HEAT TRANSFER TO AN ACOUSTICALLY EXCITED IMPINGING AIR JET

Transcription

1 HEAT TRANSFER TO AN ACOUSTICALLY EXCITED IMPINGING AIR JET Abstract T. S. O Donovan 1, D. B. Murray 2 1 Hriot-Watt Univrsity, Edinburgh, Unitd Kingdom 2 Trinity Collg Dublin, Irland Jt impingmnt hat transfr is known as a mthod of achiving particularly high hat transfr cofficints. It is thrfor mployd in many applications including th cooling olctronics, turbin blads and manufacturing procsss such as grinding. Svral paramtrs influnc th shap and magnitud of th surfac hat transfr distribution to an impinging air jt. Includd in ths paramtrs ar th jt Rynolds numbr (R), non-dimnsional surfac to impingmnt surfac spacing (H/D) tc. Rcnt rsarch has shown that vortics that roll up at th nozzl xit also hav an influnc on th surfac hat transfr at low nozzl to impingmnt surfac spacings (H/D 2). Th currnt study sks to isolat th ffct of vortics in an impinging jt flow by using acoustic xcitation as an activ control tchniqu of th vortx frquncis. Th study was conductd for a singl Rynolds numbr (R = 10000) and low surfac to impingmnt surfac spacings (H/D = 0.5 to 2.0). Th xcitation frquncy was varid from zro to th naturally occurring frquncy of th jt. Whil acoustic xcitation has bn shown to rduc th magnitud of th hat transfr ovrall, it is anticipatd that xcitation abov th natural frquncy of th jt has th potntial to nhanc th hat transfr significantly. Th currnt rsarch has dmonstratd an ffctiv mans of vortx control and has shown that th natural frquncy of a jt flow is yt anothr paramtr to b considrd for optimum surfac cooling. Nomnclatur D Diamtr of Jt, [m] f h Convctiv Hat Transfr Cofficint, [W/m 2 K] H Hight of Nozzl abov Impingmnt Surfac, [m] k Thrmal Conductivity, [W/mK] Nu Nusslt numbr (hd/k), [-] q Rat of Hat Transfr, [W] q'' Hat Flux, [W/m 2 ] r Radial distanc from Stagnation Point, [m] R Rsistanc, [Ω] R Rynolds numbr (ρu j D/μ), [-] St Strouhal numbr (fd/u j ), [-] T Tmpratur, [K] U j Jt Vlocity, [m/s] V Voltag, [V] ρ Dnsity, [kg/m 3 ] μ Viscosity, [Ns/m 2 ] δ Snsor Thicknss, [m] 1 Introduction Jt impingmnt hat transfr is known as a mthod of achiving particularly high hat transfr cofficints. It is thrfor mployd in many applications including th cooling olctronics, turbin blad cooling and manufacturing procsss such as grinding. Th flow structur of an impinging air jt is complx and is influncd by svral oprating and gomtric paramtrs; includd in ths paramtrs ar jt Rynolds numbr (R), non-dimnsional surfac to impingmnt surfac spacing (H/D), angl of impingmnt, jt xit turbulnc intnsity,

2 confinmnt of th jt flow tc. Each of ths paramtrs also has an influnc on th shap and magnitud of th surfac hat transfr distribution. Svral othr paramtrs such as confinmnt and submrgnc of th jt flow hav also bn shown to influnc th hat transfr. In rcnt yars, vortics which occur naturally in an impinging jt flow hav also bn shown to influnc th surfac hat transfr. Comprhnsiv studis of th man fluid flow charactristics of both a fr and an axially symmtric impinging air jt hav bn prsntd by Donaldson and Sndkr (1971) and Bltaos (1976) and rviws of th hat transfr to impinging jts hav bn prsntd by Martin (1977), Jambunathan t al. (1992) and Polat t al. (1989). Many tchniqus, including jt swirl and turbulnc promotrs, hav bn invstigatd to nhanc th ovrall hat transfr to an impinging jt. On potntial nhancmnt tchniqu is acoustic xcitation of th jt, as studid by Liu and Sullivan (1996). Prior to studying acoustic xcitation, O'Donovan and Murray (2007a, 2007b) invstigatd th influnc of naturally occurring vortics in a jt flow on th surfac hat transfr. In a jt flow, vortics