Rapid filling/emptying of pipes is commonly encountered in water supply and sewer systems, during which pressure transients may cause unexpected large pressure and/or geyser events. In the present study, a linearized analytical model is first developed to obtain the approximate solutions of the maximum pressure and the characteristics of pressure oscillations caused by the pressurization of trapped air in a horizontal pipe when there is no or insignificant air release. The pressure pattern is a typical periodic wave, analogous to sinusoidal motion. The oscillation period and the time when the pressure attains the peak value are significantly influenced by the driving pressure and the initial length of the entrapped air pocket. When there is air release through a venting orifice, analysis by a three-dimensional computational fluid dynamics model using ANSYS Fluent was also conducted to furnish insights and details of air–water interactions. Flow features associated with the pressurization and air release were examined, and an air–water interface deformation that one-dimensional models are incapable of predicating was presented. Modelling results indicate that the residual air in the system depends on the relative position of the venting orifice. There are mainly two types of pressure oscillation patterns: namely, long or short-period oscillations and waterhammer. The latter can be observed when the venting orifice is located near the end of the pipe where the air is trapped.

A physical model study was conducted on jet impingement in a plunging dropshaft with different drop heights of 3.38 and 1.88 m. Experimental observations show that an upward splash, annular flow, and downward bounced jet could be formed when the approaching jet hits the opposite shaft wall. The impinging pressure on the shaft wall was mainly dominated by the incoming flow velocity, and the mean pressure on the shaft wall can be reasonably well-predicted when considering the bounced flow. The pulsation of the impinging pressure on the shaft wall was significant, with the maximum pressure being approximately 1.4–3.8 times the mean value. The impinging pressure at the shaft bottom was primarily determined by the velocity at which the falling jet reached the pool. The mean value can be well estimated using the annular flow and bounced jet assumption. The pulsation intensity increased with an increase in drop height or flow rate, which could be alleviated by a plunging pool with a larger depth. However, for flows in dropshafts under study, the impinging pressure and the hydrostatic pressure of the cushion layer were within the same order of magnitude; thus, the increase of the pool depth leads to a reduction of the energy-dissipation rate.

Rapid filling of a horizontal pipe with an entrapped air pocket has attracted significant attention as overpressurization induced by air compression may cause safety concerns. This study developed a linearized model for a rapidly filling horizontal pipe, by using a Jacobian linearization around the equilibrium point of the nonlinear system. The analytical expressions explicitly show the relationship between the characteristics of pressure oscillation and parameters including the driving head, the length of the water column, the length of the entrapped air pocket, the location of the equilibrium point, and the polytropic exponent. The oscillation frequency increases with the driving head whereas it decreases with the length of the air pocket. The obtained analytical solution compares well with the rigid-column model for a limited range, and it is improved by means of introducing power-law fitting for general cases. The linearization method also can be used in other cases, such as rapid filling in a horizontal pipe with the entrapped air pocket above an initial water layer or in slope/vertical pipes.

Uncontrolled filling is often seen in storm sewers under wet weather conditions. This study develops a rigid-column model for rapid filling in a partially filled horizontal pipe with entrapped air. Numerical solutions compare very well with experimental measurements from earlier studies. Parametric analysis is conducted by nondimensionalizing the governing equations, and two typical scenarios are numerically investigated in detail: one with a fixed air pocket length and the other with a fixed air pocket volume under different tailwater depths. For the cases with a fixed air pocket length, the peak pressure becomes greater as the tailwater depth increases when the length ratio of the water column and the air pocket is large, whereas the trend is reversed when the length ratio is small. And the critical length ratio is system-dependent. In cases with a fixed air volume, the peak pressure is monotonically reduced with the increase in the tailwater depth. The proposed model can also be adapted for rapid filling with ventilation and surges in closed-conduit flows.

Rainfall-derived inflow/infiltration (RDII) modelling during heavy rainfall events is essential for sewer flow management. In this study, two machine learning algorithms, random forest (RF) and long short-term memory (LSTM), were developed for sewer flow prediction and RDII estimation based on field monitoring data. The study implemented feature engineering for extracting physically significant features in sewer flow modelling and investigated the importance of the relevant features. The results from two case studies indicated the superior capability of machine learning models in RDII estimation in the combined and separated sewer systems, and LSTM model outperformed the two models. Compared to traditional methods, machine learning models were capable of simulating the temporal variation in RDII processes and improved prediction accuracy for peak flows and RDII volumes in storm events.