Application of the Standard Torbulance Model and the Volume of Fluid Method in Prediction of the Water Surface Profiles in a Hydraulic Jumps on the Triangular Corrugated Beds

Subject Areas : Article frome a thesis

Esmaeil Heidari Fahvande ¹ , Nader Barahmand ²

1 - دانشجوی کارشناسی ارشد سازه‌های هیدرولیکی، گروه مهندسی عمران، واحد لارستان، دانشگاه آزاد اسلامی، لارستان، ایران
2 - استادیار، گروه مهندسی عمران، واحد لارستان، دانشگاه آزاد اسلامی، لارستان، ایران.

Received: 2016-06-25 Accepted : 2016-06-25 Published : 2016-06-21

Keywords: Hydraulic jump, fluent, Triangular corrugated beds, VOF method, Torbulance model, Tail water,

Abstract :

The hydraulic jump is one of the most important topics In the field of open channel flow, which has been extensively investigated. When a flow condition changes from a supercritical to a subcritical regime, the result is an abrupt rise in the water surface level accompanied by turbulent rollers. This phenomenon is called a hydraulic jump.Many researches have shown that the corrugated beds caused the conjugate depth and length of the hydraulic jump are reduced as compared to those of smooth beds. In this study, a 2D numerical simulation of hydraulic jump on a triangular corrugated bed was simulated using various turbulence models (Standard and RNG k – model and  (SST) model) and Fluent software. Also, the free surface was determined, using the VOF method. Hydraulic jump was simulated in a rectangular channel with a triangular corrugated bed, using various Froude numbers within a range of 3-7.5. The numerical results showed that the  turbulence model and the VOF method were suitable for predicting the free surface profiles of hydraulic jumps on triangular corrugated beds. The relative error of the predicted free surface profiles and measured value were within a range of 3%- 7%. Also, the results confirmed that on everage, the tailwater depth on triangular corrugated beds was 34.8% less than that of smooth beds under similar hydraulic conditions. The numerical model indicated that as the distance from jump’s toe is increased, the turbulent kinematic energy (K) is reduce; Moreover the maximum value of bed shear stress was obtained on jump’s toe.

References:

1. ابریشمی، ج. و م. حسینی. 1385. هیدرولیک نهرهای باز. چ چهاردهم. انتشارات دانشگاه امام رضا (ع).


2. بدیع زادگان، ر. ک. اسماعیلی، م. فغور مغربی، و م. صانعی.1390. مشخصات پرش آبی در حوضچه های آرامش نهرهای آبیاری با بستر موجدار. نشریه آب و خاک. 25: 687-676.


3. برهمند، ن. و س­.ر. موسوی. 1392. مقایسه­ی شبیه­های مختلف آشفتگی به منظور شبیه سازی مناسب جریانهای چگال در مجاورت محل کاهش شیب بستر. مجله مهندسی منابع آب دوره 6 : 79-93.


4. پارسامهر، پ. ع. حسین زاده دلیر، د. فرسادیزاده، و ا. عباسپور.1391. پرش آبیهیدرولیکی بر روی بستر بازبریهای نیم استوانه ای شکل. نشریه آب وخاک. 26: 775.


5. عباسپور، ا. و س. هاشمی کیا. 1392. شبیه سازی عددی جریان بر روی سرریز استوانه ای با در نظر گرفتن مولفه­ی زبری با استفاده از شبیه معیار. مجله مهندسی منابع آب. 6. (18): 87-98.


6. غزالی، م. ح. صمدی بروجنی، ب. قربانی، و ر.ر. فتاحی نافچی. 1389. تاثیر بستر موجدار مثلثی بر مشخصات پرشآبی. مجله پژوهش آب ایران. سال 4: 108- 99.
   
   
   1. Abbaspour, A. A. Hosseinzadeh-Dalir, D. farsadizadeh, and A.A. Sadraddini, 2009. Effect of sinusoidal corrugated bed on hydraulic jump characteristics. Appl. Sci.  9: 2045-2055.
   
   
   2. Belanger, J.B. 1828. Essay on numerical solution of some problems relative to Steady flow of water. Carilan-Goeury, Paris,France.
   
   
   3. Choudhury, D. 1993. Introduction to the renormalization group method and turbulence modeling.  FLUENT Inc. Technical Memorandum TM-107.
   
   
   4. Durbin, P.A. 1995. Separated low computations with model. AIAA J. 33: 659-664.
   
   
   5. Ead, S.A. and N. Rajaratnam, 2000. Turbulent open channel flow in circular corrugated culverts. J. Hydraul. Eng. 126: 750-757.
   
   
   6. Ead, S.A. and N. Rajaratnam, 2002. Hydraulic jumps on corrugated bed. J. Hydrau. Eng. ASCE. 128:656-663.
   
   
   7. Elsebaie, I.H. and Sh. Shabayek, 2010. Formation of hydraulic jumps on corrugated beds. civil & Environ. Eng. 10: 40- 45.
   
   
   8. Hirt, C.W. and B.D. Nichols, 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phy. 39: 201–225. 
   
   
   9. Leutheusser, H.J. and E.J. Schiller, 1975. Hydraulic jump in a rough channel. Water Power Dam Constr.186-191.
   
   
   10. Parneix, S. P. Durbin, and M. Behnia, 1998. Computation of 3-D turbulent boundary layer using the model. Flow, Turbul. Combus, 60: 19-46.
   
   
   11. Rajaratnam, N. 1968. Hydraulic jump on rough bed. Trans.Eng. Lnst. Canada. 11:1-8.
   
   
   12. Shafai Bejestan, M. and K. Neisi, 2009. A new roughened bed hydraulic jump stilling basin. App. Sci. 2: 436-445.
   
   
   13. Tokyay, N.D. 2005. Effect of channel bed corrugations on hydraulic jumps. Impacts of Global Climate Change Conference Proc. Paper, EwRI, Anchorage,Alaska, USA. 408-416.
   
   
   14. Versteeg, H. K. and W. Malalasekera, 1995. An introduction to computational fluid dynamics: The finite volume method. Longman Scientific & Technical. ISBN 0-582-21884-5.
   
   
   15. Zho, Q., and S.K. Misra, 2004. Numerical study of a turbulent hydraulic jump. Eng. Mech. Conf. University of Delaware, New york. 78-85.