Detection and numerical analysis of the most efforted places in turbine blades under real working conditionsTomasz Sadowski ⇑,Przemysław GolewskiLublin University of Technology,Department of Solid Mechanics,Nadbystrzycka 40Str.,20-618Lublin,Polanda r t i c l e i n f o Article history:Received 31October 2011Received in revised form 19February 2012Accepted 29February 2012Available online 24March 2012Keywords:Turbine bladesThermal Barrier Coatings Numerical modeling Crack propagation XFEM methoda b s t r a c tBlades of combustion turbines are elements which transfer an operative energy to an engine rotor.The blade consists of two pieces:a working piece called a profile covered by Thermal Barrier Coating (TBC)and a footer.The most dangerous parts of the blades are subjected to very high stress concentrations.They are situated in the profile section with the footer connection,where the maximum values of bending moments occur resulting from centrifugal forces and pressure of a working medium on the profile sec-tion.In the work we propose an extension of the turbine blade design strategy (in comparison to [5,12,13])by application of submodeling technique to perform more detailed analysis of damage process and pro-gressive fracturing of the most efforted cross sections of the blade.In particular cracking direction of the TBC was analyzed numerically with application of the XFEM technique.The critical values of rotor speeds were estimated at which damage process initiates and further develops.The damage of TBC can lead to destruction of protective covering and exposures the whole turbine blade core (made of alloys)to sudden thermal shock.Ó2012Elsevier B.V.All rights reserved.1.IntroductionDevelopment of super alloys,as material for production of tur-bine blades of combustion engines,took place in second half of twentieth century.The main reason of their use was lack of yield limit decrease with simultaneous increase of operation tempera-ture of the blade work.For _ZS6U alloy,applied for the blade pro-duction,this decrease is not higher than 1%for the temperaturesinterval from 20to 800°C.The blades of jet engines are subjected to extremal working requirements described by the following factors:Àwork environment (high temperature,fuel,oxygenation,solid particles),Àhigh mechanical stresses (acting from centrifugal force [1,3],vibration [2]),Àhigh thermal stresses (e.g.[5–11])(in results of large gradients of temperatures).Therefore designing of the turbine blades are very complex prob-lem,which can be solved partly by application of analytical methods,but numerical one play more significant role.The problem is more complex,when the turbine blade is covered by Thermal Barrier Coat-ing (TBC)and is additionally protected by a cooling channels system, e.g.[5,12].It is also necessary to introduce to the analysis description of the damage processes,which develop during operation.In the present paper analytical methods of stress estimation in the turbine blade were presented as an introduction to solution of the problem.However,because of complex turbine blade shape these methods are not enough in designing process.The aim of the present work is an extension of the numerical methods in the turbine blade design by application of submodeling technique.It allows to perform more detailed analysis of damage process and progressive fracturing of the most efforted places of the turbine blade.In particular the work was concentrated on the profile with the footer connection in order to define direction of damage devel-opment,e.g.cracking of the TBC.The progressive damage was modeled numerically with application of the XFEM technique [4].The critical values of rotor speeds were estimated at which damage process initiates and further develops.The damage of TBC can lead to destruction of protective covering and further exposures the whole turbine blade core (made of alloy)to sudden thermal shock.2.Blade loads of jet-propelled enginesLoads of the blades of whirling machines with axial medium flow can be divided into three principal groups: loads from medium flow, body forces,0927-0256/$-see front matter Ó2012Elsevier B.V.All rights reserved./10.1016/matsci.2012.02.048Corresponding author.Tel.:+48815381386;fax:+48815256948.E-mail address:t.sadowski@pollub.pl (T.Sadowski).thermal loads.Thefirst loads are caused by dynamics offlowing medium around the profiled part of the blade.The body forces include:cen-trifugal