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At least 1,549 records · Page 86

A computational method for helicopter vortex wakes

A method for calculating the wake geometry and blade loads for a hovering helicopter rotor is presented. The approach incorporates a simplified free wake model of the rotor in a finite difference calculation of the flow field. A variation of the 'cloud-in-cell' technique, modified to eliminate self-induced velocity errors for curved vortex filaments, is used. Simple lifting line theory is used to calculate the blade loads. Calculations showing the effect of vortex core size and the number of vortex filaments representing the wake are presented. For large numbers of vortices, it is seen that the wake geometry fails to converge. However, only a few vortices are needed to adequately represent the wake. Comparisons with experimental results are also presented.

Roberts, T. W.↗

Performance of the h, p and h-p versions

There are three basic versions of the finite element method, called the h, p and h-p versions. They are characterized by the way in which the finite element meshes and polynomial degree of elements are chosen. They differ in computer implementation (program architecture) and mathematical analysis. The manner in which the meshes and polynomial degree of the elements affect the accuracy of finite element solutions is examined. The approach is to fix certain parameters and increase the number of degrees of freedom so that the finie element solutions converge to the exact solution. Such a systematic increase of the number of degrees of freedom is called extension because it can be interpreted as a systematic extension of finite element spaces.

Babuska, I.↗

Experiences with digital processing of images at INPE

Four different research experiments with digital image processing at INPE will be described: (1) edge detection by hypothesis testing; (2) image interpolation by finite impulse response filters; (3) spatial feature extraction methods in multispectral classification; and (4) translational image registration by sequential tests of hypotheses.

Mascarenhas, N. D. A.↗

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.

Thoenes, J.↗

Effects of numerical dissipation on finite-volume solutions of compressible flow problems

The effects of numerical dissipation upon solutions to the Euler equations are considered, and results for transonic flows past airfoils are presented to demonstrate the effects of the dissipative terms. The equations are approximated using a finite-volume spatial approximation with added dissipation provided by an adaptive mixture of second and fourth differences. The resulting difference equations are solved using either an explicit multistage Runge-Kutta method or a diagonalized implicit method. It is found that errors in surface values can be introduced by the averaging required to calculate derived quantities of interest.

Caughey, David A.↗

Numerical investigation of laminar-turbulent transition in a flat plate wake

Lamina-turbulent transition of high-deficit flat plate wakes is investigated by direct numerical simulations using the complete Navier Stokes equations. The simulations are based on a spatial model so that both the base flow and the disturbance flow can develop in the downstream direction. The Navier Stokes equations are used in a vorticity-velocity form and are solved using a combination of finite difference and spectral approximations. Fourier series are used in the spanwise direction. Second-order finite-differences are used to approximate the spatial derivatives in the streamwise and transverse directions. For the temporal discretion, a combination of ADI, Crank-Nicolson, and Adams-Bashforth methods is employed. The discretized velocity equations are solved using fast Helmholtz solvers. Code validation is accomplished by comparison of the numerical results to both linear stability and to experiments. Calculations of two- and/or three-dimensional sinuous and mode disturbances in the wake of flat plate are undertaken. For calculations of two-dimensional disturbances, the wake is forced at an amplitude level so that nonlinear disturbance development may be observed. In addition, the forcing amplitude is varied in order to determine its effect on the disturbance behavior. To investigate the onset of three-dimensionality, the wake is forced with a small-amplitude three-dimensional disturbance and a larger amplitude two-dimensional disturbance. The two-dimensional forcing amplitude is varied in order to determine its influence on the three-dimensional flow field.

Fasel, Hermann F.↗

Converting gravity bins to spherical harmonic coefficients

The gravity bin technique as originally formulated recovers the local gravity field from the bin parameters by finite differencing. The spherical harmonic coefficients of the gravity field are then computed by an orthogonal transformation of the local gravity field. The result differs from that of the traditional method. This paper discusses the difference and proposes a new algorithm to convert the bin parameters to spherical harmonic coefficients. It is shown that the new method produces the same gravity field as the traditional method and maintains the high computational efficiency of the basic gravity bin technique.

