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Research Papers

Transmission Line Modeling of Inclined Compressible Fluid Flows

[+] Author and Article Information
Ala E. Omrani

Department of Mechanical Engineering,
University of Houston,
4726 Calhoun Road,
N285 Engineering Building 1,
Houston, TX 77204
e-mail: aomrani@uh.edu

Matthew A. Franchek

Professor
Department of Mechanical Engineering,
University of Houston,
4726 Calhoun Road,
W214 Engineering Building 2,
Houston, TX 77204
e-mail: mfranchek@central.uh.edu

Karolos Grigoriadis

Professor
Department of Mechanical Engineering,
University of Houston,
4726 Calhoun Road,
W212 Engineering Building 2,
Houston, TX 77204
e-mail: karolos@uh.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 10, 2017; final manuscript received June 13, 2017; published online August 28, 2017. Assoc. Editor: Heikki Handroos.

J. Dyn. Sys., Meas., Control 140(1), 011001 (Aug 28, 2017) (12 pages) Paper No: DS-17-1078; doi: 10.1115/1.4037133 History: Received February 10, 2017; Revised June 13, 2017

Compressible fluid flow modeling for inclined lines is a challenging phenomenon due to the nonlinearity of the governing equations and the spatial–temporal dependency of the fluid density. In this paper, the transmission line analytical model is applied to the determination of inclined compressible fluid flow's dynamics. To establish this model, an exact transcendent solution is developed by solving the Navier–Stokes equation in the Laplace domain. A transfer function approximation, allowing the fluid flow transients determination, is recovered from the exact solution using residual calculations. The error resulting from the polynomial fraction approximation of the transfer functions is circumvented through frequency response corrections for the approximation to meet the exact function steady-state behavior. The effect of gravity and fluid compressibility on the fluid flow dynamics as well as the interplay between those two factors are illustrated through the pressure and flow rate's frequency and time responses.

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References

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Figures

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Fig. 1

Transmission line model architecture

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Fig. 3

Pipeline inclination effect on Qout(s) to Pout(s) and Qout(s) to Qin(s) transfer functions in Eq. (33)

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Fig. 4

Pipeline inclination effect on Pin(s) to Pout(s) and Pin(s) to Qin(s) transfer functions in Eq. (33)

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Fig. 5

Pipe inclination effect on TF11(s) and TF12(s) transfer functions, in Eq. (33), for a fluid density of 790 kg/m3

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Fig. 6

Fluid compressibility effect on TF21(s) and TF22(s) transfer functions in Eq. (33), for a pipeline inclination of 30 deg

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Fig. 7

Fluid compressibility effect on TF11(s) and TF12(s) transfer functions in Eq. (33), for a pipeline inclination of 30 deg

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Fig. 8

Precorrected inlet pressure to inlet flow rate transfer function

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Fig. 9

Corrected inlet pressure to inlet flow rate transfer function

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Fig. 10

Transfer functions polynomial approximation

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Fig. 11

Dynamic relative outlet flow rate time response for different pipeline inclinations

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Fig. 12

Dynamic inlet pressure time response for different pipeline inclinations

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Fig. 13

Effect of pipeline inclination on the system first mode damping ratio and resonant frequency

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