DSMC Method and Its Application Þ...qsol = solar constant rth = radius of thrust throat r0 = radius of thruster exit T0 = chamber temperature x , y,z = coordinates t = time step T

AIAA JOURNAL

Vol 42 No 8 August 2004

Direct Simulation Monte Carlo Analysisof Thruster PlumesSatellite Base Region Interaction

Jae Hyun Parklowast and Seung Wook Baekdagger

Korea Advanced Institute of Science and Technology Daejon 305-701 Republic of Koreaand

Jeong Soo KimDagger

Korea Aerospace Research Institute Daejon 305-333 Republic of Korea

The interaction of thruster plumes with satellite components is investigated with emphasis on undesirable effectssuch as disturbance forcetorque thermal loading and species deposition in the Korea Multipurpose Satellite-II(KOMPSAT-II) base region The actual configuration of the satellite is simplified by the consideration of fourmajor components of hydrazine thrusters the S-band antenna and the surrounding ring For the numericalsimulation a fully unstructured three-dimensional discrete simulation Monte Carlo (DSMC) code is developedand validated The DSMC computation allows for examination of the detailed flowfield dynamics as well as thewall conditions which otherwise would not be possible from a simplified engineering analysis The computationsshow that the present thruster arrangement used in KOMPSAT-II incurs a negligible disturbance forcetorque andthermal loading compared with its nominal thrusttorque and solar heating The simulations also indicate that thespecies deposition is insignificant due to the high surface temperature of the satellite body Of the chemical speciesconsidered (H2 N2 and NH3) more H2 molecules collide with the S-band antenna cone This study clearly showsthe usefulness of DSMC calculations for analysis of plume effects in the development phase of a satellite

NomenclatureP0 = chamber pressureqsol = solar constantrth = radius of thrust throatr0 = radius of thruster exitT0 = chamber temperaturex y z = coordinatest = time stepσT = thermal accommodation coefficient

Subscript

BOL = beginning of life

Introduction

S ATELLITE motion is usually controlled by gas exhaustion fromthe thrusters into near-vacuum surroundings Then an unde-

sirable interaction between plume and spacecraft body may causeconsiderable adverse effects such as disturbance forcetorque ther-mal loads and contamination of sensitive equipment and sensorsBecause these effects would result in a reduction of the satellitemission lifetime their accurate modeling and predictions are veryimportant at the design stage of a satellite12

Received 16 April 2003 revision received 14 November 2003 acceptedfor publication 14 November 2003 Copyright ccopy 2004 by the AmericanInstitute of Aeronautics and Astronautics Inc All rights reserved Copiesof this paper may be made for personal or internal use on condition that thecopier pay the $1000 per-copy fee to the Copyright Clearance Center Inc222 Rosewood Drive Danvers MA 01923 include the code 0001-145204$1000 in correspondence with the CCC

lowastPhD Candidate Division of Aerospace Engineering 373-1 Kusung-dong Yusung-ku currently Postdoctoral Associate Beckman Insti-tute for Advanced Science and Technology University of Illinois atUrbanandashChampaign 405 North Mathews Avenue Urbana IL 61801jaeparkuiucedu Member AIAA

daggerProfessor Division of Aerospace Engineering 373-1 Kusung-dongYusung-ku swbaekkaistackr Senior Member AIAA

DaggerPrincipal Researcher Satellite Research and Development DivisionYusung-ku currently Professor School of Mechanical and Automotive En-gineering Sunchon National University 315 Maegok Sunchon Jeonnam540-742 Republic of Korea jskimsuchonackr Member AIAA

The examination of the interaction between the exhausted plumeand the satellite components through ground-based experiments isquite complicated and expensive because it requires constructionand operation of high vacuum facilities to reproduce the desired op-erating conditions such as nozzle pressure ratio and MachReynoldsnumber at the nozzle exit As a result a numerical analysis ispreferred Among many numerical methods the direct simulationMonte Carlo3 (DSMC) technique is usually adopted for this kindof problem because the flowfield around a satellite involves a broadrange of flow regimes from the near continuum in the vicinity ofthe nozzle exit through the transitional regime to free-molecularflow in the region far from the nozzle

Many researchers have investigated the fundamental character-istics of plume exhaust by comparing DSMC results with the ex-perimental data145 However recent studies concentrate more onthe plume interactions in realistic spacecraft missions Lumpkin etal6 and Rault7 examined plume effects in the shuttleMir dockingwhereas Giordano et al8 considered the x-ray multimirror mission(XMM) satellite Gatsonis et al9 investigated the induced pressureenvironment incurred by the firing of small cold-gas altitude con-trol thrusters onboard the suborbital environment monitor package(EMP) spacecraft Other than the use of a DSMC method a sim-plified plume analysis method10 was developed earlier based onthe approximate relations11minus13 and continuum analysis HoweverMarkelov et al14 have pointed out that such an approach may causelow accuracy in the analysis of a practical complex system becauseit neglects some physical phenomena such as semishadow and mul-tiple reflections

