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I am working on a project which involves air nozzles. I am interested in estimating the time it takes for air particles after they leave the nozzle to reach a particular distance away. I have the following information--- a converging nozzle, the speed with which it is coming out of the nozzle(I know when the air is choked it comes out at Mach number). I am aware that this problem is complex and would be very difficult to solve it precisely without intensive Mathematical Models. I just want a rough idea/guideline. Any help will be appreciated.

http://postimg.org/image/cw53jnibx/

Above is a profile of the nozzle

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  • $\begingroup$ Is the flow subsonic or supersonic when it exits? If supersonic, is it overexpanded or underexpanded? $\endgroup$ – tpg2114 Nov 19 '15 at 5:07
  • $\begingroup$ Also, is it a round exit or another shape? Jets exiting a nozzle are self-similar and so their cross-sections have the same shape regardless of distance downstream when scaled properly. And the shape function itself can be approximated using some relatively basic expressions. But it depends on the flow conditions which ones apply. $\endgroup$ – tpg2114 Nov 19 '15 at 5:09
  • $\begingroup$ I am assuming that the flow is choked. So I believe the air will come out speed of sound. The exit is round shaped. What basic expressions can be used? Sorry mt background in thermo is quite limited. I am trying to read up on the relevant material $\endgroup$ – Bayko Nov 19 '15 at 7:20
  • $\begingroup$ Well... the outlet speed will depend on the shape of things. A choked nozzle is choked at its smallest point (the throat) -- is the smallest point the outlet of the nozzle or does it expand after the smallest point? The expressions I mentioned don't come from thermo, they come from the study of turbulent flows but I can't point you to one particular source without more details of your geometry and operating conditions. A sketch would help immensely. $\endgroup$ – tpg2114 Nov 19 '15 at 7:31
  • $\begingroup$ I have added an image above which reflects the profile of the nozzle. $\endgroup$ – Bayko Nov 19 '15 at 23:47
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Without more details, we can't find a specific case that will match what you are doing. However, I did find a decent example to show you what to look for to answer your question.

Data for a nearly-sonic round jet can be found in this paper. If you look at Figure 5(a), you'll see how the normalized centerline velocity from several experiments collapses together and has essentially a hyperbolic tangent shape. You could find experimental data for conditions near your operating point (speed, Reynolds number) and create a tanh function that approximates the data and go from there.

You can find similar figures and/or correlations for the width of the jet as a function of downstream coordinate also. Standard textbooks on turbulence should have the subsonic jet correlations, but for a sonic jet I can't think of any off the top of my head that will definitely have it. But you can search through the literature using keywords learned in the paper I linked to and you should be able to find what you need.

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  • $\begingroup$ Thank you. I will look into this. Also I have edited the post and added an image link. It now contains the nozzle profile. $\endgroup$ – Bayko Nov 19 '15 at 23:48

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