Over the previous summer I studied mixing of a passive tracer by flow in a straight cylindrical pipe, under the supervision of prof. Bernoff. The mixing process can be thought of as the successive action of advection by the fluid flow and diffusion modeled by random walks. With this method we were able to distinguish three different regimes. For short times, diffusion is more relevant than advection and we observed a Gaussian longitudinal distribution of the concentration. In an intermediate regime, advection by the shear is dominant over longitudinal diffusion and we observed a distinctively asymmetric distribution which spread much faster than would be expected by the action of diffusion alone. Finally when the tracer had completely mixed across the pipe’s cross- section, we recovered the classical Taylor regime with a longitudinal Gaussian distribution. In each regime we have analytical prediction of tracer distribution, confirmed by numerical calculation. The object of this thesis is to extend our results to curved pipes; we will start by considering curved planar pipes and helical pipes. We will try to determine if mixing in these geometries displays the same three distinctive regimes of mixing. The pipe’s curvature introduces a secondary flow in the form of a transverse recirculation with a dipolar form, discovered by Dean (1928). We believe this transverse flow should enhance mixing, which explains why curved pipes are used in cooling systems and other situations where heat exchange is relevant. Our object is to first understand existing analytical approximations to the flow in a curved pipe due to Dean and others and then to study analytically and numerically the spread of a passive scalar in these flows.

Thesis (M.S.)--Ohio State University, 1981. / Includes bibliographical references (leaves 89-91). Available online via OhioLINK's ETD Center

The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Title from PDF of title page (University of Missouri--Columbia, viewed on January 14, 2010). Thesis advisor: Dr. James Bryan. Includes bibliographical references.

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb 25, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Dr. Hongbin Ma. Vita. Includes bibliographical references.

The development of a mid-temperature range (250°C--500°C) heat pipe for high heat flux applications has been the focus of numerous researchers during the last 40 years. However, until this work a viable working substance for the heat pipe has eluded researchers. While the most mentioned element has been sulfur, its unusual viscosity-temperature relationship has prevented the commercialization of a sulfur-based heat pipe. / The recent development (and patenting) of the McGill heat pipe revived the question of whether sulfur would be viable in such a unit. Extensive testing showed that it is possible to make a high heat flux heat pipe with sulfur as the working substance. Given the lack of scientific details about the McGill heat pipe, a focused research program was undertaken to quantify the operation of the McGill heat pipe prior to studying the sulfur based unit. / One study looked at the two-phase flow characteristics of the McGill heat pipe. Both qualitative (videos) and quantitative data like the pressure drop and returning velocity were measured as a function of gas flow rate. Moreover, a new non-dimensional parameter, the modified swirler number was proposed. Further, the Lockhart-Martinelli method was used to analyze the pressure drop. / In the McGill heat pipe, the centrifugal force that is produced by the vortexing flow pushes liquid up against the walls and increases the critical heat flux. A theoretical model consisting of 4 sub-models was developed to predict the critical heat flux for defined situations. / The development of the sulfur-based heat pipe followed the empirical and mathematical modeling work that was carried out. A McGill heat pipe with sulfur as the working substance was designed, built and tested. The design was arrived at by considering the modeling work that was originally carried out. A number of interesting features were discovered with the sulfur-based heat pipe. A model based on mass, energy, and flow balances between the condenser and the evaporator was also developed. The model can be used to calculate the void fraction, quality, wall temperature, local heat flux distribution, heat load, cooling flow rate, and working substance temperature. The experimental results fit well the calculated ones.

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