Previous DSMC studies regarding satellites have usually focusedon the nominal influences by the plume rather than its undesir-able side effects89 Given these factors in the present study theinteraction between the thruster plume and the satellite base regionis investigated by the use of the DSMC method with emphasison the estimation of plume disturbance effects To deal success-fully with the extremely complicated configuration of the satellitebase region (in which the thrusters are installed and most exhaustgas mixture resides) a three-dimensional unstructured DSMC codeis developed and validated through comparison with experimentaldata It is then applied to the base region of the Korea Multipur-pose Satellite-II (KOMPSAT-II) with firing thrusters The exhaustedplume interacts with various base region components such as the

1622

PARK BAEK AND KIM 1623

dual thruster module DTM S-band antenna adapter ring uppermarmon ring etc Throughout this study the flow structure insidethe base region is investigated for diverse operating conditions andthe consequential dynamic and thermal disturbances are discussedBased on the present numerical results we can determine whetheror not the DTMs are optimally arranged in the base region of theKOMPSAT-II

KOMPSAT-II and Problem DefinitionThe KOMPSAT project is a Republic of Korea government pro-

gram to establish the space technology of the Republic of Koreastarting from a mission of Earth observation The first model(KOMPSAT-I) was already designed manufactured and success-fully launched and the upgraded second model (KOMPAST-II) iscurrently being developed The overview of KOMPSAT-II is shownin Fig 1a The KOMPSAT-II propulsion system (PS) employs a 10-lbf (445 N) MRE-1 monopropellant hydrazine liquid rocket engineThe thrusting impulse is provided by the catalytic decomposition ofmonopropellant grade hydrazine (N2H4) in a propellant tank andthe combustion products therefore consist of H2 N2 and NH3Its actual configuration is shown in Fig 1b Only the major com-ponents in Fig 1b are considered in the DSMC computation suchas the S-band antenna DTM propulsion platform upper marmon

a)

b)

Fig 1 Actual configuration of KOMPSAT-II a) overview and b) magnified view of base region and major components therein

ring and adapter ring The exhaust plumes from the thrusters inthe DTM interact with those satellite components For an efficientgeneration of necessary thrustmomentum each thruster is inclinedto the xz plane (base plate) by 16 deg and is parallel to the yz planeThe exit plane of the thruster is tilted outward (+y or minusy) by 30 degConsequently the angle between the base plate and the normal vec-tor of the thruster exit plane is 14 deg In this study the flowfieldin the KOMPSAT-II base region is obtained under various operat-ing conditions by application of the DSMC method Results fromthe computations are used to estimate and discuss the undesirableplume interaction effects such as disturbance forcetorque thermalloading and species deposition

DSMC Method and Its ApplicationThe basic algorithms in DSMC are well described by Bird3 In

this study a three-dimensional DSMC code is developed by theuse of a fully unstructured grid system to deal with severe ge-ometrical complexity in the satellite base region The simulatedparticles are traced via the intersection between the particle trajec-tory and the faces of the computational cells being sought15 Thevariable hard sphere (VHS) model is used for molecular collisionwhereas the no time counter (NTC) method is employed for collisionsampling For the calculation of internal energy exchange between

1624 PARK BAEK AND KIM

the colliding molecules the BorgnakkendashLarsen phenomenologicalmodel is adopted Because the medium temperature inside the baseregion is relatively low rotational excitation is considered onlywhereas chemical reaction and vibrational modes are neglectedThis is justified because Kewley16 reported that chemical reactionand vibrational energy became frozen just beyond the nozzle throatThe unstructured grid system is obtained from a commercial pack-age called GRIDGEN17 using the Delaunay technique The cell sizeis carefully determined to be smaller than the local mean free pathin every cell The developed code is implemented on a personalcomputer cluster in which message passing interface18 (MPI) andMETIS19 software are used for data communication between pro-cessors and domain decomposition respectively

Similar to previous work2021 the present code is validated throughcomparison with experimental data for a three-dimensional nitro-gen plume impingement The schematic of this problem is givenin Fig 2 For the DSMC computation the inlet flow at the orificeis modeled as a uniform stream along the plume axis in whichnegligible boundary-layer effects are assumed The inlet propertiesare therefore calculated from isentropic relations for the stagna-tion conditions of 1000 Pa and 300 K The impingement surfaceis modeled as a fully diffuse wall with full thermal accommoda-tion (σT = 10) and the fully unstructured grid system is obtainedfrom GRIDGEN The typical computing conditions in this problemare as follows grid cells = 30000 number of particles = 100000transient steps = 150000 and sampling steps = 5000

In Fig 3 the present and previous DSMC results are comparedwith the experimental data for β = 45 deg Figure 3 reveals threecomparisons for surface pressure shear stress and heat flux distri-butions along the wall and shows strong a similarity between thepresent DSMC results the experiments and previously reportedDSMC results21 Although not shown here comparisons were alsomade for β = 0 and 90 deg and the results were also found to becomparably accurate

Fig 2 Schematic of plume impingement problem

a) b) c)

Fig 3 Comparisons between experiment previous DSMC data21 and present DSMC result for plume impingement with β = 45 deg a) surfacepressure b) surface shear stress and c) surface heat flux

