Implicit Stabilization Method for Numerical Modeling of Fluid Dynamics Problems

Transcription

1 Procgs o 4 WSEAS Iraoal Corc o Fl Mcacs a Aroyacs Eloa Grc Ags Ilc Salzao Mo or rcal Molg o Fl Dyacs Prols K ARTEMYE Is or Pyscs a Powr Egrg Sa Scc Cr o Rssa Frao Boaro Sq Os Kalga Rgo 4933 RUSSIA aryv@r Asrac: - I s wor lc rcal o or solvg D a 3D-soal l cacs a a ass rasr qaos s rs Dscrzao o govrg qaos s carr o o as o oooos alac ral MB rc scs wc allow o so ora gral rors o ral oraors A rc qao or rssr s rv ro rc coy a o qaos T scr qaos oa ar olar so larzao s roc a lc salzao rav rocr s vlo or ylg covrg solo Elc col acorzao o s loy or solvg larz o a a ass rasr rc qaos a a vara o o sg Cysv acclrao s al or solvg rssr qao Rsls o D woas low a 3D aral covco rcal ss ar rs Ky-Wors: - Fl cacs a a ass rasr qaos lc rcal salzao o col acorzao o wo-as low aral covco Iroco Ilc rcal cq [-] was sccsslly loy aalysg l cacs a a ass rasr rols aly or corssl orc covco lows A rs o s vlo or rcal rco o aral a covco rols wo-as lows a ors I gral cas l yacs rocsss ar govr y a sys o aral ral qaos wc volvs coy o a a ass rasr qaos sa qao c I a vcor or coy qao a qaos o oo Ryols qaos ay wr as ollows: 3 v U U U U U F v µ µ v U K 3 Mo qaos av orla accog or Bossss yoss w srss ε sor a vlocy orao sor coos g µ ε 3g µ v U K 3 wr s a sy µ µ µ a coc o olclar a rlc vscosy ar coos o Ecla rc sor s a rssr K a rl c rgy U a vlocy vcor Υ sor o vlocy orao F a oy orc vcor I a rasr rocsss ar r cosrao a sys -3 s a y a rgy qao U qv v q 4 wr s a aly q v - a volrc a grao q a a l Drc Aroaos Dscrzao o govrg qaos s carr o sg oooos alac ral MB rc scs wc allow o so ora gral rors o ral oraors A rvao MB rc sc s as o o cosrao o coy qao a rasr qao For sa o slcy cosr ollowg sys a o oa 5 g

2 Λ wr Λ A ssac ay a vlocy coo a aly a cocrao c A oooos scs sla ora rory o a l low as a owsra rasr o so srac o a covco oo A alac cosrvao rory s a scr aalog o Osrogras-Gass or: 7 wr s vcor oral o oary Aor rory o oraor Λ cocrs ll coro o rs scrg coco rasr o rgy ssao law ral avor ay orla or o gral rlaos U 8 T acco o rory 8 s scally ora rg log- rcal slao o l yacs rols Gr os a gr sacgs ar a rglar rgo Π Π as: 3 ; 5 ; ; 5 ; 5 ; wr s a l a s r - a sacg o scrzao I ollowg orlas sor oaos o gr co ar s: ± ± ± or s a l- avg or oso T qao 9 s o rcly cl lc rav rocr s as or rvao o rssr rc qao Prssr rar cocrao ar co crs o lary vol ] [ coos o vlocy vcor - crs o acs Bo MB sc a a slac o cooras o a gr cos al o oa yscally ralsc ls o co vals Drc coy qao s wr as ξ 9 Trasr qao s gra ovr a lary vol s a -rco coarso w ] [ Krocr s syol MB aroao o qao as ollowg or: A O A Λ a a Oraor A ca wr ollowg rc or: Procgs o 4 WSEAS Iraoal Corc o Fl Mcacs a Aroyacs Eloa Grc Ags

3 a c A a ν 5 ν 5 a c c ν I raccal calclaos co c ay rlac w asly co rsso 3 c 3 arzao Procr a Ilc Salzao Mo A rssr scr qao s oa sg o rc qaos or a rc coy qao 9 I s cas ssac s a vlocy coo a rg ar o coas A gral or o rssr scr qao ca rs as P 3 a c P Ts yroyacs scr rol volvs o-lar qaos or vlocy coos or rssr a gral cas sa qao Ilc salzao o s vlo or solvg o-lar sys o rc qaos arzg s carr o sc a way a oraor A cos lar rlavly o w s ow os a r o rao or a r o salzao s Ilc rcal rocr s wr as ollows A τ P τ wr τ s a s o salzao I sol o a lar oraor P s sl-ao cas a Sccssl raccal ralzao o lc rcal algor s o a o or solvg lar rc qaos rs o all llcoo rssr qao Coaoal cls av ovrca w sag o col acorzao o rs sggs y Blv [3] Ilc rcal rocr or rco o rssr a vlocy ls volvs ollowg sags o calclaos Usg ro rvos rao cocs o rc qaos ar calcla Eloyg col acorzao o w Cysv acclrao [] sl-ao rssr qao s solv a sg orary vara o o w calcla vlocy coos Iraos o crr layr ar so w a rs accracy ς o ll o rc coy qao s rac: Procgs o 4 WSEAS Iraoal Corc o Fl Mcacs a Aroyacs Eloa Grc Ags

