Search results

Filters

  • Journals
  • Authors
  • Keywords
  • Date
  • Type

Search results

Number of results: 2
items per page: 25 50 75
Sort by:
Download PDF Download RIS Download Bibtex

Abstract

The laminar flow around two side-by-side circular cylinders was numerically investigated using a vortex-in-cell method combined with a continuous-forcing immersed boundary method. The Reynolds number (Re) of the flow was examined in the range from 40 to 200, and the distance between the cylinders varies from 1.2 D to 6 D, where D is the cylinder diameter. Simulation results show that the vortex wake is classified into eight patterns, such as single-bluff-body, meandering-motion, steady, deflected-in-one-direction, flip-flopping, anti-phase-synchronization, in-phase-synchronization, and phase-difference-synchronization, significantly depending on the Re, the cylinder distance, and the initial external disturbance effects. The anti-phase-synchronization, in-phase-synchronization, and phase-difference-synchronization vortex patterns can be switched at a low Re after a long time evolution of the flow. In particular, the single-bluff-body and flip-flopping vortex patterns excite the oscillation amplitude of the drag and lift coefficients exerted on the cylinders.
Go to article

Bibliography

[1] S. Ishigai, E. Nishikawa, K. Nishimura, and K. Cho. Experimental study on structure of gas flow in tube banks with tube axes normal to flow: Part 1, Karman vortex flow from two tubes at various spacings. Bulletin of JSME, 15(86):949–956, 1972. doi: 10.1299/jsme1958.15.949.
[2] P.W. Bearman and A.J.Wadcock. The interaction between a pair of circular cylinders normal to a stream. Journal of Fluid Mechanics, 61(3):499–511, 1973. doi: 10.1017/S0022112073000832.
[3] M.M. Zdravkovich. The effects of interference between circular cylinders in cross flow. Journal of Fluids and Structures, 1(2):239–261, 1987. doi: 10.1016/S0889-9746(87)90355-0.
[4] C.H.K. Williamson. Evolution of a single wake behind a pair of bluff bodies. Journal of Fluid Mechanics, 159:1–18, 1985. doi: 10.1017/S002211208500307X.
[5] H.J. Kim and P.A. Durbin. Investigation of the flow between a pair of circular cylinders in the flopping regime. Journal of Fluid Mechanics, 196:431–448, 1988. doi: 10.1017/S0022112088002769.
[6] K.-S. Chang and C.-J.. Song. Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement. International Journal for Numerical Methods in Fluids, 11(3):317–329, 1990. doi: 10.1002/fld.1650110305.
[7] S. Kang. Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers. Physics of Fluids, 15(9):2486, 2003. doi: 10.1063/1.1596412.
[8] A. Slaouti and P.K. Stansby. Flow around two circular cylinders by the random-vortex method. Journal of Fluids and Structures, 6(6):641–670, 1992. doi: 10.1016/0889-9746(92)90001-J.
[9] J.R. Meneghini, F. Saltara, C.L.R. Siqueira, and J.A. Ferrari Jr. Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. Journal of Fluids and Structures, 15(2):327–350, 2001. doi: 10.1006/jfls.2000.0343.
[10] W. Jester and Y. Kallinderis. Numerical study of incompressible flow about fixed cylinder pairs. Journal of Fluids and Structures, 17(4):561–577, 2003. doi: 10.1016/S0889-9746(02)00149-4.
[11] C.K. Birdsall and D. Fuss. Clouds-in-clouds, clouds-in-cells physics for many-body plasma simulation. Journal of Computational Physics, 3(4):494–511, 1969. doi: 10.1016/0021-9991(69)90058-8.
[12] I.P. Christiansen. Numerical simulation of hydrodynamics by the method of point vortices. Journal of Computational Physics,13(3):363–379,1973. doi: 10.1016/0021-9991(73)90042-9.
[13] G.-H. Cottet and P.D. Koumoutsakos. Vortex Methods: Theory and Practice. Cambridge University Press, 2000.
[14] V.L. Nguyen, R.Z. Lavi, and T. Uchiyama. Numerical simulation of flow around two tandem cylinders by vortex in cell method combined with immersed boundary method. Advances and Applications in Fluid Mechanics, 19(4):781–804, 2016. doi: 10.17654/FM019040787.
[15] V.L. Nguyen, T. Takamure, and T. Uchiyama. Deformation of a vortex ring caused by its impingement on a sphere. Physics of Fluids, 31(10):107108, 2019. doi: 10.1063/1.5122260.
[16] V. L. Nguyen, T. Nguyen-Thoi, and V. D. Duong. Characteristics of the flow around four cylinders of various shapes. Ocean Engineering, 238:109690, 2021.