Analysis by Engineering MethodAlong with DSMC analysis an engineering analysis was per-

formed by ASTRIUM-France for the present problem2 Theirapproach follows the well-established classical plume analysisprocedure2223 The prediction of the plume effects by ASTRIUMin France consists of two steps first the plume flowfield visualiza-tion and second the plume impingement calculation The flowfieldsimulation begins with the analysis of the combustion chamber Thechemical compositions and physical properties are calculated underthe assumption of thermodynamic as well as chemical equilibriumThe chamber pressure and temperature are computed as P0 = 98bar and T0 = 975 K for the typical nominal thrust of 323 N andmass flow rate of 00015 kgs respectively24 The resultant molefraction of H2 N2 and NH3 are 0664 0333 and 00377 as listedin Table 1

The subsonic and supersonic flowfield inside the thruster nozzle issimulated by the solution of the axisymmetric NavierndashStokes equa-tion The medium is modeled as a single specie with averaged den-sity and properties based on equilibrium compositions The vicinityof the nozzle exit is analyzed under the assumption of inviscid flowSuch an approach is known to be more suitable for a small thruster(less than 20 N in thrust) such as the MRE-1 in this study ratherthan a method of characteristics (MOC) analysis The accuracy ofthe NavierndashStokes and Euler solvers at ASTRIUM-France has al-ready been confirmed through comparison of their numerical resultswith experimental data for various thrusters other than the 10-lbfmonopropellant rocket engine The continuum flow at the nozzleexit is expanded into space by a source flow method1213

Figure 4 shows the exit properties from the engineering methodThese are also utilized as the thruster outlet conditions for the DSMCcomputation in the following section Because the adiabatic condi-tion is imposed on the nozzle wall the temperature drastically in-creases across the boundary layer whereas the axial velocity shrinksto zero However the density has its maximum near the edge ofboundary layer where the high velocity and the low medium temper-ature are observed In correspondence with the density profile theKnudsen number reaches a minimum there When the grid systemis generated for the particle simulation the cell size at the vicinityof the thruster exit should be set sufficiently smaller than the localmean free path to guarantee good accuracy

The flowfield properties resulting from the source point methodin the first step are utilized as the input condition for the

Table 1 Chamber condition and species compositionof combustion product for KOMPSAT-II thruster

Property Value

Chamber pressure 98 barChamber temperature 975 KOperating thrust 323 NOperating mass flow rate 00015 kgsSpecies composition H2N2NH3 = 0664033300377


a)

b)

c)

d)

Fig 4 ASTRIUM-Francersquos results for nozzle exit properties of MRE-1 thruster at a given chamber conditions of P0 = 98 bar and T0 = 975K (ASTRIUM-France analysis does not consider each species of combustion mixture mean free path computed based on averaged density andmolecular diameter of mixture) a) number density b) temperature c) velocity and d) mean free path

a) Wall heat flux b) Wall pressure

Fig 5 Analysis by engineering method only one thruster (inside circle) in on mode others in off mode a) wall heat flux and b) pressure distribution(in ASTRIUM-Frances analysis base region of satellite simplified by considering four thruster modules S-band antenna and surrounding ring onlyentire satellite body has not been taken into account in the computation)

DSMC estimation Of course the whole geometry is discretizedinto a number of elements The gas stream at impingement isclassified according to the local Knudsen number Then theforce mass flux and heat transfer at the element are distinc-tively obtained from Newtonrsquos theory for the continuum regimeor the gas kinetic theory for free-molecular flows If it is inthe translational regime a local bridging method is adopted11

Also the total dynamic thermal and contamination effects are

determined by summation of all of the elemental disturbanceproperties

Figure 5 shows the distribution of wall heat flux and pressurecaused by firing of a single thruster located in x gt 0 and y gt 0 ofthe satellite coordinate system Higher pressure and heat flux arefound only at some parts of the S-band antenna surrounding ringand base plate close to the on-mode thruster The molecules emittedfrom the thruster keep traveling freely until they arrive at the solid


surface Table 2 lists the disturbance forcetorque and maximumwall heat flux when only one primary thruster in x gt 0 and y gt 0 isbeing fired Disturbance force and torque are defined by

Fdisturbance =int

surface

f dS (1)

τdisturbance =int

surface

(r times f ) dS (2)

where Fdisturbance is the total disturbance force over the KOMPSAT-IIbase regionτ disturbance is the total disturbance torque with respect to agiven reference position f is the force acting on the surface elementand r is the distance vector from the reference position In the presentstudy the torque is computed with respect to beginning of life (BOL)mass center at the beginning stage of operation Its position is givenby (xBOL yBOL zBOL) = (minus978 minus192 minus7751) mm if the originis set at the center of the base plate The center of mass of a satellitechanges during the mission due to the continuous consumption ofpropellant

However the engineering analysis may not be proper for a morepractical situation like the simultaneous firing of multiple thrustersin rarefied surroundings in which the plumeplume interaction andspecies separation would be significant

Results and DiscussionThe DSMC code validated in the preceding section is applied to

the flowfield analysis for the KOMPSAT-II base region For the nu-

Table 2 Disturbance forcetorque and maximum thermal loadingfrom the engineering analysis by ASTRIUM-Francea

