Utilization of Universal Controls Analysis Tool and CFD in Parallel for a Cold Nozzle Flow

Transcription

1 46th AIAA/ASME/SAE/ASEE Joint Propulsion Confrnc & Exhibit 5-8 July 010, Nashvill, TN AIAA Utilization of Univrsal Controls Analysis Tool and CFD in Paralll for a Cold Nozzl Flow Jol M. Faur 1, Sunil Chintalapati, Niroshn Divitotawla 3, Danil R. Kirk 4 and Héctor Gutiérrz 5 Florida Institut of Tchnology, Mlbourn, FL, 3901 Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / DOF CFD LSP NIST QE UCAT A * A Cp Cv dt dt h h m& m M P a P P R T T T u Th NASA Knndy Spac Cntr Launch Srvics Program s Univrsal Controls Analysis Tool (UCAT) is usd to analyz th flight prformanc of a sris of spcific launch vhicls. In ordr to dmonstrat th modling tool as a uniqu Launch Srvics Program s capability, a sris of non-propritary, gnric launch vhicls that ar availabl in opn litratur. Currntly, th UCAT has various analytical modls, and lookup tabls for launch vhicls which do not yild high fidlity. Th purpos of this papr is to link UCAT with ANSYS FLUENT which will b abl to simulat a transint cold flow nozzl. This papr xplains th stps usd to validat th Analytical and CFD modls basd on xprimntal rsults of a conical cold flow nozzl. Thn a compar th Analytical and CFD modls for a largr cold flow nozzl. Finally, link UCAT with both analytical and CFD modls, and compar thir prformancs on a simpl launch vhicl. Nomnclatur = Six Dgrs of Frdom = Computational Fluid Dynamics = Launch Srvics Program = National Institut of Standards and Tchnology = Quadrant Elvation = Univrsal Controls Analysis Tool = Chok ara of nozzl = Exit ara of nozzl = Spcific hat at constant prssur of th control volum = Spcific hat at constant volum of th control volum = Tim rat chang of tmpratur in th control volum = Spcific nthalpy of th control volum = Exit (static) spcific nthalpy = Mass flow rat = Mass of control volum = Exit Mach numbr = Ambint Prssur = Chambr, or control volum prssur = Exit (static) Prssur = Gas constant = Thrust = Chambr, or control volum tmpratur = Exit (static) tmpratur of nozzl = Spcific intrnal nrgy of th control volum 1 Graduat Rsarch Assistant, Mchanical and Arospac Enginring Dpartmnt, Snior AIAA mmbr. Undrgraduat Rsarch Assistant, Mchanical and Arospac Enginring Dpartmnt, AIAA studnt mmbr 3 Graduat Rsarch Assistant, Mchanical and Arospac Enginring Dpartmnt, AIAA studnt mmbr. 4 Associat Profssor, Mchanical and Arospac Enginring Dpartmnt, Snior AIAA mmbr. 5 Associat Profssor, Mchanical and Arospac Enginring Dpartmnt. 1 Amrican Institut of Aronautics and Astronautics Copyright 010 by th Amrican Institut of Aronautics and Astronautics, Inc. All rights rsrvd.

