Experiment shows that the steady axisymmetric flow past a sphere becomes unstable in the range 120 < Re < 300. The resulting time-dependent nonaxisymmetric flow gives rise to nonaxisymmetric vortex shedding at higher Reynolds numbers. The present work reports a computational investigation of the linear stability of the axisymmetric base flow. When the sphere is towed, fixed, or otherwise constrained, stability is determined solely by the Reynolds number. On the other hand, when the sphere falls due to gravity, the present work shows that a additional parameter, the ratio of fluid density to sphere density (β = ρ(f)/ρ(s)) is involved. We use a spectral technique to compute the steady axisymmetric flow, which is in closer agreement with experiment than previous calculations. We then perform a linear stability analysis of the base flow with respect to axisymmetric and nonaxisymmetric disturbances. A spectral technique similar to that employed in the base flow calculation is used to solve the linear disturbance equations in streamfunction form for axisymmetric disturbances, and in a modified primitive variable form for nonaxisymmetric disturbances. For the density ratio β = 0, which corresponds to a fixed sphere, the analysis shows that the axisymmetric base flow undergoes a Hopf bifurcation at Re = 175.1, with the critical disturbance having azimuthal wavenumber m = 1. The results are favorably compared to previous experimental work.

A Petrov-Galerkin method for the solution of the compressible Euler and Navier-Stokes equations is presented. The method is based on the introduction of an anisotropic balancing diffusion in the local direction of the propogation of the scalar variables. The direction in which the diffusion is added and its magnitude are automatically calculated locally using a criterion that is optimal for one-dimensional transport equations. Algorithms are developed using bilinear quadrilateral and linear triangular elements. The triangular elements are used in conjunction with an adaptive scheme using unstructured meshes. Several applications are presented that show the exceptional stability and accuracy of the method, including the ram accelerator concept for the acceleration of projectiles to ultrahigh velocities. Both two-dimensional and axisymmetric models are employed to evaluate multiple projectile configurations and flow conditions.

The unsteady two-dimensional flow around an array of circular cylinders submerged in a uniform onset flow is analyzed. The fluid is taken to be viscous and incompressible. The array of cylinders consists of two horizontal rows extending to infinity in the upstream and downstream directions. The center-to-center distance between adjacent cylinders is a constant. The Biot-Savart law of induced velocities is used to determine the velocity field due to the free vorticity in the surrounding fluid and the bound vorticity distributed on the surface of each cylinder. The bound vorticity is needed to enforce the no-penetration condition and to account for the production of free vorticity in the solid surfaces. It is governed by a Fredholm integral equation of the second kind. This equation is solved by numerical techniques. The transport of free vorticity in the flow field is governed by the vorticity transport equation. This equation is discretized for a control volume and is solved numerically. Advantage is taken of spatially periodic boundary conditions in the flow direction. This reduces the computational domain to a rectangular region surrounding a single circular cylinder, but necessitates use of a non-orthogonal grid. In order to test the numerical techniques, the simpler case of unsteady flow over a single circular cylinder at various Reynolds numbers if first considered. Results compare favorably with previous experimental and numerical data. Three cases for Reynolds numbers of 10², 10³, and 10⁴ are presented for the array of cylinders. The center-to-center distance is fixed at three diameters. The time development of constant vorticity contours as well as drag, lift, and moment coefficients are shown for each Reynolds number. The motion of stagnation and separation points with time is also given. It is found that the drag for a cylinder in the array may be as low as five percent of that for flow over a single cylinder at the same Reynolds number.

