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DOE OSTI2024

Discrete-Element and Material-Point Method (DEM and MPM) Based Solvers for Sustainable Technologies

We present the use of discrete element method (DEM) and material point method (MPM) in three relevant green technology applications that include biomass feedstock handling, lithium-ion battery manufacturing, and high-pressure reverse osmosis. Our open-source DEM and MPM solvers are developed using performance portable grid and particle management library, AMReX, thus enabling superior performance on NVIDIA and AMD GPUs with > 100 million particles. Our DEM solver resolves the motion of individual particles in a granular system and includes a bonded sphere method for modeling non-spherical particles along with Hertzian and liquid bridge-based contact models. We simulate highly variable biomass feedstock flows in large-scale hoppers for biofuel production and electrode calendering in battery manufacturing using DEM. Our simulations predict flow blockage in large scale biomass hoppers and electrode microstructure variations, thus providing valuable information for biofuel and battery manufacturers, respectively. The second half of the talk will be on MPM and its application towards pore resolved simulations of reverse osmosis membranes under compressive loads. We present a validation study of our MPM simulations with membrane microscopy imaging thus providing useful insights on membrane stability under high pressure conditions. We also present a spectral stability analysis of using linear hat, quadratic and cubic spline basis in MPM indicating regions of numerical stability.

BIOMASS FUELS,MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

The principal features of the discrete-ordinates finite-element method are reviewed, and the applicability of general-purpose discrete-ordinates codes to atmospheric radiative transfer and remote sensing problems is demonstrated. In particular, numerical results for typical problems arising in meteorology, climatology, and remote sensing are shown to be in good agreement with results from other methods and measurements. A sample two-dimensional calculation demonstrates that specific capabilities available in the discrete-ordinates code TWOTRAN can produce new results that are valuable in the characterization of atmospheric effects on remote sensing (e.g., the adjacency effect). The intrinsic limitations of the method are also considered, and it is concluded that the strengths of the discrete-ordinates finite-element method outweigh its weaknesses.

Gerstl, S. A. W.↗

NASA NTRS1999

Recent Development in the Analytical Investigation of Shipboard Rotorcraft Engage and Disengage Operations

This paper presents an overview of recent developments in an effort to predict transient aeroelastic rotor response during shipboard engage and disengage sequences. The blade is modeled as an elastic beam undergoing in flap, lag, extension and torsion. The blade equations of motion are formulated using Hamilton's principle and they are spatially discretized using the finite element method. The discretized blade equations of motion are integrated for a specified rotor speed run-up or run-down profile. Blade element theory is used to calculate quasi-steady or unsteady aerodynamic loads in linear and nonlinear regimes. The analysis is capable of simulating both articulated, hingeless, and gimballed rotor systems. Validation of the rotor code is discussed, including correlation with droop stop impact tests and wind tunnel experiments. Predictions of safe engagement and disengagement envelopes, limited by excessive blade tip deflections or hub moments, are presented. Future directions of study are also discussed.

Smith, Edward C.↗

NASA NTRS1976

The Relation of Finite Element and Finite Difference Methods

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Vinokur, M.↗

NASA NTRS1993

A multigrid solver for the semiconductor equations

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

Bachmann, Bernhard↗

NASA NTRS1988

Computer-aided modeling and prediction of performance of the modified Lundell class of alternators in space station solar dynamic power systems

The main purpose of this project is the development of computer-aided models for purposes of studying the effects of various design changes on the parameters and performance characteristics of the modified Lundell class of alternators (MLA) as components of a solar dynamic power system supplying electric energy needs in the forthcoming space station. Key to this modeling effort is the computation of magnetic field distribution in MLAs. Since the nature of the magnetic field is three-dimensional, the first step in the investigation was to apply the finite element method to discretize volume, using the tetrahedron as the basic 3-D element. Details of the stator 3-D finite element grid are given. A preliminary look at the early stage of a 3-D rotor grid is presented.

Demerdash, Nabeel A. O.↗

NASA NTRS1992

Electromagnetic scattering and radiation from microstrip patch antennas and spirals residing in a cavity

A new hybrid method is presented for the analysis of the scattering and radiation by conformal antennas and arrays comprised of circular or rectangular elements. In addition, calculations for cavity-backed spiral antennas are given. The method employs a finite element formulation within the cavity and the boundary integral (exact boundary condition) for terminating the mesh. By virtue of the finite element discretization, the method has no restrictions on the geometry and composition of the cavity or its termination. Furthermore, because of the convolutional nature of the boundary integral and the inherent sparseness of the finite element matrix, the storage requirement is kept very low at O(n). These unique features of the method have already been exploited in other scattering applications and have permitted the analysis of large-size structures with remarkable efficiency. In this report, we describe the method's formulation and implementation for circular and rectangular patch antennas in different superstrate and substrate configurations which may also include the presence of lumped loads and resistive sheets/cards. Also, various modelling approaches are investigated and implemented for characterizing a variety of feed structures to permit the computation of the input impedance and radiation pattern. Many computational examples for rectangular and circular patch configurations are presented which demonstrate the method's versatility, modeling capability and accuracy.

