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Optimisation 3D du nez d'un SuperSonic Business Jet basée sur l'adaptation de maillages. Application à la réduction du bang sonique

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(1)Optimisation 3D du nez d’un SuperSonic Business Jet basée sur l’adaptation de maillages. Application à la réduction du bang sonique Frédéric Alauzet, Bijan Mohammadi. To cite this version: Frédéric Alauzet, Bijan Mohammadi. Optimisation 3D du nez d’un SuperSonic Business Jet basée sur l’adaptation de maillages. Application à la réduction du bang sonique. [Rapport de recherche] RR-5053, INRIA. 2003. �inria-00071530�. HAL Id: inria-00071530 https://hal.inria.fr/inria-00071530 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Optimisation 3D du nez d’un SuperSonic Business Jet basée sur l’adaptation de maillages. Application à la réduction du bang sonique Frédéric Alauzet — Bijan Mohammadi. N° 5053 17 décembre 2003. ISSN 0249-6399. ISRN INRIA/RR--5053--FR. THÈME 4. apport de recherche.

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(144)  1 . ~s‡ h‚wnyx{zŠh‚wv~s‡ x{~,tH™ “ h/tHqŠ x{rehgziqsvwnprpnytHzov qszehf “ vwcex € h € h ~s‡ x{~,tH™—tHvwnyx{z € h‚~,tH‡tHfidgvw‡ h‚ €s“ ƒg‡wnpºtHz—v}r § x{z € h € h"~s‡ h‚ wnyx{z ²  ¦t‚ºšhF¨Çx{‡wf ~,tH‡tHfihgv hg‡}fihgvwcex € ³ !p‘7’# ¶ b¹x{qsv hF¨Çx{ny·¼¹rut`fix €s“ rpnytHvwnyx{z € hir §Á“ ƒ‚x{qsryhgfihgz—vihgz f “ ƒ·tHzsny´oqeh € h‚4Éeqsn € h‚² “ ´—q,tHvwnyx{ze €D§ÁÄ qsryhg‡®³h‚wvvw‡wn € npfihgzewnyx{zszehgrpryh/hgv zex{z µrpnpz “ tHnp‡ h¼ tHryx{‡  ´oqeh rut"~s‡ x{~,tH™—tHvwnyx{zh‚wvqszifix € dgryh rpnpz “ tHnp‡ h/hgzqszeh € npfihgzewnyx{z@¶ †0x{qs‡¦´oqeh}ryh8ƒ‚x{qs~srutH™šh" x{npv ºtHrpn € h¼onpr,¨tHqsv ´oqeh8rut4 x{rpqsvwnyx{z € q ƒc,tHfM~˜~s‡ xoƒceh t “ ‡ x € Rz,tHfMny´—qeh  x{npvt „Rny of “ vw‡wny´oqeh¶š¥¦hgvwv h¦ƒ‚x{z € npvwnyx{zMh‚wv0z “ ƒ‚h‚ tHnp‡ h¦~?x{qs‡ ~s‡ hgz € ‡ h˜hgz¾ƒ‚x{fM~sv hv x{qe}ryh‚ “ r “ fihgzov  € hrutŠ™ “ x{f “ vw‡wnyh € h4r § t·ºonyx{zвK¨©qe hgrutH™šh¼DtHnpryh‚·¼0¶p¶p¶Ø³F¶ †%tH‡ ƒ‚x{ze “ ´—qehgzov·¼š~?x{qs‡ x{”sv hgzsnp‡ qszeh”9x{zszeh~s‡ “‚€ nyƒgvwnyx{z € qi”,tHzs™ x{zsny´—qeh¼šnpr,h‚wv z “ ƒ‚h‚ ®tHnp‡ h €D§ x{”sv hgzsnp‡MqszehÂx{rpqsvwnyx{z ~s‡ “ ƒgny h € qЃ c,tHfM~ ~s‡ xRƒ cehÂwq ŠtHfMfihgzoviryx{npz € q ~s‡ xHÃer¶†&x{qs‡ ‡ “ x{q € ‡ hkƒ‚h"~s‡ x{”srydgfih¼ezex{qe8~s‡ x{~9x x{ze €D§ qsvwnprpny hg‡r § t € tH~svtHvwnyx{z € h"fŠtHnprprutH™šh¶ ¸¹tÂfix €s“ rpnytHvwnyx{z € hMr §Á“ ƒ‚x{qsryhgfihgz—vMh‚wvnprprpqewvw‡ “ hŠ ƒc “ fŠtHvwny´—qehgfihgzovMwqs‡4rut 0np™qs‡ h#je¶ ¥¦x{fMfih4rut˜~s‡ x{~,tH™—tHvwnyx{z € h‚8x{z € h‚/tHq| x{r¹h‚ v¨ÇtHnpv h4hgz`~?xwv¿µ~s‡ xoƒ‚h‚wnpzs™e¼sr § qsvwnprpnytHvwnyx{z € h € *n  “ ‡ hgz—v %ƒ‚x € h‚ € h ~s‡ x{~?x{™—tHvwnyx{z˜zeh ƒ c,tHzs™šh hgz‡wnyhgzr § tH~s~s‡ xRƒ ceh qsvwnprpny “ h € tHze%ƒ‚hgvwv h “ vwq € h¶  ΚË9Ÿ&Ï o¡  > Ì  > ¡ªœo!Î

(145) > ?D@Ÿ —ž %ož Ÿ ? % —ž ¸ §Á“ ƒ‚x{qsryhgfihgzov € qƒc,tHfM~M~s‡ xoƒcehtHqsv x{qs‡ € hir § t‚ºRnyx{z\h‚wv'fix €s“ rpny “ ~,tH‡ryh‚ “ ´—q,tHvwnyx{ze €D§ÁÄ qsryhg‡·¶&¸@hM™—tH­Šh‚wv € x{zeƒŠwqs~s~?x “ ~,tH‡¿¨tHnpv·¼ npr/h‚wvŠzex{z+ºony´—qehgq „Òhgv#npr8z § Òt¢~,t{ € h € *n 9qewnyx{z+vwcehg‡wfMny´—qeh¶»}z+zex{v h ρ rut € hgzewnpv “ ¼ r §Á“ zehg‡w™nyh4v x{vtHryh¼ ~ = (u , u , u ) ryhkºšh‚ƒgv hgqs‡ºonpv h‚ h¼ T rut˜v hgfM~ “ ‡tHvwqs‡ h¼ E = T + U § “ € u r  t s ~. ‡ ‚ h. .  y n { x \ z ‚ t š º ‚ h ƒ g h v r { x ~  ‡ H t. v g h s q  ‡  ™  ‡ t y n g h — z · v ¶0¸@h‚ “ ´oq,tHvwnyx{ze p = (γ − 1)ρT γ = 1.4 ∇ €D§ÁÄ qsryhg‡8 §Á“ ƒg‡wnpºšhgz—v/ x{qe ¨Çx{‡wfihkƒ‚x{ze hg‡wºtHvwnpºšh € h'rutfŠtHzsnydg‡ hk qsnpº{tHzov hÀ 1. 2. ~ k2 kU 2. 3.  ∂ρ  ~) = 0, + ∇. (ρU    ∂t   ∂(ρU ~) ~ ⊗U ~ ) + ∇p = 0 , + ∇. (ρU ∂t     ∂(ρE)  ~) = 0,  + ∇. ((ρE + p)U ∂t. ,.-[v, á.

