Entrainment and Jet Diameter Growth

[mm391]

Hello,

I am looking for some help in understanding jet diameter growth due to entrainment. I have an impingement plate positioned approximately 20 cm from the nozzle exit. Is there an equation or information that will allow me to figure out how a free jets diameter grows the further it gets from the nozzle exit. This is so that the rig I have that holds the impingement plate in place does not interfere with the jet growth.

Many Thanks

Mark.

 

[bigfooted]

When the jet is laminar, there are analytical equations available that describe the jet growth. When the jet is fully turbulent, the jet is self-similar and the spreading is described by the Reynolds-independent spreading rate S, but it is only valid when you are more than 30 initial jet diameters away from your inlet. So it is important to first estimate your jet Reynolds number to determine if your jet is laminar or turbulent.
A good description of the turbulent round jet case is given in Pope - Turbulent Flows and most other books that deal with turbulence.

 

[RandomGuy88]

Keep in mind that your impingement plate will interfere with the growth of your jet. So I think it is unlikely that any equation that describes the free jet will be accurate when there is an impingement plate. If there is a region in which an analytic expression, derived for the free jet, is valid it will be far from the plate (in terms of the ratio of jet diameter to distance to plate).

You also need to consider that just because you have placed something (to hold your rig) outside of the jet diameter, this does not mean it will not interfere with jet growth. If you have something near the jet, possibly even a few diameters away, it may interfere with the flow being entrained and therefore effect jet growth. Unfortunately this can be a difficult problem and I do not know of any analytic expressions that directly apply to your situation. Of course that doesn't mean they don't exist. But this may require some experiments to verify you have place the rig holder far enough away.

 

[etudiant]

Entrainment is very poorly captured by models and even full scale test rigs fail to reproduce real life performance.
Rockwell tried a couple of decades back to use entrainment to improve the effectiveness of vertical lift jets.
The models worked a treat, with about a 20% boost, reduced to about 12% if memory serves in the full scale mockup. Unfortunately, real life improvement was under 5% and the XV-12 project was terminated.

 

[RandomGuy88]

Perhaps I am not understanding what you mean by "use entrainment to improve the effectiveness of vertical lift jets." When a VTOL aircraft (like the F-35) is near the ground attempting to lift off vertically, entrainment actually makes it more difficult. The entrained air accelerates beneath the aircraft and the pressure drops below ambient. This results in a suction force towards the ground reducing the net thrust.

I had never heard of the XV-12 until now, its a pretty interesting aircraft.

 

[etudiant]

The idea had been to augment the vertical lift of the engines with air sucked into the jet exhaust with the help of a specialized exhaust nozzle.
VSTOL jets have to be horrendously overpowered to take off, which results in wretched fuel economy, because turbines don't run at partial speed very well. The hope had been that ejector entrainment would improve things, but the tests dashed that hope.