Thermal State Investgatons of Two-stage Thruster wth Anode Layer IEPC-2007-127 Presented at the 30 th Internatonal Electrc Propulson Conference, Florence, Italy Mtroshn A.S. *, Garkusha V.I., Semenkn A.V. and Solodukhn A.E. Central Research Insttute of Machne Buldng (TsNIIMASH), Ponerskaya 4, Korolev, Moscow regon, Russa 141070, Phone: (8-495) 513-44-46, Fax: (8-495) 516-59-10 Abstract: Thermal analyss s crtcally mportant for development of EP thruster and modern anode layer thrusters (TAL) n partcular. Absence and/or uncertanty of thermal boundary condtons s the one of the man prncple dffculty appearng durng heat calculatons of the thruster constructon. The purpose of the work was accurate defnton of thruster heat emssve characterstcs and verfcaton of exstng heat calculaton methods. Necessary heat boundary condtons were obtaned and verfed by usng of sememprcal method. Two approaches of temperature felds calculatons were used: analytcal and varaton one (Fnte Elements Method FEM). Comparson of these methods was carred out. Based on smulaton experment performed wth the help of ohmc heatng emssve characterstcs of outer TAL surfaces were obtaned. Temperature felds modelng by teratve method for dfferent thruster modes was carred out. Expermental data were compared wth calculated ones. It resulted n obtanng of heat generaton dstrbuton n the thruster. Emssve data table was composed for consdered type of thrusters. Thruster thermal balance was analyzed. ε σ T k Q A F I U W = emssvty factor = Stefan-Boltzmann constant = temperature = thermal-conductvty coeffcent = heat generaton = element area = vew factor = current strength = voltage = power Nomenclature * R&D Engneer, Electrc Propulson Laboratory, avs@tse.ru Head of Department, avs@tse.ru Head of Laboratory, Electrc Propulson Laboratory, avs@tse.ru Group Leader, Electrc Propulson Laboratory, asolodukhn@mtu-net.ru 1
I. Introducton Thermal analyss s crtcally mportant for development of EP thruster and modern anode layer thrusters (TAL) n partcular 1,2. TAL constructon thermal ntensty defnes and lmts appled constructonal materals as well as ther treatment. It s ncorrect to determne thruster operatng modes characterstcs wthout takng nto account thermal dstrbuton, snce the thruster effcency drectly depends on thermal ntensty. Thruster heat balance analyss allows to ncrease nput power range and to optmze thruster operaton n dfferent modes, ncludng transent modes. There are several thruster temperature feld smulatng approaches for now. All of them can be dvded to two man types: analytc and numercal. Analytc approaches are based on system heat balance equatons and classcal heat transfer equatons. The prncple of numercal methods (for example, fnte element method) les n the approxmaton of a sought temperature value varyng contnuously by volume of a body, by ts dscrete model. Advantage of numercal approach s precse descrpton of nvestgated model and operatng mode condtons. Snce modern computer equpment allows calculatng large equatons set-up (more than 1 mllon of equatons). To realze these two calculaton approaches heat transfer boundary condtons defnton s needed. Manly radant heat transfer takes place n TAL, so for thruster parts besdes standard materal propertes surface emssvty factor value (ε) s also needed to know. For the frst test run ε can be taken as nomnal value for part materal, but n case of contnuous operatng surface propertes wll change and t wll lead to heat fluxes redstrbuton. The second needed boundary condtons are the thruster parts heat generaton values (Q), whch s determned wth help of total thruster heat balance equaton. Hence boundary condtons data tabulaton s mportant task needed for new thruster constructon thermal ntensty quck estmaton under development stage. Task of boundary condtons defnton can be solved by sememprcal approach, combnng expermental data and numercal smulaton. II. Motvaton Two-stage TAL D-80-type wth average dameter of dscharge channel about 60 mm (see Fg.1) was chosen for thermal analyss. Thruster uses xenon as a propellant and t can be operated n modes wth nput power up to 2 kw. Thermal analyss data obtaned for ths sample can be appled for all two-stage xenon TAL. A. Bref TAL Desgn Descrpton The thruster conssts of two man parts (see Fg.2): Magnet system. Anode unt. Magnet system, n turns, conssts of followng man components: mountng flange (#6); nner col wth magnetc pole (#3); outer cols (#4); outer pole pece (#5). The anode unt s mounted on magnet mountng flange. It ncludes gas dstrbutng anode (#1), frst stage cathode (#2), guard rngs (#7), nsulators (#8), screen (#9). Anode unt components whch are under dfferent potental are solated from each other wth the help of Fgure 1. Photo of TAL wth thermocouples. nsulators (#8). Magnet system poles are protected from on sputterng by guard rngs (#7). Heat n the thruster constructon s generated by the frst and the second stages dscharge plasma and by magnet system cols. 2
