TY - JOUR

T1 - Bubble deformation by a turbulent flow

AU - Perrard, Stéphane

AU - Rivière, Aliénor

AU - Mostert, Wouter

AU - Deike, Luc

N1 - Funding Information:
This work was supported by the NSF CAREER award 1844932 to L.D., and the American Chemical Society Petroleum Research Fund Grant 59697-DNI9 to L.D. A.R. was supported by an International Fund grant from Princeton University to L.D. S.P. and A.R. were supported by the Labex ENS-ICFP. We would like to acknowledge high-performance computing support from Cheyenne ( doi:10.5065/D6RX99HX ) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. Computations were also performed on the Princeton supercomputer Tiger2, as well as on Stampede, through XSEDE allocations to L.D. and W.M., XSEDE is an NSF funded program 1548562.
Funding Information:
This work was supported by the NSF CAREER award 1844932 to L.D., and the American Chemical Society Petroleum Research Fund Grant 59697-DNI9 to L.D. A.R. was supported by an International Fund grant from Princeton University to L.D. S.P. and A.R. were supported by the Labex ENS-ICFP. We would like to acknowledge high-performance computing support from Cheyenne (doi:10.5065/D6RX99HX) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. Computations were also performed on the Princeton supercomputer Tiger2, as well as on Stampede, through XSEDE allocations to L.D. and W.M., XSEDE is an NSF funded program 1548562.
Publisher Copyright:
© 2021 The Author(s). Published by Cambridge University Press.

PY - 2021

Y1 - 2021

N2 - We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations, considering a low-density bubble in the high-density turbulent flow at various Weber numbers (the ratio of turbulent and surface tension forces) using the air-water density ratio. We discuss a theoretical framework for the bubble deformation in a turbulent flow using a spherical harmonic decomposition. We propose, for each mode of bubble deformation, a forcing term given by the statistics of velocity and pressure fluctuations, evaluated on a sphere of the same radius. This approach formally relates the bubble deformation and the background turbulent velocity fluctuations, in the limit of small deformations. The growth of the total surface deformation and of each individual mode is computed from the direct numerical simulations using an appropriate Voronoi decomposition of the bubble surface. We show that two successive temporal regimes occur: the first regime corresponds to deformations driven only by inertial forces, with the interface deformation growing linearly in time, in agreement with the model predictions, whereas the second regime results from a balance between inertial forces and surface tension. The transition time between the two regimes is given by the period of the first Rayleigh mode of bubble oscillation. We discuss how our approach can be used to relate the bubble lifetime to the turbulence statistics and eventually show that at high Weber numbers, bubble lifetime can be deduced from the statistics of turbulent fluctuations at the bubble scale.

AB - We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations, considering a low-density bubble in the high-density turbulent flow at various Weber numbers (the ratio of turbulent and surface tension forces) using the air-water density ratio. We discuss a theoretical framework for the bubble deformation in a turbulent flow using a spherical harmonic decomposition. We propose, for each mode of bubble deformation, a forcing term given by the statistics of velocity and pressure fluctuations, evaluated on a sphere of the same radius. This approach formally relates the bubble deformation and the background turbulent velocity fluctuations, in the limit of small deformations. The growth of the total surface deformation and of each individual mode is computed from the direct numerical simulations using an appropriate Voronoi decomposition of the bubble surface. We show that two successive temporal regimes occur: the first regime corresponds to deformations driven only by inertial forces, with the interface deformation growing linearly in time, in agreement with the model predictions, whereas the second regime results from a balance between inertial forces and surface tension. The transition time between the two regimes is given by the period of the first Rayleigh mode of bubble oscillation. We discuss how our approach can be used to relate the bubble lifetime to the turbulence statistics and eventually show that at high Weber numbers, bubble lifetime can be deduced from the statistics of turbulent fluctuations at the bubble scale.

KW - bubble dynamics

KW - multiphase flow

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U2 - 10.1017/jfm.2021.379

DO - 10.1017/jfm.2021.379

M3 - Review article

AN - SCOPUS:85104059564

SN - 0022-1120

VL - 920

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

M1 - A15

ER -