[17] J.J. Monaghan. Extrapolating B splines for interpolation. Journal of Computational Physics, 60(2):253–262, 1985. doi: 10.1016/0021-9991(85)90006-3.
[18] J.H. Walther and P. Koumoutsakos. Three-dimensional vortex methods for particle-laden flows with two-way coupling. Journal of Computational Physics, 167(1):39–71, 2001. doi: 10.1006/jcph.2000.6656.
[19] C.S. Peskin. Flow patterns around heart valves: a numerical method. Journal of Computational Physics, 10(2):252–271, 1972. doi: 10.1016/0021-9991(72)90065-4.
[20] P. Angot, C.-H. Bruneau, and P. Fabrie. A penalization method to take into account obstacles in incompressible viscous flows. Numerische Mathematik, 81:497–520, 1999. doi: 10.1007/s002110050401.
[21] E.A. Fadlun, R. Verzicco, P. Orlandi, and J. Mohd-Yusof. Combined immersed-boundary finitedifference methods for three-dimensional complex flow simulations. Journal of Computational Physics, 191(1):35–60, 2000. doi: 10.1006/jcph.2000.6484.
[22] N.K.-R. Kevlahan and J.-M. Ghidaglia. Computation of turbulent flow past an array of cylinders using a spectral method with Brinkman penalization. European Journal of Mechanics - B/Fluids, 20(3):333–350, 2001. doi: 10.1016/S0997-7546(00)01121-3.
[23] M. Coquerelle and G.-H.Cottet. Avortex level set method for the two-way coupling of an incompressible fluid with colliding rigid bodies. Journal of Computational Physics, 227(21):9121– 9137, 2008. doi: 10.1016/j.jcp.2008.03.041.
[24] F. Noca, D. Shiels, and D. Jeon. A comparison of methods for evaluating time-dependent fluid dynamic forces on bodies, using only velocity fields and their derivatives. Journal of Fluids and Structures, 13(5):551–578, 1999. doi: 10.1006/jfls.1999.0219.
[25] C. Mimeau, F. Gallizio, G.-H. Cottet, and I. Mortazavi. Vortex penalization method for bluff body flows. International Journal for Numerical Methods in Fluids, 79(2):55–83, 2015. doi: 10.1002/fld.4038.
[26] J.-I. Choi, R.C. Oberoi, J.R. Edwards, and J.A. Rosati. An immersed boundary method for complex incompressible flows. Journal of Computational Physics, 224(2):757–784, 2007. doi: 10.1016/j.jcp.2006.10.032.
[27] AB. Harichandan and A. Roy. Numerical investigation of low Reynolds number flow past two and three circular cylinders using unstructured grid CFR scheme. International Journal of Heat and Fluid Flow, 31(2):154–171, 2010. doi: 10.1016/j.ijheatfluidflow.2010.01.007.
[28] M. Braza, P. Chassaing, and H. Ha Minh. Numerical study and physical analysis of the pressure and velocity fields in the near wake of a circular cylinder. Journal of Fluid Mechanics, 165:79– 130, 1986. doi: 10.1017/S0022112086003014.
[29] K. Supradeepan and A. Roy. Characterisation and analysis of flow over two side by side cylinders for different gaps at low Reynolds number: A numerical approach. Physics of Fluids, 26(6):063602, 2014. doi: 10.1063/1.4883484.
[30] V.L. Nguyen, T. Degawa, and T. Uchiyama. Numerical simulation of annular bubble plume by vortex in cell method. International Journal of Numerical Methods for Heat and Fluid Flow, 29(3):1103–1131, 2019. doi: 10.1108/HFF-03-2018-0094.
Go to article

Authors and Affiliations

Van Luc Nguyen
1
ORCID: ORCID
Duy Knanh Ho
1

  1. Institute of Engineering and Technology, Thu Dau Mot University, Binh Duong Province, Vietnam
Download PDF Download RIS Download Bibtex

Abstract

For a deeper understanding of the inner ear dynamics, a Finite-Element model of the human cochlea is developed. To describe the unsteady, viscous creeping flow of the liquid, a pressure-displacement-based Finite-Element formulation is used. This allows one to efficiently compute the basilar membrane vibrations resulting from the fluid-structure interaction leading to hearing nerve stimulation. The results show the formation of a travelingwave on the basilar membrane propagating with decreasing velocity towards the peaking at a frequency dependent position. This tonotopic behavior allows the brain to distinguish between sounds of different frequencies. Additionally, not only the middle ear, but also the transfer behavior of the cochlea contributes to the frequency dependence of the auditory threshold. Furthermore, the fluid velocity and pressure fields show the effect of viscous damping forces and allow us to deeper understand the formation of the pressure difference, responsible to excite the basilar membrane.

