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Dynamic stall and three-dimensional wake effects on isolated rotor trim and stability with experimental correlation and parallel fast-Floquet analysis

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Date Issued:
1996
Summary:
Hingeless rotors are susceptible to instabilities of the lead-lag or lag modes, which are at best weakly damped. The lag mode derives its damping primarily from the complex rotor flow field that is driven by interdependent dynamics of airfoil stall and rotor downwash or wake. Therefore, lag-damping prediction requires an aerodynamic representation that adequately accounts for quasisteady stall, dynamic stall and three-dimensional dynamic wake. Accordingly, this dissertation investigates these stall and wake effects on lag damping and demonstrates the strengths and weaknesses of the aerodynamic representation with a comprehensive experimental correlation. The database refers to a three-bladed rotor operated untrimmed and to a fourbladed rotor operated trimmed; for both rotors, the blade collective pitch and shaft tilt angles are set prior to each test run. The untrimmed rotor is tested with advance-ratios as high as 0.55 and shaft angles as high as 20°, and it has intentionally builtin structural simplicity: torsionally stiff blades and no swash plate. The trimmed rotor has torsionally soft blades; it is trimmed in the sense that the longitudinal and lateral cyclic pitch controls are adjusted through a swash plate to minimize l/rev root flap moment. Therefore, for the untrimmed rotor, the database refers to lagdamping levels, and for the trimmed rotor, it refers to lag-damping levels as well as to trim results of lateral and longitudinal cyclic pitch controls and steady root flap moments. The dynamic stall representation is based on the ONERA models of lift, drag and pitching moment, and the unsteady wake is described by a finite-state three-dimensional wake model. The root-flexure-blade assembly of the untrimmed rotor is represented by a root-restrained rigid flap-lag model as well as by an elastic flap-lag-torsion model. Similarly, the trimmed rotor is represented by an elastic flaplag- torsion model. The predictions are from three aerodynamic theories ranging from a quasisteady stall theory to a fairly comprehensive dynamic stall and wake theory. This dissertation also addresses the computational aspects of lag-damping predictions by parallel F!oquct analysis based on classical and fast Floquet theories. In a typical trimmed flight, the Floquet analysis comprises (i) trim or equilibrium analysis, (ii) generation of the Floquet transition matrix (FTM) about the trim position, and (iii) eigenanalysis of the FTM. The trim analysis involves the computations of the unknown control inputs that satisfy flight conditions of required thrust and force-moment equilibrium as well as the initial conditions that guarantee periodic forced response. The shooting method is increasingly used for the trim analysis since it generates the FTM as a byproduct and is not sensitive to damping levels. The QR method is used almost exclusively for the FTM eigenanalysis. Presently, the Floquet analysis with shooting and QR methods is widely used for small-order systems (number of states or order M < 100). However, it has been found to be practical neither for design nor for comprehensive-analysis models that lead to large systems (A11 > 100); the run time on a conventional sequential computer is simply prohibitive. Nevertheless, all three parts of Floquet analysis can be algorithmically structured such that they lend themselves well to parallelism or concurrent computations. Furthermore, the conventional Floquet analysis requires integrations of equations of motion through one complete period T; and the bulk of the run time is for repeated integrations over one period. However, for rotors with Q identical blades, it is computationally advantageous to use the fast Floquet analysis, which requires integration through a period T/Q. Accordingly, this dissertation develops parallel algorithms for classical Floquet analysis with classical shooting and for the fast Floquet analysis with fast shooting; in each case the FTM eigenanalysis is baseJ on a parallel QR tibrary routine. The computational reliability· of the sequential anJ parallel Floquet analyses is quantified by (i) the condition number of the converged Jacobian matrix in Newton iteration of trim analysis, (ii) the condition numbers of the FTM eigenvalues of interest, and (iii) the corresponding residual errors of the eigenpairs (eigenvalue and the corresponding eigenYector). These algorithms are applied to study (i) linear flap stability with dynamic wake, (ii) nonlinear flaplag stability with dynamic wake under propulsive- or flight-trim conditions. and (iii) noniinear fiap-iag stabiiity with dynamic staii and wake under flight trim conditions. The parallel and sequential algorithms are compared with respect to computational reliability, saving in run time and growth of run time with increasing system order. Other parallel performance metrics such as speedup, efficiency, and sequential and parallel fractions are included as well. The computational reliability figures of the four algorithms - classical and fast-Floquet analyses each in sequential and parallel modes - are comparable. The fast-Floquet analysis brings in nearly Q-fold reduction in run time in both the sequential and parallel modes; that is, its advantages apply equally to both the modes. 'While the run times for the classical- and fast-Floquet analyses in sequential mode grow in between quadratically and cubically with the system order, the corresponding run times in parallel mode are far shorter and more importantly remain nearly constant. These results offer considerable promise in making large-scale Floquet analysis practical for rotorcrafts with identical as well as with dissimilar blades.
Title: Dynamic stall and three-dimensional wake effects on isolated rotor trim and stability with experimental correlation and parallel fast-Floquet analysis.
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Name(s): Subramanian, Shanmugasundaram.
Florida Atlantic University, Degree grantor
Gaonkar, Gopal H., Thesis advisor
College of Engineering and Computer Science
Department of Ocean and Mechanical Engineering
Type of Resource: text
Genre: Electronic Thesis Or Dissertation
Issuance: monographic
Date Issued: 1996
Publisher: Florida Atlantic University
Place of Publication: Boca Raton, Fla.
Physical Form: application/pdf
Extent: 330 p.
