Accelerating Steady-State Convergence of Compressible Flow Simulations via Nonlinear Elimination
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Computational Fluid Dynamics↗
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Nonlinear critical layers eliminate the upper branch of spatially growing Tollmien-Schlichting waves
This letter is concerned with the effect of nonlinear critical layers on spatially growing Tollmien-Schlichting waves in a Blasius boundary layer. It is shown that they effectively eliminate the upper branch of the neutral stability curve predicted by strictly linear theory.
Goldstein, M. E.↗
On the removal of ill conditioning effects in the computation of optimal controls
Ill conditioning effects eliminated in nonlinear programming algorithms for optimal controls
Polak, E.↗
Effect of Malmquist bias on correlation studies with IRAS data base
The relationships between galaxy properties in the sample of Trinchieri et al. (1989) are reexamined with corrections for Malmquist bias. The linear correlations are tested and linear regressions are fit for log-log plots of L(FIR), L(H-alpha), and L(B) as well as ratios of these quantities. The linear correlations for Malmquist bias are corrected using the method of Verter (1988), in which each galaxy observation is weighted by the inverse of its sampling volume. The linear regressions are corrected for Malmquist bias by a new method invented here in which each galaxy observation is weighted by its sampling volume. The results of correlation and regressions among the sample are significantly changed in the anticipated sense that the corrected correlation confidences are lower and the corrected slopes of the linear regressions are lower. The elimination of Malmquist bias eliminates the nonlinear rise in luminosity that has caused some authors to hypothesize additional components of FIR emission.
Verter, Frances↗
Bearings Incorporating Deadband Rollers
Bearings in high-pressure turbopump redesigned to incorporate rollers allowing limited axial motion within small deadband. Does not permit radial deadband motion. Axial deadband motion used for rotor-thrust-balance control. Design eliminates some nonlinearities in dynamics of pump rotor and assists in suppressing vibrations at harmonics of frequency of rotation.
Gualtieri, Guy V.↗
An improved panel method for the solution of three-dimensional leading-edge vortex flows. Volume 1: Theory document
An improved panel method for the solution of three dimensional flow and wing and wing-body combinations with leading edge vortex separation is presented. The method employs a three dimensional inviscid flow model in which the configuration, the rolled-up vortex sheets, and the wake are represented by quadratic doublet distributions. The strength of the singularity distribution as well as shape and position of the vortex spirals are computed in an iterative fashion starting with an assumed initial sheet geometry. The method calculates forces and moments as well as detail surface pressure distributions. Improvements include the implementation of improved panel numerics for the purpose of elimination the highly nonlinear effects of ring vortices around double panel edges, and the development of a least squares procedure for damping vortex sheet geometry update instabilities. A complete description of the method is included. A variety of cases generated by the computer program implementing the method are presented which verify the mathematical assumptions of the method and which compare computed results with experimental data to verify the underlying physical assumptions made by the method.
Johnson, F. T.↗
Self-Frequency-Doubling Glass-Fiber Laser
Specially prepared germanium and phosphorous-doped glass optical fiber doped with neodymium shown to act as self-frequency-doubling laser. Self-frequency-doubling fiber laser with further refinements, eliminates need for expensive, easily damaged, nonlinear crystals currently used. Enables one to avoid loss and damage mechanisms associated with interfaces of nonlinear crystals as well as to eliminate angle/temperature phase-matching tuning.
Selker, Mark D.↗
Feedback control laws for highly maneuverable aircraft
During the first half of the year, the investigators concentrated their efforts on completing the design of control laws for the longitudinal axis of the HARV. During the second half of the year they concentrated on the synthesis of control laws for the lateral-directional axes. The longitudinal control law design efforts can be briefly summarized as follows. Longitudinal control laws were developed for the HARV using mu synthesis design techniques coupled with dynamic inversion. An inner loop dynamic inversion controller was used to simplify the system dynamics by eliminating the aerodynamic nonlinearities and inertial cross coupling. Models of the errors resulting from uncertainties in the principal longitudinal aerodynamic terms were developed and included in the model of the HARV with the inner loop dynamic inversion controller. This resulted in an inner loop transfer function model which was an integrator with the modeling errors characterized as uncertainties in gain and phase. Outer loop controllers were then designed using mu synthesis to provide robustness to these modeling errors and give desired response to pilot inputs. Both pitch rate and angle of attack command following systems were designed. The following tasks have been accomplished for the lateral-directional controllers: inner and outer loop dynamic inversion controllers have been designed; an error model based on a linearized perturbation model of the inner loop system was derived; controllers for the inner loop system have been designed, using classical techniques, that control roll rate and Dutch roll response; the inner loop dynamic inversion and classical controllers have been implemented on the six degree of freedom simulation; and lateral-directional control allocation scheme has been developed based on minimizing required control effort.
