Abstract
Liquid sloshing in storage tanks is of critical concern for the fluid management in space. In the present study, oscillation of liquid in a partially filled capsule storage tank was numerically studied using the volume of fluid method and taking into account the dynamic contact angle. The filling ratios of tank ranging from 10% to 90% and the gravity levels of 10−3 g0 and 0 g0 were considered as the controlling variables. The temporal evolution of characteristic points of free surface and the law of oscillation frequencies were analyzed. The results show that for different filling ratios, the oscillations of free surfaces present different damping types, in which the small and large filling ratios correspond to the underdamping and the intermediate filling ratios to the critical damping. The present study provides fundamental insights into the free surface oscillations depending on the filling ratios and residual gravity level, which is useful for the corresponding utilization in space.
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References
Almohammadi, H., Amirfazli, A.: Droplet impact: viscosity and wettability effects on splashing. J Colloid Interface Sci. 553, 22–30 (2019). https://doi.org/10.1016/j.jcis.2019.05.101
Blake, T.D., Batts, G.N.: The temperature-dependence of the dynamic contact angle. J Colloid Interface Sci. 553, 108–116 (2019). https://doi.org/10.1016/j.jcis.2019.06.006
Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J Comput Phys. 100((2)), 335–354 (1992)
Chang, S., Ding, L., Song, M., Leng, M.: Numerical investigation on impingement dynamics and freezing performance of micrometer-sized water droplet on dry flat surface in supercooled environment. Int J Multiphase Flow. 118, 150–164 (2019). https://doi.org/10.1016/j.ijmultiphaseflow.2019.06.011
Chiba, M., Magata, H.: Influence of liquid sloshing on dynamics of flexible space structures. J Sound Vib. 401, 1–22 (2017). https://doi.org/10.1016/j.jsv.2017.04.029
Cox, R.G.: The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. J Fluid Mech. 168, 169–194 (1986). https://doi.org/10.1017/S0022112086000332
Dai, J., Han, M., Ang, K.K.: Moving element analysis of partially filled freight trains subject to abrupt braking. Int J Mech Sci. 151, 85–94 (2019). https://doi.org/10.1016/j.ijmecsci.2018.11.011
Dalmon, A., Lepilliez, M., Tanguy, S., Pedrono, A., Busset, B., Bavestrello, H., Mignot, J.: Direct numerical simulation of a bubble motion in a spherical tank under external forces and micro-gravity conditions. J Fluid Mech. 849, 467–497 (2018). https://doi.org/10.1017/jfm.2018.389
Dalmon, A., Lepilliez, M., Tanguy, S., Alis, R., Popescu, E.R., Roumiguié, R., Miquel, T., Busset, B., Bavestrello, H., Mignot, J.: Comparison between the FLUIDICS experiment and direct numerical simulations of fluid sloshing in spherical tanks under microgravity conditions. Microgravity Sci Technol. 31(1), 123–138 (2019). https://doi.org/10.1007/s12217-019-9675-4
Deng, M.L., Yue, B.Z.: Attitude tracking control of flexible spacecraft with large amplitude slosh. Acta Mech Sinica. 33(6), 1095–1102 (2017). https://doi.org/10.1007/s10409-017-0700-9
Fernandez, J., Sanchez, P.S., Tinao, I., Porter, J., Ezquerro, J.M.: The CFVib experiment: control of fluids in microgravity with vibrations. Microgravity Sci Technol. 29(5), 351–364 (2017). https://doi.org/10.1007/s12217-017-9556-7
