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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 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

A General Theory of Unsteady Compressible Potential Aerodynamics

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the potential is obtained for both supersonic and subsonic flow. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface, sigma, of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface sigma. For the important practical case of small harmonic oscillation around a rest position, the equation reduces to a two-dimensional Fredholm integral equation of second-type. It is shown that this equation reduces properly to the lifting surface theories as well as other classical mathematical formulas. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings.

Morino, L.↗
NASA NTRS1981

Correct generalized solar radiation pressure force on a circular cylinder in an arbitrary orientation

In response to the inconsistency seen in Geogevic (1973) with respect to the solution for solar radiation pressure in the case of a circular cylinder, a succinct derivation of the correct solution is presented. Numerical comparisons of the two sets of results confirm that the new formulation yields physically reasonable results for both general and special cases. A detailed graphic representation of the mathematical model used is included.

Tang, C. C. H.↗
NASA NTRS1985

Error Correction for Tandem Data-Transmission Paths

Mathematical analysis for digital data transmission calculates optimum number of binary error-correcting repeaters to install in given number of wideband channel links. Asymptotic results compared to computed numerical results.

Posner, E. C.↗
NASA NTRS1985

On the probability density function of the squared envelope of a sum of random phase vectors

Weber et al. (1980) have found that a generic problem arises in the study of multiuser FHMA/MFSK systems. According to this problem, the presence of the other channel users acts as interference to reception of the desired user's transmission. The present investigation is concerned with a recursive solution in which the recursion parameter is the number of vectors in the sum. A mathematical characterization of such a solution is presented, taking into account the simple two-vector case in which a well-known closed form result is possible. Some numerical results are also discussed. It is pointed out that the considered recursive solution provides a break in the bottleneck associated with the exact computation of the error probability performance of multiuser FHMA/MFSK systems and single access MFSK systems corrupted by multitone jamming.

Simon, M. K.↗
NASA NTRS1991

Kinetic theory model for the flow of a simple gas from a three-dimensional axisymmetric nozzle

A system of nonlinear integral equations equivalent to the Krook kinetic equations for the steady state is the mathematical basis used to develop a computer code to model the flowfields for low-thrust three-dimensional axisymmetric nozzles. The method of characteristics is used to solve numerically by an iteration process the approximated Boltzmann equation for the number density, temperature, and velocity profiles of a simple gas as it expands into a vacuum. Results predict backscatter and show the effect of the nozzle wall boundary layer on the external flowfields.

Riley, B. R.↗
NASA NTRS1998

Numerical Analysis of a Radiant Heat Flux Calibration System

A radiant heat flux gage calibration system exists in the Flight Loads Laboratory at NASA's Dryden Flight Research Center. This calibration system must be well understood if the heat flux gages calibrated in it are to provide useful data during radiant heating ground tests or flight tests of high speed aerospace vehicles. A part of the calibration system characterization process is to develop a numerical model of the flat plate heater element and heat flux gage, which will help identify errors due to convection, heater element erosion, and other factors. A 2-dimensional mathematical model of the gage-plate system has been developed to simulate the combined problem involving convection, radiation and mass loss by chemical reaction. A fourth order finite difference scheme is used to solve the steady state governing equations and determine the temperature distribution in the gage and plate, incident heat flux on the gage face, and flat plate erosion. Initial gage heat flux predictions from the model are found to be within 17% of experimental results.

