An Analytical Approach for Modeling Fluid-structure Interaction Problems in Axisymmetric Domains

Document Type : Original Research Paper


Mechanical Engineering Department, Babol Noshirvani University of Technology, Babol, Iran.


 Few analytical approaches have been proposed so far for solving FluidStructure Interaction (FSI) problems in the literature. In fact, FSI is generally so complicated that its analytical solution remains almost unavailable. Inspired by this fact, here an analytical methodology is presented for modeling steady-state fluid-structure interaction problems in axisymmetric domains. For this purpose, the Navier-Stokes equations for the flow of the incompressible viscous fluid, and the linear elasticity equations for the deformation of the solid structure are expressed in axisymmetric coordinates. Appropriate boundary conditions are also employed that are capable of coupling the fluid and solid domains by imposing kinematic and dynamic constraints on the fluid-structure interaction interface. The set of fluid and structure equations are solved by MATLAB symbolic toolbox. The accuracy of the presented analytical approach is verified in two different ways. First, by specializing the results for the simple case of a thick cylindrical pressure vessel, second, by comparing the analytical results for flow through a nozzle with numerical results obtained by ANSYS/CFX simulation. Variation of the stress components is obtained in the nozzle wall. The results of the analytical approach are in good agreement with those of the numerical modeling. The proposed methodology can be used for fast yet efficient solution of fluid-structure interaction problems in axisymmetric configuration.  


