Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical approximations”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 793 records · Page 44
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Pulse Detonation Engine Modeled

Pulse Detonation Engine Technology is currently being investigated at Glenn for both airbreathing and rocket propulsion applications. The potential for both mechanical simplicity and high efficiency due to the inherent near-constant-volume combustion process, may make Pulse Detonation Engines (PDE's) well suited for a number of mission profiles. Assessment of PDE cycles requires a simulation capability that is both fast and accurate. It should capture the essential physics of the system, yet run at speeds that allow parametric analysis. A quasi-one-dimensional, computational-fluid-dynamics-based simulation has been developed that may meet these requirements. The Euler equations of mass, momentum, and energy have been used along with a single reactive species transport equation, and submodels to account for dominant loss mechanisms (e.g., viscous losses, heat transfer, and valving) to successfully simulate PDE cycles. A high-resolution numerical integration scheme was chosen to capture the discontinuities associated with detonation, and robust boundary condition procedures were incorporated to accommodate flow reversals that may arise during a given cycle. The accompanying graphs compare experimentally measured and computed performance over a range of operating conditions for a particular PDE. Experimental data were supplied by Fred Schauer and Jeff Stutrud from the Air Force Research Laboratory at Wright-Patterson AFB and by Royce Bradley from Innovative Scientific Solutions, Inc. The left graph shows thrust and specific impulse, Isp, as functions of equivalence ratio for a PDE cycle in which the tube is completely filled with a detonable hydrogen/air mixture. The right graph shows thrust and specific impulse as functions of the fraction of the tube that is filled with a stoichiometric mixture of hydrogen and air. For both figures, the operating frequency was 16 Hz. The agreement between measured and computed values is quite good, both in terms of trend and magnitude. The error is under 10 percent everywhere except for the thrust value at an equivalence ratio of 0.8 in the left figure, where it is 14 percent. The simulation results shown were made using 200 numerical cells. Each cycle of the engine, approximately 0.06 sec, required 2.0 min of CPU time on a Sun Ultra2. The simulation is currently being used to analyze existing experiments, design new experiments, and predict performance in propulsion concepts where the PDE is a component (e.g., hybrid engines and combined cycles).

Paxson, Daniel E.↗
NASA NTRS2006

Newly-Developed 3D GRMHD Code and its Application to Jet Formation

We have developed a new three-dimensional general relativistic magnetohydrodynamic code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated constrained transport scheme is used to maintain a divergence-free magnetic field. We have performed various 1-dimensional test problems in both special and general relativity by using several reconstruction methods and found that the new 3D GRMHD code shows substantial improvements over our previous model. The . preliminary results show the jet formations from a geometrically thin accretion disk near a non-rotating and a rotating black hole. We will discuss the jet properties depended on the rotation of a black hole and the magnetic field strength.

Mizuno, Y.↗
NASA NTRS2006

GRMHD Simulations of Jet Formation with a New Code

We have developed a new three-dimensional general relativistic magnetohydrodynamic (GRMHD) code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-interpolated, constrained transport scheme is used to maintain a divergence-free magnetic field. Various one-dimensional test problems in both special and general relativity show significant improvements over our previous model. We have performed simulations of jet formations from a geometrically thin accretion disk near both nonrotating and rotating black holes. The new simulation results show that the jet is formed in the same manner as in previous work and propagates outward. In the rotating black hole cases, jets form much closer to the black hole's ergosphere and the magnetic field is strongly twisted due the frame-dragging effect. As the magnetic field strength becomes weaker, a larger amount of matter is launched with the jet. On the other hand, when the magnetic field strength becomes stronger, the jet has less matter and becomes poynting-flux dominated. We will also discuss how the jet properties depend on the rotation of a black hole.

