An experimental and numerical study of the influence of viscosity on the behavior of dam-break flow
Tóm tắt
In this paper, experimental and numerical methods are presented to investigate the dam-break flow in a horizontal rectangular section flume. In the experimental part of the research, different configurations have been tested: dry flume and the presence of shallow ambient water downstream with varied depth. In addition, experiments with viscosity changes in the fluid have been conducted. Numerically, the volume of the fluid method associated with the shear-stress transport turbulence model was used to examine the dam-break flow dynamics. Based on a review of analytical models in the literature, formulas for free water surfaces and propagation fronts were detailed. Qualitatively, various experimental snapshots of free water surfaces were obtained from the digitized images and compared with numerical predictions. Typical jet-like and mushroom-like formations have been observed. Experimental free surface profiles have been plotted against analytical and numerical results for different flow stages. The simulation of high-viscous fluid was conducted to emphasize the role of viscosity in negative wavefront velocity. By the comparison of the dam-break front locations from analytical, experimental, and numerical data, the effects of viscosity on the dam-break flow have been examined. In line with this, the influence of ambient water depth on the front propagation’s average velocity has been investigated. Finally, the air bubble characteristics, such as area, shape, and lifetime under the effects of fluid viscosity and surface tension, have been explored.
Tài liệu tham khảo
Aguirre-Pe, J., Plachco, F.P., Quisca, S.: Tests and numerical one-dimensional modelling of a high-viscosity fluid dam-break wave. J. Hydraul. Res. 33(1), 17–26 (1995). https://doi.org/10.1080/00221689509498681
Ancey, C., Cochard, S., Andreini, N.: The dam-break problem for viscous fluids in the high-capillary-number limit. J. Fluid Mech. 624, 1–22 (2009). https://doi.org/10.1017/S0022112008005041
Aureli, F., Mignosa, P., Tomirotti, M.: Numerical simulation and experimental verification of dam-break flows with shock. J. Hydraul. Res. 38(3), 197–206 (2000). https://doi.org/10.1080/00221680009498337
Bell, S.W., Elliot, R.C., Chaudhry, M.H.: Experimental results of two dimensional dam-break flows. J. Hydraul. Res. 30(2), 225–252 (1992). https://doi.org/10.1080/00221689209498936
Castro-Orgaz, O., Chanson, H.: Ritter’s dry-bed dam-break flows: positive and negative wave dynamics. Environ. Fluid Mech. 17, 665–694 (2017). https://doi.org/10.1007/s10652-017-9512-5
Castro-Orgaz, O., Chanson, H.: Undular and broken surges in dam-break flows: a review of wave breaking strategies in a Boussinesq-type framework. Environ. Fluid Mech. (2020). https://doi.org/10.1007/s10652-020-09749-3
Chanson, H.: Drag reduction in open channel flow by aeration and suspended load. J. Hydraul. Res. 32(1), 87–101 (1994). https://doi.org/10.1080/00221689409498791
Chanson, H.: Analytical Solutions of Laminar and Turbulent Dam Break Wave. Proc. Intl Conf. Fluvial Hydraulics River Flow 2006, Lisbon, Portugal, 6-8 Sept., Topic A3, paper A3008 (2006)
Deike, L., Kendall Melville, W., Popinet, S.: Air entrainment and bubble statistics in breaking waves. J. Fluid Mech. 801, 91–129 (2016). https://doi.org/10.1017/jfm.2016.372
