Laminar Flow in a Baffled Stirred Mixer

This exercise exemplifies the use of the rotating machinery features in the CFD Module. The Rotating Machinery interfaces allow you to model moving rotating parts in, for example, stirred tanks, mixers, and pumps.

The Rotating Machinery framework formulates the Navier-Stokes equations in a rotating coordinate system. Parts that are not rotated are expressed in the fixed spatial coordinate system. The rotating and fixed parts need to be coupled together by an identity pair, where a flux continuity boundary condition is applied.

You can use the rotating machinery predefined setup in cases where it is possible to divide the modeled device into rotationally invariant geometries. The desired operation can be, for example, to rotate an impeller in a baffled tank. This is exemplified in Figure 1, where the impeller rotates from position 1 to 2. The first step is to divide the geometry into two parts that are both rotationally invariant, as shown in Step 1a. The second step is to specify the parts to model using a rotating frame and the ones to model using a fixed frame (Step 1b). COMSOL Multiphysics automatically handles the coordinate transformation and the joining of the fixed and moving parts (Step 2a).

Figure 1: The modeling procedure in the Rotating Machinery setup in COMSOL Multiphysics.

Model Definition

The model you treat in this example is that of a baffled stirred mixer. Figure 2 shows the modeled geometry. The impeller rotates counterclockwise at a speed of 10 RPM, and the fluid in the mixer is water.

The model equations are the Navier-Stokes equations formulated in a rotating frame in the inner domain and in fixed coordinates in the outer one.

At the mixer’s fixed walls, no slip boundary conditions apply. The boundary condition on the rotating impeller are set to rotate with the same velocity as the no slip counterclockwise rotation conditions. This is done automatically when the in the section of the Wall feature is set to .

The implementation, applying the predefined set up for the Rotating Machinery, Laminar Flow interface, is straightforward. First you draw the geometry using two separate non-overlapping domains for the fixed and rotating parts. The next step is to form an assembly and create an identity pair, which makes it possible to treat the two domains as separate parts. You then specify which part uses a rotating frame. Once you have done this, you can proceed to the usual steps of setting the fluid properties and the boundary conditions, and finally to meshing and solving the problem.

Figure 2: Geometry of the baffled stirred mixer. The inner domain is represented by a rotating frame and the outer domain by a fixed (spatial) frame.

Results and Discussion

Figure 3 shows the shear rate at the last time step, when the mixer has rotated with full speed for 6 seconds. The shear rate can be important for example when the mixture consists of living cells which are sensitive to too high shear rates.

Figure 3: The shear rate after 6 seconds. The plot shows that the shear rate reaches its maximum value at the tip of the impeller blades.

In Figure 3, you can clearly see that the shear rate is highest where the impeller speed is highest, which is expected. If the shear rate is too high, consider to redesign the impeller with sharp leading and trailing edges.

Figure 4 shows the velocity field in the yz-plane at t = 5.5 s. It is clear that the impeller is creating a downward flow where the blades pass through the fluid.