Propertyb x y z

Main thrust N 0 minus0783 314Disturbance force N 397 times 10minus3 136 times 10minus2 169 times 10minus3

Main torque N middot m minus0427 minus0596 minus0149Disturbance torque N middot m 127 times 10minus2 minus402 times 10minus3 165 times 10minus3

aResult is for case in which only one primary thruster in x gt 0 and y gt 0 is being firedbMaximum wall heat flux asymp 150 Wm2

Fig 6 Simplified configuration of satellite base region for DSMC simulation schematic consists of triangular grid system on the satellite surface

merical simulation the actual configuration in Fig 1 is simplifiedby choosing only the major equipment and structural parts such asthe S-band antenna adapter ring upper marmon ring propulsionplatform and four primary thrusters Figure 6 presents the modelconfiguration and its surface grid system used in this study The un-desirable plume effects on the satellite originate primarily from theplumesatellite interaction in the base region whereas the contribu-tion by outside molecules is negligible Therefore the surroundingvacuum does not have much involvement with the total computa-tional domain It is extended to just 09 m in radius 01 m in depthand 05 m in height from the base region of KOMPSAT-II As aboundary condition the surface temperature of each component inTable 3 is determined by the values at the worst condition duringKOMPSAT-II maneuvering24 The worst condition corresponds tothe coldest condition during the mission such as when the satellitehas the smallest solar heat flux the smallest thermal absorption bythe satellite surface and the smallest heat dissipation through theelectrical equipment Because the operating altitude of KOMPSAT-II ranges from 670 to 700 km the environment is assumed to bea vacuum Consequently all of the boundaries except for the solidwall are presumed as a particle sink in the DSMC computationNumerical calculations are performed for four representative mis-sion conditions as listed in Table 4 In case A all four thrusters arefired simultaneously to produce the maximum thrust which cor-responds to orbit transfer The other cases B C and D are madeby a combination of two thrusters in on mode and the other twoin off mode to achieve the required attitude control motion of thesatellite

Table 3 Temperature of satellite componentsin the base region at worst case

Satellite component TemperatureC

S-band antenna minus330Propulsion platform (MLI)a minus1350DTM (MLI) minus960Upper marmon ring minus130Adapter ring (MLI) minus122

aMultilayer insulation blanket (MLT)


Fig 7 Distribution of density (kilograms per cubic meter) in the satellite base region for case A a) x = minusminus018 m b) x = 0 m c) x = 018 m d) z =02 m e) z = 03 m and f) z = 04 m

Table 4 Operating conditions considered

Case TH1P TH2P TH3P TH4P

A On On On OnB On On Off OffC On Off On OffD On Off Off On

The present DSMC computations do not include the flow in-side the thruster nozzle that is the nozzle exit is regarded as par-ticle source The Knudsen number at the nozzle exit is computedbased on the exit diameter The nozzle exit properties as shownin Fig 4 indicate that the thruster nozzle exit flow can be con-sidered to be near continuum Therefore the DSMC approach isused over the whole base region rather than by division of thisregion into separate continuum and rarefied regimes The compu-tational domain consists of about 120000 cells and the numberof simulated particles amounts to about 320000 at steady stateHowever a large number of computing cells is concentrated inthe central area to resolve the plumeplume interaction there ac-curately A sufficient number of molecules per cell (ge10) is main-tained in the central region of the flow and flow properties areaveraged over a large number of sampling steps (Nsmp = 5000) tominimize statistical scatter The domain is divided into several sub-domains for parallel implementation accordingly The time step isselected as t = 75 times 10minus8 s and this value is sufficiently smallcompared to the collision time in every computational cell Steadystate is typically accomplished after 5000 transient steps An ad-ditional 10000 sampling steps are conducted to obtain the time-averaged flow properties All of the solid boundaries in the baseregion are modeled as a diffusely reflected surface with completeenergy accommodation The microscopic properties of participat-ing species are taken from those in Birdrsquos text3 The simulatedparticles are initially introduced through the firing thrusters andspread over the empty space As indicated in the preceding section

ASTRIUM-Francersquos equilibrium NavierndashStokes simulation data forthe MRE-1 thruster are used as the nozzle exit conditions for DSMCcomputation

Figure 7 shows the density distributions in the base region for caseA Because the vacuum environment is assumed all four thrusterplumes expand rapidly near the thruster nozzle tip Because of theblockage by the surrounding ring most combustion products aredistributed inside the base region where the z coordinate is shorterthan the height of the surrounding ring and then expand primarilydownward in the +z direction whereas only a tiny amount of the gasstream moves toward the upper parts of the satellite As they spreadout along the downstream direction each exhaust plume merges withthe adjacent one Thereby two-high density zones appear inside thebase region as seen in Fig 7d The one in the +x side is formed by theplumes from thruster 1P (TH1P) and thruster 4P (TH4P) whereasthe other in the minusx side is from thruster 2P (TH2P) and thruster3P (TH3P) The two-high density zones formed inside the baseregion are again combined in the outside of the base region wherethe z coordinate is longer than the height of the surrounding ring(Figs 7e and 7f) In the engineering approach by ASTRIUM-Francethese plumeplume interactions cannot be taken into considerationand they may lead to lower accuracy in the analysis of a practicalapplication