initiat in th shar layr du to Klvin Hlmholtz instabilitis. As th vortics mov downstram of th jt nozzl ach vortx can b wrappd and dvlop into a thr dimnsional structur du to scondary instabilitis. Ths scondary instabilitis can lad to th cut and connct procss as dscribd by Hui t al. (1999) and Hussain (1986) in which th toroidal vortics brak down into smallr scal motions, gnrating high turbulnc. Vortics, dpnding on thir siz and strngth, affct th jt sprad, th potntial cor lngth and th ntrainmnt of ambint fluid. In crtain cass jt vortics can pair, forming largr but wakr vortics. In gnral, vortics pass in th shar layr of th jt at th sam frquncy as that at which thy roll up but in th vortx pairing cas th passing frquncy halvs as th vortics pair off. Turbulnt jts hav a fundamntal frquncy at which th pairing procss stabiliss and this is dtrmind by th turbulnc lvl of th jt. With distanc from th jt nozzl th vortics brak down into random small scal turbulnc. It is clar that vortics influnc th arrival vlocity of th impinging jt flow and thrfor influnc th shap and magnitud of th hat transfr distribution. In rcnt tims control of th jt vortx flow has attractd much rsarch intrst as th latst paramtr idntifid as important for impinging jt hat transfr. Hui t al. (1999) and Gao t al. (2003) installd mchanical tabs at th nozzl xit to instigat stramwis vortical structurs. Ths hav th ffct of incrasing th scondary instabilitis in th jt and thrfor hastn th cut and connct procss that braks th vortics down into small scal turbulnc. Hwang t al. (2001) invstigatd th ffct of acoustic xcitation on a coaxial jt flow and xplord th rsulting ffct on hat transfr. Hwang and Cho (2003) continud this rsarch for a widr rang of tst paramtrs. Liu and Sullivan (1996) xcitd an impinging air jt acoustically and rportd on th rsulting flow and hat transfr distributions. It was found that, dpnding on th frquncy oxcitation, th ara avragd hat transfr could b nhancd or rducd at low nozzl to impingmnt surfac spacings. Whil th rsarch to dat has shown possibl nhancmnt of th man hat transfr at various xcitation frquncis, much of this has bn attributd to changs in th arrival vlocitis. O'Donovan and Murray (2007a, 2007b) hav shown that for H/D < 2 th arrival flow vlocity and turbulnc intnsity dos not chang significantly. Thr is howvr a significant variation in th siz of th scondary paks in this rang. It was shown that th magnitud of ths paks is influncd by th vortics within th jt flow. Strong small-scal vortics instigat larg vlocity fluctuations normal to th surfac in th wall jt rsulting in nhancd hat transfr. Artificial jt xcitation can control th dvlopmnt of vortics in th jt flow and thrfor has th potntial to nhanc hat transfr from th surfac. For an axisymmtric air jt th Strouhal (St) numbr is th non-dimnsional form of th vortx passing frquncy and is constant for all jt Rynolds numbrs and nozzl diamtrs. Diffrnt nozzl gomtris, howvr, can hav a significant influnc on th naturally occurring vortics and associatd frquncis. Th motivation for rsarch in this ara, thrfor, is to dtrmin an optimum vortx frquncy for nhancd hat transfr. This could lad to th dsign of a jt nozzl

