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Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows
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Kalogirou, A, Cimpeanu, Radu and Blyth, M. G. (2020) Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows. European Journal of Mechanics - B/Fluids , 80 . pp. 195-205. doi:10.1016/j.euromechflu.2019.10.011 ISSN 0997-7546.
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WRAP-asymptotic-modelling-direct-mumerical-pressure-driven-Cimpeanu-2019.pdf - Accepted Version - Requires a PDF viewer. Available under License Creative Commons Attribution Non-commercial No Derivatives 4.0. Download (1769Kb) | Preview |
Official URL: https://doi.org/10.1016/j.euromechflu.2019.10.011
Abstract
The nonlinear dynamics of two immiscible superposed viscous fluid layers in a channel is examined using asymptotic modelling and direct numerical simulations (DNS). The flow is driven by an imposed axial pressure gradient. Working on the assumption that one of the layers is thin, a weakly-nonlinear evolution equation for the interfacial shape is derived that couples the dynamics in the two layers via a nonlocal integral term whose kernel is determined by solving the linearised Navier–Stokes equations in the thicker fluid. The model equation incorporates salient physical effects including inertia, gravity, and surface tension, and allows for comparison with DNS at finite Reynolds numbers. Direct comparison of travelling-wave solutions obtained from the model equation and from DNS show good agreement for both stably and unstably stratified flows. Both the model and the DNS indicate regions in parameter space where unimodal, bimodal and trimodal waves co-exist. Nevertheless, the asymptotic model cannot capture the dynamics for a sufficiently strong unstable density stratification when interfacial break-up and eventual dripping occurs. In this case, complicated interfacial dynamics arise from the dominance of the gravitational force over the shear force due to the underlying flow, and this is investigated in detail using DNS.
Item Type: | Journal Article | ||||||||
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Subjects: | Q Science > QA Mathematics | ||||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | European Journal of Mechanics - B/Fluids | ||||||||
Publisher: | Elsevier | ||||||||
ISSN: | 0997-7546 | ||||||||
Official Date: | March 2020 | ||||||||
Dates: |
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Volume: | 80 | ||||||||
Page Range: | pp. 195-205 | ||||||||
DOI: | 10.1016/j.euromechflu.2019.10.011 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Date of first compliant deposit: | 5 November 2019 | ||||||||
Date of first compliant Open Access: | 4 November 2020 | ||||||||
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