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NASA NTRS1987

Time-dependent approximation schemes for some problems of parameter estimation in distributed systems

A parameter estimation method that can be used to estimate functional parameters in delay differential equations and moving boundary problems is discussed. In either problem, the original model equation (which is infinite-dimensional) is approximated by a system of ordinary differential equations that can be solved numerically in an efficient way. The approximation scheme is based on time-dependent spline elements. For the delay equation with time-varying delay, convergence results are presented that indicate the estimates obtained using the approximating system. Numerical test examples converge in some sense to a best-fit parameter for the original system are included by means of which time-varying and state-dependent delays and a time-varying diffusion coefficient in a one-phase, one-dimensional Stefan problem are estimated.

Murphy, K. A.↗

NASA NTRS1992

Particle simulation of rarefied aeropass maneuvers of the Magellan spacecraft

Rarefied and free molecular flowfields corresponding to proposed aeropass maneuvers through the atmosphere of Venus by the Magellan spacecraft are computed with a vectorized particle simulation method. The significance of rarefaction and reaction effects are assessed and surface heat flux, drag coefficients, and flowfield properties are computed. A simple surface heat transfer model is coupled directly to the simulation and assumes that each surface element is in radiative equilibrium with deep space. This allows direct computation of surface temperature distributions rather than requiring prescribed isothermal boundary conditions. Uncoupled dual-node heat transfer models, which account for heat capacity and thermal conductivity within each structural component, permit more accurate determination of surface temperatures. Such temperatures restrict the allowable altitudes and entry speeds of the aeropass maneuvers, and must therefore be estimated accurately. Simulations with an entry velocity of 8600 m/s at altitudes between 125 and 140 km reveal that allowable surface temperatures occur only at the highest altitudes where the flowfield is appropriately modeled as free-molecular. Excessive surface heat flux occurs at lower altitudes where molecular collisions are significant.

Haas, Brian L.↗

NASA NTRS1996

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Manteuffel, Thomas A.↗

NASA NTRS1999

Numerical Predictions of Wind Turbine Power and Aerodynamic Loads for the NREL Phase II and IV Combined Experiment Rotor

Accurate, reliable and robust numerical predictions of wind turbine rotor power remain a challenge to the wind energy industry. The literature reports various methods that compare predictions to experiments. The methods vary from Blade Element Momentum Theory (BEM), Vortex Lattice (VL), to variants of Reynolds-averaged Navier-Stokes (RaNS). The BEM and VL methods consistently show discrepancies in predicting rotor power at higher wind speeds mainly due to inadequacies with inboard stall and stall delay models. The RaNS methodologies show promise in predicting blade stall. However, inaccurate rotor vortex wake convection, boundary layer turbulence modeling and grid resolution has limited their accuracy. In addition, the inherently unsteady stalled flow conditions become computationally expensive for even the best endowed research labs. Although numerical power predictions have been compared to experiment. The availability of good wind turbine data sufficient for code validation experimental data that has been extracted from the IEA Annex XIV download site for the NREL Combined Experiment phase II and phase IV rotor. In addition, the comparisons will show data that has been further reduced into steady wind and zero yaw conditions suitable for comparisons to "steady wind" rotor power predictions. In summary, the paper will present and discuss the capabilities and limitations of the three numerical methods and make available a database of experimental data suitable to help other numerical methods practitioners validate their own work.