3 chvron which would oprat as a passiv flow control tchniqu to achiv nhancd hat transfr. Th currnt phas of th study, howvr, sks to isolat th ffct of vortics in an impinging jt flow by using acoustic xcitation as an activ control tchniqu of th vortx frquncis. Th study was conductd for a singl Rynolds numbr (R = 10000) and low surfac to impingmnt surfac spacings (H/D = 0.5 to 2.0). Th xcitation frquncy was varid from zro to th naturally occurring frquncy of th jt. 2 Exprimntal Rig Th main lmnts of th xprimntal rig ar a nozzl and an impingmnt surfac. Both ar mountd on indpndnt carriags that can mov on orthogonal tracks. Th flat impingmnt surfac is instrumntd with two singl point hat flux snsors and th ability of th carriags to mov in this way nabls th jt to b positiond rlativ to th snsors at any location in a two dimnsional plan. Th rig dsign is prsntd in figur 1. Figur 1: Exprimntal Tst Rig As illustratd in figur 1 th jt issus from a contourd nozzl at on nd of a cylindrical chambr. Air is supplid by a comprssor to th chambr via four sparat inlts locatd nar th top of th chambr. An Alicat Scintific Inc. Prcision Gas Flow Mtr is installd on th comprssd air lin to monitor both th air volum flow rat and tmpratur. An 8Ω Visaton acoustic spakr is positiond dirctly opposit th jt nozzl and is drivn by a sin wav producd by a TTI TG210 function gnrator with an acoustic amplifir. Th impingmnt surfac is a flat plat, masuring 425mm x 550mm, that consists of two main layrs mountd on a carriag. Th top surfac is a 5mm thick coppr plat. A silicon rubbr hatr mat, approximatly 1mm thick, is fixd to th undrsid of th coppr plat with a thin layr of adhsiv. Th plat assmbly is such that it approximats a uniform wall tmpratur boundary condition; oprating typically at a surfac tmpratur of 60ºC. Groovs ar machind in th impingmnt surfac to allow th flush mounting of th hat flux snsors. Ths ar positiond in a cntral location and, togthr with th nozzl and plat carriag arrangmnt, allow for hat transfr masurmnts byond 20 diamtrs from th gomtric cntr of th jt. For th prsnt study, tsting has only bn concrnd with a rgion xtnding to 6 diamtrs from th gomtric cntr. An RdF Micro-Foil Hat Flux Snsor is flush mountd on th hatd surfac. This snsor contains a diffrntial thrmopil that masurs th tmpratur abov and blow a known thrmal barrir. Th hat flux through th snsor is thrfor dfind by quation 1.

4 ΔT q = ks (1) δ whr k s is th thrmal conductivity of th barrir (kapton) and ΔT is th tmpratur diffrnc across th thicknss (δ) of th barrir. A singl pol thrmocoupl is also mbddd in this snsor to masur th tmpratur locally. A Snflx hot film snsor oprats in conjunction with a Constant Tmpratur Anmomtr to masur th fluctuating hat flux to th impinging jt, as it has highr tmporal rsolution than th Micro-Foil snsor and can accuratly acquir data in xcss of 8kHz. This quats to a Nyquist frquncy of 4096Hz and for th maximum jt xit vlocity invstigatd th Strouhal numbr is calculatd to b approximatly 5. This uppr valu was not rquird howvr as th maximum Strouhal numbr associatd with cohrnt structurs within th impinging jt flow is lss than 2. Th snsor consists of a nickl snsor lmnt that is lctron bam dpositd onto a 0.051mm thick Upilx S polyimid film. Th hot film lmnt has a thicknss of < 0.2μm and covrs an ara of approximatly 0.1mm x 1.4mm. Th typical cold rsistanc of th snsor is btwn 6 and 8 Ohms. Coppr lads ar also dpositd on th film to provid trminals for connction to th CTA. Th lads hav a rsistanc of approximatly 0.002W/mm. A Dantc StramLin Constant Tmpratur Anmomtr is usd to control th tmpratur of th hot film. It maintains th tmpratur of th film at a slight ovrhat ( 5ºC) abov th hatd surfac. Th powr rquird to maintain this tmpratur is qual to th hat dissipatd from th film. A CTA is ssntially a Whatston bridg whr th prob, or hot film in this cas, forms on arm of th bridg. Th rsistanc of th film varis with tmpratur and thrfor, by varying a dcad rsistanc that forms anothr arm of th bridg, th tmpratur of th film is controlld. Th voltag rquird to maintain th tmpratur of th film constant is proportional to th hat transfr to th air jt as