COMSOL 6.4 - Circulating Fluidized Bed

This model simulates the operation of a circulating fluidized bed (CFB). In this apparatus, the dispersed phase, consisting of solid spherical particles, is fluidized by a gas and transported through a vertical riser. Upon reaching the outlet, the dispersed phase is reinjected in the vicinity of the gas inlet at the bottom of the bed. To study the flow in the fluidized bed, the model uses the Euler–Euler model. The phase properties and model setup follow those in Ref. 1.

Model Definition

Figure 1 displays the geometry of the fluidized bed and schematically describes its means of operation. The fluid phase, consisting of air, is injected at the bottom of the bed. The dispersed phase, particles with a diameter of 54 μm, are fluidized by the gas flow and transported upward. At the outlet, particles and gas exit the bed. The particles are fed back into the bed through reinjection inlets on the vertical walls near the gas inlet. The dispersed-phase flux matches that at the outlet, creating a circulating fluidized bed. Table 1 summarizes the bed geometries and the properties of the phases. The values correspond to those used in Ref. 1.

Table 1: Fluidized bed Properties.
Property	Value
Particle diameter	54 μm
Particle density	930 kg/m3
Gas density (air)	1.2 kg/m3
Gas dynamic viscosity (air)	1.8·10-5 kg/m3
Gas inlet velocity	1.52 m/s
Bed width	0.09 m
Bed height	10.6 m

Figure 1: Schematic of the circulating fluidized bed. The geometry is not to scale.

Governing Equations

Use the Euler–Euler model to solve for the flow of the continuous and dispersed phase. Both phases are then modeled as interpenetrating continua governed by a separate set of Navier-Stokes equations. The model also includes a transport equation for the dispersed-phase volume fraction. For details of the equations and assumptions used, see the theory section for the Euler–Euler Model, Laminar Flow interface in the CFD Module User’s Guide. To specify the transport properties of the fluidized bed, apply the settings below.

The viscosity of the dispersed phase is defined from the Gidaspow model as

where ϕd is the dispersed-phase volume fraction.

Assume the momentum transfer to be dominated by the drag force and the drag acting on each phase is given by a drag coefficient β in the manner of

Here, the subscripts “d” and “c” indicate properties of dispersed and continuous phase, respectively, and the slip velocity is defined as

To model the drag coefficient, use the Gidaspow drag model (Ref. 2)

for ϕc > 0.8 and

for ϕc < 0.8.

The dispersed phase transport resulting from particle–particle interaction, collisions, friction between particles, and so on, is included by the solids pressure term in the dispersed phase momentum equations. To model this term, the following expression is used (Ref. 1):

Initial Conditions

Initially all dispersed particles are positioned in a packed bed section at the bottom of the column. The packed bed section is 1.855 m high and consists of 50% particles. To avoid discontinuities at the start and end of the packed bed section, use a smoothly varying rectangle function to define the packed bed column.

Boundary Conditions

To fluidize the bed, air is injected at the bottom. Set the dispersed phase volume fraction at the inlet to zero.

Use pressure normal flow conditions for both phases at the outlet. To prevent the dispersed phase from falling back into the bed at the outflow boundary, remove the gravitational volume force in a region prior to the outlet using a smoothly varying step function.

At the vertical reinjection inlets, gas and solids are injected in a manner that matches the top outflux. This is achieved by using two coupling operators integrating the solid phase mass flux on the left and right sides of the bed center, each feeding the reinjection inlet on the respective side; see Figure 1. Apply solid mass flux which matches the mass outflux at the top. Use a gas velocity that equals that of the particles, assuming that the particle reinjection drags the gas phase along with it.

Along the solid bed walls, apply a no-slip condition for the continuous phase and a slip condition for the dispersed phase.

Results and Discussion

This section shows the results from the simulation. Note that the model is not deterministic and the plots may differ between computations performed on different platforms.

Figure 2 shows the startup phase of the fluidized bed simulation, plotting the dispersed-phase volume fraction during the first five seconds of simulation. Note that the packed bed section is pushed upward by the gas, primarily in the center of the bed. Due to the lower gas velocity close to the walls, the heavy solid phase is able to accumulate and fall down along the walls creating pockets with high concentration of solids. After about 6 s, the solid phase reaches the top of the bed and starts exiting the bed. You can verify this by inspecting the solids mass flux at the outlet; see Figure 3. This corresponds to the start of the re-injection of solids at the bottom. In the same figure, note that the bed reaches steady-state operations after about 15 s, after which the outflux of particles fluctuates around 11.5 kg/(m·s), which approximates to the experimental value reported in Ref. 1. Figure 4 shows snapshots of the dispersed-phase volume fraction during steady-state operation.

Figure 5 shows profiles of the averaged gas-phase streamwise velocity, giving an insight in the flow development. The gas-phase volume-fraction profiles at the corresponding positions are displayed in Figure 6.

Figure 2: Snapshots of the dispersed-phase volume fraction during the startup phase. Black indicates high volume fraction. The bed width has been scaled by a factor of ten.

