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Influence of large-scale motions on the frictional drag in a turbulent boundary layer

Published online by Cambridge University Press:  26 September 2017

Jinyul Hwang  and
Hyung Jin Sung Open the ORCID record for Hyung Jin Sung [Opens in a new window]
Jinyul Hwang
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
Hyung Jin Sung*
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulation data of a turbulent boundary layer ($Re_{\unicode[STIX]{x1D70F}}=1000$) were used to investigate the large-scale influences on the vortical structures that contribute to the local skin friction. The amplitudes of the streamwise and wall-normal swirling strengths ($\unicode[STIX]{x1D706}_{x}$ and $\unicode[STIX]{x1D706}_{y}$) were conditionally sampled by measuring the large-scale streamwise velocity fluctuations ($u_{l}$). In the near-wall region, the amplitudes of $\unicode[STIX]{x1D706}_{x}$ and $\unicode[STIX]{x1D706}_{y}$ decreased under negative $u_{l}$ rather than under positive $u_{l}$. This behaviour arose from the spanwise motions within the footprints of the large-scale low-speed ($u_{l}<0$) and high-speed structures ($u_{l}>0$). The intense spanwise motions under the footprint of positive $u_{l}$ noticeably strengthened the small-scale spanwise velocity fluctuations ($w_{s}$) below the centre of the near-wall vortical structures as compared to $w_{s}$ within the footprint of negative $u_{l}$. The streamwise and wall-normal components were attenuated or amplified around the modulated vortical motions, which in turn led to the dependence of the swirling strength on the $u_{l}$ event. We quantified the contribution of the modulated vortical motions $\langle -w\unicode[STIX]{x1D714}_{y}\rangle$, which were related to a change-of-scale effect due to the vortex-stretching force, to the local skin friction. In the near-wall region, intense values of $\langle -w\unicode[STIX]{x1D714}_{y}\rangle$ were observed for positive $u_{l}$. By contrast, these values were low for negative $u_{l}$, in connection with the amplification of $w_{s}$ and $\unicode[STIX]{x1D706}_{y}$ by the strong spanwise motions of the positive $u_{l}$. The resultant skin friction induced by the amplified vortical motions within $u_{l}^{+}>2$ was responsible for 15 % of the total skin friction generated by the change-of-scale effect. Finally, we applied this analysis to a drag-reduced flow and found that the amplified vortical motions within the footprint of positive $u_{l}$ were markedly diminished, which ultimately contributed to the total drag reduction.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulent Flows
Type
Papers
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Journal of Fluid Mechanics , Volume 829 , 25 October 2017 , pp. 751 - 779
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© 2017 Cambridge University Press 

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