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At least 793 records · Page 44

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NASA NTRS1991

Grid generation about complex three-dimensional aircraft configurations

The problem of obtaining three dimensional grids with sufficient resolution to resolve all the flow or other physical features of interest is addressed. The generation of a computational grid involves a series of compromises to resolve several conflicting requirements. On one hand, one would like the grid to be fine enough and not too skewed to reduce the numerical errors and to adequately resolve the pertinent physical features of the flow field about the aircraft. On the other hand, the capabilities of present or even future supercomputers are finite and the number of mesh points must be limited to a reasonable number: one which is usually much less than desired for numerical accuracy. One technique to overcome this limitation is the 'zonal' grid approach. In this method, the overall field is subdivided into smaller zones or blocks in each of which an independent grid is generated with enough grid density to resolve the flow features in that zone. The zonal boundaries or interfaces require special boundary conditions such that the conservation properties of the governing equations are observed. Much work was done in 3-D zonal approaches with nonconservative zonal interfaces. A 3-D zonal conservative interfacing method that is efficient and easy to implement was developed during the past year. During the course of the work, it became apparent that it would be much more feasible to do the conservative interfacing with cell-centered finite volume codes instead of the originally planned finite difference codes. Accordingly, the CNS code was converted to finite volume form. This new version of the code is named CNSFV. The original multi-zonal interfacing capability of the CNS code was enhanced by generalizing the procedure to allow for completely arbitrarily shaped zones with no mesh continuity between the zones. While this zoning capability works well for most flow situations, it is, however, still nonconservative. The conservative interface algorithm was also implemented but was not completely validated.

Klopfer, Goetz H.↗

NASA NTRSDate not supplied

A Numerical Method for Computing the State Transition Matrix Using Poincare Integral Invariants

The Poincare integral invariants describe the volumes of sets in Hamiltonian phase space. We use these invariants to derive a new numerical procedure for obtaining the state transition matrix (STM), which can be applied to both conservative and nonconservative systems. The method is analogous to a finite difference approximation of the STM, where perturbed states are numerically propagated along with the reference trajectory. We discuss the mathematical similarities between this new STM and existing methods, show numerical results for orbital motion and uncertainty propagation, and discuss new insights afforded by the Hamiltonian properties of phase flow.

state transition matrix↗

DOE OSTI2024

Oil-Pressure Based Apparatus for In-Situ High-Energy Synchrotron X-Ray Diffraction Studies During Biaxial Deformation

Background: Understanding biaxial loading response at the microstructural level is crucial in helping better design sheet manufacturing processes and calibrate/validate material deformation models. Objective: The objective of this work was to develop a low-cost testing apparatus to probe, with sufficient spatial resolution, the micro-mechanical response of a sheet material in-situ under biaxial loading conditions. Methods: The testing apparatus fabricated as a part of this study operates in a similar fashion to a standard bulge test and uses oil pressure to generate biaxial loading conditions. This biaxial testing apparatus was operated within a synchrotron beamline to characterize the mechanical response of a flash-processed steel sheet using in-situ high-energy X-ray diffraction (XRD) measurements. Further, the GSAS-II package was utilized to develop a workflow for the analysis of the large volume of diffraction data acquired. The workflow was then used to extract the peak position, width, and integrated intensity of the XRD peaks corresponding to the major body-centered cubic phase. Results: The equi-biaxial nature of the loading in the measured area was independently corroborated using experimental (XRD) and simulation (finite element analysis) methods. Furthermore, we discuss the evolution of elastic strain in the major body-centered cubic phase as a function of applied oil pressure and location on the steel sheet. Conclusions: A key advantage of the biaxial apparatus fabricated in this synchrotron study is demonstrated using the results obtained for the flash-processed steel sheet – i.e., mapping the lattice plane-dependent response to biaxial loading for a relatively large sample area in a spatially resolved manner.

36 MATERIALS SCIENCE↗

NASA NTRS1969

ELAS: A general-purpose computer program for the equilibrium problems of linear structures. Volume 2: Documentation of the program

A general purpose digital computer program for the in-core solution of linear equilibrium problems of structural mechanics is documented. The program requires minimum input for the description of the problem. The solution is obtained by means of the displacement method and the finite element technique. Almost any geometry and structure may be handled because of the availability of linear, triangular, quadrilateral, tetrahedral, hexahedral, conical, triangular torus, and quadrilateral torus elements. The assumption of piecewise linear deflection distribution insures monotonic convergence of the deflections from the stiffer side with decreasing mesh size. The stresses are provided by the best-fit strain tensors in the least squares at the mesh points where the deflections are given. The selection of local coordinate systems whenever necessary is automatic. The core memory is used by means of dynamic memory allocation, an optional mesh-point relabelling scheme and imposition of the boundary conditions during the assembly time.

