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.

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.

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.

This paper is concerned with the use of leaky Lamb waves for the nondestructive evaluation (NDE) of damage in anisotropic materials such as fiber-reinforced composites. Two fundamental acoustic properties of the material, namely, the wave speed and attenuation have been measured. Stiffness is deduced from the wave speed. The damage mode selected for this study is matrix cracking. As expected, the in-plane stiffness decreases and the attenuation increases with an increase in the linear crack density.

A new nonequilibrium turbulence closure model has been developed for computing wall bounded two-dimensional turbulent flows. This two-layer eddy viscosity model was motivated by the success of the Johnson-King model in separated flow regions. The influence of history effects are described by an ordinary differential equation developed from the turbulent kinetic energy equation. The performance of the present model has been evaluated by solving the flow around three airfoils using the Reynolds time-averaged Navier-Stokes equations. Excellent results were obtained for both attached and separated flows about the NACA 0012 airfoil, the RAE 2822 airfoil, and the Integrated Technology A 153W airfoil. Based on the comparison of the numerical solutions with the available experimental data, it is concluded that the new nonequilibrium turbulence model accurately captures the history effects of convection and diffusion on turbulence.

The details of an interacting boundary layer algorithm capable of calculating large scale laminar separation past airfoils at low speeds is given. Rationale behind various convergence acceleration methods is given. It is shown that linear based acceleration methods are limited to 50% savings in convergence rate. A nonlinear extrapolation method is proposed and tested on two simple model problems. Savings exceed the 50% limitation of the previous methods. Boundary layer results for laminar flow past symmetric airfoils at zero incidence are presented as a test of the methods. Leading edge marginal separation results at finite Reynolds numbers are presented. Richardson extrapolation of successive calculations is used to improve accuracy. Results for a zero thickness uncambered plate at angle of attack are presented.

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.

A time accurate compressible interactive boundary layer procedure for airfoils using the quasi-simultaneous method of Veldman is developed. It couples the high frequency transonic small disturbance equation with the complete set of unsteady compressible boundary equations in Levy-Lees variable form, using a pseudo-time derivative of displacement thickness for enhanced stability. Included is a simple procedure for time accurately updating the viscous wake location. The basis of the interaction is an extension of the asymptotic matching condition of Davis for unsteady compressible interaction. This analysis identifies several possible unsteady transonic separation structures and highlights the importance of the pseudo-time derivative in stabilizing the interaction. The method is applied to oscillating airfoils experiencing light shock-induced stall. Comparisons are made with several standard turbulence models. Shock-induced oscillatory flow about the 18% circular arc airfoil is investigated with this method and found to be modeled quite accurately.

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.

Over the past forty years, the problem of nonspecular reflection of bounded beams from fluid-solid interfaces has been studied extensively. Early studies by Schoch and Bertoni and Tamir have concentrated on planar structures, both halfspaces and plates. More recent studies of reflection of sound from cylinders have concentrated on effectively planar incident fields, where the sound wave field does not vary appreciably over the cylinder diameter.

The problem discussed here, nonspecular Gaussian beam reflection from cylindrical shells, differs from the previous studies in that the incident field has a substantial spatial variation over the cylinder radius. Zeroug and Felsen studied the theoretical aspects of nonspecular reflection of divergent and collimated beams from planar and cylindrical interfaces. In their analysis, the plane interface results were extended to the cylindrical case by mapping the problem geometry to cylindrical coordinates 'k and solving in terms of cylinder functions, while assuming locally planar conditions.