Multiphysics Finite Element Modeling of Current Generation of Bare Flexible Electrodynamic Tether
Abstract
The paper develops a coupled multiphysics finite element method to analyze satellite deorbit by a bare flexible electrodynamic tether. Unlike the existing approaches, the current method assumes that the tether is flexible and deflectable, and its efficiency of electron collection varies along the tether length depending on tether deflection. The orbital motion limited theory, which dictates the electron collection by a bare tether, is discretized and solved with the same finite element mesh as the tether dynamics to couple the electron collection with the tether flexural deflection. The advantages of the new method are demonstrated by numerical simulations. Compared with a reference method based on straight tether assumption, the coupling effect between the electron collection and tether deflection is significant, leading to the dynamic variation of electrodynamic force acting on the tether. Although the deorbit rates predicted by these two methods are almost the same, the new method predicts a shorter stable deorbit period than the reference method. It demonstrates that the new method is more accurate, and it should be used for detailed engineering design.
References
[1] , “Risks in Space from Orbiting Debris,” Science, Vol. 311, No. 5759, 2006, pp. 340–341. doi:https://doi.org/10.1126/science.1121337 SCIEAS 0036-8075
[2] “Space Debris Mitigation Guidelines of the Committee on the Peaceful Uses of Outer Space,” Steering Group ansd Working Group 4, Inter-Agency Space Debris Coordination Committee, TR A/62/20 (2007), 2008.
[3] , “Concept-of-Operations Disposal Analysis of Spacecraft by Gossamer Structure,” Journal of Spacecraft and Rockets, Vol. 52, No. 2, 2015, pp. 517–525. doi:https://doi.org/10.2514/1.A32919 JSCRAG 0022-4650
[4] , “Benefits and Risks of Using Electrodynamic Tethers to De-Orbit Spacecraft,” Acta Astronautica, Vol. 64, Nos. 5–6, 2009, pp. 571–588. doi:https://doi.org/10.1016/j.actaastro.2008.10.007 AASTCF 0094-5765
[5] , “Review and Comparison of Active Space Debris Capturing and Removal Methods,” Progress in Aerospace Sciences, Vol. 80, Jan. 2016, pp. 18–32. doi:https://doi.org/10.1016/j.paerosci.2015.11.001 PAESD6 0376-0421
[6] , “Versatile Electro-Dynamic Tethers Dynamics Simulator for Debris Mitigation Tools Design,” Proceedings of the 13th Symposium on Advanced Space Technologies in Robotics and Automation, European Space Agency Paper 209B-96077, Noordwijk, The Netherlands, 2015.
[7] , “Effect of Electromagnetic Forces on the Orbital Dynamics of Tethered Satellites,” Journal of Guidance, Control, and Dynamics, Vol. 28, No. 6, 2005, pp. 1309–1315. doi:https://doi.org/10.2514/1.1759 JGCODS 0731-5090
[8] , “Generator Regime of Self-Balanced Electrodynamic Bare Tethers,” Journal of Spacecraft and Rockets, Vol. 43, No. 6, 2006, pp. 1359–1369. doi:https://doi.org/10.2514/1.20471 JSCRAG 0022-4650
[9] , “Orbital Debris Mitigation Through Deorbiting with Passive Electrodynamic Drag,” Proceedings of the 63rd International Astronautical Congress, The International Astronautical Federation Paper IAC-12-D9.2.8, Naples, Italy, 2012.
[10] , “Deorbiting Performance of Bare Electrodynamic Tethers in Inclined Orbits,” Journal of Guidance, Control, and Dynamics, Vol. 36, No. 5, 2013, pp. 1550–1556. doi:https://doi.org/10.2514/1.58428
[11] , “Libration and Transverse Dynamic Stability Control of Flexible Bare Electrodynamic Tether Systems in Satellite Deorbit,” Aerospace Science and Technology, Vol. 49, Feb. 2016, pp. 112–129. doi:https://doi.org/10.1016/j.ast.2015.11.036
[12] , “Dynamics of Nanosatellite Deorbit by Bare Electrodynamic Tether in Low Earth Orbit,” Journal of Spacecraft and Rockets, Vol. 50, No. 3, 2013, pp. 691–700. doi:https://doi.org/10.2514/1.A32336 JSCRAG 0022-4650
[13] , “Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling,” Journal of Guidance, Control, and Dynamics, Vol. 39, No. 3, 2016, pp. 642–654. doi:https://doi.org/10.2514/1.G001338 JGCODS 0731-5090
[14] , “Cost-Effective End-of-Mission Disposal of LEO Microsatellites: The Terminator Tape,” Proceedings of the 24th Annual AIAA/USU Conference on Small Satellite, Mission Enabling Technologies 1, Utah State Univ. Research Foundation, Paper SSC-10-X-9, North Logan, UT, 2010.