Mizuno, Y.↗
NASA NTRS2006

GRMHD Simulations of Jet Formation with a Newly-Developed GRMHD Code

We have developed a new three-dimensional general relativistic magnetohydrodynamic code by using a conservative, high-resolution shock-capturing scheme. The numerical fluxes are calculated using the HLL approximate Riemann solver scheme. The flux-CT scheme is used to maintain a divergence-free magnetic field. Various 1-dimensional test problems show significant improvements over our previous GRMHD code. We have performed simulations of jet formations from a geometrically thin accretion disk near a non-rotating and a rotating black hole. The new simulation results show that the jet is formed by the same manner as in previous works and propagates outward. As the magnetic field strength becomes weaker, larger amount of matter launches with the jet. On the other hand when the magnetic field strength becomes stronger, the jet has less-matter and becomes poynting flux dominated. We will also discuss how the jet properties depend on the rotation of a black hole.

Mizuno, Y.↗
NASA NTRS2009

Stability of Detached Solidification

Bridgman crystal growth can be conducted in the so-called "detached" solidification regime, where the growing crystal is detached from the crucible wall. A small gap between the growing crystal and the crucible wall, of the order of 100 micrometers or less, can be maintained during the process. A meniscus is formed at the bottom of the melt between the crystal and crucible wall. Under proper conditions, growth can proceed without collapsing the meniscus. The meniscus shape plays a key role in stabilizing the process. Thermal and other process parameters can also affect the geometrical steady-state stability conditions of solidification. The dynamic stability theory of the shaped crystal growth process has been developed by Tatarchenko. It consists of finding a simplified autonomous set of differential equations for the radius, height, and possibly other process parameters. The problem then reduces to analyzing a system of first order linear differential equations for stability. Here we apply a modified version of this theory for a particular case of detached solidification. Approximate analytical formulas as well as accurate numerical values for the capillary stability coefficients are presented. They display an unexpected singularity as a function of pressure differential. A novel approach to study the thermal field effects on the crystal shape stability has been proposed. In essence, it rectifies the unphysical assumption of the model that utilizes a perturbation of the crystal radius along the axis as being instantaneous. It consists of introducing time delay effects into the mathematical description and leads, in general, to stability over a broader parameter range. We believe that this novel treatment can be advantageously implemented in stability analyses of other crystal growth techniques such as Czochralski and float zone methods.

Mazuruk, K.↗
NASA NTRS2014

S-NPP ATMS Instrument Prelaunch and On-Orbit Performance Evaluation

The first of a new generation of microwave sounders was launched aboard the Suomi-National Polar-Orbiting Partnership satellite in October 2011. The Advanced Technology Microwave Sounder (ATMS) combines the capabilities and channel sets of three predecessor sounders into a single package to provide information on the atmospheric vertical temperature and moisture profiles that are the most critical observations needed for numerical weather forecast models. Enhancements include size/mass/power approximately one third of the previous total, three new sounding channels, the first space-based, Nyquist-sampled cross-track microwave temperature soundings for improved fusion with infrared soundings, plus improved temperature control and reliability. This paper describes the ATMS characteristics versus its predecessor, the advanced microwave sounding unit (AMSU), and presents the first comprehensive evaluation of key prelaunch and on-orbit performance parameters. Two-year on-orbit performance shows that the ATMS has maintained very stable radiometric sensitivity, in agreement with prelaunch data, meeting requirements for all channels (with margins of ~40% for channels 1-15), and improvements over AMSU-A when processed for equivalent spatial resolution. The radiometric accuracy, determined by analysis from ground test measurements, and using on-orbit instrument temperatures, also shows large margins relative to requirements (specified as <1.0K for channels 1, 2, and 16-22 and <0.75 K for channels 3-15). A thorough evaluation of the performance of ATMS is especially important for this first proto-flight model unit of what will eventually be a series of ATMS sensors providing operational sounding capability for the U.S. and its international partners well into the next decade.

temperature↗
NASA NTRSDate not supplied

Least Squares Reverse Time Migration (LSRTM) for Damage Imaging in Composite Laminates

