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At least 253 records · Page 14

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NASA NTRS1993

A note on the distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate

The purpose of this note is to construct a local solution that eliminates a residual velocity discontinuity in the inviscid portion of a solution obtained in a recent paper by Goldstein, Leib and Cowley (1992). This result is of importance because it shows that the solution obtained in that paper is entirely non-singular outside the viscous wall boundary layer and that any singularity in the problem will have to arise in the usual way through a breakdown in the viscous boundary layer.

Goldstein, M. E.↗

NASA NTRS1978

Two-dimensional radiative transfer. I - Planar geometry

Differential-equation methods for solving the transfer equation in two-dimensional planar geometries are developed. One method, which uses a Hermitian integration formula on ray segments through grid points, proves to be extremely well suited to velocity-dependent problems. An efficient elimination scheme is developed for which the computing time scales linearly with the number of angles and frequencies; problems with large velocity amplitudes can thus be treated accurately. A very accurate and efficient method for performing a formal solution is also presented. A discussion is given of several examples of periodic media and free-standing slabs, both in static cases and with velocity fields. For the free-standing slabs, two-dimensional transport effects are significant near boundaries, but no important effects were found in any of the periodic cases studied.

Mihalas, D.↗

NASA NTRS1976

On the role of constant-stress surfaces in the problem of minimizing elastic stress concentration

Cases involving antiplane shear deformation, axisymmetric torsion, and plane strain theory, with surfaces of constant stress magnitude optimal in terms of minimizing stress, are investigated. Results for the plane theory refer to exterior doubly connected domains. Stresses generated by torsion of an elastic solid lying within a radially convex region of revolution with plane ends, body force absent, and lateral surface traction-free, are examined. The unknown portion of the boundary of such domains may involve a hole, fillet, or notch.

Wheeler, L.↗

NASA NTRS1972

An analytical study of reduced-gravity liquid reorientation using a simplified marker and cell technique

A computer program called HOPI was developed to predict reorientation flow dynamics, wherein liquids move from one end of a closed, partially filled, rigid container to the other end under the influence of container acceleration. The program uses the simplified marker and cell numerical technique and, using explicit finite-differencing, solves the Navier-Stokes equations for an incompressible viscous fluid. The effects of turbulence are also simulated in the program. HOPI can consider curved as well as straight walled boundaries. Both free-surface and confined flows can be calculated. The program was used to simulate five liquid reorientation cases. Three of these cases simulated actual NASA LeRC drop tower test conditions while two cases simulated full-scale Centaur tank conditions. It was concluded that while HOPI can be used to analytically determine the fluid motion in a typical settling problem, there is a current need to optimize HOPI. This includes both reducing the computer usage time and also reducing the core storage required for a given size problem.

Betts, W. S., Jr.↗

NASA NTRS1990

Time development of a perturbed-spherical nucleus in a pure supercooled liquid. I - Power-law growth of morphological instabilities. II - Nonlinear development

The linear growth stage of the morphological instabilities developing at the liquid-solid interface during crystal growth from an axisymmetric spherical nucleus is analyzed. The corresponding growth rate parameters are calculated numerically, and it is shown that morphological instabilities for free growth evolve according to a power law in agreement with WKB results and contrary to an exponential law found in a quasi-stationary approximation. The time evolution of an arbitrary perturbed liquid-solid interface from a linear into the nonlinear stage is studied. The initial perturbations include the eigenfunctions for the linear problem, localized perturbations of the grain-boundary type, and a stochastic noise. It is shown that the perturbations grow and spread in a wavelike manner. The formation of a predendritic growth stage is characterized by establishment of constant values of tip radius and velocity.

Pines, V.↗

NASA NTRS1992

Large-amplitude finite element flutter analysis of composite panels in hypersonic flow

Consideration is given to a finite-element approach for determining the nonlinear flutter characteristics of 3D thin laminated composite panels using the full third-order-piston transverse-loading aerodynamic theory. The unsteady hypersonic aerodynamic theory and the von Karman large-deflection-plate theory are used to formulate the aeroelasticity problem. Nonlinear flutter analyses are performed to assess the influence of the higher-order aerodynamic theory on the structure's limit-cycle amplitude and the dynamic pressure of the flow velocity. A solution procedure is presented to solve the nonlinear panel flutter and large-amplitude free-vibration finite-element equations. Nonlinear flutter analyses are performed for different boundary support-conditions and for various system parameters. Linear finite-element flutter for isotropic and composite panels and large-amplitude isotropic panel flutter results are compared with existing classical solutions. The large-amplitude panel flutter results using the full third-order piston aerodynamic theory are presented to assess the influence of the nonlinear aerodynamic theory.

