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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A weighted Shifted Boundary Method for free surface flow problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods and was recently introduced for the Poisson, linear advection/diffusion, Stokes, Navier-Stokes, acoustics, and shallow-water equations. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Navier-Stokes flows with moving free-surfaces, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach prevents spurious pressure oscillations in time, which would otherwise be produced if the total active fluid volume were to change abruptly over a time step. In fact, the proposed weighted SBM method induces small mass (i.e., volume) conservation errors, which converge quadratically in the case of piecewise-linear finite element interpolations, as the grid is refined. Finally, we present an extensive set of two- and three-dimensional tests to demonstrate the robustness and accuracy of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Modeling of High-Temperature Corrosion of Zirconium Alloys Using the eXtended Finite Element Method (X-FEM)

Oxidation modeling in modern nuclear fuel performance codes is currently limited by the lack of coupling with mechanics, thus preventing proper description of how high-temperature oxidation impacts mechanical properties. This is mostly due to the fact that the finite difference formalism adopted in corrosion models is incompatible with the direct coupling with mechanics in the finite element modeling employed in modern nuclear fuel performance codes. In this study, a physically based zirconium alloy corrosion model called the Coupled-Current Charge Compensation (C4) model, which was initially developed for operating temperature conditions, has been updated to include high-temperature corrosion in order to provide additional critical information (e.g., oxygen concentration profile) under loss-of-coolant accident (LOCA) conditions—information lacking in existing empirical models. The C4 model was implemented in the MOOSE finite-element framework developed at Idaho National Laboratory, enabling it to be used in the BISON nuclear fuel performance code based on the MOOSE framework. To precisely track the different interfaces at a relatively low computational cost, the eXtended Finite Element Method (X-FEM) was applied in MOOSE. The model’s results were compared to those of existing empirical models as well as metallographic analysis of high-temperature oxidized Zircaloy-4 coupons. Oxygen diffusivities in the a and ß phases resulting from this comparison closely agree with those found in the literature. The C4 model implemented with X-FEM in MOOSE now has the capability to accurately predict oxide, oxygen-stabilized a, and prior ß phase layer growth kinetics under isothermal exposure at high temperature (1000–1500°C). Furthermore, in contrast with the empirical models, the C4 model accounts for the finite thickness of the fuel cladding. It can predict the oxygen concentration profile evolution through the whole cladding, enabling evaluation of the remaining ductile thickness—a crucial variable for modeling the mechanical behavior of the fuel cladding under LOCA. Furthermore, this implementation allows direct coupling with mechanics, at a low computing cost, using finite-element-based nuclear fuel performance codes such as BISON.

36 MATERIALS SCIENCE↗
NASA NTRS1972

Leading-edge force features of the aerodynamic finite element method.

Description of a practical procedure for computing the wing leading-edge thrust distribution by the finite element method. When incorporated into a wing-body aerodynamic computer program, the technique is capable of predicting (at subsonic and supersonic speeds) the leading-edge thrust distribution (and therefore, the lateral-directional stability derivatives due to roll) and the nonlinear aerodynamic characteristics of low aspect-ratio wings with leading edge separation due to the application of suction technology.

Lan, C.-T.↗
DOE OSTI2020

Dirichlet absorbing boundary conditions for classical and peridynamic diffusion-type models

Diffusion-type problems in (nearly) unbounded domains play important roles in various fields of fluid dynamics, biology, and materials science. The aim of this paper is to construct accurate absorbing boundary conditions (ABCs) suitable for classical (local) as well as nonlocal peridynamic (PD) diffusion models. The main focus of the present study is on the PD diffusion formulation. The majority of the PD diffusion models proposed so far are applied to bounded domains only. In this study, we propose an effective way to handle unbounded domains both with PD and classical diffusion models. For the former, we employ a meshfree discretization, whereas for the latter the finite element method (FEM) is employed. The proposed ABCs are time-dependent and Dirichlet-type, making the approach easy to implement in the available models. The performance of the approach, in terms of accuracy and stability, is illustrated by numerical examples in 1D, 2D, and 3D.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Development, Implementation, and Verification of Partially-Ionized Collisional Multifluid Plasma Models in Drekar

