Speaker
Description
The outflow of a gas from a pressurised vessel is one of the classical fundamental problems in fluid mechanics. However, the compressible and subcritical case is more complex than one might think and there is no general analytical solution. This case was examined in more detail.
Based on the Bernoulli’s equation, a fast and accurate model for the prediction of transient gas outflow from vessels is derived. The system is considered adiabatic, isentropic, and subcritical and the gas is considered ideal and compressible. Two cases are considered. In the first case, a thin-wall vessel is considered in which frictional pressure losses are negligible. This case leads to the Inertial Loss Model (ILM). In the second case, a thick-wall vessel is considered in which frictional pressure losses inside the outlet must be taken into account. This leads to the Frictional Inertial Loss Model (FILM). For the first case, a dimensionless number is to be identified based on the pi‑theorem according to Buckingham, which is to be used to describe any subcritical, adiabatic discharge. The model and the dimensionless number are validated by numerical simulations and experiments.
A plot of the dimensionless number against the dimensionless pressure difference results in a single curve that obtains all parameter settings. This means that it is possible to determine all isentropic, subcritical discharges from thin-wall, adiabatic pressure vessels with two equations within a few seconds. The mean deviation of the inertial loss model to the simulations is only 1.939 % and of the correlation to the simulations only ‑2.343 %. The correlation is characterised by its generality, fast and accurate solution, and is therefore a practical tool for calculating the discharge duration of any isentropic, adiabatic, subcritical pressure discharge. In particular, because it does not require complex numerical simulations or calculations of differential equations, it is a practical tool in daily engineering life.
The mean deviation between the FILM for thick-wall vessels and the experiments is ‑1.75 %. This shows that it is possible to determine the outflow duration, even for more complex problems with frictional pressure losses, quickly and accurately.
