chemical model has a profound impact on the flame size, shape, and ignition location. However, without quantitative experimental data, it is

Transcription

1 Abstact KISLT PATIK G. A Vaable Tblent Pandtl and Scdt Nbe Model Stdy fo Scaet Applcatons. (Unde te decton of D. assan A. assan.) A tblence odel tat allows fo te calclaton of te vaable tblent Pandtl (P t ) and Scdt (Sc t ) nbes as pat of te solton s pesented. Te odel also acconts fo te nteactons between tblence and cesty by odelng te coespondng tes. Fo eqatons ae added to te baselne -ζ tblence odel two eqatons fo entalpy vaance and ts dsspaton ate to calclate te tblent dffsvty and two eqatons fo te concentatons vaance and ts dsspaton ate to calclate te tblent dffson coeffcent. Te ndelyng tblence odel aleady acconts fo copessblty effects. Te vaable P t /Sc t tblence odel s valdated and tned by slatng a wde vaety of epeents. Inclded n te epeents ae two-densonal asyetc and tee-densonal ng and cobston cases. Te cobston cases nvolved ete ydogen and a o ydogen etylene and a. Two cecal netc odels ae eployed fo eac of tese statons. Fo te ydogen and a cases a seven speces/seven eacton odel wee te eacton ates ae tepeate dependent and a nne speces/nneteen eacton odel wee te eacton ates ae dependent on bot pesse and tepeate ae sed. Fo te cases nvolvng etylene a 5 speces/44 eacton edced odel tat s bot pesse and tepeate dependent s sed along wt a speces/8 global eacton edced odel tat aes se of te qas-steady-state appoaton. In geneal fa to good ageeent s ndcated fo all slated epeents. Te tblence/cesty nteacton tes ae fond to ave a sgnfcant pact on flae locaton fo te two-densonal cobston case wt ecellent epeental ageeent wen te tes ae nclded. In ost cases te ydogen cecal ecanss beave nealy dentcally bt fo one case te pesse dependent odel wold not ato-gnte at te sae condtons as te epeent and te ote cecal odel. Te odel was atfcally gnted n tat case. Fo te cases nvolvng etylene cobston te

2 cecal odel as a pofond pact on te flae sze sape and gnton locaton. oweve wtot qanttatve epeental data t s dffclt to detene wc one s oe stable fo ts patcla applcaton.

3 A Vaable Tblent Pandtl and Scdt Nbe Model Stdy fo Scaet Applcatons by Patc Kestle A dssetaton sbtted to te Gadate Faclty of Not aolna State Unvesty n patal flfllent of te eqeents fo te Degee of Docto of Plosopy Mecancal and Aeospace ngneeng aleg Not aolna 009 APPVD B Fed. Deanette Jac. dwads Pee A. Gead Mno epesentatve assan A. assan ottee aan

4 Bogapy Patc Gaett Kestle was bon n oncod Not aolna on May st 98. ne of te ao nflences on s edcatonal coces was s patcpaton n te A Foce Jno T at ental abas g Scool. Dng ts te s nteest n avaton was spaed. obned wt an nteest n pyscs and ateatcs te obvos coce was to stdy aeospace engneeng. Te coce to attend N State Unvesty was also an easy one not only fo te convenence bt also fo te eptaton of te engneeng scool. It was not ntl s seno yea tat e too an ntodcton to coptatonal aeodynacs cose. Tat epose was enog fo to decde tat coptatonal fld dynacs was wat e wanted to pse n s gadate stdes and beyond. Patc as been attendng gadate scool at N State Unvesty snce 004 dng wc te e eceved s Mastes degee n aeospace engneeng. e plans to coplete s PD by Mac 009 at wc pont e wll begn wong at ovd Tecnologes n Mooesvlle Not aolna.

5 Acnowledgeents Tee ae a nbe of people I wold le to tan fo te sppot tog te cose of ts wo. Fst y tess advso D. assan A. assan wo as tagt e any valable lessons povded ecellent gdance and always ept y best nteests n nd. D. Jac dwads as also been an nvalable soce of nfoaton and sppot tog classes and consltatons. I wold also le to tan y offce ate Jon Boles fo patcpatng n feqent dscssons abot o wo and fo gong to lnc wt e nealy evey day. Fnally I wold le to tan y faly fo te contned otvaton and sppot togot y college caee. Te nteest tey sow n y wo s vey encoagng.

6 v Table of ontents Lst of Fges... v Lst of Tables... Lst of Sybols... Intodcton... Govenng qatons eactng Gas qaton Set Nave-Stoes qatons Teodynac elatons Govenng qatons n Vecto Fo eynolds and Fave Aveagng ecal Knetcs /A ecal Knetc Mecanss Jacows ecal Mecans onnae et al. ecal Mecans /A ecal Knetc Mecanss Golasnan et al. edced ecal Mecans Zabon and ella edced ecal Mecans Tblence lose ζ Model Vaable Tblent Pandtl Nbe Model Vaable Tblent Scdt Nbe Model Tblence / esty Inteactons oplete qaton Set Solton Metods peental vevew Bows and Kov peent... 8

7 v 3. SD Test Meda ffects peents Ln tylene Mng peent Te SLA peent peental Data Fttng ysot peent Ipleentaton Mltbloc Paallel Appoac optatonal Geoety Bows and Kov Gd Geoety SD Test Meda ffects Gd Geoety Ln tylene Mng Gd Geoety SLA Gd Geoety ysot Gd Geoety Bonday ondtons Syety Wall Bondaes Sbsonc Inflow and tflow Spesonc Inflow and tflow Specal ases eslts and Dscsson Bows and Kov peent Wtot Tblence/esty Inteactons Wt Tblence/esty Inteactons SD-Test Meda ffects peent Mng ases ydogen only ase ydogen/tylene Mte ase Ln tylene Mng peent... 7

8 v 5.3. opason wt peent opason wt LS/ANS ybd Model SLA peent Inflow and Bondaes ent eslts ysot peent opason wt peent opason wt onstant Pandtl/Scdt Nbe Slaton onclsons... 9 efeences Appendces... 0 Append A Govenng qatons Vectos... 0 Append B Tansfoaton to Genealzed oodnates Append ecal Knetc Mecans Paaetes Append D oplete qaton Set n Vecto Fo... 8 Append Necal Folaton... 3 Append F act and Modeled Tblence qatons... 35

9 v Lst of Fges Fge 3. Sceatc of Bows and Kov Spesonc obsto... 8 Fge 3. Sceatc of SD-TM peent Fge 3.3 Sceatc of Ln tylene Mng peent... 3 Fge 3.4 Sceatc of SLA peent Fge 3.5 Detal of Vectoed ydogen Inecto Fge 3.6 aple of AS Measeents and ve Ft (Plane 6 y 8. ) Fge 3.7 Sceatc of ysot ngne Model Fge 4. Bloc Layot and Detal fo Bows and Kov peent... 4 Fge 4. Bloc Layot fo SD-TM peent... 4 Fge 4.3 Bloc Layot fo Ln tylene Mng peent Fge 4.4 Bloc Layot and Inecto Detal fo SLA peent Fge 4.5 SLA Bloc Layot wt AS Svey Planes glgted Fge 4.6 Bloc Layot fo ysot peent Fge 5. Speces Pofles n te Absence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows) Fge 5. opted Mole Facton ontos n te Absence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows) Fge 5.3 opted ddy Vscosty (top) Tblent Dffson oeffcent (cente) and Tblent Dffsvty (botto) n te Absence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows) Fge 5.4 Speces Pofles n te Pesence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows)... 56

10 v Fge 5.5 opted Mole Facton ontos n te Pesence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows) Fge 5.6 opted ddy Vscosty (top) Tblent Dffson oeffcent (cente) and Tblent Dffsvty (botto) n te Pesence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows) Fge 5.7 Speces Pofles n te Pesence of Tblence/esty Inteactons fo Bows and Kov peent (onnae) Fge 5.8 opted and Meased Tepeate Pofles fo SD-TM Mng ases... 6 Fge 5.9 adal Tepeate Pofles at 40 c Staton fo SD-TM Mng ases 6 Fge 5.0 opted and Meased entelne Aal Velocty fo SD-TM Mng ases Fge 5. adal Pofles of Aal Velocty fo SD-TM Mng ases Fge 5. opted Mole Facton ontos fo SD-TM Mng ases Fge 5.3 opted ddy Vscosty (top) and Tblent Dffson oeffcent (botto) fo SD-TM Mng ases Fge 5.4 Infaed Iage of SD-TM n Fge 5.5 opted Mole Facton ontos fo SD-TM n Fge 5.6 opted ddy Vscosty ontos fo SD-TM n Fge 5.7 opted Tblent Dffson oeffcent (top) and Tblent Dffsvty ontos fo SD-TM n Fge 5.8 Vsble Iages of n 40 Pase A (top) and n 40 Pase B (botto)70 Fge 5.9 opted Mole Facton ontos fo SD-TM n 40 Pase A7 Fge 5.0 opted Mole Facton ontos fo SD-TM n 40 Pase B7 Fge 5. A Densty ontos on ente Plane fo Ln peent Fge 5. peental (left) and opted (gt) tylene Mte Facton fo Ln Mng peent... 74

11 Fge 5.3 opted Tblent Scdt Nbe ontos fo Ln Mng peent Fge 5.4 alclatons of LS/ANS Model (left) and Pesent Model (gt) Mte Factons fo Ln Mng peent Fge 5.5 opted Tblent Mass Fl opason fo Ln Mng peent.. 77 Fge 5.6 Ptot Pesse Pofle at Vtated A Nozzle t fo SLA Fge 5.7 Wall Tepeate vs. n Te at Tee Locatons (ef [3]) Fge 5.8 opted and Meased Pesse Dstbton fo SLA... 8 Fge 5.9 Sface Fts of AS Tepeate Measeents fo SLA... 8 Fge 5.30 opted (left) and Meased (gt) Tepeate Dstbtons fo SLA Fge 5.3 opted and Meased Mole Factons fo Ntogen (left) and ygen (gt) fo SLA Fge 5.3 opted P t (left) and Sc t (gt) ontos fo SLA Fge 5.33 opted Tblent Dffsvty (left) and Tblent Dffson oeffcent (gt) fo SLA Fge 5.34 opted and Meased Pesse Dstbton fo ysot ase # Fge 5.35 opted Tepeate ontos fo ysot ase # Fge 5.36 opted Tblent Pandtl Nbe fo ysot ase # Fge 5.37 opted Tblent Scdt Nbe fo ysot ase # Fge 5.38 opason of Pesent Model wt Pevos onstant P t /Sc t Slaton ysot ase # Fge 5.39 Pesse Gadent Magntde fo Slatons of ysot ase #

12 Lst of Tables Table. Toe Paaetes fo onnae et al. Mecans... 6 Table. -ζ Model lose oeffcents... Table.3 Vaable Pandtl Nbe Model onstants... 3 Table.4 Vaable Scdt Nbe Model onstants... 5 Table 3. SD-Test Meda ffects peent ondtons... 3 Table 3. Inflow ondtons fo tylene Mng peent Table 3.3 Inflow ondtons fo SLA peent Table 3.4 Inflow ondtons ysot peent (#7678) Table. Abdged Jacows Mecans eactons Table. Abdged Jacows Mecans Paaetes Table.3 onnae et al. Mecans eactons Table.4 onnae et al. Mecans Paaetes... 0 Table.5 onnae et al. Mecans Td Body ffcences... Table.6 Golasnan et al. Mecans eactons... Table.7 Golasnan et al. Mecans Paaetes... 4 Table.8 Golasnan et al. Mecans Td Body ffcences... 6 Table.9 Toe Paaetes fo Golasnan et al. Mecans... 6 Table.0 Zabon and ella Mecans Global eactons... 7

13 Lst of Sybols oan Sybols A Pe-eponental facto / face aea A G le Iplct at coeffcents a Speed of sond at * T ** T *** Fall-off eacton ate constants a b Teodynac cve ft coeffcents β Vaable Pandtl nbe odel constants Speces concentaton Mte concentaton p Specfc eat ato at constant pesse p Mte specfc eat ato at constant pesse β Vaable Scdt nbe odel constants µ ζ -ζ odel close coeffcents D Bnay dffson coeffcent D t Tblent dffson coeffcent Total enegy a Actvaton enegy F G y and z decton nvscd fles ˆ Fˆ Gˆ ξ η and ζ decton nvscd fles F G Aveage nteface fles v Fv Gv y and z decton vscos fles ˆ v Fˆ v Gˆ v ξ η and ζ decton vscos fles e Speces ntenal enegy e Mte ntenal enegy F Fall-off eacton ate fncton F Fl vecto ĝ Gbbs fee enegy pe ole Total entalpy f ĥ ntalpy vaance Speces eat of foaton Speces entalpy Speces entalpy pe ole Mte entalpy

