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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

FVCOM-plume – A Three-dimensional Lagrangian Outfall Plume Dilution and Transport Model for Dynamic Tidal Environments: Model Development

Although numerous steady-state effluent plume dilution models are in use, their application in tidal environments remains a challenge. Three-dimensional dynamic circulation models are also inadequate, often due to the lack of required resolution and simplifying assumptions. To overcome these limitations, we present FVCOM-plume—an outfall plume dilution and transport model that operates within the Finite Volume Coastal Ocean Model (FVCOM) framework. It provides simultaneous inclusion of near-field dilution and far-field plume transport processes. The near-field is based on UM3 model using Lagrangian Control Volume approach to compute buoyant plume trajectory and dilution from multiport diffusers. The far-field uses neutrally buoyant particles with point masses and the random walk method to solve unsteady advection-diffusion processes. A density kernel approach is used to compute concentrations at point locations and analyze far-field plume characteristics. The results demonstrate the ability of FVCOM-plume to simultaneously capture near-field and far-field effluent plume dynamics in tidal environments.

Plume Dilution Models↗
DOE OSTI2019

Physical conditions for UO formation in laser-produced uranium plumes

Laser-induced plasma spectroscopy is a powerful method for elemental detection and analysis, however the broadening and merging of densely packed spectral lines can make it especially challenging for studying high-Z elements such as uranium and other actinides. In order to understand the processes occurring in laser-induced plasma, it is necessary to evaluate the variation of its thermodynamic parameters. We performed spatiotemporal diagnostics of uranium species in plasma plumes produced by nanosecond near-infrared laser pulses in low- pressure environment. Spatially- and temporally-resolved emission spectroscopy experiments are supported by modeling of uranium emission and its persistence in the plume. Saha-Eggert equation as well as Boltzmann diagrams generated from numerous U I transitions are used to infer temperature. We report the rst measurements of uranium Stark broadening parameters for U I 499.01 nm and U II 500.82 nm transitions. The Stark widths of selected U transitions were measured by comparing their linewidths with the broadening of O I 777.19 nm line. Electron density was found to be on the order of 1016 cm??3, while the temperature was found to be in the range of 3000{8000 K. In addition to enhancing the fundamental understanding of high-Z plasmas under reduced-pressure environments, the knowledge of Stark broadening parameters could improve modeling capabilities and analytical performance of techniques that rely on emission plasma spectroscopy.

(140.3440) Laser-induced breakdown, (280.4788) Opt↗
DOE OSTI2019

Plume dynamics and gas-phase molecular formation in transient laser-produced uranium plasmas

The dynamics of expansion, thermodynamics, and chemical reactions in laser-produced plasmas is of general interest for all laser ablation applications. This study investigates the complex morphology and behavior of reactive species in nanosecond laser-produced uranium plasmas. Comparing plasma morphology in various inert and reactive ambient gases provides information about the role of gas-phase chemistry in plume hydrodynamics. Background gases including nitrogen and argon foster collisional interactions leading to more significant plume confinement and the increase in persistence of uranium species. On the other hand, environments containing reactive gases such as oxygen promote chemical reactions between the plasma and ambient species. By comparing the expansion dynamics of uranium plumes in nitrogen, air, and argon, we discover that chemical reactions modify the hydrodynamics of the plume at later times of its evolution in the air background. Furthermore, we observe that varying the concentration of oxygen in the fill gas promotes different reaction pathways that lead to the formation of uranium oxides. The reaction pathways from atoms to diatomic to polyatomic molecules strongly vary with ambient oxygen concentration. Lower oxygen concentrations enhance the formation of uranium monoxide from atomic uranium, whereas higher oxygen concentrations tend to depopulate both atomic uranium and uranium monoxide concentrations through the formation of more complex uranium oxides.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Aerosol size distribution changes in FIREX-AQ biomass burning plumes: the impact of plume concentration on coagulation and OA condensation/evaporation

