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At least 163 records · Page 9

Real-time gross actinide monitoring in extreme (10 6 :1) beta-gamma background fluid streams using mini-ATMFDs

Real-time, trace alpha activity monitoring in extreme mixed radiation fields is a well-known challenge in fission product-rich streams containing mixtures of beta-gamma-alpha radiation-emitting isotopes, arising due to the extreme 10 6 :1 ratio of background beta-gamma vs. alpha radiation activity levels. This paper presents results from a novel approach to addressing this challenge, based on Tensioned Metastable Fluid Detector (TMFD) sensing technology. An acoustically driven technique was developed and tested at Purdue University (using dissolved Rn-Po and U-chain alpha emitters), and validated (with dissolved Pu) at Savannah River National Laboratory for real-time monitoring of alpha activity in the 100–10,000 dpm/mL range.

Environmental Monitoring↗

Film Cooling Performance Predictions For Air And Supercritical CO 2

The current study explores the possibility of cooling the vanes and blades of a direct-fired sCO 2 turbine using film cooling geometries. The operating conditions of a direct-fired sCO 2 cycle and thermophysical properties of the fluid at those conditions can alter the flow field characteristics of the coolant jet and its mixing with the mainstream. Very little information is present in the literature regarding the performance of film cooling geometries employing a supercritical fluid. The objective of this study is to estimate the resulting film cooling effectiveness while also capturing the effects of the crossflow-to-mainstream velocity ratio on the coolant jet. A computational fluid dynamic model is used to study the coolant jet exiting a cylindrical hole located on a flat plate, with the coolant fed by an internal channel. Steady-state RANS equations were solved along with the SST kω model to provide the turbulence closure. The operating conditions for the direct-fired sCO 2 turbine are obtained using an in-house Cooled Turbine Model. Numerical predictions revealed that the crossflow effects and jet lift-off were more pronounced in the case of sCO 2 when compared to air. Spatial distribution of flow field and cooling effectiveness will be presented at different operating conditions. Recommendations for future studies will be given wherever applicable.

42 ENGINEERING↗

Subsurface Characterization for Evaluating Geothermal Resource Potential from Existing Oil and Gas Wells in Tuttle, Oklahoma: Preprint

Oil and gas (O&G) wells often encounter co-produced hot water, possibly suitable for geothermal direct-use applications. The City of Tuttle is located on the eastern part of the Anadarko sedimentary basin in Oklahoma with high heat-in-place potential and recovery capability at depth. This study aims at demonstrating the potential of geothermal energy production for direct-use applications in two public schools and 250 nearby houses in Tuttle via repurposing existing O&G wells. In this scope, geochemistry, geology, and borehole log data were collected and incorporated into a 3D conceptual subsurface model. A digital elevation model (DEM) was used to represent the study area topography with four O&G wells. In addition, hydrogeochemical characteristics of the geothermal fluid and scaling potential were analyzed using ternary diagrams and chemical ratios to develop mixing models. The subsurface geology model indicated that the study area primarily consists of Permian to Mississippian Sandstone and Limestone formations, implying a porosity ranging between 12% and 22%, and a permeability up to 3.90E-14 m2 in certain reservoir levels. The reservoir temperature is expected to be ranging between 80 degrees C to 95 degrees C around 3 km depth with an average temperature gradient of 22.8 degrees C/km. Chemical geothermometers also estimated the reservoir temperature as 90 degrees C. Findings of the chemical model demonstrated that the geothermal fluid is Sodium-Potassium-Chloride-Sulfate type and possibly mixed with shallow groundwater resulting in higher Ca and Mg concentrations and lower Na/K ratio implying lower calcite scaling. These results comprehensively characterize the potential of geothermal resources in the study area and imply that geothermal energy production by repurposing existing O&G wells is suitable for low-temperature direct-use applications.