14 J 0 b eq eq P f M M t nˆ NS P P t p p p Q q ˆ ± S S ˆ Sc Sc t s T T TB T t U U ˆ U V W U V W vw Tansfoaton Jacoban Teal condctvty / tblent netc enegy Low pesse eacton ate coeffcent Bacwad eacton ate coeffcent qlb constant based on concentatons qlb constant based on patal pesses Fowad eacton ate coeffcent Speces teal condctvty g pesse eacton ate coeffcent Mac nbe Tblent Mac nbe Fowad and bacwad eacton ode ell face noal vecto Total nbe of speces Pandtl nbe Tblent Pandtl nbe Pesse Speces patal pesse edced pesse Tblent eat fl vecto eat fl vecto esdal vecto Unvesal gas constant Mte gas constant eacton ate Adacent slope atos Soce vecto Scdt nbe Tblent Scdt nbe Instantaneos stan ate tenso Tepeate eynolds stess tenso Speces td body effcency Tblence ntensty Te onsevatve vaable vecto ontavaent veloctes Speces contavaent veloctes atesan velocty n nde notaton atesan velocty coponents

15 V V Wˆ yz ell vole Speces dffson velocty n nde notaton Speces olecla wegt atesan coodnates atesan coodnates n nde notaton Mass facton vaance Speces ass facton Tblent speces dffson vecto Gee Sybols α Teal dffsvty α t Tblent teal dffsvty Dffeent opeato δ Konece delta ε Dsspaton ate of ε Dsspaton ate of entalpy vaance ε Petaton tenso ε Dsspaton ate of σ γ Mte specfc eat ato η Tepeate eponent κ Paaete sed n appa scee µ Molecla vscosty µ Speces olecla vscosty µ t Tblent vscosty ν Kneatc vscosty ν t Tblent neatc (eddy) vscosty ν ν Speces eactant and podct stocoetc coeffcents θ d Actvaton tepeate Densty Speces densty σ Syste spectal ads σ S of ass facton vaances τ Lana stess tenso ω Votcty vecto ω& Speces podcton ate ξηζ Genealzed oodnate Dectons ξ η ζ Metc devatves n nde notaton Ψ ζ Lte fncton Votcty vaance (enstopy)

16 v Sbscpts b Bacwad ontavaant V ontol vole dwads (LDFSS) eq qlb f Fowad Gd ndces / nde notaton ell faces L Left Speces Mte popety NS Nbe of speces gt t Tblent V Vscos VL van Lee w Wall Feestea Spescpts I n P onvectve Invscd Te step Pesse Accents eynolds aveaged Fave aveaged / aveage nteface fl ^ Pe ole. Te ate of cange eynolds flctaton / eactants Fave flctaton / podcts Abbevatons AS FD oeent ant-stoes spectoscopy optatonal Fld Dynacs

17 v FL DNS N ILU LDFSS LS LMA MPI NASA SD PDF QSS ANS SST TM TVD d oant Fedcs and Lewy Dect necal slaton ssentally non-oscllatoy Incoplete Lowe Uppe Low dffson fl splttng scee Lage eddy slaton Law of Mass Acton Message Passng Inteface Natonal A and Space Adnstaton ffce of te Secetay of Defense Pobablty densty fncton Qas-steady-state eynolds aveaged Nave-Stoes Sea stess tanspot Test Meda ffects Total vaaton dnsng Mnod te sybols Patal devatve Gadent opeato

18 Intodcton Tee as always been a need fo a-beatng aeospace vecles to tavel ge and faste. Wete t s fo oe affodable access to obt o fo defense applcatons te need fo engnes tat ae capable of popellng an acaft to ypesonc speeds s clea. Tadtonal tboets n te etee case can opeate fo zeo velocty p to aond Mac 3. At ts pont te copesso stats to do oe a tan good. By eovng te copesso and ts te need fo a tbne a aet engne s ceated. aets can opeate n te ange fo Mac 3 o 4 to abot Mac 5 [5]. At Mac 5 deceleatng te flow to sbsonc speeds fo cobston becoes neasonable de to te ecessve tepeates and ts dssocaton of fel ate tan cobston. Ts llstates te need fo a spesonc cobston aet also nown as a scaet. ate tan ng and cobstng fel at sbsonc speeds te ncong a s allowed to ean spesonc. Te tas of ng and cobstng spesoncally s a dantng one and te slaton of ts pocess can be eqally dffclt. Ipotant factos n te slaton of tese types of flows nclde bt ae not lted to te specfcaton of te tblent Pandtl and Scdt nbes and te consdeaton of tblence/cesty nteactons. Te tblent Pandtl and Scdt nbes ae neently vaable n te cople teedensonal flows tat ae caactestc of cent poposed scaet desgns. Snce classc tblence odels asse tese nbes to be constant and specfed aead of te a new tblence odel tat allows tese nbes to vay and also acconts fo tblence/cesty nteactons s eqed [][65]. ne sc odel s tlzed een. Anote facto tat as eceved lttle attenton n te lteate s te ole of copessblty on g speed ng and cobston. It s well nown tat nglaye gowt ate deceases wt nceasng Mac nbe [6]. Ts penoenon becoes especally potant n spesonc cobston devces de to te fact tat copessblty effects edce te ablty of te fel to wt a at spesonc speeds

19 esltng n less oveall cobston. Te cecal netc ecans also plays an potant ole n spesonc cobston. Dffeences aong cecal odels can affect te gnton locaton o te condtons at wc te slaton wll ato-gnte. Soe effots ave been ade to ove towad te calclaton ate tan te specfcaton of te tblent Pandtl and Scdt nbes as pat of te solton. Metods based on te ng lengt ave been eployed as ealy as 975 by eynolds to calclate bot te tblent Pandtl and Scdt nbes [49]. In 988 Nagano developed a two eqaton odel fo calclatng te tblent dffsvty wc was sed n conncton wt te -ε tblence odel [43]. oweve te odel was not developed fo g speed flow and ts does not nclde te effects of copessblty. Ts odel povded te faewo fo ost of te wo to follow. In 993 Soe et al. developed a vaable tblent Pandtl nbe odel sng etods vey sla to tose sed by Nagano [54]. Ts odel was also deved fo te ncopessble enegy eqaton ate tan te copessble enegy eqaton so copessblty pesse gadent and dsspaton effects wc ae qte potant n g speed flows ae not acconted fo. Two addtonal eqatons wee added to te base ncopessble -ε tblence odel tepeate vaance and ts dsspaton ate. Solvng tese fo eqatons allowed fo te calclaton of te tblent dffsvty. In geneal te eslts fo g Mac nbe low wall tepeate cases wee poved ove tose tlzng te -ε odel alone. In 999 anote appoac was taen by Go et al. to ceate a vaable tblent Scdt nbe odel [4]. In addton to te -ε tblence odel Go odeled te tblent speces dffson vecto wt a sngle tanspot eqaton. A genetc algot tecnqe was appled to effcently obtan te odel constants. Agan te eslts wee poved ove te baselne -ε odel fo a et-n-cossflow applcaton. A copany nown as obston eseac and Flow Tecnology Inc. (AFT Tec) ave been nvestgatng te se of vaable tblent Pandtl nbe etodology fo poplsve type flows snce 000 [36]. Te folaton s based lagely on te wo of Soe and Nagano bt tey dd also nvestgate algebac stess odels n addton

20 3 to te -ε odel. Agan te odel eqatons fo tepeate vaaton and ts dsspaton ate ae based on te low speed enegy eqaton. Te pesse gadent te and te te esponsble fo enegy dsspaton ae gnoed. Te cent wo does not ae tese splfcatons snce sc assptons ae not vald fo scaet type flows. Te odel was late appled by AFT Tec to a Lage ddy Slaton (LS) of eactng and non-eactng sea layes at g speeds [8][9]. Te ppose of ts wo was to geneate data to be sed n povng ANS odels. opessblty coectons wee appled n ts wo bt te odel constants wee odfed n an ad oc anne wtot sgnfcant valdaton. Te odel was etended to nclde vaable P t and vaable Sc t n 005 [6]. In 008 te odel was sown to povde sgnfcant poveents ove any constant P t /Sc t solton [39] fo vaos classcal valdaton cases ncldng te SLA case. In 005 Xao et al. pesented two sla appoaces one fo calclatng te tblent Pandtl nbe (P t ) as pat of te solton [64] and one fo calclatng te tblent Scdt nbe (Sc t ) as pat of te solton [63]. ac of tese new odels sed te -ζ tblence odel of obnson and assan as a base [50]. Wt te addton of two eqatons eac entalpy vaance and ts dsspaton ate fo te vaable P t odel and concentatons vaance and ts dsspaton ate fo te vaable Sc t odel te tblent dffsvty and te tblent dffson coeffcent wee able to be detened. Ipoveents wee obseved fo a coaal et flow [] wt te vaable Sc t odel and poveents n eat fl pedctons wee seen wt te vaable P t odel. Te vaable Sc t odel was late appled to te spesonc cobston epeent of Bows and Kov [7] wle sng a pobablty densty fncton (PDF) to addess te tblence/cesty nteactons. In geneal te vaable Sc t folaton woed well fo bot ng and eactng spesonc flows; oweve te PDF etod fo addessng tblence/cesty nteactons dd not necessaly pove te eslts [3]. A coplete tblence odel wee bot te P t and Sc t ae calclated as pat of te solton was pesented by Xao et al. n 006 [65]. Ts wo wc eployed a new

21 4 odelng appoac fo te tblence/cesty nteactons sowed poveent n pedctons fo bot te coaal et and te Bows and Kov cobsto. Te wo also enfoced te fact tat te tblence/cesty nteactons st be acconted fo. Fo 005 to 009 te fll odel was appled to te SLA spesonc cobston epeents [33][34][35]. Med eslts wee obtaned and soe fne tnng of te odel constants was eqed bt te fnal eslts copaed qte well wt te epeent. Te latest wo s on te SD-Test Meda ffects epeents [3]. Tee s vey lttle epeental data fo tese cases so ost of copasons wee qaltatve. All of te cases tat tlze te fll odel ae dscssed n detal n apte 5. Te SLA cobsto as been slated etensvely by odgez and tle n conncton wt te actal epeents. Intally only ng was consdeed [7] ten te eactng case []. odgez and tle late contned te wo n a oe copeensve stdy [5]. Te slaton tlzed te VULAN FD code developed at NASA Langley eseac ente. Te -ω tblence odel was sed wt vaos constant vales of P t and Sc t. Te copted eslts wee seen to vay geatly wt te specfcaton of tese paaetes. Te best eslts wee obtaned wt P t 0.9 and Sc t.0 teefoe te constant P t /Sc t ns n te cent wo se tese vales. Te coptatonal gd sed n te cent wo was also developed fo a gd ognally geneated by odgez. Ingento and Bno fo te Unvesty of oe ave also pefoed etensve coptatons of te SLA epeent [7][8]. A new type of LS odel was sed and n te late case wc allowed fo vaable tblent Scdt nbe. Te eslts wee easonable bt te gds sed n all cases wee qte coase even fo a ANS slaton. Peteson and andle fo te Unvesty of Mnnesota also sed te SLA epeent n a nbe of stdes [47][48]. A odfed type of detaced eddy slaton (DS) was sed fo tese slatons. Te coptatonal gd contaned appoately 40 llon cells wc s consstent wt LS o DS slatons. Te

22 5 odel ses constant tblent Pandtl and Scdt nbes bt te specfc vales sed wee not ndcated. Te eslts obtaned sow fa ageeent wt te epeent bt dd not eac a steady solton de to a lage oscllaton of te bonday laye sepaaton between te necto locaton and a locaton pstea of te step.

