Detailed Validation Assessment of Turbine Stage Disc Cavity Rotating Flows. Shezan Kanjiyani

Transcription

1 Detaled Valdaton Assessment of Tbne Stage Dsc Cavty Rotatng Flows by Shean Kanyan A Thess Pesented n Patal Flfllment of the Reqements fo the Degee Maste of Scence Appoved Decembe 05 by the Gadate Spevsoy Commttee: Taewoo Lee, Cha Alexande Mamoghadam He-Png Hang ARIZONA STATE UNIVERSITY May 06

2 ABSTRACT The sbect of ths thess s concened wth the amont of coolng a assgned to seal hgh pesse tbne m cavtes whch s ctcal fo pefomance as well as component lfe. Insffcent a leads to excessve hot annls gas ngeston and ts penetaton deep nto the cavty compomsng dsc lfe. Excessve pge a, advesely affects pefomance. Expements on a otatng tbne stage g whch nclded a otostato fowad dsc cavty wee pefomed at Aona State Unvesty. The tbne g has vanes and 8 blades, whle the m cavty s composed of a sngle-tooth m lab seal and a m platfom ovelap seal. Tme-aveaged statc pesses wee meased n the gas path and the cavty, whle mansteam gas ngeston nto the cavty was detemned by measng the concentaton dstbton of tace gas (cabon doxde). Addtonally, patcle mage velocmety (PIV) was sed to mease fld velocty nsde the m cavty between the lab seal and the ovelap. The data fom the expements wee compaed to an 360-degee nsteady RANS (URANS) CFD smlatons. Althogh not able to match the tme-aveaged test data satsfactoly, the CFD smlatons boght to lght the nsteadness pesent n the flow dng the expement whch the slowe esponse data dd not flly capte. To nteogate the valdty of URANS smlatons n captng complex otatng flow physcs, the scope of ths wo also nclded to valdatng the CFD tool by compang ts pedctons aganst expemental LDV data n a closed oto-stato cavty. The enclosed cavty has a statonay shod, a otatng hb, and mass flow does not ente o ext the system. A fll 360 degee nmecal smlaton was pefomed compang Flent LES, wth URANS tblence models. Reslts fom these nvestgatons pont to URANS state of at nde-pedctng closed cavty tangental

3 velocty by 3% to 43%, and open m cavty effectveness by 50% compaed to test data. The goal of ths thess s to assess the valdty of URANS tblence models n moe complex otatng flows, compae accacy wth LES smlatons, sggest CFD settngs to bette smlate tbne stage mansteam/dsc cavty nteacton wth ngeston, and ecommend expementaton technqes.

4 To Mothe and Fathe

5 ACKNOWLEDGMENTS Ths thess wold not have been possble wthot the sppot of many people. Fst, I wold le to than D. Alexande Mamoghadam, who allowed get nvolved n ths nteestng poect and also too hs tme to advse me on vaos aspects on ths sbect. Also, thans to my academc advsos, D. Taewoo Lee who ageed to be the thess commttee cha, and D. He-Png Hang who also ageed to on my commttee. I wold also le to than Reddaah Vshnmolaala and Lavan Gndet fom Honeywell Technology Soltons Lab n Inda fo pefom the CFD analyss dscssed n chapte 6 of ths wo. Fnally, I wold also le to than Honeywell fo lettng me pse a Maste s Degee n Mechancal Engneeng so that I can enhance my techncal slls. v

6 TABLE OF CONTENTS Page LIST OF NOMENCLATURE... v Gee... x Sbcpts... x Aconyms... x LIST OF TABLES... x LIST OF FIGURES... x CHAPTER INTRODUCTION Bacgond: Gas Tbnes... Bacgond: Pevos Wo... 3 THEORETICAL DISCUSSION... 8 Lamna Flow Ove A Fee Dsc... Flow Between A Rotatng And A Statonay Dsc... 4 Flow Between A Rotatng And A Statonay Dsc: CFD Smlaton... 7 Geomety... 7 Mesh... 8 Bonday Condtons... 9 Reslts... 9 Dscsson... 3 TURBULENCE MODELS... 3 v

7 CHAPTER Page Reynolds Aveagng... 3 Reynolds Aveaged Nave-Stoes (RANS) Eqatons... 4 Tblence Modellng... 6 Spalat-Allmaas Model... 7 Standad K-ε Model... 8 (Renomalaton Gop) RNG K-ε Model Realable K-ε Model... 3 Standad K-ω Model Shea Stess Tanspot (SST) K-ω Model Reynold Stess Model (RSM) Lage Eddy Smlaton (LES) DESCRIPTION OF TEST: ASU TURBINE STAGE RIM SEAL CAVITY Geomety Statc Pesse Measement Concentaton Measement Patcle Image Velocmety (PIV) CFD MODEL DESCRIPTION: ASU TURBINE STAGE RIM SEAL CAVITY 5 6 RESULTS AND DISCUSSION: ASU TURBINE STAGE RIM SEAL CAVITY..56 Labynth Seal Cleaance CFD Compason Wth Flow Path Data CFD Compason Wth Cavty Data... 6 v

8 CHAPTER Page Dscsson RESULTS AND DISCUSSION:VALIDATION OF URANS AND LES Comptatonal Detals Reslts URANS Vs. LES... 8 Dscsson SUMMARY AND RECOMMENDATIONS REFERENCES APPENDIX A SAMPLE PIV RAW DATA v

9 LIST OF NOMENCLATURE b B c p Rads to stato angle wng nne sface, m Blade Specfc Heat at Constant Pesse (KJ/(g K)) Cw Non-dmensonal pge spply flow, m h sp ( R) Cw.mn Mnmm vale of Cw to pevent ngeston Cp Non-dmensonal pesse asymmety pesse coeffcent, Pmax h ( mn V ) C Mass Concentaton, g/m 3 Gc f Non-dmensonal adal o axal cleaance, = s/rh Body Foces (N) Tblent netc enegy pe nt mass, m /s and Themal condctvty (W/(m K) m spply Cavty pge/coolng spply flow (g/s) p Pesse Vecto (Pa) P Pesse, N/m P P t,r ReΩ s Pandtl Nmbe Tblent Pandtl Nmbe Rads, m Rotatonal Reynolds nmbe, = ρrh Ω/µ Axal spacng between oto and stato; adal o axal gap, m v

10 S s Spatal (.e. ccmfeental) coodnate, m Stan Rate Tenso (/s) T T V X Z Themocople; Tempeate, K Velocty Vecto (m/s) Knematc Vscosty (m /s) Tblent Vscosty (g/m-s) Velocty, m/s; Vane Axal coodnate fom centelne, m CFD based axal ct plane locaton n cavty GREEK Dffeence (staton- mns staton-) ε Dsspaton Rate m /s 3 ηc Cavty a sealng effectveness, [C() C(mansteam)]/[C(pge) C(mansteam)] Θ dynamc vscosty (g/m-s) Teta, Local secto angle, non-dmensonal (blade local sweep/total ptch) ρ Fld densty (g/m 3 ) φ Ω ω Amthal Coodnate Shea Stess (Pa) Angla velocty (ad/s) Specfc Dsspaton (/s) x

11 SUBSCRIPTS b h hb Stato nne sface angel wng locaton Tbne cavty hb locaton Tbne cavty local popety at hb locaton,,3 Ccmfeental blade/vane cont ndex max mn max-mn s t Maxmm Mnmm Maxmm Mns Mnmm Qantty Lab Seal Tooth Tp Locaton Tangental; total popety Axal decton ACRONYMS ASU B cfm CFD HPT LDV LES PIV RANS RSM SST Aona State Unvesty Blade Cbc feet pe mnte Comptatonal Fld Dynamcs Hgh pesse tbne Lase Dopple Velocmety Lage Eddy Smlaton Patcle Image Velocmety Reynolds aveaged Nave Stoes Reynolds Stess Model Shea Stess Tanspot x

12 Sp URANS Spply Unsteady Reynolds-Aveaged Nave Stoes x

13 LIST OF TABLES Table Page. Comptatonal Paametes x

14 LIST OF FIGURES Fge Page. Gas Tbne.... Tbne Stage Mansteam/Dsc Cavty Cylndcal Coodnates Flow Ove a Fee Dsc MATLAB Lamna Flow Fee Dsc Rotatng and a Statonay Dsc MATLAB Flow Between a Rotatng and a Statonay Dsc MATLAB Flow Between a Rotatng and a Statonay Dsc Tempeate Smlaton Geomety Mesh fo CFD Smlaton Radal Velocty Contos Radal Velocty at R=. m Tempeate at R=. m Aona State Unvesty Rg Geomety and nstmentaton Locatons Ccmfeental Locatons of Statc Pesse Taps on Vane Platfom n Man Gas Flow Annls at Platfom Lp Rotatng Rg and CFD Bonday Condtons Locaton of Concentaton Pobes x

15 Fge Page 8. PIV Lase Sheet Locatons Sngle Secto CFD Peodc Model CFD Mesh: Stato and Roto CFD Mesh fo the Roto-Sde Mansteam/Dsc Cavty Cavty Statc Wall Y+ Contos Mesh Independent Stdy Labynth Seal Senstvty Stdy vs. Radal Locaton Expemental and CFD Pesse Dstbtons n Flow Path Expemental and CFD Pesse Dstbtons n Flow Path Expemental and CFD Pesse Dstbtons n Flow Path Expemental and CFD Pesse Dstbtons n Flow Path Expemental and CFD Compason of Cavty Data vs. Radal Poston Expemental and CFD Compason of Cavty Data vs. Radal Poston Expemental and CFD Compason of Cavty Data vs. Radal Poston Expemental and CFD Compason of Cavty Data vs. Radal Poston PIV Radal Velocty Measements fo Cw=540 at Locaton x/s= PIV Radal Velocty Measements fo Cw=540 at Locaton x/s= Radal Velocty Contos fom Unsteady CFD, m/s Statc Pesse Monto Ponts fom Revoltons 8 to Statc Pesse Monto Ponts fom Revoltons 8 to Enclosed Roto-Stato Cavty xv

16 Fge Page 39. Closed Roto-Stato Dsc Cavty Model Tangental Velocty CFD vs Expement Re=e Radal Velocty CFD vs Expement Re=e Tangental Velocty CFD vs Expement Re=4e Radal Velocty CFD vs Expement Re=4e Tangental Velocty CFD vs Expement Re=e Radal Velocty CFD vs Expement Re=e PIV Measement (600HZ) vs LES Smlaton xv

17 CHAPTER INTRODUCTION Rotatng and swlng flows ae one of the most complex phenomena n heat tansfe and fld mechancs, and they appea n many engneeng and scentfc applcatons sch as et engnes, pmps, tp votex on a-caft wngs, tonadoes, geophyscs and astophyscs []. The goal of ths nvestgaton s to bette ndestand flow n oto-stato dsc cavtes whch ae applcable to gas tbne engnes. In gas tbnes, the amont of coolng a assgned to seal hgh pesse tbne m cavtes s ctcal fo pefomance as well as component lfe. Insffcent a leads to excessve hot annls gas ngeston and ths penetaton deep nto the cavty compomses dsc o cove plate lfe. Excessve pge a, on the othe hand, advesely affects pefomance. Consdeable effot s beng taen to mpove the ndestandng of coolng technology and ths wo wll focs on advancng smlaton technqes that capte the nteactng mansteam pge-a nsteady-non peodc flow physcs. BACKGROUND: GAS TURBINES Fge shows an example of a tbo-fan gas tbne engne. A tbo-fan can typcally be dvded nto 5 sectons: fan, compesso, combsto, tbne, and exhast. The fan daws the a fom the sondng envonment nto the bypass and the coe of the engne. The coe a s then compessed n the compesso secton, ths hgh pesse a s then delveed to the combsto. The fel a mxte s then gnted n the combsto chambe. Ths expanded gas entes the tbne secton, whee the enegy s

