Search NASA⌕ Search

SEARCH · Search NASA

Results for “Closure problem”

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

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

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Neural network representability of fully ionized plasma fluid model closures

The closure problem in fluid modeling is a well-known challenge to modelers aiming to accurately describe their systems of interest. Over many years, analytic formulations in a wide range of regimes have been presented but a practical, generalized fluid closure for magnetized plasmas remains an elusive goal. Here, as a first step toward constructing a novel data-based approach to this problem, we apply ever-maturing machine learning methods to assess the capability of neural network architectures to reproduce crucial physics inherent in known magnetized plasma closures. We find encouraging results, indicating the applicability of neural networks to closure physics, but also arrive at recommendations on how one should choose appropriate network architectures for the given locality properties dictated by the underlying physics of the plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRSDate not supplied

Advancement of the General Aviation Synthesis Program Using Python to Enable Optimization-Based Hybrid-Propulsion Aircraft Design

In support of Electrified Powertrain Flight Demonstrator and Advanced Air Transport Technologies programs at NASA, engineers at NASA Ames and NASA Glenn Research Centers have developed a new tool for coupled engine and airframe optimization and analysis. The new tool combines the engineering-level analysis methods of the FORTRAN General Aviation Synthesis Program (GASP) with the OpenMDAO framework to handle highly coupled problems that legacy tools struggle to optimize. The tool has been verified to match GASP with good agreement on a 737 MAX8 baseline vehicle closure problem, and preliminary efforts have been made to integrate the pyCycle thermodynamic cycle analysis tool for electrified engine optimization in the context of a vehicle optimization problem.

Kenneth R. Lyons↗
NASA NTRS1989

Theoretical investigation of EM wave generation and radiation in the ULF, ELF, and VLF bands by the electrodynamic orbiting tether

The problem of electromagnetic wave generation by an electrodynamic tethered satellite system is important both for the ordinary operation of such systems and for their possible application as orbiting transmitters. The tether's ionospheric circuit closure problem is closely linked with the propagation of charge-carrying electromagnetic wave packets away from the tethered system. Work is reported which represents a step towards a solution to the problem that takes into account the effects of boundaries and of vertical variations in plasma density, collision frequencies, and ion species. The theory of Alfen wave packet generation by an electrodynamic tethered system in an infinite plasma medium is reviewed, and brief summary of previous work on the problem is given. The consequences of the presence of the boundaries and the vertical nonuniformity are then examined. One of the most significant new features to emerge when ion-neutral collisions are taken into account is the coupling of the Alfven waves to the fast magnetosonic wave. This latter wave is important, as it may be confined by vertical variations in the Alfven speed to a sort of leaky ionospheric wave guide, the resonances of which could be of great importance to the signal received on the Earth's surface. The infinite medium solution for this case where the (uniform) geomagnetic field makes an arbitrary angle with the vertical is taken as the incident wave-packet. Even without a full solution, a number of conclusions can be drawn, the most important of which may be that the electromagnetic field associated with the operation of a steady-current tethered system will probably be too weak to detect on the Earth's surface, even for large tethered currents. This is due to the total reflection of the incident wave at the atmospheric boundary and the inability of a steady-current tethered system to excite the ionospheric wave-guide. An outline of the approach to the numerical problem is given. The use of numerical integrations and boundary conditions consistent with a conducting Earth is proposed to obtain the solution for the horizontal electromagnetic field components at the boundary of the ionosphere with the atmospheric cavity.

Estes, Robert D.↗
DOE OSTI2025

A geometric perspective on kinetic matter–radiation interaction and moment systems

Here, in this paper, we provide a geometric perspective on the kinetic interaction of matter and radiation, based on a pair bracket approach. We discuss the interaction of kinetic theories via dissipative brackets, with our fundamental example being the coupling of matter, described by the Boltzmann equation, and radiation, described by the radiation transport equation. We explore the transition from kinetic systems to their corresponding moment systems, provide a Hamiltonian description of such moment systems, and give a geometric interpretation of the moment closure problem for kinetic theories. As an application, we discuss in detail diffusion radiation hydrodynamics as an example of a pair bracket formulation on a space of moments corresponding to kinetic matter–radiation interaction. Additionally, using the variable moment closure framework of Burby [J. W. Burby, Variable-moment fluid closures with Hamiltonian structure, Sci. Rep. 13 (2023) 18286, doi:10.1038/s41598-023-45416-5], we show how to construct Hamiltonian moment closures for kinetic transport equations with arbitrary Hamiltonian. Using this general construction, we derive novel Hamiltonian moment closures for pure radiation transport.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Machine learning surrogate models for Landau fluid closure