23 6 Govenng qatons Ts capte wll descbe te set of patal dffeental eqatons tat govens te pyscs of spesonc lt-coponent eactng gasses.. eactng Gas qaton Set.. Nave-Stoes qatons Te govenng eqatons fo lt-coponent copessble cecally eactng flows at g speeds ae te Nave-Stoes eqatons wc consst of consevaton of ass oent and enegy along wt a set of speces ass consevaton eqatons. Te nbe of speces eqatons eqed s NS wee NS s te nbe of speces. By ncldng all of te speces eqatons te contnty eqaton ay be eoved snce te s of te speces ass consevaton eqatons eslts n te contnty eqaton. If etenal foces sc as gavty and body foces ae neglected and teal eqlb s assed te eqatons ae as follows t t ( ) 0 ( ) ( δ pτ ) 0 (.) (.) ( ) ( q τ ) 0 (.3) t

24 7 t ( ) ( V ) & ω (.4) In tese eqatons s te densty s te velocty p s te pesse τ s te stess tenso and q s te eat fl vecto. Fo te speces ass consevaton eqatons s te speces ass facton V s te dffson velocty and ω& s te podcton ate. Note tat te s of te ass facton wegted dffson veloctes acoss all speces eslts n te bl velocty of te fld. wtten as Te vscos stess tenso nde te asspton of a Newtonan fld can be τ µ s µ s δ (.5) 3 (.6) wee µ s te olecla vscosty and s s te nstantaneos stan ate tenso. Te eat fl vecto s evalated sng te s of Foe s Law and te eat fl de to dffson. q T NS V (.7) wee q s te eat fl vecto s te teal condctvty T s te tepeate and s te speces entalpy. Sla to te vscos stess and eat fl a lnea elatonsp can be developed fo te speces dffson ass fl. Ts s called Fc s Law [37] and t states tat te dffson ass fl s popotonal to te speces concentaton gadents. D V (.8) Te bnay dffson coeffcent D s defned by te Scdt nbe (Sc). µ Sc (.9) D Te total enegy and total entalpy ae defned by te followng eqatons.

25 8 p (.0) (.) Te te specfc entalpy s defned by a ass facton wegted s. NS (.) Te speces entalpes wll be defned n Secton... Te eqaton of state s sed to elate te pesse bl densty and tepeate. It s nown as Dalton s Law of Patal Pesses. p NS p T (.3) Ts law states sply tat te pesse s te s of te patal pesses of eac speces. ˆ (.4) NS W ˆ Wˆ s te olecla wegt of speces and ˆ s te nvesal gas constant. Te total enegy can also be wtten n te fo of qaton (.). e (.5) Te te ntenal enegy e s also defned n tes of te speces entalpes. e NS e T ˆ Wˆ (.6).. Teodynac elatons Fo a g tepeate cecally eactng flow typcal of tat n a scaet engne te flow s assed to be teally pefect. Unle te assptons of a

26 9 calocally pefect gas te specfc eats at constant pesse and vole ae no longe assed constant. Tey ae nstead fnctons of tepeate. A teally pefect gas s based on te asspton tat te ntenal enegy odes of a olecle ae always n a state of eqlb. Tee ae soe types of flows wee ts asspton wold not old sc as n te aea bend te bow soc of a eenty vecle. ve fts gven n [40] ae sed to calclate te specfc eats along wt ote elated popetes. Te speces entalpy can easly be obtaned fo tese cve fts sng te followng eqaton. ˆ 3 4 T T T T b a a a3 a4 a5 (.7) T ˆ T Te speces entalpy n ts eqaton s defned on a pe ole bass. To obtan te entalpy pe nt ass sply ltply by te speces olecla wegt. Specfc eat entopy and Gbbs fee enegy can be calclated n a sla anne. Te ato of specfc eats fo te te γ can be calclated sng p γ (.8) p p NS p (.9) Fnally te lana vscosty and teal condctvty st be detened. Fst te lana vscosty fo eac speces s calclated sng anote set of McBde cve fts [4]. A set of coeffcents ae povded fo eac speces fo two o oe tepeate anges. Te speces vscosty s ten detened fo te followng eqaton. B lnµ A ln T D (.0) T T Ts eqaton povdes vscosty n nts of copose (µp) wc st be conveted to standad nts befoe t s sed. Te lana teal condctvty s ten calclated fo te followng elaton to te lana Pandtl nbe. µ p (.) P

27 0 Ten sng Wle s fola [37] te speces vscostes and teal condctvtes ae cobned nto a bl o te vscosty and teal condctvty.. Govenng qatons n Vecto Fo A convenent way to ewte te Nave-Stoes eqatons s n copact vecto fo. Ts aes fte folatons c sple. Te geneal fo s as follows. U ( v) ( F Fv) ( G Gv) S (.) t y z Te defntons of tese vectos can be fond n Append A..3 eynolds and Fave Aveagng Wle te Nave-Stoes eqatons descbe contn fld flow down to te sallest scales of tblent oton te dscete coptatonal gds on wc te eqatons ae solved ae nable to esolve sc sall scales of oton. oweve te sall tblence scales ae vey potant n dsspatng enegy fo lage scale oton and te ean flow. Te tadtonal appoac to ts poble s not to esolve te sallest feates of te flow bt ate to odel te sng te local caactestcs and te stoy of te flow. Ts povdes a acoscopc vew of te affects of tblence on te ean flow. Tee ae cetanly altenatves to odelng te tblence. ne sc altenatve s dect necal slaton (DNS) n wc te eact Nave-Stoes eqatons ae esolved down to te sallest tblence scales. Ts eqes any tes oe gd ponts tan a solton wee te tblence s copletely odeled. Te appoate

28 nbe of gd ponts eqed fo a DNS solton s e 9/4 so a flow wt a eynolds nbe of 0000 wold eqe abot 0 9 cells. Anote altenatve s to esolve soe of te lage scale tblent feates and odel te scales tat occ on te sb-gd level. Ts s nown as lage eddy slaton (LS). Ts s a copose bt t stll eqes a sgnfcantly ge esolton tan slatons tat odel all tblence scales. De to te sze of oden engneeng pobles and te lted coptng powe tat s avalable a copletely odeled appoac s adopted n te cent wo. A etod called eynolds aveagng s sed to convet te govenng eqatons to solve fo te ean flow popetes ate tan te nstantaneos popetes. Tee ae a nbe of ways to aveage te flow popetes bt fo statonay tblence sc as tat n steady flows te aveagng s te ost appopate [6]. Te followng eqaton epesents ts te aveagng pocess. t T F T ( ) l f( t) dt (.3) T T t Te nstantaneos flow popety s epesented by f( t) wle F T ( ) s te te aveaged flow popety. Te nstantaneos flow popetes can ten be epessed by te te aveaged ean popety pls a flctaton. q q q (.4) ee q epesents any flow popety; q s te te aveaged qantty and q s te flctaton. Ts aveagng s appled to all flow vaables. Applyng ts te aveagng tecnqe to te Nave-Stoes eqatons eslts n wat s nown as te eynolds Aveaged Nave-Stoes (ANS) eqatons. Wle ts etod wos well fo constant densty flows oe coelatons appea wen consdeng copessble flows wc eqe odelng. To allevate ts poble a dffeent type of aveagng s ntodced Fave o ass-wegted aveagng. Ts aveage s obtaned fo te followng eqaton. t T q l T T t ( t) q( t) dt (.5)

29 ee q epesents te Fave aveaged qantty and st as befoe te nstantaneos qantty can be wtten as q q q (.6) Te densty pesse stess tenso eat fl and speces podcton ate ae decoposed sng te eynolds aveage wle te ote vaables se te Fave aveage. q q q p p p & ω & ω & ω τ τ τ V V V T T T (.7) (.8) Sbstttng tese qanttes nto te Nave-Stoes eqatons and pefong te aveagng eslts n te Fave aveaged Nave-Stoes eqatons stll nown as te ANS eqatons [65]. Wen te aveagng te eqatons coelaton tes appea tat ae not necessaly zeo. onsde te aveagng of te podct of any two vaables. ( ϕ ϕ )( ψ ψ ) ϕψ ϕψ ψϕ ϕψ ϕψ ϕ ψ ϕψ (.9) Te tes wt only one flctatng te becoe zeo wen aveaged bt te podct of two flctatng popetes s not necessaly zeo f tee s a coelaton between te. Te Fave/eynolds aveaged ean consevaton eqatons ae as follows. t t t ( ) 0 ( ) ( ) D & ω t p ( ) ( ) [ τ ] (.30) (.3) (.3) ( ) ( ) [ ( τ )] ( q ) (.33) Tee new tes ae ntodced n ts fo of te eqatons te tblent stess tenso te tblent eat fl vecto and te tblent speces dffson

30 3 vecto. Tese tes ae appoated by te tblence odel to be defned n Secton.5. Te tblent stess tenso s also nown as te eynolds stess tenso..4 ecal Knetcs Fnte ate cecal netcs s sed to tac cecal eactons n te pesent wo. Ts etod s based on te Law of Mass Acton (LMA) [37]. Ts law detenes te ate of cange of te concentaton of a sngle speces n a ltcoponent flow. Ts ate s ten ncopoated nto te soce te fo te speces consevaton eqatons. A cecal ecans conssts of a collecton of ecange/ecobnaton eactons and td body eactons wc wen cobned eslt n te global eacton sc as tat fo ydogen odaton. Te Law of Mass Acton fo ecange/ecobnaton eactons s NS f NS ν ν b (.34) Fo td body eactons wc eqe any td olecle to ntate te eqaton becoes NS NS NS ν ν f b TB (.35) s te speces concentaton o ola densty wc s te speces densty dvded by te olecla wegt. Te stocoetc coeffcents fo te eactants ae desgnated by ν and fo te podcts ν. Te effects of te td body ae cobned nto a sngle te called te td body effcency TB. ac speces as a td body effcency fo eac td body eacton. Te fowad eacton ate coeffcent f s detened by te Aens Law. It taes te followng fo.

31 4 f η AT ep( θ / T ) (.36) d Te paaetes A η and θ d ae specfc to te cecal netc ecans and wll be dscssed n Sectons.4. and.4.. ate tan eqe a sepaate set of paaetes fo te bacwad ate coeffcent b s calclated sng te eqlb coeffcent wt te followng elaton. f b ( ) P eq eq P T ˆ (.37) wee P s te standad pesse of one atospee n Pascals. Te above eqaton also deonstates te conveson of te eqlb constant fo a patal pesse bass to a concentaton bass as ndcated by te sbscpts. Te eqlb constant fo a patcla eacton can be calclated fo te cange n Gbbs fee enegy. eq P gˆ ep T ˆ (.38) NS gˆ ( ν ν ) gˆ (.39) Te podcton ate of eac speces can be detened sng te pecedng nfoaton. wee Wˆ s te speces olecla wegt. N ω& ( ν ) W ˆ (.40) ν.4. /A ecal Knetc Mecanss.4.. Jacows ecal Mecans Te abdged cecal netc ecans of Jacows s one of two odels sed fo ydogen/a eactons n ts wo [9]. Te ecans conssts of seven

32 5 speces and seven eactons. Te speces ae N and. Te eactons ae lsted n Table. of Append. Note tat te fst two eactons ae td body eactons wee M epesents te td body. Ts eac eqaton eqes a td body (TB) effcency fo eac speces. Te speces as TB.5 fo bot eactons and as TB 6.0 fo bot eactons. All ote speces ave a td body effcency of.0 fo bot eactons. Te ecans paaetes sc as te pe-eponental facto and actvaton eneges ae lsted n Table onnae et al. ecal Mecans Te second cecal odel fo ydogen/a eactons s tat of onnae et al. [0]. Ts odel eploys nne speces and nneteen eactons. It s slgtly oe coplcated tan te Jacows ecans not st n te agntde of speces and eactons bt n te coplety of te ate epessons. Te eactons ae lsted n Table.3 of Append. Te ecans paaetes and td body effcences tat ae not eqal to one ae also lsted n Append. Note tat soe of te eactons ave two lstngs. eactons 4 and 9 ae epessed as te s of two ate epessons. eactons 9 and 5 eploy a dffeent etod fo coptng te fowad ate constant. Wle te classc defnton of te ate constant s a fncton of te tepeate any cecal eactons ae also a fncton of te pesse. eactons 9 and 5 ae eaples of ts. At vey g pesses te ate constant ay be defned by one set of paaetes and at vey low pesses by anote set of paaetes and soe blend of te two n between. Ts s nown as a fall-off ate constant [37]. Te A and B potons of eactons 9 and 5 epesent te lowe and ppe pesse bonds espectvely. A etod pesented by Toe et al. s sed to blend tese two ltng cases fo nteedate pesses []. Usng te two sets of paaetes specfed fo te eqaton a gpesse lt ate constant and a low-pesse lt ate constant 0 ae detened. Te fnal fowad ate constant s detened fo te followng eqaton.

