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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

The experiments on this project proceeded on the premise that adding an array of auxiliary jets behind a main jet injector would alleviate the large region of low pressure typically found downstream of a normal, sonic injector in supersonic flow and also possibly increase in intensity of the upstream high-pressure region. The secondary jet would, in theory, "push" the primary jet further into the flow, increasing the size of the obstacle as seen by the flow. The resulting increased high pressure upstream of the flow would increase the force on the body. Also, the presence of secondary jets would reduce the intensity of the primary jet's low-pressure region. These results would be beneficial to increase the force and decrease the nose-down moment associated with sonic, normal injection into a supersonic crossflow. Therefore, in application to hypersonic, high-altitude missile maneuvering, the firing of a thruster with such an array would result in both added force and a reduction of the moment usually associated with the pressure field on the missile. Such an array could allow the missile to perform purely translational maneuvers with less fuel, all the while keeping the target in view. To accomplish this task, some modern missiles use a second injector far downstream from the primary injector. This second injector's primary function is to negate the nose-down moment, and it adds little to the overall jet effectiveness. To this end, two sets of experiments were conducted: one with low jet pressure ratio, Poj/P1 = 13.65, and low Mach number of 2.4 with Po,inf = 3.74 atm and To,inf = 293K for proof of concept and one at primary conditions Poj/P1 = 620, M1 = 4, Po,inf = 10.21 atm, To,inf = 293K. Spark Shadowgraphs were taken at both of these cases to study the structures present in the flow field and to qualitatively assess the effects of the secondary jet injectors. Placed under the Mach disk of the main jet, the secondary jets are hypothesized to push the plume of the main jet further up into the flow, increasing the force on the plate, and Shadowgraphs were used to test this hypothesis. Schlieren pictures were taken at the high M1, high-pressure ratio test case to further study the interaction of the secondary jets with the main jet. Pressure Sensitive Paint, PSP, was used in both cases to gain a greater understanding of the surface pressure near the injectors for different jet configurations. It was discovered that the addition of secondary jets could indeed both increase the force generated by the main jet and reduce the undesirable nose-down moment created by the main jet. In the low M1, low pressure ratio conditions, the addition of one pair of jets manipulated the surface pressure such that the force on the plate increased by 17% and the nose-down moment was increased by 9% over the main jet only case. The further addition of one more pair of injectors increased the surface pressure force on the plate by 34% and increased the nose-down moment on the plate by 3% when compared to the Main Jet Only case. It is important to note that, these increases are due solely to the manipulation of the surface pressure force field and not the thrust of the secondary jets. The added thrust would increase the force on the plate and their position would insure an increase of a nose-up moment. One pair of secondary jets increases the injectant mass flow by about 2.3%. Therefore, the effects reported above are seen to be disproportionate to the amount of added injectant. For the primary test conditions (M1 = 4, Poj/P1 = 620, Po = 10.21 atm, To = 293K) the addition of two pairs of secondary jets had a force increase of 62% and a nose-down moment decrease of 38% over that of the main jet only case. Three pairs increased the force 71% and the decreased the nose-down moment by 26% and four pairs increased the force 91% but increased the nose-down moment by 33%. These values do not account for the thrust of the secondary jets. Accounting for the beneficial effects of the thrust of the secondary jets, the force on the plate for two pairs of secondary jets increased the force 70% and decreased the moment 42%. Three pairs increased the force 83% and decreased the moment 35%. The increase of force for four pairs of secondary jets was 106% and the increase in nose-down moment was only 21%. A point of diminishing returns was reached. As more pairs of injectors are added further and further from the main injector, the beneficial force effects are offset by a growing moment penalty. By considering the locations of the secondary injectors to the main injector for both the low Mach number, low-pressure ratio tests and the main tests conditions, it can be surmised that the greatest benefit from the secondary jets can be extracted when the jets are placed within the main injector's downstream low-pressure region. / Master of Science

A numerical procedure is presented which uses the truncation error injection methodology to efficiently achieve accurate approximations to complex problems having disparate length scales in the context of solving viscous, transonic flow over an airfoil. The truncation error distribution is estimated using the solution on a coarse grid. Local fine grids are formed which improve the resolution in regions of large truncation error. A fast fourth-order accurate scheme is presented for interpolating and relating the solutions between the generalized curvilinear coordinate systems of the local and global grids. It is shown that accurate solutions can be obtained on a global coarse grid with correction information obtained on local fine grids, which may or may not be topologically similar to the global grid as long as they are capable of resolving the local length scale. Dirichlet boundary conditions for the local grid yield the best results. The scheme also serves as the basis of a local refinement technique wherein a grid local to the nose of an airfoil is used to resolve a supersonic zone terminated by a shock and its interaction with a turbulent boundary layer. The solution on the local grid reveals details of the shock structure and a jet-like flow emanating from the root of the normal shock in the shock boundary layer interaction zone.

