consistent with theory relating impulse, circulation, and spreading rate for dry thermals proposed in previous papers and extended here to moist thermals, predicting they will spread less than dry thermals. Tests adding heating to dry thermals, either spread uniformly across the thermal volume or concentrated in the inner core, indicate that dR / dz and ε are smaller for moist thermals because latent heating is confined mostly to their cores. Additional axisymmetric moist simulations using modified lapse rates and large-eddy simulations support this analysis. Overall, these results indicate that slow spreading rates are a fundamental feature of moist thermals caused by latent heating that alters the spatial distribution of buoyancy within them relative to dry thermals.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

DRDMannTurb: A Python package for scalable, data-driven synthetic turbulence

Synthetic turbulence models (STMs) are used in wind engineering to generate realistic flow fields and are employed as inputs to industrial wind simulations. Examples include prescribing inlet conditions in large eddy simulations that model loads on wind turbines and tall buildings. We are interested in STMs capable of generating fluctuations based on prescribed second-moment statistics since such models can simulate environmental conditions that closely resemble on-site observations. To this end, the widely used Mann model (see Mann, 1994, 1998) is the inspiration for DRDMannTurb. The Mann model is described by three physical parameters: a magnitude parameter influencing the global variance of the wind field and corresponding to the Kolmogorov constant multiplied by the rate of viscous dissipation of the turbulent kinetic energy to the two-thirds, αϵ 2/3 , a turbulence length scale parameter L, and a nondimensional parameter Γ related to the lifetime of the eddies. A number of studies, as well as international standards (e.g., those by the International Electrotechnical Commission (IEC)), include recommended values for these three parameters with the goal of standardizing wind simulations according to observed energy spectra. Yet, having only three parameters, the Mann model faces limitations in accurately representing the diversity of observable spectra. This Python package enables users to extend the Mann model and more accurately fit field measurements through flexible neural network models of the eddy lifetime function. Following Keith et al. (2021), we refer to this class of models as Deep Rapid Distortion (DRD) models. DRDMannTurb also includes a general module implementing an efficient method for synthetic turbulence generation based on a domain decomposition technique. This technique is also described in Keith et al. (2021).

17 WIND ENERGY↗
DOE OSTI2021

Computational and Experimental Validation of Fractal-Fin, Dimpled Solar Heat Collector

A 3 foot x 3 foot x 3 foot aluminum solar collector was manufactured using computer numerical control. The interior of the device included six triangular dimpled fins for enhanced heat transfer. The interior vertical wall on the south side was also dimpled. The solar collector working fluid was based on water, and the collector consisted solely of passive heat transfer mechanisms (no moving parts), making it ideal for off-the-grid and rural applications. Two types of heat transfer experiments were conducted. One experiment had external flat heaters attached on the top and the front side, while the other four sides were insulated. Except for the bottom surface, the second experiment had all its exterior surfaces sprayed with black solar paint to collect as much solar heat as possible. Temperature data as a function of time was collected using 14 thermocouples spread strategically throughout the solar collector. In addition, computational fluid dynamics (CFD) simulations were conducted using the dynamic Smagorinsky large eddy simulation turbulence model. The first simulation considered that both the top and front surfaces were exposed to a fixed temperature of 313.7 K (105 °F), while the remaining four surfaces were insulated. For the second simulation, all conditions were the same, except that the temperature for both heated surfaces was raised to 350 K (170.3 °F). The two temperatures are expected to bound the solar collector operational temperature during the late- Spring, Summer, and early-Fall months. The solar collector design, experimental data, CFD output, and a discussion of five manufacturing approaches and costs are documented in this report.

14 SOLAR ENERGY↗
DOE OSTI2025

Comparison of wind farm control strategies under realistic offshore wind conditions: turbine quantities of interest