33 6 p p F (.4) Te edced pesse p s elated to te concentaton of te te. p 0 (.4) Te te concentaton can be detened by dvdng te bl densty by te olecla wegt of te te. Te fncton F n te fall-off ate constant s detened fo te followng elatons. log F log p n d c log F (.43) cent ( log p c) wee c log F F cent cent ( a) ep( T / T *** n log Fcent d 0.4 * ** ) a ep( T / T ) ep( T / T ) (.44) eqed npts ae a T * T ** and T ***. Tese vales ae lsted n Table. fo eactons 9 and 5. Table. Toe Paaetes fo onnae et al. Mecans eacton 9 5 a T *** T * T **

34 /A ecal Knetc Mecanss.4.. Golasnan et al. edced ecal Mecans Fo tose slated cases nvolvng cobston of etylene n a anote two cecal ecanss ae consdeed. De to te coplety of ydocabon cobston te two cosen ecanss ae edced ang t feasble to se n tee-densonal scaet-le envonents. Te fst s tat of Golasnan et al. [3]. Ts ecans tlzes a sngle step eacton between 4 and esltng n. Ts step s followed by a detaled ecans fo / / eacton nvolvng 4 speces not ncldng te net speces N and 4 eactons. Te eactons ae lsted n Table.6 of Append. Te paaetes fo eac eacton td body effcences and Toe paaetes ae also lsted n Append..4.. Zabon and ella edced ecal Mecans Te second edced cecal ecans eployed fo etylene cobston s tat of Zabon and ella [66]. Ts odel aes se of te qas-steady-state (QSS) appoaton fo cetan speces and also eoves cetan fast eleentay eactons. Ts allows fo te tacng of fewe scala vaables and ts sgnfcantly deceases te coptatonal epense. Ts type of etod sally eqes an plct solton of algebac eqatons to detene te QSS speces concentatons wc nvolves coptatonally epensve sb teatons. Te ey feate of Zabon and ella s etod s te eplct solton of te QSS speces concentatons wc ae sed n detenng te eacton ates of te eleentay eactons.

35 8 Ts patcla odel s not pleented n te sae anne as te pevos tee. It s based on te sae pncples of fnte ate cesty and te Law of Mass Acton bt ate tan codng te new eplct QSS pocede fo scatc a sees of sbotnes atoatcally geneated by Zabon and ella ae sed n place of te noal fnte ate cesty fnctons. Two edced odels ae eaned n efeence [66] a 5-step odel and an 8- step odel. Te 8-step odel s sed ee. Te 8 global eactons can be fond n Table.0 of Append. Tee ae speces nvolved n tese 8 global eactons and eac of tese speces s taced n te solton. Te nne speces assed to be n QSS ae and *..5 Tblence lose As dscssed n Secton.3 te eynolds and/o Fave aveagng of te govenng eqatons eslts n te addton of tee tes. Tese tes contan oe tan one flctatng vaable and f tese two vaables ae coelated te podct does not go to zeo wen aveaged. To aceve close tese tes te eynolds stess tenso te tblent eat fl vecto and te tblent speces dffson vecto st be odeled. A coon asspton fo coptng te eynolds stess s called te Bossnesq eddyvscosty appoaton [6]. A new popety s defned called te eddy-vscosty. Sla to te Newtonan appoaton te eynolds stess tenso s assed to be a lnea fncton of te ate of stan tenso wt te vscosty µ eplaced by te tblent vscosty µ t. Ts edces te nbe of nnowns fo s to one. Tee ae a nbe of ways of specfyng te eddy-vscosty sc as algebac odels o one/two eqaton odels. Te pesent wo tlzes a two eqaton odel wc eqes one eqaton to detene a caactestc velocty of tblent flctatons and a second eqaton to

36 9 detene a tblence lengt scale o eqvalent. Te -ζ tblence odel s te two eqaton odel sed n te cent wo and s descbed n Secton.5.. An agent sla to Foe s Law s sed to detene te tblent eat fl sng te tblent dffsvty α t and an agent sla to Fc s Law s sed to detene te tblent speces dffson vecto sng te tblent dffson coeffcent D t. Typcally tese two eta vaables ae defned by a constant tblent Pandtl nbe and tblent Scdt nbe essentally te sae way as te lana contepats. oweve n te cent wo tese two paaetes ae odeled sng two eqatons fo eac tat caacteze te tblent eat condcton and tblent speces dffson. Te folaton of tese eqatons can be fond n Sectons.5. and ζ Model Te tblence odel sed n te cent wo s based on te -ζ odel of obnson and assan [][50][5]. Ts odel as a nbe of desable qaltes ncldng te absence of dapng and wall fnctons coodnate syste ndependence tensoal consstency and Gallean nvaance. Te defnton of te tblent netc enegy o vaance of velocty s (.45) Te enstopy ζ s te vaance of votcty and s defned by ζ ω ω (.46) Te eddy-vscosty s detened fo tese two qanttes tog te followng elaton. ν t µ /νζ (.47)

37 0 All odel constants ae lsted n Table.. Te eact Fave aveaged tblent netc enegy eqaton and te eact votcty vaance (enstopy) eqaton ae lsted n Append F. Tese two eqatons ae odeled te by te to etan as c of te pyscs as possble. Te dsspaton ate n te eqaton s defned as follows wt te asspton of neglgble coelatons between velocty gadent and neatc vscosty flctatons. [( ) ] 4 ε ν (.48) ( ω ) ( ) 3 ν Te second te n qaton (.48) s sply added to te dffson te. Tee ae two copessblty tes tat appea n te eqaton te fst of wc s te dlatatonal dsspaton te ν 4 3 ( ). It s odeled as follows. ν ) / (.49) 4 3 ( τ wee (.50) τ Typcally ts copessblty te s odeled as popotonal to te tblent Mac nbe M t /a. Fo ncopessble flows te sond speed s teoetcally nfnte and te tblent Mac nbe goes to zeo bt fo a te sond speed s fnte and ts te odeled te neve goes to zeo even at low Mac nbes. Fo constant densty flows sc as tose at low Mac nbes te -ζ odeled te s essentally eoved. Te second copessblty te n te eqaton s te pesse wo te. Te te s odeled as follows. P P ν t P (.5) Ts te also contans a densty gadent so tat fo constant densty flows te copessblty effects ae agan eoved. At g Mac nbes copessblty

38 effects estct te speadng ate of fee sea layes [6]. Ts can ave a pofond pact on ng and cobston so t s potant tat tese effects ae odeled popely. Te fnal vesons of te odeled and ζ eqatons ae lsted n Append F. Table. -ζ Model lose oeffcents onstant κ α β β β β β σ µ Vale onstant σ σ p / σ / σ δ ζ ζ Vale Vaable Tblent Pandtl Nbe Model Te tblent Pandtl nbe s an potant paaete n spesonc flows. It as a sgnfcant nflence on eat fl at g speeds and te typcal asspton tat ts nbe s constant s often naccate. A odel tat calclates te tblent Pandtl nbe as pat of te solton s sed n te pesent wo [64]. To aceve ts goal two new eqatons ae deved and odeled one fo te entalpy vaance and one fo te dsspaton ate of te entalpy vaance. Usng tese newly calclated paaetes te tblent dffsvty s defned by te followng elaton.

39 wee α.5( τ ν / β ) (.5) t 0 t τ / ε ε α (.53) and β ae odel constants. All te odel constants fo te vaable Pandtl nbe odel can be fond n Table.3. Te fst step n devng te entalpy vaance eqaton and ts dsspaton ate eqaton s to epess Fave aveaged enegy eqaton as follows. t Dp q ) ( ) φ ( ) (.54) Dt ( wee φ τ ε ε νζ NS Q α t Dt (.55) Wen ltple eactng speces ae pesent qaton (.54) st be ewtten n a way so as to splt te entalpy nto te sensble entalpy and tat de to eactons. pdt f (.56) NS NS p dt NS f (.57) Fo ts one can deve te eact eqatons fo te entalpy vaance and ts dsspaton ate ε. Tey ae lsted along wt te odeled eqatons n Append F. f s te eat of foaton of speces. τ s a paaete sed n te vaable tblent Scdt nbe folaton to be defned n Secton.5.3. Note te fnal te n te NS f odeled entalpy vaance eqaton ω&. Ts te s a ecans fo

40 3 tblence/cesty nteactons and te odelng of ts te s descbed n Secton.5.4. Table.3 Vaable Pandtl Nbe Model onstants onstant Vale onstant β Vale Vaable Tblent Scdt Nbe Model Jst as wt te tblent Pandtl nbe te specfcaton of te tblent Scdt nbe can ave a pofond nflence on te slaton of a spesonc cecally eactng flow. Agan ts vale s tadtonally specfed as a constant dependng on te type of poble bt fo cople tee-densonal flows ts asspton s typcally nvald. Te specfcaton of a tblent Scdt nbe tat s too g can eslt n a flae blowot wle on te ote end of te spect f te nbe s too low te slaton ay nstat. A etod sla to tat of te vaable tblent Pandtl nbe s adopted fo te vaable tblent Scdt nbe n te pesent wo [63]. Two eqatons ae deved and odeled one fo te concentatons vaance and one fo ts dsspaton ate. Usng tese new paaetes te tblent bnay dffson coeffcent s defned as follows.

41 4 wee D t.5( τ ν / β ) (.58) 0 t NS NS τ σ / ε σ ε D (.59) σ s te s of te ass facton vaances and ε s ts dsspaton ate. Te devaton of odel eqatons fo eac of tese qanttes begns wt te eact Fave aveaged speces consevaton eqaton. t ( ) ( ) D ω (.60) Fo ts one can deved te eact eqatons govenng te s of te ass facton vaances and ts dsspaton ate. Tey ae lsted n Append F. Tese eqatons ae odeled sng te sae tecnqes sed fo te eqatons n te -ζ odel and te vaable Pandtl nbe odel. Tese odeled eqatons ae also lsted n Append F. eqaton All of te odel constants can be fond n Table.4. Note te last te n te σ NS ω&. Sla to te vaable Pandtl nbe odel ts te s also a ecans fo tblence/cesty nteactons. Te odelng of ts te s dscssed n Secton.5.4. &

42 5 Table.4 Vaable Scdt Nbe Model onstants onstant Vale onstant p β Vale Tblence / esty Inteactons As entoned n Sectons.5. and.5.3 tes ase n te entalpy vaance and concentatons vaance eqatons tat act as ecanss fo te nteactons between tblence and cesty. Tee ae a lttde of etods avalable fo te estaton of tese two tes. A coon etod aes se of ete an assed o an evolton Pobablty Densty Fncton (PDF). It as been fond tat assed PDF s ae nable to easonably calclate ge ode tes sc as tose contanng cecal podcton soce tes [3]. volton PDF s on te ote and ay be able to accately calclate tese tes bt te cost n coptaton te nceases daatcally potentally by a facto of ten. onsdeng tese ltatons a odelng appoac s adopted n te nteest of savng coptatonal te and etanng te effects of te tes [65]. Te etod n geneal povdes good ageeent wt valdaton epeents. Te tblence/cesty nteacton tes along wt te coespondng odels ae lsted below. Te te tat appeas n te entalpy vaance eqaton s & ω f & ω f (.6)

43 6 Te te tat appeas n te concentatons vaance eqaton s Fo bot of tese odels & ω 8 & ω (.6) ω& s calclated sng te ean tepeate and ass factons. efe to Table.3 and Table.4 fo te odel constants..6 oplete qaton Set nce te s tblence eqatons ae ncopoated nto te eactng gas eqaton set te eslt s a syste of 0 NS copled nonlnea patal dffeental eqatons. Fo a detaled eplanaton of te solton etods eployed efe to Append. Jst as befoe te syste of eqatons can be wtten n copact vecto fo fo a genealzed coodnate syste. See qaton (B.). efe to Append D fo tese vectos..6. Solton Metods A fnte vole etod s sed to solve ts set of eqatons. An ssentally Non-scllatoy (N) and/o Total Vaaton Dnsng (TVD) scee s sed n conncton wt te Low Dffson Fl Splttng Scee (LDFSS) of dwads and te syste s advanced n te sng a plana plct scee. Te vscos and dffson tes ae evalated sng cental dffeences. An altenate veson of te code was developed wc solved te tblence eqatons sepaately. Te speces oent and enegy eqatons wee solved sng te plana plct scee ten te s tblence eqatons wee solved seqentally sng a tee-densonal scee. Ts odfed veson eqes c salle FL nbes to eep te esdal fo nceasng so te eslt s a tade off. Te code ns

44 7 c faste bt wt a salle FL. Altenatvely te odfed veson does se a sgnfcantly salle aont of eoy de to te fact tat a salle at needs to be nveted. Ts te avalablty of copte esoces detenes te oe effcent solton etod. Append contans a oe detaled eplanaton of te necal folaton.