[15] , “Model Development and Code Verification for Simulation of Electrodynamic Tether System,” Journal of Guidance, Control, and Dynamics, Vol. 32, No. 6, 2009, pp. 1713–1722. doi:https://doi.org/10.2514/1.44638 JGCODS 0731-5090
[16] , “Bare Wire Anodes for Electrodynamic Tethers,” Journal of Propulsion and Power, Vol. 9, No. 3, 1993, pp. 353–360. doi:https://doi.org/10.2514/3.23629 JPPOEL 0748-4658
[17] , “Analysis of Bare-Tether Systems for Deorbiting Low-Earth-Orbit Satellites,” Journal of Spacecraft and Rockets, Vol. 39, No. 2, 2002, pp. 198–205. doi:https://doi.org/10.2514/2.3820 JSCRAG 0022-4650
[18] , “Impact of Nonideal Effects on Bare Electrodynamic Tether Performance,” Journal of Propulsion and Power, Vol. 31, No. 3, 2015, pp. 951–955. doi:https://doi.org/10.2514/1.B35393 JPPOEL 0748-4658
[19] , “Efficient Computation of Current Collection in Bare Electrodynamic Tethers in and Beyond OML Regime,” Journal of Aerospace Engineering, Vol. 28, No. 6, 2015, Paper 04014144. doi:https://doi.org/10.1061/(ASCE)AS.1943-5525.0000479 JAEEEZ 0893-1321
[20] , “Libration Dynamics And Stability of Electrodynamic Tethers in Satellite Deorbit,” Celestial Mechanics and Dynamical Astronomy, Vol. 116, No. 3, 2013, pp. 279–298. doi:https://doi.org/10.1007/s10569-013-9489-4
[21] , “Determination of Hollow Cathode Plasma Contactor System Requirements Using an Electrodynamic Tether System Simulation Tool,” Proceedings of the 13th Spacecraft Charging and Technology Conference, NASA, JPL Paper 2014-121, Pasadena, CA, 2014.
[22] , “Electrodynamic Tether at Jupiter—1: Capture Operation and Constraints,” IEEE Transactions on Plasma Science, Vol. 36, No. 5, 2008, pp. 2450–2458. doi:https://doi.org/10.1109/TPS.2008.2002580 ITPSBD 0093-3813
[23] , “Dynamic Modeling of Cable Towed Body Using Nodal Position Finite Element Method,” Ocean Engineering, Vol. 38, No. 4, 2011, pp. 529–540. doi:https://doi.org/10.1016/j.oceaneng.2010.11.016 OCENBQ 0029-8018
[24] , “Long-Term Dynamic Modeling of Tethered Spacecraft Using Nodal Position Finite Element Method and Symplectic Integration,” Celestial Mechanics and Dynamical Astronomy, Vol. 123, No. 4, 2015, pp. 1–24. doi:https://doi.org/10.1007/s10569-015-9640-5
[25] , “Sensitivity Analysis of Bare-Wire Space Tether Systems,” Computer Methods in Applied Mechanics and Engineering, Vol. 190, No. 42, 2001, pp. 5495–5503. doi:https://doi.org/10.1016/S0045-7825(01)00163-3 CMMECC 0045-7825
[26] , “AIM Microsatellite Platform: A Canadian Multi-Mission Satellite Bus Solution,” 30th AIAA International Communications Satellite System Conference, AIAA Paper 2012-15190, Sept. 2012. doi:https://doi.org/10.2514/6.2012-15190