Unsteady aerodynamic theories are essential in the analysis of bird and insect flight. The study of these types of locomotion is vital in the development of flapping wing aircraft. This paper uses potential flow aerodynamics to extend the unsteady aerodynamic theory of Theodorsen and Garrick (which is restricted to rigid airfoil motion) to deformable thin airfoils. Frequency-domain lift, pitching moment and thrust expressions are derived for an airfoil undergoing harmonic oscillations and deformation in the form of Chebychev polynomials. The results are validated against the time-domain unsteady aerodynamic theory of Peters. A case study is presented which analyzes several combinations of airfoil motion at different phases and identifies various possibilities for thrust generation using a deformable airfoil. / Master of Science

It has been widely anticipated that thrust vectoring could be an effective method of providing sufficient levels of stability and control for highly manoeuvrable and flexible Unmanned Combat Air Vehicles (UCAVs). The present project aims to understand the interactions of delta wing vortical flows and thrust vectoring, with an emphasis on unsteady aspects. Food-colouring dye flow visualization, Laser-induced fluorescent flow visualization, Particle Image Velocimetry (PIV) and force measurements were conducted in the water and wind tunnels over a range of dimensionless frequencies and jet momentum coefficients. Both slender and nonslender wings were tested with the purpose of understanding the effect of sweep angle on the aerodynamics-propulsion interaction. The interaction of statically pitched trailing-edge jets with leading-edge vortices over stationary delta wings was studied. It was found that under-vortex blowing with rectangular nozzle at stall and post-stall regimes could yield the maximum effectiveness of trailing-edge blowing, due to the promotion of earlier reattachment and delay of vortex breakdown. The effect of nozzle geometry can be important, because the entrainment effect of the jet depends on it. Studies of the flow field reveal strong jet-vortex interactions, distortion of jet vortices, and merging of wing and jet vortices. The dynamic responses of wing vortical flows to dynamic trailing-edge blowing exhibit hysteresis and phase lag, which increases with the increasing dimensionless frequency of jet momentum. Time delay for the decelerating jet is significantly larger than that for the accelerating jet. Sweep angle has no significant influence on the effect of unsteady trailing-edge blowing. From a design aspect, hysteresis and time delay need to be considered for the flight control systems.

Vortices interacting with the solid surface of aerodynamic bodies are prevalent across a broad range of geometries and applications, such as dynamic stall on wind turbine and helicopter rotors, the separated flows over flapping wings of insects, birds, formation of the vortex wakes of bluff bodies, and the lift-producing vortices formed by aircraft leading-edge extensions and delta wings. This study provides fundamental insights into the formation and evolution of such vortices by considering the leading-edge vortices formed in variations of a canonical flapping wing problem. Specifically, the vorticity transport for three distinct maneuvers are examined, a purely rolling wing, a purely pitching wing and a rolling and pitching wing, of aspect-ratio two. Once the maneuvers are characterized, a passive bleed hole will be introduced to a purely rolling wing, to alter flow topology and vorticity transport governing the circulation on the wing. Three-dimensional representations of the velocity and vorticity fields were obtained via plenoptic particle image velocimetry (PPIV) measurements are used to perform a vorticity flux analysis that serves to identify the sources and sinks of vorticity within the flow. Time-resolved pressure measurements were obtained from the surface of the airfoil, and used to characterize the flux of vorticity diffusing from the solid surface. Upon characterizing all of the sources and sinks of vorticity, the circulation budget was found to be fully accounted for. Interpretation of the individual vorticity balance contributions demonstrated the Coriolis acceleration did not contribute to vorticity generation and was a correction term for the apparent vorticity. The transport characteristics varied among the three cases that were investigated. The spanwise convective contribution was signification over various spanwise locations for the pure roll case. For the pure pitch the shear layer contribution and the diffusive contribution. The circulation was dependent the pitch rate, which was evident only at the beginning of the motion, and circulation growth at later times depended only on the pitch angle.The combined pitch roll cases, the transport behavior strongly resembled that of pitch, with little evidence of roll influence, despite that the flow structure and circulation distribution on the inboard part of the wing exhibited roll-like behaviors. In the final case where the wing is pitching and rolling , the shear layer contribution was balanced by the diffusive contribution, similar to that of the pure pitch case. By adding a passive bleed hole to the purely rolling cases, it was found to alter the both the flow topology and vorticity transport.