45 8 3 peental vevew Ts capte descbes te epeents tat ae sed fo odel valdaton n te pesent stdy. A nbe of cases ave been eaned ncldng two-densonal asyetc and tee-densonal ng and cobston epeents. Te sectons below descbe te vaos epeental confgatons as well as te easeent tecnqes sed. 3. Bows and Kov peent Te fst epeent s te Bows and Kov spesonc cobsto [7]. Ts cobsto s two-densonal wt aal fel necton along te botto wall. A sceatc of te epeent can be seen n Fge 3.. Fge 3. Sceatc of Bows and Kov Spesonc obsto

46 9 ydogen fel s nected tog a ncel necto paallel to te an vtated a flow. Te Mac nbe of te an flow s.44 and te statc condtons at te entance to te test secton ae a pesse of at and a tepeate n te ange K. Te ydogen fel s nected at Mac and s pesse atced. Te stagnaton tepeate of te fel s only slgtly above te abent tepeate. Te an epeental easeents tat ae sed fo copason n ts stdy ae vaos vetcal pofles at te cente of te et of te test secton. f patcla nteest ae te vole factons of N and snce tese ndcate te sze and locaton of te flae at te et of te cobsto. 3. SD Test Meda ffects peents Te second set of epeents s pat of te ffce of te Secetay of Defense s (SD) Test Meda ffects (TM) poga [8]. Te ppose of ts poga s to eane te effects of te dffeences between gond and flgt tests of spesonc cobstos. In patcla te se of vtated a n place of egla a and t s effects on flae oldng and ote aspects of pefoance elated to cecal netcs [4][6]. Vtated a s te eslt of ydogen bnng n oygen enced a. Ts tecnqe s sed to ase te entalpy of te ncong gas to tat of ypesonc flgt condtons. A Sceatc of te SD-TM epeent s sown n Fge 3..

47 30 Wate passages Teocoples obsto Faclty eate Nozzle Bloc Pesse tap Matng flange ondensaton etacton flange 5 oflow nozzle Poos plate oflow plen D. n Fge 3. Sceatc of SD-TM peent Te cente et n ts asyetc devce otpts vtated a at Mac.6. Te test entalpes ange fo Mac 5 to Mac 7 flgt. Te fel s nected at low sbsonc speeds tog a coflow nozzle angled 30 towad te an et. Te pesse at eac of te nozzle ets s atospec and te total tepeate n te colfow nozzle s nea abent. peents wee condcted wtot coflow fel as well as wt ydogen alone etylene alone and a ydogen/etylene. Te ns cosen fo slaton ae lsted n Table 3..

48 3 Table 3. SD-Test Meda ffects peent ondtons n Nbe M7 - M75 M79 - M a 40b ntalpy Mac 5.5 Mac 5.5 Mac 5.5 Mac 6 Mac 6 P ( Pa) T 0 ( K) φ φ Te cases wtot coflow fel ae efeed to as ng cases ndcated by te M pecedng te n nbe. Slaly te case nvolvng ydogen only s peceded by an and te case nvolvng bot ydogen and etylene s peceded by an. Te easeent tecnqe sed n ts epeent s a cobnaton of dal pp coeent ant-stoes aan spectoscopy (AS) and ntefeoetc ayleg scatteng (IS) pefoed sltaneosly sng te sae lase [4][56][57]. Te AS- IS tecnqe allows fo sltaneos and nstantaneos easeents of tepeate speces concentatons and two velocty coponents. To obtan tese easeents a lase s focsed on a sngle pont wtn te flow feld. Te tanstted bea s ten obseved wt a caea and analyzed to obtan te condtons. Te eo assocated wt tese easeents s K fo te tepeates and /s fo te veloctes. 3.3 Ln tylene Mng peent Te td case s tat of Ln et al. [38]. Te epeent conssts of sonc etylene necton tog a ond ofce nto a Mac a stea. Te ppose of Ln s stdy was to eane te effects of dffeent types of fls wall nectos on ple sze

49 3 penetaton egt and fel concentaton. Tese popetes play an potant ole n gnton flae oldng and ote ctcal aspects of scaet engne opeaton. Vaos necto angles daetes and oent fl atos wee eaned n te ognal epeent bt only one of tose cases s slated n te cent wo. Te cosen case eploys a 3/6 daete necto at an angle of 90 and a oent fl ato of 0.5. A sceatc of ts patcla epeental confgaton can be seen n Fge 3.3. Note tat te an stea tepeate s sc tat no cobston taes place as te ppose of te epeent was to obseve only te ng caactestcs. Mac A tylene Fge 3.3 Sceatc of Ln tylene Mng peent A aan scatteng tecnqe was sed to obtan te te facton of te fel at fo dffeent planes pependcla to te flow decton. Te planes ae and 50 daetes down stea of te cente of te et. Mte facton s defned by te followng fola. Z s ) /( s ) (3.) ( f o o 0 f 0 o 0 In te above eqaton s s te stocoetc odze/fel ass ato defned by te followng. s X Wˆ ) /( X Wˆ ) at stocoetc condton (3.) ( o o f f

50 33 Te sbscpt o denotes odze and f denotes fel wc ae oygen and etylene n ts case. o0 epesents te ass facton of odze n te odze stea and f0 epesents te ass facton of fel n te fel stea. In ts case tey ae 0.33 and.0 espectvely. Table 3. Inflow ondtons fo tylene Mng peent Locaton Man Flow (A) Inecto (tylene) Mac Nbe.0.0 Stagnaton Pesse 0.43 MPa Tepeate 99.8 K Pesse 0.76 MPa Tepeate 34.8 K 3.4 Te SLA peent Te SLA epeents wee pefoed at NASA Langley eseac ente s Dect onnect Spesonc obston Test Faclty (DSTF) [3][44][58]. Te epeents wee condcted wt te ntenton of beng sed fo FD valdaton of spesonc cobston. Te odel conssts of ydogen beng nected at a 30 angle to a vtated a stea at Mac.0. Te epeent was desgned sng te VULAN FD code [6] wt epass on avodng lage egons of sbsonc flow. Ts eslted n a staton wee cecal eactons lagged ng and cobston dd not ntate ntl fa downstea of te necto. Te ydogen s nected at Mac.5 and an angle of 30 to te vtated a stea. A sceatc of te epeent s sown n Fge 3.4.

51 34 Fge 3.4 Sceatc of SLA peent Te planes at wc AS easeents ae taen ae labeled n ts fge as well. Te planes ae nbeed and 7. Te cobsto conssts of a stagt solato secton followng te vtated a nozzle. Tee s ten a sall otwad step on te ppe wall followed by anote sot stagt secton. Te eande of te dct as a 3 dvegence on te top wall. Te ydogen necto s located at te begnnng of te dvegent secton. Note te dffeent ateal tlzed n te constcton of te cobsto. Te secton aond te ydogen necto eacng to st downstea of plane 5 s ade of coppe. Te eanng downstea secton s ade of steel. Te dct was not cooled and ts ns wee lted to abot 0 seconds wt te dct beng allowed to cool between ns. As a eslt of ts te wall tepeates ae constantly nceasng wt a ate dependng on te locaton and local wall ateal. Measeents ae avalable fo te wall tepeates as a fncton of te [3] bt te slaton s not te accate and ts tese easeents cannot be sed to povde a tepeate bonday condton. Te specfcaton of wall tepeates s dscssed fte n Secton Fo clafcaton a detal vew of te ydogen necto egon s sown n Fge 3.5.

52 35 Fge 3.5 Detal of Vectoed ydogen Inecto Te entalpy of te vtated a stea s set to be tat of Mac 7 flgt and te eqvalence ato s.0. Lsted n Table 3.3 ae te stagnaton condtons and flow ates fo bot te eate and te ydogen necto. Table 3.3 Inflow ondtons fo SLA peent Locaton eate Inecto Flow ates 0.95± g/s A 0.084± ± g/s g/s oesponds to eqvalence ato of.0 Stagnaton Pesse 0.765± MPa Tepeate 87± 75 K Pesse 3.44± MPa Tepeate 30± 4 K Along wt pesse and tepeate easeents along te fo walls of te cobsto two-densonal slces of tepeate and speces ole factons wee

53 36 etacted sng te pevosly entoned AS tecnqe. Tese easeents wee taen at a nbe of planes pstea and downstea of te ydogen necto. Te slots tog wc te lase tavels ae located on ete sde of te dct at te dstances ndcated n te fges above. ac slot s 4.8 wde and as a wndow onted at te Bewste angle to nze eflectons. To avod condensaton on te wndows wa dy a s blown ove te nsde of te wndow between t and te dct wall. Soe of ts ay be entaned n te flow wtn te cobsto bt as been decded to ave neglgble effects. Ts a (400 K) ay sew te tepeate easeents slgtly nea te left and gt walls oweve. Also t tns ot tat te ognal easeents fo ydogen ole factons ay contan eos and ae ts eclded fo analyss n te cent wo peental Data Fttng peental data fttng s an potant sse wen copang wt FD slatons. Te AS data as a lage aont of scatte ts any easeents ae eqed to obtan spatally esolved aveages. Becase t s not pactcal to acclate a lage saple necal tecnqes wee sed to soot and pesent te data. A poga called Table ve 3D was sed to geneate te sface fts fo te D aay of data at eac plane. A lage nbe of etods ae avalable to geneate tese aveages any of wc ae eaned n efeence [5] to detene te best opton fo te data tat was obtaned. A pelnay FD analyss was condcted n efeence [7] and te etods fo copason wt coptaton and epeent wee nvestgated n an attept to detene te best way to analyze te two sets of data. Fge 3.6 sows an eaple of te AS scatte data fo tepeate and te sface ft tat as been appled to t. Ts data epesents a ozontal slce of plane 6 abot alf way between te top and botto walls (at y 8. ).

54 T eased T cve ft Tepeate (K) z () Fge 3.6 aple of AS Measeents and ve Ft (Plane 6 y 8. ) 3.5 ysot peent Te fnal epeent was pefoed by eseaces n te ysot poga at te Unvesty of Qeensland n Astala [45][46]. Ts epeent conssts of a coplete scaet engne odel. A sceatc of te odel can be seen n Fge 3.7. Te ppose of tese epeents ote tan deonstatng sstaned scaet opeaton was not to podce optal tst bt ate to eane te effects of cobsto egt eqvalence ato and feestea entalpy on gnton and steady opeaton of te scaet engne. Te oveall desgn was dven by atteptng to nze dag wc lead to fls wall fel nectos te absence of ng enanceent devces and an nlet desgned wt two ld copessons ate tan one. Te fel nectos wee placed on te nlet ap n an attept to copensate fo te lac of tese ng ecanss. Te eseaces attbte te sccessfl opeaton of te engne to te adcal fang

55 38 penoenon [45]. Te sde walls of te odel n te nlet secton ae ct away n a V sape to edce bonday laye gowt and allow te odel to be self statng. Inlet obsto Nozzle Inflow Fel Inectos Fge 3.7 Sceatc of ysot ngne Model Te total lengt of te odel s 0.65 and te wdt s Tee ae a total of egt sonc fel nectos on te nlet sface fo on te top ap and fo on te botto ap. Tese nectos ae eqally spaced between te sde walls and angled 45 wt espect to te nlet sface. Te nlet sfaces ae nclned at 9 and wle te nozzle s a constant 9 epanson. Te cobsto egt fo te patcla case pesented n te cent wo s 4. Te test condtons fo ts case ae lsted n Table 3.4. Te eqvalence ato fo tese condtons s 0.5. Table 3.4 Inflow ondtons ysot peent (#7678) M P T & Inlet Pa 4 K 755. g/s M P T 0 0 & Fel Pa 300 K g/s

56 39 Te only epeental data avalable fo ts case s te pesse along te cente of te lowe wall. Ts case was also te sbect of an n dept nvestgaton by Sta [55] te eslts of wc ae also sed fo copason n te cent wo.

