ANALYSIS OF FLOW IN CONVERGENT-DIVERGENT ROCKET ENGINE NOZZLE USING COMPUTATIONAL FLUID DYNAMICS

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1 HENRI COANDA AIR FORCE ACADEMY ROMANIA INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 5 Brasov, 8-3 May 5 GENERAL M.R. STEFANIK ARMED FORCES ACADEMY SLOVAK REPUBLIC ANALYSIS OF FLOW IN CONVERGENT-DIVERGENT ROCKET ENGINE NOZZLE USING COMPUTATIONAL FLUID DYNAMICS Bogdan-Alxandru Blga*, Trung Duc Nguyn** *Military Tchnical Acadmy, Bucharst, Romania, **Paul Sabatir Univrsity, Toulous, Franc Abstract: Nozzl is a dvic dsignd to control th rat of flow, sd, dirction, mass, sha, and/or th rssur of th stram that xhaust from thm. Nozzls com in a varity of shas and sizs dnding on th mission of th rockt, this is vry imortant for th undrstanding of th rformanc charactristics of rockt. By th ror gomtrical dsign of th nozzl, th xhaust of th rollant gass will b rgulatd in such a way that maximum ffctiv rockt vlocity can b rachd. Convrgnt divrgnt nozzl is th most commonly usd nozzl sinc in using it th rollant can b hatd in combustion chambr. Aftr gtting hatd th rollant first convrgs at th throat of th nozzl and thn xands undr constant tmratur in th divrgnt art. In th rsnt ar, flow through th convrgnt divrgnt nozzl study is carrid out by using a finit volum rwarding cod, FLUENT 6.3. Th nozzl gomtry modling and msh gnration has bn don using GAMBIT.4 Softwar. Comutational rsults ar in good acctanc with th xrimntal rsults takn from th litratur. Kywords: CFD, flunt, nozzl, Gambit, combustion chambr.. INTRODUCTION Th nozzl is usd to convrt th chmicalthrmal nrgy gnratd in th combustion chambr into kintic nrgy. Th nozzl convrts th low vlocity, high rssur, high tmratur gas in th combustion chambr into high vlocity gas of lowr rssur and tmratur. Th gnral rang of xhaust vlocity is to 4.5 kilomtr r scond. Th convrgnt and divrgnt (also known as convrgntdivrgnt nozzl figur ) ty of nozzl is known as DE-LAVAL nozzl. [,3] Th inlt Mach numbr is lss than on, Convrgnt sction acclrats it to sonic vlocity at th throat and furthr acclratd to sursonic vlocitis by th divrging sction. Figur Convrgnt-divrgnt nozzl In this rojct th dsigning and analysis of CD nozzl gomtry is don in th CFD (Comutational Fluid Dynamics softwar). Firstly th dsign of nozzl is mad in Gambit softwar and thn th nozzl gomtry is furthr analyzd in flunt softwar in ordr to analyz th flow insid th CD nozzl and to gt th viw of th bhavior of fluid insid th convrgnt-divrgnt sction of nozzl. [,]

2 . NOZZLE GEOMETRY ANALYSIS. Rockt nozzl quations. Th function of th nozzl is to acclrat gass roducd by th rollant to maximum vlocity in ordr to obtain maximum thrust. Th amount of thrust roducd by th ngin dnds on th mass flow rat through th ngin, th xit vlocity of th flow, and th rssur at th xit of th ngin. Th valu of ths thr flow variabls ar all dtrmind by th rockt nozzl dsign. For stadily orating rockt roulsion systm moving through a homognous atmoshr total thrust and scific imuls ar: F m v A () F Is () m g Th first trm is th momntum thrust and th scond trm rrsnts th rssur thrust. Th rockt nozzl is usually so dsignd that th xhaust rssur is qual or slightly highr than th ambint fluid rssur. Bcaus changs in ambint rssur affct th rssur thrust, thr is a variation of th rockt thrust with altitud (btwn % and 3%). Vlocity of sound and Mach numbr: a R T (3) v M (4) a Th stagnation rortis of a flow ar thos rortis which would rsult if th flow is isntroic. Stagnation rortis ar constant in an isntroic flow. Thus, rortis along th nozzl ar bst rfrncd against th stagnation rortis. With ths assumtions of idal gas and isntroic flow, ratios of rssur, dnsity and tmratur can b rlatd to th stagnation rssur, dnsity and tmratur at a givn Mach numbr. T M T (5) M M (6) (7) Additionally, th ratio of th local ara to th throat ara can b scifid by th Mach numbr: A M M (8) In a convrging-divrging nozzl a larg fraction of th thrmal nrgy of th gass in th chambr is convrtd into kintic nrgy. Th flow vlocity can b obtaind from th consrvation of total nthaly : h v h h (9) From th isntroic rlations th quation bcoms: RT v () M An incras of th ratio M T will incras th rformanc of th rockt. Th influncs of th rssur ratio and of th scific hat ratio ar lss ronouncd. Th nozzl ara xansion ratio ( ) is an imortant nozzl dsign aramtr: A () Th maximum gas flow r unit ara occurs at th throat (critical valus): t Tt T ().83.9 (3) t Throat vlocity v t is:.6.63 (4) vt RT RTt (5) To attain sonic/sursonic flow: (6) Th mass flow rat as a function of nozzl gomtry and fluid rortis can b found

