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Unifying constitutive law of vibroconvective turbulence in microgravity

Published online by Cambridge University Press:  16 May 2024

Ze-Lin Huang
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
Jian-Zhao Wu*
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China Shanghai Institute of Aircraft Mechanics and Control, Zhangwu Road, Shanghai 200092, PR China
Xi-Li Guo
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
Chao-Ben Zhao
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
Bo-Fu Wang
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
Kai Leong Chong
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China Shanghai Institute of Aircraft Mechanics and Control, Zhangwu Road, Shanghai 200092, PR China
Quan Zhou*
Affiliation:
Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, PR China
*
Email addresses for correspondence: jianzhao_wu@shu.edu.cn, qzhou@shu.edu.cn
Email addresses for correspondence: jianzhao_wu@shu.edu.cn, qzhou@shu.edu.cn

Abstract

We report the unified constitutive law of vibroconvective turbulence in microgravity, i.e. $Nu \sim a^{-1} Re_{os}^\beta$ where the Nusselt number $Nu$ measures the global heat transport, $a$ is the dimensionless vibration amplitude, $Re_{os}$ is the oscillational Reynolds number and $\beta$ is the universal exponent. We find that the dynamics of boundary layers plays an essential role in vibroconvective heat transport and the $Nu$-scaling exponent $\beta$ is determined by the competition between the thermal boundary layer (TBL) and vibration-induced oscillating boundary layer (OBL). Then a physical model is proposed to explain the change of scaling exponent from $\beta =2$ in the TBL-dominant regime to $\beta = 4/3$ in the OBL-dominant regime. Our finding elucidates the emergence of universal constitutive laws in vibroconvective turbulence, and opens up a new avenue for generating a controllable effective heat transport under microgravity or even microfluidic environment in which the gravity effect is nearly absent.

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Type
JFM Papers
Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Supplementary material: File

Huang et al. supplementary movie 1

Instantaneous flow structures visualized by volume rendering of temperature anomaly in three-dimensional microgravity vibroconvection at ω = 105, a = 10-2 and Pr=4.38, corresponding to figure 1(a) left. The time is scaled by the vibration period.
Download Huang et al. supplementary movie 1(File)
File 7.2 MB
Supplementary material: File

Huang et al. supplementary movie 2

Instantaneous flow structures visualized by volume rendering of temperature anomaly in three-dimensional microgravity vibroconvection at ω = 106, a = 10-2 and Pr=4.38, corresponding to figure 1(a) middle. The time is scaled by the vibration period.
Download Huang et al. supplementary movie 2(File)
File 4 MB
Supplementary material: File

Huang et al. supplementary movie 3

Instantaneous flow structures visualized by volume rendering of temperature anomaly in three-dimensional microgravity vibroconvection at ω = 107, a = 10-2 and Pr=4.38, corresponding to figure 1(a) right. The time is scaled by the vibration period.
Download Huang et al. supplementary movie 3(File)
File 5.3 MB