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NASA NTRS1995

Femtolensing: Beyond the semiclassical approximation

Femtolensoing is a gravitational lensing effect in which the magnification is a function not only of the position and sizes of the source and lens, but also of the wavelength of light. Femtolensing is the only known effect of 10(exp -13) - 10(exp -16) solar mass) dark-matter objects and may possibly be detectable in cosmological gamma-ray burst spectra. We present a new and efficient algorithm for femtolensing calculation in general potentials. The physical optics results presented here differ at low frequencies from the semiclassical approximation, in which the flux is attributed to a finite number of mutually coherent images. At higher frequencies, our results agree well with the semicalssical predictions. Applying our method to a point-mass lens with external shear, we find complex events that have structure at both large and small spectral resolution. In this way, we show that femtolensing may be observable for lenses up to 10(exp -11) solar mass, much larger than previously believed. Additionally, we discuss the possibility of a search femtolensing of white dwarfs in the Large Magellanic Cloud at optical wavelengths.

Ulmer, Andrew↗

NASA NTRS1999

Ames Optimized TCA Configuration

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Cliff, Susan E.↗

NASA NTRS2004

Reduced-Order Blade Mistuning Analysis Techniques Developed for the Robust Design of Engine Rotors

The primary objective of this research program is to develop vibration analysis tools, design tools, and design strategies to significantly improve the safety and robustness of turbine engine rotors. Bladed disks in turbine engines always feature small, random blade-to-blade differences, or mistuning. Mistuning can lead to a dramatic increase in blade forced-response amplitudes and stresses. Ultimately, this results in high-cycle fatigue, which is a major safety and cost concern. In this research program, the necessary steps will be taken to transform a state-of-the-art vibration analysis tool, the Turbo-Reduce forced-response prediction code, into an effective design tool by enhancing and extending the underlying modeling and analysis methods. Furthermore, novel techniques will be developed to assess the safety of a given design. In particular, a procedure will be established for using eigenfrequency curve veerings to identify "danger zones" in the operating conditions--ranges of rotational speeds and engine orders in which there is a great risk that the rotor blades will suffer high stresses. This work also will aid statistical studies of the forced response by reducing the necessary number of simulations. Finally, new strategies for improving the design of rotors will be pursued. Several methods will be investigated, including the use of intentional mistuning patterns to mitigate the harmful effects of random mistuning, and the modification of disk stiffness to avoid reaching critical values of interblade coupling in the desired operating range. Recent research progress is summarized in the following paragraphs. First, significant progress was made in the development of the component mode mistuning (CMM) and static mode compensation (SMC) methods for reduced-order modeling of mistuned bladed disks (see the following figure). The CMM method has been formalized and extended to allow a general treatment of mistuning. In addition, CMM allows individual mode mistuning, which accounts for the realistic effects of local variations in blade properties that lead to different mistuning values for different mode types (e.g., mistuning of the first torsion mode versus the second flexural mode). The accuracy and efficiency of the CMM method and the corresponding Turbo-Reduce code were validated for an example finite element model of a bladed disk.

Min, James B.↗

NASA NTRS1991

A finite mixtures algorithm for finding classes in images

The authors describe an algorithm for estimating the proportions of classes in a SAR (synthetic aperture radar) image without any user interaction. The method assumes that the image is a mixture of a known number of different pixel types. A maximum likelihood estimate of the parameters of the resulting mixture distribution is then used to find the proportions for the various classes. The technique was successfully applied to aircraft SAR images of sea ice. Computer simulations were used to determine the relative errors of the technique. The technique performs well even with extremely noisy images.

