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DOE OSTI2023

Sierra/Solid Mechanics 5.16 User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutions of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.

36 MATERIALS SCIENCE↗

NASA NTRS1983

Computational methods for ideal compressible flow

Conservative dissipative difference schemes for computing one dimensional flow are introduced, and the recognition and representation of flow discontinuities are discussed. Multidimensional methods are outlined. Second order finite volume schemes are introduced. Conversion of difference schemes for a single linear convection equation into schemes for the hyperbolic system of the nonlinear conservation laws of ideal compressible flow is explained. Approximate Riemann solvers are presented. Monotone initial value interpolation; and limiters, switches, and artificial dissipation are considered.

Vanleer, B.↗

NASA NTRS1989

Determination of near and far field acoustics for advanced propeller configurations

A method has been studied for predicting the acoustic field of the SR-3 transonic propfan using flow data generated by two versions of the NASPROP-E computer code. Since the flow fields calculated by the solvers include the shock-wave system of the propeller, the nonlinear quadrupole noise source term is included along with the monopole and dipole noise sources in the calculation of the acoustic near field. Acoustic time histories in the near field are determined by transforming the azimuthal coordinate in the rotating, blade-fixed coordinate system to the time coordinate in a nonrotating coordinate system. Fourier analysis of the pressure time histories is used to obtain the frequency spectra of the near-field noise.

Korkan, K. D.↗

NASA NTRS1994

Optimized design of a hypersonic nozzle

Conventional procedures for designing nozzles involve the design of an inviscid contour (using the method of characteristics) that is corrected with a displacement thickness calculated from boundary-layer theory. However, nozzles designed using this classical procedure have been shown to exhibit poor flow quality at Mach numbers characteristic of hypersonic applications. The nozzle to be designed will be a part of the NASA HYPULSE facility which is being used for hypervelocity flight research. Thus, the flow quality of the nozzle is a critical question that needs to be addressed. Design of nozzles for hypersonic applications requires a proper assessment of the effects of the thick boundary layer on the inviscid flowfield. Since the flow field is largely supersonic, the parabolized form of the Navier-Stokes (PNS) equations can be used. The requirement of a uniform flow at the exit plane of the nozzle can be used to define an objective function as part of an optimization procedure. The design procedure used in this study involves the coupling of a nonlinear (least-squares) optimization algorithm with an efficient, explicit PNS solver. The thick boundary layers growing on the walls of the nozzle limit the extent of the usable core region (region with uniform flow) for testing models (especially rectangular). In order to maximize the region of uniform flow, it was decided to have the exit plane of this nozzle to be (nearly) rectangular. Thus, an additional constraint on the nozzle shape resulted, namely the nozzle will have a shape transitioning from a circular one at the inlet to that of a rectangle at the exit. In order to provide for a smooth shape transition, the cross sectional contour of the nozzle is defined by a superellipse. The nozzle is taken to be a meter in length. The axial variations of the major and minor radii of the superellipse are governed by cubic splines. The design parameters are the coefficients of the splines associated with the local nozzle wall slopes. Extensive calculations have been made (with a three-dimensional Euler code) to understand the effects of various parameters such as location of the knot points of the spline function, different ways of characterizing the uniformity of the flow in the exit plane, as well as the effect of constraining the area of the nozzle to be invariant. Turbulent flow (measurements indicate that the flow at the nozzle inlet is turbulent) calculations are now being performed (with the inviscidly designed nozzle contours) to assess the flow quality.

Krishnamurthy, Ramesh↗

NASA NTRS1999

Development of a Multiobjective Optimization Procedure for Sonic Boom Minimization

A design optimization procedure for improved sonic boom and aerodynamic performance of high speed aircraft is presented. The multiobjective optimization procedure simultaneously minimizes the sonic boom at a given distance from the aircraft and the drag-to-lift ratio (C(sub D)/C(sub L)) Of the aircraft. Upper and lower bounds are also imposed on the lift coefficient. The Kreisselmeier - Steinhauser function is used for the multiobjective optimization formulation. A discrete semi-analytical aerodynamic sensitivity analysis procedure coupled with an analytical grid sensitivity analysis technique is used for evaluating design sensitivities. The use of the semi-analytical sensitivity analysis techniques results in significant computational savings. The flow equations are solved using a three-dimensional parabolized Navier-Stokes solver. Sonic boom analysis is performed using an extrapolation procedure. A nonlinear programming technique and an approximate analysis procedure are used for the optimization. The optimization procedure developed is applied to the design of two high speed configurations, namely, a doubly swept wing-body configuration and a delta wing-body configuration. For the two sweep case only, minimization of the first peak in the pressure signature is performed first by optimizing only the nose radius and length of the aircraft. Minimization of the second peak in the pressure signature is performed next by optimizing only the wing geometric parameters. Significant improvements are obtained in the sonic boom characteristics and the aerodynamic performance of the wing-body configurations.

