Abstrct LABYINTH SALS DYNAMIC COFFICINTS AND CITICAL SPD SACH BASD ON CHILDS MODL M Wensheng, Hung Hi, Feng Guoqun AVIC Shenyng Aeroengine eserch Institute, Shenyng, Chin Keywords:lbyrinth sels, dynmics coefficients, criticl speed, Childs model Mthemticl method re used to clculte the dynmic coefficients nd Criticl of lbyrinth sels. It is importnt to know the ccurte dynmic coefficients of lbyrinth sels for predicting the instbility of the rotor-sel system. Lbyrinth sel dynmic coefficients t different rdil clernces, pre-swirl rtios, rotor speeds, sel lengths nd dimeters re presented in this pper. Criticl speed t different sel length nd dimeters re lso studied in this pper. Title of Section (e.g. Generl Introduction) Lbyrinth sels re non-contcting nnulr sels, nd re widely used in stem turbines, gs turbines nd gs compressors. The lbyrinth sel hs mny dvntges, such s simplicity, relibility, nd tolernce for high temperture nd high pressure. The lbyrinth sel hs improved over the yers. There were severl mjor stges in the development of methods to study the forces nd dynmic coefficients of the sel: experiments, bulk flow, nd finite volume methods. ch stge led to new understnding bout the performnce nd dynmic chrcteristics of lbyrinth sels. Originlly, most of the work focused upon experimentl dt nd simplified rotordynmic systems. Alford [] studied lbyrinth sel with vrying inlet nd outlet res. He concluded tht when the inlet re exceeds the outlet re, n excittion force is produced tht cuses rotor in the direction of the rottion. Conversely, Alford concluded tht no excittion force would be produced when the outlet re exceeds the inlet re. These conclusions hve unfortuntely resulted in undesirble results in high pressure centrifugl compressors lbyrinth sels. More experimentl work ws crried out by Bencker nd Wchter [], nd they were ble to clculte spring coefficients for the sels. A bulk flow design code for lbyrinth sels ws developed by Kirk [3] nd the results were used to evlute rotor system stbility tht were fvorbly compred to the resulting stbility of compressors on test nd in the field. jkumr nd Sisto [4] more recently performed experiments to determine the circumferentil pressure distributions nd forces within lbyrinth sel. Strting in the mid 980s, more robust methods were brought into use to study the dynmic coefficients of lbyrinth sel. There were two min methods used: bulk flow nd finite volume. Wyssmnn et l. [5] used two control volume pproch to model the flow through lbyrinth sel. The two control volume pproch is simplified pproch to finite volume method. For tht reson, the modeled flow through the sel ws oversimplified nd could only be used for generl comprisons nd trends. hode nd Sobolik [6] used finite difference pproximtion to predict the lekge flow through lbyrinth sel.. Nordmnn [7] got rotordynmmic coefficients of turbine lbyrinth sels by the comprison CFD models nd experiments. Lbyrinth Sel Coefficients This reserch focuses on the stge centrifugl compressor impeller eye lbyrinth sel coefficients. The impeller eye lbyrinth sel is used to reduce lekge nd fcilitte
M wensheng, Hung Hi pressure drop from the high pressure dischrge into the region of lower pressure inlet flow. This is ccomplished by creting flow pth for the working fluid tht converts the pressure hed into kinetic energy. The kinetic energy is then dissipted. The stright lbyrinth cn be divided into two ctegories: tooth-on-sttor nd toothon-rotor. A tooth on rotor lbyrinth sel is shown in Fig. Figure shows tooth on sttor lbyrinth sel with selected nomenclture. Tble nd Tble show the dimensions nd conditions used for the clcultions to be discussed in this pper. This clcultion ssumes the fluid to be n idel gs nd the entire flow to be turbulent. The k-ε model is used for turbulence. Figure Jeffcott rotor-sel system Figure Stright lbyrinth sel dimensions Tble. Lbyrinth Sel Geometric Dimensions Dimension Vlue Dimeter, Ds 50mm dil Clernce, Cr 0.3mm Pitch, Ts 4mm Height, Th 3.5mm Tip width, Tw 0.3mm Number of Teeth 5 Tble. Sel Operting Conditions Dimension Vlue Speed 033PM Inlet Pressure 0.68MP Dischrge Pressure 8.8MP Inlet Temperture 5. ºC Dischrge.