A method for adapting least squares reverse time migration (LSRTM) for ultrasonic guided wave imaging of composite laminates is proposed in this paper. As composites become more widely used in fields such as the aerospace industry, the need for high-resolution imaging in structural health monitoring (SHM) and nondestructive evaluation (NDE) is also growing. For instance, delamination is a common problem in composite laminates, which has led to a certain degree of apprehension in the use of composite materials for load-bearing structures. Although the solver-based imaging techniques using conventional reverse time migration (RTM) methods illuminate damage with a wide range of damage-scattering effects, the resulting images do not fully define the damage regions due to the limited data acquisition aperture, sensor density, frequencies/wavelengths, and incompleteness of adjoint reconstruction. Previously, the LSRTM theory was derived by incorporating a least squares migration (LSM) algorithm into RTM, and benchmarked its high-resolution damage imaging performance for isotropic plates. To improve damage imaging in composite laminates, a process to create an ultrasonic guided wave-based LSRTM method for anisotropic materials is proposed in this paper. The derivation of the forward modeling operator and the adjoint operator is presented. Numerical case studies were conducted to show the improvement of LSRTM over RTM in mapping damage in composite plates. Multiple damage sites or damage with a complex shape were created in the numerical studies based on 1) Born approximation-based modeling or 2) reduction of the plate stiffness-based modeling. LSRTM begins by using a forward modeling process. The forward modeling accuracy for the flexural wave solver used in this study for LSRTM was also compared with the results from a three-dimensional rotated staggered grid (RSG) elastodynamic finite difference solver, previously open-sourced by NASA Langley Research Center. These benchmarking studies have shown that the LSRTM method is more effective in reducing artifacts, improving resolution, and enhancing damage model reconstruction compared to RTM in composite laminates.

Jiaze He↗
DOE OSTI2020

Toroidal States of the 12 C Nucleus

Among the states of 12 C, there is an important subset of $K$ = 0 and $K$ = I planar intrinsic states in which the intrinsic motion of the nucleons are confined in the planar region defined by the three-alpha cluster or by their generated toroid. The intrinsic nuclear densities of these states are toroidal in nature. In this work we study these 12 C toroidal states from the generator-coordinate viewpoints in both the alpha cluster model and the toroidal shell model. Numerical solutions in the toroidal mean field approximation are examined to pave the way for future extensions and refinements.

12C Hoyle state↗
DOE OSTI2021

Coordinated Optimization and Control of Residential Solid State Power Substations in Electrical Distribution Network

This paper proposes a computationally efficient mixed integer linear programming (MILP) model for the coordinated optimization of solid-state power substations (SSPSs) in a feeder considering the full unbalanced three-phase structure of the distribution grid and its characteristics. The proposed model determines the optimal real and reactive power of each SSPS at the point of common coupling (PCC) that minimizes the operating cost and maximizes the system performance, e.g., voltage regulation and phase balancing. To improve the computational efficiency, an inscribed octagon is introduced to approximate the quadratic capacity constraints of components. Numerical simulation results show the effectiveness of the proposed model and significant improvements in voltage profiles and power imbalance between phases.

Liu, Guodong↗
DOE OSTI2025

Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference

In this work, we present two neural network approaches that approximate the solutions of static and dynamic conditional optimal transport (COT) problems. Both approaches enable conditional sampling and conditional density estimation, which are core tasks in Bayesian inference—particularly in the simulation-based (“likelihood-free”) setting. Our methods represent the target conditional distribution as a transformation of a tractable reference distribution. Obtaining such a transformation, chosen here to be an approximation of the COT map, is computationally challenging even in moderate dimensions. To improve scalability, our numerical algorithms use neural networks to parameterize candidate maps and further exploit the structure of the COT problem. Our static approach approximates the map as the gradient of a partially input convex neural network. It uses a novel numerical implementation to increase computational efficiency compared to state-of-the-art alternatives. Our dynamic approach approximates the conditional optimal transport via the flow map of a regularized neural ODE; compared to the static approach, it is slower to train but offers more modeling choices and can lead to faster sampling. We demonstrate both algorithms numerically, comparing them with competing state-of-the-art approaches, using benchmark datasets and simulation-based Bayesian inverse problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1985

