COMSOL 6.4 - Modular Mixer

Set up the rotating domain conditions in Definitions.


Property	Variable	Value	Unit	Property group
Density	rho	972	kg/m³	Basic
Dynamic viscosity	mu	1	Pa·s	Basic

In the text field, type Silicone oil Si1000.

Moving Mesh

Rotating Domain 1

In the window, under > click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the f text field, type 40.

Use the predefined selections to set up the physics features.

Laminar Flow (spf)

Interior Wall 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Interior Wall 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

As an alternative, the union selection for and can be done.

Symmetry 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Pressure Point Constraint 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Define the postprocessing variables for the torque and power draw.

Variables 1

In the toolbar, click

In the window for , locate the section.


Name	Expression	Unit	Description
tau_riw	x(spf.T_trac_uy+spf.T_trac_dy)-y(spf.T_trac_ux+spf.T_trac_dx)	N/m	Torque per area (interior walls)
tau_rw	x(spf.T_tracy)-y(spf.T_tracx)	N/m	Torque per area (rotating walls)
P_riw	tau_riw*rot1.alphat	W/m²	Power draw per area (rotating interior walls)
P_rw	tau_rw*rot1.alphat	W/m²	Power draw per area (rotating walls)

Integration 1 (intop1)

Define a nonlocal integration coupling on to evaluate its contributions to the torque and power draw.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Integration 2 (intop2)

Define a nonlocal integration coupling on to evaluate its contributions to the torque and power draw.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Mesh 1

In the window, under click .

In the window for , locate the section.

In the table, clear the checkbox for .

button in the toolbar.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 1

In the window for , locate the section.

Clear the checkbox, because the plot can be added later using the .

In the toolbar, click

Result Templates

In the toolbar, click

and choose .

Go to the window.

In the tree, select > > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Cut Plane 1

In the toolbar, click

Multislice 1

In the window, expand the node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 0.

Locate the section. From the list, choose .

Arrow Surface 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 0.

Locate the section. In the text field, type 1000.

Locate the section. From the list, choose .

Select the checkbox. In the associated text field, type 0.005.

From the list, choose .

Surface 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 1.

Locate the section. From the list, choose .

From the list, choose .

Selection 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

In the window, under click .

In the window for , type Velocity: Magnitude and Vectors in the text field.

Click to expand the section. From the list, choose .

In the text area, type Velocity: magnitude and in-plane vectors.

Locate the section. Clear the checkbox.

Before finalizing the plot, generate a dedicated view with a subfeature that allows an unobstructed view of the impeller inside the vessel.

In the window, under right-click and choose .

Hide for Physics 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

In the window, click .

In the window for , locate the section.

Select the checkbox having rotated the geometry to give a good view of the impeller.

Define the surface used to calculate the flow number.

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the toolbar, click

Parametric Surface 1

In the toolbar, click

and choose .

In the window for , locate the section.

Find the subsection. In the text field, type 2*pi.

Find the subsection. In the text field, type -Da/10.

In the text field, type Da/10.

Locate the section. In the text field, type 0.186*T*cos(s1).

In the text field, type 0.186*T*sin(s1).

In the text field, type s2.

The surface for the calculation of the flow number is now visualized in the window.

Evaluate the torque on the impeller and the power draw using the postprocessing variables you defined.

Torque

In the toolbar, click

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

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
abs(intop1(tau_riw)+intop2(tau_rw))	N*m

Power Draw

In the toolbar, click

In the window for , type Power Draw in the text field.

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
abs(intop1(P_riw)+intop2(P_rw))	W

Evaluate the flow number.

Flow Number

In the toolbar, click

and choose > .

In the window for , type Flow Number in the text field.

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
(ucos(s1)+vsin(s1))/40[1/s]/Da^3	1

This example uses the frozen-rotor study type. Due to the topology variations resulting from the relative motion between the rotating impeller and baffled vessel, the flow field is really time dependent. The frozen-rotor solution should in this case be viewed as a quasi-steady approximation to the flow field. The solution gives a general idea of the circulation pattern set up in the mixing vessel, and may produce good approximations of certain averaged flow quantities, such as the power draw.

Turbulent Mixing — k-ε Model

In the second example, turbulent mixing of water is simulated in a dished bottom mixer with a pitched four blade impeller rotating at 20 rpm. This simulation is set up using a Rotating Machinery, Turbulent Flow, k-ε interface with the frozen-rotor study type. The geometry is built from the supplied geometry file: modular_mixer_turbulent_geom.mph using the parameters in Table 2 below. Periodicity is utilized to reduce the computational time and hence a quarter of the domain is simulated in this case.

