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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?

enter image description here

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    $\begingroup$ Might Engineering be better suited for this question? $\endgroup$
    – Kyle Kanos
    Mar 26, 2015 at 13:37
  • $\begingroup$ Can I leave it here and post it there too? Actually, I agree the part about design standards/rules is for Engineering but perhaps a physicist can explain us what is under the hood... $\endgroup$
    – vooorka
    Mar 26, 2015 at 13:47
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    $\begingroup$ Cross-posting is typically frowned upon. $\endgroup$
    – Kyle Kanos
    Mar 26, 2015 at 13:48
  • $\begingroup$ So, if you agree, I'll let it here for a while. If nothing comes up, I'll move it there. $\endgroup$
    – vooorka
    Mar 26, 2015 at 13:51
  • $\begingroup$ Just found this article (cool-grind.com/wp-content/uploads/2013/05/…). I guess case 1 is better because at the inlet of the nozzle, eddies would form in case 2. $\endgroup$
    – vooorka
    Mar 26, 2015 at 14:10

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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):

enter image description here

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.

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  • $\begingroup$ Floris, your reasoning sounds perfect to me not your drawing. See this other article (sscentral.org/docs/Theobald_1981_FSJ.pdf): profile 10 is the best as said in the discussion at the end. Profile 10 keeps the section wide till the very end then it inverts curvature (widely) and exits very quickly. $\endgroup$
    – vooorka
    Mar 26, 2015 at 15:03
  • $\begingroup$ @vooorka - I did intend for this to be "just a sketch" - but have updated with a slightly more realistic shape in accordance with Profile 10 in your link. $\endgroup$
    – Floris
    Mar 26, 2015 at 15:14
  • $\begingroup$ I am in the hope I can use these "atomizers" profiles for my air application as I should not care about compressibility effects at low Mach and linked papers refer to both turbulent and laminar flows. $\endgroup$
    – vooorka
    Mar 26, 2015 at 15:23
  • $\begingroup$ This discussion (researchgate.net/post/…) should be added herein. Two issues at low speed: 1) such a long path as profile 10's increases the Reynolds number; 2) the same holds true for a high contraction ratio (=>pressure drop). Likely, air is quite a viscous fluid. $\endgroup$
    – vooorka
    Mar 26, 2015 at 18:35
  • $\begingroup$ Reynolds number quickly becomes quite large... and obviously if your aperture (diameter) constricts by say 5x, the velocity (and Reynolds number) will increase by 25x. Hard to have truly laminar flow in air. Recall that Reynolds number scales with the inverse of viscosity - low viscosity = high Reynolds number. $\endgroup$
    – Floris
    Mar 26, 2015 at 18:42

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