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(153) 98&!. ‘‘. x |x{z`tMwqeƒ‚ƒ‚h‚ wnpºšhgfihgzov8ryh‚ “ ´oq,tHvwnyx{ze € h4ƒ‚x{ze hg‡wº{tHvwnyx{z € h"rut˜fŠt{  h¼ € qÂfix{fihgz—v"hgv € h r §Á“ zehg‡w™nyh4hF„R~s‡wnpf “ h‚} x{qe ¨Çx{‡wfih'v hgze x{‡wnyhgrpryh¶ 0hgv·np¼Rzsqsny¸¹0zetwh/qs‡ ‡ “‡ h‚€ ƒ‚x{h‚x{rpqs¹zevwfŠwnyvwx{‡wtHzqenprpƒgzoruvwtHqsny™šx{f h‚z 0“ ‡w€zenyh/x{´—z qevÞµoh w~?vw€ ‡wh h‚qe  ƒg“vw'qs´oq,‡ ms“ tH¥¦ vwny¸ª!px{‘·ze• hg#v ¶{€D€»}§Áh‚Ä z qsqsrprynpvwhgfMnp‡%rpnpnyv hhgh qs¨rytH‡ h npv&Ée€ q ~,h „ tH‡0€ rutHh tz‹}f Æ8xo“ h rpvw”,ce~9t x x{€ €qsth‡0~?ru€ tx{h‚qs‡ “‡x{x{x{”srprpqsqsv vwfihgnyzsx{h‚npz ‡ qszeh#~s‡ “ ƒgnywnyx{z €D§ x{‡ € ‡ h € hgq „ ²PrpnpfMnpv “ ³hgz h‚w~,t{ƒ‚h¶&¸ § tHrp™šx{‡wnpvwcsfihqsvwnprpny “ h‚wvhF„ ~srpnyƒgnpv hhgz v hgfM~e¦hgv qsz ƒ c “ fŠt € h}v R~9h}‹qszs™šhFµ "qsvwvt 'vw‡ x{ny ~,t{ h‚wv qsvwnprpny “ ~?x{qs‡ r § npzov “ ™‡tHvwnyx{zÂhgz v hgfM~e7¶  r h‚wv4”snyhgz ƒ‚x{zszoq ´oqeh#r § t € tH~svtHvwnyx{z € hŠfŠtHnprprutH™šh~?hg‡wfihgv˜rut`ƒ·tH~svwqs‡ h € h‚˜ƒ cexRƒ‚ € h fŠtHzsnydg‡ h4~s‡ “ ƒgny hkryx{npz € tHze8ryh € x{fŠtHnpzeh € hƒ·tHryƒgqsr0hgz°‡ “‚€ qsny®tHz—v € h'¨t !‚x{z|wnp™zsn Ã,ƒ·tHvwnpºšhryh v hgfM~e € h ƒ·tHryƒgqsr !p‘ # ¶{†0x{qs‡ ryh ƒ·tHryƒgqsr € h r §Á“ ƒ‚x{qsryhgfihgzov € tHze%ryhƒ c,tHfM~M~s‡ xRƒ ceh¼{zex{qe%qsvwnprpnyhFµ ‡ x{ze ryh‚ v h‚ƒcszsny´—qeh‚ €D§ t € tH~svtHvwnyx{z € hfŠtHnprprutH™šh¼o´oqsn, hg‡ x{zov ~s‡ “  hgzov “ h‚ € tHze rut4mRh‚ƒgvwnyx{z ¼ t Ãez €D§ x{”sv hgzsnp‡4qszehM x{rpqsvwnyx{zÅ~s‡ “ ƒgny hMwq ŠtHfMfihgzovkryx{npz € qÅ~s‡ xHÃer¶ /x{qe'h‚w~9dg‡ x{zetHnpzewn x{”sv hgzsnp‡8qszeh'fihgnprpryhgqs‡ hk~s‡ “‚€ nyƒgvwnyx{z € h"rutMwnp™z,tHvwqs‡ h € h"rut˜~s‡ h‚wnyx{z`tHq` x{r¶ W  dË I