Abstract. Wind farm flow control is a strategy to increase the efficiency and therefore lower the levelized cost of energy of a wind farm. This is done using turbine settings such as the yaw angle, blade pitch angles, or generator torque to manipulate the flow behind the turbine, affecting downstream turbines in the farm. Two inherently different wind farm flow control methods have been identified in the literature: wake steering and wake mixing. This paper focuses on comparing the turbine quantities of interest between these methods for a simple two-turbine wind farm setup, while a companion article (Brown et al., 2025) focuses on the wake quantities of interest for a single wind turbine setup. Both papers use the same set of wind farm simulations based on high-fidelity large-eddy simulations (LESs) coupled with OpenFAST turbine models. First, precursor simulations are executed in order to match wind conditions measured with lidars in an offshore wind farm off the east coast of the USA. These measurements show general wind conditions that exhibit substantially higher vertical wind shear and veer than any of the LES studies performed with wind farm flow control strategies currently available in the literature. The precursors are used to evaluate the effectiveness of the control methods. In the LES, the wind veer leads to highly skewed wakes, which have considerable influence on the power uplift of wind farm flow control strategies. In addition to a baseline controller, four different control strategies, each of which uses either pitch or yaw control, are performed on the upstream turbine of a simple two-turbine wind farm. Assuming that the wind direction is known and constant over time, the simulations show that wake steering is generally the superior wind farm flow control strategy, considering both wind farm power production and turbine damage equivalent loads when substantial wind veer is present. This result is consistent over different wind speeds and wind directions. On the other hand, for similar wind conditions with lower veer, wake mixing was found to yield the highest power production, although at the expense of generally higher loads. This leads us to conclude that the effect of wind veer, which has so far not usually been considered, can not be neglected when determining the optimal wind farm flow control strategy.

17 WIND ENERGY↗
DOE OSTI2024

Wind farm structural response and wake dynamics for an evolving stable boundary layer: computational and experimental comparisons

Abstract. The wind turbine design process requires performing thousands of simulations for a wide range of inflow and control conditions, which necessitates computationally efficient yet time-accurate models, especially when considering wind farm settings. To this end, FAST.Farm is a dynamic-wake-meandering-based mid-fidelity engineering tool developed by the National Renewable Energy Laboratory targeted at accurately and efficiently predicting wind turbine power production and structural loading in wind farm settings, including wake interactions between turbines. This work is an extension of a study that addressed constructing a diurnal cycle evolution based on experimental data (Quon, 2024). Here, this inflow is used to validate the turbine structural and wake-meandering response between experimental data, FAST.Farm simulation results, and high-fidelity large-eddy simulation results from the coupled Simulator fOr Wind Farm Applications (SOWFA)–OpenFAST tool. The validation occurs within the nocturnal stable boundary layer when corresponding meteorological and turbine data are available. To this end, we compared the load results from FAST.Farm and SOWFA–OpenFAST to multi-turbine measurements from a subset of a full-scale wind farm. Computational predictions of blade-root and tower-base bending loads are compared to 10 min statistics of strain gauge measurements during 3.5 h of the evolving stable boundary layer, generally with good agreement. This time period coincided with an active wake-steering campaign of an upstream turbine, resulting in time-varying yaw positions of all turbines. Wake meandering was also compared between the computational solutions, generally with excellent agreement. Simulations were based on a high-fidelity precursor constructed from inflow measurements and using state-of-the-art mesoscale-to-microscale coupling.

17 WIND ENERGY↗
DOE OSTI2023

Multi‐Scale Temporal Variability of Turbulent Mixing During a Monsoon Intra‐Seasonal Oscillation in the Bay of Bengal: An LES Study

A process study using large‐eddy simulations is carried out to explore the dominant 1‐D processes that affect mixed layer (ML) properties during an event of summer Monsoon Intra‐seasonal Oscillations (MISO) in the Bay of Bengal (BOB). These simulations use realistic air‐sea fluxes and initial conditions that were collected during the summer 2018 MISO‐BOB field experiment to explore the roles of thermal inversion layer (TIL) and Langmuir turbulence (LT) in modulating ML properties. The simulations span an active period with heavy rain and strong winds and a break period with strong solar heat flux and little rain. The mixed layer depth (MLD), sea surface temperature (SST) and sea surface salinity (SSS) are most affected by the presence of near‐inertial oscillations, solar heating and precipitation, all of which occur at different timescales. The subsurface warming induced by the TIL reduces the SST variability at the MISO timescale when compared with the simulation without TIL. Comparison of simulations with and without LT indicates that LT enhances subsurface warming during the active phase and reduces diurnal SST modulation during the break phase. Finally, simulations with 1‐D mixing models show a wide disparity in the evolution of MLD, SST, and SSS.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

CFD simulations of electric motor end ring cooling for improved thermal management

