Comsol (Femlab) Tutorial: Physical properties at 27 C

COMSOL (FEMLAB) TUTORIAL Example 3 (MOMENTUM TRANSFER)

Consider two immiscible and viscous liquids A and B flowing at 27 C in the z-direction in a °

horizontal thin slit of length 0.5 m and width 0.1 m under the influence of a pressure gradient. Both liquids can be considered as incompressible. The inlet velocities are 25 cm/s and 45 cm/s for A and B, respectively. Determine the corresponding velocity profile for each fluid. Liquid

Density 3 (kg/m )

Viscosity (Pa.s)

A

800

1.0

B

1200

0.4

Physical properties at 27  C  °    °   

To simplify the analysis it is convenient to define two subdomains or regions. The first subdomain comprises the liquid A phase and the second one the liquid B phase. Navier-Stokes equation seems to be suitable to perform the simulation and therefore this equation needs to be defined as an application mode within each subdomain. Boundary conditions are supposed to be the same on the interface. The geometry of the system may may be defined as follows.

Solution using Comsol Graphical User Interface.

1. In the Model Navigator we choose the 2D

coordinate

system

given

the

geometry of the system. In the same window we must click on the Steadystate analysis option of the application

mode Incompressible Navier-Stokes in the folder Momentum balance within the Chemical Engineering Module. This application mode is to

determine the velocity profile of liquid A

and

therefore

the

dependant

variables are to be called ua, va, pa, which are the x and y components of  the velocity and the pressure of A, respectively.

Le

us

name

this

application mode aph (from A phase).

2. Before clicking on OK, we must define another application mode for the liquid B phase and to do so the Multiphysics mode must be activated by clicking on

the button Multyphisics located at the bottom

of

Navigator.

the

window

Model

3. After clicking on this button the window Model Navigator will change and a new button Add will

show up at the top of the right-hand side of this window. The application mode just defined for A must be included in the list of modes of the option Multiphysics. This can be done by clicking on the

button Add.

We must be able to see the application mode aph in the list and also the name of the dependant variables we have defined in this mode.

4. The gasoline phase is to be solved using Navier-Stokes as well, but with different dependant variables. For this mode we can use ub, vb and pb for the x and y components of the velocity and the pressure, respectively. In addition, let us name this mode bph (for B phase). After doing this, we must click one more time on the button Add to include this application mode into our model.

5. Next, we must specify the geometry of the system. Let us draw two rectangles with a common side and with the properties shown below.

Thus, the geometry of the model is defined by the following figure.

Each rectangle corresponds to one phase. R1 is for the A phase (the less dense fluid) and R2 for the B phase (the more dense fluid). 6. Next, we must specify the physical properties of the fluids in each subdomain. The currently active subdomain is indicated by a black dot to the left of the name of the application mode in the menu Multiphysics. To change the active subdomain we just have to do one click on the mode we want to activate. To define the settings in the mode bph (which is currently active) we press the key F8. In the window Subdomain Parameters we select the subdomain 1 (B is more dense) and specify the properties of the fluid B as indicated below.

Subdomain 2 must be inactive for this mode. To deactivate this subdomain we select it in

the same window and clear the box Active this domain. After this, click OK.

7. To do the same with the other mode we must activate it. This can be done by clicking on its name in the menu Multiphysics. 8. After pressing the key F8 we must be able to specify the active and inactive subdomains and the physical properties for this application mode. Let us deactivate the subdomain 1 as explained above.

In the subdomain 2 we specify the physical properties of the fluid A, as shown below.

9. After clicking OK we are ready to specify the boundary conditions. To do so, we must press the key F7 and the windows Boundary Settings will show up. The active mode is aph and

therefore

the

boundary conditions will be defined for this mode. In the boundary 3 we must specify

the

inlet

velocity, which is assumed only

to

have

x-component.

To do this, we select the option Inflow/  Outflow

velocity

flow and type the value velocity.

of

the

Next, we select the 4

boundary

and

specify the velocity which is supposed to be the same for both fluids

at

the

interface, this is, x and y components must be the same. It is

important

to

mention at this point that

to

avoid

the

boundary to move we must equal the ycomponent velocity interface to 0. The boundary 5 is defined by the nonslip condition.

of at

the the

Finally,

in

the

boundary 7 we must specify the pressure. To do this, we select the option Outflow  /Pressure and

type

the value of  0 for the pressure. This value makes sense if we use relative

pressure

instead of the absolute one.

The

results

should be the same although a zero value reduces

the

computation time. 10. Once we have entered the

boundary

con-

ditions for the mode aph we must click  OK and then activate

the

bph

mode

repeat

the

to

same

procedure to set the boundary

conditions

for that mode.

To visualize the velocity profiles at each subdomain in the same plot we must define subdomain expressions. Let us define U as the module of the velocity anywhere within our system. This variable will be equal to sqrt(ub^2+vb^2) within the subdomain 1 and sqrt(ua^2+va^2) within the subdomain 2. To do so, let us click on the option Subdomain Expressions in the menu Options, as shown below.

In the window Subdomain Expressions we enter the expressions that define U, as follows.

Postprocessing

After running the model the following surface plot showing the velocity field of A will be displayed.

To visualize both velocity fields, A and B, at the same time we must use the subdomain expression just created. To do this, we press the key F12 to open the window Plot Parameters. In this window we select the tab Surface and in the field Expression we type the name of the subdomain expression, U, as shown below.

After clicking OK we should be able to visualize both velocity profiles as surface plots.

It is possible to visualize the velocity fields using arrows. To achieve this, let us select the tab Arrow at the top of the window Plot Parameters. Next, we must

check the box Arrow plot to activate this option and then to specify any quantity that

we

want

to

be

displayed this way. For our case,

let

us

select

the

velocity field of A (aph).

We can also choose the color of the arrows by clicking Color.

on

the

button

The velocity field of A will be now displayed as shown below.

The velocity profile is obtained by using the option Cross-Section

Plot

Parameters

in

the

menu

Postprocessing.

Let us visualize the velocity profile in the middle of the slit. To do this, we select the tab Line/Extrusion and specify two points to define this section. The values are entered in the field Cross-section line data. In the field Expression we type the

name of the subdomain expression U that was defined earlier.

To add labels and title to our plot we select the tab General in the window Cross-Section Plot Parameters and click on the button Title/Axis.

In doing so, the window Title/Axis Settings will show up. Now we can type the labels and title for our graph.

Finally, we click OK and the velocity profile will be displayed as shown below.