Advertisement

Computational Mechanics

, Volume 39, Issue 4, pp 453–476 | Cite as

Collapse of a Liquid Column: Numerical Simulation and Experimental Validation

  • Marcela A. Cruchaga
  • Diego J. Celentano
  • Tayfun E. Tezduyar
Original Paper

Abstract

This paper is focused on the numerical and experimental analyses of the collapse of a liquid column. The measurements of the interface position in a set of experiments carried out with shampoo and water for two different initial column aspect ratios are presented together with the corresponding numerical predictions. The experimental procedure was found to provide acceptable recurrence in the observation of the interface evolution. Basic models describing some of the relevant physical aspects, e.g. wall friction and turbulence, are included in the simulations. Numerical experiments are conducted to evaluate the influence of the parameters involved in the modeling by comparing the results with the data from the measurements. The numerical predictions reasonably describe the physical trends.

Keywords

Moving interfaces Two-fluid flows Computational fluid mechanics Experimental validation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    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 32:199–259CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:239–349CrossRefMathSciNetGoogle Scholar
  3. 3.
    Liu WK (1981) Finite element procedures for fluid-structure interactions and application to liquid storage tanks. Nucl Eng Des 65:221–238CrossRefGoogle Scholar
  4. 4.
    Huerta A, Liu W (1988) Viscous flow with large free surface motion. Comput Methods Appl Mech Eng 69:277–324CrossRefzbMATHGoogle Scholar
  5. 5.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Tezduyar TE, Behr M, Liu 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 94:339–351CrossRefzbMATHGoogle Scholar
  7. 7.
    Tezduyar TE, Behr M, Mittal S, Liu 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-surfaces flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94: 353–371CrossRefzbMATHGoogle Scholar
  8. 8.
    Braess H, Wriggers P (2000) Arbitrary Lagrangian–Eulerian finite element analysis of free surface flow. Comput Methods Appl Mech Eng 190:95–109CrossRefzbMATHGoogle Scholar
  9. 9.
    Feng YT, Perić D (2003) A spatially adaptive linear space-time finite element solution procedure for incompressible flows with moving domains. Int J Numer Methods Fluids 43:1099–1106CrossRefzbMATHGoogle Scholar
  10. 10.
    Rabier S, Medale M (2003) Computation of free surface flows with a projection FEM in a moving mesh framework. Comput Methods Appl Mech Eng 192:4703–4721CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Koshizuka S, Oka Y (1996) Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nucl Sci Eng 123:421–434Google Scholar
  12. 12.
    Bonet J, Kulasegaram S, Rodriguez-Paz MX, Profit M (2004) Variational formulation for the smooth particle hydrodynamics (SPH) simulation of fluid and solid problems. Comput Methods Appl Mech Eng 193:928–948CrossRefGoogle Scholar
  13. 13.
    Kulasegaram S, Bonet J, Lewis RW, Profit M (2004) A variational formulation based contact algorithm for rigid boundaries in two-dimensional SPH applications. Comput Mech 33:316–325CrossRefzbMATHGoogle Scholar
  14. 14.
    Xie H, Koshizuka S, Oka Y (2004) Modelling of a single drop impact onto liquid film using particle method. Int J Numer Methods Fluids 45:1009–1023CrossRefzbMATHGoogle Scholar
  15. 15.
    Idelsohn S, Storti M, Oñate E (2003) A Lagrangian meshless finite element method applied to fluid-structure interaction problems. Comput Struct 81:655–671CrossRefGoogle Scholar
  16. 16.
    Tezduyar T, Aliabadi S, Behr M (1998) Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 155:235–248CrossRefzbMATHGoogle Scholar
  17. 17.