18 extacted to dve the oto. The netc enegy s then sed fo thst as the gas entes the exhast secton and mxes wth the bypass flow. FIGURE. GAS TURBINE The amont of coolng o seconday flow whch s allocated fom the compesso to cool the tbne secton s one of dvng factos n nflencng effcency of the system. In an effot to mpove tbne effcency, eseaches and desgnes ae always loong to edce ths coolng flow. One of these aeas s the tbne stage dsc cavty pge flow whee mansteam/dsc cavty flow nteacton occs. As shown n Fge, tbne stage mansteam/dsc cavty s the complex nteacton between hot annls flow and coole pge flow n the oto-stato dsc wheel space. Allocatng nsffcent pge flow wold case ngeston of the hot mansteam gas to tavel nsde the cavty, ths asng the metal tempeates of the statonay and otatng components. On the othe hand, assgnng excessve pge flow wold degade

19 pefomance. In ode to optme the pge flow, accate CFD (Comptatonal Fld Dynamcs) smlatons of the tbne stage mansteam/dsc cavty needs to be pefomed. Befoe enteng dscssons on smlaton technqes sed n ths wo, an ovevew s pesented below on how flows n a otatng cavtes ncldng the tbne stage mansteam/dsc cavtes have been analyed hstocally. Hot Annls Flow Cool Pge Flow FIGURE. TURBINE STAGE MAINSTREAM/DISC CAVITY BACKGROUND: PREVIOUS WORK Befoe detaled CFD smlatons wee boght to maet, tbomachney desgnes sed theoetcal and expemental stdes pefomed on fee otatng dsc flows n ode to ndestand the fld mechancs n a tbne dsc cavty. Hee wo of pevos athos that began nvestgatng flows n otatng dscs ae smmaed. In 905 Eman [3] theoetcally explaned the fomaton of cent spals n the ote laye of the ocean. Late Von Kámán [4] showed that fo lamna flows ove an nfnte otatng dsc, exact soltons fo the Nave-Stoes eqatons can be fond. He dd ths by smplfyng the govenng eqatons fo a fee dsc assmng axsymmetc flow. Ths showed that the fee dsc pmps the fld thogh the bonday laye that foms adally 3

20 ove the dsc. Von Kámán also showed tblent soltons by sng momentm ntegal methods wth powe law velocty pofles. Afte ths, Batchelo [5] solved a case of two otatng dscs of nfnte ads. He obseved that bonday layes fomed on the sface of each dsc, and confned between the bonday layes was a non-vscos coe. Flow between a closed otatng and a statonay dsc was descbed by Mello [6]. In ths case, a bonday laye foms on both the otatng and statonay dsc; theefoe the ente cavty s descbed by two bonday layes. The theoetcal mass flow ate was also eo snce the setp dd not ntodce mass flow nto the system. Mello also fond that fo the case of oto-stato cavty the solton s not nqe. Ths was late confmed by Daly and Nece [7] n 960 who also pefomed expements n closed oto-stato cavtes. They fond the exstence of fo types of flows accodng to the otatonal Reynolds nmbe and the cavty non dmensonal adal heght. Thee ae two lamna and two tblent egmes, each of whch coesponds ethe to meged o sepaated bonday layes. Bayley and Owen [8] pefomed expements specfcally elated to tbomachney shoded dsc cavtes, and they detemned the mnmm non-dmensonal gas sealng flow (Cw,mn) to pevent man gas path ngeston was a fncton of non-dmensonal axal cleaance (Gc) between the oto and stato shod and otatonal Reynolds nmbe (ReΩ). Phade and Owen [9] tested seven sealng geometes, developed elatons fo Cw,mn fo each geomety, and sed flow vsalaton to obseve man gas path ngeston flow stcte. The above bacgond was a bef smmay of theoetcal and expemental eseach on dsc cavtes spannng fom 905 to 988. When compaed to CFD 4

21 smlatons, these analytcal and expemental technqes seem otdated, bt desgnes n the ndsty stll se ths nowledge when they need to mae qc decsons. Detaled CFD smlatons can eqe comptng tme of wees o even months, ths s ndesable when facng poblems n engne test whee mmedate esponses ae needed. Nmecal smlatons have been pefomed on m seal dsc cavtes. A evew of ecent lteate wth focs on nmecal smlatons of m cavty ngeston s shown below. In 009, Mamoghadam et al. [0] n 009 looed at the nflence of tbne mansteam bonday condtons on the HP tbne dsc cavty mnmm sealng flow sng 3D CFD. The secto model ns wee made sng the steady state model wth the mxng plane located aft of the cavty. The assessment of the mxng plane locaton compaed to the nsteady solton evealed the aft located mxng plane to be moe epesentatve of cavty hb/mansteam ngeston dynamcs; bt the oveall conclson of the wo showed that an nsteady solton was eqed. The athos also showed the applcablty of desgn coelatons coespondng to the otatonal ndced vess mansteam pesse asymmety ngeston mechansms epoted eale by Phade and Owen [9]. Dnn and Roy et al. [] n 00 conclded that a 360 degee smlaton may gve moe nsght nto the nsteady flow feld as elated to lage scale flow stctes. Ths obsevaton was confmed by Wang et al. [] n the 360 degee nsteady CFD valdaton stdy sng tbne stage ngeston g data. One of the man conclsons was that fo the lowe sppled pge flows, the ngess ccmfeental velocty dstbtons thogh the platfom ovelap seal do not have the peodcty assocated wth 5

22 ethe the blade bow wave o vane ext pesse vaatons. The fll ng nsteady CFD stdy set the stage fo fte wo wth dffeent cavty/m geomety vaatons n ode to mpove the ndestandng of the m seal ngeston pocess. Stll, secto steady/nsteady CFD stdes pefomed the same yea by Mamoghadam et al. [3] on the nflence of hgh pesse tbne fowad dsc cavty platfom axal ovelap geomety evealed nteestng eslts on ppe m cavty effectveness(ηc) vess sppled pge flow. Ths eseach extends the wo of Wang et al. by pefomng a 360 nsteady CFD valdaton on the same g wth a dffeent ovelap geomety and m seal. Wang et al. showed thogh the 360 degee nsteady CFD valdaton that the flow thogh the m seal s non-peodc, bt dd not comment o povde sffcent evdence that the flow had stabled. Heen, flow stablaton s defned as an nsteady ngess/egess phenomenon that can be non-peodc bt whose secto cont emans wthn a cetan lmt followng a ctcal nmbe of evoltons. Wth only 6 evoltons, the CFD pefomed by Wang et al nde-pedcts the sealng effectveness (ηc) fo low pge flow condton, whch mght have occed becase the flow stcte n the cavty has not eached ts fnal state n the smlaton. Ths the sealng effectveness (ηc) s not pedcted accately. Caft [4] showed n hs smlaton of dsc cavtes sng a two-eqaton tblence model, that the flow does not each steady state even afte 70 evoltons. The pesent wo smlates the expemental g geomety as ASU modfed by Honeywell and docmented by Balasbamanan et al. [5]. The 360 degee nsteady CFD model ns the smlaton nde g condtons, and then compaes the CFD pedctons of 6

23 pesse, velocty, and concentaton-based cavty effectveness (ηc) wth the expemental data of [5]. Ths data ncldes patcle mage velocmety (PIV) measements to monto the fld velocty nsde the cavty between the lab seal and the m seal. The qeston of eachng convegence n ctcal aeas wll be nvestgated by fthe analyng the nsteady data and smlatng addtonal evoltons. The data fom the expements wll be compaed to tme-dependent CFD smlatons sng FLUENT CFD softwae. 7

24 CHAPTER THEORETICAL DISCUSSION Althogh the mansteam/ dsc cavty poblem s mch moe complex n a gas tbne, stdyng smple oto-stato cavtes gves nsght and ntton to the physcs whch domnate fld mechancs. In dong ths, the D Nave-Stoes and Enegy eqatons wll be solved theoetcally sng pevos wo as gde to help mae ey assmptons abot the flow. Ths theoetcal ovevew wll lead to a deepe ndestandng of the complex flow n a ds cavty, whch wll lead to a geate ndestandng of CFD eslts of a tbne stage dsc cavty. The contnty, the Nave-Stoes, and the enegy eqatons ae sed to descbe the flow n otatng systems, whee the contnty eqaton s deved fom the consevaton of mass, the Nave-Stoes eqatons ae deved fom the consevaton of momentm and the enegy eqatons ae deved fom the consevaton of enegy. Addtonally these govenng eqatons ae vald povded the followng assmptons hold te [6]: The fld s a contnm The fld stess tenso s symmetc The fld s sotopc The fld s Newtonan If the flow s assmed to be lamna, ncompessble, and steady the contnty, the Nave-Stoes, and the enegy eqatons become [6]: 8

25 0 ( ) eq. ( ) f p eq. c p ( ) T T eq. 3 The above eqatons ae descbed sng symbolc notaton, whee, c p,, and T ae densty, specfc heat at constant pesse, themal condctvty, and tempeate espectvely. Vecto descbes velocty of the patcle, vecto p descbes the pesse, vecto f descbes any body foces actng on the fld, and tenso descbes the stess n the fld. The symbolc notaton s vald fo any abtay coodnate system bt the most convenent coodnate system fo ths egme s the cylndcal coodnate system sng a statonay o Elean fame of efeence. As shown n Fge 3, the otaton taes place abot the -axs, the adal dstance s mapped by the -axs and φ nceases wth ght-handed otaton []: FIGURE 3. CYLINDRICAL COORDINATES Fo a vscos fld, a constttve elaton between stess and the ate of defomaton tenso states that they have a lnea elatonshp and the popotonalty 9

26 0 constant whch descbes ths elatonshp s µ o the vscosty of the fld. The stess tenso s shown below [6]: ) ( ) ( ) ( eq. 4 The contnty, the Nave-Stoes and the enegy eqatons can now be shown n expanded fom fo lamna flow: 0 eq. 5 f p... eq. 6 f p... eq. 7 f p... eq. 8 T T T T T T c p... eq. 9

27 LAMINAR FLOW OVER A FREE DISC Flow ove a fee dsc occs when a otatng dsc at angla velocty cases a movement n a statonay fld as shown n Fge 4. A bonday laye develops n whch the tangental velocty of the fld deceases fom to ts fee steam velocty otsde of the bonday laye. Mass entes the system thogh axal flow as thee ae centfgal foces geneated between the otatng dsc and the fld. Mass also leaves the system thogh adal otflow, theefoe as descbed by Chlds, the fld s pmped ot of the system and consevaton of mass s satsfed [7]. FIGURE 4. FLOW OVER A FREE DISC [7] If the flow s assmed to be symmetc abot the -axs and lamna, tems that contan ae elmnated, addtonally tems that contan ae nsgnfcant n magntde compaed to othe vscos tems so they ae elmnated as well. If s taen to be eo at the dsc and nfnty when the bonday laye ends, then the bonday condtons at the otatng and fee sfaces ae as follows [7] [8]: 0,, 0 at 0 eq. 0

