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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS2012

High Accuracy Liquid Propellant Slosh Predictions Using an Integrated CFD and Controls Analysis Interface

Coupling computational fluid dynamics (CFD) with a controls analysis tool elegantly allows for high accuracy predictions of the interaction between sloshing liquid propellants and th e control system of a launch vehicle. Instead of relying on mechanical analogs which are not valid during aU stages of flight, this method allows for a direct link between the vehicle dynamic environments calculated by the solver in the controls analysis tool to the fluid flow equations solved by the CFD code. This paper describes such a coupling methodology, presents the results of a series of test cases, and compares said results against equivalent results from extensively validated tools. The coupling methodology, described herein, has proven to be highly accurate in a variety of different cases.

Marsell, Brandon↗
NASA NTRS2012

Unsteady Adjoint Approach for Design Optimization of Flapping Airfoils

This paper describes the work for optimizing the propulsive efficiency of flapping airfoils, i.e., improving the thrust under constraining aerodynamic work during the flapping flights by changing their shape and trajectory of motion with the unsteady discrete adjoint approach. For unsteady problems, it is essential to properly resolving time scales of motion under consideration and it must be compatible with the objective sought after. We include both the instantaneous and time-averaged (periodic) formulations in this study. For the design optimization with shape parameters or motion parameters, the time-averaged objective function is found to be more useful, while the instantaneous one is more suitable for flow control. The instantaneous objective function is operationally straightforward. On the other hand, the time-averaged objective function requires additional steps in the adjoint approach; the unsteady discrete adjoint equations for a periodic flow must be reformulated and the corresponding system of equations solved iteratively. We compare the design results from shape and trajectory optimizations and investigate the physical relevance of design variables to the flapping motion at on- and off-design conditions.

Lee, Byung Joon↗
NASA NTRS2011

AutoBayes Program Synthesis System System Internals

This lecture combines the theoretical background of schema based program synthesis with the hands-on study of a powerful, open-source program synthesis system (Auto-Bayes). Schema-based program synthesis is a popular approach toward program synthesis. The lecture will provide an introduction into this topic and discuss how this technology can be used to generate customized algorithms. The synthesis of advanced numerical algorithms requires the availability of a powerful symbolic (algebra) system. Its task is to symbolically solve equations, simplify expressions, or to symbolically calculate derivatives (among others) such that the synthesized algorithms become as efficient as possible. We will discuss the use and importance of the symbolic system for synthesis. Any synthesis system is a large and complex piece of code. In this lecture, we will study Autobayes in detail. AutoBayes has been developed at NASA Ames and has been made open source. It takes a compact statistical specification and generates a customized data analysis algorithm (in C/C++) from it. AutoBayes is written in SWI Prolog and many concepts from rewriting, logic, functional, and symbolic programming. We will discuss the system architecture, the schema libary and the extensive support infra-structure. Practical hands-on experiments and exercises will enable the student to get insight into a realistic program synthesis system and provides knowledge to use, modify, and extend Autobayes.

Statistical Algorithms↗
NASA NTRS1995

Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Bibel, G. D.↗
DOE OSTI2022

The MP{sub N} method: a new angular discretization method based on piecewise polynomial interfaces fluxes

In transport calculations, it is well known how S{sub N} method is extremely inefficient in problems where the particle physics is dominated by streaming. The ray-effect eventually produced by the insufficient angular discretization, appears to be extremely persistent with respect to the refinement of the angular quadrature. The MP{sub N} method, that relies on continuous angular representation, offers a robust remedy to such an issue. MP{sub N} is based on the decomposition of the unit sphere into solid angles and on a piecewise continuous definition of interface fluxes, which are expanded in polynomials in each solid angle. This allows propagating more than one angular degree of freedom simultaneously while maintaining unaltered the block-diagonal pattern of the displacement plus removal operator. The method is therefore well suited for the flux resolution by means of a conventional sweep algorithm. Furthermore, unlike the S{sub N} method, MP{sub N} does not rely on discrete directions and, thus, on an angular quadrature formula, but rather constructs a set of linear equations solving for the angular moments of the flux for all discrete solid angles within the sweep. MP{sub N} shows an error convergence rate higher than S{sub N} at the expense of an increased size of the coefficient matrices, so of the computational cost. Although MP{sub N} is not free from ray-effect, the latter is effectively mitigated and less persistent with respect to the increase of the angular refinement order. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Solving Coupled Cluster Equations by the Newton Krylov Method