dscribd in quation 2. Corrctions du to th slight ovrhat of th snsor abov th impingmnt surfac tmpratur wr mad to acquir accurat masurmnts. q dissipatd 2 Vout (2) R Both th RdF Micro-Foil hat flux snsor and th Snflx hot film snsor wr calibratd in situ against a rfrnc stagnation point hat transfr cofficint prsntd by Shadlsky (1983). Th calibration of th snsors compard favourably with that providd by th manufacturr s spcification. Hat transfr rsults ar prsntd as distributions of th tim avragd man Nusslt numbr (Nu) and fluctuating Nusslt numbr (Nu'). Th magnitud of th fluctuations of th Nusslt numbr (Nu') is th root-man-squar (rms) of th Nusslt numbr signal. Th man and fluctuating Nusslt numbrs hav calculatd uncrtaintis of 5.7% and 30% rspctivly and ar basd on th local hat transfr cofficint that is dfind by quation 3: h () r = q&& ( r) () r ( T ) surf T j (3) whr q is th hat flux signal (corrctd for losss) from th surfac, T j is th jt xit tmpratur and T surf is th local surfac tmpratur. Ths uncrtaintis ar basd on a worst cas scnario whr th uncrtainty is a prcntag of th smallst masurmnts. It is clar from th rsults prsntd that th uncrtainty in Nu' is, in gnral, lss than 30%. A complt calibration and uncrtainty analysis for this xprimntal st-up is prsntd by O'Donovan (2005).

5 3 Rsults & Discussion Th primary objctiv of th currnt rsarch is to stablish a powr lvl for th acoustic xcitation systm that can ffctivly control th vortx passing frquncy in an impinging air jt. Acoustic xcitation is mployd to triggr vortx dtachmnt from th lip of th jt nozzl and it is not intndd that th xcitation should nhanc th jt xit turbulnc intnsity. Nu W 3 W 6 W 9 W 12 W r/d Figur 2: Man Nusslt Numbr Distribution, R = 10000, H/D = 1, f = 315 Hz Figur 2 prsnts distributions of th man Nusslt numbr for a rang oxcitation lvls and othrwis similar xprimntal paramtrs whr th Rynolds numbr is 10000, th nozzl to impingmnt surfac spacing is 1 diamtr and th xcitation frquncy is 315 Hz (half th natural frquncy of th jt). It can b sn for th unxcitd jt (0 W) that th pak hat transfr occurs at th stagnation point and scondary paks xist at a radial location btwn r/d = 1 and 2. At high lvls of acoustic xcitation, from 6 to 12 Watts, th ovrall hat transfr throughout th distribution is shown to incras with incrasing xcitation powr. This nhancmnt of hat transfr is attributd to th acoustic xcitation pulsing th flow or incrasing th turbulnc in th impinging jt flow. For th lowr xcitation lvl (3W) th hat transfr distribution is largly unaffctd by th acoustic xcitation in th stagnation rgion and in th far wall jt rgion. In th intrmdiat rgion howvr (1 < r/d < 2) oftn trmd th transitional wall jt rgion th scondary pak is liminatd from th hat transfr distribution. This will b discussd in gratr dtail latr but is considrd an indication that this powr lvl oxcitation succssfully triggrs th dtachmnt of vortics from th jt nozzl at th xcitation frquncy, without incrasing th mainstram jt turbulnc. = 0 Hz = 315 Hz = 472 Hz = Figur 3: Spctral Analysis of Surfac Hat Transfr Signals, R = 10000, H/D = 1, r/d = 0.3

6 Figurs 3 prsnts spctral analysis of th surfac hat transfr within th stagnation rgion that xtnds up to r/d = ± 0.5, for a rang oxcitation frquncis and an xcitation lvl of 3 Watts. It can b sn that all spctra within th stagnation zon ar broadly similar to that of th unxcitd jt (f = 0 Hz). Frquncy paks gratr than 1000 Hz can b ignord as thy hav bn attributd to xtrnal lctrical nois and ar not considrd to b an artfact of th flow or hat transfr. Th magnitud of th surfac hat transfr fluctuations for ach xcitation frquncy is similar across th spctral frquncy rang