28 0, 0, at eq. In ode to solve the -D Nave-Stoes eqatons, one has to tansfom them nto a set of odnay dffeental eqatons. The tansfomatons ae based on pevos nowledge of flow behavo based on expemental eslts, and also expeence solvng patal dffeental eqatons. In the case of otatng flows t s assmed that the velocty pofles ae smla and can be mapped onto one non dmensonal axs *. The coodnate tansfomaton fom cylndcal to the dmensonless coodnate system s shown below [6]: * * * * * * *, ( ), ( ), ( ) eq. Eqatons 5-8 become a set of odnay dffeentals eqatons wth coespondng bonday condtons shown below: d d * * * 0 eq. 3 * * d * d * * 0 * * eq. 4 d d d * * d * d * * * 0 * eq. 5 d * * * * 0,, 0 at 0 eq. 6 * * * 0, 0, at eq. 7 The eqatons wee solved by wtng them as a system of fst ode eqatons and by employng MATLAB s bonday vale poblem solve bvp4c. The eslts of the solton ae shown n Fge 5:

29 0.8 * *theta * * pme FIGURE 5. MATLAB LAMINAR FLOW FREE DISC The fee dsc bonday laye thcness s defned as the dstance away fom the dsc whee the tangental velocty s % of the dsc speed, ths coesponds to a of 5.5. Theefoe, the bonday laye thcness on the fee dsc fo lamna flow s: * vale 5. 5 eq. 8 The mass flow ate pmped by the dsc can be fond by the ntegaton: * m d.779 eq. 9 The nmecal eslts ae n ageement wth eslts geneated by Owens and expemental eslts []: 3

30 4 FLOW BETWEEN A ROTATING AND A STATIONARY DISC Flow between a otatng and a statonay dsc s descbed by Fge 6, n whch case a bonday laye foms on both the otatng and statonay dsc theefoe the ente cavty s descbed by two bonday layes. The theoetcal mass flow ate s also eo snce the otatng dsc does not ntodce mass flow nto the system [6]. FIGURE 6. ROTATING AND A STATIONARY DISC If the flow s assmed to be symmetc abot the -axs and lamna, tems that contan ae elmnated. The smplfed -D eqatons ae shown below: 0 eq. 0 p eq. eq. p eq. 3 T T T T c p eq. 4

31 Addtonally tems that contan ae nsgnfcant n magntde compaed to othe vscos tems so they ae elmnated as well. The bonday condtons fo a otatng and a statonay dsc ae shown below, whee l s the dstance between the two dscs: 0,, 0 T Tmax at 0 eq. 5 0, 0, 0 T T at l eq. 6 mn It s also assmed that the velocty pofles ae smla and can be mapped onto one non dmensonal axs *. The coodnate tansfomaton fom cylndcal to the dmensonless coodnate system s shown below [6]: * * p ( l *, ) * * ( ), p l l * * ( ), l T Tmn T T max mn * ( * ), eq.7 Eqatons 0-3 become a set of odnay dffeentals eqatons wth coespondng l bonday condtons shown below whee R s the Reynolds nmbe, and s an nnown paamete to be detemned fom the bonday condtons [6]. d R d d d d d d 3 * * * * * ( ) *3 * * eq. 8 * * d * d 0 * * eq. 9 d d * * * R d '' * * ' P( ) 0 eq. 30 * * * * 0, 0, 0, 0 at 0 eq. 3 5

32 * * * * 0,, 0, at eq. 3 The eqatons wee solved by wtng them as a system of fst ode dffeental eqatons and by employng MATLAB s bonday vale poblem solve bvp4c. The eslts of the solton ae shown n Fge 7 and 8 fo the case whee R=50:. *pme *theta v pme FIGURE 7. MATLAB FLOW BETWEEN A ROTATING AND A STATIONARY DISC 6

33 0.9 Tempeate T pme FIGURE 8. MATLAB FLOW BETWEEN A ROTATING AND A STATIONARY DISC TEMPERATURE The nmecal eslts fo the fld mechancs ae n ageement wth eslts geneated by Mello and expemental eslts [6]. Heat tansfe measements o analytcal pedcton fo ths confgaton was not fond n the lteate evew: theefoe, one way to valdate ths pedcton s to pefom CFD analyss of the expemental setp descbed by Mello ncldng heat tansfe. FLOW BETWEEN A ROTATING AND A STATIONARY DISC: CFD SIMULATION Geomety The CFD smlaton was pefomed sng commecally avalable ANSYS Flent softwae. Fst, the -D geomety was geneated sng ANSYS Desgn Modele. The dmensons of the geomety wee dplcated fom Mello s expement. Althogh Mello dd not have nflow o otflow n hs cavty, ths was needed to pefom a steady state 7

34 smlaton. The mass nflow was lmted to a small amont so the eslts mmc a -D closed cavty. Fge 9 shows dmensons of the geomety n SI nts. FIGURE 9. SIMULATION GEOMETRY Mesh Meshng was pefomed sng ANSYS meshng, 69 qadlateal elements wee ceated. The mesh s fne nea the stato and of the oto n ode to capte the detals of the bonday layes nea the two walls. Fge 0 shows the mesh of the fld one. 8

35 FIGURE 0. MESH FOR CFD SIMULATION Bonday Condtons Mello [6] obseved that hs expement was pefomed n the lamna flow egme, theefoe the analyss was pefomed sng lamna flow. The oto wall has a otatonal velocty of 730 pm. Tempeate at the oto wall s specfed at 350K, and the tempeate at the stato wall s 300K. The nflow s defned by a velocty nlet at. m/s, otflow s defned by a pesse otlet at atm. Lastly the fld s assmed to be a. Reslts Below ae Fges -3 show the adal velocty conto, and plots of the adal velocty, and tempeate at =.m. 9

36 FIGURE. RADIAL VELOCITY CONTOURS FIGURE. RADIAL VELOCITY AT R=. M 0

37 FIGURE 3. TEMPERATURE AT R=. M The CFD eslts fo fld mechancs ae n ageement wth eslts geneated by Mello s nmecal eslts, bt thee ae dscepances between the tempeate pofle pedcted by the CFD and nmecal eslts. The nmecal eslts show a lnea tempeate pofle between the stato and the oto, whle the CFD shows the tempeate pofle s smla to the tangental velocty pofle. Snce the flow nsde the cavty s domnated by the tangental velocty, t s expected that the tempeate pofle wold follow the tangental velocty pofle. Althogh the nmecal method accately pedcts the flow feld, smplfyng assmptons sacfce detals needed to accately pedct tempeate. Dscsson Althogh the mansteam/ dsc cavty poblem s mch moe complex n a gas tbne, stdyng smple oto-stato cavtes gves nsght and ntton to the physcs whch domnate fld mechancs and heat tansfe. Fo example, the adal velocty plots

38 ae postve on the oto sde and negatve nea the stato sde. Ths ndcates that the oto s pmpng the flow ot of the cavty and hot mansteam gas ngeston occs nea the stato. The adal velocty conto plot fom the CFD smlaton also shows that the pge/coolng flow s entaned by oto sde bonday laye whch s pmpng the fld ot of the cavty. Ths means that most of the coolng flow s sewed becase t s entaned n the oto sde bonday laye, bt ngeston occs on the stato sde wall. Fte wo of smple cavtes can expement wth dffeent cavty geometes, and coolng technqes (flm coolng, et mpngement, and poos medm). Ths can help dentfy soltons to mansteam/ dsc cavty ngeston poblem.

39 CHAPTER 3 TURBULENCE MODELS The pevos secton descbed lamna flows n a otatng dsc cavty, whch s a smplfed poblem of the oto-stato dsc cavtes seen n gas tbne engnes. In addton to otatng flows, a mansteam dsc cavty ncldes the man gas path, the otostato cavty, and nsteady nteacton between the two fld egmes. Fthemoe, le most engneeng fld mechancs poblems, the flow n the mansteam dsc cavty s hghly tblent. Cently, vey lmted theoetcal analyss of tblence can be done, so ths secton wll descbe tblence and the dffeent modellng technqes sed n nmecal smlatons. Moe detals on the dscsson on tblence can be fond n Fndamentals of Tblence Modellng by Chen [9]. REYNOLDS AVERAGING Fo tblent flows t s sefl to sepaate the vaables nto mean and flctatng vales show below: eq. 33 p p p eq. 34 Whee the tme-aveaged mean vale s shown by an ove ba ( ), and ths tme aveagng pocess s nown as Reynolds Aveagng: t t t t dt eq. 35 3

40 Hee the peod, t s selected so that small scale and hgh feqency flctatons ae flteed ot and only the lage scales nsteady flow feates eman. s the flctatng vale whose mean s eo. Ths appoach whee the vaables ae decomposed nto a mean and flctatng vales s done fo a cople of easons. Fst, expementally flow qanttes ae most commonly meased n the mean vales sng a pocess smla to Reynolds Aveagng. Secondly, becase the Nave-Stoes eqatons ae solved nmecally, t wold eqe a vey fne fld mesh and fne esolton n tme steppng to esolve the hgh feqency/hgh flctatng tblent scales. Instead, tblence models ae sed to estmate these small scale behavos, theefoe comptatonal esoces ae saved. REYNOLDS AVERAGED NAVIER-STOKES (RANS) EQUATIONS The decomposton dscssed above s sed to deve the aveaged Nave-Stoes eqatons and the vaables. p and q shown hee nclde aveaged and flctatng qanttes and have the followng popetes: p q... p q... eq. 36 p p eq. 37 pq pq eq. 38 pq pq pq eq. 39 p x p x eq. 40 p 0 eq. 4 4

41 p p 0 eq. 4 p q 0 eq. 43 p q 0 eq. 44 It s mpotant to note that n eqatons 4 and 43, the podct of aveages of two flctatons s non-eo. Ths tem leads to the close poblem and wll be dscssed n moe detal when tblence modellng s dscssed. Expandng the Nave-Stoes eqatons efeenced n eqaton and, the ncompessble contnty and Nave-Stoes eqatons n consevatve fom ae: x 0 eq. 45 t x p ( ) (s ) x x eq. 46 And the stan-ate tenso s s gven by s x x eq. 47 Insetng eqatons 33, 34 nto eqatons 45, 46 and by sng the popetes n eqatons 36 th 44 yelds the Reynolds Aveaged Nave-Stoes (RANS) eqatons. x 0 eq. 48 p ( ) (s ) eq. 49 t x x x And the aveaged stan-ate tenso s s gven by: 5

42 s x x eq. 50 Eqatons can be fthe smplfed nto eqaton 5. t x p x x x x eq. 5 Whee, and s defned as the nematc vscosty, and the tem epesents the Reynolds stess tenso. The tenso s symmetc and epesents the 6 addtonal nnown qanttes de to tblence. TURBULENCE MODELLING As allded to befoe, the close poblem occs n the RANS eqatons above becase of the non-lnea Reynolds Stess tem. The system of eqatons has addtonal nnown qanttes wthot addng eqatons to solve fo, theefoe ths tem s modelled n ode to close the system of eqatons. Moe detals on tblence modelng can be fond n ANSYS Flent Theoy Gde [0]. Fo the Spalat-Allmaas, -ε, and, ω tblence models, the Bossnesq hypothess s appled. It elates the Reynolds stesses to the mean velocty gadents shown n eqaton 5. T x x T 3 x eq. 5 Hee T s the tblent vscosty and s the tblent netc enegy. One assmpton of the Bossnesq hypothess s that the tblent vscosty s sotopc, whch s not te fo all flows. Ths assmpton s expected to be vald fo shea domnated flows sch as wall bonday layes and ets. Bt n cases whee ansotopy of tblence s domnant 6

