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Aerospace Engineering

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#### Solution of viscous flow problems by using the boundary element method

A scheme based on the Boundary Element Method (BEM) for solving the problem of steady flow of an incompressible viscous fluid is presented in this thesis. The problem is governed by both Navier-Stokes (N-S) equations and the continuity equation. The fundamental solution of the two-dimensional N-S is derived, and the partial differential equations are converted to an integral equation;The computer code is flexible enough to handle a variety of boundary and domain elements with different degrees of interpolation polynomial. Boundary and domain integrals over corresponding elements are evaluated analytically. The Newton Raphson iteration scheme accompanied by a relaxation factor is used to solve the nonlinear equations. The code includes a post processor that calculates the velocity components at any point inside the domain;The scheme has been applied to three test problems. The first concerns Couette flow, which has been used as a test case for testing the rate of convergence and accuracy. The second and the third concern the driven cavity and the flow in a stepped channel, respectively;In the integral equation formulation, the primary unknowns are tractions on the domain boundary and velocities in the interior. Because the shear stress, drag, and lift can be simply computed from the values of tractions along the boundary, such a formulation is markedly superior to either the finite-difference or the finite-element formulation. In customary pressure-velocity or streamfunction-vorticity formulations, employed in the finite-difference or finite-element methods, calculation of stress, drag, and lift involves extensive postprocessing.

#### Design, analysis, and modeling of giant magnetostrictuve transducers

The increased use of giant magnetostrictive, Terfenol-D transducers in a wide variety of applications has led to a need for greater understanding of the materials performance. This dissertation attempts to add to the Terfenol-D transducer body of knowledge by providing an in-depth analysis and modeling of an experimental transducer. A description of the magnetostriction process related to Terfenol-D includes a discussion of material properties, production methods, and the effect of mechanical stress, magnetization, and temperature on the material performance. The understanding of the Terfenol-D material performance provides the basis for an analysis of the performance of a Terfenol-D transducer. Issues related to the design and utilization of the Terfenol-D material in the transducers are considered, including the magnetic circuit, application of mechanical prestress, and tuning of the mechanical resonance. Experimental results from two broadband, Tonpilz design transducers show the effects of operating conditions (prestress, magnetic bias, AC magnetization amplitude, and frequency) on performance. In an effort to understand and utlilize the rich performance space described by the experimental results a variety of models are considered. An overview of models applicable to Terfenol-D and Terfenol-D transducers is provided, including a discussion of modeling criteria. The Jiles-Atherton model of ferromagnetic hysteresis is employed to describe the quasi-static transducer performance. This model requires the estimation of only six physically-based parameters to accurately simulate performance. The model is shown to be robust with respect to model parameters over a range of mechanical prestress, magnetic biases, and AC magnetic field amplitudes, allowing predictive capability within these ranges. An additional model, based on electroacoustics theory, explains trends in the frequency domain and facilitates an analysis of efficiency based on impedance and admittance analysis. Results and discussion explain the importance of the resonance of the electromechanical system, as distinct from the mechanical resonance. Conclusions are drawn based on the experimental work, transducer analysis, and modeling approaches.

#### Scattering investigation based on acoustical holography

The objective of this research is to investigate sound scattering by an object using a two-surface measurement technique that separates the incident field and the scattered field. The separation technique is developed in cartesian and cylindrical coordinates. The decomposition method in the cartesian coordinate system is based on the principle that any wave form can be decomposed into plane-wave components by using a two dimensional spatial Fourier transform. For the cylindrical coordinate system, a two plane separation technique is based on decomposing the sound field into cylindrical waves. Numerical simulations are performed and the effect of various parameters are investigated. Specifically, the distance between two measurement surfaces, the distance between measurement points, and the aperture size are investigated. In addition, experimental studies were conducted inside an anechoic chamber with a baffled loudspeaker as a source, illuminating four different scatterers. The decomposed scattered field is then used to estimate the far-field target strength. The experiments demonstrate the feasibility of the field separation technique.

