Onset of instabilities in rotating flows by direct numerical simulation

Liu, Ziyao; Ladd, Anthony J.C.

doi:10.1017/jfm.2022.566

Onset of instabilities in rotating flows by direct numerical simulation

Journal Article · Tue Jul 26 00:00:00 EDT 2022 · Journal of Fluid Mechanics

DOI:https://doi.org/10.1017/jfm.2022.566· OSTI ID:1907355

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Univ. of Florida, Gainesville, FL (United States); University of Florida
Univ. of Florida, Gainesville, FL (United States)

A rotating disk is the canonical experiment for measuring surface reaction rates in geochemical and electrochemical systems. Using the similarity solution for laminar flow around an infinite disk, the mass transfer coefficient can be simply related to the intrinsic reaction rate at the surface. However, measurements of mass transfer rates use a finite-size disk within a larger container of solution; here the flow is no longer strictly laminar, but there must always be some recirculation. Our interest was initially in the assumption of a uniform radial concentration field, how this breaks down near the perimeter of the disk, and what effect that might have on the measured mass transfer rates. However, our numerical simulations suggest that the flow around a finite-size disk becomes time dependent at Reynolds number ($$\textit{Re}$$) below 1000, which is much smaller than the typical values in mass-transfer measurements ($$\textit{Re}$$~10⁴). In this work, we observe the formation of coherent structures in the flow, which suggest a non-uniform mass transfer at the disk surface. The rotating-disk flow follows a similar sequence of instabilities to the Taylor–Couette flow: a centrifugal instability leading an axisymmetric, time-invariant flow, followed by a Hopf bifurcation to a time-periodic flow. To minimise the possibility that our results are a numerical artefact, we have also simulated the instability in the stationary boundary layer of a rotor–stator flow, comparing with self-similar solutions at low $$\textit{Re}$$ and with spectral methods near the critical Reynolds number.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Florida, Gainesville, FL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division

Grant/Contract Number:: SC0018676

OSTI ID:: 1907355

Alternate ID(s):: OSTI ID: 1991223

Journal Information:: Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 945; ISSN 0022-1120

Publisher:: Cambridge University PressCopyright Statement

Country of Publication:: United States

Language:: English

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