Hydraulic characteristics of flow over the asymmetric hydrofoil weirs

Document Type : Research Article


1 elhambahman69@gmail.com

2 Associate Professor, Department of Civil Engineering, Isfahan University of Technology

3 Department of Civil Engineering, Isfahan University of Technology


Weirs are one of the most common hydraulic structures and are used to regulate the upstream approach flow depth, measure the flow discharge, and evacuate the excess flow discharge in dams, irrigation and drainage networks. Based on the ratio of the total head of the upstream approach flow to the length of the weir, weirs of finite crest length are categorized into four main groups, namely sharp-crested, short-crested, broad-crested, and long-crested type weirs. The thickness of the crest results in different velocity and pressure profiles over the weir crest and consequently tends to various flow behaviors. The short-crested weirs are categorized as three different types, including ogee, circular-crested, and hydrofoil weirs. The hydrofoil weirs are a type of short-crested weirs that are designed on the basis of airfoil theory. This kind of weirs has some merits compared to the other types, such as high discharge coefficient, stability and submergence limit, and low fluctuations of pressure and water free-surface profile. Despite the extensive studies have been carried out on the hydraulic characteristics of the ogee and circular-crested weirs, there is a lack of comprehensive studies on the hydrofoil weirs, and therefore the flow characteristics over the hydrofoil weirs are still unknown.

A hydrofoil weir is designed, on the basis of the Joukowsky transformation function to the equation of a reference circle on the source coordinate plane. The weir pattern generated on the destination coordinate plane is a function of the radius and the coordinate of the center of the circle on the source coordinate plane. If the center of a circle in the source coordinate plane is offset just on the horizontal axis, the Joukowsky transformation yields a symmetric hydrofoil. In this situation, if the center of a circle in the source coordinate plane is offset as large as the radius of the reference circle, the Joukowsky transformation yields a circular-crested weir. On the other hand, if the center of the circle in the source coordinate plane is offset on both the horizontal- and vertical axis, the Joukowsky transformation yields an asymmetric hydrofoil. So far, only three published studies have investigated the flow characteristics over symmetrical hydrofoil weirs. In symmetric hydrofoil weirs, the height of the weir is small, therefore these weirs have received less attention by the researchers till now. Whereas, by applying the asymmetric hydrofoil weirs instead of the symmetric ones, the weir height increases to be used for practical purposes. The present research subjects to study the flow behavior over the asymmetric hydrofoil weirs using experimental and numerical models. An experimental and numerical investigation was conducted, applying three and five models of the asymmetric hydrofoil weirs, respectively, designed on the basis of the Joukowsky transform function. Numerical simulations were performed using open source, OpenFoam v.4.0.1, CFD software. The interFoam solver and the VOF (volume of fluid) method is used to achieve the water free surface profiles and the other hydrodynamic characteristics of the flow field. The PIMPLE (pressure implicit method for pressure linked equations) algorithm was applied to couple the pressure and velocity equations in two-phase flows. In the present study, structured meshes with hexahedral elements were created by the blockMesh utility of OpenFOAM software. To generate a finer grid mesh close to the weir body and along the water free surface, snappyHexMesh utility was applied. To validate the numerical results, former experimental results and the present experimental data of different hydrofoil weirs were applied. Based on the recommendations of former studies, the k-ω SST turbulence model was used for the determination of flow characteristics over the hydrofoil weirs.

Results and discussion
The results of the numerical simulations including different geometrical characteristics, showed that the asymmetric hydrofoil weirs decrease the possibility of cavitation and the range of positive pressure downstream of the weir compared to those of circular-crested weirs, without decreasing the weir height. Also, in the asymmetric hydrofoil weirs, the results demonstrated that the greatest bed shear stresses and the compressive forces occur at the downstream end of the hydrofoil weir with a more camber, therefore, the downstream zone of these weirs is responsible for large values of bed erosion. Furthermore, the possibility of the downstream bed erosion is the same for the circular-crested weirs and the asymmetric hydrofoil weirs, having equal height.
Finally, by applying asymmetric hydrofoil weirs instead of circular-crested weirs, unfavorable flow conditions would be removed, leading to a more safe and economic hydraulic structures, without decreasing the weir structural height.
Keywords: Bed shear stress, Joukowsky transform function, OpenFoam software, Pressure distribution, Velocity profile.


