0
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

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

Ahmad Nourbakhsh

Professor
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.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

IEC, 1991, “Field Acceptance Tests to Determine the Hydraulic Performance of Hydraulic Turbines, Storage Pumps and Pump-Turbines,” 3rd ed., International Electrotechnical Commission, Geneva, Switzerland, Standard No. IEC 60041. https://www.saiglobal.com/pdftemp/previews/osh/iec/iec60000/60000/iec60041%7Bed3.0%7Den_d.img.pdf
IS, 1996, “Structural Design of Penstocks-Criteria—Part 3: Specials for Penstocks,” Bureau of Indian Standards code, New Delhi, India, Standard No. IS 11639-3. https://archive.org/details/gov.in.is.11639.3.1996
Adamkowski, A. , and Janicki, W. , 2008, “A New Approach to Using the Classic Gibson Method to Measure Discharge,” 15th International Seminar on Hydropower Plants, Vienna, Austria, pp. 511–522.
Jonsson, P. P. , Cervantes, M. J. , and Finnstrom, M. , 2007, “Numerical Investigation of the Gibson Method-Effects of Connecting Tubing,” Second IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Timisoara, Romania, Oct. 24–26, pp. 305–310. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.561.3565&rep=rep1&type=pdf
Jonsson, P. P. , Ramdal, J. , and Cervantes, M. J. , 2008, “Experimental Investigation of the Gibson's Method Outside Standards,” 24th IAHR Symposium on Hydraulic Machinery and Systems, Foz Do Iguassu, Brazil, Oct. 27–31, pp. 1–9. http://www.diva-portal.org/smash/record.jsf?pid=diva2%3A1000930&dswid=-6150
Adamkowski, A. , and Janicki, W. , 2009, “A Method for Measurement of Leakage Through Closed Turbine Wicket Gates,” HYDRO2009, International Conference and Exhibition, Lyon, France, Oct. 26–28, pp. 1–8.
Dahlhaug, O. G. , Nielsen, T. K. , Brandastro, B. , Franco, H. H. , Wiborg, E. J. , and Hulaas, H. , 2006, “Comparison Between Pressure-Time and Thermodynamic Efficiency Measurements on a Low Head Turbine,” Sixth IGHEM Symposium, Portland, OR, July 30–Aug. 1, pp. 1–8. http://ighem.org/Paper2006/d5.pdf
Castro, L. , Urquiza, G. , Adamkowski, A. , and Reggio, M. , 2011, “Experimental and Numerical Simulations Predictions Comparison of Power and Efficiency in Hydraulic Turbine,” Model. Simul. Eng., 2011, pp. 1–8. [CrossRef]
Bortoni, E. C. , and Santos, A. H. M. , 2004, “On the Leakage Flow Measurement in Gibson Method Applied for Hydropower Plant,” WSEAS International Conference, Miami, FL, Apr. 21–23. http://www.wseas.us/e-library/conferences/miami2004/papers/484-147.pdf
Adamkowski, A. , Krzemianowski, Z. , and Janicki, W. , 2009, “Improved Discharge Measurement Using the Pressure-Time Method in a Hydropower Plant Curved Penstock,” ASME J. Eng. Gas Turbines Power, 131(5), pp. 1–6. [CrossRef]
Adamkowski, A. , and Janicki, W. , 2010, “Selected Problems in Calculation Procedures for the Gibson Discharge Measurement Method,” IGHEM 2010, AHEC, IIT Roorkee, India, Oct. 21–23, pp. 73–80.
Ghidaoui, M. , Zhao, M. , Mclnnis, D. A. , and Axworthy, D. H. , 2005, “A Review of Water Hammer Theory and Practice,” ASME Appl. Mech. Rev., 58(1), pp. 49–76. [CrossRef]
Vardy, A. E. , and Hwang, K. L. , 1991, “A Characteristic Model of Transient Friction in Pipes,” J. Hydraul. Res., 29(5), pp. 669–685. [CrossRef]
Pezzinga, G. , 1999, “Quasi-2D Model for Unsteady Flow in Pipe Networks,” J. Hydraul. Eng., 125(7), pp. 676–685. [CrossRef]
Ghidaoui, M. S. , Mansour, G. S. , and Zhao, M. , 2002, “Applicability of Quasi-Steady and Axisymmetric Turbulence Models in Water Hammer,” J. Hydraul. Eng., 128(10), pp. 917–924. [CrossRef]
Zhao, M. , and Ghidaoui, M. S. , 2006, “Investigation of Turbulence Behavior in Pipe Transient Using a k-ε Model,” J. Hydraul. Res., 44(5), pp. 682–692. [CrossRef]
Raisi, A. , Nourbakhsh, A. , and Raisee, M. , 2009, “Unsteady Turbulent Pipe Flow Due to Water Hammer Using k-ω Turbulence Model,” J. Hydraul. Res., 47(4), pp. 429–437. [CrossRef]
Cebeci, T. , and Smith, A. M. O. , 1974, Analysis of Turbulent Boundary Layers, Academic Press, New York.
Kita, Y. , Adachi, Y. , and Hirose, K. , 1980, “Periodically Oscillating Turbulent Flow in a Pipe,” Bull. JSME, 23(179), pp. 656–664. [CrossRef]
