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A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems

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Abstract

Interactions between an incompressible fluid passing through a flexible tube and the elastic wall is one of the strongly coupled fluid–solid interaction (FSI) problems frequently studied in the literature due to its research importance and wide range of applications. Although incompressible fluid is a prevalent model in many simulation studies, the assumption of incompressibility may not be appropriate in strongly coupled FSI problems. This paper narrowly aims to study the effect of the fluid compressibility on the wave propagation and fluid–solid interactions in a flexible tube. A partitioned FSI solver is used which employs a finite volume-based fluid solver. For the sake of comparison, both traditional incompressible (ico) and weakly compressible (wco) fluid models are used in an Arbitrary Lagrangian–Eulerian (ALE) formulation and a PISO-like algorithm is used to solve the unsteady flow equations on a collocated mesh. The solid part is modeled as a simple hyperelastic material obeying the St-Venant constitutive relation. Computational results show that not only use of the weakly compressible fluid model makes the FSI solver in this case more efficient, but also the incompressible fluid model may produce largely unrealistic computational results. Therefore, the use of the weakly compressible fluid model is suggested for strongly coupled FSI problems involving seemingly incompressible fluids such as water especially in cases where wave propagation in the solid plays an important role.

Article highlights

  • Flow in a flexible tube is a strongly coupled FSI problem.

  • The weakly compressible fluid model has computational merits in FSI problems.

  • The incompressibility assumption for liquids leads to unrealistic results in some FSI cases.

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Notes

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References

  1. Gerbeau J-F, Vidrascu M (2003) A quasi-newton algorithm based on a reduced model for fluid–structure interaction, problems in blood flows. Math Model Numer Anal 37:631–647

    Article  MathSciNet  Google Scholar 

  2. Causin P, Gerbeau J-F, Nobile F (2005) Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput Methods Appl Mech Eng 194:4506–4527

    Article  MathSciNet  Google Scholar 

  3. Förster C, Wall WA, Ramm E (2007) Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput Methods Appl Mech Eng 196:1278–1293

    Article  MathSciNet  Google Scholar 

  4. Badia S, Quaini A, Quarteroni A (2008) Modular vs non-modular preconditioners for fluid-structure systems with large added-mass effect. Comput Methods Appl Mech Eng 197:4216–4232

    Article  MathSciNet  Google Scholar 

  5. He T (2015) Partitioned coupling strategies for fluid–structure interaction with large displacement: explicit, implicit and semi-implicit schemes. Wind Struct 20(3):423–448

    Article  Google Scholar 

  6. Le Tallec P, Mouro J (2001) Fluid structure interaction with large structural displacements. Comput Methods Appl Mech Eng 190:3039–3067

    Article  Google Scholar 

  7. De Santiago E, Law KH (1999) A robust distributed adaptive finite element program for coupled fluid-structure problems. Eng Comput 15:137–154

    Article  Google Scholar 

  8. Parker G, Guilkey J, Harman T (2006) A component-based parallel infrastructure for the simulation of fluid–structure interaction. Eng Comput 22:277–292

    Article  Google Scholar 

  9. Deiterding R, Radovitzky R, Mauch SP, Noels L, Cummings JC, Meiron DI (2006) A virtual test facility for the efficient simulation of solid material response under strong shock and detonation wave loading. Eng Comput 22:325–347

    Article  Google Scholar 

  10. Degroote J, Swillens A, Bruggeman P, Haelterman R, Segers P, Vierendeels J (2010) Simulation of fluid–structure interaction with the interface artificial compressibility method. Int J Numer Methods Biomed Eng 26:276–289

    Article  MathSciNet  Google Scholar 

  11. Raback P, Jarvinen E, Ruokolainen J (2008) Computing the artificial compressibility field for partitioned fluid–structure interaction simulations. Eighth World Congress on Computational Mechanics, 5th European Congress on computational methods in applied sciences and engineering, Venice, Italy