    Osher S, Fedkiw P (2001) Level set methods: and overview and some recent results. J Comput Phys 169:463–502CrossRefzbMATHMathSciNetGoogle Scholar
  18. 18.
    Sethian JA (2001) Evolution, implementation, and application of level set and fast marching methods for advancing fronts. J Comput Phys 169:503–555CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130zbMATHGoogle Scholar
  20. 20.
    Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575CrossRefzbMATHMathSciNetGoogle Scholar
  21. 21.
    Kim MS, Lee WI (2003) A new VOF-based numerical scheme for the simulation of fluid flow with free surface. Part I: New free surface-tracking algorithm and its verification. Int J Numer Methods Fluids 42:765–790CrossRefzbMATHGoogle Scholar
  22. 22.
    Minev P, Chen T, Nandakumar K (2003) A finite element technique for multifluid incompressible flow using Eulerian grids. J Comput Phys 187:255–273CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Sochnikov V, Efrima S (2003) Level set calculations of the evolution of boundaries on a dynamically adaptive grid. Int J Numer Methods Eng 56:1913–1929CrossRefzbMATHMathSciNetGoogle Scholar
  24. 24.
    Yue W, Lin CL, Patel VC (2003) Numerical simulation of unsteady multidimensional free surface motons by level set method. Int J Numer Methods Fluids 42:853–884CrossRefzbMATHGoogle Scholar
  25. 25.
    Tezduyar TE, Sathe S (2004) Enhanced-discretization space-time technique (EDSTT). Comput Methods Appl Mech Eng 193:1385–1401CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Kohno H, Tanahashi T (2004) Numerical analysis of moving interfaces using a level set method coupled with adaptive mesh refinement. Int J Numer Methods Fluids 45:921–944CrossRefzbMATHMathSciNetGoogle Scholar
  27. 27.
    Wang JP, Borthwick AGL, Taylor RE (2004) Finite-volume-type VOF method on dynamically adaptive quadtree grids. Int J Numer Methods Fluids 45:485–508CrossRefzbMATHGoogle Scholar
  28. 28.
    Greaves D (2004) Simulation of interface and free surface flows in a viscous fluid using adapting quadtree grids. Int J Numer Methods Fluids 44:1093–1117CrossRefzbMATHGoogle Scholar
  29. 29.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2004) Modeling of moving interface problems with the ETILT. In: Computational mechanics proceedings of the WCCM VI in conjunction with APCOM’04. Tsinghua University Press and Spring-Verlag, Beijing, ChinaGoogle Scholar
  30. 30.
    Tezduyar TE (2004). Finite elements methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, De Borts R, Hughes TJR (eds). Encyclopedia of computational mechanics, Fluids, vol 3, chapt 17. Wiley, New YorkGoogle Scholar
  31. 31.
    Tezduyar TE (2004). Moving boundaries and interfaces. In: Franca LP, Tezduyar TE, Masud A (eds). Finite element methods: 1970’s and beyond. CIMNE, Barcelona, pp 205–220Google Scholar
  32. 32.
    Cruchaga MA, Celentano DJ, Tezduyar TE (2005) Moving-interface computations with the edge-tracked interface locator technique (ETILT). Int J Numer Methods Fluids 47:451–469CrossRefzbMATHGoogle Scholar
  33. 33.
    Tezduyar TE (2006) Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces. Comput Methods Appl Mech Eng (published online)Google Scholar
  34. 34.
    Cruchaga MA, Oñate E (1999) A generalized streamline finite element approach for the analysis of incompressible flow problems including moving surfaces. Comput Methods Appl Mech Eng 173:241–255CrossRefzbMATHGoogle Scholar
  35. 35.
    Martin J, Moyce W (1952) An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philos Trans R Soc Lond 244:312–324CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Marcela A. Cruchaga
    • 1
  • Diego J. Celentano
    • 1
  • Tayfun E. Tezduyar
    • 2
  1. 1.Departamento de Ingeniería MecánicaUniversidad de Santiago de ChileSantiagoChile
  2. 2.Team for Advanced Flow Simulation and Modeling (T*AFSM), Mechanical EngineeringRice UniversityHoustonUSA

Personalised recommendations