Gray, Carl E., Jr.↗

NASA NTRS1997

Towards Perfectly Absorbing Boundary Conditions for Euler Equations

In this paper, we examine the effectiveness of absorbing layers as non-reflecting computational boundaries for the Euler equations. The absorbing-layer equations are simply obtained by splitting the governing equations in the coordinate directions and introducing absorption coefficients in each split equation. This methodology is similar to that used by Berenger for the numerical solutions of Maxwell's equations. Specifically, we apply this methodology to three physical problems shock-vortex interactions, a plane free shear flow and an axisymmetric jet- with emphasis on acoustic wave propagation. Our numerical results indicate that the use of absorbing layers effectively minimizes numerical reflection in all three problems considered.

Hayder, M. Ehtesham↗

NASA NTRS1976

Interlaminar stresses in composite laminates: A perturbation analysis

A general method of solution for an elastic balanced symmetric composite laminate subject to a uniaxial extension was developed based upon a perturbation analysis of a limiting free body containing an interfacial plane. The solution satisfies more physical requirements and boundary conditions than previous investigations, and predicts smooth continuous interlaminar stresses with no instabilities. It determines the finite maximum intensity for the interlaminar normal stress in all laminates, provides mathematical evidences for the singular stresses in angle-ply laminates, suggests the need for the experimental determination of an important problem parameter, and introduces a viable means for solving related problems of practical interest.

Hsu, P. W.↗

NASA NTRS1981

Calculation of two-dimensional inlet flow fields by an implicit method including viscous effects: User's manual

Inlet flow fields for airbreathing missiles are calculated by the adaptation of a two dimensional computational method developed for the flow around airfoils. A supersonic free stream is assumed to allow the forebody calculation to be uncoupled from the inlet calculation. The inlet calculation employs an implicit, time marching finite difference procedure to solve the thin layer Navier-Stokes equations formulated in body fitted coordinates. The mathematical formulation of the problem and the solution algorithm are given. Numerical stability and accuracy as well as the initial and boundary conditions used are discussed. Instructions for program use and operation along with the overall program logic are also given.

Biringen, S.↗

NASA NTRS1997

Improvements in Block-Krylov Ritz Vectors and the Boundary Flexibility Method of Component Synthesis

A method of dynamic substructuring is presented which utilizes a set of static Ritz vectors as a replacement for normal eigenvectors in component mode synthesis. This set of Ritz vectors is generated in a recurrence relationship, proposed by Wilson, which has the form of a block-Krylov subspace. The initial seed to the recurrence algorithm is based upon the boundary flexibility vectors of the component. Improvements have been made in the formulation of the initial seed to the Krylov sequence, through the use of block-filtering. A method to shift the Krylov sequence to create Ritz vectors that will represent the dynamic behavior of the component at target frequencies, the target frequency being determined by the applied forcing functions, has been developed. A method to terminate the Krylov sequence has also been developed. Various orthonormalization schemes have been developed and evaluated, including the Cholesky/QR method. Several auxiliary theorems and proofs which illustrate issues in component mode synthesis and loss of orthogonality in the Krylov sequence have also been presented. The resulting methodology is applicable to both fixed and free- interface boundary components, and results in a general component model appropriate for any type of dynamic analysis. The accuracy is found to be comparable to that of component synthesis based upon normal modes, using fewer generalized coordinates. In addition, the block-Krylov recurrence algorithm is a series of static solutions and so requires significantly less computation than solving the normal eigenspace problem. The requirement for less vectors to form the component, coupled with the lower computational expense of calculating these Ritz vectors, combine to create a method more efficient than traditional component mode synthesis.

Carney, Kelly Scott↗

NASA NTRS1975

A numerical method for determining the natural vibration characteristics of rotating nonuniform cantilever blades

A method is presented for determining the free vibration characteristics of a rotating blade having nonuniform spanwise properties and cantilever boundary conditions. The equations which govern the coupled flapwise, chordwise, and torsional motion of such a blade are solved using an integrating matrix method. By expressing the equations of motion and matrix notation, utilizing the integrating matrix as an operator, and applying the boundary conditions, the equations are formulated into an eigenvalue problem whose solutions may be determined by conventional methods. Computer results are compared with experimental data.

White, W. F., Jr.↗

NASA NTRS1988

BEM for wave equation with boundary in arbitrary motion and applications to compressible potential aerodynamics of airplanes and helicopters

The wave equation for an object in arbitrary motion is investigated analytically using a BEM approach, and practical applications to potential flows of compressible fluids around aircraft wings and helicopter rotors are considered. The treatment accounts for arbitrary combined rotational and translational motion of the reference frame and for the wake motion. The numerical implementation as a computer algorithm is demonstrated on problems with prescribed and free wakes, the former in compressible flows and the latter for incompressible flows; results are presented graphically and briefly characterized.

