ON THE ACCURACY OF NUMERICAL PREDICTION IN TRANSONIC-SUPERSONIC FLOW ARROUND MISSILES

Transcription

1 U.P.B. Sc. Bll., Seres D, Vol. 7, Iss. 3, ISSN ON THE ACCURACY OF NUMERICAL PREDICTION IN TRANSONIC-SUPERSONIC FLOW ARROUND MISSILES Crsna MIHAILESCU, Teodor Vorel CHELARU, Seran DANAILA 3, Cornel BERBENTE 4, Coscă SAVA 5 Scopl lcrăr ese de a valda n model nmerc prn comparaţe c daele epermenale esene penr o confgraţe alngă c ampena canard. Penr acesa sn consderae 4 confgraţ de bază penr care sn analzae comparav rezlaele epermenale ş eorece. Modelarea nmercă s-a fac lzând programl FLUENT (v6..). Penr comparaţe s-a folos rezlaele epermenale obne în nell aerodnamc. In fnal se vor prezena o sere de conclz prvnd acraeţea meode dezvolae. The am of he paper s o valdae a nmercal model sng a comparson wh avalable epermenal daa for a slender body confgraon wh canard fns. For basc confgraons are consdered, for whch he heorecal resls are analyzed n comparson wh epermenal ones. The nmercal model was developed sng he commercal code FLUENT (v6..). For comparson epermenal resls obaned n aerodynamc wnd nnel were sed. Fnally, some conclsons relaed o he accracy of hs mehod are presened. Key words: canard-conrolled mssle, aerodynamc characerscs. Inrodcon Over he pas decade, sac Compaonal Fld Dynamcs (CFD) smlaons over ncreasngly comple vehcles have become commonplace. Many aerodynamc predcon codes are sed o provde vales for aerodynamc coeffcens. B how well hese coeffcens reflec realy s a problem of accracy. Nowadays, hs problem s presened n many papers, beng par of code valdaons [], error esmaons [], mesh refnemen [3], [4] and ohers. Obanng he aerodynamc coeffcens for mssles s a problem ha Drd. Eng., Facly of Aerospace Engneerng, Unversy POLITEHNICA of Bchares, Romana Reader., Facly of Aerospace Engneerng, Unversy POLITEHNICA of Bchares, Romana 3 Prof., Facly of Aerospace Engneerng, Unversy POLITEHNICA of Bchares, Romana 4 Prof., Facly of Aerospace Engneerng, Unversy POLITEHNICA of Bchares, Romana, e- mal: berbene@yahoo.com 5 Drd. Eng., Facly of Aerospace Engneerng, Unversy POLITEHNICA of Bchares, Romana

2 86 Crsna Mhalesc, Teodor Vorel Chelar, Seran Danala, Cornel Berbene, Cosca Sava nvolves hgh responsbles from researchers n fld flow doman. To oban hese aerodynamc daa, many models cold be bl and esed n a wnd nnel, wh dfferen posons relaed o he flow. Sch ess are epensve and reqre also an epensve model eecon. Compaonal Fld Dynamcs (CFD) s an alernave o wnd nnel esng, b he necessary reqremen of sng sch a nmercal model s ha he resls ha yeld ms be a realsc smlaon of a fld n moon. Tha s why s necessary o compare nmercal resls wh epermenal ones. Canard conrol s also qe commonly sed, especally on shor-range mssles. The prmary advanage of canard conrol s beer manoevrably a low angles of aac, b canards end o become neffecve a hgh angles of aac de o flow separaon ha cases he srfaces o sall. Snce canards are ahead of he cener of gravy, hey case a desablzng effec and reqre large fed als o eep he mssle sable. For he case of a slender body confgraon wh fns and canards, sdes abo he nflence of canard deflecon on aerodynamc characerscs for mssle are necessary. Ths s de o ar deflecon n presence of canards, a phenomenon ha can prodce commands nverson, especally for he case of asymmercal deflecon of canards for roll conrol. The am of hs sdy s o mae a comparson beween epermenal and nmercal daa of aerodynamc coeffcens for a gded mssle and o evalae he accracy of nmercal predcon n ransonc-spersonc flow arond mssles wh canard fns. Smlar sdes nvolvng canard-conrolled mssles were performed by James DeSpro e al. [5], [6], [7] a Army Research Laboraory beween and 4, wh good agreemen beween nmercal and epermenal daa.. Mahemacal model The hree-dmensonal Reynolds-Averaged Naver-Soes eqaons are: ( ) p l ( ) ( ) δ ( ) where he Reynolds sresses can be epress n erms of mean velocy gradens sng he Bossnesq approach: 3 l () ()