Narayan, J. R.↗

NASA NTRS2002

Development of Reduced-Order Models for Aeroelastic and Flutter Prediction Using the CFL3Dv6.0 Code

A reduced-order model (ROM) is developed for aeroelastic analysis using the CFL3D version 6.0 computational fluid dynamics (CFD) code, recently developed at the NASA Langley Research Center. This latest version of the flow solver includes a deforming mesh capability, a modal structural definition for nonlinear aeroelastic analyses, and a parallelization capability that provides a significant increase in computational efficiency. Flutter results for the AGARD 445.6 Wing computed using CFL3D v6.0 are presented, including discussion of associated computational costs. Modal impulse responses of the unsteady aerodynamic system are then computed using the CFL3Dv6 code and transformed into state-space form. Important numerical issues associated with the computation of the impulse responses are presented. The unsteady aerodynamic state-space ROM is then combined with a state-space model of the structure to create an aeroelastic simulation using the MATLAB/SIMULINK environment. The MATLAB/SIMULINK ROM is used to rapidly compute aeroelastic transients including flutter. The ROM shows excellent agreement with the aeroelastic analyses computed using the CFL3Dv6.0 code directly.

Silva, Walter A.↗

NASA NTRS2017

Comparisons Between NO PLIF Imaging and CFD Simulations of Mixing Flowfields for High-Speed Fuel Injectors

The current work compares experimentally and computationally obtained nitric oxide (NO) planar laser induced fluorescence (PLIF) images of the mixing flowfields for three types of high-speed fuel injectors: a strut, a ramp, and a rectangular flushwall. These injection devices, which exhibited promising mixing performance at lower flight Mach numbers, are currently being studied as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center. The EIMP aims to investigate scramjet fuel injection and mixing physics, and improve the understanding of underlying physical processes relevant to flight Mach numbers greater than eight. In the experiments, conducted in the NASA Langley Arc-Heated Scramjet Test Facility (AHSTF), the injectors are placed downstream of a Mach 6 facility nozzle, which simulates the high Mach number air flow at the entrance of a scramjet combustor. Helium is used as an inert substitute for hydrogen fuel. Both schlieren and PLIF techniques are applied to obtain mixing flowfield flow visualizations. The experimental PLIF is obtained by using a UV laser sheet to interrogate a plane of the flow by exciting fluorescence from the NO molecules, which are present in the AHSTF air. Consequently, the absence of signal in the resulting PLIF images is an indication of pure helium (fuel). The computational PLIF is obtained by applying a fluorescence model for NO to the results of the Reynolds-averaged simulations (RAS) of the mixing flow field carried out using the VULCAN-CFD solver. This approach is required because the PLIF signal is a nonlinear function of not only NO concentration, but also pressure, temperature, and the flow velocity. This complexity allows additional flow features to be identified and compared with those obtained from the computational fluid dynamics (CFD) simulations, however, such comparisons are only semiquantitative. Three-dimensional image reconstruction, similar to that used in magnetic resonance imaging, is also used to obtain images in the streamwise and spanwise planes from select cross-stream PLIF plane data. Synthetic schlieren is also computed from the RAS data. Good agreement between the experimental and computational results provides increased confidence in the CFD simulations for investigations of injector performance.

Drozda, Tomasz G.↗

NASA NTRSDate not supplied

Comparisons Between NO PLIF Imaging and CFD Simulations of Mixing Flowfields for High-Speed Fuel Injectors

The current work compares experimentally and computationally obtained nitric oxide (NO) planar laser-induced fluorescence (PLIF) images of the mixing flowfields for three types of high-speed fuel injectors: a strut, a ramp, and a rectangular flushwall. These injection devices, which exhibited promising mixing performance at lower flight Mach numbers, are currently being studied as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center. The EIMP aims to investigate scramjet fuel injection and mixing physics, and improve the understanding of underlying physical processes relevant to flight Mach numbers greater than eight. In the experiments conducted in the NASA Langley Arc-Heated Scramjet Test Facility (AHSTF), the injectors are placed downstream of a Mach 6 facility nozzle, which simulates the high Mach number air flow at the entrance of a scramjet combustor. Helium is used as an inert substitute for hydrogen fuel. Both schlieren and PLIF techniques are applied to obtain mixing flowfield flow visualizations. The experimental PLIF is obtained by using a UV laser sheet to interrogate a plane of the flow by exciting fluorescence from the NO molecules that are present in the AHSTF air. Consequently, the absence of signal in the resulting PLIF images is an indication of pure helium (fuel). The computational PLIF is obtained by applying a fluorescence model for NO to the results of the Reynolds-averaged simulations (RAS) of the mixing flowfield carried out using the VULCAN-CFD solver. This approach is required because the PLIF signal is a nonlinear function of not only NO concentration, but also pressure, temperature, and the flow velocity. This complexity allows additional flow features to be identified and compared with those obtained from the computational fluid dynamics (CFD) simulations, however, such comparisons are only semiquantitative. Three-dimensional image reconstruction, similar to that used in magnetic resonance imaging, is also used to obtain images in the streamwise and spanwise planes from select cross-stream PLIF plane data. Synthetic schlieren is also computed from the RAS data. Good agreement between the experimental and computational results provides increased confidence in the CFD simulations for investigations of injector performance.