Duque, Earl P. N.↗

NASA NTRS2007

Shuttle Entry Imaging Using Infrared Thermography

During the Columbia Accident Investigation, imaging teams supporting debris shedding analysis were hampered by poor entry image quality and the general lack of information on optical signatures associated with a nominal Shuttle entry. After the accident, recommendations were made to NASA management to develop and maintain a state-of-the-art imagery database for Shuttle engineering performance assessments and to improve entry imaging capability to support anomaly and contingency analysis during a mission. As a result, the Space Shuttle Program sponsored an observation campaign to qualitatively characterize a nominal Shuttle entry over the widest possible Mach number range. The initial objectives focused on an assessment of capability to identify/resolve debris liberated from the Shuttle during entry, characterization of potential anomalous events associated with RCS jet firings and unusual phenomenon associated with the plasma trail. The aeroheating technical community viewed the Space Shuttle Program sponsored activity as an opportunity to influence the observation objectives and incrementally demonstrate key elements of a quantitative spatially resolved temperature measurement capability over a series of flights. One long-term desire of the Shuttle engineering community is to calibrate boundary layer transition prediction methodologies that are presently part of the Shuttle damage assessment process using flight data provided by a controlled Shuttle flight experiment. Quantitative global imaging may offer a complementary method of data collection to more traditional methods such as surface thermocouples. This paper reviews the process used by the engineering community to influence data collection methods and analysis of global infrared images of the Shuttle obtained during hypersonic entry. Emphasis is placed upon airborne imaging assets sponsored by the Shuttle program during Return to Flight. Visual and IR entry imagery were obtained with available airborne imaging platforms used within DoD along with agency assets developed and optimized for use during Shuttle ascent to demonstrate capability (i.e., tracking, acquisition of multispectral data, spatial resolution) and identify system limitations (i.e., radiance modeling, saturation) using state-of-the-art imaging instrumentation and communication systems. Global infrared intensity data have been transformed to temperature by comparison to Shuttle flight thermocouple data. Reasonable agreement is found between the flight thermography images and numerical prediction. A discussion of lessons learned and potential application to a potential Shuttle boundary layer transition flight test is presented.

Horvath, Thomas↗

NASA NTRS1975

The finite element method in low speed aerodynamics

The finite element procedure is shown to be of significant impact in design of the 'computational wind tunnel' for low speed aerodynamics. The uniformity of the mathematical differential equation description, for viscous and/or inviscid, multi-dimensional subsonic flows about practical aerodynamic system configurations, is utilized to establish the general form of the finite element algorithm. Numerical results for inviscid flow analysis, as well as viscous boundary layer, parabolic, and full Navier Stokes flow descriptions verify the capabilities and overall versatility of the fundamental algorithm for aerodynamics. The proven mathematical basis, coupled with the distinct user-orientation features of the computer program embodiment, indicate near-term evolution of a highly useful analytical design tool to support computational configuration studies in low speed aerodynamics.

Baker, A. J.↗

NASA NTRS1985

Energy Stability of Thermocapillary Convection in Models of the Float Zone Process

The energy-stability of thermocapillary convection in models of the float-zone, crystal-growing process was studied. Stability limits, as functions of pertinent parameters, that will identify conditions which will not allow the existence of an undesirable oscillatory flow instability were determined. Such instabilities may occur in the space processing of semiconductor materials. The determination of the stability limits will involve two sets of numerical computations: (1) solution of the nonlinear governing equations together with the appropriate boundary conditions to determine the basic state (in general, velocity, pressure and temperature fields and the displacement of free surfaces and interfaces); and (2) solution of a nonlinear Euler-Lagrange systems for the energy-stability limit. Both computations, while difficult, should be within the scope of available computer capability and available concepts in numerical analysis. Finite-element methods are attractive candidates for the numerical work.

Neitzel, G. P.↗

NASA NTRS1989

Overview of the fatigue/fracture/life working group program at the Lewis Research Center

Constitutive and life prediction models are developed and verified for materials typically used in hot gas path components of reusable space propulsion systems over the range of relevant operating environments. The efforts were centered on the development of crack initiation life prediction methods, while the efforts of a counterpart group were centered on the development of cyclic crack propagation life prediction methods. The complexion of the active tasks are presented. A significant new task started this year will incorporate the various material constitutive and life prediction models developed in this program into a comprehensive creep-fatigue damage analysis and life assessment computer code. The program will function as a postprocessor to general structural analysis programs (such as finite element or boundary element codes) using the output of such analyses (stress, strain, and temperature fields as functions of time) as the input to the damage analysis and life assessment code. The code will be designed to execute on engineering/scientific workstations and will feature a windowing, mouse-driven user interface. Current plans call for the code to be finished and made available for use in mid 1991.