43 7 sch as hgh swlng flows, ths Bossnesq hypothess s not expected to povde accate eslts. SPALART-ALLMARAS MODEL The fst model that wll be dscssed s the Spalat-Allmaas model, t s a one eqaton model to solve fo the tanspot eqaton of the modfed tblent vscosty ~. The tblent netc enegy as shown n the Bossnesq hypothess s assmed to be eo. Ths model s sefl fo most aeodynamc flow sch as bonday laye flows and flows typcally seen n tbomachney flow path. The model has lage eos fo fee shea and swlng flows, and s not expected to pedct accate eslts fo the decay of homogenos sotopc tblence. The tanspot eqatons shown below fo the modfed tblent vscosty was developed sng empcsm and dmensonal analyss. ~ ~ ~ ~ ) ~ ( ) ~ ( ) ~ ( S Y x C x x G x t v b v eq. 53 Hee v G s the podcton tem, ~ ~ ~ ) ~ ( b x C x x s the dffson tem, and v Y s the destcton tem. The tblent vscosty s calclated sng the elatonshps descbes by eqatons t v v v t X C X X f f ~ ~ eq Whee v f s the vscos dampng fncton. The modelng of the podcton tem s

44 8 ~ ~ ~ ~ v v v b v Xf X f f d S S S C G eq Whee S s the scala mease of votcty, x x S eq. 60, 6 The destcton tem s modeled as: 6 6 / ~ ~ ) ( ~ d S C g C g C g f d f C Y w w w w w w v eq Model constants n the above eqaton have the followng vales n ANSYS Flent: ) ( ~ ~ w w b b w v b b C C C C C C C C eq STANDARD K-ε MODEL One of the most popla two eqaton tblence models s the -ε tblence model, and t ncldes tanspot eqatons fo both (tblence netc enegy) and ε (dsspaton ate). The model leads to stable calclatons and povdes easonable pedctons fo many flows. Lmtatons of ths model ncldes poo pefomance n complex flows sch as flow wth lage pesse gadents, stong sepaatons and lage swls. The eqatons sed to descbe tblence netc enegy and the ate of dsspaton ae shown below: m b t S Y G G x x x t eq. 74

45 9 S C G C G C x x x t b t 3 ) ( eq. 75 Hee the x tem s the convectve tanspot, the t x x tem s the dffsve tanspot. G s the podcton of tblence netc enegy, ts exact defnton s estmated accodng to the Bossnesq hypothess and as shown n eqatons 76 and 77. x G eq. 76 S G t eq. 77 S S S eq. 78 b G s the accmlaton of tblence netc enegy de to boyancy and the contbtos of ths enegy geneaton ae gavtatonal feld and tempeate gadents. t t b x T g G P eq. 79 T p eq. 80 t t b x g G P eq. 8 In the eqatons above the t P s the tblent Pandtl nmbe wth defalt vale 0.85 and g s the gavtatonal vecto. Eqaton 80 descbes the themal coeffcent of expanson and eqaton 8 shows the enegy geneaton b G fo deal gasses.

46 Y m s nclded n the modelled tblence netc enegy eqaton to accont fo the compessblty effects of hgh speed flow whch deceases the speadng ate. Y m eq. 8 M t M t eq. 83 a a RT eq. 84 In the eqatons above M t s the tblent Mach nmbe and a s the speed of sond. S and S ae se defned soce tems to nclde effects sch as mlt-phase flows and tblent vscosty s compted by eqaton 85. t C eq. 85 Othe model constants ae defned below: C.44 C.9 C eq (RENORMALIZATION GROUP)RNG K-ε MODEL The RNG -ε model s smla to the -ε model dscssed bt t has addtons fom a statstcal technqe called the enomalaton gop theoy. These modfcatons nclde an addtonal tem n the ε eqaton to mpove pedctons of shea flows. Also nclded s nceased accacy of swlng flows, analytcal fomla fo tblent Pandtl nmbe and dffeental fomla fo effectve vscosty. Ths model shold povde mpoved accacy fo modeately complex flows sch as et mpngement, modeately swlng flows and seconday flows. The tanspot eqatons sed to descbe tblence netc enegy and the ate of dsspaton ae shown below: 30

47 t t eq. 9 x x x a eff G Gb Ym S x x x ( eq. 9 a eff C G C3 Gb ) C R S x Hee the tem s the convectve tanspot, the a x eff x tem s the dffsve tanspot tem. G s the podcton of tblence netc enegy, ts appoxmaton accodng to the Bossnesq hypothess s shown n eqatons 76 and 77. G b s the accmlaton of tblence netc enegy de to boyancy, Y m s shown n eqatons 8-84, and S, S ae se defned soce tems. a and a ae nvese effectve Pandtl nmbes and ae calclated sng the fomla below: 0.63 a.399 a.399 a0.399 a mol eff eq. 93 Addtonally, the RNG theoy eslts n a dffeental eqaton fo tblent vscosty, d.7 ˆ 3 ˆ C v d ˆ eq. 94 eff ˆ eq. 95 The R tem s the man dffeence between the standad -ε tblence model and RNG -ε tblence model and ts eqatons s defned below: 3 C / 0 R eq

48 S / eq. 97 Ths tem maes a negatve contbton to the ε eqatons n the pesence of lage stan ates, whch means that the RNG model yelds a lowe tblent vscosty and s moe eactve to lage stans and steamlne cvates. Fnally, the model constants ae defned below: C C.4 C.68 eq All othe constants have the same vale as dscssed n the standad -ε secton. REALIZABLE K-ε MODEL The ealable -ε model s smla to the -ε model dscssed bt t has two mao dffeences. Fst, the ealable -ε model ncldes an altenate elatonshp fo the tblent vscosty, and t contans an mpoved eqaton fo ε. These modfcatons ense that eslts pedcted by ths model ae ealable o the Reynolds stesses physcally possble. Ths s done by havng a vaable C so that when the stan s lage, negatve nomal stesses and physcally mpossble shea stesses ae coected. Ths shows mpoved eslts fo flow egmes that have votces, cvates, otatons and bonday layes nde stong advese pesse gadents. The tanspot eqatons sed to descbe tblence netc enegy and the ate of dsspaton ae shown below: t G Gb Ym S t x x eq. 03 x t x x x eq. 04 t C S C C C3 Gb S 3

49 x Hee the tem s the convectve tanspot, the x t tem x s the dffsve tanspot tem. G s the podcton of tblence netc enegy, ts appoxmaton accodng to the Bossnesq hypothess s shown n eqatons 76 and 77. G b s the accmlaton of tblence netc enegy de to boyancy, Y m s shown n eqatons 8-84, and S, S ae se defned soce tems. Pe eqaton 85, the fomla to compte eddy vscosty s smla to the -ε model, bt C s no longe a constant vale. C eq. 05 U A0 As * ~ ~ U* S S eq. 06 ~ eq. 07 eq. 08 A 6 cos eq. 09 s cos 6W eq. 0 3 SS S W ~ S 3 eq. S ~ S S eq. The eqatons above show that C depends on the mean stan, otaton ates and the angla velocty, tblence netc enegy, and dsspaton. 33

50 Fnally, the model constants ae defned below: C max 0.43, A C C.0..9 eq. 3-8 All othe constants have the same vale as dscssed n the standad -ε secton. STANDARD K-ω MODEL The standad -ω s an empcally deved model based on the tblent netc enegy and the specfc dsspaton (ω), o the ato of ε to. It demonstates accate pedctons fo wall-bonded, low Reynolds nmbe flows and pefoms well nde advese pesse gadents. Convesely, ths model has toble pedctng flow sepaaton and othe complex flow egmes. The tanspot eqatons sed to descbe tblence netc enegy and the specfc dsspaton ate ae shown below: t eq. 9 x x x G Y S t x x x G Y S eq. 0 x Hee the tem s the convectve tanspot, the x x tem s the dffsve tanspot. S, S ae se defned soce tems. G s the podcton of tblence netc enegy, ts appoxmaton accodng to the Bossnesq hypothess s shown n eqatons 76 and 77. G epesents the podcton of specfc dsspaton and descbed as: 34

51 G a G eq. a a 0 Ret/ Re a eq. a * Ret/ Re a 0 * Ret/ Re a* a eq. 3 Ret/ Re Re t eq. 4 a 0 * eq. 5 3 and epesent the effectve dffsvtes of and ω espectvely, t eq. 6 t Y and Y show the dsspaton of of and ω, Y * * f eq. 7 X 0 f * 680X eq. 8 X 0 400X X 3 x x eq. 9 * * * F( M t ) eq

52 4 Re t/ R Ret/ R 4 /5 * * 4 eq. 3 Y f eq. 3 f 70X eq X S X eq. 34 * 3 * * F ( M t ) eq M t M t0 F ( M t ) M t M t0 M t M t0 eq. 36 M t a eq. 37 The tblent vscosty s compted as follows: t a * eq. 38 Fnally, the model constants ae defned below: R 6 * M t R.95 a * *.5 a 0.5 R 8 a 0 9 eq SHEAR STRESS TRANSPORT (SST) K-ω MODEL The Shea Stess Tanspot (SST) -ω model was fomlated to combne the 36

53 accacy of the -ω model n the nea wall egon wth the fee steam accacy of the -ε model. Ths s done by a blendng fncton whch actvates n the nea wall egon and becomes eo n the fa feld. Also the modelng constants ae modfed. These changes mae the SST -ω model moe accate n pedctng a vaety of flows whch nclde, flows wth advese pesse gadents, afols, tansonc shoc waves. Ths model stll stggles wth vey complex flows sch as fee shea flows and flows wth hgh amont of swl as a eslt of the sotopc eddy vscosty assmpton. The tanspot eqatons sed to descbe tblence netc enegy and the specfc dsspaton ate ae shown below: t eq. 5 x x x G Y S t x x x G Y D S eq. 5 x Hee the tem s the convectve tanspot, the x x tem s the dffsve tanspot. S, and S ae se defned soce tems. G s the podcton of tblence netc enegy, ts appoxmaton accodng to the Bossneq hypothess s shown n eqatons 76 and 77. G epesents the podcton of specfc dsspaton. G a G eq. 53 t Whee a s defned n eqaton, whee a s evalated as eqaton 54 and the fncton F epesents the blend fncton. a F a eq. 54, ( F ) a, 37

54 , a, eq. 55 * * w,, a, eq. 56 * * w, F tanh( 4 ) eq mn max,, 0.09y y,d y eq D max,0, x x eq. 59 F eq. 60 tanh 500 max, 0.09y y eq. 6 Hee, y s the dstance to the next sface and dffson s tem defned below. D D whch the postve poton of the coss F eq. 6, x x Y and Y epesent the dsspaton of tblence netc enegy and specfc dsspaton, and s defned by the thee eqatons below. Y * eq. 63 Y eq. 64 F, F eq. 65, The effectve dffsvtes fo ths model ae gven by and. 38