Language(s): English
Summary: Hingeless rotors are susceptible to instabilities of the lead-lag or lag modes, which are at best weakly damped. The lag mode derives its damping primarily from the complex rotor flow field that is driven by interdependent dynamics of airfoil stall and rotor downwash or wake. Therefore, lag-damping prediction requires an aerodynamic representation that adequately accounts for quasisteady stall, dynamic stall and three-dimensional dynamic wake. Accordingly, this dissertation investigates these stall and wake effects on lag damping and demonstrates the strengths and weaknesses of the aerodynamic representation with a comprehensive experimental correlation. The database refers to a three-bladed rotor operated untrimmed and to a fourbladed rotor operated trimmed; for both rotors, the blade collective pitch and shaft tilt angles are set prior to each test run. The untrimmed rotor is tested with advance-ratios as high as 0.55 and shaft angles as high as 20°, and it has intentionally builtin structural simplicity: torsionally stiff blades and no swash plate. The trimmed rotor has torsionally soft blades; it is trimmed in the sense that the longitudinal and lateral cyclic pitch controls are adjusted through a swash plate to minimize l/rev root flap moment. Therefore, for the untrimmed rotor, the database refers to lagdamping levels, and for the trimmed rotor, it refers to lag-damping levels as well as to trim results of lateral and longitudinal cyclic pitch controls and steady root flap moments. The dynamic stall representation is based on the ONERA models of lift, drag and pitching moment, and the unsteady wake is described by a finite-state three-dimensional wake model. The root-flexure-blade assembly of the untrimmed rotor is represented by a root-restrained rigid flap-lag model as well as by an elastic flap-lag-torsion model. Similarly, the trimmed rotor is represented by an elastic flaplag- torsion model. The predictions are from three aerodynamic theories ranging from a quasisteady stall theory to a fairly comprehensive dynamic stall and wake theory. This dissertation also addresses the computational aspects of lag-damping predictions by parallel F!oquct analysis based on classical and fast Floquet theories. In a typical trimmed flight, the Floquet analysis comprises (i) trim or equilibrium analysis, (ii) generation of the Floquet transition matrix (FTM) about the trim position, and (iii) eigenanalysis of the FTM. The trim analysis involves the computations of the unknown control inputs that satisfy flight conditions of required thrust and force-moment equilibrium as well as the initial conditions that guarantee periodic forced response. The shooting method is increasingly used for the trim analysis since it generates the FTM as a byproduct and is not sensitive to damping levels. The QR method is used almost exclusively for the FTM eigenanalysis. Presently, the Floquet analysis with shooting and QR methods is widely used for small-order systems (number of states or order M < 100). However, it has been found to be practical neither for design nor for comprehensive-analysis models that lead to large systems (A11 > 100); the run time on a conventional sequential computer is simply prohibitive. Nevertheless, all three parts of Floquet analysis can be algorithmically structured such that they lend themselves well to parallelism or concurrent computations. Furthermore, the conventional Floquet analysis requires integrations of equations of motion through one complete period T; and the bulk of the run time is for repeated integrations over one period. However, for rotors with Q identical blades, it is computationally advantageous to use the fast Floquet analysis, which requires integration through a period T/Q. Accordingly, this dissertation develops parallel algorithms for classical Floquet analysis with classical shooting and for the fast Floquet analysis with fast shooting; in each case the FTM eigenanalysis is baseJ on a parallel QR tibrary routine. The computational reliability· of the sequential anJ parallel Floquet analyses is quantified by (i) the condition number of the converged Jacobian matrix in Newton iteration of trim analysis, (ii) the condition numbers of the FTM eigenvalues of interest, and (iii) the corresponding residual errors of the eigenpairs (eigenvalue and the corresponding eigenYector). These algorithms are applied to study (i) linear flap stability with dynamic wake, (ii) nonlinear flaplag stability with dynamic wake under propulsive- or flight-trim conditions. and (iii) noniinear fiap-iag stabiiity with dynamic staii and wake under flight trim conditions. The parallel and sequential algorithms are compared with respect to computational reliability, saving in run time and growth of run time with increasing system order. Other parallel performance metrics such as speedup, efficiency, and sequential and parallel fractions are included as well. The computational reliability figures of the four algorithms - classical and fast-Floquet analyses each in sequential and parallel modes - are comparable. The fast-Floquet analysis brings in nearly Q-fold reduction in run time in both the sequential and parallel modes; that is, its advantages apply equally to both the modes. 'While the run times for the classical- and fast-Floquet analyses in sequential mode grow in between quadratically and cubically with the system order, the corresponding run times in parallel mode are far shorter and more importantly remain nearly constant. These results offer considerable promise in making large-scale Floquet analysis practical for rotorcrafts with identical as well as with dissimilar blades.
Identifier: 9780591029277 (isbn), 12462 (digitool), FADT12462 (IID), fau:9356 (fedora)
Collection: FAU Electronic Theses and Dissertations Collection
Note(s): College of Engineering and Computer Science
Thesis (Ph.D.)--Florida Atlantic University, 1996.
Subject(s): Rotors (Helicopters)
Stalling (Aerodynamics)
Drag (Aerodynamics)
Wakes (Aerodynamics)
Floquet theory
Held by: Florida Atlantic University Libraries
Persistent Link to This Record: http://purl.flvc.org/fcla/dt/12462
Sublocation: Digital Library
Use and Reproduction: Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
Use and Reproduction: http://rightsstatements.org/vocab/InC/1.0/
Host Institution: FAU
Is Part of Series: Florida Atlantic University Digital Library Collections.