Compressible air flow thorugh pipe

[munni]

Hi guys:

I am wondering with issue regarding high speed (subsonic) compressible air flow thorugh a pipe exit to atmosphere. So here is 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

 

[Q_Goest]

Hi munni,
This question comes up fairly often regarding vent headers on industrial processes, especially for example, relief valve outlets.

Whether or not a shock wave exists at the exit of a pipe is dependant on the flow rate. The flow rate may depend on the pressure drop throughout the piping system, but eventually you need to determine both pressure drop and flow rate through the pipe. Whether or not a shock wave is found at the pipe discharge is an integral part of that flow calculation.

In the case of a relief valve discharging through a vent header system to atmosphere, the flow rate is determined by the flow through the RV. Knowing this flow, you can determine if the exit velocity must exceed mach 1 or not. If the velocity doesn't need to exceed mach 1, there won't be a shock wave at the pipe exit.

In other cases, such as if you only have a pressure drop through the piping system, the flow rate and discharge velocity must be determined together.

 

[ravenprp]

Hi Munni,

To answer your first question, the flow will not always reach M=1 at the exit of the pipe regardless of the pipe length. The Mach number at the exit depends on various factors such as the initial conditions, pipe length, and pressure conditions at the exit. If the pipe length is long enough and the pressure conditions at the exit are favorable, the flow may not reach M=1. However, if the pipe length is short and the pressure conditions at the exit are not favorable, the flow may reach M=1. The key factor here is the pressure conditions at the exit, which can greatly affect the Mach number of the flow.

Regarding your second question, numerical analysis can provide a good approximation of the flow behavior, but it is important to validate the results with experimental data. If your simulation consistently shows a choked flow at the exit, it could be due to the boundary conditions you are using. Atmospheric pressure at the outlet may not accurately represent the actual pressure conditions at the exit, which can affect the Mach number of the flow. It would be beneficial to compare your simulation results with experimental data or use more accurate boundary conditions to improve the accuracy of your results.

I hope this helps. Best of luck with your project!