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Fluid-Structure Interaction in Microchannel Using Lattice Boltzmann Method and Size-Dependent Beam Element

Published online by Cambridge University Press:  03 June 2015

V. Esfahanian ,
E. Dehdashti  and
A. M. Dehrouyeh-Semnani
V. Esfahanian*
Affiliation:
School of Mechanical Engineering, University of Tehran, Tehran 14395-515, Iran
E. Dehdashti*
Affiliation:
School of Mechanical Engineering, University of Tehran, Tehran 14395-515, Iran
A. M. Dehrouyeh-Semnani*
Affiliation:
School of Mechanical Engineering, University of Tehran, Tehran 14395-515, Iran
*
Corresponding author. Email: [email protected]
Email: [email protected]
Email: [email protected]
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Abstract

Fluid-structure interaction (FSI) problems in microchannels play prominent roles in many engineering applications. The present study is an effort towards the simulation of flow in microchannel considering FSI. Top boundary of the microchannel is assumed to be rigid and the bottom boundary, which is modeled as a Bernoulli-Euler beam, is simulated by size-dependent beam elements for finite element method (FEM) based on a modified couple stress theory. The lattice Boltzmann method (LBM) using D2Q13 LB model is coupled to the FEM in order to solve fluid part of FSI problem. In the present study, the governing equations are non-dimensionalized and the set of dimensionless groups is exhibited to show their effects on micro-beam displacement. The numerical results show that the displacements of the micro-beam predicted by the size-dependent beam element are smaller than those by the classical beam element.

Keywords

74F1074N1574A6080M1076T99Fluid-structure interactionmicrochannellattice Boltzmann methodsize-dependent beam element
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 3 , June 2014 , pp. 345 - 358
Copyright
Copyright © Global-Science Press 2014

