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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Singular asymptotic expansions in nonlinear rotordynamics

During hot firing ground testing of the Space Shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.

Day, W. B.↗
NASA NTRS1985

Singular asymptotic expansions in nonlinear rotordynamics

During hot firing ground testing of the Space shuttle's Main Engine, vibrations of the liquid oxygen pump occur at frequencies which cannot be explained by the linear Jeffcott model of the rotor. The model becomes nonlinear after accounting for deadband, side forces, and rubbing. Two phenomena present in the numerical solutions of the differential equations are unexpected periodic orbits of the rotor and tracking of the nonlinear frequency. A multiple scale asymptotic expansion of the differential equations is used to give an analytic explanation of these characteristics.

Day, W. B.↗
DOE OSTI2021

Analytical solutions of the Arrhenius-Semenov problem for constant volume burn

Analytical solutions to the Semenov thermal ignition problem for constant volume burn governed by Arrhenius reaction kinetics are derived. Specifically, an approximate analytical solution technique for the Arrhenius-Semenov differential equation is derived for reaction orders n ϵ R> 0 and exact solutions are also constructed for reaction orders n ϵ N : n ≤ 3. The approximation technique relies on expansion of the respective nondominant terms in the differential equation at the lower and upper bounds of the reaction progress variable in order to create a pair of integrable series. The two integrated series are then connected to create a single continuous analytical solution. Excellent agreement is observed between the analytical approximation and solutions obtained numerically. The presented approximation constitutes a simple and robust strategy for solving the Arrhenius-Semenov problem analytically.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1999

Steady Secondary Flows Generated by Periodic Compression and Expansion of an Ideal Gas in a Pulse Tube

This study establishes a consistent set of differential equations for use in describing the steady secondary flows generated by periodic compression and expansion of an ideal gas in pulse tubes. Also considered is heat transfer between the gas and the tube wall of finite thickness. A small-amplitude series expansion solution in the inverse Strouhal number is proposed for the two-dimensional axisymmetric mass, momentum and energy equations. The anelastic approach applies when shock and acoustic energies are small compared with the energy needed to compress and expand the gas. An analytic solution to the ordered series is obtained in the strong temperature limit where the zeroth-order temperature is constant. The solution shows steady velocities increase linearly for small Valensi number and can be of order I for large Valensi number. A conversion of steady work flow to heat flow occurs whenever temperature, velocity or phase angle gradients are present. Steady enthalpy flow is reduced by heat transfer and is scaled by the Prandtl times Valensi numbers. Particle velocities from a smoke-wire experiment were compared with predictions for the basic and orifice pulse tube configurations. The theory accurately predicted the observed steady streaming.

Lee, Jeffrey M.↗
NASA NTRS1987

A low dimensional dynamical system for the wall layer

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Aubry, N.↗
DOE OSTI2024

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. Here we use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2000

T Lymphocyte Activation Threshold is Increased in Reduced Gravity

There have been substantial advances in molecular and cellular biology that have provided new insight into the biochemical and genetic basis of lymphocyte recognition, activation and expression of distinct functional phenotypes. It has now become evident that for both T and B cells, stimuli delivered through their receptors can result in either clonal expansion or apoptosis. In the case of T cells, clonal expansion of helper cells is accompanied by differentiation into two major functional subsets which regulate the immune response. The pathways between the membrane and the nucleus and their molecular components are an area of very active investigation. This meeting will draw together scientists working on diverse aspects of this problem, including receptor ligand interactions, intracellular pathways that transmit receptor mediated signals and the effect of such signal transduction pathways on gene regulation. The aim of this meeting is to integrate the information from these various experimental approaches into a new synthesis and molecular explanation of T cell activation, differentiation and death.

