Hi guys:

I am wondering with issue regarding high speed (subsonic) compressible air flow through a pipe exit to atmosphere. So here are detail:

Air coming from a reservoir and flowing thorugh an adiabatic constant area pipe and exit to atmosphere at the end of the pipe. Due to high velocity (M>0.3) we have to use compressible flow. Now my question is:

1. from physical point of view will the flow reach M =1 at the exit always? I mean regardless of the pipe length. Since the air discharging to the atmosphere, I found from some forum they are saying it will be sonic velocity all the time.

2. from numerical analysis point: I did some simulation and i found no matter what pipe lentgh I use, the flow is choke at the exit (M = 1). If this is not right from physical point of view, how can overcome this issue. I am using atmosphereic pressure (0 gauge) at the outlet of the pipe as my boundary condition.

Comments are welcome.

Munni

1. No. The velocity of the flow at exit will be driven by the total to static pressure ratio. The only way you can have sonic exit conditions it if the pressure ratio is above the critical value (1.85 for air if I remember correctly ... or anyway around this value).

Anyway, since the duct is constant area, the velocity will be almost constant, won't it? The only acceleration will be due to boundary layer thickening at the walls

2. The length of the pipe won't change that much the solution (as I said it only influences slightly pressure losses and boundary layer thickening). You change the massflow rate and hence the velocity by changing the discharge pressure. You have to go below the critical value to get subsonic flow (this means you need to increase the exit pressure)

Check your gasdynamics book for "Fanno" flow to get a more detailed description. Once you understand it, it might be a good idea to add it to the CFD Wiki.

Thanks guys for your input. Actually Fanno flow was my first guide. I went through that and got some info. Tiz, you are right the ratio between stagnation/static pressure should have to be more than 1.89 for air. And if I use atmospheric pressure at the outlet, I get less than that which is choking at the outlet. If I change the pressure at the outlet (increase so that ratio is more than 1.89) then it does not choke. But the problem I am simulating where the air discharged to the atmosphere. So now what would be the right approach? Comments are welcome.

Munni

What drives the flow in a pipe is only (as a first approximation) the total to static pressure ratio. If the ratio is above 1.89 (the critical value) you will have a choked nozzle with expansion waves outside the nozzle itself to adapt the exit pressure to the discharge pressure. (of course I am supposing simply convergent nozzles and not convergent-divergent ones where you can develop supersonic flow ...).

In your case, the exit pressure is fixed by your data. The only way to reduce the flow speed is to reduce the inlet total pressure. If the ratio is BELOW the critical value you start having subsonic flow (all this supposing you give inlet total conditions and exit static pressure as boundary conditions)

Hope this helps

Tiz

[nikhilchotai@gmil.com]

Hi Munni if you found any Proper solution/answer then Plz can you mail me
As in my case in additioin My flow has heat is also there (Solar heating of Pipe)