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At least 1,117 records · Page 62

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NASA NTRS1993

A solution scheme for the Euler equations based on a multi-dimensional wave model

A scheme for the solution of scalar advection on an unstructured mesh has been developed, tested, and extended to the Euler equations. The scheme preserves a linear function exactly, and yields nearly monotone results. The flux function associated with the Euler scheme is based on a discrete 'wave model' for the system of equations. The wave model decomposes the solution gradient at a location into shear waves, entropy waves and acoustic waves and calculates the speeds, strengths and directions associated with the waves. The approach differs from typical flux-difference splitting schemes in that the waves are not assumed to propagate normal to the faces of the control volumes; directions of propagation of the waves are instead computed from solution-gradient information. Results are shown for three test cases, and two different wave models. The results are compared to those from other approaches, including MUSCL and Galerkin least squares schemes.

Powell, Kenneth G.↗

NASA NTRS1988

Design of magnets inside cylindrical superconducting shields

The design of magnets inside closed, cylindrical, superconducting shields is discussed. The Green function is given for the magnetic vector potential for cylindrically symmetric currents inside such a shield. The magnetic field everywhere inside the shield can be obtained from this function, which includes the effects of the induced shield currents exactly. The field is given for a thin solenoid as an example and the convergence of the series solution for this case is discussed. The shield can significantly reduce the strength and improve the homogeneity of a magnet. The improvement in homogeneity is of particular importance in the design of correction coils. These effects, and the maximum field on the shield, are examined for a typical solenoid. The results given are also useful, although not exact, for long shields with one or two open ends.

Rigby, K. W.↗

NASA NTRS1973

Analytical method for predicting the pressure distribution about a nacelle at transonic speeds

The formulation and development of a computer analysis for the calculation of streamlines and pressure distributions around two-dimensional (planar and axisymmetric) isolated nacelles at transonic speeds are described. The computerized flow field analysis is designed to predict the transonic flow around long and short high-bypass-ratio fan duct nacelles with inlet flows and with exhaust flows having appropriate aerothermodynamic properties. The flow field boundaries are located as far upstream and downstream as necessary to obtain minimum disturbances at the boundary. The far-field lateral flow field boundary is analytically defined to exactly represent free-flight conditions or solid wind tunnel wall effects. The inviscid solution technique is based on a Streamtube Curvature Analysis. The computer program utilizes an automatic grid refinement procedure and solves the flow field equations with a matrix relaxation technique. The boundary layer displacement effects and the onset of turbulent separation are included, based on the compressible turbulent boundary layer solution method of Stratford and Beavers and on the turbulent separation prediction method of Stratford.

Keith, J. S.↗

NASA NTRS1975

Attenuation of sound in ducts with acoustic treatment: A generalized approximate equation

A generalized approximate equation for duct lining sound attenuation is presented. The specification of two parameters, the maximum possible attenuation and the optimum wall acoustic impedance is shown to completely determine the sound attenuation for any acoustic mode at any selected wall impedance. The equation is based on the nearly circular shape of the constant attenuation contours in the wall acoustic impedance plane. For impedances far from the optimum, the equation reduces to Morse's approximate expression. The equation can be used for initial acoustic liner design. Not least important is the illustrative nature of the solutions which provide an understanding of the duct propagation problem usually obscured in the exact calculations. Sample calculations using the approximate attenuation equation show that the peak and the bandwidth of the sound attenuation spectrum can be represented by quite simple functions of the ratio of actual wall acoustic resistance to optimum resistance.