B. Research stages The work was amed on creaton of boundary condtons data base of exstng thrusters. These data s needed for new thruster constructon thermal ntensty quck estmaton under development stage and thermal analyss. Man steps were the followng: Thruster constructon parts thermal ntensty prelmnary calculaton, wth help of reference and boundary condton emprcal data; For two thruster operatng modes temperature feld measurement; Obtaned results analyss and boundary condtons correcton; More accurate calculaton; Thruster heat balance analyss. Calculaton algorthm s gven n Fg. 3. Fgure 2. Two-stage TAL prncple desgn scheme. Calculaton Scheme Input boundary condton data: Q, ε Calclulate by THeat1 smulaton Changng of boundary condtons False Obtanng of Temperature feld T Comparson wth experment True Temperature feld Т, Heat generaton Q End of Calculaton Fgure 3. Calculaton algorthm. 3
III. Thruster Thermal State Smulaton Thruster temperature feld was calculated by both analytcal methods and fnte element method (FEM). THeat1 bundled software (developed n TsNIIMASH) was used for analytcal nvestgatons. The software was specally developed and optmzed for TAL temperature feld smulaton. A. Prerequstes Program algorthm contans classcal heat transmsson equatons, partcularly radant heat exchange one. Heat transfer between surfaces was descrbed by equaton 1 (see Fg.4). Q rad 4 4 = σ ε A F ( T T ) (1) where F vew factor between surfaces and ε - emssvty factor of surface A - area of radaton surface T, T - surfaces and temperatures accordngly Vew factor F has a man nfluence for two surface heat nteracton descrpton. It defnes heat quantty transferred from surface to surface takng nto account ther postonal relatonshp. For two elementary surfaces looks as follows: cos( θ ) cos( θ ) df = da 2 π R Where da and da vew factor θ, θ - drecton angles between perpendcular to surface and lne (2) In ntegral form vew factor looks as follows: 1 cos( θ ) cos( θ ) F = da da A 2 π R 1 (3) A1 A2 B. THeat1 smulaton THeat1 bundled software permts quck heat feld calculaton of both: thruster statonary state and no statonary one. Calculatng speed was the man advantage of ths program. It allows organzng teraton algorthm of boundary condtons selecton. Also t s necessary to mark that THeat1 s adapted ust for TAL radaton smulaton. Ths program models all necessary condtons of radaton heat transfer, whch are typcal for thruster operaton. Calculatng model s presented as axsymmetrc one. It can be explaned, that the most of TAL constructon parts have sold of revoluton shape, excludng outer magnet cols. However, these four cols have been equally dstrbuted around a crcle, that allows ntegrally 4 F Fgure 4. Calculaton algorthm Fgure 5. THeat1 smulaton model R, whch connected two surfaces.
consderng ones contrbuton n heat transfer by flat axsymmetrc examnaton. Nomnal value of Emssvty ε was gven for all thruster surfaces. Heat generaton Q was gven for thruster surfaces also. Vew factor was defned between all radant nteracton surfaces. THeat1 smulaton scheme was presented n Fg. 5. As a frst approach the calculaton was carred out once wthout teratons. The result of ths smulaton was taken as a reference pont for further calculatons and comparson wth expermental data. Fgure 6. THeat1 smulaton results (presented temperature has averaged by thruster parts) C. Verfcaton For verfcaton of the THeat1 code smlar task has been performed wth help of well known Fnte Elements Method. The used boundary condtons (ε and Q)and thruster model were the same as the one n the THeat1. Consdered fnte element model s shown n Fgure 7. The calculatons have been done by ANSYS software. The temperature dstrbuton obtaned by both methods - THeat1 and ANSYS are shown correspondngly on Fgures 6 and 7. As one can see from the Table 1 below, the dfference of the temperature values calculated by both methods do not exceed 5%. Ths result confrms that THeat1 s good enough for quck calculatons of the thruster part temperature mode. Fgure 7. ANSYS verfcaton smulaton results 5
