Date of Award

Spring 2022

Project Type

Dissertation

Program or Major

Applied Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Gregory Chini

Second Advisor

John McHugh

Third Advisor

Mark Lyon

Abstract

Acoustic streaming refers to time-averaged flows generated by time-periodic sound waves. In classic“Rayleigh streaming”, the mean flow is generated by the interaction of a standing acoustic wave with a solid boundary (e.g., a channel wall). Applications of acoustic streaming include inducing fluid mixing in microfluidic medical devices, improving the efficiency of chemical reactions, and enhancing heat transfer. Recently, Chini et al. [J. Fluid Mech., Vol. 744 (2014)] and Michel & Chini [J. Fluid Mech., Vol. 858 (2019)] demonstrated that strong acoustic streaming flows can be generated in gases subjected to an imposed cross-channel temperature gradient. In contrast with Rayleigh streaming, standing acoustic waves of O(ϵ) amplitude acquire vorticity owing to torques arising from the misalignment of pressure and density isosurfaces throughout the domain rather than via viscous torques acting in oscillatory boundary layers adjacent to channel walls. More significantly, these “baroclinically-driven” streaming flows have a magnitude that is O(ϵ), i.e. comparable to that of the sound waves, leading to fully two-way wave/mean-flow coupling. The present investigation extends these earlier studies by relaxing the restriction to small aspect-ratio domains, thereby enabling the (forced) heat transport across the channel to be quantified as a function of aspect ratio and other system parameters. This extension requires the numerical solution of a non-separable two-dimensional eigenvalue problem for the sound-wave frequency and mode structure. Nevertheless, the resulting computations are orders of magnitude faster than direct numerical simulation of the compressible Navier-Stokes equations. The prospect for using baroclinic acoustic streaming as a lightweight, fan-less cooling technology is evaluated.

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