Investigation of instable fluid velocity in pipes with internal nanofluid flow based on Navier-Stokes equations
Document Type : Research Paper
Authors
Department of Mechanical Engineering, Kashan Branch, Islamic Azad University, Kashan, Iran
Abstract
In this article, the instable fluid velocity in the pipes with internal nanofluid is studied. The fluid is mixed by SiO2, AL2O3, CuO and TiO2 nanoparticles in which the equivalent characteristic of nanofluid is calculated by rule of mixture. The force induced by the nanofluid is assumed in radial direction and is obtained by Navier-Stokes equation considering viscosity of nanofluid. The displacements of the structure are described by first order shear deformation theory (FSDT). The final equations are calculated by Hamilton's principle. Differential quadrature method (DQM) is utilized for presenting the instable fluid velocity. The influences of length to radius ratio of pipe, volume fraction, diameter and type of nanoparticles are shown on the instable fluid velocity. The outcomes are compared with other published articles where shows good accuracy. Numerical results indicate that with enhancing the volume fraction of nanoparticles, the instable fluid velocity is increased. In addition, the instable fluid velocity of SiO2-water is higher than other types of nanoparticles assumed in this work.
Keywords
[1] Paidoussis M.P., Li G.X., 1993, Pipes conveying fluid: a model dynamical problem, Journal of Fluids and Structures, 7: 137–204.
[2] Amabili M., 2008, Nonlinear Vibrations and Stability of Shells and Plates, Cambridge University Press, New York.
[3] Toorani M.H., Lakis A.A., 2001, Dynamic analysis of anisotropic cylindrical shells containing flowing fluid, Journal of Pressure Vessels and Technology Transection ASME, 123: 454–60.
[4] Zhang X.M., Liu G.R., Lam K.Y., 2001, Frequency analysis of cylindrical panels using a wave propagation approach, Applied Acoustics, 62: 527–543.
[5] Jayaraj K., Ganesan N., Chandramouli P., 2002, A semi-analytical coupled finite element formulation for composite shells conveying fluids, Journal of Sound and Vibration, 258: 287–307.
[6] Zhang Y.L., Reese J.M., Gorman D.G., 2002, Initially tensioned orthotropic cylindrical shells conveying fluid: A vibration analysis, Journal of Fluids and Structures, 161: 53–70,.
[7] Kadoli R., Ganesan N., 2003و Free vibration and buckling analysis of composite cylindrical shells conveying hot fluid, Composite Structures, 60: 19–32.
[8] Wang L., Ni Q., 2006, A note on the stability and chaotic motions of a restrained pipe conveying fluid, Journal of Sound and Vibration, 296: 1079–1083.
[9] Modarres-Sadeghi Y., Païdoussis M.P., 2009, Nonlinear dynamics of extensible fluid-conveying pipes, supported at both ends, Journal of Fluids and Structures, 25: 535-543.
[10] Meng D., Guo H., Xu S., 2011, Non-linear dynamic model of a fluid-conveying pipe undergoing overall motions, Applied Mathematical Modelling, 35:, pp. 781-796.
[11] Ni Q., Zhang Z.L., Wang L., 2011و Application of the differential transformation method to vibration analysis of pipes conveying fluid, Applied Mathematical and Computation, 217: 7028-7038.
[12] Dai H.L., Wang L., Qian Q., Gan J., 2012, Vibration analysis of three-dimensional pipes conveying fluid with consideration of steady combined force by transfer matrix method, Applied Mathematical and Computation 219: 2453-2464.
[13] Gay-Balmaz F., Putkaradze V., 2015, On flexible tubes conveying fluid: geometric nonlinear theory, stability and dynamics, Journal of Nonlinear Science, 25: 889-936.
[14] Zhang T., Ouyang H., Zhang Y.O., Lv B.L., 2016, Nonlinear dynamics of straight fluid-conveying pipes with general boundary conditions and additional springs and masses, Applied Mathematical Modelling, 40: 7880-7900.
[15] Gu J., Tianqi M., Menglan, D., 2016, Influence of aspect ratio on the dynamic response of a fluid-conveying pipe using the Timoshenko beam model, Ocean Engineering, 114: 185–191.
[16] Li B., Wang Zh., Jing L., 2018, Dynamic Response of Pipe Conveying Fluid with Lateral Moving Supports, Shock and Vibration, 24: ID 3295787.
[17] Bai Y., Xie W., Gao W., Xu W., 2018, Dynamic analysis of a cantilevered pipe conveying fluid with density variation, Journal of Fluids and Structures, 81: 638-655.
[18] Hu Y.J., Zhu W., 2018, Vibration analysis of a fluid-conveying curved pipe with an arbitrary undeformed configuration, Applied Mathematical Modelling, 64: 624-642.