Go to article

Bibliography

[1] L. Robles and M.A. Ruggero. Mechanics of the mammalian cochlea. Physiological Reviews, 81(3):1305–1352, 2001. doi: 10.1152/physrev.2001.81.3.1305.
[2] M. Fleischer. Mehrfeldmodellierung und Simulation der äußeren Haarsinneszelle der Cochlea (Multifield modelling and simulation of the outer hair cells of the cochlea). Doctoral Thesis. Technische Universität Dresden, Germany, 2012. (in German).
[3] J. Baumgart. The hair bundle: Fluid-structure interaction in the inner ear. Doctoral Thesis. Technische Universität Dresden, Germany, 2010 .
[4] J. Tian, X. Huang, Z. Rao, N. Ta, and L. Xu. Finite element analysis of the effect of actuator coupling conditions on round window stimulation. Journal of Mechanics in Medicine and Biology, 15(4):1–19, 2015. doi: 10.1142/S0219519415500487.
[5] R.Z. Gan, B.P. Reeves, and X. Wang. Modeling of sound transmission from ear canal to cochlea. Annals of Biomedical Engineering, 35:2180–2195, 2007. doi: 10.1007/s10439-007-9366-y.
[6] L. Xu, X. Huang, N. Ta, Z. Rao, and J. Tian. Finite element modeling of the human cochlea using fluid-structure interaction method. Journal of Mechanics in Medicine and Biology, 15(3):1–13, 2015. doi: 10.1142/S0219519415500396.
[7] H.W. Ades and H. Engström. Anatomy of the inner ear. In: Keidel W.D., Neff W.D. (eds) Auditory System. Handbook of Sensory Physiology, vol. 5/1. Springer, Berlin, 1974. doi: 10.1007/978-3-642-65829-7_5.
[8] C.R. Steele, G.J. Baker, J.A. Tolomeo, and D.E. Zetes-Tolometo. Cochlear mechanics. In: J.D. Bronzino (ed.) The Biomedical Engineering Handbook, CRC Press, 2006.
[9] S. Iurato. Functional implications of the nature and submicroscopic structure of the tectorial and basilar membranes. The Journal of the Acoustical Society of America, 34(9):1386–1395, 1962. doi: 10.1121/1.1918355.
[10] H. Herwig. Strömungsmechanik: Einführung in die Physik von technischen Strömungen (Introduction to the Physics of Technical Flows). Springer Vieweg, Wiesbaden; 2008. (in German).
[11] H. Schlichting and K. Gersten. Boundary-Layer Theory, vol. 7. Springer-Verlag, Berlin, 2017.
[12] G.H. Keulegan and L.H. Carpenter. Forces on cylinders and plates in an oscillating fluid. Journal of Research of the National Bureau of Standards, 60:423–440, 1958.
[13] E. Zwicker. Über die Viskosität der Lymphe im Innenohr des Hausschweines (About the viscosity of the lymph in the inner ear of the domestic pig). Acta Otolaryngologica, 78(1-6): 65–72, 1974. (in German). doi: 10.3109/00016487409126327.
[14] M. Lesser and D. Berkley. Fluid mechanics of the cochlea. Part 1. Journal of Fluid Mechanics, 51(3):497–512, 1972. doi: 10.1017/S0022112072002320.
[15] A. De Paolis, H. Watanabe, J. Nelson, M. Bikson, M. Marom, M. Packer, and L. Cardoso. Human cochlear hydrodynamics: A high-resolution μCT-based finite element study. Journal of Biomechanics, 50:209–216, 2017. doi: 10.1016/j.jbiomech.2016.11.020.
[16] L. Papula. Mathematische Formelsammlung (Mathematical Formula Collection). Springer Verlag, Wiesbaden, 2014. (in German).
[17] O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu. The Finite Element Method: Its Basis and Fundamentals, 6 ed. Elsevier Butterworth-Heinemann, Oxford, 2006.
[18] J.E. Sader. Frequency response of cantilever beams immersed in viscous fluids with applications to the atomic force microscope. Journal of Applied Physics, 84(1):64–76, 1998. doi: 10.1063/1.368002.
[19] E. de Boer. Auditory physics. Physical principles in hearing theory. Part 1. Physics Reports, 62(2):87–174, 1980. doi: 10.1016/0370-1573(80)90100-3.
[20] M.J. Wittbrodt, C.R. Steele, and S. Puria. Developing a physical model of the human cochlea using microfabrication methods. Audiology and Neurotology, 11(2):104–112, 2006. doi: 10.1159/000090683.
