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Results for “differential expansion”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate

A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.

Carlson, John R.↗
DOE OSTI2021

Crystal Structure Evolution of UCl 3 from Room Temperature to Melting

We report uranium trichloride (UCl 3 ) is actively researched to develop and improve applications ranging from molten salt reactors to actinide processing, including spent fuel reprocessing. Here, we report for the first time the crystal structure evolution between room temperature and melting point from in situ high-temperature neutron diffraction to quantify, for example, the thermal expansion of the hexagonal a and c lattice parameters. The results are compared with density functional theory calculations. The melting point of UCl 3 is determined by differential scanning calorimetry to be 1108.2 ± 0.2 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Linearised Fokker–Planck collision model for gyrokinetic simulations

We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids 19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys. 391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Nonperturbative random matrix model of N = 2 JT supergravity

It is shown how to nonperturbatively define a random matrix model that captures key physics of N = 2 Jackiw-Teitelboim supergravity, going well beyond the perturbative topological expansion defined recently by Turiaci and Witten. A decomposition into an infinite family of certain multicritical models is derived, leading to the definition of a nonlinear ordinary differential equation from which the physics may be computed. Bogomol’nyi-Prasad-Sommerfield (BPS) states are naturally described by the model. The nonperturbative completions of the spectral densities for non-BPS multiplets are readily extracted. Published by the American Physical Society 2024

Johnson, Clifford V. (ORCID:0000000189645830)↗
NASA NTRS1981

Boundary-layer effects in composite laminates: Free-edge stress singularities, part 6

A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.

Wanag, S. S.↗
NASA NTRS1996

Further Development of a New, Flux-Conserving Newton Scheme for the Navier-Stokes Equations

This paper is one of a series of papers describing the development of a new numerical approach for solving the steady Navier-Stokes equations. The key features in the current development are (1) the discrete representation of the dependent variables by way of high order polynomial expansions, (2) the retention of all derivatives in the expansions as unknowns to be explicitly solved for, (3) the automatic balancing of fluxes at cell interfaces, and (4) the discrete simulation of both the integral and differential forms of the governing equations. The main purpose of this paper is, first, to provide a systematic and rigorous derivation of the conditions that are used to simulate the differential form of the Navier-Stokes equations, and second, to extend our previously-presented internal flow scheme to external flows and nonuniform grids. Numerical results are presented for high Reynolds number flow (Re = 100,000) around a finite flat plate, and detailed comparisons are made with the Blasius flat plate solution and Goldstein wake solution. It is shown that the error in the streamwise velocity decreases like r(sup alpha)(Delta)y(exp 2), where alpha approx. 0.25 and r = delta(y)/delta(x) is the grid aspect ratio.

Scott, James R.↗
NASA NTRS2007

Continued Investigation of Leakage and Power Loss Test Results for Competing Turbine Engine Seals

Seal leakage decreases with increasing surface speed due to reduced clearances from disk centrifugal growth. Annular and labyrinth seal leakage are 2-3 times greater than brush and finger seal leakage. Seal leakage rates increase with increasing temperature because of seal clearance growth due to different coefficients of thermal expansion between the seal and test disk. Seal power loss is not strongly affected by inlet temperature. Seal power loss increases with increasing surface speed, seal pressure differential, mass flow rate or flow factor, and radial clearance. The brush and finger seals had nearly the same power loss. Annular and labyrinth seal power loss were higher than finger or brush seal power loss. The brush seal power loss was the lowest and 15-30% lower than annular and labyrinth seal power loss.

Delgado, Irebert R.↗
DOE OSTI2022

Cavitation in a soft porous material

Abstract We study the collapse and expansion of a cavitation bubble in a deformable porous medium. We develop a continuum-scale model that couples compressible fluid flow in the pore network with the elastic response of a solid skeleton. Under the assumption of spherical symmetry, our model can be reduced to an ordinary differential equation that extends the Rayleigh–Plesset equation to bubbles in soft porous media. The extended Rayleigh–Plesset equation reveals that finite-size effects lead to the breakdown of the universal scaling relation between bubble radius and time that holds in the infinite-size limit. Our data indicate that the deformability of the porous medium slows down the collapse and expansion processes, a result with important consequences for wide-ranging phenomena, from drug delivery to spore dispersion.

