Date of Award

Fall 1999

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Computational Analysis and Modeling

First Advisor

Hisham Hegab

Abstract

Micro-channel flows have been computed to investigate the influence of Navier-Stokes formulation for the slip-flow boundary condition, and a micro-polar fluid model, respectively.

The results of the slip boundary condition show that the current methodology is valid for slip-flow regime (i.e., for values of Knudsen number less than approximately 0.1). Drag reduction phenomena apparent in some micro-channels can be explained by slip-flow theory. These results are in agreement with some computations and experiments.

An ad hoc micro-polar fluid model is developed to investigate the influence of micro effects, such as micro-gyration, in micro-scale flows. The foundation of the ad hoc micro-polar fluid is based on Eringen's micro simple fluid, and is simplified for incompressible, two-dimensional, iso-thermal, and micro-isotropic case. Our model contains two material constants, μ and κ, one scale parameter, m × Kn, and one boundary condition parameter n. The number of parameters is significantly reduced from general micro-polar fluid model and makes the theory practical.

The scale parameter m × Kn introduces the Knudsen number into the micro-polar fluid dynamics by statistical explanation. Therefore, the effect of rarefaction can be accounted into the model by modeling this parameter.

The parameter μ is classical bulk viscosity. The vortex Viscosity κ is related to micro-gyration, and needs modeling at current time. It affects the flow field in two aspects, by modifying the apparent viscosity and by introducing the effect of microgyration. In the simplest case of fully-developed channel flow, the overall effect is equivalent to lessen the Reynolds number by (I + k/ 2).

The current micro-polar fluid model explains the drag increase phenomenon in some micro-channel flows from both experimental and computational data. This result is exactly opposite to that predicted by slip-flow theory. The existence of micro-effect needs to be taken into account for the micro-scale flow.

A projection method is used as a numerical technique for both models to solve the difficulty of implicit pressure equation, with the help of staggered grids. An explicit Euler scheme is used for solving the steady flow.

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