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Direct numerical simulation of a bubble motion in a spherical tank under external forces and microgravity conditions

Published online by Cambridge University Press:  21 June 2018

A. Dalmon ,
M. Lepilliez ,
S. Tanguy Open the ORCID record for S. Tanguy [Opens in a new window] ,
A. Pedrono ,
B. Busset ,
H. Bavestrello  and
J. Mignot
A. Dalmon*
Affiliation:
Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS, 2 allée du Professeur Camille Soula, 31400 Toulouse, France Airbus Defence and Space, 31 Avenue des Cosmonautes, 31402 Toulouse CEDEX 4, France Centre National d’Études Spatiales, 18 Avenue Edouard Belin, 31401 Toulouse CEDEX 9, France
M. Lepilliez
Affiliation:
Airbus Defence and Space, 31 Avenue des Cosmonautes, 31402 Toulouse CEDEX 4, France
S. Tanguy
Affiliation:
Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS, 2 allée du Professeur Camille Soula, 31400 Toulouse, France
A. Pedrono
Affiliation:
Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS, 2 allée du Professeur Camille Soula, 31400 Toulouse, France
B. Busset
Affiliation:
Airbus Defence and Space, 31 Avenue des Cosmonautes, 31402 Toulouse CEDEX 4, France
H. Bavestrello
Affiliation:
Airbus Defence and Space, 31 Avenue des Cosmonautes, 31402 Toulouse CEDEX 4, France
J. Mignot
Affiliation:
Centre National d’Études Spatiales, 18 Avenue Edouard Belin, 31401 Toulouse CEDEX 9, France
*
†Email address for correspondence: [email protected]
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Abstract

We present, in this paper, numerical simulations of bubble sloshing in a spherical tank, resulting from a tank rotation around a fixed axis in microgravity conditions. This configuration is of great interest in space applications where sloshing can have harmful effects on the stability of satellites. Depending on the dimensionless numbers characterising this phenomenon, our study is focused on the motion and the deformation of a bubble, initially at rest, which is set in motion when the manoeuvre is starting until it reaches a constant rotation speed around the axis. It is shown in this article that, during the first stage of the manoeuvre, the motion of the bubble is essentially driven by the inertial force that depends on the angular acceleration. Next, when the angular velocity is increasing, the centrifugal force being dominant, the trajectory of the bubble is pushed towards the direction between the centre of the tank and the axis of rotation. Finally, when the angular velocity becomes constant, the bubble, reaching a quasi-steady position, is deformed and pressed against the solid boundary of the tank. A quantified description of these phenomena is proposed through a parametric study varying the essential dimensionless numbers, i.e. the Bond number based on the angular velocity, and another Bond number based on the angular acceleration. As the temporal evolution of the forces acting on the satellite wall is of utmost importance for designing satellites and manoeuvres, we also present an analysis characterising the latter. We also detail the first comparisons between the numerical simulations and the Fluidics experiment performed in the International Space Station (ISS) in microgravity conditions. Thanks to these comparisons, we can validate the simulations in configurations of interest.

JFM classification

Drops and Bubbles: Bubble dynamics Mathematical Foundations: Computational methods Drops and Bubbles: Drops and Bubbles
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 467 - 497
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Copyright
© 2018 Cambridge University Press 

