# Rotating Frame of Reference

What Does a Rotating Frame of Reference Do?

A rotating frame of reference is used to model flows in rotating machines. In these cases, the flow is unsteady in an inertial frame (non-accelerating coordinate system in the inertial frame) because the blades or rotors sweep the domain periodically. However, it is possible to perform the calculations in a domain that moves with the rotating coordinate which is fixed on the rotating part. In this approach, the flow is steady relative to the rotating (non-inertial) frame, which reduces the expensive computations needed for an accurate analysis.

This approach is appropriate when the flow at the boundary between the rotating parts and the stationary parts is weakly affected by the interaction. It provides a reasonable time-averaged simulation result for many applications. Rotating frames don't physically rotate anything and therefore do not show transient effects due to the real motion. Instead, a quasi-steady state solution is calculated due to the rotating equipment. Any problems where transient effects due to rotor-stator interaction are small are candidates to use the rotating frame of reference approach. A typical example is the mixing tank where the impeller-baffle interactions are relatively weak; large-scale transient effects are not present.

Single versus Multiple Rotating Frames of Reference:

 Caution The boundary of the part that has rotating components must be axisymmetric about the rotation axis. (Both geometry and loads need to be axisymmetric.) This may require additional steps when creating the model. In the case of 2-D models, this capability may limit what can be analyzed. The surfaces that actually rotate do not need to be axisymmetric.

Here's how to visualize the above capability. The rotation rate is applied by the user to the surfaces of the mesh that rotate; the rest of the surfaces are stationary. Think of the analysis as switching the stationary and rotating surfaces, performing the calculations, and then transforming the results back to make the stationary surfaces have a 0 velocity and the rotating surfaces have an angular velocity. This only works when the stationary surfaces are axisymmetric about the rotation axis. See Figure 1.

 (a) View in the absolute frame. The user specifies the angular velocity W on the surfaces of the rotating component. (b) View in the rotating reference frame. The stationary surfaces rotate at the angular velocity of –W and the rotating surfaces are fixed. (c) After the analysis, the results are transformed back to the absolute frame. To the user, it appears that the blades are rotating.

The model in figure 1 uses a single rotating frame of reference because the stationary walls are axisymmetric to the rotating surfaces. How can something like Figure 2 be analyzed? In this situation, the stationary walls are not axisymmetric about the rotation axis.

Figure 2: The Stationary Walls are not Axisymmetric

To handle this situation, the model can be split into two parts. The surface of the part surrounding the rotating surfaces is axisymmetric about the rotation axis. This creates a multiple rotating frames of reference. One frame is rotating and one frame is stationary. See Figure 3(a).

(a) The model from Figure 2 is split into multiple parts. The boundary of the rotating part 1 is axisymmetric to the rotation axis. Part 2 is stationary.

(b) If the inner blades were to rotate at one velocity and the outer surface were to rotate at a different velocity, then three parts would be required. The surface of each rotating part is axisymmetric with respect to rotation axis. Two rotating frames (parts 1 and 3) and one stationary frame (part 2) are created.

 Note In multiple rotating frames of reference, the boundary of a part that is rotating must be attached to a stationary part. Thus, the model requires three parts instead of two parts. Rotating part 1 is connected to stationary part 2. So is rotating part 3. If part 2 were eliminated, then rotating part 1 would be connected to rotating part 3, and this is not supported.

Figure 3: Multiple Rotating Frames of Reference

The capabilities of the software to handle single and multiple rotating frames of reference are summarized in Table 1. Additional examples of single and multiple rotating frames of reference are given in Figure 4.

 Model/Analysis Type Single Rotating Frame of Reference Multiple Rotating Frame of Reference 2-D Axisymmetric Steady Fluid Flow Yes* No 2-D Planar Steady Fluid Flow Yes * Yes 2-D Axisymmetric Unsteady Fluid Flow No No 2-D Planar Unsteady Fluid Flow Yes** Yes** 3-D Steady Fluid Flow Yes Yes 3-D Unsteady Fluid Flow Yes** Yes** Flow through Porous Media No No Open Channel Flow No No

* The processor treats the entire model as one part, regardless of how many parts are actually used. Thus, the stationary surfaces are at the walls of the model, not at the boundaries between parts. Therefore, only a single rotating frame of reference can be analyzed.

** Although a rotating frame of reference can be used in an unsteady fluid flow analysis, the rotation is still treated as steady. The rotating components need to be rotating fast enough that the effects in the inertial frame can be treated as steady. Other effects remote from the rotating components will show the transient effects accurately.

 Multiple rotating frames of reference: two parts. Single rotating frame of reference: one part. Multiple rotating frames of reference: two parts. Multiple rotating frames of reference: two parts. Multiple rotating frames of reference: three parts.

Applying a Rotating Frame of Reference:

First, you must create the rotating frame of reference. This is done by right clicking on the "Rotating Frames of Reference" heading in the tree view and selecting the "New..." command. Specify the rotational velocity in RPM in the "Angular Velocity" field. Next, specify the point about which the part is rotating in the "Center of Rotation" section. (Any point on the rotation axis is acceptable.) Next, specify the axis about which the part is rotating in the "Axis of Rotation" field. Next, specify the load curve that the rotating frame of reference will follow. Click the "OK" button to finish the definition.

Once the rotating frame of reference is defined, you must apply it to the model using the surfaces. This is done by right clicking on the heading for the surface or surfaces in the tree view (or selecting the item in the display area by using the "Selection: Select" menu) and selecting the "Rotating Frames of Reference" pull-out menu. Select the ID of the rotating frame of reference that you want to apply.

 Note The rotating frames of reference should only be applied to the surfaces that physically rotate; that is, the surfaces of the equipment that moves. The slip boundary and/or walls should not be assigned to a rotating frame of reference. Thus, the rotating frames of reference should not be applied to an entire part or to all surfaces within a part. Tip To see which nodes have a rotation assigned to them, right-click on the desired rotating frames of reference branch in the tree view and choose "Show". Or, use the "View: Options: Rotating Frame of Reference Directions".   Also, the part and surface entries in the tree view will have a rotation symbol next to them, such as the following figure. (Note how surface 1 and 2 are not assigned to the rotating frame).

Note that only one rotating frame of reference can be assigned to a part; that is, different surfaces within a part cannot be assigned to two different rotating frames. The same rotating frame of reference can be assigned to two or more parts.

Rotating Frame of Reference Calculations:

The assigned surfaces rotate with the rotating frame, and the part associated with the surfaces will become a rotating part. Interior surfaces on the rotating parts – faces that match to another part – will be treated as slip surfaces. The results at these slip surfaces (velocity and pressure) will be calculated iteratively during the analysis.

Coriolis force and centrifugal forces are handled by the processor; they are treated as body forces. However, angular acceleration terms are not included in the solution.