Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-17T14:56:23.294Z Has data issue: false hasContentIssue false
  • English
  • Français

Study on Rigid-Liquid Coupling Dynamics of the Spacecraft With Arbitrary Axisymmetrical Tanks

Published online by Cambridge University Press:  10 May 2018

Y. L. Yan  and
B. Z. Yue
Y. L. Yan
Affiliation:
Department of MechanicsSchool of Aerospace EngineeringBeijing Institute of TechnologyBeijing, China
B. Z. Yue*
Affiliation:
Department of MechanicsSchool of Aerospace EngineeringBeijing Institute of TechnologyBeijing, China
*
*Corresponding author ([email protected])
Get access

Abstract

This article focus on the rigid-liquid coupling dynamics of the spacecraft with arbitrary axisymmetrical tanks with curved walls and top. The carrier velocity potential function was obtained according to the motion equations of a representative point in the tank of spacecraft, and the relative velocity potential function can be expressed as Gauss hypergeometric series. The Hamilton's variational principle was applied to derive the governing equations of liquid sloshing based on the profile of hydrostatic shape of free liquid surface. The dynamic equations of modal coordinates were established through the Galerkin method. The state equations of coupled motion of main rigid platform of the spacecraft were deduced by using the Lagrange's equations in term of general quasi-coordinates. Thruster firing was actuated to the coupled system to analyze the rigid-liquid coupled dynamic behaviors. Computer numerical simulations was carried out to confirm the validity of the method developed in this paper.