[21] C.R. Steele and J.G. Zais. Effect of coiling in a cochlear model. The Journal of the Acoustical Society of America, 77(5):1849–1852, 1985. doi: 10.1121/1.391935.
[22] J. Wysocki. Dimensions of the human vestibular and tympanic scalae. Hearing Research, 135(1-2):39–46, 1999. doi: 10.1016/S0378-5955(99)00088-X.
[23] M. Thorne, A.N. Salt, J.E. DeMott, M.M. Henson, O.W. Henson, and S.L. Gewalt. Cochlear fluid space dimensions for six species derived from reconstructions of resonance images. Annals of Otology, Rhinology & Laryngology, 109(10):1661–1668, 1999. doi: 10.1097/00005537-199910000-00021.
[24] G. Herrmann and H. Liebowitz. Mechanics of Bone Fractures. Academic Press, New York, 1972.
[25] J. Kirikae. The Middle Ear. Tokyo: University of Tokyo Press, 1960.
[ 26] F. Atturo, M. Barbara, and H. Rask-Andersen. Is the human round window really round? An anatomic study with surgical implications. Otology and Neurotology, 35(8):1354–1360, 2014. doi: 10.1097/MAO.0000000000000332.
[27] M.V. Goycoolea and L. Lundman. Round window membrane. Structure, function and permeability. A review. Microscopy Research and Technique, 36(3):201–211, 1997. doi: 10.1002/(SICI)1097-0029(19970201)36:3201::AID-JEMT8>3.0.CO;2-R.
[28] M. Kwacz, M. Mrówka, and J. Wysocki. Round window membrane motion before and after stapedotomy surgery. An experimental study. Acta of Bioengineering and Biomechanics, 13(3):27–33, 2011.
[29] X. Zhang and R.Z. Gan. Dynamic properties of human round window membrane in auditory frequencies running head: Dynamic properties of round window membrane. Medical Engineering & Physics, 35(3):310–318, 2013. doi: 10.1016/j.medengphy.2012.05.003.
[30] A.A. Poznyakovskiy, T. Zahnert, Y. Kalaidzidis, N. Lazurashvili, R. Schmidt, H.J. Hardtke, B. Fischer, and Y.M. Yarin. A segmentation method to obtain a complete geometry model of the hearing organ. Hearing Research, 282(1-2):25–34, 2011. doi: 10.1016/j.heares.2011.06.009.
[31] P. Leichsenring. Aufbereitung von Geometriedaten der menschlichen Cochlea (Preparation of geometry data for the human cochlea). Master Thesis. Technische Universität Dresden, Germany, 2012. (in German).
[32] E.G. Wever. The width of the basilar membrane in man. Annals of Otology, Rhinology & Laryngology, 47:37–47, 1938.
[33] F. Böhnke. Finite Elemente Analysen zur Berechnung der Signalverarbeitung in der Cochlea (Analyses for computation of signal processing in the cochlea). Doctoral Thesis. Technische Universität Ilmenau, Germany, 1999. (in German).
[34] L.M. Cabezudo. The ultrastructure of the basilar membrane in the cat. Acta Oto-Laryngologica, 86(1-6):160–175, 1978. doi: 10.3109/00016487809124733.
[35] S. Newburg, A. Zosuls, P. Barbone, and D. Mountain. Mechanical response of the basilar membrane to lateral micromanipulation. In: Concepts and Challenges in the Biophysics of Hearing. Proceedings of the 10th International Workshop on the Mechanics of Hearing, pages 240–246, 2009. doi: 10.1142/9789812833785_0038.
[36] V. Tsuprun and P. Santi. Ultrastructure and immunohistochemical identification of the extracellular matrix of the chinchilla cochlea. Hearing Research, 129(1-2):35–49, 1999. doi: 10.1016/S0378-5955(98)00219-6.
[37] I.U. Teudt and C.P. Richter. The hemicochlea preparation of the guinea pig and other mammalian cochleae. Journal of Neuroscience Methods, 162(1-2):187–197, 2007. doi: 10.1016/j.jneumeth.2007.01.012.
[38] M. Fleischer, R. Schmidt, and A.W. Gummer. Compliance profiles derived from a three-dimensional finite-element model of the basilar membrane. The Journal of the Acoustical Society of America, 127(5):2973–2991, 2010. doi: 10.1121/1.3372752.
[39] J. Baumgart, M. Fleischer, and C. Steele. The traveling wave in the human inner ear studied by means of a finite-element model including middle and outer ear. In: Proceedings of the 23rd International Congress on Sound and Vibration, Greece, 2016.