2 u V γ ε ρ = Exit vlocity = Volum = Spcific hat ratio = Expansion ratio of xit ara to chok ara = Dnsity of control volum Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / I. Introduction h NASA Launch Srvic Program s (LSP) Univrsal Controls Analysis Tool (UCAT) is usd to analyz th T guidanc, navigation, and control dynamics of launch vhicls [1]. Many launch vhicls ar modld in UCAT, but all prsnt vhicl modls contain propritary information which prohibits th sharing of ths modls with potntial usrs and dvloprs or rporting th rsults in opn litratur. Florida Institut of Tchnology in clos collaboration with NASA LSP has dvlopd a gnric, non-propritary vrsion of UCAT which us launch vhicls that ar availabl in opn litratur. This modl could b shard with potntial usrs, shar with potntial dvloprs of nw faturs and capabilitis. UCAT is dvlopd undr Math Works Simulink program [], which nabls objct orintd programming which maks it asir to visualiz how crtain blocks of cod intract with th main program. Currntly most rockts ar simulatd at ground lvl which do not tak includ ambint atmosphric ffcts ovr th prformanc of thrust for rockt ngins. Equation 1 shows that th thrust quation is dirctly affctd by altitud which rquirs a non-linar kinmatic quation usd in UCAT. ( P P) T = m& u + A (1) a Th purpos of this documnt is to prov th importanc and capability of Computational Fluid Dynamics simulation running in paralll with UCAT for high fidlity rockt simulations. As th rockt taks off, th ambint conditions start to chang, and high acclrations not sn in static tst fir ar ncountrd. Th mthod of solution is to crat a CFD and Analytical modl basd on th xprimntal stup for a cold nozzl flow. Aftr both th Analytical modl and CFD agr with th xprimntal data, th nxt stp will b to scal th rockt with a significantly largr storag tank, and nozzl. Compar th Analytical and CFD modl togthr, and thn simulat both modls in UCAT. II. Validation Background Th intndd procdur for validation of th CFD modl was to tak th initial conditions for th Florida Tch air cylindr and compar th xprimntal data to th two modls (Analytical, and CFD). Th Florida Tch air cylindr is a prssurizd air aluminum cylindr 8 ft long and 8 inchs in diamtr capabl of raching prssurs up to 3.45 MPa (gaug) as sn in Figur 1. Figur 1. Florida Tch air cylindr fittd with a toroidal arospik nozzl for 3.45 MPa (gaug) tst fir Th tank is connctd to a solnoid ball valv which is connctd to a conical nozzl. Th Florida Tch air cylindr has bn xtnsivly tstd on th Florida Tch 6-DOF thrust stand which masurs forc and torqu along th longitudinal axis, and two additional forcs orthogonal to th longitudinal axis [3]. Th Florida Tch air cylindr was idal for comparison mainly du to th larg amounts of data collctd, availability, and known accuracy of th Amrican Institut of Aronautics and Astronautics

3 thrust stand. Th only portion of th thrust stand data of intrst was th thrust in th axial (longitudinal dirction). Th two computr modls wr dvlopd indpndntly and corrlatd wll with ach othr, howvr both did not match up to th xprimntal data as sn in Figur. Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / Figur. Comparison btwn CFD, Exprimntal, and Analytical rsults of th Florida Tch air cylindr Th discrpancis btwn th computr modls and th xprimntal rsults basd on th following diffrncs: th solnoid valv has a dlay for opning and shutting, th valv orific whn th valv is opn choks th air coming out of th tank, and unknown prssur drops across th valv. Ths diffrncs which ar not simulatd insid th computr modls would xplain ths discrpancis in th rsults. Th tim for th valv to opn and clos would affct th pak thrust bcaus th prssur, tmpratur, and mass insid th tank has alrady droppd. Bcaus of this addd complication it was dcidd to drop th xprimntal data and procd with validation btwn th Analytical and numrical modls xclusivly. Th concptual dsigns of th nozzl gomtry ar basd on th Florida Tch air cylindr. Aftr th validation of th Florida Tch air cylindr btwn th Analytical, and numrical modls hav bn mad, th nxt stp was to scal th tank, and nozzl to provid nough thrust to gt it off of th ground. Th nozzl throat ara and tank volum wr paramtrs that varid, until it has attaind a larg altitud without making th tank too larg and provid a transition of undr xpansion to ovr xpansion. Th dimnsions dtrmind from th Analytical modl ar usd insid th CFD modl, and Pro Enginr Wildfir 5.0 to gt th mass proprtis such as cntr of gravity location, and momnt of inrtia at th cntr of gravity. III. Analytical Stup Th Analytical modl simulats th transint ffcts insid th prssur tank, and uss stady-stat isntropic conditions for th xit conditions such as Mach numbr, xit prssur, and tmpratur. Th control volum ncompasss th tank, and th nozzl. Th contact surfac is only along th xit plan of th nozzl, with a ambint prssur forc bing applid to it. Th walls along th tank and nozzl ar adiabatic for simplicity. Whil many sourcs for th fluid proprtis of air xist, a dcision was mad to us th National Institut of Standards and Tchnology (NIST). Sinc air is not an availabl matrial proprty in th NIST databas, Nitrogn was usd as an analog. Svral scripts hav bn dvlopd at Florida Tch to xtract th isobaric data from NIST 3 Amrican Institut of Aronautics and Astronautics

