Analysis of unsteady flow forces acting on the thermowell in a steam turbine control stage

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1 Jounal of Physics: Confnc is PAPER OPEN ACCE Analysis of unsady flow focs acing on h hmowll in a sam ubin conol sag To ci his aicl: J Badu al 216 J. Phys.: Conf Viw h aicl onlin fo updas and nhancmns. This conn was downloadd fom IP addss on 4/1/218 a 15:9

2 XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 Analysis of unsady flow focs acing on h hmowll in a sam ubin conol sag J Badu 1,2, Kon 1,3, D ławińsi 1 and P Ziółowsi 1,4 1 Engy Consion Dpamn, Th zwalsi Insiu of Fluid-Flow Machiny PA-ci, Fisza 14, Gdańs, Poland 2 jb@imp.gda., 3 son@imp.gda., 4 pziolowsi@imp.gda. Absac. In h psn pap h phnomnon of unsady flow focs acing on h hmowll fo masuing sam mpau in a sam ubin conol sag has bn psnd. Th non-saionaiy of fluid acing on h hmowll such as: ouhal fquncy, pssu amiud, pssu pas, pssu fild, lociy fild c. ha bn sudid analyically and numically. Th ha bn xamind wo cass of flow wih changing mass flow a, pssu and mpau in h conol sag chamb of a ubin high-pssu cylind. Th poblm of ny ino sonanc by hmowll has bn dscibd in h AME sandad PTC19.3 TW-21 wih poiding daild guidlins fo hmowll dsigns. 1. Inoducion Gnally, fom h scinific and ngining poin of iw, unsady flow focs acing on a solid sucu a a y impoan issu. Thfo, in h pap, in od o spcify h similaiy bwn piodical phnomna and o a ino accoun h cas of non-saionay flows focs acing on h hmowll fo masuing sam mpau in a sam ubin conol sag, a nol CFD+CD appoach has bn usd. How, i should b undlind ha h psnc of a cylindical lmn in h sam flow is a ason of occunc of h ox shdding phnomnon, wh h flowing sam dachs fom h cylind sufac caing downsam a ox sucu [1]. Th accompanying pssu pulsaions gna flow-inducd ibaions which may lad o hmowll damag du o high-cycl faigu [2,3]. Th poblm is dscibd in h AME sandad PTC19.3 TW-21 [4] poiding daild guidlins fo hmowll calculaions Rsonanc and ouhal numb h In od o spcify h similaiy bwn piodical phnomna and non-saionay flows, h ouhal numb h is inoducd, which is h similaiy numb dfind as [5]: a a f h, (1) wh: a - chaacisic dimnsion, - sady ambin lociy of h unifom flow, - piod of sd phnomnon, f - fquncy of h phnomnon. Conn fom his wo may b usd und h ms of h Cai Commons Aibuion 3. licnc. Any fuh disibuion of his wo mus mainain aibuion o h auho(s) and h il of h wo, jounal ciaion and DOI. Publishd und licnc by Ld 1

