Analytical study on water hammer pressure in pressurized conduits with a throttled surge chamber for slow closure

This paper presents an analytical investigation of water hammer in a hydraulic pressurized pipe system with a throttled surge chamber located at the junction between a tunnel and a penstock, and a valve positioned at the downstream end of the penstock. Analytical formulas of maximum water hammer pressures at the downstream end of the tunnel and the valve were derived for a system subjected to linear and slow valve closure. The analytical results were then compared with numerical ones obtained using the method of characteristics. There is agreement between them. The formulas can be applied to estimating water hammer pressure at the valve and transmission of water hammer pressure through the surge chamber at the junction for a hydraulic pipe system with a surge chamber.

THEORETICAL,NUMERICAL AND EXPERIMENTAL STUDY OF WATER HAMMER IN PIPE SYSTEM WITH COLUMN SURGE CHAMBER

A new kind of governing equations for water hammer based on the elasticcolumn theory was proposed and adopted to analyse water hammer phenomenon in the pipe system with avertical column surge chamber and water level fluctuation in the surge chamber during pressuretransient. The wrongness existing in the classical governing equations for water hammer wasanalysed. A typical reservoir-valve pipe system was chosen as an example to verify the new governingequations numerically and experimentally. The finite difference method based on the method ofcharacteristics was used to solve numerically the nonlinear characteristic equations. The temporalevolutions of transient volume flux and head and of water level fluctuation for various surgechamber configurations were worked out, assuming that the air in the surge chamber are compressible.The relevant experiment was conducted to verify the new governing equations and numerical method.The numerical and experimental results show that the new governing equations are valid and theconventional assumption that the pressure head at the base of a surge chamber equals that of thestatic head above it during pressure transient is not always valid. The surge chamber generallyreises the period of transient pressure wave in pipe system, reduces the maximum pressure envelopeand lifts the minimum envelope substantially. The water level fluctuation in the surge chamber wasnumerically and experimentally observed. Increasing the size of the surge chamber and/or decreasingthe initial air pressure in the surge chamber enhance the effectiveness of the surge chamber insuppressing pressure wave.

3-D simulation of transient flow patterns in a corridor-shaped air-cushion surge chamber based on computational fluid dynamics

The 3-D characteristics of the water-air flow patterns in a corridor-shaped air-cushion surge chamber during hydraulic transients need to be considered in the shape optimization. To verify the reliability of the water-air two-phase model, namely, the volume of fluid model, the process of charging water into a closed air chamber is successfully simulated. Using the model, the 3-D flow characteristics under the load rejection and acceptance conditions within the air-cushion surge chamber of a specific hydro- power station are studied. The free surface waves, the flow patterns, and the pressure changes during the surge wave process are analyzed in detail. The longitudinal flow of water in the long corridor-shaped surge chamber is similar to the open channel flow with respect to the wave propagation, reflection and superposition characteristics. The lumped parameters of the 3-D numerical simulation agree with the results of a 1-D calculation of hydraulic transients in the whole water conveying system, which validates the 3-D method. The 3-D flow structures obtained can be applied to the shape optimization of the chamber.

NUMERICAL STUDY OF WATER LEVEL FLUCTUATION IN BULL-HORN SURGE CHAMBER IN PIPE SYSTEM DURING WATERHAMMER

The method of characteristics was adopted to analyze water level fluctuationexisting in Bull-Horn surge chamber in reservoir-valve pipe system during waterhammer caused byvalve closure operation. The Finite Difference Method (FDM) based on the method of characteristicswas used to solve numerically the nonlinear two-parameter characteristic equations governingwaterhammer. The finite fixed mesh was applied to obtaining the discrete form of the governingequations and discrete flow-field. The temporal trends of the y -directional flow, water level,velocity of water level and head difference for different heights of water in surge chamber,diameters of cylinder, cutting angles of surge chamber, lengths of horizontal cylinder and lengthsof inclined cylinder were obtained under the condition that the air in surge chamber iscompressible. The conclusions on water level fluctuation in Bull-Horn surge chamber were given basedon the analyses of the obtained transient numerical results. These conclusions can play a guidingrole in designing pipe system and executing surge suppression.