#### Nonlinear and hysteretic magnetomechanical model for magnetostrictive transducers

The growing interest on magnetostrictive materials for generation of strains and forces in smart structure systems motivates the development of increasingly accurate models of the performance of these materials as used in transducers. The proposed magnetomechanical model provides a characterization of the material magnetization as well as the strain and force output by a transducer in response to quasistatic applied magnetic fields. The model is built in three steps. In the first, the mean field model for ferromagnetic hysteresis originally developed by Jiles and Atherton is used to compute the magnetization arising from the application of magnetic fields. While this model provides an accurate characterization of the field-induced magnetization at constant stress, it is insufficient in cases where the stress state of the magnetostrictive driver varies significantly during operation. To model the stress-induced magnetization changes, or magnetomechanical effect, a 'law of approach' to the anhysteretic magnetization is considered. The magnetization hysteresis model in combination with this law of approach provides a more realistic representation of the bidirectional energy transduction taking place in magnetostrictive transducers. In the second step, an even-term series expansion posed in terms of the magnetization is employed to calculate the magnetostriction associated with magnetic moment rotations within domains. While the magnetostriction provides a good description of the total material strain at the low field levels where elastic dynamics are of secondary significance, it is highly inaccurate at higher drive levels, in which the elastic response gains significance. This elastic or material response is considered in the third and last step, by means of force balancing in the form of a PDE system with magnetostrictive inputs and boundary conditions consistent with the transducer mechanical design. The solution to this PDE system provides the longitudinal displacements and corresponding strains and forces generated by the magnetostrictive driver. Since the formulation precludes analytic solution, a Galerkin discretization is employed to express the PDE in the form of a temporal system, which is subsequently solved using finite difference approximations. The ability of the model to accurately characterize the magnetomechanical behavior of magnetostrictive transducers is demonstrated via comparison of model simulations with experimental measurements collected from two Terfenol-D transducers.

#### Numerical solution of inverse problems in nondestructive evaluation using the boundary element method and multivariate adaptive regression splines

Flaw identification is an important inverse problem that underlies techniques for nondestructive evaluation (NDE). In this study, a known steady state thermal field is used to identify multiple flaws in a material. The problem is to determine locations and sizes of the multiple flaws if the number of flaws and the temperature at certain probe locations on the boundary are known. The boundary element method (BEM) is used as a computational tool in this task;Earlier work in this area has dealt with the case of a single flaw, while we address the case of multiple flaws. The identification of the multiple flaws is difficult because it is impossible to identify the disturbances caused by each individual fLaw; As a result, the iterative methods, used in the single flaw identification, typically fail to converge unless approximate locations of the multiple flaws are known;In our method, the characterization of flaws is performed in two stages. First, the specimen probe data is compared with a set of known cases of probe data (training set) to predict the approximate locations and sizes of the multiple flaws. Second, the final prediction of flaws is determined using a nonlinear optimization method;To prepare the training set, we need only the information of a single flaw of fixed size at various locations. The superposition principle and a special scaling are used to create the multiple flaws information. This procedure is developed as an extension of the theory of potential flows in fluid mechanics. The distinguishing feature of this technique is that only a small training set is stored in the memory;In this study, the final characterizations are made by two different methods. One of them is an iteration method, which minimizes an error functional. The other is called the multivariate adaptive regression splines (MARS). Various test cases yielded excellent solutions. The tolerance of both methods to experimental errors is also discussed. It is found that the iterative method performs better than MARS.

