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Research Papers: Techniques and Procedures

Propagation and Attenuation of Pressure Waves in Dispersed Two-Phase Flows

[+] Author and Article Information
Jaqueline Costa Martins

São Carlos School of Engineering,
University of São Paulo,
Avenida Trabalhador Sãocarlense, 400,
São Carlos, SP 13566-590, Brazil
e-mail: jaquelinebft@yahoo.com.br

Paulo Seleghim, Jr.

São Carlos School of Engineering,
University of São Paulo,
Avenida Trabalhador Sãocarlense, 400,
São Carlos, SP 13566-590, Brazil
e-mail: seleghim@sc.usp.br

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 8, 2015; final manuscript received July 21, 2016; published online October 18, 2016. Assoc. Editor: Mark R. Duignan.

J. Fluids Eng 139(1), 011304 (Oct 18, 2016) (13 pages) Paper No: FE-15-1906; doi: 10.1115/1.4034370 History: Received December 08, 2015; Revised July 21, 2016

The propagation and attenuation of pressure waves in highly dispersed gas–liquid flows are investigated in this work, and an indirect measurement method is proposed to assess the attenuation coefficient in short pipelines. Additionally, a mechanistic acoustic energy dissipation model is derived from the oscillatory solutions of one-dimensional (1D) nondimensionalized mass and momentum equations to facilitate the interpretation of the results. Tests were performed on a 1500 m long, 50 mm internal diameter pipeline in which pressure disturbances were induced by suddenly opening leak valves. The results are consistent and in good agreement with the proposed attenuation model (±10% for 103 < Re < 104), therefore validating the proposed model and indirect measurement method.

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Figures

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Fig. 1

Schematic representation of the structure of a pressure signal sensed by a pressure probe placed at a distance ℓ from the inlet, in response to a pressure disturbance caused by opening a leak valve (negative pressure wave)

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Fig. 2

Schematic representation of the multiphase flow (air–oil–water) test loop (positions of the pressure sensors (◇) and leakage valves (▪) are relative to the input pressure sensor indicated by    Ⓐ )

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Fig. 3

Typical input (continuous) and output (dotted) flow rates and pressure signals, respectively, measured by the electromagnetic flow meters and pressure sensor, corresponding to the automated test procedure

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Fig. 4

Visual assessment of the arrival times and disturbance amplitudes sensed by pressure sensors installed along the pipeline at known positions

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Fig. 5

Evolution of the acoustic propagation speed, void fraction, and inlet flow pressure for all the tested flow rates

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Fig. 6

Direct attenuation coefficients (λdir) assessed from pressures waves sensed by each one of the ten sensors in the pipe loop, for disturbances generated by opening one leakage valve at a time for all the tested flow rates: (a) 154.5 l/min, (b) 143.9 l/min, (c) 127.6 l/min, (d) 111.4 l/min, (e) 94.6 l/min, (f) 77.5 l/min, (g) 33.8 l/min, and (h) 14.9 l/min

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Fig. 7

Examples of the temporal damping coefficient of the multiple echo signals measured by pressure sensors 4 and 6, respectively, up and downstream of leak valve 10 which was opened to generate the acoustic disturbance

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Fig. 8

Acoustic attenuation coefficients assessed via three different approaches: directly measured (▪), indirectly measured (▲), and theoretically from Eq. (21) (continuous curve)

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Fig. 9

Schematic representation sequential calculations leading to the theoretical attenuation coefficient

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Fig. 10

Probability distributions of the theoretical attenuation coefficient: (a) Re = 6.95 × 103, (b) Re = 1.58 × 104, (c) Re = 3.61 × 104, (d) Re = 4.41 × 104, (e) Re = 5.19 × 104, (f) Re = 5.95 × 104, (g) Re = 6.71 × 104, and (h) Re = 7.20 × 104

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