Acoustic Vibrations in Gas Pipelines

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Journal of Sound and Vibration (1995) 184(2), 343–368

HIGH AMPLITUDE VORTEX-INDUCED PULSATIONS IN A GAS TRANSPORT SYSTEM P. C. K, M. C. A. M. P, A. H  A. P. J. W Eindhoven University of Technology, W & S 1.53, P.O. Box 513, Eindhoven, The Netherlands

A. I, G. R  R. P University ‘La Sapienza’, Via Eudossiana 18, 00184 Rome, Italy

 J. C. B
TPD/TNO, P.O. Box 155, 2600 AD Delft, The Netherlands (Received 17 January 1994, and in final form 7 June 1994) High Reynolds number, low Mach number gas flows in pipe systems with closed side branches exhibit spectacular low frequency self-sustained pulsations driven by periodic vortex shedding at specific values of the Strouhal number. A detailed study is presented of the behaviour of the flow in a system with two opposite closed side branches of equal length in a cross configuration. For junctions with both sharp and rounded edges the acoustic flow velocity amplitude is comparable to the main flow velocity. A two-dimensional potential flow model based on the vortex blob method, used to simulate the flow in the junction, describes accurately the flow visualization and laser Doppler data obtained in pipes with square cross-sections and with sharp edged junctions. The numerical simulation is used to calculate the acoustical power generated by the vortical flow at a given amplitude of the acoustic velocity field and Strouhal number. In reality, for a pulsation with constant amplitude, this power is balanced by the viscothermal losses and acoustic radiation, which is the basis for the indirect measurement of the source power. It is shown that, for the acoustic amplitude observed, radiation losses due to the generation of non-resonating harmonics by wavesteepening has to be taken into account in the energy balance. This finding is confirmed by the appearance of shock waves in the geometry with rounded edges. 7 1995 Academic Press Limited

1. INTRODUCTION

The present research project was initiated by the occurrence of severe flow-induced pulsations in one of the compressor stations of the N.V. Nederlandse Gasunie, which operates the gas transport system of the Netherlands. Measurements by Gasunie demonstrated that pulsations occurred in the presence of closed side branches. In a previous study, Bruggerman et al. [1–4] identified the tandem-branch configuration shown in Figure 1, two closed side-branches of length L placed at a distance 2mL apart, with m an integer number, as a critical configuration in which acoustics velocity amplitudes uac could reach ˆ values comparable to the main flow velocity U0†. The particular case m = 0, which will † In practice uac is determined from the acoustic pressure amplitude pac measured at the end of a closed side ˆ ˆ branch by using the approximation uac = pac /r0 c0 , where r0 is the mean density and c0 is the speed of sound. ˆ ˆ

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0022–460X/95/270343 + 26 $12.00/0 7 1995 Academic Press Limited

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. .   .

Figure 1. The lowest excited acoustic modes for cross and tandem side branch geometry.

be referred to as the cross-junction geometry, has been studied experimentally by Chen [5] and Ziada and Buhlmann [6]. ¨ It has been demonstrated by Bruggeman [2] that a simplified (single vortex) model for the flow in the junction connecting the main pipe and the side branch can be used to predict the Strouhal conditions for acoustic resonance and the order of magnitude of the pulsation level. Furthermore, the theory was used to explain qualitatively the dramatic influence of the geometry of the junction’s edges on the pulsation level. This resulted in the design of very efficient spoilers which can be placed at the upstream edges of the junctions to reduce or prevent pulsations. Alternative geometries of spoilers have later been proposed by Jungowski et al. [7, 8]. In the present paper we focus on a more quantitative description of the flow in the junction using the two-dimensional...
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