• Journal of Korea Water Resources Association
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• v.46 no.4
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• pp.389-400
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• 2013

In this study, a conventional pipeline unsteady friction model has been integrated into Levenberg Marquardt method to calibrate friction coefficient in a pipeline system. The method of characteristics has been employed as the modeling platform for the frequency dependant model of unsteady friction. In order to obtain Hessian and Jacobian matrix for optimization, the direct differentiation of pressure to friction factor was calculated and sensitivities to friction for heads and discharges were formulated for implementation to the integration constant in the characteristic method. Using a hypothetical simple pipeline system, time series of pressure, introduced by a sudden valve closure, were obtained for various Reynolds numbers. Convergency in fiction factors were evaluated both in steady and unsteady friction models. The comparison of calibration performance between the proposed method and genetic algorithm indicates that faster and stabler behaviour of Levenberg Marquardt method than those of evolutionary calibration.

• Journal of Korea Water Resources Association
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• v.45 no.5
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• pp.455-464
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• 2012

In this study, a combined unsteady friction model has been developed to simulate the waterhammer phenomenon for the pipeline system. The method of characteristics has been employed as the modeling platform for the integration of the acceleration based model and the frequency dependant model for unsteady friction. Both Zielke's model and Ramos model were also compared with pressure measurements of a pilot plant pipeline system. In order to validate the modeling approach, a pipeline system equipped with the high frequency pressure data acquisition system was fabricated. The time series of pressure, introduced by a sudden valve closure, were obtained for two Reynolds numbers. A trial and error method was used to calibrate parameters for unsteady friction model. The comparison between different unsteady friction contributions in pressure variation provided the comprehensive understanding in the pressure damping mechanism of waterhammer. The proper evaluation of unsteady friction impact is a critical factor for accurate simulation of hydraulic transient.

• Journal of Korean Society of Water and Wastewater
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• v.22 no.6
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• pp.657-664
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• 2008

This research compared several unsteady friction models for transient analysis of pipeline system. Unsteady friction is an important factor for accurate simulation of hydraulic transient. Steady friction, quasi-steady friction, Zielke's model and two versions of Brunone model were compared with measurement data of identical pipeline conditions. This study showed that the existing simple steady friction model can be useful for the safer design of pipeline system due to its overestimation of waterhammer, but introduction of more elaborate models are required for advanced analysis such as inverse transient analysis of friction or leakage and the preliminary analysis of water quality prediction of water distribution system.