Analysis of water hammer attenuation in the Brunone model of unsteady friction
Authors:
E. Yao, G. Kember and D. Hansen
Journal:
Quart. Appl. Math. 72 (2014), 281-290
MSC (2010):
Primary 74G10, 93C70
DOI:
https://doi.org/10.1090/S0033-569X-2014-01354-6
Published electronically:
February 10, 2014
MathSciNet review:
3186237
Full-text PDF Free Access
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Abstract: A multiple-scales asymptotic analysis is used to describe the attenuation of a water hammer pressure wave in the Brunone model of unsteady friction. The method is applied to water hammer caused by sudden valve closure in water reservoir pipelines. The analytical results explain the parametric dependence of the Brunone unsteady friction pressure-wave attenuation. It is also found that viscous head in an extended steady friction model may provide an alternative to the unsteady friction basis for increased attenuation in cases where the attenuation has a weak spatial dependence and is primarily time-dependent. All results are numerically verified using the method of characteristics.
References
- A. Bergant, A. R. Simpson, and J. Vitkovsky, Review of unsteady friction models in transient pipe flow, The Work Group On The Behaviour Of Hydraulic Machinery Under Steady Oscillatory Conditions, 1999, 12pp.
- A. Bergant and A. S. Tijsseling, Parameters affecting water-hammer wave attenuation, shape and timing, Proceedings of the 10th International Meeting of the IAHR Work Group on the Behaviour of Hydraulic Machinery under Steady Oscillatory Conditions, 2001, Paper C2, 12pp.
- A. Bergant, A. S. Tijsseling, J. P. Vitkovsky, D. I. C. Covas, A. R. Simpson, and M. F. Lambert, Parameters affecting water-hammer wave attenuation, shape, and timing part ii: Case studies, IAHR J. of Hydraulic Research 46(3) (2008), 382–391.
- A. Bergant, J. Vitkovsky, A. R. Simpson, and M. Lambert, Performance of instantaneous acceleration models of unsteady skin friction in practical applications, 3rd Unsteady Friction Group Meeting, University of Dundee, 2002, 14pp.
- B. Brunone and U. M. Golia, Improvements in modelling of water hammer and cavitating flow - experimental verification, Proc. of the XXII Italian Conference on Hydraulics and Hydraulic Constructions, 1990, pp. 147–160.
- ---, Some considerations on velocity profiles in unsteady pipe flows, Proc. of the Int. Conf. on Entropy and Energy Dissipation in Water Resources, 1991, pp. 481–487.
- B. Brunone, U. M. Golia, and M. Greco, Some remarks on the momentum equations for fast transients, Hydraulic Transients with Column Separation (9th and Last Round Table of the IAHR Group), IAHR, 1995, pp. 201–209.
- Vardy A. E. and Brown J. M. B., Transient, turbulent, smooth pipe flow, Proc. Int. Conf. on Pressure Surges and Fluid Transients, BHR Group, 1996, pp. 289–311.
- M. Greco, Recent findings on column separation during water hammer, G.N.I. Edizioni Libreria Progetto, 1990, pp. 261–272.
- S. Y. Han, D. Hansen, and G. Kember, Multiple scales analysis of water hammer attenuation, Quart. Appl. Math. 69 (2011), no. 4, 677–690. MR 2893995, DOI https://doi.org/10.1090/S0033-569X-2011-01258-9
- Golia U. M., On the evaluation of the friction term in water hammer, Dept. of Hydraulics, Univ. of Napoli ‘Frederico II’, 1990, Rep. 639.
- J. P. Vitkovsky and A. R. Simpson, A critique of the Brunone et al. unsteady state friction method, Tech. report, Hydraulics Technical Memorandum No. 90/1, Dept. of Civil and Envir. Engrg., University of Adelaide, 1998.
- E. B. Wylie and V. L. Streeter, Fluid transients in systems, Prentice-Hall, Englewood Cliffs, NJ, 1993.
- E. Yao, G. C. Kember, and D. H. Hansen, Analysis of water hammer attenuation in sudden valve closure applications, J. Engng. Mech. (submitted).