Garrard, William L.↗
Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades
The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree geometric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.
Subrahmanyam, K. B.↗
Influence of third-degree geometric nonlinearities on the vibration and stability of pretwisted, preconed, rotating blades
The governing coupled flapwise bending, edgewise bending, and torsional equations are derived including third-degree goemetric nonlinear elastic terms by making use of the geometric nonlinear theory of elasticity in which the elongations and shears are negligible compared to unity. These equations are specialized for blades of doubly symmetric cross section with linear variation of Pretwist over the blade length. The nonlinear steady state equations and the linearized perturbation equations are solved by using the Galerkin method, and by utilizing the nonrotating normal modes for the shape functions. Parametric results obtained for various cases of rotating blades from the present theoretical formulation are compared to those produced from the finite element code MSC/NASTRAN, and also to those produced from an in-house experimental test rig. It is shown that the spurious instabilities, observed for thin, rotating blades when second degree geometric nonlinearities are used, can be eliminated by including the third-degree elastic nonlinear terms. Furthermore, inclusion of third degree terms improves the correlation between the theory and experiment.
Subrahmanyam, K. B.↗
Triaxial digital fluxgate magnetometer for NASA applications explorer mission: Results of tests of critical elements
Tests performed to prove the critical elements of the triaxial digital fluxgate magnetometer design were described. A method for improving the linearity of the analog to digital converter portion of the instrument was studied in detail. A sawtooth waveform was added to the signal being measured before the A/D conversion, and averaging the digital readings over one cycle of the sawtooth. It was intended to reduce bit error nonlinearities present in the A/D converter which could be expected to be as much as 16 gamma if not reduced. No such nonlinearities were detected in the output of the instrument which included the feature designed to reduce these nonlinearities. However, a small scale nonlinearity of plus or minus 2 gamma with a 64 gamma repetition rate was observed in the unit tested. A design improvement intended to eliminate this small scale nonlinearity was examined.
Mcleod, M. G.↗
Optimum sensitivity derivatives of objective functions in nonlinear programming
The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.
Barthelemy, J.-F. M.↗
Nonlinear sensitivity coefficients and corrections in system identification
The evaluation of sensitivity coefficients which are the changes in the eigencharacteristics with respect to changes in the structural parameters is important in the identification of structural systems. In such studies the commonly used linearized sensitivity coefficients for system identification have occasionally resulted in poor convergence or even divergence during the iteration process to update analytical models for better correlation with the test data. Nonlinear sensitivity coefficients and nonlinear correction terms, usually eliminated during the linearization process, have been developed to evaluate sensitivity coefficients of linear systems. Application to computer simulated example problems indicates a more rapid and stable convergence of the iteration processes to update the analytical model for the improvement of the correlation with test data. The successful application of combining the nonlinear sensitivity coefficients and nonlinear correction terms with the Multiple Boundary Condition Tests enhances the ability to validate large space structures by ground tests.