Utku, S.↗

DOE OSTI2021

Powder spreading, densification, and part deformation in binder jetting additive manufacturing

Binder jetting additive manufacturing (AM) can print complex structures in economical and scalable manner. Binder jetting AM comprises of deposition and weak binding of particles, known as green part, at room temperature and subsequent binder removal and sintering densification at high temperatures. However, during the densification (i.e., sintering), the part significantly deforms due to volume shrinkage. The deformation during sintering is difficult to predict, which prevents the widespread application of this technology. In this research, powder spreading simulation using discrete element method (DEM) was performed first to capture local variations in powder bed configuration. Second, finite element method (FEM) with a phenomenological continuum constitutive model was used to predict part shrinkage during the sintering process. DEM simulation showed variations in packing density, particle segregation, formation of uneven powder bed surface, and shift in particle size distribution (PSD). The sintering simulation modeled part deformation with a reasonable accuracy of 3% for solid-state sintering and intermediate liquid phase sintering. A demonstration case with non-uniform initial packing density showed that inhomogeneous green part density and PSD should be accounted for prediction of part deformation in binder jetting AM.

36 MATERIALS SCIENCE↗

NASA NTRS1988

Three-dimensional multigrid algorithms for the flux-split Euler equations

The Full Approximation Scheme (FAS) multigrid method is applied to several implicit flux-split algorithms for solving the three-dimensional Euler equations in a body fitted coordinate system. Each of the splitting algorithms uses a variation of approximate factorization and is implemented in a finite volume formulation. The algorithms are all vectorizable with little or no scalar computation required. The flux vectors are split into upwind components using both the splittings of Steger-Warming and Van Leer. The stability and smoothing rate of each of the schemes are examined using a Fourier analysis of the complete system of equations. Results are presented for three-dimensional subsonic, transonic, and supersonic flows which demonstrate substantially improved convergence rates with the multigrid algorithm. The influence of using both a V-cycle and a W-cycle on the convergence is examined.

Anderson, W. Kyle↗

NASA NTRS1994

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Slack, David C.↗

NASA NTRS1995

Implicit method for the computation of unsteady flows on unstructured grids

An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.

Venkatakrishnan, V.↗

NASA NTRS2017

The Root Cause of the Overheating Problem

Previously we identified the receding flow, where two fluid streams recede from each other, as an open numerical problem, because all well-known numerical fluxes give an anomalous temperature rise, thus called the overheating problem. This phenomenon, although presented in several textbooks, and many previous publications, has scarcely been satisfactorily addressed and the root cause of the overheating problem not well understood. We found that this temperature rise was solely connected to entropy rise and proposed to use the method of characteristics to eradicate the problem. However, the root cause of the entropy production was still unclear. In the present study, we identify the cause of this problem: the entropy rise is rooted in the pressure flux in a finite volume formulation and is implanted at the first time step. It is found theoretically inevitable for all existing numerical flux schemes used in the finite volume setting, as confirmed by numerical tests. This difficulty cannot be eliminated by manipulating time step, grid size, spatial accuracy, etc, although the rate of overheating depends on the flux scheme used. Finally, we incorporate the entropy transport equation, in place of the energy equation, to ensure preservation of entropy, thus correcting this temperature anomaly. Its applicability is demonstrated for some relevant 1D and 2D problems. Thus, the present study validates that the entropy generated ab initio is the genesis of the overheating problem.

