Hydraulic behavior modeling of the simple tank using the Finite Difference Method: a comparison of four different methods

Document Type : Original Article

Author

Assistant Professor, Department of Civil Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan

Abstract

In this paper, the hydraulic modeling of a simple surge tank with two assumptions of with or without friction condition at both gradually and suddenly valve closing is studied. The four different kinds of the finite difference method called the Explicit Euler, Implicit Euler, Predictor-Corrector Euler and Rung-Kutta methods are used to solve hydraulic equations and the results are presented and compared. Comparison of the results shows that in all cases, by using the Implicit Euler method, the fluid level variation is less than other available methods. In other words, the fluid level variation obtained using Implicit Euler is about 3 percent less than that obtained using Rung-Kutta method at without friction condition. In addition, at friction condition, the fluid level variation obtained using Implicit Euler is about 4, 3 and 2 percent less than that obtained using Explicit Euler, Predictor-Corrector Euler and Rung-Kutta methods, respectively. Moreover, the results converge faster than the other methods at without friction condition using Implicit Euler method and finally the results converge faster than the other methods at friction condition using Rung-Kutta method.

Keywords


[1] Izquierdo, J., & Iglesias, P.L. (2002), “Mathematical modeling of hydraulic transients in simple systems”, Mathematical and Computational Modeling, 35(7), 801–812.
[2] Wood, D.J., Lindireddy, S., Boulos, P.F., Karney, B., & Mcpherson, D.L. (2005), “Numerical methods for modeling transient flow”, Journal of American Water Works Association, 97(7), 104–15.
[3] Zhao, M., & Ghidaoui, M. (2004), “Godunov-type solutions for water hammer flows”, ASCE Journal of Hydraulic Engineering, 130(4), 341–8.
[4] Kendir, T.E., & Ozdamar, A. (2013), “Numerical and experimental investigation of optimum surge tank forms in hydroelectric power plant”, Renewable Energy, 60, 323-331.
[5] Sutton, B.A. (1960), “Series solutions of some surge tank problems”, Proc. Inst. Civil Engrs, 16, 225-233.
[6] France, P.W. (1977), “Comparison between experimental and numerical investigations of the motion of the water surface in a model surge tank”, Advances in Water Resources, 1(1), 49-51.
[7] France, P.W. (1980), “Surge tank water level variations following rapid valve opening”, Advances in Water Resources, 3(1), 41-3.
[8] France, P.W. (1983), “Finite element solution for mass oscillations in a surge tank”, Advances in Water Resources, 6(2), 200-204.
[9] France, P.W. (1984), “Mathematical models for surge analysis”, Engineering Analysis, 1(2), 107-9.
[10] France, P.W. (1996), “Finite element solution for mass oscillations in a surge tank on sudden valve opening”, Advances in Engineering Software, 26(3), 185-7.
[11] Gulhan, A. (1984). Study of water hammer in hydroelectric power plants by taking turbine and regulation characteristics into account. Master of Science Thesis, ITU, Istanbul [in Turkish].
[12] Gill, M.A., & Eke, O.C. (1987), “Mass oscillations in surge tanks on sudden opening of the valve”, Water Power Dam Constr., 36-39.
[13] Selek, B. (1993). Computerized calculation of surge tank oscillations and water hammers in hydraulic power plants. Master of Science Thesis, Adana: Cukurova University, [in Turkish].
[14] Vournas, C.D., & Papaioannou, G. (1995), “Modelling and stability of a hydro plant with two surge tanks”, Energy Conversion, IEEE Transaction, 10(2), 368-75.
[15] Nicolet, C., Avellan, F., Prénat, J.E., Sapin, A., & Simond, J.J. (2001), “A new tool for the simulation of dynamic behaviour of hydroelectric power plants”, In: 10th international meeting of the work group on the behaviour of hydraulic machinery under steady oscillatory conditions, project LMH e SIMSEN. Lausanne: IMHEF/EPFL, Norway.
[16] Nicolet, C. (2007). Hydroacoustic modelling and numerical simulation of unsteady operation of hydroelectric systems. Ph.D. Thesis. Lausanne, EPFL n_3751.
[17] Klasinc, R., & Bilus, I. (2009), “Experimental and numerical approach to surge tank improvements”, In: International symposium on water management and hydraulic engineering, paper A100, 339-48.
[18] Kim, S.H.(2010), “Design of surge tank for water supply systems using the impulse response method with the GA algorithm”, Journal of Mechanical Science and Technology, 24 (2), 629-636.
[19] Guo, L., Liu, Z., Geng, J., Li, D., & Du, G.S. (2013), “Numerical study of flow fluctuation attenuation performance of a surge tank”, Journal of Hydrodynamics, Ser. B, 25(6), 938-943.
[20] An, J.F., Zhang, J., Yu, X.D., & Chen, S. (2014), “Influence of flow field on stability of throttled surge tanks with standpipe”, Journal of Hydrodynamics, 25(2), 294-299.
[21] Skulovich, O., Perelman, L., & Osteld, A. (2013), “Bi-level Optimization of Closed Surge Tanks Placement and Sizing in Water Distribution System Subjected to Transient Events”, 16th Conference on Water Distribution System Analysis, WDSA 2014, Procedia Engineering, 89, 1329-1335.
[22] Chaudhry, M.H. (1979). Applied Hydraulic Transients. New York, USA: Van Nostrand Reinhold Company.
CAPTCHA Image