We describe using the Newton Krylov method to solve the coupled cluster equation. The method uses a Krylov iterative method to compute the Newton correction to the approximate coupled cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each step of a Krylov iterative method such as the Generalized Minimum Residual (GMRES) method, is carried out through a finite difference approximation, and requires an additional residual evaluation. The overall cost of the method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss the termination criterion used for the inner iteration and show how to apply pre-conditioners to accelerate convergence. We will also examine the use of regularization technique to improve the stability of convergence and compare the method with the widely used direct inversion of iterative subspace (DIIS) methods through numerical examples.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1987

An Exponential Finite Difference Technique for Solving Partial Differential Equations

An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.

Handschuh, Robert F.↗
NASA NTRS1989

Algorithms and software for solving finite element equations on serial and parallel architectures

Over the past 15 years numerous new techniques have been developed for solving systems of equations and eigenvalue problems arising in finite element computations. A package called SPARSPAK has been developed by the author and his co-workers which exploits these new methods. The broad objective of this research project is to incorporate some of this software in the Computational Structural Mechanics (CSM) testbed, and to extend the techniques for use on multiprocessor architectures.

George, Alan↗
DOE OSTI2025

One-shot learning for solution operators of partial differential equations

Learning and solving governing equations of a physical system, represented by partial differential equations (PDEs), from data is a central challenge in many areas of science and engineering. Traditional numerical methods can be computationally expensive for complex systems and require complete governing equations. Existing data-driven machine learning methods require large datasets to learn a surrogate solution operator, which could be impractical. Here, we propose a solution operator learning method that requires only one PDE solution, i.e., one-shot learning, along with suitable initial and boundary conditions. Leveraging the locality of derivatives, we define a local solution operator in small local domains, train it using a neural network, and use it to predict solutions of new input functions via mesh-based fixed-point iteration or meshfree neural-network based approaches. We test our method on various PDEs, complex geometries, and a practical spatial infection spread application, demonstrating its effectiveness and generalization capabilities.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1996

Error and Complexity Analysis for a Collocation-Grid-Projection Plus Precorrected-FFT Algorithm for Solving Potential Integral Equations with LaPlace or Helmholtz Kernels

In this paper we derive error bounds for a collocation-grid-projection scheme tuned for use in multilevel methods for solving boundary-element discretizations of potential integral equations. The grid-projection scheme is then combined with a precorrected FFT style multilevel method for solving potential integral equations with 1/r and e(sup ikr)/r kernels. A complexity analysis of this combined method is given to show that for homogeneous problems, the method is order n natural log n nearly independent of the kernel. In addition, it is shown analytically and experimentally that for an inhomogeneity generated by a very finely discretized surface, the combined method slows to order n(sup 4/3). Finally, examples are given to show that the collocation-based grid-projection plus precorrected-FFT scheme is competitive with fast-multipole algorithms when considering realistic problems and 1/r kernels, but can be used over a range of spatial frequencies with only a small performance penalty.

Phillips, J. R.↗
NASA NTRS1986

An efficient method for solving the steady Euler equations

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

Liou, M. S.↗
DOE OSTI2022

GW-PINN: A deep learning algorithm for solving groundwater flow equations

Machine learning methods provide new perspective for more convenient and efficient prediction of groundwater flow. In this study, a deep learning method “GW-PINN” without labeled data for solving groundwater flow equations with wells was proposed. GW-PINN takes the physics inform neural network (PINN) as the backbone and uses either the hard or soft constraint in the loss function for training. A locally refined sampling strategy (LRS) is adopted to generate the consistent spatial sampling points for problems with strong hydraulic head change, and then combined with an appropriate temporal sampling scheme to obtain the final spatial-temporal sampling points. A snowball-style two-stage training strategy by dividing the temporal domain into two subdomains is designed to decrease the sampling points. Five cases were designed to test the training performance of GW-PINN under different sampling strategies and two constraints. The predicted results of GW-PINN were compared with MODFLOW and the analytical solution. The results demonstrate that GW-PINN possesses strong ability in capturing the hydraulic head change for both confined and un-confined aquifers. The hard constraint owns more robust learning ability than the soft constraint. The LRS strategy can generate more accurate results with much fewer sampling points than traditional sampling strategies, and the snowball-style two-stage training strategy is significantly efficient for problems with the drastic change of hydraulic head. Additionally, the application of GW-PINN as a surrogate model for parameterized groundwater flow equations is illustrated. This study provides an option tool for efficient groundwater flow simulation, especially for those with local refinements are needed.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1994