4 Procgs o 4 WSEAS Iraoal Corc o Fl Mcacs a Aroyacs Eloa Grc Ags aς ς 4 y s 8 U 79 s volrc vo raco 4 rcal Molg o Trl Two-Pas l low Dvlo lc rcal o wosoal cas av ralz as FUIDD co T co as o varos alcaos a o o s rcal rco or rl wo-as low w sal -sa vo raco rol T rc ral vsgaos g [4 ] a local caracrscs col sy o l o-qlr wo-as lows av rval arclar cs o aoalos wall rco acors a a rasr cocs cras coos w roaly wall cocrao vo a o gas vaor as a low vlocs o orc low D o o-or sro o gas ovr cross sco war gas-lq lows wall sar srsss ca y 9 s gr a or sgl-as low Maacal a rcal olg o aov o rgs o gas-lq lows s colca rol so o ros o rcal vsgaos s o oa vlocy rssr ls a sar srsss sg ral raal vo raco rols Two-as low sy s calcla as wr - vo raco a g sy o l a gas corrsogly Hyroyacs qaos ar wr r-z gory or ro o ras R Trl vscosy g µ s sv o wo µ o r coos µ µ µ o lq rlc o rlav oo o ls a or µ o aoal rlc cas y l agao Mor al aacal ol s scr [7-8] I sol oc a oary layrs ar vry ror corrc sar srss scro as al gr ar wall Ilc rcal o allows o loy g rrglar gr w logarc corssly oary layrs zos So rsls o rcal ss or woas war l low ar rs g -3 T vlocy rol raal vo raco sro ol cross-sco o ar 83 ar sow Fg Erac l vloc- U s Y Fg : q aal vlocy a vo raco rol; - calclao - ral aa; vo raco U λ λ Blaz zr Fg : Rlav rco acor; calclao - r Y Fg 3 q aal vlocy R U 8 s ; - calclao - r

5 Procgs o 4 WSEAS Iraoal Corc o Fl Mcacs a Aroyacs Eloa Grc Ags Rlav rco acor rs g sows ssal cras coarso w Blass acor or sgl as low rcal rsls ar sasacory agr w ral aa [4] I g 3 vlocy rols ar rs solss or wr Y rr Y Y τ µ solss coora τ τ w - rco vlocy; τ w wall sar srss; z τ - rco scal vlocy I ca s a rcal ol scrs oary layr zo w goo accracy o Y 5 rcal Rsls or 3-D Covco Bcar Prol Tr-soal cas o lc rcal o s ralz as FUID3D co As a s o rcal o a co car coaos av ror T ars [9 ] coas ral rsls or a covco a ccal ar-ll closr Ts rol s sggs as 3-D car rcs A sc o rs [9 ] s sow Fg 4 coarsos ar rs al a g 5-8 Tal Avrag ssl r rsls E Ra [9 ] 383 ± ± 8 79 ± ± ± ± 9 Y Prs ar [] [] X Fg 5 Flow ars la z5 9 Ra Fg 4 Scacs o ccal cavy car W o cc s 7 clao agl s s o 45 a 9 c swall rar vars larly ro col ac o o ac T c 3 K T 37 K Gas rors ar vala a a rar T 335 K Pr7 rssr s qal o rssr a gvs sr Raylg r Calclaos ar coc sg or a o-or grs a r r o gr os: So rcal rsls a Y X Fg Dsro o local ssl r o 7 col wall 9 Ra

6 Procgs o 4 WSEAS Iraoal Corc o Fl Mcacs a Aroyacs Eloa Grc Ags Y X Fg 7 rar coors la z5 45 Ra s Fg 8 Avrag ssl r o col wall Ra Coclso Ilc rcal o or solvg D a 3Dsoal l cacs a a ass rasr qaos s scr Ilc o s sal a covrg als o larg s a rc coaoal rs Prs rsls o D wo-as low a 3D aral covco rcal ss sow oal ossls o o Goo agr w ral aa s rac Acowlgs Ts wor was sor y Rssa Foao or Faal Ss a Govr o Kalga Rgo r Gra Rrcs: [] Aryv K Ilc Mo or Solvg o avr-sos Eqaos aral arals Molg Mcacs ovosrs ol [] Aryv K Dvlo o rcal Mos or Solvg Fl Dyacs Prols Tss Is o Pyscs a Powr Egrg Os Rssa 997 [3] Blv I A rcal Mo or Solo o Two-Dsoal a Tr-Dsoal Eqaos o Dso Ma S [4] aoryaov E Kassy O ocal Caracrscs o Uwar Gas-q Flows I J Mlas Flow ol [5] Kassy O & Ra Dowwar Bly Gas-q Flow a rcal P I J Mlas Flow ol [] Sao Y Saao M Sogc K Mo a Ha Trasr Two-Pas Bl Flow-II A Coarso w Eral Daa a Torcal Calclaos I J Mlas Flow ol [7] Aryv K Koro Y Two- Dsoal Molg o Two Pas Bl Flows o Bass o Sgl-Fl Dscro Mo a Algor Cocaos o Hgr Scools clar Powr Egrg [8] Aryv K Koro Y rcal Ss o o-mooo o Fraco Prols Ecs o Hyroyacs a Ha Trasr Two-Pas Bl Flows Coarso w Er Cocaos o Hgr Scools clar Powr Egrg [9] og WH Hollas KGT a Brgr AP O a Pyscally-ralzal Bcar Prol Iral aral Covco I J Ha Mass Trasr 998 ol [] og WH Hollas KGT a Brgr AP Eral ssl rs or a ccal-cavy car rol aral covco I J Ha Mass Trasr 999 ol [] Mossa R Prco o aral Covco a Ar-Fll Ccal Cavy sg Fl Sowar ICHMT I Sy o Av Co Ha Trasr Pal Cov Qsla Asrala May [] Krr K CHT : alao Ercs: aral Covco a Ar-Fll Ccal Cavy ICHMT I Sy o Av Co Ha Trasr Pal Cov Qsla Asrala May