forces of the blades(together with elements connected with them)as well as forces caused by springy vibrations of the blades and the whole rotor.The blade,being in the stream of a very hot medium,warms not uniformly.This generates additional forces and internal stresses.The state of stresses,created during the turbine blades opera-tion and in axial compressors are very complex.One can distin-guish the following resistance states:1.Stretching–caused by the centrifugal forces of whirling massesof the blade and bandage.2.Bending–due to medium pressure on the profiled part.3.Bending–as a result of centrifugal forces of the whirling mass of the blade.4.Cutting–due to twist moments caused byflowing medium.5.Cutting–by twist moments due to body forces of the blade.6.Bending–caused by transverse vibration of the blade.7.Cutting–due to twisting vibrations of the working part of the blade.In designing process of the turbine blades we assume,that nor-mal resultant stresses in any transverse section of the bade are equal to(according to superposition rule)an algebraical sum of the normal component stresses due to above specified strength states.We are looking for the most efforted turbine places(cross sections),e.g.where the largest normal or the reduced stresses occur.3.Turbine blade materialFor our investigation we assumed that the turbine blades mate-temperatures from500°C to700°C the small increase of the yield limit was observed in comparison with the room temperature.For the temperature above700°C a decrease of mechanical properties of alloy is visible.4.The analytic method of the state of stress estimation in the most efforted cross section of the blade4.1.Stretching of the bladeThe blade with the length of the working part l([m])is sub-jected to the centrifugal force(Fig.2).Let us denote by c[N/m3] specific weight of material;by–F,F i,F0[m2]cross sections areas of the blade in distances r and r i as well as R0[m]from axis of rota-tion.Moreover angular velocity of the rotor is designated by x [rpm].In the cross-sections(characterized by distances r i and R0)the tensile stresses are equal to:rri¼x2gFiZ lx ic FðR0þxÞdxð1Þr Ro¼x2gFZ lc FðR0þxÞdxð2Þwhere g is a gravitational acceleration[m/s2].Fig.3shows the level of the tensile stress and the centrifugal force in relation to the length of the blade.The extreme value,equal to378MPa,was ob-served at the basis blade.The corresponding rotor angular velocity was equal to30,000r.p.m.and dimensions of the blade approxi-mately equal to:length–60mm,width–21mm,thickness–1.3mm.4.2.Bending of the blade due to centrifugal force286T.Sadowski,P.Golewski/Computational Materials Science64(2012)285–288total moments in the cross section and in relation to axis x and y are:M xd¼cgx2Z R1riFðyriÀy i rÞdr M yd¼cgx2Z R1r iFðxÀx iÞrdrand near the footer of the blade:MðsÞxd ¼cx2R0Z R1R0Fydr MðsÞyd¼cgx2Z R1R0FxrdrThe above defined bending moments along axes x and y,can be decomposed along main central axis x0,y0receiving resultant mo-ment in direction of the axis x0–M x0as well as in direction of the axis y0–M y0.Due to change of the cross section area for any ray va-lue,calculations of bending moments were conducted with the use of tabular method for ten specified values of rays r.The largest bending stresses takes place in points of the cross-section denoted by letters A,B,C,D(Fig.5)and they are equal to:r0gA;B;C;B¼M y0y0x A;B;C;D r00gA;B;C;D¼M x0x0yA;B;C;Dwhere J x0,J y0are the main central moments of inertia of the blade cross section[m4]x A,B,C,D and y A,B,C,D are co-ordinates of points A, B,C,D related to the central main axis[m].5.The numerical method of the stress state calculation in the most efforted places of the bladeThe aim of the numeric simulation was assessment of the most efforted places in the turbine blade to compare obtained results with the analytic method.The assembly consisted of the blade as well as the part of the socket in which the blade was installed.Due to the complicated shape of the blade and the socket a linear tetrahedron elements C3D4were used to create thefinite element mesh for FEA simula-tion with the help of ABAQUS code.The total quantity of thefinite elements was66,222(51,540for the blade and14,682for the sock-et).The simulation was a static type and two types of loads were applied:the rotary speed with value27,000rot/min and the pres-sure applied to the surface of the working part of the blade equal to 0.22MPa.As a results the distribution of Mises reduced stresses was obtained.The simulation confirmed,that the extreme values of stresses are at the level of454MPa(Fig.6)placed in a small dis-tance from the leading edge on the suction side of the blade.The second stage of the numerical simulation consisted in sep-aration from the global model of the blade a volume,where the largest stress concentration occured(creation of the submodel) [14].The new model was divided into partition and a thin protec-tive TBC layer(ZrO2)of thickness about0.3mm was additionally selected.In order to include a damage process in the TBC material model description(e.g.