Advances in aircraft and spacecraft science

  • 제10권5호
  • /
  • Pages.439-455
  • /
  • 2023
  • /
  • 2287-528X(pISSN)
  • /
  • 2287-5271(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Frequency analysis of liquid sloshing in prolate spheroidal containers and comparison with aerospace spherical and cylindrical tanks

  • Mohammad Mahdi Mohammadi (Faculty of the Mechanic, Malek Ashtar University of Technology) ;
  • Hojat Taei (Faculty of the Mechanic, Malek Ashtar University of Technology) ;
  • Hamid Moosazadeh (Faculty of the Mechanic, Malek Ashtar University of Technology) ;
  • Mohammad Sadeghi (Department of Aerospace Engineering, Tarbiat Modares University)
  • 투고 : 2022.10.20
  • 심사 : 2023.11.13
  • 발행 : 2023.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

Free surface fluid oscillation in prolate spheroidal tanks has been investigated analytically in this study. This paper aims is to investigate the sloshing frequencies in spheroidal prolate tanks and compare them with conventional cylindrical and spherical containers to select the best tank geometry for use in space launch vehicles in which the volume of fuel is very high. Based on this, the analytical method (Fourier series expansion) and potential fluid theory in the spheroidal coordinate system are used to extract and analyze the governing differential equations of motion. Then, according to different aspect ratios and other parameters such as filling levels, the fluid sloshing frequencies in the spheroidal prolate tank are determined and evaluated based on various parameters. The natural frequencies obtained for a particular tank are compared with other literature and show a good agreement with these results. In addition, spheroidal prolate tank frequencies have been compared with sloshing frequencies in cylindrical and spherical containers in different modes. Results show that when the prolate spheroidal tank is nearly full and in the worst case when the tank is half full and the free fluid surface is the highest, the prolate spheroidal natural frequencies are higher than of spherical and cylindrical tanks. Therefore, the use of spheroidal tanks in heavy space launch vehicles, in addition to the optimal use of placement space, significantly reduces the destructive effects of sloshing.

키워드

참고문헌

  1. Albright, N. (1977), Small-Amplitude Periodic Sloshing Modes of a Liquid in a Vertical Right Circular Cylinder With a Concave Spheroidal Bottom, Lawrence Berkeley National Laboratory.
  2. Bao, G. (1994), "Numerical calculation of steady meniscus of liquid in a slow spin container under a micro gravity field", J. Eng. Mech., 14(2), 147-154.
  3. Bauer, H. and Eidel, W. (1989), "Liquid oscillations in a prolate spheroidal container", Ingenieur-Archive, 59(5), 371-381. https://doi.org/10.1007/BF00534067
  4. Chatjigeorgiou, I.K. and Miloh, T. (2014), "Free-surface hydrodynamics of a submerged prolate spheroid in finite water depth based on the method of multipole expansions", Quart. J. Mech. Appl. Math., 67(4), 525-552. https://doi.org/10.1093/qjmam/hbu016.
  5. Concus, P., Crane, G.E. and Satterlee, H.M. (1969), "Small amplitude lateral sloshing in spheroidal containers under low gravitational conditions", Final Report, No. NASA-CR-72500.
  6. Coney, T.A. and J. Salzman (1971), Lateral Sloshing in Oblate Spheroidal Tanks Under Reduced-and Normal-Gravity Conditions, National Aeronautics and Space Administration.
  7. Coogan, S.B. and Green, S. (2019), "critical review of damping prediction methods for annular ring slosh baffles", AIAA Propulsion and Energy 2019 Forum, 4436. https://doi.org/10.2514/6.2019-4436.
  8. Dodge, F.T. and Kana, D.D. (1987), "Dynamics of liquid sloshing in upright and inverted bladdered tanks", J. Fluid. Eng., 109(1), 58-63. https://doi.org/10.1115/1.3242617.
  9. Eidel, W. (1989), "Non-linear liquid oscillations in prolate spheroidal containers", Zeitschrift fur Flugwissenschaften and Weltraumforschung, 159-165.
  10. Howard, A. Flanderstrw Systems Group under Contract to Manned Spacecraft Center (1972), Prolate Spheroidal Slosh Model for Fluid Motion, National Aeronautics and Space Administration.
  11. Ibrahim, R.A. (2005), Liquid Sloshing Dynamics: Theory and Applications, Cambridge University Press, UK.
  12. Leonard, H.W. and Walton, W.C. (1961), An Investigation of The Natural Frequencies and Mode Shapes of Liquids in Oblate Spheroidal Tanks, National Aeronautics and Space Administration.
  13. Mavrakos, S.A. and Chatjigeorgiou, I.K. (2012), "Hydrodynamic exciting forces on immersed prolate spheroids", 27th International Workshop of Water Waves and Floating Bodies, April.
  14. Stephens, D.G., Leonard, H.W. and Silveira, M.A. (1961), An Experimental Investigation of The Damping of Liquid Oscillations in An Oblate Spheroidal Tank with and Without Baffles, National Aeronautics and Space Administration.
  15. Storey, J.M. and Kirk, D.R. (2020), "Experimental investigation of spherical tank slosh dynamics with water and liquid nitrogen", J. Spacecraft Rocket., 57(5), 930-944. https://doi.org/10.2514/1.A34471.
  16. Storey, J.M., Kirk, D., Marsell, B. and Schallhorn, P. (2020), "Progress towards a microgravity CFD validation study using the ISS SPHERES-SLOSH experiment", AIAA Propulsion and Energy 2020 Forum, 3814. https://doi.org/10.2514/6.2020-3814.
  17. Sumner, I.E. (1965), Experimentally Determined Pendulum Analogy of Liquid Sloshing in Spherical and Oblate-Spheroidal Tanks, National Aeronautics and Space Administration.
  18. Turner, M. and Bridges, T. (2013), "Nonlinear energy transfer between fluid sloshing and vessel motion", J. Fluid Mech., 719, 606-636. https://doi.org/10.1017/jfm.2013.29.
  19. Utsumi, M. (2008), "Slosh analysis for teardrop tank", J. Spacecraft Rocket., 45(5), 1053-1060. https://doi.org/10.2514/1.35156.
  20. Weingarten, V.I., Seide, P. and Peterson, J.P. (1968), Buckling of Thin-Walled Circular Cylinders, National Aeronautics and Space Administration.
  21. Yang, H. and Peugeot, J. (2010), "Propellant sloshing parameter extraction from CFD analysis", 46th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. https://doi.org/10.2514/6.20106889.
  22. Yang, H.Q., West, J., Brodnick, J. and Eberhart, C. (2016), "Development of semi-empirical damping equation for baffled tank with oblate spheroidal dome", JANNAF Modeling and Simulation (MSS) Meeting (No. M16-5415), December
  23. Zang, Q., Liu, J., Zhou, Y. and Lin, G. (2021), "On investigation of liquid sloshing in cylindrical tanks with single and multiply connected domains using isogeometric boundary element method", J. Press. Ves. Technol., 143(2), 021402. http://doi.org/10.1002/stc.2184.