Didden, N., Maxworthy, T.: The viscous spreading of plane and axisymmetric gravity currents. J. Fluid Mech. 121, 27–42 (1982). https://doi.org/10.1017/S0022112082001785
Dressler, R.: Comparison of theories and experiments for the hydraulic dam-break wave. Proc. Int. Assoc. Sci. Hydrol. Assemblée Générale Rome 3(38), 319–328 (1954)
Dutykh, D., Mitsotakis, D.: On the relevance of the dam-break problem in the context of non-linear shallow water equations. Discrete Contin. Dyn. Syst. Ser. S 3(2), 1–20 (2010). https://doi.org/10.1080/002216895094986810
Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39, 201–225 (1981). https://doi.org/10.1080/002216895094986811
Houltd, P.: Oil spreading on the sea. Ann. Rev. Fluid Mech. 4, 341–368 (1972). https://doi.org/10.1080/002216895094986812
Hui, J., Shao, S., Huang, Y., Hussain, K.: Evaluations of SWEs and SPH numerical modelling techniques for dam break flows. Eng. Appl. Comput. Fluid Mech. 7(4), 544–563 (2013). https://doi.org/10.1080/002216895094986813
Huppert, H.E.: The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58 (1982). https://doi.org/10.1080/002216895094986814
Jánosi, I.M., Jan, D., Szabo, K.G., Tel, T.: Turbulent drag reduction in dam-break flows. Exp. Fluids 37, 219–229 (2004). https://doi.org/10.1080/002216895094986815
Kleefsman, K.M.T., Fekken, G., Veldman, A.E.P., Iwanowski, B., Buchner, B.: A volume-of-fluid based simulation method for wave impact problems. J. Comput. Phys. 206, 363–393 (2005). https://doi.org/10.1080/002216895094986816
Kocaman, S., Ozmen-Cagatay, H.: The effect of lateral channel contraction on dam break flows: laboratory experiment. J. Hydrol. 432–433, 145–153 (2012). https://doi.org/10.1080/002216895094986817
Lauber, G., Hager, W.H.: Experiments to dam-break wave: sloping channel. J. Hydraul. Res. 36(5), 761–773 (1998). https://doi.org/10.1080/002216895094986818
Leal, J., Ferreira, R.M.L., Cardoso, A.H.: Dam-break wave-front celerity. J. Hydraul. Eng. 132(1), 69–76 (2006). https://doi.org/10.1080/002216895094986819
Li, X., Zhao, J.: Dam-break of mixtures consisting of non-Newtonian liquids and granular particles. Powder Technol. 338, 493–505 (2018). https://doi.org/10.1017/S00221120080050410
Lister, J.R.: Viscous flows down an inclined plane from point and line sources. J. Fluid Mech. 242, 631–653 (1992). https://doi.org/10.1017/S00221120080050411
Lobovský, L., Botia-Vera, E., Castellana, F., Mas-Soler, J., Souto-Iglesias, A.: Experimental investigation of dynamic pressure loads during dam break. J. Fluids Struct. 48, 407–434 (2014). https://doi.org/10.1017/S00221120080050412
Menter, F.R., Kuntz, M., Langtry, R.: Ten Years of Industrial Experience with the SST Turbulence Model. Turbulence, Heat and Mass Transfer 4, ed: K. Hanjalic, Y. Nagano, and M. Tummers, Begell House, Inc. ISBN:1567001963. pp. 625–632 (2003)
Mokrani, C., Abadie, S.: Conditions for peak pressure stability in VOF simulations of dam break flow impact. J. Fluids Struct. 62, 86–103 (2016). https://doi.org/10.1016/j.jfluidstructs.2015.12.007
Motozawa, M., Sawada, T., Ishitsuka, S., Iwamoto, K., Ando, H., Senda, T., Kawaguchi, Y.: Experimental investigation on streamwise development of turbulent structure of drag-reducing channel flow with dosed polymer solution from channel wall. Int. J. Heat Fluid Flow 50, 51–62 (2014). https://doi.org/10.1016/j.ijheatfluidflow.2014.05.009
Nistor, I., Palermo, D., Nouri, Y., Murty, T., Saatcioglu, M.: Tsunami-induced forces on structures. Handb. Coast. Ocean Eng. (2009). https://doi.org/10.1142/9789812819307_0011
