Special approaches are needed when dealing with the modeling and analysis of various complex rotating systems having a stator and a rotor, in single or multistage, with change in the frame of reference from fixed to rotating (namely fans, pumps, compressors, turbines, propellers, impellers, diffusers, stators, vanes etc.). Indeed, all parts attached to the rotating shaft will be rotating with a certain angular velocity with respect to the machine axis, while the stationary parts such as stator, casing, inlet(s), exit(s) etc., do not move. When viewed by a stationary observer, the flow around the moving parts is always unsteady, even if the flow is apparently of steady state. When viewed by an observer stationed on the rotor, such a flow appears steady. For unsteady flow problems such as transients, it does not matter whether the observer is situated on the stationary or moving parts.

So, the important issue is the transfer of information from one stationary frame to the moving reference frame and vice-versa. By changing the frame of reference, quantities like normal, shear and deformation stress tensors are invariant. However, quantities like velocity, acceleration and rotating tensors depend on the frame of reference, e.g. static pressure does not change with change in coordinate frame (P_static); but total pressure changes with the coordinate frame. Additional complexities in rotating systems arise from three dimensionality, complex shapes with curvature, accelerated/decelerated flows, rotor-wake-stator/stator-wake-rotor interactions, etc.

Hence, special approaches/models come in handy to convert a very complex transient problem into a steady state problem and thus reduce the modeling and analysis time drastically. Proven approaches are:

1. Body Force Model (also known as lumped parameter model, mostly applicable for fans),
2. Multiple Reference Frame model (MRF),
3. Mixing Plane Model (MPM),
4. Sliding Mesh method.

All the above models are made available in CFD-ACE+. This tip describes the Multiple Reference Frame (MRF) feature. If you are interested in this tip please read on.

The MRF model accounts for complete blade design and fan details to simulate complex turbo machinery. It is a steady state approximation where the fluid zone in the fan region is modeled as a rotating frame of reference and the surrounding zones are modeled in a stationary frame. Contrary to the Body Force Model, the MRF model includes the geometry of the fan blades. The fan blades are modeled stationary but since the fluid domains surrounding them are in a rotating frame, the pressure jump and the swirl components are given by the presence of blades as wall without the need of experimental data as an input.

The major difference between MRF and Mixing Plane Methods is that the MRF directly translates the properties of the flow at the interfaces between the rotating and stationary zones, whereas the MPM averages the properties of the flow circumferentially. The MPM avoids flow field non-uniformities that arise from the fact that the fan blades are modeled stationary.

The steady state approximation of MRF allows individual cell zones to rotate or translate with different speeds. This is achieved by dividing the whole problem domain (say a rotor/stator interaction for rotating machinery) into separate zones where the flow is solved in stationary or rotating coordinate systems. The MRF approach is good when the flow (say between two rotors moving in counter directions or a rotor and a stator) is nearly uniform.

MRF and Navier-Stokes Equations of Motion:

The MRF transforms the fluid velocities from stationary to rotating frames using the following relation:

Stationary Frame

Rotating Frame

Where:     Velocity Relative to Rotating Frame  =  Absolute Velocity  -  Whirl Velocity  

Solving the equations of motion in the rotating reference frame results in additional acceleration terms in the momentum equation. Also, for a reference frame rotating at a constant angular velocity, the body force per unit mass includes both Coriolis and centrifugal forces. MRF solves the equations of motion in both stationary frame (for absolute velocity) and rotating frame (velocity in the rotating reference frame). Therefore, with the general MRF capability, steady state analysis can be performed on various components of the rotating system using local reference frames, either stationary or rotating as appropriate.

As shown in figure 2, CFD-ACE+ offers three options under MRF. They are:

Figure 2: CFD-ACE+ Multiple Reference Frame Options

1. Frame (Global): Select this option when you would like to solve the system as a Rotating Frame Reference to yield relative velocity solutions. Inputs are: Point on axis of rotation and Angular velocity vector.
2. Multiple Frame (VC Based): Select this option for more than one rotating frame of reference, like for fans and impellers. Inputs are: Point on axis of rotation and Angular velocity vector.
3. Multiple Frame (Geometry based, see figure 3): Use this option when the rotating domains are not defined as separate volume conditions. Here, a virtual cylinder will be created to define the rotating region. Two levels adjacent to this region are used as the rotating frame boundaries. Inputs are: center location, normal direction, thickness, radius of virtual cylinder geometry and angular rotation speed.

Figure 3: CFD-ACE+ Multiple Reference Frame - Geometry Based Option

To work with the first two options of MRF, select ‘Rotation’ under ‘MO’ tab. Select ‘Rotation’ under ‘VC’ tab, activate ‘Rotating Frame’, choose Fluid zone to be rotated from Explorer and specify the values for input fields.

Select Multiple frame (Geometry based) option from ‘Rotation’ under ‘MO’ tab. Select ‘MRF’ tab adjacent to ‘BC’ tab in ACE-GUI control panel, hit on ‘Add’ button in the Explorer window to add a multiple reference frame, choose virtual cylinder zone ‘MRF’ from Explorer and specify the values for input fields.

Convention followed in CFD-ACE+ for Angular rotation speed; angle is positive for counter-clockwise rotation and negative for clockwise rotation.

All the boundary conditions values must be specified in absolute frame of reference. Walls that rotate and appear in absolute frame of reference, e.g. blade surfaces must be specified as rotating walls. The ACE-SOLVER will automatically convert all velocities specified from the absolute frame to the rotating frame using the frame information provided in the Problem Type setting.

Try using the MRF feature next time. If you have any questions about this feature or would like us to discuss other topics in the future please let us know.

Regards,
Shivakumar GT
ESI CFD Support Team