Rice, E. J.↗

NASA NTRS1975

Attenuation of sound in ducts with acoustic treatment - A generalized approximate equation

Rice, E. J.↗

NASA NTRS1980

Mark 3 interactive data analysis system

The interactive data analysis system, a major subset of the total Mark 3 very long baseline interferometry (VLBI) software system is described. The system consists of two major and a number of small programs. These programs provide for the scientific analysis of the observed values of delay and delay rate generated by the VLBI data reduction programs and product the geophysical and astrometric parameters which are among the ultimate products of VLBI. The two major programs are CALC and SOLVE. CALC generates the theoretical values of VLBI delay rate as well as partial derivatives based on apriori values of the geophysical and astronometric parameters. SOLVE is a least squares parameters estimation program which yields the geophysical and astrometric parameters using the observed values by the data processing system and theoretical values and partial derivatives provided by CALC. SOLVE is a highly interactive program in which the user selects the exact form of the recovered parameters and the data to be accepted into the solution.

Ryan, J. W.↗

NASA NTRS1982

Asymptotic Expansions and Estimates for the Capillary Problem

The asymptotic properties for the small Bond number B of the equilibrium capillary interface interior to a circular cylindrical tube vertically dipped in an infinite reservoir of liquid are discussed. (The Bond number B is a dimensionless parameter which is the ratio of gravitational to capillary forces.) The formal expansion in powers of B of the solution to the differential equation describing the equilibrium surface (as can be obtained by standard perturbation methods) is proved to be truly asymptotic -- to all orders and uniformly in the variable and parameter gamma, the contact angle. Sequences of general estimates, in closed form, from above and from below, are also given for the solution and related functions. The M-th term in these sequences are asymptotically exact to order m. An idiosyncrasy of the problem, crucial in obtaining these estimates, is the absolute monotonicity of the structural function of the system in integral form.

Brulois, F. P.↗

NASA NTRS1982

Pole placement and order reduction in two-time-scale control systems through Riccati iteration

A transformation of variables taken from singular perturbations may be applied to two-time-scale linear systems in state space form to reduce the system to block-diagonal form with slow and fast modes decoupled. The transformation is easily computed by applying the new Riccati iteration. The iteration yields a solution to the nonsymmetric algebraic Riccati equation obtained by partitioning the original system matrix A. The numerical procedure is initiated with the trivial iterate L(0) = 0, and is globally convergent to the desired unique time scale decoupling solution. After transformation, the decoupled system may be used in controller design to achieve exact closed loop pole placement in the slow subsystem without altering the poles of the fast subsystem. The decoupled form may also be used to reduce system order by wetting a small parameter to zero. Provided the fast subsystem is stable, the order reduction can be expected to yield a good approximation to the original system. These methods are demonstrated using the 16th order linear model of a turbofan engine.

Anderson, L. R.↗

NASA NTRS1986

Quasi-generalized variables

The numerical solution of a system of differential and algebraic equations is difficult, due to the appearance of numerical instabilities. A method is presented here which permits numerical solutions of such a system to be obtained which satisfy the algebraic constraint equations exactly without reducing the order of the differential equations. The method is demonstrated using examples from mechanics.

Baumgarten, J.↗

NASA NTRS1986

Phase propagation of the solar modulation of galactic cosmic rays

The phase of the 11-yr galactic cosmic ray variation, due to a varying rate of emission of long-lived, propagating regions of enhanced scattering, travels faster than the scattering regions themselves. The radial speed of the 11-yr phase in the quasi-steady force field approximation is exactly twice the speed of the individual episodic decreases. A time-dependent numerical solution for 1-GeV protons at 1 and 30 AU gives a phase speed which is 1.85 times the propagation speed of the individual decreases.

Forman, M. A.↗

NASA NTRS1992

A considerable effect of stratospheric aerosol on lidar-detected ozone profile and a three-wavelength inversion technique for both ozone and aerosol

As far as the Differential Absorption Lidar (DIAL) technique is concerned, it is important that the off-line wavelength is close to the on-line wavelength in order to avoid a messy computation of the atmospheric aerosol scattering. However, the two wavelengths of ozone-DIAL are usually considerably different. Usually, an excimer laser of 308nm (on-line) and Raman shifting of 353nm or the third harmonic of a Nd-YAG laser with 355nm (off-line) are selected for measurements of the stratospheric ozone, and there is a difference of 45nm or 47nm between them. Because of the difference there is a difference in the atmospheric scatterings of the two wavelengths. This can cause some error in the retrieved ozone profile if the aerosol scattering is neglected. This paper is devoted to a study of the effect of the stratospheric aerosol on the ozone solution, and a three-wavelength detection technique is proposed for obtaining the more exact ozone profile and the aerosol profile in the stratosphere.

