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Research Papers: Fundamental Issues and Canonical Flows

Use of Pipeline Wave Propagation Model for Measuring Unsteady Flow Rate

[+] Author and Article Information
Nigel Johnston, Min Pan, Sylwester Kudzma, Pengfei Wang

Department of Mechanical Engineering,
University of Bath,
Bath BA2 7AY, UK

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 25, 2013; final manuscript received November 20, 2013; published online January 24, 2014. Assoc. Editor: Michael G. Olsen.

J. Fluids Eng 136(3), 031203 (Jan 24, 2014) (8 pages) Paper No: FE-13-1052; doi: 10.1115/1.4026106 History: Received January 25, 2013; Revised November 20, 2013

A novel method for estimation of unsteady flow rate using pressure at two or three points along a pipeline is described in this paper. The pressure data are processed using a wave propagation model to determine the unsteady flow. The comparison and analysis of two-transducer and three-transducer techniques are investigated through simulation. The proposed method is shown to be effective for unsteady flow rate measurement over a high bandwidth. However, if the pressure values from two transducers are used, inaccuracies exist at certain frequencies when the transducer spacing coincides with multiples of half a wavelength. The accuracy can be improved by adding a third transducer with unequal spacing. The three-transducer method has been implemented in experiments and has been found to be robust and reliable.

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References

Figures

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Fig. 1

Characteristics line of pipe [8]

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Fig. 2

System schematic of two-transducer technique

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Fig. 3

Errors in estimated flow ripple at transducers 1 and 2 with a 1% error in calibration factor for transducer 2

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Fig. 4

Errors at transducers 1 and 2 with a 1% error in speed of sound

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Fig. 5

System schematic for three-transducer technique

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Fig. 6

Errors at transducer 2 by using different transducer pairs (MOC estimator) with a 1% error in calibration factor for transducer 2

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Fig. 7

Errors at transducer 2 by using different transducer pairs (MOC estimator) with a 1% error in speed of sound

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Fig. 8

Coupling of MOC estimators

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Fig. 9

Errors using a three-transducer technique with a 1% error in calibration of transducer 2: (a) errors at transducers 1 and 3, and (b) errors at transducer 2

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Fig. 10

Errors using a three-transducer technique with a 1% error in speed of sound: (a) errors at transducers 1 and 3, and (b) errors at transducer 2

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Fig. 11

Schematic of the test rig

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Fig. 12

Experimental and simulated pressures (simulated results were obtained using measured downstream boundary condition): (a) transducer 1 (upstream), (b) transducer 2 (midstream), and (c) transducer 3 (downstream) measured pressure

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Fig. 13

Unsteady flow rates (estimated results used three transducer MOC estimator technique; simulated results were obtained using measured downstream boundary condition): (a) transducer 1 (upstream), (b) transducer 2 (midstream), and (c) transducer 3 (downstream)

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Fig. 14

Estimated unsteady flow rate at transducer 2 by using the two-transducer method with the transducer pair 1 and 2, compared with the three-transducer method

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Fig. 15

Estimated unsteady flow rate at transducer 2 by using the two-transducer method with the transducer pair 2 and 3, compared with the three-transducer method

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