With the present drive in turbomachine engine developmenttowards thinner and lighter bladings, closer spaced blade rowsand higher aerodynamic loads per blade row and blade, advanceddesign criteria and accurate prediction methods for vibrationalproblems such as forced response become increasingly importantin order to be able to address and avoid fatigue failures ofthe machine early in the design process. The present worksupports both the search for applicable design criteria and thedevelopment of advanced prediction methods for forced responsein transonic turbine stages. It is aimed at a betterunderstanding of the unsteady aerodynamic mechanisms thatgovern forced response in transonic turbine stages and furtherdevelopment of numerical methods for rotor stator interactionpredictions. The investigation of the unsteady aerodynamic excitationmechanisms is based on numerical predictions of thethree-dimensional unsteady flow field in representative testturbine stages. It is conducted in three successive steps. Thefirst step is a documentation of the pressure perturbations onthe blade surface and the distortion sources in the bladepassage. This is performed in a phenomenological manner so thatthe observed pressure perturbations are related to thedistortion phenomena that are present in the blade passage. Thesecond step is the definition of applicable measures toquantify the pressure perturbation strength on the bladesurface. In the third step, the pressure perturbations areintegrated along the blade arc to obtain the dynamic bladeforce. The study comprises an investigation of operationvariations and addresses radial forcing variations. With thehelp of this bottom-up approach the basic forcing mechanisms oftransonic turbine stages are established and potential routesto control the aerodynamic forcing are presented. For the computation of rotor stator interaction aerodynamicsfor stages with arbitrary pitch ratios a new numerical methodhas been developed, validated and demonstrated on a transonicturbine test stage. The method, which solves the unsteadythree-dimensional Euler equations, is formulated in thefour-dimensional time-space domain and the derivation of themethod is general such that both phase lagged boundaryconditions and moving grids are considered. Time-inclination isutilised to account for unequal pitchwise periodicity bydistributing time co-ordinates at grid nodes such that thephase lagged boundary conditions can be employed. The method isdemonstrated in a comparative study on a transonic turbinestage with a nominal non integer blade count ratio and anadjusted blade count ratio with a scaled rotor geometry. Thepredictions show significant differences in the blade pressureperturbation signal of the second vane passing frequency, whichwould motivate the application of the new method for rotorstator predictions with non-integer blade count ratios.

The leading edge flow structure of the NACA 0012 airfoil is experimentally investigated under dynamic stall conditions (M = 0.1; α = 16.7◦, 22.4◦; Rec = 1× 10^6) using planar particle image velocimetry. The airfoil was dynamically pitched about the 1/4 chord at a reduced frequency, k = 0.1. As expected, on the upstroke the flow remains attached in the leading edge region above the static stall angle, whereas during downstroke, the flow remains separated below the static stall angle. A phase averaging procedure involving triple velocity decomposition in combination with the Hilbert transform enables the entire dynamic stall process to be visualized in phase space, with the added benefit of the complete phase space composed of numerous wing oscillations. The formation and complex evolution of the leading edge vortex is observed. This vortex is seen to grow, interact with surrounding vorticity, detach from the surface, and convect downstream. A statistical analysis coupled with instantaneous realizations results in the modification of the classical dynamic stall conceptual model, specifically related to the dynamics of the leading edge vortex.

