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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 1,333 records · Page 74
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

An investigation of impurity centers in semiconductors of variable composition. Part 1: General theory and some applications

A theory of deep point defects imbedded in otherwise perfect semiconductor crystals is developed with the aid of pseudopotentials. The dominant short-range forces engendered by the impurity are sufficiently weakened in all cases where the cancellation theorem of the pseudopotential formalism is operative. Thus, effective-mass-like equations exhibiting local effective potentials derived from nonlocal pseudopotentials are shown to be valid for a large class of defects. A two-band secular determinant for the energy eigenvalues of deep defects is also derived from the set of integral equations which corresponds to the set of differential equations of the effective-mass type. Subsequently, the theory in its simplest form, is applied to the system Al(x)Ga(1-x)As:Se. It is shown that the one-electron donor level of Se within the forbidden gap of Al(x)Ga(1-x)As as a function of the AlAs mole fraction x reaches its maximum of about 300 meV (as measured from the conduction band edge) at the cross-over from the direct to the indirect band-gap at x = 0.44 in agreement with experiments.

Vonroos, O. H.↗
NASA NTRS1983

Modeling of steady, rotational, transonic winds from rotating stars and galaxies

The theory of steady transonic winds from condensed bodies is extended to general, two-dimensional, axisymmetric systems. A stream function is used to reduce the gasdynamics equations to a single, second-order differential equation plus an algebraic equation for the density. The approach extends Parker's (1958) quasi-one-dimensional theory, which uses Bernoulli's theorem, to a complete two-dimensional calculation which includes vorticity and rotation. The conceptual basis of the stream function approach is described in detail, and a numerical method for solving the resulting equations is presented. The applications illustrate solutions for stellar (spherical source surface) and galactic (oblate spheroidal source surface) models. Among other things, it is found that for rapidly rotating stellar models the Coriolis force dominates the centrifugal terms and the streamlines bend toward the rotation axis as a consequence of the axisymmetry. For both the rotating and nonrotating galaxy models, the streamlines bend toward the equator.

Kopriva, D. A.↗
NASA NTRS1985

Error Reduction Program

The details of a study to select, incorporate and evaluate the best available finite difference scheme to reduce numerical error in combustor performance evaluation codes are described. The combustor performance computer programs chosen were the two dimensional and three dimensional versions of Pratt & Whitney's TEACH code. The criteria used to select schemes required that the difference equations mirror the properties of the governing differential equation, be more accurate than the current hybrid difference scheme, be stable and economical, be compatible with TEACH codes, use only modest amounts of additional storage, and be relatively simple. The methods of assessment used in the selection process consisted of examination of the difference equation, evaluation of the properties of the coefficient matrix, Taylor series analysis, and performance on model problems. Five schemes from the literature and three schemes developed during the course of the study were evaluated. This effort resulted in the incorporation of a scheme in 3D-TEACH which is usuallly more accurate than the hybrid differencing method and never less accurate.

Syed, S. A.↗
NASA NTRS1986

On the solution of the generalized wave and generalized sine-Gordon equations

The generalized wave equation and generalized sine-Gordon equations are known to be natural multidimensional differential geometric generalizations of the classical two-dimensional versions. In this paper, a system of linear differential equations is associated with these equations, and it is shown how the direct and inverse problems can be solved for appropriately decaying data on suitable lines. An initial-boundary value problem is solved for these equations.

Ablowitz, M. J.↗
NASA NTRS1986

Linear stability analysis of the Vlasov-Poisson equations in high density plasmas in the presence of crossed fields and density gradients

The equations for the single-particle orbits in a nonneutral high density plasma in the presence of inhomogeneous crossed fields are obtained. Using these orbits, the linearized Vlasov equation is solved as an expansion in the orbital radii in the presence of inhomogeneities and density gradients. A model distribution function is introduced whose cold-fluid limit is exactly the same as that used in many previous studies of the cold-fluid equations. This model function is used to reduce the linearized Vlasov-Poisson equations to a second-order ordinary differential equation for the linearized electrostatic potential whose eigenvalue is the perturbation frequency.

Kaup, D. J.↗
NASA NTRS1988

A Mathematical Formulation of the SCOLE Control Problem. Part 2: Optimal Compensator Design

The study initiated in Part 1 of this report is concluded and optimal feedback control (compensator) design for stability augmentation is considered, following the mathematical formulation developed in Part 1. Co-located (rate) sensors and (force and moment) actuators are assumed, and allowing for both sensor and actuator noise, stabilization is formulated as a stochastic regulator problem. Specializing the general theory developed by the author, a complete, closed form solution (believed to be new with this report) is obtained, taking advantage of the fact that the inherent structural damping is light. In particular, it is possible to solve in closed form the associated infinite-dimensional steady-state Riccati equations. The SCOLE model involves associated partial differential equations in a single space variable, but the compensator design theory developed is far more general since it is given in the abstract wave equation formulation. The results thus hold for any multibody system so long as the basic model is linear.

