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NASA NTRS1992

Order reduction of z-transfer functions via multipoint Jordan continued-fraction expansion

The order reduction problem of z-transfer functions is solved by using the multipoint Jordan continued-fraction expansion (MJCFE) technique. An efficient algorithm that does not require the use of complex algebra is presented for obtaining an MJCFE from a stable z-transfer function with expansion points selected from the unit circle and/or the positive real axis of the z-plane. The reduced-order models are exactly the multipoint Pade approximants of the original system and, therefore, they match the (weighted) time-moments of the impulse response and preserve the frequency responses of the system at some characteristic frequencies, such as gain crossover frequency, phase crossover frequency, bandwidth, etc.

Lee, Ying-Chin↗

NASA NTRS1992

Flight-test guidance for airbreathing hypersonic vehicles

A guidance solution for aerospace planes is given based on a family of energy-heading extremal solutions that can be used for feedback implementations. Test conditions are developed as steady-cruise solutions by means of energy-heading extremal solutions to a time/fuel-range flight-optimization problem. Feedback charts are derived that give control as a function of energy and heading-to-go, and the reduced-order model is compared to numerically optimized point-mass solutions for flight optimization. The energy-heading model is shown to provide feedback-control charts that yield fuel-efficient turn/acceleration maneuvers with significant weight-change as compared to the point-mass solutions. Such variables as Mach number, dynamic pressure, and lift are found to influence the solutions significantly.

Cliff, Eugene M.↗

NASA NTRS1991

Control-structure interaction study for the Space Station solar dynamic power module

The authors investigate the feasibility of using a conventional PID (proportional plus integral plus derivative) controller design to perform the pointing and tracking functions for the Space Station Freedom solar dynamic power module. Using this simple controller design, the control/structure interaction effects were also studied without assuming frequency bandwidth separation. From the results, the feasibility of a simple solar dynamic control solution with a reduced-order model, which satisfies the basic system pointing and stability requirements, is suggested. However, the conventional control design approach is shown to be very much influenced by the order of reduction of the plant model, i.e., the number of the retained elastic modes from the full-order model. This suggests that, for complex large space structures, such as the Space Station Freedom solar dynamic, the conventional control system design methods may not be adequate.

Cheng, J.↗

NASA NTRS1993

On eigensystem assignment with dissipativity constraints

Stability of the closed-loop system is of vital importance when controller synthesis is being performed using a reduced order model of the open-loop plant. For passive systems such as flexible space structures, closed-loop stability is often ensured by low-authority dissipative controllers using collocated and compatible sensors and actuators. This paper considers the problem of eigensystem assignment for flexible structures using constant-gain output feedback, under the dissipativity constraints requiring that the gain matrices be nonnegative definite. A novel method is developed in which a sequential procedure is used to assign one complex-conjugate pair of closed-loop eigenvalues in each step. At each step, an iterative technique is employed for generating a nonnegative definite gain matrix that assigns a new pair while keeping the previously assigned pairs unchanged. This method can assign up to m closed-loop system eigenvalues, where m is the number of control inputs. A numerical example of damping enhancement for a large flexible structure is presented to demonstrate the approach.

Maghami, Peiman G.↗

NASA NTRS1989

Residual mode filters and adaptive control in large space structures

One of the most difficult problems in controlling large systems and structures is compensating for the destructive interaction which can occur between the reduced-order model (ROM) of the plant, which is used by the controller, and the unmodeled dynamics of the plant, often called the residual modes. The problem is more significant in the case of large space structures because their naturally light damping and high performance requirements lead to more frequent, destructive residual mode interaction (RMI). Using the design/compensation technique of residual mode filters (RMF's), effective compensation of RMI can be accomplished in a straightforward manner when using linear controllers. The use of RMF's has been shown to be effective for a variety of large structures, including a space-based laser and infinite dimensional systems. However, the dynamics of space structures is often uncertain and may even change over time due to on-orbit erosion from space debris and corrosive chemicals in the upper atmosphere. In this case, adaptive control can be extremely beneficial in meeting the performance requirements of the structure. Adaptive control for large structures is also based on ROM's and so destructive RMI may occur. Unfortunately, adaptive control is inherently nonlinear, and therefore the known results of RMF's cannot be applied. The purpose is to present the results of new research showing the effects of RMI when using adaptive control and the work which will hopefully lead to RMF compensation of this problem.

Davidson, Roger A.↗

NASA NTRS1993

Some experiences with Krylov vectors and Lanczos vectors

This paper illustrates the use of Krylov vectors and Lanczos vectors for reduced-order modeling in structural dynamics and for control of flexible structures. Krylov vectors and Lanczos vectors are defined and illustrated, and several applications that have been under study at The University of Texas at Austin are reviewed: model reduction for undamped structural dynamics systems, component mode synthesis using Krylov vectors, model reduction of damped structural dynamics systems, and one-sided and two-sided unsymmetric block-Lanczos model-reduction algorithms.

