Unsteady flows in moving reference frame

Transcription

1 Usay flows i moig fc fam Ralf Hiich TAU Taiig, auschwig, 5h Fbuay 8 TAU Taiig Usay flows i moig fc fam Oiw Moiaio Nai-oks quaios i gal moig fc fam Tim igaio fo usay flows imilaiis a iffcs bw im iscizaio fo say & usay applicaios Tam of gi lociis Exampls, paam sigs a his Pichig oscillaio Tmpoal o of TAU Equial s cass fo cosiscy chck o Kámá s TAU Taiig

2 Usay flows i moig fc fam Moiaio Usay ffcs i aoyamics Aolasic phoma Ifluc of guss Mauig aicaf.g. halig qualiis ox bus Flow spaaio... always if i is gig agous... Th picio of usay ailoas plays a sigifica ol i h aicaf sig pocss 3 TAU Taiig Usay flows i moig fc fam Nai-oks quaios i gal fc fam aig poi fo h iaio of N-quaios fo moig fc fam i TAU N balac quaios fo abiay cool olum / bouay moig wih h flui sp D D D D D D T, / Mass of flui iclu wihi T T isc pe T q ubsaial iai ufac of olum Δ Δ 4 TAU Taiig

3 Usay flows i moig fc fam Nai-oks quaios i gal fc fam This fom of balac quaios is o y appopia fo umical am Usag of Ryols aspo hom o asfom o cool olum fix i spac a im D * * * * D * * moig wih flui sp moig wih abiay sp 5 TAU Taiig Usay flows i moig fc fam Nai-oks quaios i gal fc fam D D D T T T isc pe D, D T q D / N i iial sysm fo cool olum fix i spac a im T [ ] T q D D * * * 6 TAU Taiig 3

4 4 TAU Taiig 7 Usay flows i moig fc fam Nai-oks quaios i gal fc fam Chag of.g. mass i abiay moig cool olum moig wih lociy TAU Taiig 8 Usay flows i moig fc fam Nai-oks quaios i gal fc fam T q T N i iial sysm fo abiay moig cool olum Disaaag: Mic is im pa

5 5 TAU Taiig 9 Usay flows i moig fc fam Nai-oks quaios i gal fc fam Chag fom basis of iial sysm o basis cos lik lociy:,, 3,, a NOT alig wih lai lociis!! wok wih h absolu lociy co TAU Taiig Usay flows i moig fc fam Nai-oks quaios i gal fc fam Poblm : asis of oaig sysm is im pa ϖ λ λ λ λ λ λ λ λ λ λ

6 6 TAU Taiig Usay flows i moig fc fam Nai-oks quaios i gal fc fam T ϖ q T N i moig cooia sysm fo abiay moig cool olum TAU Taiig Usay flows i moig fc fam Nai-oks quaios i gal fc fam,, flx o as

7 Tim igaio fo usay flows Explici im sppig impls way o pfom im accua simulaio wih TAU Us h xplici basic Rug-Kua im igaio schm us fo say poblms, UT wich of all cogc acclaio chiqus, bcaus hy soy h im accuacy NO local im sppig, siual smoohig, muligi To b im accua, h im sp Δ has o h sam fo ach cll global im sp To b sabl, you ha o slc h miimum of all local im sps fom h fil Δ miδ i R-K / LUG local.s. muligi 3 TAU Taiig Tim igaio Explici im sppig y wll sui, if gi h aiaio of h gi spacig of a msh is small hock-ub poblm Δ mi Δ i CFLΔx i mi λmax hock-ub poblm, lis of cos. siy Expasio fa Coac sufac shock High pssu low pssu 4 TAU Taiig 7

8 Tim igaio Explici im sppig a fficicy fo mshs wih fi local soluio.g. i bouay lay Pichig NACA, Ma.755, k.6, α.6 lif mom Gi: 6 x 3 Abou pysical im sps p pio fo xplici Eul calculaio Esimaio of im sp siz fo iscous flows: igifica fqucy: Hz Δx mi : -5 m a 34 m/s Δ ~ 3x -8 s << T 6-7 im sps p pio c m 5 TAU Taiig Tim igaio fo usay flows Implici im sppig: Dual im sppig How o bypass h poblms of h xplici basic schm?? Us of a implici im iscizaio fo biy fo cosa mic R Δ R Iai soluio usig h ual im sppig mho Jamso τ ν R ν ν 4Δ R τ τ R τ 4 3 τ psuo say sa τ ν 6 TAU Taiig 8

