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    Quantifying Linearization Error When Modeling Fluid Pipeline Transients Using the Frequency Response Method

    Source: Journal of Hydraulic Engineering:;2010:;Volume ( 136 ):;issue: 010
    Author:
    Pedro J. Lee
    ,
    John P. Vítkovský
    DOI: 10.1061/(ASCE)HY.1943-7900.0000246
    Publisher: American Society of Civil Engineers
    Abstract: The unsteady mass and momentum equations for pipe flow can be solved in the frequency domain and provides additional insight into the behavior of fluid transients. Additionally, this approach has significant computational advantages compared to the method of characteristics because it is not based on a rigid time-space grid. Despite its advantages, the frequency domain approach must be used with care as it uses linearized forms of the steady friction and orifice equations—which can deviate significantly from the true nonlinear solution. The conditions in which the frequency response method can be accurately used are currently unknown. This paper investigates and quantifies the error in the frequency-domain method, via comparison to a highly discretized time-domain model that uses the method of characteristics, and describes situations where the frequency response method can be used with accurate results. A reservoir-pipe-valve system was used in this study with transients generated by perturbation of the valve. The error consists of errors from two sources: the linear approximations of the steady friction and the steady orifice equations. The frequency response method was shown to produce identical results to the method of characteristics when these two sources of error are minimized. The error in the frequency-domain model was quantified as functions of the perturbation magnitude, frequency, and system parameters. The results indicate that errors are significant when the perturbation size is more than 25% of the steady-state condition and this error is frequency dependent with the largest errors occurring at the harmonic peaks of the system.
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      Quantifying Linearization Error When Modeling Fluid Pipeline Transients Using the Frequency Response Method

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    contributor authorPedro J. Lee
    contributor authorJohn P. Vítkovský
    date accessioned2017-05-08T21:50:52Z
    date available2017-05-08T21:50:52Z
    date copyrightOctober 2010
    date issued2010
    identifier other%28asce%29hy%2E1943-7900%2E0000269.pdf
    identifier urihttp://yetl.yabesh.ir/yetl/handle/yetl/64079
    description abstractThe unsteady mass and momentum equations for pipe flow can be solved in the frequency domain and provides additional insight into the behavior of fluid transients. Additionally, this approach has significant computational advantages compared to the method of characteristics because it is not based on a rigid time-space grid. Despite its advantages, the frequency domain approach must be used with care as it uses linearized forms of the steady friction and orifice equations—which can deviate significantly from the true nonlinear solution. The conditions in which the frequency response method can be accurately used are currently unknown. This paper investigates and quantifies the error in the frequency-domain method, via comparison to a highly discretized time-domain model that uses the method of characteristics, and describes situations where the frequency response method can be used with accurate results. A reservoir-pipe-valve system was used in this study with transients generated by perturbation of the valve. The error consists of errors from two sources: the linear approximations of the steady friction and the steady orifice equations. The frequency response method was shown to produce identical results to the method of characteristics when these two sources of error are minimized. The error in the frequency-domain model was quantified as functions of the perturbation magnitude, frequency, and system parameters. The results indicate that errors are significant when the perturbation size is more than 25% of the steady-state condition and this error is frequency dependent with the largest errors occurring at the harmonic peaks of the system.
    publisherAmerican Society of Civil Engineers
    titleQuantifying Linearization Error When Modeling Fluid Pipeline Transients Using the Frequency Response Method
    typeJournal Paper
    journal volume136
    journal issue10
    journal titleJournal of Hydraulic Engineering
    identifier doi10.1061/(ASCE)HY.1943-7900.0000246
    treeJournal of Hydraulic Engineering:;2010:;Volume ( 136 ):;issue: 010
    contenttypeFulltext
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