Quantitative benchmark computations of two-dimensional bubble dynamics

Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two‐dimensional bubbles rising in liquid columns, are proposed. The benchmark quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor...

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Veröffentlicht in:	International journal for numerical methods in fluids Jg. 60; H. 11; S. 1259 - 1288
Hauptverfasser:	Hysing, S., Turek, S., Kuzmin, D., Parolini, N., Burman, E., Ganesan, S., Tobiska, L.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Chichester, UK John Wiley & Sons, Ltd 20.08.2009 Wiley
Schlagworte:	ALE Benchmarking Bubbles Computational fluid dynamics Computational methods in fluid dynamics Drops and bubbles Exact sciences and technology finite-element method Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) level set method Mathematical models Monitors multiphase flow Nonhomogeneous flows Numerical analysis numerical simulation Physics rising bubble Two dimensional Geometrical shape Euler Lagrange equation Computational fluid dynamics benchmarking Bubble ascent Digital simulation Computation code Boundary conditions finite-element method Finite element method Bubbles rising bubble level set method multiphase flow Modelling ALE Incompressible fluid numerical simulation Navier-Stokes equations
ISSN:	0271-2091, 1097-0363, 1097-0363
Online-Zugang:	Volltext
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Abstract	Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two‐dimensional bubbles rising in liquid columns, are proposed. The benchmark quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor convergence toward a reference solution. Comprehensive studies are undertaken by three independent research groups, two representing Eulerian level set finite‐element codes and one representing an arbitrary Lagrangian–Eulerian moving grid approach. The first benchmark test case considers a bubble with small density and viscosity ratios, which undergoes moderate shape deformation. The results from all codes agree very well allowing for target reference values to be established. For the second test case, a bubble with a very low density compared to that of the surrounding fluid, the results for all groups are in good agreement up to the point of break up, after which all three codes predict different bubble shapes. This highlights the need for the research community to invest more effort in obtaining reference solutions to problems involving break up and coalescence. Other research groups are encouraged to participate in these benchmarks by contacting the authors and submitting their own data. The reference data for the computed benchmark quantities can also be supplied for validation purposes. Copyright © 2008 John Wiley & Sons, Ltd.
AbstractList	Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two‐dimensional bubbles rising in liquid columns, are proposed. The benchmark quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor convergence toward a reference solution. Comprehensive studies are undertaken by three independent research groups, two representing Eulerian level set finite‐element codes and one representing an arbitrary Lagrangian–Eulerian moving grid approach. The first benchmark test case considers a bubble with small density and viscosity ratios, which undergoes moderate shape deformation. The results from all codes agree very well allowing for target reference values to be established. For the second test case, a bubble with a very low density compared to that of the surrounding fluid, the results for all groups are in good agreement up to the point of break up, after which all three codes predict different bubble shapes. This highlights the need for the research community to invest more effort in obtaining reference solutions to problems involving break up and coalescence. Other research groups are encouraged to participate in these benchmarks by contacting the authors and submitting their own data. The reference data for the computed benchmark quantities can also be supplied for validation purposes. Copyright © 2008 John Wiley & Sons, Ltd. Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two-dimensional bubbles rising in liquid columns, are proposed. The benchmark quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor convergence toward a reference solution. Comprehensive studies are undertaken by three independent research groups, two representing Eulerian level set finite-element codes and one representing an arbitrary Lagrangian-Eulerian moving grid approach. Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two‐dimensional bubbles rising in liquid columns, are proposed. The benchmark quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor convergence toward a reference solution. Comprehensive studies are undertaken by three independent research groups, two representing Eulerian level set finite‐element codes and one representing an arbitrary Lagrangian–Eulerian moving grid approach. The first benchmark test case considers a bubble with small density and viscosity ratios, which undergoes moderate shape deformation. The results from all codes agree very well allowing for target reference values to be established. For the second test case, a bubble with a very low density compared to that of the surrounding fluid, the results for all groups are in good agreement up to the point of break up, after which all three codes predict different bubble shapes. This highlights the need for the research community to invest more effort in obtaining reference solutions to problems involving break up and coalescence. Other research groups are encouraged to participate in these benchmarks by contacting the authors and submitting their own data. The reference data for the computed benchmark quantities can also be supplied for validation purposes. Copyright © 2008 John Wiley & Sons, Ltd.
Author	Turek, S. Kuzmin, D. Parolini, N. Tobiska, L. Burman, E. Hysing, S. Ganesan, S.