Qiu, Jinhuan↗

NASA NTRS1997

Application of the Two-Step Filter to Process Ranging Measurements for Relative Navigation in an Elliptical Orbit

This estimator breaks a nonlinear estimation problem into a set of over determined 'first step' states which are linear in the observations and 'second step' states which are ultimately the states of interest. Linear estimation methods are applied to filter the observations and produce the optimal first step state estimate. The 'second step' states are obtained through iterative nonlinear parameter estimation considering the first step states as observations. It has been shown that this process exactly minimizes the least squares cost function for static problems and provides a better solution than the iterated extended Kalman filter (EKF) for dynamic problems. The two step filter is applied in this paper to process range and range rate measurements between the two spacecraft. Details of the application of the two step estimator to this problem will be given, highlighting the use of a test for ill-conditioned covariance estimates that can result from the first order covariance propagation. A comparison will be made between the performance of the two step filter and the IEKF.

Garrison, James L.↗

NASA NTRS2002

Solutal Convection Around Growing Protein Crystal and Diffusional Purification in Space

This work theoretically addressed two subjects: 1) onset of convection, 2) distribution of impurities. Onset of convection was considered analytically and numerically. Crystal growth was characterized by slow surface incorporation kinetics, i.e. growth kinetic coefficient beta (cm/s) small as compared to the typical bulk diffusion rate, D(sub 1)/h, where D(sub 1) is diffusivity of major crystallizing protein and h is the crystal size. Scaling type analysis predicted two laws on how the convection rate, v, essentially the Peclet number, Pe exactly equal to vh/D(sub 1), depends on dimensionless kinetic coefficient a exactly equal to beta h/D(sub 1). Namely: Pe = C(sub 2/5)(aRa(sup 2/5)) and Pe = C(sub 1) aRa. Here, Reynolds number Ra = rho(sub 1)(sup 0)gh(sup 3)(rho(sub p) - rho(sub w))/rho(sup p)rho(sub 1)vD(sub 1), v being solution viscosity. The constants C(sub 2/5), exactly equal to 0.28 and C(sub 1) exactly equal to 10(exp -2) found from the full scale computer simulation for a cylindrical crystal inside big cylindrical vessel. The linear boundary conditions connecting protein and impurity concentration at the interface with the flux to/from the interface was applied. No-slip condition for Navier-Shocker equations was employed. With these conditions, flow and concentration distributions were calculated. Validity of the Pe(Ra) dependencies follows for wide range of parameters for which numerical calculations have been accomplished and presented by various points.

Chernov, A. A.↗

NASA NTRS1975

ISOFINEL: Isoparametric finite element code for elastic analysis of two-dimensional bodies

A formulation is presented for the development of a finite element program for the elastic analysis of two-dimensional bodies using the eight-node isoparametric quadrilateral. The program solves for both plane stress and plane strain problems. The finite element formulation based on the isoparametric displacement functions is presented. The program structure is given in the form of flow diagrams with descriptions of the numerical procedure used to obtain the element stiffness matrix, and the solution method employed to solve for nodal displacements. Three numerical examples (a plate under uniaxial tension, a plate under pure shear, and a beam under pure bending) are presented to illustrate the capability and limitations of the element implementation. The first problem is solved exactly by the element, as predicted by the form of its displacement functions. In the other two problems the accuracy of the solution is highly dependent upon the slenderness of the element, the number of elements in the map, and the numerical integration scheme used to build the element stiffness matrix.