Leng, Yu↗
NASA NTRS2011

Microgravity-Enhanced Stem Cell Selection

Stem cells, both embryonic and adult, promise to revolutionize the practice of medicine in the future. In order to realize this potential, a number of hurdles must be overcome. Most importantly, the signaling mechanisms necessary to control the differentiation of stem cells into tissues of interest remain to be elucidated, and much of the present research on stem cells is focused on this goal. Nevertheless, it will also be essential to achieve large-scale expansion and, in many cases, assemble cells in 3D as transplantable tissues. To this end, microgravity analog bioreactors can play a significant role. Microgravity bioreactors were originally conceived as a tool to study the cellular responses to microgravity. However, the technology can address some of the shortcomings of conventional cell culture systems; namely, the deficiency of mass transport in static culture and high mechanical shear forces in stirred systems. Unexpectedly, the conditions created in the vessel were ideal for 3D cell culture. Recently, investigators have demonstrated the capability of the microgravity bioreactors to expand hematopoietic stem cells compared to static culture, and facilitate the differentiation of umbilical cord stem cells into 3D liver aggregates. Stem cells are capable of differentiating into functional cells. However, there are no reliable methods to induce the stem cells to form specific cells or to gain enough cells for transplantation, which limits their application in clinical therapy. The aim of this study is to select the best experimental setup to reach high proliferation levels by culturing these cells in a microgravity-based bioreactor. In typical cell culture, the cells sediment to the bottom surface of their container and propagate as a one-cell-layer sheet. Prevention of such sedimentation affords the freedom for self-assembly and the propagation of 3D tissue arrays. Suspension of cells is easily achievable using stirred technologies. Unfortunately, in conventional bioreactors, stirring invokes deleterious forces that disrupt cell aggregation and results in cell death. First-generation rotating bioreactors provided rotation on the horizontal axis, which resulted in the suspension of cells without stirring, thus providing a suitable environment to propagate cells without sedimentation to a surface. The rotating wall bioreactors did not provide a way to remove air bubbles that were causing shear and disrupting 3D cultures. Johnson Space Center successfully engineered the hydrofocusing bioreactor (HFB) that resolved the problem of removing the air bubbles from the fluid medium of NASA's rotating-wall space bioreactors. The HFB uses the principle of hydrodynamic focusing that simultaneously produces a low-shear fluid culture environment and a variable hydrofocusing force that can control the movement, location, and removal of suspended cells, tissues, and air bubbles from the bioreactor. The HFB is a rotating, domeshaped cell culture vessel with a centrally located sampling port and an internal viscous spinner. The vessel and spinner can rotate at different speeds either in the same or opposite directions. Rotation of the vessel and viscous interaction at the spinner generate a hydrofocusing force. Adjusting the differential rotation rate between vessel and spinner controls the magnitude of the force.

Claudio, Pier Paolo↗
DOE OSTI2019

Low-Rank Solution Methods for Stochastic Eigenvalue Problems

In this report, we study efficient solution methods for stochastic eigenvalue problems arising from discretization of self-adjoint partial differential equations with random data, where the underlying operators depend linearly on the random parameters. With the stochastic Galerkin approach, the solutions are represented as generalized polynomial chaos expansions. When these solutions can be approximated well by low-rank objects, we introduce a low-rank variant of the inverse subspace iteration algorithm for computing one or several minimal eigenvalues and corresponding eigenvectors of parameter-dependent matrices. In the algorithm, the iterates are approximated by low-rank matrices, which leads to significant cost savings. Furthermore, the algorithm is tested on two benchmark problems, a stochastic diffusion problem with some poorly separated eigenvalues, and an operator derived from a discrete stochastic Stokes problem whose minimal eigenvalue is related to the inf-sup stability constant. Numerical experiments show that the low-rank algorithm produces accurate solutions compared to the Monte Carlo method, and it uses much less computational time than the original algorithm without low-rank approximation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Fast Glazing of Alumina/Silica Tiles

Technique for applying ceramic coating to fibrous silica/alumina insulation tiles prevents cracks and substantially reduces firing time. To reduce thermal stresses in tile being coated, high-temperature, shorttime firing schedule implemented. Such schedule allows coating to mature while substrate remains at relatively low temperature, reducing stress differential between coating and substrate. Technique used to repair tiles with damaged coatings and possibly used in heat-treating objects made of materials having different thermal-expansion coefficients.

Creedon, J. F.↗
NASA NTRS1986

Physical aging in epoxy matrices and composites

Postcured specimens of Thornell 300 carbon-fiber/Fiberite 934 epoxy as well as Fiberite 934 epoxy resin were quenched from above the glass transition temperature and annealed at 140, 110, or 80 C for times up to 100,000 min. No weight gain or loss was observed during annealing at these temperatures, but significant time-dependent variations were observed in density, modulus, hardness, damping, moisture absorption ability, and thermal expansion characteristics. The relations between the excess thermodynamic properties of epoxy glasses and their time-dependent behavior are discussed. The discussion is illustrated by results obtained by differential scanning calorimetry, dynamic mechanical analysis, tensile testing, solid state nuclear magnetic resonance spectroscopy, and small-angle X-ray scattering.

