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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.

We consider the flow of nonlinear Maxwell fluids in the unsteady quasistatic case, where the effect of inertia is neglected. We study the well-posedness of the resulting PDE initial-boundary value problem. This well-posedness depends on the unique solvability of an elliptic boundary value problem. We first present results for the 3D case, locally and globally in time, with sufficiently small initial data, and for a simple shear flow problem, locally in time with arbitrary initial data; after that we extend our results to some 3D flow problems, locally in time, with large initial data. Additionally, we present results for models of White-Metzner type in 3D flow, locally and globally in time, with sufficiently small initial data. We solve our problem using an iteration between elliptic and hyperbolic linear subproblems. The limit of the iteration provides the solution of our original problem. / Ph. D.

The harmonic oscillatory tests for a fighter aircraft configuration using the Dynamic Plunge-Pitch-Roll (DyPPiR) model mount at Virginia Tech Stability Wind Tunnel are described and analyzed. The corresponding data reduction methods are developed on the basis of multirate digital signal processing techniques. Since the model is sting-mounted to the support system of DyPPiR, the Discrete Fourier Transform (DFT) is first used to identify the frequencies of the elastic modes of sting. Then the sampling rate conversion systems are built up in digital domain to resample the data at a lower rate without introducing distortions to the signals of interest. Finally linear-phase Finite Impulse Response (FIR) filters are designed by Remez exchange algorithm to extract the aerodynamic characteristics responses to the programmed motions from the resampled measurements. These data reduction procedures are also illustrated through examples. The results obtained from the harmonic oscillatory tests are then illustrated and the associated flow mechanisms are discussed. Since no significant hysteresis loops are observed for the lift and the drag coefficients for the current angle of attack range and the tested reduced frequencies, the dynamic lags of separated and vortex flow effects are small in the current oscillatory tests. However, large hysteresis loops are observed for pitch moment coefficient in the current tests. This observation suggests that at current flow conditions, pitch moment has large pitch rate and alpha-dot dependencies. Then the nondimensional maximum pitch rate q__max is introduced to characterize these harmonic oscillatory motions. It is found that at current flow conditions, all the hysteresis loops of pitch moment coefficient with same nondimensional maximum pitch rate are tangential to one another at both top and bottom of the loops, implying approximately same maximum offset of these loops from static values. Several cases are also illustrated. Based on the results obtained and those from references, a state-space model is developed to describe the unsteady aerodynamic characteristics up to the high angle of attack regime. A nondimensional coordinate is introduced as the state variable describing the flow separation or vortex burst. First-order differential equation is used to govern the dynamics of flow separation or vortex bursting through this state variable. To be valid for general configurations, Taylor series expansions in terms of the input variables are used in the determination of aerodynamic characteristics, resembling the current approach of the stability derivatives. However, these derivatives are longer constant. They are dependent on the state variable of flow separation or vortex burst. In this way, the changes in stability derivatives with the angle of attack are included dynamically. The performance of the model is then validated by the wind-tunnel measurements of an NACA 0015 airfoil, a 70 degree delta wing and, finally two F-18 aircraft configurations. The results obtained show that within the framework of the proposed model, it is possible to obtain good agreement with different unsteady wind tunnel data in high angle-of-attack regime. / Ph. D.

The unsteady interaction of shock waves emerging from the trailing edge of modern turbine nozzle guide vanes and impinging on downstream rotor blades is modeled in a linear cascade. The Reynolds number based on blade chord and exit conditions (5*10^6) and the exit Mach number (1.2) are representative of modern engine operating conditions. The relative motion of shocks and blades is simulated by sending a shock wave along the leading edges of the linear cascade instead of moving the blades through an array of stationary shock waves. The blade geometry is a generic version of a modern high turning rotor blade with transonic exit conditions. The blade is equipped with a showerhead film cooling scheme. Heat flux, surface pressure and surface temperature are measured at six locations on the suction side of the central blade. Pressure measurements are taken with Kulite XCQ-062-50a high frequency pressure transducers. Heat flux data is obtained with Vatell HFM-7/L high speed heat flux sensors. High speed heat flux and pressure data are recorded during the time of the shock impact with and without film cooling. The data is analyzed in detail to find the relative magnitudes of the shock effect on the heat transfer coefficient and the recovery temperature or adiabatic wall temperature (in the presence of film cooling). It is shown that the variations of the heat transfer coefficient and the film effectiveness are less significant than the variations of recovery temperature. The effect of the shock is found to be similar in the cases with and without film cooling. In both cases the variation of recovery temperature induced by the shock is shown to be the main contribution to the overall unsteady heat flux. The unsteady heat flux is compared to results from different prediction models published in the literature. The best agreement of data and prediction is found for a model that assumes a constant heat transfer coefficient and a temperature difference calculated from the unsteady surface pressure assuming an isentropic compression. / Ph. D.