4 onlin using MATLAB, organiz th data, and us th data as a 3-D lookup tabl. Th tim to xtract th data taks too long, though robust and accptd diffrnt typs of data inputs, a simplifid fastr program was dvlopd for this simulation which taks a mr fraction of th tim to output th ncssary data, howvr it rquirs prssur as an input, and any othr input such as tmpratur as an input for th lookup tabl function. First som input paramtrs ar rquird such as: fluid proprtis of nitrogn gas, xpansion ratio, chok ara, volum of th control volum which all should rmain as constants. Th tim snsitiv information for th simulation ar th following: ambint prssur, mass of th control volum, and tmpratur of th control volum. Th assumptions ar th following: idal gas, isntropic flow insid th nozzl, singl gas phas only, proprtis do no chang insid th nozzl (spcific hat ratio dos not chang at any point insid th nozzl), idal xpansion, inviscid flow, chokd flow only occurs, adiabatic conditions at th walls, and 1st law of thrmodynamics. Th Analytical solution is dtrmind by first to gt th molar mass, dnsity of th gas, and total prssur in th control volum as sn in Eqs. -3 [4]. Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / ρ = m V P =ρ R T Nxt go into th Florida Tch-NIST lookup tabl function and input both prssur and tmpratur of th control volum to gt th spcific intrnal nrgy, spcific nthalpy, spcific hat at constant prssur, and spcific hat at constant volum. Thn calculat th spcific hat ratio at constant volum as sn in Eq. 4 [4]. Cp = Cv γ (4) Nxt dtrmin whthr th flow is chokd by chcking th ambint prssur to chambr prssur ratio is gratr than th chokd flow condition as sn in Eq. 5 [4] which indicats that it is no longr chokd. If th flow is no longr chokd thn it outputs all zros, and xits th function, othrwis it will continu. Pa P γ γ 1 > γ + 1 Thn solv for th xit Mach numbr as sn in Eq. 6 [4] basd on isntropic conditions. ( γ+ 1) ( γ 1) 1 γ 1 ε (6) = M 1+ γ + 1 M M Mass flow of th nozzl is dpndnt on th following isntropic conditions at th chok point as sn in Eq. 7 [4]. () (3) (5) * ( γ+ 1) ( γ 1) A P m& = (7) R T γ γ + 1 Th xit prssur, and tmpratur, vlocity and static nthalpy ar dtrmind via isntropic rlations as sn in Eqs [4]. γ 1 γ γ 1 P = P 1+ M (8) 4 Amrican Institut of Aronautics and Astronautics

5 T u γ 1 1 = M γ R T = T + M h = h u 1 (9) (10) (11) Nxt calculat thrust using Eq. 1, and th tmpratur rat chang in Eq. 1 [5]. Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / dt dt = m m& Cp u h u Th thrust, mass flow, tim rat chang of tmpratur ar all outputtd to Simulink, which will thn tak th intgral of th mass flow, and tmpratur tim rat chang to b inputtd for th nxt tim stp. This will rpat until critrion has bn mt for ithr of th following: tim, thrust lvl, or chokd flow condition. Th intrfac for th propulsion block in Figur 3 for th mask and Figur 4 for th Simulink block diagram allows th usr to chang various paramtrs for th Analytical modl. (1) Figur 3. Mask of Analytical propulsion block Figur 4. Analytical block at sa-lvl IV. Computation Stup Th CFD simulations wr prformd using ANSYS FLUENT 1.1 [6]. Th D gomtry was cratd and mshd using Gambit (vrsion.4), prprocssor for FLUENT. Figur 5 shows th domain along with boundary conditions. All th simulation for th currnt papr was axi-symmtric. A doubl prcision, dnsity basd implicit solvr with a scond ordr discrtization for flow was prfrrd. Viscous modl usd was ralizabl k-psilon (two quation turbulnc) modl with standard wall function. Idal gas was usd for dnsity formulation and Suthrland 5 Amrican Institut of Aronautics and Astronautics

