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A numerical investigation of fluid flows induced by the oscillations of thin plates and evaluation of the associated hydrodynamic forces

Published online by Cambridge University Press:  15 July 2019

Artem N. Nuriev Open the ORCID record for Artem N. Nuriev [Opens in a new window] ,
Airat M. Kamalutdinov  and
Andrey G. Egorov
Artem N. Nuriev*
Affiliation:
The Research Institute for Mechanics, Lobachevsky State University of Nizhni Novgorod, 23, Gagarina pr., Nizhnii Novgorod, 603950, Russian Federation
Airat M. Kamalutdinov
Affiliation:
Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga region) Federal University, 18, Kremlyovskaya St., Kazan, Tatarstan 420008, Russian Federation
Andrey G. Egorov
Affiliation:
Lobachevskii Institute of Mathematics and Mechanics, Kazan (Volga region) Federal University, 18, Kremlyovskaya St., Kazan, Tatarstan 420008, Russian Federation
*
†Email address for correspondence: Artem.Nuriev@kpfu.ru
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Abstract

The paper is devoted to the problem of harmonic oscillations of thin plates in a viscous incompressible fluid. The two-dimensional flows caused by the plate oscillations and their hydrodynamic influence on the plates are studied. The fluid motion is described by the non-stationary Navier–Stokes equations, which are solved numerically on the basis of the finite volume method. The simulation is carried out for plates with different thicknesses and shapes of edges in a wide range of control parameters of the oscillatory process: dimensionless frequency and amplitude of oscillations. For the first time in the framework of one model all two-dimensional flow regimes, which were found earlier in experimental studies, are described. Two new flow regimes emerging along the stability boundaries of symmetric flow regimes are localized. The map of flow regimes in the frequency–amplitude plane is constructed. The analysis of the hydrodynamic influence of flows on the plates allow us to establish new effects associated with the influence of the shape of the plates on the drag and inertia forces. Due to these effects, the values of hydrodynamic forces can differ by 90 % at the same parameters of the oscillation. The lower and upper estimates of hydrodynamic forces obtained in the work have a good agreement with the experimental data presented in the literature.

JFM classification

Vortex Flows: Vortex shedding Wakes/Jets: Separated flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 1057 - 1095
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Copyright
© 2019 Cambridge University Press 