3 On accracy of nmercal predcon n ransonc-spersonc flow arrond mssles 87 δ 3 (3) and: C (4) For rblence modellng, a modfed form of he - wo-eqaon rblence model proposed by Shh e al. [8], called Realzable - model was sed. I dffers from he sandard - model becase conans a new formlaon for he rblen vscosy and a new ranspor eqaon for he dsspaon rae. The ranspor eqaons for and for Realzable - model are: ( ) ( ) M Y G σ (5) and ( ) ( ) ν σ 3 C C C C S (6) where 5.43, ma η η C, η S, S S S, S (7) For hs model, C s no longer a consan. Insead, s comped from: * U A A C s (8) where A and A s are consans. The erm G represens he prodcon of rblence energy and s defned as: G (9) The erm Y M represens he dlaaon dsspaon erm for hgh Mach nmber flows. Ths erm s modelled accordng o Sarar [9], as: RT Y M γ () The Realzable - Eqaon ( 6) canno be appled o wall-bonded flows drecly. For he wall-bonded flows, we ms specfy he bondary

4 88 Crsna Mhalesc, Teodor Vorel Chelar, Seran Danala, Cornel Berbene, Cosca Sava condons approprae o a sold bondary for velocy, rblence nec energy and dsspaon rae. The wall fncon s sed o avod he nphyscal behavor of he and eqaons nsde he vscos sb layer regon and o mach he oer flow o he wall. The no-slp condon:,v,w s sed on he wall. Ths model was valdaed for many flow ypes ncldng srong sreamlne crvare, vorces, and roaon. For all hese cases, he Realzable - model showed sbsanal mprovemens over he sandard - model. 3. Nmercal solon All compaons were performed for seady-sae case sng he commercal CFD code FLUENT (v6..). The geomery and nsrcred meshes were generaed sng he preprocessor GAMBIT. The nmber of erahedral cells for he resled meshes s presened n Table. Becase of he necessy o analyze he nflence of dfferenal canard deflecon, was mpossble o fnd a symmery plan for he doman flow. Tha s why he analyses are performed n hree-dmensonal space. In generaon of meshes, he bondary layer mesh spacng was sed near he mssle body and fn srfaces. The doman was large enogh, s eenson on O as was beween -5L before mssle and L afer, where L s he oal lengh of he mssle. On Oy and Oz as he dsance from mssle o he oer bondary was abo 6L. The mposed bondary condons were: - For mssle s sold srfaces, wall bondary condon was sed; - A far-feld pressre bondary condon a he downsream, psream, and oer bondary wh mposed vales for free sream drecon, speed and pressre was sed; - The deal gas hypohess for ar and Sherland law for vscosy was sed. 4. The nflence of canard geomery In hs sdy he aerodynamc coeffcens for a gded mssle wll be evalae consderng dfferen canard deflecons. The confgraon has for canard fns, whch can be defleced n a range of -5 5, o realze he gdance of mssle, and s fns. The mssle confgraon s presened n Fg.. The analyses were performed a Mach nmber. for a range of ncdences -4 for for cases wh dfferen confgraons presened n Table. The epermenal resls sed for comparson have been obaned only for cases B, C and D n he wnd nnel [] for a range of aac angle of -4 5.