Proper thermal management of an electric motor for vehicle applications extends its operating range. One cooling approach is to impinge Automatic Transmission Fluid (ATF) onto the rotor end ring. Increased ATF coverage correlates to enhanced heat transfer. Computational Fluid Dynamics (CFD) analytical tools provide a mechanism to assess motor thermal management prior to hardware fabrication. The complexity of the fluid flow (e.g., jet atomization, interface tracking, wall impingement) and heat transfer makes these simulations challenging. Computational costs are high when solving these flows on high-speed rotating meshes. Typically, a Volume-of Fluid (VOF) technique (i.e., two-fluid system) is used to resolve ATF dynamics within this rotating framework. Suitable numerical resolution of the relevant physics for thin films under strong inertial forces at high rotor speeds is computationally expensive, further increasing the run times. In this work, a numerical study of rotor-ring cooling by ATF is presented using a patent automated Cartesian cut-cell based method coupled with Automatic Mesh Refinement (AMR). This approach automatically creates the Cartesian mesh on-the-fly and can effectively handle complex rotating geometries by adaptively refining the mesh based on local gradients in the flow field which results in better resolution of the air-ATF interface. A Single non-inertial Reference Frame (SRF) approach is used to account for the rotating geometry and to further improve the overall computational efficiency. Quasi-steady state conditions are targeted in the analysis of the results. Important physics such as ATF jet structure, velocity detail near the air-jet interface, ATF coverage/accumulation on the ring surface, and cooling capacity are presented for a low-resolution Reynolds averaged Navier-Stokes (RANS), high-resolution RANS, and high-resolution Large-Eddy Simulation (LES) models. Computations are scaled over hundreds of cores on a supercomputer to maximize turnaround time. Each numerical approach is shown to capture the general trajectory of the oil jet prior to surface impingement. The high-resolution LES simulation, however, is superior in capturing small scale details and heat transfer between the free jet and surrounding air.

42 ENGINEERING↗
DOE OSTI2020

Description of the LASSO Data Bundles Product

The U. S. Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) user facility began a pilot project in May 2015 to design a routine, high-resolution modeling capability to complement ARM’s extensive suite of measurements. This modeling capability has evolved into the Large-Eddy Simulation (LES) ARM Symbiotic Simulation and Observation (LASSO) datastream. The datastream, broadly termed data bundles, contains high-resolution model output, input files, observations for evaluation, and skill scores for the simulations. The initial focus of LASSO is on shallow convection at the ARM Southern Great Plains (SGP) atmospheric observatory. The availability of LES simulations with concurrent observations serves many purposes. LES helps bridge the scale gap between DOE ARM observations and models, and the use of routine LES adds value to observations. It provides a self-consistent representation of the atmosphere and a dynamical context for the observations. Further, it elucidates unobservable processes and properties. LASSO generates a simulation library for researchers that enables statistical approaches beyond a single-case mentality. It also provides tools necessary for modelers to reproduce the LES and conduct their own sensitivity experiments. The LASSO library of data bundles is designed to facilitate a wide range of research. For an observationalist, LASSO can help inform instrument remote-sensing retrievals, conduct observation system simulation experiments (OSSEs), and test implications of radar scan strategies or flight paths. For a theoretician, LASSO can help calculate estimates of fluxes and co-variability of values, and test relationships without having to run the model personally. For a modeler, LASSO can help one know ahead of time which days have good forcing, have co-registered observations at high-resolution scales, and have simulation inputs and corresponding outputs to test parameterizations. Further details on the overall LASSO project are available at https://www.arm.gov/capabilities/modeling/lasso.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Assessment of Low-Altitude Atmospheric Turbulence Models for Aircraft Aeroelasticity

We investigate the dynamic aeroelastic response of large but slow aircraft in low-altitude atmospheric turbulence. To this end, three turbulence models of increasing fidelity, namely, the one-dimensional von Kármán model, the two-dimensional Kaimal model and full three-dimensional wind fields extracted from large-eddy simulations (LES) are used to simulate ambient turbulence near the ground. Load calculations and flight trajectory predictions are conducted for a representative high-aspect-ratio wing aircraft, using a fully coupled nonlinear flight dynamics/aeroelastic model, when it operates in background atmospheric turbulence generated by the aforementioned models. Comparison of load envelopes and spectral content, on vehicles of varying flexibility, shows strong dependency between the selected turbulence model and aircraft aeroelastic response (e.g. 58% difference in the predicted magnitude of the wing root bending moment between LES and von Kármán models). This is mainly due to the presence of large flow structures at low altitudes that have comparable dimensions to the vehicle, and which despite the relatively small wind speeds within the Earth boundary layer, result in overall high load events for slow-moving vehicles. Results show that one-dimensional models that do not capture those effects provide fairly non-conservative load estimates and are unsuitable for very flexible airframe design.

