This investigation, in consideration of the sudden separation increase involved in wing drop, was to determine if the incorporated 2-D airfoil exhibits abnormal shock sensitivity. A comparative airfoil study was used to determine if this particular transonic airfoil is prone to abrupt shock movement, resulting in increased regions of separation. / Master of Science

An experimental study of active control of fully separated flow over a symmetrical circular-arc airfoil at high angles of attack was performed. The experiments were carried out in a low-speed, open circuit wind tunnel. Angles of attack from 10 to 40 degrees were tested. Low-power input, unsteady excitation was applied to the leading or trailing edge shear layers. The actuation was provided by the periodic oscillation of a 4-percent-chord flap placed on the suction side of the airfoil and facing the sharp edge. Vortex-shedding frequencies were measured and harmonic combinations selected as the applied actuator frequencies. Pressure measurements over the airfoil show that the control increased the normal force coefficient by up to 70%. This supports the idea of vortex capture in the time-averaged sense, enhancing the lift on the airfoil by managing the shear layer roll up. The results indicate the viability of the control of large-scale flow fields by exploiting the natural amplification of disturbances triggered by small-scale actuators. The application of flow control on sharp-edged aircraft wings could lead to improved maneuverability, innovative flight control and weight reduction. These can be achieved by inexpensive, low-power, rugged actuators. / Master of Science

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Piezoelectrics offer high actuation authority and sensing over a wide range of frequencies. A Macro-Fiber Composite is a type of piezoelectric device that offers structural flexibility and high actuation authority. A challenge with piezoelectric actuators is that they require high voltage input; however the low power consumption allows for relatively lightweight electronic components. Another challenge, for piezoelectric actuated aerodynamic surfaces, is found in operating a relatively compliant, thin structure (desirable for piezoceramic actuators) in situations where there are relatively high external (aerodynamic) forces. Establishing an aeroelastic configuration that is stiff enough to prevent flutter and divergence, but compliant enough to allow the range of available motion is the central challenge in developing a piezocomposite airfoil. The research proposed here is to analyze and implement novel electronic circuits and structural concepts that address these two challenges. Here, a detailed theoretical and experimental analysis of the aerodynamic and electromechanical systems that are necessary for a practical implementation of a piezocomposite airfoil is presented. First, the electromechanical response of Macro-Fiber Composite based unimorph and bimorph structures is analyzed. A distributed parameter electromechanical model is presented for interdigitated piezocomposite unimorph actuators. Necessary structural features that result in large electrically induced deformations are identified theoretically and verified experimentally. A novel, lightweight electrical circuitry is proposed and implemented to enable the peak-to-peak actuation of Macro-Fiber Composite bimorph devices with asymmetric voltage range. Next, two novel concepts of supporting the piezoelectric material are proposed to form two types of variable-camber aerodynamic surfaces. The first concept, a simply-supported thin bimorph airfoil, can take advantage of aerodynamic loads to reduce control input moments and increase control effectiveness. The structural boundary conditions of the design are optimized by solving a coupled fluid-structure interaction problem by using a structural finite element method and a panel method based on the potential flow theory for fluids. The second concept is a variable-camber thick airfoil with two cascading bimorphs and a compliant box mechanism. Using the structural and aerodynamic theoretical analysis, both variable-camber airfoil concepts are fabricated and successfully implemented on an experimental ducted-fan vehicle. A custom, fully automated low-speed wind tunnel and a load balance is designed and fabricated for experimental validation. The airfoils are evaluated in the wind tunnel for their two-dimensional lift and drag coefficients at low Reynolds number flow. The effects of piezoelectric hysteresis are identified. In addition to the shape control application, low Reynolds number flow control is examined using the cascading bimorph variable-camber airfoil. Unimorph type actuators are proposed for flow control in two unique concepts. Several electromechanical excitation modes are identified that result in the delay of laminar separation bubble and improvement of lift. Periodic excitation to the flow near the leading edge of the airfoil is used as the flow control method. The effects of amplitude, frequency and spanwise distribution of excitation are determined experimentally using the wind tunnel setup. Finally, the effects of piezoelectric hysteresis nonlinearity are identified for Macro-Fiber Composite bimorphs. The hysteresis is modeled for open-loop response using a phenomenological classical Preisach model. The classical Preisach model is capable of predicting the hysteresis observed in 1) two cantilevered bimorph beams, 2) the simply-supported thin airfoil, and 3) the cascading bimorph thick airfoil. / Ph. D.

Continuous adjoint methods and optimal control theory are applied to a pressure-matching inverse design problem of quasi 1-D nozzle flows. Pontryagin’s Minimum Principle is used to derive the adjoint system and the reduced gradient of the cost functional. The properties of adjoint variables at the sonic throat and the shock location are studied, revealing a logarithmic singularity at the sonic throat and continuity at the shock location. A numerical method, based on the Steger-Warming flux-vector-splitting scheme, is proposed to solve the adjoint equations. This scheme can finely resolve the singularity at the sonic throat. A non-uniform grid, with points clustered near the throat region, can resolve it even better. The analytical solutions to the adjoint equations are also constructed via Green’s function approach for the purpose of comparing the numerical results. The pressure-matching inverse design is then conducted for a nozzle parameterized by a single geometric parameter. In the second part, the adjoint methods are applied to the problem of minimizing drag coefficient, at fixed lift coefficient, for 2-D transonic airfoil flows. Reduced gradients of several functionals are derived through application of a Lagrange Multiplier Theorem. The adjoint system is carefully studied including the adjoint characteristic boundary conditions at the far-field boundary. A super-reduced design formulation is also explored by treating the angle of attack as an additional state; super-reduced gradients can be constructed either by solving adjoint equations with non-local boundary conditions or by a direct Lagrange multiplier method. In this way, the constrained optimization reduces to an unconstrained design problem. Numerical methods based on Jameson’s finite volume scheme are employed to solve the adjoint equations. The same grid system generated from an efficient hyperbolic grid generator are adopted in both the Euler flow solver and the adjoint solver. Several computational tests on transonic airfoil design are presented to show the reliability and efficiency of adjoint methods in calculating the reduced (super-reduced) gradients. / Ph. D.

The application of smart materials to control the flight dynamics of a Micro Air Vehicle (MAV) has numerous benefits over traditional servomechanisms. Under study is wing morphing achieved through the use of piezoelectric Macro Fiber Composites (MFCs). These devices exhibit low power draw but excellent bandwidth characteristics. This thesis provides a background in the 2D analytical and computer modeling tools and methods needed to design and characterize an MFC-actuated airfoil. A composite airfoil is designed with embedded MFCs in a bimorph configuration. The deflection capabilities under actuation are predicted with the commercial finite element package NX Nastran. Placement of the piezoelectric actuator is studied for optimal effectiveness. A thermal analogy is used to represent piezoelectric strain. Lift and drag coefficients in low Reynolds number flow are explored with XFOIL. Predictions are made on static aeroelastic effects. The thin, cambered Generic Micro Aerial Vehicle (GenMAV) airfoil is fabricated with a bimorph actuator. Experimental data are taken with and without aerodynamic loading to validate the computer model. This is accomplished with in-house 2D wind tunnel testing. / Master of Science