SIMULATION OF THE FLOW AND ACOUSTIC FIELD OF A FAN

Cofeece o Modellg Flud Flow (CMFF 9) The 14 th Iteatoal Cofeece o Flud Flow Techologes Budapest, Hugay, Septembe 9-1, 9 SIMULATION OF THE FLOW AND ACOUSTIC FIELD OF A FAN Q Wag 1, Mchael Hess, Bethold Matyscho, Pete Pelz 1 Coespodg Autho. Depatmet of Mechacal Egeeg, Cha of Flud Systems Techology Techsche Uvestät Damstadt, Petesest., 6487 Damstadt, Gemay. E-mal: q.wag@fst.tu-damstadt.de ABSTRACT The focus of the peset wo s the steady ad usteady umecal smulato of flow feld ad flow-duced acoustc feld of a fa usg a hybd appoach. The steady smulato of the flow feld s caed out wth a ealzable -epslo tubulece model. I a secod step the esult ae used fo the evaluato of the acoustc souces, whch ae used as put data of the Boadbad Nose Model. Fom ths computatoal acoustcs (CA) we get a qualtatve map of acoustc powe level the ete computatoal doma. Fom steady flow felds wth dffeet mass flows as let bouday codto the chaactestc cuve of the fa (pessue vs. mass flow) s evaluated. I the usteady smulato, the acoustc ose popagato s computed usg the Ffowcs Wllams ad Hawgs (FW-H) aalogy. The souce tem the acoustc popagato equato s acheved fom the CFD esult. Wth ths usteady smulato the taset acoustc powe level evey locato ca be calculated, whch eables a FFT-aalyss of the acoustc feld. Keywods: axal fa, computatoal flud dyamcs (CFD), computatoal acoustcs (CA), acoustc aalogy. NOMENCLATURE Z IB [-] umbe of mpelle blades Z g [-] umbe of gude vae f z [Hz] fequecy [s -1 ] otatoal speed ρ [g/m ] flud desty ρ [g/m ] upetubed flud desty ρ [g/m ] flud desty petubato t [s] ecepto tme τ [s] emsso tme H [-] Heavsde fucto δ(f) [-] Dac delta fucto p [Pa] pessue of the udstubed medum p [Pa] soud pessue p t [Pa] total pessue P [Pa] compessve stess teso T [g/ms ] Lghthll stess teso τ gap [-] dmesoless gap wdth s [m] gap wdth D IB [m] damete mpelle blades C µ [-] costat ψ [-] dmesoless total pessue se ψ deal [-] dmesoless deal total pessue se ψ V [-] dmesoless total pessue se loss ϕ [-] dmesoless volume flux u [m/s] flud velocty v [m/s] suface velocty [m] dstace fom souce to obseve M [-] mach umbe Q [m /s] volume flux η [-] effcecy S Ω [s -1 ] defomato teso S [s -1 ] mea ate of sta teso 1. INTRODUCTION The acoustc emsso of fas s a cosdeable ose souce coolg system. Nose fom axal fa ases maly due to the tubulet flow aoud fa blades (boadbad) ad teacto of popelle ad fo example gude vae o suppot stuts (toal). The latte oe s depedet o the moutg aagemet of the fa blades. The fa blades ae most cases equdstat ccumfeetal decto ad cause dscete fequecy compoet ad ts hamocs wth 1m each otato, whch deped o the speed ad the umbe of the popelle blades: f z ZIB. Fo axal fas the ampltudes accodg to z f ceases due to teacto of the popelle ad gude vae o suppot stuts. Blade umbe atos Z IB / Z g of 1 ad.5 ae to be avoded, othewse toal soud powe level would stogly cease. I ths wo the vestgated fa has 9 mpelle blades ad 1 gude vaes. 1