Jacobs, E.N., Ward, K.E. and Pinkerton, R.M. (1933). The characteristics of 78 related airfoil sections from tests in the variable-density wind tunnel. National Advisory Committee for Aeronautics Report. 460, 299–354.
Montes, J.S. (1970). Flow over round-crested weirs. L’Energia Elettrica. 47(3), 155–164.
Sarginson, E. J. (1972). The influence of surface tension on weir flow. J. Hydraulic Res. 10(4), 431–446.
Tennekes, H. and Lumley, J.L. (1972). A First Course in Turbulence. The MIT Press. Massachusetts, United States, 300 p.
Lakshmana Rao, N.S. and Jagannadha Rao, M.V. (1973). Characteristics of hydrofoil weirs. J. Hydraulic Div., 99(HY2), 259–283.
Bos, M.G. (1976). Discharge measurement structures. International Institute for Land    Reclamation and Improvement. Wageningen, The Netherlands, 401 p.
Hager, W.H. (1991). Experiments on standard spillway flow. Proc. Instn Civ. Engrs., 91(3), 399–416.
Ramamurthy, A. S. and Vo, N. D. (1993). Characteristic of circular crested weir. J. Hydraulic Eng., 119(9), 1055–1063.
Chanson, H. and Montes, J. S. (1998). Overflow characteristics of circular weir. J. Irrig. Drain. Eng., 124(3), 152–162.
Savage, B. and Johnson, M. (2001). Flow over ogee spillway: Physical and numerical model case study. J. Hydraulic Eng., 127(8), 640–649.
Heidarpour, M. and Chamani, M. R. (2006). Velocity distribution over cylindrical weir. J. Hydraulic Res., 44(5), 708–711.
Johnson, M. and Savage, B. (2006). Physical and numerical comparison of flow over ogee spillway in the presence of tailwater. J. Hydraulic Eng., 132(12), 1353–1357.
Castro-Orgaz, O. (2008). Curvilinear flow over round-crested weirs. J. Hydraulic Res., 46(4), 543–547.
Jensch, C., Pfingsten, K.C. and Radespiel, R. (2008). Numerical investigation of leading edge blowing and optimization of the slot geometry for a circulation control airfoil. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 112, 183-190.
Schmocker, L., Halldórsdóttir, B. R. and Hager, W. H. (2011). Effect of weir face angles on circular-crested weir flow. J. Hydraulic Eng., 137(6), 637–643.
Tullis, B. P. (2011). Behavior of submerged ogee crest weir discharge coefficients. J. Irrig. Drain. Eng., 137(10), 677–681.
Lopes, P. (2013). Free-surface flow interface and air-entrainment modeling using OpenFoam. PhD Thesis, University of Coimbra, Portugal, 187p.
Castro-Orgaz, O. and Hager, W. H. (2014). Scale effects of round-crested weir flow, J. Hydraulic Res., 52(5), 653–665.
Kabiri-Samani, A. and Bagheri, S. (2014). Discharge coefficient of circular-crested weirs based on combination of flow around a cylinder and circulation. J. Irrig. Drain. Eng., 140(5), 04014010.
Kabiri-Samani, A., Rabiei, M.H., Safavi, H. and Borghei, S.M. (2014). Experimental-analytical investigation of super- to subcritical flow transition without a hydraulic jump. J. Hydraulic Res., 52(1), 129–136.
Olver, P.J. (2014). Introduction to Partial Differential Equations. Springer, New York, 636 p.
Hu, Z.Z., Greaves, D. and Raby, A. (2016). Numerical wave tank study of extreme waves and wave-structure interaction using OpenFoam®. J. Ocean Eng. 126, 329-342.
Bagheri, S. (2017). Hydraulic characteristics of flow over the streamlined weirs. PhD Thesis, Isfahan University of Technology, Isfahan, 106 p. (in Persian)
Bagheri, S. and Kabiri-Samani, A. (2017). Hydraulic characteristics of flow over the streamlined weirs. Modares Civil Engineering Journal. 17(6), 29–42. (in Persian)
Castro-Orgaz, O. and Hager, W. H. (2017). Non-Hydrostatic Free Surface Flows. Springer, New York, 696 p.
Farshi, F., Kabiri-Samani, A.R., Chamani, M.R. and Atoof, H. (2018). Evaluation of the secondary current parameter and depth-averaged velocity in curved compound open channels. J. Hydraulic Eng. 144(9), 04018059.
Gourbesville, P., Cunge, J. and Caignaert, G. (2018). Advances in Hydroinformatics. Springer, New York, 560 p.
Hong, H. H., Sturm, T. W. and González-Castro, J. A. (2018). Transitional flow at low-head ogee spillway. J. Hydraulic Eng. 144(2), 04017062.