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 Title
 Frequencytime spectral analysis of helicopter turbulence and response in forward flight.
 Creator
 Vellathottam, George V., Florida Atlantic University, Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The atmospheric turbulence that a blade station experiences is called bladefixed turbulence. It can qualitatively differ from the conventional bodyfixed turbulence such as experienced by an element of the body or fuselage. This difference is due to the rotational ,elocity, which causes foreandaft motions of the blade station through the turbulence waves. A closedform solution of a frequencytime spectrum for the dominant vertical turbulence velocity at an arbitrary blade station is dc,...
Show moreThe atmospheric turbulence that a blade station experiences is called bladefixed turbulence. It can qualitatively differ from the conventional bodyfixed turbulence such as experienced by an element of the body or fuselage. This difference is due to the rotational ,elocity, which causes foreandaft motions of the blade station through the turbulence waves. A closedform solution of a frequencytime spectrum for the dominant vertical turbulence velocity at an arbitrary blade station is dc,·eloped. This solution makes it possible to explain qualitatively the turbulence cllcrgy transfer due to rotational velocity from the lowfrequency region (< 1P or 1/ rcv.) to the highfrequency(> 1P) region with the occurrence of spectral peaks and split peaks at 1P /2, 1P, 3P /2, 2P etc. Comparison of blade responses to bladeand bodyfixed turbulence is also presented over a comprehensive range of turbulcuce scale length and advance ratio; the comparison covers frequencytime spectra, correlations including standard deviations, and average thresholdcrossing rates of a flapping blade. A major contribution is to formulate both the cyclostationary turbulence and blade response by the frequencytime spectra, which predict simultaneously the time ancl frequencydependent characteristics such as the energy culltained in the frequency and time intervals. For lowaltitude and lowadvanceratio flights, such as napofthe earth or NOE flights, rotational velocity effects on turbulence modeling qualitatively affect the prediction of turbulence ancl response statistics.
Show less  Date Issued
 1991
 PURL
 http://purl.flvc.org/fcla/dt/14683
 Subject Headings
 Turbulence, Rotors (Helicopters)
 Format
 Document (PDF)
 Title
 Dynamic stall and threedimensional wake effects on trim, stability and loads of hingeless rotors with fast Floquet theory.
 Creator
 Chunduru, Srinivas Jaya., Florida Atlantic University, Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

This dissertation investigates the effects of dynamic stall and threedimensional wake on isolatedrotor trim, stability and loads. Trim analysis of predicting the pilot's control inputs and the corresponding periodic responses is based on periodic shooting with the fast Floquet theory and damped Newton iteration. Stability analysis, also based on the fast Floquet theory, predicts damping levels and frequencies. Loads analysis uses a forceintegration approach to predict the rotatingblade...
Show moreThis dissertation investigates the effects of dynamic stall and threedimensional wake on isolatedrotor trim, stability and loads. Trim analysis of predicting the pilot's control inputs and the corresponding periodic responses is based on periodic shooting with the fast Floquet theory and damped Newton iteration. Stability analysis, also based on the fast Floquet theory, predicts damping levels and frequencies. Loads analysis uses a forceintegration approach to predict the rotatingblade root shears and moments as well as the hub forces and moments. The blades have flap bending, lag bending and torsion degrees of freedom. Dynamic stall is represented by the ONERA stall models of lift, drag and pitching moment, and the unsteady, nonuniform downwash is represented by a threedimensional, finitestate wake model. Throughout, full bladestallwake dynamics is used in that all states are included from trim to stability to loads predictions. Moreover, these predictions are based on four aerodynamic theoriesquasisteady linear theory, quasisteady stall theory, dynamic stall theory and dynamic stall and wake theoryand cover a broad range of system parameters such as thrust level, advance ratio, number of blades and blade torsional frequency. The investigation is conducted in three phases. In phase one, the elastic flaplagtorsion equations are coupled with a finitestate wake model and with linear quasisteady airfoil aerodynamics. The investigation presents convergence characteristics of trim and stability with respect to the number of spatial azimuthal harmonics and radial shape functions in the wake representation. It includes a comprehensive parametric study over a broad range of system parameters. The investigation also includes correlation with the measured lagdamping data of a threebladed isolated rotor operated untrimmed. In the correlation, three structural models of the rootflexureblade assembly are used to demonstrate the strengths and the weaknesses of lagdamping predictions. Phase two includes dynamic stall in addition to threedimensional wake to generate trim and stability results over a comprehensive range of system parameters. It addresses the degree of sophistication necessary in blade discretization and wake representation under dynamically stalled conditions. The convergence and parametric studies isolate the effects of wake, quasisteady stall and dynamic stall on trim and stability. Finally, phase three predicts the rotating blade loads and nonrotating hub loads; the predictions are based on the blade, wake and stall models used in the preceding trim and stability investigations. Although an accurate evaluation of loads requires a more refined blade description, the results isolate and demonstrate the principal dynamic stall and wake effects on the loads.
