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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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Computer solutions of Wu's equations for compressible flow through turbomachines

Two computers programs, known as Matrix Through-Flow and Matrix Blade-To-Blade, for analyzing the meridional and blade-to-blade flow patterns are described. The numerical solutions are obtained by finite difference approximations to the governing Poisson-type differential equations for the stream function. Solutions for several turbomachines, giving flow patterns and velocity distributions, are included.

Smith, D. J. L.↗
NASA NTRS1975

Cost performance satellite design using queueing theory

A modified Poisson arrival, infinite server queuing model is used to determine the effects of limiting the number of broadcast channels (C) of a direct broadcast satellite used for public service purposes (remote health care, education, etc.). The model is based on the reproductive property of the Poisson distribution. A difference equation has been developed to describe the change in the Poisson parameter. When all initially delayed arrivals reenter the system a (C plus 1) order polynomial must be solved to determine the effective value of the Poisson parameter. When less than 100% of the arrivals reenter the system the effective value must be determined by solving a transcendental equation. The model was used to determine the minimum number of channels required for a disaster warning satellite without degradation in performance. Results predicted by the queuing model were compared with the results of digital simulation.

Hein, G. F.↗
DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗
NASA NTRS1991

Charge collected by diffusion from an ion track under mixed boundary conditions

Charge-carrier diffusion from an ion track in a silicon substrate at least a few hundred microns thick is analyzed. The substrate upper surface is treated as reflective except for a small section, intended to represent a reverse-biased junction, which is treated as a sink. Total charge collected by the sink is calculated by assuming transport to be governed by an ambipolar diffusion equation with temporally constant and spatially uniform carrier lifetime and diffusion coefficient. Present results apply to a normally incident track but could easily be generalized to arbitrary track direction. The collected charge is found to depend on track length and on the electrostatic capacitance, rather than the area, of the sink. Theoretical predictions are compared to the results of a numerical simulation called the Poisson and Continuity Equation Solver (PISCES) for three cases and are found to agree within a factor of two in the worst case.

Edmonds, Larry D.↗
NASA NTRS1995

Multiparameter linear least-squares fitting to Poisson data one count at a time

A standard problem in gamma-ray astronomy data analysis is the decomposition of a set of observed counts, described by Poisson statistics, according to a given multicomponent linear model, with underlying physical count rates or fluxes which are to be estimated from the data. Despite its conceptual simplicity, the linear least-squares (LLSQ) method for solving this problem has generally been limited to situations in which the number n(sub i) of counts in each bin i is not too small, conventionally more than 5-30. It seems to be widely believed that the failure of the LLSQ method for small counts is due to the failure of the Poisson distribution to be even approximately normal for small numbers. The cause is more accurately the strong anticorrelation between the data and the wieghts w(sub i) in the weighted LLSQ method when square root of n(sub i) instead of square root of bar-n(sub i) is used to approximate the uncertainties, sigma(sub i), in the data, where bar-n(sub i) = E(n(sub i)), the expected value of N(sub i). We show in an appendix that, avoiding this approximation, the correct equations for the Poisson LLSQ (PLLSQ) problems are actually identical to those for the maximum likelihood estimate using the exact Poisson distribution. We apply the method to solve a problem in high-resolution gamma-ray spectroscopy for the JPL High-Resolution Gamma-Ray Spectrometer flown on HEAO 3. Systematic error in subtracting the strong, highly variable background encountered in the low-energy gamma-ray region can be significantly reduced by closely pairing source and background data in short segments. Significant results can be built up by weighted averaging of the net fluxes obtained from the subtraction of many individual source/background pairs. Extension of the approach to complex situations, with multiple cosmic sources and realistic background parameterizations, requires a means of efficiently fitting to data from single scans in the narrow (approximately = 1.2 keV, HEAO 3) energy channels of a Ge spectrometer, where the expected number of counts obtained per scan may be very low. Such an analysis system is discussed and compared to the method previously used.

Wheaton, Wm. A.↗
NASA NTRS2005

Full Multigrid Flow Solver

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Mineck, Raymond E.↗
NASA NTRS1988

Consistent boundary conditions for reduced Navier-Stokes (RNS) scheme applied to three-dimensional internal viscous flows

Three-dimensional internal viscous flow problems are presently addressed by a consistent and efficient set of boundary conditions for the multisweep space-marching, pressure-elliptic Reduced Navier-Stokes scheme. Since continuity is by this means directly satisfied at all points in the flow domain, the first-order momentum equations are directly solvable for pressure without the requirement for a Poisson pressure-correction equation. Incompressible flow solutions are obtained for straight and curved ducts of square cross section, in order to validate the procedure. Usefulness is demonstrated for internal flows with strong interactions, as would be found in turbomachine geometries.

