Scale Effects Investigation in Physical Modeling of Recirculating Shallow Flow Using Large Eddy Simulation Technique

Document Type : Regular Article


1 Department of Civil Engineering, Parahyangan Catholic University, Jl. Ciumbuleuit No. 94, Bandung, West Java 40141, Indonesia

2 Water Research Laboratory, University of New South Wales, 110 King St, Sydney 2093, Australia



In this study, the Large Eddy Simulation (LES) model in OpenFOAM was used to investigate the scale effects in the physical modeling of recirculating shallow flow at low Froude numbers. A laboratory test of turbulent flow through a submerged conical island with a Reynolds number of 6,210 was selected. The lab prototype was scaled with factors of 3 and 10 for both undistorted and distorted models. Our study employed the Froude similarity as the gravitational force is more dominant than the others (viscous, drag, and cohesion forces). Because the fluid (water) used for the prototype and model is the same, it is impossible to match the Reynolds, Weber, and Froude numbers simultaneously, resulting in the scale effects. For a scale of 1:1, the LES model could simulate the experimental data by appropriately capturing the vortices behind the conical island. For the undistorted models with scales of 3 and 10, the numerical model captured weaker magnitudes of vortices than the 1:1 scale, indicated by the discrepancies in velocity. In fact, the magnitudes of vortices became weaker with the distorted models. We also observed a significant increment in energy loss behind the conical island (where recirculating flows exist) as the scale increased. However, no significant discrepancies in velocity were observed between the results of the 1:1 scale and the scaled models in front of the conical island, where vortices were absent. These results indicate that the scale effects due to the Froude similarity are quite significant provided that recirculating turbulent flow occurs.


Main Subjects

Chanson, H. (2008). Physical modelling, scale effects, and self-similarity of stepped spillway flows. Proceedings of the World Environmental and Water Resources Congress 2008.
Chanson, H. (2009). Turbulent air–water flows in hydraulic structures: dynamic similarity and scale effects. Environmental Fluid Mechanics, 9(2), 125–142.
Chanson, H., & Murzyn, F. (2008). Froude similitude and scale effects affecting air entrainment in hydraulic jumps. Proceedings of the World Environmental and Water Resources Congress 2008.
Chanson, H., Aoki, S., & Hoque, A. (2004). Physical modelling and similitude of air bubble entrainment at vertical circular plunging jets. Chemical Engineering Science, 59(4), 747–758.
Chaudhry, M. H. (1993). Open-channel flow. Prentice-Hall, Inc., Englewood Cliffs.
Ferziger, J. H., & Perić, M. (1996) Computational Methods for Fluid Dynamics. Springer, Berlin.
Fröhlich, J., & Rodi, W. (2002). Introduction to Large Eddy Simulation of Turbulent Flows. In B. Launder & N. Sandham (Eds.), Closure Strategies for Turbulent and Transitional Flows (pp. 267-298). Cambridge: Cambridge University Press.
Ginting, B. M., & Ginting, H. (2019). Hybrid Artificial Viscosity–Central-Upwind Scheme for Recirculating Turbulent Shallow Water Flows. Journal of Hydraulic Engineering, 145(12), 04019041.
Heller, V. (2007). Massstabseffekte im hydraulischen Modell (Scale effects in hydraulic modelling). Wasser Energie Luft, 99(2), 153–159 [in German].
Heller, V. (2011). Scale effects in physical hydraulic engineering models. Journal of Hydraulic Research, 49(3), 293–306.
Hughes, S. A. (1993). Physical models and laboratory techniques in coastal engineering. World Scientific, London.
Kim, W. W., & Menon, S. (1995). A new dynamic one-equation subgrid-scale model for large eddy simulations. 33rd Aerospace Sciences Meeting and Exhibit, Reno, NV, United States.
Lesieur, M., & Metais, O. (1996). New trends in large-eddy simulations of turbulence. Annual Review of Fluid Mechanics, 28(1), 45–82.
Lloyd, P. M., & Stansby, P. K. (1997). Shallow-water flow around model conical islands of small side slope. II Submerged. Journal of Hydraulic Engineering, 123(12), 1068–1077.
Martin, H., & Pohl, R. (2000). Technische Hydromechanik 4 (Technical hydromechanics). Verlag für Bauwesen, Berlin [in German].
Menon, S., & Yeung, P. K. (1994). Analysis of subgrid models using direct and large-eddy simulations of isotropic turbulence. Proc. AGARD 74th Fluid Dynamics Symp. on Application of Direct and Large Eddy Simulation to Transition and Turbulence, AGARD-CP-551.
Menon, S., Yeung, P. K., & Kim, W. W. (1994). Effect of subgrid models on the computed interscale energy transfer in isotropic turbulence. 25th AIAA Fluid Dynamics Conference, Colorado Springs, CO, United States.
Novak, P., Guinot, V., Jeffrey, A., & Reeve, D. E. (2010). Hydraulic modelling: an introduction: principles, methods and applications (1st ed.). CRC Press.
Novak, P., Moffat, A. I. B., Nalluri, C., & Narayanan, R. (2007). Hydraulic Structures (4th ed.). CRC Press.
Ouro, P., Wilson, C. A. M. E., Evans, P., & Angeloudis, A. (2017). Large-eddy simulation of shallow turbulent wakes behind a conical island. Physics of Fluids, 29(12), 126601.
Piomelli, U. (1999). Large-eddy simulation: achievements and challenges. Progress in Aerospace Sciences, 35(4), 335–362.
Pope, S. (2000). Turbulent Flows. Cambridge: Cambridge University Press.
Rodi, W. (2017). Turbulence modeling and simulation in hydraulics: A historical review. Journal of Hydraulic Engineering, 143(5), 03117001.
Sagaut, P. (2006). Large eddy simulation for incompressible flows: an introduction (Third Ed.). Springer-Verlag Berlin Heidelberg.
Sharma, H., Singh, D., & Singh, A. K. (2021). Large eddy simulation of film cooling over a flat plate in supersonic flow. Journal of Thermal Science and Engineering Applications, 13(4), 041019.
Singh, D., Udayraj Singh, A. N., & Handique, J. (2022). Experimental and LES study of unconfined jet impingement on a smooth flat heated plate with slots of different widths. Experimental Heat Transfer
Stoesser, T. (2014). Large-eddy simulation in hydraulics: Quo Vadis? Journal of Hydraulic Research, 52(4), 441–452.
Suerich-Gulick, F., Gaskin, S. J., Villeneuve, M., & Parkinson, É. (2014). Free surface intake vortices: scale effects due to surface tension and viscosity. Journal of Hydraulic Research, 52(4), 513–522.
Torres, C., Borman, D., Matos, J., & Neeve, D. (2022). CFD modeling of scale effects on free-surface flow over a labyrinth weir and spillway. Journal of Hydraulic Engineering, 148(7), 4022011.
Tullis, B. (2018). Size-Scale Effects of Labyrinth Weir Hydraulics. 7th IAHR International Symposium on Hydraulic Structures, Aachen, Germany.
Versteeg, H. K.,  &Malalasekera, W. (2007). An introduction to computational fluid dynamics: the finite volume method 2nd edition. Edinbugh: Pearson Prentice Hall
Yoshizawa, A. (1993). Bridging between eddy-viscosity-type and second-order turbulence models through a two-scale turbulence theory. Physical Review E, 48(1), 273–281.