The first result of applying the machine/deep learning technique to the fluid closure problem is presented in this letter. As a start, three different types of neural networks (multilayer perceptron (MLP), convolutional neural network (CNN) and two-layer discrete Fourier transform (DFT) network) were constructed and trained to learn the well-known Hammett-Perkins Landau fluid closure in configuration space. We found that in order to train a well-preformed network, a minimum size of training data set is needed; MLP also requires a minimum number of neurons in the hidden layers equals to the degrees of freedom in Fourier space despite training data is fed in configuration space. Out of three models DFT performs the best for the clean data most likely due to the existence of nice Fourier expression for Hammett-Perkins closure but it is least robust with respect to input noise. Overall, with appropriate tuning and optimization, all three neural networks are able to accurately predict Hammett-Perkins closure and reproduce the inherit nonlocal feature, suggesting a promising path to calculate more sophisticated closures with the machine/deep learning technique.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

Laguerre–Hermite pseudo-spectral velocity formulation of gyrokinetics

First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a pseudo-spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower resolution three-dimensional (3-D) gyrofluid representation and the conventional but more expensive 5-D gyrokinetic representation. Our formulation is a projection of the nonlinear gyrokinetic equation onto a Laguerre–Hermite velocity-space basis. We discuss issues related to collisions, closures and entropy. While any collision operator can be used in the formulation, we highlight a model operator that has a particularly sparse Laguerre–Hermite representation, while satisfying conservation laws and the H theorem. Free streaming, magnetic drifts and nonlinear phase mixing each give rise to closure problems, which we discuss in relation to the instabilities of interest and to free energy conservation. We show that the model is capable of reproducing gyrokinetic results for linear instabilities and zonal flow dynamics. Thus the final model is appropriate for the study of instabilities, turbulence and transport in a wide range of geometries, including tokamaks and stellarators.

Physics↗
DOE OSTI2022

A learned closure method applied to phase mixing in a turbulent gradient-driven gyrokinetic system in simple geometry

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ( $12\,\%$ ) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Memory-based parameterization with differentiable solver: Application to Lorenz ’96

Physical parameterizations (or closures) are used as representations of unresolved subgrid processes within weather and global climate models or coarse-scale turbulent models, whose resolutions are too coarse to resolve small-scale processes. These parameterizations are typically grounded on physically based, yet empirical, representations of the underlying small-scale processes. Machine learning-based parameterizations have recently been proposed as an alternative solution and have shown great promise to reduce uncertainties associated with the parameterization of small-scale processes. Yet, those approaches still show some important mismatches that are often attributed to the stochasticity of the considered process. This stochasticity can be due to coarse temporal resolution, unresolved variables, or simply to the inherent chaotic nature of the process. To address these issues, we propose a new type of parameterization (closure), which is built using memory-based neural networks, to account for the non-instantaneous response of the closure and to enhance its stability and prediction accuracy. We apply the proposed memory-based parameterization, with differentiable solver, to the Lorenz ’96 model in the presence of a coarse temporal resolution and show its capacity to predict skillful forecasts over a long time horizon of the resolved variables compared to instantaneous parameterizations. This approach paves the way for the use of memory-based parameterizations for closure problems.

Mathematics↗
NASA NTRS1977

Model for premixed turbulent flames

Flame speed and mean degree of reaction profiles are determined for an ensemble mean one-dimensional premixed turbulent flame. Elementary closure models are employed to treat turbulence closure problems arising from the nonlinear convective and chemical reaction rate terms in the time-dependent fuel conservation equation; a constant eddy diffusivity is useed to model correlation terms derived from the convective term. An expression developed for fuel consumption is solved to obtain the turbulent flame speed and the variation of mean fuel mass fraction across the flame. Comparison of the numerical analysis with experimental data indicates the importance of the quenching of the combustion reaction in high-wavenumber eddies.