Table 2: Turbulent mixer geometry parameters
H	0.5[m]	Vessel height
T	H	Vessel diameter
C	1/4*H	Clearance
B	4	Number of baffles
bw	T/12	Baffle width
Boz	0	Baffle offset from bottom
Rd	T/10	Minor radius of dished bottom
Da	1/2*T	Impeller diameter
shaft_diameter	1/10*Da	Shaft diameter
blade_width	Da/5	Width of impeller blade
alpha	-45[deg]	Pitch angle
N_blades	4	Number of blades for pitched blade impeller

The pitched blade impeller expels the fluid axially as well as radially, and a large zonal vortex, extending from the bottom to the top of the vessel, is formed. A smaller zonal vortex forms below the impeller and may in certain cases cause aggregation of heavy dispersed particles at the bottom center of the vessel.

Figure 6 shows a surface plot of the velocity magnitude and a projection of the velocity vectors on the yz-plane for the turbulent simulation with the k-ε turbulence model.

Figure 6: Velocity magnitude and in-plane velocity vectors (yz-plane) for turbulent mixing in a dished bottom mixer with a pitched blade impeller using the k-ε turbulence model.

The torque on the impeller, given by

where A is the surface area of the impeller and T is the total stress, is 0.016 Nm. The power draw is obtained from

where Ω is the angular-velocity vector. The power draw is 0.033 W in this case.

The process of setting up a time-dependent study with the results of the frozen-rotor simulation as initial conditions is a bit more involved in this case because of the geometry reduction. You can either use general extrusions to define the solution on the remaining three quarters of the domain, or, you can recompute the frozen-rotor simulation on the full domain.

Modeling Instructions

Root

Begin by loading the geometry file.

From the menu, choose .

Browse to the model’s Application Libraries folder and double-click the file modular_mixer_turbulent_geom.mph.

Use the predefined selections to set up the physics features.

button in the toolbar.

Add Physics

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > > > > ε.

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Turbulent Flow, k-ε (spf)

Interior Wall 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Interior Wall 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Symmetry 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Use a to account for the excluded domain.

Periodic Flow Condition 1

In the toolbar, click

and choose .

Select Boundaries 2, 6, 22, and 23 only.

Pressure Point Constraint 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Moving Mesh

Rotating Domain 1

In the window, under > click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the f text field, type 20[rpm].

Add postprocessing variables for the torque and power draw.

Variables 1

In the toolbar, click

In the window for , locate the section.


Name	Expression	Unit	Description
tau_riw	x(spf.T_trac_uy+spf.T_trac_dy)-y(spf.T_trac_ux+spf.T_trac_dx)	N/m	Torque per area (interior walls)
tau_rw	x(spf.T_tracy)-y(spf.T_tracx)	N/m	Torque per area (rotating walls)
P_riw	tau_riw*rot1.alphat	W/m²	Power draw per area (rotating interior walls)
P_rw	tau_rw*rot1.alphat	W/m²	Power draw per area (rotating walls)

Integration 1 (intop1)

Define a nonlocal integration coupling on to evaluate its contributions to the torque and power draw.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Integration 2 (intop2)

Define a nonlocal integration coupling on to evaluate its contributions to the torque and power draw.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Mesh 1

In the window, under click .

In the window for , locate the section.

In the table, clear the checkbox for .

Right-click > and choose .

Size

In the window, under > click .

In the window for , locate the section.

Click the button.

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

Size 1

Select Boundaries 1, 15, 16, and 25 only.

button in the toolbar to see the interior of the geometry.

In the window, click .

Size

In the window, right-click and choose .

Size 2

In the window, right-click and choose .

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 3 and 17 only.

Locate the section. From the list, choose .

From the list, choose .

Click the button.

Refine the mesh in the domain defined by the control surfaces.

Size 3

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Domain 3 only.

Locate the section. From the list, choose .

From the list, choose .

Click the button.

Locate the section.

Select the checkbox. In the associated text field, type 0.0114.

Select the checkbox. In the associated text field, type 0.00123.

Select the checkbox. In the associated text field, type 1.08.

Refine the mesh further near the blade’s surface.

Size 4

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundary 9 only.

button in the toolbar to disable wireframe rendering.

Locate the section. From the list, choose .

From the list, choose .

