Research Papers: Techniques and Procedures

Numerical Investigation of the Pressure-Time Method Considering Pipe With Variable Cross Section

[+] Author and Article Information
Simindokht Saemi

School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 1439955961, Iran;
Division of Fluid and Experimental Mechanics,
Lulea University of Technology,
Lulea SE 971 87, Sweden
e-mail: si.saemi@ut.ac.ir

Mehrdad Raisee

Associate Professor
Hydraulic Machinery Research Institute,
School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 1439955961, Iran
e-mail: mraisee@ut.ac.ir

Michel J. Cervantes

Division of Fluid and
Experimental Mechanics,
Lulea University of Technology,
Lulea SE 971 87, Sweden
e-mail: Michel.Cervantes@ltu.se

Ahmad Nourbakhsh

Hydraulic Machinery Research Institute,
School of Mechanical Engineering,
College of Engineering,
University of Tehran,
Tehran 1439955961, Iran
e-mail: anour@ut.ac.ir

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 26, 2018; final manuscript received June 26, 2018; published online August 6, 2018. Assoc. Editor: Ioannis K. Nikolos.

J. Fluids Eng 140(10), 101401 (Aug 06, 2018) (15 pages) Paper No: FE-17-1320; doi: 10.1115/1.4040718 History: Received April 26, 2018; Revised June 26, 2018

A common method to calculate the flow rate and consequently hydraulic efficiency in hydropower plants is the pressure-time method. In the present work, the pressure-time method is studied numerically by three-dimensional (3D) simulations and considering the change in the pipe cross section (a contraction). Four different contraction angles are selected for the investigations. The unsteady Reynolds-averaged Navier–Stokes (URANS) equations and the low-Reynolds k–ω shear stress transport (SST) turbulence model are used to simulate the turbulent flow. The flow physics in the presence of the contraction, and during the deceleration period, is studied. The flow rate is calculated considering all the losses: wall shear stress, normal stresses, and also flux of momentum in the flow. The importance of each term is evaluated showing that the flux of momentum plays a most important role in the flow rate estimation while the viscous losses term is the second important factor. To extend the viscous losses calculations applicability to real systems, the quasi-steady friction approach is employed. The results showed that considering all the losses, the increase in the contraction angle does not influence the calculated errors significantly. However, the use of the quasi-steady friction factor introduces a larger error, and the results are reliable approximately up to a contraction angle of ϴ = 10 deg. The reason imparts to the formation of a local recirculation zone upstream and inside the contraction, which appears earlier as the contraction angle increases. This feature cannot be captured by the quasi-steady friction models, which are derived based on the fully developed flow assumption.

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Fig. 1

Schematic of the experimental test rig employed in Refs. [5] and [24]

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Fig. 2

Schematic of the experimental test rig employed in Ref.[32]

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Fig. 3

Pipe geometry: (a) schematic of the pipe with contraction, (b) pipe cross section grid, and (c) part of the pipe geometry close to the gate valve

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Fig. 4

Valve closure obtained from the experiments and used for the first part of the simulations

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Fig. 5

The wall shear stress variation in time

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Fig. 6

The pressure difference variation with time between two cross section z = 27.3 m and z = 36.3 m

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Fig. 7

The wall shear stress variation time averaged between the measuring cross section

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Fig. 8

Streamlines of the flow inside the pipe after the valve closure, z = 0 m corresponds to the pipe inlet and z = 40 m to the gate position: (a) streamlines at 16 < z < 40 m and (b) zoomed streamlines at 38 < z < 40 m

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Fig. 9

The pressure contours and velocity vectors in various cross section close to the valve

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Fig. 10

The axial velocity profile at several cross section close to the valve at (a) t = 3.9 s and (b) t = 4.4 s

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Fig. 11

Velocity profiles (left column) and turbulent kinetic energy (right column) at three sections: zA = 5.08, zB = 5.393, and zC = 5.843 m. The experimental results are obtained from Ref. [32].

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Fig. 12

Pressure difference variation between cross sections, Δz = 27.3–30.3 m, Δz = 30.3–33.3 m and Δz = 33.3–36.3 m considering cases 1 and 2

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Fig. 13

Averaged axial wall shear stress variation between the cross sections at z = 27.3–30.3 m, 30.3–33.3 m, and 33.3–36.3 m considering cases 1 and 2

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Fig. 14

Velocity profiles for cases 1 and 2 at different times at sections z = 27.3 m and 36.3 m

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Fig. 15

The turbulent shear stress profiles in two cases and different times considering the sections at z = 27.3 m and 36.3 m

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Fig. 16

Variation of the terms in Eq. (5) with time: the terms ΔB, ΔC, and ΔD are explained in Sec. 2.4

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Fig. 17

Appearance of a recirculation zone near the contraction inlet

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Fig. 18

Control volume used to derive the relation to calculate the flow rate



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