Mcgaw, Michael A.↗

NASA NTRS1995

Dynamic sensitivity analysis of frictional contact/impact response of axisymmetric composite structures

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic frictional contact/impact response of axisymmetric composite structures. The structures are assumed to consist of an arbitrary number of perfectly bonded homogeneous anisotropic layers. The material of each layer is assumed to be hyperelastic, and the effect of geometric nonlinearity is included. The sensitivity coefficients measure the sensitivity of the response to variations in different material, lamination and geometric parameters of the structure. A displacement finite element model is used for the discretization. The normal contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the nodal displacements, and the Lagrange multipliers associated with the contact conditions. The Lagrange multipliers are allowed to be discontinuous at interelement boundaries. Tangential contact conditions are incorporated by using a penalty method in conjunction with the classical Coulomb's friction model. Temporal integration is performed by using Newmark method. The Newton-Raphson iterative scheme is used for the solution of the resulting nonlinear algebraic equations, and for the determination of the contact region, contact conditions (sliding or sticking), and the contact pressures. The sensitivity coefficients are evaluated by using a direct differentiation approach. Numerical results are presented from the frictional contact/impact response of a composite spherical cap impacting on a rigid plate.

Karaoglan, Levent↗

NASA NTRSDate not supplied

Development of a C-ELS Specimen-Based Numerical Benchmark for Mode II Delamination and Assessment of Two VCCT-Based Propagation Strategies

A finite element (FE) benchmark example inspired by the calibrated end-loaded split (C-ELS) specimen is developed and used to assess the performance of delamination propagation capabilities based on linear elastic fracture mechanics (LEFM). The C-ELS specimen has the advantage of a longer region of stable delamination propagation compared to the existing mode II benchmark case. The new benchmark example may therefore provide a better assessment tool by enabling more stable crack growth in regions further away from the boundary conditions or load application. First, a benchmark result is created manually using two-dimensional finite element models of the C-ELS specimen with different delamination lengths. Second, the performance of the virtual crack closure technique (VCCT) delamination propagation capabilities in the Abaqus/Standard®1 FE code and the recently developed Progressive Release eXplicit-VCCT (PRX-VCCT) method are assessed by comparing the results to the benchmark case. Two examples with different starter delamination lengths are studied. A shorter starter length is chosen to create a scenario with unstable delamination propagation. A longer delamination encourages stable delamination propagation. Detailed results from three-dimensional analyses with aligned and misaligned meshes and two levels of mesh refinement are provided. In general, good agreement can be achieved between the results obtained from the quasi-static propagation analysis and the benchmark analysis. Numerical artifacts including anomalous unreleased nodes in the crack wake and zig-zag crack fronts occur for propagation analyses using Abaqus/Standard VCCT. In comparison, continuous, smooth, delamination fronts are observed for PRX-VCCT. The use of the benchmark case to assess different VCCT-based propagation strategies illustrates the value of establishing benchmark cases.

Composite Materials↗

NASA NTRS2001

Development of an Unstructured Mesh Code for Flows About Complete Vehicles

This report describes the research work undertaken at the Massachusetts Institute of Technology, under NASA Research Grant NAG4-157. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of flow simulations about complete vehicle configurations. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms, flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the code which incorporates real gas effects, has been produced. The FELISA system is also a component of the STARS aeroservoelastic system developed at NASA Dryden. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. We show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although this initial results were encouraging it became apparent that in order to develop a fully functional capability for viscous flows, several advances in solution accuracy, robustness and efficiency were required. In this grant we set out to investigate some novel methodologies that could lead to the required improvements. In particular we focused on two fronts: (1) finite element methods and (2) iterative algebraic multigrid solution techniques.

Peraire, Jaime↗

NASA NTRS1978

Two-dimensional computer code for design assessment of SRM aft closure environment

A general interpolants method for constructing numerical analogs of the partial differential equations of continuum mechanics and which combines the best features of both finite element and finite difference methods was used in a two dimensional axisymmetric analysis of the space shuttle solid motor aft closure region flowfield. The numerical technique used is discussed as well as the results of the analysis. A steady state solution for the submerged nozzle nose region indicates the development of an area gas flow recirculation near the propellant burning surface boundary and in the region of the underside of the nozzle nose. This recirculation region remains spatially fixed for successive iterations (greater than 800) of the solution.

Freeman, J. A.↗

NASA NTRS1985

On the Interconnection of Incompatible Solid Finite Element Meshes Using Multipoint Constraints

Incompatible meshes, i.e., meshes that physically must have a common boundary, but do not necessarily have coincident grid points, can arise in the course of a finite element analysis. For example, two substructures may have been developed at different times for different purposes and it becomes necessary to interconnect the two models. A technique that uses only multipoint constraints, i.e., MPC cards (or MPCS cards in substructuring), is presented. Since the method uses only MPC's, the procedure may apply at any stage in an analysis; no prior planning or special data is necessary.