Fricke, M., Koehne, M., Bothe, D.: A kinematic evolution equation for the dynamic contact angle and some consequences. Physica D-Nonlinear Phenomena. 394, 26–43 (2019). https://doi.org/10.1016/j.physd.2019.01.008
Frosina, E., Senatore, A., Andreozzi, A., Fortunato, F., Giliberti, P.: Experimental and Numerical Analyses of the Sloshing in a Fuel Tank. Energies. 11((3)), (2018). https://doi.org/10.3390/en11030682
Gueyffier, D., Li, J., Nadim, A., Scardovelli, R., Zaleski, S.: Volume-of-fluid interface tracking with smoothed surface stress methods for three-dimensional flows. J Comput Phys. 152(2), 423–456 (1999)
Han, M., Dai, J., Wang, C.M., Ang, K.K.: Hydrodynamic analysis of partially filled liquid tanks subject to 3D vehicular Manoeuvring. Shock Vib. 2019, 1–14 (2019). https://doi.org/10.1155/2019/6943879
Hasheminejad, S.M., Soleimani, H.: An analytical solution for free liquid sloshing in a finite-length horizontal cylindrical container filled to an arbitrary depth. Appl Math Model. 48, 338–352 (2017). https://doi.org/10.1016/j.apm.2017.03.060
Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys. 39(1), 201–225 (1981)
Hoffman, R.L.: A study of the advancing interface, I. Interface shape in liquid—gas systems. J Colloid Interface Sci. 50(2), 228–241 (1975)
Issa, R.I.: Solution of implicitly discretized fluid flow equations by operator splitting. J Comput Phys. 62, 40–65 (1986)
Jiang, T.S., Soo-Gun, O.H., Slattery, J.C.: Correlation for dynamic contact angle. J Colloid Interface Sci. 69(1), 74–77 (1979)
Kistler, S.F.: Hydrodynamics of wetting. in Wettability, edited by J. C. Berg (Marcel Dekker, New York, 1993), p.311 (1993)
Li, J.C., Lin, H., Zhao, J.-F., Li, K., Hu, W.-R.: Dynamic behaviors of liquid in partially filled tank in short-term microgravity. Microgravity Sci Technol. 30(6), 849–856 (2018). https://doi.org/10.1007/s12217-018-9642-5
Luppes, R., Helder, J.A., Veldman, A.E.P.: The Numerical Simulation of Liquid Sloshing in Microgravity. In: Computational Fluid Dynamics 2006. pp. 607–612. (2009)
Malgarinos, I., Nikolopoulos, N., Marengo, M., Antonini, C., Gavaises, M.: VOF simulations of the contact angle dynamics during the drop spreading: standard models and a new wetting force model. Adv Colloid Interf Sci. 212(3), 1–20 (2014)
Miao, N., Li, J., Wang, T.: Equivalent mechanical model of large-amplitude liquid sloshing under time-dependent lateral excitations in low-gravity conditions. J Sound Vib. 386, 421–432 (2017). https://doi.org/10.1016/j.jsv.2016.08.029
Ohayon, R., Soize, C.: Vibration of structures containing compressible liquids with surface tension and sloshing effects, Reduced-order model. Comput Mech. 55(6), 1071–1078 (2015). https://doi.org/10.1007/s00466-014-1091-4
Popinet, S., Zaleski, S.: Simulation of Axisymmetric Free Surface Viscous Flow around a Non-spherical Bubble in the Sonoluminescence Regime. In, Third International Conference on Multiphase Flow (1998)
Quetzeri-Santiago, M.A., Yokoi, K., Castrejon-Pita, A.A., Castrejon-Pita, J.R.: Role of the Dynamic Contact Angle on Splashing. Phys Rev Lett. 122((22)), (2019). https://doi.org/10.1103/PhysRevLett.122.228001
Sanapala, V.S., Rajkumar, M., Velusamy, K., Patnaik, B.S.V.: Numerical simulation of parametric liquid sloshing in a horizontally baffled rectangular container. J Fluids Struct. 76, 229–250 (2018). https://doi.org/10.1016/j.jfluidstructs.2017.10.001
