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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.
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Natural frequencies of a bubble near a solid sphere
This paper presents an analytical and computational method to describe natural frequencies of a spherical bubble residing near a solid sphere of an arbitrary size in an otherwise unbounded fluid. Under low capillary and Reynolds number limits, the relevant hydrodynamic fields are converted into time-invariant but frequency-dependent quantities by temporal Fourier transform. Then, the spatial variations in the velocity and the pressure can be expressed in terms of two sets of harmonic basis functions involving spherical coordinates centered around the particle and the bubble. A subsequent derivation of transformation coefficients between the aforementioned two sets allows a matrix equation relating the unknown amplitudes to the boundary conditions at all interfaces. Finally, natural frequencies corresponding to different modes of pulsation are obtained from the eigenvalues of the constructed matrix. The results show fast convergence of the computed frequencies with the increasing number of basis functions. These values change significantly with the distance of the bubble from the particle and even decay to zero for some modes when their surface-to-surface separation vanishes. Furthermore, bubble oscillation near a solid plate is also discussed when the radius of the solid sphere is increased to an infinitely large dimension. Thus, this article renders a comprehensive study of naturally pulsating submerged bubbles in the presence of a nearby solid surface of various kinds.
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- Award ID(s):
- 2137638
- PAR ID:
- 10597258
- Publisher / Repository:
- American Institute of Physics
- Date Published:
- Journal Name:
- AIP Advances
- Volume:
- 12
- Issue:
- 8
- ISSN:
- 2158-3226
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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