GEOTHERMAL ENERGY↗

Subsurface Characterization for Evaluating Geothermal Resource Potential from Existing Oil and Gas Wells in Tuttle, Oklahoma

Oil and gas (O&G) wells often encounter co-produced hot water, possibly suitable for geothermal direct-use applications. The City of Tuttle is located on the eastern part of the Anadarko sedimentary basin in Oklahoma with high heat-in-place potential and recovery capability at depth. This study aims at demonstrating the potential of geothermal energy production for direct-use applications in two public schools and 250 nearby houses in Tuttle via repurposing existing O&G wells. In this scope, geochemistry, geology, and borehole log data were collected and incorporated into a 3D conceptual subsurface model. A digital elevation model (DEM) was used to represent the study area topography with four O&G wells. In addition, hydrogeochemical characteristics of the geothermal fluid and scaling potential were analyzed using ternary diagrams and chemical ratios to develop mixing models. The subsurface geology model indicated that the study area primarily consists of Permian to Mississippian Sandstone and Limestone formations, implying a porosity ranging between 12% and 22%, and a permeability up to 3.90E-14 m2 in certain reservoir levels. The reservoir temperature is expected to be ranging between 80 degrees C to 95 degrees C around 3 km depth with an average temperature gradient of 22.8 degrees C/km. Chemical geothermometers also estimated the reservoir temperature as 90 degrees C. Findings of the chemical model demonstrated that the geothermal fluid is Sodium-Potassium-Chloride-Sulfate type and possibly mixed with shallow groundwater resulting in higher Ca and Mg concentrations and lower Na/K ratio implying lower calcite scaling. These results comprehensively characterize the potential of geothermal resources in the study area and imply that geothermal energy production by repurposing existing O&G wells is suitable for low-temperature direct-use applications.

gas wells↗

Implications of real-gas behavior on refractive index calculations for optical diagnostics of fuel–air mixing at high pressures

Three models to compute the refractive index of gaseous mixtures at real gas conditions are presented with the purpose to improve the accuracy of state relationships between refractive index and thermodynamic properties. Models are compared with experimental data to determine one that is applicable to high pressure mixtures with non-ideal thermodynamic behavior near or above a fluids’ critical point. The optimal model is applied to analyze adiabatic thermal mixing of fuel and air at typical diesel engine conditions. Our results show that the ideal gas mixture law is appropriate in the vapor region, assuming it is known, for example, from experimental measurements. Finally, the model is applied for binary fuel-air mixing at supercritical conditions to demonstrate its full potential.

02 PETROLEUM↗

An Open-Source Framework for the Computational Analysis and Design of Autothermal Chemical Processes

The main project object was to develop software tools for simulating non-equilibrium autothermal processes, improving the prospects for identifying and designing such systems. The project demonstrates the use of these tools to simulate autothermal pyrolysis, a process recently developed at the pilot-plant scale at Iowa State University. In such process, instead of externally heating a reactor to pro-vide the enthalpy of pyrolysis, sufficient oxygen in the form of air is introduced into the reactor to support partial oxidation of reactants and products with the exothermic energy released supporting endothermic pyrolysis reactions. A fluidized bed is used to assure good mixing of biomass and oxidant and provide an isothermal reaction environment. The amount of oxygen required depends upon the kind of biomass being pyrolyzed and parasitic heat losses from the reactor. For example, for woody biomass pyrolyzed under conditions that simulate adiabatic operation, equivalence ratios can be as low as 0.06, compared to 0.20 or higher for autothermal gasifiers. By removing the heat transfer bottleneck of conventional pyrolysis, operation in autothermal mode allowed a significant increase in reactor throughput process, approaching five times the throughput of the conventionally operated pyrolyzer. Different simulation strategies were considered and developed: a zero-dimensional chemistry model was used to verify the applicability of kinetic schemes to predict biomass fast pyrolysis in autothermal conditions. Conventional chemical reactor models such as the plug flow reactor and the partially stirred reactor were used to investigate the role of mixing in the fluidized bed pyrolyzer and to establish the impact of mixing time on the gas-phase reactions. A comprehensive multiphase computational fluid dynamics (mCFD) framework, including polydisperse granular phase modeling and detailed chemical kinetics was formulated and used to model the experimental setup for autothermal biomass fast pyrolysis at ISU. Multiphase CFD was also used to investigate the role of biomass feed positioning on the mixing of biomass in the pyrolizer. Finally, a reduced order model (ROM), suitable to be implemented in process simulators was obtained. Both the mCFD and the ROM were validated against experiments.