[13])the maximum stress criterion was applied. The loadings for the submodel were obtained from simulation of the global model.To make the mesh offinite elements C3D8R lin-ear hexahedral elements were used;total quantity about104,987. After calculations of the submodel,the same values of displace-ments were received,as in global one.However,the Mises stresses were about18.6%larger in relation to the global model.A several simulations were conducted for different values of the rotor speeds,observing initiation and development of the damage which appeared in the thin layer TBC.The relation between rotor speed and the quantity of damaged elements is presented in Fig.7.6.Final conclusionsThe obtained results lead to the following conclusions:The convergence of results obtained for both models:analytical and numerical was achieved.The maximum of the reduced Misses stresses occured in the basis of blade.Tensile stress and the centrifugal force in relation to the lengthofFig.4.Bending of the blade due to centrifugal force.The normal stress coming from stretching(about378MPa)and bending(about46MPa)has the local maximum in point B (Fig.5)and is equal to424MPa.After taking into account shear stresses the maximum value of the Misses stress are above point B also on the edge of cross section with value454MPa. The submodeling technique,applied in numerical calculations, permitted for creation veryfine thefinite element mesh for detailed analysis of the selected fragment of the turbine blade.In the global model this fragment was described by772ele-ments,meanwhile the submodel possessed104,987elements.This approach allows for more exact calculation of the Misses stress values,which were about18.6%larger in relation to glo-bal model(taking into consideration maximum value).Using the X-FEM technique we assessed the critical threshold of the rotor speed with the turbine blade at the thin TBC layer does not undergo damage.After exceeding of the speed level equal to 26,750rpm,it comes to quick damaging of elements until the speed limit27,500rpm.Then the damage growth is smaller for higher values of the rotor speed.The presented approach of detecting the most efforted places in the turbine blades can be useful in engineering design in order to avoid or at least decrease numbers of expensive experimental tests.AcknowledgmentsThe research leading to these results has received funding from:(1)Financial support of Structural Funds in the Operational Pro-gramme–Innovative Economy(IE OP)financed from the European Regional Development Fund–Project‘‘Modern material technolo-gies in aerospace industry’’,No.POIG.0101.02-00-015/08is grate-fully acknowledged(RT-10:Modern barrier covers on critical engine parts).(2)The European Union Seventh Framework Programme(FP7/ 2007–2013),FP7–REGPOT–2009–1,under Grant Agreement No.:245479.References[1]E.Poursaeidi,M.Aieneravaei,M.R.Mohammadi,Eng.Fail.Anal.15(2008)1111–1129.[2]J.Li,S.T.Lie,Z.Cen,Finite Elem.Anal.Des.35(2000)337–348.[3]L.Chen,Y.Liu,L.Xie,Int.J.Fatigue29(2007)10–19.[4]P.Michlik,C.Berndt,Surf.Coat.Technol.201(2006)2369–2380.[5]T.Sadowski,P.Golewski,Comput.Mater.Sci.50(2011)1326–1335.[6]T.Sadowski,Non-symmetric thermal shock in ceramic matrix composite(CMC)materials,in:R.de Borst,T.Sadowski(Eds.),Lecture Notes on Composite Materials–Current Topics and Achievements,Springer,2008.[7]T.Sadowski,S.Ataya,K.Nakonieczny,Comput.Mater.Sci.46(2009)687–693.[8]T.Sadowski,K.Nakonieczny,Comput.Mater.Sci.43(2008)171–178.[9]T.Sadowski,M.Boniecki,Z.Librant,K.Nakonieczny,Int.J.Heat Mass Transfer50(2007)4461–4467.[10]K.Nakonieczny,T.Sadowski,Comput.Mater.Sci.44(2009)1307–1311.[11]K.Nakonieczny,T.Sadowski,Comput.Mater.Sci.47(2010)867.[12]M.Białas,Surf.Coat.Technol.202(2008)6002–6010.[13]T.Sadowski,P.Golewski,Comput.Mater.Sci.52(2012)293–297.[14]Abaqus6.10Documentation.。