Create a plot of the velocity magnitude and in-plane velocity vectors using the previously created datasets.

button in the toolbar.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 1

In the window for , locate the section.

Clear the checkbox, because the desired plots can be added manually later.

In the toolbar, click

In the window, expand the node.

Right-click and choose .

In the window for , type Velocity: Magnitude and Vectors in the text field.

Click to expand the section. From the list, choose .

In the text area, type Velocity: magnitude and in-plane vectors.

Surface 1

Right-click and choose .

Selection 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Surface 1

In the window, click .

In the window for , locate the section.

In the text field, type 1.

Locate the section. From the list, choose .

From the list, choose .

In the window, click .

In the window for , locate the section.

Clear the checkbox.

Surface 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Selection 1

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 2 and 6 only.

In the toolbar, click

button in the toolbar.

Cut Plane 1

In the window, expand the > node.

Right-click > and choose .

Arrow Surface 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the text field, type 0.

Locate the section. In the text field, type 500.

Locate the section. From the list, choose .

Select the checkbox. In the associated text field, type 0.26.

From the list, choose .

In the toolbar, click

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

button in the toolbar.

Evaluate the torque on the impeller and the power draw using the imported postprocessing variables.

In the window, under > click .

In the window for , locate the section.

Select the checkbox.

Due to the periodicity conditions, multiply by 4 to get the torque on the whole impeller.

Torque

In the toolbar, click

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

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
4*abs(intop1(tau_riw)+intop2(tau_rw))	N*m

Multiply by 4 to get the full power draw.

Power Draw

In the toolbar, click

In the window for , type Power Draw in the text field.

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
4*abs(intop1(P_riw)+intop2(P_rw))	W

Turbulent Mixing — k-ω Model

In the third example, similarly to the second example, turbulent mixing of water is simulated in a dished bottom mixer with a pitched four blade impeller rotating at 20 rpm. Here, the simulation is set up using a Rotating Machinery, Turbulent Flow, k-ω interface with the frozen-rotor study type. The k-ω model is better suited for flows with recirculation regions but, due to the strong nonlinearity in the turbulence coefficients, takes longer to converge than the k-ε model. By using the previous k-ε model as initial condition for the flow and turbulence variables, a faster convergence can be obtained. In the interfaces for turbulent fluid flow, there is a global option for creating a new turbulent flow interface. This option will add a new turbulent flow interface with the desired turbulence model, and automatically add settings for the initial values so that the previous solution is used in a new study.

The torque on the impeller, given by

Figure 7 shows a surface plot of the velocity magnitude and a projection of the velocity vectors on the yz-plane for the turbulent simulation with the k-ω turbulence model.

Figure 7: Velocity magnitude and in-plane velocity vectors (yz-plane) for turbulent mixing in a dished bottom mixer with a pitched blade impeller using the k-ω turbulence model.

Similarly to the k-ε simulation, the flow pattern is dominated by a large zonal vortex but its core appears to be more stretched in the vertical direction. The smaller zonal vortex below the impeller appears to be stretched in the radial direction.

where A is the surface area of the impeller and T is the total stress, is 0.025 Nm. The power draw is obtained from

where Ω is the angular-velocity vector. The power draw is 0.053 W in this case. These values are higher than the corresponding results from the k-ε simulation. Although the k-ω model is better suited for these types of flows, experimental results are needed to determine whether these results are indeed more accurate.

The process of setting up a time-dependent study with the results of the frozen-rotor simulation as initial conditions is a bit more involved because of the geometry reduction. You can either use general extrusions to define the solution on the remaining three quarters of the domain, or, you can recompute the frozen-rotor simulation on the full domain.

Modeling Instructions

Root

Begin by loading the model file with the k-ε-model that contains the solution.

From the menu, choose .

Browse to the model’s Application Libraries folder and double-click the file modular_mixer_ke.mph.

Component 1 (comp1)

Add a new k-ω turbulent flow interface and a study that use the solution from the k-ε-model as initial values.

Turbulent Flow, k-ε (spf)

Generate New Turbulence Model Interface 1

In the window, expand the node.

Right-click > ε (spf) and choose .

In the window for , locate the section.

From the list, choose ω.

Locate the section. Click .

Since the new interface has different variable names for the stress components, duplicate the current variables from the previous model and replace the respective interface tag spf with spf2 to create new variables for torque and power for the k-ω-model.

Variables 2

In the window, expand the > node.

Right-click > > and choose .

In the window for , locate the section.