CFD for Rotating Systems Explained: Moving Reference Frame (MRF) vs Rigid Body Motion (RBM)

Overview

This article demonstrates the capabilities and limitations of modeling rotational flow problems using the Moving Reference Frame (MRF) approach through two case studies. The first case examines internal turbulent flow in a duct with a rotating two-blade fan. The second case builds on the first by introducing a blockage just upstream of the fan. For each problem, three simulations are conducted to evaluate the effect of blade orientation (clocking angle):

1. 0° steady-state MRF
   
2. 90° steady-state MRF
   
3. Rotating mesh transient RBM

Background - MRF

Mesh motion is defined relative to a reference frame, which may be stationary (laboratory frame) or rotating/translating with respect to the laboratory frame. In steady-state simulations—or transient simulations that do not require time-accurate solutions—the MRF approach allows modeling of rotational and translational motion while keeping the mesh stationary. Applying MRF to a region does not alter the position of cell vertices. Instead, it introduces a Grid Flux term in the governing equations, calculated based on the reference frame properties rather than local mesh motion. Grid flux is computed at every wall boundary cell face within the MRF region.

The MRF approach is computationally cheaper than RBM because it assumes steady-state behavior and produces a time-averaged result. In contrast, RBM is a transient solution that produces a time-accurate solution. For RBM simulations, the time step is typically restricted so that the blade does not rotate more than 1° per time step to maintain numerical accuracy. Additionally, up to 10 full revolutions are often required to reach a steady solution, significantly increasing computational cost compared to MRF.

MRF Capabilities and Limitations

The MRF approach yields physically realistic results only when the surrounding flow is axisymmetric. If a significant component of the external flow is perpendicular to the axis of rotation, it leads to unphysical results that scale with the magnitude of that perpendicular flow component. Common examples include:

1. crosswind on a wind turbine
   
2. angled inlet flow into a fan or pump
   
3. side flow in a mixing tank
   
4. tangential blower
   
5. non-uniform flow in HVAC systems
   

A key assumption of the MRF (Frozen Rotor) method is its steady-state approximation. It provides a time-averaged solution and is NOT suitable for problems requiring time-accurate results. In such cases, rigid body motion (RBM) approach must be adopted.

Another consideration is the clocking effect, especially for configurations with a low blade count. Clocking refers to the angular position of rotating components relative to stationary components or boundary conditions. Different clocking angles can influence performance metrics such as pressure rise, thrust, and efficiency.

Case Study 1 – Axisymmetric internal flow

Problem 1 involves a two-blade fan rotating at 7000 RPM inside a duct. Boundary conditions include a stagnation inlet and a pressure outlet at atmospheric pressure and room temperature, as shown in the below figures. The goal is to assess how blade orientation (clocking angle) affects pressure rise using:

1. Steady-state MRF at 0° and 90°
   
2. Transient RBM (time-accurate)
   

Problem 1 Domain and Boundary Conditions – No Blockage

Problem 1 (a) 0 deg and (b) 90 deg - MRF clocking angle with static mesh, and (c) transient RBM with rotating mesh

Pressure rise is taken between the inlet and outlet boundaries for each case. The two MRF cases with blade orientations at 0° and 90° calculate 61.1 Pa and 61.0 Pa, respectively. They agree within 2% of the time-accurate RBM benchmark case, as described in the table below. Therefore, clocking orientation of the two-blade fan does not have a significant effect on pressure rise.

Table 1: Problem 1 - Duct Inlet/Outlet Pressure Rise

Run ID	Pressure Rise (Pa)	% Difference, RBM
MRF 0°	61.1	1.7
MRF 90°	61.0	1.5
RBM	60.1	-

Velocity line integral convolution and vector plots upstream of the fan show flow aligned with the axis of rotation, confirming axisymmetric flow. Thus, the MRF solution closely matches the time-accurate RBM results.

Problem 1 velocity vector results at 0 deg blade orientation

Case Study 2 – Internal Flow with Blockage

Problem 2 introduces a rectangular blockage upstream of the fan, disrupting the flow path, as shown in the figure below.

Problem 2 Blockage (a) 0 deg and (b) 90 deg - MRF clocking angle with static mesh, and (c) transient RBM with rotating mesh

Pressure rise results for the MRF cases are 47.1 Pa and 50.1 Pa, showing poor agreement with each other and with the RBM benchmark (mean 54.4 Pa):

Table 2: Problem 2 - Duct Inlet/Outlet Pressure Rise

Run ID	Pressure Rise (Pa)	% Difference, RBM
MRF 0°	47.1	-13.4
MRF 90°	50.1	-7.9
RBM (mean)	54.4	-

Velocity plots reveal vortex formation downstream of the blockage, introducing significant perpendicular flow components in the MRF region, as shown in the below figures. This violates the axisymmetric assumption, leading to degraded MRF accuracy.

Problem 2 velocity vector results at 0 deg blade orientation

Conclusion

Problem 1 pressure rise results indicate the clocking angle of the two-blade fan has minimal impact on the results because the flow is axisymmetric about the axis of rotation. However, the same cannot be said for problem 2. The blockage disrupts the flow path and induces perpendicular flow in the surrounding volume of the MRF region, thus requiring a time accurate solution.

In Problem 1, the clocking angle of the two-blade fan has minimal impact due to axisymmetric flow, allowing MRF to produce accurate results. In Problem 2, the upstream blockage introduces perpendicular flow to the volume surround the MRF region and invalidating the MRF assumptions. The RBM approach is necessary for time-accurate modeling in such cases.

Summary

MRF is a time-averaged method that performs well under axisymmetric conditions. When significant perpendicular flow components are present, MRF accuracy degrades, and transient RBM approach becomes essential.

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