Craig, Roy R., Jr.↗

NASA NTRS1999

Acoustic Reflection and Transmission of 2-Dimensional Rotors and Stators, Including Mode and Frequency Scattering Effects

A reduced order modeling scheme has been developed for the unsteady acoustic and vortical coupling between blade rows of a turbomachine. The essential behavior of the system is governed by modal scattering coefficients (i.e., reflection and transmission coefficients) of the rotor, stator, inlet and nozzle, which are calculated as if they were connected to non-reflecting ducts. The objective of this report is to identify fundamental behavior of these scattering coefficients for a better understanding of the role of blade row reflection and transmission in noise generation. A 2D flat plate unsteady cascade model is used for the analysis with the expectation that the general behavior presented herein will carry over to models that include more realistic flow and geometry. It is shown that stators scatter input waves into many modes at the same frequency whereas rotors scatter on frequency, or harmonic order. Important cases are shown here the rotor reflection coefficient is greater than unity; a mode at blade passing frequency (BPF) traveling from the stator with unit sound power is reflected by the rotor with more than unit power at 2xBPF and 3xBPE Analysis is presented to explain this unexpected phenomenon. Scattering curves are presented in a format chosen for design use and for physical interpretation. To aid in interpretation of the curves, formulas are derived for special condition where waveforms are parallel to perpendicular to the rotor.

Hanson, Donald B.↗

NASA NTRS2004

The Application of Probabilistic Methods to the Mistuning Problem

FMM is a reduced order model for efficiently calculating the forced response of a mistuned bladed disk. FMM ID is a companion program which determines the mistuning in a particular rotor. Together, these methods provide a way to acquire data on the mistuning in a population of bladed disks, and then simulate the forced response of the fleet. This process is tested experimentally, and the simulated results are compared with laboratory measurements of a fleet of test rotors. The method is shown to work quite well. It is found that accuracy of the results depends on two factors: the quality of the statistical model used to characterize mistuning, and how sensitive the system is to errors in the statistical modeling.

Griffin, J. H.↗

NASA NTRS2007

Simultaneous Excitation of Multiple-Input Multiple-Output CFD-Based Unsteady Aerodynamic Systems

A significant improvement to the development of CFD-based unsteady aerodynamic reduced-order models (ROMs) is presented. This improvement involves the simultaneous excitation of the structural modes of the CFD-based unsteady aerodynamic system that enables the computation of the unsteady aerodynamic state-space model using a single CFD execution, independent of the number of structural modes. Four different types of inputs are presented that can be used for the simultaneous excitation of the structural modes. Results are presented for a flexible, supersonic semi-span configuration using the CFL3Dv6.4 code.

Silva, Walter A.↗

NASA NTRS2008

Simultaneous Excitation of Multiple-Input Multiple-Output CFD-Based Unsteady Aerodynamic Systems

Silva, Walter A.↗

NASA NTRS2008

A Numerical Investigation of Turbine Noise Source Hierarchy and Its Acoustic Transmission Characteristics

Understanding the relative importance of the various turbine noise generation mechanisms and the characteristics of the turbine acoustic transmission loss are essential ingredients in developing robust reduced-order models for predicting the turbine noise signature. A computationally based investigation has been undertaken to help guide the development of a turbine noise prediction capability that does not rely on empiricism. The investigation relies on highly detailed numerical simulations of the unsteady flowfield inside a modern high-pressure turbine (HPT). The simulations are developed using TURBO, which is an unsteady Reynolds-averaged Navier-Stokes (URANS) code capable of multi-stage simulations. The purpose of this study is twofold. First, to determine an estimate of the relative importance of the contributions to the coherent part of the acoustic signature of a turbine from the three potential sources of turbine noise generation, namely, blade-row viscous interaction, potential field interaction, and entropic source associated with the interaction of the blade rows with the temperature nonuniformities caused by the incomplete mixing of the hot fluid and the cooling flow. Second, to develop an understanding of the turbine acoustic transmission characteristics and to assess the applicability of existing empirical and analytical transmission loss models to realistic geometries and flow conditions for modern turbine designs. The investigation so far has concentrated on two simulations: (1) a single-stage HPT and (2) a two-stage HPT and the associated inter-turbine duct/strut segment. The simulations are designed to resolve up to the second harmonic of the blade passing frequency tone in accordance with accepted rules for second order solvers like TURBO. The calculations include blade and vane cooling flows and a radial profile of pressure and temperature at the turbine inlet. The calculation can be modified later to include the combustor pattern factor at the turbine inlet to include that contribution to turbine noise. We shall present preliminary analysis of the results obtained so far in order to assess the validity of such an approach and to seek feedback on improving the approach. This work addresses both Area 1 (Turbine Tone Noise) and Area 5 (Influence of the Turbine on Combustor Noise) topics.