6 mthod was usd to comput viscosity. Tim-stp siz for th Florida Tch air cylindr simulation was 1-05 whil a tim-stp siz of 5-05 was usd for CFD at sa lvl and in-flight. Th whol tank was modld as an adiabatic wall boundary condition and th ambint surroundings wr st as prssur outlt boundary condition. Car was takn so that th prssur outlt boundary condition was far away from th nozzl xit and wouldn t affct th flow downstram. Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / Figur 5. Domain and boundary condition Th whol computational domain was mshd using structurd quad clls. Th total cll count for th currnt cas is clls (s Figur 5). Th msh dnsity was highr at th nozzl and th xit and spannd out to th outlt boundary conditions. Stady stat simulation with varying grid was compltd prior to transint simulation to chck for grid dpndncy of th simulation. A similar computational modl was usd in combind xtrnal and intrnal flow. Domain for this st-up is axisymmtric, doubl prcision, dnsity basd implicit solvr. Turbulnc is computd using ralizabl k-psilon modl. Domain of air rockt and clos up fatur of th rockt ar givn in Figur 6. Domain was cratd using structurd quad with total cll count around (s Figur 6). Static prssur and tmpratur chang du to altitud chang was incorporatd by updating gag static prssur and tmpratur trm in prssur-far fild boundary conditions at vry incrmntal tim-stp. Front nd Nozzl Domain with air rockt Figur 6. Domain and boundary conditions with clos look at rockt faturs Nozzl -clos 6 Amrican Institut of Aronautics and Astronautics

7 A. Prlim Computational Rsults Th initial convrgnc critria for stady stat cass wr 1-03 but th latr incrasd to 1-06 to improv th accuracy of th solution and chck for grid dpndncy. Transint simulation wr run on a ight cor machin running at 3.6 GHz with FLUENT using six cors and MATLAB using th othr two cor. Rsults from th Florida Tch air cylindr transint simulation ar shown blow in Figur 7. Prliminary analysis show th rsults agr with th thortical prdiction and th flow bhavior is in much agrmnt with thory. Rsults of th simulation wr compard with Analytical modl and xprimntal data givn in Figur. Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / Contours of Vlocity Magnitud Contours of static prssur Contours of dnsity Figur 7. Prliminary rsults; Florida Tch air cylindr transint simulation at 0. scond flow tim V. Rockt Simulation Procdur Th mthod of solution diffrd slightly dpnding on whthr it was a lookup tabl or in-flight for both Analytical, and CFD. Howvr th consistnt outputs wr mass flow, and axial thrust. Th axial thrust was put into a vctor, and th mass flow was intgratd and outputtd to th mass proprtis block, th cntr of gravity location, and momnt of inrtia ar a function of mass, and ar linarly intrpolatd. Th diffrncs vary btwn th inputs for th propulsion block, if th sa-lvl simulations for both th Analytical and CFD ar usd, thn tim is th only input rquird. Howvr for th in-flight Analytical simulation, th ambint prssur is th only xtrnal tim dpndnt input rquird. Th CFD rquirs th ambint Mach numbr, prssur and tmpratur as xtrnally tim dpndnt inputs. Th rockt simulation program, UCAT runs insid Simulink, at a fixd tim stp with a major tim stp siz of 1-4 sconds. Th solvr typ is Bogacki-Shampin a fixd-stp solvr, with minor tim stps which follows th squnc: 0, 0.5, and 0.75 of th major stp siz. Each minor tim stp rpats dpnding on th numbr of algbraic loops, th first of ths rpatd tim stps is usd in th Analytical, and CFD propulsion modul, whil oprating on th assumption that any diffrncs btwn rpatd tim stps would b too subtl, and would tak unncssarily long to comput for lss than marginally diffring rsults. Th Analytical modl dvlops th tim rat chang for both mass and tmpratur laving th rockt, and outputs th rsults to Simulink intgrator blocks which intgrats dpnding on th solvr slctd, in this cas it's th Bogacki-Shampin. Th mass, and tmpratur of th control volum ar fd back into th Analytical function, manwhil at any tim chang, th Analytical function looks into a data fil which savs th outputs of th function to a fil including th sampl tim, if th tim diffrnc btwn what's rcordd and sampl tim inputtd into th function diffrs by mor than sconds thn it calculats th output. Othrwis it outputs th valus from th data fil. Du to limitd oprational tim, th thrust is limitd from 0 to 0.6 sconds, aftr that tim has lapsd th function outputs 0 for all outputs simulating a valv instantly closing. Th CFD modl function is similar to th Analytical modl; th only diffrnc is that FLUENT dos all of th computations with th xcption of thrust calculation which is calculatd aftr convrgnc at vry tim stp. Th inputs ar th following: tim, logical thrshold, ambint Mach numbr, tmpratur and prssur. Whn th sampl tim is 0.5-4, (th first minor tim stp) and th monitor fils do not xist thn it initializs th CFD modl using th Florida Tch-FLUENT link. It computs th modls, and savs th data to a monitor fil. Thn it computs th thrust basd on th data collctd from th monitor fils, and outputs th rsults. If th sampl tim diffrnc is lss than 1-5 thn it calculats thrust basd on th prviously itratd monitor fil. Othrwis it taks th Mach numbr, ambint tmpratur and prssur, and adjusts th tim-stp siz to fit th diffrnc btwn what was in th monitor fil, 7 Amrican Institut of Aronautics and Astronautics