Figure 8 shows a distribution of translational temperature forcase A Because a large number of molecules reside inside the baseregion the translational temperature there does not diminish signif-icantly with respect to the exit value A high temperature of over400 K is found in the vicinity of the S-band antenna cone along thex axis due to the strong molecular stream from the nearby high-density zones Although not shown here the distribution of rota-tional temperature is qualitatively similar to that of the translationalone

The density distribution strongly affects the surface propertiessuch as pressure and heat flux distribution Figure 9 shows surfaceheat flux distribution for case A Figure 9 consists of distributionson five components as follows 1) S-band antenna and four thrusters


Fig 8 Distribution of translational temperature (kelvin) in the satellite base region for case A a) x = minusminus018 m b) x = 0 m c) x = 018 m d) z = 02 me) z = 03 m and f) z = 04 m

Fig 9 Distribution of wall heat flux (watts per square meter) in the satellite base region for case A a) three-dimensional view (+x) b) three-dimensionalview (minusminusx) c) three-dimensional view with base plate d) surrounding ring inside and e) surrounding ring outside


Fig 10 Surface distribution of wall species H2 number (per second square meter) flux in the satellite base region for case A a) three-dimensionalview (+x) b) three-dimensional view (minusminusx) c) three-dimensional view with base plate d) surrounding ring inside and e) surrounding ring outside

Table 5 Maximum values of wall properties for variousoperating conditions for maximum wall heat flux

watts per square meter

Case S-band antenna Inner surrounding ring

A 9065 7705B 5275 6950C 5859 5852D 8824 5129

(viewing from +x side) 2) S-band antenna and four thrusters (view-ing from minusx side) 3) antenna thrusters and base plate 4) inner sur-rounding ring and 5) outer surrounding ring In Fig 9 whereas twohigh heat flux zones are observed on the S-band antenna along thex axis the top periphery of the inner surrounding ring is also heatedup along the y axis The S-band antenna is strongly influenced bythe two nearby high-density zones each of which is generated by apair of thrusters at the same x location However the two thrustersat the same y location mostly affect the inner surrounding ringIn Table 5 the maximum heat fluxes on S-band antenna and innersurrounding ring are compared for the operating conditions in thisstudy The largest heat flux is found on the S-band antenna in caseA where all four thrusters are fired However its value of 100 Wm2

is quite small compared with the solar constant of qsol = 1353 Wm2

(Ref 25) It is therefore concluded that the thermal loading dueto impinging plumes on the satellite base region is negligible

As described in the preceding section the exhaust gas consistsof three major species of H2 N2 and NH3 Among them only thedistribution of H2 is presented in Fig 10 because N2 and NH3 arefound to be negligible compared with H2 in the base region NH3

is inherently expected to be so because its initial amount in the ex-haust mixture is very small as listed in Table 1 However for thecase of N2 its negligible quantity is due to species separation Inother words the light H2 molecules are remarkably separated fromthe main stream and expanded diffusely throughout the flow do-main whereas the heavy N2 molecules reside in the main flow and

Table 6 Maximum values of wall properties for variousoperating conditions for maximum number flux

number per second square meter


AndashH2 17626 times 1022 11619 times 1022

AndashN2 11128 times 1020 30890 times 1019

BndashH2 79878 times 1021 91489 times 1021

BndashN2 43066 times 1011 40393 times 1019

CndashH2 88575 times 1021 77215 times 1021

CndashN2 80557 times 1019 38465 times 1019

DndashH2 16425 times 1022 67032 times 1021

DndashN2 97642 times 1019 27360 times 1019

escape the base area without interfering with satellite structuresTable 6 compares the maximum number fluxes of H2 and N2 at theS-band antenna and inner surrounding ring for four cases Becauseof species separation the maximum value for N2 does not reach 1of that for H2 The position of the maximum number flux is almostthe same as that of the maximum thermal loading because greatermolecular impingement toward the wall can transfer more energyonto the wall Because in the DSMC results most of the heat istransported by lighter molecules of H2 the maximum wall heat fluxis smaller than that obtained from the engineering analysis whichmodels the medium as an overall mixture without the considerationof species composition For instance as seen in Table 2 the engi-neering approach yields the maximum heat flux of 150 Wm2 whenone thruster is fired However in the DSMC results it is still lessthan 100 Wm2 even though all four thrusters are simultaneouslyfired Consequently the engineering analysis is considered to havean inherent shortcoming in the investigation of details of the inter-action between the thruster plume and the satellite base region Thepoor estimation of flow properties may lead to severe error in thedesign stage

The final discussion for case A concerns contamination The cap-ture temperature for H2 is known to be only 4 K (Refs 26 and 27)


Fig 11 Distribution of wall heat flux (watts per square meter) in the satellite base region for case B a) three-dimensional view (+x) b) three-dimensional view (minusminusx) and c) surrounding ring inside

Fig 12 Distribution of wall heat flux (watts per square meter) in the satellite base region for case C a) three-dimensional view (+x) b) three-dimensional view (minusminusx) and c) surrounding ring inside

