Publicado 4 números por año
ISSN Imprimir: 1065-3090
ISSN En Línea: 1940-4336
Indexed in
LINEAR STABILITY ANALYSIS OF NAPPE OSCILLATIONS
SINOPSIS
The falling liquid curtain at a low-head condition subjected to an air cushion on one side develops longitudinal oscillations. These oscillations can generate considerable sound energy that can induce vibrations in the nearby structures. Thus, stability analysis and flow visualization of these liquid sheets is vital for safeguarding the structures housing them. In the present study, global behavior of gravitational inviscid liquid sheet subjected to an adjacent compressible air cushion is analyzed. The linear stability analysis is carried out by formulating the eigenvalue problem. Moreover, the effect of Froude number, domain size, and nozzle width on the oscillations is investigated. It is demonstrated that an increase in the inertia forces and nozzle width destabilize the liquid sheet. However, an increase in air cushion size stabilizes the liquid sheet oscillations. Moreover, global eigenmodes for pressure and sheet deflection are compared. It is depicted that the growth of perturbations occur until the pressure oscillations are in phase with the liquid sheet oscillations, whereas amplitude dampening occurs when both are out of phase. In addition, numerical simulation has been performed, taking into consideration viscosity and surface tension forces, to visualize the temporal behavior of the gravitational liquid nappe. It is depicted that due to confinement, the pressure builds up near the wall, causing the sheet to deflect away from it.
-
Anderson, A. and Tullis, B.P., Finite Crest Length Weir Nappe Oscillation, J. Hydraulic Eng., vol. 144, no. 6, p. 04018020,2018.
-
Arote, A., Bade, M., and Banerjee, J., Numerical Investigations on Stability of the Spatially Oscillating Planar Two-Phase Liquid Jet in a Quiescent Atmosphere, Phys. Fluids, vol. 31, no. 11, p. 112103,2019.
-
Arote, A., Bade, M., and Banerjee, J., On Coherent Structures of Spatially Oscillating Planar Liquid Jet Developing in a Quiescent Atmosphere, Phys. Fluids, vol. 32, no. 8, p. 082111, 2020. DOI: 10.1063/5.0016480. DOI: 10.1063/5.0016480
-
Arote, A., Bade, M., and Banerjee, J., Behavior of Synchronous and Asynchronous Spatially Oscillating Planar Liquid Jets in Tandem, Phys. Fluids, vol. 33, no. 5, p. 052102,2021a. DOI: 10.1063/5.0046990. DOI: 10.1063/5.0046990
-
Arote, A., Bade, M., and Banerjee, J., Numerical Investigations into the Effect of Confinement on the Stability of an Oscillating Planar Liquid Jet, IOP Conf. Ser.: Mater. Sci. Eng., vol. 1128, no. 1, p. 012032, 2021b.
-
Binnie, A.M. and A, P.R.S.L., Resonating Waterfalls, Proc. Roy. Soc. London. A: Math. Phys. Sci, vol. 339, no. 1619, pp. 435-449,1974.
-
Casperson, L.W., Fluttering Fountains: Simplified Models, J. Appl. Phys., vol. 74, no. 8, pp. 4894-4898, 1993.
-
Casperson, L.W., Fluttering Fountains: Stability Criteria, Journal of Applied Physics, vol. 75, no. 10, pp. 4892-4894,1994.
-
Chanson, H., Hydraulics of Nappe Flow Regime above Stepped Chutes and Spillways, Australian Civil/Structural Engineering Transactions, vol. CE36, no. 1, pp. 69-76,1994.
-
Chanson, H., Some Hydraulic Aspects during Overflow above Inflatable Flexible Membrane Dam, Department of Civil Engineering, The University of Queensland, vol. CH47/86, Australia, 1996.
-
Coppola, G., De Rosa, F., and de Luca, L., Surface Tension Effects on the Motion of a Free-Falling Liquid Sheet, Phys. Fluids, vol. 25,no. 6,p. 062103,2013. DOI: 10.1063/1.4810751. DOI: 10.1063/1.4810751
-
De Rosa, F., Girfoglio, M., and de Luca, L., Global Dynamics Analysis ofNappe Oscillation, Phys. Fluids, vol. 26, no. 12, pp. 1-25,2014.
