Numerical Investigation On Rapid Filling Transients In Pipelines

Filling transients in pipelines are common phenomena in hydraulic engineering.The interaction of air-water two phase flows may cause violent surge pressures during the rapid filling process of complex pipelines,which could threaten the safe operation of water systems.In order to guide the accurate prediction of pipeline filling transients and formulate the effective protection measures,more comprehensive pipeline filling models are built based on the interface tracking method and more effective transient analysis is conducted.The steady,quasi-steady and unsteady friction models are introduced to investigate the effects of steady,quasi-steady and unsteady friction coefficients on filling transients in a simple reservoir valve pipeline system.It is found that the filling velocities predicted by the variable friction coefficients determined by quasi-steady or unsteady friction models are lower than that by constant friction coefficients determined by steady friction model.However,the pressure heads at the outlet of the valve predicted by the variable friction coefficients determined by quasi-steady or unsteady friction models are higer than that by constant friction coefficients determined by steady friction model.Moreover,the calculation difference between the variable friction coefficients determined by quasi-steady or unsteady friction models and the constant friction coefficients determined by steady friction model increases with the decresing in driving head or the increasing in valve's opening time.In order to solve the problem that the coulumn separation could not be predicted effectively by the existing branched pipeline filling models,a branched pipeline filling model with atmospheric outlet is proposed.In this model,the velocity head is included into the energy equation of branch junction and the column separation model is also employed.The filling transients are analyzed basing on the proposed model in a branched pipeline with atmospheric outlet.It is found that the intensity of column separation occurring at the local high point is predicted to decrease with the slope of ascending line but increase with the slope of the descending branched line.In order to solve the problem that the interation of air-water is ignored by the existing dividing-and-reuniting pipeline filling models,a dividing-and-reuniting pipeline filling model is proposed.In this model,the polytropic law for the air phase is firstly considered.The filling transients are analyzed basing on this model in a dividing-and-reuniting pipeline with atmospheric outlet.The results show that an increase in the distance to the upstream reservoir or the size of the bypass line decreases the magnitude of resulting overpressures in the dividing-and-reuniting pipelines without entrapped air and that an increase in the length of the submain line increases the magnitude of the pressure surge in the dividing-and-reuniting pipelines with entrapped air.The proposed branched pipeline filling model improves the calculation accuracy of column separation and the proposed dividing-and-reuniting pipeline filling model expands the filling model scope of application.In order to achieve the filling transient analysis in pipelines with submerged outlet,the filling model of pipeline with submerged outlet is proposed.In this model,the equation of submerged outlet boundary is developed by introducing the term of submerged depth into the orifice equation.This model could be equivilient to the dead-end boundary when the air pressure head is lower than the submerged depth of water and the submerged outlet boundary when the air pressure head is higher than the submerged depth of water.Based on this model,the filling transients are analyzed in a pipeline with submerged outlet.It is found that air flow decreases with the increasing of submerged depth of downstream reservoir and that the resulted maximum and minimum pressure heads are both increasing when the submerged depth of downstream reservoir becomes greater.This model fills the gap on the filling model of pipeliens with submerged outlet and discovers the effect of submerged depth on filling transients in the actual pipeliens with submerged outlet.In order to solve the problem that the spurious numerical oscillation could occur when the air valve model is solved by the existing Newton iteration method during filling process,the improved Newton iteration method to solve the air valve model is proposed by judging twice the air pressure in air valve.Thus,a method that combines improved Newton iteration method with direct solving method is proposed in order to calculate the air valve model during the filling process of pipelines.Basing on the proposed numerical method of air valve model,the effects of type,diameter and flow discharge coefficient of air valve on the effectiveness of preventing the pipelines from column separation are studied systematically.The results show that the air inlet and micro exhaust valve is the most appropriate air valve type for the water hammer protection during pipeline filling process and that the air valve with smaller diameter and smaller flow discharge coefficient of released air benefits the water hammer protection.This numerical method improves the calculation accuracy of air valve model and makes the prediction of water hammer protection more effective.The investigation achievements in this paper provide theoretical innovation for the accurate prediction of pipeline filling transients,which is of great significance in engineering practices to guarantee the safe operation of pipeline systems.