This article deals with the gas reservoir and the blow-off pipe as a unit. Implicit relations for sonic and subsonic outflows through pipes of any length are presented. Explicit approximate relations are provided as well. The formulas have been applied to determine valve influence on depressurization and blow-through of a compressor yard. The theoretical results have been verified by experimental data.
Depressurization, pressurization and blow-through of a tank or a compressor pipe yard are quite common processes. In spite of this, they are rarely well described. Reason of the problem is in the used lengths and cross-sections of inlet or outlet pipes:
The most occurring pipe lengths L are longer than ten pipe diameters D but shorter than thousands of the diameters D. For these lengths, there is no simple formula for calculation of a gas flow, therefore a more general approach is necessary, e.g., Oswatitsch equations. Moreover, at such lengths, a significant gas pressure drop and the velocity increase occurs both in the reservoir and along the pipe as well. Thus the reservoir and the blow-off pipe have to be treated as an inseparable unit.
A pure knowledge of a pipe cross-section is insufficient, since a gas flows into the blow-off pipe from the sides of reservoir. The side velocity component is maintained by inertia so it narrows the gas flow cross-section. Hence the unknown cross-section of a flow jet can be considerably smaller than the known geometric cross-section of a pipe. Moreover, the flow through the outlet pipe is also limited by a mostly unknown, changing cross-section of an outlet valve.
This article deals with the unit comprised of a reservoir and inlet or outlet pipes. It provides implicit relations for sonic and subsonic flows through pipes of any length. Also, an explicit approximate relation is presented. The theoretical formulas are proven by data from Frössel experiments and are applied to simulation of a real depressurization and blow-through of a compressor yard. A comparison of the simulated and measured data has enabled to determine the changing cross-section of an outlet valve, the effective cross-section of a blow-off pipe (chimney) and the amount of gas losses during a depressurization of compressor pipe yard.