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At least 811 records · Page 45

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NASA NTRS1981

An asymptotic unsteady lifting-line theory with energetics and optimum motion of thrust-producing lifting surfaces

A low frequency unsteady lifting-line theory is developed for a harmonically oscillating wing of large aspect ratio. The wing is assumed to be chordwise rigid but completely flexible in the span direction. The theory is developed by use of the method of matched asymptotic expansions which reduces the problem from a singular integral equation to quadrature. The wing displacements are prescribed and the pressure field, airloads, and unsteady induced downwash are obtained in closed form. The influence of reduced frequency, aspect ratio, planform shape, and mode of oscillation on wing aerodynamics is demonstrated through numerical examples. Compared with lifting-surface theory, computation time is reduced significantly. Using the present theory, the energetic quantities associated with the propulsive performance of a finite wing oscillating in combined pitch and heave are obtained in closed form. Numerical examples are presented for an elliptic wing.

Ahmadi, A. R.↗

NASA NTRS1981

Scaled Runge-Kutta algorithms for handling dense output

Low order Runge-Kutta algorithms are developed which determine the solution of a system of ordinary differential equations at any point within a given integration step, as well as at the end of each step. The scaled Runge-Kutta methods are designed to be used with existing Runge-Kutta formulas, using the derivative evaluations of these defining algorithms as the core of the system. For a slight increase in computing time, the solution may be generated within the integration step, improving the efficiency of the Runge-Kutta algorithms, since the step length need no longer be severely reduced to coincide with the desired output point. Scaled Runge-Kutta algorithms are presented for orders 3 through 5, along with accuracy comparisons between the defining algorithms and their scaled versions for a test problem.

Horn, M. K.↗

NASA NTRS1981

A comparative study of nonreflecting far-field boundary condition procedures for unsteady transonic flow computation

Various nonreflecting far-field boundary condition procedures are compared by implementing them in the computer code LTRAN2. This code solves the implicit finite-difference representation of the small-disturbance equations for transonic flows about airfoils. The first- and second-approximate nonreflecting conditions, as proposed by Engquist and Majda, are compared with the condition derived from the full-characteristic equation. The far-field boundary conditions and the description of the algorithm for implementing these conditions in LTRAN2 are discussed. Various cases are computed and compared with results from the older, more conventional procedures. One concludes that the full-characteristic equation produces the most effective results, thus allowing the far-field boundary to be located closer to the airfoil; this decreases the computer time required to obtain the solution because fewer mesh points are required.

Kwak, D.↗

NASA NTRS1980

A rapid method for the approximate determination of nonlinear solutions Application to aerodynamic flows

A method for determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameters, is developed and evaluated. The procedure consists of defining a unit perturbation by employing two or more nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, and then using that unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is used in determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Although the procedure is generally applicable, results are presented here for nonlinear aerodynamic applications. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Flows past both isolated airfoils and compressor cascades involving a variety of flow and geometry parameter changes are considered. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure. Computational time is trivial.

Stahara, S. S.↗

NASA NTRS1980

Evaluation of several schemes for classification of remotely sensed data

Various numerical analysis schemes for the classification of remotely sensed data are evaluated with respect to their capabilities for crop identification. A per point Gaussian maximum likelihood classifier, per point sum-of-normal-densities classifier, per point linear classifier, per point Gaussian maximum likelihood decision tree classifier and a texture-sensitive per field Gaussian maximum likelihood classifier were applied to seven sets of Landsat MSS data on several crop types and regions. The results of the implementation of the classifiers indicate that, given a representative set of training statistics, the choice of classification algorithm of the differentiation of corn and soybeans from one another and from other crop types made relatively little difference in accuracy, whereas the use of a different training method affected the accuracy significantly. In addition, the linear classifier is found to be the easiest for the analyst to use and to cost least in computer time per classification.

Hixson, M.↗

NASA NTRS1981

New approach to the solution of large, full matrix equations

A new approach to the solution of matrix equations resulting from integral equations is presented and applied to the solution of two-dimensional Neumann problems describing the inviscid, incompressible flow past an airfoil. The problem is reformulated in terms of a preselected set of mode functions giving an equivalent matrix equation to be solved for the mode-function expansion coefficients. Because of the inherent smoothness of the original problem, the coefficient problem can be solved approximately without significantly affecting the accuracy of the final solution. Very promising two-dimensional results are obtained and the extension of the method to three-dimensional problems is investigated. On the basis of these results it is shown that the computing time for the matrix solution for a large three-dimensional panel method calculation could be reduced by an order of magnitude compared with that required for a direct solution.