and crucially no dominant frquncy pak occurs at th xcitation frquncy. It can also b sn from figur 4 that th magnitud of th root-man-squar distribution, which is an indication of th unstadinss in th flow clos to th surfac, is not significantly influncd by th xcitation frquncy. Thrfor it is concludd that this lvl oxcitation dos not contribut to th mainstram jt turbulnc. Nu f = 0 Hz f = 315 Hz f = 472 Hz f = r/d Figur 4: RMS Nusslt Numbr Distributions, R = 10000, H/D = 1 = 0 Hz Broadband Pak = 315 Hz 315 Hz Harmonic 945 Hz Harmonic = 472 Hz 472 Hz Broadband Pak 944 Hz Harmonic = Broadband Pak 1260 Hz Figur 5: Spctral Analysis of Surfac Hat Transfr Signals, R = 10000, H/D = 1, r/d = 1.3 Figur 5 prsnts spctral analysis of surfac hat transfr signals in th wall jt at a radial location of r/d = 1.3. It can b sn that vn at this low lvl oxcitation (3 Watts) th surfac hat transfr signals ar influncd by th acoustic xcitation. This is a location in th transitional wall jt that is just bfor th point whr vortics brak-up and, in so doing, contribut to an incras in th turbulnc rsponsibl for th scondary pak (O'Donovan and Murray (2007a, 2007b)). For f = 0 Hz, thr xists a broadband frquncy pak with cntr frquncy qual to which is quivalnt to a Strouhal numbr of approximatly 1. Exciting th jt at a frquncy of 315 Hz (half th natural frquncy) has provn to succssfully control th passing frquncy of th vortics. By triggring th dtachmnt ovry scond naturally occurring vortx, it has ncouragd th pairing of vortics. This rsults in largr but wakr vortics braking up in th wall jt flow. This xcitation frquncy dos not liminat th highr frquncis of in th flow howvr. Similarly at th highr xcitation frquncy of 472 Hz th dominant frquncy occurs at th xcitation frquncy

7 but dos not liminat th natural frquncy. Finally by xciting th jt at a frquncy corrsponding to th natural frquncy, th vortx strngth is nhancd. Th influnc of this control on surfac hat transfr is prsntd in figur 6. Onc th appropriat acoustic xcitation lvl was dtrmind it was possibl to invstigat th ffct of vortx passing frquncy on th surfac hat transfr to an impinging air jt. Figurs 6 prsnts th distribution of th man Nusslt numbr for R = 10000, H/D = 1 and a rang oxcitation frquncis from 0 to th natural frquncy of th jt. Nu f = 0 Hz f = 315 Hz f = 472 Hz f = r/d Figur 6: Man Nusslt Numbr Distributions, R = 10000, H/D = 1 It can b sn in figur 6 that th xcitation frquncy has no influnc on th magnitud of th surfac hat transfr in th stagnation zon or in th far wall jt rgion (r/d > 2). Th xcitation frquncy simply changs th magnitud of th scondary pak. O'Donovan and Murray (2007a, O'Donovan and Murray (2007b) hav shown that naturally occurring vortics in an impinging jt flow influnc th magnitud of th scondary pak. Thy hav shown that th brak-up of vortics in th wall jt incrasd th magnitud of local vlocity fluctuations normal to th impingmnt surfac. Rsults prsntd in figur 6 show that by controlling th passing frquncy, ths vlocity fluctuations can also b controlld. At th xcitation frquncy of 315 Hz, th vortics ar larg and wak and upon brak up do not incras th turbulnc significantly. As th xcitation frquncy incrasd towards th natural frquncy of th jt howvr, th vortics ar smallr and strongr and upon brak-up in th wall jt incras th wall jt turbulnc which rsults in nhancing th surfac hat transfr to a scondary pak. Ovrall, th currnt rsarch has shown that acoustic xcitation rducs th local and ara avragd hat transfr. It is anticipatd that, by improving th xcitation mthod to nabl th jt to b xcitd at frquncis abov its natural frquncy, th magnitud of th hat transfr at th scondary paks will b incrasd. This will significantly improv th ovrall cooling capacity of impinging air jts. Ths rsults will also hlp inform futur nozzl dsign as th natural frquncy of an impinging jt can b a passiv mans onhancing hat transfr. 