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References

An, H., Cheng, L. & Zhao, M. 2009 Steady streaming around a circular cylinder in an oscillatory flow. Ocean Engng 36 (14), 1089–1097.Google Scholar
An, H., Cheng, L. & Zhao, M. 2011 Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan–Carpenter number. J. Fluid Mech. 666, 77–103.Google Scholar
An, H., Cheng, L. & Zhao, M. 2015 Two-dimensional and three-dimensional simulations of oscillatory flow around a circular cylinder. Ocean Engng 109, 270–286.Google Scholar
Aureli, M. & Porfiri, M. 2010 Low frequency and large amplitude oscillations of cantilevers in viscous fluids. Appl. Phys. Lett. 96 (16), 164102.Google Scholar
Aureli, M., Porfiri, M. & Basaran, M. E. 2012 Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids. J. Sound Vib. 331 (7), 1624–1654.Google Scholar
Aureli, M., Prince, C., Porfiri, M. & Peterson, S. D. 2010 Energy harvesting from base excitation of ionic polymer metal composites in fluid environments. Smart Mater. Struct. 19 (1), 015003.Google Scholar
Bearman, P. W. 1971 An investigation of the forces on flat plates normal to a turbulent flow. J. Fluid Mech. 46 (01), 177–198.Google Scholar
Bearman, P. W., Downie, M. J., Graham, J. M. R. & Obasaju, E. D. 1985 Forces on cylinders in viscous oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 154 (1), 337–356.Google Scholar
Bearman, P. W., Graham, J. M. R. & Singh, S. 1979 Forces on cylinders in harmonically oscillating flow. In Proc. Mechanics of Wave-induced Forces on Cylinders, pp. 437–449. Pitman Advanced Publishing Program.Google Scholar
Bearman, P. W. & Obasaju, E. D. 1982 An experimental study of pressure fluctuations on fixed and oscillating square-section cylinders. J. Fluid Mech. 119 (1), 297–321.Google Scholar
Bidkar, R. A., Kimber, M., Raman, A., Bajaj, A. K. & Garimella, S. V. 2009 Nonlinear aerodynamic damping of sharp-edged flexible beams oscillating at low Keulegan–Carpenter numbers. J. Fluid Mech. 634, 269–289.Google Scholar
Brooks, A. N. & Hughes, T. J. R. 1982 Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput. Meth. Appl. Mech. Engng 32 (1), 199–259.Google Scholar
Buzhinskii, V. A. 1998a Vortex damping of sloshing in tanks with baffles. Z. Angew. Math. Mech. J. Appl. Math. Mech. 62 (2), 217–224.Google Scholar
Buzhinskii, V. A. 1998b Vibrations of liquid in tanks involving structural components with sharp edges. Dokl. Phys. 43 (11), 697–699.Google Scholar
De Rosis, A. & Lévêque, E. 2015 Harmonic oscillations of a thin lamina in a quiescent viscous fluid: a numerical investigation within the framework of the lattice Boltzmann method. Comput. Struct. 157, 209–217.Google Scholar
Dutsch, H., Durst, F., Becker, S. & Lienhart, H. 1998 Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers. J. Fluid Mech. 360, 249–271.Google Scholar
Egorov, A. G., Kamalutdinov, A. M. & Nuriev, A. N. 2018 Evaluation of aerodynamic forces acting on oscillating cantilever beams based on the study of the damped flexural vibration of aluminium test samples. J. Sound Vib. 421, 334–347.Google Scholar
Egorov, A. G., Kamalutdinov, A. M., Nuriev, A. N. & Paimushin, V. N. 2014 Theoretical-experimental method for determining the parameters of damping based on the study of damped flexural vibrations of test specimens 2. Aerodynamic component of damping. Mech. Compos. Mater. 50 (3), 267–278.Google Scholar
Egorov, A. G., Kamalutdinov, A. M., Nuriev, A. N. & Paimushin, V. N. 2017 Experimental determination of damping of plate vibrations in a viscous fluid. Dokl. Phys. 62 (5), 257–261.Google Scholar
Elston, J. R., Blackburn, H. M. & Sheridan, J. 2006 The primary and secondary instabilities of flow generated by an oscillating circular cylinder. J. Fluid Mech. 550, 359–389.Google Scholar
Erturk, A. & Inman, D. J. 2011 Piezoelectric Energy Harvesting. Wiley.Google Scholar
Ferziger, J. H. & Peric, M. 2002 Computational Methods for Fluid Dynamics. Springer.Google Scholar
Graham, J. M. R. 1980 The forces on sharp-edged cylinders in oscillatory flow at low Keulegan–Carpenter numbers. J. Fluid Mech. 97 (02), 331–346.Google Scholar
Greenshields, C.2018 OpenFOAM user guide: CFD direct, architects of OpenFOAM.Google Scholar
Guoqiang, T., Liang, C., Lin, L., Yunfei, T., Ming, Z. & Hongwei, A. 2018 Effect of oscillatory boundary layer on hydrodynamic forces on pipelines. Coast. Engng 140, 114–123.Google Scholar
Honji, H. 1981 Streaked flow around an oscillating circular cylinder. J. Fluid Mech. 107, 509–520.Google Scholar