Equilibrium structure of solar magnetic flux tubes: Energy transport with multistream radiative transfer

We examine the equilibrium structure of vertical intense magnetic flux tubes on the Sun. Assuming cylindrical geometry, we solve the magnetohydrostatic equations in the thin flux-tube approximation, allowing for energy transport by radiation and convection. The radiative transfer equation is solved in the six-stream approximation, assuming gray opacity and local thermodynamic equilibrium. This constitutes a significant improvement over a previous study, in which the transfer was solved using the multidimensional generalization of the Eddington approximation. Convection in the flux tube is treated using mixing-length theory, with an additional parameter alpha, characterizing the suppression of convective energy transport in the tube by the strong magnetic field. The equations are solved using the method of partial linearization. We present results for tubes with different values of the magnetic field strength and radius at a fixed depth in the atmosphere. In general, we find that, at equal geometric heights, the temperature on the tube axis, compared to the ambient medium, is higher in the photosphere and lower in the convection zone, with the difference becoming larger for thicker tubes. At equal optical depths the tubes are generally hotter than their surroundings. The results are comparatively insensitive to alpha but depend upon whether radiative and convective energy transport operate simultaneously or in separate layers. A comparison of our results with semiempirical models shows that the temperature and intensity contrast are in broad agreement. However, the field strengths of the flux-tube models are somewhat lower than the values inferred from observations.

Hasan, S. S.↗
NASA NTRS1985

Numerical solutions of 3-dimensional Navier-Stokes equations for closed bluff-bodies

The Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallelepiped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDc VPS 32 computer. The codes are written in 32-bit (half word) FORTRAN, which provides an approximate factor of two decreasing in computational time and doubles the memory size compared to the 54-bit word size.

Abolhassani, J. S.↗
NASA NTRS1989

Numerical modeling for primary atomization of liquid jets

In the proposed numerical model for primary atomization, surface-wave dispersion equations are solved in conjunction with the jet-embedding technique of solving mean flow equations of a liquid jet. Linear and approximate nonlinear models have been considered. In each case, the dispersion equation is solved over the whole wavelength spectrum to predict drop sizes, frequency, and liquid-mass breakup rates without using any empirical constants. The present model has been applied to several low-speed and high-speed jets. For the high-speed case (the LOX/H2 coaxial injector of the Space Shuttle Main Engine Preburner), predicted drop sizes and liquid breakup rates are in good agreement with the results of the CICM code, which have been calibrated against measured data.

Przekwas, A. J.↗
NASA NTRS2006

Rapid Aeroelastic Analysis of Blade Flutter in Turbomachines

The LINFLUX-AE computer code predicts flutter and forced responses of blades and vanes in turbomachines under subsonic, transonic, and supersonic flow conditions. The code solves the Euler equations of unsteady flow in a blade passage under the assumption that the blades vibrate harmonically at small amplitudes. The steady-state nonlinear Euler equations are solved by a separate program, then equations for unsteady flow components are obtained through linearization around the steady-state solution. A structural-dynamics analysis (see figure) is performed to determine the frequencies and mode shapes of blade vibrations, a preprocessor interpolates mode shapes from the structural-dynamics mesh onto the LINFLUX computational-fluid-dynamics mesh, and an interface code is used to convert the steady-state flow solution to a form required by LINFLUX. Then LINFLUX solves the linearized equations in the frequency domain to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. A post-processor uses the unsteady pressures to calculate generalized aerodynamic forces, response amplitudes, and eigenvalues (which determine the flutter frequency and damping). In comparison with the TURBO-AE aeroelastic-analysis code, which solves the equations in the time domain, LINFLUX-AE is 6 to 7 times faster.

Trudell, J. J.↗