Approved for public release; distribution is unlimited / A computational fluid dynamic (CFD) investigation is presented that provides predictions of the aerodynamic impact of uniform and non-uniform coatings applied to the leading edge of a compressor airfoil in a cascade. Using a NACA 65(12)10 airfoil, coating profiles of varying leading edge non-uniformity were added. This non-uniformity is typical of that expected due to fluid being drawn away from the leading edge during the coating process. The CFD code, RVCQ3D, is a steady, quasi-three-dimensional Reynolds Averaged Navier-Stokes (RANS) solver. A k-omega turbulence model was used for the Reynolds' Stress closure. The code predicted that these changes in leading edge shape can lead to alternating pressure gradients in the first few percent of chord that create small separation bubbles and possibly early transition to turbulence. The change in total pressure loss and trailing edge deviation are presented as a function of the coating non-uniformity parameter. Results are presented for six leading edge profiles over a range of incidences and inlet Mach numbers from 0.6 to 0.8. Reynolds number was 600,000 and free-stream turbulence was 6%. A two-dimensional map is provided that shows the allowable degree of coating non-uniformity as a function of incidence and inlet Mach number. / Lieutenant Commander, United States Navy

<div>A sharp, circular 7° half-angle cone was tested in the Boeing/AFOSR Mach-6 Quiet Tunnel</div><div>at 6° angle of attack, extending several previous experiments on the growth and breakdown of</div><div>stationary crossflow instabilities in the boundary layer. </div><div><br></div><div>Measurements were made using infrared</div><div>imaging and surface pressure sensors. Detailed measurements of the stationary and traveling</div><div>crossflow vortices, as well as various secondary instability modes, were collected over a large</div><div>region of the cone.</div><div><br></div><div>The Rod Insertion Method (RIM) roughness, first developed for use on a flared cone, was</div><div>adapted for application to crossflow work. It was demonstrated that the roughness elements were</div><div>the primary factor responsible for the appearance of the specific pattern of stationary streaks</div><div>downstream, which are the footprints of the stationary crossflow vortices. In addition, a roughness</div><div>insert was created with a high RMS level of normally-distributed roughness to excite the naturally</div><div>most-amplified stationary mode.</div><div><br></div><div>The nonlinear breakdown mechanism induced by each type of roughness appears to be</div><div>different. When using the discrete RIM roughness, the dominant mechanism seems to be the</div><div>modulated second mode, which is significantly destabilized by the large stationary vortices. This</div><div>is consistent with recent computations. There is no evidence of the presence of traveling crossflow</div><div>when using the RIM roughness, though surface measurements cannot provide a complete picture.</div><div>The modulated second mode shows strong nonlinearity and harmonic development just prior</div><div>to breakdown. In addition, pairs of hot streaks merge together within a constant azimuthal</div><div>band, leading to a peak in the heating simultaneously with the peak amplitude of the measured</div><div>secondary instability. The heating then decays before rising again to turbulent levels. This nonmonotonic</div><div>heating pattern is reminiscent of experiments on a flared cone and earlier computations</div><div>of crossflow on an elliptic cone.</div><div><br></div><div>When using the distributed roughness there are several differences in the nonlinear breakdown</div><div>behavior. The hot streaks appear to be much more uniform and form at a higher wavenumber,</div><div>which is expected given computational results. Furthermore, the traveling crossflow waves become</div><div>very prominent in the surface pressure fluctuations and weakly nonlinear. In addition there</div><div>appears in the spectra a higher-frequency peak which is hypothesized to be a type-I secondary instability</div><div>under the upwelling of the stationary vortices. The traveling crossflow and the secondary</div><div>instability interact nonlinearly prior to breakdown.</div>