مدل سازی عددی شکست موج در کانال با مانع با استفاده از روش هیدرودینامیک ذرات هموار شده تراکم ناپذیر

نوع مقاله : مقاله پژوهشی

نویسندگان

1 فارغ التحصیل دکتری سازه‌های هیدرولیکی، بخش مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه شهید باهنر کرمان

2 استاد، بخش مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه شهید باهنر کرمان.

3 دانشیار، بخش مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه شهید باهنر کرمان،

چکیده

شکست موج پدیده­ای است که در جریان­های مخاطره­آمیز سیلاب اتفاق می­افتد. از این رو شبیه­سازی چنین جریان­هایی با روشی مناسب از اهمیت ویژه­ای برخوردار است. در این تحقیق شکست امواج روی بستر ناهموار با استفاده از روش هیدرودینامیک ذرات هموار­شده تراکم­ناپذیر (ISPH) مدل­سازی شده است. روش ISPH یک روش لاگرانژی و مبتنی بر ذره بوده که برای مدل­سازی جریان دارای سطوح آزاد پیچیده قدرتمند می­باشد. معادله­های حاکم در این مدل، معادله­های بقای جرم و اندازه حرکت (معادله­های ناویر استوکس) می­باشند که با روش دو گام جزیی حل شده اند. به­منظور بررسی کارایی مدل حاضر، مسئله شکست سد درکانال با مانع با انتهای باز و بسته مورد بررسی قرار گرفته است. نتایج مدل­سازی نشان می­دهد که بسیاری از پدیده­های پیچیده که در جریان­های دارای امواج شکننده اتفاق می­افتند، به خوبی با روش ISPH قابل مدل­سازی است. حداکثر خطای به­دست آمده با مقایسه نتایج مدل عددی و داده­های آزمایشگاهی، 3/15 درصد محاسبه شده است که نشان­دهنده دقت خوب مدل ISPH برای شبیه­سازی مسائل پیچیده مانند جریان­های ناشی از سیلاب در شکست سد می­باشد.

کلیدواژه‌ها


عنوان مقاله [English]

Numerical Modeling of Wave Breaking in a Bumpy Channel Using Incompressible Smoothed Particles Hydrodynamics

نویسندگان [English]

  • Sajedeh Farmani khanekahdani 1
  • Gholamabbas Barani 2
  • Mahnaz Ghaeini Hessaroeyeh 3
1 Ph.D. Graduate, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Iran
2 Professor, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Iran.
3 Associate Professor, Department of Civil Engineering, Faculty of Engineering, Shahid Bahonar University of Kerman, Iran.
چکیده [English]

Wave breaking can occur in dam break phenomenon. These waves can be summarized as an uncontrolled release of water flow instantaneously from rest by the sudden removal of a vertical barrier that initially contains water. This occurrence usually causes huge loss of lives and destructions of properties and environment. Therefore, prediction of water level position, velocity and pressure is essential.
Recently meshless methods have been used for numerical modeling of free surface flows. One of the oldest meshless methods is the Smoothed Particle Hydrodynamics (SPH). This method is robust to simulate problems with large deformations. Furthermore, SPH method has used successfully to model the fixed-bed dam break waves on a dry-bed and wet-bed downstream channel (Lee et al. 2008 and Khayed & Gotoh, 2010). SPH simulations of the incompressible flows can be performed by two methods: 1) approximately simulating incompressible flows with a small compressibility, namely Weakly Compressible SPH (WCSPH); 2) simulating flows by enforcing incompressibility, namely Incompressible SPH (ISPH). In WCSPH method, the flow is considered as slightly compressible, with a state equation for the pressure calculation (Monaghan, 1994). In ISPH method the pressure-velocity coupling is generally achieved by the projection method (Hu and Adams, 2007). This paper presents a two-dimensional ISPH model to simulate dam break waves in a bed with a hump.

کلیدواژه‌ها [English]

  • Waves breaking
  • ISPH method
  • Fractional step method
  • Dam break
1-    Ataie-Ashtiani, B., Shobeiry, G. and Farhadi, L., 2006. Modified Incompressible SPH method for simulating free surface problem. Fluid Dynamic Research. 40, pp. 637-661.
 
2-    Chang, T.J., Kao, H.M., Chang, K.H. and Hsu M.H., 2011. Numerical simulation of shallow water dam break flows in open channels using smoothed particle hydrodynamics. Journal of Hydrology. 408, pp. 78-90.
 