VanZante, Dale↗

NASA NTRS2010

Minnowbrook VI: 2009 Workshop on Flow Physics and Control for Internal and External Aerodynamics

Topics covered include: Flow Physics and control for Internal and External Aerodynamics (not in TOC...starts on pg13); Breaking CFD Bottlenecks in Gas-Turbine Flow-Path Design; Streamwise Vortices on the Convex Surfaces of Circular Cylinders and Turbomachinery Blading; DNS and Embedded DNS as Tools for Investigating Unsteady Heat Transfer Phenomena in Turbines; Cavitation, Flow Structure and Turbulence in the Tip Region of a Rotor Blade; Development and Application of Plasma Actuators for Active Control of High-Speed and High Reynolds Number Flows; Active Flow Control of Lifting Surface With Flap-Current Activities and Future Directions; Closed-Loop Control of Vortex Formation in Separated Flows; Global Instability on Laminar Separation Bubbles-Revisited; Very Large-Scale Motions in Smooth and Rough Wall Boundary Layers; Instability of a Supersonic Boundary-Layer With Localized Roughness; Active Control of Open Cavities; Amplitude Scaling of Active Separation Control; U.S. Air Force Research Laboratory's Need for Flow Physics and Control With Applications Involving Aero-Optics and Weapon Bay Cavities; Some Issues Related to Integrating Active Flow Control With Flight Control; Active Flow Control Strategies Using Surface Pressure Measurements; Reduction of Unsteady Forcing in a Vaned, Contra-Rotating Transonic Turbine Configuration; Active Flow Control Stator With Coanda Surface; Controlling Separation in Turbomachines; Flow Control on Low-Pressure Turbine Airfoils Using Vortex Generator Jets; Reduced Order Modeling Incompressible Flows; Study and Control of Flow Past Disk, and Circular and Rectangular Cylinders Aligned in the Flow; Periodic Forcing of a Turbulent Axisymmetric Wake; Control of Vortex Breakdown in Critical Swirl Regime Using Azimuthal Forcing; External and Turbomachinery Flow Control Working Group; Boundary Layers, Transitions and Separation; Efficiency Considerations in Low Pressure Turbines; Summary of Conference; and Final Plenary Session Transcript.

LaGraff, John E.↗

NASA NTRS2010

External and Turbomachinery Flow Control Working Group

Broad Flow Control Issues: a) Understanding flow physics. b) Specific control objective(s). c) Actuation. d) Sensors. e) Integrated active flow control system. f) Development of design tools (CFD, reduced order models, controller design, understanding and utilizing instabilities and other mechanisms, e.g., streamwise vorticity).

Ahmadi, G.↗

NASA NTRS2013

Dry wind tunnel system

This invention is a ground flutter testing system without a wind tunnel, called Dry Wind Tunnel (DWT) System. The DWT system consists of a Ground Vibration Test (GVT) hardware system, a multiple input multiple output (MIMO) force controller software, and a real-time unsteady aerodynamic force generation software, that is developed from an aerodynamic reduced order model (ROM). The ground flutter test using the DWT System operates on a real structural model, therefore no scaled-down structural model, which is required by the conventional wind tunnel flutter test, is involved. Furthermore, the impact of the structural nonlinearities on the aeroelastic stability can be included automatically. Moreover, the aeroservoelastic characteristics of the aircraft can be easily measured by simply including the flight control system in-the-loop. In addition, the unsteady aerodynamics generated computationally is interference-free from the wind tunnel walls. Finally, the DWT System can be conveniently and inexpensively carried out as a post GVT test with the same hardware, only with some possible rearrangement of the shakers and the inclusion of additional sensors.

Chen, Ping-Chih↗

NASA NTRS2017

Economical Unsteady High-Fidelity Aerodynamics for Structural Optimization with a Flutter Constraint

Structural optimization with a flutter constraint for a vehicle designed to fly in the transonic regime is a particularly difficult task. In this speed range, the flutter boundary is very sensitive to aerodynamic nonlinearities, typically requiring high-fidelity Navier-Stokes simulations. However, the repeated application of unsteady computational fluid dynamics to guide an aeroelastic optimization process is very computationally expensive. This expense has motivated the development of methods that incorporate aspects of the aerodynamic nonlinearity, classical tools of flutter analysis, and more recent methods of optimization. While it is possible to use doublet lattice method aerodynamics, this paper focuses on the use of an unsteady high-fidelity aerodynamic reduced order model combined with successive transformations that allows for an economical way of utilizing high-fidelity aerodynamics in the optimization process. This approach is applied to the common research model wing structural design. As might be expected, the high-fidelity aerodynamics produces a heavier wing than that optimized with doublet lattice aerodynamics. It is found that the optimized lower skin of the wing using high-fidelity aerodynamics differs significantly from that using doublet lattice aerodynamics.

