Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Mechanical and Materials Engineering

Supervisor

Dr. Jerzy Maciej Floryan

Abstract

Responses of annular and planar flows to the introduction of grooves on the bounding surfaces have been analyzed. The required spectral algorithms based on the Fourier and Chebyshev expansions have been developed. The difficulties associated with the irregularities of the physical domain have been overcome using either the immersed boundary conditions (IBC) concept or the domain transformation method (DT).

Steady flows in annuli bounded by walls with longitudinal grooves have been studied. Analysis of pressure losses showed that the groove-induced changes can be represented as a superposition of a pressure drop due to a change in the average position of the bounding cylinders and a pressure drop due to the flow modulations induced by the shape of the grooves. The former effect can be evaluated analytically while the latter requires explicit computations. It has been shown that the reduced-order model is an effective tool for extraction of features of the groove geometry that lead to flow modulations relevant to drag generation. It has been shown that the presence of the longitudinal grooves may lead to a reduction of the pressure loss in spite of an increase of the wetted surface area. The form of the optimal grooves from the point of view of the maximization of the drag reduction has been determined.

When mixing augmentation is not available, heat can be transported across micro-channels by conduction only. A method to increase this heat flow has been proposed. The method relies on the use of grooves parallel to the flow direction. It has been shown that it is possible to find grooves that can increase the heat flow and, at the same time, can decrease the pressure losses. The optimal groove shape that maximizes the overall system performance has been determined. Since it has been assumed that the flow must be laminar, it is of interest to determine the maximum Reynolds number for which this assumption remains valid.

The stability characteristics of flow in a grooved channel have been studied. Only disturbances corresponding to the travelling waves in the limit of zero groove amplitude have been found. It has been shown that disturbances corresponding to the two-dimensional waves in a smooth channel play the critical role in the grooved channel. The highly three-dimensional disturbance flow topology at the onset of the instability has been described. It has been demonstrated that the presence of the grooves leads to flow stabilization for the groove wave numbers 4.22 and flow destabilization for larger . The stabilizing/destabilizing effects increase with the groove amplitude. Variations of the critical Reynolds number over the whole range of the groove wave numbers and the groove amplitudes of interest have been determined. Special attention has been paid to the effects of the long wavelength, drag reducing grooves. It has been shown that such grooves lead to a small increase of the critical Reynolds number compared with the smooth channel.

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