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Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows

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Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows. / Kalogirou, Anna; Cimpeanu, Radu; Blyth, Mark.

In: European Journal of Mechanics - B/Fluids, Vol. 80, 03.2020, p. 195-205.

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@article{b05c9ecd7ac64389be1883f80ea1c71b,
title = "Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows",
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.",
keywords = "ADAPTIVE SOLVER, Direct numerical simulation, INSTABILITY, INTERFACE, Interfacial instability, LINEAR-STABILITY, LONG-WAVE, Multilayer flow, POISEUILLE FLOW, Poiseuille flow, Thin films, VISCOSITY, VISCOUS FLUIDS",
author = "Anna Kalogirou and Radu Cimpeanu and Mark Blyth",
year = "2020",
month = mar,
doi = "10.1016/j.euromechflu.2019.10.011",
language = "English",
volume = "80",
pages = "195--205",
journal = "European Journal of Mechanics - B/Fluids",
issn = "0997-7546",
publisher = "Elsevier",

}

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TY - JOUR

T1 - Asymptotic modelling and direct numerical simulations of multilayer pressure-driven flows

AU - Kalogirou, Anna

AU - Cimpeanu, Radu

AU - Blyth, Mark

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

KW - ADAPTIVE SOLVER

KW - Direct numerical simulation

KW - INSTABILITY

KW - INTERFACE

KW - Interfacial instability

KW - LINEAR-STABILITY

KW - LONG-WAVE

KW - Multilayer flow

KW - POISEUILLE FLOW

KW - Poiseuille flow

KW - Thin films

KW - VISCOSITY

KW - VISCOUS FLUIDS

UR - http://www.scopus.com/inward/record.url?scp=85076549270&partnerID=8YFLogxK

U2 - 10.1016/j.euromechflu.2019.10.011

DO - 10.1016/j.euromechflu.2019.10.011

M3 - Article

VL - 80

SP - 195

EP - 205

JO - European Journal of Mechanics - B/Fluids

JF - European Journal of Mechanics - B/Fluids

SN - 0997-7546

ER -

ID: 169274247