Fig 13 Distribution of wall heat flux (watts per square meter) in the satellite base region for case D a) three-dimensional view (+x) b) three-dimensional view (minusminusx) and c) surrounding ring inside

The present surface temperatures of the base region are much higherthan this even for the worst case Subsequently the H2 moleculesare hardly deposited on the solid walls and the contamination ofthe satellite base region may be negligible

Figures 11 12 and 13 show the distributions of wall heat fluxesfor cases B C and D respectively Similar to case A the highthermal loading zone is found over the S-band antenna cone as wellas around the periphery of the inner surrounding ring in all casesTheir distributions are strongly dependent on which thrusters arebeing fired For cases B C and D the total number of moleculescontained in the computing domain is about one-half of that forcase A however the maximum values of wall heat flux and numberflux are not linearly reduced because the interaction between theplumes results in its nonlinear behavior For case B in which onlythe TH1P and TH2P are being fired together the maximum heatflux on the inner surrounding ring is greater than that on the S-band antenna whereas the maximum heat flux is almost the same

on the inner surrounding ring and S-band antenna for case C asseen in Tables 5 and 6 As a result the maximum thermal loadingat the surrounding ring and antenna cone is influenced more by thepositions of thrusters Thus contrary to case B for case D in whichtwo close thrusters are being fired the stronger thermal loading isobserved on the antenna cone For case D although the total numberof occupied molecules is one-half of that for case A the maximumnumber flux is close to that for case A Note that the molecularnumber flux impinging on the hardware surface is closely related tothe thermal loading therein

Tables 7 and 8 list the disturbance force and torque and theirpercentage ratios to the nominal values respectively All of the ratiosare found to be less than 41 Such levels are known only rarely toinfluence the main satellite dynamics and propellant budget Basedon this it can be judged that the DTM equipped in KOMPSAT-IIare properly arranged to minimize the disturbance effects caused bythe plume


Table 7 Disturbance forcetorque vs nominal thrusttorque for various operating conditions

Parameter x y z

Case ANominal thrust N 0 0 12536Disturbance force N 1823 times 10minus2 1009 times 10minus2 minus23 times 10minus4

Nominal torque N middot m 2407 times 10minus2 minus01226 0Disturbance torque N middot m minus1817 times 10minus3 4297 times 10minus3 2041 times 10minus3

Case BNominal thrust N 0 minus15628 6286Disturbance force N 521 times 10minus3 19849 times 10minus3 23647 times 10minus5

Nominal torque N middot m 20063 minus61301 times 10minus3 minus15284 times 10minus2

Disturbance torque N middot m 35857 times 10minus3 99724 times 10minus3 minus96059 times 10minus4

Case CNominal thrust N 0 0 6286Disturbance force N 6281 times 10minus3 38048 times 10minus3 14126 times 10minus5

Nominal torque N middot m 1203 times 10minus2 minus61301 times 10minus3 minus28130 times 10minus1

Disturbance torque N middot m minus6022 times 10minus4 3368 times 10minus3 2087 times 10minus3

Case DNominal thrust N 0 0 6286Disturbance force N 124 times 10minus2 6989 times 10minus3 minus33 times 10minus4

Nominal torque N middot m 1203 times 10minus2 minus11895 0Disturbance torque N middot m 1985 times 10minus3 16094 times 10minus3 6103 times 10minus4

Table 8 Percentage ratio of disturbancesto their nominal values

Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022

ConclusionsIn this study a DSMC analysis of the interaction between the

exhaust plumes and the satellite base region has been performed Tothis end a three-dimensional DSMC code was developed by the useof an unstructured grid system and validated by comparison withexperimental meaasurements and other DSMC calculations ThisDSMC code was then applied to the analysis of the KOMPSAT-II base region with four hydrazine thrusters S-band antenna andinner and outer surrounding rings With dependence on the com-bination of firing thrusters four operating conditions were consid-ered For each case the detailed flowfield and surface propertieswere visualized and the resultant undesirable effects such as thedisturbance forcetorque and thermal loading were estimated anddiscussed Heat flux due to molecule impingement was found tobe significant on both the inner surrounding ring and S-band an-tenna Their maximum value was totally dependent on the degree ofplumeplume interaction determined by the thruster position How-ever the quantitative comparison concluded that the disturbanceforcetorque as well as thermal loading were all negligible withrespect to their nominal thrusttorque and solar heating In otherwords the placement of the DTM is such that undesirable effectsby plume interaction are expected to be small and within tolerablelevels Among three species in the exhaust gas only considerableamounts of H2 were observed to reach the S-band antenna becauseof species separation effects However H2 deposition onto the conesurface hardly occurred because the surface temperature was toohigh to capture H2 molecules Furthermore it was also found thatthe maximum heat flux estimated from an engineering analysis washigher than that from the DSMC computation

AcknowledgmentsThe authors gratefully acknowledge the financial support of the

Agency for Defense Development and the Center for ElectroOpticsat the Korea Advanced Institute of Science and Technology

References1Boyd I D and Stark J P W ldquoModeling of a Small Hydrazine Thruster

Plume in the Transition Flow Regimerdquo Journal of Propulsion and PowerVol 6 No 2 1990 pp 121ndash126