#### The effect of rib attachment properties on structural acoustics

Sound Pressure measurements were taken of several 2.44m long thin beams which had 0.635cm wide t-ribs centered on them. The beams were excited by a chirp signal with the frequency range of 500Hz to 1500Hz. Two rib attachment methods were used on the beams. One group of beams were machined out of thick stock to the geometry of a rib welded to a beam to ensure that the rib and attachment were one continuous media. The other group of beams had ribs that were welded on. Fillets from the welding process were subjected to heat-treatment and machining to determine the effect of static stress in fillets. Farfield sound radiation from the beam and phase speeds of waves propagating through the beam were used to investigate the effects of the rib and its attachment properties on the beam response;The experimental results showed that the geometry and stress state of the attachment are the main parameters that alter wave propagation and sound radiation. Also, the maximum sound radiation from the rib was not centered directly over the rib, but rather ahead of the rib location. Furthermore, substantial phase speed increases were observed around the shaker location and the rib location;Attachment geometry and stress information were incorporated into a Euler-Bernoulli wave-based model. This wave-based model reproduced the static stress effect on the farfield sound radiation, but didn't reproduce the position of the sound radiation from the rib nor the experimental phase speed increases around the shaker or rib locations;An energy-based model was derived that included the geometry of the rib and attachment. The model used the Extended Hamilton's Principle. Cubic spline weighting functions were applied via Galerkin's method of weighted residuals. This energy-based model did reproduce both the position and the magnitude of the peak in the sound radiation field from the rib. It also reproduced the phase speed increases around the shaker and the rib locations.

#### Drag on object moving through foam

Foams consist of small gas bubbles separated by thin liquid films. Although many complex models have been developed to describe the rheological properties of foam, very little information is available concerning the flow charateristics of foam flowing past an object. The purpose of this research was to investigate foam flow properties by performing simple experiments to determine the drag charateristics of simple-shaped bodies moving through foam;A rotating tank apparatus was built and used as the equivalent of a wind tunnel in aerodynamic testing. Foam with consistent properties was produced and models of various shapes were suspended in the moving foam. The drag on the model moving through the foam was obtained by using a simple strain gauge force balance. The foams were made from liquid soap, water, and air. By varying the percent of these quantities, foams with various properties were produced;The drag was measured as a function of velocity, foam properties, and body type (spheres, disks, ellipsoids, and flat plates). Various surface roughnesses were tested to determine the dependence of drag on surface texture. This is especially important for foam flows because of their "slip" condition at solid surfaces;The experimental data obtained indicate that a foam flow has a Bingham plastic charateristic with a yield stress. The drag was a consistent function of the foam quality and soap-water solution's viscosity. For the case of rough surface specimens, the drag increment differs from that of Newtonian laminar flow.

#### Modeling of ultrasonic scattering experiments with applications to system and transducer characterization

The voltage signal output by the receiver electronics, which represents the observable quantity in an ultrasonic scattering experiment, is written as a product, in the frequency domain, of two factors: the system efficiency and the scattering coefficient. The system efficiency represents the combined electrical properties of both the generator and receiver electronics and is a function of frequency only. The scattering coefficient represents the acoustic nature of the experiment (the radiation, propagation, scattering and reception of ultrasonic waves) and depends on the distributed field properties of the transducers involved and their locations and orientations, on the number and type of scattering obstacles and their locations and orientations, on the acoustic properties of the media through which the waves travel, and on the nature and shape of any interfaces through which the waves pass. Based on a generalized principle of electroacoustic reciprocity, formulae are developed for the evaluation of the scattering coefficient. The most general of these involve an integration over either the volume or the surface of the scattering obstacle. More specific formulae are also developed which express the scattering coefficient in terms of either the spherical wave transition matrix or the plane wave scattering amplitude of the obstacle;In order to demonstrate the use of the formulae developed, the calculation of the scattering coefficient is considered for two common ultrasonic scattering experiments. The first experiment involves the pulse-echo scattering from an infinite, flat elastic plate immersed in water. This arrangement is often used for the measurement of the velocity and attenuation of elastic waves, and also as a reference experiment for the determination of the system efficiency. The second experiment involves the pulse-echo scattering from an elastic sphere immersed in water. Particular attention is given to the specular reflection component of the scattering, which is demonstrated to be approximately equivalent to a point measurement of the pressure field radiated by the transducer. This approximation is subsequently used as the basis for obtaining experimental data for transducer characterization. The characterization itself is based on expanding in a set of basis functions, each weighted by an unknown coefficient, the normal velocity profile across the plane flush with the face of the probe. Values for the coefficients are obtained by determining the best fit between the experimental pressure data and the pressure calculated from the assumed velocity profile. Results are presented for two commercially manufactured immersion transducers, one planar (unfocused) and the other focused.

