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At least 163 records · Page 9

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NASA NTRS1976

New convergence criteria for the vortex-lattice models of the leading-edge separation

The convergence criterion for the vortex-lattice technique which deals with delta wings exhibiting significant leading-edge separation was studied. It was shown that one can predict pressure distributions without irregularities which agree fairly well with experimental data (which show some irregularities of their own) by replacing the system of discrete vortex lines with a single concentrated core. This core has a circulation equal to the algebraic sum of the circulations around the discrete lines and is located at the centroid of these lines. Moreover, there is a requirement that the position and strength of the core must converge as the number of elements increases. Because the calculation of the position and strength of the core is much less involved than the calculation of the loads, this approach has the additional desirable feature of requiring less computational time.

Kandil, O. A.↗

NASA NTRS1976

Convergence of an iterative procedure for large-scale static analysis of structural components

The paper proves convergence of an iterative procedure for calculating the deflections of built-up component structures which can be represented as consisting of a dominant, relatively stiff primary structure and a less stiff secondary structure, which may be composed of one or more substructures that are not connected to one another but are all connected to the primary structure. The iteration consists in estimating the deformation of the primary structure in the absence of the secondary structure on the assumption that all mechanical loads are applied directly to the primary structure. The j-th iterate primary structure deflections at the interface are imposed on the secondary structure, and the boundary loads required to produce these deflections are computed. The cycle is completed by applying the interface reaction to the primary structure and computing its updated deflections. It is shown that the mathematical condition for convergence of this procedure is that the maximum eigenvalue of the equation relating primary-structure deflection to imposed secondary-structure deflection be less than unity, which is shown to correspond with the physical requirement that the secondary structure be more flexible at the interface boundary.

Austin, F.↗

NASA NTRS1976

Relaxed controls and the convergence of optimal control algorithms

This paper presents a framework for the study of the convergence properties of optimal control algorithms and illustrates its use by means of two examples. The framework consists of an algorithm prototype with a convergence theorem, together with some results in relaxed controls theory.

Williamson, L. J.↗

NASA NTRS1978

Interpolation and extrapolation of creep rupture data by the minimum commitment method. I - Focal-point convergence

The minimum commitment method has been applied to the analysis of creep-rupture data. The method is based on a parameter representing the focal point of convergence of all isothermals when extended to the long or short times necessary for such convergence to occur. The technique may be applied by manual-graphic analysis on computer code. It is illustrated for the nickel-base alloy Astroloy.

Manson, S. S.↗

NASA NTRS1978

On the accuracy and convergence of implicit numerical integration of finite element generated ordinary differential equations

A study of accuracy and convergence of linear functional finite element solution to linear parabolic and hyperbolic partial differential equations is presented. A variable-implicit integration procedure is employed for the resultant system of ordinary differential equations. Accuracy and convergence is compared for the consistent and two lumped assembly procedures for the identified initial-value matrix structure. Truncation error estimation is accomplished using Richardson extrapolation.

Baker, A. J.↗

NASA NTRS1980

The effect of throat contouring on two-dimensional converging-diverging nozzles at static conditions

An experiment was conducted at static conditions to determine the internal performance effects of nozzle throat contouring, the result of increasing the circular-arc throat radius. Five nonaxisymmetric converging-diverging nozzles were tested at nozzle pressure ratios up to 9.0. Data are presented as internal thrust ratios, discharge coefficients, and static-pressure distributions. Comparisons of internal performance data for the five nozzles show that throat contouring increases the value of discharge coefficient but has no significant effect on internal thrust ratio except in cases of internal flow separation. To illustrate the use of the two dimensional converging-diverging (2-D C-D) nozzle data base, a two dimensional inviscid theory was applied to the five configurations. The generally good agreement of data with theoretical results indicates that two-dimensional inviscid theory can be successfully applied to the prediction of 2-D C-D nozzle internal flow.

