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Abstract
The dispersion of bubbles in homogeneous and isotropic turbulence is numerically examined. The fluid velocity field evolves according to the Navier–Stokes equations that are solved by direct numerical simulation. The bubble paths are followed by Lagrangian tracking. The aim of the work is to quantify dispersion properties of bubbles in a regime ranging from low- to high-turbulence velocity fluctuations as compared to the bubble velocity scale, and to compare them to those of fluid particles. Moreover, the forces that are relevant for the bubble dispersion are analysed and their probability density functions, as well as their intermittency characteristics, are compared to those of fluid particle accelerations.
Highlights
The dispersion of microbubbles with response time τb much smaller than the Kolmogorov time τk has been studied in homogeneous isotropic turbulence and compared to the dispersion of fluid particles
Inertial forces are fundamental in the dispersion: the numerical results deviate from the analytical theory mainly owing to the interaction with eddies, which is caused by the flow pressure gradient term in the bubble equation of motion
Such analysis can only be achieved by a full direct simulation of the flow, i.e., including a proper representation of the small scales, which is not provided by hitherto performed kinematic simulation
Summary
Kin is a subset of small wavenumbers defined according to: Kin = {k such that(L0/(2π))k = ±(−1, 2, 2), ±(2, −1, −1) + permutations} This type of forcing has been successfully applied in many of our previous simulations [9], [14]–[16]. The Kolmogorov length, time, and velocity scales can be evaluated according to: η = (ν3/ )1/4, τk = (ν/ )1/2 and vk = ( ν)1/4, respectively. 1 u2x π rx =0 ux(0)ux(rx) rx, because the velocity autocorrelation function ux(0)ux(rx) in turbulence simulations driven by the forcing (2) presents a negative loop on the large scales: for rx = π it is ux(0)ux(rx) / ux(0)2 ≈ −0.17, whereas for larger rx the correlation increases again due to the periodic boundary conditions.
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