CFD BASED APPROACH TO PREDICT THE WINDAGE HEATING EFFECT IN STEAM TURBINE LABYRINTH SEALS

Transcription

1 Proeedings of the st Global Power and Proplsion Form GPPF 07 Jan 6-8, 07, Zrih, Switzerland GPPF CFD ASED APPROACH TO PREDICT THE WINDAGE HEATING EFFECT IN STEAM TURINE LAYRINTH SEALS Simon Heker Rheinstr. 00, Mülheim Rhr, Germany Christian Msh Rheinstr. 00, Mülheim Rhr, Germany Andreas Penkner Rheinstr. 00, Mülheim Rhr, Germany Stefan Glos Rheinstr. 00, Mülheim Rhr, Germany ASTRACT Today s steam trbine power plants are designed for highest steam inlet temperatres p to 60 C to maximize thermal effiieny. This leads to elevated thermal stresses in rotors and asings of the trbines. Hene, temperatre distribtions of the omponents have to be predited with highest aray at varios load points in the design proess to assre reliable operation and long life time. This paper desribes the windage heating effet in fll labyrinth seals sed in steam trbines. An analytial approah is presented, based on CFD simlations, to predit the reslting steam temperatres. A broad appliation range from very low to highest Reynolds nmbers representing different trbine operation onditions from partial to fll load is addressed. The effet of varying Reynolds nmber on the flow frition behavior is aptred by sing an analogy to the flow over a flat plate. Additionally, the impat of different labyrinth geometries on the frition oeffiient is evalated with the help of more than 00 CFD simlations. A meta-model is derived from the nmerial reslts. Finally, the analytial windage heating model is validated against measrements. The presented approah is a fast and reliable method to find the best performing labyrinth geometries with lowest steam temperatres. INTRODUCTION Steam trbine manfatrers want to realize the highest trbine and yle effiieny for power plants. The aim is to rede the green hose gas otpt as mh as possible to rede environmental impats. This aim an be ahieved by optimizing the trbine blade and flow paths, reding leakages between stationary and rotating omponents, sing improved seals or by inreasing the main steam onditions sh as pressre and temperatre. Sine trbine omponents sh as asings or rotors are highly stressed e.g. by thermal gradients in the materials, the temperatre distribtion in eah load ase has to be known as arately as possible. The more preisely the stress distribtion is known in the design proess, the more exat the life time of the omponents an be predited. A ontra diretional effet an or in labyrinth seals optimization: windage heating ors de to rotor rotation. Windage heating leads to a temperatre inrease of the steam that flows throgh the labyrinth. The smaller the radial learane of the seal, the lower the mass flow throgh it is, whih an reslt in large temperatre inreases. The effet is strong in ase where the labyrinth is long with many fins, e.g. labyrinth seals on a thrst balane piston. If the design goal is to minimize leakage mass flow by se of sh types of seals in ombination with higher inlet temperatres, then the effet of windage heating may beome an important design onsideration. CURRENT STATE OF RESEARCH The first law of thermodynamis desribes the effet of rotor rotation on total enthalpy inrease h t : M h t () m De to rotor rotation with the freqeny, a torqe M ats onto the steam mass flow m throgh the labyrinth. This leads to irmferential shear in the flow, whih ats against the rotor torqe. The power M reslts in a total enthalpy inrease h t and therefore a temperatre inrease in the flid passing throgh the labyrinth seal. This work is liensed nder a Creative Commons Attribtion-NonCommerial-NoDerivatives 4.0 International Liense