Curved Finite Elements and Curve Approximation

The approximation of parameterized curves by segments of parabolas that pass through the endpoints of each curve segment arises naturally in all quadratic isoparametric transformations. While not as popular as cubics in curve design problems, the use of parabolas allows the introduction of a geometric measure of the discrepancy between given and approximating curves. The free parameters of the parabola may be used to optimize the fit, and constraints that prevent overspill and curve degeneracy are introduced. This leads to a constrained optimization problem in two varibles that can be solved quickly and reliably by a simple method that takes advantage of the special structure of the problem. For applications in the field of computer-aided design, the given curves are often cubic polynomials, and the coefficient may be calculated in closed form in terms of polynomial coefficients by using a symbolic machine language so that families of curves can be approximated with no further integration. For general curves, numerical quadrature may be used, as in the implementation where the Romberg quadrature is applied. The coefficient functions C sub 1 (gamma) and C sub 2 (gamma) are expanded as polynomials in gamma, so that for given A(s) and B(s) the integrations need only be done once. The method was used to find optimal constrained parabolic approximation to a wide variety of given curves.

Baart, M. L.↗
NASA NTRS1995

Hybrid Upwind Splitting (HUS) by a Field-by-Field Decomposition

We introduce and develop a new approach for upwind biasing: the hybrid upwind splitting (HUS) method. This original procedure is based on a suitable hybridization of current prominent flux vector splitting (FVS) and flux difference splitting (FDS) methods. The HUS method is designed to naturally combine the respective strengths of the above methods while excluding their main deficiencies. Specifically, the HUS strategy yields a family of upwind methods that exhibit the robustness of FVS schemes in the capture of nonlinear waves and the accuracy of some FDS schemes in the resolution of linear waves. We give a detailed construction of the HUS methods following a general and systematic procedure directly performed at the basic level of the field by field (i.e. waves) decomposition involved in FDS methods. For such a given decomposition, each field is endowed either with FVS or FDS numerical fluxes, depending on the nonlinear nature of the field under consideration. Such a design principle is made possible thanks to the introduction of a convenient formalism that provides us with a unified framework for upwind methods. The HUS methods we propose bring significant improvements over current methods in terms of accuracy and robustness. They yield entropy-satisfying approximate solutions as they are strongly supported in numerical experiments. Field by field hybrid numerical fluxes also achieve fairly simple and explicit expressions and hence require a computational effort between that of the FVS and FDS. Several numerical experiments ranging from stiff 1D shock-tube to high speed viscous flows problems are displayed, intending to illustrate the benefits of the present approach. We assess in particular the relevance of our HUS schemes to viscous flow calculations.

Coquel, Frederic↗
DOE OSTI2021

Various facets of magnetic charge correlation: Micromagnetic and distorted-wave Born approximation simulations study

The emergent concept of the magnetic charge quasiparticle provides a new realm to study the evolution of magnetic properties in two-dimensional artificially frustrated magnets. Here we report on the exploration of magnetic phases due to various magnetic charge correlation using the complementary numerical techniques of micromagnetic and distorted-wave Born approximation simulations in artificial permalloy honeycomb lattice. The honeycomb element length varies between 10 nm and 100 nm, while the width and thickness are kept within the single domain limit. In addition to the charge ordered loop state, we observe disordered charge arrangement, characterized by the random distribution of ±Q charges, in single domain size honeycomb lattice. As the length of the honeycomb element increases, low multiplicity magnetic charges tend to form contiguous bands in thinner lattice. Thin honeycomb lattice with 100 nm element length exhibits a perfect spin ice pattern, which remains unaffected by the modest increase in the width of element size. We simulate scattering profiles under the pretext of distorted-wave Born approximation formalism for the micromagnetic phases. The results are expected to provide useful guidance in the experimental investigation of magnetic phases in an artificial honeycomb magnet.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

