Revisiting frequency domain analysis method for water hammer effects on pipeline systems
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(2020) 42:599
TECHNICAL PAPER
Revisiting frequency domain analysis method for water hammer effects on pipeline systems Lazhar Ayed1 · Zahreddine Hafsi1 Received: 26 August 2020 / Accepted: 17 October 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract This paper revisits frequency domain analysis method for water hammer study in a hydraulic system. Detailed investigation of the effect of the flow parameters is conducted. Weaknesses on previous research works were pointed out. A brief presentation of the frequency response function determined from motions equations of transient water flow is firstly presented. A special emphasis was devoted to the effect of frictional flow on resonance pulsations. It was obtained that, unlike previous findings, resonance frequencies in a frictional flow are decayed from odd harmonics. This decay is more or less significant depending on the friction coefficient. The observations related to various effects are also illustrated through a set of test cases that were numerically analyzed. Additionally relative uncertainties highlighting the frictional flow effect on the accuracy of resonant pulsations detection are evaluated. Keywords Water hammer · Impedance method · Resonance pulsations · Spectrum
1 Introduction Transient water flow in pipelines leading to the so-called water hammer phenomenon is governed by continuity and momentum equations. These partial differential equations were solved in time domain using different methods, viz. the method of characteristics [1, 2], the finite element method [3] and the finite volume method [1, 4, 5]. Furthermore, solving water hammer equations in frequency domain arises as an alternative approach for predicting the pressure evolution in a given section of the pipe. The impedance method [6, 7] and the transfer matrix method [8, 9] are based on linearized forms of the equations of motion in the frequency domain. Mpesha et al. [10] utilized the fast Fourier transform (FFT) for the transposition of the time solutions of the motion equations into the frequency domain to analyze and predict the evolution of the water hammer wave as a function of the frequency. Technical Editor: Daniel Onofre de Almeida Cruz. * Lazhar Ayed [email protected] 1
Laboratory of Applied Fluids Mechanics Process and Environment Engineering, University of Sfax, National Engineering School of Sfax, 3038 Sfax, Tunisia
Classical dynamic analysis of hydraulic systems is performed using the transient response of the system by analyzing the fluctuation of the pressure head at a measurement point after the occurrence of a transient event. This analysis depends on the type of the input signal. For different types of input events, different transient responses over time will result although the state of the system itself has remained unchanged. A more concise definition of the state of a hydraulic system can be determined by extracting the system’s response function. To this end, for frequency response analysis, the partial differential equ
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