Improved method for simulating transients of turbulent pipe flow

Zarzycki, Z.; Kudźma, S.; Urbanowicz, K.

Artykuł - szczegóły

Tytuł artykułu

Improved method for simulating transients of turbulent pipe flow

Autorzy

Zarzycki Z. , Kudźma S. , Urbanowicz K.

Treść / Zawartość

Pełne teksty:

httpwww_ptmts_org_pl2011-1-zarzycki-in.pdf

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Języki publikacji

Abstrakty

The paper presents the problem of modelling and simulation of transients during turbulent fluid flow in hydraulic pipes. The instantaneous wall shear stress on a pipe wall is presented in the form of integral convolution of a weighting function and local acceleration of the liquid. This weighting function depends on the dimensionless time and Reynolds number. Its original, very complicated mathematical structure is approximated to a simpler form which is useful for practical engineering calculations. The paper presents an efficient way to solve the integral convolution based on the method given by Trikha (1975) for laminar flow. An application of an improved method with the use of the Method of Characteristic for the case of unsteady flow (water hammer) is presented. This method is characterised by high efficiency compared to traditional numerical schemes.

Artykuł przedstawia zagadnienie modelowania i symulacji przebiegów przejściowych podczas turbulentnego przepływu cieczy w przewodach ciśnieniowych. Chwilowe naprężenie styczne na ściance przewodu przedstawiono w postaci całki splotowej z funkcji wagi i przyspieszenia cieczy. Funkcja wagi dla naprężenia stycznego na ściance przewodu zależy od czasu bezwymiarowego i liczby Reynoldsa. Ma ona zawiłą postać matematyczną, dlatego aproksymowano ją do prostszej postaci, przydatnej do praktycznych obliczeń inżynierskich. Przedstawiono efektywny sposób rozwiązania całki splotowej, opierając się na metodzie podanej przez Trikha (1975) dla przepływu laminarnego. Podano zastosowanie ulepszonej metody symulacji naprężenia stycznego do metody charakterystyk podczas uderzenia hydraulicznego. Charakteryzuje się ona dużą efektywnością w stosunku do metody tradycyjnej.

Słowa kluczowe

unsteady pipe flow transients waterhammer efficient numerical simulation

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2011

Tom

Vol. 49 nr 1

Strony

135--158

Opis fizyczny

Bibliogr. 46 poz., rys.

Twórcy

autor

Zarzycki Z.

autor

Kudźma S.

autor

Urbanowicz K.

West Pomeranian University of Technology, Faculty of Mechanical Engineering and Mechatronics, Szczecin, Poland, zbigniew.zarzycki@zut.edu.pl