09 BIOMASS FUELS↗

Scaling relationships for the elastic moduli and viscosity of mixed lipid membranes

The elastic and viscous properties of biological membranes play a vital role in controlling cell functions that require local reorganization of the membrane components as well as dramatic shape changes such as endocytosis, vesicular trafficking, and cell division. These properties are widely acknowledged to depend on the unique composition of lipids within the membrane, yet the effects of lipid mixing on the membrane biophysical properties remain poorly understood. Here, we present a comprehensive characterization of the structural, elastic, and viscous properties of fluid membranes composed of binary mixtures of lipids with different tail lengths. We show that the mixed lipid membrane properties are not simply additive quantities of the single-component analogs. Instead, the mixed membranes are more dynamic than either of their constituents, quantified as a decrease in their bending modulus, area compressibility modulus, and viscosity. While the enhanced dynamics are seemingly unexpected, we show that the measured moduli and viscosity for both the mixed and single-component bilayers all scale with the area per lipid and collapse onto respective master curves. This scaling links the increase in dynamics to mixing-induced changes in the lipid packing and membrane structure. More importantly, the results show that the membrane properties can be manipulated through lipid composition the same way bimodal blends of surfactants, liquid crystals, and polymers are used to engineer the mechanical properties of soft materials, with broad implications for understanding how lipid diversity relates to biomembrane function.

59 BASIC BIOLOGICAL SCIENCES↗

Detailed Simulations of a Three-Stage Supercritical Carbon Dioxide Axial Compressor with a Focus on the Shrouded Stator Cavities Flow

This paper describes the findings of detailed simulations performed to investigate the impact of seal teeth cavity leakage flow on the aerodynamic and thermal performance of a three-stage supercritical CO 2 axial compressor. The study compares a shrouded stator configuration (with cavities) to a cantilevered stator configuration (without cavities) to highlight their differences. High-fidelity computational fluid dynamics simulations were performed using non-linear harmonic (NLH) and mixing plane assumptions, considering various possible rotor/stator interface configurations for mixing plane calculations. The key performance parameters for each case were compared, and the best-performing configuration selected for further analysis. The individual stage performance parameters are also examined and compared between the cantilevered and shrouded configurations. It was observed that in the shrouded case, the leakage flow enters the cavity downstream of the stator trailing edge and gets entrained into the primary flow upstream of the stator, leading to boundary layer changes at the hub and degradation of stator and downstream rotor performance. Vortical flow structures were also observed in the stator wells, which tended to change the flow angles around the region, thereby affecting mixing and velocity distribution, resulting in a slight deterioration of compressor performance. Additionally, the study examines windage heating due to shear work from rotating walls, including the seal teeth surface. The amount of shear work done on the leakage flow and the corresponding rise in fluid temperature were quantified, tabulated, and further compared with a simple analytical model, showing good agreement between them and, hence, validating the numerical approach used.

42 ENGINEERING↗

Entropy generation from hydrodynamic mixing in inertial confinement fusion indirect-drive targets

The increase in entropy from the physical mixing of two adjacent materials in inertial confinement fusion (ICF) implosions and gas-filled hohlraums is analytically assessed. An idealized model of entropy generation from the mixing of identical ideal-gas particles across a material interface in the presence of pressure and temperature gradients is applied. Physically, mix-driven entropy generation refers to the work done by the gases in expanding into a larger common volume from atomic mixing under the condition of no internal energy change, or work needed to restore the initial unmixed state. Furthermore, the effect of a mix-generated entropy increase is analytically shown to lead to less compression of the composite ICF fluid under adiabatic conditions. The amount of entropy generation is estimated to be ~10 J for a Rayleigh–Taylor-induced micrometer-scale annular mixing layer between the solid deuterium–tritium fuel and (undoped) high-density carbon pusher of an imploding capsule at the National Ignition Facility (NIF). This level of entropy generation is consistent with lower-than-expected fuel compressions measured on the NIF [Hurricane et al., Phys. Plasmas 26, 052704 (2019)]. The degree of entropy increase from mixing of high-Z hohlraum wall material and low-Z, moderate- to high-density gas fills is estimated to lead to ~100 kJ of heat generation for NIF-scale experiments [Moody et al., Phys. Plasmas 21, 056317 (2014)]. This value represents a significant fraction of the inferred missing x-ray drive energy based on observed delays in capsule implosion times compared with mainline simulations [Jones et al., Phys. Plasmas 19, 056315 (2012)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Numerical investigation of mixing and heat transfer in a 7.9 m JP-8 pool fire