Reddy, D. R.↗
DOE OSTI2026

Ion Transport in Charged Membranes: Linking Electric-Field-Driven Mechanisms to Pore Size via Perturbation Analysis

Ion-exchange membranes are a critical component in electrochemical systems. Nevertheless, the understanding and modeling of ion transport within these porous structures have been limited by particular complexity reductions, either ignoring the dimensionality of their porous network architecture or imposing geometric assumptions (i.e., overlapping double layers). Before addressing this morphology-transport gap, a framework that relates the driving forces of transport to the geometry of a single pore is required. In this work, our modeling domain consists of a two-dimensional single pore with charged walls, connecting two identical electrolyte reservoirs. Using the Poisson-Nernst-Planck equations and regular perturbation theory, we decouple the electric fields and analyze the driving forces of ion transport, specifically electromigration and induced electroosmosis within the pore. These processes are described as analytical functions of the interaction aspect ratio, ?, defined as the ratio of the pore radius to the Debye length. Using this parameter, our study (i) describes the interplay between electromigrative and electroosmotic mechanisms that set ionic conductivity, (ii) identifies a dimensionless group of intrinsic electrolyte properties that indicates the predominant driving force, and (iii) provides a qualitative, confinement-dependent perspective on selectivity in ion-conducting membranes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Large deviations of ionic currents in dilute electrolytes

Here, we evaluate the exponentially rare fluctuations of the ionic current for a dilute electrolyte by means of macroscopic fluctuation theory. We consider the fluctuating hydrodynamics of a fluid electrolyte described by a stochastic Poisson–Nernst–Planck equation. We derive the Euler–Lagrange equations that dictate the optimal concentration profiles of ions conditioned on exhibiting a given current, whose form determines the likelihood of that current in the long-time limit. For a symmetric electrolyte under small applied voltages, number density fluctuations are small, and ionic current fluctuations are Gaussian with a variance determined by the Nernst–Einstein conductivity. Under large applied potentials, the ionic current distribution is generically non-Gaussian. Its structure is constrained thermodynamically by Gallavotti–Cohen symmetry and the thermodynamic uncertainty principle.

Farhadi, Jafar [University of California, Berkeley↗
DOE OSTI2025

Cosmological perturbation theory for large scale structure in phase space

We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of negligible velocity dispersion underlying the Standard Perturbation Theory (SPT). We apply the new method to rederive the usual SPT kernels up to third order in the perturbative expansion. We also show that a counterterm, identical to the one introduced by standard Effective Field Theory (EFT) methods, naturally arises within our framework. We finish by making a precise connection to EFT techniques, which reveals the necessity of the EFTofLSS to self-consistently model the long-wavelength fluid, and illustrates the importance of having theoretical control over short distance fluctuations.

Cosmological perturbation theory in GR and beyond↗
NASA NTRS1977

Flow study in the cross sectional planes of a turbine scroll

A numerical study of the nonviscous flow characteristics in the cross-sectional planes of a radial inflow turbine scroll is presented. The velocity potential is used in the formulation to determine the flow velocity in these planes resulting from the continuous mass discharge. The effect of the through flow velocity is simulated by a continuous distribution of source/sink in the cross-section. A special iterative procedure is devised to handle the solution of the resulting Poisson's differential equation with Neumann boundary conditions in a domain with generally curved boundaries. The analysis is used to determine the effects of the radius of curvature, the location of the scroll section and its geometry on the flow characteristics in the turbine scroll.

Hamed, A.↗
NASA NTRS1983

A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution

A numerical method is presented for studying one-dimensional electron plasma evolution under typical interplanetary conditions. The method applies the Fourier-Fourier transform approach to a plasma model that is a generalization of the electrostatic Vlasov-Poisson system of equations. Conservation laws that are modified to include the plasma model generalization and also the boundary effects of nonperiodic solutions are given. A new conservation law for entropy in the transformed space is then introduced. These conservation laws are used to verify the numerical solutions. A discretization error analysis is presented. Two numerical instabilities and the methods used for their suppression are treated. It is shown that in interplanetary plasma conditions, the bump-on-tail instability produces significant excitation of plasma oscillations at the Bohm-Gross frequency and its second harmonic. An explanation of the second harmonic excitation is given in terms of wave-wave coupling during the growth phase of the instability.

