## Dissertations, Master's Theses and Master's Reports

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2019

#### Document Type

Campus Access Dissertation

#### Degree Name

Doctor of Philosophy in Mechanical Engineering-Engineering Mechanics (PhD)

#### Administrative Home Department

Department of Mechanical Engineering-Engineering Mechanics

Chunpei Cai

Lyon Brad King

Youngchul Ra

Zhen Liu

#### Abstract

This dissertation is comprised of two parts.

Part I includes the study of the compressible gas boundary layer (BL) flows over a flat plate with velocity-slip, and temperature-jump boundary conditions (BCs). The work mainly focuses on the BCs effects on base flow profiles, shear stress and heat transfer on the plate surface. The governing ordinary differential equations (ODE) for the flow and temperature fields stay the same. However, the BCs on the plate surface change. With the new BCs, it is still possible to form self-similar solutions. Also, the shooting methods are still applicable to solve the velocity profiles station by station. There are two types of velocity-temperature field couplings where the temperature field may or may not affect the velocity field. In the velocity profiles, there may be a deflection point, which indicates a higher probability of flow instability.

Part I also includes linear stability analysis on high-speed, compressible, rarefied boundary layer flows over a flat plate. The base boundary layer flows consider the velocity-slip effect, but no temperature-jumps are considered. The eigenvectors for the perturbations have larger amplitudes indicating a higher chance of flow instability. The relative larger eigenvalue $\alpha_i$ also confirms this point.

The second part of work concentrates on a simple model for micro-plasma jet end flow and electric field. It is assumed that the jet exit is planar, the spray is in vacuum, and the gas at the exit is Maxwellian. The gaskinetic theory is adopted to compute the flowfield properties. The gas is also assumed to be weakly charged, and the Boltzmann relation is adopted to compute the potential and electric fields. A set of analytical solutions for flowfield density, velocity, temperature components, and potential and electric fields are obtained. Further, corresponding farfield solutions for these properties were also obtained. These solutions offer many insights, for example, the Simons' plume model or the cosine law may be improper to describe the plume flows. Also, at farfield, the particles shot out along straight lines, and the detailed density, velocity components, and fluxes solutions were provided. It shall be mentioned that the electric field solutions are very crude, however, they are analytical solutions and serve as a starting point to develop a more advanced model. By comparison, if numerical simulations can only offer a significant amount of data which buries physical insights. These analytical solutions can be used as a proper sub-grid model, which can properly connect the upstream Taylor Cone-Jet model which may be studied with an analytical method, and its downstream plasma plume flows which must be simulated with particle methods.

errata.pdf (380 kB)
Errata submitted by Xin He

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