The response of objects engulfed in, and adjacent to, large-scale pool fires is of interest in accident and safety assessments. In this study, Fuego, a low-Mach turbulent reacting flow code was used to study conjugate heat transfer in a 7.9 m diameter JP-8 pool fire. Simulations were designed to replicate past experimental measurements (Blanchat et al., 2006) of incident heat flux to three cylindrical calorimeters in and around the pool fire. Two turbulent combustion models were compared directly - the eddy dissipation concept and a more recently developed unsteady flamelet model. First and second order spatial and temporal discretization schemes were also compared to assess the performance of low-dissipation numerical operators. Heat flux predictions to the transportation size calorimeter outside the fire were within experimental uncertainties. Inside the fire, experimental measurements were higher than predicted values and may have been a consequence of soot deposition and augmented participating media radiation from soot and fuel vapor. Simulation predictions improved in cases where turbulent kinetic energy and mixing were more resolved. This work, and others referenced herein, suggest that spatial resolution on the order of 0.5–1.0 cm may be required to fully resolve fluid instabilities, vortex production between fire plumes and crosswind, soot production, and fuel-air mixing. This presents a substantial computational challenge for safety assessments of engulfed objects in fully turbulent pool fires.

Conjugate heat transfer↗

Fluid dynamic mathematical aspects of supernova remnants

Supernovae—explosions of stars—are a central problem in astrophysics since they contain information on the entire process of stellar evolution and nucleosynthesis. Rayleigh–Taylor (RT) and Richtmyer–Meshkov (RM) instabilities, developing during the supernova blast, lead to intense interfacial RT/RM mixing of the star's materials and couple astrophysical to atomic scales. This work analyzes some fluid dynamic mathematical aspects of the titanic task of supernova's blast. We handle mathematical challenges of RT/RM dynamics in supernova relevant conditions by directly linking the conservation laws governing RT/RM dynamics to symmetry-based momentum model, by exactly deriving the model parameters in the scale-dependent and scale-invariant regimes, and by exploring the special self-similar class for RT/RM interfacial mixing with variable accelerations. Here we reveal that RT/RM dynamics is strongly influenced by deterministic (the initial and the flow) conditions in the scale-dependent linear and nonlinear regimes and in the self-similar mixing regime. The theory outcomes are consistent with the observations of supernova remnants, explain the results of the scaled laboratory experiments in high energy density plasmas, and yield the design of future experiments for the accurate quantification of RT/RM dynamics in supernova relevant conditions. We find that from fluid dynamic mathematical perspectives, supernovae can be regarded as an astrophysical initial value problem. Along with the guidance of what explodes at microscopic scales, supernova remnants encapsulate information on the explosion hydrodynamics and the associated deterministic conditions at macroscopic scales. We urge such effects be considered in interpretations of the observational data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A combined experimental and modelling study of granite hydrothermal alteration

Geochemical reactions can induce significant changes of rock reservoir porosity and permeability via mineral dissolution and precipitation processes, affecting the long-term fluid behaviour within various geological systems. Here, the understanding and quantification of these reactions rely on field and experimental studies and on the predictions of reactive transport models. The present study was aimed at assessing the extent to which current geochemical models integrating available mineral dissolution/precipitation rate equations can reproduce the experimental data obtained from 4 to 17-day long hydrothermal alteration experiments of a muscovite-biotite granite and, thus, help provide an accurate description of the evolution of geothermal systems within granitic reservoirs. The experiments were conducted at a constant temperature of 180 °C and over an aqueous fluid pH range of 2 to 8.5, using both mixed-flow and static batch reactors. Modelled major element (K, Al, Si, Ca, and Mg) concentrations were generally in satisfactory agreement with the corresponding measured elemental fluxes – the differences between modelled and experimental values were generally within a factor of 5 – and the predicted identity and mass of formed secondary phases were consistent with the microscopic observations of the reacted solids. However, larger differences between measured and modelled element concentrations were observed when significant amounts of secondary phases formed, notably at pH 2 to 3, and for longer-term batch experiments. Much of this concentration difference stems from the underestimation of the amounts of Al-phases formed at acid to near-neutral pH. Although an idealized rock composition was considered, the observed mismatch between model calculations and experimental data can be attributed to inadequate mineral precipitation reaction rates and a poor description of reactive surface areas in existing geochemical modelling codes. More accurate quantification of precipitation kinetics, including nucleation and growth, and improved descriptions of the temporal change of mineral surface area would enhance the predictive capabilities of reactive transport models and benefit, particularly, the efforts aimed at increasing the sustainability of EGS reservoirs.