Abstract. The evolution of organic aerosol (OA) and aerosol size distributions within smoke plumes is uncertain due to the variability in rates of coagulation and OA condensation/evaporation between different smoke plumes and at different locations within a single plume. We use aircraft data from the FIREX-AQ campaign to evaluate differences in evolving aerosol size distributions, OA, and oxygen to carbon ratios (O:C) between and within smoke plumes during the first several hours of aging as a function of smoke concentration. The observations show that the median particle diameter increases faster in smoke of a higher initial OA concentration (>1000 µg m−3), with diameter growth of over 100 nm in 8 h – despite generally having a net decrease in OA enhancement ratios – than smoke of a lower initial OA concentration (<100 µg m−3), which had net increases in OA. Observations of OA and O:C suggest that evaporation and/or secondary OA formation was greater in less concentrated smoke prior to the first measurement (5–57 min after emission). We simulate the size changes due to coagulation and dilution and adjust for OA condensation/evaporation based on the observed changes in OA. We found that coagulation explains the majority of the diameter growth, with OA evaporation/condensation having a relatively minor impact. We found that mixing between the core and edges of the plume generally occurred on timescales of hours, slow enough to maintain differences in aging between core and edge but too fast to ignore the role of mixing for most of our cases.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

VENTSAR V3.0: A Python GUI for Estimating Contaminant Concentrations on or Near Buildings Due to Building Effects and Plume Rise and For Calculating Inhalation and Plume Shine Doses

VENTSAR: Originated as VENTAX (Smith and Weber 1983) on the IBM Mainframe at the Savannah River Site (SRS) as a Fortran program. Updated to VENTSAR XL V1.0 (Simpkins 1997) as a spreadsheet version using macros created in Microsoft Excel. Later updated to VENTSAR XL V2.0 (Dixon 2018) as a spreadsheet executing a modified version of the original VENTAX Fortran code. Estimates contaminant concentrations on or near a building from a release at a nearby location. Calculates concentrations for a given meteorological exceedance probability or for a given stability and wind speed combination. Can model a single building with or without a penthouse on top or a ground location from either a stack or ground release. Plume rise can be considered. Contaminant releases can be chemical or radioactive with downwind concentrations determined at user-specified distances. Wind passing over and around buildings creates a complicated dispersion pattern. Air-intake vents may be located on building roofs or near the ground downwind of a release source. An estimation of pollutant concentrations on or near a structure is important in determining expected pollutant levels. Meteorological data are selected based on a specific area of the site. Fortran-based VENTAX able to make fast, complex mathematical calculations. Not user-friendly VENTSAR XL V1.0 no longer supported due to obsolete Excel macros. VENTSAR XL V2.0 an interim solution using an Excel spreadsheet to interface with the modified VENTAX Fortran code. Requires user to have Microsoft Excel. Not an intuitive interface for someone unfamiliar with VENTSAR. Does not perform dose calculations. VENTSAR V3.0 goal to combine the strengths of previous versions of VENTSAR into a single, powerful yet user-friendly program with a Graphical User Interface (GUI). Not dependent upon a specific program or plug-ins. Self-contained package to be used on any computer running Microsoft Windows. User-friendly, intuitive GUI created in Python for parameter input. Executes same modified VENTAX Fortran code as VENTSAR XL V2.0. Outputs formatted text file of completed calculations for easy review and dissemination. Performs inhalation and plume shine dose calculations for up to 11 user-selected nuclides from a nuclide dose factor library of almost 500 nuclides. 12 test cases were created for verification of V1.0 and V2.0. Same test cases run in V3.0 to verify correct performance. V3.0 produced similar results to V1.0. Confirmed GUI did not alter calculations in any way. Comparisons of the test case results confirm the V3.0 GUI does not influence the VENTSAR calculations. Simply passes same input parameters to VENTAX Fortran code for execution. Provides end user an easy-to-use, intuitive tool to quickly make building effect and plume rise calculations, as well as, inhalation and plume shine dose calculations. No experience with or working knowledge of Fortran, Excel, command line, or macros required. Self-contained package allows VENTSAR be deployed to any Windows computer without the need for specific programs or plug-ins.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Hyperfine structures and isotopic shifts of uranium transitions using tunable laser spectroscopy of laser ablation plumes

We report isotopic shifts and hyperfine structures of selected U transitions employing tunable spectroscopy viz: laser-induced fluorescence and laser absorption spectroscopy of laser ablation plumes. The laser-produced plasmas were produced during ns laser ablation on a natural U metal which contains 0.7% 235U. Our results show that isotopic shifts between 238U and 235U are entangled with hyperfine structures of 235U. The isotopic ratio obtained using laser-induced fluorescence is affected by optical saturation effect. Time-resolved laser absorption spectroscopy is carried out for evaluating the optical absorption and estimating the hyperfine constants.

