Experimental Apparatus for Roll-Wave Measurements and Comparison with a 1D Mathematical Model
Publication: Journal of Hydraulic Engineering
Volume 143, Issue 11
Abstract
An experimental approach to examine the instabilities present on free surfaces of non-Newtonian fluid flow occurring in inclined channels is presented. When these flows occur in favorable conditions of inclination and discharge, it is observed that the propagation of instabilities can evolve into a specific type of wave, known as roll waves. The experimental apparatus developed allows simulation of stabilized roll waves in many scenarios for Newtonian and non-Newtonian rheology fluids, thereby constituting a highly useful approach for the understanding and control of roll waves. The fluid test for the non-Newtonian case used a gel rheometrically representative of the muddy material presented in natural disasters, such as mudflows. A low-cost, high-performance, and nonintrusive level measurement system (ultrasonic transducer) is proposed. A comparison between the experimental results obtained and a one-dimensional (1D) mathematical model exhibited good amplitude and wave-period estimations.
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Acknowledgments
The authors wish to acknowledge CNPq and FAPESP for financial support under Processes 449550/2014-1 and 2015/25518-8, respectively. Thanks are also given to CNPq for the postdoctoral (502961/2013-9) and Ph.D. scholarships (201557/2012-6) of the second and fourth authors, respectively. Finally, the authors thank Professor Doctor Edson Del Rio Vieira from the Mechanical Engineering Department of Unesp Ilha Solteira—SP for his collaboration.
References
Ancey, C. (2007). “Plasticity and geophysical flows: A review.” J. Non-Newtonian Fluid Mech., 142(1–3), 4–35.
Aranda, A., Amigo, N., Ihle, C., and Tamburrino, A. (2016). “Digital image correlation applied to the calculation of the out-of-plane deformation induced by the formation of roll waves in a non-Newtonian fluid.” Opt. Eng., 55(6), 064101.
Balmforth, N. J., Bush, J. W. M., and Craster, R. V. (2005). “Roll waves on flowing cornstarch suspensions.” Phys. Lett. A, 338(6), 479–484.
Borger, D. V., and Walters, K. (1993). Rheological phenomena in focus, Elsevier, Amsterdam, Netherlands, 155.
Brock, R. R. (1969). “Development of roll-wave trains in open channels.” J. Hydraulics Div., 95(4), 1401–1427.
Brookfield Viscometers. (1998). Operational manual R/S rheometer, Harlow, U.K., 112.
Burger, J., Haldenwang, R., and Alderman, N. (2010). “Friction factor-Reynolds number relationship for laminar flow of non-Newtonian fluids in open channels of different cross-sectional shapes.” Chem. Eng. Sci., 65(11), 3549–3556.
Burton, I. (2005). “The social construction of natural disasters: An evolutionary perspective.” Know risk, T. Jeggle, ed., Tudor Rose, Geneva, 35–36.
Coussot, P. (1994). “Steady, laminar, flow of concentrated mud suspensions in open channel.” J. Hydraul. Eng., 32(4), 535–559.
Coussot, P. (1997). Mudflow rheology and dynamics, A.A. Balkema, Rotterdam, Netherlands.
Di Cristo, C., Iervolino, M., and Vacca, A. (2013). “On the applicability of minimum channel length criterion for roll-waves in mud-flows.” J. Hydrol. Hydromech., 61(4), 286–292.
Di Cristo, C., and Vacca, A. (2005). “On the convective nature of roll waves instability.” J. Appl. Math., 2005(3), 259–271.
Dressler, R. F. (1949). “Mathematical solution of the problem of roll waves in inclined open channels.” Commun. Pure Appl. Math., 2(2–3), 149–194.
EMFAL. (2015). “Ficha de Informação Técnica.” ⟨⟩ (Oct. 5, 2016) (in Portugese).
Ferreira, F. O. (2013). “Estabilidade e controle dinâmico de roll waves, 204 f.” Ph.D. thesis Faculdade de Engenharia, Universidade Estadual Paulista, Ilha Solteira, Brazil (in Portugese).
