New efficient approximation of weighting functions for simulations of unsteady friction losses in liquid pipe flow

• Autorzy: Urbanowicz K. , Zarzycki Z.

Warianty tytułu

PL

Nowe efektywne funkcje wagowe umożliwiające symulację niestacjonarnych oporów hydraulicznych podczas przepływówniestacjonarnych oporów hydraulicznych podczas przepływów cieczy w przewodach ciśnieniowych

• Języki publikacji: EN

Abstrakty

EN

Most papers dealing with calculations and simulations of the unsteady liquid pipe flow are based on the assumption that the formula for quasi-steady friction (Darcy-Weisbach formula) can be applied. In the case of fast changes, like fast transients e.g. water hammer, it fails. In this work, the wall shear stress is presented as a sum of quasi-steady and unsteady component. The unsteady component of the wall shear stress is modeled as a convolution of local fluid acceleration and a weighting function. The original weighting function has usually a very complicated structure, and what is more, makes impossible to carry out an efficient simulation of dynamical runs. In this paper, in order to enable efficient calculation of the unsteady component of the wall shear stress, new weighting functions are presented as sums of exponential components.

PL

W dużej części prac, dotyczących obliczania oraz symulacji niestacjonarnego przepływu cieczy w przewodach ciśnieniowych, opory wyznacza się jedynie z dobrze znanej formuły Darcy-Weisbacha. Niestety w szybkozmiennych przepływach, takich jak np. uderzenie hydrauliczne, założenie quasi-stacjonarności oporów jest poważnym błędem. Wponiższej pracy naprężenie styczne na ściance przewodu wyznacza się z sumy quasi-stacjonarnego składnika oraz niestacjonarnego. Niestacjonarny składnik naprężenia stycznego modelowany jest jako splot lokalnego przyśpieszenia cieczy oraz funkcji wagi. Klasyczne funkcje wagi mają skomplikowaną postać, co uniemożliwia efektywne wyznaczanie oporów. W tej pracy przedstawione zostały nowe efektywne postacie funkcji wagowych o rozszerzonych zakresach stosowalności.

Słowa kluczowe

EN

transient flow; weighting function; friction losses

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2012
• Tom: Vol. 50 nr 2
• Strony: 487--508
• Opis fizyczny: Bibliogr. 31 poz., rys., tab.

Twórcy

autor

Urbanowicz K.

autor

Zarzycki Z.

• West Pomeranian University of Technology, Faculty of Mechanical Engineering and Mechatronics, Szczecin, Poland,