9 Tim igaio fo usay flows Implici im sppig: Dual im sppig Cogc of h pichig oscillaio of a aifoil a b a R-K / LUG local.s. muligi b siual 7 TAU Taiig Tim igaio fo usay flows Implici im sppig: Dual im sppig τ s R 4Δ Poi implici R τ α sδτ Δ s s R oluio wih Rug-Kua o LUG abiliy sicio fo saa Rug-Kua CFL Δx Δτ mi, Δ λ s Δτ α Δ s α sδτ Δ α sδτ s ν Δ s R ν 8 TAU Taiig 9

10 Tim igaio fo usay flows Implici im sppig: Tmpoal o of TAU I TAU you ca slc bw s, o 3 o accuacy wih spc o im: Δ 4 Δ R 3 R 8 9 R 6Δ 9 TAU Taiig Tam of gi lociis Iial sysm T Moig sysm as o ω, flx T, TAU Taiig

11 Tam of gi lociis aa am of whilfluxs:,, ϖ TAU Taiig Tam of gi lociis aa am of whilfluxs: fsam cosiscy chck appoxima whilfluxs,, ϖ TAU Taiig

12 Tam of gi lociis Exac am of whilfluxs: fsam cosiscy chck xac whilfluxs N ϖ i N ϖ ϖ i i N i i i i 3 TAU Taiig Tam of gi lociis Gomic cosaio law ha happs solig h balac quaios fo fomig mshs u fsam coiios? Oly fafil bouais a ps, o soli walls! All quaiis shoul mai cosa! Coiuiy quaio is simplifi fom o This quaio is us as aiioal balac quaio fo h cool olums! This sus h so call fsam cosiscy 4 TAU Taiig

13 3 TAU Taiig 5 Tam of gi lociis Gomic cosaio law Usag fo o mpoal iscizaio 4 3 Δ R 4 3 Δ R ν τ 4 3, Δ facs i i i Δ facs i i i, 3 TAU Taiig 6 GCL off GCL o c p isibuio fo wo iff ims wih a wihou GCL Tam of gi lociis pscib mom of cyli ip Fsam cosiscy TAU ig cyli msh wih fafil bouais flowfil iiialilz wih fsam quaiis Cp~O -4 Cp~O -5

14 Exampls, paam sigs a his Pichig oscillaio of a aifoil Task: compuaio of h pichig oscillaio of a aifoil aou is qua poi O flow Mach umb: Ma.755 ma agl of aack: α Pich ampliu: Δα. 5 Ruc fqucy: k.68 ω c k f ω Rfc lgh cho: c f m Th agl of aack ca h b compu as α α Δα si ω π T pio c f m 7 TAU Taiig Exampls, paam sigs a his Pichig oscillaio of a aifoil p : pfom say compuaio NACA, Ma.755, α..8 - siy siual lif MG-cycl 8 TAU Taiig 4

15 Exampls, paam sigs a his Pichig oscillaio of a aifoil p : ppa usay compuaio Dual im : - Usay calculaio: ual Usay show psuo im sps /: Usay physical im sps: 5 Usay i iaios p im sp: Miimum umb of i iaios p im sp: Usay implici schm o: Usay xapolaio o: Compu hamoics of global focs /..: Compu hamoics o sufac /: Dfaul alu is o say compuaio ual ual im sppig global global im sppig 9 TAU Taiig Exampls, paam sigs a his Pichig oscillaio of a aifoil p : ppa usay compuaio Moig gi : - Typ of mom: pioic Oigi of local cooia sysm:.5 Dg of Foui sis fo oaio: ω cf Ruc fqucy fo oaio:.68 k Ruc fqucy fc lgh: Foui cofficis fo oaio cos yaw: Foui cofficis fo oaio cos pich: Foui cofficis fo oaio cos oll: Foui cofficis fo oaio si yaw: Foui cofficis fo oaio si pich:.5 Foui cofficis fo oaio si oll: mf α α Δα si ω Numb of imsps p pio: 5 3 TAU Taiig 5

