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At least 559 records · Page 31

High Order Difference Method for Low Mach Number Aeroacoustics

A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved analytically using separation of variables.

Mueller, B.↗

Steady-state and transient analysis of a squeeze film damper bearing for rotor stability

A study of the steady-state and transient response of the squeeze film damper bearing is presented. Both the steady-state and transient equations for the hydrodynamic bearing forces are derived. The bearing equivalent stiffness and damping coefficients are determined by steady-state equations. These coefficients are used to find the bearing configuration which will provide the optimum support characteristics based on a stability analysis of the rotor-bearing system. The transient analysis of rotor-bearing systems is performed by coupling the bearing and journal equations and integrating forward in time. The effects of unbalance, cavitation, and retainer springs are included in the analysis. Methods of determining the stability of a rotor-bearing system under the influence of aerodynamic forces and internal shaft friction are discussed with emphasis on solving the system characteristic frequency equation and on producing stability maps. It is shown that for optimum stability and low force transmissability the squeeze bearing should operate at an eccentricity ratio epsilon 0.4.

Barrett, L. E.↗

A methodology for formulating a minimal uncertainty model for robust control system design and analysis

In the design and analysis of robust control systems for uncertain plants, the technique of formulating what is termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents the transfer function matrix M(s) of the nominal system, and delta represents an uncertainty matrix acting on M(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unstructured uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, and for real parameter variations the diagonal elements are real. As stated in the literature, this structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the literature addresses methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty. Since have a delta matrix of minimum order would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta model would be useful. A generalized method of obtaining a minimal M-delta structure for systems with real parameter variations is given.

Belcastro, Christine M.↗

Application of spectral collocation techniques to the stability of swirling flows

The linearized stability equations in cylindrical coordinates of a Chebyshev spectral collocation method for the temporal and spatial stability of swirling flows are presently solved with the eigenvalues obtained through the use of the QZ routine. The algorithm thus created is robust and easily adaptable to a range of flow configurations encompassing internal and external flows with minor boundary condition application modifications. Accuracy and efficiency tests of the method are made for the cases of plane Poiseulle, rotating-pipe, and trailing line vortex flows.

Khorrami, Mehdi R.↗

Longitudinal stability and control derivatives of a jet fighter airplane extracted from flight test data by utilizing maximum likelihood estimation

A method of parameter extraction for stability and control derivatives of aircraft from flight test data, implementing maximum likelihood estimation, was developed and successfully applied to actual longitudinal flight test data from a modern sophisticated jet fighter. The results of this application establish the merits of the estimation technique and its computer implementation(allowing full analyst interaction with the program) as well as provide data for the validation of a portion of the differential maneuvering simulator (DMS). The results are presented for all flight test runs in tabular form and as time history comparisons between the estimated states and the actual flight test data. Comparisons between extracted and manufacturer's values for five major derivatives are presented and reveal good agreement for these principal derivatives with one exception. This particular derivative is extensively investigated by utilizing the interactive capabilities of the computer program. The results of this investigation verify the numbers extracted by maximum likelihood estimation.

Steinmetz, G. G.↗

Lateral stability and control derivatives of a jet fighter airplane extracted from flight test data by utilizing maximum likelihood estimation

A method of parameter extraction for stability and control derivatives of aircraft from flight test data, implementing maximum likelihood estimation, has been developed and successfully applied to actual lateral flight test data from a modern sophisticated jet fighter. This application demonstrates the important role played by the analyst in combining engineering judgment and estimator statistics to yield meaningful results. During the analysis, the problems of uniqueness of the extracted set of parameters and of longitudinal coupling effects were encountered and resolved. The results for all flight runs are presented in tabular form and as time history comparisons between the estimated states and the actual flight test data.

Parrish, R. V.↗

Implicit methods in CFD

A class of implicit approximate factorization schemes is examined for stability and convergence characteristics. These schemes include Newton's method, factorization, and flux-vector splitting. Examples are used to show that all practical methods suffer from some limited stability or asymptotic convergence restriction. A three-dimensional factored scheme is shown which suffers from unconditional instability which can only be ameliorated by added artificial dissipation. An F3D + or - flux split scheme is described which avoids unconditional instability, but in the end has similar convergence characteristics.

Pulliam, Thomas H.↗

Procedure for estimating stability and control parameters from flight test data by using maximum likelihood methods employing a real-time digital system

A maximum likelihood parameter estimation procedure and program were developed for the extraction of the stability and control derivatives of aircraft from flight test data. Nonlinear six-degree-of-freedom equations describing aircraft dynamics were used to derive sensitivity equations for quasilinearization. The maximum likelihood function with quasilinearization was used to derive the parameter change equations, the covariance matrices for the parameters and measurement noise, and the performance index function. The maximum likelihood estimator was mechanized into an iterative estimation procedure utilizing a real time digital computer and graphic display system. This program was developed for 8 measured state variables and 40 parameters. Test cases were conducted with simulated data for validation of the estimation procedure and program. The program was applied to a V/STOL tilt wing aircraft, a military fighter airplane, and a light single engine airplane. The particular nonlinear equations of motion, derivation of the sensitivity equations, addition of accelerations into the algorithm, operational features of the real time digital system, and test cases are described.

