Frequency domain modelling of pipe transient flow with the virtual valves method to reduce linearization errors. (15th September 2019)

• Record Type: Journal Article
• Authors: Ranginkaman, Mohammad Hadi; Haghighi, Ali; Lee, Pedro Jose
• Is Part Of: Mechanical systems and signal processing. Volume 131(2019)
• Page Start: 486
• Page End: 504
• Publication Date: 2019-09-15
• Subjects: Transient flow -- Frequency Response Method -- Linearization error -- Virtual valves; Structural dynamics -- Periodicals; Vibration -- Periodicals; Constructions -- Dynamique -- Périodiques; Vibration -- Périodiques; Structural dynamics; Vibration; Periodicals; 621
• DOI: 10.1016/j.ymssp.2019.05.065
• Languages: English
• ISSNs: 0888-3270

Abstract

Highlights: Reviewing the accuracy of the standard Frequency Response Method (FRM). Introducing the modified-FRM by defining the valve correction factors. Introducing the Virtual Valve Method to capture the response at the higher-order frequencies. Applying the developed approaches to a series of theoretical examples. Abstract: For Modeling the transient flow in a pipeline by Frequency Response Method (FRM), the nonlinear terms of the governing equations and boundary conditions should be linearized. Significant nonlinearities are associated with the steady friction and valve equations. This study reviews the FRM and its range of validity in accordance with the linearization errors and, proposes some remedies to reduce the errors. To improve the FRM accuracy, the linearization of valve equation is modified and a new frequency-dependent correction factor is introduced. Also, to capture the system responses at the higher-order frequencies due to the nonlinear terms, the method of virtual valves is introduced. Through this method, the system's real nonlinear valve oscillating at a main frequency ω is represented by a number of linear virtual valves oscillating at the main and some higher-order frequencies 2 ω, 3 ω, ⋯ that may appear in the system's response spectra due to the nonlinearity of valve equation. The modified FRM (M-FRM) is compared with the standard FRM (S-FRM) as well as the Method of Characteristics (MOC) on the energy phase diagram. The results demonstrate that the modifications dramatically improve the validity of the FRM even for large sizes of valve perturbation. The generality of the method is also validated by solving several pipe-reservoir-valve systems with different specifications.