Show less  Date Issued
 1995
 PURL
 http://purl.flvc.org/fcla/dt/12426
 Subject Headings
 Floquet theory, Helicopters, Rotors (Helicopters), Vibration (Aeronautics)
 Format
 Document (PDF)
 Title
 FastFloquet method of hingelessrotor trim and stability including comparisons with experiments and approximate methods.
 Creator
 Ma, Guifa., Florida Atlantic University, Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The trim and stability of an isolated hingeless rotor in forward flight are predicted for two coning angles with advance ratio, shaft angle and collective pitch variations. These predictions are correlated with measurements from a test model with four softinplane, softtorsion blades. The test was conducted by the U.S. Army Aeroflightdynamics Directorate at Ames. The collective pitch and shaft angle are set prior to each test point, and the rotor is trimmed as follows: the longitudinal and...
Show moreThe trim and stability of an isolated hingeless rotor in forward flight are predicted for two coning angles with advance ratio, shaft angle and collective pitch variations. These predictions are correlated with measurements from a test model with four softinplane, softtorsion blades. The test was conducted by the U.S. Army Aeroflightdynamics Directorate at Ames. The collective pitch and shaft angle are set prior to each test point, and the rotor is trimmed as follows: the longitudinal and lateral cyclic pitch controls are adjusted through a swashplate to minimize the 1/rev flapping moment at the 12% radial station. The database includes the cyclic pitch controls, steady rootflap moment and lag regressivemode damping. The predictions are based on a modal approach with both nonrotating and rotating modes, the ONERA dynamic stall models of lift, drag and pitching moment, and a threedimensional statespace wake model. The periodic shooting method, with damped Newton iteration and the fastFloquet theory, is used to predict the cyclic pitch controls and the corresponding periodic responses; the equivalent Floquet transition matrix (EFTM) comes out as a byproduct. The eigenvalues and eigenvectors of the EFTM lead to the frequencies and damping levels. The steady rootflap moment is calculated by both the force integration and modedeflection methods. Although exact, the fastFloquet theory requires a finitestate representation of all states and is not applicable to numerically and experimentally generated data of response histories. Therefore, the stability is also predicted by three related approximations: generalized Floquet (fastFloquet) theory and Sparse Time Domain (STD) technique. These approximations can be applied with a finitestate representation of an arbitrary number of states and to response histories; their convergence characteristics and accuracy are examined as well. Two major findings are: (1) The dynamic wake dramatically improves the correlation of the lateral cyclic pitch controls, and (2) all three approximations have excellent convergence characteristics and the converged values agree well with the exact values.
Show less  Date Issued
 2000
 PURL
 http://purl.flvc.org/fcla/dt/12648
 Subject Headings
 Floquet theory, Rotors (Helicopters), Stability of helicopters
 Format
 Document (PDF)
 Title
 Turbulence modeling and simulation and related effects on helicopter response with wake dynamics using finite elements and parallelism.
 Creator
 Dang, Ying Yi., Florida Atlantic University, Gaonkar, Gopal H.