Grove, R. D.↗

A method for the early detection of instabilities in rotordynamics

For a simple Jeffcott model with deadband, a method is developed to determine stability margins by an analysis of the Discrete Fourier transform of the system response. The viability of this method is demonstrated by means of numerical simulations. The circular behavior of the system response on the stability boundary is also explained.

Zalik, Richard A.↗

Innovative Trajectory Designs to meet Exploration Challenges

This document is a viewgraph presentation of the conference paper. Missions incorporated into NASA's Vision for Space Exploration include many different destinations and regions; are challenging to plan; and need new and innovative trajectory design methods to enable them. By combining proven methods with chaos dynamics, exploration goals that require maximum payload mass or minimum duration can be achieved. The implementation of these innovative methods, such as weak stability boundaries, has altered NASA's approach to meet exploration challenges and is described to show how exploration goals may be met in the next decade. With knowledge that various perturbations play a significant role, the mission designer must rely on both traditional design strategies as well as these innovative methods. Over the past decades, improvements have been made that would at first glance seem dramatic. This paper provides a brief narrative on how a fundamental shift has occurred and how chaos dynamics improve the design of exploration missions with complex constraints.

Folta, David C.↗

Design and application of squeeze film dampers for turbomachinery stabilization

The steady-state transient response of the squeeze film damper bearing was investigated. Both the steady-state and transient equations for the hydrodynamic bearing forces are derived; the steady-state equations were used to determine the damper equivalent stiffness and damping coefficients. These coefficients are used to find the damper configuration which will provide the optimum support characteristics based on a stability analysis of the rotor-bearing system. The effects of end seals and cavitated fluid film are included. The transient analysis of rotor-bearing systems was conducted by coupling the damping and rotor equations and integrating forward in time. The effects of unbalance, cavitation, and retainer springs are included. Methods of determining the stability of a rotor-bearing system under the influence of aerodynamic forces and internal shaft friction are discussed.

Gunter, E. J.↗

The VISAR Process

The Video Image Stabilization And Registration (VISAR) process is an award winning video image processing software developed at NASA's Marshall Space Flight Center. VISAR has a wide variety of application areas where the refinement of digital video is needed. It is used to correct jitter, rotation, and zoom effects by registering and processing on individual image captures that are a part of normal video capturing. Its most prominent uses were the 1996 Olympic Bombing case and in identifying Saddam Hussein during the Iraq war. Based on first-hand knowledge, this paper describes the VISAR process, which consists of several steps designed to refine digital video using VISAR software. The process determines the differences between two video images so that one, or both, of the images can be changed in ways that make them match as well as possible. Corrections include changes in position (horizontal and vertical image shifts), changes in orientation (image rotation), and changes in magnification (image zoom). While much of the VISAR process is automated, in its current embodiment it requires the user to initially identify the area of interest and to reset a threshold parameter if the default gives unacceptable results. The basic process that is used is an old tried and true method that determines how well the two images match. This process is called cross-correlation. It gives a single number, the correlation coefficient, that is equal to 1.0 if the images are perfectly matched, is equal to 0.0 if the images have nothing in common, and is equal to -1.0 if one image is the negative of the other. This basic process is used by many image stabilization methods. With VISAR we use it in a manner that provides statistical information needed to best determine orientation and magnification.

Hathaway, David↗

Stability and resonance in grooved-channel flows

Numerical simulation using the spectral element method is used to study the stability and resonant response of incompressible moderate-Reynolds-number flows in periodically-grooved channels. For Reynolds numbers below a critical value, the flow is shown to approach a stable steady-state, and the least stable modes resemble Tollmien-Schlichting channel waves. For Reynolds numbers greater than the critical value, self-sustained oscillations result. Oscillatory perturbation of the grooved-channel flow at the frequency of the least stable mode of the linearized system is found to result in subcritical resonant excitation as the critical Reynolds number is approached. The importance of nonhomogeneous geometry in the forced response of the flow is discussed.

Ghaddar, Nasreen K.↗

A review of nonstatistical techniques for the estimation of vertical atmospheric structure from remote infrared measurements

Mathematical techniques used in atmospheric profile inversion are reviewed, with the discussion limited to methods that do not require extensive information on the statistical properties of the profiles. The basic problem of the calculation of vertical profiles from noise contaminated infrared spectral measurements is examined. Three specific examples of methods of solution are given: the iterative minimum estimation method, a second linear iterative method, and the algorithm of Chahine. Satellite data are used in an empirical comparison of the methods. Several factors are considered, including the stability of solutions, convergence behavior of the iterative methods, and dependence of the solutions on the first guess, a factor that is particularly important in the treatment of data from other planets.