57 40 4 Ipleentaton Te code sed n te pesent wo s called ATMB [0] wc as been nde developent at N State Unvesty fo te past seveal yeas. It s a paallel geneal ppose Nave-Stoes solve fo lt-pase lt-coponent eactve flows at all speeds. It eploys a second ode essentally non-oscllatoy and/o total vaaton dnsng scee based on te Low Dffson Fl Splttng Scee (LDFSS) of dwads wc s descbed n Append. 4. Mltbloc Paallel Appoac Paallelzaton s aceved tog doan decoposton. Te gd s dvded nto any salle blocs wc ae dstbted aong a nbe of pocessng nodes n a coptng clste. Te Message Passng Inteface (MPI) s ten sed fo concaton aong pocessos [53]. Te data fo te edges of eac bloc s passed to te pocesso contanng te adacent bloc. Te coptatons wee caed ot on te IBM Blade ente at N State Unvesty s g Pefoance optng ente. 4. optatonal Geoety Te coptatonal geoetes fo te fve cases wee geneated sng te GIDGN poga. Te gds wee ten atoatcally decoposed sng a poga

58 4 developed at N State Unvesty. Te dstbton of blocs ove te nbe of pocessos allocated fo te ob s detened by a poga called KMTIS [30]. 4.. Bows and Kov Gd Geoety Te bloc layot and necto egon detal fo te Bows and Kov epeent can be seen n Fge 4.. Note tat te cobsto egon s te only geoety nfoaton tat s povded fo te ognal epeent. Te vtated a nozzle was geneated tog an teatve pocess wt te goal of atcng te bonday laye tcness at te entance to te test secton. Te ydogen necto was geneated vsally based on te povded sceatcs. Fge 4. Bloc Layot and Detal fo Bows and Kov peent

59 4 Te efned gd conssts of 5 blocs and contans 0448 cells. As seen n Fge 4. bot te ydogen and vtated a nozzles ae nclded n te solton. Ts was necessay to povde ealstc bonday laye pofles at te entance to te test secton. 4.. SD Test Meda ffects Gd Geoety Te bloc layot fo te SD-TM gd s sown n Fge 4.. Ts gd contans 74 blocs and cells. Te efned gd contans blocs and cells bt te efneent dd not affect te solton so te eslts pesented n te cent stdy all tlze te 74 bloc gd. Fge 4. Bloc Layot fo SD-TM peent Te otflow bonday on te gt s placed sc tat te spesonc et as te to etn to a flly sbsonc pofle. Ts allows a sngle bonday condton to be sed

60 43 on te et plane. Te nflow bonday on te top left allows fo entanent and s placed so as to not be affected by te aea aond te et. Te ppe bonday s sloped as t s so tat t can be foced to be a sbsonc otflow sface. If te bonday wee ozontal t wold not be possble to detene te bonday condton aead of te. Te lowe bonday s of cose te as of syety Ln tylene Mng Gd Geoety Te bloc layot fo te Ln etylene ng epeent can be seen n Fge 4.3. Te Gd conssts of 48 blocs and appoately 3.7 llon cells. nly alf of te geoety s epesented to tae advantage of te syety. nly te nozzle and lowe wall epesent pyscal geoety n ts case. Te sze of te gd s sc tat te egons of nteest ae capted and tat te bondaes do not ntefee wt tose eslts. nly te fst tee epeental planes ae nclded n ts egon de to te fact tat te fot plane s 50 daetes downstea.

61 44 Fge 4.3 Bloc Layot fo Ln tylene Mng peent 4..4 SLA Gd Geoety Te bloc layot fo te SLA epeent s sown n Fge 4.4. Te fge also sows a detal of te ydogen necto wt all gd ponts actvated. A bttefly type gd topology s sed n ts egon to avod snglates and oddly saped cells. Note tat syety s sed on te vetcal centeplane so tat only alf of te cobsto needs to be odeled.

62 45 Fge 4.4 Bloc Layot and Inecto Detal fo SLA peent Te gd fo ts case eploys 378 blocs and appoately 7.5 llon gd ponts. It ns on 50 pocessos. Fo clafcaton a vew fo te sde of te syety plane s sown n Fge 4.5 ncldng te svey planes fo te AS syste.

63 46 Fge 4.5 SLA Bloc Layot wt AS Svey Planes glgted 4..5 ysot Gd Geoety Te bloc layot fo te ysot epeent can be seen n Fge 4.6. Te gd eploys 400 blocs and 5.43 llon cells. Te left and top bondaes as vewed n Fge 4.6 ae bot syety planes so te coptatonal odel s only one qate of te epeental odel. Te ble set of blocs s te nlet secton and te geen set of blocs to te gt s te spllage egon eqed fo te V saped ctot of te sde walls. Note tat te sde walls n te coptatonal odel ae nfntely tn. Also ate tan odelng te ydogen nectos eactly a dffeent bonday condton s eployed on te wall ove te egon wee eac necto wold be posng a nfo sonc fel necton pofle.

64 47 Fge 4.6 Bloc Layot fo ysot peent n te epeental odel te ccla fel nectos ntesect te nlet sface at a 45 angle ts fong an ellpse. Fo splcty te nectos ae odeled as ectangles bt wt te sae aea as te epeental nectos ts te ass flow ate of fel s te sae. 4.3 Bonday ondtons Fo te epesentaton of bonday condtons te gost cell etod s eployed. ate tan posng bonday condtons dectly on te fles at a wall o fld nteface an agnay cell on te opposte sde of te bonday s ceated. Te data n

65 48 tese cells s defned n a way sc tat te fl at te nteface between te coesponds to te pyscal bonday condtons sc as te no-slp velocty condton and constant o adabatc wall tepeate. Wen ge ode fl econstcton scees ae sed ltple layes of cells ay be eqed. Te code can accoodate p to tee layes of gost cells Syety Snce syety s tlzed to edce te coptatonal coplety n a nbe of te pesent cases a syety bonday condton s necessay. Ts s aceved by sply copyng all scala popetes nto te gost cells fo te nteo cells. ae st be taen wt te velocty vecto n tat t st be oed acoss te syety plane ate tan sply coped Wall Bondaes A nbe of dffeent wall bonday condtons ae eqed fo te pesent slaton. Te fst condton coesponds to te no-slp condton. v w 0 (4.) w w w p n w 0 (4.) Te decton noal to te wall s epesented by n. Te veloctes becoe zeo at te wall by applyng te negatve of all tee velocty coponents to te gost cells. Te zeo pesse gadent s enfoced by sply settng te gost cell pesse to te neaest ntenal cell pesse. ge ode appoatons of ts ae also possble.

66 49 Fo te speces eqatons te noal concentaton gadent st be zeo at te wall. n w 0 (4.3) Ts s enfoced n a anne sla to te pesse. Tee ae vaos optons fo te wall tepeate. Te fst and splest condton s an adabatc wall. Snce te speces dffson velocty n te noal decton at te wall st be zeo te eat fl n te noal decton at te wall s popotonal to te tepeate gadent. Ts eans tat te noal tepeate gadent at te wall st be zeo fo t to be adabatc. ondtons sla to te pesse and ass factons can be sed fo ts. Te second possblty s to ave an soteal wall eanng tat te tepeate s constant. To accopls ts te tepeate s etapolated fo te fst ntenal laye of cells tog te wall nto te gost cell. Many tes ts can eslt n a negatve tepeate n te gost cell. Ts of cose st be lted to a sall postve vale o te calclaton of te vscosty o ote teal popetes n tat cell wll case te poga to cas. A td opton s te soteal gost cell wall. Ts s soewee between an adabatc wall and an soteal wall. Te wall tepeate s allowed to cange bt stll eans close to te specfed gost cell vale. Fo te tblence odel 0 at te walls. Fo ζ te wall condton edces to te followng. νζ w ν (4.4) n n Te bonday condtons fo te vaable tblent Pandtl/Scdt nbe odels ae w sla to tose of te -ζ odel. σ and st be zeo at te walls and a condton sla to qaton (4.4) olds fo te dsspaton ates.

67 Sbsonc Inflow and tflow Fo cases wt vtated a nozzles and/o fel nozzles te nflow bonday s lely sbsonc. Fo gd algned sbsonc flow tee ae two caactestcs tat popagate n te flow decton and one caactestc tat popagates bacwads ot of te doan [6]. Te two caactestcs n te flow decton ae eld constant n te gost cells wle te td s calclated fo te nteo cells and etapolated nto te gost cells. Te gost cell popetes ae ten ecalclated gven ts nfoaton. Te pstea entanent bonday fo te SD-TM epeent s also sbsonc. Fo te -ζ tblence odel te ncong tblence ntensty T and te ntal tblence scale (ν t / ν) st be specfed. Slaly fo te vaable tblent Scdt nbe and tblent Pandtl nbe odels ntal qanttes st be specfed by sla eans. nly te SD-TM epeent eqes te se of sbsonc otflow bondaes. Te ppe and downstea bondaes ae bot sbsonc. In tese cases te two caactestcs n te flow decton ae popagatng ot of te doan and te td one s ovng nto te doan. Te fst two caactestcs ae calclated n te nteo cells and etapolated to te gost cells wle te td s eld constant based on a specfed bac pesse. Te popetes n te gost cells ae ten ecalclated gven ts nfoaton Spesonc Inflow and tflow Spesonc nflow s eqed fo te Ln etylene ng epeent and te ysot epeent. Ts s c sple tan te sbsonc case as all tee caactestcs ae popagatng n te flow decton. All popetes n te gost cells ae sply eld constant. Ts s also nown as a Dclet bonday condton [6].

68 5 Fo spesonc otflow te opposte s te. All caactestcs ae popagatng ot of te doan and ts all popetes st be etapolated to te gost cells fo te nteo. Ts condton s sally efeed to as etapolaton. All of te otflow bondaes sed n ts stdy ae spesonc ecept fo te SD-TM case. Te etapolaton condton s also sed n cases wee te flow s ostly paallel to te bonday bt fa fo egons of nteest n te flow so as not to nflence te solton Specal ases Tee ae two specal cases n te cent wo bot nvolvng te ysot epeent. Te fst as entoned n Secton 4..5 s fo te fel nectos. A sonc Dclet bonday condton s posed ove te aea of te nectos n cells tat wold noally be consdeed wall bondaes. A nfo flow of ydogen s posed at 45 to te nlet sface. Te condton ad to be ad coded fo ts case. Te second condton petans to te V saped ctot of te sde wall n te nlet. Snce te blocs coposng te nlet and te blocs coposng te spllage egon ae contnosly connected te solve wold typcally asse tese wee contnos fld ntefaces. Fo ts specfc case an eqaton s sppled to specfy te locaton of te wall. Fo cells on te nteface tat sold be pat of te sdewall te noal contnos fld nteface bonday condton s ovedden wt te wall condtons descbed n Secton 4.3..

69 5 5 eslts and Dscsson Ts capte pesents te eslts tat ave been obtaned sng te pocedes and odels descbed n te pevos captes fo te fve epeents. Below s a lst of te potant factos nvestgated n ts wo. ole of tblence/cesty nteactons. ole of cecal netc ecanss. ole of te copessblty te. Vaable vs. constant tblent Pandtl/Scdt nbes. Gd esolton and efneent. Wall tepeates and teal bonday condtons. Specfcaton of vaos nflow condtons sc as tblence ntensty tblcne scale (ν t / ν) and concentaton. 5. Bows and Kov peent Te fst epeent s te spesonc cobsto of Bows and Kov [7] descbed n Secton 3.. Te ey aspect of ts nvestgaton s te ole of tblence/cesty nteactons. f te avalable epeental data te speces ole facton pofles at te cobsto et ae of an nteest. Fo bot of te slatons te tblence eqatons ae nclded n te te advanceent scee. Note tat bot cases also tlze te Jacows cecal ecans as te cecal odel was fond to ave a nal effect on te solton.