 Abstract/Description

Future helicopters will require allweather capability for stabilized flight through severe atmospheric turbulence. This requirement has brought into focus the effect of turbulence on handling qualities. Accordingly, there is renewed interest in modeling and simulating turbulence and predicting turbulenceinduced rotor oscillations. This thesis addresses three fundamental aspects of the problem: (1) modeling and simulation of turbulence including crosscorrelation; (2) threedimensional...
Show moreFuture helicopters will require allweather capability for stabilized flight through severe atmospheric turbulence. This requirement has brought into focus the effect of turbulence on handling qualities. Accordingly, there is renewed interest in modeling and simulating turbulence and predicting turbulenceinduced rotor oscillations. This thesis addresses three fundamental aspects of the problem: (1) modeling and simulation of turbulence including crosscorrelation; (2) threedimensional dynamicwake effects on rotor response to turbulence and (3) prediction of turbulence and response statistics. The analysis is based on the theory of isotropic and homogeneous turbulence and Taylor's frozenfield approximation. Quasisteady airfoil aerodynamics and a threedimensional wake are used. Both the isolated blades and isolated rotors are treated. The parallelization is carried out on a massively parallel MasPar SIMD computer. Major conclusions include: (i) The effects of crosscorrelation are negligible when two stations lie on the same blade and appreciable when two stations lie on different blades. (ii) In modeling the threedimensional wake, 3 harmonics are required and dynamic wake has dominant influence on response statistics. (iii) With increasing comprehensiveness of helicopterturbulence modeling, the sequential execution times increase dramatically; by comparison, the parallel execution times are far lower and, more significantly, remain nearly constant.
Show less  Date Issued
 1995
 PURL
 http://purl.flvc.org/fcla/dt/15117
 Subject Headings
 Helicopters, Turbulence, Rotors (Helicopters), Boundary layer noise
 Format
 Document (PDF)
 Title
 Computations of normal vortex interaction with blades and circular cylinders.
 Creator
 Yalamanchili, Ramakrishna., Florida Atlantic University, Marshall, Jeffrey S., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

A numerical model for the simulation of threedimensional normal bladevortex interaction has been developed to study the bending and variation of core radius of the vortex due to the influence of the blade and the subsequent unsteady force on the blade. For thin blades, a procedure to enable instantaneous cutting of the vortex has been employed to study the vortex response to cutting. The vortex is represented by a filament model which includes axial flow within the core and nonuniform core...
Show moreA numerical model for the simulation of threedimensional normal bladevortex interaction has been developed to study the bending and variation of core radius of the vortex due to the influence of the blade and the subsequent unsteady force on the blade. For thin blades, a procedure to enable instantaneous cutting of the vortex has been employed to study the vortex response to cutting. The vortex is represented by a filament model which includes axial flow within the core and nonuniform core area. The vortex is convected with selfinduced velocities given by the BiotSavart line integral, and the effect of the cylinder is obtained using a vortex sheet panel method. The governing equations for the vortex axial velocity have a form similar to that of the onedimensional gas dynamics equations and admit "shocklike" discontinuities. The results indicate that the amount of vortex bending due to interaction with the blade is primarily dependent on the ratio of blade thickness T to ambient vortex core radius sigma o, although for a given amount of bending of the vortex axis, increase in cylinder forward speed results in a decrease in vortex core radius. For blades with T/sigma o < 0(1), very little bending is observed for attack angles under the stall limit. In the case of vortex cutting by a blade, vortex shocks and expansion waves are observed to propagate on the vortex axis away from the blade.
Show less  Date Issued
 1993
 PURL
 http://purl.flvc.org/fcla/dt/14985
 Subject Headings
 Helicopters, BladesNoise, Rotors (Helicopters), Vortexmotion
 Format
 Document (PDF)
 Title
 Helicopter stability during aggressive maneuvers.
 Creator
 Mohan, Ranjith., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The dissertation investigates helicopter trim and stability during level bankangle and diving bankangle turns. The level turn is moderate in that sufficient power is available to maintain level maneuver, and the diving turn is severe where the power deficit is overcome by the kinetic energy of descent. The investigation basically represents design conditions where the peak loading goes well beyond the steady thrust limit and the rotor experiences appreciable stall. The major objectives are:...