Conrath, B. J.↗

Parametric stability margin for multilinear interval control systems

Recently, a necessary and sufficient condition to determine the robust stability of a multilinear interval control system has been reported as an extension of the well-known Box theorem which deals with the linear affine case. A simple but computationally efficient algorithm, based on the above result, to check the robust stability of such systems is introduced. The method is also extended to find the parametric stability margin of such a system.

Keel, L. H.↗

Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence

A stable high-order numerical scheme for direct numerical simulation (DNS) of shock-free compressible turbulence is presented. The method is applicable to general geometries. It contains no upwinding, artificial dissipation, or filtering. Instead the method relies on the stabilizing mechanisms of an appropriate conditioning of the governing equations and the use of compatible spatial difference operators for the interior points (interior scheme) as well as the boundary points (boundary scheme). An entropy-splitting approach splits the inviscid flux derivatives into conservative and nonconservative portions. The spatial difference operators satisfy a summation-by-parts condition, leading to a stable scheme (combined interior and boundary schemes) for the initial boundary value problem using a generalized energy estimate. A Laplacian formulation of the viscous and heat conduction terms on the right hand side of the Navier–Stokes equations is used to ensure that any tendency to odd–even decoupling associated with central schemes can be countered by the fluid viscosity. The resulting methods are able to minimize the spurious high-frequency oscillations associated with pure central schemes, especially for long time integration applications such as DNS. For validation purposes, the methods are tested in a DNS of compressible turbulent plane channel flow at low values of friction Mach number, where reference turbulence data bases exist. It is demonstrated that the methods are robust in terms of grid resolution, and in good agreement with published channel data. Accurate turbulence statistics can be obtained with moderate grid sizes. Stability limits on the range of the splitting parameter are determined from numerical tests.

N.D. Sandham↗

On the formulation of a minimal uncertainty model for robust control with structured uncertainty

In the design and analysis of robust control systems for uncertain plants, representing the system transfer matrix in the form of what has come to be termed an M-delta model has become widely accepted and applied in the robust control literature. The M represents a transfer function matrix M(s) of the nominal closed loop system, and the delta represents an uncertainty matrix acting on M(s). The nominal closed loop system M(s) results from closing the feedback control system, K(s), around a nominal plant interconnection structure P(s). The uncertainty can arise from various sources, such as structured uncertainty from parameter variations or multiple unsaturated uncertainties from unmodeled dynamics and other neglected phenomena. In general, delta is a block diagonal matrix, but for real parameter variations delta is a diagonal matrix of real elements. Conceptually, the M-delta structure can always be formed for any linear interconnection of inputs, outputs, transfer functions, parameter variations, and perturbations. However, very little of the currently available literature addresses computational methods for obtaining this structure, and none of this literature addresses a general methodology for obtaining a minimal M-delta model for a wide class of uncertainty, where the term minimal refers to the dimension of the delta matrix. Since having a minimally dimensioned delta matrix would improve the efficiency of structured singular value (or multivariable stability margin) computations, a method of obtaining a minimal M-delta would be useful. Hence, a method of obtaining the interconnection system P(s) is required. A generalized procedure for obtaining a minimal P-delta structure for systems with real parameter variations is presented. Using this model, the minimal M-delta model can then be easily obtained by closing the feedback loop. The procedure involves representing the system in a cascade-form state-space realization, determining the minimal uncertainty matrix, delta, and constructing the state-space representation of P(s). Three examples are presented to illustrate the procedure.

Belcastro, Christine M.↗

Impact of Aerodynamics and Structures Technology on Heavy Lift Tiltrotors

Rotor performance and aeroelastic stability are presented for a 124,000-lb Large Civil Tilt Rotor (LCTR) design. It was designed to carry 120 passengers for 1200 nm, with performance of 350 knots at 30,000 ft altitude. Design features include a low-mounted wing and hingeless rotors, with a very low cruise tip speed of 350 ft/sec. The rotor and wing design processes are described, including rotor optimization methods and wing/rotor aeroelastic stability analyses. New rotor airfoils were designed specifically for the LCTR; the resulting performance improvements are compared to current technology airfoils. Twist, taper and precone optimization are presented, along with the effects of blade flexibility on performance. A new wing airfoil was designed and a composite structure was developed to meet the wing load requirements for certification. Predictions of aeroelastic stability are presented for the optimized rotor and wing, along with summaries of the effects of rotor design parameters on stability.

Acree, C. W., Jr.↗