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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 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The role of collective elasticity on activated structural relaxation, yielding, and steady state flow in hard sphere fluids and colloidal suspensions under strong deformation

In this work, we theoretically study the effect of external deformation on activated structural relaxation and aspects of the nonlinear mechanical response of glassy hard sphere fluids in the context of elastically collective nonlinear Langevin equation theory. This microscopic force-based approach describes activated relaxation as a coupled local–nonlocal event involving caging and longer range collective elasticity, with the latter becoming more important and ultimately dominant with increasing packing fraction under equilibrium conditions. The central new question we address is how this physical picture of activated relaxation, and the relative importance of local caging vs collective elasticity physics, depends on external deformation. Theoretical predictions are presented for deformation-induced enhancement of mobility, the onset of relaxation speed up at remarkably low values of stress, strain, or shear rate, apparent power law thinning of the steady state structural relaxation time and viscosity, a non-vanishing activation barrier in the shear thinning regime, an apparent Herschel–Bulkley form of the rate dependence of the steady state shear stress, exponential growth of different measures of a dynamic yield or flow stress with the packing fraction, and reduced fragility and dynamic heterogeneity under deformation. The results are contrasted with experiments and simulations, and qualitative or better agreement is found. An overarching conclusion is that deformation strongly reduces the importance of longer range collective elastic effects relative to the local caging aspect for most, but not all, physical questions, with deformation-dependent fragility and dynamic heterogeneity phenomena being qualitatively sensitive to collective elasticity. Overall, nonlinear rheology is predicted to be a more local problem than quiescent structural relaxation, albeit with deformation-modified activated processes still important.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

SOLPS analysis of the necessary conditions for detachment cliff

SOLPS modeling including full cross-filed drifts is used, for the first time, to reproduce the step-like detachment onset observed in the DIII-D tokamak previously simulated with UEDGE [Jaervinen A. E. et al., 2018 Phys. Rev. Lett.121 075001], and to further investigate the underlying physics processes. The SOLPS analysis reveals a strong interplay between the E×B drift-driven flows and carbon radiation in DIII-D. The modeling shows that the high confinement H-mode facilitates the formation of such a detachment cliff due to the narrow SOL width and hence steep radial gradients near the separatrix, which enhances the poloidal E×B drift. Furthermore, the SOLPS modeling indicates that carbon radiation also plays a key role in the formation of the detachment cliff in DIII-D without additional impurity seeding. These findings may have significant implications for the control and maintenance of divertor detachment for the steady-state operation of high-power fusion devices.

Physics - Plasma physics↗
DOE OSTI2022

A Phase-Field Model for In-Space Manufacturing of Binary Alloys

The integrity of the final printed components is mostly dictated by the adhesion between the particles and phases that form upon solidification, which is a major problem in printing metallic parts using available In-Space Manufacturing (ISM) technologies based on the Fused Deposition Modeling (FDM) methodology. Understanding the melting/solidification process helps increase particle adherence and allows to produce components with greater mechanical integrity. We developed a phase-field model of solidification for binary alloys. The phase-field approach is unique in capturing the microstructure with computationally tractable costs. The developed phase-field model of solidification of binary alloys satisfies the stability conditions at all temperatures. The suggested model is tuned for Ni-Cu alloy feedstocks. We derived the Ginzburg-Landau equations governing the phase transformation kinetics and solved them analytically for the dilute solution. We calculated the concentration profile as a function of interface velocity for a one-dimensional steady-state diffuse interface neglecting elasticity and obtained the partition coefficient, k, as a function of interface velocity. Numerical simulations for the diluted solution are used to study the interface velocity as a function of undercooling for the classic sharp interface model, partitionless solidification, and thin interface.