We consider the development of multifluid models for partially ionized multispecies plasmas. The models are composed of a standard set of five-moment fluid equations for each species plus a description of electromagnetics. The most general model considered utilizes a full set of fluid equations for each charge state of each atomic species, plus a set of fluid equations for electrons. The fluid equations are coupled through source terms describing electromagnetic coupling, ionization, recombination, charge exchange, and elastic scattering collisions in the low-density coronal limit. The form of each of these source terms is described in detail, and references for required rate coefficients are identified for a diverse range of atomic species. Initial efforts have been made to extend these models to incorporate some higher-density collisional effects, including ionization potential depression and three- body recombination. Some reductions of the general multifluid model are considered. First, a reduced multifluid model is derived which averages over all of the charge states (including neutrals) of each atomic species in the general multifluid model. The resulting model maintains full consistency with the general multifluid model from which it is derived by leveraging a quasi-steady-state collisional ionization equilibrium assumption to recover the ionization fractions required to make use of the general collision models. Further reductions are briefly considered to derive certain components of a single-fluid magnetohydrodynamics (MHD) model. In this case, a generalized Ohm's law is obtained, and the standard MHD resistivity is expressed in terms of the collisional models used in the general multifluid model. A number of numerical considerations required to obtain robust implementations of these multifluid models are discussed. First, an algebraic flux correction (AFC) stabilization approach for a continuous Galerkin finite element discretization of the multifluid system is described in which the characteristic speeds used in the stabilization of the fluid systems are synchronized across all species in the model. It is demonstrated that this synchronization is crucial in order to obtain a robust discretization of the multifluid system. Additionally, several different formulations are considered for describing the electromagnetics portion of the multifluid system using nodal continuous Galerkin finite element discretizations. The formulations considered include a parabolic divergence cleaning method and an implicit projection method for the traditional curl formulation of Maxwell's equations, a purely- hyperbolic potential-based formulation of Maxwell's equations, and a mixed hyperbolic-elliptic potential-based formulation of Maxwell's equations. Some advantages and disadvantages of each formulation are explored to compare solution robustness and the ease of use of each formulation. Numerical results are presented to demonstrate the accuracy and robustness of various components of our implementation. Analytic solutions for a spatially homogeneous damped plasma oscillation are derived in order to verify the implementation of the source terms for electromagnetic coupling and elastic collisions between fluid species. Ionization balance as a function of electron temperature is evaluated for several atomic species of interest by comparing to steady-state calculations using various sets of ionization and recombination rate coefficients. Several test problems in one and two spatial dimensions are used to demonstrate the accuracy and robustness of the discretization and stabilization approach for the fluid components of the multifluid system. This includes standard test problems for electrostatic and electromagnetic shock tubes in the two-fluid and ideal shock-MHD limits, a cylindrical diocotron instability, and the GEM challenge magnetic reconnection problem. A one-dimensional simplified prototype of an argon gas puff configuration as deployed on Sandia's Z-machine is used as a demonstration to exercise the full range of capabilities associated with the general multifluid model.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Islet: interpolation semi-Lagrangian element-based transport

Abstract. Advection of trace species, or tracers, also called tracer transport, in models of the atmosphere and other physical domains is an important and potentially computationally expensive part of a model's dynamical core. Semi-Lagrangian (SL) advection methods are efficient because they permit a time step much larger than the advective stability limit for explicit Eulerian methods without requiring the solution of a globally coupled system of equations as implicit Eulerian methods do. Thus, to reduce the computational expense of tracer transport, dynamical cores often use SL methods to advect tracers. The class of interpolation semi-Lagrangian (ISL) methods contains potentially extremely efficient SL methods. We describe a finite-element ISL transport method that we call the interpolation semi-Lagrangian element-based transport (Islet) method, such as for use with atmosphere models discretized using the spectral element method. The Islet method uses three grids that share an element grid: a dynamics grid supporting, for example, the Gauss–Legendre–Lobatto basis of degree three; a physics parameterizations grid with a configurable number of finite-volume subcells per element; and a tracer grid supporting use of Islet bases with particular basis again configurable. This method provides extremely accurate tracer transport and excellent diagnostic values in a number of verification problems.

58 GEOSCIENCES↗
DOE OSTI2024

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Here, we present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1984

Loads and aeroelasticity division research and technology accomplishments for FY 1983 and plans for FY 1984

Research was done in the following areas: development and validation of solution algorithms, modeling techniques, integrated finite elements for flow-thermal-structural analysis and design, optimization of aircraft and spacecraft for the best performance, reduction of loads and increase in the dynamic structural stability of flexible airframes by the use of active control, methods for predicting steady and unsteady aerodynamic loads and aeroelastic characteristics of flight vehicles with emphasis on the transonic range, and methods for predicting and reducing helicoper vibrations.

