Influence of aeration on the head loss along the pipeline

This study aimed to clarify the variation law of head loss along aerated pipelines, explore the impact of aeration rate on the hydraulic performance of water-air two-phase flow in pipelines, and establish a reliable calculation method for head loss along aerated pipelines. The goal was to provide theoretical guidance and technical support for the hydraulic design of aeration irrigation systems. An automated water-air aeration irrigation system was constructed based on a programmable logic controller (PLC), consisting of a water source, pipeline system, variable frequency water pump, aeration device, valves, and measurement instruments. The pipeline used was a horizontal PVC pipe with an outer diameter of 32 mm and a wall thickness of 3 mm. A full factorial experiment was conducted with 3 water head levels (11, 17, 22 m) and 8 aeration rates (ranging from 0-1.33×10⁻³ m³/s), resulting in 24 working conditions. For each condition, measurements were taken for 5 minutes after stabilization, repeated 3 times, and the average value was used. Flow rate was measured by an intelligent electronic water meter, aeration rate by a gas mass flowmeter, and water head by pressure transmitters installed at 5 positions along the pipeline. Regression analysis was applied to establish relationships between variables, and the proposed calculation formula was verified through specific working conditions. The results showed that aeration had an inhibitory effect on the average pipeline flow rate. The maximum inhibition rate was 3.81% when the aeration rate was 1.08×10⁻³ m³/s. Both water head and aeration rate, as well as their interaction, had significant effects on the flow rate (P<0.05 or P<0.01). For aerated pipelines, a higher pressure was required compared to pure water pipelines. The pipeline pressure increased with the aeration rate, with an approximate 3 m increase for every 1×10⁻³ m³/s increment in aeration rate, and it was jointly affected by water head and aeration rate. Along the pipeline, pressure decreased with increasing length, and the decrease rate tended to slow down, which was consistent with the variation in pure water flow; higher aeration rates led to higher pressures. A calculation formula for head loss along aerated pipelines was established, considering the effects of aeration rate on resistance coefficient and flow velocity. Verification results indicated that the error between calculated and measured values ranged from 0.2% to 1.6%, confirming the formula's reliability. This formula was applicable to horizontal circular pipes with bubbly flow, gas content between 0-50%, initial pressure between 11 and 22, and Reynolds number above 70 000. Aeration rate exerts dual effects on pipeline hydraulic performance: increasing pipeline pressure and slightly inhibiting flow rate, with the overall impact within an engineering acceptable range. The established calculation formula for head loss along aerated pipelines, with high reliability, provides an important theoretical basis for hydraulic calculation and optimal design of aeration irrigation systems, especially facilitating pressure compensation and flow control balance in hilly areas by adjusting aeration rate.