The water level in an open well tapping a confined formation is influenced by natural forces including the solid Earth tide (SET) and atmospheric pressure variation (APV). The spectral method is used to derive an analytical solution for well response to both the random and the periodic components of the combined SET and APV (CSA) forcings. Previously posed models for the individual SET and APV forcings are subsets of this more general model. An inverse theory and an algorithm are developed in order to provide improved results when using such models to estimate the hydraulic parameters associated with a given formation. A complex vector estimation criterion is used in developing a nonlinear, Gauss-Marquardt estimation algorithm. When compared to previous methods of fitting modulus and phase, the complex vector estimation methodology has less bias and variance, and is more robust. An examination of the response surface of the estimation criterion reveals that storativity (S) is relatively non-unique, and thus is not considered in the context of the parameter estimation problem. However, since there is little correlation between transmissivity (T) and S estimators, a good estimate for T is still possible independent of having knowledge of S. An estimate of T is possible only if the data contain sufficient information so that the analysis occurs within an identifiability window, which is defined with respect to the dimensionless transmissivity of the system. The CSA estimation methodology is compared to individual SET and APV schemes. The CSA scheme gives the greatest probability that sufficient information is contained in a data record so that T is identifiable. The results of applications to synthetic data indicate that the OEA scheme gives a T estimate with the most precision, and also that it requires collecting fewer observations.

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Digitized by Kansas Correctional Industries

Jets in crossflow are used in a wide range of engineering applications and have been studied for more than 60 years. The transversal penetration and structure of a jet placed in a crossflow is known to be strongly three-dimensional. It is believed that, by using a pulsed jet inclined in the crossflow direction, the momentum transport can be controlled in two very efficient ways: the pulse can increase the jet penetration and the mixing downstream, while the inclination avoids the creation of a reverse flow at the jet exit and may extend the mixing area further downstream. Although some results are available in the literature focusing on components of this problem, none addresses the combination of these two factors. Moreover, most of these studies use elaborate flow visualizations and 2-D velocity measurement methods that may not be adequate to elucidate the complexity of such a flow. This study addresses these issues by using stereoscopic PIV measurements for a steady and fully modulated jet at a constant mean velocity ratio, V[subscript r], of 3.4. For the steady jet case, the effect of the jet Reynolds number, Re[subscript j], is investigated. For the pulsed case, the effect of a low pulsing frequency is considered as well as the pulse duty cycle. For each case, the mean three-component velocity field is examined. Proper Orthogonal Analysis (POD) of vorticity and turbulent kinetic energy are used to further evaluate the vortical and turbulent characteristics of the jet. In addition, a vortex detection algorithm, and 3D rendering of the flow streamlines are used to study the near field vortical flow structure of the jet flow. / Graduation date: 2006

Droplet formation from a rigid and a vibration nozzle driven by a pulsing pressure is simulated. Droplet formation is simulated by using one-dimensional model. For the case of droplet formation from a vibration nozzle, the nozzle vibration is simulated by large deflection plate vibration equation. Droplet formation from a rigid nozzle is studied simply by setting the nozzle deflection always to be zero. The one-dimensional model is solved by MacCormack method. The large deflection plate vibration equation is solved by mode shape approximation and Runga--Kuta time integration method. Three different effect factors, the driving pressure thrust input effects, the fluid viscosity effects, and the nozzle vibration effects, on droplet formation are studied. The driving pressure thrust input effects and the fluid viscosity effects are studied based on a rigid nozzle. The nozzle vibration effects are studied by comparing the results from a vibration nozzle with the results from a rigid nozzle. Results show: 1) the primary droplet break-off time is constant if the driving pressure magnitude is high, but the primary droplet volume and primary droplet velocity increase slightly as the driving pressure thrust input increase; 2) higher thrust input can possibly result in the occurrence of overturn phenomenon; 3) increasing the fluid viscosity cause the primary droplet break-off later, but the primary droplet volume and the primary droplet velocity does not change significantly by fluid viscosity; 4) the nozzle vibration effect on the primary droplet break-off time and the primary droplet size is small, but the nozzle vibration cause the primary droplet velocity to increase by an amount of the nozzle vibration velocity magnitude; 5) nozzle vibration cause longer liquid thread to form and the total satellite droplet volume to increase significantly which eventually break into multiple satellite droplet. / Graduation date: 2004

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

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