OPTIMIZING A SPACE MISSION USING ION PROPULSION

Transcription

1 Review of the Air Force Acadey No 3 (30) 015 OPTIMIZING A SPACE MISSION USING ION PROPULSION Grigore CICAN National Research and Develoent Institute for Gas Turbines COMOTI, Bucharest, Roania DOI: / Abstract: The urose of this aer is to describe a ethod of otiizing a sace ission using ion roulsion, the calculation ethod of the araeters that belong to a sacecraft equied with ion roulsion, the seed variation of a sacecraft deending on the evacuation seed of the articles for variation t, variation α and other araeters. The following eleents will be calculated: the evacuation seed variation deending on the otential acceleration, force variation deending on the otential acceleration, flow rate variation deending on the otential acceleration. Keywords: ission, ion roulsion, otiization, araeters, ayload, roellant 1. INTRODUCTION Fro the oldest ties one of the biggest dreas of huans was the flight, esecially the flight to other lanets. One of the first reviews of this idea was the great scientist Konstantin Eduardovitch Tsiolkovsky [3]. We can say that the history of odern rocket flying and astronautics starts in 1903 with the faous article Investigation of Universal Sace by Means of Reactive Devices, [6] fro which the following quote is taken. That article contains the rocket equation of Tsiolkovsky in differential for, which is the fundaental atheatical exression in the field of sace roulsion. In the field of electricity the first scientists who see the ossibility and the otential of electrical roulsion are: Robert H. Goddard [8], in 1906, exressed any of the just as sile inforation; Konstantin Eduardovitch Tsiolkovsky which in 1911 ublished an idea of electric roulsion: It is ossible that in tie we ay use electricity to roduce a large velocity for the articles ejected fro a rocket device [6] and Professor Heran Oberth, which in 199, included a chater on electric roulsion in his classic book about rockets and sace travel [5]. There are three tyes of electrical roulsion systes: electro-theral, electrostatic (ionic) and electroagnetic; a detailed descrition of these roulsion systes can be found in reference [1]. For studying the travel to Mars it was chosen the electrostatic (ionic) roulsion syste. This roulsion syste was develoed since the beginning of 60 s by rojects NASTAR. Over the tie this systes were ade and erfected esecially for satellites, in order to do the orbit correction and satellite transfer fro an orbit to another. After erfecting these roulsion systes they were used during soe Terra outer sace issions, the first success ission which used ionic roulsion was in 1998 during the Aerican Dee sace ission 1 [10]. Another successful ission which used the ionic roulsion was the Jaanese ission Hayabusa [11] fro the year 003 which had as ain objective the study of an asteroid. The last ajor success ission which used the ionic roulsion was Dawn [1] launched in 007, the urose of the ission was to study the Vesta and Ceres asteroids, which arrived at her destination in 015 assing near Mars by using the lanet s gravity in order to continue the travel. A future interlanetary ission will be ade by ESA and JAXA in 017 and it will be a travel to Mercury lanet, the nae of the ission is BeiColobo [13]. In this aerwork we try the otiization the erforances of a sacecraft, esecially by otiizing the roulsion syste seeing the technological actual liits and the calculation extension of the iroveent ossibilities. 89

2 Otiizing a Sace Mission Using Ion Proulsion. THE RUNNING PRINCIPLE OF THE ELECTRIC PROPULSION SYSTEMS The running rincile of electrical roulsion systes consists of aking the gas olecules or, in general the articles which have to be ejected, sensitive to the action of an electric field and to send the the desired energy using this field. The known ethod for aking a conductor fro a gas it is by ionizing it, in this case the gas becoes sensitive to the action of an electric or agnetic field. If we ionize a gas in a given chaber we obtain negative and ositive charges. In a ionic rocket the charges are searated first, the negatives fro the ositives and the ion obtained are accelerated in a article accelerator. Electrostatic roulsion, regardless of tye, consists of the sae series of basic ingredients, a roellant source, several fors of electric ower, an ionizing chaber, an accelerator region, and the eans of neutralizing the exhaust. While Coulob accelerators require a net charge density of one olarity, the exhaust bea ust be neutralized to avoid a sacecharge build-u outside of the craft which could easily cancel the oeration of the thruster. The neutralization is given by the injection of electrons downstrea as in icture 1, a scheatic diagra of the NASTAR ion thruster, as used on Dee Sace 1 [7]. The neutralization of the ion fascicle as one of the ost difficult robles of this roulsion syste. Fig 1 The scheatic diagra of the NASTAR ion thruster. The evacuation seed at which the articles arrive it is deterined in a article accelerator. We analyzed the direct article accelerator because it is the ost used article accelerator. This article accelerator is described in reference []. According to reference [9] we will resent the calculation ethod for the ionic engine. For starters it will be analyzed the situation of an ion which has the load q and ass located in an electric field E r, deterined by the tension Vacc = V - V1 which alies between A anode and C cathode, as it can be seen in the icture below. Fig The scheatic diagra of the electric field. The ion is accelerated until it gets a seed v e deterined by the next equality: the kinetic energy of the electron it is equal with the kinetic energy variation of the article, conditioned by the electric field action. 1 q V v q V v acc e = acc e = (1) The below exression is valid if the article takes off fro the ion source with the seed 0, during the acceleration interval there is an unifor electric field U E = () d where d is the distance between the two electrodes. In order to calculate the roulsion force roduced by the ionic engine we used the exression below: 90