Show moreThe dissertation investigates helicopter trim and stability during level bankangle and diving bankangle turns. The level turn is moderate in that sufficient power is available to maintain level maneuver, and the diving turn is severe where the power deficit is overcome by the kinetic energy of descent. The investigation basically represents design conditions where the peak loading goes well beyond the steady thrust limit and the rotor experiences appreciable stall. The major objectives are: 1) to assess the sensitivity of the trim and stability predictions to the approximations in modeling stall, 2) to correlate the trim predictions with the UH60A flight test data, and 3) to demonstrate the feasibility of routinely using the exact fastFloquet periodic eigenvector method for mode identification in the stability analysis. The UH60A modeling and analysis are performed using the comprehensive code RCAS (Army's Rotorcraft Comprehensive Analysis System). The trim and damping predictions are based on quasisteady stall, ONERAEdlin vi (Equations Differentielles Lineaires) and LeishmanBeddoes dynamic stall models. From the correlation with the test data, the strengths and weaknesses of the trim predictions are presented.
Show less  Date Issued
 2012
 PURL
 http://purl.flvc.org/FAU/3342237
 Subject Headings
 Helicopters, Aerodynamics, Helicopters, Control systems, Rotors (Helicopters), Aerodynamics, Stability of helicopters, Vibration (Aeronautics), Damping
 Format
 Document (PDF)
 Title
 Dynamic stall and threedimensional wake effects on isolated rotor trim and stability with experimental correlation and parallel fastFloquet analysis.
 Creator
 Subramanian, Shanmugasundaram., Florida Atlantic University, Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

Hingeless rotors are susceptible to instabilities of the leadlag 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, lagdamping prediction requires an aerodynamic representation that adequately accounts for quasisteady stall, dynamic stall and threedimensional dynamic wake. Accordingly, this dissertation investigates these...
Show moreHingeless rotors are susceptible to instabilities of the leadlag 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, lagdamping prediction requires an aerodynamic representation that adequately accounts for quasisteady stall, dynamic stall and threedimensional 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 threebladed 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 advanceratios 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 lagdamping 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 finitestate threedimensional wake model. The rootflexureblade assembly of the untrimmed rotor is represented by a rootrestrained rigid flaplag model as well as by an elastic flaplagtorsion 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 lagdamping 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 forcemoment 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 smallorder systems (number of states or order M < 100). However, it has been found to be practical neither for design nor for comprehensiveanalysis 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 flighttrim conditions. and (iii) noniinear fiapiag 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 fastFloquet analyses each in sequential and parallel modes  are comparable. The fastFloquet analysis brings in nearly Qfold 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 fastFloquet 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 largescale Floquet analysis practical for rotorcrafts with identical as well as with dissimilar blades.
Show less  Date Issued
 1996
 PURL
 http://purl.flvc.org/fcla/dt/12462
 Subject Headings
 Rotors (Helicopters), Stalling (Aerodynamics), Drag (Aerodynamics), Wakes (Aerodynamics), Floquet theory
 Format
 Document (PDF)
 Title
 Parallelcomputing concepts and methods toward largescale floquet analysis of helicopter trim and stability.
 Creator
 Nakadi, Rajesh Mohan., Florida Atlantic University, Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The rotorcraft trim solution involves a search for control inputs for required flight conditions as well as for corresponding initial conditions for periodic response or orbit. The control inputs are specified indirectly to satisfy flight conditions of prescribed thrust levels, rolling and pitching moments etc. In addition to the nonlinearity of the equations of motion and control inputs, the control inputs appear not only in damping and stiffness matrices but also in the forcingfunction or...