36 MATERIALS SCIENCE↗
NASA NTRS1987

Computational interferometric description of nested flow fields

Computer graphics and theoretical descriptions of density are used to obtain computer generated flow visualizations called computational interferograms. Computational interferograms are pictorially analogous to optical interferograms, and examples showing the fringe pattern for the flow about a sharp tip cone in a supersonic air stream are presented. To ascertain the effect of unsteady behavior, local density disturbances are added to the steady state flow field. This introduces irregularities to the computational interferogram like those seen in the optical interferograms. These theoretical disturbances can be varied in geometry, density description, translated with time, and strengthened or dissipated. The accuracy of computational interferometry relies on the accuracy of the theoretical density descriptions and therefore, it provides a way of verifying existing models of flow fields, especially those containing unsteady or turbulent behavior. In addition to being a unique method of flow visualization, computational interferometry can be used to develop and modify theories or numerical solutions to both simple and complex flow fields. The presented research is a general description of this process.

Havener, A. George↗
NASA NTRS1996

Bubble Dynamics on a Heated Surface

In this work, we study the combined thermocapillary and natural convective flow generated by a bubble on a heated solid surface. The interaction between gas and vapor bubbles with the surrounding fluid is of interest for both space and ground-based processing. On earth, the volumetric forces are dominant, especially, in apparatuses with large volume to surface ratio. But in the reduced gravity environment of orbiting spacecraft, surface forces become more important and the effects of Marangoni convection are easily unmasked. In order to delineate the roles of the various interacting phenomena, a combined numerical-experimental approach is adopted. The temperature field is visualized using Mach-Zehnder interferometry and the flow field is observed by a laser sheet flow visualization technique. A finite element numerical model is developed which solves the two-dimensional momentum and energy equations and includes the effects of bubble surface deformation. Steady state temperature and velocity fields predicted by the finite element model are in excellent qualitative agreement with the experimental results. A parametric study of the interaction between Marangoni and natural convective flows including conditions pertinent to microgravity space experiments is presented. Numerical simulations clearly indicate that there is a considerable difference between 1-g and low-g temperature and flow fields induced by the bubble.

Kassemi, Mohammad↗
NASA NTRS2002

Quasi-One-Dimensional Modeling of Pulse Detonation Rocket Engines

Pulsed detonation rocket engines (PDREs) have generated considerable research interest in recent years as a chemical propulsion system potentially offering improved performance and reduced complexity compared to conventional rocket engines. The detonative mode of combustion employed by these devices offers a thermodynamic advantage over the constant-pressure deflagrative combustion mode used in conventional rocket engines and gas turbines. However, while this theoretical advantage has spurred a great deal of interest in building PDRE devices, the unsteady blowdown process intrinsic to the PDRE has made realistic estimates of the actual propulsive performance problematic. The recent review article by Kailasanath highlights some of the difficulties in comparing the available experimental measurements with numerical models. In a previous paper by the author, parametric studies of the performance of a single, straight-tube PDRE were reported. A 1-D, unsteady method of characteristics code, employing a constant-gamma assumption behind the detonation front, was developed for that study. Models of this type are computationally inexpensive, and are particularly useful for parametric performance comparisons. For example, a plot showing the specific impulse of various PDRE and steady-state rocket engine (SSRE) configurations as a function of blowdown pressure ratio. The performance curves clearly indicate that a straight-tube PDRE is superior in specific impulse to a SSRE with a sonic nozzle over the entire range of pressure ratios. Note, however, that a straight-tube PDRE in general does not compare favorably to a SSRE fitted with an optimized de Laval supersonic nozzle, particularly at the high pressure ratios typical for boost or in-space rocket applications. However, the calculations also show that if a dynamically optimized, supersonic de Laval nozzle could be could be fitted to a PDRE, then the specific impulse of the device would exceed that of a comparable SSRE. While such a nozzle is a considerable idealization, it is clear that nozzle design and optimization will play a critical role in whether the performance potential of PDREs can be effectively realized in practice. In order to study PDRE nozzle issues with greater accuracy, a quasi-one-dimensional, finite-rate chemistry CFD code has been developed by the author. Comparisons of the code with both the previous MOC model and experimental data from Stanford University are reported. The effect of constant-gamma and finite-rate chemistry assumptions on the flowfield and performance is examined. Parametric studies of the effect of nozzle throat size and expansion ratio, at various blowdown pressure ratios, are reported.