[40] H. Altenbach, J.W. Altenbach, and W. Kissing. Mechanics of Composite Structural Elements. Springer-Verlag, Berlin, 2013.
[41] R.C. Naidu and D.C. Mountain. Basilar membrane tension calculations for the gerbil cochlea. The Journal of the Acoustical Society of America, 121(2):994–1002, 2007. doi: 10.1121/1.2404916.
[42] S. Liu and R.D. White. Orthotropic material properties of the gerbil basilar membrane. The Journal of the Acoustical Society of America, 123(4):2160–2171, 2008. doi: 10.1121/1.2871682.
[43] C.E. Miller. Structural implications of basilar membrane compliance measurements. The Journal of the Acoustical Society of America, 77(4):146–1474, 1985. doi: 10.1121/1.392041.
[44] L. Schweitzer, C. Lutz, M. Hobbs, and S.P. Weaver. Anatomical correlates of the passive properties underlying the developmental shift in the frequency map of the mammalian cochlea. Hearing Research, 97(1-2):84–94, 1996. doi: 10.1016/S0378-5955(96)80010-4.
[45] R.C. Naidu and D.C. Mountain. Measurements of the stiffness map challenge. A basic tenet of cochlear theories. Hearing Research, 124(1-2):124–131, 1998. doi: 10.1016/S0378-5955(98)00133-6.
[46] H. Wada and T. Kobayashi. Dynamical behavior of middle ear: Theoretical study corresponding to measurement results obtained by a newly developed measuring apparatus. The Journal of the Acoustical Society of America, 87(1):237–245, 1990. doi: 10.1121/1.399290.
[47] M. Kwacz, P. Marek, P. Borkowski, and M. Mrówka. A three-dimensional finite element model of round window membrane vibration before and after stapedotomy surgery. Biomechanics and Modeling in Mechanobiology, 12:1243–1261, 2013. doi: 10.1007/s10237-013-0479-y.
[48] P. Wahl. Simulation der Fluidströmung und Basilarmembranschwingung im menschlichen Innenohr (Simulation of fluid flow and basilar membrane vibrations in the human inner ear). Doctoral Thesis. Universität Stuttgart, Germany, 2018. (in German).
[49] J.H. Sim, M. Chatzimichalis, M. Lauxmann, C. Röösli, A. Eiber, and A. Huber. Complex stapes motion in human ears. Journal of the Association for Research in Otolaryngology, 11(3):329–341, 2010. doi: 10.1007/s10162-010-0207-6.
[50] S. Huang and E.S. Olson. Auditory nerve excitation via a non-traveling wave mode of basilar membrane motion. Journal of the Association for Research in Otolaryngology, 12:559–575, 2011. doi: 10.1007/s10162-011-0272-5.
[51] G. von Békésy. Experiments in Hearing. McGraw-Hill, New York, 1960.
[52] T.Ren. Longitudinal pattern of basilar membrane vibration in the sensitive cochlea. Proceedings of the National Academy of Sciences, 99(26):17101–17106, 2002. doi: 10.1073/pnas.262663699.
[53] S. Stenfelt, S. Puria, N. Hato, and R.L. Goode. Basilar membrane and osseous spiral lamina motion in human cadavers with air and bone conduction stimuli. Hearing Research, 181(1-2):131–143, 2003. doi: 10.1016/S0378-5955(03)00183-7.
[54] S. Ramamoorthy, N.V. Deo, and K. Grosh. A mechano-electro-acoustical model for the cochlea: response to acoustic stimuli. The Journal of the Acoustical Society of America, 121(5):2758–2773, 2007. doi: 10.1121/1.2713725.
[55] W.E. Langlois and M.O. Deville. Slow Viscous Flow. 2nd ed. Springer, Cham, 2014. doi: 10.1007/978-3-319-03835-3.
[56] E. Olson. Direct measurement of intra-cochlear pressure waves. Nature, 402:526–529, 1999. doi: 10.1038/990092.
[57] D.D. Greenwood. A cochlear frequency-position function for several species – 29 years later. The Journal of the Acoustical Society of America, 87(6):2592–2605, 1990. doi: 10.1121/1.399052.
[58] H.G. Boenninghaus and T. Lenarz. HNO: Hals-Nasen-Ohrenheilkunde (Otorhinolaryngology). Springer, Berlin, 2007. (in German).
Go to article

Authors and Affiliations

Philipp Wahl
1
Pascal Ziegler
1
Peter Eberhard
1

  1. Institute of Engineering and Computational Mechanics, University of Stuttgart, Germany

This page uses 'cookies'. Learn more