On the motion of gas bubbles in homogeneous isotropic turbulence

Abstract

This paper is concerned with the motion of small gas bubbles, equivalent diameter about 1.0 mm, in isotropic turbulent flows. Data on the mean velocity of rise and the dispersion of the bubbles have been obtained numerically by simulating the turbulence as a sum of Fourier modes with random phases and amplitudes determined by the Kraichnan and the von Kármán–Pao energy-spectrum functions, and by calculating the bubble trajectories from a reasonably well-established equation of motion. The data cover the range β[les ]1, where β is the ratio between the turbulence intensity and the velocity of rise of the bubbles in still fluid. An approximate analysis based on the assumption that β is small yields results that compare favourably with the numerical data, and clarifies the important role played by the lift forces exerted by the fluid.

Lagrangian statistics for fluid particles and bubbles in turbulence

“…Therefore, we separately compute the lateral diffusivity Bubble dispersion has been approached analytically by Spelt and Biesheuvel [6,7] (henceforth indicated as SB97 [6] and SB98 [7]) and the predictions have been compared to the numerical results obtained by kinematic simulations of turbulence. The various regimes have been characterized by two dimensionless parameters, namely…”

“…In order to fix reference values for the analysis of bubbles, we measure the dispersion of fluid particles by tracking the motion of N p = 40 960 particles that evolve according to equation (6). …”

“…Later, analytical investigations have been carried out for heavy particles that, owing to inertia, do not follow all the turbulence fluctuations [4,5], and, most recently, also for air bubbles [6]- [8].…”

The effect of microbubbles on developed turbulence

“…Recent work has either focused on the forces acting on single particles or bubbles 1-5 or on collective effects, such as dispersion or local concentration evolution. 6 Among the latter one can distinguish between work focusing on passive particles or bubbles, i.e., without momentum transfer to the flow, [7][8][9][10][11] and work taking into account the back reaction of the particles and bubbles on the flow ͑two-way coupling͒. [12][13][14][15][16][17][18] In turbulent flow initially uniformly distributed bubbles cluster in regions of low pressure and high vorticity.…”

“…The microbubbles are assumed to be spherical with fixed radius a, which is small compared to the scales on which the flow varies, and their density is considered to be negligible as compared to the fluid density. The bubble motion can then be modeled by the equation 11,16,17,23 …”