55 t eq. 66 t eq. 67 t eq. 68 SF max, a* a F eq. 69 /, ( F ) /, F F eq. 70 /, ( ) /, Fnally, the model constants ae defned below: a, ,, ,, ,.68 eq All othe constants have the same vale as dscssed n the standad -ω secton. REYNOLD STRESS MODEL (RSM) The Reynolds Stess Model (RSM) closes the Reynolds-Aveaged Nave-Stoes eqatons by solvng fo the addtonal tanspot eqatons fo the sx ndependent Reynolds stesses dscssed n eqaton 5. The one and two eqaton tblence models dscssed above mae the assmpton that the eddy vscosty s sotopc. Ths assmpton s avoded fo the RSM, theefoe t s expected to gve accate pedctons fo complex flows sch as cyclone flows, swlng combsto flows, otatng flow passages, seconday flows, and flows nvolvng sepaaton. Howeve, modelng assmptons ae stll made n the RSM n ode to close the exact tanspot eqatons 39

56 40 becase some tems ae nnown. These assmptons ae not valdated as extensvely as the assmptons n the one and two eqaton tblence models, theefoe the RSM s not always expected to gve moe accate eslts. The tanspot eqatons sed to descbe the Reynolds stess ae deved by tang the moment of the momentm eqaton and ae shown below: se m m m m S x x x x p g g x x x x x x t ) ( ) ( ) ( eq. 78 Fo convenence the tanspot eqaton can also be wtten n a shot fom. se L T S F G P D D C t R,, eq. 79 Whee R s the Reynolds stesses, C s the convecton tem, T D, s the tblent dffson, L D, s the molecla dffson, P s the stess podcton, G s the boyancy podcton, s the pesse stan, s dsspaton, F s podcton by system otaton, and se S s the se defned soce tem. Of these tems, C, L D,, P, and F

57 do not eqe modellng, bt D T,, G,, and need to be modeled to close the eqatons. The pesse stan and the dsspaton ate tems ae the most dffclt to model, and ceate the lagest eo when RSM fals to pedct flows popely. In ode to model the eqatons above the tanspot eqatons fo netc enegy and dsspaton ate ae needed t P G M t S t x x eq. 80 x t x x x 3 eq. 8 t C ( P C G C S Whee M t was defned n eqaton 37. ) The tblent dffson s modelled sng a scala tblent dffsvty, t D T, eq. 8 x x Whee t s compted sng eqaton 85 smla to the -ε model. The pesse stan tem s modeled by sng the decomposton below: eq. 83,,, w Hee the, tem s the slow pesse-stan tem,, s the apd pesse stan tem and, w s the wall-eflecton tem. The slow pesse stan tem s modeled as:, C eq The apd pesse stan tem s modelled as: 4

58 P F 5/ 6G C P 5/ G C, C 6 eq P P G G C C eq. 86 The wall-eflecton tem, w, edstbtes the nomal stess nea the wall by dampng the nomal stesses nea the wall and enhancng the paallel stesses paallel to the wall., w 3 C mnnm n n C m, 3 nnm, n n 3 C nn d 3, C nn d 3/ 3/ eq. 87 3/ 4 C C eq. 88 The podcton tem G de to boyancy s modeled as follows, G t P t g g x x eq. 89 The dsspaton tenso s modeled as, ( YM ) eq And Y M s defned above n eqaton 8. Fnally, the model constants ae defned below C C.44 C C.80.9 C eq LARGE EDDY SIMULATION (LES) RANS tblence modellng s chaacteed by esolvng the lagest eddes that have the chaactestc length scale of the mean flow, these lage eddes ae thee 4

59 dmensonal, poblem dependent and the flow chaactestcs of these eddes depend on geomety and bonday condtons. The thee dmensonal stcte of tblence s chaacteed by votex stetchng and most of the netc enegy s assocated wth lage stctes. The netc enegy s then tansfeed to smalle stctes tll the dsspaton of ths enegy nto heat occs at the smallest length scales. The soce of ths enegy ae the lage scale motons whee thee s an npt of enegy. Othewse, all the netc enegy wold decay by vscos dsspaton. At the smallest length scales tblence s nvesal, sotopc, and two dmensonal. Theefoe, t s possble to model small eddes by a nvesal tblence model. A nmecal smlaton appoach called dect nmecal smlaton (DNS) esolves that ente ange of tblence fom the lagest to the smallest stctes. The comptatonal cost to n ths smlaton s popotonal to 3 Re, and ths appoach s not feasble pactcal engneeng poblem whch nvolve hgh Reynolds nmbe flows. In lage eddy smlaton (LES), the lage eddes ae esolved and only the smallest eddes ae modelled. Ths allows fo a mch coase mesh when compaed to DNS, bt LES n an nsteady smlaton appoach that eqes a fne mesh when compaed nsteady RANS (URANS) calclatons. The contnty and momentm LES eqatons ae shown below: x 0 eq. 99 t x p x x x eq

60 Althogh, the LES eqatons ae smla to the RANS eqatons, n LES the ove-ba desgnates spatal flteng. The flte s a fncton of gd se, and tblent scales smalle than the gd se ae emoved and modeled by a sb-gd scale defned as. Ths means that eddes lage than the gd se ae solved nmecally by the flteed N-S eqatons. Theefoe flctatons of the flow feld that tansfe momentm at the smalle scales ae capted by the LES eqatons. The tem s splt nto ts sotopc and devatoc pats eq Whee s the devatoc tem and s the sotopc tem. The devatoc 3 3 pat of the sbgd-scale stess tenso s calclated sng the Smagonsy model: 3 t S 3 S eq. 0 p eq. 03 M sgs Whee M sgs s the sbgd Mach nmbe, and fnally, t s calclated sng the Smagonsy-Llly model: S eq. 04 t L s S S S eq. 05 Whee Ls s the mxng length fo sbgd scales and s calclated as, L mn d, C s eq. 06 s 44

61 Hee C s s the Smagonsy constant and has a vale of 0. and s the local gd scale and s calclated by the volme of the comptatonal cell. /3 V eq

62 CHAPTER 4 DESCRIPTION OF TEST: ASU TURBINE STAGE RIM SEAL CAVITY Wth the analytcal bacgond povded by the pevos two sectons, ths secton descbes the expemental test whch wll be the sbect of the CFD eslts compason. As mentoned n the ntodcton, the pesent wo smlates the expemental g geomety ASU-Hang as docmented by Balasbamanan et al. [5] n a 360 nsteady CFD model, ns the smlaton nde g condtons, and then compaes the CFD pedctons of pesse, velocty, and concentaton-based cavty effectveness (ηc) wth the expemental data of [5]. Also nclded s the patcle mage velocmety (PIV) measements to monto the fld velocty nsde the cavty between the lab seal and the m seal. The data fom the expements wll be compaed to nsteady CFD smlatons sng FLUENT CFD softwae. P P P P C, T, P 4 Blade (8) P Vane () Man a flow C, P (= 87) 5. C, P (= 73) C, P (= 6) C, P (= 48) R= 7.8 R= 8.6 R= 95.7 b= 9. R= 84.7 Rs= Labynth seal cleaance = 0.6mm C, P (= 3) C, P (= 04) R= 38.0 R= C, P (= 8) s = 6.5 C, P (= 45) T C, P 9. =9. Pge a flow All dmensons ae n mm FIGURE 4. ARIZONA STATE UNIVERSITY RIG GEOMETRY AND INSTRUMENTATION LOCATIONS (C: CONCENTRATION TAP, P: PRESSURE PROBE, T: THERMOCOUPLE) 46

63 GEOMETRY The tbne m seal g at Aona State Unvesty, shown n Fge 5 was sed to n expements nvestgatng man gas path ngeston n the fowad dsc m cavty. The g conssts of patal heght bt fll length vanes and 8 patal heght, ctbac blades; the patal heght and lengths ae sed to edce the powe eqed to n the g. Pge a s nected fom the stato sde of the cavty at the centelne boe, and a sngle tooth labynth seal sepaates the nne cavty fom the ote cavty. The labynth seal has adal cleaance of 0.6mm. An axally and adally ovelappng m seal sepaates the ote cavty fom the man gas path. Both the axal and adal ovelap cleaances ae each.6mm. The expemental condtons of the g, whch wee also the bonday condtons n the CFD model ae shown n Fges 5 and 6. FIGURE 5. CIRCUMFERENTIAL LOCATIONS OF STATIC PRESSURE TAPS ON VANE PLATFORM IN MAIN GAS FLOW ANNULUS AT PLATFORM LIP 47

64 Man nlet mass flow ate C w = 3.5X0 5 Inlet pge mass flow ate: C w =540 (0.435%man) C w =3080 (0.87%man) C w =46 (.304%man) C w = 66 (.739%man) FIGURE 6. ROTATING RIG (PURGE FLOW IS IN % OF TESTED MAINSTREAM FLOW) AND CFD BOUNDARY CONDITIONS Otlet statc pesse: 96.Pa Roto Speed: 400 pm STATIC PRESSURE MEASUREMENT Fo the pesse measement, a dffeental pesse tansdce (Valdyne)- Scanvalve (48-channel) was sed to mease the tme-aveaged statc pesse on the man gas flow annls ote shod at 33 ccmfeental locatons ove two vane ptches as shown n Fge 5. The locaton of these tansdces ae mm, 5 mm and 5.5 mm downsteam of the vane talng edge. Thee ae also tansdces at 33 ccmfeental locatons on the hb ove two vane ptches as shown n Fge 5, mm downsteam of the vane talng edge plane and mm psteam of the platfom lp. Also pe Fge 5, on the stato sface at nne adal postons, thee ae 7 ccmfeental locatons ove one vane ptch at =87 mm, and 6 ccmfeental locatons ove one vane ptch at =73 mm. The measng feqency of ths pesse tansdce s 0 H and the ncetanty n the pesse measements, estmated based on nstment and data acqston system ncetantes, s ± 0.5% of the meased statc gage pesse pe Balasbamanan et al. [5]. 48

65 CONCENTRATION MEASUREMENT CO concentaton was sed to mease the mxng between the mansteam and cavty a. The tace gas was nected nto the pge a va a 5-hole, mm damete tbe at appoxmately.6 m psteam of the ds cavty entance. Fo ths expement cabon doxde volmetc concentaton n the pge a was mantaned at a constant vale n the ange of 3.7% to 4.0%. Althogh the concentaton was montoed dng each expement by a concentaton measement psteam of the cavty entance pe Fge 4, the adally nnemost locaton n the nne cavty ( =45 mm) was detemned to be epesentatve of the flly mxed cabon doxde concentaton n the pge a sppled de to the 90 o tn of the pge a afte enteng the cavty. The cabon doxde volmetc concentaton was also meased at eght othe adal locatons n the ds cavty whch s shown below n Fge 7 FIGURE 7. LOCATION OF CONCENTRATION PROBES 49

66 Hee the ed dots epesent the locatons whee concentaton measements wee taen on the stato sface, and ble dots epesent the locatons whee axal tavese pobes meased concentaton on both the stato sface and axally wthn the oto-stato gap. The cabon doxde volmetc concentaton n the gas sample was meased by an NDIR gas analye. The ncetanty n the meased cabon doxde volmetc concentaton s ± 0.% cabon doxde concentaton pe Balasbamanan et al. [5], and ts measng feqency s 3 H. PARTICLE IMAGE VELOCIMETRY (PIV) Patcle Image Velocmety (PIV) technqe s sed to mease the fld velocty feld nsde the cavty between the lab seal and the m seal pe Fge 8. The pge gas was seeded wth the olve ol doplets (seed patcles) befoe ts enty nto the ds cavty. Afte the doplets wee geneate the lght sheet optcs system podced a lght sheet n the adal-amthal plane shown n Fge 8. Thee wee thee axal locatons of the thee vaos lase planes, the lght sheet was ntodced thogh the tanspaent and optcally polshed ote shod. Images wee capted by means of a hgh-esolton camea thogh the tanspaent and optcally polshed stato wall. The PIV measement has a capte ate of 3.3 H. 50