ºC Temperture Gs Air Turbulence model k-ε 3 Lbyrinth sels dynmics model Childs formulted bulk flow model using Hirs lubriction eqution, which the linerized forces cting on the rotor generted in sel re: F F x y kxx kxy x c xx c xy x mf x () k k y c c y m y xy xx xy xx The restoring forces re proportionl to displcement, velocity nd ccelertion. A fundmentl reltionship between the totl xil pressure drop nd the men xil gs velocity is: ( ) P V () Where L (3) Cr nd ( ) V defines the inlet pressure drop. It shows tht the inlet pressure drop is greter in the region where the clernce is lrger due to high velocity thn the region where the clernce is smll. Childs formulted the sel dynmic coefficients bsed on Hirs lubriction eqution, which included in the momentum equtions nd the inlet swirl is lso included. The circumferentil velocity of the gs entering the sel is commonly expressed s frction of shft surfce speed (Ω): uc (4) The coefficients re summrized in the following: k k xx P 5 T v 4 4 6 xy 0 e e B B v 0 6 e P T B P T B cxx (7) 6 P T 0 c xy 6 e where v e P 6 mf T (9) f (5) (6) (8)
LABYINTH SALS DYNAMIC COFFICINTS AND CITICAL SPD SACH BASD ON CHILDS MODL 0.5 0.066 c 4b 0.375 (0) VCr () Cr () b c V (3) ( 0.75 ) (4) (5) 4b B 3b (6) B L V 4 Lbyrinth Sel Dynmics Coefficients Study T (7) (8) esults for the lbyrinth sel model of Fig using Childs experimentl conditions [5] re shown in Fig 8. The lbyrinth sel geometric conditions re follows: Sel length is 5. mm, sel dimeter is 50 mm nd rdil clernce is 0.3mm. The results re presented s dynmic coefficients versus rotor speed, pre-swirl, sel length nd lbyrinth sel clernce. The Childs experimentl conditions were ir temperture 300K, ir density.5kg/m 3, nd pressure 8.8 0 6 P. Cross-coupled stiffness is mjor reson of instbility in berings, hence the lbyrinth sel system is more likely to be unstble when the cross-coupled stiffness is greter. It is lso known tht direct dmping cn improve system stbility, hence cross-coupled stiffness nd direct dmping re the min reserch in this pper. Figure 3() shows the reltion of lbyrinth sel rdil clernce nd cross-coupled stiffness for different rotor speeds. otor speed is shown for 5000 rpm nd 0000 rpm. Figure 3() shows tht cross-coupled stiffness will decrese s the lbyrinth sel clernce is incresing. The crosscoupled stiffness decresed shrply when the lbyrinth rdil clernce incresed from 0.mm to mm, but they chnged little when the lbyrinth sel clernce is more thn 0.mm. The sel hs less destbilizing cross-coupled stiffness when lbyrinth sel rdil clernce is more thn 0.mm. Figure 3(b) gives the result for lbyrinth sel cross-coupled stiffness for two different lbyrinth sel clernces plotted versus pre-swirl rtio. The two lbyrinth sel clernces used were 0. mm nd 0.3 mm. This result clerly shows tht the cross-stiffness will increse with higher pre-swirl rtio. Lbyrinth rdil clernce is mde s smll s possible to control lekge in rel mchine, so it is better prctice to mke the lbyrinth system more stble by reducing the pre-swirl rtio with mechnicl or erodynmic swirl brkes. Figure 3(c) show cross-coupled stiffness for three different pressure drops plotted versus rotor speed, the three pressures being 5 0 5 P nd 0 0 5 P. It cn be seen tht crosscoupled stiffness will increse with rotor speed nd lso s the pressure drop increses. Hence system will be less stble s rotor speed nd pressure drop increse. However the dynmics of mchine will be more stble for stiffer shft nd higher criticl speed, so the importnt prmeter to reduce when possible is the pressure drop. Figure 3(d) shows the direct dmping for different lbyrinth sel dimeters plotted versus sel length. Lbyrinth sel length vries from 6 mm to 0 mm, nd the lbyrinth sel dimeters re 00 mm nd 50 mm. Figure 3(d) shows tht the direct dmping will increse s lbyrinth sel length increses nd lso s the lbyrinth sel dimeter increses. From prcticl stndpoint, reduction in dimeter is the importnt method to reduce the destbilizing forces in sel. 3
