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NASA NTRS1980

An improved panel method for the solution of three-dimensional leading-edge vortex flows. Volume 1: Theory document

An improved panel method for the solution of three dimensional flow and wing and wing-body combinations with leading edge vortex separation is presented. The method employs a three dimensional inviscid flow model in which the configuration, the rolled-up vortex sheets, and the wake are represented by quadratic doublet distributions. The strength of the singularity distribution as well as shape and position of the vortex spirals are computed in an iterative fashion starting with an assumed initial sheet geometry. The method calculates forces and moments as well as detail surface pressure distributions. Improvements include the implementation of improved panel numerics for the purpose of elimination the highly nonlinear effects of ring vortices around double panel edges, and the development of a least squares procedure for damping vortex sheet geometry update instabilities. A complete description of the method is included. A variety of cases generated by the computer program implementing the method are presented which verify the mathematical assumptions of the method and which compare computed results with experimental data to verify the underlying physical assumptions made by the method.

Johnson, F. T.↗

NASA NTRS1980

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

Chakravarthy, S. R.↗

NASA NTRS1980

Hybrid vortex method for lifting surfaces with free-vortex flow

A Nonlinear Hybrid Vortex method (NHV-method) has been developed for predicting the aerodynamic characteristics of wings exhibiting leading- and side-edge separations. This method alleviates the drawbacks of the Nonlinear Discrete Vortex method (NDV-method, also known as the multiple line vortex method.) The NHV-method combines continuous-vorticity and vortex-line representations of the wing and its separated free shear layers. Continuous vorticity is used in the near-field calculations, while discrete vortex-lines are used in the far-field calculations. The wing and its free shear layers are divided into quadrilateral vortex panels having second-order vorticity distributions. The aerodynamic boundary conditions and continuity of the vorticity distributions are satisfied at certain nodal points on the vortex panels. An iterative technique is used to satisfy these conditions in order to obtain the vorticity distribution and the wake shape. Distributed and total aerodynamic loads are then calculated.

Kandil, O. A.↗

NASA NTRS1981

The stability of pseudospectral-Chebyshev methods

The pseudospectral-Chebyshev methods are shown to be convergent in variable coefficient problems and, in some cases, hyperbolic problems. The analysis demonstrates that the rate of convergence is greater for finite difference methods or the finite element method. For a single first-order hyperbolic equation, the method is seen as remaining stable even when the coefficient changes sign, although in this case it is specified that care must be taken to have adequate spatial resolution. It is noted that this fact, combined with the fact that collocation methods are easy to apply in the nonlinear case, shows that the pseudospectral method is in general preferable to the Galerkin or Tau methods.

Gottlieb, D.↗

NASA NTRS1981

A Galerkin type finite element method for rotary-wing aeroelasticity in hover and forward flight

A Galerkin finite element method for the spatial discretization of the nonlinear, nonselfadjoint, partial differential equations governing rotary-wing aeroelasticity is presented. This method reduces algebraic manipulative labor significantly when compared to the global Galerkin method based on assumed modes. Furthermore, the Galerkin finite element method is ideally suited to treat rotor blades with discontinuous mass and stiffness distribution and structurally redundant configurations as they appear in bearingless rotors. Implementation of the method is illustrated for the coupled flap-lag aeroelastic problem of hingeless rotor blades in hover and forward flight. Numerical results for stability and response illustrate the numerical properties and convergence behavior of the method. It is concluded that the Galerkin finite element method is a practical tool for solving rotary-wing aeroelastic stability and response problems.

Straub, F. K.↗

NASA NTRS1982

Application of the reduced basis method to nonlinear transient thermal analysis

An effort to apply the reduced basis method to nonlinear transient thermal analysis is described. The method combines the classical Rayleigh-Ritz and modal superposition techniques with contemporary finite element methods to retain modeling versatility as the degrees of freedom in a problem are reduced. The essence of the method is to use a few thermal modes from eigenvalue analyses as basis vectors to represent the temperature response for a given thermal problem similar to the use of vibration modes to represent displacements in a dynamic response problem. Approximate temperature distributions were obtained using the reduced basis method for a small section of the Shuttle Orbiter lower wing undergoing reentry heating. Good agreement was obtained between the reduced basis method solutions and full system solutions with reductions in the degrees of freedom of up to a factor of four. The good agreement indicates the reduced basis method has the potential for significant reduction in computing effort for thermal analysis; however, considerable work remains to determine techniques for selecting the type and number of basis vectors needed for approximate solutions to more complex transient thermal problems.