67 Blade (8) Vane () Man a flow (Vane/blade hb ads, R h ) Labynth seal cleaance = 0.6mm coss-coelaton camea R= 8.6 R= 95.7 b= 9. R= 38.0 R= 84.7 Rs= 3.8 R= 86.6 thee-dmensonal tavese s = =9. Pge a flow All dmensons ae n mm Fge 8. PIV Lase Sheet Locatons 5

68 CHAPTER 5 CFD MODEL DESCRIPTION: ASU TURBINE STAGE RIM SEAL CAVITY The fll 360 degee ASU CFD model s smla to the geomety dscssed n the pevos secton. The model and the CFD analyss was done by Reddaah Vshnmolaala, Lavan Gndet fom Honeywell Techncal Sevces Lab n Hydeabad, Inda. Mesh was ceated only fo sngle peodc channel fo stato and oto sepaately sng ANSYS ICEM CFD stcted mesh wth blocng stategy. The stato peodc secto CFD model s shown n Fge 9 along wth the sldng nteface. Stato peodc secto contans 7 elements ccmfeentally excldng 4 O-gd elements on blade sface and 33 elements along the span (see Fge 0). Roto blade had 6 elements ptch wse excldng 4 O-gd elements on the blade sface to bette capte the bonday laye physcs, and 33 elements span wse, whch ncldes tp cleaance (see Fges 0 and ). Bonday laye mesh s ceated on all the walls wth the taget Y+ of less than. Fge shows the vales along the dsc cavty statc wall. FIGURE 9. SINGLE SECTOR CFD PERIODIC MODEL 5

69 FIGURE 0. CFD MESH: STATOR (LEFT) AND ROTOR (RIGHT) Ths sngle secto peodc mesh was ead n to ANSYS FLUENT solve and copes wee ceated ccmfeentally to bld the fll 360 degee CFD model. The fll 360 degee model contans a total of 3.6 mllon cells followng demonstaton of mesh ndependent stdes as shown n Fge 3. The coeffcent of pesse (.e. pesse asymmety nomaled wth the dynamc pesse) at cavty statc wall s only slghtly changng between 9 and 3.6 mllon. A non confomal sldng nteface s ceated between the oto and stato. Fge llstates a oomed vew nto the cavty platfom/m seal mesh. Compessble a deal gas s sed as the fld. -ω based SST Tblence model wth Low-Re coecton and compessblty effects s sed fo Solton comptatons. Mass flow n and statc pesse ot type bonday condtons fo the CFD model wee appled. Roto doman set p wthn FLUENT was tested nde Relatve Fame moton and Mesh moton to capte senstvty of eslts to these settngs []. 53

70 FIGURE. CFD MESH FOR THE ROTOR-SIDE MAINSTREAM/DISC CAVITY INCLUDING ZOOMED OUT REGIONS OF THE RIM SEALS FIGURE. CAVITY STATIC WALL Y+ CONTOURS 54

71 Cp mllon elements 9 mllon elements 3.6 mllon elements Radal Poston (/Rh) FIGURE 3. MESH INDEPENDENT STUDY: DISC PRESSURE COMPARISON ON STATIC WALL 55

72 CHAPTER 6 RESULTS AND DISCUSSION: ASU TURBINE STAGE RIM SEAL CAVITY Dect compasons between the expements and the eslts of the smlaton ae dscssed n ths secton. The expemental data whch wll be compaed to the nsteady smlaton nclded tme-aveaged pesse and concentaton measements. Also, compason between PIV eslt, whch was sed to mease fld velocty nsde the cavty between the lab seal and the m seal wll be made wth CFD velocty gaphs. The CFD smlatons boght to lght the nsteadness pesent n the flow dng the expement whch the slowe esponse data dd not flly capte. LABYRINTH SEAL CLEARANCE When pefomng expements n a otatng g, cetan dmensonal ncetantes ae nevtable. One of these ncetantes s the measement of the labynth seal cleaance. It s not possble to mease the lab seal cleaance dng the assembled condton of the test g; theefoe, the adal heghts of the sngle tooth lab seal on the oto dsc and coespondng land on the stato wall wee meased n the nassembled condton. The dffeence of the two measements s assmed as the lab seal cleaance dng the assembled condton. Dng nnng, howeve, the lab seal cleaance shold only slghtly decease de to centfgal foce becase the tests wee pefomed at oom tempeate, ths elmnatng dffeental adal gowth de to themal expanson. Unde oto fame moton settng, engne test data wee ntally obtaned at an assemblymeased lab seal cleaance of 0.6mm acoss the specfed ange of pge flows. In a second ond of tests wth e-assembled hadwae and a cleaance of 0.5mm, cavty statc 56

73 Statc Pesse, KPa pesses wee consstently hghe by oghly 600 Pa as shown n Fge 4. De to ncetanty n the meased lab seal cleaance, the nsteady FLUENT CFD smlatons wee pefomed by applyng the mass flow n-statc pesse ot bonday condtons to compae the 0.6 and 0.5mm cleaance at the low pge flow of Cw=540 (see Fge 4). It can be seen that the statc pesse pedcted by CFD at the smalle cleaance shows a slght elevaton n vale fo the lowe cavty bt afte the lab seal, the devaton nceases. On the othe hand, the coespondng data fo the lage cleaance show a bette match wth the data acoss all ad. Snce the dffeence falls wthn the ncetanty n pesse measements [7], the CFD smlatons wee pefomed wth 0.6mm acoss the ange of pge flows Measement, Cw=540, 0.6mm LS Measement, Cw=540, 0.5mm LS Flent Unsteady, Cw=540, 0.6mm LS Flent Unsteady, Cw=540, 0.5mm LS Radal Poston, (/Rh) FIGURE 4. LABYRINTH SEAL SENSITIVITY STUDY VS. RADIAL LOCATION 57

74 CFD COMPARISON WITH FLOW PATH DATA In Flent, fst, steady state analyss was caed ot, and ths steady state eslt was sed as ntal solton fo tansent smlaton. A smmay of the compason between nsteady CFD smlaton and flow path test g data follows. To compae the tme-aveaged pesse measements wth the data obtaned fom FLUENT smlatons, CFD pesse coeffcent dstbtons wee obtaned fom 4 to 6 evoltons, and then aveaged ove the coespondng tme to mmc the statc pesse data acqston. The compason s acoss all pge flows n Fges 5 and 6. In all of the plots, the test data ponts ae mostly on top of each othe fo all pge flows, and fo ths eason, Cw=66 was omtted fom the plot. Fge 5 shows pesse coeffcent compason between the expements and the CFD smlatons mm downsteam of the vane talng edge (6.7mm psteam of cavty gap) acoss one vane ptch. The pesse dstbtons geneated fom the expements and the smlatons ae pedctable as they have a pea to pea feqency of pe evolton whch matches the vane cont. To vefy the convegence of the pesse coeffcent dstbtons shown, a smlaton of the Cw=540 pge flow ate was caed ot thogh 5 evoltons. Tme aveaged data of 4 to 6 evoltons wee compaed wth the tme aveaged data of 9 to 5 evoltons. The maxmm pesse coeffcent dffeence n pecent between tme aveaged smlatons was 0.5%; theefoe, t was conclded that the solton had conveged at 4 to 6 evoltons. The data at the low pge flow s n good ageement wth the nsteady smlatons at the nd half of the vane ptch angle, whee both types of cves have a pea to pea feqency of pe evolton. One of the dffeences between the pesse coeffcent dstbtons geneated by the measements and the nmecal smlatons s that the nmecal 58

75 smlaton geneates cves wth hghe ampltdes. Ths can occ becase the pesse monto pont n Fge 5 s n the vcnty of the dsc cavty. Thee, the nsteadness of the flow can case t to oscllate at a feqency whch s ndetectable by the statc pesse measement, bt s capted by the nsteady CFD smlaton. Ths hypothess can be tested by placng an nsteady pesse measement downsteam of the vane talng edge m seal. FIGURE 5. EXPERIMENTAL AND CFD PRESSURE DISTRIBUTIONS IN FLOW PATH 59

76 FIGURE 6. EXPERIMENTAL AND CFD PRESSURE DISTRIBUTIONS IN FLOW PATH The pesse monto pont at the vane talng edge ote shod acoss two vane ptches shown n Fge 6 s solated fom the nsteadness stemmng fom both the dsc cavty and the blade tp. Fo ths eason, the pesse coeffcent dstbton n Fge 6 s n excellent ageement wth the test data. Both the feqency and the ampltde geneated by the statc pesse measements and the nsteady nmecal smlatons match. Sgnfcant nsteadness ases nea the blade tp, and ths s shown when compang the pesse coeffcent dstbtons acoss two vane ptches n both Fges 60

77 7 and 8. The pesse dstbtons geneated fom the expements and the smlatons have a pea to pea feqency of pe evolton, whch matches the vane cont; bt the slow esponse pesse measement s nable to capte the blade-vane nteacton. Addtonally, the tme-aveaged data extacted fom the nsteady CFD smlaton s nable to capte the hgh feqency oscllatons nea the blade tp. Sgnfcant wo needs to be pefomed to gan nsght nto blade-vane nteactons nea the blade tp. Fte wo focsng on ths sbect shold nclde nsteady pesse measements nea the blade tp, and an nsteady CFD smlaton wth mesh devoted to captng the blade-vane nteactons. FIGURE 7. EXPERIMENTAL AND CFD PRESSURE DISTRIBUTIONS IN FLOW PATH 6

78 FIGURE 8. EXPERIMENTAL AND CFD PRESSURE DISTRIBUTIONS IN FLOW PATH CFD COMPARISON WITH CAVITY DATA Fge 9 and 30 shows statc pesse and sealng effectveness (ηc) measements at the stato wall nsde the dsc cavty. The CFD eslt n Fge 30 coesponds to Roto Fame moton set-p, and Fges 3 and 3 coespond to Mesh moton set p. To compae the tme-aveaged pesse measements wth the data obtaned fom nmecal smlatons, a smla pocess as descbed n the flow path secton of the eslts was sed. The pesse dstbton was fst aveaged ove the ccmfeence n the adal decton, and then aveaged ove tme (4 to 6 evoltons). Sealng effectveness (ηc) on the stato wall was obtaned expementally by seedng the pge a wth CO tace gas, whee ngeston nto the cavty edces the CO gas 6

79 Statc Pesse, KPa concentaton. Ths concentaton was meased by a gas analye, ths by nowng the ntal gas concentaton of the pge flow and the gas concentaton at dffeent locatons on the stato wall, sealng effectveness (ηc) was expementally calclated. Seedng pge a wth CO gas was also pefomed n the CFD smlatons. The CO gas dstbton was fst aveaged ove the ccmfeence n the adal decton then aveaged ove tme (4 to 6 evoltons). In compang Fame vess Mesh moton settngs, sealng effectveness patclaly at the lowe pge flows matches the data bette wth mesh moton set p as compaed to Fame moton (see Fges 30 and 3) Measement, Cw=540 Flent Unsteady, Cw=540 Measement, Cw=3080 Flent Unsteady, Cw=3080 Measement, Cw=46 Flent Unsteady, Cw=46 Measement, Cw=66 Flent Unsteady, Cw= Radal Poston, /Rh a) Ds Pesse Compason on Cavty Statc Wall FIGURE 9. EXPERIMENTAL AND CFD COMPARISON OF CAVITY DATA VS. RADIAL POSITION 63