Liou, Meng-Sing↗

DOE OSTI2022

Hardness Prediction by Incorporating Heat Transfer and Molten Pool Fluid Flow in a Multi-pass, Multi-layer Weld for Onsite Repair of Grade 91 steel

Introduction: In the current fleet of fossil-fired power plants, creep strength enhanced ferritic steels (CSEF) are used to sustain the harsh service conditions. Enhanced properties of Grade 91 steel result from tempered martensite with a fine distribution of MX and M23C6 carbides. Grade 91 steel is subjected to onsite welding repair to remedy their degradation due to extreme service condition. Knowledge of weld repairability of these steels, such as as-welded hardness distribution, is essential to establishing sound repair procedures. Experimental trial and error tests can consume a lot of time as many welding variables need to be studied. For numerical modelling, most of the multi-pass multi-layer models are based on finite element method, which are limited to solve the heat conduction equation and ignore convective heat transfer due to melt flow. Moreover, the mesh has to be pre-built based on a known or assumed weld cross-section geometry. These finite element based models thus have limited predictive capability as defects are not considered and nugget size are pre-assumed. This research aims at developing a thermal and microstructure evolution model incorporating molten pool dynamics in a multi-pass multi-layer material deposition to predict the as-welded hardness distribution. Technical Approach: All the thermal, physical, and metallurgical properties of Grade 91 as a function of temperature are collected from the literature and inputted into the thermo-fluid model based on Flow-3D, a computational fluid dynamics software. A multi-pass, multi-layer material deposition is simulated where the melting of filler wire into the molten pool is directly considered based on the volume of fluid (VOF) method. The flow behaviour of the molten pool is used to understand the formation of deposition geometry and defects. The temperature profiles during the multi-pass, multi-layer welding are calculated. The results computed using the new model are compared against the experimental data of fusion zone geometry and thermal cycles. Hardness prediction in the heat-affected zone (HAZ) are made using Johnson-Mehl-Avrami (JMA) equation for solid-state phase transformation kinetics. The JMA parameters are extracted from the experimental data available in the literature. For comparison, a standard finite element heat conduction model is also developed to predict the thermal cycles and hardness distribution in the multi-pass, multi-layer weld. Expected Result: Results obtained using the molten pool dynamic simulation versus the finite element heat conduction model are compared. Specifically, the effects of convective heat transfer on the accuracy of the calculated thermal history, bead shape and size, and HAZ hardness distribution are examined.

Modeling, Grade 91 steel, Multi-pass multi-layer d↗

NASA NTRS1996

Coupled Structural, Thermal, Phase-change and Electromagnetic Analysis for Superconductors, Volume 2

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromag subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermel and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. Volume 1 describes mostly formulation specific problems. Volume 2 describes generalization of those formulations.

Felippa, C. A.↗

DOE OSTI2025

Response tailoring of elasto-plastic trusses

Abstract In this work we tailor the response of trusses loaded beyond their yield limit. The truss structures are modeled using finite strain theory and rate-independent elasto-plasticity. We design trusses with a tailored mechanical response that is between “elastic” and “elastic-ideal-plastic” subject to the volume constraint. The design updates are generated by the gradient-based Method of Moving Asymptotes (MMA) solver and the sensitivities of the response functions are computed using a path-dependent adjoint sensitivity analysis. The computations are performed in Matlab.

42 ENGINEERING↗

DOE OSTI2026

Scattering Processes from Quantum Simulation Algorithms for Scalar Field Theories

We provide practical simulation methods for scalar field theories on a quantum computer that yield improved asymptotics as well as concrete gate estimates for the simulation and physical qubit estimates using the surface code. We achieve these improvements through two optimizations. First, we consider a finite volume approach for estimating the elements of the S-matrix. This approach is appropriate in general for 1+1D and for certain low-energy elastic collisions in higher dimensions. Second, we implement our approach using a series of different fault-tolerant simulation algorithms for Hamiltonians formulated both in the field occupation basis and field amplitude basis. Our algorithms are based on either second-order Trotterization or qubitization. The cost of Trotterization in occupation basis scales as O ( λ N 7 | Ω | 3 / ( M 5 / 2 ϵ 3 / 2 ) ) where λ is the coupling strength, N is the occupation cutoff, | Ω | is the volume of the spatial lattice, M is the mass of the particles and ϵ is the uncertainty in the energy calculation used for the S -matrix determination. Qubitization in the field basis scales as O ( | Ω | 2 ( k 2 Λ + k M 2 ) / ϵ ) , where k is the cutoff in the field and Λ is a scaled coupling constant. We find in both cases that the bounds suggest physically meaningful simulations can be performed using on the order of 4 × 10 6 physical qubits and 10 12 T -gates which corresponds to roughly one day on a superconducting quantum computer with surface code and a cycle time of 100 ns. This places the simulation of scalar field theory within striking distance of the gate counts for the best available chemistry simulation results.

