Abstract

Numerical simulation of undular hydraulic jumps, which occur at an inflow Froude number slightly above unity, remain an important and enigmatic challenge in hydraulic engineering. In this study, a systematic assessment of the two-dimensional (2D) Reynolds averaged Navier Stokes–volume of fluid (RANS-VOF) equations coupled with the kω shear stress transport (SST) turbulence model was carried out for the simulation of undular jumps. The modeling strategies adopted for obtaining a stable undular jump profile are highlighted in this paper. The correlation between turbulence intensity at the jump toe and jump characteristics is also demonstrated. Comparison of laboratory observations with results obtained from experiments conducted under different discharge, approach Froude number, and inflow conditions demonstrated that the proposed 2D RANS model can accurately reproduce the key free-surface characteristics corresponding to undular jumps. The model was capable of reproducing the velocity and pressure fields with greater accuracy than the depth-averaged model. The model was also successful in reproducing the bottom recirculation region below the first wave crest for undular jumps with partially developed boundary layer at the jump toe. The proposed 2D RANS-VOF computational fluid dynamics (CFD) model coupled with the k–ω SST turbulence closure equation is, therefore, recommended as an efficient tool for hydraulic computations, especially for the simulation of weak undular jumps.

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Data Availability Statement

Some or all data, models, or code generated or used during the study are available from the corresponding author by request. This includes information related to the implementation of the model in the OpenFOAM software package.