5 On accracy of nmercal predcon n ransonc-spersonc flow arrond mssles 89 The normal force (Cz,), aal force (C,), and pchng momen (Cm,) coeffcens are presened n a mssle s as sysem. The resls obaned n prevos condons have been graphcally represened for a comparson wh epermenal resls. In hs way, n Fg., 3, 4 and 5 he force coeffcens and he momens coeffcens respecvely are represened for every case. For case A (Fg. ) he accracy of nmercal resls s good and predc n good condons he ncrease of lf coeffcen wh he ncdence angle. In he same manner, he nmercal resls for he momen coeffcen C m predc n a reasonable way he nflence of ncdence. For drag coeffcen he accracy s raher poor, b he conclson s ha nmercal resls for drag force coeffcens are hgher han he epermenal daa. The same resls referrng o he drag coeffcen are obaned for all hree cases A, B and C. For cases B and C (Fg.3 and Fg.4) he accracy s a lle poorer han for case A boh for lf and momen coeffcens, b he slope of he dagrams s ep. In he absence of epermenal daa, for case D represened n Fg.5, only nmercal resls are avalable and hey predc lf, drag and momen coeffcens for he case of confgraon who canard fns. We apprecae ha resls for hs case have he same accracy le n prevos cases. Referrng o nflence of canard deflecon angle, a maor nflence on ncrease of he canard deflecon angle s he ncrease of aal force coeffcen C. The lf coeffcen Cz s no nflenced when he deflecon s asymmerc, b, when he canards are defleced symmercally n crren flow (Case C, Fg.8) an ncrease of Cz can be observed. The nflence of asymmerc deflecon angle of canards (case A and B) s qe small comparave o he case of symmerc deflecon angle (case C) relaed o momen coeffcen Cm. All hese comparave graphs are represened n Fg. 6, 7 and 8. Table Cells nmber for meshes Case Nmber of cells A 654 B C 5453 D 6474 Confgraons Case Deflecon of horzonal canard A /-.5 B /-5 C D No canard fns Table

6 9 Crsna Mhalesc, Teodor Vorel Chelar, Seran Danala, Cornel Berbene, Cosca Sava Fg. Mssle s confgraon 4 3 Cz presen Cz eperm C presen C eperm Cz C ncdence [grad] Fg. Forces and momens coeffcens for case A Cz presen Cz eperm C presen C eperm Cz C Cm presen Cm eperm ncdence [grad] ncdence [grad] Fg. 3 Forces and momens coeffcens for case B

7 On accracy of nmercal predcon n ransonc-spersonc flow arrond mssles C presen C eperm Cz presen Cz eperm ncdence [grad] Cz C Cm presen Cm eperm ncdence [grad] Fg. 4 Forces and momens coeffcens for case C.5 Cz presen C presen Cm presen ncdence [grad] ncdence [grad] Fg. 5 Forces and momens coeffcens for case D 7,,7 6,,65 5,,6 4, C,55,5,45 /-.5 degree /-5 degree degree Cz 3,,, /-.5 degree /-5 degree degree,4,, ,,3 -,, , ncdence [degree] Fg. 6 Inflence of canard deflecon angle on C ncdence [degree] Fg. 7 Inflence of canard deflecon angle on Cz

8 9 Crsna Mhalesc, Teodor Vorel Chelar, Seran Danala, Cornel Berbene, Cosca Sava,5,,5, Cm -,5 -, -,5 /-.5 degree /-5 degree degree -, -,5-3, -3,5 ncdence [degree] Fg. 8 Inflence of canard deflecon angle on Cm Fg. 9 Mssle model drng wnd nnel ess 5. Conclsons Usng he FLUENT posprocessor, he vscos and pressre forces were negraed along he mssle body and fn srfaces o calclae he aerodynamc coeffcens. The pchng momen s epressed abo he nose of he mssle. The

