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published_or_final_version / abstract / toc / Mechanical Engineering / Doctoral / Doctor of Philosophy

The two-dimensional, viscous flow around an elliptic cylinder undergoing prescribed unsteady motions is analyzed. The fluid is taken to be incompressible. Departing from the conventional vorticity-stream function approach, the Biot-Savart law of induced velocities is utilized to account for the contribution to the velocity field of the different vorticity fields comprising the flow. These include the internal vorticity due to the rotation of the body, the free vorticity in the fluid surrounding the body, and the bound vorticity distributed along the body contour. In order to apply the method, the body must be assumed to be replaced by fluid of the same density as the undisturbed surroundings. The replacement fluid must have a rigid motion exactly the same as the actual body motion. This can be achieved by placing suitable distributed vorticity fields within and on the surface of the body. The bound vorticity on the body surface is in the form of a vortex sheet, and its distribution is governed by a Fredholm integral equation of the second kind. The equation is derived in detail. It is solved numerically. The motion of the free vorticity in the flow field is governed by the Navier-Stokes equations written in terms of vorticity. The descretized vorticity transport equation is derived for a control volume and is solved numerically using an explicit method with a forward-difference for the time derivative, and a central-difference for the diffusive terms. An upwind method is used for convection terms. The results obtained using the present method are compared with a number of special cases available in the literature. Viscous flows around a circular cylinder rotating in any arbitrary fashion possess an exact solution, as presented in Chapter 2. Two cases of this flow are chosen for comparison. In the first case the circular cylinder is initially given an impulsive twist such that it rotates with a constant velocity about its axis. In the second case, the angular velocity of the circular cylinder increases with time exponentially. For a Reynolds number of 100, based on the cylinder radius and the internal vorticity, the exact solutions are compared with the numerical results. Viscous flow around an elliptic cylinder of .0996 aspect ratio rotating with a constant angular velocity is another special case, available in the literature, which is chosen for comparison. For this case the Reynolds number, based on the cylinder semi-major-axis and internal vorticity is 202. The agreement in all above-mentioned cases is excellent. Finally, viscous flow around an elliptic cylinder of .25 aspect ratio undergoing a combined translation and pitching oscillation is presented. A Reynolds number of 500, based on the semi-major-axis and body translational velocity, is chosen for this case. No similar case has been reported until now. This case, however, is only one of the many cases that can be handled by the present method.

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This thesis is on the Navier-Stokes equations which model the motion of compressible viscous fluid. A minimum principle on the temperate variable is established. Under the thermo-insulated boundary conditions and some reasonable assumptions on the solution, the minimum of the temperature does not increase. To our best knowledge, that's the first result on the minimum principle of the temperature variable in the compressible Navier-Stokes equation. As an application of the minimum principle, global in time existence of the weak solution for the Navier-Stokes equations is established when the viscosities and heat conductivity are power functions of the temperature. In this model the temperature is coupled with density which may have vacuum or concentration and the heat conductivity has possible degeneracy. However the temperature is proved to obey the minimum principle, which secured the dissipative mechanism of the system, and paved the road to the existence theory.

Thesis (Ph.D.)--Tufts University, 1992. / Submitted to the Dept. of Mechanical Engineering. Adviser: Vincent P. Manno. Includes bibliographical references (leaves 183-193). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

Diss. (sammanfattning) Uppsala : Univ., 2003. / Härtill 6 uppsatser.