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Internal hydraulic jump in plane Poiseuille two-layer flow: theoretical, numerical and experimental study

Published online by Cambridge University Press:  16 February 2021

Mrinmoy Dhar ,
Subhabrata Ray ,
Gargi Das Open the ORCID record for Gargi Das [Opens in a new window]  and
Prasanta Kumar Das Open the ORCID record for Prasanta Kumar Das [Opens in a new window]
Mrinmoy Dhar
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur721302, India
Subhabrata Ray
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kharagpur721302, India
Gargi Das*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology, Kharagpur721302, India
Prasanta Kumar Das
Affiliation:
Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur721302, India
*
† Email address for correspondence: [email protected]
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Abstract

This paper discusses a hitherto unexplored flow phenomenon, namely the internal hydraulic jump in thin films during co-current and counter-current two-layer flow between parallel plates. The problem corresponds to a special case of plane Poiseuille flow where the velocity profile changes continuously in the streamwise distance. Since an exact solution of Navier–Stokes equations is not possible, we reformulate the approximate shallow water theory, conventionally adopted to analyse viscous jumps in single-layer laminar flow. The standalone theory has been extensively validated with experimental data for coflow of the two phases and numerical simulations for both co- and counter-current flow. In the limit of zero viscosity ratio, the theoretical results reduce to the expression proposed by Dhar et al. (J. Fluid Mech., vol. 884, no. A11, 2020, pp. 1–26) for single-layer viscous jumps. For a holistic understanding, numerical simulations are used to unravel the physics at the jump, where the analysis displays singularity. The theory in conjunction with simulation reveals recirculation zones even in co-current laminar flow and delineates wavy, smooth and submerged jumps, displayed as a phase diagram. We thus demonstrate the efficacy of shallow water theory which, despite the approximations involved, can be used as a reliable tool for a priori prediction of viscous jumps in two-layer flow with much less effort and resources compared to numerical simulations. Use of an approximate analysis to obtain multifaceted results for a complex flow phenomenon has rarely been explored previously. This paper is also the first study reporting experiments on viscous jumps for two-layer flow in a shallow water analogue.

JFM classification

Interfacial Flows (free surface): Thin films Geophysical and Geological Flows: Shallow water flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A45
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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