80 Effectveness Effectveness Measement, Cw=540 Flent Unsteady, Cw=540 Measement, Cw=3080 Flent Unsteady, Cw=3080 Measement, Cw=46 Flent Unsteady, Cw=46 Measement, Cw=66 Flent Unsteady, Cw= Radal Poston (/Rh) b) Sealng Effectveness Compason on Cavty Statc Wall, Fame Moton FIGURE 30. EXPERIMENTAL AND CFD COMPARISON OF CAVITY DATA VS. RADIAL POSITION (WHERE DASHED LINES REPRESENT RADIAL POSITIONS AT ROTOR-SIDE LAB SEAL INNER WALL, STATOR-SIDE LAB SEAL OUTER WALL, AND PLATFORM ROTOR-SIDE MID- RADIUS WING) Measement, Cw=540 Flent Unsteady, Cw=540, MM Measement, Cw=3080 Flent Unsteady, Cw=3080, MM Measement, Cw=46 Flent Unsteady, Cw=46, MM Measement, Cw=66 Flent Unsteady, Cw=66, MM Radal Poston (/Rh) c) Sealng Effectveness Compason on Cavty Statc Wall, Mesh Moton FIGURE 3. EXPERIMENTAL AND CFD COMPARISON OF CAVITY DATA VS. RADIAL POSITION (WHERE DASHED LINES REPRESENT RADIAL POSITIONS AT ROTOR-SIDE LAB SEAL INNER WALL, STATOR-SIDE LAB SEAL OUTER WALL, AND PLATFORM ROTOR-SIDE MID- RADIUS WING) 64

81 Effectveness Ccmfeentally aveaged sealng effectveness vess evoltons n was checed to assess pedcton accacy. The 5.3 evoltons data fom Wang et al. [] wee also added to bette demonstate the mpact. As shown n Fge 3, the mpovement fom 7 to evoltons of ths stdy on aveage s vey small, and beyond evoltons, thee s hadly any change. Howeve, between [] and ths stdy, t s nclea whethe the obseved dffeence n ppe m cavty effectveness (.e. 5 to 6 evoltons) s de to the m lab seal geomety/locaton whch fo ths stdy s at a lowe ads and conssts of a sngle tooth compaed to the axal gap of [] evoltons evoltons 6 evoltons Wang [Ref.3] Radal Poston (/Rh) d) Sealng effectveness on Cavty Statc Wall at dffeent locaton, Mesh Moton FIGURE 3. EXPERIMENTAL AND CFD COMPARISON OF CAVITY DATA VS. RADIAL POSITION (WHERE DASHED LINES REPRESENT RADIAL POSITIONS AT ROTOR-SIDE LAB SEAL INNER WALL, STATOR-SIDE LAB SEAL OUTER WALL, AND PLATFORM ROTOR-SIDE MID-RADIUS WING ) The data compason between CFD and the g test n Fges 9-3 show that patclaly n the m cavty, both the pesse and sealng effectveness (ηc) dffe fo all 65

82 pge flow ates. The geneal tend s that the nmecal smlatons nde pedct sealng effectveness (ηc) and ove pedct pesses,.e. hghe statc pesse along the m cavty stato wall s dven by ngess. Eo meased md-ads of oto platfom wng s % and 50% at hgh and low pge flow. These eslts ndcate that the flow feld podced n the cavty by the expements s dffeent than the flow feld geneated by the CFD smlatons. In ode to gan nsght nto the fld stcte n the cavty, Balasbamanan et al. [5] obtaned adal and tangental veloctes sng patcle mage velocmety (PIV) ove a sqae lase sheet whch encompasses appoxmately 90 degees nsde the oto-stato dsc ote cavty. Fo the pge flow ate of Cw=540, ten nstantaneos mages wee ceated at a captng feqency of 3.3 H, o one mage evey. oto evoltons. It was obseved n the adal velocty conto plots that fve mages had ngess secto and the emanng fve had ngess sectos. Ths eslt scaled p to a 360 degee mage wold podce 4 to 8 ngess sectos. Two nstantaneos adal velocty vecto plots llstatng the two types of ngess sectos ae shown n Fges 33 and 34. The veloctes ae meased n the plane x/s=0.84. Fge 35 shows nstantaneos adal velocty contos fo 7,, and 6 evoltons n the ote cavty podced by 360 degees nsteady CFD smlatons at plane x/s=0.83. The ngess sectos shown n Fge 35 vay fom 8 to 3 and confm the tends n aveaged sealng effectveness eslts shown n Fges

83 FIGURE 33. PIV RADIAL VELOCITY MEASUREMENTS FOR CW=540 AT LOCATION X/S=.84 FIGURE 34. PIV RADIAL VELOCITY MEASUREMENTS FOR CW=540 AT LOCATION X/S=.84 Fthe nvestgaton nto Fge 35 shows that flow nsde the cavty s nonpeodc; also, the nmbe and poston of the ngess and egess sectos ae changng 67

84 wth the nmbe of evoltons,.e. satsfes the defnton of nstable flow. Moeove, ndvdal pesse ponts as well as ccmfeentally aveaged (Z plane) at ad 44mm, 48mm, 6mm, 73mm, 79mm, and 8mm wee montoed fo convegence fom evoltons 8 to 6, see Fges 36 and 37. The dsceet pont pesse plses had non epeatng peas ove tme whch confms the obsevaton of nstable flow noted n Fge 35. Ccmfeental non-peodcty was confmed by pevos 360 degee nsteady CFD smlatons, bt t s dffclt to tell f the obseved nstable fld stcte physcally epesents what occed n the test g snce the fld stcte cannot be obtaned fo ths geomety expementally. FIGURE 35. RADIAL VELOCITY CONTOURS FROM UNSTEADY CFD, M/S 68

85 (a) Dsceet ponts along dsc ads as shown above (b) Z plane ct nea the stato dsc wall FIGURE 36. STATIC PRESSURE MONITOR POINTS FROM REVOLUTIONS 8 TO 6 (360 TIME STEPS PER REVOLUTION) 69

86 Statc Pesse, Pa 9650 Statc Pesse Z-4._R44 Z-4._R48 Z-4._R Z-4._R73 Z-4._R79 Z-4._R Tme Step (a) Aveaged at axal (Z) plane along each ads (b) Dsc adal cts FIGURE 37. STATIC PRESSURE MONITOR POINTS FROM REVOLUTIONS 8 TO 6 (360 TIME STEPS PER REVOLUTION) Expemental flow vsalaton data obtaned by Cany et al.[] showed that fo a wde ange of condtons, stable votex stctes ae fomed n smple oto-stato 70

87 cavtes. Caft [4] pefomed URANS smlatons of the above mentoned expements. The smlaton of the dsc cavty was done sng a two-eqaton tblence model, and smla to the eslts pesented n ths epot, Caft s smlatons dd not each stablty even afte 70 evoltons. To ths atho s nowledge, expemental flow stctes of smple oto-stato cavtes have yet to be eplcated n URANS o LES models. DISCUSSION The above wo demonstates the challenges n oto-stato smlatons. The lmtatons n nmecal smlatons need to be valdated wth moe sophstcated expemental measements capable of captng ngess/egess flow stctes. The slow esponse sealng effectveness measements and PIV eslts obtaned at 3.3 H (one mage pe. oto evoltons) do not mease the apdly changng ngess sectos. On the othe hand, the nsteady smlaton pesented n ths wo s able to capte the fld stcte at a ate of 4.4 H (360 tme steps pe evolton). Theefoe, one eason the smlatons pesented n ths pape ae n dsageement wth the tbne g data s becase slow esponse expemental data ae beng compaed to fast esponse CFD smlatons. Anothe eason s that the fld stcte shown n the smlatons has not eached ts fnal state. Even afte 6 evoltons, the ngess sectos have not conveged to what was expementally obseved. Wang et al. [] pefomed a 360 nsteady CFD valdaton on the same g wth a dffeent ovelap geomety and m seal. Wang et al. showed thogh the 360 degee nsteady CFD valdaton that the flow thogh the m seal s non-peodc, bt dd not comment o povde sffcent evdence that the flow had stabled afte 6 oto 7

88 evoltons. The CFD pefomed to sppot ths thess shows the flow stcte n the cavty s nstable ccmfeentally and stll evolvng afte 6 evoltons, albet the ccmfeentally aveaged sealng effectveness seems to not change afte evoltons. Ths povdes one explanaton on why the sealng effectveness (ηc) does not match the data, ths ngeston nto the cavty s ove pedcted at hghe stato wall statc pesse. As stated pevosly, anothe eason why the nmecal eslts do not match what was meased n the expements s becase fast esponse CFD eslts ae beng compaed to slow esponse sealng effectveness and PIV eslts. Fom ths wo alone t can be conclded that mpovements need to be made n expemental measng technqes and smlaton methodology. The nmecal analyss pefomed n ths wo shows the flow stcte n the cavty s nstable ccmfeentally and stll evolvng afte 6 evoltons. Fthemoe, Caft [4] showed n hs smlaton of dsc cavtes sng a two-eqaton tblence model, that the flow does not each steady state even afte 70 evoltons. Ths povdes one explanaton on why the sealng effectveness (ηc) does not match the data. Nevetheless, the CFD valdaton eslts pesented n ths secton extend the database fo pacttones nvolved wth nsteady mansteam/dsc cavty nteacton. Fo example, t was shown that Mesh moton set p n FLUENT eslted n an mpovement n matchng sealng effectveness data as compaed to Fame Moton. Ths evelaton sggests the mpotance of locatng the optmm oto-stato mesh assmpton acoss all physcal vaables beng compted. Fom the expemental sde, flow vsalaton nsde a tbne dsc cavty s not cently avalable and wll be vey dffclt to obtan. Theefoe, t s poposed that fte wo on ths sbect pefom CFD valdaton of the 7

89 smlaton method wth dffeent settngs sng moe sophstcated expemental measements capable of captng the evolvng ngess/egess flow stctes. Recommendatons to mpove expemental technqes and smlaton methodology s dscssed late n ths wo. 73

90 CHAPTER 7 RESULTS AND DISCUSSION: VALIDATION OF URANS AND LES SOLUTIONS IN A CLOSED ROTOR-STATOR DISC CAVITY The pevos secton ponted ot that cent smlaton methodology sed to pedcted m seal cavty concentaton measements can be mpoved, ths secton tes to addess these shotcomngs valdatng the CFD tool by compang ts pedctons aganst expemental LDV data n a closed oto-stato cavty. The enclosed cavty has a statonay shod, a otatng hb, and mass flow does not ente o ext the system. A fll 360 degee nmecal smlaton s pefomed compang Flent LES, wth nsteady RANS sng Spalat-Allmaas, RNG -ε, Realable -ε, Reynolds Stess, -ω, and SST -ω tblence models. The obectve of ths tas s to assess the valdty of URANS tblence models n moe complex otatng flows, compae accacy wth LES smlatons, and sggest CFD settngs to bette smlate tbne stage mansteam/dsc cavty nteacton wth ngeston. The closed sothemal oto-stato cavty has a statonay shod, a otatng hb, and mass flow does not ente o ext the system as shown n Fge 38. If t can be shown fo a oto stato poblem that nmecal smlatons agee wth expemental eslts, ths blds confdence that the same smlaton settngs may gve sefl eslts fo the tbne stage mansteam/dsc cavty poblem wthot pefomng extensve CFD evaldaton. 74

