MRF and steady state solution
 

Hi everyone,

I am new to CFD and I am working on a rotating problem and investigating SRF and MRF models.

I understand the overall logic of the two methodologies, but I do not fully understand the output of the MRF model. I explain myself.

In the SRF case I am sitting on the rotor moving at constant angular speed and observe the velocity field when stationary. This is fine.

On the other hand, in the case of the MRF model I don't understand what is meant by stationary solution. As soon as there is an obstacle in the periphery that interacts with the rotor blade, the velocity field is never going to be stationary (= $$\partialu/\partialt=0$$).
Is this solution to be considered as if the rotor is frozen at a given position? (I don't think so, the solution would depend on the position of the rotor w.r.t. the stator).
I don't understand how stator-rotor interactions are interpreted in a steady state framework.

Bonus: does anyone know where I can find the full mathematical development of the MRF model plus the equations solved by the CFD software (openFoam)?
I found the equations in the link below, but it is not explained how they are used, especially at the interface.
https://openfoamwiki.net/index.php/S...RF_development

In order for the MRF to be physically sound, the mesh of a moving zone should actually move with respect to others having different motion.

In the MRF you start instrad from different zones with different frames, where their solution is locally sound, and can be steady. The approximation is them in how they see the neighbor zones with different motion, as they don't see them moving

I am not sure to understand what you mean. In the MRF approach meshes are not moving. This approach, as far as I know, gives a steady state solution.

I found this video quite insightful:
https://youtu.be/oa-xcE0_0UY

On the other hand I still don't understand how the relative motion is taken into account. I think equations are solved for the rotor at a frozen position. I am going to check that as soon as I have time.

Please correct me if what I am saying is wrong!

I was referring to the fact that, generally speaking, any CFD simulation of a moving object, steady or not, can be correctly done without actually moving the mesh if you can find a reference frame where the object doesn't change its geometry. That's how you do CFD for, say, airplanes. This is the SRF approach.

So far so good.

When you have multiple objects moving with different velocities, except for trivial cases, you can't pick up a single reference frame where all the objects are standing still. In this case, your only option for a physically sound simulation is using a moving mesh, and the unsteadyness is a direct consequence of this (you can't do that in a steady manner).

So, what is the MRF approach? Except for the trivial cases mentioned above (steady or not), it is an approximation. The idea is that, for different moving objects, you can pick up different frames where the said object is standing still (and so can be the mesh). So you split your domain in different zones, each one with its reference frame. At this point, each of these zones could be solved correctly, steady or not, in their reference frame if it was alone, without moving the mesh. The problem is that they are not and are coupled with neighbor zones, so here comes the approximation of the MRF you solve each zone in its reference frame as it was alone and, at the interface between zones you just take the neighbor zone velocity transformed in the local frame.

The approximation is indeed in the fact that each zone sees the others as still, which is not correct. Yet, the idea is that the relative transformed velocity field is still better than nothing, some sort of average along the relative motion direction.

This has only a partial connection with the steady vs unsteady approach. You can use the MRF approach with an unsteady computation, but that wouldn't make it more accurate.