Balakrishnan, A. V.↗
NASA NTRS1992

Linear-stability theory of thermocapillary convection in a model of float-zone crystal growth

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities will remain partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases.

Neitzel, G. P.↗
NASA NTRS1994

Chaotic dynamics of corotating magnetospheric convection

The corotating plasma convection system of the Jovian magnetosphere is analyzed. The macroscopic (mhd) model introduced by Summers and Mu, (1992) that incorporates the effects of microdiffusion is extended by including previously neglected density effects. We reduce the governing partial differential equations to a third-order ordinary differential system by the Galerkin technique of mode truncation. We carry out such a severe truncation partly in the interests of tractability, and leave open the question of the efficacy of adding additional modes. Exhaustive numerical integrations are carried out to calculate the long-term solutions, and we discover that a rich array of plasma motions is possible, dependent on the value of the height-integrated ionospheric Pederson conductivity Sigma. If Sigma is less than a certain critical value Sigma(sub c), then plasma motion can be expected to be chaotic (or periodic), while if Sigma is greater than Sigma(sub c), then steady state convection is expected. In the former case, whether the plasma motion is chaotic or periodic (and, if periodic, the magnitude of the period) can be very sensitive to the value of Sigma. The value of Sigma(sub c), which is a function of a parameter q that occurs in the assumed form of the stationary radial profile (varies as L(exp -q) of the plasma mass per unit magnetic flux, lies well within the accepted range of values of Sigma for Jupiter, i.e. Sigma greater than or equal to 0.1 mho and less than or equal to 10 mho.

Summers, Danny↗
NASA NTRS1995

Analysis of composite ablators using massively parallel computation

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

Shia, David↗
NASA NTRS2001

Filtered Mass Density Function for Design Simulation of High Speed Airbreathing Propulsion Systems

The objective of this research is to develop and implement new methodology for large eddy simulation of (LES) of high-speed reacting turbulent flows. We have just completed two (2) years of Phase I of this research. This annual report provides a brief and up-to-date summary of our activities during the period: September 1, 2000 through August 31, 2001. In the work within the past year, a methodology termed "velocity-scalar filtered density function" (VSFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function (PDF) of all of the components of the velocity and scalar vectors. An exact transport equation is derived for the VSFDF in which the effects of the unresolved SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source terms appear in closed form. The remaining unclosed terms in this equation are modeled. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VSFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by an Eulerian LES procedure in which the corresponding transport equations for the first two SGS moments are solved. The unclosed SGS convection, SGS velocity-scalar source, and SGS scalar-scalar source in the Eulerian LES are replaced by corresponding terms from VSFDF equation. The consistency of the results is then analyzed for a case of two dimensional mixing layer.

Drozda, T. G.↗
NASA NTRS2002

Dynamics of Diffusion Flames in von Karman Swirling Flows Studied

Von Karman swirling flow is generated by the viscous pumping action of a solid disk spinning in a quiescent fluid media. When this spinning disk is ignited in an oxidizing environment, a flat diffusion flame is established adjacent to the disk, embedded in the boundary layer (see the preceding illustration). For this geometry, the conservation equations reduce to a system of ordinary differential equations, enabling researchers to carry out detailed theoretical models to study the effects of varying strain on the dynamics of diffusion flames. Experimentally, the spinning disk burner provides an ideal configuration to precisely control the strain rates over a wide range. Our original motivation at the NASA Glenn Research Center to study these flames arose from a need to understand the flammability characteristics of solid fuels in microgravity where slow, subbuoyant flows can exist, producing very small strain rates. In a recent work (ref. 1), we showed that the flammability boundaries are wider and the minimum oxygen index (below which flames cannot be sustained) is lower for the von Karman flow configuration in comparison to a stagnation-point flow. Adding a small forced convection to the swirling flow pushes the flame into regions of higher strain and, thereby, decreases the range of flammable strain rates. Experiments using downward facing, polymethylmethacrylate (PMMA) disks spinning in air revealed that, close to the extinction boundaries, the flat diffusion flame breaks up into rotating spiral flames (refs. 2 and 3). Remarkably, the dynamics of these spiral flame edges exhibit a number of similarities to spirals observed in biological systems, such as the electric pulses in cardiac muscles and the aggregation of slime-mold amoeba. The tail of the spiral rotates rigidly while the tip executes a compound, meandering motion sometimes observed in Belousov-Zhabotinskii reactions.

Nayagam, Vedha↗
NASA NTRS2012

Assessing Tsunami Vulnerabilities of Geographies with Shallow Water Equations

Tsunami preparedness is crucial for saving human lives in case of disasters that involve massive water movement. In this work, we develop a framework for visual assessment of tsunami preparedness of geographies. Shallow water equations (also called Saint Venant equations) are a set of hyperbolic partial differential equations that are derived by depth-integrating the Navier-Stokes equations and provide a great abstraction of water masses that have lower depths compared to their free surface area. Our specific contribution in this study is to use Microsoft's XNA Game Studio to import underwater and shore line geographies, create different tsunami scenarios, and visualize the propagation of the waves and their impact on the shore line geography. Most importantly, we utilized the computational power of graphical processing units (GPUs) as HLSL based shader files and delegated all of the heavy computations to the GPU. Finally, we also conducted a validation study, in which we have tested our model against a controlled shallow water experiment. We believe that such a framework with an easy to use interface that is based on readily available software libraries, which are widely available and easily distributable, would encourage not only researchers, but also educators to showcase ideas.