3 XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 I should b addd, ha h ouhal numb h is usd in h ngining chnology o analysis of.g. flow aound h ibaing body (aofoil, od, hmowll), flow hough a blad ow mound in h oo disc, flow aound a oaing pol o scw pol, c. Th is boad liau discussing h poblm of h fomaion of oics, changs in hi sucu, h impac of ox sucus on objcs on which hy fom. Th sach on h oiciy and h fomaion of sucus a flow has bn caid ou fo hundds yas, wha is idncd by schs of Lonado da Vinci [6]. Ga impoanc in h dlopmn of nowldg of piodical phnomna had wos of on Kámán abou oics gnaion and wos of ouhal abou fquncy of hi fomaion. Daild dscipion of hs issus can b found in h wos of h pions [7,8] and of conmpoay auhos [5,9]. Mos of h publishd aicls lad o h nonsaionay sucus in flow, concn h xpimnal wo and analysis [1-13], bu h impoanc of numical wos is gowing [14-16]. Th fundamnal wo in his gad is h analysis of h fomaion and dlopmn of ox sucus in a flow aound obsacls. A significan numb of sudis in his fild concns laminaubuln ansiion in h aa, wh uncognizd and no wll cognizd phnomna in singl hoy occus. Th a nown wos, in which h obsacl has h fom of sph [13], oaing sph [12], apz [1] o cub [11]. Espcially impoan is h poblm of oics focing ibaions, and ic sa - h ibaion of dics affcing h ox sucu. In h las dcad, a numb of wos was publishd [15] concning inacion of fluid and sucus aising in i, which suld in caion of a nw nom fo AME PTC 19.3 TW-21. How, h main aim of his pap is analysis of inacion bwn sam and hmowll. am mpau masumns in hmal ubins a conducd using hmocous acd in hmowll which is insd ino h sam flow. Th hmowll pocs h mpau snso agains dimnal acion of sam, simulanously inoducing o h masumn sysm a hmal inia suling fom h solid dsign of hmowll. Th psnc of a cylindical lmn in h sam flow is a ason of occunc of h ox shdding phnomnon, wh h flowing sam dachs fom h cylind sufac caing downsam a ox sucu [17]. Th accompanying pssu pulsaions gna flow-inducd ibaions which may lad o hmowll damag du o high-cycl faigu [1,18-21]. Th poblm is wll dscibd in h AME sandad PTC19.3 TW-21 [4] poiding daild guidlins fo hmowll calculaions. How, hmal and sngh analyss of lmns woing in high-pssu w psnd in [18-21]. Oh sudis [22,23] ha modlld and pdicd h sss upu of alloys and h sidual lif of h mos ciical componns whil considing h ffcs of cp, hmo-mchanical faigu, coosion, and oxidaion. In h famwo of oo caus analysis, sam flow, dynamic and mchanical ingiy calculaions w pfomd aiming a dmining sam xciaions acing on h hmowll, is naual fquncis and safy magins. Fo his pupos, CFD+CD (Compuaional Fluid-olid Dynamic) appoach has bn adopd. 2. Modl dscipion In analyss cas, h similaiy ciion is h fquncy of h foc which can b dicly compad wih h f ibaion fquncy of h dic, so ha i can b dmind whh h sonanc occus. An impoan ool in h analysis of his phnomnon is h combinaion of CFD + CD, ofn calld FI - Fluid olid Inacion o Fluid ucu Inacion CFD Tadiionally, h fi balanc quaions (ha consis of on mass balanc quaion, h momnum balanc quaions and on ngy balanc quaion) and wo oluion quaion fo paams dfining ubulnc (quaion fo ubuln inic ngy oluion and quaion fo ubulnc dissipaion oluion ) ha bn dscibd in [6,22]. To maximiz h us of h asily immnabl maix calculus, h saing poin fo CFD compuaion is fomulaion of unisal s 2

4 of mass, momnum and ngy balanc quaions fo h fluid, supmnd wih quaions fo ubulnc oluion - in h fom of: p p c s s b J J q I di di (2) wh: x, - fluid dnsiy, gnally dpndn on im and locaion, x i i - fluid lociy, p - hmodynamic pssu, j i j i I - uni nso, s = u lam - sss flux componns, lamina nd ubuln spcily, b - mass foc of ah gaiy, u - sum of innal and inic ngy, q - ha flux, J, J ε - diffusi flux of and diffusi flux of wih soucs, (aious dfiniions of diffn auhos xis in liau). Fo ach fini olum of h compuaional gid, sn quaions a sold (on fo mass, ngy, and anspo balanc quaion and h momnum balanc quaions) [6] CD Th poblm of naual ibaion has bn discussd in [2,6]. Th poblm of dminaion of nonsaionay load coming fom sam flow, amiuds of xciaion fom non-saionay flow and paial load ha cnly bn discussd in [2,6,21]. In analogy o CFD, h appopia s of CD goning quaions is dmind as follows [6]: α b J q σ σ α α di di 1 (3) wh: σ - nso of solid ssss; - nso of asic sain; α - inmaic hadning; - isoopic hadning; J - diffusi flux of ;,, α soucs of asiciy, inmaic and isoopic hadning ypical fo h Chaboch modl. Ou analysis and calculaions in solid body a basd on h 3D modal and hamonic analysis ypical fo h CD [2]. CD is poin-blan analogy of CFD (Compuaional Fluid Dynamics). Boh mhods us h sam balanc quaions (mass, momnum and ngy). Discizaion mhod fo h CD and CFD is abiay (FEM, FVM, c) bu h goning quaions a idnical. This achicu of soling quaions galy simifis FI (Fluid olid Inacion) [2,6] and hmal-fi [22] analyss. 3. Analysis 3.1. Gomy and bounday condiions Th hmowll analyzd h opad in h conol sag chamb of a ubin high-pssu cylind (figu 1). Figu 2 psns h gomy modl discizd wih fini olum msh which was usd o simula h gnal sam flow condiions wihin h conol sag. I shows fou inl piins, nozzl scos, conol sag oaing whl and chamb, and fis full-ac admission sag. XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 3

In od o b dscib h flow condiions and obain a al picu of h conol sag flow, h compuaional domain was xndd o h fis nogulad sag.