  12. Bogaers AEJ, Kok S, Reddy BD, Franz T (2015) Extending the robustness and efficiency of artificial compressibility for partitioned fluid–structure interactions. Comput Methods Appl Mech Eng 283:1278–1295

    Article  MathSciNet  Google Scholar 

  13. He T, Wang T, Zhang H (2018) The use of artificial compressibility to improve partitioned semi-implicit fsi coupling within the classical chorin-témam projection framework. Comput Fluids 166:64–77

    Article  MathSciNet  Google Scholar 

  14. Marrone S, Colagrossi A, Di Mascio A, Le Touzé D (2015) Prediction of energy losses in water impacts using incompressible and weakly compressible models. J Fluids Struct 54:802–822

    Article  Google Scholar 

  15. Andersson H, Nordin P, Borrvall T, Simonsson K, Hilding D, Schill M, Krus P, Leidermark D (2017) A co-simulation method for system-level simulation of fluid-structure couplings in hydraulic percussion units. Eng Comput 33:317–333

    Article  Google Scholar 

  16. Chorin AJ (1967) A numerical method for solving incompressible viscous flow problems. J Comput Phys 2:12–26

    Article  MathSciNet  Google Scholar 

  17. Pierre B, Oger G, Guilcher P, Touze DL (2017) A weakly-compressible cartesian grid approach for hydrodynamic flows. Comput Phys Commun 220:31–43

    Article  MathSciNet  Google Scholar 

  18. Seo JH, Moon YJ (2006) Linearized perturbed compressible equations for low mach number aeroacoustics. J Comput Phys 218:702–719

    Article  MathSciNet  Google Scholar 

  19. Hirt CW, Amsden AA, Cook JL (1974) An arbitrary Lagrangian–Eulerian computing method for all flow speeds. J Comput Phys 14(3):227–253

    Article  Google Scholar 

  20. Hughes THR, Liu WK, Zimmermann TK (1981) Lagrangian–Eulerian finite element formulation for incompressible viscous flow. Comput Methods Appl Mech Eng 29:329–349

    Article  MathSciNet  Google Scholar 

  21. Barlowa AJ, Maire PH, Rider WJ, Rieben RN, Shashkov MJ (2016) Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows. J Comput Phys 322:603–665

    Article  MathSciNet  Google Scholar 

  22. Greenshields CJ, Weller HG, Ivankovic A (1999) The finite volume method for coupled fluid fow and stress analysis. Comput Model Simul Eng 4:213–218

    Google Scholar 

  23. Kochupillai J, Ganesan N, Padmanabhan C (2005) A new finite element formulation based on the velocity of flow for water hammer problems. Int J Press Vessels Pip 82:1–14

    Article  Google Scholar 

  24. Daude F, Tijsseling AS, Galon P (2018) Numerical investigations of water-hammer with column- separation induced by vaporous cavitation using a one-dimensional finite-volume approach. J Fluids Struct 83:91–118

    Article  Google Scholar 

  25. Formaggia L, Gerbeau JF, Nobile F, Quarteroni A (2001) On the coupling of 3D and 1D Navier–Stokes equations for flow problems in compliant vessels. Comput Methods Appl Mech Eng 191(6–7):561–582

    Article  MathSciNet  Google Scholar 

  26. Gee MW, Küttler U, Wall WA (2011) Truly monolithic algebraic multigrid for fluid–structure interaction. Int J Numer Meth Eng 85:987–1016

    Article  MathSciNet  Google Scholar 

  27. Eken A, Sahin M (2016) A parallel monolithic algorithm for the numerical simulation of large-scale fluid structure interaction problems. Int J Numer Meth Fluids 80:687–714

    Article  MathSciNet  Google Scholar 

  28. Lozovskiya A, Olshanskii MA, Vassilevski YV (2019) Analysis and assessment of a monolithic FSI finite element method. Comput Fluids 179:277–288