I the desg phase t s mpotat to have a clea pctue of the expected hydodyamc ad acoustc pefomace of the fa. To acheve ths, a hybd method s ecommeded. Oe possble hybd method amog othes s to use CFD the ea-feld povdes put data fo a acoustc tegal fomulato to calculate adated ose. I ths wo a steady state CFD aalyss of a axal fa s caed out to get the chaactestc cuve ad the boadbad ose emsso of the fa. A usteady state flow smulato s caed out fo the CA usg the FW-H aalogy [1], whch s based o Lghthll s Acoustc Aalogy (LAA) [] deved fom the cosevato equato of mass ad mometum.. PROBLEM FORMULATION The vestgated axal fa cotas sucto ad pessue chael o the left ad ght sde espectvely. A s suced by the fa though the let ozzle followed by the aechoc chael ad sucto chael. O the pessue sde at the ed of the aechoc chael a choe seves fo adustg the fa wog pots. The total soud powe s measued the sucto chael ad pessue chael. The fa has a.% elatve gap, defed as τ s /. The otatoal speed was ept gap D IB costat at 41.67 s -1.. THE HYBRID APPROACH.1 Flow feld The flow feld s modelled wth the ealzable -epslo two equato tubulece model [] fo the Reyolds-aveaged Nave-Stoes (RANS) equato. Ths model cotas a taspot equato fo the dsspato ate based o the dyamc equato of the mea-squae votcty fluctuato ad a fomulato fo the tubulet vscosty µ t volvg a vaable C whch esues the postve µ omal stesses. It s mathematcally descbed by the followg equatos (1-): η C1 max.4,, η+ 5 η SΩ, S S Ω 1 ( S S u u + ) I these equatos, G ad G b deotes the geeato of tubulece etc eegy due to the mea velocty gadets ad buoyacy espectvely. Y epesets the cotbuto of the fluctuatg M dlatato compessble tubulece to the oveall dsspato ate. C ad C 1 ae costats. σ ad σ ae the tubulet Padtl umbes espectvely fo ad. S ad S ae use-defed souce tems.. Acoustc feld..1 Boadbad model Dect smulato ad acoustc aalogy methods ae vey tme expesve. Fo desg pupose a detaled acoustc fomato s ofte ot eeded, so that boadbad models ca be suffcet. Boadbad models eque oly fomato extacted fom steady RANS calculatos (mea flow feld, tubulet etc eegy, ad the dsspato ate ). The soud eegy s dstbuted ove a boad age of fequeces. The fst type of a boadbad models s deved by Poudma [4] fo sotopc tubulece ose (quadupole souces) usg Lghthll's acoustc aalogy. A othe type of the boadbad models s based o the Lghthll-Cule s [5] equato fo dpole ose, whch ases tubulet bouday laye ea a sold body suface. The boadbad models ae developed fo specfc poblems ad ot applcable geeal. They ae lmted to the boadbad ose chaactestcs pedcto ad do ot povde ay toal fomato. t t wth ( ρ) + ( ρu ) ( ρ) + ( ρu ) ρc S 1 μ t μ + x σ + G +G ρ Y + S ρc +C1 + ν b μ t μ + x σ + C M G b + S (1) ().. The FW- H tegal methods The Lghthll equato s oly applcable to cases wthout a body wth the flud. Cule [5] exteded the Lghthll equato to ovecome ths estct. Late Ffowcs Wllams-Hawgs (FW-H) [1] exteded the Lghthll-Cule s equato futhe ad povded a stadad appoach fo the pedcto of ose ogated fom otatg blades. Moe ecetly, usg the so called pemeable suface fomulato, the FW-H equato s capable to pedct the soud geeated by equvalet acoustc souces such as moopoles, dpoles ad quadupoles. Assumg a suface S : f ( x, t) to be a close movg suface pemeable to the flud, whch evey teacto of sold suface ad the

