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At least 649 records · Page 36
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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 NTRS1981

A more accurate modeling of the effects of actuators in large space structures

The paper deals with finite actuators. A nonspinning three-axis stabilized space vehicle having a two-dimensional large structure and a rigid body at the center is chosen for analysis. The torquers acting on the vehicle are modeled as antisymmetric forces distributed in a small but finite area. In the limit they represent point torquers which also are treated as a special case of surface distribution of dipoles. Ordinary and partial differential equations governing the forced vibrations of the vehicle are derived by using Hamilton's principle. Associated modal inputs are obtained for both the distributed moments and the distributed forces. It is shown that the finite torquers excite the higher modes less than the point torquers. Modal cost analysis proves to be a suitable methodology to this end.

Hablani, H. B.↗
NASA NTRS1981

Analysis of Lageos' altitude decrease

The paper treats the inverse problem of celestial mechanics which consists of determining the force field or potential from given or observed orbit(s). From the observational information, according to which Lageos loses approximately 1 mm altitude per day, a linear partial differential equation is formulated. The solution of this equation gives the field responsible for the above-mentioned, as yet unexplained, small but well established secular decrease in the semi-major axis. Note that the altitude-loss is not due to air-drag because of the very high altitude of this satellite.

Szebehely, V.↗
NASA NTRS1981

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Chen, C.-J.↗
NASA NTRS1981

Nonparallel stability of three-dimensional flows

The linear stability of three-dimensional incompressible, isothermal, nonparallel boundary-layer flows has been investigated. The method of multiple scales is used to derive the partial-differential equations that describe the spatial modulations of the amplitude, phase and wavenumber of a disturbance. Group velocities are used to determine the disturbance growth direction. The envelope method is used to calculate the logarithmic amplitude growth rate N. The theory is applied to the flows over a swept-back tapered wing with boundary-layer suction. Results of such analysis for the X-21 wing are discussed. It is found that the nonparallel effects for this wing is substantial.

Padhye, A. R.↗
NASA NTRS1981

Instability of non-zonal baroclinic flows - Multiple-scale analysis

The linear instability of a non-zonal flow can be reduced to an eigenvalue-eigenfunction problem, governed by a nonseparable partial differential equation (Niehaus, 1980). Approximate solutions, found by the method of multiple scales, are derived here and compared with earlier results found using a spectral method. The amplitude maxima are correctly located. The zonal variations of local wavenumber and of amplitude are qualitatively correct, but not sufficiently extreme. Because the method is oversensitive to local conditions, and less sensitive to global constraints, this comparison provides theoretical limits to the possibility of parameterizing transient eddies in terms of the local time mean state of the atmosphere. The method can be extended easily to flows with more realistic vertical structure.

Niehaus, M. C. W.↗
NASA NTRS1980

The control and estimation of large space structures

A shape control or estimation problem for a large space structure can be modeled by a partial differential equation which represents changes in shape with respect to space and time, together with spatially discrete forcing functions or observations which represent the placement of actuators or sensors at discrete points along the structure. The use of Green's functions to convert boundary value problems into integral equations provides a convenient treatment of this mixture of continuous and discrete mathematics. Control and estimation algorithms are developed for the one-dimensional static beam to illustrate this technique.

Weeks, C.↗
NASA NTRS1982

Higher-Order Panel Method for Aerodynamic Flow Analysis

PANAIR uses high-order panel method to predict inviscid subsonic or supersonic flows about arbitrary configuration. Panel method solves linear partial differential equation numerically by approximating configuration surface with panels on which unknown "singularity strengths" are defined. PANAIR includes advanced software technology as well as advanced aerodynamic technology.

Erickson, L.↗
NASA NTRS1982

Numerical solution of potential flow about arbitrary 2-dimensional multiple bodies

A procedure for the finite-difference numerical solution of the lifting potential flow about any number of arbitrarily shaped bodies is given. The solution is based on a technique of automatic numerical generation of a curvilinear coordinate system having coordinate lines coincident with the contours of all bodies in the field, regardless of their shapes and number. The effects of all numerical parameters involved are analyzed and appropriate values are recommended. Comparisons with analytic solutions for single Karman-Trefftz airfoils and a circular cylinder pair show excellent agreement. The technique of application of the boundary-fitted coordinate systems to the numerical solution of partial differential equations is illustrated.

Thompson, J. F.↗
NASA NTRS1981

Applications of estimation theory to numerical weather prediction

Numerical weather prediction (NWP) is an initial value problem for a system of nonlinear partial differential equations in which the initial values are known only incompletely and inaccurately. Data at initial time can be supplemented, however, by observations of the system distributed over a time interval preceding it. Estimation theory was successful in approaching such problems for models governed by systems of ordinary differential equations and of linear PDEs. Estimation-theoretic methods for NWP are developed. A model exhibiting many features of large scale atmospheric flow important in NWP is the one governed by the shallow fluid equations. The estimation problem for a linearized formulation of these equations is studied. A finite difference version of the equations is used as a forecast model to simulate the numerical models used in NWP.