    Article  MathSciNet  Google Scholar 

  29. Soloukhin RI (1966) Shock waves and detonations in gases. Mono Books

  30. Zhang G, Setoguchi T, Kim HD (2015) Numerical simulation of flow characteristics in micro shock tubes. J Therm Sci 24(3):246–253

    Article  Google Scholar 

  31. Prandtl L (1925) Uber die ausgebildete Turbulenz. ZAMM 5:136–139

    Article  Google Scholar 

  32. Issa RI (1985) Solution of implicitly discretized fluid flow equations by operator-splitting. J Comput Phys 62:40–65

    Article  Google Scholar 

  33. Jang DS, Jetli R, Acharya S (1986) Comparison of the PISO, SIMPLER and SIMPLEC algorithms for the treatment of the pressure-velocity coupling in steady flow problems. Numer Heat Transf 10:209–228

    Article  Google Scholar 

  34. Greenshields CJ, Weller HG (2005) A unified formulation for continuum mechanics applied to fluid–structure interaction in flexible tubes. Int J Numer Meth Eng 64:1575–1593

    Article  MathSciNet  Google Scholar 

  35. Demirdzic I, Peric M (1988) Space conservation law in finite volume calculations of fluid flow. Int J Numer Meth Fluids 8:1037–1050

    Article  MathSciNet  Google Scholar 

  36. Maneeratana K (2000) Development of finite volume method for non-linear structure applications. PhD Thesis, Department of Mechanical Engineering Imperial College of Science, Technology and Medicine, London

  37. Jasak H, Tukovic Z (2007) Upadted lagrangian finite volume solver for large deformation dynamic response of elastic. Trans FAMENA 31(1):55–70

    Google Scholar 

  38. Donea J, Huerta A, Ponthot J-Ph, Rodriguez-Ferran A (2004) Arbitrary Lagrangian–Eulerian methods. Encyclopedia of computational mechanics; Chapter 14

  39. Ryzhakov P, Marti J, Idelsohn S, Oñate E (2017) Fast fluid–structure interaction simulations using a displacement-based finite element model equipped with an explicit streamline integration prediction. Comput Methods Appl Mech Eng 315:1080–1097

    Article  MathSciNet  Google Scholar 

  40. Mok D, Wall WA (2001) Partitioned analysis schemes for the transient interaction of incompressible flows and nonlinear flexible structures. In: Wall WA, Bletzinger KU, Schweitzerhof K (eds) Trends in computational structural mechanics. CIMNE, Barcelona

    Google Scholar 

  41. Küttler U, Wall WA (2008) Fixed-point fluid–structure interaction solvers with dynamic relaxation. Comput Mech 43:61–72

    Article  Google Scholar 

  42. Pielhop K, Klaas M, Schröder W (2015) Experimental analysis of the fluid–structure interaction in finite-length straight elastic vessels. Eur J Mech B/Fluids 50:71–88

    Article  Google Scholar 

  43. Geoghegan PH, Buchmann NA, Soria PHG, Jermy MC (2013) Time-resolved PIV measurements of the flow field in a stenosed, compliant arterial model. Exp Fluids 54:1528. https://doi.org/10.1007/s00348-013-1528-0

    Article  Google Scholar 

  44. Tijsseling AS (2007) Water hammer with fluid–structure interaction in thick-walled pipes. Comput Struct 85:844–851

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, K. N. Toosi University of Technology, P.O.B. 19395-1999, Tehran, Iran

    Emad Tandis & Ali Ashrafizadeh

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  1. Emad Tandis
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  2. Ali Ashrafizadeh
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Correspondence to Emad Tandis.

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Tandis, E., Ashrafizadeh, A. A numerical study on the fluid compressibility effects in strongly coupled fluid–solid interaction problems. Engineering with Computers 37, 1205–1217 (2021). https://doi.org/10.1007/s00366-019-00880-4

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  • DOI: https://doi.org/10.1007/s00366-019-00880-4

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