Aras, Rifat↗
NASA NTRS2018

Instability Wave–Streak Interactions in a High Mach Number Boundary Layer at Flight Conditions

The interaction of stationary streaks undergoing nonmodal growth with modally unstable instability waves in a hypersonic boundary-layer flow is studied using numerical computations. The geometry and flow conditions are selected to match a relevant trajectory location from the ascent phase of the HIFiRE-1 flight experiment; namely, a 7 degree half-angle, circular cone with 2.5 mm nose radius, freestream Mach number equal to 5.30, unit Reynolds number equal to 13.42 m -1 , and wall-to-adiabatic temperature ratio of approximately 0.35 over most of the vehicle. This paper investigates the nonlinear evolution of initially linear optimal disturbances that evolve into finite-amplitude streaks, followed by an analysis of the modal instability characteristics of the perturbed, streaky boundary-layer flow. The investigation is performed with stationary direct numerical simulations (DNS) and plane-marching parabolized stability equations (PSE), in conjunction with partial-differential-equation-based planar eigenvalue analysis. The overall effect of streaks is to reduce the peak amplification factors of instability waves, indicating a possible downstream shift in the onset of laminar-turbulent transition. The present study confirms previous findings that the mean flow distortion of the nonlinear streak perturbation reduces the amplification rates of the Mack-mode instability. More importantly, however, the present results demonstrate that the spanwise varying component of the streak can produce a larger effect on the Mack-mode amplification. The study with selected azimuthal wavenumbers for the stationary streaks reveals that a wavenumber of approximately 1.4 times larger than the optimal wavenumber is more effective in stabilizing the planar Mack-mode instabilities. In the absence of unstable first-mode waves for the present cold-wall condition, transition onset is expected to be delayed until the peak streak amplitude increases to nearly 35 percent of the freestream velocity, when intrinsic instabilities of the boundary-layer streaks begin to dominate the transition process. For streak amplitudes below that limit a significant net stabilization is achieved, yielding a potential transition delay that can exceed 100 percent of the length of the laminar region in the uncontrolled case.

Boundary layer stability↗
DOE OSTI2022

Nonlocal Kernel Network (NKN): a Stable and Resolution-Independent Deep Neural Network.

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known partial differential equation (PDE) for a single instance of the input parameters at a fixed resolution, neural operators approximate the solution map of a family of PDEs [6, 7]. Despite their success, the uses of neural operators are so far restricted to relatively shallow neural networks and confined to learning hidden governing laws. In this work, we propose a novel nonlocal neural operator, which we refer to as nonlocal kernel network (NKN), that is resolution independent, characterized by deep neural networks, and capable of handling a variety of tasks such as learning governing equations and classifying images. Our NKN stems from the interpretation of the neural network as a discrete nonlocal diffusion reaction equation that, in the limit of infinite layers, is equivalent to a parabolic nonlocal equation, whose stability is analyzed via nonlocal vector calculus. The resemblance with integral forms of neural operators allows NKNs to capture long-range dependencies in the feature space, while the continuous treatment of node-to-node interactions makes NKNs resolution independent. The resemblance with neural ODEs, reinterpreted in a nonlocal sense, and the stable network dynamics between layers allow for generalization of NKN’s optimal parameters from shallow to deep networks. This fact enables the use of shallow-to-deep initialization techniques [8]. Our tests show that NKNs outperform baseline methods in both learning governing equations and image classification tasks and generalize well to different resolutions and depths.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A Stochastic Calculus Approach to Boltzmann Transport

Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within source iteration are associated with the adjoint flux density and the adjoint particle paths are associated with the flux density. Here, we make our assertion rigorous through the use of stochastic calculus by representing the particle path used in source iteration as a solution to a stochastic differential equation (SDE). The solution to the adjoint Boltzmann equation is then expressed in terms of the same SDE, and the solution to the Boltzmann equation is expressed in terms of the SDE associated with the adjoint particle process. An important consequence is that the particle paths used within source iteration simultaneously provide Monte Carlo samples of the flux density and adjoint flux density in the detector and source regions, respectively. The significant practical implication is that particle trajectories can be reused to obtain both forward and adjoint quantities of interest. To the best our knowledge, the reuse of entire particles paths has not appeared in the literature. Monte Carlo simulations are presented to support the reuse of the particle paths.

Boltzmann transport↗
DOE OSTI2020

Deep learning of free boundary and Stefan problems

Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/DeepStefan.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