Morino, Luigi↗

NASA NTRS1991

On the wall-normal velocity of the compressible boundary-layer equations

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Pruett, C. David↗

NASA NTRS1972

Electrophoresis demonstration on Apollo 16

Free fluid electrophoresis, a process used to separate particulate species according to surface charge, size, or shape was suggested as a promising technique to utilize the near zero gravity condition of space. Fluid electrophoresis on earth is disturbed by gravity-induced thermal convection and sedimentation. An apparatus was developed to demonstrate the principle and possible problems of electrophoresis on Apollo 14 and the separation boundary between red and blue dye was photographed in space. The basic operating elements of the Apollo 14 unit were used for a second flight demonstration on Apollo 16. Polystyrene latex particles of two different sizes were used to simulate the electrophoresis of large biological particles. The particle bands in space were extremely stable compared to ground operation because convection in the fluid was negligible. Electrophoresis of the polystyrene latex particle groups according to size was accomplished although electro-osmosis in the flight apparatus prevented the clear separation of two particle bands.

Snyder, R. S.↗

NASA NTRS1987

A generalized method for optimization of active noise controllers in three-dimensional spaces

In this investigation, the formulation of an optimal active noise controller for harmonic, enclosed sound fields is derived using an indirect boundary element method. The optimal active noise controller is defined as the volume velocity secondary source strengths which minimize the sound pressure level at a number of discrete interior locations. In addition, the formulation of an optimal active noise controller which minimizes the free field power radiated from a generalized, distributed noise source is presented. Representative results are provided for each formulation. For the enclosure problem, results are given for global control, local control, and passive wall treatments using a rectangular cavity. For the free field radiation problem, the effects of secondary source location and quantity on active noise controller performance are investigated. The relative merits of each formulation are discussed.

Mollo, C. G.↗

NASA NTRS1991

Compressible turbulent flows: Modeling and similarity considerations

With the recent revitalization of high speed flow research, compressibility presents a new set of challenging problems to turbulence researchers. Questions arise as to what extent compressibility affects turbulence dynamics, structures, the Reynolds stress-mean velocity (constitutive) relation, and the accompanying processes of heat transfer and mixing. In astrophysical applications, compressible turbulence is believed to play an important role in intergalactic gas cloud dynamics and in accretion disk convection. Understanding and modeling of the compressibility effects in free shear flows, boundary layers, and boundary layer/shock interactions is discussed.

Zeman, Otto↗

NASA NTRS1961

The General Equations of Equilibrium of Rotationally Symmetric Membranes and some Static Solutions for Uniform Centrifugal Loading

The general equations of equilibrium of a rotationally symmetrical body undergoing large arbitrary deflections but small strains are derived by means of the principle of virtual work. All deflections are referred to a reference surface which, in general, may be taken to coincide with any intermediate state of the membrane. Static solutions of the general equations for steadily rotating membranes are considered for the cases in which the final or the initial configuration of the membrane is specified. For problems in which the final configuration is specified, conditions are given under which such a configuration is obtainable from a stress-free initial state. Such conditions being satisfied, it is shown that the stresses and radial displacements are determinate while axial displacements may be obtained by quadrature. For problems in which the initial configuration is given, the determination of the stresses and deflections is reduced to the solution of a second-order nonlinear differential equation for a stress function. An approximate method of solution based on boundary-layer considerations is presented for the case of a spinning sphere of constant thickness. Specific examples are given for both classes of problems.

Simmonds, James G.↗

NASA NTRS1949

Behavior of the Laminar Boundary Layer for Periodically Oscillating Pressure Variation

The calculation of the phenomena within the boundary layer of bodies immersed in a flow underwent a decisive development on the basis of L. Prandtl's trains of thought, stated more than forth years ago, and by numerous later treatises again and again touching upon them. The requirements of the steadily improving aerodynamics of airplanes have greatly increased with the passing of time and recently research became particularly interested in such phenomena in the boundary layer as are caused by small external disturbances. Experimental results suggest that, for instance, slight fluctuations in the free stream velocities as they occur in wind tunnels or slight wavelike deviations of outer wing contours from the prescribed smooth course as they originate due to construction inaccuracies may exert strong effects on the extent of the laminar boundary layer on the body and thus on the drag. The development of turbulence in the last part of the laminar portion of the boundary layer is, therefore, the main problem, the solution of which explains the behavior of the transition point of the boundary layer. A number of reports in literature deal with this problem,for instance, those of Tollmien, Schlichting, Dryden, and Pretsch. The following discussion of the behavior of the laminar boundary layer for periodically oscillating pressure variation also purports to make a contribution to that subject.

Quick, august Wilhelm↗