Wu, J. T.↗

Elliptic flow computation by low Reynolds number two-equation turbulence models

A detailed comparison of ten low-Reynolds-number k-epsilon models is carried out. The flow solver, based on an implicit approximate factorization method, is designed for incompressible, steady two-dimensional flows. The conservation of mass is enforced by the artificial compressibility approach and the computational domain is discretized using centered finite differences. The turbulence model predictions of the flow past a hill are compared with experiments at Re = 10 exp 6. The effects of the grid spacing together with the numerical efficiency of the various formulations are investigated. The results show that the models provide a satisfactory prediction of the flow field in the presence of a favorable pressure gradient, while the accuracy rapidly deteriorates when a strong adverse pressure gradient is encountered. A newly proposed model form that does not explicitly depend on the wall distance seems promising for application to complex geometries.

Michelassi, V.↗

A spectral overlay method for dissimilar materials

The spectral overlay method is applied to examine the stress distribution along the interface between the two different materials. The essential feature of the spectral overlay method is that the high resolution of localized steep gradients can be achieved by overlaying a spectral interpolant on a standard finite element mesh. In order to evaluate this method and compare it with conventional finite element method, a test problem with high gradients in Poisson equation has been devised. The results show that this method is very powerful in capturing the shape of the gradient field and its peak value. Solutions for two problems with interfaces between dissimilar materials are then given to illustrate the effectiveness of this method.

Belytschko, T.↗

Numerical simulation of thermocapillary flow under zero and low gravity conditions

This paper discusses the numerical solution methods and results of steady and unsteady thermocapillary (surface-tension) and buoyancy driven flows in 2D cavities and liquid columns. The 2D cavity was assumed to be square with one free surface with a zero Capillary number (i.e., the free surface was constrained to be flat). A pseudospectral method was used to solve steady and unsteady surface tension-driven and mixed buoyancy-surface tension flows in a square cavity. For the liquid column a finite-difference scheme based on a Picard iteration was used to solve for the flow, temperature and free surface shape. The surface of the liquid column was allowed to deform and, as for the 2D cavity, the surface tension was assumed to depend on temperature.

Alexander, J. I. D.↗

Effect of Apex Flap Deflection on Vertical Tail Buffeting

A computational study of the effect of vortex breakdown location on vertical tail buffeting is conducted. The position of the breakdown is modified by employing an apex flap deflected by an experimentally determined optimal angle. The delayed breakdown flow and buffeting response is then compared to the nominal undeflected case. This multidisciplinary problem is solved sequentially for the fluid flow, the elastic tail deformations and the grid displacements. The fluid flow is simulated by time accurately solving the unsteady, compressible, Reynolds-averaged Navier-Stokes equations using an implicit, upwind, flux-difference splitting finite volume scheme. The elastic vibrations of the tails are modeled by uncoupled bending and torsion beam equations. These equations are solved accurately in time using the Galerkin method and a five-stage Runge-Kutta-Verner scheme. The grid for the fluid dynamics calculations is continuously deformed using interpolation functions to disperse the displacements smoothly throughout the computational domain. An angle-of-attack of 35 deg.is chosen such that the wing primary-vortex cores experience vortex breakdown and the resulting turbulent wake flow impinges on tile vertical tails. The dimensions and material properties of the vertical tails are chosen such that the deflections are large enough to insure interaction with the flow, and the natural frequencies are high enough to facilitate a practical computational solution. Results are presented for a baseline uncontrolled buffeting case and a delayed breakdown case in which the apex flap has been deflected 15 deg. The flap was found to be very effective in delaying the breakdown, increasing the location from 50%c to 94%c, which resulted in a 6% increase in lift coefficient and pitching moment. However, the integrated buffet loads and tip responses were roughly equivalent for the two cases.

Massey, Steven J.↗

Analysis Method for Inelastic, Adhesively Bonded Joints with Anisotropic Adherends

A one-dimensional analysis method for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives with nonlinear material behavior is presented in the proposed paper. The strain and resulting stress field in a general, bonded joint overlap are determined by using a variable-step, finite-difference solution algorithm to iteratively solve a system of first-order differential equations. Applied loading is given by a system of combined extensional, bending, and shear forces that are applied to the edge of the joint overlap. Adherends are assumed to behave as linear, cylindrically bent plates using classical laminated plate theory that includes the effects of first-order transverse shear deformation. Using the deformation theory of plasticity and a modified von-Mises yield criterion, inelastic material behavior is modeled in the adhesive layer. Results for the proposed method are verified against previous results from the literature and shown to be in excellent agreement. An additional case that highlights the effects of transverse shear deformation between similar adherends is also presented.