Samadani, Ramin↗

NASA NTRS1986

An explicit finite-volume time-marching procedure for turbulent flow calculations

A method was developed which calculates two-dimensional, transonic, viscous flow in ducts. The finite-volume, time-marching formulation is used to obtain steady flow solutions of the Reynolds-averaged form of the Navier-Stokes equations. The entire calculation is performed in the physical domain. Control volumes are chosen so that smoothing of flow properties, typically required for stability, is not required. Different time steps are used in the different governing equations. A new pressure interpolation scheme is introduced which improves the shock capturing ability of the method. A multi-volume method for pressure changes in the boundary layer allows calculations which use very long and thin control volumes (length/height - 1000). The method is compared with two test cases. Essentially incompressible turbulent boundary layer flow in an adverse pressure gradient is calculated and the computed distributions of mean velocity and shear are in good agreement with the measurements. Transonic viscous flow in a converging diverging nozzle is calculated; the Mach number upstream of the shock is approximately 1.25. The agreement between the calculated and measured shock strength and total pressure losses is good.

Nicholson, Stephen↗

NASA NTRS1987

An explicit finite-volume time-marching procedure for turbulent flow calculations

Nicholson, Stephen↗

NASA NTRS1991

Computation of viscous blast wave flowfields

A method to determine unsteady solutions of the Navier-Stokes equations was developed and applied. The structural finite-volume, approximately factored implicit scheme uses Newton subiterations to obtain the spatially and temporally second-order accurate time history of the interaction of blast-waves with stationary targets. The inviscid flux is evaluated using MacCormack's modified Steger-Warming flux or Roe flux difference splittings with total variation diminishing limiters, while the viscous flux is computed using central differences. The use of implicit boundary conditions in conjunction with a telescoping in time and space method permitted solutions to this strongly unsteady class of problems. Comparisons of numerical, analytical, and experimental results were made in two and three dimensions. These comparisons revealed accurate wave speed resolution with nonoscillatory discontinuity capturing. The purpose of this effort was to address the three-dimensional, viscous blast-wave problem. Test cases were undertaken to reveal these methods' weaknesses in three regimes: (1) viscous-dominated flow; (2) complex unsteady flow; and (3) three-dimensional flow. Comparisons of these computations to analytic and experimental results provided initial validation of the resultant code. Addition details on the numerical method and on the validation can be found in the appendix. Presently, the code is capable of single zone computations with selection of any permutation of solid wall or flow-through boundaries.

Atwood, Christopher A.↗

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 NTRS1986

Adaptive computational methods for SSME internal flow analysis

Adaptive finite element methods for the analysis of classes of problems in compressible and incompressible flow of interest in SSME (space shuttle main engine) analysis and design are described. The general objective of the adaptive methods is to improve and to quantify the quality of numerical solutions to the governing partial differential equations of fluid dynamics in two-dimensional cases. There are several different families of adaptive schemes that can be used to improve the quality of solutions in complex flow simulations. Among these are: (1) r-methods (node-redistribution or moving mesh methods) in which a fixed number of nodal points is allowed to migrate to points in the mesh where high error is detected; (2) h-methods, in which the mesh size h is automatically refined to reduce local error; and (3) p-methods, in which the local degree p of the finite element approximation is increased to reduce local error. Two of the three basic techniques have been studied in this project: an r-method for steady Euler equations in two dimensions and a p-method for transient, laminar, viscous incompressible flow. Numerical results are presented. A brief introduction to residual methods of a-posterior error estimation is also given and some pertinent conclusions of the study are listed.

Oden, J. T.↗

NASA NTRS1975

Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Anderson, E. C.↗

NASA NTRS1975

Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Anderson, E. C.↗

NASA NTRS1980

Application of advanced computational procedures for modeling solar-wind interactions with Venus: Theory and computer code

Computational procedures are developed and applied to the prediction of solar wind interaction with nonmagnetic terrestrial planet atmospheres, with particular emphasis to Venus. The theoretical method is based on a single fluid, steady, dissipationless, magnetohydrodynamic continuum model, and is appropriate for the calculation of axisymmetric, supersonic, super-Alfvenic solar wind flow past terrestrial planets. The procedures, which consist of finite difference codes to determine the gasdynamic properties and a variety of special purpose codes to determine the frozen magnetic field, streamlines, contours, plots, etc. of the flow, are organized into one computational program. Theoretical results based upon these procedures are reported for a wide variety of solar wind conditions and ionopause obstacle shapes. Plasma and magnetic field comparisons in the ionosheath are also provided with actual spacecraft data obtained by the Pioneer Venus Orbiter.

