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Computational Mechanics

, Volume 63, Issue 5, pp 985–998 | Cite as

An oil sloshing study: adaptive fixed-mesh ALE analysis and comparison with experiments

  • Ernesto Castillo
  • Marcela A. CruchagaEmail author
  • Joan Baiges
  • José Flores
Original Paper
  • 70 Downloads

Abstract

We report in this work a numerical analysis of the sloshing of a squared tank partially filled with a domestic vegetable oil. The tank is subject to controlled motions with a shake table. The free-surface evolution is captured using ultrasonic sensors and an image capturing method. Only confirmed data within the error range is reported. Filling depth, imposed amplitude and frequency effects on the sloshing wave pattern are specifically evaluated. The experiments also reveal the nonlinear wave behavior. The numerical model is based on a stabilized finite element method of the variational multi-scale type. The free-surface is captured using a level set technique developed to be used with adaptive meshes in Arbitrary Lagrangian–Eulerian framework. The numerical results are compared with the experiments for different sloshing conditions near the first sloshing mode. The simulations satisfactorily match the experiments, providing a reliable tool for the analysis of this kind of problems.

Keywords

Sloshing Experimental validation Arbitrary Lagrangian–Eulerian (ALE) Stabilized finite element methods Adaptive mesh 

Notes

Acknowledgements

The support provided by the Chilean Council for Research and Technology CONICYT (CONICYT-FONDECYT Projects 1170620 and 11160160); the Scientific Research Projects Management Department of the Vice Presidency of Research, Development and Innovation (DICYT-VRID) of Universidad de Santiago de Chile (USACH); and Project Basal USA1555, are gratefully acknowledged.