Table 1. Two smulaton methods results Smulaton type THeat1 Ansys Frst stage cathode 403 C 421 C Anode 462 C 479 C Out guard rng 413 C 425 C Inner guard rng 430 C 449 C Outer pole 180 C 171 C Inner pole 301 C 312 C Thermal screen 298 C 304 C IV. Expermental thruster temperature measurements TAL temperature dstrbuton study was carred out n TsNIIMASH laboratory by thermocouples specally mbedded n the structure. Scheme of thermocouple locaton s presented n Fg. 8. Thermocouples status: Т1 nner pole; T2 thermal screen; T3 mountng flange ; T4 mountng frame; T5 cover; T6 out pole; Т7 out guard rng. Average temperature of magnetc cols was obtaned by measurements of col resstance durng thruster heatng/test and standard ohmc thermal dependence for col materal. Two phase TAL thermal feld measurng experment was carred out, when n use nvestgatons: Fgure 8. Scheme of thermocouple locaton Frst phase (preparatory) thermal feld measurng wth operaton (means ohmc heatng) of magnetc system only; Second phase (man) thermal feld measurng wth thruster frng at nomnal mode; Mode parameters presented n Table 2. Table 2. Thruster mode parameters Mode parameters Magnetc system operate Nomnal mode Inner col current, Inn, А 5 1.75 Inner col voltage, Unn, V 10.4 4.5 Out cols current, Iout, A 5 1.2 Out cols voltage, Uout, V 7 2 Frst stage current, Id, А 2.75 Frst stage voltage, Ud, V 150.8 Second stage current, Iа, А 2.5 Second stage voltage, Uа, V 553 Summary thruster power, W, W 87 1800 6
In vew of falng dscharge by only magnetc system operaton maxmum convenent mbeddng thermocouple n thruster parts was possble. Magnetc system heat generaton Q was determned va measurements of magnet col currents and voltages. Man thermal feld measurng experment phase was carred out at nomnal thruster operaton mode (W=1800w). Expermental data was processed and used for surfaces emssvty and heat generaton accurate defnton. It took about 4 hour to reach thermal equlbrum. The temperature data versus tme s shown on Fgures 9,10. As a result of the two expermental phases temperature dstrbuton has been obtaned for two cases (see Table 3): Ohmc heatng by magnetc col currents Total thruster heatng at nomnal operaton regme Fgure 9. Thermocouple data for the thruster wth magnetc system operaton/heatng mode It s mportant to note, that for the frst case heat flux nto the thruster elements s known, thus obtaned preparatory results was used for smulaton scheme verfcaton. Fgure 10. Thermocouple data for nomnal operate mode Table 3. Thruster mode parameters Thruster parts temperature T, С Mode Magnetc system operate Nomnal mode Т1 nner pole 242 Т2 thermal screen 167 322 Т3 mountng flange 159 228 Т4 mountng frame 137 203 Т5 cover 143 207 Т6 out pole 151 311 Т7 out guard rng 368 Tnn Inner col 301 407 Tout Out cols 148 206 7
V. Gettng thermal boundary condtons database Obtaned expermental temperature dstrbuton and heat flux known for preparatory case allowed to determne and clarfy boundary condtons. The boundary condtons were determned va followng teratons: Prelmnary calculatons wth pre-selected boundary condtons; Comparson of the calculated and expermental data; Correcton of the boundary condtons n accordance wth result of comparson (see Fgure 12). The teratons were made untl the agreement between the calculatons and experment. The allowable dfference between the data were not than 5% (see Fgure 11). Temperature T, C 450 400 350 300 250 200 150 100 50 0 nner col out col outpole out guard rng mountng flange thermal screen Measurement Smulaton Fgure 11. Fnal dfference between the data Fnally the calculated temperature dstrbuton was fully equvalent to the measured one. So that, one can conclude, that the boundary condtons selected for the fnal calculatons are correct and represents real parameters of the used hardware and can be for further analyss of smlar thrusters. The performed study allowed to get correct data about heat dsspaton n the thruster durng operaton. Heat flux from the dscharge and magnet col ohmc heatng dd not exceed 17% of total electrc power consumpton value of 1800 W. Values of emssvty factor for thruster surfaces (shown n the Table) has been determned as a result of performed analyss. Table 4. Boundary condtons Data base structure Element Value ε Value Q, W Out guard rng (nner sde) 0.95 Out guard rng (out sde) 0.88 Inner guard rng (nner sde) 0.91 Inner guard rng (out sde) 0.97 Anode (nner sde) 0.25 Anode (out sde) 0.21 90 Frst stage cathode (nner sde) 0.20 Frst stage cathode (out sde) 0.24 40 ect 8
VI. Concluson Dedcated study of two stage anode layer thruster thermal mode has been performed. By the comparson of expermental data and results of calculatons thermal boundary condtons and emssvty of the thruster surfaces have been determned and proven. Obtaned data base s the one necessary as well as for further thruster operaton mode and desgn mprovement as for development of a new thrusters mplementng two stage scheme. Fgure 12. THeat1 fnal smulaton results (presented temperature has averaged by thruster parts) operate mode 9
References 1 Solodukhn A.E., Semenkn A.V. "Study of dscharge channel eroson n mult mode anode layer thruster", IEPC 2003-0204, 28th Internatonal Electrc Propulson Conference, March 17-21, Toulouse, France. 2 Solodukhn A.E., Semenkn A.V. "Operaton of Two-stage Thruster wth Anode Layer n "Floatng Electrode" scheme", IEPC 2005-0145, 29th Internatonal Electrc Propulson Conference. 10