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TECHNICAL PAPERS

A Universal, Nonintrusive Method for Correcting the Reading of a Flow Meter in Pipe Flow Disturbed by Installation Effects

[+] Author and Article Information
C. Wildemann, W. Merzkirch

Lehrstuhl für Strömungslehre, Universität Essen, D-45117 Essen, Germany

K. Gersten

Institut für Thermo- und Fluiddynamik, Ruhr-Universität Bochum, D-44780 Bochum, Germany

J. Fluids Eng 124(3), 650-656 (Aug 19, 2002) (7 pages) doi:10.1115/1.1478065 History: Received June 29, 2001; Revised February 28, 2002; Online August 19, 2002
Copyright © 2002 by ASME
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References

Figures

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Comparison of measured error shift, ΔCD exp, and error shift predicted by the artificial neural network, ΔCD ANN, for the gate (installation shown in Fig. 4). No data measured with this installation were used for the training of the ANN.
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Probability density functions (PDF) as defined and shown in Fig. 9 for different numbers of measuring positions used in determining the distributions Tax(θ) and Ttan(θ)
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(a) Pair of two counter-rotating vortices (“secondary flow”) as caused by a 90 deg single bend and definition of the azimuthal angle with respect to the orientation of the bend. (b) Principal distribution of the tangential component of the wall shear stress downstream of the 2.9 deg out-of-plane bend: (1) contribution of swirl, (2) contribution of superimposed pair of counter-rotating vortices.
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Azimuthal distribution of wall shear stress downstream of the 90 deg single bend: Coordinate of the axial component, τax, is on the left, coordinate of the tangential component, τtan, on the right. Pipe Reynolds number ReD=2.2⋅105. The values of τax and τtan(=0) for fully developed flow are indicated. (a) Axial distance from bend x/D=3, Fourier decomposition of τax and τtan is included. List of Fourier coefficients: a0tan=−0.0206,a0ax=0.319,a1tan=−0.199,a1ax=0.0128,b1tan=−0.0080,b1ax=0.112,a2tan=−0.0051,a2ax=0.0517,b2tan=0.0781,b2ax=−0.0003. (b) x/D=41.
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Azimuthal distribution of wall shear stress downstream of the 2⋅90 deg out-of-plane double bend: The value of τax for fully developed flow is indicated. (a) x/D=3,ReD=2.2⋅105. Fourier decomposition of τax and τtan is included. List of Fourier coefficients: a0tan=−0.246,a0ax=0.122,a1tan=0.0654,a1ax=0.0838,b1tan=0.0974,b1ax=−0.157,a2tan=−0.0553,a2ax=0.0021,b2tan=−0.0145,b2ax=0.0413. (b) x/D=41,ReD=2.0⋅105.
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Circular flat plate (gate valve) inserted from above into the pipe of diameter D as an installation
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Error shift ΔCD measured for the venturi meter downstream of the 90 deg out-of-plane double bend (above) and the 90 deg single bend (below) as function of the axial distance x/D between installation and meter (horizontal scale)
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Error shift ΔCD measured for the β=0.65 orifice meter downstream of the 90 deg out-of-plane double bend (above) and the 90 deg single bend (below) as function of the axial distance x/D between installation and meter (horizontal scale)
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Fourier coefficients a0,c1=√(a12+b12) determined at various distances (horizontal scale) downstream of the 2⋅90 deg out-of-plane double bend and 90 deg single bend; pipe Reynolds number ReD=1⋅105
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Comparison of measured error shift, ΔCD exp, and error shift predicted by the artificial neural network, ΔCD ANN, for the venturi meter. The data that were used for the training of the ANN is marked as full squares.
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Probability density function (PDF) of the scatter of the data shown in Fig. 7
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Comparison of measured error shift, ΔCD exp, and error shift predicted by the artificial neural network, ΔCD ANN, for the β=0.8 orifice meter. The data that were used for the training of the ANN is marked as full squares.
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Comparison of measured error shift, ΔCD exp, and error shift predicted by the artificial neural network, ΔCD ANN, for the β=0.65 orifice meter. The data that were used for the training of the ANN is marked as full squares.

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