Adams, Charley L.↗
DOE OSTI2021

Soliton Generation in Negative Thermal Expansion Materials

Strain solitons have been observed statically in several 2D materials and dynamically in substrate materials using ultrafast laser pulses. The latter case relies on lattice relaxation in response to ultrafast heating in a light-absorbing transducer material, a process which is sensitive to the thermal expansion coefficient. Here we consider an unusual case where the sign of the thermal expansion coefficient is negative, a scenario which is experimentally feasible in light of rapid and recent advances in the discovery of negative thermal expansion materials. We present numerical solutions to a nonlinear differential equation which has been repeatedly demonstrated to quantitatively model experimental data and discuss the salient results using realistic parameters for material linear and nonlinear elasticity. The solitons that emerge from the initial value problem with negative and positive thermal expansion are qualitatively different in several ways. The new case of negative thermal expansion gives rise to a nearly-periodic soliton train with chirped profile and free of an isolated shock front. We suggest this unanticipated result may be realized experimentally and assess the potential for certain applications of this generic effect.

36 MATERIALS SCIENCE↗
NASA NTRS1974

Method of fabricating an article with cavities

An article having a cavity with a thin bottom wall is provided by assembling a thin sheet, for example, a metal sheet, adjacent to the surface of a member having one or more apertures. A bonding adhesive is interposed between the thin sheet and the subadjacent member, and the thin sheet is subjected to a high fluid pressure. In order to prevent the differential pressure from being exerted against the thin sheet, the aperture is filled with a plug of solid material having a linear coefficient of thermal expansion higher than that of the member. When the assembly is subjected to pressure, the material is heated to a temperature such that its expansion exerts a pressure against the thin sheet thus reducing the differential pressure.

Dale, W. J.↗
NASA NTRS1960

Slow-Neutron Scattering by Rotators. II

The methods developed in a previous paper for extending the neutron scattering formalism of Zemach and Glauber to any type of molecular rotator have been employed to derive generalized forms generalized forms of the differential cross sections for rotator scattering. A mass-ratio expansion for the treatment of the high-energy limit is illustrated on the classical cross section and then employed in the treatment of the more general quantum-mechanical expression for the differential cross section. The results apply to an arbitrarily asymmetric rotator. The very low energy approximation is carried out for the symmetric rotator, and the procedure is compared with the explicit summing of the partial cross sections for individual rotational transitions. The inelastic correction to the static approximation for interference scattering is calculated to an accuracy of first order in the mass ratios for the case of the symmetric rotator.

Volkin, Howard C.↗
NASA NTRS1983

The determination of the elastodynamic fields of an ellipsoidal inhomogeneity

The determination of the elastodynamic fields of an ellipsoidal inhomogeneity is studied in detail via the eigenstrain approach. A complete formulation and a treatment of both types of eigenstrains for equivalence between the inhomogeneity problem and the inclusion problem are given. This approach is shown to be mathematically identical to other approaches such as the direct volume integral formulation. Expanding the eigenstrains and applied strains in the polynomial form in the position vector and satisfying the equivalence conditions at every point, the governing simultaneous algebraic equations for the unknown coefficients in the eigenstrain expansion are derived. The elastodynamic field outside an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the induced displacement field, as well as the differential and total cross sections are formally given in series expansion form for the case of uniformly distributed eigenstrains.

Fu, L. S.↗
DOE OSTI2022

University of Missouri Research Reactor (MURR) Design Demonstration Element End Fitting Structural Rigidity Analysis

The primary objective of this work is to assess the extent to which the stiffness (measured by means of maximum displacement) of the end fittings in the DDE contributes to the stiffness of the entire element, and how it compares to the equivalent stiffness of the end fittings in the LEU element. Structural analysis of both the LEU element and the DDE were performed using COMSOL 5.3a finite element software. Supporting combs are used on the leading and trailing edges of fuel plates for both the LEU element and the DDE. Therefore, simulations with and without combs are performed as two bounding boundary conditions on the leading edge of the fuel plates. Three types of loads are analyzed in this work: the hydraulic load due to the channel flow disparity-induced pressure differential, the thermal load due to the thermal expansion of the fuel plates, and a point load equal in magnitude to the LEU element’s weight.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Tuning Thermal and Mechanical Properties of Polydimethylsiloxane with Carbon Fibers