Bibliografia

• 1. Adamkowski A., Lewandowski M., 2004, Experimental examination of unsteady friction models for transient pipe flow simulation, 9th Int. conf. on Pressure Surges BHR 2004, Proc., II, 421-437
• 2. Bergant A., Simpson A., Vtkovsk´y J., 2001, Developments in unsteady pipe flow friction modelling, Journal of Hydraulic Research, IAHR, 39, 3, 249-257
• 3. Brown F.T., 1969, A quasi method of characteristics with application to fluid lines with frequency dependent wall shear and heat transfer, Trans. ASME, J. Basic Engineering, 91, 2, 217-227
• 4. Brown F.T., Margolis D.L., Shah R.P., 1969, Small-amplitude frequency behaviour of fluid lines with turbulent flow, Trans. ASME, J. Basic Engineering, 678-693
• 5. Brunone B., Golia U.M., Greco M., 1991, Some remarks on the momentum equations for fast transients, Proceedings of the International Meeting on Hydraulic Transients with Column Separation, 9th Round Table, IAHR, Valencia, Spain, 201-209
• 6. Bughazem M.B., Anderson A., 2000, Investigation of an unsteady friction model for waterhammer and column separation, Proceedings of the 8th International Conference on Pressure Surges, BHR Group Conf. Series Publ., The Hague, The Netherlands, 483-498
• 7. Carstens M.R., Roller J.E., 1959, Boundary-shear stress in unsteady turbulent pipe flow, ASCE Journal of the Hydraulics Division, 85, HY2, 67-81
• 8. 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, J. Basic Engineering, 78, July, 1071-1077
• 9. Holmboe E.L., Rouleau W.T., 1967, The effect of viscous shear on transients in liquid lines, Journ. of Basic Eng., Trans. ASME, s. D, 89, 11, 174-180
• 10. Kagawa T., Lee I., Kitagawa A., Takenaka T., 1983, High speed and accurate computing method of frequency-dependent friction in laminar pipe flow for characteristics method, Trans. Jpn. Soc. Mech. Eng., Ser. A, 49, 447, 2638-2644 [in Japanese]
• 11. Kudźma S., 2005, Modeling and simulation dynamical runs in closed conduits of hydraulics systems using unsteady friction model, PhD Thesis, Szczecin University of Technology [in Polish]
• 12. Ohmi M., Kyomen S., Usui T., 1985, Numerical analysis of transient flow in a liquid line, Bulletin of JSME, 28, 239, 799-806
• 13. Popov D.N., 1982, Unsteady-State Hydromechanical Processes, Moscow, Mashinostroenie [in Russia]
• 14. Safwat H.H., Polder J. van Den, 1973, Experimental and analytic data correlation study of water column separation, Journal of Fluids Engineering, March, 91-97
• 15. Schohl G.A., 1993, Improved approximate method for simulating frequency – dependent friction in transient laminar flow, Journal of Fluids Engineering, Trans. ASME, 115, September, 420-424
• 16. Shuy E.B., Aplet C.J., 1987, Experimental studies of unsteady shear stress in turbulent flow in smooth round pipes, Conf. on Hydraulics in Civil Engineering, Melbourne, Australia, 137-141
• 17. Suzuki K., Taketomi T., Sato S., 1991, Improving Zielke’s method of simulating frequency – dependent friction in laminar liquid pipe flow, Journal of Fluids Engineering, Trans. ASME, 113, December, 569-573
• 18. Trikha A.K., 1975, An efficient method for simulating frequency-dependent friction in transient liquid flow, Journal of Fluids Engineering, Trans. ASME, March, 97-105
• 19. Vardy A.E., Brown J.M.B., 1995, Transient, turbulent, smooth pipe friction, J. Hydraul. Res., 33, 435-456
• 20. Vardy A.E., Brown J.M.B., 1996, On turbulent unsteady, smooth – pipe friction, Proc. of the 7th International Conf. on Pressure Surges – BHR Group, Harrogate, United Kingdom, 289-311
• 21. Vardy A.E., Brown J.M.B., 2003, Transient turbulent friction in smooth pipe flows, Journal of Sound and Vibration, 259, 5, 1011-1036
• 22. Vardy A.E., Brown J.M.B., 2004a, Efficient approximation of unsteady friction weighting functions, Journal of Hydraulic Engineering, ASCE, 130, 11, 1097-1107
• 23. Vardy A.E., Brown J.M.B., 2004b, Transient turbulent friction in fully rough pipe flows, Journal of Sound and Vibration, 270, 233-257
• 24. Vardy A., Brown J., 2007, Approximation of turbulent wall shear stresses in highly transient pipe flows, Journal of Hydraulic Engineering, 133, 11, 1219-1228
• 25. Vardy A.E., Hwang K.L., Brown J.M.B., 1993, A weighting function model of transient turbulent pipe friction, J. Hydraul. Res., 31, 4, 533-548
• 26. Vitkovsky J., Lambert M., Simpson A., Bergant A., 2000, Advances in unsteady friction modelling in transient pipe flow, Proceedings of the 8th International Conference on Pressure Surges, BHR Group Conf. Series Publ., The Hague, The Netherlands, 471-482
• 27. Vtkovsk´y J.P., Stephens M.L., Bergant A., Simpson A.R., Lambert M.F., 2004, Efficient and accurate calculation of Zilke and Vardy-Brown unsteady friction in pipe transients, 9th International Conference on Pressure Surges, Chester, United Kingdom, 405-419
• 28. Zarzycki Z., 1994, A Hydraulic Resistance’s of Unsteady Liquid Flow in Pipes, Published by Technical University of Szczecin, No 516, Szczecin [in Polish]
• 29. Zarzycki Z., 2000, On weighting function for wall shear stress during unsteady turbulent flow, Proc. of 8th International Conference on Pressure Sergues, The Hague, The Netherlands, BHR Group Conference Series, 39, 529-534
• 30. Zarzycki Z., Kudźma S., 2004, Simulations of transient turbulent flow in liquid lines using time – dependent frictional losses, Proceedings of the 9th International Conference on Pressure Surges, BHR Group, Chester UK, 439-455
• 31. Zielke W., 1968, Frequency-dependent friction in transient pipe flow, Journal of ASME, 90, March, 109-115