Volakis, J. L.↗

NASA NTRSDate not supplied

Statistical Descriptors of Composite Fiber Aggregation

This study introduces a method of characterizing fiber aggregation and resin rich regions in composite microstructures. Microscale models of representative elements (RVE) need to be indicative of the extend of clustering (i.e. close fiber-to-fiber interaction) and resin rich “pools” which may impact the overall strength and performance of a composite structure. This algorithm was used to evaluate different unidirectional 2-D microstructure scans, which will be compared to their manufacturing method or any special treatment processes. These cluster and pool scan statistics can be used as criteria to judge statistical equivalency of artificially constructed microstructures.

Statistics↗

NASA NTRS1983

A refined finite element for vibration analysis of twisted blades based on beam theory

A finite element method of discretizing beam segments of pretwisted rotating blades is presented. Employing the matrix displacement method, stiffness and mass properties are developed from basic mechanics of a pretwisted beam theory. By introducing the proper displacement functions, the effect of rotor blade rotational motion on the stiffness matrix is obtained systematically from the kinetic energy expression. Comparing with other beam elements the derivation of this element is more fundamental. This allows one to apply the same approach to more complicated problems including nonlinear effects or complex dynamic motions. Illustrative examples are given comparing numerical results with available data and other numerical solutions from rotating and nonrotating force fields. These examples show that accurate prediction of vibration frequencies for pretwisted blades can be obtained by employing a quite modest number of degrees of freedom.

Sisto, F.↗

NASA NTRS2022

Multi-Scale Modelling of the Bound Metal Deposition Manufacturing of Ti6Al4V

Nonlinear shrinkage of the metal part during manufacturing by bound metal deposition, both on the ground and under microgravity, is considered. A multi-scale physics-based approach is developed to address the problem. It spans timescales from atomistic dynamics on the order of nanoseconds to full-part shrinkage on the order of hours. This approach enables estimation of the key parameters of the problem, including the widths of grain boundaries, the coefficient of surface diffusion, the initial redistribution of particles during the debinding stage, the evolution of the microstructure from round particles to densely-packed grains, the corresponding changes in the total and chemical free energies, and the sintering stress. The method has been used to predict shrinkage at the levels of two particles, of the filament cross-section, of the sub-model, and of the whole green, brown, and metal parts.

Nonlinear shrinkage↗

DOE OSTI2024

A high-resolution pseudo-polygon discrete element model for regional sea ice

Here, this work presents a pseudo-polygon discrete element model for high-resolution sea ice simulations. A scale-invariant bonded particle contact model is proposed to model joints between sea ice floes based on the smeared fracture model and a lattice spring beam model, and the Mohr–Coulomb failure criterion is implemented to represent the shearing failure mechanism of sea ice packings under complex loadings. All mechanical parameters of the bond model can be directly determined from laboratory tests. Validations of the proposed model are made by investigations of mechanical response and failure criteria of field sea ice sheets. Compared with the field observations of sea ice from satellite radar and in situ stress sensors, the proposed model is capable of reproducing the typical constitutive behavior and the Coulomb friction envelope of field sea ice. Finally, the proposed discrete element sea ice model is used to study the effect of loading rates on mechanical behavior including failure strength of regional sea ice.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Unified cohesive zone model (UCZM) for fracturing and fragmenting solids

Here, a Unified Cohesive Zone Model (UCZM), which inherits most of the advantages while overcoming the shortcomings of existing Cohesive Zone Models (CZMs), is proposed. Similar to the traditional extrinsic CZM approach, UCZM dynamically inserts the cohesive elements into the system based on local material states (e.g., stress, strain). However, the transition from continua to discontinua is smoothly achieved, thereby eliminating the “time-discontinuous” issue seen in the extrinsic CZM. Moreover, within the novel UCZM framework, the point of transition from continua to discontinua is controllable through the introduction of crack initialization criteria. As a result, the UCZM allows any material models (e.g., elastic, plastic, damage models) for continuum solids and for discrete fracture behavior to work together. In essence, both an enhanced extrinsic cohesive zone model and an intrinsic cohesive zone model can be represented by the proposed unified model. The proposed UCZM has been verified through different numerical examples. The work demonstrates that the UCZM is a highly effective approach for modeling fracture and fragmentation processes in solids.