M wensheng, Hung Hi Figure 3 Lbyrinth sel dynmics coefficients effect fctors () Cross-coupled stiffness versus sel clernce 5 Criticl Speed Study Fig.4 () is rotor-bering-sel system model which include shft, bering, sel disk nd mss disk. The shft length is 560 mm, the shft disk spcing is 00mm. The sel disk is 0 kg nd mss disk is 5 kg in this model. The geometric conditions re shown in the Tb. nd operting conditions re shown in the Tb.. otorbering-sel DyoBes model is shown in Fig.8 (b). It cn clculte rotor-bering-sel criticl speed mode shpe s shown in Fig.5. First-order criticl speed mode shpe is shown in Fig.5 () nd second-order criticl speed mode shpe is shown in Fig.5 (b). (b) Cross-coupled stiffness versus rtio of pre-swirl rtio () otor-bering-sel system dimensions (c) Cross-coupled stiffness versus rotor speed (b) otor-bering-sel system DyoBes model Figure 5 otor-bering-sel system model () First-order criticl speed mode shpe (d) Direct dmping versus sel length 4
LABYINTH SALS DYNAMIC COFFICINTS AND CITICAL SPD SACH BASD ON CHILDS MODL (Sel dimeter=50mm) 6 Conclusions (b) Second-order criticl speed mode shpe Figure 5 otor-bering-sel system criticl speed mode shpe Fig.6 is rotor-bering-sel system criticl speed effect study in different sel length when the sel dimeter is 00mm. Fig.7 is rotorbering-sel system criticl speed effect study in different sel length when the sel dimeter is 50mm. Fig.6 nd Fig.7 shows the sel length effect to first-order criticl speed. Sel length is shown for 6 mm nd 0 mm. The results show tht first-order criticl speed will increse s the sel lenth is incresing. Figure 6 Criticl speed of different sel length (Sel dimeter=00mm) The pper presents the impct of rotor lbyrinth sel dynmic coefficients nd criticl speed by mthemticl method. The sel clernce, pre-swirl rtio, sel length, sel dimeter were vried to determine the effect on compressible flow pttern for the lbyrinth sel dynmics coefficients nd criticl speed. Lbyrinth sel clernce could be incresed to reduce the instbility cused by cross-coupled stiffness. A system will be less stble when rotor speed, pressure, sel length nd sel dimeter re incresing. The lbyrinth sel system cn hve better stbility when the lbyrinth sel clernce is incresing. eferences [] Alford, J. S (965). Protecting turbomchinery from self-excited rotor whirl. Journl of ngineering for Power, v. 87, 333-334. [] Benckert, H. Wchter, J. (980). Flow induced spring coefficients of lbyrinth sels for ppliction in rotor dynmics. NASA CP 33, 89-. [3] Kirk,.G (988). vlution of erodynmic instbility mechnisms for centrifugl compressors prt II: dvnced nlysis. Journl of Vibrtion, Acoustics, Stress, nd elibility in Design, v. 0, 07-. [4] jkumr, C. Sisto, F. (990). xperimentl investigtions of rotor whirl excittion forces induced by lbyrinth sel flow. Journl of ngineering for Gs Turbines nd Power, v. 06, 63-7. [5] Wyssmnn, H.., Phm T.C., Jenny.J. (984). Prediction of stiffness nd dmping coefficients for centrifugl compressor lbyrinth sels. Journl of ngineering for Gs turbines nd Power, v.06, 90-96. [6] hode D.L. Sobolik S.. (986). Simultion of subsonic flow through generic lbyrinth sel. Journl of ngineering for Gs Turbines nd Power, v. 08, 674-680. [7] J. Schettel nd. Nordmnn. (004). otordynmics of turbine lbyrinth sels- comprison of CFD models to experiments. IMCH 8th Interntionl Conference on Vibrtions in otting Mchinery. Figure 7 Criticl speed of different sel length Contct Author mil Address mil: mwensheng980@gmil.com 5
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