A high pressure jet is a stream of pressurized fluid that is released from an environment at a significantly higher pressure than ambient pressure from a nozzle or orifice, due to operational or accidental release. In the field of safety engineering, the release of toxic and flammable gases has been the subject of many R&D studies because of the major risk that they pose to the health and safety of workers, equipment and environment. Intentional or accidental release may occur in an industrial settings like natural gas processing plants, oil refineries and hydrogen storage facilities. A main focus during a risk assessment process is the estimation of the gas cloud extension and dissipation, important parameters that allow to evaluate and establish safety limits that must be respected in order to minimize the possible damage after a high pressure release.
Mechanism and structure of a gaseous jet
Subsonic and sonic flow When a pressurized gas is released, the velocity of the flow will heavily depend on the pressure difference between stagnant pressure and downstream pressure. By assuming an isentropic expansion of an ideal gas from its stagnant conditions (P0 , meaning the velocity of the gas is zero) to downstream conditions (P1, positioned at the exit plane of the nozzle or orifice), the subsonic flow rate of the source term is given by Ramskill's formulation:
Q = C D A o ρ 1 2 P 0 ρ 0 [ γ γ − 1 ] [ 1 − ( P 1 P 0 ) γ − 1 γ ] {\displaystyle Q\;=\;C_{D}\;A_{o}\;\rho _{1}\;{\sqrt {\;2\;{\frac {P_{0}}{\rho _{0}\ }}\;\left[{\frac {\gamma \ }{\gamma \ -1}}\right]\left[1-\;\,\left({\frac {\;P_{1}}{P_{0}}}\right)^{\frac {\gamma \ -1}{\gamma \ }}\;\right]}}}
As the ratio between downstream condition pressure and stagnant condition pressure decreases, the flow rate of the ideal gas will increase. This behavior will continue until a critical value is reached (in air, P1/P0 is roughly 0.528, dependent on the heat capacity ratio, γ), changing the condition of the jet from a non-choked flow to a choked flow. This will lead to the a newly defined expression for the aforementioned pressure ratio and, sub-sequentially, the flow rate equation. The critical value for the pressure ratio is defined as:
P 1 P 0 = [ 2 γ + 1 ] ( γ γ − 1 ) {\displaystyle {\frac {\;P_{1}}{P_{0}}}\;=\;\left[{\frac {2}{\gamma \ +1}}\right]^{\left({\frac {\gamma \ }{\gamma \ -1}}\right)}}
This newly defined ratio can then be used to determine the flow rate for a sonic choked flow:
Q = C D A o ρ 1 V c {\displaystyle Q\;=\;C_{D}\;A_{o}\;\rho _{1}\;V_{c}}
The flow rate equation for a choked flow will have a fixed velocity, which is the speed of sound of the medium, where the Mach number is equals to 1:
… excerpt ends here. Continue reading the full article.
