NO MATTER WHAT ONE DOES.

I have tried and then tried some more, I have been very, very trying. This is as good as the water simulation is going to get. I will have another look in the future, I think I read that Blender 2.90 is due in July, hopefully they will have polished the Mantaflow job up a bit by then. How many particle bakes I have run is beyond count and I even started taking screen grabs of the settings not to mention wasting valuable paper scribbling stuff down. All to no or little determinable  improvement. It's time to move on and think of something else to occupy my little grey cells. I have enjoyed the modelling aspect of this project so am tempted to resurrect the old Steam Punk motorbike. It could be done in Blender but FreeCAD is a better tool for that job.
It would have been quicker to 3D print the waterwheel. I can model waterwheels in about half an hour so if anyone with a printer who fancies an Stl. file, I'll send one free from my computer. You can then pop it under the kitchen tap and film a video in minutes.
I thought I had cracked it with this version.

Unfortunately the water is too lumpy, the spray too small and it's still getting through the mesh. I quite like the RSJ (That dates me. 'I' beams they are called now), support structure and the plumber blocks and fasteners they came out a treat. Modelled from scratch and not downloaded as Obj. files from the bearing folks catalogue. It's nice to look at something and just extrude, scale, fill meshes.
Here is the video. I win some I lose some.

This is rendered in EEVEE the reason the water looks opaque is not because I forgot to set roughness to zero, it's because I have too much spray and foam in the job. 
Onto the next project.

I see we are getting blue post boxes. Must be to celebrate the new blue passports.

Have fun.