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Direct numerical simulation of turbulent, generalized Couette–Poiseuille flow

Published online by Cambridge University Press:  23 October 2024

Y. Zhang ,
D.I. Pullin Open the ORCID record for D.I. Pullin [Opens in a new window] ,
W. Cheng Open the ORCID record for W. Cheng [Opens in a new window]  and
X. Luo Open the ORCID record for X. Luo [Opens in a new window]
Y. Zhang
Affiliation:
School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
D.I. Pullin
Affiliation:
Graduate Aerospace Laboratories, California Institute of Technology, CA 91125, USA
W. Cheng*
Affiliation:
School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
X. Luo
Affiliation:
School of Engineering Science, University of Science and Technology of China, Hefei 230026, PR China
*
†Email address for correspondence: [email protected]
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Abstract

We present direct numerical simulation (DNS) and modelling of incompressible, turbulent, generalized Couette–Poiseuille flow. A particular example is specified by spherical coordinates $(Re,\theta,\phi )$, where $Re = 6000$ is a global Reynolds number, $\phi$ denotes the angle between the moving plate, velocity-difference vector and the volume-flow vector and $\tan \theta$ specifies the ratio of the mean volume-flow speed to the plate speed. The limits $\phi \to 0^\circ$ and $\phi \to 90^\circ$ give alignment and orthogonality, respectively, while $\theta \to 0^\circ,\ \theta \to 90^\circ$ correspond respectively to pure Couette flow in the $x$ direction and pure Poiseuille flow at angle $\phi$ to the $x$ axis. Competition between the Couette-flow shear and the forced volume flow produces a mean-velocity profile with directional twist between the confining walls. Resultant mean-speed profiles relative to each wall generally show a log-like region. An empirical flow model is constructed based on component log and log-wake velocity profiles relative to the two walls. This gives predictions of four independent components of shear stress and also mean-velocity profiles as functions of $(Re,\theta,\phi )$. The model captures DNS results including the mean-flow twist. Premultiplied energy spectra are obtained for symmetric flows with $\phi =90^\circ$. With increasing $\theta$, the energy peak gradually moves in the direction of increasing $k_x$ and decreasing $k_z$. Rotation of the energy spectrum produced by the faster moving velocity near the wall is also observed. Rapid weakening of a spike maxima in the Couette-type flow regime indicates attenuation of large-scale roll structures, which is also shown in the $Q$-criterion visualization of a three-dimensional time-averaged flow.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence modelling
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 997 , 25 October 2024 , A76
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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