flud eclosed (Fg. 1). The fucto f s defed as f < sde S, f > outsde S ad f, wth whch the omal vecto ca be calculated. Accodg to Fg. 1 FW-H [1] exteds the Lghthll s acoustc equato by combg mass ad mometum equatos of flud mechacs usg the Heavsde fucto H ( f ) to the followg equato: 1 a t x p' t p' {[ ρ( u v ) + ρ v ] δ( f )} [ P + ρu ( u v )] δ( f ) { } { T H ( f )} + () The ght-had sde equato () ae souce tems fo the wave equato. The fst two tems o the ght-had sde ae the thcess, loadg ose souces espectvely ad behave le moopole ad dpole souce tem. The last tem s a volume tem, whch s called quadupole souce tem dstbuted the aeodyamc feld exteo to souce (emsso) suface, ad s the double dvegece of the Lghthll s stess teso: T ρu u + P a ρ ) δ wth P f > f < u pδ µ ( ρ (4) u + u f S : f ( x, t) Fgue 1. The pemeable tegato suface δ (5) Oe ca get Reyolds stess teso ρ u u fom tme-aveaged Lghthll s stess teso. Because of popagato effect o the adato path betwee the souces of the petubatos ad the obseve, all the ght-had sde souce tems ae geeally eglgble outsde a lmted doma (souce doma). By tegato of equato (), the fst ad secod tem lead to a suface tegal whle the thd tems leads to a volume tegal o a ego of space V outsde of to the tegato suface. Whe f cocdes wth the body suface, usg the mpemeablty codto u v ad the Gee s fucto ad eglectg the quadupole souce tem, equato () leads to the followg tegal fom. 4πp ( x,t) ρ U + U ds + f (1 ) τ ρ U { M + a ( M f (1 ) 1 L ds a + f (1 ) τ L L M ds + f (1 ) τ 1 L { M + a ( M a f (1 ) wheeτ t / a ad U L v / ( + ρ ρ u P ˆ + ρu ( u v ) v ) )} ds + τ )} τ ds (6) (7) Ths acoustc fomulato s based o Faassat s [6] 1A soluto of the FW-H equato. The 1A fomulato s a soluto of the FW-H equato fo thcess ad loadg ose souces obtaed by tegato o the body suface ad eglectg the quadupole tem. The FW-H aalogy s wdely used fo lea aeo-acoustc poblems such as the flow though fa mpelle. The mpotat lmtato of the FW-H aalogy FLUENT 6..6 [7] s that t does ot accout ay effect of the flow o popagatg soud. 4. SIMULATION SETUP I the chael, hexahedal elemets ae used fo the mesh. Aoud the fa tetaede elemets ae used to efe the mesh fo captug the flow feld moe exactly. The mesh cossts of 1.7eG elemets. The let s defed as a massflow let ad the outlet s specfed as a pessue outlet. The fa s modelled wth the foze-oto appoach fo steady state smulato ad sldg mesh appoach fo usteady state smulato. The mateal data of a desty of 1.5 g/m ad a dyamc vscosty of 1.7894e-5 Pa.s ae used. The flud s dealed as compessble.

5. RESULTS COMPARISON WITH EXPERIMENT The smulatos ae caed out wth FLUENT 6..6. Each steady state smulato u taes appoxmately 4 days ad the taset smulatos 7 days o a Itel XEON-pocessos wth Quadcoes mache ug Lux. Fg. shows the total pessue se acheved fom steady state smulato, compaso wth expemet data gaed by Kastadt [9]. It shows deal total pessue se (ψ deal ) ad total pessue se loss (ψ V ) all vaables ae elato to the effcecy optmum. The dffeece betwee the calculated/expemetal data ad ths deal oe s pessue se loss. The dmesoless total pessue se ad mass flux ae defed as follows: 4Q ϕ π DIB (8) pt ψ ρπ D IB Fom the measued o smulated values the deal cuve ad the pessue loss s gaed ψ ψ deal, ψ V ψ deal ψ. η (9) Thee s a clea dffeece betwee the computato ad measuemets what epesets a aveage dffeece of about 1% total pessue se. The cuves of deal total pessue se fom smulato ad expemet should be theoetcaly detcal. The dffeece of these two cuves s due to eo smulato ad expemet as well. I compaso to expemet, lage total pessue se ad lowe total pessue se loss ae acheved fom smulato. The easos fo ths dffeece ae as follows: a) Thee s a small dffeet agle of gude vae betwee smulato ad expemet. b) The used tubulece model s ealzable - epslo model. I ths model C µ, used fo calculato tubulet vscosty µ t, s ot a costat as the stadad -epslo [8] model, but a