Bibliografia

1. Abreu J.W., Almeida A.B., 2000, Pressure transients dissipative effects: a contribution for their computational prediction, 8th International Conference on Pressure Surges, BHR Group, The Hague, Netherlands, 449-517
2. Bergant A., Simpson A.R., 1994, Estimating unsteady friction in transient cavitating pipe flow, Proc., 2nd Int. Conf. On Water Pipeline Systems, BHRA Group Conf. Series Publ., 10, UK, Edinburgh, 24-26 May, 2-15
3. Bergant A., Simpson A.R., Vitkovsky J.P., 1999, Review of unsteady friction models in transients pipe flow, 9th International Meeting of the Work Group om the Behaviour of Hydraulic Machinery under Steady Oscillatory Conditions, IAHR, Brno, Czech Republic, September 1-12
4. Brown F.T., Margolis D.L., Shah R.P., 1969, Small amplitude frequency behavior of fluid lines with turbulent flow, Journ. of Basic Eng., Trans. ASME, s. D, 4, 678-692
5. Brunone B., Golia U.M., Greco M., 1994, Estimating unsteady friction in transient cavitating pipe flow, Proceedings of the 2nd International Conference on Water Pipeline Systems, Edinburgh 1994, BHR Group, 1-16
6. Brunone B., Golia U.M., Greco M., 1995, Effects of two-dimensionality on pipe transients modeling, Journal of Hydraulic Engineering, ASCE, 121, 12, 906-912
7. Bughazem M.B., Anderson A., 2000, Investigation of an unsteady friction model for waterhammer and column separation, 8th International Conference on Pressure Surges, BHR Group, The Hague, Netherlands 2000, 483-498
8. Carstens M.R., Roller J.E., 1959 Boundary-shear stress in unsteady turbulent pipe flow, Journ. of Hydraulics Division, Proceedings of the American Society of Civil Engineers, February, 67-81
9. Dailey J.W. Hankey W.L., Olive R.W., Jordan J.M., 1956, Resistance coefficient for accelerated and decelerated flows through smooth tubes and orifices, J. Basic Eng., 78, 1071-1077
10. Ferrante M., Brunone B., 2007,Wavelets for the analysis of transient pressure signals for leak detection, Journal of Hydraulic Engineering, ASCE, 133, November, 1274-1284
11. Ghidaoui M.S., Mansour S., 2002, Efficient treatment of the Vardy-Brown unsteady shear in pipe transients, Journal of Hydraulic Engineering, ASCE, January, 102-112
12. Hinze J.O., 1953, Turbulence, Mc Graw-Hill, New York
13. 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, March, 89, 11, 174-180
14. Hussain A.K.M.F., Reynolds W.C., 1975, Measurements in fully developed turbulent channel flow, ASME Journal of Fluids Engineering, December, 568-580
15. Kim S.H., 2008, Impulse response method for pipeline system equipped with water hammer prediction devices, Journal of Hydraulic Engineering, ASCE, 134, July, 961-963
16. Kudźma S., 2005, Modeling and simulation of dynamical runs in closed conduits of hydraulics systems using unsteady friction model, PhD work at Szczecin University of Technology [in Polish]
17. Kwon H.J., Lee J.J., 2008, Computer and experimental models of transient flow in a pipe involving backflow preventers, Journal of Hydraulic Engineering, ASCE, 134, April, 426-433
18. Liiv U.R., 1965, On Losses for acceleratedmotion of liquid in pressure conduits, Trudy Tallinskogo, Politkhicheskogo Instituta, Series A, 223, 43-50 [in Russian]
19. Ohmi M., Iguchi M., Usui T., Minami M., 1980-1981, Flow pattern and frictional losses in pulsating pipe flow, (Part 1-7), Bulletin of JSME, 23, 24
20. Ohmi M., Kyonen S., Usui T., 1985, Numerical analysis of transient turbulent flow in a liquid line, Bulletin of JSME, 28, 239, May, 799-806
21. Pezzinga G., 1999, Quasi 2D model for unsteady flow in pipe networks, Journal of Hydraulic Engineering, ASCE, 125, 7, 676-685
22. Rahl F.M., Barlamont J., 1996, Unsteady pipe flow simulations using unsteady friction flow formulae, 7th International Conference on Pressure Surges and Transients in Pipeline and Open Channels, BHR Group, Harrogate, UK, 313-322
23. Safwat H.H., Polder J., 1973, Friction-frequency dependence for oscillatory flows in circular pipe, Journal of the Hydraulics Division, ASCE, 99, HY 11, 1933-1945
24. Satlar A.M., Chaudhry M.H., Kassen A.A., 2008, Partial blockage detection in pipelines by frequency response method, Journal of Hydraulic Engineering, ASCE, 134, January, 76-89
25. Satlar A.M., Dicherson J.R., Chaudhry M.H., 2009, Wavelet-Galerkin solution to the water hammer equations, Journal of Hydraulic Engineering, ASCE, 135, April, 283-295
26. Schohl G.A., 1993, Improved approximate method for simulating frequency dependent friction in transient laminar flow, Journal of Fluids Eng., Trans. ASME, 115, September, 420-424
27. Solodovnikov V.V., 1964, Statistical Dynamic of Linear Control Systems, WNT, Warszawa
28. 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
29. Trikha A.K., 1975, An efficient method for simulating frequency-dependent friction in transient liquid flow, Journ. of Fluids Eng., Trans. ASME, March, 97-105
30. Vardy A.E., 1980, Unsteady flows: fact and friction, Proc. 3rd International Conference on Pressure Surges, Cantenbury, UK, 1-14
31. Vardy A.E, Brown J.M.B., 1995, Transient, turbulent, smooth pipe friction, Jurnal of Hydraulic Research, 33, 4, 435-456
32. Vardy A.E., Brown J., 1996, On turbulent, unsteady, smooth-pipe friction, Proc. of 7th International Conference on Pressure Surges, BHRA, Fluid Eng., 289-311, Harrogate, UK, 16-18 April, 289-311
33. Vardy A.E., Brown J.M.B., 2003, Transient turbulent friction in smooth pipe flows, Journal of Sound and Vibration, 259, 5, 1011-1036
34. Vardy A.E., Brown J.M.B., 2004, Transient turbulent friction in fully rough pipe flows, Journal of Sound and Vibration, 270, 233-257
35. Vardy A.E., Brown J.M.B., 2007, Approximation of turbulent wall shear stress in highly transient pipe flows, Journal of Hydraulic Engineering, ASCE, November, 1219-1228
36. Vardy A.E., Hwang K.L., Brown J.M.B., 1993, A weighting function model of transient turbulent pipe friction, Jurnal of Hydraulic Research, 31, 4, 553-548
37. Wichowski R., 1984, One-dimensional theory of water-hammer phenomenon in water-supply system conduits, Part II, Archiwum Hydrotechniki, 1/2, 39-58
38. Wylie E.B., Streeter V.L., 1993, Fluid Transient in Systems, Prentice Hall, Englewood Cliffs, NY
39. Vitkowsky J., Lambert W., Simpson A., 2000, Advances in unsteady friction modeling in transient pipe flow, 8th International Conference on Pressure Surges, BHR Group, The Hague, Netherlands, 471-482
40. Wood J.D., Funk J.E., 1970, A boundary-layer theory for transient viscous losses in turbulent flow, Journ. of Basic. Eng., Trans. ASME, December, 865-873
41. Zarzycki Z., 1993, Friction factor in a pulsating turbulent pipe flow, Trans. of the Institute of Fluid-Flow Machinery, 95, 179-196
42. Zarzycki Z., 1994, A hydraulic resistance’s of unsteady fluid flow in pipes, To be published by Technical University of Szczecin, No 516, Szczecin [in Polish]
43. Zarzycki Z., 2000, On weighting function for wall shear stress during unsteady turbulent pipe flow, 8th International Conference on Pressure Surges, BHR Group, The Hague, 529-543
44. Zarzycki Z., Kudźma S., 2004, Simulations of transient turbulent flow in liquid lines using time-dependent frictional losses, The 9th International Conference on Pressure Surges, BHR Group, Chester, UK, 24-26 March, 439-455
45. Zarzycki Z., Kudzma S., Kudzma Z., Stosiak M., 2007, Simulation of transients flow in a hydrostatic system with a long liquid line, Journal of Theoretical and Applied Mechanics, 45, 4
46. Zielke W., 1968, Frequency-dependent friction in transient pipe flow, Journal of Basic Eng., Trans. ASME, March, 109-115

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Bibliografia

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