atmospheric turbulence↗
DOE OSTI2020

Relationships between Immersion Freezing and Crystal Habit for Arctic Mixed-Phase Clouds—A Numerical Study

Abstract The number concentration of ice particles in Arctic mixed-phase clouds is a major controlling factor of cloud lifetime. The relationships between ice nucleation mode and ice crystal habit development are not yet constrained by observations. This study uses a habit-predicting microphysical scheme within a 3D large-eddy simulation model to evaluate the relationship between immersion freezing and ice habit in a simulated Arctic mixed-phase cloud case. Three immersion freezing parameterizations are considered: a volume-dependent freezing scheme (VF), a parameterization limited to activated droplets (C-AC), and a parameterization limited to coarse aerosol particles (C-CM). Both C-AC and C-CM are based on classical nucleation theory. The freezing rate with VF is found to be greater in downdraft regions than in updraft regions due to the downdraft having a higher number concentration of large droplets. The C-AC cases show active freezing of small droplets near cloud top, whereas in the C-CM cases, mainly the 8–32- μ m-sized droplets freeze in updraft regions near the cloud base. Because the initial crystal size is assumed to affect the axis ratio of hexagonal plates, the VF cases produce crystals with larger axis ratios, resulting in smaller mode radii than the C-AC cases. In all cases, irregular polycrystals dominate near cloud top and a band-like structure develops within the cloud, which qualitatively agrees with previous observations. In the VF and C-CM cases, unactivated large droplets arising from coarse-mode aerosol particles contributed significantly to the freezing rate, producing an important influence on crystal habit.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Wind Fields in Category 1–3 Tropical Cyclones Are Not Fully Represented in Wind Turbine Design Standards

Abstract Offshore wind energy deployment in the U.S. is expected to increase in the years to come, with proposed wind farm sites located in regions with high risk for tropical cyclones. Yet, the wind turbine design criteria outlined by the International Electrotechnical Commission for extreme events may not account for wind field characteristics unique to tropical cyclones. To evaluate if current design standards capture the extreme conditions of these storms, we perform idealized large‐eddy simulations of three tropical cyclones (one Category 1, one Category 2, and one Category 3 storms) using the Weather Research and Forecasting model. Wind conditions near the eyewall of Cat‐1, Cat‐2, and Cat‐3 storms can exceed current design standards for offshore wind turbines. Winds at 90 m can be faster than outlined in the design criteria for Class I and Class T turbines for 50‐year recurrence periods. Wind speed shear across the turbine rotor layer is also larger than assumed in design specifications. Moreover, vertical variations in wind direction across the turbine rotor layer are large for tropical cyclones of all intensity levels, suggesting design standards should include veer, which can amplify loads in wind turbines. The existence of hurricane wind field characteristics that are not represented in design standards does not imply that damage or failure will certainly occur. Engineering safety factors incorporated in the design of the turbine's blades and structural components may prevent damage from occurring.

17 WIND ENERGY↗
DOE OSTI2025

A simple three-component mixing problem for the evaluation of a new reaction rate model

A simple computational mixing problem is presented which can be utilized to assess the behavior of Reynolds-averaged reaction rate models in a problem with temporally varying mixedness. In this problem, three mixing components are homogeneously distributed but initially separated in a triply periodic domain. Further, these components are initialized within a Taylor–Green-like velocity field, which creates a mixing history evolving from the so-called “no-mix limit” to a well-mixed state. Large-eddy simulation results from this problem in configurations involving both premixed and nonpremixed reactants are then compared with zero-dimensional Reynolds-averaged Navier–Stokes results utilizing a new model for multicomponent reacting mixtures. The new model is shown to appropriately respect the no-mix limit and outperforms an earlier model (Morgan, 2022), particularly at early times when components are near the no-mix limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