Relieving pressure in critical and sub-critical flow regimes in backpressure conditions

A method comprising:

• receiving a pressurized fluid flow by an inlet of a pressure relief valve;
• lifting a plunger from a valve seat within the pressure relief valve responsive to receiving the pressurized fluid flow;
• lowering a pressure and increasing a velocity of the fluid flow by a throat of the pressure relief valve, the throat defining a throat flow area;
• increasing the pressure and decreasing the velocity of the fluid flow by an exit of a plunger within the pressure relief valve, the plunger at least partially defining a curtain flow area;
• and
• directing the fluid flow to a relief header by the pressure relief valve, the relief header having a backpressure, wherein a flow area ratio of the throat flow area to the curtain flow area is 0.428 or less.

A pressure relief system comprising:

• a pressurized system;
• a relief header;
• and
• a pressure relief valve coupling the pressurized system to the relief header, the pressure relief valve configured to direct fluid flow from the pressurized system to the relief header when a pressure within the pressurized system exceeds a specified threshold, the pressure relief valve comprising:
• a housing defining an inlet and an outlet, the housing defining a flow passage between the inlet and the outlet;
• a seat defined by the housing, the seat defining a throat flow area;
• a plunger configured to rest upon the seat, the plunger blocking the flow passage when in a closed position, the plunger configured to actuate between a fully open position and the closed position, the plunger and the seat at least partially defining a curtain flow area;
• and
• a bias directing the plunger towards the seat,
• wherein a ratio of throat flow area to curtain flow area, when the plunger is in the fully open position, is sized to cause supersonic flow velocities during critical flow conditions and subsonic velocities during subcritical flow conditions.