#### Determination of secondary sources in noise cancellation with boundary element method

The direct boundary element method is proposed in this thesis to solve acoustic radiation problems as well as to achieve regional noise cancellation in half space with uniform finite impedance over the surface. The boundary integral equation and half space Green's function were derived to accomplish these goals. Those formulations were verified by comparing numerical simulations with theoretical solutions as well as experimental results. In addition, the above formulations were extended to achieve regional noise cancellation in half space by applying the boundary element method;Two methods were investigated to obtain noise cancellation in desired regions. They are the iterative control method and the coupled equation method. A set of Fortran programs including discretizing of geometries, incorporating boundary integral equations, and accommodating the noise cancellation technique were developed. Various problems concerning ill-conditioned matrices in numerical simulation and practical application of noise cancellation technique were discussed as well. Finally, data banks for various configurations of sound sources were set up for quick reference of the locations and driving functions of secondary sources. Thus, noise reduction in a designated area is shown to be feasible;A 6" speaker was used to simulate a noise source with uniform surface velocity. In addition, a ribbed aluminum plate with the dimension 71.12cm x 60cm was used to simulate a noise source with variable surface velocity. Four 10" speakers were used as secondary sources to achieve noise reduction in desired regions at certain frequencies. A multi-channel digital/analog converter was used in order to control desired driving functions for each individual secondary sources. The computer-controlled scanning system including a 2-channel controller, 2-D scanner, and stepping motors was used to place a quarter-inch microphone at certain locations. The acoustic pressure on a 120cm by 120cm plane at various distances above the source plane was measured. A Bruel and Kjaer model 2032 FFT analyzer was used to acquire and process signals from the microphone. The experimental results agreed well with numerical simulations. This indicated that the proposed noise cancellation technique attenuated the acoustic noise level successfully.

#### Numerical investigation of Type II non-Newtonian de/anti-icing fluid effects on take-off performance for general aviation aircraft

Ground icing, while preventable with glycol based freezing point depressant fluids, accounts for nearly 40-50 civil accidents a year according to one account. More viscous than Type I fluids, Type II fluids are inherently non-linear in their shear stress-rate of strain relationship having smaller relative viscosity at higher shear rates. The non-linearity makes properly scaled wind-tunnel testing difficult and computational methods are employed in this study to look at the aerodynamic effects of the deicing fluid on global performance during typical take-off maneuvers for general aviation. The method is tested on a two-dimensional NACA 0012 airfoil under typical take-off simulation parameters;A modified PANEL method arrives at potential flow solutions which account for the accelerating freestream, rotation maneuver, and shed vorticity while time-dependent Boundary Layer equations are solved using an implicit finite difference scheme. Viscid-inviscid interaction is accomplished in an inverse method through the specification of normal velocities induced on each panel during potential flow calculations to account for displacement thickness effects. Deicing fluid motion is driven by shear stresses at the interface of the fluid and gas-dynamic boundary layer and pressure gradients based on the outer flow solution. Slip velocities and shear stresses are then matched at the interface to insure kinematic and dynamic continuity. The displacement thickness effect of the deicing fluid is accounted for in the viscid-inviscid interaction;The deicing fluid is assumed Newtonian in this study and exhibits a fluid bucking effect which may point to reasons for reported losses in lift. The large shear stresses toward the leading edge drag the fluid to the center of the airfoil while large pressure gradients in the back push the fluid to the center. The buckling phenomena is shown to be brought on by (1) increased fluid viscosity, (2) deeper initial depths of deicing fluid and (3) higher rotation speeds where shear stresses and pressure gradients are larger. In simulations which did not exhibit fluid buckling, the effect on maximum lift coefficient was found to be minimal. The current programming is not equipped to handle this aspect of fluid stability and remains an issue for further investigation.