2Puyoo O Theroude C and Cheoux-Damas P ldquoPlume Im-pingement Analysis on the KOMSAT-2 Spacecraftrdquo ASTRIUMMOSNTOP368275201 Toulouse France Feb 2002

3Bird G A Molecular Gas Dynamics and the Direct Simulation of GasFlows Clarendon Oxford 1994

4Boyd I D Penko P F Meissner D L and DeWitt K J ldquoExperi-mental Investigations of Low Density Nozzle and Plume Flows of NitrogenrdquoAIAA Journal Vol 30 No 10 1992 pp 2453ndash2461

5Chung C H Kim S C and Stubbs R M and DeWitt K J ldquoLow-Density Nozzle Flow by the Direct Simulation Monte Carlo and ContinuumMethodsrdquo Journal of Propulsion and Power Vol 11 No 1 1995 pp 64ndash70

6Lumpkin III F E Stuart P C and LeBeau G J ldquoEnhanced Analysisof Plume Impingement During ShuttlendashMir Docking Using a CombinedCFD and DSMC Methodologyrdquo AIAA Paper 96-1877 June 1996

7Rault D F G ldquoMethodology for Thruster Plume Simulation and Im-pingement Effects Characterized Using DSMCrdquo AIAA Paper 95-2032 June1995

8Giordano D Ivanov M Kashkovsky A Markelov G Tumino Gand Koppenwallner G ldquoApplication of Numerical Multizone Approach tothe Study of Satellite Plumesrdquo Journal of Spacecraft and Rockets Vol 35No 4 1998 pp 502ndash508

9Gatsonis N A Nanson R A and Lebeau G J ldquoSimulations ofCold-Gas Nozzle and Plume Flows and Flight Data Comparisons Journalof Spacecraft and Rockets Vol 37 No 1 2000 pp 39ndash48

10Koppenwallner G Johannsmeiwe D Klinkrad H Ivanov M andKashkowski A ldquoA Rarefied Aerodynamic Modelling System for EarthSatellites (RAMSES)rdquo Proceedings of the 19th International Symposiumon Rarefied Gas Dynamics edited by J Harvey and G Lord Oxford UnivPress Oxford 1995 pp 1366ndash1372

11Matting F W ldquoApproximate Bridging Relation in the TransitionalRegime Between Continuum and Free-Molecular Flowsrdquo Journal of Space-craft and Rockets Vol 8 No 1 1971 pp 35ndash40

12Mayer E Hermel J and Rogers A W ldquoThrust Loss Due to PlumeImpingement Effectsrdquo Journal of Spacecraft and Rockets Vol 23 No 61986 pp 554ndash560

13Mirels H and Mullen J F ldquoExpansion of Gas Clouds and HypersonicJet Bounded by a Vacuumrdquo AIAA Journal Vol 1 No 3 1963 pp 596ndash602

14Markelov G N Kashkovsky A V and Ivanov M ldquoSpace StationMir Aerodynamics Along the Descent Trajectoriesrdquo Journal of Spacecraftand Rockets Vol 38 No 1 2001 pp 43ndash50

15Dietrich S and Boyd I D ldquoScalar and Parallel Optimized Implemen-tation of the Direct Simulation Monte Carlo Methodrdquo Journal of Computa-tional Physics Vol 126 1996 pp 328ndash342

16Kewley D J ldquoPredictions of the Exit Conditions Including SpeciesConcentrations and the Ratio of Specific Heats of Hydrazine DecompositionThrustersrdquo DFVLR Internal Rept IB 222-85 A05 Gottingen Germany1985


17ldquoGRIDGEN User Manualrdquo ver 133 Pointwise Inc Fort Worth TX1997

18Gropp W and Lusk E ldquoUserrsquos Guide for mpich a Portable Im-plementation of MPIrdquo Argonne National Lab ANLMCS-TM-ANL 966Argonne IL 1996

19Karypis G and Kumar V ldquoMETIS A Software Package for Par-titioning Unstructured Graphs Partitioning Meshes and Computing Fill-Reducing Orderings of Sparse Matricesrdquo Dept of Computer Science andEngineering Univ of Minnesota Minneapolis MN Sept 1998 also URLhttpwwwcsumnedusimkarypis [cited 26 April 2004]

20Hyakutake T and Nishida M ldquoDSMC Simulation of ParallelOblique and Normal Free Jet Impingements on a Flat Platerdquo Transactionsof Japan Society of Aeronautics and Space Science Vol 43 No 139 2000pp 1ndash7

21Kannenberg K C and Boyd I D ldquoThree-Dimensional Monte CarloSimulations of Plume Impingementrdquo Journal of Thermophysics and HeatTransfer Vol 13 No 2 1999 pp 226ndash235

22Cheoux-Damas P and Koeck C ldquoThermal Effects of Plume Impinge-mentrdquo Proceedings of the 3rd European Symposium on Space Thermal Con-trol and Life Support Systems SP-288 ESA Noordwijk The Netherlands1988 pp 273ndash279