2 For a given mass flow and labyrinth geometry, the most important vale to be allated is the rotor torqe to predit the temperatres in the labyrinth. The link between M and the irmferential shear in the flow an be expressed as M r da () with the rotor radis r and the wetted rotor srfae A. desribes the wall shear in irmferential diretion, whih an also be expressed by a frition oeffiient f aording f. (3) ² The variables and shown in eqation (3) represent flid density and irmferential flow veloity. Different windage heating models are available in the literatre; the models of e.g. MGreehan and Ko [] and Millwards and Edwards [] are most poplar. The model given in [] is based on the momentm balane in eah labyrinth hamber; at a given inlet momentm the rotor and stator torqes as well as the exit momentm an be allated hamber wise and iteratively. The frition oeffiients at rotor and stator are expressed by eqations, whih depend on a loal irmferential Reynolds nmber. Millwards and Edwards [] give an empirially determined relationship for the irmferential frition oeffiient to be sed for allation of the rotor torqe. In addition to the geometry the frition oeffiient also depends on the mass flow and irmferential Reynolds nmber. Also, eqations are available in the literatre whih model the temperatre inrease in a rotating labyrinth by approximating it to a single rotating shaft and diss. Sores for information are the pbliations of Hütte [3], Stoff [4] and Polkowski [5]. Deneke et al. [6] smmarize parameters, whih inflene the windage heating effet and the leakage in a labyrinth seal. They arried ot an analytial and a nmerial stdy on short stepped labyrinths to find ot that e.g. pressre ratio, geometry, axial Reynolds nmber, irmferential Mah nmber and flid parameters mostly inflene the windage and leakage behavior. Yan et al. [7] analyze the inflene of honeyomb strtres, applied to the stator, on windage heating behavior nmerially. The labyrinth investigated is again a stepped labyrinth with for fins. They point ot that the windage heating effet inreases with the pressre ratio. It is observed frther that the gap width between stator and the fins inflenes the temperatre in sh a way that it beomes high in ase the gap width is low. Finally the nmerial allations are validated against measrements. In a frther stdy Yan et al. [8] simlated the flow in a stepped labyrinth seal sing CFD with and withot honeyombs applied to the asing wall. They varied pressre ratio, pre swirl in front of the labyrinth and the honeyomb design. The reslt shows that the pre-swirl has a weak inflene on the leakage flow, while the windage heating is inflened strongly by it. Another reslt is that the honeyomb design inflenes leakage. Nayak and Dtta [9] analyze the inflene of grooves in the asing of a see-throgh-labyrinth de to rotor stator ontat. The aim of this stdy is to explore the windage heating effet nmerially and experimentally. The athors analysed honeyombs applied to the asing. The reslts are ompared to reslts from the MGreen and Ko model. One reslt is that it is possible to inrease the leakage by p to three times in ase of no honeyombs with wear grooves and a small radial learane. In the ase of small radial learanes, the ontat grooves reslt in lower windage heating in labyrinths with honeyomb applied. He et al. [0] allate the windage heating in a stepped labyrinth with three fins and diabati wall onditions with CFD. In addition, thermal models of the rotor and the stator are inlded in the simlations. They also fossed on a labyrinth with honeyomb strtres applied to the asing. One major otome is that pre-swirl strongly inflenes windage heating, whih is more prononed in ase of smooth walls. It is also observed that the pressre ratio inflenes windage heating. The literatre review shows that many athors analyze very short and stepped labyrinths nmerially as well as experimentally. Frther, many athors state that the pressre ratio, pre swirl, irmferential Reynolds nmber and the state of the flid are the important parameters, whih most inflene windage heating. To the athors knowledge no models are available whih aptre the inflene of all these parameters for different types of very long fll labyrinth geometries. WINDAGE HEATING CORRELATIONS The present paper desribes an analytial method for prediting the windage heating effet in long labyrinth seals, by sing frition and ontration oeffiients allated with CFD: It is assmed that the irmferential flow veloity in a single hamber does not hange in axial diretion z: d 0 dz In eah hamber of the labyrinth the average irmferential flow veloity is approx. 50 % of the rotor srfae veloity: (4) U r (5) This relationship is exat for laminar oette flow and sffiiently exat for desribing flly trblent flow (Stoff [4]). Sine the axial veloity omponent inflenes the windage heating effet [, 6, 7], a maximm axial flow veloity ax between rotor and fin is allated from ax p ² p ² (6) p n Copyright 07 by Siemens AG