(020.3260) Isotope shifts↗
DOE OSTI2022

Basin Management of Geologic CO2 Storage: Effect of Well Spacing on CO2 Plume and Pressure Interference

This is the conference paper accompanying an oral presentation made at the Society of Petroleum Engineers (SPE) Western Regional Meeting (WRM) held in Bakersfield, California, April 26–28, 2022. The paper provides the results of a basin-scale CO2 storage modeling project investigating subsurface pressure interference among CO2 injection wells located in proximity to each other.

Wijaya, Nur↗
DOE OSTI2021

Changing chemistry of particulate manganese in the near- and far-field hydrothermal plumes from 15°S East Pacific Rise and its influence on metal scavenging

Dissolved Mn(II) in the hydrothermal plume is known to be microbially oxidized to form Mn(III/IV) oxides, and the Mn oxides scavenge other trace elements in seawater. In the GEOTRACES GP16 cruise, dissolved Mn (dMn) and particulate Mn (pMn) were found to be transported over 4000 km westwards from the Southern Eastern Pacific Rise. Previous studies in this plume showed different removal rates of dMn and pMn as well as pMn size distribution between the near-field (<80 km from the ridge axis) and far-field (>80 km) plumes. In order to understand Mn cycling in these plumes, spatial distribution, oxidation states, and mineral structures of Mn in small size fraction (SSF; 0.8–51 μm) and large size fraction (LSF; >51 μm) particles from the near-field and far-field plumes were examined using micro X-ray fluorescence spectrometry (μ-XRF), X-ray absorption near-edge structure spectroscopy (XANES), chemical species mapping, and extended X-ray absorption fine-structure spectroscopy (EXAFS). In the near-field plume, pMn in the SSF is dominated by oxidized Mn with Mn(III) fractions of ~30%. They are a mixture of δ-MnO 2 and triclinic birnessites that is known to be formed as a result of autocatalytic Mn(II) oxidation at the surface of freshly-formed δ-MnO2, suggesting that both microbial and autocatalytic Mn oxidation occur in the near-field plume. The LSF pMn in the near-field plume is also oxidized and often found in large aggregates several hundreds of μm in size. These aggregates settle out in the near-field and during transport, and are not found in the far-field plume. In the far-field plume where Mn oxides are not newly formed, pMn in the SSF is oxidized, but their Mn(III) fractions are smaller than in the near-field pMn. Unlike the SSF, the far-field plume LSF pMn is dominated by reduced Mn, implying very slow aggregation of pMn in the far-field plume. The different characteristics of pMn between the near-field and far-field plumes affect its scavenging of other trace elements. In the near-field plume, Co, Mo, 231 Pa are associated with pMn, but not in the far-field plume. 231 Pa is adsorbed to pFe rather than pMn in the far-field plume, and Pb is adsorbed to pFe in the entire plume. The result shows that freshly-formed Mn oxides in the near-field plume have higher scavenging capacity than the far-field plume pMn. Our findings suggest that the mineralogical age of Mn oxides may be an important parameter that controls the scavenging of many other trace elements and isotopes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Sensitivities of Large Eddy Simulations of Aerosol Plume Transport and Cloud Response

Abstract Cloud responses to surface‐based sources of aerosol perturbation partially depend on how turbulent transport of the aerosol to cloud base affects the spatial and temporal distribution of aerosol. Here, scenarios of plume injection below a marine stratocumulus cloud are modeled using large eddy simulations coupled to a prognostic bulk aerosol and cloud microphysics scheme. Both passive plumes, consisting of an inert tracer, and active plumes are investigated, where the latter are representative of saltwater droplet plumes such as have been proposed for marine cloud brightening. Passive plume scenarios show higher in‐plume cloud brightness (relative to out‐of‐plume) due to the predominant transport of the passive plume tracer from the near‐surface to the cloud layer within updrafts. These updrafts rise into brighter areas within the cloud deck, even in the absence of an aerosol perturbation associated with an active plume. Comparing albedo at in‐plume to out‐of‐plume locations associates the inert plume with the brightest cloud locations, without any causal effect of the plume on the cloud. Numerical sensitivities are first assessed to establish a suitable model configuration. Then sensitivity to particle injection rate is investigated. Trade‐offs are identified between the number of injected particles and the suppressive effect of droplet evaporation on plume loft and spread. Furthermore, as the near‐field in‐plume brightening effect does not depend significantly on injection rate given a suitable definition of perturbed versus unperturbed regions of the flow, plume area is a key controlling factor on the overall cloud brightening effect of an aerosol perturbation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Deep learning inversion of gravity data for detection of CO 2 plumes in overlying aquifers