Klimas, A. J.↗
NASA NTRS1986

Elliptic generation of composite three-dimensional grids about realistic aircraft

An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid generation method are presented along with results of the present application, a wing-body configuration based on the F-16 fighter aircraft.

Sorenson, R. L.↗
NASA NTRS1986

Missing matter in the vicinity of the sun

The Poisson and Vlasov equations are solved numerically for realistic Galaxy models which include multiple disk components, a Population II spheroid, and an unseen massive halo. The total amount of matter in the vicinity of the sun is determined by comparing the observed distributions of tracer stars, samples of F dwarfs, and K giants with the predictions of the Galaxy models. Results are obtained for a number of different assumed distributions of the unseen disk mass. For all the observed samples, typical models imply that about half of the mass in the solar vicinity must be in the form of unobserved matter. The volume density of unobserved material near the sun is about 0.1 solar mass/cu pc; the corresponding column density is about 30 solar mass/sq pc. This so far unseen material must be in a disk with an exponential scale height of less than 0.7 kpc.

Bahcall, John N.↗
NASA NTRS1987

Dark matter in the galactic disk

Observational data on the distributions of tracer stars, F dwarfs and K giants were used as input to obtain self-consistent solutions for the Poisson and Vlasov equations to set bounds on the amount of missing matter in the solar neighborhood. The numerical computations were carried out using Galaxy models which feature multiple disk components and an unseen massive halo. The star data included the mass components and velocity dispersions. Consideration of various possible distributions of the unseen matter leads to the conjecture that half of the disk material in the solar neighborhood has yet to be observed. Techniques for determining if brown dwarfs are a significant component of the missing mass are discussed, as are improved models which would use limited numbers of tracer stars to set further constraints on the amount and distribution of the missing mass.

Bahcall, John N.↗
NASA NTRS1986

Elliptic generation of composite three-dimensional grids about realistic aircraft

An elliptic method for generating composite grids about realistic aircraft is presented. A body-conforming grid is first generated about the entire aircraft by the solution of Poisson's differential equation. This grid has relatively coarse spacing, and it covers the entire physical domain. At boundary surfaces, cell size is controlled and cell skewness is nearly eliminated by inhomogeneous terms, which are found automatically by the program. Certain regions of the grid in which high gradients are expected, and which map into rectangular solids in the computational domain, are then designated for zonal refinement. Spacing in the zonal grids is reduced by adding points with a simple, algebraic scheme. Details of the grid-generation method are presented along with results of the present application, a wing/body configuration based on the F-16 fighter aircraft.

Sorenson, Reese L.↗
NASA NTRS1989

The 3DGRAPE book: Theory, users' manual, examples

A users' manual for a new three-dimensional grid generator called 3DGRAPE is presented. The program, written in FORTRAN, is capable of making zonal (blocked) computational grids in or about almost any shape. Grids are generated by the solution of Poisson's differential equations in three dimensions. The program automatically finds its own values for inhomogeneous terms which give near-orthogonality and controlled grid cell height at boundaries. Grids generated by 3DGRAPE have been applied to both viscous and inviscid aerodynamic problems, and to problems in other fluid-dynamic areas. The smoothness for which elliptic methods are known is seen here, including smoothness across zonal boundaries. An introduction giving the history, motivation, capabilities, and philosophy of 3DGRAPE is presented first. Then follows a chapter on the program itself. The input is then described in detail. A chapter on reading the output and debugging follows. Three examples are then described, including sample input data and plots of output. Last is a chapter on the theoretical development of the method.

Sorenson, Reese L.↗
NASA NTRS1989

Calculation of the electron wave function in a graded-channel double-heterojunction modulation-doped field-effect transistor

Three double-heterojunction modulation-doped field-effect transistor structures with different channel composition are investigated theoretically. All of these transistors have an In(x)Ga(1-x)As channel sandwiched between two doped Al(0.3)Ga(0.7)As barriers with undoped spacer layers. In one of the structures, x varies from 0 from either heterojunction to 0.15 at the center of the channel quadratically; in the other two, constant values of x of 0 and 0.15 are used. The Poisson and Schroedinger equations are solved self-consistently for the electron wave function in all three cases. The results showed that the two-dimensional electron gas (2DEG) concentration in the channel of the quadratically graded structure is higher than the x = 0 one and slightly lower than the x = 0.15 one, and the mean distance of the 2DEG is closer to the center of the channel for this transistor than the other two. These two effects have important implications on the electron mobility in the channel.

Mui, D. S. L.↗