Jiang, Shanjuan↗
NASA NTRS2005

Simulations of Evaporating Multicomponent Fuel Drops

A paper presents additional information on the subject matter of Model of Mixing Layer With Multicomponent Evaporating Drops (NPO-30505), NASA Tech Briefs, Vol. 28, No. 3 (March 2004), page 55. To recapitulate: A mathematical model of a three-dimensional mixing layer laden with evaporating fuel drops composed of many chemical species has been derived. The model is used to perform direct numerical simulations in continuing studies directed toward understanding the behaviors of sprays of liquid petroleum fuels in furnaces, industrial combustors, and engines. The model includes governing equations formulated in an Eulerian and a Lagrangian reference frame for the gas and drops, respectively, and incorporates a concept of continuous thermodynamics, according to which the chemical composition of a fuel is described by use of a distribution function. In this investigation, the distribution function depends solely on the species molar weight. The present paper reiterates the description of the model and discusses further in-depth analysis of the previous results as well as results of additional numerical simulations assessing the effect of the mass loading. The paper reiterates the conclusions reported in the cited previous article, and states some new conclusions. Some new conclusions are: 1. The slower evaporation and the evaporation/ condensation process for multicomponent-fuel drops resulted in a reduced drop-size polydispersity compared to their single-component counterpart. 2. The inhomogeneity in the spatial distribution of the species in the layer increases with the initial mass loading. 3. As evaporation becomes faster, the assumed invariant form of the molecular- weight distribution during evaporation becomes inaccurate.

Bellan, Josette↗
DOE OSTI2024

A conservative discontinuous-Galerkin-in-time (DGiT) multirate time integration framework for interface-coupled problems with applications to solid–solid interaction and air–sea models

In this paper we extend the DGiT multirate framework, developed in Connors and Sockwell (2022) for scalar transmission problems, to a solid–solid interaction (SSI) problem involving two coupled elastic solids and a coupled air–sea model with the rotating, thermal shallow water equations. In so doing we aim to demonstrate the broad applicability of the mathematical theory and governing principles established in Connors and Sockwell (2022) to coupled problems characterized by subproblems evolving at different temporal scales. Further, multirate time integration algorithms employing different time steps, optimized for the dynamics of each subproblem, can significantly improve simulation efficiency for such coupled problems. However, development of multirate algorithms is a highly non-trivial task due to the coupling, which can impact accuracy, stability or other desired properties such as preservation of system invariants. DGiT provides a general template for multirate time integration that can achieve these properties. To elucidate the manner in which DGiT accomplishes this task, we fully detail each step in the application of the framework to the SSI and air–sea coupled problems. Numerical examples illustrate key properties of the resulting multirate schemes for both problems.

42 ENGINEERING↗
NASA NTRS2008

Oxidation Behavior of Carbon Fiber-Reinforced Composites

OXIMAP is a numerical (FEA-based) solution tool capable of calculating the carbon fiber and fiber coating oxidation patterns within any arbitrarily shaped carbon silicon carbide composite structure as a function of time, temperature, and the environmental oxygen partial pressure. The mathematical formulation is derived from the mechanics of the flow of ideal gases through a chemically reacting, porous solid. The result of the formulation is a set of two coupled, non-linear differential equations written in terms of the oxidant and oxide partial pressures. The differential equations are solved simultaneously to obtain the partial vapor pressures of the oxidant and oxides as a function of the spatial location and time. The local rate of carbon oxidation is determined at each time step using the map of the local oxidant partial vapor pressure along with the Arrhenius rate equation. The non-linear differential equations are cast into matrix equations by applying the Bubnov-Galerkin weighted residual finite element method, allowing for the solution of the differential equations numerically.

Sullivan, Roy M.↗
DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d -dimension ( \(d=2,3\) ). This method uses polynomials of degree \(k+1\) for the stress and of degree k for the displacement ( \(k\ge 0\) ). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any \(k \ge 0\) , the \(H(\mathrm{div})\) -like error estimate for the stress and \(L^2\) error estimate for the displacement are optimal. We further establish the optimal \(L^2\) error estimate for the stress provided that the \({\mathcal {P}}_{k+2}-{\mathcal {P}}_{k+1}^{-1}\) Stokes pair is stable and \(k \ge d\) . Finally, we also provide numerical results of MDG showing that the orders of convergence are actually sharp.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems

The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an adjoint analysis, which requires the numerical solution of large high-contrast linear elastic problems with features spanning several length scales. The size of the discretized problems forces the utilization of iterative linear solvers with solution time dependent on the quality of the preconditioner. The lack of clear separation between the scales, as well as the high-contrast, imposes severe challenges on the standard preconditioning techniques. Thus, here we propose new methods for the high-contrast elasticity equation with performance independent of the high-contrast and the multi-scale structure of the elasticity problem. The solvers are based on two-levels domain decomposition techniques with a carefully constructed coarse level to deal with the high-contrast and multi-scale nature of the problem. The construction utilizes spectral equivalence between scalar diffusion and each displacement block of the elasticity problems and, in contrast to previous solutions proposed in the literature, is able to select the appropriate dimension of the coarse space automatically. The new methods inherit the advantages of domain decomposition techniques, such as easy parallelization and scalability. Finally, the presented numerical experiments demonstrate the excellent performance of the proposed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Stochastic modeling and statistical calibration with model error and scarce data

This paper introduces a procedure to assess the predictive accuracy of stochastic models subject to model error and sparse data. Model error is introduced as uncertainty on the coefficients of appropriate polynomial chaos expansions (PCE). The error associated with finite sample size allows us to conceive of these coefficients as statistics of the data that we describe as random variables whose influence on output quantities of interest is evaluated through the extended polynomial chaos expansion (EPCE). A Bayesian data assimilation scheme is introduced to update these expansions by considering the resulting nested chaos expansion as a hierarchical probabilistic model. Stochastic models of quantities of interest (QoI) are thus constructed and efficiently evaluated. Here, the Metropolis–Hastings Markov chain Monte Carlo procedure is used to sample the posterior. Two illustrative analytical and numerical problems are used to demonstrate the proposed approach.

Bayesian inference↗
DOE OSTI2023

Constraining chaos: Enforcing dynamical invariants in the training of reservoir computers

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants—such as the Lyapunov exponent spectrum and the fractal dimension—in the systems of interest, enabling longer and more stable forecasts when operating with limited data. The technique is demonstrated in detail using reservoir computing, a specific kind of recurrent neural network. Finally, results are given for the Lorenz 1996 chaotic dynamical system and a spectral quasi-geostrophic model of the atmosphere, both typical test cases for numerical weather prediction.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Numerical integration of stochastic contact Hamiltonian systems via stochastic Herglotz variational principle

Within this work, we establish a stochastic contact variational integrator and its discrete version via stochastic Herglotz variational principle for stochastic contact Hamiltonian systems. A general structure-preserving stochastic contact method is provided to seek the stochastic contact variational integrators. Numerical experiments are performed to verify the validity of this approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Fusion by beam ions in a low collisionality, high mirror ratio magnetic mirror

Abstract The classical problem of neutral beam ions slowing down in a magnetic mirror geometry is revisited to provide predictive capability for the new Wisconsin HTS Axisymmetric Mirror under development at the University of Wisconsin. A Fokker–Planck model named fast beam ion solver (FBIS) is developed to include the spatial non-uniformity of a physical mirror geometry. The mathematical framework allows for efficient orbit averaging of the pitch-angle scattering operator, and permits a determination of the axial profile of the ambipolar potential confining the electrons. The numerical results from FBIS are consistent with earlier work, but further show how mirror-ratio and a near square magnetic well optimizes the fusion gain. The numerical results are also applied to inform the conceptual design of WHAM++, a low capital-cost breakeven-class magnetic mirror device.

Egedal, J. (ORCID:0000000177531529)↗
DOE OSTI2023

Model averaging approaches to data subset selection

Model averaging is a useful and robust method for dealing with model uncertainty in statistical analysis. Often, it is useful to consider data subset selection at the same time, in which model selection criteria are used to compare models across different subsets of the data. Two different criteria have been proposed in the literature for how the data subsets should be weighted. We compare the two criteria closely in a unified treatment based on the Kullback-Leibler divergence and conclude that one of them is subtly flawed and will tend to yield larger uncertainties due to loss of information. Here, analytical and numerical examples are provided.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