58 GEOSCIENCES↗

Supercritical water co-liquefaction of LLDPE and PP into oil: properties and synergy

The major plastic wastes are always mixtures, which are difficult to separate to treat in practice. Because of some possible cross-reactions, the degradation behaviors of plastics could not be mathematically represented by a simple addition of each polymer according to their proportions. This work examines supercritical water (scH 2 O) to liquefy poly-ethylene and poly-propylene mixtures into an oil with special interest in the oil quality and positive effect. Additionally, linear low-density polyethylene (LLDPE) and polypropylene (PP) were chosen as parent materials because of their high proportions in plastic wastes. The results show that a high conversion rate of around 99.75% was achieved with as high as 90.7 wt% oil yield without additional catalysts or hydrogen. The scH 2 O co-liquefaction of the LLDPE/PP mixture was different from that of the single polymer along with an improvement in the oil yield. Cyclic hydrocarbon ( i.e. , cyclic) generation was promoted while the production of paraffins was hindered in scH 2 O co-liquefaction using a mixture of LLDPE/PP. TGA reveals that the scH 2 O co-liquefaction of LLDPE/PP mixtures generated more diesel and lubricant oils and less gasoline and (jet fuel + light diesel) oils, thus slightly lowering the oil quality. Overall, the supercritical fluid technology was a powerful and promising means to liquefy mixed plastic wastes into oil at a high conversion rate free of catalysts or hydrogen.

42 ENGINEERING↗

Photochemically induced acousto-optics in gases

Acousto-optics consists of launching acoustic waves in a medium (usually a crystal) in order to modulate its refractive index and create a tunable optical grating. Here, in this article, we present the theoretical basis of an alternative scheme to generate acousto-optics in a gas, where the acoustic waves are initiated by the localized absorption (and thus gas heating) of spatially modulated UV light, as was demonstrated by Michine and Yoneda [Commun. Phys. 3, 24 (2020)]. We identify the chemical reactions initiated by the absorption of UV light via the photodissociation of ozone molecules present in the gas, and calculate the resulting temperature increase in the gas as a function of space and time. Solving the Euler fluid equations shows that the modulated, isochoric heating initiates a mixed acoustic-entropy wave in the gas, whose high-amplitude density (and thus refractive index) modulation can be used to manipulate a high-power laser. We calculate that diffraction efficiencies near 100% can be obtained using only a few millimeters of gas containing a few percent ozone fraction at room temperature, with UV fluences of less than 100 mJ/cm 2 —consistent with the experimental measurements. Our analysis suggests possible ways to optimize the diffraction efficiency by changing the buffer gas composition. Gases have optics damage thresholds 2–3 orders of magnitude beyond those of solids; these optical elements should therefore be able to manipulate kilojoule-class lasers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

EGS Collab Experiment 1: SIMFIP Notch-164 GRL Paper

Characterizing the stimulation mode of a fracture is critical to assess the hydraulic efficiency and the seismic risk related to deep fluid manipulations. We have monitored the three-dimensional displacements of a fluid-driven fracture during water injections in a borehole at ~1.5 km depth in the crystalline rock of the Sanford Underground Research Facility (USA). The fracture initiates at 61% of the minimum horizontal stress by micro-shearing of the borehole on a foliation plane. As the fluid pressure increases further, borehole axial and radial displacements increase with injection time highlighting the opening and sliding of a new hydrofracture growing ~10 m away from the borehole, in accordance with the ambient normal stress regime and in alignment with the microseismicity. Our study reveals how fluid-driven fracture stimulation can be facilitated by a mixed-mode process controlled by the complex hydromechanical evolution of the growing fracture. The data presented in this submission refer to the SIMFIP measurements and analyses of the stimulation tests conducted on the 164 ft (50 m) notch of the Sanford Underground Research Facility (SURF), during the EGS-Collab test 1. In addition to the datafiles, there is the draft of a manuscript submitted to Geophysical Research Letters (GRL).