Smeltzer, Stanley S., III↗

Applications of Quantum Chemistry to the Study of Carbon Nanotubes

For several years, scientists at NASA Ames have been studying the properties of carbon nanotubes using various experimental and computational methods. In this talk, I will compare different strategies for using quantum chemistry calculations to describe the electronic structure, deformation and chemical functionalization of single wall carbon nanotubes (SWNT) and the physisorption of small molecules on nanotube surfaces. The SWNT can be treated as an infinite (periodic) or finite length carbon cylinder or as a polycyclic aromatic hydrocarbon (PAH) molecule with an imposed curvature maintained by external constraints (as if it were cut out of the SWNT surface). Calculations are carried out using DFT and MP2 methods and a variety of atomic orbital basis sets from minimal (STO-3G) to valence triple zeta. The optimal approach is based on the particular SWNT property of interest. Examples to be discussed include: nanotube fluorination and other functionalization reactions; coating of nanotubes by water vapor and low-molecular weight organic molecules; and the nature of the interface between SWNT and liquids such as water and amines. In many cases, the quantum chemistry calculations are used to parameterize or validate force fields for molecular dynamics simulations. The results of these calculations have helped explain experimental data and contributed to the design of novel materials and sensors based on carbon nanotubes. Some of this research is described in the following papers:

Jaffe, Richard L.↗

Efficient Entropy Stable Gauss Collocation Methods

The construction of high-order entropy stable collocation schemes on quadrilateral and hexahedral elements has relied on the use of Gauss-Legendre-Lobatto collocation points and their equivalence with summation-by-parts (SBP) finite difference operators. In this work, we show how to efficiently generalize the construction of semidiscrete, entropy stable schemes on tensor product elements to Gauss points and generalized SBP operators. Numerical experiments suggest 8 that the use of Gauss points significantly improves accuracy on curved meshes.

Jesse Chan↗

A review and assessment of the stress-intensity factors for surface cracks

The stress-intensity factor solutions proposed for a surface crack in a finite plate subjected to uniform tension are reviewed. Fourteen different solutions for the stress-intensity factors are compared. These solutions were obtained over the past 16 years using approximate analytical methods, experimental methods, and engineering estimates. The accuracy is assessed of the various solutions by correlating fracture data on surface-cracked tension specimens made of a brittle epoxy material. Fracture of the epoxy material was characterized by a constant value of stress-intensity factor at failure. Thus, the correctness of the various solutions is judged by the variations in the stress-intensity factors at failure. The solutions were ranked in order of minimum standard deviation. The highest ranking solutions correlated 95 percent of data analyzed within + or - 10 percent, whereas the lowest ranking solutions correlated 95 percent of data analyzed within + or - 20 percent. However, some solutions could be applied to all data considered, whereas others are limited with respect to crack shapes and crack sizes that could be analyzed.

Newman, J. C., Jr.↗

Developments in the simulation of compressible inviscid and viscous flow on supercomputers

In anticipation of future supercomputers, finite difference codes are rapidly being extended to simulate three-dimensional compressible flow about complex configurations. Some of these developments are reviewed. The importance of computational flow visualization and diagnostic methods to three-dimensional flow simulation is also briefly discussed.

Steger, J. L.↗

Developments in the simulation of compressible inviscid and viscous flow on supercomputers

In anticipation of future supercomputers, finite difference codes are rapidly being extended to simulate three-dimensional compressible flow about complex configurations. Some of these developments are reviewed. The importance of computational flow visualization and diagnostic methods to three-dimensional flow simulation is also briefly discussed.

Steger, J. L.↗

Design sensitivity analysis with Applicon IFAD using the adjoint variable method

A numerical method is presented to implement structural design sensitivity analysis using the versatility and convenience of existing finite element structural analysis program and the theoretical foundation in structural design sensitivity analysis. Conventional design variables, such as thickness and cross-sectional areas, are considered. Structural performance functionals considered include compliance, displacement, and stress. It is shown that calculations can be carried out outside existing finite element codes, using postprocessing data only. That is, design sensitivity analysis software does not have to be imbedded in an existing finite element code. The finite element structural analysis program used in the implementation presented is IFAD. Feasibility of the method is shown through analysis of several problems, including built-up structures. Accurate design sensitivity results are obtained without the uncertainty of numerical accuracy associated with selection of a finite difference perturbation.

Frederick, Marjorie C.↗