References
- A. Bergant, A. R. Simpson, and J. Vitkovsky, Review of unsteady friction models in transient pipe flow, The Work Group On The Behaviour Of Hydraulic Machinery Under Steady Oscillatory Conditions, 1999, 12pp.
- A. Bergant and A. S. Tijsseling, Parameters affecting water-hammer wave attenuation, shape and timing, Proceedings of the 10th International Meeting of the IAHR Work Group on the Behaviour of Hydraulic Machinery under Steady Oscillatory Conditions, 2001, Paper C2, 12pp.
- A. Bergant, A. S. Tijsseling, J. P. Vitkovsky, D. I. C. Covas, A. R. Simpson, and M. F. Lambert, Parameters affecting water-hammer wave attenuation, shape, and timing part ii: Case studies, IAHR J. of Hydraulic Research 46(3) (2008), 382–391.
- A. Bergant, J. Vitkovsky, A. R. Simpson, and M. Lambert, Performance of instantaneous acceleration models of unsteady skin friction in practical applications, 3rd Unsteady Friction Group Meeting, University of Dundee, 2002, 14pp.
- B. Brunone and U. M. Golia, Improvements in modelling of water hammer and cavitating flow - experimental verification, Proc. of the XXII Italian Conference on Hydraulics and Hydraulic Constructions, 1990, pp. 147–160.
- ---, Some considerations on velocity profiles in unsteady pipe flows, Proc. of the Int. Conf. on Entropy and Energy Dissipation in Water Resources, 1991, pp. 481–487.
- B. Brunone, U. M. Golia, and M. Greco, Some remarks on the momentum equations for fast transients, Hydraulic Transients with Column Separation (9th and Last Round Table of the IAHR Group), IAHR, 1995, pp. 201–209.
- Vardy A. E. and Brown J. M. B., Transient, turbulent, smooth pipe flow, Proc. Int. Conf. on Pressure Surges and Fluid Transients, BHR Group, 1996, pp. 289–311.
- M. Greco, Recent findings on column separation during water hammer, G.N.I. Edizioni Libreria Progetto, 1990, pp. 261–272.
- S. Y. Han, D. Hansen, and G. Kember, Multiple scales analysis of water hammer attenuation, Quart. Appl. Math. 69 (2011), no. 4, 677–690. MR 2893995 (2012j:76072), DOI https://doi.org/10.1090/S0033-569X-2011-01258-9
- Golia U. M., On the evaluation of the friction term in water hammer, Dept. of Hydraulics, Univ. of Napoli ‘Frederico II’, 1990, Rep. 639.
- J. P. Vitkovsky and A. R. Simpson, A critique of the Brunone et al. unsteady state friction method, Tech. report, Hydraulics Technical Memorandum No. 90/1, Dept. of Civil and Envir. Engrg., University of Adelaide, 1998.
- E. B. Wylie and V. L. Streeter, Fluid transients in systems, Prentice-Hall, Englewood Cliffs, NJ, 1993.
- E. Yao, G. C. Kember, and D. H. Hansen, Analysis of water hammer attenuation in sudden valve closure applications, J. Engng. Mech. (submitted).
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Additional Information
E. Yao
Affiliation:
Department of Engineering Mathematics, Dalhousie University, 1340 Barrington St., Halifax, NS, Canada, B3J 1B7
Email:
Edward.Yao@dal.ca
G. Kember
Affiliation:
Department of Engineering Mathematics, Dalhousie University, 1340 Barrington St., Halifax, NS, Canada, B3J 1B7
Email:
Guy.Kember@dal.ca
D. Hansen
Affiliation:
Department of Civil and Resource Engineering, Dalhousie University, 1360 Barrington St., Halifax, NS, Canada, B3H 4R2
Email:
David.Hansen@dal.ca
Received by editor(s):
June 18, 2012
Published electronically:
February 10, 2014
Article copyright:
© Copyright 2014
Brown University
The copyright for this article reverts to public domain 28 years after publication.