Gouldin, F. C.↗
NASA NTRS1978

On the interactions between large-scale structure and fine-grained turbulence in a free shear flow. II - The development of spatial interactions in the mean

The interactions between large-scale structure and fine-grained turbulence in a spatially developing mixing layer are investigated. Both a conditioned average and a time average are employed to separate the nonrandom and random fluctuations in the kinetic energy treatment of the interactions. Shape assumptions applying to the interaction integrals are adopted to obtain a solution to the closure problem. Energy-transfer mechanisms among the mean flow, the fine-grained turbulence and the large-scale structure are discussed. The magnitude of the large-scale structure and its streamwise lifetime both prove to be important in accounting for fine-grained turbulence enhancement.

Alper, A.↗
NASA NTRS1995

PDF methods for turbulent reactive flows

Viewgraphs are presented on computation of turbulent combustion, governing equations, closure problem, PDF modeling of turbulent reactive flows, validation cases, current projects, and collaboration with industry and technology transfer.

Hsu, Andrew T.↗
NASA NTRS1993

Development and analysis of prognostic equations for mesoscale kinetic energy and mesoscale (subgrid scale) fluxes for large-scale atmospheric models

Generated by landscape discontinuities (e.g., sea breezes) mesoscale circulation processes are not represented in large-scale atmospheric models (e.g., general circulation models), which have an inappropiate grid-scale resolution. With the assumption that atmospheric variables can be separated into large scale, mesoscale, and turbulent scale, a set of prognostic equations applicable in large-scale atmospheric models for momentum, temperature, moisture, and any other gaseous or aerosol material, which includes both mesoscale and turbulent fluxes is developed. Prognostic equations are also developed for these mesoscale fluxes, which indicate a closure problem and, therefore, require a parameterization. For this purpose, the mean mesoscale kinetic energy (MKE) per unit of mass is used, defined as E-tilde = 0.5 (the mean value of u'(sub i exp 2), where u'(sub i) represents the three Cartesian components of a mesoscale circulation (the angle bracket symbol is the grid-scale, horizontal averaging operator in the large-scale model, and a tilde indicates a corresponding large-scale mean value). A prognostic equation is developed for E-tilde, and an analysis of the different terms of this equation indicates that the mesoscale vertical heat flux, the mesoscale pressure correlation, and the interaction between turbulence and mesoscale perturbations are the major terms that affect the time tendency of E-tilde. A-state-of-the-art mesoscale atmospheric model is used to investigate the relationship between MKE, landscape discontinuities (as characterized by the spatial distribution of heat fluxes at the earth's surface), and mesoscale sensible and latent heat fluxes in the atmosphere. MKE is compared with turbulence kinetic energy to illustrate the importance of mesoscale processes as compared to turbulent processes. This analysis emphasizes the potential use of MKE to bridge between landscape discontinuities and mesoscale fluxes and, therefore, to parameterize mesoscale fluxes generated by such subgrid-scale landscape discontinuities in large-scale atmospheric models.

Avissar, Roni↗
NASA NTRS1995

A new approach to the formulation of scalar flux closure

This report shows that if a stochastic differential equation (Langevin equation) for velocity fluctuation vector is known, it is possible to derive the equations for scalar flux transport. Durbin and Speziale (1994) showed that the second moment of this stochastic differential equation gives an equation for the evolution of Reynolds stress tensor. Similarly, the stochastic equation will give an equation for scalar flux. Therefore, a coupling between these two is present. The basis for the present work is that there should be Langevin equations that can produce acceptable models for both the Reynolds stress tensor and the scalar flux vector. Having found this basic Langevin equation, the amount of work needed to model the second order closure problems is reduced; using the well developed models for Reynolds stress equations, it will be possible to derive corresponding models for scalar flux equation.

Shabany, Y.↗
NASA NTRS1996

LES, DNS, and RANS for the Analysis of High-Speed Turbulent Reacting Flows

A filtered density function (FDF) method suitable for chemically reactive flows is developed in the context of large eddy simulation. The advantage of the FDF methodology is its inherent ability to resolve subgrid scales (SGS) scalar correlations that otherwise have to be modeled. Because of the lack of robust models to accurately predict these correlations in turbulent reactive flows, simulations involving turbulent combustion are often met with a degree of skepticism. The FDF methodology avoids the closure problem associated with these terms and treats the reaction in an exact manner. The scalar FDF approach is particularly attractive since it can be coupled with existing hydrodynamic computational fluid dynamics (CFD) codes.