Fox, G. L.↗

NASA NTRS1987

Probabilistic structural analysis to evaluate the structural durability of SSME critical components

NASA Lewis Research Center is currently developing probabilistic structural analysis methods for select Space Shuttle Main Engine (SSME) structural components. Briefly, the deterministic, three-dimensional, inelastic analysis methodology developed under the Hot Section Technology (HOST) and R and T Base Programs is being augmented to accommodate the complex probabilistic loading spectra, the thermoviscoplastic material behavior, and the material degradation associated with the environment of space propulsion system structural components representative of the SSME such as turbine blades, transfer ducts, and liquid-oxygen posts. The development of probabilistic structural analysis methodology consists of the following program elements: (1) composite load spectra; (2) probabilistic structural analysis methods; (3) probabilistic finite element theory - new variational principles; and (4) probabilistic structural analysis application. In addition, the program includes deterministic analysis elements: (1) development of structural tailoring computer codes (SSME/STAEBL); (2) development of dynamic creep buckling/ratcheting theory; (3) evaluation of the dynamic characteristics of single-crystal SSME blades; (4) development of SSME blade damper technology; and (5) development of integrated boundary elements for hotfluid structure interaction.

Chamis, Christos C.↗

NASA NTRS1986

A Petrov-Galerkin finite element method for the compressible Euler and Navier-Stokes equations

An overview of a new finite element method for the compressible Euler and Navier-Stokes equations is presented. The discretization is based on entropy variables. The method is developed within the framework of a Petrov-Galerkin formulation. Two perturbations are added to the weighting function; one is a generalization of the SUPG operator and the other is designed to enhance shock capturing capability. The treatment of boundary conditions and the consistent calculation of boundary fluxes are addressed. Results of numerical tests are presented which confirm the robustness and wide applicability of the method.

Franca, L. P.↗

NASA NTRS1987

Model-size reduction for the analysis of symmetric structures with asymmetric boundary conditions

A simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (1) restructuring the governing finite-element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (2) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite-element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The effectiveness of the computational procedure is demonstrated by means of numerical examples of linear static problems of shells, and its potential for solving nonlinear problems is discussed.

Noor, Ahmed K.↗

NASA NTRS1984

Large-Scale Advanced Prop-Fan (LAP) blade design

This report covers the design analysis of a very thin, highly swept, propeller blade to be used in the Large-Scale Advanced Prop-Fan (LAP) test program. The report includes: design requirements and goals, a description of the blade configuration which meets requirements, a description of the analytical methods utilized/developed to demonstrate compliance with the requirements, and the results of these analyses. The methods described include: finite element modeling, predicted aerodynamic loads and their application to the blade, steady state and vibratory response analyses, blade resonant frequencies and mode shapes, bird impact analysis, and predictions of stalled and unstalled flutter phenomena. Summarized results include deflections, retention loads, stress/strength comparisons, foreign object damage resistance, resonant frequencies and critical speed margins, resonant vibratory mode shapes, calculated boundaries of stalled and unstalled flutter, and aerodynamic and acoustic performance calculations.

Violette, John A.↗

NASA NTRS1988

Efficient vibration mode analysis of aircraft with multiple external store configurations

A coupling method for efficient vibration mode analysis of aircraft with multiple external store configurations is presented. A set of low-frequency vibration modes, including rigid-body modes, represent the aircraft. Each external store is represented by its vibration modes with clamped boundary conditions, and by its rigid-body inertial properties. The aircraft modes are obtained from a finite-element model loaded by dummy rigid external stores with fictitious masses. The coupling procedure unloads the dummy stores and loads the actual stores instead. The analytical development is presented, the effects of the fictitious mass magnitudes are discussed, and a numerical example is given for a combat aircraft with external wing stores. Comparison with vibration modes obtained by a direct (full-size) eigensolution shows very accurate coupling results. Once the aircraft and stores data bases are constructed, the computer time for analyzing any external store configuration is two to three orders of magnitude less than that of a direct solution.

Karpel, M.↗