Show moreThe rotorcraft trim solution involves a search for control inputs for required flight conditions as well as for corresponding initial conditions for periodic response or orbit. The control inputs are specified indirectly to satisfy flight conditions of prescribed thrust levels, rolling and pitching moments etc. In addition to the nonlinearity of the equations of motion and control inputs, the control inputs appear not only in damping and stiffness matrices but also in the forcingfunction or input matrix; they must be found concomitantly with the periodic response from external constraints on the flight conditions. The Floquet Transition Matrix (FTM) is generated for perturbations about that periodic response; usually, a byproduct of the trim analysis. The damping levels or stability margins are computed from an eigenanalysis of the FTM. The Floquet analysis comprises the trim analysis and eigenanalysis and is routinely used for small order systems (order N < 100). However, it is practical for neither design applications nor comprehensive analysis models that lead to large systems (N > 100); the execution time on a sequential computer is prohibitive. The trim analysis takes the bulk of this execution time. Accordingly, this thesis develops concepts and methods of parallelism toward Floquet analysis of large systems with computational reliability comparable to that of sequential computations. A parallel shooting scheme with damped Newton iteration is developed for the trim analysis. The scheme uses parallel algorithms of RungeKutta integration and linear equations solution. A parallel QR algorithm is used for the eigenanalysis of the FTM. Additional parallelism in each iteration cycle is achieved by concurrent operations such as perturbations of initial conditions and control inputs, followup integrations and formations of the columns of the Jacobian matrix. These parallel shooting and eigenanalysis schemes are applied to the nonlinear flaplag stability with a threedimensional dynamic wake (N ~ 150). The stability also is investigated by widely used sequential schemes of shooting with damped Newton iteration and QR eigenanalysis. The computational reliability is quantified by the maximum condition number of the Jacobian matrices in the Newton iteration, the eigenvalue condition numbers and the residual errors of the eigenpairs. The saving in computer time is quantified by the speedup, which is the ratio of the execution times of Floquet analysis by sequential and parallel schemes. The work is carried out on massively parallel MasPar MP1, a distributedmemory, singleinstruction multipledata or SIMD computer. A major finding is that with increasing system order, while the parallel execution time remains nearly constant, the sequential execution time increases nearly cubically with N. Thus, parallelism promises to make largescale Floquet analysis practical.
Show less  Date Issued
 1994
 PURL
 http://purl.flvc.org/fcla/dt/15085
 Subject Headings
 Floquet theory, HelicoptersControl systems, Rotors (Helicopters), Parallel processing (Electronic computers)
 Format
 Document (PDF)
 Title
 An experimental study of vortex response during cutting by a blade or cylinder.
 Creator
 Krishnamoorthy, Srikanth., Florida Atlantic University, Marshall, Jeffrey S., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

An experimental study of the vortex response to interaction with and cutting by a thin flat plate or circular cylinders of various diameters has been performed. The direction of motion of the flat plate (or circular cylinder) is normal to the vortex axis in the experiments. The vortex is generated by withdraw of fluid at an orifice at the bottom of an "inner cylinder" immersed in a rectangular tank, and the flow field is visualized with both water soluble and immiscible dyes. In the...
Show moreAn experimental study of the vortex response to interaction with and cutting by a thin flat plate or circular cylinders of various diameters has been performed. The direction of motion of the flat plate (or circular cylinder) is normal to the vortex axis in the experiments. The vortex is generated by withdraw of fluid at an orifice at the bottom of an "inner cylinder" immersed in a rectangular tank, and the flow field is visualized with both water soluble and immiscible dyes. In the experiments with circular cylinders, the bending of the vortex is compared to computational predictions from [15], and the mechanism of subsequent breakup of the vortex as it gets closer to the cylinder is studied. The vortex is observed to bend farther without breakup for larger forward speeds of the circular cylinder. Very little bending is observed when the vortex interacts with the flat plate, except for angles of attack exceeding the stall limit Following cutting of the vortex by the flat plate or circular cylinder, a vortex shock is observed to form and propagate up the vortex axis. No vortex shock is observed on the opposite side of the blade. The various forms of these vortex shocks have been photographed, and they appear very similar to travelling vortex breakdowns. The propagation speed of the shocks is compared to an analytical solution for instantaneous vortex cutting by a flat plate of zero thickness.
Show less  Date Issued
 1993
 PURL
 http://purl.flvc.org/fcla/dt/14977
 Subject Headings
 Vortexmotion, BladesNoise, Cylinders, Rotors (Helicopters), HelicoptersNoise
 Format
 Document (PDF)