Analysis of beat phenomena during transients in pipelines with a trapped air pocket

Abstract

Trapped gas pockets may cause severe operational problems in liquid piping systems. The severity of the resulting transients depends on the size and position of the trapped air pocket. Previous numerical simulations by the authors have indicated that a beat is possible to develop for ‘medium’ size air pockets. This paper investigates the beat phenomenon in detail, both theoretically and experimentally. Trapped air pockets are incorporated as boundary conditions (discrete gas cavities) into two distinct numerical solution schemes: (1) the method of characteristic scheme (MOC) and (2) a conservative solution scheme (CSS). The classical discrete gas cavity model (DGCM) allows gas cavities to form at computational sections in the MOC. A discrete gas cavity is governed by the water hammer compatibility equations, the continuity equation for the gas cavity volume, and the equation of state of an ideal gas. A novel CSS-based DGCM solves the system of unsteady pipe flow equations and respective state equations for four dependent variables (pressure, density, cross-sectional area, flow velocity) rather than two variables (pressure, flow velocity) in the classical MOC approach. In the MOC-based DGCM, the Courant number is equal to unity. This condition is difficult to fulfil (without using interpolations) in complex pipe networks without modification of wave speeds and/or pipe lengths. The CSS-based DGCM offers flexibility in the selection of computational time and space steps, however, the numerical weighting coefficients in the scheme should be carefully selected. Both models incorporate a convolution-based unsteady friction model. Experimental investigations of beat phenomena have been carried out in the University of Adelaide laboratory apparatus (reservoirpipeline-valve system). A trapped air pocket is captured at the midpoint of the pipeline in a specially designed device. The transient event is initiated by rapid closure of a side-discharge solenoid valve. Predicted and measured results are compared and discussed. It is shown that the fully-developed beat is strongly attenuated by unsteady friction and not so by steady friction.