8 and th currnt sampl tim, and itrats. Thn th modl calculats thrust and continus until th logical condition has a non-zro valu (only occurs whn th sampl tim is gratr than 0.1 sconds), and th tim is gratr 0.6 sconds. Onc th tim has xcdd 0.6 sconds a logical oprator changs th output of thrust and mass flow to zro, and outputs a 1 which is thn addd to a logical output in Simulink, if this is th first occurrnc it outputs a sum of 1 to th function at th nxt tim stp, which outputs zro mass flow and thrust out of th propulsion block function, closs th CFD program, and outputs a 1 in th logical. Thn th output snds a sum of back into th function whr it outputs a 1 in th logical, and outputs only zro mass flow and thrust out, and no longr calls th CFD program anymor. Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / VI. Rsults All th simulations hav th sam simulation conditions, no wind, initial altitud is zro, and lvation angl st to QE 90 dgrs. Th sa-lvl Analytical and CFD modls ar pr-procssd and us tim as an xtrnal input for mass flow, and thrust. Th Analytical in-flight modl uss both tim, and ambint prssur as an xtrnal input. Th CFD in-flight modl uss tim, Mach numbr, and both ambint prssur and tmpratur as xtrnal inputs. Th Analytical modls hav vry littl diffrncs from ach othr du to th slight incras in altitud at burnout, which was causd by th ambint prssur bing lowr in-flight than th sa-lvl cas. In comparison to th CFD rsults th Analytical modl appars to ovr prdict th thrust, mass flow, and xit plan prssur diffrnc as sn in Figur 8. Figur 8. Thrust and Thrust componnts vs. Tim Th Analytical modl at sa-lvl appars to hav marginally total impuls and avrag thrust, howvr thir pak thrust is th sam. This is du to both modls having th sam altitud, and thus sam conditions at th instanc in tim which yild th sam rsults. Th CFD modls obviously hav lowr total impuls, pak thrust and avrag thrust. This is most likly attributd to th transint conditions in th CFD modl whil stady stat conditions ar utilizd in th Analytical modl. 8 Amrican Institut of Aronautics and Astronautics

9 Tabl 1. Motor prformanc of computational modls Modl Typ Total Impuls (kn s) Pak Thrust (kn) Avrag Thrust (kn) Analytical modl at sa-lvl Analytical modl in-flight CFD modl at sa-lvl CFD modl in-flight Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / Transint air rockt simulations ran on six cor machin, utilizing paralll capability of ANSYS FLUENT 1.1 [6]. Sampl of qualitativ rsults of th air rockt simulation at in-flight is givn blow in Figur 9, flow tim in th simulation is 0.3 sconds. Th top lft pictur is a zoomd viw of nozzl with contour of Mach numbr. This pictur clarly shows th formation of shocks in th nozzl at this tim prssur losss that would impact th ovrall prformanc in thrust. Monitors rcording th tank prssur, tank tmpratur, mass flow at xit, xit vlocity and xit prssur givs th thrust and othr variabl for th simulation. Tabl 1 shows th motor prformancs of all four cass. Computational run tim was massiv owing to th comprssibl natur of th simulation and basd on th altrnating tim-stp sizs of to sconds. Th total-run tim for CFD in-flight cas including th intrrupts and updat from MATLAB was approximatly 48 days on a six cor machin running at 3.6GHz. Th total run-tim for CFD sa lvl cas did not includ any intrrupts from MATLAB was around 18 days on an ight cor machin running at 3.6GHz. Contours of Mach numbr Contours of static prssur Contours of vlocity magnitud Figur 9. Simulation of air rockt at in-flight at 0.3 scond flow tim Contours of tmpratur 9 Amrican Institut of Aronautics and Astronautics