In this work, we developed an effective U-Net based deep learning (DL) model for inversion of surface gravity data on a rectangular grid to predict 2-D high-resolution subsurface CO 2 distribution along a vertical cross-section due to CO 2 leakage through a wellbore within a deep CO 2 storage reservoir. We used synthetic data to model two types of CO 2 leakage scenarios: one CO 2 plume in a shallow aquifer (single plume case), and two plumes present at different depths (double plume case). The 3-D synthetic plume samples were created by sampling among predetermined CO 2 plume depths, saturations, and volumes. The corresponding surface gravity data on a rectangular grid were generated by a 3-D forward model. The U-Net model detected 72% of single-plume samples, and one or both plumes in 75% of double-plume samples. Most of the undetected single plumes have small gravity field strengths below the typical noise level of 5 μGal. This model generated reproducible, reliable predictions with acceptable errors and demonstrated improved spatial resolution over the conventional least-squares inversion. In contrast to the conventional least-squares inversion, which often overestimates the size of its target and underestimates its density, this U-Net model accurately delineated the boundary of a target. Furthermore, this DL inversion detected deep, small, or low saturation CO 2 plumes that are often more difficult to resolve with conventional gravity inversion methods. We note the limitations of this feasibility study, including the use of synthetic data with regular CO 2 plume shapes, and the prediction of a 2-D plume cross-section rather than the full 3-D plume, as well, we recognize the lower detection fraction for double-plume scenarios. Nevertheless, this study demonstrates that DL gravity inversion is a promising and potentially superior method to conventional least-squares inversion. Our U-Net based deep learning inversion approach may be adapted for inversion of other types of geophysical data. DL inversion can facilitate near real-time monitoring of geologic carbon sequestration to provide site operators with prompt information about subsurface CO 2 distribution for risk management and mitigation.

58 GEOSCIENCES↗
DOE OSTI2024

Mixing of the Connecticut River Plume During Ambient Flood Tides: Spatial Heterogeneity and Contributions of Bottom–Generated and Interfacial Mixing

The Connecticut River plume is influenced by energetic ambient tides in the Long Island Sound receiving waters. The objectives of this modeling study are (a) characterizing the spatial heterogeneity of turbulent buoyancy fluxes, (b) partitioning turbulent buoyancy fluxes into bottom-generated and interfacial shear contributions, and (c) quantifying contributions to plume-integrated mixing within the tidal plume. The plume formed during ambient flood tides under low river discharge, spring tides, and no winds is analyzed. Turbulent buoyancy fluxes (B) and depth-integrated B through the plume (Bd) are characterized by pronounced spatial heterogeneity. Strong mixing (Bd ~ 10 –5 -10 –4 m 3 /s 3 ) occurs near the mouth, in the nearfield plume turning region, over shoals, and nearshore shallow areas. Low to moderate mixing (Bd ~ 10 –8 -10 –6 m 3 /s 3 ) occupies half the plume. Buoyancy fluxes are first partitioned based on the depth of the shear stress minimum between plume-generated and bottom-generated shear maxima. Four other tested partitioning methods are based on open channel flow and stratified shear flow parameterizations. Interfacial and bottom-generated shear contribute to different areas of intense and moderate mixing. All methods indicate a significant plume mixing role for bottom-generated mixing, but interfacial mixing is a bigger contributor. Plume-integrated total and interfacial mixing peak at max ambient flood and the timing of peak bottom-generated mixing varies among partitioning methods. Two-thirds of the mixing occurs in concentrated intense mixing areas. A parameter space with the ambient tidal Froude number and plume thickness to depth ratio as axes indicates many tidally modulated plumes are moderately to dominantly influenced by bottom-generated tidal mixing.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Stability of a Uranium-Contaminated Plume in a Karst Aquifer in Northwest New Mexico - 19574