3 with the pressre in front and behind the labyrinth p and p, the density in front of it, the nmber of fins n and the average density of the flid. The absolte wall shear at the rotor srfae in rotating frame of referene qantifies all ating shear fores, whereas the irmferential omponent of the wall shear is the rial omponent for windage heating. Figre gives the geometrial relationships. U/ ax w ; U w ; Figre : Veloity triangle desribing the flow sitation nder one asing fin is aligned with the relative flow veloity w, whih an be allated aording to w² ² w ² (7) ² ax with the absolte flow veloity, whih is eqal to w in ase of flly developed irmferential flow. It is assmed that the frition behavior of the bondary layer an be expressed by w². (8) f The irmferential omponent of the wall shear is allated by geometri relationship with the eqation w² os. (9) f It is observed that the windage heating behavior depends on the Reynolds nmber in the labyrinth [-6]. So a Reynolds nmber relationship between the frition oeffiient f and the Reynolds nmber is sed in the form wd A A h f (Re) Re (0) to aptre this effet; with a onstant A, the hydrali diameter D h, the dynami visosity and an exponent. The eqation is based on the assmption that the frition behavior is eqivalent to the frition behavior on a flat plat with a bondary layer development in eah labyrinth hamber. is hosen as = -0. as proposed by Shlihting []. Eqation (0) an be rearranged to w f (Re) ADh. () The ombination of eqations (9) and () leads to an expression for the irmferential wall shear, depending on flow veloity, flid properties and labyrinth geometry: w ADh w² os () If the frition behavior as well as the hydrali diameter is a fntion of the labyrinth geometry, then eqation () an be rewritten to w C(Geom) w² os (3) with a windage oeffiient C(Geom), to be allated e.g. nmerially or via measrements for eah labyrinth onfigration. Frthermore, the torqe M of eah single hamber is allated with help of eqation (). The torqe of the whole labyrinth an be ompted by smmation of the torqes at eah hamber. It is neessary to ompte the mass flow m for allation of the total enthalpy inrease as expressed by eqation (). This an be done by the well known eqation p ² p² m (Geom) Agap (4) p n with the ontration oeffiient (Geom) and the free gap width nder the fins A gap. The windage oeffiient C(Geom) and the ontration oeffiient (Geom) of eah labyrinth hamber, whih depends on geometri parameters, is allated by CFD. The detailed presentation of the nmerial model follows below. NUMERICAL MODELS CFD simlations are arried ot to gain neessary information abot C (Geom) and (Geom) to ompte eqation (3) and eqation (4). Frther information an be fond in Cremanns [] and in the following: h s s T t T asing inlet dt otlet rotor Figre : CFD model of the labyrinth setion The CFD model of the labyrinth as depited in Figre ontains 4 labyrinth fins; seven of them are applied at the rotor, the remaining at the asing. All srfaes of the rotor, inlding the rotor fins are treated as rotating walls. An inlet dt in front of the first fin with the rotating rotor wall is 3 Copyright 07 by Siemens AG