References

  1. 1.
    Jiang S, Wang Z, Zhou G, Yang W (2007) An implicit control-volume finite element method and its time step strategies for injection molding simulation. Comput Chem Eng 31(11):1407–1418.  https://doi.org/10.1016/j.compchemeng.2006.12.001 CrossRefGoogle Scholar
  2. 2.
    Yu JD, Sakai S, Sethian J (2007) Two-phase viscoelastic jetting. J Comput Phys 220(2):568–585.  https://doi.org/10.1016/j.jcp.2006.05.020 MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Favero J, Secchi A, Cardozo N, Jasak H (2010) Viscoelastic fluid analysis in internal and in free surface flows using the software OpenFOAM. Comput Chem Eng 34(12):1984–1993.  https://doi.org/10.1016/j.compchemeng.2010.07.010. 10th international symposium on process systems engineering, Salvador, Bahia, Brasil, 16–20 August 2009
  4. 4.
    Cruchaga M, Battaglia L, Storti M, D’Elía J (2016) Numerical modeling and experimental validation of free surface flow problems. Arch Comput Methods Eng 23(1):139–169.  https://doi.org/10.1007/s11831-014-9138-4 MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Baiges J, Codina R, Pont A, Castillo E (2017) An adaptive fixed-mesh ALE method for free surface flows. Comput Methods Appl Mech Eng 313:159–188.  https://doi.org/10.1016/j.cma.2016.09.041 MathSciNetCrossRefGoogle Scholar
  6. 6.
    Castillo E, Baiges J, Codina R (2015) Approximation of the two-fluid flow problem for viscoelastic fluids using the level set method and pressure enriched finite element shape functions. J Non-Newton Fluid Mech 225:37–53.  https://doi.org/10.1016/j.jnnfm.2015.09.004 MathSciNetCrossRefGoogle Scholar
  7. 7.
    Moraga NO, Castillo EF, Garrido CP (2012) Non Newtonian annular alloy solidification in mould. Heat Mass Transf 48(8):1415–1424.  https://doi.org/10.1007/s00231-012-0983-0 CrossRefGoogle Scholar
  8. 8.
    Escobar A, Celentano D, Cruchaga M, Lacaze J, Schulz B, Dardati P, Parada A (2014) Experimental and numerical analysis of effect of cooling rate on thermal-microstructural response of spheroidal graphite cast iron solidification. Int J Cast Met Res 27(3):176–186CrossRefGoogle Scholar
  9. 9.
    Benedetti L, Cervera M, Chiumenti M (2016) High-fidelity prediction of crack formation in 2D and 3D pullout tests. Comput Struct 172:93–109.  https://doi.org/10.1016/j.compstruc.2016.05.001 CrossRefGoogle Scholar
  10. 10.
    Baiges J, Codina R (2017) Variational multiscale error estimators for solid mechanics adaptive simulations: an orthogonal subgrid scale approach. Comput Methods Appl Mech Eng 325:37–55.  https://doi.org/10.1016/j.cma.2017.07.008 MathSciNetCrossRefGoogle Scholar
  11. 11.
    Moure M, Otero F, García-Castillo S, Sánchez-Sáez S, Barbero E, Barbero E (2015) Damage evolution in open-hole laminated composite plates subjected to in-plane loads. Compos Struct 133:1048–1057.  https://doi.org/10.1016/j.compstruct.2015.08.045 CrossRefGoogle Scholar
  12. 12.
    Tezduyar T (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8:83–130CrossRefzbMATHGoogle Scholar
  13. 13.
    Tezduyar T (2006) Interface-tracking and interface-capturing techniques for finite element computation of moving boundaries and interfaces. Comput Methods Appl Mech Eng 195:2983–3000MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Huerta A, Liu W (1988) Viscous flow with large free surface motion. Comput Methods Appl Mech Eng 69(3):277–324CrossRefzbMATHGoogle Scholar
  15. 15.
    Hughes TJ, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29(3):329–349.  https://doi.org/10.1016/0045-7825(81)90049-9 MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Tezduyar T, 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 94:339–351MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Tezduyar T, 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 94:353–371MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    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
  19. 19.
    Tezduyar T, Aliabadi S (2000) EDICT for 3D computation of two-fluid interfaces. Comput Methods Appl Mech Eng 190:403–410CrossRefzbMATHGoogle Scholar
  20. 20.
    Díez P, Huerta A (1999) A unified approach to remeshing strategies for finite element h-adaptivity. Comput Methods Appl Mech Eng 176(1):215–229.  https://doi.org/10.1016/S0045-7825(98)00338-7 CrossRefzbMATHGoogle Scholar
  21. 21.
    Askes H, Sluys LJ (2000) Remeshing strategies for adaptive ALE analysis of strain localisation. Eur J Mech A/Solids 19(3):447–467.  https://doi.org/10.1016/S0997-7538(00)00176-5 CrossRefzbMATHGoogle Scholar
  22. 22.
    Codina R, Houzeaux G, Coppola-Owen H, Baiges J (2009) The fixed-mesh ALE approach for the numerical approximation of flows in moving domains. J Comput Phys 228(5):1591–1611.  https://doi.org/10.1016/j.jcp.2008.11.004 MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Coppola-Owen H, Codina R (2011) A free surface finite element model for low Froude number mould filling problems on fixed meshes. Int J Numer Methods Fluids 66(7):833–851.  https://doi.org/10.1002/fld.2286 CrossRefzbMATHGoogle Scholar
  24. 24.
    Baiges J, Codina R, Coppola-Owen H (2011) The Fixed-Mesh ALE approach for the numerical simulation of floating solids. Int J Numer Methods Fluids 67(8):1004–1023.  https://doi.org/10.1002/fld.2403 MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Akyildız H, Erdem Ünal N (2006) Sloshing in a three-dimensional rectangular tank: numerical simulation and experimental validation. Ocean Eng 33(16):2135–2149CrossRefGoogle Scholar
  26. 26.
    Cruchaga M, Celentano D, Tezduyar T (2007) Collapse of a liquid column: numerical simulation and experimental validation. Comput Mech 39(4):453–476CrossRefzbMATHGoogle Scholar
  27. 27.
    Liu D, Lin P (2008) A numerical study of three-dimensional liquid sloshing in tanks. J Comput Phys 227(8):3921–3939CrossRefzbMATHGoogle Scholar
  28. 28.
    Cruchaga M, Celentano D, Tezduyar T (2009) Computational modeling of the collapse of a liquid column over an obstacle and experimental validation. J Appl Mech 76(2):021202CrossRefGoogle Scholar
  29. 29.
    Eswaran M, Singh A, Saha U (2011) Experimental measurement of the surface velocity field in an externally induced sloshing tank. Proc Inst Mech Eng Part M J Eng Marit Environ 225(2):133–148Google Scholar
  30. 30.
    Cruchaga M, Löhner R, Celentano D (2012) Spheres falling into viscous flows: experimental and numerical analysis. Int J Numer Methods Fluid 69(9):1496–1521CrossRefGoogle Scholar
