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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Enforcing global constraints for the dispersion closure problem: τ 2 -SIMPLE algorithm

Permeability and effective dispersion tensors are critical parameters to characterize flow and transport in porous media at the continuum scale. Homogenization theory defines a framework in which such effective properties are first computed from solving a closure problem in a repeating unit cell of the periodic microstructure and then used in a macroscopic formulation for efficient computation. The closure problem is formulated as a local boundary value problem subjected to global constraints, which guarantee the uniqueness of the solution and can be difficult to satisfy for complex geometries and at high flow conditions. These constraints also ensure that pore-scale pressure, velocity, and concentration fields can be accurately reconstructed from the closure variable. Building on a previous work, here we present a framework that allows to satisfy global constraints associated to both the permeability and the dispersion closure problems by introducing two artificial time scales. The algorithm, called τ 2 -SIMPLE, computes both permeability and effective dispersion given an arbitrarily complex geometry and flow condition. Furthermore, this algorithm is demonstrated to be accurate for both 2D and 3D geometries across varying flow conditions, and thus it can be used to quickly characterize effective properties from porous media images in many applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Mesh-connected processor arrays for the transitive closure problem

The main purpose in this paper is to lay a theoretical foundation for the design of mesh-connected processor arrays for the transitive closure problem. Using a simple path-algebraic formulation of the problem and observing its similarity to certain well-known smoothing problems that occur in digital signal processing, it is shown how to draw upon existing techniques from the signal processing literature to derive regular iterative algorithms for determining the transitive closure of the graph. The regular iterative algorithms that are derived using these considerations, are then analyzed and synthesized on mesh-connected processor arrays. Among the vast number of mesh-connected processor arrays that can be designed using this unified approach, the systolic arrays reported in the literature for this problem are shown to be special cases.

Rao, S. K.↗
NASA NTRS1992

Turbulent fluid motion IV-averages, Reynolds decomposition, and the closure problem

Ensemble, time, and space averages as applied to turbulent quantities are discussed, and pertinent properties of the averages are obtained. Those properties, together with Reynolds decomposition, are used to derive the averaged equations of motion and the one- and two-point moment or correlation equations. The terms in the various equations are interpreted. The closure problem of the averaged equations is discussed, and possible closure schemes are considered. Those schemes usually require an input of supplemental information unless the averaged equations are closed by calculating their terms by a numerical solution of the original unaveraged equations. The law of the wall for velocities and temperatures, the velocity- and temperature-defect laws, and the logarithmic laws for velocities and temperatures are derived. Various notions of randomness and their relation to turbulence are considered in light of ergodic theory.

Deissler, Robert G.↗
NASA NTRS1985

The closure problem for turbulence in meteorology and oceanography

The dependent variables used for computer based meteorological predictions and in plans for oceanographic predictions are wave number and frequency filtered values that retain only scales resolvable by the model. Scales unresolvable by the grid in use become 'turbulence'. Whether or not properly processed data are used for initial values is important, especially for sparce data. Fickian diffusion with a constant eddy diffusion is used as a closure for many of the present models. A physically realistic closure based on more modern turbulence concepts, especially one with a reverse cascade at the right times and places, could help improve predictions.

Pierson, W. J., Jr.↗
NASA NTRS2018

TPSAS-NF1676L-30451-DND

The fundamental laws of the physics of fluid flow in the continuum regime are embedded in a somewhat "simple" set of partial differential equations describing the transport of mass, momentum, energy, and/orentropy. These basic equations can be manipulated to construct other important physical quantities such as vorticity that help further elucidate flow physics. Additionally, these equations can be nondimensionalized to identify important nondimensional groups governing compressible, reacting fluid flows, most prominently Reynolds, Mach, Froude, Prandtl, Lewis, Schmidt, Damkohler, and Zeldovich numbers. In this lecture, we present these governing equations and discuss the significance of the different terms and nondimensional groups. Furthermore, since these equations cannot be solved directly on current supercomputers for turbulent flows at Reynolds numbers of engineering interest, a scale reduction by averaging or filtering is introduced, which leads to a "closure" problem. The closure is then provided by introducing some common models. The current introduction is by no means complete, but it and the references herein may serve as a good starting point for learning about the most common approaches to turbulent reacting flows.

Tomasz (Tom) G Drozda↗
DOE OSTI2024

Scientific machine learning for closure models in multiscale problems: A review

Here, closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Simulation of Multistage Turbine Flows

The numerical simulation of turbine flows serves to enhance the understanding of the flow phenomena within multistage turbomachinery components. The direct benefit of this activity is improved modeling capability, which can be used to improve component efficiency and durability. A hierarchy of equations was formulated to assess the difficulty in analyzing the flow field within multistage turbomachinery components. The Navier-Stokes equations provides the most complete description. The simplest description is given by a set of equations that govern the quasi-one-dimensional flow. The number of unknowns to be solved for increases monotonically above the number of equations. The development of the additional set of equations needed to mathematically close the system of equations forms the closure problem associated with that level of description. For the Navier-Stokes equation there is no closure problem. For the quasi-one-dimensional equation set random flow fluctuations, unsteady fluctuations, nonaxisymmetric flow variations, and hub-to-shroud variations on the quasi-one-dimensional flow must be accounted for.