Figure 3: Dispersed-phase bed outflux.

Figure 4: Snapshots of the dispersed-phase volume fraction during the steady-state operation. Black indicates high volume fraction. The bed width has been scaled by a factor of ten.

Figure 5: Averaged streamwise continuous-phase velocities at three vertical positions.

Figure 6: Averaged continuous-phase volume fractions at three vertical positions.

Notes About the COMSOL Implementation

The current model includes a slender geometry with an aspect ratio of about 100. When plotting and inspecting the solution over the whole modeling domain, it is therefore hard to distinguish any details. To produce the plots in Figure 2 and Figure 4, the view was stretched ten times in the x direction.

The flow in the fluidized bed is turbulent with Reynolds number around 9000. Nevertheless, a laminar flow model is used here. The effects of additional stresses from meso-scale structures are included in the models for solid pressure and inter-phase drag. See Ref. 4 for further details.

References

1. N. Yang, W. Wang, W. Ge, and J. Li, “CFD simulation of concurrent-up gas–solid flow in circulating fluidized beds with structure-dependent drag coefficient,” J. Chem. Eng., vol. 96, pp. 71–80, 2003.

2. D. Gidaspow, Multiphase Flow and Fluidization, Academic Press, San Diego, 1994.

3. H. Enwald, E. Peirano, and A.-E. Almstedt, “Eulerian Two-Phase Flow Theory Applied to Fluidization,” Int. J. Multiphase Flow, vol. 22, pp. 21–66, 1996.

4. K. Agrawal and others, “The Role of Meso-scale Structures in Rapid Gas-solid Flows,” J. Fluid Mech., vol. 445, pp. 151–185, 2001.

CFD_Module/Multiphase_Flow/fluidized_bed

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file fluidized_bed_parameters.txt.

Geometry 1

Rectangle 1 (r1)

In the toolbar, click

In the window for , locate the section.

In the text field, type bedW.

In the text field, type bedH.

Locate the section. In the text field, type inlH.

Rectangle 2 (r2)

In the toolbar, click

In the window for , locate the section.

In the text field, type bedW.

In the text field, type solidH0.

Locate the section. In the text field, type inlH.

Rectangle 3 (r3)

In the toolbar, click

In the window for , locate the section.

In the text field, type bedW.

In the text field, type inlH.

Line Segment 1 (ls1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Locate the section. In the text field, type 0.02.

Locate the section. In the text field, type 0.02+injH.

Line Segment 2 (ls2)

Right-click and choose .

In the window for , locate the section.

In the text field, type bedW.

Locate the section. In the text field, type bedW.

Point 1 (pt1)

In the toolbar, click

In the window for , locate the section.

In the text field, type bedW/2.

In the text field, type bedH+inlH.

In the toolbar, click

Edit the view scale manually to rescale the geometry in the x direction and reduce the aspect ratio of plots.

Definitions

In the window, expand the > node.

Axis

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

In the text field, type 10.

Click

Click the

button in the toolbar.

In the toolbar, click

In the window for , locate the section.

Select the checkbox.

Axis

In the window, expand the node, then click .

In the window for , locate the section.

In the text field, type -0.01.

In the text field, type 0.105.

In the text field, type 0.4.

In the text field, type -0.025.

From the list, choose .

In the text field, type 10.

Click

In the window toolbar, click

next to

, then choose .

Create a step function to use for ramping up the bottom inlet velocity from zero to its full value over the initial 0.002 s.

Global Definitions

Step 1 (step1)

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type 1e-3[s].

Click to expand the section. In the text field, type 2e-3.

Click

to view the step function.

Next, create another step function to use for ramping up the volume fraction at the reinjection slots.

Step 2 (step2)

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type bedH.

In the text field, type 1.

In the text field, type 0.

Locate the section. In the text field, type 0.15.

Create a rectangle function to specify the initial conditions for the solid volume fraction.

Rectangle 1 (rect1)

In the toolbar, click

and choose > .

In the window for , locate the section.

In the text field, type inlH.

In the text field, type solidH0+inlH.

Click to expand the section. In the text field, type bedW.

Click

Create two integration operators at the outlet. You will use these to compute the dispersed phase outlet flux in the left and right bed halves as well as the corresponding reinjection velocities.

Definitions

Integration 1 (intop1)

In the toolbar, click

and choose .

In the window for , type intopL in the text field.

Locate the section. From the list, choose .

Select Boundary 9 only (top-left boundary)

Integration 2 (intop2)

In the toolbar, click

and choose .

In the window for , type intopR in the text field.

Locate the section. From the list, choose .

Select Boundary 10 only (top-right boundary)

Variables 1

In the window, right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
outfluxdL	intopL(phid*max(udy,0[m/s]))	m²/s	Dispersed phase outflux, left side
outfluxdR	intopR(phid*max(udy,0[m/s]))	m²/s	Dispersed phase outflux, right side