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References

Abramson, N. H.1967 The dynamic behaviour of liquids in moving containers, with applications to space vehicle technology. Tech. Rep. NASA SP 106.Google Scholar
Borges, R., Carmona, M., Costa, B. & Don, W. S. 2008 An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws. J. Comput. Phys. 227, 3191–3211.Google Scholar
Chorin, A. 1967 A numerical method for solving incompressible viscous flow problems. J. Comput. Phys. 2, 12–26.Google Scholar
Dendy, J. E. 1982 Black box multigrid. J. Comput. Phys. 48, 366–386.Google Scholar
Dodge, F. T.2000 The new dynamic behaviour of liquids in moving containers. Tech. Rep., Southwest Reaserch Institute.Google Scholar
Faltinsen, O. M., Firoozkoohi, R. & Timokha, A. N. 2011 Steady-state liquid sloshing in a rectangular tank with a slat-type screen in the middle: quasilinear modal analysis and experiments. Phys. Fluids 23, 042101.Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2010 A multimodal method for liquid sloshing in a two-dimensional circular tank. J. Fluid Mech. 665, 457–479.Google Scholar
Faltinsen, O. M. & Timokha, A. N. 2013 Multimodal analysis of weakly nonlinear sloshing in a spherical tank. J. Fluid Mech. 719, 129–164.Google Scholar
Fedkiw, R., Aslam, T., Merriman, B. & Osher, S. 1999 A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152, 457–492.Google Scholar
Gibou, F., Cheng, L.-T., Nguyen, D. & Banerjee, S. 2007 A level set based sharp interface method for the multiphase incompressible Navier–Stokes equations with phase change. J. Comput. Phys. 222, 536–555.Google Scholar
Gibou, F., Fedkiw, R., Cheng, L.-T. & Kang, M. 2002 A second-order-accurate symmetric discretization of the poisson equation on irregular domains. J. Comput. Phys. 176, 205–227.Google Scholar
Huber, G., Tanguy, S., Bera, J. & Gilles, B. 2015 A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves. J. Comput. Phys. 302, 439–468.Google Scholar
Huber, G., Tanguy, S., Sagan, M. & Colin, C. 2017 Direct numerical simulation of nucleate pool boiling at large microscopic contact angle and moderate Jakob number. Intl J. Heat Mass Transfer 113, 662–682.Google Scholar
Ikeda, T., Ibrahim, R. A., Harata, Y. & Kuriyama, T. 2012 Nonlinear liquid sloshing in a square tank subjected to obliquely horizontal excitation. J. Fluid Mech. 700, 304–328.Google Scholar
Kang, M., Fedkiw, R. & Liu, X.-D. 2000 A boundary condition capturing method for multiphase incompressible flow. J. Sci. Comput. 15, 323–360.Google Scholar
Lalanne, B., Chebel, N. A., Vejrazka, J., Tanguy, S., Masbernat, O. & Risso, F. 2015a Non-linear shape oscillations of rising drops and bubbles: experiments and simulations. Phys. Fluids 27, 123305.Google Scholar
Lalanne, B., Villegas, L. R., Tanguy, S. & Risso, F. 2015b On the computation of viscous terms for incompressible two-phase flows with level set/ghost fluid method. J. Comput. Phys. 301, 289–307.Google Scholar
Langbein, D. 2002 Capillary Surfaces: Shape Stability Dynamics, in Particular Under Weightlessness, vol. 178. Springer Tracts in Modern Physics.Google Scholar
Lepilliez, M.2015 Simulation numérique des ballotements d’ergols dans les réservoirs de satellites en microgravité et à faible nombre de Reynolds. PhD thesis, Université Toulouse 3 Paul Sabatier.Google Scholar
Lepilliez, M., Popescu, E. R., Gibou, F. & Tanguy, S. 2016 On two-phase flow solvers in irregular domains with contact line. J. Comput. Phys. 321, 1217–1251.Google Scholar
Liu, D. & Lin, P. 2008 A numerical study of three-dimensional liquid sloshing in tanks. J. Comput. Phys. 227, 3921–3939.Google Scholar
Liu, X.-D., Fedkiw, R. & Kang, M. 2000 A boundary condition capturing method for poissons equation on irregular domain. J. Comput. Phys. 160, 151–178.Google Scholar
MacLachlan, S. P., Tang, J. M. & Vuik, C. 2008 Fast and robust solvers for pressure-correction in bubbly flow problems. J. Comput. Phys. 227 (23), 9742–9761.Google Scholar
Mignot, J., Pierre, R., Berhanu, M., Busset, B., Roumiguié, R., Bavestrello, H., Bonfanti, S., Miquel, T., Marot, L. O. & Llodra-Perez, A. 2017 Fluid dynamic in space experiment. In 68th International Astronautical Congress (IAC), Adelaide, Australia (IAC-17-A2.62).Google Scholar
Ng, Y. T., Min, C. & Gibou, F. 2009 An efficient fluid–solid coupling algorithm for single-phase flows. J. Comput. Phys. 228, 8807–8829.Google Scholar
Osher, S. & Sethian, J. A. 1988 Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys. 79, 12–49.Google Scholar
Papac, J., Gibou, F. & Ratsch, C. 2010 Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions. J. Comput. Phys. 229, 875–889.Google Scholar
Rueda Villegas, L., Alis, R., Lepilliez, M. & Tanguy, S. 2016 A ghost fluid/level set method for boiling flows and liquid evaporation: application to the Leidenfrost effect. J. Comput. Phys. 316, 789–813.Google Scholar
Rueda Villegas, L., Tanguy, S., Castanet, G., Caballina, O. & Lemoine, F. 2017 Direct numerical simulation of the impact of a droplet onto a hot surface above the Leidenfrost temperature. Intl J. Heat Mass Transfer 104, 1090–1109.Google Scholar
Stephan, P. C. & Busse, C. A. 1992 Analysis of the heat transfer coefficient of grooved heat pipe evaporator walls. Intl J. Heat Mass Transfer 35 (2), 383–391.Google Scholar
Sussman, M., Smereka, P. & Osher, S. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146–159.Google Scholar
Sussman, M., Smith, K. M., Hussaini, M. Y., Ohta, M. & Zhi-Wei, R. 2007 A sharp interface method for incompressible two-phase flows. J. Comput. Phys. 221, 469–505.Google Scholar
Tanguy, S. & Berlemont, A. 2005 Application of a level set method for simulation of droplet collisions. Intl J. Multiphase Flow 31, 1015–1035.Google Scholar
Tanguy, S., Menard, T. & Berlemont, A. 2007 A level set method for vaporizing two-phase flows. J. Comput. Phys. 221, 837–853.Google Scholar
Tanguy, S., Sagan, M., Lalanne, B., Couderc, F. & Colin, C. 2014 Benchmarks and numerical methods for the simulation of boiling flows. J. Comput. Phys. 264, 1–22.Google Scholar
Urbano, A., Tanguy, S., Huber, G. & Colin, C. 2018 Direct numerical simulation of nucleate boiling in micro-layer regime. Intl J. Heat Mass Transfer 123, 1128–1137.Google Scholar
Veldman, A. E. P., Gerrits, J., Luppes, R., Helder, J. A. & Vreeburg, J. P. B. 2007 The numerical simulation of liquid sloshing on board spacecraft. J. Comput. Phys. 224, 82–99.Google Scholar

Dalmon et al. supplementary movie

Example of bubble motion during the tank rotation

Download Dalmon et al. supplementary movie(Video)
Video 8.3 MB