Bartels, Robert E.↗

NASA NTRS2018

Multidisciplinary Design Optimization and Cruise Mach Number Study of Truss-Braced Wing Aircraft

The Subsonic Ultra Green Aircraft Research (SUGAR) Phase III was led by Dr. Rakesh K. Kapania and Dr. Joseph A. Schetz at the Multidisciplinary Analysis and Design Center for Advanced Vehicles, Department of Aerospace and Ocean Engineering, Virginia Tech, Blacksburg VA. The research was performed from December 2014 to December 2015. Three major areas were investigated: Multidisciplinary Design Optimization (MDO) studies of truss braced wing (TBW) and strut braced wing (SBW) vehicles at cruise Mach numbers of 0.7 and 0.8 for a flight mission similar to current market single aisle configurations. The performance and the characteristics of the optimized vehicles were compared to the SUGAR Phase II TBW vehicle. These results were obtained without applying any of the extended transonic aerodynamic and aeroelastic tools that will be discussed later. It was found that the cruise Mach number has a large effect on the best “truss” configuration. At Mach 0.7, an SBW has a better fuel consumption and better take-off gross weight (TOGW). However, at Mach 0.8, the TBW is superior because the jury strut aids in satisfying the flutter constraint; Two-dimensional, steady, transonic aerodynamic analysis of the Boeing Airfoil J (BACJ) airfoil was performed for a range of thickness ratios, Mach numbers and lift coefficients. Reynolds-averaged Navier-Stokes (RANS) equations were solved to obtain the lift-curve slope, wave drag coefficient, the location of the center of pressure and to predict the separation at the trailing edge, which may lead to buffeting. One of the goals was to develop a database of lift-curve slope and the location of center of pressure, which could be used in a transonic aeroelastic analysis. Another goal was to compare the wave drag coefficients to those predicted by Lock’s fourth-power law and also to compare the transonic effects obtained from RANS simulations to those predicted by the Korn equations. A third goal was to develop a buffet boundary, which can be integrated into the MDO framework to prevent the optimized designs from probable buffeting; A state-space transonic aeroelastic analysis tool was developed, which can incorporate the nonlinear transonic effects in the unsteady aerodynamics but is yet computationally cheap when used within the VT MDO framework. The aeroelastic analysis uses Leishman- Beddoes (LB) indicial functions, which generated a state-space representation of the aeroelastic system. The indicial functions allow the incorporation of data for steady lift-curve slope and location of the center of pressure. Thus, the steady transonic effects are included, and the unsteady aerodynamic responses are a linearization about the steady results. The aeroelastic approach discretizes the wing into numerous strips, which results in a large eigenvalue problem as each strip has eight augmented aerodynamic states as per the LB theory. Thus, to reduce the computation expense, a reduced order model (ROM) was developed. The approach was validated using a few examples.

Kapania, Rakesh K.↗

NASA NTRS2018

Application of Rapid Distortion Theory to the Prediction of Integrated Propulsion System Noise

This presentation reviews past and current work done using inhomogeneous Rapid Distortion Theory (RDT) to develop reduced-order models for the prediction of noise generated by flow/surface interactions in geometries representative of propulsion systems which are tightly integrated with the airframe. The specific applications considered are: trailing-edge noise, generated by the interaction of a turbulent jet with a semi-infinite flat plate, and turbulence distortion and noise generation in a boundary-layer ingesting inlet. The inhomogeneous RDT formulation is briefly reviewed, a sampling of available results are shown and the current status and future plans for work on these two applications are discussed.

Leib, Stewart J.↗

NASA NTRS2021

Thermal Inspection of a Composite Fuselage Section Using theMethod of Proper Generalized Decomposition

Proper Generalized Decomposition (PGD) is a reduced order modeling technique for the simulation of physical systems whose governing equations depend on boundary conditions, initial conditions, material properties, and geometric parameters. It uses separated representations of system covariates combined with an iterative approximation method known as successive enrichment in order to compute an accurate parameter-dependent approximation to the full governing equations. PGD can also be used as an alternative to the Singular Value Decomposition (SVD) of a matrix and therefore as an alternative to PCA thermography. In this paper PGD was used to analyze data derived from the inspection of a composite fuselage forward section using flash thermography, and the results were compared against the standard PCA approach.

Nondestructive Evaluation↗