5 XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 Figu 1. Locaion of h hmowll (mad in d) in h conol sag chamb. Fo appopia dscipion of h flow nau wihin h conol sag chamb, h numical modl pcisly dscibs dimnsions of h conol sag (64 blads), nozzl ings whos shap xacly dscibs h gomy of al sag. In od o b dscib h flow condiions and obain a al picu of h conol sag flow, h compuaional domain was xndd o h fis nogulad sag. Th whol modl was discizd using sucud msh poiding h mos liabl suls wih opimum dnsiy. Th aas of xpcd big gadins w addiionally find, which suld in h numb of lmns aching 6 million. Figu 2. Gomy modl wih paially shown msh fo com compuaions of ni conol sag (na nozzl box B was locad h hmowll; boh nozzl boxs A and C includs 14 nozzls, nx pai of nozzl boxs (B and D) includ 9 nozzls). Bounday condiions fo CFD calculaions a psnd in abl 1. Th w considd wo cass of wo of h conol sag a ducd pssu and mass flow a of sam - nigh wo wih 18 MW and daily wo wih 38 MW a nominal paams. Piously dscibd modl was usd. How h idal gas was considd so iscosiy ffc was omid. Tabl 1. Bounday condiions such as ( m, p, T ) assumd o calculaions fo wo cass of wo ( N ). Paam Uni Daily wo full load Nigh wo paial load m g/s p ba T o C N MW Calibaion of h CFD modl In od o confim h cocnss of h suls, som sulan poins fom [2] w mad on h diagam psning dpndnc of Rynolds numb on ouhal numb (figu 3), an fom h AME nom [4]. Th posiion of poins in figu 3 should b considd as saisfacoy bcaus hy a wihin h aa dfind xpimnally. I is woh mnioning ha h diagam fom fs o h obsacls, immsd in h whol high of h channl wih a unifom coss-scion, and in h cas of analyss hmowll h flow was only paially disubd, and addiionally h hmowll has h shap of a uncad con. 4

XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 Figu 3. Compaison of (R) fom AME PTC 19.3 TW-21 wih numical suls. 3.3. Bounday condiion of h CD modl Fig.

As h maial of h hmowll was an sl T12. In h Fig. 4a), h a mad acs (p) of apicaion h aodynamic loads, which alus w dmind on h basis of pssu fild on h sufac psnd on Fig.4 b). a) b) Figu 4.

Rsuls and discussion Numical simulaions w caid ou wih bounday condiions dscibing ubin opaion wih nominal and pa load.

6 XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 Figu 3. Compaison of (R) fom AME PTC 19.3 TW-21 wih numical suls Bounday condiion of h CD modl Fig. 4a) shows h gomy of h hmowll af maing discizaion which was usd o calcula h fquncy of f ibaions of h housing of sam mpau snso. To moun a sucu, 6 dgs of fdom was an away fom h aa mad by bold lins. As h maial of h hmowll was an sl T12. In h Fig. 4a), h a mad acs (p) of apicaion h aodynamic loads, which alus w dmind on h basis of pssu fild on h sufac psnd on Fig.4 b). a) b) Figu 4.a) Th housing of h hmowll af maing discizaion and wih mad ac (p) of apicaion of h bounday condiions. b) sufac usd o dmin pssu fild acing on solid. 4. Rsuls and discussion Numical simulaions w caid ou wih bounday condiions dscibing ubin opaion wih nominal and pa load. Figu 5a) psns spaial filds of saic pssu compud fo on full oaion of h oo a nominal load. Th suls w psnd fo slcd im sp mainly =.36 s. Th im sp was qual o Δ=.312 [s] which cosponds o 1 sps p ach in-blad channl fo 64 oo blads. Local pssu aiaions do no xhibi significan flucuaions. A his phas, af xamining disibuion of h flow paams and is chaac, i can b sad ha h flow a h conol sag chamb is sabl and dos no xhibi sympoms of big oscillaions. Th subsqun figus show h local aiaions of flow paams. Figu 5b),c) psns h saic pssu filds calculad a iniial phas of oo oaion a h conol sag chamb: Fig.5b) af h conol sag a h inl o conol sag chamb and; Fig.5c) oul of h conol sag chamb bfo h fis no-gulad sag. Th suls fom Figu 5b) and 5c) cospond o h ubin opaing wih paial load. This opaion mod diffs fom h nominal load by opning of wo nozzl boxs only. Th maining wo a fully closd by h sop als and sam is flowing only hough h boxs wih a small numb of nozzls (compa wih Figu 5a - nominal load). Consqunly, high non-unifomiy of pssu Fig.5b) and lociy disibuion Fig.6 is obsd fo h sam laing h oo blads. Figu 5c) psns saic pssu aiaions a h xi an of 5

XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 h conol sag chamb. Th xi is locad clos o h inl o saionay blads of h fis nongulad sag.

