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Pulsed inductive thruster, which employs pulsed inductive magnetic field to ionize propellant and accelerate a bulk of plasma, is accompanied with complicated phenomena such as plasma physics, magnetohydrodynamics and the strong coupling effect between the drive-circuit and plasma load. Simulations employing a snowplow circuit model or present magnetohydrodynamic model might be insufficient to capture these important phenomena simultaneously and self-consistently. Therefore the validity of currently existing numerical models remain to be verified. In this paper, a novel circuit-coupled magnetohydrodynamic model is proposed. The flow process of the plasma in the acceleration channel and the discharge process of the circuit are solved simultaneously in a bi-directionally coupled method by calculating the voltage drop across the drive-coil according to the drive-coil geometry and the temporal electric field distribution. The magnetohydrodynamic field is solved with Navier-Stokes equations coupled with Maxwell equations, while the plasma thermodynamic parameters and transport parameters are calculated by employing the local thermal equilibrium model. And the circuit process is solved with a set of circuit equations based on Kirchhoff's law. All the physics fields are computed by the finite element method in COMSOL MultiphysicsTM. Numerical simulation for American TRW Inc.'s MK-1 thruster successfully reproduces its working process. The numerical magnetic field distribution in plasma, the time-dependent collective Lorentz force and the specific impulse and efficiency of the thruster under varying working voltages agree well with the corresponding experimental data. Numerical results imply that a compact azimuthal plasma current sheet is established in the initial 1-2 s in the near-face region of the drive-coil. This plasma current sheet, which entrains the majority of the propellant, is excluded and accelerated by the Lorentz force derived from the drive-coil magnetic field. Most of the propellant acceleration is accomplished within the first half period of the circuit current, which is about 7-8 s. Furthermore, the bi-directional coupling effect is quantitatively analyzed with the current model. Numerical results indicate that the coupling plasma load generally tends to increase the effective resistance and reduce the effective inductance of the drive-circuit. Moreover, this effect changes as the plasma structure varies. When the plasma current sheet moves away from the drive-coil, the mutual inductance between plasma load and drive-coil decreases monotonically. That implys that the plasma current sheet decouples gradually from the dirve-circuit in the process. In conclusion, bidirectional coupling effect between plasma load and drive-circuit plays an important role in the operation of the thruster. This model could be used to predict the performances of pulsed inductive thrusters and might be helpful in designing a more effective thruster.
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Keywords:
- plasma physics /
- electric propulsion /
- magnetohydrodynamic /
- plasma simulation
[1] Polzin K A 2011 J. Prop. Power. 27 3
[2] Martin A K, Dominguez A, Eskridge R H 2015 34th International Electric Propulsion Conference Hyogo-Kobe, Japan, July 4-10, 2015 p50
[3] Russell D, Poylio J H, Goldstein W 2004 Space Conference and Exhibit San Diego, America, September 28-30, 2004 p6054
[4] Dailey C L, Loveberg R H 1987 Pulsed Inductive Thruster Component Technology AFAL TR 07 012
[5] Dailey C L, Loveberg R H 1989 AIAA/ASME/SAE/ ASEE 25th Joint Propulsion Conference Monterey, America, July 10-12, 1989 p2266
[6] Dailey C L, Lovberg R H 1993 The PIT MkV Pulsed Inductive Thruster NASA CR 19 1155
[7] Polzin K A, Choueiri E Y 2006 IEEE Trans. Plasma Sci.. 34 3
[8] Polzin K A 2006 Ph. D. Dissertation.(Princeton: Princeton University)
[9] Polzin K A, Sankaran K, Ritchie A G, Reneau J P 2013 J. Phys. D: Appl. Phys. 46 475201
[10] Martin A K 2016 J. Phys. D: Appl. Phys. 49 025201