Baldwin, B. S. , and Lomax, H. , 1978, “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” 16th Aerospace Sciences Meeting, Huntsville, AL, Jan. 16–18, pp. 1–8.
Fan, S. , Lakshminarayana, B. , and Barnett, M. , 1993, “Low-Reynolds-Number Model for Unsteady Turbulent Boundary-Layer Flows,” AIAA J., 31(10), pp. 1777–1784. [CrossRef]
Menter, F. R. , 1994, “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications,” AIAA J., 32(8), pp. 1598–1605. [CrossRef]
Saemi, S. , Raisee, M. , Cervantes, M. , and Nourbakhsh, A. , 2014, “Computation of Laminar and Turbulent Water Hammer Flows,” WCCM-ECCM-ECFD 2014 Congress: 11th World Congress on Computational Mechanics (WCCM XI) 5th European Conference on Computational Mechanics (ECCM V) 6th European Conference on Computational Fluid Dynamics (ECFD VI), Barcelona, Spain, July 20–25, pp. 5496–5507. http://congress.cimne.com/iacm-eccomas2014/admin/files/fileabstract/a1099.pdf
Jonsson, P. P. , Ramdal, J. , and Cervantes, M. J. , 2012, “Development of the Gibson Method-Unsteady Friction,” J. Flow Meas. Inst., 23, pp. 19–25. [CrossRef]
Saemi, S. D. , Cervantes, M. , Raisee, M. , and Nourbakhsh, A. , 2017, “Numerical Investigation of the Pressure-Time Method,” J. Flow Meas. Inst., 55, pp. 44–58. [CrossRef]
Shuy, E. B. , 1996, “Wall Shear Stress in Accelerating and Decelerating Turbulent Pipe Flows,” J. Hydraul. Res., 34(2), pp. 173–183. [CrossRef]
He, S. , and Jackson, J. D. , 2000, “A Study of Turbulence Under Conditions of Transient Flow in a Pipe,” J. Fluid Mech., 408, pp. 1–38. [CrossRef]
He, S. , Ariyaratne, C. , and Vardy, A. E. , 2008, “A Computational Study of Wall Friction and Turbulence Dynamics in Accelerating Pipe Flows,” Comput. Fluids, 37(6), pp. 674–689. [CrossRef]
Ariyaratne, C. , He, S. , and Vardy, A. E. , 2010, “Wall Friction and Turbulence Dynamics in Decelerating Pipe Flows,” J. Hydraul. Res., 48(6), pp. 810–821. [CrossRef]
Seddighi, M. , He, S. , Orlandi, P. , and Vardy, A. E. , 2011, “A Comparative Study of Turbulence in Ramp-Up and Ramp-down Unsteady Flows,” Flow Turbul. Combust., 86(3–4), pp. 439–454. [CrossRef]
Saka, H. , Ueda, Y. , Nishihara, K. , Ilegbusi, O. , and Iguchi, M. , 2015, “Transition Phenomena and Velocity Distribution in Constant-Deceleration Pipe Flow,” Exp. Ther. Fluid Sci., 62, pp. 175–182. [CrossRef]
Spencer, E. A. , Heitor, M. V. , and Castro, I. P. , 1995, “Intercomparison of Measurements and Computations of Flow Through a Contraction and a Diffuser,” J. Flow Meas. Inst., 6(1), pp. 3–14. [CrossRef]
Korteweg, D. J. , 1878, “Uber Die Fortpflanzungsgeschwindigkeit Des Schalles in Elastischen Rohren,” Ann. Phys. Chem., 241(12), pp. 525–542. [CrossRef]
Haaland, S. E. , 1983, “Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow,” ASME J. Fluids Eng., 105(1), pp. 89–90. [CrossRef]
Churchill, S. W. , 1977, “Friction-Factor Equation Spans All Fluid-Flow Regimes,” Chem. Eng., 84(24), pp. 91–92.
Jain, A. K. , 1976, “Accurate Explicit Equation for Friction Factor,” J. Hydraul. Div., 102(5), pp. 674–677. http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0025295
Zigrang, D. J. , and Sylvester, N. D. , 1982, “Explicit Approximations to the Solution of Colebrook's Friction Factor Equation,” AIChE J., 28(3), pp. 514–515. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 4

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

Grahic Jump Location
Fig. 5

The wall shear stress variation in time

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 9

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

Grahic Jump Location
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

Grahic Jump Location
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].

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
Fig. 14

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 16

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

Grahic Jump Location
Fig. 17

Appearance of a recirculation zone near the contraction inlet

Grahic Jump Location
Fig. 18

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

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In