3 HENRI COANDA AIR FORCE ACADEMY ROMANIA INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 5 Brasov, 8-3 May 5 GENERAL M.R. STEFANIK ARMED FORCES ACADEMY SLOVAK REPUBLIC from basic continuity whr v th avrag vlocity is, A is th nozzl ara, is th dnsity and m is flowrat: m va cons tant (7) Aftr substitutions w hav D Saint Vnant s Equation: m A RT (8) Whn sonic vlocity is rachd at th throat, it is not ossibl to incras th throat vlocity or th flow rat in th nozzl by furthr lowring th xit rssur (choking th flow). Choking is a comrssibl flow ffct that obstructs th flow, stting a limit to fluid vlocity bcaus th flow bcoms sursonic and rturbations cannot mov ustram; in gas flow, choking taks lac whn a subsonic flow rachs M. Mass flow rat: m tvt RT m (9) RT whr Th ara ratio is: A () Th vlocity ratio is: v () vt. Calculatd valus for nozzl dimnsions and gomtry. Th dimnsions of th convrgnt-divrgnt nozzl gomtry ar obtaind through th following quations which ar usd in vry saccraft availabl during th rsnt day. Mass flow in rockt is calculatd by: Fthrust m () v whr F thrust.mn and v 35m / s Putting th givn valus in th quation w obtain: m 34.86kg / s For high altitud ( km or highr) xansion ratio in nozzl, givn by (), ar btwn 4 and. Ara of th nozzl throat: m A (3) t Pc M RuTc Givn: M ; J R u 87 ; kg K T c 3K ;. ; P c MPa and utting ths valus in (3) w gt:.9m Now by using quation () w can gt th valu of A for 74 : A.95m Also th xit ara of nozzl is givn by: A r (4)

4 obtaining: r,55m Convrgnc ara in Nozzl is: A 3 c A t (5) Ac.387m Radius of throat: rt (6) r t.64m Combustion radius: Ac rc (7) r c.m Givn 5 and 6 w can calculat divrging Nozzl lngth: A Ldn (8) tan L dn.4m Lngth of th convrging nozzl: Ac Lcn (9) tan L cn.8m Lngth of th combustion chambr: * L Lc (3) rc A aramtr dscribing th chambr volum rquird for comlt combustion is * th charactristic chambr lngth, L, which is givn by: * Vc L (3) whr V c is th chambr volum (including th convrging sction of th nozzl) and A t is th nozzl throat ara. For gasous oxygn/hydrocarbon fuls, an L * of.7 to.54 mtrs is aroriat. For L *. 7m, chambr lngth is: L c.43m 3. METHODOLOGY AND IMPLEMENTATION 3. Modling th nozzl. Th gomtry of th nozzl was cratd using th Gomtry workbnch of GAMBIT modling ackag for dvloing th wir fram which rsmbls th cross-sction of th rockt nozzl (figur ). A tri-dimnsional gomtry of th nozzl was cratd by using th valu of A ;r ; A ;r ; L ; A ;r ; L ; L ; t. t t dn c c cn c wall Figur Nozzl Gomtry 3. Mshing in Gambit. Th nxt task was to msh th gomtry cratd. In GAMBIT th msh usd was ttrahdral msh lmnts and ror car is takn whil mshing th rgions nar th walls of th nozzl so as to gt mor rfinmnt in that articular rgions. As any comutational rocss rquirs a msh to carry comutation this st is a rimary and most imortant to start th roblm. Th msh cratd in GAMBIT is as shown blow figur.3. Figur 3 Nozzl Gomtry (Msh) W can s that th mshing nar th boundary of th nozzl is mor rfind whn comard to othr rgions of msh. Th msh was rfind to th third dgr using th rfinmnt otion of th GAMBIT. Aftr mshing, th inlt, th axis and th outlt boundaris wr namd. 3.3 Boundary Conditions usd. Scification of th boundary zons has to b don in GAMBIT only, thr is no ossibility to scify th boundary zons in FLUENT. Accordingly th gomtry of th nozzl is dividd into zons and boundary conditions givn to ths ar: th insid nozzl surfacs