Mason, M. L.↗

NASA NTRS1979

Trace gas concentrations, intertropical convergence, atmospheric fronts, and ocean currents in the tropical Pacific

Descriptions of the intertropical convergence zones (ITCZ) in the tropical Pacific have been obtained from shipboard measurements of Rn-222, CO, and CH4 in combination with conventional meteorological data and satellite images. The intertropical convergence zone is marked by light shifting waves near an area of heavy cloud cover and precipitation, and appears to be located north and south of the south equatorial current. A 'second' ITCZ with the same atmospheric features was encountered just north of the south equatorial current in the Southern Hemisphere. Atmospheric Rn-222 increases north of the ITCZ and serves as a sensitive indicator for this atmospheric boundary.

Wilkniss, P. E.↗

NASA NTRS1981

Finite element analysis of transonic flows in cascades: Importance of computational grids in improving accuracy and convergence

The finite element method is applied for the solution of transonic potential flows through a cascade of airfoils. Convergence characteristics of the solution scheme are discussed. Accuracy of the numerical solutions is investigated for various flow regions in the transonic flow configuration. The design of an efficient finite element computational grid is discussed for improving accuracy and convergence.

Ecer, A.↗

NASA NTRS1980

Intensification and refraction of acoustical signals in partially choked converging ducts

A computer code based on the wave-envelope technique is used to perform detailed numerical calculations for the intensification and refraction of sound in converging hard walled and lined circular ducts carrying high mean Mach number flows. The results show that converging ducts produce substantial refractions toward the duct center for waves propagating against near choked flows. As expected, the magnitude of the refraction decreases as the real part of the admittance increases. The pressure wave pattern is that of interference among the different modes, and hence the variation of the magnitude of pressure refraction with frequency is not monotonic.

Nayfeh, A. H.↗

NASA NTRS1981

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

The Galerkin-weighted residuals formulation is employed to derive an implicit finite element solution algorithm for a generally non-linear initial-boundary value problem. Solution accuracy and convergence with discretization refinement are quantized in several error norms, for the non-linear parabolic partial differential equation system governing laminar boundary layer flow, using linear, quadratic and cubic 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 non-linear equations characteristic of laminar boundary layer flow.

Soliman, M. O.↗

NASA NTRS1981

On the convergence of unsteady generalized aerodynamic forces

Variations in generalized forces calculated by different computer programs are traced to improper mathematical modeling techniques. Comparisons of generalized forces calculated by three theoretical methods are presented to illustrate difficulties involved in obtaining prediction convergence for increasing wave number. Use of a sufficiently dense chordwise paneling arrangement, in finite panel methods, results in predictions that are essentially identical to predictions of converged solutions. Procedural modifications are suggested for application in finite panel methods to increase prediction accuracy and reduce computer usage costs.

Rowe, W. S.↗

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 NTRS1983

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Molusis, J. A.↗

NASA NTRS1983

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed.

Johnson, G. M.↗

NASA NTRS1984

Static internal performance including thrust vectoring and reversing of two-dimensional convergent-divergent nozzles

The effects of geometric design parameters on two dimensional convergent-divergent nozzles were investigated at nozzle pressure ratios up to 12 in the static test facility. Forward flight (dry and afterburning power settings), vectored-thrust (afterburning power setting), and reverse-thrust (dry power setting) nozzles were investigated. The nozzles had thrust vector angles from 0 deg to 20.26 deg, throat aspect ratios of 3.696 to 7.612, throat radii from sharp to 2.738 cm, expansion ratios from 1.089 to 1.797, and various sidewall lengths. The results indicate that unvectored two dimensional convergent-divergent nozzles have static internal performance comparable to axisymmetric nozzles with similar expansion ratios.

Re, R. J.↗

NASA NTRS1983

Convergence of generalized MUSCL schemes

Semi-discrete generalizations of the second order extension of Godunov's scheme, known as the MUSCL scheme, are constructed, starting with any three point ""E" scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

Osher, S.↗

NASA NTRS1984

Convergence of generalized MUSCL schemes

Semi-discrete generalizations of the second order extension of Godunov's scheme, known as the MUSCL scheme, are constructed, starting with any three point E scheme. They are used to approximate scalar conservation laws in one space dimension. For convex conservation laws, each member of a wide class is proven to be a convergent approximation to the correct physical solution. Comparison with another class of high resolution convergent schemes is made.

Osher, S.↗

NASA NTRS1984

Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem

The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison.

Halyo, N.↗