4 Conclusions Acoustic xcitation has bn succssfully mployd to control th passing frquncy of vortics in an impinging air jt flow. It has bn shown that at low powr lvls ( 3 Watts) th acoustic xcitation triggrs th dtachmnt of vortics from th jt nozzl. At highr powr lvls th acoustic xcitation is rsponsibl for incrasd turbulnc in th mainstram jt flow which nhancs th surfac hat transfr ovrall. Furthr rsarch is rquird in this ara, but this is not th

8 focus of th currnt rsarch, which sks to isolat th ffct of vortx passing frquncy on th surfac hat transfr. For a Rynolds numbr of and a nozzl to impingmnt surfac spacing of 1 diamtr th xcitation frquncy of th jt has bn incrasd from 0 to th natural frquncy of th jt ( 630 Hz). At low xcitation frquncis, th magnitud of th scondary pak is rducd and at half th naturally occurring frquncy it dos not xist at all. As th frquncy is incrasd toward th naturally occurring frquncy th magnitud of th scondary pak is rstord. A mor ffctiv mthod oxciting th air jt is rquird to ffctivly triggr vortics at frquncis highr than th natural frquncy. It is anticipatd that this would rsult in nhancmnt of th surfac hat transfr. 5 Rfrncs Bltaos, S., 1976, Obliqu Impingmnt of Circular Turbulnt Jts, Journal of Hydraulic Rsarch, 14, Donaldson, C. D. & Sndkr, R. S., 1971, A study of fr jt impingmnt, Part I Man proprtis of fr impinging jts, Journal of Fluid Mchanics, 45, Gao, N., Sun, H. & Ewing, D., 2003, Hat transfr to impinging round jts with triangular tabs, Intrnational Journal of Hat and Mass Transfr, 46, Hui, H., Kobayashi, T., Wu, S. & Shn, G., 1999, Changs to th vortical and turbulnt structur of jt flows du to mchanical tabs, Procdings of th Institution of Mchanical Enginrs, 213, Hussain, A. K. M. F., 1986, Cohrnt structurs and turbulnc, Journal of Fluid Mchanics, 173, Hwang, S. D. & Cho, H. H., 2003, Effcts of acoustic xcitation positions on hat transfr and flow in axisymmtric impinging jt: main jt xcitation and shar layr xcitation, Intrnational Journal of Hat and Fluid Flow, 24, Hwang, S. D., L, C. H. & Cho, H. H., 2001, Hat transfr and flow structurs in axisymmtric impinging jt controlld by vortx pairing, Intrnational Journal of Hat and Fluid Flow, 22, Jambunathan, K., Lai, E., Moss, M. A. & Button, B. L., 1992, A rviw of hat transfr data for a singl circular jt impingmnt, Intrnational Journal of Hat Fluid Flow, 13, Liu, T. & Sullivan, J. P., 1996, Hat transfr and flow structurs in an xcitd circular impinging jt, Intrnational Journal of Hat and Mass Transfr, 39, Martin, H., 1977, Hat and mass transfr btwn impinging gas jts and solid surfacs, Advancs in Hat Transfr, 13, O'Donovan, T. S. (2005) Fluid flow and hat transfr of an impinging air jt. Mchanical & Manufacturing Enginring. Trinity Collg Dublin. O'Donovan, T. S. & Murray, D. B., 2007a, Jt impingmnt hat transfr - Part I: Man and rootman-squar hat transfr and vlocity distributions, Intrnational Journal of Hat and Mass Transfr, 50, O'Donovan, T. S. & Murray, D. B., 2007b, Jt impingmnt hat transfr - Part II: A tmporal invstigation of hat transfr and local fluid vlocitis, Intrnational Journal of Hat and Mass Transfr, 50, Polat, S., Huang, B., Mujumdar, A. S. & Douglas, W. J. M., 1989, Numrical flow and hat transfr undr impinging jts: a rviw, Annual Rviw of Numrical Fluid Mchanics Hat Transfr, 2, Shadlsky, P. S., 1983, Stagnation point hat transfr for jt impingmnt to a plan surfac, AIAA Journal, 21,