When searching for this online I did not seem to be able to find any examples of this, which might imply that this idea does not work (or I did not use the right search terms). I have seen the use of two counter rotating fans, but this would probably still impart rotational energy to the flow after the second fan. I think a jet engine is an example of what I mean, but I at least have not seen other applied use cases. Intuitively I would think that adding stationary blades after the driven rotating ones could improve performance (if the total weight is not an issue). Namely those stationary blades can convert some of the rotational energy of the fluid, imparted by the rotating fan blades, into (linear) kinetic energy of the fluid. So increase the mean flow rate and/or head pressure. Also converting and thus reducing the rotational energy should also reduce friction between the fluid and the wall of the duct. Since a rotating fluid flowing through a duct has a higher velocity near the wall then a none rotating fluid.
Would (some of) these gains be counteracted by a higher torque required to keep the rotating blades spinning at the same speed? Or might the gains at typical speeds be too low?