<p>With the present drive in turbomachine engine developmenttowards thinner and lighter bladings, closer spaced blade rowsand higher aerodynamic loads per blade row and blade, advanceddesign criteria and accurate prediction methods for vibrationalproblems such as forced response become increasingly importantin order to be able to address and avoid fatigue failures ofthe machine early in the design process. The present worksupports both the search for applicable design criteria and thedevelopment of advanced prediction methods for forced responsein transonic turbine stages. It is aimed at a betterunderstanding of the unsteady aerodynamic mechanisms thatgovern forced response in transonic turbine stages and furtherdevelopment of numerical methods for rotor stator interactionpredictions.</p><p>The investigation of the unsteady aerodynamic excitationmechanisms is based on numerical predictions of thethree-dimensional unsteady flow field in representative testturbine stages. It is conducted in three successive steps. Thefirst step is a documentation of the pressure perturbations onthe blade surface and the distortion sources in the bladepassage. This is performed in a phenomenological manner so thatthe observed pressure perturbations are related to thedistortion phenomena that are present in the blade passage. Thesecond step is the definition of applicable measures toquantify the pressure perturbation strength on the bladesurface. In the third step, the pressure perturbations areintegrated along the blade arc to obtain the dynamic bladeforce. The study comprises an investigation of operationvariations and addresses radial forcing variations. With thehelp of this bottom-up approach the basic forcing mechanisms oftransonic turbine stages are established and potential routesto control the aerodynamic forcing are presented.</p><p>For the computation of rotor stator interaction aerodynamicsfor stages with arbitrary pitch ratios a new numerical methodhas been developed, validated and demonstrated on a transonicturbine test stage. The method, which solves the unsteadythree-dimensional Euler equations, is formulated in thefour-dimensional time-space domain and the derivation of themethod is general such that both phase lagged boundaryconditions and moving grids are considered. Time-inclination isutilised to account for unequal pitchwise periodicity bydistributing time co-ordinates at grid nodes such that thephase lagged boundary conditions can be employed. The method isdemonstrated in a comparative study on a transonic turbinestage with a nominal non integer blade count ratio and anadjusted blade count ratio with a scaled rotor geometry. Thepredictions show significant differences in the blade pressureperturbation signal of the second vane passing frequency, whichwould motivate the application of the new method for rotorstator predictions with non-integer blade count ratios.</p>

The present thesis aims at shedding some light for future applications of &amp / #956 / AVs by investigating the hovering mode of flight by flapping motion. In this study, a detailed numerical investigation is performed to investigate the effect of some geometrical parameters, such as the airfoil profile shapes, thickness and camber distributions and as well as the flapping motion kinematics on the aerodynamic force coefficients and vortex formation mechanisms at low Reynolds number. The numerical analysis tool is a DNS code using the moving grid option. Laminar Navier-Stokes computations are done for flapping motion using the prescribed kinematics in the Reynolds number range of 101-103. The flow field for flapping hover flight is investigated for elliptic profiles having thicknesses of 12%, 9% and 1% of their chord lengths and compared with those of NACA 0009, NACA 0012 and SD 7003 airfoil profiles all having chord lengths of 0.01m for numerical computations. Computed aerodynamic force coefficients are compared for these profiles having different centers of rotation and angles of attack. NACA profiles have slightly higher lift coefficients than the ellipses of the same t/c ratio. And one of the most important conclusions is that the use of elliptic and NACA profiles with 9% and 12% thicknesses do not differ much as far as the aerodynamic force coefficients is concerned for this Re number regime. Also, two different sinusoidal flapping motions are analyzed. Force coefficients and vorticity contours obtained from the experiments in the literature and present study are compared. The validation of the present computational results with the experimental results available in the literature encourages us to conclude that present numerical method can be a reliable alternative to experimental techniques.

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This dissertation presents both analytical and numerical approaches to optimizing thrust and thrust efficiency of harmonically deforming thin airfoils and membrane wings. A frequency domain unsteady aerodynamic theory for deformable thin airfoils, with Chebychev polynomials as the basis functions is presented. Stroke-averaged thrust and thrust efficiency expressions are presented in a quadratic matrix form. The motion and deformation of the airfoil is optimized for maximum thrust and efficiency. Pareto fronts are generated showing optimum deformation conditions (magnitude and phase) for various reduced frequencies and constraints. It is shown that prescribing the airfoil to deform in a linear combination of basis functions with optimal magnitude and phase results in a larger thrust as compared to rigid plunging, especially at low reduced frequencies. It is further shown that the problem can be constrained significantly such that thrust is due entirely to pressure with no leading edge suction, and associated leading edge separation. The complete aeroelastic system for a membrane wing is also optimized. The aerodynamic theory for deformable thin airfoils is used as the forcing in a membrane vibration problem. Due to the nature of the two dimensional theory, the membrane vibration problem is reduced to two dimensions via the Galerkin method and nondimensionalized such that the only terms are nondimesional tension, mass ratio and reduced frequency. The maximum thrust for the membrane wing is calculated by optimizing the tension in the membrane so that the the aeroelastic deformation due to wing motion leads to optimal thrust and/or efficiency. A function which describes the optimal variation of spanwise tension along the chord is calculated. It is shown that one can always find a range of membrane tension for which the flexible membrane wings performs better than the rigid wing. These results can be used in preliminary flapping wing MAV design. / Ph. D.