Shore, C. P.↗

NASA NTRS1984

X-ray Topographic Methods and Application to Analysis of Electronic Materials

Three supplementary X-ray techniques new to semiconductor applications are discussed. These are the Computer Aided Rocking Curve Analyzer, the Divergent Beam Method and a new method based on enhanced X-ray flourescence. The first method is used for quantitative mapping of an elastic or plastic strain field while the other two methods are used only to measure elastic strains. The divergent beam method is used for measuring the full strain tensor while the microfluorescence method is useful for monitoring strain uniformity. These methods are discussed in detail and examples of their application is presented. Among these are determination of the full strain ellipsoid in state-of-the-art liquid phase epitaxy deposited III-V epitaxial films; mapping of the plastic strain concentrations in tensile deformed Si; and quantitative determination of damage in V3Si due to ion implantation.

Mayo, W. E.↗

NASA NTRS1984

Implementation of uniform perturbation method for potential flow past axisymmetric and two-dimensional bodies

The aerodynamic characteristics of potential flow past an axisymmetric slender body and a thin airfoil are calculated using a uniform perturbation analysis method. The method is based on the superposition of potentials of point singularities distributed inside the body. The strength distribution satisfies a linear integral equation by enforcing the flow tangency condition on the surface of the body. The complete uniform asymptotic expansion of its solution is obtained with respect to the slenderness ratio by modifying and adapting an existing technique. Results calculated by the perturbation analysis method are compared with the existing surface singularity panel method and some available analytical solutions for a number of cases under identical conditions. From these comparisons, it is found that the perturbation analysis method can provide quite accurate results for bodies with small slenderness ratio. The present method is much simpler and requires less memory and computation time than existing surface singularity panel methods of comparable accuracy.

Wong, T. C.↗

NASA NTRS1984

Ultrasonic velocity measurement using phase-slope cross-correlation methods

Computer implemented phase-slope and cross-correlation methods are introduced for measuring time delays between pairs of broadband ultrasonic pulse-echo signals for determining velocity in engineering materials. The phase-slope and cross-correlation methods are compared with the overlap method which is currently in wide use. Comparison of digital versions of the three methods shows similar results for most materials having low ultrasonic attenuation. However, the cross-correlation method is preferred for highly attenuating materials. An analytical basis for the cross-correlation method is presented. Examples are given for the three methods investigated to measure velocity in representative materials in the megahertz range.

Hull, D. R.↗

NASA NTRS1983

Comparison of three methods for measuring acoustic properties of bulk materials

Three methods for measuring the acoustic properties of bulk materials have been evaluated. The methods differ from one another in their practical implementation and reliability. The two more convenient methods exploit changes in surface impedance of test samples resulting from a change in the test sample geometry or boundary conditions. The results from these surface methods are compared with that obtained using Scott's method. In Scott's method the propagation constant is obtained by a 'direct' measurement inside the test material by means of a probe tube. The comparisons suggest that the surface methods will provide reliable and accurate results when the test sample behaves as a rigid porous structure.

Smith, C. D.↗

NASA NTRS1985

A Uniform Subdivision Method for Triangular Bezier Patches

A subdivision method for Bezier triangles is presented that parallels the development of Lane-Riesenfeld for Bezier Curves. The method is developed from the mathematical description of the patch, and the resulting algorithm does not require evaluation of the blending functions. This method subdivides the triangle uniformly so that the lengths of the sides of the subtriangles are uniformly reduced. This method is a member of the class of methods first presented by Goldman, which contain subdivision methods that arise from degenerate subdivision of Bezier tetrahedra. It is shown that a certain method is a natural extension of the Lane-Riesenfeld results for Bezier curves.

Joy, K. I.↗

NASA NTRS1985

Comparison of Two Algebraic Methods for Curve/curve Intersection

Most geometric modeling systems use either polynomial or rational functions to represent geometry. In such systems most computational problems can be formulated as systems of polynomials in one or more variables. Classical elimination theory can be used to solve such systems. Here Cayley's method of elimination is summarized and it is shown how it can best be used to solve the curve/curve intersection problem. Cayley's method was found to be a more straightforward approach. Furthermore, it is computationally simpler, since the elements of the Cayley matrix are one variable instead of two variable polynomials. Researchers implemented and tested both methods and found Cayley's to be more efficient. Six pairs of curves, representing mixtures of lines, circles, and cubic arcs were used. Several examples had multiple intersection points. For all six cases Cayley's required less CPU time than the other method. The average time ratio of method 1 to method 2 was 3.13:1, the least difference was 2.33:1, and the most dramatic was 6.25:1. Both of the above methods can be extended to solve the surface/surface intersection problem.