70 Wtot Tblence/esty Inteactons Te fst slaton eploys te fll odel as pesented above wt vaable tblent Pandtl and Scdt nbes. Fo te case wtot tblence/cesty nteactons te copted and eased speces ole factons at te cobsto et can be seen n Fge 5.. Te locaton of te flae as ndcated by te pea concentaton of s consdeably close to te wall tan te epeental flae locaton. Fge 5. Speces Pofles n te Absence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows) Te copted ole facton dstbton can be seen n Fge 5.. Note tat te gnton locaton s appoately 3 c fo te entance of te cobsto. Fge 5.3 sows te copted eddy vscosty tblent dffson coeffcent and tblent

71 54 dffsvty. Tese tee plots ave te sae eponental conto level dstbton so tat tey ay be copaed dectly to one anote. Te tblent Scdt and Pandtl nbes ae sply atos of tese vales. Te copted tblent dffson coeffcent s nealy constant togot te cobston egon wle te copted tblent dffsvty appeas to follow te sae tend as te flae tself n tat aeas wt ge concentatons te tblent dffsvty s ge. Fge 5. opted Mole Facton ontos n te Absence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows)

72 55 Fge 5.3 opted ddy Vscosty (top) Tblent Dffson oeffcent (cente) and Tblent Dffsvty (botto) n te Absence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows)

73 Wt Tblence/esty Inteactons Te second slaton eploys te fll odel as descbed above ncldng te odelng of tblence/cesty nteactons. Te speces pofles at te cobsto et ae sown n Fge 5.4. Ts slaton sows ecellent ageeent wt te eased flae locaton. Te pea vale of also atces qte well. Te only dscepancy n ts slaton s te flae tcness. Te dffeence n te copted and epeental data nea te wall ndcates tat te copted flae s soewat tnne tan te actal flae. Fge 5.4 Speces Pofles n te Pesence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows)

74 57 Te copted ole facton contos fo te case wt tblence/cesty nteactons s sown n Fge 5.5. Te tcness and pea of te flae bot ncease n ts case wle te gnton locaton eans ncanged. Sla to te above pesentaton te eddy vscosty tblent dffson coeffcent and tblent dffsvty ae sow fo ts case n Fge 5.6. Wt te addton of tblence/cesty nteactons tee s a daatc ncease n te tblent dffsvty togot te flae egon wle te tblent dffson coeffcent only sows a slgt ncease nea te cente of te flae. Note tat te floo vale fo bot te tblent Pandtl and Scdt nbes n ts case s Ts s accoplsed tog ltng te a tblent dffsvty and tblent dffson coeffcent to be less tan o eqal to twenty tes te copted eddy vscosty. In te entalpy vaance eqaton te tblence/cesty nteacton te acts as a podcton te wen tee s even a slgt aont of cobston occng. Ts nceases te calclated tblent dffsvty to a level c ge tan even 0 tes te eddy vscosty. Ts te Pandtl nbe always eaces te specfed floo vale togot any cobston egon. Fge 5.5 opted Mole Facton ontos n te Pesence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows)

75 58 Fge 5.6 opted ddy Vscosty (top) Tblent Dffson oeffcent (cente) and Tblent Dffsvty (botto) n te Pesence of Tblence/esty Inteactons fo Bows and Kov peent (Jacows)

76 59 Te sae calclaton ncldng tblence/cesty nteactons was also caed ot sng te onnae ecans. Te copted and eased speces pofles ae sown n Fge 5.7. Note tat tee s vey lttle dffeence n te flae tcness flae sze and pea ole facton fo te two cecal odels. Fge 5.7 Speces Pofles n te Pesence of Tblence/esty Inteactons fo Bows and Kov peent (onnae) 5. SD-Test Meda ffects peent Te second set of epeents s pat of te SD-Test Meda ffects (SD-TM) poga descbed n Secton 3.. Te patcla cases nvestgated ae lsted n Table 3.. All of te followng slatons tlze te fll pesented odel and te tblence

77 60 eqatons ae nclded n te te advanceent scee. Tese epeents ae nqe n tat tey nvolve bot te cobston of ydogen and etylene. Fo eac case two sepaate cecal odels ae consdeed. Tese odels ae descbed n detal n Secton Mng ases Te fst set of ns slated only tlzes te an vtated a et wt no coflow fel. Tese ae nown as te ng cases. Tee ae two sets of data fo te ng cases of te SD-TM epeents. Te fst set contans adal tepeate pofles at egt dffeent steawse locatons. Tese easeents wee obtaned sng te AS poton of te AS-IS syste. Te second set of data contans two coponents of velocty along te centelne and along two adal pofles. Tese easeents wee obtaned sng te IS poton of te AS-IS syste. Te aveage stagnaton tepeate fo te nea feld easeents wc wee taen n ns M7-M75 s sgnfcantly lowe tan te aveage fo te fa feld easeents wc wee taen n ns M79-M95. Te sae tend s obseved n te stagnaton pesse. Slatons wee caed ot sng bot of tese aveages and ae pesented togete wt te epeental data. Te taget entalpy fo tese cases s tat of Mac 5.5 flow. Fge 5.8 sows eased and copted tepeate pofles fo egt dffeent steawse locatons. Fo te ost pat tee s good ageeent. Note tat tee s soe asyety n te epeental data. Ts s ost lely de to a sfted efeence pont n te easeents not an asyety n te et tself. Also note te appeaance of two dffeent epeental pofles at te 40 c staton. Ts as been attbted to te fact tat alf of te easeents cae fo te ge aveage tepeate ns. Fge 5.9 sows te 40 c staton only. Te blac sybols and lne epesent te pstea easeents wc wee at a lowe stagnaton tepeate and te ed sybols and lne epesent te downstea easeents wc wee taen at a

78 6 ge stagnaton tepeate. Pedctons ae wtn te standad devaton fo all bt tee ponts. 000 K 5.5 c Lowe Aveage ge Aveage peent 000 K 3.5 c Lowe Aveage ge Aveage peent 0 c 40 c T T 6.5 c 55 c 3 c 70 c y () y () Fge 5.8 opted and Meased Tepeate Pofles fo SD-TM Mng ases

79 Upstea Downstea Lowe Aveage ge Aveage 800 T (K) y (c) Fge 5.9 adal Tepeate Pofles at 40 c Staton fo SD-TM Mng ases Fge 5.0 sows te eased and copted aal veloctes along te centelne of te et. Te eased veloctes ae sgnfcantly ge tan ete of te copted pofles. Ts case of ts dffeence s nnown. Gven te eased tepeates along te centelne tese veloctes coespond to appoately Mac.8-.9 flow. Te nozzle s desgned fo Mac.6 opeaton wc bot of te slatons pedct. Te two adal pofles at /d.6 and /d ae sown n Fge 5.. As epected te ageeent s poo nea te centelne wt slgtly bette ageeent fte fo te cente. Note tat te epeental ponts n ts case ae te aveage of vey few easeents and at te /d locaton te ponts off te centelne ae only a sngle easeent.

80 peent ge Aveage Lowe Aveage 00 Aal Velocty (/s) /d Fge 5.0 opted and Meased entelne Aal Velocty fo SD-TM Mng ases peent Lowe Aveage ge Aveage peent Lowe Aveage ge Aveage (/s) 600 (/s) y/d (/d.6) y/d (/d ) Fge 5. adal Pofles of Aal Velocty fo SD-TM Mng ases

81 64 Te copted ole facton dstbton s sown n Fge 5.. Fo efeence te gt sde of ts fge s at appoately 83 c. Fge 5.3 sows te copted eddy vscosty and tblent dffson coeffcent. Agan tese two plots ave te sae conto levels so tat tey ay be copaed dectly. Note tat te enfoced Scdt nbe ange s between 0. and.0 so te tblent dffson coeffcent s estcted to te ange between v t and fve tes v t. Fge 5. opted Mole Facton ontos fo SD-TM Mng ases

82 65 Fge 5.3 opted ddy Vscosty (top) and Tblent Dffson oeffcent (botto) fo SD-TM Mng ases 5.. ydogen only ase Te second n slated nvolves te necton and cobston of ydogen only. Wle tee s no epeental data fo n 57 of te SD-TM epeent an

83 66 nfaed age s nclded fo qaltatve copason. Ts age can be seen n Fge 5.4. Te ydogen s nected at atospec pesse and tepeate wt a ass flow ate coespondng to an eqvalence ato of.0. Te taget entalpy fo ts case s tat of Mac 5.5 flow. Fge 5.4 Infaed Iage of SD-TM n 57 Te ppose of tese coptatonal ns s to copae te two ydogen/a cecal odels. Fge 5.5 sows te copted ole factons fo eac of te cecal odels wt Jacows on te top alf and onnae on te botto alf. Note tat wle te soltons ae sla te onnae odel s c less lely to ato-gnte. In ts case t was estated fo an gnted Jacows n at wc pont t sstaned te cobston and podced sla eslts to tose of te Jacwos ecans. Te eslts obseved n tese fges also sggest a degee of nsteadness n te vcnty of te fel necto. Tese oscllatons do not affect te sze sape o gnton locaton of

84 67 te flae downstea bt deally te copted soltons sold be te aveage of a te-accate slaton. oweve te cent copte esoces do not allow ts. Fge 5.5 opted Mole Facton ontos fo SD-TM n 57 Fge 5.6 sows te copted eddy vscosty fo tese ns and te tblent dffson coeffcent and tblent dffsvty ae sown n Fge 5.7. Te tblent dffson coeffcent s slgtly ge tan te eddy vscosty n te flae egon ndcatng a tblent Scdt nbe lowe tan one bt te tblent dffsvty s eactly fve tes te eddy vscosty togot te flow feld eanng tat te tblent Pandtl nbe s beng lted to 0. eveywee. Ts s te sae beavo obseved n te above slatons. It s clea tat te tblent Pandtl nbe s qte senstve to te tblence/cesty nteacton te. Te odel constants contaned n ts te ay need to be adsted n te fte to avod sc sevee ltng of te tblent dffsvty.

85 68 An addtonal n was pefoed sng te Jacows ecans on a efned gd wc dobled te nbe of cells n te steawse decton. Te gnton locaton and te oveall solton eaned ncanged. Fge 5.6 opted ddy Vscosty ontos fo SD-TM n 57

86 69 Fge 5.7 opted Tblent Dffson oeffcent (top) and Tblent Dffsvty (botto) ontos fo SD-TM n ydogen/tylene Mte ase Te td n slated of te SD-TM epeents s n 40. Ts n s splt nto two pases 40a and 40b. Dng te fst pase te coflow contans only

87 70 ydogen wt a taget eqvalence ato of 0.5. Dng te second pase wc s ntated afte steady cobston s aceved n te fst pase etylene s added to te coflow fel sc tat t contans bot ydogen and etylene eac wt a taget eqvalence ato of 0.5. Te actal eqvalence atos fo ts patcla n can be seen n Table 3.. Note tat te taget entalpy s tat of Mac 6 flow. A vsble age of eac pase s sown n Fge 5.8. Fge 5.8 Vsble Iages of n 40 Pase A (top) and n 40 Pase B (botto)

88 7 As wt n 57 tee s no qanttatve data avalable and slaly ts case s sed as a copason of te two edced etylene ecans descbed above te 5 speces odel of Galasnan et al. and te speces odel of Zabon and ella. Tese odels ae descbed n detal n Sectons.4.. and.4... Fge 5.9 sows te contos fo n 40a wee only ydogen s pesent n te coflow fel. Te 5 speces odel s on top and te speces odel s oed on te botto. Te speces odel pedcts a c eale gnton and an oveall salle flae. Te sae tend s obseved fo n 40b wc s sown n Fge 5.0. Te stcte s essentally te sae bt fo te speces odel te gnton locaton oves slgtly downstea wen te etylene s ntodced. efeng bac to vsble ages n Fge 5.8 ts slgt oveent s to be epected. Tee s agan obvos nsteadness n te egon aond te necto bt as wt te pevos case te flae sape sze and gnton locaton ae not affected. Fge 5.9 opted Mole Facton ontos fo SD-TM n 40 Pase A

89 7 Fge 5.0 opted Mole Facton ontos fo SD-TM n 40 Pase B 5.3 Ln tylene Mng peent Te td epeent as descbed n Secton 3.3 s te Ln etylene ng epeent [38]. Te slaton s copaed wt epeental data as well as wt slatons pefoed by Boles et al. [5] sng an LS/ANS ybd odel. Te copted a densty on te cente plane s sown n Fge 5.. Ts fge s nclded to sow te geneal stcte of te flow and to ndcate te locatons of te easeent planes. Te coptaton tlzes te fll pesented odel and te tblence eqatons ae nclded n te plct te advanceent scee.

90 73 Fge 5. A Densty ontos on ente Plane fo Ln peent 5.3. opason wt peent Te fst and only epeental copason fo te Ln etylene ng epeent s te etylene te facton as eased by a aan scatteng tecnqe on te tee planes. Te copason s sown n Fge 5.. n te left ae te eased qanttes and on te gt ae te contos copted sng te cent odel. Te top ddle and botto faes coespond to te 5 0 and 5.3 daete locatons. Mte facton wc s sla to vole facton n ts case s defned by qaton (3.). Te blac lne on te fge epesents te stocoetc te facton wc s 6.36% n te case of etylene and oygen.

