COMPUTATION OF 1D SIDE WEIR FLOW BY FINITE ELEMENT METHOD

L. AMARA, A. BERREKSI

Abstract


In this work, a numerical approach using finite element method is proposed for the integration of the nonlinear differential equation of the side weir flow in rectangular channel. After recalling the ordinary differential equation governing the problem, the numerical modeling is given by use of the Galerkin weighting residual method. The problem being of Cauchy with initial value, the element matrix obtained was rewritten in recurrence formula. The non-linearity of the latter is treated by an iterative technique for the variables; flow depth and lateral outflow. The performances of the numerical approach are confronted with experimental measurements available in the literature according to different flow regimes. The results obtained show a good agreement with the experimental observations.

Keywords


Side weir, Numerical model, Finite elements, weighted residuals, Galerkin’s method.

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References


AMARA L., BERREKSI A., ACHOUR B., ABDOUNE K. (2014). Numerical Computation of Water Level Fluctuation in Surge Tanks Using the Galerkin Method. Dam Engineering, vol. 25, no 1, pp. 23-35.

BALMFORTH D. J., SARGINSON E. J. (1983). The effects of curvature in supercritical side weir flow. Journal of Hydraulic Research, vol. 21, no 5, pp. 333-343.

CASTRO-ORGAZ O., HAGER W. H. (2011). Spatially-varied open channel flow equations with vertical inertia. Journal of Hydraulic Research, vol. 49, no 5, pp. 667-675.

CASTRO-ORGAZ O., HAGER W. H. (2012). Subcritical side-weir flow at high lateral discharge. Journal of Hydraulic Engineering, vol. 138, no 9, pp. 777-787.

CONNOR J. J., BREBBIA C. A. (1976). Finite element techniques for fluid flow. Newness-Butterworths, London, 310 p.

DE MARCHI G. (1934). Saggio di teoria funzionamento degli stramazzi laterali. Energia Elettrica, 11, pp. 849-860.

FAVRE H., BRAENDLE F. (1937). Expériences sur le mouvement permanent de l'eau dans les canaux découverts, avec apport ou prélèvement le long du courant. Bulletin Technique de la Suisse Romande, vol. 63, pp.93-96, pp.109-114, pp.129-134.

FEATHERSTONE R. E., NALLURI C. (1995). Civil engineering hydraulics: Essential theory with worked examples. Blackwell Science Ltd, 401 p.

GHODSIAN M. (2003). Supercritical flow over a rectangular side weir. Canadian Journal of Civil Engineering, vol. 30, no 3, pp. 596-600.

GRANATA F., DE MARINIS G., GARGANO R. (2013). A Flow Power Based Approach For Side Weirs. In : 35 th IAHR Congress, Chengdu, China.

HAGER W. H. (1981). Die Hydraulik von Verteikanaelen (L’hydraulique des canaux à débit décroissant). Thèse de Doctorat en sciences techniques, Ecole Polytechnique Fédérale de Zurich, ETH, Zurich, Suisse, N°6948, partie I, 332 p, partie II, 322 p.

HAGER W. H. (1986). L'écoulement dans des déversoirs latéraux. Canadian Journal of Civil Engineering, vol. 13, no 5, pp. 501-509.

HAGER W. H. (1987). Lateral outflow over side weirs. Journal of Hydraulic Engineering, vol. 113, no 4, pp. 491-504.

HAGER W. H., HAGER K. (1985). Streamline curvature effects in distribution channels. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, vol. 199, no 3, pp. 165-172.

HAGER W. H., VOLKART P. U. (1986). Distribution channels. Journal of Hydraulic Engineering, vol. 112, no 10, pp. 935-952.

MAY R. W. P., BROMWICH B. C., GASOWSKI Y., RICKARD C.E. (2003) Hydraulic design of side weirs. Thomas Telford, London, 133 p.

MICHELAZZO G. (2015). New analytical formulation of De Marchi’s model for a zero-height side weir. Journal of Hydraulic Engineering, vol. 141, no 12, pp. 04015030.

MIZUMURA K., YAMASAKA M., ADACHI J. (2003). Side outflow from supercritical channel flow. Journal of Hydraulic Engineering, vol. 129, no 10, pp. 769-776.

RAO K. D., PILLAI C. R. S. (2008). Study of flow over side weirs under supercritical conditions. Water resources management, vol. 22, no 1, pp. 131-143.

REDDY J. N. (2005). An introduction to the finite element method, Me Graw Hill, India, 755 p.

ROBINSON D. I., MCGHEE T. J. (1993). Computer modeling of side-flow weirs. Journal of irrigation and drainage engineering, vol. 119, no 6, pp. 989-1005.

SUBRAMANYA K., AWASTHY S. C. (1972). Spatially varied flow over side-weirs. Journal of the Hydraulics Division, vol. 98, no 1, pp. 1-10.

SUBRAMANYA K. (2009). Flow in Open Channels. 3e, Tata McGraw-Hill Education, New Delhi, 547 p.

ZIENKIEWICZ O. C., TAYLOR R. L. (2000). The finite element method: The basis (Vol. 1). Butterworth-heinemann, 689 p.


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