[11] Che B X 2015 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese) [车碧轩 2015 硕士学位论文 (长沙: 国防科技大学)]
[12] Mikellides P G, Neilly C 2007 J. Prop. Power 23 51
[13] Mikellides P G, Ratnayake N 2007 J. Prop. Power 23 854
[14] Mikellides P G, Villarreal J K 2007 J. Appl. Phys. 102 103301
[15] Cheng Y G, Xia G Q 2017 Acta Phys. Sin. 66 075204(in Chinese) [成玉国, 夏广庆 2017 物理学报 66 075204]
[16] Cheng Y G 2015 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [成玉国 2015 博士学位论文 (长沙: 国防科技大学)]
[17] Li M, Liu H, Ning Z X 2015 IEEE Trans. Plasma Sci. 43 12
[18] John D A (translated by Yang Y) 2011 Hypersonic and High-Temperature Gas Dynamics.(2nd Ed.) (Beijing: Aviation Industry Press) pp421-422 (in Chinese) [小约翰 D A 著 (杨永 译) 2011 高超声速和高温气体动力学(第二版)(北京: 航空工业出版社)第421422页]
[19] Cheng X 2009 Thermal Plasma Heat Transfer and Flow (Bejiing: Science Press) pp50-55 (in Chinese) [陈熙 2009 热等离子体传热与流动(北京: 科学出版社) 第5055页]
[20] Deb P, Agarwal R K 2001 AIAA Aerospace Sciemces Meeting . Exhibit Reno, America 2001, p794
[21] Tian Z Y 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [田正雨 2008 博士学位论文 (长沙: 国防科学技术大学)]
[22] Ahangar M, Ebrahimi R, Shams M 2014 Acta Astronaut. 103 129
[23] Heiermann J 2002 Ph. D. Dissertation. (Stuttgart: Universitat Stuttgart)
[24] Sankaran K 2005 Ph. D. Dissertation (Princeton: Princeton University)
[25] Glumb R J, Krier H 1986 AIAA J. 24 1331
[26] Lovberg R H, Dailey C L 1982 AIAA/JSASS/DGLR 16th International Electric Propulsion Conference New Orleans, America, November 17-19, 1982 p1921
[27] Lovberg R H, Dailey C L 1982 AIAA J. 20 971
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[1] Polzin K A 2011 J. Prop. Power. 27 3
[2] Martin A K, Dominguez A, Eskridge R H 2015 34th International Electric Propulsion Conference Hyogo-Kobe, Japan, July 4-10, 2015 p50
[3] Russell D, Poylio J H, Goldstein W 2004 Space Conference and Exhibit San Diego, America, September 28-30, 2004 p6054
[4] Dailey C L, Loveberg R H 1987 Pulsed Inductive Thruster Component Technology AFAL TR 07 012
[5] Dailey C L, Loveberg R H 1989 AIAA/ASME/SAE/ ASEE 25th Joint Propulsion Conference Monterey, America, July 10-12, 1989 p2266
[6] Dailey C L, Lovberg R H 1993 The PIT MkV Pulsed Inductive Thruster NASA CR 19 1155
[7] Polzin K A, Choueiri E Y 2006 IEEE Trans. Plasma Sci.. 34 3
[8] Polzin K A 2006 Ph. D. Dissertation.(Princeton: Princeton University)
[9] Polzin K A, Sankaran K, Ritchie A G, Reneau J P 2013 J. Phys. D: Appl. Phys. 46 475201
[10] Martin A K 2016 J. Phys. D: Appl. Phys. 49 025201
[11] Che B X 2015 M. S. Thesis (Changsha: National University of Defense Technology) (in Chinese) [车碧轩 2015 硕士学位论文 (长沙: 国防科技大学)]
[12] Mikellides P G, Neilly C 2007 J. Prop. Power 23 51
[13] Mikellides P G, Ratnayake N 2007 J. Prop. Power 23 854
[14] Mikellides P G, Villarreal J K 2007 J. Appl. Phys. 102 103301
[15] Cheng Y G, Xia G Q 2017 Acta Phys. Sin. 66 075204(in Chinese) [成玉国, 夏广庆 2017 物理学报 66 075204]
[16] Cheng Y G 2015 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [成玉国 2015 博士学位论文 (长沙: 国防科技大学)]
[17] Li M, Liu H, Ning Z X 2015 IEEE Trans. Plasma Sci. 43 12
[18] John D A (translated by Yang Y) 2011 Hypersonic and High-Temperature Gas Dynamics.(2nd Ed.) (Beijing: Aviation Industry Press) pp421-422 (in Chinese) [小约翰 D A 著 (杨永 译) 2011 高超声速和高温气体动力学(第二版)(北京: 航空工业出版社)第421422页]
[19] Cheng X 2009 Thermal Plasma Heat Transfer and Flow (Bejiing: Science Press) pp50-55 (in Chinese) [陈熙 2009 热等离子体传热与流动(北京: 科学出版社) 第5055页]
[20] Deb P, Agarwal R K 2001 AIAA Aerospace Sciemces Meeting . Exhibit Reno, America 2001, p794
[21] Tian Z Y 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese) [田正雨 2008 博士学位论文 (长沙: 国防科学技术大学)]
[22] Ahangar M, Ebrahimi R, Shams M 2014 Acta Astronaut. 103 129
[23] Heiermann J 2002 Ph. D. Dissertation. (Stuttgart: Universitat Stuttgart)
[24] Sankaran K 2005 Ph. D. Dissertation (Princeton: Princeton University)
[25] Glumb R J, Krier H 1986 AIAA J. 24 1331
[26] Lovberg R H, Dailey C L 1982 AIAA/JSASS/DGLR 16th International Electric Propulsion Conference New Orleans, America, November 17-19, 1982 p1921
[27] Lovberg R H, Dailey C L 1982 AIAA J. 20 971
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