Hardy, Andrew [Toronto U.] (ORCID:0000000235817382↗

NASA NTRS1976

Numerical simulation of low gravity draining

A boundary value problem was solved numerically for a liquid that is assumed to be inviscid and incompressible, having a motion that is irrotational and axisymmetric, and having a constant (5 degrees) solid-liquid contact angle. The avoidance of excessive mesh distortion, encountered with strictly Lagrangian or Eulerian kinematics, was achieved by introducing an auxiliary kinematic velocity field along the free surface in order to vary the trajectories used in integrating the ordinary differential equations simulating the moving boundary. The computation of the velocity potential was based upon a nonuniform triangular mesh which was automatically revised to varying depths to accommodate the motion of the free surface. These methods permitted calculation of draining induced axisymmetric slosh through the many (or fractional) finite amplitude oscillations that can occur depending upon the balance of draining, gravitational, and surface tension forces. Velocity fields, evolution of the free surface with time, and liquid residual volumes were computed for three and one half decades of Weber number and for two Bond numbers, tank fill levels, and drain radii. Comparisons with experimental data are very satisfactory.

Bizzell, G. D.↗

NASA NTRS1990

Surface-crack growth: Models, experiments, and structures; Proceedings of the Symposium, Sparks, NV, Apr. 25, 1988

The present volume on surface-crack growth modeling, experimental methods, and structures, discusses elastoplastic behavior, the fracture analysis of three-dimensional bodies with surface cracks, optical measurements of free-surface effects on natural surfaces and through cracks, an optical and finite-element investigation of a plastically deformed surface flaw under tension, fracture behavior prediction for rapidly loaded surface-cracked specimens, and surface cracks in thick laminated fiber composite plates. Also discussed are a novel study procedure for crack initiation and growth in thermal fatigue testing, the growth of surface cracks under fatigue and monotonically increasing load, the subcritical growth of a surface flaw, surface crack propagation in notched and unnotched rods, and theoretical and experimental analyses of surface cracks in weldments.

Reuter, Walter G.↗

NASA NTRS1993

Two-dimensional CFD modeling of wave rotor flow dynamics

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. The Roe approximate Riemann solution scheme or the computationally less expensive Advection Upstream Splitting Method (AUSM) flux-splitting scheme are used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passage and the distribution of flow variables in the stationary inlet port region.

Welch, Gerard E.↗

NASA NTRS1994

Two-dimensional CFD modeling of wave rotor flow dynamics

A two-dimensional Navier-Stokes solver developed for detailed study of wave rotor flow dynamics is described. The CFD model is helping characterize important loss mechanisms within the wave rotor. The wave rotor stationary ports and the moving rotor passages are resolved on multiple computational grid blocks. The finite-volume form of the thin-layer Navier-Stokes equations with laminar viscosity are integrated in time using a four-stage Runge-Kutta scheme. Roe's approximate Riemann solution scheme or the computationally less expensive advection upstream splitting method (AUSM) flux-splitting scheme is used to effect upwind-differencing of the inviscid flux terms, using cell interface primitive variables set by MUSCL-type interpolation. The diffusion terms are central-differenced. The solver is validated using a steady shock/laminar boundary layer interaction problem and an unsteady, inviscid wave rotor passage gradual opening problem. A model inlet port/passage charging problem is simulated and key features of the unsteady wave rotor flow field are identified. Lastly, the medium pressure inlet port and high pressure outlet port portion of the NASA Lewis Research Center experimental divider cycle is simulated and computed results are compared with experimental measurements. The model accurately predicts the wave timing within the rotor passages and the distribution of flow variables in the stationary inlet port region.

Welch, Gerard E.↗

NASA NTRS1998

Congruence Approximations for Entrophy Endowed Hyperbolic Systems

Building upon the standard symmetrization theory for hyperbolic systems of conservation laws, congruence properties of the symmetrized system are explored. These congruence properties suggest variants of several stabilized numerical discretization procedures for hyperbolic equations (upwind finite-volume, Galerkin least-squares, discontinuous Galerkin) that benefit computationally from congruence approximation. Specifically, it becomes straightforward to construct the spatial discretization and Jacobian linearization for these schemes (given a small amount of derivative information) for possible use in Newton's method, discrete optimization, homotopy algorithms, etc. Some examples will be given for the compressible Euler equations and the nonrelativistic MHD equations using linear and quadratic spatial approximation.

Barth, Timothy J.↗