5 HENRI COANDA AIR FORCE ACADEMY ROMANIA INTERNATIONAL CONFERENCE of SCIENTIFIC PAPER AFASES 5 Brasov, 8-3 May 5 GENERAL M.R. STEFANIK ARMED FORCES ACADEMY SLOVAK REPUBLIC ar givn as WALL; th inlt is givn as mass flow inlt; th outlt is givn as rssur outlt. With all th zons dfind rorly th msh is xortd to th solvr. Th solvr usd in this ar is FLUENT. Th xortd msh fil is rad in flunt for solving th roblm. Th flunt conditions to th dsign nozzl gomtry ar nrgy quation includd, viscous modl- K silon, matrials ar Hydrogn and Titanium for fluid flow and wall rsctivly, mass flow rat (Inlt) kg / s and outlt gaug rssur and tmratur ar and 73 k rsctivly. 3.4 Solving. Aftr initiating th numrical analysis, convrgnc was obtaind aftr 33th itration in cas of nozzl analyzd. Th stady axisymmtric imlicit formulation with could solvr with K- turbulnc modl is chosn. Th mass flow of th burning solid rollant was modld using a usr-dfind function. [4, 5] In figur 4 and figur 5 vlocity distribution and absolut rssur of nozzl gomtry is shown rsctivly. It is clarly sn th vlocity is incrasing along with th lngth of th nozzl. Du to shocking in th nozzl, th vlocity dcrasd for a whil but latr bgan to incras as th fluid xandd through th divrgnt ortion. Prssur gradually dcrasd along th lngth of th nozzl xct a slight ris during th shocking. Howvr, th ris was not significant comaring to th total fall in rssur. According to Brnoulli s quation, rssur dcras as vlocity incrass along th xansion zon. Figur 6 Total tmratur distribution of nozzl gomtry Figur 4 Vlocity distribution of nozzl gomtry Figur 7 Wall shar strss distribution of nozzl gomtry Figur 5 Absolut rssur distribution of nozzl gomtry In figur 6 and figur 7 total tmratur and wall shar strss of nozzl gomtry is shown rsctivly. It is sn that tmratur dcrasd gradually xct a slight incras. Th slight

6 incras occurs in th shock zon whr raid chang of fluid rortis taks lac. But th ris in tmratur was not significant with rsct to th fall in tmratur throughout th distanc. 4. CONCLUSIONS & ACKNOWLEDGMENT Aftr succssfully comlting this simulation of a dsign cratd, th dcisions wr finally confind into th following oints. From th analysis, it is clarly obsrvd that nozzl cratd basd on xit aramtrs it is in accord with th sco.. REFERENCES Mohan Kumar G., Dominic Xavir Frnando, R. Muthu Kumar, - Dsign and Otimization of D Lavl Nozzl to Prvnt Shock Inducd Flow Saration - Advancs in Arosac Scinc and Alications. ISSN Volum 3, Numbr (3), Mayur Chakravarti - Dsign analysis of flow in convrgnt divrgnt rockt nozzl - Univrsity of Ptrolum and nrgy studis, Dartmnt of Arosac Enginring, Dhradun, India,. 3. Viul Sharma, Ravi Shankar, Gaurav Sharma, - CFD Analysis of Rockt Nozzl - Univrsity of Ptrolum and nrgy studis, Dartmnt of Arosac Enginring, Dhradun, India,. 4. Biju Kuttan P, M Sajsh - Otimization of Divrgnt Angl of a Rockt Engin Nozzl Using Comutational Fluid Dynamics - Th Intrnational Journal Of Enginring And Scinc, volum, ags 96-7, 3, ISSN: MD. Safayt Hossain, Muhammad Frdous Raiyan, Nahd Hassan Jony - Comarativ study of sursonic nozzls - Intrnational Journal of Rsarch in Enginring and Tchnology, volum 3, ags , oct.4 ISSN: