This exercise was part of my continuing effort to climb the learning curve for CAD & 3D printing.
The screw itself is pretty much sorted. Apparently the eight-vane configuration is somewhat optimal. (Found a paper on the subject.)
Note the design (in Onshape) is parameterized (partly) and properly(?) constrained. You might want to keep the size of the screw small (by changing the "length" parameter) when doing test prints, to save print time. You could make a larger screw (by changing the "length" and "case" parameters) and the rest of the partsshould adjust properly.
The top end of the screw can be turned by the hand crank. Alternatively, you could remove the crank and turn the screw with an 8mm Allen key - perhaps attached to an electric motor or drill.
Designed in Onshape

The author marked this model as their own original creation. Imported from Thingiverse.