4 P / P base [ - ] P / P base [ - ] modelled to garantee that the irmferential flow veloity is flly developed in front of the first fin and onstant along the labyrinth, so that no frther flow aeleration in irmferential diretion ors in the hambers. The CFD model represents a small setor of the whole labyrinth sing a irmferential-yli interfae. Total pressre p t and total temperatre T t are set at the inlet of the model; the pressre p is presribed at the otlet. The steam is modelled as real gas, sine varying steam parameters sh as visosity, or thermodynami effets sh as the Jole-Thomson effet, are desired to be taken into aont. The Menter baseline (SL) eddy-visosity-trblene model (Menter [3]) is sed to simlate the inflene of trblene on the veloity, pressre and temperatre fields. A seond order arate iteration sheme is sed to allate the flow field. The nmerial grid sed is a qad dominant mesh, extrded in irmferential diretion. The bondary layer is resolved by 0 nodes leading to y + vales from seven to 30 at the rotor. The geometry of the nmerial model is bilt p parametrially (Figre ). So varios labyrinth geometries an be investigated with the aim to parameterize the windage oeffiient C(Geom) and the ontration oeffiient (Geom). The hamber an be desribed geometrially by the radial learanes s and s, the axial distanes between the fins T and T as well as the fin thikness t. t is set to a onstant vale for this investigation. The asing fin height is h. Modelling one hamber and patterning the model seven times in the axial diretion leads to the 3D-model as shown in Figre. An atomati seqene for model and mesh generation as well as flow omptation is observed: at first 00 different geometry designs are hosen by a Latin Hyperbe sampling method. The mesh generator meshes eah model afterwards. The CFD soltion proess sing Ansys CFX is arried ot after mesh generation. The final reslt is reahed in less than 000 iteration steps for eah labyrinth with se of a proper start soltion. The main onvergene riterion beside maximm residals being lower than is a negligible variation of loal pressre, temperatre and veloity at single monitor points in the domain from step to step of the solver rn. The harateristi otpt parameters of the flow field are allated atomatially, whih are then stored together with the geometry parameter desribing the allated labyrinth. These harateristi otpt parameters are the ontration oeffiient and the windage oeffiient. A hybrid meta model is sed to parametrize the ontration and the windage oeffiients depending on s, s, T and h. So the inflene of different labyrinth geometries on flow behavior is approximated by analytial relationships. This method replaes frther CFD simlations and gives the opportnity for optimization (Cremanns []). The meta model is able to ompte the importane of single inflene parameter on the objetive riterion. Sine T is less important in the observed range of variation for the desired riteria (Cremanns []), the eqation allated by the meta model does not inlde this parameters, bt the most important ones. CALIRATION OF THE ALGERAIC MODEL The windage power P of the labyrinth is analyzed for one geometry onfigration. In the pper diagram of the Figre 3, P is shown relative to P base of the referene onfigration; depending on different pressre ratios at different rotor speeds. For eah rotor speed, the irmferential Reynolds nmber is kept onstant, sine the average pressre is onstant for all onditions. CFD base P / P base [ - ] CFD base n / n base [ - ] n base 0.75 n base 0.5 n base 0.5 n base.3p base.6p base p base 0.89p base 0.87p base Figre 3: Windage power relative to power of base onfigration for different pressre ratios and rotor speeds. The dots represent CFD reslts, the lines ome from the analytial model The pressre ratio p inflenes the windage heating: the presented orrelation shows that the windage power is inreased at higher pressre ratios. This is in agreement with Yan et al. [7]. The reason for this behavior is that the sqare of the flow veloity inflenes the wall shear. This effet is ompensated to a ertain degree sine the flow angle is 4 Copyright 07 by Siemens AG