Scardovelli, R., Zaleski, S.: Direct Numerical Simulation of Free-Surface and Interfacial Flow. Annu Rev Fluid Mech. 31((1)), 567–603 (1999)
Šikalo, Š., Wilhelm, H.D., Roisman, I.V., Jakirlić, S., Tropea, C.: Dynamic contact angle of spreading droplets: Experiments and simulations. Phys Fluids. 17((6)), (2005). https://doi.org/10.1063/1.1928828
Snoeijer, J.H., Andreotti, B.: Moving contact lines: scales, regimes, and dynamical transitions. Annu Rev Fluid Mech. 45(1), 269–292 (2013). https://doi.org/10.1146/annurev-fluid-011212-140734
Stange, M., Dreyer, M.E., Rath, H.J.: Capillary driven flow in circular cylindrical tubes. Phys Fluids. 15(9), 2587–2601 (2003). https://doi.org/10.1063/1.1596913
Sui, Y., Ding, H., Spelt, P.D.M.: Numerical simulations of flows with moving contact lines. Annu Rev Fluid Mech. 46(1), 97–119 (2014). https://doi.org/10.1146/annurev-fluid-010313-141338
Utsumi, M.: Slosh damping caused by friction work due to contact angle hysteresis. AIAA J. 55(1), 265–273 (2017). https://doi.org/10.2514/1.j055238
Viola, F., Brun, P.T., Gallaire, F.: Capillary hysteresis in sloshing dynamics: aweakly nonlinear analysis. J Fluid Mech. 837, 788–818 (2018). https://doi.org/10.1017/jfm.2017.860
Vreeburg, J.P.B.: Simulation of liquid dynamics onboard Sloshsat FLEVO. Paper presented at the AIP Conference Proceedings (1999). https://doi.org/10.1063/1.57704
Wang, J., Sun, S.L., Hu, J.: The coupling analysis of tank motion and sloshing by a fully nonlinear decoupling method. Nonlinear Dyn. 89(2), 971–985 (2017). https://doi.org/10.1007/s11071-017-3495-0
Wang, X., Zhou, B., Jiang, M.: Technical challenges in numerical simulation of droplet behaviors with dynamic contact angle in microchannels. Int J Energy Res. 43(9), 4828–4839 (2019). https://doi.org/10.1002/er.4633
Yang, W.J., Zhang, T.T., Li, C., Li, S.M., Xu, X.H.: Numerical Simulation of Pitching Sloshing under Microgravity. J Appl Fluid Mech. 12((5)), 1527–1537 (2019). https://doi.org/10.29252/jafm.12.05.29677
Youngs, D.L.: Time-Dependent Multi-material Flow with Large Fluid Distortion. In: Morton, W., Baines, M.J. (eds.) Numerical Methods in Fluid Dynamics, pp. 273–285. Academic Press (1982)
Zhang, F., Zhang, X., Liu, Y.: An augmented incompressible material point method for modeling liquid sloshing problems. Int J Mech Mater Des. 14(1), 141–155 (2018). https://doi.org/10.1007/s10999-017-9366-5
Zhao, D.Y., Hu, Z.Q., Chen, G., Chen, X.B., Feng, X.Y.: Coupling analysis between vessel motion and internal nonlinear sloshing for FLNG applications. J Fluids Struct. 76, 431–453 (2018). https://doi.org/10.1016/j.jfluidstructs.2017.10.008
Acknowledgements
This research is supported by the Key Research Program of Frontier Sciences, CAS (Grant No. QYZDY-SSWJSC040), the National Nature Science Foundation of China (Gant No. 11672311) and Strategic Project of Leading Science and Technology (class A), CAS (Grant No. XDA15012700).
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LI, JC., LIN, H., LI, K. et al. Liquid Sloshing in Partially Filled Capsule Storage Tank Undergoing Gravity Reduction to Low/Micro-Gravity Condition. Microgravity Sci. Technol. 32, 587–596 (2020). https://doi.org/10.1007/s12217-020-09801-3
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DOI: https://doi.org/10.1007/s12217-020-09801-3