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Correlations between wall heat flux and Reynolds shear stress/turbulent heat flux in compressible turbulent boundary layers

Published online by Cambridge University Press:  14 November 2024

Yitong Fan Open the ORCID record for Yitong Fan [Opens in a new window] ,
Melissa Kozul Open the ORCID record for Melissa Kozul [Opens in a new window] ,
Weipeng Li Open the ORCID record for Weipeng Li [Opens in a new window]  and
Richard D. Sandberg Open the ORCID record for Richard D. Sandberg [Opens in a new window]
Yitong Fan
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
Melissa Kozul
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
Weipeng Li*
Affiliation:
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, Shanghai 200240, PR China
Richard D. Sandberg
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3010, Australia
*
†Email address for correspondence: liweipeng@sjtu.edu.cn
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Abstract

This study investigates the correlation between the fluctuating wall heat flux, and the distribution and transport of Reynolds shear stress and turbulent heat flux in compressible boundary layers at Mach number 5.86 and friction Reynolds number 420, with a relatively weaker and a stronger wall cooling imposed. As illustrated from the probability density functions of the wall-heat-flux perturbations, with increasing wall cooling, the extreme wall heat flux is intensified and tends to be more negatively skewed. To examine the role of the extreme events in the transport of the momentum and heat, conditional analysis of the extreme positive and negative wall-heat-flux-perturbation events is conducted. In most regions of the boundary layer, the positive events are predominantly associated with an increase in Reynolds shear stress and a decrease in turbulent heat flux. Joint probability density functions of velocity and wall-heat-flux perturbations in the near-wall region indicate that the extreme positive events tend to be more correlated with ejections, which is particularly evident in the stronger wall-cooling case. To further shed light on the underlying mechanisms of the connections between wall heat flux and transport budgets, a transport equation for turbulent heat flux is derived, in a similar manner to that for Reynolds shear stress. The energy balance is inspected, with conditional analysis applied to budget terms and mean flow properties so as to quantify the correlation between wall-heat-flux fluctuations and energy evolution.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulent boundary layers

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 999 , 25 November 2024 , A52
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© The Author(s), 2024. Published by Cambridge University Press

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