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References

[1]Karniadakis, G., Beskok, A. AND Aluru, N. R., Microflows and Nanoflows: Fundamentals and Simulation, Springer, 2005.Google Scholar
[2]Walhorn, E., Kölke, A., Hwbner, B. and Dinkler, D., Fluidstructure coupling within a monolithic model involving free surface flows, Comput. Struct., 83 (2005), pp. 2100–2111.Google Scholar
[3]Letallec, P. and Mouro, J., Fluid structure interaction with large structural displacements, Comput. Method. Appl. Mech. Eng., 190 (2001), pp. 3039–3067.CrossRefGoogle Scholar
[4]Küttler, U. and Wall, W., Vector extrapolation for strong coupling fluid-structure interaction solvers, J. Appl. Mech., 2 (2009), 76.Google Scholar
[5]Löhner, R., Cebral, J. R., Camelli, F. F., Baum, J. D., Mestreau, E. L. and Soto, O. A., Adaptive embedded/immersed unstructured grid techniques, Arch. Comput. Method. Eng., 14 (2007), pp. 27–31.Google Scholar
[6]Bathe, K. J., Nitikipaiboon, C. and Wang, X., A mixed displacement-based finite element formulation for acoustice fluid-structure interaction, Comput. Struct., 56 (1995), pp. 225–237.CrossRefGoogle Scholar
[7]Kwon, Y. W. and Mcdermott, P. M., Effects of void growth and nucleation on plastic deformation of plates subjected to fluid-structure interaction, ASME J. Pres. Ves. Technol., 123 (2001), pp. 480–485.Google Scholar
[8]Everstine, G. C. and Henderson, F. M., Coupled finite element/boundary element approach for fluid-structure interaction, J. Acoust. Soc. Am., 87 (1990), pp. 1938–1947.CrossRefGoogle Scholar
[9]Giordano, J. A. and Koopmann, G. H., State space boundary element-finite element coupling for fluid-structure interaction analysis, J. Acoust. Soc. Am., 98 (1995), pp. 363–372.Google Scholar
[10]Dubini, G., Pietrabissa, R. and Montevecchi, F. M., Fluid-structure interaction problems in bio-fluid mechanics: a numerical study of the motion of an isolated particle freely suspended in channel flow, Med. Eng. Phys., 17 (1995), pp. 609–617.Google Scholar
[11]Tienfuan, K., Lee, L. L. and Wellford, L. C., Transient fluid-structure interaction in a control valve, J. Fluids Eng., Trans. ASME, 119 (1997), pp. 354–359.Google Scholar
[12]Mcfarland, A. W. and Colton, J. S., Role of material microstructure in plate stiffness with relevance to microcantilever sensors, J. Micromech. Microeng., 15 (2005), pp. 1060–1067.Google Scholar
[13]Maranganti, R. and Sharma, P., A novel atomistic approach to determine strain-gradient elasticity constants: tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir) relevance for nanotechnologies, J. Mech. Phys. Solids, 55 (2007), pp. 1823–1852.Google Scholar
[14]Park, S. K. and Gao, X. L., Bernoulli-Euler beam model based on a modified couple stress theory, J. Micromech. Microeng, 16 (2006), pp. 2355–2359.Google Scholar
[15]Yang, F., Chong, A. C. M., Lam, D. C. C. and Tong, P., Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39 (2002), pp. 2731–2743.Google Scholar
[16]Kahrobaiyan, M. H., Khajehpour, M. and Ahmadian, M. T., A size-dependent beam element based on the modified couple stress theory, ASME Conf. P., 8 (2011), pp. 591–597.Google Scholar
[17]Suga, K., Takenaka, S., Ito, T. AND Kaneda, M., Lattice Boltzmann flow simulation in a combined nanochannel, Adv. Appl. Math. Mech., 2 (2010), pp. 609–625.Google Scholar
[18]Swift, M. R., Orlandini, E., Osborn, W. R. and Yeomans, J. M., Lattice Boltzmann simulations ofliquid-gas and the binary uid systems, Phys. Rev. E, 54 (1996), pp. 5041–5052.Google Scholar
[19]Soe, M., Vahala, G., Pavlo, P., Vahala, L. and Chen, H., Thermal lattice Boltzmann simulations of variable Prandtl number turbulent ows, Phys. Rev. E, 57 (1998), pp. 4227–4237.Google Scholar
[20]Peng, Y., Shu, C. and Chew, Y. T., Simplied thermal lattice Boltzmann model for incompressible thermal ows, Phys. Rev. E, 68 (2003), 026701.Google Scholar
[21]Ladd, A., Numerical simulations of partiuclate suspensions via a discretized Boltzmann equation: part 1: theoretical foundations, J. Fluid Mech., 271 (1994), 285.Google Scholar
[22]Ladd, A., Numerical simulations of partiuclate suspensions via a discretized Boltzmann equation. Part 2: numerical results, J. Fluid Mech., 271 (1994), 311.Google Scholar
[23]Krafczyk, M., Tolke, J., Rank, E. and Schulz, M., Two-dimensional simulation of fluid- structure interaction using lattice-Boltzmann methods, Comput. Struct., 79 (2001), pp. 2031–2037.Google Scholar
[24]Kwon, Y. W., Development of coupling technique for LBM and FEM for FSI application, Eng. Comput., 23 (2006), pp. 860–875.CrossRefGoogle Scholar
[25]Kollmannsberger, S., Geller, S., Düster, A., Tölke, J., Sorger, C., Krafczyk, M. and Rank, E., Fixed-grid uid-structure interaction in two dimensions based on a partitioned Lattice Boltzmann and p-FEM approach, Int. J. Numer. Meth. Eng., 79 (2009), pp. 817–845.CrossRefGoogle Scholar
[26]Frisch, U., Hasslacher, B. and Pomeau, Y., Lattice-gas automata for the Navier-Stokes equations, Phys. Rev. Lett., 56 (1986), pp. 1505–1508.Google Scholar
[27]Bhatnagar, P. L., Gross, E. P., AND Krook, M. k., A model for collision process in gases: I: small amplitude processes in charged and neutral one-component system, Phys. Rev., 94 (1954), pp. 511–525.CrossRefGoogle Scholar
[28]Kong, S., Zhou, s., Nie, Z. and Wang, K., The size-dependent natural frequency of Bernoulli-Euler micro-beams, Int J. Eng. Sc., 46 (2008), pp. 427–437.Google Scholar
[29]Bungartz, H-J, Mehl, M. AND SchäFer, M., Fluid Structure Interaction II: Modelling, Simulation, Optimization, Springer-Verlag Berlin Heidelberg, 2010, pp. 285–299.Google Scholar
[30]Toschi, F. and Succi, S., Lattice Boltzmann method atfinite-Knudsen numbers, Europhys. Lett., 69 (2005), 549.Google Scholar
[31]Nguyen,, N. T. and Wereley, S. T., Fundamentals and Applications of Microfluidics, Artech House, Boston, MA, Chapter 2.Google Scholar
[32]Guo, Z. L., Zheng, C. G. and Shi, B. C., Non-equilibrium extrapolation method for velocity and pressure boundary conditions in the lattice Boltzmann method, Chin. Phys. Soc., 11 (2002), 366.Google Scholar