Nonlinear stability analysis of acoustic streaming using the energy method

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Abstract/Contents

Abstract: Acoustic streaming is recently used in lithium metal batteries to inhibit the formation of dendrites. We review the concepts of hydrodynamic stability and its necessity for finding critical parameters. The energy method is further explored to study the nonlinear stability of outer Rayleigh streaming in a channel. Dimensionless analysis yields a critical parameter in the form of an acoustic Reynolds number and the resulting Euler-Lagrange equations contain nonlinear eigenvalues. The eigenvalue problem is solved numerically and an optimization algorithm is introduced to deal with the nonlinearity. Discontinuities in the domain were handled by solving and matching two models, and energy stability curves were generated for different wave amplitude ratios and channel thicknesses. The obtained critical numbers showed that monotonic stability is maintained longer in thinner channels due to smaller velocities in the base flow. Instabilities are guaranteed to be absent for acoustic Reynolds number less than 259 for thin channels and 0.011 for thick channels. The results proved to be in-line with experimental observations of acoustic flows in batteries. With the provided nonlinear stability thresholds, minimum requirements for instabilities in a channel are better understood.

Type of resource	text
Date created	June 2020

Author	Boukarim, Anthony
Primary advisor	Tartakovsky, Daniel
Degree granting institution	Stanford University, Energy Resources Engineering

Subject	School of Earth Energy & Environmental Sciences
Subject	stability analysis
Subject	acoustic streaming
Subject	energy method
Genre	Thesis

Location	https://purl.stanford.edu/hy190rj3116

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License: This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).

Preferred Citation: Boukarim, Anthony. (2020). Nonlinear stability analysis of acoustic streaming using the energy method. Stanford Digital Repository. Available at: https://purl.stanford.edu/hy190rj3116

Master's Theses, Doerr School of Sustainability

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