[1] D. Cinquegrana, P.L. Vitagliano, Validation of a new fluid-structure interaction framework for nonlinear instabilities of 3D aerodynamic configurations, J. Fluids Struct., 103 (2021) 103264.
[2] E. Alaei, H. Afrasiab, M. Dardel, Analytical and numerical fluid-structure interaction study of a microscale piezoelectric wind energy harvester, Wind Energy., 23(6) (2020) 1444-1460.
[3] S. Meduri, M. Cremonesi, A. Frangi, U. Perego, A lagrangian fluid-structure interaction approach for the simulation of airbag deployment, Finite Elem. Anal. Des., 198 (2022) 103659.
[4] J. Boustani, M.F. Barad, C.C. Kiris, C. Brehm, An immersed boundary fluid-structure interaction method for thin, highly compliant shell structures, J. Comput. Phys., 438 (2021) 110369.
[5] A. Morvan, M. Sacher, A. Nˆeme, J.B. Leroux, C. Jochum, N. Abiven, Efficient jib-mainsail fluidstructure interaction modelling Validations with semi-rigid sails experiments, Ocean Eng., 243 (2022) 110210.
[6] H. Afrasiab, M.R. Movahhedy, A. Assempour, Proposal of a new design for valveless micropumps, Sci. Iran., 18(6) (2011) 1261-1266.
[7] H. Safi, N. Phillips, Y. Ventikos, R. Bomphrey, Implementing fluid-structure interaction computational and empirical techniques to assess hemodynamics of abdominal aortic aneurysms, Artery Res., 20(C) (2017) 55-56.
[8] M. Kazemiyan, H. Afrasiab, M.H. Pashaei, Comparison of the plaque rupture risk in different double-stenosis arrangements of coronary arteries by modeling fluid-structure interaction, Modares Mech. Eng., 16(2) (2016) 10-18.
[9] Z. Xie, X. Wang, W. Zhu, Theoretical and experimental exploration into the fluid structure coupling dynamic behaviors towards water-lubricated bearing with axial asymmetric grooves, Mech. Syst. Signal Process., 168 (2022) 108624.
[10] J. Pirnar, B. Širok, A. Bombač, Effect of airway  surface liquid on the forces on the pharyngeal wall: Experimental fluid-structure interaction study, J. Biomech., 63 (2017) 117-124.
[11] T. Gleim, P. Birken, M. Weiland, D. Kuhl, A. Meister, O. Wünsch, Experimental and numerical aspects of a thermal fluid-structure phenomenon, AIP Conf. Proc., 1863(1) (2017) 410004.
[12] A. Hessenthaler, N.R. Gaddum, O. Holub, R. Sinkus, O.  Röhrle, D. Nordsletten, Experiment for validation of fluid-structure interaction models and algorithms, Int. J. Numer. Methods Biomed. Eng., 33(9) (2017) e2848.
[13] P.B. Ryzhakov, E. Oñate, A finite element model for fluid-structure interaction problems involving closed membranes, internal and external fluids, Comput. Methods Appl. Mech. Eng., 326 (2017) 422-445.
[14] M. Abbadeni, I. Zidane, H. Zahloul, A. Fatu, M. Hajjam, Finite element analysis of fluid-structure interaction in the hydromechanical deep drawing process, J. Mech. Sci. Technol., 31(11) (2017) 5485-5491.
[15] A.K. Slone, K. Pericleous, C. Bailey, M. Cross, Dynamic fluid-structure interaction using finite volume unstructured mesh procedures, Comput. Struct., 80(5-6) (2002) 371-390.
[16] D.R. Wilkes, A.J. Duncan, Acoustic coupled fluidstructure interactions using a unified fast multipole boundary element method, J. Acoust. Soc. Am., 137(4) (2015) 2158-2167.
[17] H. Yao, H. Zhang, H. Liu, W. Jiang, Numerical study of ow-excited noise of a submarine with full appendages considering fluid structure interaction using the boundary element method, Eng. Anal. Bound. Elem., 77 (2017) 1-9.
[18] L. Wang, G.M.D. Currao, F. Han, A.J. Neely, J. Young, F.-B. Tian, An immersed boundary method for fluid-structure interaction with compressible multiphase ows, J. Comput. Phys., 346 (2017) 131-151.
[19] A. Gerstenberger, W.A. Wall, An extended finite element method/lagrange multiplier based approach for fluid-structure interaction, Comput. Methods Appl. Mech. Eng., 197(19-20) (2008) 1699-1714.
[20] D.J. Munk, T. Kipouros, G.A. Vio, G.P. Steven, G.T. Parks, Topology optimisation of micro fluidic mixers considering fluid-structure interactions with a coupled lattice Boltzmann algorithm, J. Comput. Phys., 349 (2017) 11-32.
[21] A. Zhang, P. Sun, F. Ming, A. Colagrossi, Smoothed particle hydrodynamics and its applications in fluid-structure interactions, J. Hydrodyn. Ser B., 29(2) (2017) 187-216.
[22] D. Soares Jr., Fluid-structure interaction analysis by optimised boundary element-finite element coupling procedures, J. Sound Vib., 322(1-2) (2009) 184-195.
[23] X. Cui, X. Yao, Z. Wang, M. Liu, A hybrid wavelet-based adaptive immersed boundary finite- difference lattice Boltzmann method for twodimensional fluid-structure interaction, J. Comput. Phys., 333 (2017) 24-48.
[24] Z. Li, J. Favier, A non-staggered coupling of finite element and lattice Boltzmann methods via an immersed boundary scheme for fluid-structure interaction, Comput. Fluids., 143 (2017) 90-102.
[25] Z. Li, J. Leduc, A. Combescure, F. Leboeuf, Coupling of SPH-ALE method and finite element method for transient fluid-structure interaction, Comput. Fluids., 103 (2014) 6-17.
[26] D. Hu, T. Long, Y. Xiao, X. Han, Y. Gu, Fluidstructure interaction analysis by coupled FE-SPH model based on a novel searching algorithm, Comput. Methods Appl. Mech. Eng., 276 (2014) 266-286.
[27] J.R. Craig, W. Wayne Read, The future of analytical solution methods for groundwater ow and transport simulation, XVIII International Conference on Water Resources (CMWR), Barcelona, (2010).
[28] H. Afrasiab, M.R. Movahhedy, Treatment of the small time instability in the finite element analysis of fluid structure interaction problems, Int. J. Numer. Methods Fluids., 71(6) (2013) 756-771.
[29] H. Afrasiab, M.R. Movahhedy, A. Assempour, Fluid-structure interaction analysis in micro microfluidic devices: A dimensionless finite element approach, Int. J. Numer. Methods Fluids., 68(9) (2012) 1073- 1086.
[30] P. Xu, P.R. Wellens, Theoretical analysis of nonlinear fluid-structure interaction between largescale polymer offshore oating photovoltaics and waves, Ocean Eng., 249 (2022) 110829.
[31] S. Soni, N.K. Jain, P.V. Joshi, A. Gupta, Effect of fluid-structure interaction on vibration and deflection analysis of generally orthotropic submerged micro-plate with crack under thermal environment: an analytical approach, J. Vib. Eng. Technol., 8 (2020) 643-672.
[32] M. Fritsche, P. Epple, A. Delgado, Analytical and numerical investigation of the fluid structure interaction of an elastic beam in a water channel, Proceedings of the ASME (American Society of Mechanical Engineers Digital Collection) 2020 International Mechanical Engineering Congress and Exposition. Volume 10: Fluids Engineering. Virtual, Online. November 16-19, (2020) V010T10A049.
[33] N.K. Jain, S. Soni, R. Prajapati, Analytical treatment for vibration analysis of partially cracked orthotropic and FGM submerged cylindrical shell with consideration of fluid-structure interaction, Mech. Based Des. Struct. Mach., 49(4) (2021) 463-486.
[34] C.-C. Yu, A.S. Whittaker, Review of analytical studies on seismic fluid-structure interaction of base-supported cylindrical tanks, Eng. Struct., 233 (2021) 111589.
[35] C. Zhang, Fluid-structure interaction in rectilinear ows: Four analytical solutions, Phys. Fluids., 33(6) (2021) 063611.
[36] H. Afrasiab, M.R. Movahhedy, A. Assempour, Finite element and analytical fluid-structure interaction analysis of the pneumatically actuated diaphragm microvalves, Acta Mech., 222 (2011) 175.
[37] A. Van Hirtum, B. Wu, H. Gao, X.Y. Luo, Constricted channel ow with different cross-section shapes, Eur. J. Mech. B/Fluids., 63 (2017) 1-8.
[38] A. Sohankar, A. Joulaei, M. Mahmoodi, Fluid flow and convective heat transfer in a rotating rectangular microchannel with various aspect ratios, Int. J. Therm. Sci., 172 (Part A) (2022) 107259.
[39] A.P. Boresi, K.P. Chong, J.D. Lee, Elasticity in Engineering Mechanics, John Wiley and Sons, (2010).
[40] V. Vullo, Circular Cylinders and Pressure Vessels: Stress Analysis and Design, 2nd ed., Springer Science and Business Media, (2016).
[41] S. Murugappan, E.J. Gutmark, R.R. Lakhamraju, S. Khosla, Flow-structure interaction effects on a jet emanating from a exible nozzle, Phys. Fluids., 20(11) (2008)  117105.