10 Figur 10 shows th vrtical acclration, vlocity, and position, thr is an obvious diffrnc btwn th CFD at sa lvl and thos in th Analytical cass. Th prformancs of th Analytical to CFD ar highr for all cass in Figur 10, and this is du to th prformanc diffrncs, and assumptions usd in ach modl. Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / Inrtial Acclration and Thrust vs. Tim Figur 10. Inrtial Acclration, Thrust, and Altitud vs. Tim Altitud vs. Tim Tabl shows that thr is a marginal incras in prformanc for th in-flight Analytical modl to th Analytical sa-lvl cas. Th CFD modl has highr prformancs in both altitud and pak vlocity, which is du to th highr prformancs in thrust ovr th Analytical modls. Tabl. Inrtial prformanc of rockt Altitud at Apog Modl Typ (m) Prcnt Apog diffrnc (%) Pak Vlocity (m/s) Analytical modl at sa-lvl 15. N/A Analytical modl in-flight CFD modl at sa-lvl CFD modl in-flight Th computational tim ncssary to comput insid th UCAT nvironmnt as sn in Tabl 3 shows that prprocssing th sa-lvl cass taks only a fraction of th tim rathr than th in-flight tim which taks hours or days. Tabl 3. Computational prformanc insid th UCAT nvironmnt Modl Typ Simulation tim (s) Analytical modl at sa-lvl 1,106 Analytical modl in-flight 51,59 CFD modl at sa-lvl 1,195 CFD modl in-flight 4,74,475 VII. Futur Work Th link btwn MATLAB and FLUENT opns a whol nw ralm of possibilitis for computational modls. Namly high fidlity rockt simulations, slosh dynamics, and automation routins for dtrmining th arodynamic charactristics of xtrnal flows with th us of nural ntworks to optimiz convrgnc. Th nxt stp for this modl at Florida Tch is to compar trajctoris of a rockt basd on lookup tabl data to th stady-stat CFD data of similar gomtry, and transint CFD rsults for complt arodynamic forcs and torqus in-flight. 10 Amrican Institut of Aronautics and Astronautics

11 VIII. Conclusion Th purpos of this papr was to show th viability of using a CFD modl insid a rockt trajctory program for highr fidlity. Th cold flow modl may hav bn too simpl of a modl with littl static prssur diffrnc at th xit plan of th nozzl which did not affct th thrust in any significant way, howvr vn that small diffrnc still yildd rsults that varid from th sa-lvl cass. This mans that using tim as th only input paramtr for thrust dos not yild th most accurat rsults and can b rsponsibl to dviation of th prdictd rockt's trajctory for rockt motors that ar static tstd at sa-lvl. Acknowldgmnts W would lik to thank William Bnson, Dav Griffin, and Charls Walkr at NASA Knndy Spac Cntr Expndabl Launch Vhicl Mission Analysis Branch for thir continuing support. Downloadd by FLORIDA INSTITUTE OF TECHNOLOGY on July 7, DOI: / Rfrncs 1. Faur, Jol M.; Kirk, Danil R., Gutirrz, Hctor; Validation of Univrsal Controls Analysis Tool Six Dgr of Frdom Kinmatics ; 48 th AIAA Arospac Scincs Mting Including th Nw Horizons Forum of Arospac Exposition; Orlando, Florida; Jan. 4-7, MATLAB (R010a), Simulink 7.5 (R010a), Th MathWorks Inc., 3 Appl Hill Driv, Natick, MA , Brimhall, Zack N.; Divitotawla, Niroshn; Atkinson, Josph P.; Kirk Danil R.; Pbls, Hnry G..; Dsign and Validation of a Six Dgr of Frdom Rockt Motor Tst Stand ; 44 th AIAA/ASME/SAE/ASEE Joint Propulsion Confrnc & Exhibit; Hartford, CT; July 1-3, Hill, Philip G.; Ptrson, Carl R.; Mchanics and Thrmodynamics of Propulsion; nd d.; Addison-Wsly Publishing Company; Rading; 199; pp. 33, 35, Sonntag, Richard E.; Borgnakk, Claus; Van Wyln, Gordon J.; Fundamntals of Thrmodynamics; 6 th d.; John Wily & Sons, Inc.; Hobokn; 003; pp ANSYS 1.1 FLUENT, ANSYS, Inc. Southpoint 75 Tchnology Driv, Canonsburg, PA, Amrican Institut of Aronautics and Astronautics