Bubble interactions drag force

It must be noted here that even for Eulerian-Lagrangian simulations, although there is no complexity of averaging over trajectories, the accuracy of simulations of individual bubble trajectories depends on lumped interphase interaction parameters such as drag force, virtual mass force and lift force coefficients. All of these interphase interaction parameters will be functions of bubble size and shape, presence of other bubbles or walls, surrounding pressure field and so on. Unfortunately, adequate information is not available on these aspects. To enhance our understanding of basic... 

Bubble size is required to calculate, for example, the drag force imparted on a bubble. Most Eulerian-Eulerian CFD codes assume a single (average) bubble size, which is justified if one is modeling systems in which the bubble number density is small (e.g., bubbly flow in bubble columns). In this case, the bubble-bubble interactions are weak and bubble size tends to be narrowly distributed. However, most industrially relevant flows have a very large bubble number density where bubble-bubble interactions are significant and result in a wide bubble size distribution that may be substantially different from the average bubble size assumption. In these cases, a bubble population balance equation (BPBE) model may be implemented to describe the bubble size distribution (Chen et al., 2fX)5). 

The model closes interaction phase Mkj with effective viscosity //eff, and it is considered that the slurry phase of FTS is in the turbulent zone. The effective viscosity can be considered as turbulence viscosity, which can usually be solved by standard model, where turbulence induced by bubbles is also taken into consideration. Interaction force between the phases consists of drag, lift, and virtual mass force. The main force of interaction between phases often is overlooked. Drag force, caused by gas, drives the serious movements and the type of which is written as Eq. (28) ... 

A dimensionless drag force is a suitable scaling parameter in many cases. Increased gas-particle interaction at high pressures combined with turbulent fluctuations in the gas phase can account for increased instability of bubbles. 

The momentum interaction term Tj in the momentum equation can be calculated using the fact that the drag force experienced by the bubbles acts with equal magnitude but in the opposite direction of the liquid ... 

Apart from an increased drag force, high gas volume fractions can also lead to occurrence of coalescence and breakup of bubbles. Although the closures derived for these kinds of phenomena are rather mature for droplet-droplet interactions, this is not the case for bubble—bubble interactions. The main reason is probably the role of surfactants, which can have a considerable effect on the rigidness of the bubble surface and hence on the processes occurring on that scale. Given the fact that many closures were derived for water-air systems makes things worse, as the water quahty and in... 

The multiplicity of phenomena characteristic of flow in heated micro-channels determined the content of the book. We consider a number of fundamental problems related to drag and heat transfer in flow of a pure liquid and a two-phase mixture in micro-channels, coolant boiling in restricted space, bubble dynamics, etc. Also considered are capillary flows with distinct interfaces developing under interaction of inertia, pressure, gravity, viscous and capillary forces. 

One therefore has to decide here which components of the phase interaction force (drag, virtual mass, Saffman lift, Magnus, history, stress gradients) are relevant and should be incorporated in the two sets of NS equations. The reader is referred to more specific literature, such as Oey et al. (2003), for reports on the effects of ignoring certain components of the interaction force in the two-fluid approach. The question how to model in the two-fluid formulation (lateral) dispersion of bubbles, drops, and particles in swarms is relevant... 

Maxey and Riley [47] derived an equation of motion for a small rigid sphere of radius R in a nonuniform flow. If one considers small bubbles moving in a polar liquid, this equation might be appropriate because surfactants would tend to immobilize the surface of a bubble and make it behave like a rigid sphere. Maxey and Riley assumed that the Reynolds number based on the difference between the sphere velocity and the undisturbed fluid velocity was small compared to unity. In addition, they assumed that the spatial nonuni-formity of the undisturbed flow was sufficiently small that the modified drag due to particle rotation and the Saffman [48] lift force could be neglected. Finally, they ignored interactions between particles. 

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