5 meta model / CFD [-] meta model / CFD [-] inreasing with elevated pressre ratio, leading to a redtion of. Additionally, the frition oeffiient f redes with inreasing absolte Reynolds nmber, sine the exponent is negative. The windage heating strongly inreases with higher rotor speed as expeted (bottom diagram in Figre 3). At a given pressre ratio, the flow angle dereases with inreasing rotor speed; leading to a flow vetor pointing inreasingly towards the irmferential diretion. Additionally, the absolte flow veloity inreases, leading to higher irmferential shear fore. The symbols shown in Figre 3 show the CFD reslts of one labyrinth onfigration at different thermodynami bondary onditions. One of the simlations represents the base design and delivers the windage oeffiient C(Geom), whih is then kept onstant in the algebrai model. The disrepany between the reslts for the algebrai model and the CFD reslts is less than 5%. The largest differene is at low Reynolds nmbers (low rotor speed and/or small pressre ratio). The reason for this is the strong gradient of the fntion f (Re) at low Reynolds nmbers. Sine the fntion f (Re) beomes nearly onstant at very high Reynolds nmbers, the aray inreases if high Reynolds nmber flow exists. The meta model predits the ontration oeffiient (Geom) with a deviation smaller than 6% ompared to CFD. The windage oeffiient C(Geom) is predited with a deviation smaller than 3%. The omparison therefore shows sffiiently high prognosis qality. VALIDATION AGAINST MEASUREMENTS The verifiation sing a short labyrinth for alibration shows good agreement between CFD reslts and the model at varios thermodynami onditions. Sine the most signifiant windage heating effet in seals of real steam trbines ors in long labyrinth seals where gas dynami effets play a major role, a omparison between the analytial model, CFD and experimental data is shown for this type of labyrinth seal in the following: T heat flxes in asing aptred by FSI-CFD loal heat p of steam in front of labyrinth aptred by CFD EXTENSION TO ARITRARY GEOMETRIES The hybrid meta model delivers the model oeffiients C(Geom) and (Geom) as explained above. To assess the aray of the meta model sed, Figre 4 shows the named oeffiients for three labyrinth onfigrations; allated with the meta model and with CFD. (Geom) (Geom) Figre 4: Windage and ontration oeffiient for different labyrinth geometries at onstant Reynolds nmber Labyrinth onfigration is the one sed for alibration of the thermodynami orrelations. Labyrinth has 35 % smaller radial learane at the asing s ompared to labyrinth ; and the asing sided fin height h of labyrinth 3 is 5% smaller ompared to h in labyrinth. All parameters not mentioned are kept onstant. Figre 5: Measred trbine and the CFD proedre to aptre parasiti heat flxes, whih inflene measrement of labyrinth temperatres The measred labyrinth exit temperatre at a HP steam trbine thrst ompensation piston is available at varios load points for different power plants. The inlet temperatre measrement in front of the labyrinth is loated a ertain distane pstream of the labyrinth. Sine parasiti heat flxes exist, whih inflene the inlet temperatre, a flly opled aero-thermal CFD simlation (Flid-Solid-Interation CFD) was done to determine the deviation between measred pstream temperatre and steam temperatre diretly in front of the labyrinth (Figre 5). The differene between labyrinth exit temperatre T exit and labyrinth exit temperatre in ase of no rotor rotation T exit,0 (isenthalpi throttled inlet temperatre) is sed to qantify the windage heating effet aording to the following: T T exit T exit,0. (5) The analysis shows that the measred vales of T are inflened by approximately 30 % by the heat flxes throgh the asing walls and side effets sh as windage heating on the piston front fae in this ase. This reinfores that the parasiti heat flxes mst be taken into aont in the analysis of measrements of this kind. So the measred T in the three different trbines investigated are orreted by the allated temperatre inflene, in order to make a diret omparison between the allated and the measred 5 Copyright 07 by Siemens AG