Cohn, S.↗
NASA NTRS1982

Integrating matrix formulations for vibrations of rotating beams including the effects of concentrated masses

By expressing partial differential equations of motion in matrix notation, utilizing the integrating matrix as a spatial operator, and applying the boundary conditions, the resulting ordinary differential equations can be cast into standard eigenvalue form upon assumption of the usual time dependence. As originally developed, the technique was limited to beams having continuous mass and stiffness properties along their lengths. Integrating matrix methods are extended to treat the differential equations governing the flap, lag, or axial vibrations of rotating beams having concentrated masses. Inclusion of concentrated masses is shown to lead to the same kind of standard eigenvalue problem as before, but with slightly modified matrices.

Lakin, W. D.↗
NASA NTRS1982

Implementation of a C-1 triangular element based on the P-version of the finite element method

The implementation of a computer code CONE (for C(1) continuity) based on the p-version of the finite element method is described. A hierarchic family of triangular finite elements of degree p 5 is used. This family enforces C(1)-continuity across interelement boundaries, and the code is applicable to fourth order partial differential equations in two independent variables, in particular to the biharmonic equation. Applications to several benchmark problems in plate bending are presented. Sample results are examined and compared with theoretical predictions. In particular the analysis of the bending of a rhombic plate shows a significant improvement over othr published results.

Wang, D. W.↗
NASA NTRS1981

Determining solutions of hyperbolic systems from incomplete data

An investigation is conducted regarding first-order hyperbolic systems of partial differential equations, taking into account problems for which complete initial data are not available. Problems of the considered kind arise in geophysical applications where satellites are used to collect data. In global weather prediction, it is possible to derive atmospheric temperature and pressure reasonably well over the whole globe from satellite measurements; obtaining the wind field globally is more difficult. It is pointed out that a simple model of atmospheric flow investigated in numerical weather prediction is governed by the shallow water equations. The effect of the Coriolis term on the linearized shallow-water equations is studied.

Bube, K. P.↗
NASA NTRS1981

Accuracy and convergence of a finite element algorithm for turbulent boundary layer flow

The Galerkin-Weighted Residuals formulation is employed to derive an implicit finite element solution algorithm for the nonlinear parabolic partial differential equation system governing turbulent boundary layer flow. Solution accuracy and convergence with discretization refinement are quantized in several error norms using linear and quadratic basis functions. Richardson extrapolation is used to isolate integration truncation error in all norms, and Newton iteration is employed for all equation solutions performed in double-precision. The mathematical theory supporting accuracy and convergence concepts for linear elliptic equations appears extensible to the nonlinear equations characteristic of turbulent boundary layer flow.

Soliman, M. O.↗
NASA NTRS1981

Dynamic behavior of continuous cantilevered pipes conveying fluid near critical velocities

The plane motion of a cantilevered pipe conveying fluid is examined when the flow velocity is in the neighborhood of that generating flutter. In contrast to previous studies, the flow velocity is not prescribed as a constant, but is determined from the laws of motion. A system of two nonlinear partial differential equations which are coupled through the nonlinear terms is thereby obtained. The solution is found by the use of the Krylov-Bogoliubov averaging method and the results are discussed indicating the effect of nonlinearities.

Rousselet, J.↗
NASA NTRS1982

Estimation of distributed parameter systems

The estimation and control of large flexible space structures pose significant new control technology problems. One major problem area is the closed-loop stability of a structure that has been modeled with truncated modal dynamics. Stability problems arise due to the control design process beginning with a deficient model. This work provides the necessary conditions for the optimal estimation of infinite dimensional (partial-differential equation) systems. This approach can be particularly useful for initial control studies and for gaining considerable insight into what the optimal estimator for a truly infinite dimensional system should be. A detailed example of the estimation of the continuous shape of a string in tension is presented.

Schaechter, D. B.↗
NASA NTRS1981

Analytical description of charged particle transport along arbitrary guiding-field configurations

Focused particle transport is analyzed in terms of partial differential equations which are applicable to arbitrary spatial variations of the mean free path and the focusing length. A distribution function for transport is written in two forms of the Boltzmann equation and a coefficient of spatial diffusion is defined. Changes from a nearly coherent propagation of flare particles in regions of strong focusing near the sun to ordinary diffusion in the outer solar system are described as supercoherent transitions. A solution to the steady state problem is developed and results are presented for a monopolar guiding field configuration with isotropic diffusion gradually giving way to anisotropy in a region suggestive of a collimated beam of particles streaming away from its source.

Earl, J. A.↗
NASA NTRS1982

Estimation of atmospheric species concentrations from remote sensing data

The atmospheric species concentration distribution-estimation problem that arises from the measurement configuration of remote sensing, which involves a field of view that moves across the region, is solved by means of the partial differential equation for atmospheric diffusion and the Wiener-Hopf theory. A numerical study is also undertaken for the estimation of concentration distribution downwind of a hypothetical, continuous ground-level source of pollutants.

Omatu, S.↗