In order to meet the needs of constantly advancing technologies, fabricating materials with improved properties and predictable behavior has become vital. To that end, we have prepared polydimethylsiloxane (PDMS) polymer samples filled with carbon nanofibers (CFs) at 0, 0.5, 1.0, 2.0, and 4.0 CF loadings (w/w) to investigate and optimize the amount of filler needed for fabrication with improved mechanical properties. Samples were prepared using easy, cost-efficient mechanical mixing to combine the PDMS and CF filler and were then characterized by chemical (FTIR), mechanical (hardness and tension), and physical (swelling, thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and coefficient of thermal expansion) analyses to determine the material properties. We found that hardness and thermal stability increased predictably, while the ultimate strength and toughness both decreased. Repeated tension caused the CF-filled PDMS samples to lose significant toughness with increasing CF loadings. The hardness and thermal degradation temperature with 4 wt.% CF loading in PDMS increased more than 40% and 25 °C, respectively, compared with the pristine PDMS sample. Additionally, dilatometer measurements showed a 20% decrease in the coefficient of thermal expansion (CTE) with a small amount of CF filler in PDMS. In this study, we were able to show the mechanical and thermal properties of PDMS can be tuned with good confidence using CFs.

degradation temperature↗
NASA NTRS1972

Some efficient methods for obtaining infinite series solutions of n-th order linear ordinary differential equations

The use of the theta-operator method and generalized hypergeometric functions in obtaining solutions to nth-order linear ordinary differential equations is explained. For completeness, the analysis of the differential equation to determine whether the point of expansion is an ordinary point or a regular singular point is included. The superiority of the two methods shown over the standard method is demonstrated by using all three of the methods to work out several examples. Also included is a compendium of formulae and properties of the theta operator and generalized hypergeometric functions which is complete enough to make the report self-contained.

Allen, G.↗
NASA NTRS1986

Studies of electron-molecule collisions - Applications to e-H2O

Elastic differential and momentum transfer cross sections for the elastic scattering of electrons by H2O are reported for collision energies from 2 to 20 eV. These fixed-nuclei static-exchange cross sections were obtained using the Schwinger variational approach. In these studies the exchange potential is directly evaluated and not approximated by local models. The calculated differential cross sections, obtained with a basis set expansion of the scattering wave function, agree well with available experimental data at intermediate and larger angles. As used here, the results cannot adequately describe the divergent cross sections at small angles. An interesting feature of the calculated cross sections, particularly at 15 and 20 eV, is their significant backward peaking. This peaking occurs in the experimentally inaccessible region beyond a scattering angle of 120 deg. The implication of this feature for the determination of momentum transfer cross sections is described.

Brescansin, L. M.↗
NASA NTRS1987

Theories of multiple equilibria and weather regimes : A critical reexamination. II - Baroclinic two-layer models

Previous results based on low- and intermediate-order truncations of the two-layer model suggest the existence of multiple equilibria and/or multiple weather regimes for the extratropical large-scale flow. The importance of the transient waves in the synoptic scales in organizing the large-scale flow and in the maintenance of weather regimes was emphasized. The result shows that multiple equilibria/weather regimes that are present in lower-order models examined disappear when a sufficient number of modes are kept in the spectral expansion of the solution to the governing partial differential equations. Much of the chaotic behavior of the large-scale flow that is present in intermediate-order models is now found to be spurious. Physical reasons for the drastic modification are offered. A peculiarity in the formulation of most existing two-layer models is noted that also tends to exaggerate the importance of baroclinic processes and increase the degree of unpredictability of the large-scale flow.

Cehelsky, Priscilla↗
NASA NTRS2000

On the Dynamics of Two Dimensional Array Beam Scanning Via Coupled Oscillators

This presentation will begin with a description of the previous published work contributing to the results reported here. The previously developed one dimensional continuum model will be generalized to two dimensions and a Green's function for the resulting differential equation will be obtained as an eigenfunction expansion. This will be used to obtain dynamic solutions relevant to the steering of the radiated beam. Finally, some remarks concerning limitations on the interoscillator phase difference will be provided.

Pogorzelski, R. J.↗