Clark, R. W.↗

NASA NTRS1981

The controlled growth method - A tool for structural optimization

An adaptive design variable linking scheme in a NLP based optimization algorithm is proposed and evaluated for feasibility of application. The present scheme, based on an intuitive effectiveness measure for each variable, differs from existing methodology in that a single dominant variable controls the growth of all others in a prescribed optimization cycle. The proposed method is implemented for truss assemblies and a wing box structure for stress, displacement and frequency constraints. Substantial reduction in computational time, even more so for structures under multiple load conditions, coupled with a minimal accompanying loss in accuracy, vindicates the algorithm.

Hajela, P.↗

NASA NTRS1981

Use of global functions for improvement in efficiency of nonlinear analysis

A method for improving the efficiency of nonlinear structural analysis by the use of global displacement functions is presented. The computer programs include options to define the global functions as input or let the program automatically select and update these functions. The program was applied to a number of structures: (1) 'pear-shaped cylinder' in compression, (2) bending of a long cylinder, (3) spherical shell subjected to point force, (4) panel with initial imperfections, (5) cylinder with cutouts. The sample cases indicate the usefulness of the procedure in the solution of nonlinear structural shell problems by the finite element method. It is concluded that the use of global functions for extrapolation will lead to savings in computer time.

Almroth, B. O.↗

NASA NTRS1981

Relative performance of algorithms for autonomous satellite orbit determination

Limited word size in contemporary microprocessors causes numerical problems in autonomous satellite navigation applications. Numerical error introduced in navigation computations performed on small wordlength machines can cause divergence of sequential estimation algorithms. To insure filter reliability, square root algorithms have been adopted in many applications. The optimal navigation algorithm requires a careful match of the estimation algorithm, dynamic model, and numerical integrator. In this investigation, the relationship of several square root filters and numerical integration methods is evaluated to determine their relative performance for satellite navigation applications. The numerical simulations are conducted using the Phase I GPS constellation to determine the orbit of a LANDSAT-D type satellite. The primary comparison is based on computation time and relative estimation accuracy.

Tapley, B. D.↗

NASA NTRS1981

Boundary conditions for subsonic compressible Navier-Stokes calculations

A systematic study of inflow and outflow boundary conditions for the numerical solution of the compressible Navier-Stokes equations is presented. Combinations of several representative inflow and outflow boundary conditions are applied in the solution of subsonic flow over a flat plate in a finite computational domain. These boundary conditions are evaluated in terms of their effect on the accuracy of the solution and the rate of convergence to a steady state. It is shown that errors in the data specified at the inflow boundary can produce significant errors in the computed flow field. It is also shown that a non-reflecting outflow boundary condition can significantly reduce the total computational time required.

Rudy, D. H.↗

NASA NTRS1981

Numerical simulation of steady transonic flow about airfoils

A computer code has been developed that couples a fast transonic full-potential AF2 solver with both an efficient integral boundary-layer method and a viscous wedge approximation of the shock/boundary-layer interaction. The efficiency of the coupled analysis methods and the method of coupling has resulted in a uniquely efficient analysis tool. The airfoil geometry is modified by the displacement thickness before the shock and the displacement thickness plus the viscous wedge thickness after the shock by considering the viscous effects as an equivalent transpiration boundary condition. The flow about conventional and supercritical airfoils under moderately strong shock situations has been calculated. Comparisons with experimental data indicate that this viscous correction method has improved the accuracy of the full-potential analysis. Furthermore, the computer time required to obtain a converged solution has been reduced.