Morris, Christopher I.↗
NASA NTRS1998

Polymerization on the rocks: theoretical introduction

It is difficult if not impossible to synthesize long polymers of amino acids, nucleotides, etc., in homogeneous aqueous solution. We suggest that long polymers were synthesized on the surface of minerals in a prebiotic process analogous to solid-phase synthesis. Provided that the affinity of a mineral for an oligomer increases with the length of the oligomer, adsorption must become essentially irreversible for sufficiently long oligomers. Irreversibly adsorbed oligomers may be elongated indefinitely by repeated cycles in which the mineral with its adsorbed oligomers is first incubated with activated monomers and then washed free of deactivated monomer and side-products. We discuss in some detail the formation of oligomers of negatively-charged amino acids such as glutamic acid on anion-exchange minerals such as hydroxylapatite or illite. We show that the average length of adsorbed oligomers at steady state, n, depends on the balance between the rate of chain elongation and the rate of hydrolysis, and we derive a very approximate formula for n.

NASA Discipline Exobiology↗
NASA NTRS2012

NASA's Evolutionary Xenon Thruster (NEXT) Long-Duration Test as of 736 kg of Propellant Throughput

The NASA s Evolutionary Xenon Thruster (NEXT) program is developing the next-generation solar-electric ion propulsion system with significant enhancements beyond the state-of-the-art NASA Solar Electric Propulsion Technology Application Readiness (NSTAR) ion propulsion system to provide future NASA science missions with enhanced mission capabilities. A Long-Duration Test (LDT) was initiated in June 2005 to validate the thruster service life modeling and to qualify the thruster propellant throughput capability. The thruster has set electric propulsion records for the longest operating duration, highest propellant throughput, and most total impulse demonstrated. At the time of this publication, the NEXT LDT has surpassed 42,100 h of operation, processed more than 736 kg of xenon propellant, and demonstrated greater than 28.1 MN s total impulse. Thruster performance has been steady with negligible degradation. The NEXT thruster design has mitigated several lifetime limiting mechanisms encountered in the NSTAR design, including the NSTAR first failure mode, thereby drastically improving thruster capabilities. Component erosion rates and the progression of the predicted life-limiting erosion mechanism for the thruster compare favorably to pretest predictions based upon semi-empirical ion thruster models used in the thruster service life assessment. Service life model validation has been accomplished by the NEXT LDT. Assuming full-power operation until test article failure, the models and extrapolated erosion data predict penetration of the accelerator grid grooves after more than 45,000 hours of operation while processing over 800 kg of xenon propellant. Thruster failure due to degradation of the accelerator grid structural integrity is expected after

Shastry, Rohit↗
NASA NTRS2012

NASA's Evolutionary Xenon Thruster (NEXT) Long-Duration Test as of 736 kg of Propellant Throughput

The NASA s Evolutionary Xenon Thruster (NEXT) program is developing the next-generation solar-electric ion propulsion system with significant enhancements beyond the state-of-the-art NASA Solar Electric Propulsion Technology Application Readiness (NSTAR) ion propulsion system to provide future NASA science missions with enhanced mission capabilities. A Long-Duration Test (LDT) was initiated in June 2005 to validate the thruster service life modeling and to qualify the thruster propellant throughput capability. The thruster has set electric propulsion records for the longest operating duration, highest propellant throughput, and most total impulse demonstrated. At the time of this publication, the NEXT LDT has surpassed 42,100 h of operation, processed more than 736 kg of xenon propellant, and demonstrated greater than 28.1 MN s total impulse. Thruster performance has been steady with negligible degradation. The NEXT thruster design has mitigated several lifetime limiting mechanisms encountered in the NSTAR design, including the NSTAR first failure mode, thereby drastically improving thruster capabilities. Component erosion rates and the progression of the predicted life-limiting erosion mechanism for the thruster compare favorably to pretest predictions based upon semi-empirical ion thruster models used in the thruster service life assessment. Service life model validation has been accomplished by the NEXT LDT. Assuming full-power operation until test article failure, the models and extrapolated erosion data predict penetration of the accelerator grid grooves after more than 45,000 hours of operation while processing over 800 kg of xenon propellant. Thruster failure due to degradation of the accelerator grid structural integrity is expected after groove penetration.