PLIF↗

NASA NTRSDate not supplied

Comparisons Between NO PLIF Imaging and CFD Simulations of Mixing Flowfields for High-Speed Fuel Injectors

PLIF↗

DOE OSTI2021

Nonlinear convergence in contact mechanics: Immersed boundary finite volume

In this report we present an immersed boundary finite volume (IBM) method for simulating quasistatic contact mechanics of linearly elastic domains at small strains. In IBM, all external boundaries and internal contacts of an object are represented by embedded surfaces inside a Cartesian mesh, which need not conform to the grid lines. The contact constraints consist of the non-penetrability condition and Coulomb’s friction law, which are discretized using special interpolation stencils and enforced via penalty parameters. The resulting nonlinear system depends on displacement unknowns only. To solve it, we use the Newton method but find that it diverges frequently. To understand the divergence pattern, we analyze a simplified 2-cell problem and show that the global convergence of Newton cannot be ensured for any choice of penalty parameters. We thus propose a modified Newton solver, which guarantees convergence for the 2-cell problem and is numerically verified to converge for all the challenging simulations considered herein. While both 1 st - and 2 nd -order variants of IBM, in displacement unknowns, are proposed, the modified Newton solver applies only to the 1 st -order variant.

42 ENGINEERING↗

NASA NTRS1999

Sonic Boom Prediction and Minimization of the Douglas Reference OPT5 Configuration

Conventional CFD methods and grids do not yield adequate resolution of the complex shock flow pattern generated by a real aircraft geometry. As a result, a unique grid topology and supersonic flow solver was developed at Northrop Grumman based on the characteristic behavior of supersonic wave patterns emanating from the aircraft. Using this approach, it was possible to compute flow fields with adequate resolution several body lengths below the aircraft. In this region, three-dimensional effects are diminished and conventional two-dimensional modified linear theory (MLT) can be applied to estimate ground pressure signatures or sonic booms. To accommodate real aircraft geometries and alleviate the burdensome grid generation task, an implicit marching multi-block, multi-grid finite-volume Euler code was developed as the basis for the sonic boom prediction methodology. The Thomas two-dimensional extrapolation method is built into the Euler code so that ground signatures can be obtained quickly and efficiently with minimum computational effort suitable to the aircraft design environment. The loudness levels of these signatures can then be determined using a NASA generated noise code. Since the Euler code is a three-dimensional flow field solver, the complete circumferential region below the aircraft is computed. The extrapolation of all this field data from a cylinder of constant radius leads to the definition of the entire boom corridor occurring directly below and off to the side of the aircraft's flight path yielding an estimate for the entire noise "annoyance" corridor in miles as well as its magnitude. An automated multidisciplinary sonic boom design optimization software system was developed during the latter part of HSR Phase 1. Using this system, it was found that sonic boom signatures could be reduced through optimization of a variety of geometric aircraft parameters. This system uses a gradient based nonlinear optimizer as the driver in conjunction with a computationally efficient Euler CFD solver (NIIM3DSB) for computing the three-dimensional near-field characteristics of the aircraft. The intent of the design system is to identify and optimize geometric design variables that have a beneficial impact on the ground sonic boom. The system uses a simple wave drag data format to specify the aircraft geometry. The geometry is internally enhanced and analytic methods are used to generate marching grids suitable for the multi-block Euler solver. The Thomas extrapolation method is integrated into this system, and hence, the aircraft's centerline ground sonic boom signature is also automatically computed for a specified cruise altitude and yields the parameters necessary to evaluate the design function. The entire design system has been automated since the gradient based optimization software requires many flow analyses in order to obtain the required sensitivity derivatives for each design variable in order to converge on an optimal solution. Hence, once the problem is defined which includes defining the objective function and geometric and aerodynamic constraints, the system will automatically regenerate the perturbed geometry, the necessary grids, the Euler solution, and finally the ground sonic boom signature at the request of the optimizer.