References

Andersen, V. M. 1978. “Undular hydraulic jump.” J. Hydraul. Div. 104 (8): 1185–1188. https://doi.org/10.1061/JYCEAJ.0005048.
Bayon, A., J. P. Toro, F. A. Bombardelli, J. Matos, and P. A. López-Jiménez. 2018. “Influence of VOF technique, turbulence model and discretization scheme on the numerical simulation of the non-aerated, skimming flow in stepped spillways.” J. Hydro-environ. Res. 19 (Mar): 137–149. https://doi.org/10.1016/j.jher.2017.10.002.
Bayon, A., D. Valero, R. García-Bartual, P. A. López-Jiménez, and F. J. Vallés-Morán. 2016. “Performance assessment of OpenFOAM and FLOW-3D in the numerical modelling of a low Reynolds number hydraulic jump.” Environ. Modell. Software 80 (Jun): 322–335. https://doi.org/10.1016/j.envsoft.2016.02.018.
Bayon-Barrachina, A., and P. A. Lopez-Jimenez. 2015. “Numerical analysis of hydraulic jumps using OpenFOAM.” J. Hydroinf. 17 (4): 662–678. https://doi.org/10.2166/hydro.2015.041.
Blocken, B., and C. Gualtieri. 2012. “Ten iterative steps for model development and evaluation applied to computational fluid dynamics for environmental fluid mechanics.” Environ. Modell. Software 33 (Jul): 1–22. https://doi.org/10.1016/j.envsoft.2012.02.001.
Bombardelli, F. A., C. W. Hirt, and M. H. García. 2001. “Computations of curved free surface water flow on spiral concentrators.” J. Hydraul. Eng. 127 (7): 629–631. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:7(629).
Bombardelli, F. A., I. Meireles, and J. Matos. 2011. “Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways.” Environ. Fluid Mech. 11 (3): 263–288. https://doi.org/10.1007/s10652-010-9188-6.
Bose, S. K., O. Castro-Orgaz, and S. Dey. 2012. “Free surface profiles of undular hydraulic jumps.” J. Hydraul. Eng. 138 (4): 362–366. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000510.
Bose, S. K., and S. Dey. 2007. “Curvilinear flow profiles based on Reynolds averaging.” J. Hydraul. Eng. 133 (9): 1074–1079. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:9(1074).
Castro-Orgaz, O. 2010. “Weakly undular hydraulic jump: Effects of friction.” J. Hydraul. Res. 48 (4): 453–465. https://doi.org/10.1080/00221686.2010.491646.
Castro-Orgaz, O., W. H. Hager, and S. Dey. 2015. “Depth-averaged model for undular hydraulic jump.” J. Hydraul. Res. 53 (3): 351–363. https://doi.org/10.1080/00221686.2014.967820.
Cebeci, T. 2013. Analysis of turbulent flows with computer programs. Oxford, UK: Elsevier.
Celik, I. B., U. Ghia, and P. J. Roache. 2008. “Procedure for estimation and reporting of uncertainty due to discretization in CFD applications.” J. Fluids Eng. 130 (7): 078001. https://doi.org/10.1115/1.2960953.
Chanson, H. 1993. Characteristics of undular hydraulic jumps. St. Lucia, QLD, Australia: Dept. of Civil Engineering, Univ. of Queensland.
Chanson, H. 1995. Flow characteristics of undular hydraulic jumps: Comparison with near-critical flows. St. Lucia, QLD, Australia: Dept. of Civil Engineering, Univ. of Queensland.
Chanson, H. 2002. “Hydraulic condition for undular-jump formations.” J. Hydraul. Res. 40 (3): 379–384. https://doi.org/10.1080/00221680209499953.
Chanson, H. 2005. “Physical modelling of the flow field in an undular tidal bore.” J. Hydraul. Res. 43 (3): 234–244. https://doi.org/10.1080/00221680509500118.
Ferziger, J. H., M. Peric, and R. L. Street. 2020. Computational methods for fluid dynamics. Berlin: Springer.
Gotoh, H., Y. Yasuda, and I. Ohtsu. 2005. “Effect of channel slope on flow characteristics of undular hydraulic jumps.” WIT Trans. Ecol. Environ. 83: 33–42.
Hager, W. H., and O. Castro-Orgaz. 2019. “On the undular hydraulic jump and the undular surge.” In Vol. 1 of Proc., 38th IAHR Congress, 2030–2039. Panama City, Panama: International Association for Hydraulic Research. https://doi.org/10.3850/38WC092019-0414.
Hirt, C. W., and B. D. Nichols. 1981. “Volume of fluid (VOF) method for the dynamics of free boundaries.” J. Comput. Phys. 39 (1): 201–225. https://doi.org/10.1016/0021-9991(81)90145-5.
Issa, R. I. 1986. “Solution of the implicitly discretized fluid flow equations by operator- splitting.” J. Comput. Phys. 62 (1): 40–65. https://doi.org/10.1016/0021-9991(86)90099-9.
Larsen, B. E., D. R. Fuhrman, and J. Roenby. 2019. “Performance of interFoam on the simulation of progressive waves.” Coastal Eng. J. 61 (3): 380–400. https://doi.org/10.1080/21664250.2019.1609713.
Macián-Pérez, J. F., A. Bayón, R. García-Bartual, P. A. López-Jiménez, and F. J. Vallés-Morán. 2020. “Characterization of structural properties in high Reynolds hydraulic jump based on CFD and physical modeling approaches.” J. Hydraul. Eng. 146 (12): 04020079. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001820.
Menter, F., M. Kuntz, and R. Langtry. 2003. “Ten years of industrial experience with the SST turbulence model.” In Turbulence, heat and mass transfer, edited by K. Hanjalic, Y. Nagono, and M. Tummers, 625–632. New York: Begell House.
Menter, F. R. 1994. “Two-equation eddy viscosity turbulence models for engineering applications.” AIAA J. 32 (8): 1598–1605. https://doi.org/10.2514/3.12149.
Ohtsu, I., Y. Yasuda, and H. Gotoh. 2001. “Hydraulic conditions for undular jump formations.” J. Hydraul. Res. 39 (2): 203–209. https://doi.org/10.1080/00221680109499821.
OpenFOAM Foundation. 2013. “The OpenFOAM web page.” Accessed August 10, 2021. http://www.openfoam.org.
Patankar, S. V., and D. B. Spalding. 1972. “A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows.” J. Heat Mass Transfer 15 (10): 1787–1806. https://doi.org/10.1016/0017-9310(72)90054-3.
Reinauer, R., and W. H. Hager. 1995. “Non-breaking undular hydraulic jump.” J. Hydraul. Res. 33 (5): 683–698. https://doi.org/10.1080/00221689509498564.
Robertson, E., V. Choudhury, S. Bhushan, and D. Walters. 2015. “Validation of OpenFOAM numerical methods and turbulence models for incompressible bluff body flows.” Comput. Fluids 123 (Dec): 122–145. https://doi.org/10.1016/j.compfluid.2015.09.010.
Rodi, W. 2017. “Turbulence modeling and simulation in hydraulics: A historical review.” J. Hydraul. Eng. 143 (5): 03117001. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001288.
Roenby, J., H. Bredmose, and H. Jasak. 2016. “A computational method for sharp interface advection.” R. Soc. Open Sci. 3 (11): 160405. https://doi.org/10.1098/rsos.160405.
Romagnoli, M., M. Portapila, and H. Morvan. 2009. “Computational simulation of a hydraulic jump” [Simulaci ón computacional del resalto hidráulico]. [In Spanish.] Mecánica Computacional 28 (1): 1661–1672.
Rostami, F., S. R. S. Yazdi, M. A. M. Said, and M. Shahrokhi. 2012. “Numerical simulation of undular jumps on graveled bed using volume of fluid method.” Water Sci. Technol. 66 (5): 909–917. https://doi.org/10.2166/wst.2012.213.
Schneider, W., R. Jurisits, and Y. S. Bae. 2010. “An asymptotic iteration method for the numerical analysis of near-critical free-surface flows.” Int. J. Heat Fluid Flow 31 (6): 1119–1124. https://doi.org/10.1016/j.ijheatfluidflow.2010.07.004.
Toro, J. P., F. A. Bombardelli, J. Paik, I. Meireles, and A. Amador. 2016. “Characterization of turbulence statistics on the non-aerated skimming flow over stepped spillways: A numerical study.” Environ. Fluid Mech. 16 (6): 1195–1221. https://doi.org/10.1007/s10652-016-9472-1.
Witt, A., J. Gulliver, and L. Shen. 2015. “Simulating air entrainment and vortex dynamics in a hydraulic jump.” Int. J. Multiphase Flow 72 (Jun): 165–180. https://doi.org/10.1016/j.ijmultiphaseflow.2015.02.012.

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Go to Journal of Hydraulic Engineering
Journal of Hydraulic Engineering
Volume 147Issue 11November 2021

History

Received: Dec 29, 2020
Accepted: Jul 13, 2021
Published online: Sep 15, 2021
Published in print: Nov 1, 2021
Discussion open until: Feb 15, 2022

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Tirtha Roy Biswas [email protected]
Ph.D. Candidate, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India. Email: [email protected]
Professor, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India. ORCID: https://orcid.org/0000-0001-9764-1346. Email: [email protected]
Professor, Dept. of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721302, India (corresponding author). ORCID: https://orcid.org/0000-0002-4481-9865. Email: [email protected]; [email protected]

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