Skip to main content
Log in

Flow past two square cylinders with flexible splitter plates

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

Abstract

Fluid–structure interaction of flexible splitter plates attached to two rigid square cylinders, placed side-by-side in a uniform flow is studied. A partitioned approach is used to solve the fluid and structure problems. The results from the implementation are compared with earlier results on standard benchmarks. The Reynolds number based on the edge of the square cylinder is 100. The flexibility of the splitter plates is varied. Initially, the splitter plates undergo small amplitude oscillations that are out of phase relative to each other. The fully developed unsteady response shows in-phase variation. The frequency of the initial out-of-phase vibrations is found to be greater than the natural frequency of the structure. It approaches the natural frequency with increase in stiffness of the structure. The amplitude of the response of the structure is large when the dominant vibration frequency is close to its natural frequency. Lock-in/synchronization is observed for certain values of flexibility considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Mittal S, Kumar V, Raghuvanshi A (1997) Unsteady incompressible flows past two cylinders in tandem and staggered arrangements. Int J Numer Methods Fluids 25:1315–1344

    Article  MATH  Google Scholar 

  2. Zdravkovich MM (1977) Review of flow interference between two circular cylinders in various arrangements. J Fluids Eng Trans ASME 99:618–633

    Article  Google Scholar 

  3. Kim HJ, Durbin PA (1988) Investigation of the flow between a pair of circular cylinders in the flopping regime. J Fluid Mech 196:431–448

    Article  Google Scholar 

  4. Wong PTY, Ko NWM, Chiu AYW (1995) Flow characteristics around two parallel adjacent square cylinders of different sizes. J Wind Eng Ind Aerodyn 54–55:263–275

    Article  Google Scholar 

  5. Suqin C (2000) Numerical computation of the flow around two square cylinders arranged side-by-side. Appl Math Mech 21:147–164

    Article  MATH  Google Scholar 

  6. Kwon K, Choi H (1996) Control of laminar vortex shedding behind a circular cylinder using splitter plates. Phys Fluids 8:479–486

    Article  MATH  Google Scholar 

  7. Mansingh V, Oosthuizen PH (1990) Effects of splitter plates on the wake flow behind a bluff body. AIAA J 28:778–783

    Article  Google Scholar 

  8. Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190:321–332

    Article  MATH  Google Scholar 

  9. Bazilevs Y, Takizawa K, Tezduyar TE (2013) Computational fluid–structure interaction: methods and applications. Wiley, Hoboken

    Book  Google Scholar 

  10. Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94:339–351

    Article  MATH  MathSciNet  Google Scholar 

  11. Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94:353–371

    Article  MATH  MathSciNet  Google Scholar 

  12. Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575

  13. Mittal S (2000) On the performance of high aspect-ratio elements for incompressible flows. Comput Methods Appl Mech Eng 188:269–287

    Article  MATH  Google Scholar 

  14. Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 32:199–259

    Article  MATH  MathSciNet  Google Scholar 

  15. Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95:221–242

    Article  MATH  Google Scholar 

  16. Tezduyar TE, Behr M, Mittal S, Johnson AA (1992) Computation of unsteady incompressible flows with stabilized finite element methods: space-time formulations, iterative strategies and massively parallel implementations, New Methods in Transient Analysis, AMD Vol. 143, ASME, 7–24

  17. Tezduyar TE, Aliabadi SK, Behr M, Johnson AA, Mittal S (1993) Parallel finite element computation of 3D flows. Computer 26:27–36

    Article  Google Scholar 

  18. Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119:73–94

    Article  MATH  Google Scholar 

  19. Dhondt G, Calculix: A free software three-dimensional structural finite element program http://www.calculix.de/

  20. Dhondt G (2004) The finite element method for three-dimensional thermomechanical applications. Wiley, Hoboken

    Book  MATH  Google Scholar 

  21. Harari I, Hughes TJR (1992) What are c and h?: inequalities for the analysis and design of finite element methods. Comput Methods Appl Mech Eng 97:157–192

    Article  MATH  MathSciNet  Google Scholar 

  22. Turek S, Hron J (2006) Proposal for numerical benchmarks for fluid-structure interaction between an elastic object and laminar incompressible flow. In: Fluid–structure interaction. Modelling, simulation and optimization, Lecture notes in computational science and engineering

  23. Wall WA, Ramm E (1998) Fluidstructure interaction based upon a stabilized (ALE) finite element method. In: Idelsohn SR, Onate E (eds) 4th World congress on computational mechanics. CIMNE, Barcelona, Spain, Computational mechanics—New trends and applications, Buenos Aires, Argentina

  24. Hubner B, Walhorn E, Dinkler D (2004) A monolithic approach to fluid–structure interaction using space-time finite elements. Comput Methods Appl Mech Eng 193:2087–2104

    Article  Google Scholar 

  25. Dettmer W, Peric D (2006) A computational framework for fluidstructure interaction: finite element formulation and applications. Comput Methods Appl Mech Eng 195:5754–5779

    Article  MATH  Google Scholar 

  26. Lee J, You D (2013) Study of vortex-shedding-induced vibration of a flexible splitter plate behind a cylinder. Phys Fluids 25(110811):1–17

    MATH  Google Scholar 

  27. Khalak A, Williamson CHK (1999) Motions, force and mode transitions in vortex induced vibrations at low mass damping. J Fluids Struct 13:813–851

    Article  Google Scholar 

  28. Thomson WT, Dahleh MD (1997) Theory of vibration with applications, 5th edn. Prentice Hall, Upper Saddle River

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sanjay Mittal.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Furquan, M., Mittal, S. Flow past two square cylinders with flexible splitter plates. Comput Mech 55, 1155–1166 (2015). https://doi.org/10.1007/s00466-014-1110-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-014-1110-5

Keywords

Navigation