Shastry, Rohit↗
NASA NTRS2003

Shared motion signals for human perceptual decisions and oculomotor actions

A fundamental question in primate neurobiology is to understand to what extent motor behaviors are driven by shared neural signals that also support conscious perception or by independent subconscious neural signals dedicated to motor control. Although it has clearly been established that cortical areas involved in processing visual motion support both perception and smooth pursuit eye movements, it remains unknown whether the same or different sets of neurons within these structures perform these two functions. Examination of the trial-by-trial variation in human perceptual and pursuit responses during a simultaneous psychophysical and oculomotor task reveals that the direction signals for pursuit and perception are not only similar on average but also co-vary on a trial-by-trial basis, even when performance is at or near chance and the decisions are determined largely by neural noise. We conclude that the neural signal encoding the direction of target motion that drives steady-state pursuit and supports concurrent perceptual judgments emanates from a shared ensemble of cortical neurons.

Visual Cortex/physiology↗
NASA NTRS2004

High Power MPD Thruster Performance Measurements

High power magnetoplasmadynamic (MPD) thrusters are being developed as cost effective propulsion systems for cargo transport to lunar and Mars bases, crewed missions to Mars and the outer planets, and robotic deep space exploration missions. Electromagnetic MPD thrusters have demonstrated, at the laboratory level, the ability to process megawatts of electrical power while providing significantly higher thrust densities than electrostatic electric propulsion systems. The ability to generate higher thrust densities permits a reduction in the number of thrusters required to perform a given mission, and alleviates the system complexity associated with multiple thruster arrays. The specific impulse of an MPD thruster can be optimized to meet given mission requirements, from a few thousand seconds with heavier gas propellants up to 10,000 seconds with hydrogen propellant. In support of programs envisioned by the NASA Office of Exploration Systems, Glenn Research Center is developing and testing quasi-steady MW-class MPD thrusters as a prelude to steady state high power thruster tests. This paper provides an overview of the GRC high power pulsed thruster test facility, and presents preliminary performance data for a quasi-steady baseline MPD thruster geometry.

LaPointe, Michael R.↗
DOE OSTI2021

Deliquescence of eutectic LiCl-KCl diluted with NaCl for interim waste salt storage

Molten eutectic LiCl-KCl salt is a widely used electrolyte for electrorefining uranium from spent nuclear fuel. Due to the hygroscopic nature of this salt, careful handling and storage of solidified waste electrorefiner (ER) salt is required to avoid deliquescence and corrosion of container materials. This study investigated a potential processing path for reducing the deliquescence through dilution with NaCl. The hydration behavior of LiCl-KCl salts diluted with NaCl was evaluated in terms of mass gain due to mass of water absorption, visual evidence of deliquescence, and visual evidence of corrosion to stainless steel containers in a humid air environment. Pure eutectic LiCl-KCl exhibited a 50 mass% increase due to water absorption and showed signs of deliquescence after 24 hours. 89 mass% NaCl was required in order to prevent deliquescence. Dilution with 89% NaCl was also found to protect corrosion to stainless steel crucibles. Corrosion, thus, appears to require deliquescence. While NaCl dilution greatly decreases steady state hydration and eliminated deliquescence, storage volume is increased ~10x.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Photoinduced phase separation in the lead halides is a polaronic effect

