Filtering by
- All Subjects: engineering
The dissertation starts with a study of a volumetric expansion driven drainage flow of a viscous compressible fluid from a small capillary and channel in the low Mach number limit. An analysis based on the linearized compressible Navier-Stokes equations with no-slip condition shows that fluid drainage is controlled by the slow decay of the acoustic wave inside the capillary and the no-slip flow exhibits a slip-like mass flow rate. Numerical simulations are also carried out for drainage from a small capillary to a reservoir or a contraction of finite size. By allowing the density wave to escape the capillary, two wave leakage mechanisms are identified, which are dependent on the capillary length to radius ratio, reservoir size and acoustic Reynolds number. Empirical functions are generated for an effective diffusive coefficient which allows simple calculations of the drainage rate using a diffusion model without the presence of the reservoir or contraction.
In the second part of the dissertation, steady viscous compressible flow through a micro-conduit is studied using compressible Navier-Stokes equations with no-slip condition. The mathematical theory of Klainerman and Majda for low Mach number flow is employed to derive asymptotic equations in the limit of small Mach number. The overall flow, a combination of the Hagen-Poiseuille flow and a diffusive velocity shows a slip-like mass flow rate even through the overall velocity satisfies the no-slip condition. The result indicates that the classical formulation includes self-diffusion effect and it embeds the Extended Navier-Stokes equation theory (ENSE) without the need of introducing additional constitutive hypothesis or assuming slip on the boundary. Contrary to most ENSE publications, the predicted mass flow rate is still significantly below the measured data based on an extensive comparison with thirty-five experiments.
The objective of this thesis is to conduct a case study into the Bell X-2, an early supersonic research aircraft utilizing a modern perspective and computational tools. The Bell X-2 was the second in a series of supersonic research aircraft created by Bell Aviation Corporation, designed to help engineers to explore this new region of flight. The goal of the X-2 was to gather data on high Mach Number and high-altitude flight as well as aerodynamic heating. The X-2 had poor lateral stability resulting in it being unstable at high Mach Numbers and moderate angles of attack. The program was full of new and unforeseen technical challenges resulting in many delays and tragedies. The program ended when stability problems resulted in a fatal crash destroying the aircraft and killing the test pilot. This case study addresses the historical background of the program, human influence, the stability problems encountered and conducting a stability analysis of the aircraft. To conduct the stability analysis, the potential flow solver, VORLAX, was used to gather aerodynamic coefficient data of the X-2 and determine if these stability problems could be determined from the data obtained. By comparing the results from VORLAX to a wind tunnel study, I determined that the poor lateral directional stability and control coupling issues were foreseeable in the initial design.