Gardner, J. E.↗
DOE OSTI2020

Optimization-based, property-preserving finite element methods for scalar advection equations and their connection to Algebraic Flux Correction

In this paper, we continue our efforts to exploit optimization and control ideas as a common foundation for the development of property-preserving numerical methods. Here we focus on a class of scalar advection equations whose solutions have fixed mass in a given Eulerian region and constant bounds in any Lagrangian volume. Our approach separates discretization of the equations from the preservation of their solution properties by treating the latter as optimization constraints. This relieves the discretization process from having to comply with additional restrictions and makes stability and accuracy the sole considerations in its design. A property-preserving solution is then sought as a state that minimizes the distance to an optimally accurate but not property-preserving target solution computed by the scheme, subject to constraints enforcing discrete proxies of the desired properties. Furthermore, we consider two such formulations in which the optimization variables are given by the nodal solution values and suitably defined nodal fluxes, respectively. A key result of the paper reveals that a standard Algebraic Flux Correction (AFC) scheme is a modified version of the second formulation obtained by shrinking its feasible set to a hypercube. In conclusion, we present numerical studies illustrating the optimization-based formulations and comparing them with AFC

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

The numerical viscosity of entropy stable schemes for systems of conservation laws. I

Discrete approximations to hyperbolic systems of conservation laws are studied. The amount of numerical viscosity present in such schemes is quantified and related to their entropy stability by means of comparison.To this end, conservative schemes which are also entropy-conservative are constructed. These entropy-conservative schemes enjoy second-order accuracy; moreover, they can be interpreted as piecewise-linear finite-element methods, and hence can be formulated on various mesh configurations. It is then shown that conservative schemes are entropy stable, if and (for three-point schemes) only they contain more viscosity than that present in the above-mentioned entropy-conservative ones.

Tadmor, Eitan↗
DOE OSTI2024

Sequential formulation of all‐way coupled finite strain thermoporomechanics for largely deformable gas hydrate deposits

We develop a numerically stable sequential formulation of thermoporomechanics for largely deformable gas hydrate deposits, extended from the fixed stress split of infinitesimal transformation. Constitutive equations are based on the total Lagrangian approach for both flow and geomechanics, including dynamic full tensor permeability and thermal conductivity updated from the deformation gradient. For space discretization, we take the cell-centered finite volume and node-based finite element method for flow and geomechanics, respectively. Then, we propose a sequential implicit method for all-way coupled thermoporomechanics, where the nonisothermal multiphase flow problem of gas hydrates is solved implicitly first and then the geomechanics problem is solved implicitly at the next step. During solution of the flow problem, we fix the rate of first Pioal total stress for numerical stability as well as apply porosity correction and entropy correction to account for geomechanical effects. We test numerical examples where flow and geomechanics parameters are based on deep oceanic gas hydrate deposits. When applying depressurization, even though the results between the infinitesimal transformation and finite strain geomechanics are similar in the early stages due to small deformation, we find differences between them in the late times as deformation becomes large. Accordingly, permeability and thermal conductivity tensors become nonisotropic full tensors although they are initially isotropic. Furthermore, we identify numerical stability of the developed sequential method from the test cases that exhibit the highly complex coupled gas hydrate systems with large deformation. Thus, the proposed sequential formulation can be applied in largely deformable gas hydrate systems.

42 ENGINEERING↗
NASA NTRS1990

Adaptive quadrilateral and triangular finite-element scheme for compressible flows

The development of an adaptive mesh refinement procedure for analyzing high-speed compressible flows using the finite-element method is described. This new adaptation procedure, which uses both quadrilateral and triangular elements, was implemented with two explicit finite-element algorithms - the two-step Taylor-Galerkin and the multistep Galerkin-Runge-Kutta schemes. A von Neumann stability analysis and a rotating 'cosine hill'problem demonstrate the instability of the Taylor-Galerkin scheme when coupled with the adaptation procedure. For the same adaptive refinement scheme, the Galerkin-Runge-Kutta procedure yields stable solutions within its explicit stability limit. The utility of this new adaptation procedure for the prediction of compressible flow features is illustrated for inviscid problems involving strong shock interactions at hypersonic speeds.

Ramakrishnan, R.↗
NASA NTRS2007

An Aeroelastic Analysis of a Thin Flexible Membrane

Studies have shown that significant vehicle mass and cost savings are possible with the use of ballutes for aero-capture. Through NASA's In-Space Propulsion program, a preliminary examination of ballute sensitivity to geometry and Reynolds number was conducted, and a single-pass coupling between an aero code and a finite element solver was used to assess the static aeroelastic effects. There remain, however, a variety of open questions regarding the dynamic aeroelastic stability of membrane structures for aero-capture, with the primary challenge being the prediction of the membrane flutter onset. The purpose of this paper is to describe and begin addressing these issues. The paper includes a review of the literature associated with the structural analysis of membranes and membrane utter. Flow/structure analysis coupling and hypersonic flow solver options are also discussed. An approach is proposed for tackling this problem that starts with a relatively simple geometry and develops and evaluates analysis methods and procedures. This preliminary study considers a computationally manageable 2-dimensional problem. The membrane structural models used in the paper include a nonlinear finite-difference model for static and dynamic analysis and a NASTRAN finite element membrane model for nonlinear static and linear normal modes analysis. Both structural models are coupled with a structured compressible flow solver for static aeroelastic analysis. For dynamic aeroelastic analyses, the NASTRAN normal modes are used in the structured compressible flow solver and 3rd order piston theories were used with the finite difference membrane model to simulate utter onset. Results from the various static and dynamic aeroelastic analyses are compared.