91 74 Fge 5. peental (left) and opted (gt) tylene Mte Facton fo Ln Mng peent Tee s fa ageeent between epeent and coptaton ee. At te fve daete staton te coptaton sows a geate degee of ng tan te epeent bt ovng fte downstea te copted pofles do not spead as qcly as ndcated n te epeent. Te penetaton dstance s atced faly well bt wt an obvos ovesoot at te fst plane. Te ng of fel and a n ts type of epeent s eavly dependent on te tblent Scdt nbe. Te copted Scdt nbes ae sown n Fge 5.3. As can be seen te vale of te tblent Scdt nbe vaes geatly fo a n vale of appoately 0.5 to a a of.0. Te fact tat te vales n te fst plane ae lowe tan tose downstea sppots te tend of ecessve ntal ng followed by odeate ng downstea. Te actal copted vales of eddy vscosty tblent dffson coeffcent and tblent dffsvty ae all vey sla n ts case and ae teefoe not nclded.

92 75 Fge 5.3 opted Tblent Scdt Nbe ontos fo Ln Mng peent 5.3. opason wt LS/ANS ybd Model Te LS/ANS odel sed by Boles s a ge fdelty odel n tat t esolves te lage scales of tblence and odels te salle scales ate tan odelng all of te tblence scales. Te slaton s te accate bt also ses constant tblent Pandtl and Scdt nbes of 0.9 and 0.9. Te LS/ANS slaton eploys a gd wt 9.96 llon cells as opposed to 3.7 llon fo te pesent etod. Ts lage dffeence s typcal LS vess ANS coptatonal gds. Fge 5.4 sows copted te facton contos fo bot te LS/ANS ybd odel and te cent odel. Unle te pesent odel te LS/ANS odel sows a ge concentaton of etylene n te fst plane tan te epeent. oweve te

93 76 downstea ng pedctons ae c close to te epeental vales fo te LS/ANS odel. Ts dscepancy n te coptatons of te pesent odel s lely de to lage scale nsteady oton tat te steady solve cannot capte. Fge 5.4 alclatons of LS/ANS Model (left) and Pesent Model (gt) Mte Factons fo Ln Mng peent Also avalable fo te LS/ANS coptatons ae aveages of te tblent ass fles. Ts dect aveage obtaned fo te LS/ANS coptatons s copaed wt te coptatons of te cent odel sng te elaton n qaton (F.5). Te copason of te agntde of te tblent ass fl vecto can be seen n Fge 5.5. Te sape of te stctes s sla bt tee s a dffeence n agntde. Ts dffeence cold be de to te fact tat te pesent odel asses tat te tblent ass fl vecto s popotonal only to te speces gadent wle n ealty t s affected by tepeate and pesse gadents as well.

94 77 Fge 5.5 opted Tblent Mass Fl opason fo Ln Mng peent 5.4 SLA peent Te vectoed necton SLA epeent as been te sbect of any past nvestgatons. Te fndngs of tose pevos stdes and ow t apples to te nflow and bonday condtons n te cent wo wll be dscssed n Secton 5.4. wle te latest eslts wll be dscssed n Secton All of te slatons of ts epeent tlze te fll pesented odel and te tblence eqatons ae solved sepaately fo te ote eqatons. Te cent eslts eploy only te Jacows ecans bt pevos stdes ave stdes ave sown tat tee s vey lttle dffeence between te onnae and Jacows ecanss [34].

95 Inflow and Bondaes As entoned above one of te factos nvestgated was te effect of te nflow condtons on te solton. Te senstvtes of seveal paaetes wee eaned. Fst s te ntal tblence ntensty wc s defned as T 00 (5.) 3 Ts te s bascally sed to specfy te ntal tblent netc enegy. Soe tblence odels ae senstve to ts vale bt te -ζ odel s not. Vales fo 5% to 5% wee nspected. Lttle to no nflence on te solton was obseved. Te second facto te ntal tblence scale (ν t / ν) also ad only a no pact on te solton. Te pesse along te botto wall n te cobsto secton seeed to be loosely elated to te specfcaton of ts vale. Vales fo 5 to 000 wee sed. In te lowe ange fo 5 to 500 te pesse nceased vey slgtly wt an ncease n (ν t / ν). oweve any ncease above 500 dd not see to cange te solton. Fnally te effects of feestea concentaton wee obseved. te tan te baselne case wee te feestea ass facton was zeo vales fo.00-6 to.00-3 wee consdeed. It was obseved tat te degee of cobston nceased wt te addton of n te feestea coposton. Ts n tn podced ge pesses n te cobsto. Te feestea tblence ntensty was set to 5% fo all of te ns pesented ee and te tblence scale was 000. Te feestea ass facton was A nfo dstbton was sed fo all popetes at te nozzle entance ncldng te tblence qanttes entoned above. Te speces concentatons total tepeate and total pesse wee obtaned sng a one-densonal calclaton tat assed coplete cobston and no teal losses gven te flow ates of ydogen oygen and a nto te cobsto. Te epeental data set nclded a ptot pesse pofle fo te vtated a nozzle et. Te qalty of te flow n te cobsto clealy depends on ow well te

96 79 nozzle otpt can be atced. pofles and tee s good ageeent between te two. Fge 5.6 sows te copted and epeental 0.0 Vetcal Dstance () opted peent p 0 /p Fge 5.6 Ptot Pesse Pofle at Vtated A Nozzle t fo SLA A fnal geneal consdeaton s ow te wall tepeates wee specfed. Te fst attept eployed te adabatc wall tepeate fo all sfaces. Ts was sple to pleent bt eslted n wall tepeates and tepeates n te nea wall egon to be c ge tan te epeental vales. Ts s ndesable snce colde walls wold eove enegy fo te flow and ts cold ave a sbstantal effect on te flow downstea n te cobsto. Te second opton eploed fo te wall tepeate was te se of a constant wall tepeate. Ts s a dffclt asspton to ae snce te wall tepeate s vayng togot te geoety of te cobsto de to ateal dffeences and te fact tat te walls ae ncooled and constantly nceasng n tepeate. Te fnal solton was to se a constant gost cell tepeate etod. Ts olds te actal wall

97 80 tepeate close to te specfed vale bt lets t ncease slgtly as te tepeate n te bonday laye nceases. ate tan specfy a sngle tepeate fo te ente syste te code was odfed to allow dffeent tepeates fo dffeent potons of te dct. In Fge 5.7 taen fo efeence [3] te wall tepeates n dffeent sectons of te cobsto ae lsted aganst te n te. Usng ts data appoate aveage tepeates wee cosen fo eac secton of te cobsto. In te ydogen necto a gost cell tepeate of 300 K was sed de to te low stagnaton tepeate. ecall te cobsto ateals entoned n Secton 3.4. A tepeate of 500 K was sed fo te coppe secton and 700 K was sed fo te steel secton. All of te pevos stdes as well as te cent wo eploy te soteal gost cell etod. Fge 5.7 Wall Tepeate vs. n Te at Tee Locatons (ef [3]) A fnal consdeaton s te se of te copessblty coecton n te ndelyng tblence odel. Pevos slatons ave sown tat ecldng ete of te

98 8 copessblty tes n te eqaton eslt n an nstat. All of te pesent slatons se te odeled tes and constants descbed n Secton ent eslts As eplaned n Secton 3.4 tee ae two an sets of epeental data fo te SLA epeent pesse data along te cente of te botto wall and AS easeents on te fve planes ndcated n Fge 4.5. Te AS easeents nclde tepeate and absolte ole factons of ntogen and oygen. Te copted and eased pesse dstbtons along te botto wall ae sown n Fge 5.8. Wle tee ae soe obvos ecessve soc eflectons n te egon fo 0.4 to 0.6 te oveall pesse dstbton s atced qte well especally n te downstea secton opted Meased Pesse (Pa) dstance () Fge 5.8 opted and Meased Pesse Dstbton fo SLA

99 8 Te sface fts of te AS tepeate easeents ae sown n Fge 5.9. Ts data s sown ee by tself to pont ot tat te eased data s not syetc. Te slaton aes se of te syety n te cobsto and ts cannot podce asyetc eslts. Fge 5.9 Sface Fts of AS Tepeate Measeents fo SLA Fge 5.30 sows te copted and eased tepeate dstbtons on te AS easeent planes. Te copted data s on te left alf of eac plane and te epeental sface fts ae on te gt sde of eac plane. Tee s fa ageeent oveall bt ealy gnton s ndcated on te td plane. Note tat te etod of geneatng te sface ft ay elnate sap feates sc as tose seen n te copted contos. egadless of ts fact ealy gnton cold be an sse not only wt te odel bt also te gd te cecal odel te te advanceent scee etc.

100 83 Ignton locaton of a standoff flae s a notoosly dffclt poble fo all of tese easons. Speces ole facton contos fo bot ntogen and oygen ae sown n Fge 5.3. Agan te copted dstbton atces te epeental sface fts well. Fge 5.30 opted (left) and Meased (gt) Tepeate Dstbtons fo SLA

101 84 Fge 5.3 opted and Meased Mole Factons fo Ntogen (left) and ygen (gt) fo SLA

102 85 Te copted tblent Pandtl and Scdt nbes can be seen n Fge 5.3. Jst as n ote cobston cases te Pandtl nbe eaces te floo vale of 0. togot te ng and cobston egon. In ts case te Scdt nbe beaves n a sla anne bt stats to ecove towad te end of te dct. Note tat te floo vale fo te Scdt nbe n ts case s Fge 5.3 opted P t (left) and Sc t (gt) ontos fo SLA In ts case te vales of te tblent Pandtl and Scdt nbes ae not vey nfoatve. Altenatvely te tblent dffsvty and tblent dffson coeffcent ae sown n Fge Wt ts pesentaton t can be seen tat te tblent dffsvty eaces ts pea on plane 3 wle te tblent dffson coeffcent eaces ts pea slgtly eale on plane.

103 86 Fge 5.33 opted Tblent Dffsvty (left) and Tblent Dffson oeffcent (gt) fo SLA 5.5 ysot peent Te fnal epeent s te ysot odel scaet descbed n Secton 3.5. Te copted eslts ae copaed wt bot te epeental easeents and a pevosly condcted slaton sng constant tblent Pandtl and Scdt nbes. Te n dept nvestgaton condcted by Sta [55] eploys te Jacows cecal ecans and Mente s sea stess tanspot (SST) ybd tblence odel [4]. Te slaton pefoed by Sta s also te accate sng a dal te steppng tecnqe wle te calclatons of te pesent odel ae all steady state sng a local te steppng tecnqe. Sta s slaton sed a tblent Pandtl nbe of 0.9 and a tblent Scdt nbe of 0.5. Bot slatons se te sae gd.

104 opason wt peent Te data sed fo copason s te pesse dstbton along te cente of te botto wall. Ts patcla n (#7678) eslted n steady-state sstaned cobston. Ts patcla pesse dstbton was ecoded dng te steady state opeaton ts eplanng te se of a steady solve n te slaton. Te copted and eased pesse dstbtons ae sown n Fge Te ageeent s good tog te nlet and fst alf of te cobsto bt fo appoately 0.3 to te et of te engne te pedcted pesse s lowe tan te eased pesses Meased opted Statc Pesse (Pa) () Fge 5.34 opted and Meased Pesse Dstbton fo ysot ase #7678 Te dscepancy s ost lely de to te lac of fel cobston n te cente of te odel. Te ote fel et gntes n te fst alf of te cobsto and te flae pessts tog to te et of te nozzle bt te nne fel et does not gnte. Ts can be seen n

105 88 te copted tepeate contos wc ae sown n Fge Note tat only te gt alf of te odel s sown. Te slce n te -y decton s tog te cente of te nne fel necto as s te fst y-z slce. It s clea tat only te ote fel et gntes and does not spead to te cente of te odel. Fge 5.35 opted Tepeate ontos fo ysot ase #7678 Fge 5.36 and Fge 5.37 sow te copted tblent Pandtl and Scdt nbes espectvely. As obseved n pevos cases te Pandtl nbe eaces te floo vale (0. n ts case) n te cobston egon. In te fel et tat does not gnte te Pandtl nbe s ntally low and ten ecoves to appoately.0 by te et of te nozzle. Te Scdt nbe sows soewat sla tends vayng fo te floo vale of 0. to te a of.0. Te eddy vscosty tblent dffsvty and tblent dffson coeffcent do not povde any nqe nfoaton n ts case teefoe tey ae not nclded.