Acoustic Resonance in a Reservoir-Double Pipe-Orifice System

Abstract

Acoustic resonance in a two-pipe system is simulated with four different models for the periodic excitation. Analytical solutions are provided in full for the three linear excitations. Exact numerical results are presented for the nonlinear excitation. The influence of a large-diameter supply pipe (instead of a constant-head reservoir) on the system's fundamental frequencies and mode shapes is studied. The peculiar behaviour of wave reflection at an orifice is fully explained.

Improved One-Dimensional Models for Rapid Emptying and Filling of Pipelines

“…The water tower consists of a high tank and a vertical steel pipe below it. The tank has its free surface at an elevation of 24.25 m above the connection to the 0.2-m-diameter steel pipe and maintains a constant depth of 2 m. The vertical pipe is 22.25 m long and has a diameter of 1.0 m. The accelerations in this pipe are ignored in the simulations [17]. The inlet in the model is taken just upstream of valve V8 in Fig.…”

Acoustic Resonance Experiments in a Reservoir-Pipeline-Orifice System

“…The orifice is a horizontal slit of 100 mm width and 8 mm height. In preliminary tests and simulations [1,2] the orifice was covered between 0% and 20% by the rotating disc ( = 1/5) in order to minimise friction (and wear) while sliding in between its guiding steel plates. The outflow area varied between 800 mm 2 and 640 mm 2 .…”

“…The outflow area varied between 800 mm 2 and 640 mm 2 . In the final tests reported herein the orifice area varied in between 240 mm 2 = 21 Pa = 0.21 mbar, assuming that  = 0.02. This is very small compared to the steady pressure loss P 0 at the orifice.…”

“…The following input data are used in the numerical simulations (using conventional nomenclature [1,2] The material properties of water (at atmospheric pressure and 19 Celsius temperature) and steel are taken from handbooks. The length of the pipeline is rounded to 49 m, because it is not exactly clear where acoustic waves reflect at the upstream boundary.…”

“…The results of group C are presented and analysed herein with an emphasis on the resonance behaviour of the system. The theoretical considerations in the previous studies [1,2] are employed in the interpretation of the measurements.…”