Fluid Transients in Piping Systems
Part 2 – Pressure Transients in Liquid-Gas Lines
This is the second in a series of articles on fluid transients in piping systems.
A trapped gas pocket in a liquid system can occur in several configurations, as illustrated in Figure 1. Consider the first case where the gas pocket is trapped in-line at a dead-end, at an initial pressure Pg0. As the pump starts, the gas pocket is compressed, causing an oscillatory pressure in the gas.
The gas pressure can be calculated by closed-form solution based on mass conservation and momentum principles, with gas state equations. A closed-form solution to the differential equations (DE) is plotted in Figure 2, labeled “DE Model”.
A more realistic pressure can be calculated by computational fluid dynamics, taking into consideration the compressibility of the liquid. Figure 2 shows a comparison of the computational fluid dynamics numerical solution with liquid compressibility (labeled “Numerical”) to the rigid column differential equation closed-form solution (labeled “DE Model”). The CFD method goes one step further than just modeling compressibility; it also models the propagation of pressure waves; this is why smaller precursor pressure spikes representing the pump start-up pressure can be found before the main pressure peak.