# Bubbles¶

## Basic Concepts¶

Bubbles are Lagrangian points that can access continuous positions across the fluid lattice. They are used to model gas transport processes, gas hold-up, gasified power draws, and bubble trajectories.

Bubble positions and velocities evolve according to Newton’s Second Law using a Verlet algorithm. Included in the force summation are (i) fluid drag, (ii) gravity, (iii) buoyancy, and (iv) bubble collision forces (unless deactivated by the user).

The fluid drag force is velocity dependent and follows experimentally derived hard sphere drag data. When assigned zero density or zero diameter, bubbles are modeled as massless tracer particles with positions advanced each iteration according to the local and instantaneous fluid velocity.

Upon entering the system through a sparge, each bubble is assigned a unique ID, a birth timestamp, a diameter, and an origin ID. The birth timestamp identifies the time-step at which a bubble entered the system. This value is particularly useful in predicting bubble residence time distributions and bubble mean-age. The origin ID describes where a bubble entered the system (through which sparge domain). This value is particularly useful in predicting how bubbles from various sources blend in the system. It is also useful in predicting how bubbles with different properties (e.g. density and diameter) are affected by fluid motion (assuming different bubble properties are assigned to the different bubble origins).

Note

Bubble output files are printed at the same frequency as output slices.

## Properties¶

Volume Feed Rate

Rate at which gas is injected into the bubble sparge, [L/min]

Volume Scale

Scale factor applied to the number of bubbles entering the system, [-]

For large-scale systems with high volume feed rates, which may have billions of bubbles, the computational requirements necessary to monitor every bubble may exceed available memory. To make simulations tractable, users can specify a Volume Scale, which scales down the number of explicitly tracked bubbles by this number. The simulated volume of the bubbles will then be scaled by this cofactor for hold-up and two-way coupling interactions.

Resolved Feed Rate

Actual number of bubbles that will be fed into the system, [#/s]

The resolved feed rate describes the rate at which bubbles enter the domain through the sparge. When the Volume Scale is set to 1, the resolved feed rate is equal to the user-defined volume feed rate divided by the mean bubble volume. Otherwise, the resolved feed rate will be smaller by a factor equal to this Volume Scale.

Initial Velocity

Initial velocity vector of the bubbles entering the system, [m/s]

Start Time

Time to begin bubble injection, [s]

Stop Time

Time to end bubble injection, [s]

Bubble Density

Density of the bubble, [kg/m 3 ]

Geometry Type

The Geometry Type specifies the nature of the bubble sparge. Three different geometry types are available:

• Box: inject bubbles along the surface of a box

• Ring: inject bubbles along the surface of a ring

• Cylinder: inject bubbles along the surface of a cylinder

Note

• The sparge geometry can be edited interactively in the GUI.

• The sparge geometry can be moved or deleted by right-clicking the bubble component in the model listing.

Bubble Size Distribution

This parameter allows the bubble size to be randomly chosen from one of the following distributions at run-time.

• Single: Single value

• Uniform: Randomly chosen between min max values defined

• Normal: Randomly chosen from distribution function defined by mean and standard deviation

• Log Normal: Randomly chosen from distribution function defined by mean and standard deviation

• Rayleigh: Randomly chosen from distribution function defined by the scale parameter

Bubble Breakup Model

This parameter allows bubbles to break up according to a user defined expression

• None: the bubble diameter is constant

• Bubble Breakup : Enables the bubble break up model

Bubble Min Diameter

Minimum diameter that can be achieved through the break-up process. Bubbles smaller than this value will not break up.

Bubble Breakup Expression

An expression relating the independent variable bubble diameter [m] to the dependent variable energy dissipation rate [W/kg]. For example,:

(0.00000003)*(d^-2.326)


where d is the bubble diameter and the output of this expression is the corresponding EDR. This relationship is used to determine if bubbles will break-up.

Bubble break-up is modeled as a splitting process, wherein the original bubble is split into two equal-volume daughter bubbles with a diameter equal to (1/2)^(1/3) that of the original. This break-up process is only realized when the local EDR is higher than the equilibrium energy dissipation rate of the daughter bubbles. To illustrate this process, consider the following example, which is based on the example bubble breakup expression provided above: A 1 mm diameter bubble travels through the fluid. From the bubble breakup expression, the equilibrium energy dissipation rate for this 1 mm bubble is calculated as 0.285 W/kg, and the equilibrium energy dissipation rate for the 0.794 mm-diameter daughter bubbles is 0.488 W/kg. As the bubble travels through the fluid, it samples different energy dissipation rates. If the sampled energy dissipation rate exceeds 0.488 W/kg, a break-up is initiated, and the original 1 mm diameter bubble is split into to 0.794 mm-diameter bubble. These newly created 0.794 mm-diameter bubbles travel through the fluid along independent trajectories. As they travel, they sample various energy dissipation rates across the fluid. If the sampled energy dissipation rate of one of these bubbles exceeds 0.835 W/kg, a break-up is initiated, and the 0.794 mm-diameter bubble is split into two, 0.623 mm-diameter bubbles. This process continues et cetera. Note that intermediate bubble break-up is not allowed; if a bubble does not sample an energy dissipation rate equivalent to that of its daughter bubbles, it will not break-up. This condition is tested once at each simulation timestep.

Compute Bubble Collisions

When checked, bubbles from this sparge interact and collide with other inertial bubbles.

Two Way Coupling

Enable/Disable two-way bubble-fluid coupling

With two-way coupling activated, momentum is transferred from the bubbles to the fluid.

Export Enabled

Turns the bubble sparge on/off in the solver input file