Analytical expressions for effective weighting functions used during simulations of water hammer

Urbanowicz, K.

doi:10.15632/jtam-pl.55.3.1029

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Tytuł artykułu

Analytical expressions for effective weighting functions used during simulations of water hammer

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Urbanowicz K.

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DOI

10.15632/jtam-pl.55.3.1029

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Abstrakty

For some time, work has been underway aimed at significant simplification of the modelling of hydraulic resistance occurring in the water hammer while maintaining an acceptable error. This type of resistance is modelled using a convolution integral, among others, from local acceleration of a liquid and a certain weighting function. The recently completed work shows that during efficient calculations of the convolution integral, the effective weighting function used does not have to be characterised by large convergence with a classical function (according to Zielke during laminar flow and to Vardy-Brown during turbulent flow). However, it must be a sum of at least two or three exponential expressions so that the final results of the simulation could be considered as satisfactory. In this work, it has been decided to present certain analytical formulas using which it will be possible to determine the coefficients of simplified effective weighting functions in a simple direct way.

Słowa kluczowe

unsteady flow water hammer convolution integral frequency-dependent friction

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2017

Tom

Vol. 55 nr 3

Strony

1029--1040

Opis fizyczny

Bibliogr. 39 poz., rys., tab.

Twórcy

autor

Urbanowicz K.

kamil.urbanowicz@zut.edu.pl

West Pomeranian University of Technology, Szczecin, Poland

Bibliografia

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5. Brunone B., Golia U.M., Greco M., 1991, Some remarks on the momentum equations for fast transients, Proceedings of International Meeting on Hydraulic Transients with Column Separation, 9th Round Table, IAHR, Valencia, Spain, 201-209
6. Dailey J.W., Hankey W.L., Olive R.W., Jordaan J.M., 1956, Resistance coefficient for accelerated and decelerated flows through smooth tubes and orifices, Journal of Basic Engineering, ASME, 78, 1071-1077
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9. Karadzić U., Bulatović V., Bergant A., 2014, Valve-induced water hammer and column separation in a pipeline apparatus, Strojniˇski vestnik – Journal of Mechanical Engineering, 60, 11, 742-754
10. Keramat A., Tijsseling A.S., Hou Q., Ahmadi A., 2012, Fluid-structure interaction with pipe-wall viscoelasticity during water hammer, Journal of Fluids and Structures, 28, 1, 434-456
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21. Urbanowicz K., 2015, Simple modelling of unsteady friction factor, Proceedings of 12th International Conference on Pressure Surges, Dublin, Ireland, 18-20 November, 113-130.
22. Urbanowicz K., Firkowski M., Zarzycki Z., 2016, Modelling water hammer in viscoelastic pipelines: short brief, Journal of Physics: Conference Series, 760, paper 012037
23. Urbanowicz K., Zarzycki Z., 2012, New efficient approximation of weighting functions for simulations of unsteady friction losses in liquid pipe flow, Journal of Theoretical and Applied Mechanics, 50, 2, 487-508
24. Urbanowicz K., Zarzycki Z., 2015, Improved lumping friction model for liquid pipe flow, Journal of Theoretical and Applied Mechanics, 53, 2, 295-305
25. Urbanowicz K., Zarzycki Z., Kudźma S., 2012, Universal weighting function in modeling transient cavitating pipe flow, Journal of Theoretical and Applied Mechanics, 50, 4, 889-902
26. Vardy A.E., Brown J.M.B., 1996, On turbulent unsteady, smooth – pipe friction, Proceedings of 7th International Conference on Pressure Surges, BHR Group, Harrogate, United Kingdom, 289-311
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35. Zarzycki Z., Kudźma S., Urbanowicz K., 2011, Improved method for simulating transients of turbulent pipe flow, Journal of Theoretical and Applied Mechanics, 49, 1, 135-158
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38. Zarzycki Z., Urbanowicz K., 2006, Modelling of transient flow during water hammer considering cavitation in pressure pipes (in Polish), Chemical and Process Engineering, 27, 3, 915-933
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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)

Typ dokumentu

Bibliografia

Identyfikator YADDA

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