Acoustic Resonance in a Reservoir-Pipeline-Orifice System

Abstract

The fundamentals of oscillating flow in a reservoir-pipe-orifice system are revisited in a theoretical study related to acoustic resonance experiments carried out in a large-scale pipeline. Four different types of system excitation are considered: forcing velocity, forcing pressure, linear oscillating resistance and nonlinear oscillating resistance. Analytical solutions are given for the periodic responses to the first three excitations. Analytical and numerical results for the large-scale pipeline are presented and some peculiarities are discussed.

Acoustic Resonance in a Reservoir-Double Pipe-Orifice System

“…As already seen in Ref. [1], there is no resonance − i.e. pressure variations at least twice "Joukowsky" − for the current valve setting, because it introduces a large amount of damping.…”

“…The single-pipe solutions in Ref. [1] are obtained by taking L 1 = 0. The lengths, cross-sectional areas, initial velocities, wave speeds and wave numbers are denoted by L, A, V 0 , c and κ, where the subscripts 1 and 2 indicate the upstream and downstream pipe, respectively.…”

“…The reservoir -two-pipe -orifice system is simulated with the following input data: pipe length L 2 = 50 m, wave speed c 2 = 1250 m/s, pipe flow area A 2 = 31416 mm 2 , orifice area A or,0 = 800 mm 2 , discharge coefficient C d = 0.6, orifice cover fraction α = 0.2, mass density ρ = 1000 kg/m 3 and friction factor λ f,2 = 0. These values correspond to an idealised laboratory system [1] with pipe inner diameter D 2 = 200 mm and wall thickness e 2 = 6 mm. The pipeline leading to the elevated reservoir is simulated with the following input data: pipe length L 1 = 30 m, wave speed c 1 = 1000 m/s, pipe flow area A 1 = 785398 mm 2 , reservoir pressure P res = 2.5 bar and friction factor λ f,1 = 0.…”

“…Figure 6 shows system responses for excitation frequencies of 1, 6 and 12 Hz. The dashed blue line is the single-pipe solution [1] and the continuous red line is the MOC transient double-pipe solution. Both solutions start from the constant steady state V 0 (x) = V 0 and 0 r e s ( ) P x P =…”

“…In a previous study [1] this system was analysed without taking into account the 30 m long pipe that connects the test pipeline to the elevated reservoir. This additional steel pipe has a diameter of 1 m, a wall thickness of 10 mm, and is lined with 1.5 mm thick synthetic material.…”