Author_xml	– sequence: 1 givenname: S. surname: Hysing fullname: Hysing, S. email: shuren@cimne.upc.edu, shuren.hysing@math.uni-dortmund.de organization: Universitat Politècnica de Catalunya (UPC), Jordi Girona 1-3, Edifici C1, 08034 Barcelona, Spain – sequence: 2 givenname: S. surname: Turek fullname: Turek, S. organization: Institut für Angewandte Mathematik, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany – sequence: 3 givenname: D. surname: Kuzmin fullname: Kuzmin, D. organization: Institut für Angewandte Mathematik, TU Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany – sequence: 4 givenname: N. surname: Parolini fullname: Parolini, N. organization: MOX, Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 29, 20133 Milano, Italy – sequence: 5 givenname: E. surname: Burman fullname: Burman, E. organization: Department of Mathematics, University of Sussex, Brighton BN1 9RF, U.K – sequence: 6 givenname: S. surname: Ganesan fullname: Ganesan, S. organization: Department of Aeronautics, Imperial College, London, U.K – sequence: 7 givenname: L. surname: Tobiska fullname: Tobiska, L. organization: Institut für Analysis und Numerik, Otto-von-Guericke Universität, 39016 Magdeburg, Germany
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Cites_doi	10.1002/fld.591 10.1016/ S0045‐7825(96)01155‐3 10.1007/BF01385643 10.1007/978-3-642-58393-3 10.1063/1.1842220 10.1017/S0022112098003176 10.1007/978-3-642-61623-5 10.1017/S0022112097005570 10.1098/rsta.1952.0006 10.1016/j.apnum.2006.03.003 10.1016/j.ces.2005.01.031 10.1007/BFb0014497 10.1146/annurev.fluid.31.1.567 10.1017/S0022112099004449 10.1002/nme.1620150502 10.1002/aic.10607 10.1002/fld.395 10.1016/j.cma.2006.08.018 10.1006/jcph.2000.6537 10.1017/S002211208100311X 10.1002/fld.195 10.1016/0021‐9991(92)90307‐K 10.1007/s002110000225 10.1016/j.jcp.2004.01.015 10.1086/624040 10.1002/fld.1147 10.1016/j.ijmultiphaseflow.2006.07.003 10.1007/s00791‐003‐0120‐1 10.1006/jcph.2001.6938 10.1016/0021‐9991(88)90002‐2
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References_xml	– reference: Ye T, Shyy W, Chung JN. A fixed-grid, sharp-interface method for bubble dynamics and phase change. Journal of Computational Physics 2001; 174(2):781-815. DOI: 10.1006/jcph.2001.6938. – reference: John V, Matthies G. Higher-order finite element discretizations in a benchmark problem for incompressible flows. International Journal for Numerical Methods in Fluids 2001; 37(8):885-903. DOI: 10.1002/fld.195. – reference: Di Pietro DA, Lo Forte S, Parolini N. Mass preserving finite element implementations of the level set method. Applied Numerical Mathematics 2006; 56(9):1179-1195. DOI: 10.1016/j.apnum.2006.03.003. – reference: Annaland MS, Dijkhuizen W, Deen NG, Kuipers JAM. Numerical simulation of behavior of gas bubbles using a 3-D front-tracking method. AIChE Journal 2006; 52(1):99-110. DOI: 10.1002/aic.10607. – reference: Bonometti T, Magnaudet J. An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics. International Journal of Multiphase Flow 2007; 33(2):109-133. DOI: 10.1016/j.ijmultiphaseflow.2006.07.003. – reference: Girault V, Raviart PA. Finite Element Methods for Navier-Stokes Equations. Springer: Berlin, 1986. – reference: Ruschak KJ. A method for incorporating free boundaries with surface tension in finite element fluid-flow simulators. International Journal for Numerical Methods in Engineering 1980; 15(5):639-648. DOI: 10.1002/nme.1620150502. – reference: Esmaeeli A, Tryggvason G. Direct numerical simulations of bubbly flows. Part 1: low Reynolds number arrays. Journal of Fluid Mechanics 1998; 377:313-345. – reference: Dziuk G. An algorithm for evolutionary surfaces. Numerische Mathematik 1991; 58:603-611. – reference: Scardovelli1 R, Zaleski S. Direct numerical simulation of free-surface and interfacial flow. Annual Review of Fluid Mechanics 1999; 31:567-603. DOI: 10.1146/annurev.fluid.31.1.567. – reference: Martin J, Moyce W. An experimental study of the collapse of liquid columns on a rigid horizontal plane. Philosophical Transactions of the Royal Society of London, Series A 1952; A 244:312-324. – reference: Norman CE, Miksis MJ. Dynamics of a gas bubble rising in an inclined channel at finite Reynolds number. Physics of Fluids 2005; 17(2):022102. DOI: 10.1063/1.1842220. – reference: Chen L, Garimella SV, Reizes JA, Leonardi E. The development of a bubble rising in a viscous liquid. Journal of Fluid Mechanics 1999; 387:61-96. – reference: Kuzmin D, Turek S. High-resolution FEM-TVD schemes based on a fully multidimensional flux limiter. Journal of Computational Physics 2004; 198(1):131-158. DOI: 10.1016/j.jcp.2004.01.015. – reference: Unverdi SO, Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of Computational Physics 1992; 100(1):25-37. DOI: 10.1016/0021-9991(92)90307-K. – reference: Sussman M, Smereka P. Axisymmetric free boundary problems. 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Snippet	Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two‐dimensional bubbles rising in... Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two‐dimensional bubbles rising in... Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two-dimensional bubbles rising in...
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SubjectTerms	ALE Benchmarking Bubbles Computational fluid dynamics Computational methods in fluid dynamics Drops and bubbles Exact sciences and technology finite-element method Fluid dynamics Fluid flow Fundamental areas of phenomenology (including applications) level set method Mathematical models Monitors multiphase flow Nonhomogeneous flows Numerical analysis numerical simulation Physics rising bubble Two dimensional
Title	Quantitative benchmark computations of two-dimensional bubble dynamics
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