From an unsteady sliding mesh case of a standalone fan I would like to extract (write in a file) an average 3D field of momentum (x,y,z)
the idea behind is to “replace” the unsteady fan by a steady ROM in a big case
If your idea is to replace the Fan by a cell zone that mimics the same effect, why not to use 3D fan zone (or 2D pressure jump if simplification allows)? You can run your unsteady fan for different operating points and get the fan curve (dp vs Q) and insert this into your model.
I am not sure exporting momentum will help better in this case. You need to introduce momentum sources on a cell by cell basis to accelerate the flow to match the exported momentum. The source should be proportional to the difference between the target momentum (exported) and the actual momentum (computed in the simplified cell zone). For that matter you can create a variable rho*V and export the three components as any other variable. Then create a DEFINE_SOURCE UDF that uses (rho*V_target - rho*V_current) to add the source. This source should be 0 when V_target = V_current.