Th saic pssu filds a iniial phas of oo oaion: a) spaial disibuions; b) coss scion af h conol sag; c) coss scion bfo h fis no-gulad sag. a) b) Figu 6.

I can b noicd ha h flow foms h main co of high lociy bginning a h xi fom h conol sag and nding a h inl o h sao blads of h fis non-gulad sag.

This flow can gna oics and coninuous ciculaion of sam insid h chamb. Figu 7. Plos of oal pssu disibuion aound hmowll: lf 18MW; igh 38 MW.

7 XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 h conol sag chamb. Th xi is locad clos o h inl o saionay blads of h fis nongulad sag. Cla diffnc bwn opn and closd nozzl scos is sn fom h pssu disibuions. This disincion is isibl n hough h sams flow hough h ni conol sag chamb. a) b) c) Figu 5. Th saic pssu filds a iniial phas of oo oaion: a) spaial disibuions; b) coss scion af h conol sag; c) coss scion bfo h fis no-gulad sag. a) b) Figu 6. Vlociy disibuion a an cuing h hmowll a subsqun im sps: a).36 [s] ; b).7 [s]. Figu 6 psns h lociy filds a slcd im sps. I can b noicd ha h flow foms h main co of high lociy bginning a h xi fom h conol sag and nding a h inl o h sao blads of h fis non-gulad sag. A h boom pa of h conol sag chamb, a sagnaion gion psiss du o high dignc of h chamb and sd flow can b xpcd h. This flow can gna oics and coninuous ciculaion of sam insid h chamb. Figu 7. Plos of oal pssu disibuion aound hmowll: lf 18MW; igh 38 MW. Figu 7 psns disibuions of h oal pssu aound h hmowll a 18MW (paial load) and 38 MW (full load). Th pssu disibuion changs boh is alus and shaps wih changing load, which mans ha boh pssu amiud and sulan foc dicion ay wih ubin load. I can b hus concludd ha dicion of h pssu foc acing on h hmowll dpnds on h opaion gim (figu 7). In h cas of analyss hmowll h flow has diffn chaac of 6

XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 ubulnc and pssu diaion in compaison o h sam main flow dicion which is bhaiou as axial.

8 XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 ubulnc and pssu diaion in compaison o h sam main flow dicion which is bhaiou as axial. Ths loads xpssd as diffnc of oal pssu fo h hmowll scion insd ino h flow a psnd in figu 8. I is sn ha h aodynamic loads a on-sidd which mans ha sam pushs h hmowll in lin wih h sam flow dicion bu wih diffn im-dpndn foc. Th y ol in aiabl loading of h hmowll is ayd by h oal pssu. Th diffnc in sam pssu ais bwn ba fo pa load and -.9 ba fo full load. Figu 8. Plo of oal pssu diffnc aiaion bwn upsam and downsam sid of h hmowll scion insd ino h flow (pa load - solid lin, full load dod lin) CD Analysis Figu 9 psns a aiaion of naual fquncis wih mpau and compaison of h xciaion fquncis wih fobiddn angs of naual fquncis. As h main xciaion h ailing dg was fom 64 oaing blads w assumd and basd on his h xciaion fquncy n zw = 32 Hz was compud. Th xciaions du o non-unifom sam supy o nozzl boxs w no analyzd h, as h fquncis qual o 5 Hz and 1 Hz fo pa and full load condiions a y small compaing wih h hmowll naual fquncis. Figu 9. Vaiaion of naual fquncis wih mpau. Accoding o h AME sandad PTC 19.3 TW-21, h quid safy magin fo naual fquncy is ±2%. As i is sn fom figu 9 his condiion is saisfid wih a considabl magin fo h analyzd naual fquncis of h hmowll. Taing ino accoun h abo suls i can b concludd ha h hmowll naual fquncis a wihin a saf zon as compad wih h xciaion fquncis. 5. Conclusions ummaizing h calculaion suls i can b said ha, opaion wih paial load is chaacizd by lag amiuds of pssu acing on h hmowll. Th oal pssu amiud fo, pa load achs 4.5 ba, whil a full load is qual maximum.9 ba. Pssu disibuion cu aound h hmowll changs boh is shap and alu binging abou a aiaion of no only h pssu amiud bu also h load dicion.two majo xciaions fom h sam flow in h conol sag chamb can b disinguishd, namly du o non-unifom sam supy o h nozzl boxs and du o 7