3-    Dalrymple, R.A. and Rogers, B.D., 2006. Numerical modeling of water waves whit the SPH method. Coastal Engineering. 53, pp. 141-147.
 
4-    De Wit, L. 2006. Smoothed Particle Hydrodynamics a study of the possibilities of SPH in hydraulic engineering. MSc thesis, Delft University of Technology. Netherland.
 
5-    Kao, H.M. and Chang, T.J., 2012. Numerical modeling of dambreak-induced flood and inundation using smoothed particle hydrodynamics. Journal of Hydrology. 448, pp. 232-244.
 
6-    Lee, E.S., Moulinec, C., Xu, R., Violeau, D., Laurence, D. and Stansby, P. و2008. Comparisons of Weakly Compressible and Truly Incompressible Algorithms for the SPH Mesh Free Particle Method. Journal of Computational Physics. 227, pp. 8417-8436
 
7-    Lucy, LB., 1997. A numerical approach to the testing of the fission hypothesis. Astronomy Journal. 82 (12), pp. 1013–1024.
 
8-    Marsooli, R., Zhang, M. and Weiming, Wu., 2011. Vertical and horizontal two-dimensional numerical modeling of dam-break flow over fixed beds. World Experimental and Water Resources Congress (ASCE). pp. 2225-2233.
 
9-    Monaghan, J.J., 1992. Smoothed Particle Hydrodynamics. Anu. Rev. Astron. Astrophysics. 30, pp. 543-574.
 
10- Monaghan, J.J., 1994. Simulating free surface flows whit SPH, Journal of Computational Physics, 110, pp. 399-406.
 
11- Monaghan, J.J., 2000. SPH without a tensile instability. Journal of Computational Physics. 159, pp. 290-311.
 
12- Nomeritae., Daly E., Grimaldi S. and Hong Bui H., 2016. Explicit incompressible SPH algorithm for free- surface flow modelling: a comparison with weakly compressible schemes. Advances in Water Resources. 97, pp. 156-167.
 
13- Ozmen-Cagatay, H., Kocaman, S. and Guzel, H., 2014. Investigation of dam-break flood waves in a dry channel with a hump. Journal of Hydro-environment Research. pp.1-12.
 
14- Pahar, G. and Dhar, A., 2017. On modification of pressure gradient operator in integrated ISPH for multifluid and porous media flow with free-surface. Engineering Analysis with Boundary Elements.80, pp. 38-48
 
15- Razavi Toosi, S.L., Ayyoubzadeh, S.A. and Valizadeh, A., 2010. The influence of time scale in free surface flow simulation using Smoothed Particle Hydrodynamics (SPH). Journal of Irrigation Sciences and Engineering. 33, pp. 75-92. In Persian.
 
16- Ren, J., Jiang, T., Lu W. and Li G., 2016. An improved parallel SPH approach to solve 3D transient generalized Newtonian free surface flows. Computer Physics Communications. 205, pp. 87-105.
 
17- Rezavand, M., Taeibi-Rahni, M. and Rauch, W., 2017. An ISPH scheme for numerical simulation of multiphase flows with complex interfaces and high density ratios. Computers & Mathematics with Applications. 75, pp. 2658-2677.
 
18- Shao, S., and Lo. E., 2003. Incompressible SPH method for simulating Newtonian and non-Newtonian flows whit a free surface. Advances in Water Resources. 26, pp. 787-800.
 
19- Soares-Frazao, S., 2002. Dam-break induced flows in complex topographies. Theoretical, numerical and experimental approaches. PhD Thesis, Louvainla- Neuve: Universitá Catholique de Louvain, Civil Engineering Department, Hydraulics division, 116(8).
 
20- Xu, X. and Deng, X., 2016. An improved weakly compressible SPH method for simulating free surface flows of viscous and viscoelastic fluids. Computer Physics Communications. 201, pp. 43-46
 
21- Xu, H. and Lin, P., 2017. A new two-step projection method in an ISPH model for free surface flow computations. Coastal Engineering. 127, pp. 68-79.
 
22- Xu, R., Stansby, P.K. and Laurence, D., 2009. Accuracy and Stability in Incompressible SPH (ISPH) Based on the Projection Method and a New Approach. Journal of Computational Physics. 228 (18), pp. 6703-6725.