9 On accracy of nmercal predcon n ransonc-spersonc flow arrond mssles 93 reference area s he cross-seconal area of he mssle body, and he reference lengh s he dameer of he mssle. The calclaed coeffcens are compared o wnd nnel measremens performed a Naonal Inse for Aerospace Research "Ele Carafol" Bchares []. A maor nflence of ncreasng canard deflecon angle s he ncrease of aal force coeffcen. The lf coeffcen s no nflenced when he deflecon s asymmerc, b when he canards are defleced symmercally n crren flow (case C), an ncreasng of Cz can be observed. The nflence of asymmerc deflecon angle of canards (case A and B) s qe small comparave o he case of symmerc deflecon angle (case C) relaed o momen coeffcen Cm. All hese comparave los are represened n Fg. 6, 7 and 8. Secondly, a echncal conclson resled from hs sdy was ha he deflecon on he als s neglgble f we se small asymmercal canard deflecon and small aac angle. In hs case, we can conrol he roll of he mssle sng only canard asymmercal deflecon, who oher alary sysems. The resls were valdaed by comparng he comped aerodynamc coeffcens for he mssle agans wnd nnel measremen daa. The bes agreemen beween nmercal and epermenal resls s obaned for case A. We can see from Fgres -3 a good accracy for he lf coeffcen. We can no say he same hng abo he drag coeffcen, becase n hs case he accracy s raher poor, b he conclson s ha nmercal force coeffcens are hgher han he epermenal ones. Anyway, hey predced he same ncrease wh ncdence angle as he showed epermenal daa. The mamm dfference beween he calclaed and measred normal force coeffcen was 7%, whle he mamm dfference beween he calclaed and measred aal force coeffcen was 4%. To ncrease he accracy of nmercal resls, a fner mesh s recommended, b hs mposes an ncrease of comper memory and of compng me. In a smlar sdy performed a Army Research Laboraory, compers wh 48 and even 64 processors [6] have been sed. The fnal conclson of hs wor s ha vscos CFD analyss offers an accrae mehod for calclang he flow feld and aerodynamc coeffcens for mssles. B I B L I O G R A P H Y [] Thomas J. Sooy and Rebecca Z. Schmd. Aerodynamc Predcons, Comparsons, and Valdaons Usng Mssle DATCOM (97) and Aeropredcon 98 (AP98) Technology Servce Corporaon, Slver Sprng, Maryland 9 -Jornal of Spacecraf and Roces Vol. 4, No., March Aprl 5

10 94 Crsna Mhalesc, Teodor Vorel Chelar, Seran Danala, Cornel Berbene, Cosca Sava [] Maran Nemec Error Esmaon and Adapve Mesh Refnemen for Problems wh Complcaed Geomeres MIT ACDL Semnar May 9, 8 [3] Maran Nemec Mchael J. Afosms, Adon Error Esmaon and Adapve Refnemen for Embedded-Bondary Caresan Meshes, 8h AIAA Compaonal Fld Dynamcs Conference, Mam, FL, Jne 5 8, 7. [4] Sco M. Mrman, Mchael J. Afosms Caresan-Grd Smlaons of a Canard-Conrolled Mssle wh a Spnnng Tal AIAA-3-367, s AIAA Appled Aerodynamcs Conference, Orlando, Florda, Jne 3-6, 3 [5] James DeSpro, Harrs L. Edge, Pal Wenach, Jbara Sah and Srya Dnavah Compaonal Fld Dynamc (CFD) Analyss of a Generc Mssle wh Grd Fns Army Research Laboraory Repor No. ARL-TR-38, Sepember [6] James DeSpro, Mlon E. Vaghn, Jr., W. Davd Washngon Nmercal Invesgaons of Aerodynamcs of Canard-Conrolled Mssle Usng Planar and Grd Tal Fns, Par I: Spersonc Flow -Army Research Laboraory Repor No. ARL-TR-848, Sepember [7] James DeSpro, Mlon E. Vaghn, Jr., W. Davd Washngon Nmercal Invesgaons of Aerodynamcs of Canard-Conrolled Mssle Usng Planar and Grd Tal Fns, Par II: Sbsonc and Transonc Flow -Army Research Laboraory Repor No. ARL-TR-36, March 4 [8] T.-H. Shh, W. W. Lo, A. Shabbr, Z. Yang, and J. Zh. A New - Eddy-Vscosy Model for Hgh Reynolds Nmber Trblen Flows - Model Developmen and Valdaon. Compers Flds, 4(3):7-38, 995. [9] S. Sarar and L. Balarshnan. Applcaon of a Reynolds-Sress Trblence Model o he Compressble Shear Layer. ICASE Repor 9-8, NASA CR 8, 99. [] ***, Epermenal deermnaon of aerodynamc characerscs, Naonal Inse for Aerospace Research "Ele Carafol" code C-774, 7. [] B. E. Lander and D. B. Spaldng. The Nmercal Compaon of Trblen Flows. Comper Mehods n Appled Mechancs and Engneerng, 3:69-89, 974. [] D. C. Wlco. Trblence Modellng for CFD. DCW Indsres, Inc., La Canada, Calforna, 998.