Siclari, Michael J.↗

DOE OSTI2026

Final Technical Report - Center for Simulation of Fusion Relevant RF Actuators

We have developed a suite of 3D electromagnetic field solvers, both FEM and FDTD based, that account for the RF antenna and vacuum vessel geometries with unprecedented accuracy. Workflows were developed that make it possible to translate CAD models for the antenna and vacuum vessel to physics meshes for RF wave simulation. Nonlinear RF sheath formation has been incorporated self-consistently as a boundary condition in these solvers. We have also carried out extensive studies of the impact of RF sheaths on the ion energy angle distribution at plasma-material interfaces, using high fidelity particle-in-cell codes. Comprehensive simulation models were developed to assess the impact of blob-like edge turbulence on RF wave propagation and the impact of the RF ponderomotive force on the plasma scrape-off layer (SOL). A fluid transport solver for the far-SOL was also developed which accounts for the high parallel to perpendicular heat anisotropy on an unstructured mesh, thus making it possible to precisely represent an antenna structure in the presence of edge transport. Finally we have developed a hierarchy of core wave propagation and absorption models that self-consistently combine continuum Fokker Planck and Monte Carlo treatments of fast ion evolution with ICRF full-wave field solvers and continuum Fokker Planck treatments of fast electron evolution with both full-wave and ray tracing models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1978

Semidirect calculation of steady two- and three-dimensional flows

This paper describes a semidirect method for rapidly solving steady-state viscous flows described by the complete Navier-Stokes equations. The current results are for two-dimensional incompressible flows in general channels at arbitrary Reynolds numbers, but work in progress on compressible and three-dimensional flows is also described. The basic concept of semidirect methods is to use the recently developed fast (direct, or noniterative) linear solvers to solve linearized equations, which are then iterated to solve the nonlinearity. The method used here is an extension of the Split NOS method (Roache, 1975)

Roache, P. J.↗

NASA NTRS1979

Multi-level adaptive finite element methods. 1: Variation problems

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Brandt, A.↗

NASA NTRS1990

Trajectory optimization for real-time guidance. I - Time-varying LQR on a parallel processor

A key algorithmic element of a real-time trajectory optimization hardware/software implementation, the quadratic program (QP) solver element, is presented. The purpose of the effort is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter. Many methods of nonlinear programming require the solution of a QP at each iteration. In the trajectory optimization case the QP has a special dynamic programming structure, a LQR-like structure. QP algorithm speed is increased by taking advantage of this special structure and by parallel implementation.

Psiaki, Mark L.↗

NASA NTRS1995

A Hybrid Parallel Preconditioning Algorithm For CFD

A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.

Barth,Timothy J.↗

NASA NTRS2012

Direct Method Transcription for a Human-Class Translunar Injection Trajectory Optimization

This paper presents a new trajectory optimization software package developed in the framework of a low-to-high fidelity 3 degrees-of-freedom (DOF)/6-DOF vehicle simulation program named Mission Analysis Simulation Tool in Fortran (MASTIF) and its application to a translunar trajectory optimization problem. The functionality of the developed optimization package is implemented as a new "mode" in generalized settings to make it applicable for a general trajectory optimization problem. In doing so, a direct optimization method using collocation is employed for solving the problem. Trajectory optimization problems in MASTIF are transcribed to a constrained nonlinear programming (NLP) problem and solved with SNOPT, a commercially available NLP solver. A detailed description of the optimization software developed is provided as well as the transcription specifics for the translunar injection (TLI) problem. The analysis includes a 3-DOF trajectory TLI optimization and a 3-DOF vehicle TLI simulation using closed-loop guidance.

Witzberger, Kevin E.↗

DOE OSTI2021

Porting the Nonlinear Optimization Library HiOp to Accelerator-Based Hardware Architectures

While interior point method has been the centerpiece of nonlinear programming tools used in science and engineering, its reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it difficult to implement it effectively on hardware accelerators. HiOp optimization package attempts to provide an implementation of the interior point method suitable for hardware accelerators by compressing the original sparse problem to produce an underlying linear problem that is dense and of manageable size. Implementations of dense linear solvers are more mature and utilize hardware accelerators better than their sparse counterparts. There is a number of important domain problems, such as optimal power flow analysis for power grids, where the sparse problem can be effectively compressed and deploying dense linear solver within the interior point method can improve performance. Here we describe a portable implementation of HiOp optimization engine, which uses a linear solver from Magma library and runs entirely on hardware accelerators. To compress the problem, HiOp uses customized mixed dense-sparse linear algebra. All HiOp kernels are implemented using Umpire and RAJA portability libraries. We describe details of the implementation and discuss trade-offs between performance, portability and development cost.

97 MATHEMATICS AND COMPUTING↗