Sudden valve opening with compressible flow

[morganjp]

I am trying to determine the impulse forces on a piping system after the sudden opening of a blowdown valve. I need to be able to determine pressures, temperatures, and velocities as the flow is developing. Before the opening, natural gas at about 1200 psig is in a large header system. Downstream of the blowdown valve the piping system is at atmospheric pressure and open ended. Both sides of the valve are near ambient temperature. I know that once steady state is achieved I will have a normal shock at the end of the pipe, and I know how to calculate the conditions and flowrates. I am trying to understand the transients in going from a closed valve and no flow to the final steady state, i.e., how does the flow develop? The valve is an actuated 2-inch full port ball valve, so that may give you some idea of my anticipated opening time. There are no orifices in the system. I have gone through a couple of anlysis ideas involving moving shocks, but I was getting supersonic fluid velocities. Is this possible? I suppose as a transient it might happen, but I am pretty sure the final flow has to be subsonic.

 

[BigInch]

My thoughts are, Yes, its possible. And there is no reason to believe the final "average" flowrate will be subsonic until and if the system pressure gets low enough in relation to atmosphere to do so. That may not happen, if for example, the downstream pipe diameter is very small. But since its a blowdown system, we would hope that this pipe is sized large enough to allow eventual blowdown resulting in subsonic velocities, then finally zero velocity. In your system you have flow from the valve into the pipe, flow within the pipe, then flow from the pipe into the atmosphere. Initially you probably do have sonic flow flow across the valve element, which will continue until volumes and pressures at that point build up enough such that velocity drops below sonic, if it ever does. Flow regime depends on the pressure difference across the element, or in your case possibly along a moving front within the pipe as volume and pressures build at the valve outlet and the pipe is filled. If the pipe is of relatively small diameter, its flow resistance will be sufficient to back up pressure along the pipe such that the pressure drop across the valve may reduce velocity to subsonic levels, in which case the shock lines will proceed to move down the pipe. If the pipe is relatively large diameter, gas behind that shock wave would expand laterally, thus decreasing the advance velocity of the shock and possibly causing it to slow down to the point where the shock front advance can no longer be sustained. As pressure within the pipe outlet region increases, you will also develop particular flow regimes at the end of the pipe into the atmosphere, depending on the pressure difference there between a point just inside the pipe outlet and just outside the pipe outlet. If the shock wave inside the pipe continues to advance rapidly, you will basically have no flow at the pipe outlet until the arrival of the shock wave there, or if the shock wave advance dissipates and "normal" flow develops in the pipe as a result of subsonic velocities, pressures within the pipe outlet region would increase more gradually. It is possible that they could eventually reach pressures which would initiate supersonic velocities at the pipe outlet, with shock waves forming on discharge to the atmosphere, or remain at subsonic levels entirely. Just depends on if and at what velocity that sonic front is being sustained and its advance velocity down the pipe.

**********************
"Pumping accounts for 20% of the world’s energy used by electric motors and 25-50% of the total electrical energy usage in certain industrial facilities."-DOE statistic (Note: Make that 99% for pipeline companies)

http://virtualpipeline.spaces.live.com/