Lee, S. C.↗

NASA NTRS1981

A PANSONIC Navier-Stokes solver

A finite-difference formulation of the full Navier-Stokes equations which demonstrates a capability to economically solve two-dimensional problems has been developed. The basic algorithm was derived from the full, Reynolds-averaged, conservative, Navier-Stokes equations expressed in curvilinear coordinates. Eddy viscosity was determined by the Baldwin and Lomax algebraic turbulence model. This non-iterative, second-order accurate, implicit, numerical algorithm is based on the approximate factorization finite-difference scheme of Beam and Warming. Results indicate a facility for solving subsonic, transonic, and supersonic (hence PANSONIC) flows about arbitrary airfoils for a wide range of Reynolds numbers, Mach numbers, and angles of attack. Current computations demonstrate that vectorized implementations of this algorithm can solve steady-state, two-dimensional problems in five to ten minutes of computer time.

Cooper, G. K.↗

NASA NTRS1981

N-stream approximations to radiative transfer

Schuster's two-stream approximation (1905) is first derived from Chandrasekhar's radiative transfer equation (1950), and then extended to an arbitrary number of streams. The resulting technique for solving the transfer function similar to the discrete ordinate and spherical harmonic methods, is useful for modeling atmospheres with complicated phase functions and moderate optical depths. The resulting n coupled linear differential equations are simple and consume less computer time than other approximations, yet have the same required accuracy. The approximation is also flexible with respect to the choice of patch functions, and no approximations are made on the form of the phase function, other than its expansion into Legendre polynomials. A four-stream approximation is evaluated for a Henyey-Greenstein phase function with an asymmetry factor equal to 0.5.

Acquista, C.↗

NASA NTRS1981

Amplified crossflow disturbances in the laminar boundary layer on swept wings with suction

Solution charts of the Orr-Sommerfeld equation for stationary crossflow disturbances are presented for 10 typical velocity profiles on a swept laminar flow control wing. The critical crossflow Reynolds number is shown to be a function of a boundary layer shape factor. Amplification rates for crossflow disturbances are shown to be proportional to the maximum crossflow velocity. A computer stability program called MARIA, employing the amplification rate data for the 10 crossflow velocity profiles, is constructed. This code is shown to adequately approximate more involved computer stability codes using less than two percent as much computer time while retaining the essential physical disturbance growth model.

Dagenhart, J. R.↗

NASA NTRS1981

A vortex-filament and core model for wings with edge vortex separation

A method for predicting aerodynamic characteristics of slender wings with edge vortex separation was developed. Semiempirical but simple methods were used to determine the initial positions of the free sheet and vortex core. Comparison with available data indicates that: the present method is generally accurate in predicting the lift and induced drag coefficients but the predicted pitching moment is too positive; the spanwise lifting pressure distributions estimated by the one vortex core solution of the present method are significantly better than the results of Mehrotra's method relative to the pressure peak values for the flat delta; the two vortex core system applied to the double delta and strake wing produce overall aerodynamic characteristics which have good agreement with data except for the pitching moment; and the computer time for the present method is about two thirds of that of Mehrotra's method.

Pao, J. L.↗

NASA NTRS1981

Formulation of a dynamic analysis method for a generic family of hoop-mast antenna systems

Analytical studies of mast-cable-hoop-membrane type antennas were conducted using a transfer matrix numerical analysis approach. This method, by virtue of its specialization and the inherently easy compartmentalization of the formulation and numerical procedures, can be significantly more efficient in computer time required and in the time needed to review and interpret the results.

Gabriele, A.↗

NASA NTRS1981

Deep space navigation systems and operations

The history of the deep space navigation system developed by NASA is outlined. Its application to Mariner, Viking and Pioneer missions is reviewed. Voyager navigation results for Jupiter and Saturn are commented on and velocity correction in relation to fuel expenditure and computer time are discussed. The navigation requirements of the Gahleo and Venus orbiting imaging radar (VOIR) missions are assessed. The measurement and data processing systems are described.

Jordan, J. F.↗

NASA NTRS1980

Comparison of NASCAP modelling results with lumped circuit analysis

Engineering design tools that can be used to predict the development of absolute and differential potentials by realistic spacecraft under geomagnetic substorm conditions are described. Two types of analyses are in use: (1) the NASCAP code, which computes quasistatic charging of geometrically complex objects with multiple surface materials in three dimensions; (2) lumped element equivalent circuit models that are used for analyses of particular spacecraft. The equivalent circuit models require very little computation time, however, they cannot account for effects, such as the formation of potential barriers, that are inherently multidimensional. Steady state potentials of structure and insulation are compared with those resulting from the equivalent circuit model.

Stang, D. B.↗