This dissertation presents measurements of the far-field noise associated with the interaction of grid-generated turbulence with a series of airfoils of various chord lengths, thicknesses, and camber. The radiated noise was measured for a number of angles of attack for each airfoil to determine the effects of angle of attack on the leading edge noise. Measurements are compared with numerous theories to determine the mechanism driving the production of leading edge noise. Calculations were also made using a boundary element method to determine the effects of airfoil shape on the unsteady loading spectrum on the different airfoils to attempt to explain the far-field noise. Measurements of the unsteady surface pressure on a single airfoil were made for a number of angles of attack to determine the effects of wind tunnel interference corrections on the unsteady surface pressure. These measurements were compared with those of Mish (2003) to determine the effects of the interference correction. An attempt was also made to correlate the unsteady loading on the airfoil with the far-field noise. The airfoils studied were a 0.203-m chord NACA 0012, a 0.61-m chord NACA 0015, a 0.914-m chord NACA 0012, a 0.914-m chord DU96, and a 0.914-m chord S831. All airfoils spanned the entire 1.83-m height of the test section. Measurements were made using the Virginia Tech Stability Wind Tunnel in its acoustic configuration with an anechoic test section with side walls made of stretched Kevlar fabric to reduce aerodynamic interference. Measurements were made in grid-generated turbulence with an integral length scale of 8.2-cm and a turbulence intensity of 3.9%. Far-field noise measurements were made at Mach numbers of 0.087 and 0.117 with various configurations of up to 4 Bruel and Kjaer microphones mounted at an observer angle of 90° measured from the wind tunnel axis. Unsteady surface pressure measurements were made on the NACA 0015 airfoil immersed in the same grid generated turbulence used in the far-field noise study. An array of microphones mounted subsurface along the airfoil chord and a spanwise row was used to measure the unsteady surface pressure. These measurements were made at angles of attack from 0 through 16° in 2° increments. Far-field noise measurements of the leading edge noise show a consistent angle of attack effect. The radiated noise increases as the angle of attack is increased over the frequency range. These effects are small for large integral scale to airfoil chord ratios. The larger airfoils have been shown to generate significantly less leading edge noise at high frequencies, but this effect does not appear to be solely dependent upon the leading edge radius. The leading edge noise can be predicted with accuracy using the method of Glegg et al. (2008). Unsteady surface pressure measurements have been shown to be largely independent of the wind tunnel interference correction as shown by comparison with Mish (2008). The same low frequency reduction described by Mish was seen for an interference correction that was nearly 30% larger. The unsteady sectional lift spectra have been shown to be related to the far-field noise spectra by a factor close to the dipole efficiency factor; however, no correlation could be found between the instantaneous unsteady surface pressure and the radiated noise. The spanwise averaged unsteady pressure difference spectra have been shown to be related to the far-field noise spectra by the dipole efficiency factor. / Ph. D.

Ph. D.

Two algorithms commonly used for solving low-speed flow fields are evaluated using an unsteady turbulent flow formulation. The first algorithm is the method of artificial compressibility which solves the incompressible Navier-Stokes equations. The second is a preconditioned system for solving the compressible Navier-Stokes equations. Both algorithms have been implemented into GASP Version 4, which is the flow solver used in this investigation. Unsteady numerical simulations of unsteady, 2-D flow over square cylinders are performed with comparisons made to experimental data. Cases studied include both a single-cylinder and a three-cylinder configuration. Two turbulence models are also used in the computations, namely the Spalart-Allmaras model and the Wilcox k-ω (1998) model. The following output data was used for comparison: aerodynamic forces, mean pressure coefficient, Strouhal number, mean velocity magnitude and turbulence intensity. The main results can be summarized as follows. First, the predictions are more sensitive to the turbulence model choice than to the choice of algorithm. The Spalart-Allmaras model overall produced better results with both algorithms than the Wilcox k-ω model. Second, the artificial compressibility algorithm produced slightly more consistent results compared with experiment. / Master of Science

A two-dimensional, inviscid, incompressible procedure is presented for predicting the unsteady lift on turbomachinery blades caused by the upstream potential disturbance of downstream flow obstructions. The method is applied to a particular geometry which consists of a rotor, a downstream stator, and downstream struts which support the engine casing. Using the Douglas-Neumann singularity superposition computer program to model the downstream flow obstructions, classical equations of thin airfoil theory are then employed, to compute the unsteady lift on the upstream rotor blades. Very good agreement between the Douglas-Neumann program and experimental measurements was obtained for the downstream stator-strut flow field. The calculations for the unsteady lift due to the struts were in good agreement with the experiments in showing that the unsteady lift due to the struts decays exponentially with increased axial separation of the rotor and the struts. However, the calculations for the unsteady lift due to the stator were two orders of magnitude smaller than that measured in experiments. This is attributed to the strong viscous interaction between the rotor and stator blade rows. / M.S.