9 XXII Fluid Mchanics Confnc (KKMP216) Jounal of Physics: Confnc is 76 (216) 121 aodynamic was of oo blads ailing dgs. Th xciaion fquncy du o non-unifom sam supy o h nozzl boxs is 1 Hz fo 18 MW load and 5 Hz fo 38 MW load. Th xciaion fquncy du o aodynamic was is 32 Hz in h ni load ang. A sady sa opaions h ciia of uning h naual fquncis agains sam focs basic fquncis a m and h hmowll is f of sonanc. Rfncs [1] El-Baahgy A and Fahy G 213 Faigu failu of hmowlls in fd gas supy downsam piin a a naual gas poducion an Cas ud Eng Fail Anal 1(2) [2] Kon, ławińsi D, Ziółowsi P and Badu J 215 Analysis of unsady flow focs on h hmowll of sam mpau Tans. IFFM [3] Hasling K H 23 Flow-inducd ibaion sing of acmn hmos-wll dsigns Jounal of Fluids ucus [4] AME PTC19.3 TW-21: pfomanc s cods: hmowlls. AME 21 [5] hyy W 1994 Compuaional modling fo fluid flow and infacial anspo Do Pub. (NY) [6] Badu J 29 Dlopmn of ngy concp Wyd. IMP PAN (Gdańs) [7] Fuchs R, Hopff L and wald F 1934 Aodynami ping (Blin) [8] Pandl L 1956 Flow dynamics Tłum. J. Wysoci PWN in Polish (Waszawa) [9] Posna W J 197 Fluid mchanics PWN in Polish (Waszawa) [1] Goujon-Duand, Jnff P and Wsfid J E 1994 Downsam oluion of h Bnad-on Kámán insabiliy Physical Riw E 5 no [11] Kloz L, Goujon-Duand, Roici J and Wsfid J E 214 Expimnal insigaion of flow bhind a cub fo moda Rynolds numbs J. Fluid Mch [12] aysz M, Pyśo J, Goujon-Duand and Wsfid J E 214 Th wa bhind a oaing sph Jounal of Physics: Confnc is [13] Gumowsi K, Midzi J, Goujon-Duan, Jnff P and Wsfid J E 28 Tansiion o a im-dpndn sa of fluid flow in h wa of a sph Physical Riw E (R) [14] aha A K 26 Th-dimnsional numical sudy of flow and ha ansf fom a cub acd in a unifom flow Innaional Jounal of Ha and Fluid Flow [15] apaya T 24 A ciical iw of h ininsic nau of ox-inducd ibaions Jounal of Fluid and ucus [16] L A H, Campbll R L and Hambic A 214 Coud dlayd-dachd-ddy simulaion and sucual ibaion of a slf-oscillaing cylind du o ox-shdding Jounal of Fluids and ucus [17] Mgahd M M and Aia M 215 Failu analysis of hmowll wldmn cacing Eng Fail Anal [18] Zau G A, Cown E A, Wu T R and Liu P L-F 215 Vox shdding and oluion inducd by a soliay wa popagaing o a submgd cylindical sucu Jounal of Fluid and ucus [19] Moishia M and Dozai K 1998 Hisoy of flow-inducd ibaion incidn occud in Monju AME Tans PVP [2] Odahaa, Muaami Y, Inou M and uoa M 25 Faigu failu by in-lin flow-inducd ibaion and faigu lif aluaion JME In J, A 48(2) [21] Banasziwicz M 215 Mulill appoach o lifim assssmn of sam ubins Innaional Jounal of Faigu [22] Badu J, Ziółowsi P, ławińsi D and Kon 215 An appoach fo simaion of wa wall dgadaion wihin pulizd-coal boils Engy [23] Banasziwicz M and Rhmus-Foc A 215 ss coosion cacing of a 6 MW sam ubin oo Engining Failu Analysis

Study of Tyre Damping Ratio and In-Plane Time Domain Simulation with Modal Parameter Tyre Model (MPTM)

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