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 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
 Interaction of vortex sheet with a finite vortex.
 Creator
 Viswanathan, K. S., Florida Atlantic University, Dhanak, Manhar R., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

The rollup of a vortex sheet of elliptic span loading in the presence of a vortex of finite core size is studied in the Trefftz plane. The vorticity in the finite vortex is taken to be uniform and sign opposite to that of the sheet and the flow is assumed to be inviscid and incompressible. A numerical scheme is developed to determine the evolution of (a) the finite vortex using the Contour Dynamics technique, (b) the vortex sheet using an algorithm developed by Krasny. The interaction is...
Show moreThe rollup of a vortex sheet of elliptic span loading in the presence of a vortex of finite core size is studied in the Trefftz plane. The vorticity in the finite vortex is taken to be uniform and sign opposite to that of the sheet and the flow is assumed to be inviscid and incompressible. A numerical scheme is developed to determine the evolution of (a) the finite vortex using the Contour Dynamics technique, (b) the vortex sheet using an algorithm developed by Krasny. The interaction is shown to substantially affect the development of the vortex sheet rollup. The vortex sheet undergoes significant deformation at the rolling up tip region due to its devouring the vortex patch as well as due to the formation of secondary rollup features on the sheet. These features are believed to be important in inhibiting rollup considerably. The interaction is quantified by using a criterion developed to measure the extent of the tip vortex rollup and its characteristics are studied for a range of flow parameters. The strength of the rolling up tip region of the vortex sheet is found to be highly dependent on the location and the vorticity in the finite vortex.
Show less  Date Issued
 1994
 PURL
 http://purl.flvc.org/fcla/dt/15048
 Subject Headings
 Turbulence, Whirlwinds, Vortexmotion, Wakes (Aerodynamics)
 Format
 Document (PDF)
 Title
 Experimental study of the wakemodes for propulsion of twodimensional heaving airfoils.
 Creator
 Buzard, Alan Joe., Florida Atlantic University, von Ellenrieder, Karl
 Abstract/Description

Particle image velocimetry and flow visualization are used to characterize the wake of a heaving airfoil in a set of two experiments. In the first experiment a tandem airfoil configuration is used, with a stationary airfoil downstream of a heaving airfoil (modified Schmidt wavepropeller). Several vortex structures are identified for a forced Strouhal number (St)based on airfoil chordlength, forcing frequency, and freesteam velocityfor 0.1
Show moreParticle image velocimetry and flow visualization are used to characterize the wake of a heaving airfoil in a set of two experiments. In the first experiment a tandem airfoil configuration is used, with a stationary airfoil downstream of a heaving airfoil (modified Schmidt wavepropeller). Several vortex structures are identified for a forced Strouhal number (St)based on airfoil chordlength, forcing frequency, and freesteam velocityfor 0.1 < St < 0.7. An asymmetric average velocity profile is measured in the upper St range. In the second experiment, the wake behind a single heaving airfoil is further inspected, with the purpose of highlighting the asymmetric wake, for 0.1 < St < 1.0. A maximum wake excursion of 18 degrees is measured at St = 0.6, and a minimum excursion of 5.7 degrees occurs at St = 0.9. Using averaged velocity profiles, a virtual origin of the wake excursion is also calculated.
Show less  Date Issued
 2005
 PURL
 http://purl.flvc.org/fcla/dt/13216
 Subject Headings
 Particle acceleratorsResearch, Aerofoils, Aerodynamics, Wakes (Aerodynamics), Flow visualization
 Format
 Document (PDF)
 Title
 On the Low Order Model of Turbulence in the Wake of a Cylinder and Airfoil – URANS Approach.
 Creator
 Whelchel, Jeremiah Mark, Glegg, Stewart A. L., Florida Atlantic University, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
 Abstract/Description

This thesis has described a Reynolds Averaged Navier Stokes approach to modeling turbulence in the wake of a cylinder and airfoil. The mean flow, cross stresses, and twopoint space time correlation structure was analyzed for an untripped cylinder with a Reynolds number based on the cylinder diameter and freestream velocity of 60,000. The same features were also analyzed using this approach for an untripped NACA 0012 airfoil with a Reynolds number based on the airfoil chord and freestream...
Show moreThis thesis has described a Reynolds Averaged Navier Stokes approach to modeling turbulence in the wake of a cylinder and airfoil. The mean flow, cross stresses, and twopoint space time correlation structure was analyzed for an untripped cylinder with a Reynolds number based on the cylinder diameter and freestream velocity of 60,000. The same features were also analyzed using this approach for an untripped NACA 0012 airfoil with a Reynolds number based on the airfoil chord and freestream velocity of 328,000. These simulation results were compared to experimental and newly developed models for validation. The ultimate goal of this present study was to create the twopoint space time correlation function of a cylinder and airfoil wake using RANS calculations which contributes to a larger study where the sound radiated by an open rotor due to ingestion of turbulence.
Show less  Date Issued
 2018
 PURL
 http://purl.flvc.org/fau/fd/FA00013105
 Subject Headings
 TurbulenceNoiseMathematical models., Aerodynamic noise., Wakes (Aerodynamics)., Reynolds number.
 Format
 Document (PDF)