15 GEOTHERMAL ENERGY↗

Influence of sequential stimulation practices on geochemical alteration of shale

Water-based hydraulic fracturing fluids (HFFs) can chemically interact with formation shale, resulting in altered porosity and permeability of the host rock. Experimental investigations of spatial and temporal shale-HFF interactions are helpful in interpreting chemical compositions of the injectate, as well as predicting alteration of hydraulic properties in the reservoir due to mineral dissolution and precipitation. Most bench-top experiments designed to study shale-HFF chemical interactions, either using batch reactors or flow-through setups, are carried out assuming that the acid spearhead has already become mixed with neutral HFFs. During operations, however, HFFs are typically injected according to a sequenced pumping schedule, starting with a concentrated acid spearhead, followed by multiple additions of near-neutral pH HFFs containing chemical amendments and proppant. In this study, we use geochemical modeling to consider whether this pre-mixed experimental protocol provides results directly comparable to a sequential discrete fluid-shale interaction protocol. Our results show that for the batch system, the transient evolution in major ion concentrations is faster with the sequential procedure. After 2 h of reaction time, the two protocols converge to the same aqueous concentrations. In a flow-through geometry, the pre-mixed model predicts extensive chemical alteration close to the injection point but negligible alteration downstream. In contrast, the sequential model predicts mineral reactions over hundreds of meters along the flow path. The extent of shale alteration in the sequential model at a given location depends on shale mineralogy and where the acid spearhead resides during the shut-in period. The predictive model developed in this study can help experimentalists to design bench-top tests and operators to better translate the results of laboratory experiments into practical applications.

Li, Qingyun↗

Evaluation of RANS vs. LES simulation of fluid flow through 3 × 3 rod bundle with a simple spacer grid as a precursor to coupled fluid–structure interaction simulations

The research literature on Computational Fluid Dynamics (CFD) of coolant flow through rod bundles with spacer-grids and mixing vanes is replete, ranging from high fidelity Large Eddy Simulation (LES)/Direct Numerical Simulation (DNS) simulations to Reynolds-Averaged Navier–Stokes (RANS) modeled studies. The mixing of flow between subchannels and the pressure drop through the bundle are fundamental quantities useful for comparing and evaluating CFD methods. Less commonly observed and compared are the forces exerted onto the structure by the fluid. The present study seeks to evaluate the use of RANS simulations for predicting the structural response to fluid flow. Wall resolved RANS simulations are benchmarked against LES simulations of fluid flow at a Reynolds number of 15,000 through a 3 × 3 fuel rod bundle with a simple spacer grid. Velocity line-plots are compared showing good agreement between RANS and LES results, ascertaining that the former is capable of capturing the essential time-averaged velocity profile. Additionally, the distribution of forces on the spacer grid and fuel rods are collected as a function of time and space. The RANS methods are evaluated using the frequency and magnitude of the fluctuating forces on various portions of the structure as compared to LES. In conclusion, the power spectral density evaluation of the models reveal underprediction of force amplitude on the rod walls by RANS and also discrepancy in the prediction of high frequency spectra, especially in the immediate vicinity of spacer-grid structure, which may be attributed to the lack of random turbulence fluctuation or insufficient modeling of small-scale eddies in RANS simulation.

FIV↗

Derivation of a Multi-Species Mix Model

Multi-species flow takes place when two or more gases, plasmas or fluids are flowing and interacting with one another through particle collisions, chemical reactions, turbulence, and thermonuclear processes; this list is not exhaustive. It has a wide range of applications in geological, biological and engineering systems. In what follows species refers to different species of atoms or molecules that may or may not be partially or fully ionized. The interactions between these species takes place at an atomic or molecular level. The species are electrically neutral. These are very important points, because the coupling between species that are interacting on a mesoscale level or are immiscible would be very different than what is being considered in this work. In addition, in section 4, we present a heuristic argument to enhance the collisional mean free path to incorporate the effects of turbulent eddies by use of Prandtl’s assumption that the integral scale length of a turbulent boundary layer is proportional to the width of the turbulent layer. This leads to coupling terms that are non-Newtonian, because they are a function of the dynamics of the flow. It is also assumed that the turbulent stress terms are much smaller than the species partial pressures. This may be a good assumption if the species are hot, dense plasmas that exist in ICF targets.

74 ATOMIC AND MOLECULAR PHYSICS↗