Issa, R. I. 1986 Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62 (1), 40–65.10.1016/0021-9991(86)90099-9Google Scholar
Jasak, H.1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, Imperial College of Science, Technology and Medicine.Google Scholar
Justesen, P. 1991 A numerical study of oscillating flow around a circular cylinder. J. Fluid Mech. 222, 157–196.Google Scholar
Kanwal, R. 1955 Vibrations of an elliptic cylinder and a flat plate in a viscous fluid. Z. Angew. Math. Mech. J. Appl. Math. Mech. 35, 17–22.Google Scholar
Keulegan, G. H. & Carpenter, L. H. 1958 Forces on cylinders and plates in an oscillating fluid. J. Res. Natl Bur. Stand. 60 (5), 423–440.Google Scholar
Kopman, V. & Porfiri, M. 2013 Design, modeling, and characterization of a miniature robotic fish for research and education in biomimetics and bioinspiration. IEEE /ASME Trans. Mechatronics 18 (2), 471–483.Google Scholar
Morison, J. R., Johnson, J. W. & Schaaf, S. A. 1950 The force exerted by surface waves on piles. J. Petrol. Tech. 2 (5), 149–154.Google Scholar
Nehari, D., Armenio, V. & Ballio, F. 2004 Three-dimensional analysis of the unidirectional oscillatory flow around a circular cylinder at low Keulegan–Carpenter and 𝛽 numbers. J. Fluid Mech. 520, 157–186.Google Scholar
Nuriev, A. N., Egorov, A. G. & Zaitseva, O. N. 2018 Numerical analysis of secondary flows around an oscillating cylinder. J. Appl. Mech. Tech. Phys. 59 (3), 451–459.Google Scholar
Paimushin, V. N., Firsov, V. A., Gyunal, I., Egorov, A. G. & Kayumov, R. A. 2014 Theoretical–experimental method for determining the parameters of damping based on the study of damped flexural vibrations of test specimens. 3. Identification of the characteristics of internal damping. Mech. Compos. Mater. 50 (5), 633–646.Google Scholar
Paimushin, V. N., Firsov, V. A. & Shishkin, V. M. 2017 Modeling the dynamic response of a carbon-fiber-reinforced plate at resonant vibrations considering the internal friction in the material and the external aerodynamic damping. Mech. Compos. Mater. 53 (4), 425–440.Google Scholar
Patankar, S. V. & Spalding, D. B. 1972 A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Intl J. Heat Mass Transfer 15 (10), 1787–1806.Google Scholar
Phan, C. N., Aureli, M. & Porfiri, M. 2013 Finite amplitude vibrations of cantilevers of rectangular cross sections in viscous fluids. J. Fluids Struct. 40, 52–69.Google Scholar
Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.Google Scholar
Sarpkaya, T. 2002 Experiments on the stability of sinusoidal flow over a circular cylinder. J. Fluid Mech. 457, 157–180.Google Scholar
Shrestha, B., Ahsan, S. N. & Aureli, M. 2018 Experimental study of oscillating plates in viscous fluids: qualitative and quantitative analysis of the flow physics and hydrodynamic forces. Phys. Fluids 30 (1), 013102.Google Scholar
Singh, S.1979 Forces on bodies in oscillatory flow. PhD thesis, University of London.Google Scholar
Spalding, D. B. 1972 A novel finite difference formulation for differential expressions involving both first and second derivatives. Intl J. Numer. Meth. Engng 4 (4), 551–559.Google Scholar
Suthon, P. & Dalton, C. 2011 Streakline visualization of the structures in the near wake of a circular cylinder in sinusoidally oscillating flow. J. Fluids Struct. 27 (7), 885–902.Google Scholar
Tafuni, A. & Sahin, I. 2015 Non-linear hydrodynamics of thin laminae undergoing large harmonic oscillations in a viscous fluid. J. Fluids Struct. 52, 101–117.Google Scholar
Tao, L. & Thiagarajan, K. 2003a Low KC flow regimes of oscillating sharp edges. I. Vortex shedding observation. Appl. Ocean Res. 25 (1), 21–35.Google Scholar
Tao, L. & Thiagarajan, K. 2003b Low KC flow regimes of oscillating sharp edges. II. Hydrodynamic forces. Appl. Ocean Res. 25 (2), 53–62.Google Scholar
Tatsuno, M. 1981 Secondary flow induced by a circular cylinder performing unharmonic oscillations. J. Phys. Soc. Japan 50, 330–337.Google Scholar
Tatsuno, M. & Bearman, P. W. 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low stokes numbers. J. Fluid Mech. 211, 157–182.Google Scholar
Tuck, E. O. 1969 Calculation of unsteady flows due to small motions of cylinders in a viscous fluid. J. Engng Maths 3 (1), 29–44.Google Scholar
Wang, C.-Y. 1968 On high-frequency oscillatory viscous flows. J. Fluid Mech. 32 (1), 55–68.Google Scholar
Zhao, M., Cheng, L., Teng, B. & Dong, G. 2007 Hydrodynamic forces on dual cylinders of different diameters in steady currents. J. Fluids Struct. 23 (1), 59–83.Google Scholar