42 ENGINEERING↗

DOE OSTI2026

Energy-conserving contact dynamics of nonspherical rigid-body particles

Understanding the contact dynamics of nonspherical particles is crucial for accurately modeling colloidal and granular systems where shape anisotropy dictates structural organization and transport properties. We here introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles by implementing vertex–boundary interactions in 2D and vertex–surface and edge–edge detection in 3D. The established formulation enables continuous force evaluation and prevents particle overlap while conserving total energy during translational and rotational motion. We demonstrate the framework’s stability and its utility to capture packing behavior, anisotropic diffusion, and equations of state of polygonal and polyhedral particles as examples. The framework establishes a robust and extensible foundation for investigating nonequilibrium dynamics of complex nonspherical particulate systems, enabling enhanced understanding of phenomena across spatiotemporal scales in self- and directed-assembly, granular flows, and hydrodynamics, potentially coupled with interactions that represent underlying physical mechanisms.

Discrete element method↗

NASA NTRS1974

Subsonic and supersonic indicial aerodynamics and aerodynamic transfer function for complex configurations

A general theory for indicial-potential-compressible aerodynamics around complex configurations is presented. The motion is assumed to consist of constant subsonic or supersonic speed (steady state) and small perturbations around the steady state. Using the finite-element method to discretize the space problem, a set of differential-difference equations in time relating the potential to its normal derivative on the surface of the body was obtained. The aerodynamics transfer function was derived by using standard method of operational calculus.

Morino, L.↗

NASA NTRS1975

Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations for flutter applications

A general theory for study, oscillatory or fully unsteady potential compressible aerodynamics around complex configurations is presented. Using the finite-element method to discretize the space problem, one obtains a set of differential-delay equations in time relating the potential to its normal derivative which is expressed in terms of the generalized coordinates of the structure. For oscillatory flow, the motion consists of sinusoidal oscillations around a steady, subsonic or supersonic flow. For fully unsteady flow, the motion is assumed to consist of constant subsonic or supersonic speed for time t or = 0 and of small perturbations around the steady state for time t 0.

Tseng, K.↗

NASA NTRS1989

A multi-domain spectral computation of three-dimensional laminar horseshoe vortex flow using incompressible Navier-Stokes equations

Multidomain spectral methods are presently used to numerically simulate a strut-wall intersection's laminar horseshoe vortex flow through direct solution of the three-dimensional, incompressible, time-dependent Navier-Stokes equations. Direct expansion in Chebyshev polynomials and spectral element method spatial discretization of flow dependence are used to achieve high-order accuracy, and minimal dispersion errors. Low and moderate Reynolds number results are presented to illustrate the method application.

Tan, C. S.↗

NASA NTRS1993

LinAir: A multi-element discrete vortex Weissinger aerodynamic prediction method

LinAir is a vortex lattice aerodynamic prediction method similar to Weissinger's extended lifting-line theory, except that the circulation around a wing is represented by discrete horseshoe vortices, not a continuous distribution of vorticity. The program calculates subsonic longitudinal and lateral/directional aerodynamic forces and moments for arbitrary aircraft geometries. It was originally written by Dr. Ilan Kroo of Stanford University, and subsequently modified by the author to simplify modeling of complex configurations. The Polhamus leading-edge suction analogy was added by the author to extend the range of applicability of LinAir to low aspect ratio (i.e., fighter-type) configurations. A brief discussion of the theory of LinAir is presented, and details on how to run the program are given along with some comparisons with experimental data to validate the code. Example input and output files are given in the appendices to aid in understanding the program and its use. This version of LinAir runs in the VAX/VMS, Cray UNICOS, and Silicon Graphics Iris workstation environments at the time of this writing.

Durston, Donald A.↗

NASA NTRS2001

Displacement Models for THUNDER Actuators having General Loads and Boundary Conditions

This paper summarizes techniques for quantifying the displacements generated in THUNDER actuators in response to applied voltages for a variety of boundary conditions and exogenous loads. The PDE (partial differential equations) models for the actuators are constructed in two steps. In the first, previously developed theory quantifying thermal and electrostatic strains is employed to model the actuator shapes which result from the manufacturing process and subsequent repoling. Newtonian principles are then employed to develop PDE models which quantify displacements in the actuator due to voltage inputs to the piezoceramic patch. For this analysis, drive levels are assumed to be moderate so that linear piezoelectric relations can be employed. Finite element methods for discretizing the models are developed and the performance of the discretized models are illustrated through comparison with experimental data.

Wieman, Robert↗