Heat Transfer Enhancement by Chaotic Mixing. Annual Report, 1 September 1991-30 August 1992.

摘要

The report presents the results of three numerical studies, undertaken to determine the optimum values of various parameters for the alternating axis coil. Section I explains chaotic mixing as it applies to alternating axis coiled heat exchangers, and provides the motivation for the following numerical studies. The first numerical study, presented in section II, considers two chemically-reactive species in low Dean number flow. Because chemical reaction and heat transfer both occur through molecular diffusion, the effects of chaotic mixing are similar in each process. Reacting flows have the added advantage of providing a highly visual mass fraction profile. The mixing of the different species at a given cross-section of the coil has a significant effect on species profiles. As a result, the effects of initial conditions and geometrical parameters can be seen quite vividly. The parameters which have been studied are the initial conditions, switching length, Reynolds number, Schmidt number, Prandtl number, and reaction rate. Results show that initial conditions can be of significant importance. Also, the optimum switching length of the alternating axis coil shows a strong dependence on Reynolds number. Finally, it is shown that chaotic mixing enhances reaction for most, but not all, values of fluid parameters. Section III describes a numerical study of the heat transfer in flows outside the valid range for Dean velocity profiles, but with the assumption that axial conduction is negligible. This assumption is valid for high Reynolds numbers, and for fully developed flows. The effects of hydrodynamic and thermal entrance lengths are presented. A bifurcation is observed in the secondary flow near a Reynolds number of 2000. It is shown that this bifurcation has little effect on the system. A scaling is found which collapses the axial variation of Nusselt number at various Reynolds numbers onto a single curve. Axial diffusion cannot be neglected near the pipe entrance or in other regions were the flow is developing. Therefore the full elliptic equations must be solved for the alternating axis case. The solution of these equations is provided in section IV.