Colucci, P. J.↗
NASA NTRS1996

Model equations for simulating flows in multistage turbomachinery

A steady, three dimensional average-passage equation system was derived. The purpose was to simulate multistage turbomachinery flows. These equations describe a steady, viscous flow that is periodic from blade passage to blade passage. Moreover, these equations have a closure problem that is similar to that of the Reynolds-average Navier-Stokes equations. A scaled form of the average-passage equation system could provide an improved mathematical model for simulating the flow in the design and in the off-design conditions of a multistage machine.

Adamczyk, John J.↗
NASA NTRS1998

Investigation of EM Emissions by the Electrodynamic Tether, Inclusive of an Observational Program (EMET)

Our TSS-1/R investigation, which we shall refer to as EMET in this report, was an integral part of the effort by the TSS-1/R Investigators' Working Group (IWG) to come to an understanding of the complex interaction between the tethered satellite system and the ionosphere. All of the space-borne experiments were designed to collect data relevant to the local interaction. Only the ground- based experiments, EMET and its Italian counterpart Observations on the Earth's Surface of Electromagnetic Emissions (OESEE), held out any hope of characterizing the long range effects of the interaction. This was to be done by detecting electromagnetic waves generated by the system in the ionosphere, assuming the signal reached the Earth's surface with sufficient amplitude. As the type of plasma waves excited to carry charge away from the charge-exchange regions of the system at each end of the tether is one of the theoretical points about which there is greatest disagreement, a definitive identification of tether-generated waves could mark significant progress in the so-called current closure problem of electrodynamic tethers. Dr. Mario Grossi of the Smithsonian Astrophysical Observatory (SAO) initiated the investigation, and his experience in the field of ULF-ELF waves and their detection was invaluable throughout its course. Rice University had the responsibility of setting up the EMET ULF-VLF ground stations under a subcontract from SAO. Principal Investigator (PI) for the Rice effort was Prof. William E. Gordon, who was primary observer at the Arecibo Observatory during TSS-LR. Dr. Steve Noble handled major day-to-day operations, training, and planning for the ground-based measurements. Dr. James McCoy of NASA JSC, a member of the Mona/Arecibo team, was pilot for the numerous flights ferrying personnel and equipment between Puerto Rico and Mona Island. Final responsibility for the measurements rested with SAO, and the activities of field personnel and SAO investigators were closely co-ordinated during the mission. Dr. Enrico Lorenzini of SAO served as the eyes, ears, and brain of EMET in the Science Operations Area and PI table during the mission, whenever the PI was absent during the round-the-clock mission operations. The Rice University final report to SAO, which is included as an Appendix, contains details of the remote sites, means of communication, sensors, etc., as well as the affiliations of personnel involved in the data-gathering effort.

Estes, Robert D.↗
NASA NTRS2001

Toward a Unified Parameterization of the Boundary Layer and Moist Convection: A New Type of Mass-Flux Model - Part 1

Higher-order closure (HOC) models have been proposed for parameterization of the turbulent planetary boundary layer (PBL). HOC models must include closures for higher-order moments (e.g., fourth moments in third-order closure models), for pressure terms, and for dissipation terms. Mass-flux closure (MFC) models have been proposed for parameterization of cumulus convection and, more recently, the convective PBL. MFC models include closures for lateral mass exchanges and for pressure terms (which are usually ignored). The authors developed a new kind of model that combines HOC and MFC, which they hope will be useful for the parameterization of both the PBL and cumulus convection, in a unified framework. Such a model is particularly well suited to regimes in which the PBL turbulence and the cumulus convection are not well separated, for example, the broken stratocumulus and shallow cumulus regimes. The model makes use of an assumed joint probability distribution for the variables of interest, and the equations typically used in HOC models can be derived by integrating over the distribution. Accordingly, the model is called Assumed-Distribution Higher-Order Closure (ADHOC). The prognostic variables of ADHOC are the mean state, the second and third moments of the vertical velocity, and the vertical fluxes of other quantities of interest. All of the parameters of the distribution can be determined from the predicted moments, thereafter the joint distribution is effectively known, and so any and all moments can be constructed as needed. In this way, the usual closure problem of "higher moments" is avoided. The pressure-term parameterizations previously developed for HOC models are used to predict the convective fluxes and the moments of the vertical velocity. In companion papers, parameterizations of lateral mass exchanges and subplume-scale fluxes are presented, and then ADHOC is applied to several observationally based tropical, subtropical, and dry convective boundary layers.

Lappen, Cara-Lyn↗