Kuo, C. P.↗
Balloon Borne Arc-Second Pointer Feasibility Study
For many years scientists have been utilizing stratospheric balloons as low-cost platforms on which to conduct space science experiments. A major hurdle in extending the range of experiments for which these vehicles are useful has been the imposition of the gondola dynamics on the accuracy with which an instrument can be kept pointed at a celestial target. A significant number of scientists have sought the ability to point their instruments with jitter in the arc-second range. This paper presents the design and analysis of a stratospheric balloon borne pointing system that is able to meet this requirement. The foundation for a high fidelity controller simulation is presented. The flexibility of the flight train is represented through generalized modal analysis. A multiple controller scheme is introduced for coarse and fine pointing. Coarse azimuth pointing is accomplished by an established pointing system, with extensive flight history, residing above the gondola structure. A pitch-yaw gimbal mount is used for fine pointing, providing orthogonal axes when nominally on target. Fine pointing actuation is from direct drive dc motors, eliminating backlash problems. An analysis of friction nonlinearities and a demonstration of the necessity in eliminating static fiction are provided. A unique bearing hub design is introduced that eliminates static fiction from the system dynamics. A control scheme involving linear accelerometers for enhanced disturbance rejection is also presented. Results from a linear analysis of the total system and the high fidelity simulation are given. This paper establishes that the proposed control strategy can be made robustly stable with significant design margins. Also demonstrated is the efficacy of the proposed system in rejecting disturbances larger than those considered realistic. Finally, we see that sub arc-second pointing stability can be achieved for a large instrument pointing at an inertial target.
Ward, Philip R.↗
Demonstration of a Balloon Borne Arc-Second Pointer Design
Many designs for utilizing stratospheric balloons as low-cost platforms on which to conduct space science experiments have been proposed throughout the years. A major hurdle in extending the range of experiments for which these vehicles are useful has been the imposition of the gondola dynamics on the accuracy with which an instrument can be kept pointed at a celestial target. A significant number of scientists have sought the ability to point their instruments with jitter in the arc-second range. This paper presents the design and analysis of a stratospheric balloon borne pointing system that is able to meet this requirement. The test results of a demonstration prototype of the design with similar ability are also presented. Discussion of a high fidelity controller simulation for design analysis is presented. The flexibility of the flight train is represented through generalized modal analysis. A multiple controller scheme is utilized for coarse and fine pointing. Coarse azimuth pointing is accomplished by an established pointing system, with extensive flight history, residing above the gondola structure. A pitch-yaw gimbal mount is used for fine pointing, providing orthogonal axes when nominally on target. Fine pointing actuation is from direct drive dc motors, eliminating backlash problems. An analysis of friction nonlinearities and a demonstration of the necessity in eliminating static friction are provided. A unique bearing hub design is introduced that eliminates static friction from the system dynamics. A control scheme involving linear accelerometers for enhanced disturbance rejection is also presented. Results from a linear analysis of the total system and the high fidelity simulation are given. Results from a generalized demonstration prototype are presented. Commercial off-the-shelf (COTS) hardware was used to demonstrate the efficacy and performance of the pointer design for a mock instrument. Sub-arcsecond pointing ability from a ground hang test setup is shown from the testing results. This paper establishes that the proposed control strategy can be made robustly stable with significant design margins. Also demonstrated is the efficacy of the proposed system in rejecting disturbances larger than those considered realistic. The system is implemented and demonstrates sub arc second pointing ability using COTS hardware. Finally, we see that sub arc-second pointing stability can be achieved for a large instrument pointing at an inertial target.
DeWeese, Keith D.↗
Euler solutions for the flow around a hovering helicopter rotor
A method for computing the flow around a hovering helicopter rotor is presented. The solution procedure is divided into two parts. The first part is a finite volume solution of the Euler equations for the near field flow around a rotor blade. The second part is a free wake approach for determining the wake geometry and induced velocities. These two parts are solved in a coupled fashion. The rolled-up vortex wake of the rotor is included in the Euler computational domain through a nonlinear perturbation technique. This eliminates the numerical diffusion of the wake vorticity due to truncation error and artificial viscosity without the need for excessive grid resolution near the vortex core. The method is used to compute both hovering rotor and wing/vortex interaction flows, and the results are compared to experiment.
Roberts, T. W.↗
Zero-Deadband Ball Bearings
Proposed supports for ball bearings press outer races against balls without radial clearance. Diaphragm-like axially flexible springs eliminate deadband and consequent nonlinear radial vibrational response of rotor. If shaft needs two bearings at each end, they are supported independently or connected in series by U-spring. Mechanical stops limit axial travel of shaft.
Hine, Michael J.↗