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Image-based modelling of the skin-friction coefficient in compressible boundary-layer transition

Published online by Cambridge University Press:  26 July 2019

Wenjie Zheng ,
Shanxin Ruan ,
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window] ,
Lin He  and
Shiyi Chen
Wenjie Zheng
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
Shanxin Ruan
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China CAPT and BIC-ESAT, Peking University, Beijing 100871, China
Lin He
Affiliation:
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
Shiyi Chen
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China CAPT and BIC-ESAT, Peking University, Beijing 100871, China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology of China, Shenzhen 518055, China
*
†Email address for correspondence: yyg@pku.edu.cn
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Abstract

We develop a model of the skin-friction coefficient based on scalar images in the compressible, spatially evolving boundary-layer transition. The images are extracted from a passive scalar field by a sliding window filter on the streamwise and wall-normal plane. The multi-scale and multi-directional geometric analysis is applied to characterize the averaged inclination angle of spatially evolving filtered component fields at different scales ranging from a boundary-layer thickness to several viscous length scales. In general, the averaged inclination angles increase along the streamwise direction, and the variation of the angles for large-scale structures is smaller than that for small-scale structures. Inspired by the coincidence of the increasing averaged inclination angle and the rise of the skin-friction coefficient, we propose a simple image-based model of the skin-friction coefficient. The model blends empirical formulae of the skin-friction coefficient in laminar and fully developed turbulent regions using the normalized averaged inclination angle of scalar structures at intermediate and small scales. The model prediction calculated from scalar images is validated by the results from the direct numerical simulation at two Mach numbers, 2.25 and 6, and the relative error can be less than 15 %.

JFM classification

Boundary Layers: Boundary layer structure Compressible Flows: Compressible boundary layers Turbulent Flows: Turbulent transition
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 1175 - 1203
Copyright
© 2019 Cambridge University Press 

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