fucto of the mea sta, otato ates, the agula velocty of the system otato, ad the tubulece felds ( ad epslo). C µ cludes a tem of the agula velocty due to the system otato. Accodg to [7] smulato wth ths tem s oly tested fo sgle otatg efeece fame. Howeve, t has bee mult otatg efeece fame system ths wo, whch ths tubulece model poduces o-physcal tubulet vscostes. c) The usteady flow s smplfed as steady flow the smulato to save CPU-tme. Fg. shows the effcecy compaso wth expemet data. The dffeece betwee these two cuves s about 5%. Fg. 4 shows the esults of tubulece testy whch s defed as: Fgue. Ideal total pessue se ad total pessue se loss 4

Fgue. Effcecy compaso wth expemet wth U the mea velocty (Reyolds aveaged) ad tubulet etc eegy, whch s spu of Reyolds stess teso, acheved fom CFD. Ths tubulece testy s decsve fo the boadbad ose level peseted Fg. 5. Smla cotou ca be foud Fg. 4 ad Fg. 5. The usteady state esults wth FW-H aalogy ae peseted Fg. 6. f z ad ts hamocs ae qualtatvely coect. The souce suface f(x, t) s located o the sold body suface ad quadupole Fgue 4. Tubulet testy aoud the mpelle ad gude vae Fgue 6. Spectum of ose souce doma Fgue 5. Boadbad ose aoud the mpelle ad gude vae (1) I, U souce tem s eglected. Neglectg the quadupole tem s a pactcal appoxmato, because the volume tegato s vey tme cosumg ad ths tems ae oly mpotat fo tas/supe-soc flows [1]. Smulatos wth efed gd show o otceable dffeece total pessue se (Fg. 7). 6. CONCLUSIONS I the peset wo fluddyamcs ad acoustcs of a fa have bee studed. 5

Total pessue ses smulated wth the commecal CFD pogam FLUENT agee easoable well wth expemet statoay state. Wth the boadbad model acoustcal calculato gves oly qualtatve esults due to ts physcal fomulato (steady state, ealzable -epslo [4] I. Poudma. The Geeato of Nose by Isotopc Tubulece. Poc. Roy. Soc., A14:119, 195. [5] N. Cule. The I fluece of Sold Boudaes upo Aeodyamc Soud. Poceedgs of the Royal Socety of Lodo. Sees A, Fgue 7. Total pessue se tubulece model). Howeve ths model has advatage lmted CPU tme, The secod ma pat of ths wo s taset calculato. The calculated specta show the coect blade sequece fequeces (f z ad ts hamocs). Hee the soud level s oveestmated, because FW- H aalogy s developed fo soud adato to the ope feld. ACKNOWLEDGEMENTS The authos appecate the expemetal data povded by M. Kastadt. REFERENCES [1] Ffowcs Wllams J.E., Hawgs D.L., Soud abtay moto, Phlos. T. Roy. Soc. A 64 (A1151) (1969) 1 4. [] Lghthll M.J., O soud geeated aeodyamcally, I: geeal theoy, P. Roy. Soc. Lod. A Mat. 1 (195) 564 587. [] T.-H. Shh, W. W. Lou, A. Shabb, Z. Yag, ad J. Zhu. A New -epslo Eddy-Vscosty Model fo Hgh Reyolds Numbe Tubulet Flows - Model Developmet ad Valdato. Computes Fluds, 4():7 8, 1995. Mathematcal ad Physcal Sceces, 1:55 514, 1955. [6] Faassat, F. Ad Succ, G. P., The Pedcto of Helcopte Roto Dscete Fequecy Nose, Vetca, Vol. 7, No. 4, pp. 9-, 198. [7] Fluet Use Gude fo FLUENT 6., 6 [8] B. E. Laude ad D. B. Spaldg. Lectues Mathematcal Models of Tubulece. Academc Pess, Lodo, Eglad, 197. [9] S. Kastadt, Ifluece of the Tp Cleaace o the Acoustc ad Aeodyamc Chaactestcs of a Fa. Dploma Thess, Depatmet of Mechacal Egeeg, Cha of Flud Systems Techology, TU Damstadt, Gemay, 8 [1] K. S. Bete, Modelg Aeodyamcally Geeated Soud: Recet Advaces Roto Nose Pedcto, Peseted at 8th Aeospace Sceces Meetg ad Exhbt, AIAA - 45, Jauay 1-1, Reo, Nevada, USA,. 6