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Research Papers: Fundamental Issues and Canonical Flows

Alternative Approach for Modeling Transients in Smooth Pipe With Low Turbulent Flow

[+] Author and Article Information
David A. Hullender

Department of Mechanical and
Aerospace Engineering,
The University of Texas at Arlington,
P.O. Box 19023,
Arlington, TX 76019
e-mail: hullender@uta.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received February 24, 2016; final manuscript received July 6, 2016; published online August 19, 2016. Assoc. Editor: Alfredo Soldati.

J. Fluids Eng 138(12), 121202 (Aug 19, 2016) (10 pages) Paper No: FE-16-1120; doi: 10.1115/1.4034097 History: Received February 24, 2016; Revised July 06, 2016

A new simplified approach for modeling and simulating pressure transients resulting from the rapid acceleration or deceleration of turbulent flow in smooth-walled fluid lines is introduced. In contrast to previous approaches for modeling turbulence by modifying the head loss terms in the momentum partial differential equation, this approach is achieved by coupling the frequency domain analytical solution to the laminar flow version of the partial differential equations in series with a lumped resistance that has been sized so that the steady flow resistance for the line is equivalent to an empirical turbulent steady flow resistance. The model provides normalized pressure and flow transients that have good agreement with experimental data and with method-of-characteristics (MOC) solutions associated with previously validated turbulence models. The motivation for this research is based on the need for a practical means to simulate the effects of fluid transients in lines that are internal components within a total engineering system without the need to understand the different unsteady turbulence one- and two-dimensional (1D/2D) friction models and also be proficient with the complexities of nonlinear interaction of friction and interpolation errors encountered using MOC. This modeling approach utilizes a preprogramed inverse frequency algorithm, commonly used for system identification, which generates “equivalent” high-order normalized linear ordinary differential equations that can be coupled with models for other fluid power components and easily solved in the time domain using preprogramed numerical algorithms for ordinary differential equations.

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Figures

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Fig. 1

Schematic of a fluid transmission line with the input and output variables

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Fig. 2

(a) Demonstration of magnitude frequency response curve fit accuracy out to a normalized frequency of only 2000 and (b) demonstration of phase frequency response curve fit accuracy out to a normalized frequency of only 2000

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Fig. 3

Comparing a low-order inverse frequency model with experimental data [48] for laminar pretransient flow. DC gain = 1.0265 and valve closure time = 0.003 s.

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Fig. 4

(a) Demonstration of magnitude frequency response curve fit accuracy out to a normalized frequency of 30,000 and (b) demonstration of phase frequency response curve fit accuracy out to a normalized frequency of 30,000

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Fig. 5

Comparing the 28th order inverse frequency model with experimental data [48] for laminar pretransient flow. DC gain = 1.005 and valve closure time = 0.003 s.

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Fig. 6

Adding a lumped resistance RT to the end of a hypothetical line with pretransient laminar flow

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Fig. 7

Line of length L with a lumped resistance RT/n at the end of each line segment of length L/n

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Fig. 8

Comparing the response of the inverse frequency model with the MOC response of the Brunone et al. model [103,104] with k = 0.0209 and the Bergant et al. [49] experimental data for a copper pipe of length 37.23 m and pretransient Reynolds number of 5600. The DC gain of the inverse frequency model is 1.04, the order of the transfer function is 19, and the valve closing simulation time is 0.008 s. (Reproduced with permission from Bergant et al. [49]. Copyright 2001 by ASCE.)

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Fig. 9

Comparing the response of the inverse frequency model with the MOC response of the Brunone et al. model [103,104] using k = 0.0141 and Adamkowski et al. [48] experimental data for a copper pipe of length 98.11 m and pretransient Reynolds number of 15,800. The DC gain of the inverse frequency model is 1.0078, the transfer function is 19th order, and the valveclosing simulation time is 0.03 s. (Reproduced with permission from Adamkowski and Lewandowski [48]. Copyright 2006 by ASME.)

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Fig. 10

Comparing the response of the inverse frequency model with the MOC response of the Vardy and Brown model [35] and the Szymkiewicz and Mitosek [89] experimental data for steel pipe of length 177.4 m and pretransient Reynolds number of 8984. The DC gain of the 24th order inverse frequency transfer function is 1.0036; the simulation valve closing time was 0.05 s. (Reproduced with permission from Szymkiewicz and Mitosek [89]. Copyright 2014 by ASME.)

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Fig. 11

Comparing the response of the inverse frequency model with the MOC response of the Vardy and Brown model [35] and the Szymkiewicz and Mitosek [89] experimental data for steel pipe of length 72 m and pretransient Reynolds number of 14,989. The DC gain of the 23rd order inverse frequency transfer function is 1.001; the simulation valve closing time is 0.05 s. (Reproduced with permission from Szymkiewicz and Mitosek [89]. Copyright 2014 by ASME.)

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