The US Department of Energy (DOE) Office of Legacy Management monitors groundwater contamination resulting from ore processing operations conducted between 1953 and 1982 at a former uranium mill site on property that is now part of the Bluewater, New Mexico, Disposal Site. The site is located in the Grants Mineral Belt in northwest New Mexico at the base of the Zuni Mountains. It is estimated that prior to mill tailings encapsulation in 1995, approximately 21.6 billion liters (5.7 billion gallons) of tailings fluid seeped from the main tailings impoundment into the underlying aquifers. Today, there is remnant groundwater contamination from the mill in two aquifers: the San Andres-Glorieta (SAG) bedrock aquifer and the Ancestral Rio San Jose alluvial aquifer. Groundwater contamination in the SAG aquifer is of particular concern, as the aquifer is the primary water source in the region for municipal, agricultural, and industrial use. Municipal wells for the region are located as close as 6.4 kilometers (4 miles) southeast of the Main Tailings Disposal Cell. The SAG uranium plume extends east for more than 4.8 kilometers (3 miles) beyond the site's eastern boundary, along the direction of groundwater flow. The plume intersects the Homestake Mining Company site, another former uranium mill site undergoing active remediation. The SAG aquifer contains two formations, the Lower Permian San Andres Limestone and the Glorieta Sandstone. Most of the groundwater moving through the SAG aquifer is in ancient karst features consisting of open conduits where the limestone has dissolved, resulting in flow through solution cavities, solution channels, cavernous zones, and enlarged fracture openings. These features make the San Andres Limestone extremely permeable and capable of rapidly transporting groundwater. In addition, the karst characteristics make the aquifer difficult to evaluate and the uranium plume difficult to characterize. Numerous faults in the area, including two directly under the Main Tailings Disposal Cell, further complicate characterization by impacting groundwater flow both onsite and in the vicinity. A DOE study of the SAG aquifer uranium plume at the Bluewater site, conducted in 2014, indicated that the plume had moved offsite soon after the start of milling and effectively stabilized in its present location prior to the 1980's. An updated study completed in 2018 confirmed previous information regarding general plume stability and provided insight regarding potential localized trends east and south of the Main Tailings Disposal Cell. One such trend may be decreasing uranium concentrations east of the Main Tailings Disposal Cell, potentially attributable to regional groundwater elevation decreases. Both the 2013 and 2017 plumes suggest that the dissolved uranium contamination is derived from the leaching of a secondary mineralized zone derived from seeped tailings fluids in the geologic formations and fault zones below the Main Tailings Disposal Cell at the Bluewater site. In developing the 2013 and 2017 SAG aquifer uranium plume depictions, DOE had to address challenges associated with data quality and comparability. Analytical results used to determine the plume extent were compiled from multiple sources, including the state of New Mexico, Homestake Mining Company, and DOE. Each source used different well identifiers and coordinate systems, and well information between sources was inconsistent. Also, the integrity of some wells was questionable and necessitated review; casing integrity was found to be compromised in multiple wells. Given these uncertainties, some of these wells were excluded from the characterization. Another source of uncertainty is the paucity of wells, particularly monitoring wells, near or immediately downgradient of the leading edge of the plume. Therefore, the exact extent of the SAG aquifer uranium plume is not known at this time. There is, however, no evidence or indication of milling-related contamination in municipal wells. Furthermore, due to plume stability and direction of groundwater flow, the municipal wells are not expected to be impacted. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Standoff Infrared Measurements of Chemical Plume Dynamics in Complex Terrain Using a Combination of Active Swept-ECQCL Laser Spectroscopy with Passive Hyperspectral Imaging