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(156) eŸ ž7ËÏ †&x{qs‡Å~s‡ x{~,tH™šhg‡ªryh‚¾~?hg‡wvwqs‡w”,tHvwnyx{ze € q ƒ c,tHfM~ ~s‡ xRƒ cehÂtHq  x{r¼&zex{qe˜t·ºšx{ze €s“ ºšhgryx{~s~ “ qsz ƒ‚x € h € h#~s‡ x{~,tH™—tHvwnyx{z qsvwnprpnytHz—vMrut`f “ vwcex € h € hab cex{fŠt{ª²  ¦t·ºšhF¨©x{‡wf ~,tH‡tHfihgv hg‡Âfihgvwcex €  ³ !p‘7’ # ¶¦«"tHzeƒ‚hgvwv hÅtH~s~s‡ xRƒ ceh¼¦r § x{z € h € h ~s‡ h‚wnyx{z°h‚wvƒ·tH‡t{ƒgv “ ‡wny “ h4~,tH‡vw‡ x{ny~,tH‡tHfidgvw‡ h‚@À  m rutM~9hgzov h € h‚ hg™fihgzov  € h'r § x{z € h € h"~s‡ h‚wnyx{z@¼  ∆p º{tH‡wnutHvwnyx{z € h'~s‡ h‚ wnyx{zÂ~,tH‡8hg™fihgz—v²©hgzovw‡ hkryh‚x{z € h‚ € h"~s‡ h‚ wnyx{z i hgv i + 1 ³F¼  λ v hgfM~e8ƒ·tH‡t{ƒgv hg‡wny vwny´—qeh4~9x{qs‡ryhkhg™fihgz—v € h'r § x{z € h € h"~s‡ h‚ wnyx{z i ¶ †0x{qs‡"~s‡ x{~,tH™šhg‡"r § x{z € h € h~s‡ h‚ wnyx{z € tHze8r § tHvwfix ~scedg‡ h¼Dx{z|‡ “  x{q € qsz| Rwv dgfih € hvw‡ x{ny “ ´oq,tHvwnyx{ze € *n  “ ‡ hgz—vwnyhgrpryh‚/x{‡ € npz,tHnp‡ h‚²Pqszehk~9x{qs‡ƒc,t{´—qeh4~,tH‡tHfidgvw‡ h7³9À . . . i. i. i. dmi dt.          . d∆pi dt.         . dλi dt. t·ºšh‚ƒ'ryh‚zex{vtHvwnyx{ze@À. γ + 1 a0 , C1 = 2γ p0 cn. = C1 m2i + C2 mi , 1 C1 ∆pi (mi + mi−1 ) + C2 ∆pi , 2. =. 1 = − C1 (∆pi + ∆pi+1 ) − C1 mi λi , 2 1 C2 = 2. . 3 da0 1 dρ0 2 cn 1 A + − − a0 dt ρ0 dt cn dt A dt. . ,. x \r § npz € nyƒ‚h 0 wnp™zsn Ã,hiryh‚´—q,tHzovwnpv “  € hŠr § tHnp‡˜tHf”snutHz—vMhgv4x x{z tÂzex{v “ a rutºRnpv h‚  h € q x{z@¼ rut € hgzewnpv “ ¼ rut ºonpv h‚ h € h¾~s‡ x{~,tH™—tHvwnyx{z € h¾r § x{z € hªhgv r § tHnp‡ h € qvwqs”9h € h ‡t·šx{zeρ't{ƒ‚x{qewvwny´—qeh‚"cƒ‚x{qs~ “ ~,tH‡/ryh'¨©‡ x{z—v €D§ x{z € h š¶b¹x{qsv h‚'ƒ‚h‚ € x{zsz A“ h‚/x{z—v¨Çx{zeƒgvwnyx{z € h r § tHrpvwnpvwq € h¶,¸¹tºonpv h‚ h € h"~s‡ x{~,tH™—tHvwnyx{z € h"r § x{z € h'h‚wv € x{zsz “ h'~,tH‡@À c = a + V~ .~n x V~ &à %—(Ü '?Û Õ ‚íFç '@Õ®ß¿í® â '©åÖ ‚âH(Ü ' 'Çí®ç‚å@Ö ' 'Çâ '¹Ý Ü0× Õwï·ÖØí®ç"ÜäåDñHÕÛÇåÜ¿ç‚åDñÜÞÛñÜ¿ç{Ý7ÖØßäâH×ØÕ®ÖÁÛÜ¿ÔÜ¿ç‚å@Õâ/ß ®çHÜÝ7Üì"ÕßÞî—à , × 'Dè í®ÛÔÜäç·å@×YÜß ®çHÜ Ý7Ü0Û Õ ‚íFç '&Õß¿íFâ '©åÖ ·â (Ü ' pÜ¿ç"Õç ®× ÕÖ ' ®Û Õ 8ß¿í®çHÜ Þà n. . n. . . . ç. vv wJx!y x!z. . . . . . 0. 0. .