23Theroude C Maag M-C and Cheoux-Damas P ldquoSpace-craftThrusters Interaction New Models for Chemical Propulsionrdquo Pro-ceedings of 3rd International Conference on Spacecraft Propulsion SP-465ESA Noordwijk The Netherlands 2000 pp 609ndash618

24Kim J S ldquoTechnical Information on Input and Requirements for Out-put Generation Plume Analysis KOMPSAT-IIrdquo Korea Aerospace ResearchInst KS-D0-460-010 Taejon Republic of Korea Oct 2001

25Modest M F Radiative Heat Transfer McGrawndashHill New York1993 Chap 1

26Barewald R K and Passamaneck R S ldquoMonopropellant ThrusterPlume Contamination Measurementsrdquo Jet Propulsion Lab JPL PublicationCalifornia Inst of Technology Pasadena CA Sept 1997

27Cheoux-Damas P Theroude C and Ounougha L ldquoContaminationModelling in Space Environmentrdquo Proceedings of the 6th International Sym-posium on Material in a Space Environment SP-368 ESA Noordwijk TheNetherlands 1994 pp 45ndash50

C KaplanAssociate Editor


dual thruster module DTM S-band antenna adapter ring uppermarmon ring etc Throughout this study the flow structure insidethe base region is investigated for diverse operating conditions andthe consequential dynamic and thermal disturbances are discussedBased on the present numerical results we can determine whetheror not the DTMs are optimally arranged in the base region of theKOMPSAT-II

KOMPSAT-II and Problem DefinitionThe KOMPSAT project is a Republic of Korea government pro-

gram to establish the space technology of the Republic of Koreastarting from a mission of Earth observation The first model(KOMPSAT-I) was already designed manufactured and success-fully launched and the upgraded second model (KOMPAST-II) iscurrently being developed The overview of KOMPSAT-II is shownin Fig 1a The KOMPSAT-II propulsion system (PS) employs a 10-lbf (445 N) MRE-1 monopropellant hydrazine liquid rocket engineThe thrusting impulse is provided by the catalytic decomposition ofmonopropellant grade hydrazine (N2H4) in a propellant tank andthe combustion products therefore consist of H2 N2 and NH3Its actual configuration is shown in Fig 1b Only the major com-ponents in Fig 1b are considered in the DSMC computation suchas the S-band antenna DTM propulsion platform upper marmon

a)

b)

Fig 1 Actual configuration of KOMPSAT-II a) overview and b) magnified view of base region and major components therein

ring and adapter ring The exhaust plumes from the thrusters inthe DTM interact with those satellite components For an efficientgeneration of necessary thrustmomentum each thruster is inclinedto the xz plane (base plate) by 16 deg and is parallel to the yz planeThe exit plane of the thruster is tilted outward (+y or minusy) by 30 degConsequently the angle between the base plate and the normal vec-tor of the thruster exit plane is 14 deg In this study the flowfieldin the KOMPSAT-II base region is obtained under various operat-ing conditions by application of the DSMC method Results fromthe computations are used to estimate and discuss the undesirableplume interaction effects such as disturbance forcetorque thermalloading and species deposition

DSMC Method and Its ApplicationThe basic algorithms in DSMC are well described by Bird3 In

this study a three-dimensional DSMC code is developed by theuse of a fully unstructured grid system to deal with severe ge-ometrical complexity in the satellite base region The simulatedparticles are traced via the intersection between the particle trajec-tory and the faces of the computational cells being sought15 Thevariable hard sphere (VHS) model is used for molecular collisionwhereas the no time counter (NTC) method is employed for collisionsampling For the calculation of internal energy exchange between






a) b) c)








Property Value



a)

b)

c)

d)










Fdisturbance =int

surface

f dS (1)

τdisturbance =int

surface

(r times f ) dS (2)






Propertyb x y z




























A 9065 7705B 5275 6950C 5859 5852D 8824 5129





























Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022








































a) b) c)








Property Value



a)

b)

c)

d)










Fdisturbance =int

surface

f dS (1)

τdisturbance =int

surface

(r times f ) dS (2)






Propertyb x y z




























A 9065 7705B 5275 6950C 5859 5852D 8824 5129





























Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022




































a)

b)

c)

d)










Fdisturbance =int

surface

f dS (1)

τdisturbance =int

surface

(r times f ) dS (2)






Propertyb x y z




























A 9065 7705B 5275 6950C 5859 5852D 8824 5129





























Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022





































Fdisturbance =int

surface

f dS (1)

τdisturbance =int

surface

(r times f ) dS (2)






Propertyb x y z




























A 9065 7705B 5275 6950C 5859 5852D 8824 5129





























Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022





















































A 9065 7705B 5275 6950C 5859 5852D 8824 5129





























Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022











































A 9065 7705B 5275 6950C 5859 5852D 8824 5129





























Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022








































A 9065 7705B 5275 6950C 5859 5852D 8824 5129





























Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022













































Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022





































Parameter x y z












Case Thrust Torque

A 017 41B 009 053C 012 14D 023 022
















































Documents

DSMC Method and Its Application Þ...qsol = solar constant rth = radius of thrust throat r0 = radius of thruster exit T0 = chamber temperature x , y,z = coordinates t = time step T