How is the average exhaust gas velocity determined in complex nozzle designs?

[strive]

Hi

Can someone tell me how exactly (physically and mathematically) is the nozzle exhaust plane defined?
I “understand” the principle with simple circular openings, but not the more complex shapes (such as in the links below).

http://www.strutpatent.com/image/get/2003/full/US06532729-20030318-D00002.jpg

http://patentimages.storage.googleapis.com/US20020125340A1/US20020125340A1-20020912-D00000.png

 

[Aero_UoP]

I don't quite understand what exactly you're asking but physically, this kind of shapes enhances the mixing of the hot and cold streams with the freestream flow in order to reduce the noise. Better mixing leads to smaller length scales which means higher frequences hence faster decay.

 

[strive]

Indeed, but with this shape of the nozzle some of the exhaust mass (gas) exits the engine while some of the gas is still traveling through it thus further accelerating (as the nozzle is further converging (or diverging in case of a supersonic nozzle)).

So how do we determine the average exhaust gas velocity (in order to calculate thrust)?
Or rather where (at which point down the length of the nozzle) can we “measure” it (in a cfd simulation)?
Of course when using such a nozzle for sound suppression the difference between velocities is minimal, but consider a more pronounced version of these nozzles.