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Numerical simulation of turbulent, plane parallel Couette-Poiseuille flow

Cheng, W. and Pullin, D. I. and Samtaney, R. and Luo, X. (2023) Numerical simulation of turbulent, plane parallel Couette-Poiseuille flow. Journal of Fluid Mechanics, 955 . Art. No. A4. ISSN 0022-1120. doi:10.1017/jfm.2022.1023.

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We present numerical simulation and mean-flow modelling of statistically stationary plane Couette–Poiseuille flow in a parameter space (Re,θ) with Re = √[Re꜀² + Re²_M] and θ = arctan (Re_M/Re꜀, where Re꜀, Re_M are independent Reynolds numbers based on the plate speed U꜀ and the volume flow rate per unit span, respectively. The database comprises direct numerical simulations (DNS) at Re = 4000, 6000, wall-resolved large-eddy simulations at Re = 10000, 20000, and some wall-modelled large-eddy simulations (WMLES) up to Re = 10¹⁰. Attention is focused on the transition (from Couette-type to Poiseuille-type flow), defined as where the mean skin-friction Reynolds number on the bottom wall Re_(τ,b), changes sign at θ = θ꜀(Re). The mean flow in the (Re,θ) plane is modelled with combinations of patched classical log-wake profiles. Several model versions with different structures are constructed in both the Couette-type and Poiseuille-type flow regions. Model calculations of Re_(τ,b)(Re,θ), Re_(τ,t)(Re,θ) (the skin-friction Reynolds number on the top wall) and θ꜀ show general agreement with both DNS and large-eddy simulations. Both model and simulation indicate that, as θ is increased at fixed Re, Re_(τ,t) passes through a peak at approximately θ = 45°, while Re_(τ,b) increases monotonically. Near the bottom wall, the flow laminarizes as θ passes through θ_(c) and then re-transitions to turbulence. As Re increases, θ꜀ increases monotonically. The transition from Couette-type to Poiseuille-type flow is accompanied by the rapid attenuation of streamwise rolls observed in pure Couette flow. A subclass of flows with Re_(τ,b) = 0 is investigated. Combined WMLES with modelling for these flows enables exploration of the Re → ∞ limit, giving θ꜀ → 45° as Re → ∞.

Item Type:Article
Related URLs:
URLURL TypeDescription
Cheng, W.0000-0003-3960-4162
Samtaney, R.0000-0002-4702-6473
Luo, X.0000-0002-4303-8290
Additional Information:This work was supported by the National Natural Science Foundation of China (nos 12172352, 91952205 and 11621202). The Cray XC40, Shaheen, at KAUST was utilized for the reported DNS and WRLES.
Funding AgencyGrant Number
National Natural Science Foundation of China11621202
National Natural Science Foundation of China12172352
National Natural Science Foundation of China91952205
Record Number:CaltechAUTHORS:20230206-9037800.10
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119057
Deposited By: Research Services Depository
Deposited On:03 Mar 2023 16:12
Last Modified:03 Mar 2023 16:12

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