Ozmen-Cagatay, H., Kocaman, S., Guzel, H.: Investigation of dam-break flood waves in a dry channel with a hump. J. Hydro-environ. Res. 8, 304–315 (2014). https://doi.org/10.1016/j.jher.2014.01.005
Peregrine, D.H.: Steep Unsteady Water Waves and Boundary Integral Methods. In: Cruse T.A. (eds) Advanced Boundary Element Methods. International Union of Theoretical and Applied Mechanics. Springer, Berlin, Heidelberg (1988). https://doi.org/10.1007/978-3-642-83003-7_31
Pu, J.H.: Turbulent rectangular compound open channel flow study using multi-zonal approach. Environ. Fluid Mech. 19, 785–800 (2018). https://doi.org/10.1007/s10652-018-09655-9
Ritter, A.: Die Fortpflanzung der Wasserwellen. Vereine Deutcher Ingenieure Zeitswchrift. 36, 947–954 (1892). ((in German))
Schmitt, F.G.: About Boussinesq’s turbulent viscosity hypothesis: historical remarks and a direct evaluation of its validity. Comptes Rendus Mécanique. 335 (9–10): 617-627. https://doi.org/10.1016/j.crme.2007.08.004
Shaheed, R., Mohammadian, A., Gildeh, H.K. : A comparison of standard k–\(\varepsilon \) and realizable k–\(\varepsilon \) turbulence models in curved and confluent channels. 19: 543–568 (2019). https://doi.org/10.1007/s10652-018-9637-1
Stagonas, D., Warbrick, D., Muller, G., Magagna, D.: Surface tension effects on energy dissipation by small scale, experimental breaking waves. Coast. Eng. 58, 826–836 (2011). https://doi.org/10.1016/j.coastaleng.2011.05.009
Stansby, P.K., Chegini, A., Barnes, T.C.D.: The initial stages of dam-break flow. J. Fluid Mech. 374, 407–424 (1998). https://doi.org/10.1017/S0022112098009975
Stoker, J.J.: Water waves. Interscience publ. Inc., New York (1957)
Sturm, T.W.: Open channel hydraulics. McGraw-Hill Science, New York (2001). https://doi.org/10.1115/1.1421122
Techet, A.H., McDonald, A.K.: High Speed PIV of Breaking Waves on Both Sides of the AirWater Interface. 6th International Symposium on Particle Image Velocimetry, Pasadena, California, USA, September 21–23 (2005). https://pdfs.semanticscholar.org/9f61/7a73820047d34c61f02f2e10b39f680d81e1.pdf
Tomboulides, A., Aithal, S.M., Fischer, P.F., Merzari, E., Obabko, A.V., Shaver, D.R.: A novel numerical treatment of the near-wall regions in the k \(- \quad \omega \) class of RANS models. Int. J. Heat Fluid Flow 72, 186–199 (2018). https://doi.org/10.1016/j.ijheat?uid?ow.2018.05.017
Vallier A.: Simulations of cavitation - from the large vapour structures to the small bubble Dynamics. Thesis, Lund University, (2013). https://doi.org/10.1016/j.jfluidstructs.2015.12.0070
Wang, B., Zhang, J., Chen, Y., Peng, Y., Liu, X., Liu, W.: Comparison of measured dam-break flood waves in triangular and rectangular channels. J. Hydrol. 575, 690–703 (2019). https://doi.org/10.1016/j.jfluidstructs.2015.12.0071
Wu, G., Li, C., Huang, D., Zhao, Z., Feng, X., Wang, R.: Drag reduction by linear viscosity model in turbulent channel flow of polymer solution. J. Cent. South Univ. Technol. 15(s1), 243–246 (2008). https://doi.org/10.1016/j.jfluidstructs.2015.12.0072
Ye, Z., Zhao, Z.: Investigation of water-water interface in dam break flow with a wet bed. J. Hydrol. 548, 104–120 (2017). https://doi.org/10.1016/j.jfluidstructs.2015.12.0073
Zhang, D.: Comparison of various turbulence models for unsteady flow around a finite circular cylinder at Re=20000. J. Phys. Conf. Ser. 910, 012027 (2017). https://doi.org/10.1016/j.jfluidstructs.2015.12.0074