A Hybrid Solution for Transient Pipe Flow based on Method of Characteristics and Lax-Friedrichs Scheme | ||
| Journal of Hydraulic and Water Engineering | ||
| دوره 2، شماره 1، مهر 2024، صفحه 13-28 اصل مقاله (743.79 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22044/jhwe.2024.13086.1015 | ||
| نویسندگان | ||
| Faeze Khalighi* 1، 2؛ Ahmad Ahmadi3؛ Alireza Keramat4، 5؛ Arris Tijsseling2 | ||
| 1Department of Civil Engineering, Shahrood University of Technology, Shahrood, Iran. | ||
| 2Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands. | ||
| 3Department of Civil and Environmental Engineering, Hong Kong Polytechnic University, Hung Hom, SAR 999077, Kowloon, Hong Kong. | ||
| 4Civil and Environmental Engineering Department, Hong Kong Polytechnic University, Hong Kong | ||
| 5Research Institute for Land and Space, Hong Kong Polytechnic University, Hung Hom SAR 999077, Kowloon, Hong Kong. | ||
| چکیده | ||
| Method of Characteristics (MOC) has long been an excellent and widely established technique for analyzing transient flow, especially in a single pipeline with constant wave speed. But, this method has some limitations in terms of mesh sizing while studying multi-pipe systems or systems with different wave speeds. More specifically, it needs all pipes to satisfy the Courant number to be unity while the same time step should be chosen for all pipes. With this, one reach in each pipe remains, which does not satisfy the Courant requirement. As one possible remedy to this shortcoming, a hybrid numerical method based on MOC and a two-step variant of the Lax-Friedrichs method (MOC-LF) is suggested in the present study. This method is compared against the conventional MOC scheme, which adapts interpolation for the remaining length per pipe (MOC-MOC). In the approach, two significant effects of FSI in fluid-filled tubes, namely Poisson and junction coupling, are introduced. The computational simulations are carried out for a reservoir-pipe-valve system with instantaneous and gradual closure of the downstream valve. The results of proposed scheme and those of MOC with interpolation are in good agreement with solutions obtained by MOC with a very fine grid, which are taken as a reference. Detailed comparison of the computational methods in terms of error indicates that the proposed MOC-LF can be a good alternative for conventional MOC schemes. | ||
| کلیدواژهها | ||
| Transient flow؛ Water hammer؛ Fluid-structure interaction | ||
| مراجع | ||
|
Alatorre, L., Beguería, S., & García-Ruiz, J. M. (2010). Regional scale modeling of hillslope sediment delivery: A case study in the Barasona Reservoir watershed (Spain) using WATEM/SEDEM. Journal of Hydrology, 391(1), 109–123.
Bergant, A., Simpson, A. R., & Tijsseling, A. S. (2006). Water hammer with column separation: A historical review. Journal of Fluids and Structures, 22(2), 135–171.
Chikitkin, A. V., Rogov, B. V., & Utyuzhnikov, S. V. (2015). High-order accurate monotone compact running scheme for multidimensional hyperbolic equations. Applied Numerical Mathematics, 93(3), 150–163.
El Idrissi, A. Q., da Silva, E. G., & Zeidan, D. (2023). Numerical studies of two-phase water hammer flows using Godunov methods. Annals of Nuclear Energy, 182, 109578.
Ferras, D., Manso, P. A., Schleiss, A. J., & Covas, D. I. C. (2017). Fluid-structure interaction in straight pipelines with different anchoring conditions. Journal of Sound and Vibration, 394, 348–365.
Ferras, D., Manso, P. A., Schleiss, A. J., & Covas, D. I. C. (2018). One-dimensional fluid–structure interaction models in pressurized fluid-filled pipes: A review. Applied Sciences, 8(10), 1844.
Ghodhbani, A., Akrout, M., & Haj Taieb, E. (2019). Coupled approach and calculation of the discrete vapour cavity model. Journal of Fluids and Structures, 91, 102691.
Ghidaoui, M. S., & Karney, B. W. (1994). Equivalent differential equations in fixed-grid characteristics method. Journal of Hydraulic Engineering, 120(10), 1159–1175.
Ghidaoui, M. S., Karney, B. W., & McInnis, D. A. (1998). Energy estimates for discretization errors in water hammer problems. Journal of Hydraulic Engineering, 124(4), 384–393.
Greyvenstein, G. P. (2002). An implicit method for the analysis of transient flows in pipe networks. International Journal for Numerical Methods in Engineering, 53(5), 1127–1143.
Henclik, S. (2018). Numerical modeling of water hammer with fluid–structure interaction in a pipeline with viscoelastic supports. Journal of Fluids and Structures, 76, 469–487.
Hosseini, R. S., Ahmadi, A., & Zanganeh, R. (2020). Fluid-structure interaction during water hammer in a pipeline with different performance mechanisms of viscoelastic supports. Journal of Sound and Vibration, 487, 115527.
Hou, Q., Kruisbrink, A. C. H., Tijsseling, A. S., & Keramat, A. (2012). Simulating water hammer with corrective smoothed particle method. In S. Anderson (Ed.), Proceedings of the 11th International Conference on Pressure Surges (pp. 171–187). BHR Group.