Kong, Eric Siu-Wai↗
NASA NTRS1990

Average reflected power from a one-dimensional slab of discrete scatterers

Reflection from a one-dimensional random medium of discrete scatterers is considered. The discrete scattering medium is modeled by a Poisson impulse process with concentration lambda. By employing the Markov property of the Poisson impulse process, an exact functional integro-differential equation of the Kolmogorov-Feller type is found for the average reflected power. Approximate solutions to this equation are obtained by regular perturbation and two variable expansion techniques in the limit of small lambda. The regular perturbation results is valid for small slab thicknesses, while the two-variable result is uniformly valid for any thickness. The two-variable result shows that as the slab size becomes infinite all of the incident power is reflected on the average.

Saatchi, Sasan S.↗
NASA NTRS2002

Elliptic Relaxation of a Tensor Representation for the Redistribution Terms in a Reynolds Stress Turbulence Model

A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. Direct numerical simulation data and Reynolds stress solutions using a full differential approach are compared for the case of fully developed channel flow.

Carlson, J. R.↗
NASA NTRS2004

Optical Measurement Technique for Space Column Characterization

A simple optical technique for the structural characterization of lightweight space columns is presented. The technique is useful for determining the coefficient of thermal expansion during cool down as well as the induced strain during tension and compression testing. The technique is based upon object-to-image plane scaling and does not require any photogrammetric calibrations or computations. Examples of the measurement of the coefficient of thermal expansion are presented for several lightweight space columns. Examples of strain measured during tension and compression testing are presented along with comparisons to results obtained with Linear Variable Differential Transformer (LVDT) position transducers.

Barrows, Danny A.↗
DOE OSTI2023

Applying Quantum Computing to Simulate Power System Dynamics

Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations due to a large number of generators, loads, and transmission lines. Thus, its computational complexity grows exponentially with the system size. This paper demonstrates the potential use of quantum computing algorithms to model the power system dynamics. Leveraging a symbolic programming framework, we equivalently convert the power system dynamics’ differential algebraic equations (DAEs) into ordinary differential equations (ODEs), where the data of the state vector can be encoded into quantum computers via amplitude encoding. The system's nonlinearity is captured by Taylor polynomial expansion, the quantum state tensor, and Hamiltonian simulation, whereas state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can simulate the dynamics of the power system with high accuracy, whereas its complexity is polynomial in the logarithm of the system dimension. Our work also illustrates the use of scientific machine learning tools for implementing scientific computing concepts, e.g., Taylor expansion, DAEs/ODEs transform, and quantum computing solver, in the field of power engineering.

Tran, Huynh↗
NASA NTRS1997

A Model of the THUNDER Actuator

A THUNDER actuator is a composite of three thin layers, a metal base, a piezoelectric wafer and a metal top cover, bonded together under pressure and at high temperature with the LaRC SI polyimid adhesive. When a voltage is applied between the metal layers across the PZT the actuator will bend and can generate a force. This document develops and describes an analytical model the transduction properties of THUNDER actuators. The model development is divided into three sections. First, a static model is described that relates internal stresses and strains and external displacements to the thermal pre-stress and applied voltage. Second, a dynamic energy based model is described that allows calculation of the resonance frequencies, developed force and electrical input impedance. Finally, a fully coupled electro-mechanical transducer model is described. The model development proceeds by assuming that both the thermal pre-stress and the piezoelectric actuation cause the actuator to deform in a pure bend in a single plane. It is useful to think of this as a two step process, the actuator is held flat, differential stresses induce a bending moment, the actuator is released and it bends. The thermal pre-stress is caused by the different amounts that the constituent layers shrink due to their different coefficients of thermal expansion. The adhesive between layers sets at a high temperature and as the actuator cools, the metal layers shrink more than the PZT. The PZT layer is put into compression while the metal layers are in tension. The piezoelectric actuation has a similar effect. An applied voltage causes the PZT layer to strain, which in turn strains the two metal layers. If the PZT layer expands it will put the metal layers into tension and PZT layer into compression. In both cases, if shear force effects are neglected, the actuator assembly will experience a uniform in-plane strain. As the materials each have a different elastic modulus, different stresses will develop in each layer and these stresses will induce a bending moment. When the actuator is released from its flat configuration, the differential stresses are relieved as the actuator bends.

Curtis, Alan R. D.↗
DOE OSTI2021

Mixed Precision Fermi-Operator Expansion on Tensor Cores from a Machine Learning Perspective

Here we present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia’s A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bias values to substantially reduce the number of layers required for convergence. We also show how this machine learning approach can be used to optimize the coefficients of the recursive Fermi-operator expansion to accurately represent the fractional occupation numbers of the electronic states at finite temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