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Compared to the drawbacks of traditional experimental and numerical methods for predicting bubble migration, such as high experimental costs and complex simulation operations, the data-driven approach of using deep neural network algorithms can provide an alternative method. The objective of this paper is to construct a two-branch deep neural network (TBDNN) model in order to improve the high-fidelity bubble migration results and further reduce dependence on the quantity of experimental data. A TBDNN model is obtained by embedding the features of the Kelvin impulse into a basic deep neural network (BDNN) system. The results show that compared to the original BDNN model, TBDNN performs much better in accurately predicting bubble migration based on the same amount of training data. Using the TBDNN model, the critical condition of bubble oscillation at a fixed location can be detected under the influence of boundary properties (normalized stiffness and mass) and bubble standoff. Furthermore, the initial position of the bubble and normalized stiffness of boundaries have a positive correlation with bubble migration, whereas normalized mass has a negative impact. It was found that the normalized mass of boundaries plays the most important role in affecting bubble migration compared to the standoff and stiffness when using the method of variable sensitivity analysis.

This paper presents the results from a one-way coupled, Euler–Lagrangian, direct numerical simulation of bubbles injected into a turbulent boundary layer. The Reynolds number of the turbulent boundary layer varies from 420

Results and analysis of ground-based experiments performed to aid in designing experiments on the behavior of bubbles in a rotating liquid body on board the Shuttle in free fall are presented. Spherical shells filled with silicone oil containing a small gas bubble were spun and filmed by high speed motion picture photography. The rotation of the shell and the trajectory of the bubble motion were recorded and the film was exposed to a motion analyzer connected to a keypunch. The analyzer measured Cartesian coordinates as well as angle, frame number, and rotation rate. Optical correction equations were employed to determine the apparent bubble trajectory relative to an inertial frame of reference. An analytical model for the bubble motion was defined, yielding predictions of velocity and position at different times. Rotation of the fluid container is concluded to aid in centering the bubbles.

Thermocapillary migration of long gas bubbles in cylinders of regular-polygonal or rectangular cross sections is studied. An imposed axial temperature gradient produces a gradient of surface tension leading to a steady migration of the bubble towards the hotter region. A leading order approximation for the bubble migration speed is found by computing the volume flux of liquid through the corner regions of the cylinder, which provide a parallel channel for the flow of fluid driven by the Marangoni stress. A global mass balance is used to relate the dimensionless bubble speed to the modified capillary number Δσ*=γTβa/σ, where β is the temperature gradient, a the tube length scale, σ the mean surface tension, and γT the temperature coefficient of surface tension. The dimensionless bubble speed is found to be linear in this parameter at leading order. The approximation is improved by accounting for the deposition of a thin film on the cylinder walls at small capillary number. A modified Landau–Levich equation...

We investigate the migration of bubbles in several flow patterns occurring within the gap between a rotating inner cylinder and a concentric fixed outer cylinder. The time-dependent evolution of the two-phase flow is predicted through three-dimensional Euler-Lagrange simulations. Lagrangian tracking of spherical bubbles is coupled with direct numerical simulation of the Navier-Stokes equations. We assume that bubbles do not influence the background flow (one-way coupling simulations). The force balance on each bubble takes into account buoyancy, added-mass, viscous drag and shear-induced lift forces. For increasing velocities of the rotating inner cylinder, the flow in the fluid gap evolves from the purely azimuthal steady Couette flow to Taylor toroidal vortices and eventually a wavy vortex flow. The migration of bubbles is highly dependent on the balance between buoyancy and centripetal forces (mostly due to the centripetal pressure gradient) directed toward the inner cylinder and the vortex cores. Depending on the rotation rate of the inner cylinder, bubbles tend to accumulate alternatively along the inner wall, inside the core of Taylor vortices or at particular locations within the wavy vortices. A stability analysis of the fixed points associated with bubble trajectories provides a clear understanding of their migration and preferential accumulation. The location of the accumulation points is parameterized by two dimensionless parameters expressing the balance of buoyancy, centripetal attraction toward the inner rotating cylinder, and entrapment in Taylor vortices. A complete phase diagram summarizing the various regimes of bubble migration is built. Several experimental conditions considered by Djéridi et al.1 are reproduced; the numerical results reveal a very good agreement with the experiments. When the rotation rate is further increased, the numerical results indicate the formation of oscillating bubble strings, as observed experimentally by Djéridi et al.2. After a transient state, bubbles collect at the crests or troughs of the wavy vortices. An analysis of the flow characteristics clearly indicates that bubbles accumulate in the low-pressure regions of the flow field.