Ferreira, F. O., Maciel, G. F., Fiorot, G. H., and Cunha, E. F. (2014). “Numerical analysis of roll waves generation on non-Newtonian fluids flowing down an inclined plane.” Advanced materials research, Vol. 1006–1007, Trans Tech, Zurich, Switzerland, 160–167.
Fiorot, G. H., Maciel, G. F., Cunha, E. F., and Kitano, C. (2015). “Experimental setup for measuring roll waves on laminar open channel flows.” Flow Meas. Instrum., 41, 149–157.
Forterre, Y., and Pouliquen, O. (2003). “Long-surface-wave instability in dense granular flows.” J. Fluid. Mech., 486, 21–50.
Gao, D., Morley, N. B., and Dhir, V. (2003). “Numerical simulation of wavy falling film flow using VOF method.” J. Comput. Phys., 192(2), 624–642.
Kapitza, P. L. (1948). Wave flow of thin layers of a viscous fluid, Pergamon, Oxford, U.K., 662–709.
Kranenburg, C. (1992). “On the evolution of roll waves.” J. Fluid Mech. Res., 245(-1), 249–261.
LabVIEW version 11.0.1 [Computer software]. National Instruments, Austin, TX.
Leite, L. O. B. (2009). “Determinação física e numérica de corridas de lama em escoamentos resultantes de ruptura de barreira retendo material viscoplástico, 185 f.” Master’s dissertation, Faculdade de Engenharia, Universidade Estadual Paulista, Ilha Solteira, Brazil (in Portugese).
Liu, J., and Gollub, J. P. (1994). “Solitary wave dynamics of film flows.” Phys. Fluids, 6(5), 1702–1712.
Maciel, G. F., Ferreira, F. O., and Fiorot, G. H. (2013). “Control of instabilities in non-Newtonian free surface fluid flows.” J. Braz. Soc. Mech. Sci. Eng., 35(3), 217–229.
Maciel, G. F., Santos, H. K., and Ferreira, F. O. (2009). “Rheological analysis of water clay compositions in order to investigate mudflows developing in canals.” J. Braz. Soc. Mech. Sci. Eng., 31(1), 64–74.
MATLAB version 7.10.0 [Computer software]. MathWorks, Natick, MA.
Merkin, J., and Needham, D. (1986). “An infinite period bifurcation arising in roll waves down an open inclined channel.” Proc., R. Soc. London, Ser. A, Math. Phys. Sci., 405(1828), 103–116.
Minussi, R. B., and Maciel, G. F. (2012). “Numerical experimental comparison of dam break flows with non-Newtonian fluids.” J. Braz. Soc. Mech. Sci. Eng., 34(2), 167–178.
Montuori, C. (1963). “Discussion of ‘Stability aspect of flow in open channels’.” J. Hydr. Div., 89(HY4), 264–273.
Ng, C. O., and Mei, C. C. (1994). “Roll waves on a layer of fluid mud modelled as a power law fluid.” J. Fluid Mech., 263(-1), 151–184.
Tamburrino, A., and Ihle, C. F. (2013). “Roll wave appearance in bentonite suspensions flowing down inclined planes.” J. Hydraul. Res., 51(3), 330–335.
Vilimek, V., and Spilkova, J. (2009). “Natural hazards and risks: The view from the junction of natural and social sciences.” Geografie–Sbornik ČGS, 114(4), 332–349.
Wisner, B., Blakie, P., Cannon, T., and Davis, I. (2004). At risk: Natural hazards, people’s vulnerability and disasters, Routledge, London, 496.
Zanuttigh, B., and Lamberti, A. (2002). “Roll waves simulation using shallow water equations and weighted average flux method.” J. Hydraul. Res., 40(5), 610–622.
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Published In
Journal of Hydraulic Engineering
Volume 143 • Issue 11 • November 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: May 28, 2016
Accepted: May 1, 2017
Published online: Aug 30, 2017
Published in print: Nov 1, 2017
Discussion open until: Jan 30, 2018
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