-
Della Pia, A., Chiatto, M., and de Luca, L., Global Eigenmodes of Thin Liquid Sheets by Means of Volume-of-Fluid Simulations, Phys. Fluids, vol. 32, no. 8, p. 082112,2020.
-
Desjardins, O. and Pitsch, H., Detailed Numerical Investigation of Turbulent Atomization of Liquid Jets, Atomization Sprays, vol. 20, no. 4, pp. 311-336,2010.
-
Driscoll, T.A., Hale, N., and Trefethen, L.N., Chebfun Guide, Pafnuty Publications, Oxford, UK, 2014.
-
Girfoglio, M., De Rosa, F., Coppola, G., and de Luca, L., Global Eigenmodes of Free-Interface Vertical Liquid Sheet Flows, WIT Transactions on Engineering Sciences, vol. 79, pp. 285-295,2013.
-
Girfoglio, M., De Rosa, F., Coppola, G., and de Luca, L., Unsteady Critical Liquid Sheet Flows, J. Fluid Mech., vol. 821, pp. 219-247,2017.
-
Homma, M. and Ogihara, K., Theoretical Analysis of Flap Gate Oscillation, Doboku Gakkai Ronbunshu, vol. 1975, pp. 43-53,1975.
-
Khodier, M.A. and Tullis, B.P., PIV Measurements for Oscillating Liquid Nappe, J. Hydro-Environ. Res., vol. 19,pp. 237-242,2018. DOI: 10.1016/j.jher.2017.11.002. DOI: 10.1016/j.jher.2017.11.002
-
Li, X., On the Instability of Plane Liquid Sheets in Two Gas Streams of Unequal Velocities, Acta Mechanica, vol. 106, nos. 3-4, pp. 137-156,1994.
-
Mehring, C. and Sirignano, W.A., Nonlinear Capillary Wave Distortion and Disintegration of Thin Planar Liquid Sheets, J. Fluid Mech, vol. 388, pp. 69-113,1999.
-
Naudascher, E. and Rockwell, D., Flow-Induced Vibrations an Engineering Guide, London, UK: Taylor and Francis Group, 1994.
-
Ogihara, K. and Ueda, S., The Conditions of Self-Excited Vibration Occurring in Radial Gates, 1999. DOI: 10.1061/40440(1999)75. DOI: 10.1061/40440(1999)75
-
Petrikat, K., Vibration Tests on Weirs and Bottom Gates, Water Power, vol. 10, pp. 52-57,1958.
-
Popinet, S., Gerris: A Tree-Based Adaptive Solver for the Incompressible Euler Equations in Complex Geometries, J. Comput. Phys, vol. 190, pp. 572-600,2003.
-
Roache, P.J., Ghia, K.N., and White, F.M., Editorial Policy Statement on the Control of Numerical Accuracy, J. Fluids Eng., vol. 108, no. 1, p. 2, 1986.
-
Rocco, G., Coppola, G., and De Luca, L., The VOF Method Applied to the Numerical Simulation of a 2D Liquid Jet under Gravity, WIT Transact. Eng. Sci., vol. 69,2010.
-
Sato, Y, Miura, S., Nagamine, T., Morii, S., and Ohkubo, S., Behavior of a Falling Water Sheet, J. Environ. Eng., vol. 2, no. 2, pp. 394-406,2007.
-
Schmid, P.J. and Henningson, D.S., On the Stability of a Falling Liquid Curtain, J. Fluid Mech, vol. 463, pp. 163-171,2002.
-
Schwartz, H.I., Nappe Oscillation, J. HydraulicsDiv., vol. 90, no. 6, pp. 129-143,1964.
-
Sirignano, W.A. and Mehring, C., Review of Theory of Distortion and Disintegration of Liquid Streams, Progr. Energy Combust. Sci., vol. 26, nos. 4-6, pp. 609-655,2000.
-
Sumi, T. and Okubo, S., Vibration Characteristics of a Falling Liquid Sheet from Flap Gate, Jap. Soc. Civil Eng., vol. 20, pp. 456-457,1988.