Stahara, S. S.↗

NASA NTRS1985

A first-order time-domain Green's function approach to supersonic unsteady flow

A time-domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. The Green's function method is employed in order to convert the potential-flow differential equation into an integral one. This integral equation is then discretized, in space through standard finite-element technique, and in time through finite-difference, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. Consistent with the spatial linear (first-order) finite-element approximations, the potential and co-normalwash are assumed to vary linearly in time. The long range goal of our research is to develop a comprehensive theory for unsteady supersonic potential aerodynamics which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range.

Freedman, M. I.↗

NASA NTRS1985

One-dimensional kinematics of particle stream flow with application to solar wind simulation

A simple kinematic method for determining the particle velocity distribution of a model solar wind for which the spatial distribution of particles is given as a function of particle travel time has been developed by Hakamada and Akasofu (1982). Here their method is formalized mathematically and an inverse procedure for determining the particle distribution from a given velocity distribution is derived. This inverse procedure is then applied to a simulated velocity distribution obtained from an MHD finite difference code.

Olmsted, C.↗

NASA NTRS1985

Joint research effort on vibrations of twisted plates, phase 1: Final results

The complete theoretical and experimental results of the first phase of a joint government/industry/university research study on the vibration characteristics of twisted cantilever plates are given. The study is conducted to generate an experimental data base and to compare many different theoretical methods with each other and with the experimental results. Plates with aspect ratios, thickness ratios, and twist angles representative of current gas turbine engine blading are investigated. The theoretical results are generated by numerous finite element, shell, and beam analysis methods. The experimental results are obtained by precision matching a set of twisted plates and testing them at two laboratories. The second and final phase of the study will concern the effects of rotation.

Kielb, R. E.↗

NASA NTRS1986

Preconditioning for first-order spectral discretization

Efficient solution of the equations from spectral discretizations is essential if the high-order accuracy of these methods is to be realized. Direct solution of these equations is rarely feasible, thus iterative techniques are required. A preconditioning scheme for first-order Chebyshev collocation operators is proposed herein, in which the central finite difference mesh is finer than the collocation mesh. Details of the proper techniques for transferring information between the meshes are given here, and the scheme is analyzed by examination of the eigenvalue spectra of the preconditioned operators. The effect of artificial viscosity required in the inversion of the finite difference operator is examined. A second preconditioning scheme, involving a high-order upwind finite difference operator of the van Leer type is also analyzed to provide a comparison with the present scheme. Finally, the performance of the present scheme is verified by application to several test problems.

Streett, C. L.↗

NASA NTRS1991

Scattering of Lamb waves in a composite plate

A combined analytical and finite element technique is developed to gain a better understanding of the scattering of elastic waves by defects. This hybrid method is capable of predicting scattered displacements from arbitrary shaped defects as well as inclusions of different material. The continuity of traction and displacements at the boundaries of the two areas provided the necessary equations to find the nodal displacements and expansion coefficients. Results clearly illustrate the influence of increasing crack depth on the scattered signal.

Bratton, Robert↗

NASA NTRS1992

Thermomechanical buckling and postbuckling of multilayered composite panels

A study is made of the thermomechanical buckling and postbuckling responses of flat unstiffened composite panels. The panels are subjected to combined temperature change and applied edge displacement. The analysis is based on a first-order shear deformation, von Karman type nonlinear plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. An efficient multiple-parameter reduction method is used in conjunction with mixed finite element models, for determining the stability boundary and postbuckling response. The reduction method is also used for evaluating the sensitivity coefficients which measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of variations in the laminate stacking sequence, fiber orientation, number of layers and aspect ratio of the panels on their thermomechanical buckling and postbuckling responses and their sensitivity coefficients.

Noor, Ahmed K.↗