3 Review of the Air Force Acadey No 3 (30) 015 e I = & (3) The roulsion force is defined as: F = & ve = I V acc (4) e We have to deterine the intensity of the electric current by defining the current density I j =. S Using the Poisson s equation we obtain: d V ρe = (5) d e0 where d is the distance, e 0 is the vacuu ereation and ρe current density. Solving the equation below we obtain the current density: 3 4 e V 0 q j = acc (6) 9 d For atoic or olecular ions we obtain: V j = acc 1 (7) M d And for circular for holes we have: π D I = j S = j (8) 4 where D is the hole diaeter. acc V F = π e0 D 9 d (9) The electric ower is: The erforance of an electrical rocket can be conveniently analyzed in ters of the ower and the relevant asses [4]. Using Țsiolkovski s equation we obtain the forula: v = v ln 0 e (11) f f is the final ass of the rocket, is the roellant ass fro aboard, v is the rocket seed at the tie oent t, 0 is the initial ass of the rocket, is the ass of the rocket at t oent, v e is the evacuation seed of the roellant fro the engine. Before the rocket take off, the initial ass is given by: l + 0 = + (1) u is the ass of the ayload, ass of the ower lant fro aboard, is the α = Pe P e is the electrical ower of the ower source. Between the electrical ower of the source and the ower of the jet we have the relation: Pjet η = (13) Pe η is the syste s erforance. Pjet 1 = & v e (14) Pjet ve Pe = α s = = (15) η t η In order to deterine the rocket s erforances: where t is the tie in which the roellant is used. s, P e = I V acc = 1 & v e η (10) 91

4 Otiizing a Sace Mission Using Ion Proulsion 3. RESULTS OF MISSION OPTIMIZATION The erforances of the ission will be otiized deending on different araeters as it can be seen below: For study of the erforances we know l = 3 about the ission η=0.7, α=500,, 7 = 01. 5, t = 10 s. The following inforation is known about the ionic engine: The working fluid is xenon which olecular weight is kg/kg-ole, the distance between the acceleration grids d=.5, the diaeter of each hole of the grid D=, the nuber holes in the grid No=00. After variation the araeters obtain: Fig. 5 Rocket seed variation deending on the evacuation seed of the articles for the l. Fig. 6 s, and + s variation deending on the evacuation seed of the articles. Fig. 3 Rocket seed variation deending on the evacuation seed of the articles for variation of t. Fig. 7 Rocket seed variation deending on the evacuation seed of the articles for l. 0 Fig. 4 Rocket seed variation deending on the evacuation seed of the articles for variation of α. 9

5 Review of the Air Force Acadey No 3 (30) 015 CONCLUSIONS Fig. 8 Evacuation seed variation deending on the otential acceleration Fig. 9 Electric field variation deending on the otential acceleration As you can see in the figure 3 the variation of the shi s seed is axiu with the evacuation seed for each tie of the ission. Fro the figure 4 it can be seen that for each α there is a axiu for the seed rocket deending on the evacuation seed of the articles for variation of α. Therefore if there would be high values for the α araeters the rocket could achieve higher seeds for the shi. For choosing the roellant quantity aboard figure 5 shows that the axiu seed that can be achieved by the shi for a certain evacuation seed of the articles. Fro the figure 8 it can be seen the variation of seed of articles deending on the otential of acceleration so the higher the otential for acceleration, the higher the exhaust seed. The variation thrust and roellant flow is greater as long as the distance d between the two boards is less, so a higher electric field is resent. For a certain sace ission, a sacecraft that ust reach a certain seed, it can be chosen a certain otial exhaust seed deending on the araeters studied in this article. Fig. 10 Force variation deending on the otential acceleration Fig. 11 Flow rate evacuation deending on the otential acceleration 93

6 Otiizing a Sace Mission Using Ion Proulsion BIBLIOGRAPHY 1. Goebel, D., Ira Katz Fundaentals of Electric Proulsion: Ion and Hall Thrusters, Jet Proulsion Laboratory California Institute of Technology, 008, 3-6. JAHN, R. Physics of electric roulsion, McGRAW-HILL BOOK COMPANY, New York, 1968, ; Kosodeyansky, A. Tsiolkovsky, K. His Life and Work, translated by X. Danko, Univ. Press of the Pacific, Honolulu, Languir D., Low-Thrust Flight: Constant Exhaust Velocity in Field-Free Sace, in H. Seifert (Ed.), Sace Technology, John Wiley & Sons, New York, 1959, Chater Obert, H. Man into Sace, Harer & Row, Publishers, Incororsted, New York, Tikhonravov, M. K., (ed.), Works on Rocket Technology by E. K. Tsiolkovsky, Publishing House of the Defense Ministry, Moscow, 1947; translated fro the 1947 Russian text by NASA as NASA TT F-43, TURNER M., Rocket and Sacecraft Proulsion (Secand Edition), Chichester, UK, Stuhlinger, E. Ion Proulsion for sace Flight, cha. 1, McGraw-Hill Book Coany, New York, SUTTON G. P., BIBLARZ, O. Rocket Proulsion Eleents ( 7th ed.), JOHN WILEY & SONS, New York, 001, ; 10. htt:// 11. htt://global.jaxa.j/rojects/sat/uses_c/ index.htl 1. htt:// ain/index.htl 13. htt://sci.esa.int/beicolobo/ beicolobo-launch-oved-to-017/ 94