Air nozzle outlet profile efficiency, concave/convex I need to design a contracting nozzle for air. The application is quite simple, consider it like an hair dryer but the flow speed is even lower. So the Mach number is very low and the flow laminar.
If I wanted the highest efficiency, which is the best profile?
In particular, should it be concave or convex as a starting point.
This paper is the only one I could find that mentions concave/convex (see page 21, for example).
Perhaps, the fact that the flow is subsonic makes it (almost) trivial but according to the profile of the vena contracta, I'd go for case 2.
Are there any design standards/rules?

 A: You might want to define what you mean by "efficient" better - but assuming you want to accelerate the air flow, then the most important parameter is the ratio of input to output diameter. Next, you want to minimize the length of the nozzle (since a longer nozzle implies more drag) and in particular the length of the nozzle where your cross section is narrow (pressure drop increases quickly with decreasing area). But finally, you may worry about the direction of the flow across the exit - if your walls are at a steep angle to the flow, you will create vortices at the exit. But as you found, a steep change in direction at the inlet will also cause eddies.
All that seems to point to a nozzle like this (drawing updated based on your comment and profile 10 in your link):

Large ratio of input / output area, relatively short, and smooth transitions at both inlet and outlet; per your comment (and link) I shortened the narrow section (where most drag occurs). Note that proper design requires more knowledge about the application and the actual parameters of the flow, so consider this just a sketch as a starting point.