We present a perspective on recent observations of the photoinduced phase separation of halides in multi-component lead-halide perovskites. The spontaneous phase separation of an initial homogeneous solid solution under steady-state illumination conditions is found experimentally to be reversible, stochastic, weakly dependent on morphology, yet strongly dependent on composition and thermodynamic state. Regions enriched in a specific halide species that form upon phase separation are self-limiting in size, pinned to specific compositions, and grow in number in proportion to the steady-state carrier concentration until saturation. These empirical observations of robustness rule out explanations based on specific defect structures and point to the local modulation of an existing miscibility phase transition in the presence of excess charge carriers. A model for rationalizing existing observations based on the coupling between composition, strain, and charge density fluctuations through the formation of polarons is reviewed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

An Easily Prepared Monomeric Cobalt(II) Tetrapyrrole Complex That Efficiently Promotes the 4e – /4H + Peractivation of O 2 to Water

The selective 4e – /4H + reduction of dioxygen to water is an important reaction that takes place at the cathode of fuel cells. Monomeric aromatic tetrapyrroles (such as porphyrins, phthalocyanines, and corroles) coordinated to Co(II) or Co(III) have been considered as oxygen reduction catalysts due to their low cost and relative ease of synthesis. Furthermore, these systems have been repeatedly shown to be selective for O 2 reduction by the less desired 2e – /2H + pathway to yield hydrogen peroxide. Herein, we report the initial synthesis and study of a Co(II) tetrapyrrole complex based on a nonaromatic isocorrole scaffold that is competent for 4e – /4H + oxygen reduction reaction (ORR). This Co(II) 10,10-dimethyl isocorrole (Co[10-DMIC]) is obtained in just four simple steps and has excellent yield from a known dipyrromethane synthon. Evaluation of the steady state spectroscopic and redox properties of Co[10-DMIC] against those of Co porphyrin (cobalt 5,10,15,20-tetrakis(pentafluorophenyl)porphyrin, [Co(TPFPP)]) and corrole (cobalt 5,10,15-tris(pentafluorophenyl)corrole triphenylphosphine, Co[TPFPC](PPh 3 )) homologues demonstrated that the spectroscopic and electrochemical properties of the isocorrole are distinct from those displayed by more traditional aromatic tetrapyrroles. Further, the investigation of the ORR activity of Co[10-DMIC] using a combination of electrochemical and chemical reduction studies revealed that this simple, unadorned monomeric Co(II) tetrapyrrole is ~85% selective for the 4e – /4H + reduction of O 2 to H 2 O over the more kinetically facile 2e – /2H + process that delivers H 2 O 2 . In contrast, the same ORR evaluations conducted for the Co porphyrin and corrole homologues demonstrated that these traditional aromatic systems catalyze the 2e – /2H + conversion of O 2 to H 2 O 2 with near complete selectivity. Despite being a simple, easily prepared, monomeric tetrapyrrole platform, Co[10-DMIC] supports an ORR catalysis that has historically only been achieved using elaborate porphyrinoid-based architectures that incorporate pendant proton-transfer groups or ditopic molecular clefts or that impose cofacially oriented O 2 binding sites. Accordingly, Co[10-DMIC] represents the first simple, unadorned, monomeric metalloisocorrole complex that can be easily prepared and shows a privileged performance for the 4e – /4H + peractivation of O 2 to water as compared to other simple cobalt containing tetrapyrroles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Development of Conceptual Lead Cartridge Design to Perform Irradiation Experiments in VTR

This paper seeks to introduce the latest design of the Extended Length Test Assembly–Cartridge Lead (ELTA-CL) with associated thermal-hydraulic (TH) assessment and related experiment activities to support the critical component development performed by the ELTA-CL team (Los Alamos National Laboratory, Westinghouse Electric Company, and the University of New Mexico). The goal of the ELTA-CL program is to develop and validate an experimental capability to perform irradiation experiments in the Versatile Test Reactor (VTR) addressing Lead Fast Reactor (LFR) technology gaps, in support of the commercial development of advanced lead-cooled fast reactor concepts. Through a design maturation process and parametric study, a conceptual design is proposed to meet the requirements for material and corrosion testing. Thermal-hydraulic characteristics for the conceptual design at desired operating conditions are assessed with systems-level (one-dimensional) and computational fluid dynamics (three-dimensional) simulations. Along with the conceptual design work, experimental activities for the development of critical components such as the pump and flowmeter are undertaken. From both the modeling study and the experimental results, the design requirements of the Phase 1 ELTA-CL (e.g., 500°C and 2 m/s) are achievable with the current conceptual design. Additional design improvements and safety assessments at both steady-state and transient conditions for the final ELTA-CL design will be pursued.