Chemical plume detection and modeling in complex terrain present numerous challenges. We present experimental results from outdoor releases of two chemical tracers (sulfur hexafluoride and Freon-152a) from different locations in mountainous terrain. Chemical plumes were detected using two standoff instruments collocated at a distance of 1.5 km from the plume releases. A passive long-wave infrared hyperspectral imaging system was used to show time- and space-resolved plume transport in regions near the source. An active infrared swept-wavelength external cavity quantum cascade laser system was used in a standoff configuration to measure quantitative chemical column densities with high time resolution and high sensitivity along a single measurement path. Both instruments provided chemical-specific detection of the plumes and provided complementary information over different temporal and spatial scales. The results show highly variable plume propagation dynamics near the release points, strongly dependent on the local topography and winds. Effects of plume stagnation, plume splitting, and plume mixing were all observed and are explained based on local topographic and wind conditions. Measured plume column densities at distances ~100 m from the release point show temporal fluctuations over ~1 s time scales and spatial variations over ~1 m length scales. The results highlight the need for high-speed and spatially resolved measurement techniques to provide validation data at the relevant spatial and temporal scales required for high-fidelity terrain-aware microscale plume propagation models.

47 OTHER INSTRUMENTATION↗
DOE OSTI2026

Impact of Forest Canopy Structure on Buoyant Plume Dynamics During Wildland Fires

Heterogeneous forest canopies can generate complex turbulent structures, but in the presence of a fire plume, these interactions are not fully understood. This study investigates the influence of forest canopy heterogeneity on buoyant plume dynamics resulting from surface thermal anomalies representing wildland fires, utilizing Large Eddy Simulation (LES). The Parallelized Large-Eddy Simulation Model (PALM) was employed to simulate six canopy configurations: no canopy, homogeneous canopy, external plume-edge canopy, internal plume-edge canopy, 100 m gap canopy, and 200 m gap canopy. Each configuration was analyzed with and without a static surface heat flux patch of 5000 W ∙ m -2 , resulting in a resting buoyant plume. Simulations were conducted under three crosswind speeds: 0, 5, and 10 m ∙ s -1 . Results show that canopy structure significantly modifies plume behavior, mean flow, and turbulent kinetic energy (TKE) budgets. Plume updraft speed and tilt varied with canopy configuration and crosswind speed. Horizontal pressure gradients associated with plume-atmosphere interaction were modified based on the canopy configuration, resulting in varying crosswind speed reductions at the plume region. Strong momentum absorption was observed above the canopy for the crosswind cases, with the greatest enhancement in the gap canopies. Momentum injection from below the canopy due to the heat source was also observed, resulting in plume structure modulation based on canopy configuration. TKE was found to be the largest in the gap canopy configurations. TKE budget analysis revealed that buoyant production dominated over shear production. At the center of the heat patch, the gap canopy configurations showed enhanced buoyancy within the gap. These results improve our knowledge of fire-canopy-atmosphere interactions that can inform fire models on the impacts of canopy heterogeneity on plume dynamics and ember ejections.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Assessment of integral models for non-Boussinesq lazy plumes using numerical simulations

Integral modelling of turbulent buoyant plumes is crucial for rapid predictions of plume characteristics. While the governing equations are typically derived using self-similarity and a Boussinesq approximation, these assumptions may not hold for plumes originating from finite-area sources with large density ratios. Here, this work evaluates the accuracy of integral-scale models for non-Boussinesq lazy plumes using high-fidelity numerical simulations of turbulent helium plumes. We analyse the plume kinematics by computing vertical fluxes, plume radius and radial profiles, establishing some disparities between common practice and physical accuracy. We identify how the definition of the plume radius changes the perception of the plume structure when the flow is not self-similar and derive a relationship between the flux-based and threshold-based definitions without requiring self-similarity. We then examine the plume dynamics by evaluating the source terms from the governing plume equations. Our results support neglecting diffusive and viscous effects but emphasise the importance of the mean pressure gradient, even in the self-similar regime. Two coefficients need to be modelled: the well-known entrainment coefficient and the lesser-known momentum correction coefficient, which is a correction required for the momentum equation to account for self-similar and slender approximations. The momentum correction coefficient is found to be approximately constant and slightly greater than the assumed value of 1. The standard entrainment coefficient models perform well up to a local Richardson number three times the asymptotic value but overpredict entrainment for larger Richardson numbers. We propose a correction using the known finite limit of entrainment at infinite Richardson number.

Meehan, Michael Alexander [Sandia National Laborat↗