  31. 31.
    Battaglia L, Cruchaga M, Storti M, D’Elía J, Aedo JN, Reinoso R (2018) Numerical modelling of 3D sloshing experiments in rectangular tanks. Appl Math Model 59:357–378MathSciNetCrossRefGoogle Scholar
  32. 32.
    Cruchaga MA, Reinoso RS, Storti MA, Celentano DJ, Tezduyar TE (2013) Finite element computation and experimental validation of sloshing in rectangular tanks. Comput Mech 52(6):1301–1312.  https://doi.org/10.1007/s00466-013-0877-0 CrossRefGoogle Scholar
  33. 33.
    Hirt C, Amsden A, Cook J (1997) An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J Comput Phys 135(2):203–216.  https://doi.org/10.1006/jcph.1997.5702 CrossRefzbMATHGoogle Scholar
  34. 34.
    Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1–44MathSciNetzbMATHGoogle Scholar
  35. 35.
    Behr MA, Franca LP, Tezduyar TE (1993) Stabilized finite element methods for the velocity-pressure-stress formulation of incompressible flows. Comput Methods Appl Mech Eng 104(1):31–48MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Cruchaga M, Oñate E (1997) A finite element formulation for incompressible flow problems using a generalized streamline operator. Comput Methods Appl Mech Eng 143(1):49–67MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Tezduyar T (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575MathSciNetCrossRefzbMATHGoogle Scholar
  38. 38.
    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(1–2):241–255CrossRefzbMATHGoogle Scholar
  39. 39.
    Corsini A, Rispoli F, Santoriello A, Tezduyar T (2006) Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. Comput Mech 38:356–364MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Bazilevs Y, Hsu MC, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22(supp02):1230002CrossRefzbMATHGoogle Scholar
  41. 41.
    Hughes TJ, Feijóo GR, Mazzei L, Quincy JB (1998) The variational multiscale method–a paradigm for computational mechanics. Comput Methods Appl Mech Eng 166(1–2):3–24MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Codina R (2001) A stabilized finite element method for generalized stationary incompressible flows. Comput Methods Appl Mech Eng 190(20–21):2681–2706.  https://doi.org/10.1016/S0045-7825(00)00260-7 MathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Burman E, Fernández MA (2014) An unfitted Nitsche method for incompressible fluid-structure interaction using overlapping meshes. Comput Methods Appl Mech Eng 279:497–514.  https://doi.org/10.1016/j.cma.2014.07.007 MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Burman E, Hansbo P (2014) Fictitious domain methods using cut elements: III. A stabilized Nitsche method for stokes problem. ESAIM: M2AN 48(3):859–874.  https://doi.org/10.1051/m2an/2013123 MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Burman E (2010) Ghost penalty. C R Math 348(21):1217–1220.  https://doi.org/10.1016/j.crma.2010.006 MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Tezduyar T, Park Y (1986) Discontinuity capturing finite element formulations for nonlinear convection–diffusion-reaction equations. Comput Methods Appl Mech Eng 59:307–325CrossRefzbMATHGoogle Scholar
  47. 47.
    Aliabadi S, Tezduyar T (2000) Stabilized-finite-element/interface-capturing technique for parallel computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 190:243–261CrossRefzbMATHGoogle Scholar
  48. 48.
    Akin JE, Tezduyar TE (2004) Calculation of the advective limit of the supg stabilization parameter for linear and higher-order elements. Comput Methods Appl Mech Eng 193(21–22):1909–1922CrossRefzbMATHGoogle Scholar
  49. 49.
    Tezduyar TE (2007) Finite elements in fluids: stabilized formulations and moving boundaries and interfaces. Comput Fluids 36(2):191–206MathSciNetCrossRefzbMATHGoogle Scholar
  50. 50.
    Codina R, Principe J, Guasch O, Badia S (2007) Time dependent subscales in the stabilized finite element approximation of incompressible flow problems. Comput Methods Appl Mech Eng 196(21–24):2413–2430MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Codina R (2008) Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales. Appl Numer Math 58(3):264–283.  https://doi.org/10.1016/j.apnum.2006.11.011 MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Sussman M, Smereka P, Osher S (1994) A level set approach for computing solutions to incompressible two-phase flow. J Comput Phys 114(1):146–159CrossRefzbMATHGoogle Scholar
  53. 53.
    Adalsteinsson D, Sethian JA (1995) A fast level set method for propagating interfaces. J Comput Phys 118(2):269–277MathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    Brooks AN, Hughes TJ (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(1):199–259.  https://doi.org/10.1016/0045-7825(82)90071-8 MathSciNetCrossRefzbMATHGoogle Scholar
  55. 55.
    Battaglia L, Storti M, D’Elía J (2010) Bounded renormalization with continuous penalization for level set interface-capturing methods. Int J Numer Methods Eng 84(7):830–848MathSciNetCrossRefzbMATHGoogle Scholar
  56. 56.
    Ausas R, Dari E, Buscaglia G (2011) A geometric mass-preserving redistancing scheme for the level set function. Int J Numer Methods Fluids 65(8):989–1010CrossRefzbMATHGoogle Scholar
  57. 57.
    Baiges J, Bayona C (2017) Refficientlib: an efficient load-rebalanced adaptive mesh refinement algorithm for high-performance computational physics meshes. SIAM J Sci Comput 39(2):C65–C95.  https://doi.org/10.1137/15M105330X MathSciNetCrossRefzbMATHGoogle Scholar
  58. 58.
    Quanser (2017) STII Manual. online access: www.quanser.com
  59. 59.
    Faltinsen O, Rognebakke O, Lukovsky I, Timokha A (2000) Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. J Fluid Mech 407:201–234MathSciNetCrossRefzbMATHGoogle Scholar
  60. 60.
    Engineering B (2017) U-GAGETM S18U Series Sensors with Analog Output. On line access: www.bannerengineering.com
  61. 61.
    Technologies A (2017) Q-PRI High Speed Camera. On line access: www.aostechnologies.com
  62. 62.
    OpenCV (2017) The OpenCV Reference manual. On line access: opencv.orgGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Ernesto Castillo
    • 1
  • Marcela A. Cruchaga
    • 1
    Email author
  • Joan Baiges
    • 2
  • José Flores
    • 1
  1. 1.Departamento de Ingeniería MecánicaUniversidad de Santiago de Chile USACHSantiago de ChileChile
  2. 2.Universitat Politècnica de CatalunyaBarcelonaSpain

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