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(161) 3. h‚ vrut"ºonpv h‚ h € qiºšhgz—v¦hgv rut"zex{‡wfŠtHryh}tHqi¨P‡ x{zov €D§ x{z € h¶Rmon,x{zi qs~s~9x h8´—qeh rut"ºRnpv h‚  h € q ºšhgzov'h‚wv}zoqsrpryhitHryx{‡ "x{zÅt ~nc = a ¶?¸ § tHnp‡ h € q|vwqs”?h € h4‡t·šx{ze4t{ƒ‚x{qewvwny´oqeh‚"h‚wv/ƒ·tHryƒgqsr “ h ~,tH‡ € *n ?hg‡ hgzovwnutHvwnyx{zhgzŠ qsnpº{tHzov rut"~s‡ x{~,tH™—tHvwnyx{z € h8´—q,tHvw‡ h8‡t‚šx{ze t{ƒ‚x{qe vwny´—qeh‚/²©ƒ cex{nywny € h fŠtHzsnydg‡ ht €s“ ´—q,tHv h7³´—qsnD”?x{‡wzehgz—vryhkvwqs”9h € h'‡t·šx{ze}t{ƒ‚x{qewvwny´oqeh‚·¶ †&x{qs‡ ¨©hg‡wfihg‡ ryh Rwv dgfih¼—x{z €s“ Ãezsnpv r § tHvwfixw~scedg‡ h²      “ ºšx{rpqsvwnyx{z € hrut/v hgfM~ “ ‡tHvwqs‡ h hgv € hkrut~s‡ h‚ wnyx{z`hgz¨Çx{zeƒgvwnyx{z € h'r § tHrpvwnpvwq € h7³ € h"rut˜fŠtHzsnydg‡ hkwqsnpºtHz—v hÀ ²¿‘7³ T (z) = max(T − 6.5 z , 216.5) ,   ²Ç•š³ αz 1− p(z) = p , T x  α = 9.8 hgv γ = 1.4 ¶0«"hM~srpqe·¼¹x{z\wqs~s~9xhi´—qehŠr § tHnp‡4ºšhg‡wn Ã,hirutÂryx{n € h‚k™—tH­#~,tH‡¿¨ÇtHnpv·¶ «'tHzeƒ‚hgvwv h “ vwq € h¼ zex{qe¨ÇtHny x{zeqszeh¾coo~?x{vwced‚ hÅwqs~s~sr “ fihgzovtHnp‡ h¢wqs‡Ârut € nywvw‡wnp”sqsvwnyx{z tHvwfix ~sc “ ‡wny´—qeh/hgz—vw‡ h}r § tHrpvwnpvwq € h € qŠºšx{rhgv ryh} x{r¼zex{qe¦wqs~s~?x x{ze ´oqehrutkºonpv h‚ h € qŠºšhgzov h‚ vz—qsrpryh¶ †&x{qs‡ ‡ “  x{q € ‡ hƒ‚hw wv dgfih¼{nprewq iv €D§ npzov “ ™‡ hg‡ hgzMv hgfM~e ryh‚vw‡ x{ny h‚´oq,tHvwnyx{ze € *n  “ ‡ hgz µ vwnyhgrpryh‚x{‡ € npz,tHnp‡ h‚%~s‡ “ ƒ “‚€ hgzov h‚·¼šhgzMƒ‚x{zewn €s“ ‡tHzovv x{qsv hF¨©x{ny·¼Hqsz˜~,t{ € h¦v hgfM~ewq ŠtHfMfihgz—v ~?hgvwnpv/~9x{qs‡'´oqeh4r § x{z¾~sqsny  hwqs~s~?x hg‡"´—qehryh‚/º{tH‡wnutH”sryh‚ C hgv C  x{z—v'ƒ‚x{zewvtHzov h‚·¶D†%tH‡ tHnprpryhgqs‡ 7¼?ryh~,t{ €D§ npz—v hg™‡tHvwnyx{z € x{npv $gvw‡ h˜vw‡ x{ze´oq “M€ hfŠtHzsnydg‡ hŠt €s“ ´oq,tHv h˜ryx{‡  € h˜rut‡ “  xHµ rpqsvwnyx{z@¶ Ä z|h Dhgv·¼sryx{‡  € h'rutM~s‡ x{~,tH™—tHvwnyx{z € h'r § x{z € h € hk~s‡ h‚ wnyx{z`ryhkryx{zs™ € h‚8vw‡t ˆ¿h‚ƒgv x{np‡ h‚ € h‚i‡t‚šx{zet{ƒ‚x{qewvwny´—qeh‚7¼ € h‚izex{qsºšh·tHq „Òƒcexoƒ‚Šºšx{z—v#hƒg‡ “ hg‡#x{qДsnyhgz € h‚#ƒ cexRƒ‚iºšx{zov ¨©qewnyx{zszehg‡hgz—vw‡ h'hgq „D¶ .ƒ‚h/fix{fihgz—vr ¼RqszÂx{q~srpqewnyhgqs‡  λ v hgz € hgz—vºšhg‡  ­ “ ‡ xs¶emon?qsz € h‚ v hgz € ºšhg‡ ¦­ “ ‡ xhgzovw‡ h € hgq „Š~?x{npz—v ·¼Rryh/ hg™fihgz—v´oqsnrpqsnDh‚wvt{  xRƒgn “ h‚wv wqs~s~s‡wnpf “ hgv x{z λ t{ƒgvwq,tHrpnyh'ryh‚~,tH‡tHfidgvw‡ h‚/´—qsn@ƒ·tH‡t{ƒgv “ ‡wny hkr § x{z € h € h'~s‡ h‚ wnyx{z@¶ ¸¹t° x{rpqsvwnyx{z € hŠƒ‚hgvhgze hgf4”sryh#h‚wv4~?x wnp”sryhi n rut € nywvw‡wnp”sqsvwnyx{z\npzsnpvwnutHryh € h‚4º{tH‡wnutH”sryh‚ h‚ v t{ƒ‚ƒ‚h‚  np”sryh¶s¸ § npzsnpvwnutHrpnytHvwnyx{z`h‚wv € x{zsz “ h"~,tH‡ rut x{rpqsvwnyx{z € qƒ c,tHfM~Â~s‡ xRƒ ceh'x{”sv hgzoqeh r § tHn € h € q|ƒ‚x € h Ä qsryhg‡'{«˜¶,†rpqe}~s‡ “ ƒgny “ fihgz—v·¼ryh‚8hg™fihgz—v  € tHzezex{vw‡ hnpfM~sr “ fihgz—vtHvwnyx{z ƒ‚x{‡w‡ h‚ ~9x{z € hgzo'v ˜qszeh € ny ƒg‡ “ vwnytHvwnyx{z|qszsn ¨©x{‡wfih

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