6 K windage heating effet. For typial steam trbine appliations, T is in a range of approximately 5 to 30 K depending on labyrinth geometry and steam onditions. The omparison between ompted and measred temperatre inrease T is given for different load ases (i.e. Reynolds nmbers) in the seals of three trbines of nearly similar type (Figre 6). Figre 6: Comparison between ompted and measred vales of T in three trbines The presented model allates the temperatre inrease T in the whole trbine load spetrm with a deviation of less than K ompared to CFD. The inrease of T from high to low trbine load as a reslt of f (Re) is aptred with both allation methods. The allation reslts are in very good agreement with the measrements. The absolte temperatre and the inrease of T from high to low load is measred as predited. The predition aray of the analytial model is high sine the allation reslts are in the satter band of less than K ompared to the measrements. SUMMARY AND CONCLUSION An algebrai model for prediting the windage heating effet in fll labyrinth seals is developed from fndamental relations. This model aonts for the inflene of varying axial and irmferential flow veloities in the labyrinth hambers over a wide band of Reynolds nmbers. The impat of labyrinth geometry on the heating effet is also taken into aont. This is aomplished with the help of a meta model. The omparison with experimental data shows that the model an arately predit the temperatres in the labyrinth at varios load points. With the approah presented, a method is available for fast and reliable allation of steam temperatres in labyrinth seals to find the best performing labyrinth geometries with lowest steam temperatres. PERMISSION FOR USE The ontent of this paper is opyrighted by Siemens AG and is liensed to GPPS for pbliation and distribtion only. Any inqiries regarding permission to se the ontent of this paper, in whole or in part, for any prpose mst be addressed to Siemens AG diretly. NOMENCLATURE Latin A area [m²] A onstant [-] onstant [-] C windage oeffiient [-] veloity [m/s] D diameter [m] h enthalpy [J/kg] h fin height [m] M torqe [Nm] m mass flow [kg/s] n fin nmber [-] n rotor speed [Hz] P power [W] p pressre [Pa] Re Reynolds nmber [-] r radis [m] s learane [m] T fin distane [m] T temperatre [K] t fin thikness [m] U srfae veloity [m/s] w relative veloity [m/s] z axial oordinate [-] Greek ontration oeffiient [-] flow angle [ ] differene [-] dyn. visosity [kg/(ms)] p pressre ratio [-] density [kg/m³] wall shear [Pa] rotor anglar veloity [/s] Sbsripts 0 no rotation inlet; rotor side otlet; asing side ax axial base referene exit exit f fritional gap gap t total h hydrali irmferential 6 Copyright 07 by Siemens AG

7 REFERENCES [] MGreehan, W.F., and Ko, S.H., Power Dissipation in smooth and honeyomb labyrinth seals, Proeedings of the International Gas Trbine and Aeroengine Congress and Exposition, 989, 89-GT-0 [] Millward, J.A., and Edwards, M.F., Windage Heating of air passing throgh labyrinth seals, Proeedings of the International Gas Trbine and Aeroengine Congress and Exposition, 994, 94-GT-056 [3] Hütte, Akademisher Verein, Des Ingeniers Tashenbh, 955, 8 th Edition, erlin: W. Ernst & Sohn [4] Stoff, H., Algebraishe erehnng von integralen Kenngrößen für die inkompressible Strömng in einer Labyrinthdihtng, Forshng im Ingenierwesen, 988 Vol. 54, pp. 9-3 [5] Polkowski, J.W., Trblent Flow etween Coaxial Cylinders With The Inner Cylinder Rotating, J Eng Gas Trbines and Power, 984, pp [6] Deneke, J., Färber, J., Dllenkopf, K., and aer, H.- J., Dimensional Analysis and Saling of Rotational Seals, Proeedings of ASME Trbo Expo, 005, GT [7] Yan, X., Li, J., Song, L., and Feng, Z., Investigations on the disharge and total temperatre inrease harateristis of the labyrinth seals with honeyomb and smooth lands, J Trbomahinery, 009, Vol. 3, pp. -8 [8] Yan, X., Li, J., and Feng, Z., Effets of inlet preswirl and ell diameter and depth on honeyomb seal harateristis, J Eng Gas Trbines and Power, 00, Vol. 3, pp. -3 [9] Nayak, K.C., and Dtta, P., Effet of rb-grooves on leakage and windage heating in straight throgh labyrinth seals, ASME Aepted Mansript, 05 [0] He, K., Li, J., Yan, X., and Feng, Z., Investigations of the onjgate heat transfer and windage effet in stepped labyrinth seals, Int J Heat and Mass Transfer, 0, Vol. 55, pp [] Shlihting, H., Grenzshiht-Theorie, G. ran, 958 [] Cremanns, K., Roos, D., Heker, S., Dmstorff, P., Almstedt, H., and Msh, C., Effiient Mlti-Objetive Optimization of Labyrinth Seal Leakage in Steam Trbines ased on Hybrid Srrogate Models, ASME Trbo Expo, 06, GT [3] Menter, F.R., Two-Eqation Eddy-Visosity Trblene Models for Engineering Appliations, AIAA Jornal, 994, Vol. 3, pp Copyright 07 by Siemens AG