Analytical-numerical methods of calculations of energy and three-dimensional particle distributions in electromagnetic cascades

Analytical and numerical methods of calculation of the energy and three dimensional EPS characteristics are reported. The angular and lateral functions of electrons in EPS have been obtained by the Landau and small angle approximations A and B and compared with earlier data. A numerical method of solution of cascade equations for the EPS distribution function moments has been constructed. Considering the equilibrium rms angle as an example, errors appearing when approximating the elementary process cross sections by their asymptotic expressions are analyzed.

Ivanenko, I. P.↗
NASA NTRS1976

The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions

Necessary and sufficient conditions are given for a maximum likelihood estimate of a subset of mixture proportions. From these conditions, likelihood equations are derived satisfied by the maximum-likelihood estimate and a successive-approximations procedure is discussed as suggested by equations for numerically evaluating the maximum-likelihood estimate. It is shown that, with probability one for large samples, this procedure converges locally to the maximum-likelihood estimate whenever a certain step-size lies between zero and two. Furthermore, optimal rates of local convergence are obtained for a step-size which is bounded below by a number between one and two.

Peters, B. C., Jr.↗
NASA NTRS1989

A simple time-accurate turbomachinery algorithm with numerical solutions of an uneven blade count configuration

The present computer algorithm for the time-accurate flow analysis of rotating turbomachines is based on the finite-volume method and employs a high-resolution approximate Riemann solver for interface flux definitions and an implicit numerical scheme that possesses apparent unconditional stability. Block-block interfaces, including dynamic ones, are treated in such a way as to mimic interior block communication. The turbomachine configurations treated by way of illustration are 8-8-bladed and 11-9-bladed versions of a contrarotating unducted fan engine.

Janus, J. Mark↗
DOE OSTI2021

A sharp interface Lagrangian-Eulerian method for rigid-body fluid-structure interaction

Herein this paper introduces a sharp interface method to simulate fluid-structure interaction (FSI) involving rigid bodies immersed in viscous incompressible fluids. The capabilities of this methodology are benchmarked using a range of test cases and demonstrated using large-scale models of biomedical FSI. The numerical approach developed herein, which we refer to as an immersed Lagrangian-Eulerian (ILE) method, integrates aspects of partitioned and immersed FSI formulations by solving separate momentum equations for the fluid and solid subdomains, as in a partitioned formulation, while also using non-conforming discretizations of the dynamic fluid and structure regions, as in an immersed formulation. A simple Dirichlet-Neumann coupling scheme is used, in which the motion of the immersed solid is driven by fluid traction forces evaluated along the fluid-structure interface, and the motion of the fluid along that interface is constrained to match the solid velocity and thereby satisfy the no-slip condition. To develop a practical numerical method, we adopt a penalty approach that approximately imposes the no-slip condition along the fluid-structure interface. In the coupling strategy, a separate discretization of the fluid-structure interface is tethered to the volumetric solid mesh via stiff spring-like penalty forces. Our fluid-structure coupling scheme relies on an immersed interface method (IIM) for discrete geometries, which enables the accurate determination of both velocities and stresses along complex internal interfaces. Numerical methods for FSI can suffer from instabilities related to the added mass effect, but computational tests indicate that the methodology introduced here remains stable for selected test cases across a broad range of solid-fluid mass density ratios, including extremely small, nearly equal, equal, and large density ratios. Biomedical FSI demonstration cases include results obtained using this method to simulate the dynamics of a bileaflet mechanical heart valve in a pulse duplicator, and to model transport of blood clots in a patient-averaged anatomical model of the inferior vena cava.

97 MATHEMATICS AND COMPUTING↗