Omega-Luitex법을 이용한 수력점프 발생시 러프 베드의 와류 진화 예측 및 영향 분석
Cong Trieu Tran, Cong Ty Trinh
Abstract
The dissipation of energy downstream of hydropower projects is a significant issue. The hydraulic jump is exciting and widely applied in practice to dissipate energy. Many hydraulic jump characteristics have been studied, such as length of jump Lj and sequent flow depth y2. However, understanding the evolution of the vortex structure in the hydraulic jump shows a significant challenge. This study uses the RNG k-e turbulence model to simulate hydraulic jumps on the rough bed. The Omega-Liutex method is compared with Q-criterion for capturing vortex structure in the hydraulic jump. The formation, development, and shedding of the vortex structure at the rough bed in the hydraulic jumper are analyzed. The vortex forms and rapidly reduces strength on the rough bed, resulting in fast dissipation of energy. At the rough block rows 2nd and 3rd, the vortex forms a vortex rope that moves downstream and then breaks. The vortex-shedding region represents a significant energy attenuation of the flow. Therefore, the rough bed dissipates kinetic energy well. Adding reliability to the vortex determined by the Liutex method, the vorticity transport equation is used to compare the vorticity distribution with the Liutex distribution. The results show a further comprehension of the hydraulic jump phenomenon and its energy dissipation.
Keywords
flow-3D; hydraulic Jump; omega-liutex method; vortex breakdown
References
[1] Viti, N., Valero, D., & Gualtieri, C. (2019). Numerical Simulation of Hydraulic Jumps. Part 2: Recent Results and Future Outlook. Water, 11(1), 28. https://doi.org/10.3390/w11010028
[2] Peterka, A. J. (1978.) Hydraulic Design of Stilling Basins and Energy Dissipators. Department of the Interior, Bureau of Reclamation.
[3] Bejestan, M. S. & Neisi, K. (2009). A new roughened bed hydraulic jump stilling basin. Asian journal of applied sciences, 2(5), 436-445. https://doi.org/10.3923/ajaps.2009.436.445
[4] Tokyay, N. D. (2005). Effect of channel bed corrugations on hydraulic jumps. Impacts of Global Climate Change, 1-9. https://doi.org/10.1061/40792(173)408
[5] Nikmehr, S. & Aminpour, Y. (2020). Numerical Simulation of Hydraulic Jump over Rough Beds. Periodica Polytechnica Civil Engineering, 64(2), 396-407. https://doi.org/10.3311/PPci.15292
[6] Hunt, J. C., Wray, A. A., & Moin, P. (1988). Eddies, streams, and convergence zones in turbulent flows. Studying turbulence using numerical simulation databases. 2. Proceedings of the 1988 summer program.
[7] Gao, Y. & Liu, C. (2018). Rortex and comparison with eigenvalue-based vortex identification criteria. Physics of Fluids, 30(8), 085107. https://doi.org/10.1063/1.5040112
[8] Liu, C., Gao, Y., Tian, S., & Dong, X. (2018). Rortex – A new vortex vector definition and vorticity tensor and vector decompositions. Physics of Fluids, 30(3), 035103. https://doi.org/10.1063/1.5023001
[9] Liu, C. et al. (2019). Third generation of vortex identification methods: Omega and Liutex/Rortex based systems. Journal of Hydrodynamics, 31(2), 205-223. https://doi.org/10.1007/s42241-019-0022-4
[10] Liu, C., Wang, Y., Yang, Y. et al (2016). New omega vortex identification method. Science China Physics, Mechanics & Astronomy, (8), 56-64. https://doi.org/10.1007/s11433-016-0022-6
[11] Tran, C. T. & Pham, D. C. (2022). Application of Liutex and Entropy Production to Analyze the Influence of Vortex Rope in the Francis-99 Turbine Draft Tube. Tehnički vjesnik, 29(4), 1177-1183. https://doi.org/10.17559/TV-20210821070801
[12] Dong, X., Gao, Y., & Liu, C. (2019). New normalized Rortex/vortex identification method. Physics of Fluids, 31(1), 011701. https://doi.org/10.1063/1.5066016
[13] Wang, L., Zheng, Z., Cai, W. et al. (2019). Extension Omega and Omega-Liutex methods applied to identify vortex structures in viscoelastic turbulent flow. Journal of Hydrodynamics, 31(5), 911-921. https://doi.org/10.1007/s42241-019-0045-x
[14] Xu, H., Cai, X., & Liu, C. (2019). Liutex (vortex) core definition and automatic identification for turbulence vortex structures. Journal of Hydrodynamics, 31(5), 857-863. https://doi.org/10.1007/s42241-019-0066-5
[15] Tran, C. T. et al. (2020). Prediction of the precessing vortex core in the Francis-99 draft tube under off-design conditions by using Liutex/Rortex method. Journal of Hydrodynamics, 32, 623-628. https://doi.org/10.1007/s42241-020-0031-3
[16] Liu, C. et al. (2019). A Liutex based definition of vortex axis line. arXiv preprint arXiv:1904.10094. https://doi.org/10.48550/arXiv.1904.10094
[17] Samadi-Boroujeni, H. et al. (2013). Effect of triangular corrugated beds on the hydraulic jump characteristics. Canadian Journal of Civil Engineering, 40(9), 841-847. https://doi.org/10.1139/cjce-2012-0019
[18] Ghaderi, A. et al. (2020). Characteristics of free and submerged hydraulic jumps over different macroroughnesses. Journal of Hydroinformatics, 22(6), 1554-1572. https://doi.org/10.2166/hydro.2020.298
[19] Wu, Z. et al. (2021). Analysis of the influence of transverse groove structure on the flow of a flat-plate surface based on Liutex parameters. Engineering Applications of Computational Fluid Mechanics, 15(1), 1282-1297. https://doi.org/10.1080/19942060.2021.1968955
[20] Ji, B., et al. (2014). Numerical simulation of threedimensional cavitation shedding dynamics with special emphasis on cavitation – vortex interaction. Ocean Engineering, 87, 64-77. https://doi.org/10.1016/j.oceaneng.2014.05.005
[21] Tran, C., Bin, J., & Long, X. (2019). Simulation and Analysis of Cavitating Flow in the Draft Tube of the Francis Turbine with Splitter Blades at Off-Design Condition. Tehnicki vjesnik – Technical Gazette, 26(6). https://doi.org/10.17559/TV-20190316042929