42 ENGINEERING↗
DOE OSTI2021

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the equivalent Dancoff factor cell method performing slowing down calculations on the fly for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for pin-cell, unit-cell, and fuel assembly problems with various resonance self-shielding conditions based on very high temperature reactor, high temperature test reactor, and Empire benchmark cores, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also showed that the methodology worked well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Cross Section Generation Capability in Griffin

The Griffin code is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. The code reads multigroup cross sections in the ISOXML format generated from external deterministic or Monte Carlo cross section generation codes. The implementation of the cross section generation capability in Griffin was initiated last year by plugging in the cross section application programming interface (CSAPI) and reviewing the methodologies for treating particulate fuels. The focus this year was on improving the CSAPI integration and implementing advanced self-shielding methods for applications to advanced reactor problems with TRISO fuels. First, the process for cross section library generation was updated to accurately and rigorously produce isotopic cross section data. Second, the on-the-fly slowing down method for the resonance treatment was implemented in CSAPI to improve the accuracy of effective multigroup cross sections in the resonance energy range. Among various on-the-fly slowing down methods, the equivalent Dancoff factor cell method was employed. Third, the iterative local spatial self-shielding method was implemented under the calculation framework of the equivalent Dancoff factor cell method to accurately deal with the double heterogeneity effect of particulate fuel. The updated CSAPI with the advanced self-shielding methods, together with the cross section libraries generated based on the improved process, were tested for the very high temperature reactor (VHTR), high temperature test reactor (HTTR), and Empire benchmark problems with various resonance self-shielding conditions, indicating that the updated CSAPI in Griffin is able to produce multigroup cross sections accurately and efficiently. We also show that the methodology works well for pebble bed fuel from HTR-10, but the capability still needs to be fully integrated into CSAPI. In the future, further benchmark tests will be performed for various thermal reactor core problems, including particulate fuel-based pebble bed reactors.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1992

Lumley's energy cascade dissipation rate model for boundary-free turbulent shear flows

True dissipation occurs mainly at the highest wavenumbers where the eddy sizes are comparatively small. These high wavenumbers receive their energy through the spectral cascade of energy starting with the largest eddies spilling energy into the smaller eddies, passing through each wavenumber until it is dissipated at the microscopic scale. However, a small percentage of the energy does not spill continuously through the cascade but is instantly passed to the higher wavenumbers. Consequently, the smallest eddies receive a certain amount of energy almost immediately. As the spectral energy cascade continues, the highest wavenumber needs a certain time to receive all the energy which has been transferred from the largest eddies. As such, there is a time delay, of the order of tau, between the generation of energy by the largest eddies and the eventual dissipation of this energy. For equilibrium turbulence at high Reynolds numbers, there is a wide range where energy is neither produced by the large eddies nor dissipated by viscosity, but is conserved and passed from wavenumber to higher wavenumbers. The rate at which energy cascades from one wavenumber to another is proportional to the energy contained within that wavenumber. This rate is constant and has been used in the past as a dissipation rate of turbulent kinetic energy. However, this is true only in steady, equilibrium turbulence. Most dissipation models contend that the production of dissipation is proportional to the production of energy and that the destruction of dissipation is proportional to the destruction of energy. In essence, these models state that the change in the dissipation rate is proportional to the change in the kinetic energy. This assumption is obviously incorrect for the case where there is no production of turbulent energy, yet energy continues to cascade from large to small eddies. If the time lag between the onset on the energy cascade to the destruction of energy at the microscale can be modeled, then there will be a better representation of the dissipation process. Development of an energy cascade time scale equation is discussed.

Duncan, B. S.↗