Demontaudouin, Y.↗

NASA NTRS1984

Methods for analysis of cracks in three-dimensional solids

Analytical and numerical methods evaluating the stress-intensity factors for three-dimensional cracks in solids are presented, with reference to fatigue failure in aerospace structures. The exact solutions for embedded elliptical and circular cracks in infinite solids, and the approximate methods, including the finite-element, the boundary-integral equation, the line-spring models, and the mixed methods are discussed. Among the mixed methods, the superposition of analytical and finite element methods, the stress-difference, the discretization-error, the alternating, and the finite element-alternating methods are reviewed. Comparison of the stress-intensity factor solutions for some three-dimensional crack configurations showed good agreement. Thus, the choice of a particular method in evaluating the stress-intensity factor is limited only to the availability of resources and computer programs.

Raju, I. S.↗

NASA NTRS1984

A survey of strength analysis methods for laminates with holes

The methods for predicting the strength of composite laminates with fastener holes are reviewed for the cases of unloaded as well as loaded holes. Three categories of methods are discussed: (1) the hole-boundary stress (HBS) methods which compare the peak stresses and the laminate strength; (2) the linear elastic fracture (LEFM) methods which assume cracks emanating from the hole and predict failure when the stress intensity factor for a crack equals the laminate fracture toughness; and (3) two different two-parameter (TP) methods: the average-stress (ASTP) method, which predicts failure when the average stress over a distance from the hole equals the laminate strength; and the point-stress (PSTP) Whitney-Nuismer (1974) approach, which predicts failure when the stress near the hole equals the material strength. The PSTP is relatively accurate and is by far the most widely used of all the prediction methods. However, for large ranges of variables and cases, the current strength predictions may not always be accurate.

Crews, J. H., Jr.↗

NASA NTRS1986

Multi-color incomplete Cholesky conjugate gradient methods for vector computers

In this research, we are concerned with the solution on vector computers of linear systems of equations, Ax = b, where A is a larger, sparse symmetric positive definite matrix. We solve the system using an iterative method, the incomplete Cholesky conjugate gradient method (ICCG). We apply a multi-color strategy to obtain p-color matrices for which a block-oriented ICCG method is implemented on the CYBER 205. (A p-colored matrix is a matrix which can be partitioned into a pXp block matrix where the diagonal blocks are diagonal matrices). This algorithm, which is based on a no-fill strategy, achieves O(N/p) length vector operations in both the decomposition of A and in the forward and back solves necessary at each iteration of the method. We discuss the natural ordering of the unknowns as an ordering that minimizes the number of diagonals in the matrix and define multi-color orderings in terms of disjoint sets of the unknowns. We give necessary and sufficient conditions to determine which multi-color orderings of the unknowns correpond to p-color matrices. A performance model is given which is used both to predict execution time for ICCG methods and also to compare an ICCG method to conjugate gradient without preconditioning or another ICCG method. Results are given from runs on the CYBER 205 at NASA's Langley Research Center for four model problems.

Poole, E. L.↗

NASA NTRS1985

Measurement of ultrasonic velocity using phase-slope and cross-correlation methods

Hull, D. R.↗

NASA NTRS1986

A comparison of several methods for the calculation of vibration mode shape derivatives

Four methods for the calculation of derivatives of vibration mode shapes (eigenvectors) with respect to design parameters are reviewed and compared. These methods (finite difference method, Nelson's method, modal method and a modified modal method) are implemented in a general-purpose commercial finite element program and applied to a cantilever beam and a stiffened cylinder with a cutout. A beam tip mass, a beam root height and specific dimensions of the cylinder model comprise the design variables. Data are presented showing the amount of central processor time used to compute the first four eigenvector derivatives for each example problem; errors and rapidity of convergence of the approximate derivative to the exact derivative are taken into account. Nelson's method proved to be most reliable and efficient.

Sutter, T. R.↗

NASA NTRS1986

A comparison of computational methods for three-dimensional, turbulent turbomachinery flow fields

A space-marching method and a time-marching method have been used to compute the three-dimensional turbulent flow in an end wall cascade of airfoils. Using an identical grid and turbulence model, the two codes were used to predict a variety of flow quantities. Predictions by the two methods are compared to each other and to experimental data. In general both methods predict measured quantities well, with a small edge in prediction accuracy going to the space-marching method. Secondary flow comparisons show the time-marching solution more accurately predicting the underturning of the flow in the outer portion of the end wall boundary layer while the space-marching method more accurately predicted the overturning of the flow very near the end wall. The prediction comparisons are discussed along with computational details and other attributes of the two methods.

Kirtley, K. R.↗