16 Exampls, paam sigs a his Pichig oscillaio of a aifoil p 3: pfom usay compuaio.8 - siy siual lif MG-cycl 3 TAU Taiig Exampls, paam sigs a his Pichig oscillaio of a aifoil p 3: pfom usay compuaio.8 - siy siual lif MG-cycl 3 TAU Taiig 6

17 Exampls, paam sigs a his Pichig oscillaio of a aifoil p 3: pfom usay compuaio lif.4 lif /T pio alpha 33 TAU Taiig Exampls, paam sigs a his Pichig oscillaio of a aifoil p 3: pfom usay compuaio C p,a. -. C p,. C p,im C p X X X 34 TAU Taiig 7

18 Exampls, paam sigs a his Pichig oscillaio of a aifoil: Chck of mpoal o Ts cas lik bfo O flow Mach umb ma agl of aack: Pich ampliu: Ruc fqucy: Ma. 755 α Δα. 5 k.68 Pfom compuaios wih s, a 3 o accuacy Fo ach o compu 5 oscillaio pios wih 48, 96, 9 physical im sps p pio Pfom a fc soluio wih 8 im sps p pio Dfiiio of h o: Diffc of al pa of h lif bw fc soluio a compuaios wih 48-9 im sps p pio c L, al cl, al, REF 35 TAU Taiig Exampls, paam sigs a his Pichig oscillaio of a aifoil: Chck of mpoal o Ts cas lik bfo ps p pio N s o C L, al o C L, al 3 o C L, al Δ om Δ / Δ N c L, al cl, al, REF log o log Δ N 48 om, N 48 log log Δ N 9 om, N 9 36 TAU Taiig 8

19 Exampls, paam sigs a his Pichig oscillaio of a aifoil: Chck of mpoal o Ts cas lik bfo c L, al cl, al, REF log o log Δ N 48 om, N 48 log log Δ N 9 om, N 9 37 TAU Taiig Exampls, paam sigs a his Equial s cass fo cosiscy chck: Roaig aifoil Ts cas lik bfo Aifoil oaig aou x o y axis Th agula lociy is ajus i such a way, ha h oaioal Mach umb is.755 i boh cass If yhig is implm cocly, wihi h oaig fam a say sa shoul b ach cala quaiis lik pssu / siy shoul b fo boh cass h sam Fo lag isac o h oaio axis, h sul shoul b quial o say suls i a fix fam fo Ma TAU Taiig 9

20 Exampls, paam sigs a his Equial s cass fo cosiscy chck: Roaig aifoil Rfc Mach umb:. Rfc mpau: Usay physical im sp siz: Typ of mom: igi Oigi:.5. - Dg of polyomial fo oaio: polyomial cofficis fo oaio psi: # psi psi # # psi psi psi* psi*^... i g! # psi/ psi *psi*.. # > omga cos psi # _o.755 * sq.4 * R_gas T_f omga * R # CHECKENCHECKEN # _o.755 * sq.4 * 87 * [m/s] 5.67 [m/s] # omga _ifiiy / [s^-].556/[s] [gs/s] # T_pio pi / omga 4.867[s] 39 TAU Taiig Exampls, paam sigs a his Equial s cass fo cosiscy chck: Roaig aifoil 4 TAU Taiig

21 Exampls, paam sigs a his o Kámá ox s Lamia flow wih slf iuc usays Ma., R T 73.5K Lamia flow T D pio Ma a Ma γ RT ~. 4 TAU Taiig Exampls, paam sigs a his o Kámá ox s Lamia flow wih slf iuc usays Ma., R T 73.5K Lamia flow T D pio Ma a Ma γ RT T pio. 437 s ~. Dual im : - Usay calculaio: ual Usay physical im sp siz: Usay physical im sps: Usay i iaios p im sp: 6 Miimum umb of i iaios p im sp: Usay implici schm o: Rfcs : - Rfc mpau: 73.5 Rfc Mach umb:. # ouhal umb : D / T_pio * _if. # _if Ma * sq.4 * R * T_if #. * sq.4 * 87 * 73.5 # T_pio ~ D / _if * [s] 4 TAU Taiig

22 Exampls, paam sigs a his o Kámá ox s Lamia flow wih slf iuc usays Ma., R T 73.5K Lamia flow T D pio ~. C-lif im [s] T pio ~.4 T pio. 437 s 43 TAU Taiig