91 FIGURE 38. ENCLOSED ROTOR-STATOR CAVITY COMPUTATIONAL DETAILS The cavty shown n Fge 38 s composed of a statonay ds, otatng ds, nne otatng cylnde, and ote statonay shod. A=40 mm and b=40 mm ae the nne and ote ad of the otatng ds. h=0 mm s the nne ds spacng and Ω s the otaton ate. The otatonal Reynolds nmbe s based on the ote ads on the ds. Séveac [3] pefomed expements on ths cavty whee the fld was wate at 0 C. The expemental lase Dopple velocmety (LDV) eslts obtaned by Séveac can be sed to compae wth comptatonal pedctons. The gd se fo the 360 degee model and tme steps fo all nmecal smlatons ae pesented below n Table, and the mesh s shown n Fge 39. It was obseved fo the smlaton at Re=e5 that the solton emaned nmecally stable at.66 tme steps pe evolton of the otatng ds, ths ths paamete was mantaned fo all comptatonal ns. 75

92 TABLE. COMPUTATIONAL PARAMETERS Comptatonal Paametes Re Comptaton Gd Ө tme step (s) tme steps pe ev.00e+05 URANS/LES E+05 LES E+06 LES FIGURE 39. CLOSED ROTOR-STATOR DISC CAVITY MODEL The comptatons stated wth the fld at est. No-slp bonday condtons ae appled on all the cavty walls whee V and V ae eo on all the walls n the cavty. Vθ=Ω s appled on the oto and hb, and s eo on all othe walls. Fo otatonal Reynolds Nmbe=e5, smlatons of the closed oto-stato cavty wee pefomed sng Flent employng nsteady -ω, -ε, Spalat-Allmaas, RNG -ε, Realable -ε, Reynolds Stess, and SST -ω tblence models. Addtonally, a smlaton was pefomed wth LES (Smagonsy-Lly Sb-Gd Scale (SGS) model). These comptatonal eslts wee compaed wth expemental data. 76

93 RESULTS In the followng eslts, the nne ds spacng has been nomaled by h=0mm, theefoe the non-dmensonal axal spacng vaes fom 0-. Both the adal and tangental velocty components ae meased at md-ads and these components ae nomaled by the maxmm otatonal velocty of the system; V = V/Ω and Vt = Vt /Ω. The ccmfeental aveage was taen fo the velocty components mentoned above afte seconds of smlaton. It can be seen by the meased data that flow nsde the cavty s domnated by tangental velocty. The lagest adal velocty component s 5% of the lagest tangental velocty component. Data compason wth the tangental velocty s shown n Fge 4o. The URANS smlatons fals to capte the mean tangental velocty nea the oto, stato and the md axal plane of the cavty. The URANS pedcton at the md axal plane ange fom , bt the meased vale s nea Ths tanslates to URANS smlatons nde-pedctng closed cavty tangental velocty by 3% to 43%. On the othe hand, the LES smlaton captes the mean tangental velocty at all locatons. The URANS smlatons, capte the mean adal velocty nea the oto and the md axal plane of the cavty n Fge 4. Howeve, nea the stato t fals to match the expemental data. It s expected that the mnmm adal velocty shold appoach bt mnmm occs between two meased data ponts, ths, t s not capted by the expement. The mnmm adal velocty at the stato locaton pedcted by URANS s abot Convesely, the LES smlaton captes the mean adal velocty nea the oto, stato and the md axal plane of the cavty. Based on the eslts dscssed above the velocty pofles pedcted by the LES model moe closely esembles the LDV data. 77

94 FIGURE 40. TANGENTIAL VELOCITY CFD VS EXPERIMENT RE=E5 FIGURE 4. RADIAL VELOCITY CFD VS EXPERIMENT RE=E5 78

95 The LES model was fthe valdated n Fges 4-45 whee the nmecal pedctons wee compaed wth expements at Re=4e5 and Re=e6. Smla to the pevos data the adal and tangental velocty components ae meased at md-ads. The ccmfeental aveage was taen fo the velocty components mentoned above afte seconds of smlaton. It can be seen that as the otatonal Reynolds nmbe nceases, the domnance of the flow by tangental velocty s lage. The lagest adal velocty component s abot % of the lagest tangental velocty component at Re=4e5 and abot 0% at Re=e6. Ths tend s capted by the LES model and addtonally the model also matched the LDV data the nea the oto, stato and the md axal plane of the cavty at the hghe Reynold nmbes. In a otatng flow envonment, LES smlatons wee accately able to pedct the adal and tangental veloctes. FIGURE 4. TANGENTIAL VELOCITY CFD VS EXPERIMENT RE=4E5 79

96 FIGURE 43. RADIAL VELOCITY CFD VS EXPERIMENT RE=4E5 FIGURE 44. TANGENTIAL VELOCITY CFD VS EXPERIMENT RE=E6 80

97 FIGURE 45. RADIAL VELOCITY CFD VS EXPERIMENT RE=E6 URANS VS. LES In the nmecal stdes shown above LES has pefomed bette n smlatng flows n a closed otatng cavty when compaed aganst URANS soltons. Althogh URANS solves the tansent solton, t s nable to capte the tempoal and spatal vaaton [0]. Ths s becase n URANS smlatons, the flow popetes ae oganed nto the mean and flctatng components, and ntegaton ove tme s pefomed. The contnty and momentm eqatons descbng ths pocess wee mentoned n eqatons and ae epeated hee. x t 0 x p x x R x eq. 08 8

98 t x p x x R x eq. 09 Whee R s the Reynolds stess tenso ths closes the govenng eqatons by modelng the nnowns ntodced by the aveagng pocede. Theefoe, URANS captes the lage scale flctatons, then t models flctatons of the tblent netal and dsspaton ange. The LES eqatons ae shown n eqatons 04 and 05: Althogh, the LES eqatons ae smla to the RANS eqatons, n LES the oveba desgnates spatal flteng. The flte s a fncton of gd se, and tblent scales smalle than the gd se ae emoved and modeled by a sb-gd scale defned as τ. Ths means that eddes lage than the gd se ae solved nmecally by the flteed N-S eqatons. Theefoe flctatons of the flow feld that tansfe momentm at the smalle scales ae capted by the LES eqatons. These flctatons ae mpotant to model tblent otatng flows ths the velocty pofles pedcted by the LES models moe closely esembles the LDV data. DISCUSSION Two dffeent CFD technqes, URANS and LES smlatons wee valdated n a closed oto stato cavty to sggest CFD settngs fo bette tbne stage mansteam/dsc cavty ngeston pedctons. It was shown that n ode to accately pedct otatng flows, t s mpeatve to model the small scale flctatons. URANS s nable to accont fo these flctatons n the flow feld, as ts accacy s lmted to lage scale stctes. Ths s why URANS fals to accately pedct tbne stage mansteam/ds cavty sealng effectveness and the velocty pofles n an enclosed oto-stato cavty. LES matched expemental data of the velocty pofles n an enclosed oto-stato cavty 8

99 becase t esolves these small scale stctes. Theefoe, LES smlaton s ecommended to accately pedct tbne stage mansteam/ds cavty sealng effectveness n addton to the velocty feld. 83

100 CHAPTER 8 SUMMARY AND RECOMMENDATIONS Appoaches sed to bette ndestand ngeston n a tbne stage dsc cavty nclde analytcal, expemental, and nmecal modellng. All of these appoaches povde a dffeent nsght nto the poblem and have all been pesented hee. Despte these dffeent methodologes, pedctng ngeston n a tbne dsc cavty emans a challenge. All of the classc theoetcal models pesented n ths wo wee valdated by expementaton and ae sed by ndsty to povde qc answes n statons sch as component/engne testng whee tme fo detaled CFD smlatons and data edcton s not avalable. These analytcal appoaches ae also sefl fo ganng physcal ntton of the poblem becase of the smplfyng assmptons made. In the case of the lamna flow between a otatng and a statonay dsc, thee ae many physcal occences whch mo the tbne stage dsc cavty poblem. Fo example, the oto s pmps the flow ot of the cavty and hot mansteam gas ngeston occs nea the stato. Howeve, theoetcal models do not have the detal of nmecal smlatons and ae only accately applcable to a vey small class of flows. Expemental valdaton was anothe technqe dscssed n ths wo. Sccessfl expemental technqe se epesentatve envonments to ndestand a poblem o a desgn. Hee a scaled g s desgned to epesent a tbne stage n ode to gan nsght nto the m seal ngeston poblem. The g does not fncton n a combston envonment, theefoe ngeston s not meased n tems of tempeate bt by 84

101 concentatons meased n a m seal cavty. Usng the heat tansfe/ mass tansfe analogy t s assmed that ngeston mechansm obseved n the expement wll be smla to the mechansm seen n tbne stage m seal cavtes n combston envonments. The PIV measements show that ngeston s non peodc, concentaton measements also povde a tme-aveaged sealng effectveness of the pge flow. Lmtatons of an expemental g s that not all cased can be epesented by one expemental setp, theefoe pefomng desgn teatons and testng all desgns sng expemental technqes s expensve and tme consmng. Also, nmeased physcs go ndetected and meased data s sbected to measement eo. The fnal appoach sed to ndestand the ngeston poblem n a m seal cavty was nmecal smlatons. Althogh detaled smlatons dscssed hee can be tme consmng, bldng models fo CFD smlatons s stll cheape and less tme consmng when compaed to bldng a desgned expement. Addtonally, the data n nmecal models ae not lmted by nstmentaton. CFD smlatons fo the m seal cavty showed that ngeston s ccmfeentally non peodc and tempoally nstable. Howeve, the accacy of nmecal smlatons ae lmted by the accacy of the bonday condtons and the lmtatons of the mathematcal models sed n the smlatons. When compaed to expemental data sealng effectveness (ηc) s nde pedcted, ths ngeston nto the cavty s ove pedcted. One eason why smlaton eslts do not match what was meased n the expements s becase fast esponse CFD eslts ae beng compaed to slow esponse sealng effectveness and PIV eslts. Fom ths wo alone t can be conclded that mpovements need to be made n expemental measng technqes and smlaton methodology. 85

102 In ode to bette gan nsght nto ngeston physcs that occ n a tbne stage dsc cavty, ntegaton of both expemental and nmecal technqe s moe effectve to complement the dawbacs of each method, and bng bette nowledge fom each technqe. Ths wo showed URANS s nable to accont fo these flctatons n the flow feld, as ts accacy s lmted to lage scale stctes. Ths s why URANS fals to accately pedct tbne stage mansteam/ds cavty sealng effectveness and the velocty pofles n an enclosed oto-stato cavty. Reslts fom ths nvestgaton pont to URANS smlatons nde-pedctng closed cavty tangental velocty by 3% to 43%, and open m cavty effectveness by 50% compaed to test data. Theefoe, LES s ecommended to accately pedct tbne stage mansteam/ds cavty sealng effectveness becase t esolves these small scale stctes. On the othe hand, the slow esponse sealng effectveness measements and PIV eslts obtaned at 3.3 H (one mage pe. oto evoltons) do not mease the apdly changng ngess sectos. Theefoe expemental technqe smla to the Fge 46 efeenced below whee the PIV measement has tme esolton fom 800 H to 600 H s necessay. FIGURE 46. PIV MEASUREMENT (600HZ) VS LES SIMULATION [4] 86