Karney, B. W., & Ghidaoui, M. S. (1997). Flexible discretization algorithm for fixed-grid moc in pipelines. Journal of Hydraulic Engineering, 123(11), 1004–1011.
Khalighi, F., Ahmadi, A., & Keramat, A. (2016). Investigation of fluid-structure interaction by explicit central finite difference methods. International Journal of Engineering, 29(5), 590–598.
Khalighi, F., Ahmadi, A., & Keramat, A. (2017). Water hammer simulation by explicit central finite difference methods in staggered grids. Journal of Computational & Applied Research in Mechanical Engineering, 6(2), 69–77.
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, 434–455.
Lai, C. (1988). Comprehensive method of characteristics models for flow simulation. Journal of Hydraulic Engineering, 114(9), 1074–1097.
Laguna, A. J., & Tsouvalas, A. (2014). Transient laminar flow in hydraulic networks based on a semi-analytical impulse response method. Heron, 59(1), 37–56.
Li, Q. S., Yang, K., & Zhang, L. (2003). Analytical solution for fluid-structure interaction in liquid-filled pipes subjected to impact-induced water hammer. Journal of Engineering Mechanics, 129(12), 1408–1417.
Lu, M., Liu, X., Xu, G., & Tian, Y. (2024). Optimal pump-valve coupling operation strategy of complex long-distance water-conveyance systems based on MOC. Ain Shams Engineering Journal, 15(1), 102318.
Pal, S., Hanmaiahgari, P. R., & Karney, B. W. (2021). An overview of the numerical approaches to water hammer modelling: The ongoing quest for practical and accurate numerical approaches. Water, 13(11), 1597.
Ramos, H., Tamminen, S., & Covas, D. I. C. (2009). Water supply system performance for different pipe materials Part II: Sensitivity analysis to pressure variation. Water Resources Management, 23(2), 367–393.
Samani, H. M. V., & Khayatzadeh, A. (2002). Transient flow in pipe networks. Journal of Hydraulic Research, 34(5), 637–644.
Shampine, L. F. (2004). Two-step Lax–Friedrichs method. Applied Mathematics Letters, 18(10), 1134–1136.
Shampine, L. F. (2005). Solving hyperbolic PDEs in MATLAB. Applied Numerical Analysis & Computational Mathematics, 2(3), 346–358.
Shi, L., Zhang, J., Yu, X. D., Chen, S., Zhao, W. L., & Chen, X. Y. (2023). Water hammer protection for diversion systems in front of pumps in long-distance water supply projects. Water Science and Engineering, 16(2), 211–218.
Shimada, M., Brown, J., Leslie, D., & Vardy, A. (2006). Time-line interpolation errors in pipe networks. Journal of Hydraulic Engineering, 132(3), 294–306.
Thomas, J. W. (1995). Numerical partial differential equations: Finite difference methods (Vol. 22). Springer Science & Business Media.
Tijsseling, A. S. (2003). Exact solution of linear hyperbolic four equation system in axial liquid-pipe vibration. Journal of Fluids and Structures, 18(2), 179–196.
Tijsseling, A. S. (2009). Exact computation of the axial vibration of two coupled liquid-filled pipes. Proceedings of the ASME Pressure Vessels and Piping Division Conference (Paper PVP2009-77250). ASME.
Trangenstein, J. A. (2009). Numerical solution of hyperbolic partial differential equations. Cambridge University Press.
Twyman, J. (2016). Wave speed calculation for water hammer analysis. Obras y Proyectos, 20, 86–92.
Twyman, J. (2017). Water hammer analysis using a hybrid scheme. Revista Ingeniería de Obras Civiles, 7, 16–25.
Twyman, J. (2018). Water hammer analysis using an implicit finite difference method. Revista Chilena de Ingeniería, 26(2), 307–318.
Urbanowicz, K. (2018). Fast and accurate modelling of frictional transient pipe flow. ZAMM - Journal of Applied Mathematics and Mechanics, 98(5), 802–823.
Wan, W., Wang, Y., Chen, X., Zhan, H., Wang, T., & Zhang, B. (2023). Investigation of partially expanded surge tank with self-adaptive auxiliary system controlling water hammer in pipelines. Engineering Science and Technology, an International Journal, 40, 101379.
Wiggert, D. C., & Sundquist, M. J. (1997). Fixed-grid characteristics for pipeline transients. Journal of the Hydraulics Division, 103(12), 1403–1416.
Zhang, B., Wan, W., & Shi, M. (2018). Experimental and numerical simulation of water hammer in gravitational pipe flow with continuous air entrainment. Water, 10(7), 928.
Zhang, Q., Liao, T., Ding, L., Wang, K., Yang, H., & Lian, Z. (2023). Study on water hammer effect and tubing string vibration in high-pressure high-production gas wells. Geoenergy Science and Engineering, 229, 212147.
| ||
|
آمار تعداد مشاهده مقاله: 140 تعداد دریافت فایل اصل مقاله: 63 |
||