Scott, Robert C.↗
NASA NTRS1996

H Infinity Control of Magnetic Bearings to Ensure Both System and External Periodic Disturbance Robustness

Both self-excited and forced disturbances often lead to severe rotor vibrations in a magnetic bearing systems with long slender shafts. This problem has been studied using the H-infinity method, and stability with good robustness can be achieved for the linearized model of a magnetic bearing when small transient disturbances are applied. In this paper, the H-infinity control method for self-excited and forced disturbances is first reviewed. It is then applied to the control of a magnetic bearing rotor system. In modelling the system, the shaft is first discretized into 18 finite elements and then three levels of condensation are applied. This leads to a system with three masses and three compliant elements which can be described by six state variable coordinates. Simulation of the resultant system design has been performed at speeds up to 10,000 rpm. Disturbances in terms of different initial displacements, initial impulses, and external periodic inputs have been imposed. The simulation results show that good stability can be achieved under these different transient disturbances using the proposed controller while at the same time reducing the sensitivity to external periodic disturbances.

Jiang, Yuhong↗
DOE OSTI2021

A Segregated Approach for Modeling the Electrochemistry in the 3-D Microstructure of Li-Ion Batteries and Its Acceleration Using Block Preconditioners

Abstract Battery performance is strongly correlated with electrode microstructure. Electrode materials for lithium-ion batteries have complex microstructure geometries that require millions of degrees of freedom to solve the electrochemical system at the microstructure scale. A fast-iterative solver with an appropriate preconditioner is then required to simulate large representative volume in a reasonable time. In this work, a finite element electrochemical model is developed to resolve the concentration and potential within the electrode active materials and the electrolyte domains at the microstructure scale, with an emphasis on numerical stability and scaling performances. The block Gauss-Seidel (BGS) numerical method is implemented because the system of equations within the electrodes is coupled only through the nonlinear Butler–Volmer equation, which governs the electrochemical reaction at the interface between the domains. The best solution strategy found in this work consists of splitting the system into two blocks—one for the concentration and one for the potential field—and then performing block generalized minimal residual preconditioned with algebraic multigrid, using the FEniCS and the Portable, Extensible Toolkit for Scientific Computation libraries. Significant improvements in terms of time to solution (six times faster) and memory usage (halving) are achieved compared with the MUltifrontal Massively Parallel sparse direct Solver. Additionally, BGS experiences decent strong parallel scaling within the electrode domains. Last, the system of equations is modified to specifically address numerical instability induced by electrolyte depletion, which is particularly valuable for simulating fast-charge scenarios relevant for automotive application.

25 ENERGY STORAGE↗
NASA NTRS1987

Analysis of structures with rotating, flexible substructures applied to rotorcraft aeroelasticity in GRASP

Application to the General Rotorcraft Aeromechanical Stability Program (GRASP) of new methodology for structural dynamic analysis, including substructuring, frames of reference, nodes, finite elements, and constraints, is discussed. The structure is decomposed into a hierarchy of substructures, and discrete relative motion between substructures is analyzed exactly. The finite element method is used to treat deformation of continua, and the library of finite elements includes a nonlinear beam element incorporating aeroelastic effects. Analytical bases for the aeroelastic beam element and the screw constraint are considered, and the important role of geometric stiffness in the formulation is shown.

Hodges, Dewey H.↗
NASA NTRS1985

Numerical solution of the vertical structure equation in the normal mode method

In the present model of multilayered stability stratification, aimed at obtaining the analytic eigensolutions of the vertical structure equation, each layer is characterized by its own static stability value. By requiring continuity of pressure and vertical velocity across each interface level, and by imposing suitable upper and lower boundary conditions, matching eigensolutions are obtained in terms of the Bessel functions. Attention is given to an explicit example of a double-layered stratified atmosphere which demonstrates the mathematical manipulations involved; the resultant vertical structure functions are used to check the accuracy of the numerical solutions by the finite difference and finite element methods.

Sasaki, Y. K.↗
NASA NTRS1982

Profiles of electrified drops and bubbles

Axisymmetric equilibrium shapes of conducting drops and bubbles, (1) pendant or sessile on one face of a circular parallel-plate capacitor or (2) free and surface-charged, are found by solving simultaneously the free boundary problem consisting of the augmented Young-Laplace equation for surface shape and the Laplace equation for electrostatic field, given the surface potential. The problem is nonlinear and the method is a finite element algorithm employing Newton iteration, a modified frontal solver, and triangular as well as quadrilateral tessellations of the domain exterior to the drop in order to facilitate refined analysis of sharply curved drop tips seen in experiments. The stability limit predicted by this computer-aided theoretical analysis agrees well with experiments.

Basaran, O. A.↗