Marino, C.↗

NASA NTRS1975

Some recent developments in predicting unsteady loadings caused by control surface motions

Solution instabilities are identified within the procedures used to predict unsteady loadings due to motions of swept hingeline control surfaces. A preferred solution process that demonstrates the need of calculating smooth residual downwash distributions is described. Numerical results displaying erratic solution behavior when use is made of various forms of pressure expressions currently employed in control surface analyses are presented. A new expression of the asymptotic pressure function is derived, which exactly satisfies the change in boundary conditions around the boundary of the control surface. Results of applying the new pressure function are presented and indicate that stable converged solutions may be achieved for predicting the unsteady loadings caused by motions of swept hingeline control surfaces.

Rowe, W. S.↗

NASA NTRS2000

Light Scattering By Nonspherical Particles: Current Status and Challenging Issues

Quantitative analyses of remote sensing measurements of aerosols, clouds, precipitation, and particulate surfaces as well as computations of the Earth's radiation balance require detailed understanding of the interaction of small particles with light and other electromagnetic radiation. The convenient availability of the Lorenz-Mie theory has led to a widespread practice of treating all particles as if they were spheres. However, many natural and anthropogenic particles have nonspherical shapes, and the accumulated knowledge suggests that their scattering and radiative properties can be dramatically different from those of equivalent spheres. This presentation will summarize the recent significant progress achieved in the area of electromagnetic scattering by nonspherical particles and outline major problems that still await solution. The talk will cover the following specific topics: (1) comparison of most widely used exact and approximate theoretical techniques; (2) outline of laboratory and field measurement techniques; (3) compare theory and experiment; (4) need for a statistical approach in dealing with natural particles; (5) remote sensing and radiative transfer applications; and (6) major unsolved problems.

Mishchenko, Michael↗

NASA NTRS2004

Combined In-Plane and Through-the-Thickness Analysis for Failure Prediction of Bolted Composite Joints

Although two-dimensional methods provide accurate predictions of contact stresses and bolt load distribution in bolted composite joints with multiple bolts, they fail to capture the effect of thickness on the strength prediction. Typically, the plies close to the interface of laminates are expected to be the most highly loaded, due to bolt deformation, and they are usually the first to fail. This study presents an analysis method to account for the variation of stresses in the thickness direction by augmenting a two-dimensional analysis with a one-dimensional through the thickness analysis. The two-dimensional in-plane solution method based on the combined complex potential and variational formulation satisfies the equilibrium equations exactly, and satisfies the boundary conditions and constraints by minimizing the total potential. Under general loading conditions, this method addresses multiple bolt configurations without requiring symmetry conditions while accounting for the contact phenomenon and the interaction among the bolts explicitly. The through-the-thickness analysis is based on the model utilizing a beam on an elastic foundation. The bolt, represented as a short beam while accounting for bending and shear deformations, rests on springs, where the spring coefficients represent the resistance of the composite laminate to bolt deformation. The combined in-plane and through-the-thickness analysis produces the bolt/hole displacement in the thickness direction, as well as the stress state in each ply. The initial ply failure predicted by applying the average stress criterion is followed by a simple progressive failure. Application of the model is demonstrated by considering single- and double-lap joints of metal plates bolted to composite laminates.

Kradinov, V.↗

NASA NTRS2019

On the Calculation of Exact Cumulative Distribution Statistics for Burgers Equation

A mathematical procedure is presented for the calculation of exact cumulative distribution statistics for a viscosity-free variant of Burgers nonlinear partial differential equation (PDE) in one space dimension and time subject to sinusoidal initial data with uncertain (random variable) amplitude or phase shift. Analytical solutions of nonlinear PDEs with uncertain initial and/or boundary data are invaluable benchmarks in assessing approximate uncertainty quantification techniques. The Burgers equation solution with uncertain initial data results in nonsmooth solution behavior in both physical and random variable dimensions which provides a severe test for approximate uncertainty quantification techniques. Mathematical proofs are provided to verify that exact cumulative distribution statistics can be systematically and robustly obtained for all forward time.

Burgers↗