[19] Daneshmehr, A., Rajabpoor, A., Hadi, A., 2015, Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science, 95: 23-35.
[20] Zamani Nejad, M., Hadi, A., 2016, Non-local analysis of free vibration of bi-directional functionally graded Euler-Bernoulli nano-beams, International Journal of Engineering Science, 105: 1-11.
[21] Zamani Nejad, M., Hadi, A., 2016, Eringen's non-local elasticity theory for bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams, International Journal of Engineering Science, 106: 1-9.
[22] Zamani Nejadو M., Hadi A., Farajpour A., 2017, Consistent couple-stress theory for free vibration analysis of Euler-Bernoulli nano-beams made of arbitrary bi-directional functionally graded materials, Structural Engineering and Mechanics 63(2): 161-169.
[23] Zamani Nejad M., Jabbari M., Hadi A., 2017, A review of functionally graded thick cylindrical and conical shells, Journal of Computational Applied Mechanicsو 48(2): 357-370.
[24] Hadi A., Zamani Nejad M., Hosseini M., 2018, Vibrations of three-dimensionally graded nanobeams, International Journal of Engineering Science,128: 12-23.
[25] Hadi A., Zamani Nejad M., Rastgoo A., Hosseini M., 2018, Buckling analysis of FGM Euler-Bernoulli nano-beams with 3D-varying properties based on consistent couple-stress theory, Steel and Composite Structures, 26(6): 663-672.
[26] Zamani Nejad M., Hadi A., Omidvari A., Rastgoo A., 2018, Bending analysis of bi-directional functionally graded Euler-Bernoulli nano-beams using integral form of Eringen's non-local elasticity theory, Structural Engineering and Mechanics, 67(4): 417-425.
[27] Zarezadeh E., Hosseini V., Hadi A., 2019, Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory, Mechanics Based Design of Structures and Machines, 25: 1-16.
[28] Barati A., Hadi A., Zamani Nejad M., Noroozi R., 2020, On vibration of bi-directional functionally graded nanobeams under magnetic field, Mechanics Based Design of Structures and Machines, 23: 1-18.
[29] Dehshahri K., Zamani Nejad M., Ziaee S., Niknejad A., Hadi A., 2020, Free vibrations analysis of arbitrary three-dimensionally FGM nanoplates, Advances in nano research, 8(2): 115-134.
[30] Barati A., Adeli M.M., Hadi A., 2020, Static torsion of bi-directional functionally graded microtube based on the couple stress theory under magnetic field, International Journal of Applied Mechanics, 12(02): 2050021.
[31] Noroozi R., Barati A., Kazemi A., Norouzi S., Hadi A., 2020, Torsional vibration analysis of bi-directional FG nano-cone with arbitrary cross-section based on nonlocal strain gradient elasticity, Advances in nano research, 8(1): 13-24.
[32] Brush, D.O., Almroth, B.O. 1975, Buckling of bars, plates and shells, McGraw-Hill, New York.
[33] Baohui, L., Hangshan, G., Yongshou, L., Zhufeng, Y., 2012, Free vibration analysis of micropipe conveying fluid by wave method, Results in Physics, 2: 104–109.
[34] Sheikhzadeh G.A., Teimouri H., Mahmoodi M., 2013, Numerical study of mixed convection of nanofluid in a concentric annulus with rotating inner cylinder, Trans. Phenomen. Nano Micro Scales 1: 26-36.
[35] Bellman R., Casti J., 1971, Differential quadrature and long-term integration, Journal of Mathematical Analysis and Applications, 34: 235–238.
[36] Eiamsa-ard S., Kiatkittipong K., Jedsadaratanachai W., 2015, Heat transfer enhancement of TiO2/water nanofluid in a heat exchanger tube equipped with overlapped dual twisted-tapes, Engineering Science and Technology, an International Journal 18: 336-350.
[37] Kefayati G.R., Hosseinizadeh S.F., Gorji M., Sajjadi H., 2011, Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid, International Communications in Heat and Mass Transfer, 38: 798‒805.
[38] Abu-Nada E., 2009, Influences of variable viscosity and thermal conductivity of Al2O3-water nanofluid on heat transfer enhancement in natural convection, International Journal of Heat and Fluid Flow, 30: 679-690.
[39] Zeinali Heris S., Talaii E., Noie S.H., 2012, CuO/ Water Nanofluid Heat Transfer Through Triangular Ducts, Iranian Journal of Chemical Engineering, 9, 23-33.
[40] Qu, Y., Chen, Y., Long, X., Hua, H., Meng, G. 2013, Free and forced vibration analysis of uniform and stepped circular cylindrical shells using a domain decomposition method, Applied Acoustics, 74: 425–439.
)
Volume 51, Issue 1
June 2020Pages 122-128
- Receive Date: 01 April 2020
- Revise Date: 09 May 2020
- Accept Date: 14 May 2020