A FINITE VOLUME CENTRAL DIFFERENCING SCHEME FOR SIMULATION OF THE SHUT DOWN PROCEDURE OF A HYDRAULIC SYSTEM
Keywords:
water hammer, hydraulic system analysis, finite volume schemes, shut down procedureAbstract
A new central differencing finite volume scheme is investigated for solution of unsteady hydraulic problems as wa-ter hammer in pipe systems. Special time stepping procedure similar to Runge-Kutta algorithm is used to stabilize this second order scheme. It is monotonized by adding dissipative terms including second and fourth derivatives of the con-served variables, with coefficients proportional to derivatives of pressure or volumetric flow, which keeps the second order of accuracy in smooth flow regions. The one-dimensional unsteady incompressible equations are solved for a wa-ter hammer situation, and results are compared to existing analytical solutions. Results are also compared with numeri-cal results of classical characteristic method, which is proved to be fairly accurate. The scheme could easily be general-ized to two-dimensional case. Finally this procedure is used for analysis of the shut down procedure of a hydraulic sys-tem. Components of the system are modeled and effects of important parameters on the performance are studied.
Downloads
References
Bellos, C. V., Soulis, J. V. and Sakkas, J. G. 1991. Computation of Two-Dimensional Dam-Break In-duced Flow. Advances in Water Resour, Vol. 14(1), pp. 31-41.
Fennema, R. J. and Chaudhry, M. H. 1987. Simula-tion of One Dimensional Dam-Break Flows. J. Hydr. Res., Vol. 25(1), pp. 25-51.
Garcia-Navaho, P. and Kahawita, R. A. 1986. Nu-merical Solution of the St. Venant Equation with the MacCormack Finite Difference Scheme. Int. J. Numer. Methods in Fluid, Vol (6), pp. 507-527.
Garcia-Navaho, P., Priestley, A. and Alcrudo, F. 1994. An Implicit Method for Water Flow Model-ing in Channel and Pipe. J. Hydr. Res., Vol. 32(5), pp. 721-742.
Jameson, A., Schmidt, W. and Turkel, E. 1981. Nu-merical Solution of Euler Equation by Finite Vol-ume Methods Using Rung-Kutta Time Stepping Schemes. AIAA 14th Fluid and Plasma Dynamic Conference, Palo Alto.
Katopodes, N. D. and Sterlkoff, R. 1978. Computing Two-Dimensional Dam-Break Flood Waves. J. Hydr. Div. ASCE, Vol. 104(9), pp. 1269-1288.
Lai, C. 1979. Comprehensive Method of Characteris-tics Models for Flow Simulation. J. Hydr. Engrg, ASCE, Vol. 114(9), pp. 1074-1097.
Leaf, G. K. and Chawla, T. C. 1979. Numerical Methods for Hydraulic Transients. Numerical Heat Transfer, Vol. 2, pp. 1-34.
Mingham, C. G. and Causon, D. M. 1998. High-Resolution Finite Volume Method for Shallow Wa-ter Flow. J. Hydr. Engrg. ASCE, Vol. 124(6), pp. 605-614.
Nujic, M. 1995. Efficient Implementation of Non-Oscillatory Schemes for Computation of Free-Surface Flows. J. Hydr. Res., Delft, the Nether-lands, Vol. 33(1), pp. 101-111.
Rao, V. S. and Latha, G. 1992. A Slope Modification Method for Shallow Water Equation. Int. J. Meth-ods in Fluid, Vol. 14, pp. 189-196.
Roe, P.L. 1981. Characteristics-Based Schemes for Euler Equations. Anal.Rev. Fluid Mech., pp. 337-365.
Savic, L. J. and Holly, F. M., Jr. 1993. Dam-Break Flood Waves Computed by Modified Godunov Method. J. Hdry. Res., Delft, the Netherlands, Vol. 31(2), pp. 187-204.
Streeter, V. L. and Wylie, E. B. 1981. Fluid Mechan-ics. McGraw-Hill Book Co.
Zhao, D. H., Shen, H. W., Tabios, G. Q., Lai, J. S. and Tan, W. Y. 1994. A Finite Volume Two-Dimensional Unsteady Flow Modle for River Ba-sins. J. Hydr.Engrg. ASCE, Vol. 120(7), pp. 863-883.