Celestina, M. L.↗
NASA NTRS1989

Pdf - Transport equations for chemically reacting flows

The closure problem for the transport equations for pdf and the characteristic functions of turbulent, chemically reacting flows is addressed. The properties of the linear and closed equations for the characteristic functional for Eulerian and Lagrangian variables are established, and the closure problem for the finite-dimensional case is discussed for pdf and characteristic functions. It is shown that the closure for the scalar dissipation term in the pdf equation developed by Dopazo (1979) and Kollmann et al. (1982) results in a single integral, in contrast to the pdf, where double integration is required. Some recent results using pdf methods obtained for turbulent flows with combustion, including effects of chemical nonequilibrium, are discussed.

Kollmann, W.↗
NASA NTRS1977

Turbulence processes and simple closure schemes

The problem of closure in turbulence in the case of two-point correlations resides in the existence of two unknowns E and W, the energy spectrum function and the transfer function, respectively, in the spectrum equation. In the case of weak turbulence, W is negligible. In case of higher correlations, closure can be effective by neglecting the inertia term in the highest order term used. Specifying a certain number of spectra at an initial time is also a way of getting around the closure problem. A simple case of turbulent shear flow is then considered, where two-point correlation equations are used and the velocity is broken into mean and fluctuating components. This yields a differential equation for the energy spectrum, the three terms of which are the energy spectrum, production term and dissipation term. They are plotted for a particular time. Similar analyses and comparisons with experiment are made for pipe and boundary layer flows.

Deissler, R. G.↗
NASA NTRS1975

Turbulence processes and simple closure schemes

The closure problem in turbulence is reviewed, and some simple closure schemes are introduced. Processes occurring in turbulent flow are discussed on the basis of solutions for some elementary flows such as homogeneous turbulence with and without uniform shear. Closure by specification of initial conditions, and finally practical closure schemes for more complicated flows are considered. The latter include Reynolds stress, eddy viscosity, and mixing-length closures.

Deissler, R. G.↗
NASA NTRS1975

Turbulence processes and simple closure schemes

The closure problem in turbulence is briefly reviewed, and some simple closure schemes are introduced. Processes occurring in turbulent flow are discussed on the basis of solutions for some elementary flows such as homogeneous turbulence with and without uniform shear. Closure by specification of initial conditions, and finally practical closure schemes for more complicated flows (e.g., pipe flows) are considered briefly. The latter include Reynolds stress, eddy viscosity, and mixing-length closures.

Deissler, R. G.↗
DOE OSTI2026

Quantum mechanical closure of partial differential equations with symmetries

We develop a statistical framework for the dynamical closure of spatiotemporal dynamics governed by partial differential equations. Employing the mathematical framework of quantum mechanics to embed the original classical dynamics into a quantum mechanical representation, we use the space of quantum density operators to model the unresolved degrees of freedom of the original dynamics in a statistical sense, and the framework of quantum measurement to predict their contributions to the resolved dynamics. The embedded dynamics is discretized by a positivity preserving process, leading to a compressed representation that is invariant under the dynamical symmetries of the resolved dynamics. We present a data based formulation of the closure scheme and apply it to a closure problem for the shallow water equations. The numerical results demonstrate that our closure model can accurately predict the main features of the true dynamics, including for out of sample initial conditions.

Delay embedding↗
NASA NTRS1987

Physical mechanisms of heat, momentum and turbulence fluxes

In a qualitative way, the physical mechanisms which generate fluxes of heat, momentum, and turbulence in the atmosphere are discussed. This material is presented to acquaint people with the Earth science aspects of turbulence as important processes in the atmosphere. To attempt to describe turbulent fluxes of heat, momentum, and moisture in precise mathematical detail becomes an intractable problem. It is burdened by an eighth order set of equations involving more variables than equations. It is a closure problem which requires complicated assumptions that are not necessarily always satisfied, variable boundary conditions, and sparse observational data. Therefore, we must approach the problem in a simplified manner to obtain any kind of solution involving the variables of shear, stress, and heat, moisture, and momentum fluxes. There are other problems, of course, in which the inclusion of the planetary boundary layer is extremely important. Air pollution studies, air-sea exchanges, mesoscale models, and so on, must account for the planetary layer in very specific terms. Some of the physical mechanisms that are involved in generating fluxes are described.

Theon, John S.↗
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↗
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.↗