Keywords

Axisymmetrical tankLow-gravityRigid-liquid coupling systemLiquid-filled spacecraft
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 6 , December 2018 , pp. 817 - 828
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Dodge, F. T., The New “Dynamic Behavior of Liquids in Moving Containers”, NASA SP-106 (2000).Google Scholar
2. Deng, M. L. and Yue, B. Z., “Attitude Dynamics and Control of Liquid Filled Spacecraft with Large Amplitude Fuel Slosh,” Journal of Mechanics, 33, pp. 125–136 (2017).Google Scholar
3. Hung, R. J., Long, Y. T. and Zu, G. J., “Coupling of Gravity-Gradient-Dominated Acceleration-Induced Slosh Reaction Torques with Spacecraft Orbital Dynamics,” Control Engineering Practice, 4, pp. 939–949 (1996).Google Scholar
4. Hung, R. J., Long, Y. T. and Chi, Y. M., “Slosh Dynamics Coupled with Spacecraft Attitude Dynamics. I - Formulation and Theory,” Journal of Spacecraft and Rockets, 33, pp. 575–581 (1996).Google Scholar
5. Hastings, L. J. and Rutherford, R. I., “Low Gravity Liquid-Vapor Interface Shapes in Axisymmetric Containers and a Computer Solution,” NASA TM X-53790 (1968)Google Scholar
6. Bauer, H. F. and Eidel, W., “Free and Forced Oscillations of a Frictionless Liquid in a Long Rectangular Tank with Structural Obstructions at the Free Liquid Surface,” Archive of Applied Mechanics, 70, pp. 550–560 (2000).Google Scholar
7. Bauer, H. F. and Eidel, W., “Hydroelastic Vibrations in a Two-Dimensional Rectangular Container Filled with Frictionless Liquid and a Partly Elastically Covered Free Surface,” Journal of Fluids and Structures, 19, pp. 209–220 (2004).Google Scholar
8. Yue, B. Z., Wu, W. J. and Yan, Y. L., “Modeling and Coupling Dynamics of the Spacecraft with Multiple Propellant Tanks,” AIAA Journal, 54, pp. 3608–3618 (2016).Google Scholar
9. Peterson, L. D., Crawley, E. F. and Hansman, R., “Nonlinear Fluid Slosh Coupled to the Dynamics of a Spacecraft,” AIAA Journal, 27, pp. 1230–1240 (1989).Google Scholar
10. Sabri, F. and Lakis, A. A., “Effects of Sloshing on Flutter Prediction of Liquid-Filled Circular Cylindrical Shell,” Journal of Aircraft, 48, pp. 1829–1839 (2011).Google Scholar
11. He, Y. J., Ma, X. R., Wang, P. P. and Wang, B. L., “Low-Gravity Liquid Nonlinear Sloshing Analysis in a Tank Under Pitching Excitation,” Journal of Sound and Vibration, 299, pp. 164–177 (2007).Google Scholar
12. McIver, P., “Sloshing Frequencies for Cylindrical and Spherical Containers Filled to an Arbitrary Depth,” Journal of Fluid Mechanics, 201, pp. 243–257 (1989).Google Scholar
13. Utsumi, M., “Low-Gravity Propellant Slosh Analysis Using Spherical Coordinates,” Journal of Fluids and Structures, 12, pp. 57–83 (1998).Google Scholar
14. Utsumi, M., “Low-Gravity Sloshing in an Axisymmetrical Container Excited in the Axial Direction,” Journal of Applied Mechanics-Transactions of the ASME, 67, pp. 344–354 (2000).Google Scholar
15. Utsumi, M., “Low-Gravity Slosh Analysis for Cylindrical Tanks with Hemiellipsoidal Top and Bottom,” Journal of Spacecraft and Rockets, 45, pp. 813–821 (2008).Google Scholar
16. Yang, D. D. and Yue, B. Z., “Research on Sloshing in Axisymmetrcal Containers Under Low Gravity,” Journal of Astronautics, 34, pp. 917–925 (2013).Google Scholar
17. Utsumi, M., “Slosh Damping Caused by Friction Work Due to Contact Angle Hysteresis,” AIAA Journal, 55, pp. 265–273 (2016).Google Scholar
18. Lü, J., Wang, S. M. and Wang, T. S., “Coupling Dynamic Analysis of a Liquid-Filled Spherical Container Subject to Arbitrary Excitation,” Acta Mechanica Sinica, 28, pp. 1154–1162 (2012).Google Scholar
19. Faltinsen, O. M. and Timokha, A. N., “Analytically Approximate Natural Sloshing Modes for a Spherical Tank Shape,” Journal of Fluid Mechanics, 703, pp. 391–401 (2012).Google Scholar
20. Yue, B. Z. and Zhu, L. M., “Hybrid Control of Liquid-Filled Spacecraft Maneuvers by Dynamic Inversion and Input Shaping,” AIAA Journal, 52, pp. 618–626 (2014).Google Scholar
21. Kana, D. D., “Validated Spherical Pendulum Model for Rotary Liquid Slosh,” Journal of Spacecraft and Rockets, 26, pp. 188–195 (1989).Google Scholar
22. Ahmad, S., Yue, B. Z. and Shah, S. F., “Hamilton Structure and Stability Analysis for a Partially Filled Container,” Journal of Mechanics, 29, pp. 79–83 (2012).Google Scholar
23. Dodge, F. T., Green, S. T. and Cruse, M. W., “Analysis of Small-Amplitude Low Gravity Sloshing in Axisymmetric Tanks,” Microgravity - Science and Technology, 4, pp. 228–234 (1991).Google Scholar
24. Veldman, A. E. P., Gerrits, J., Luppes, R., Helder, J. A. and Vreeburg, J. P. B., “The Numerical Simulation of Liquid Sloshing on Board Spacecraft,” Journal of Computational Physics, 224, pp. 82–99 (2007).Google Scholar
25. Kulczycki, T., Kwaśnicki, M. and Siudeja, B., “The Shape of the Fundamental Sloshing Mode in Axisymmetric Containers,” Journal of Engineering Mathematics, 99, pp. 157–183 (2016).Google Scholar
26. Ibrahim, R. A., Liquid Sloshing Dynamics Theory and Applications, 2nd Edition, Cambridge University Press, Cambridge, pp. 294–329 (2005).Google Scholar
27. Yang, A. S., “Investigation of Liquid–Gas Interfacial Shapes in Reduced Gravitational Environments,” International Journal of Mechanical Sciences, 50, pp. 1304–1315 (2008).Google Scholar
28. Storey, J. M., Kirk, D. R., Gutierrez, H., Marsell, B. and Schallhorn, P. A. “Experimental, Numerical and Analytical Characterization of Slosh Dynamics Applied to In-Space Propellant Storage and Management,” 51st AIAA/SAE/ASEE Joint Propulsion Conference, Orlando, FL (2015).Google Scholar