Weight Optimization of Turbine Blades - Technical Paper

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This technical paper from Altair presents a study to minimize the weight of turbine blades while maintaining performance characteristics. Optimizing turbine blades leads to reduced stresses during operation resulting in increased component life.

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Weight Optimization of Turbine Blades - Technical Paper

  1. 1. Weight Optimization of Turbine Blades J.S. Rao Chief Science Officer, Altair Engineering Mercury 2B Block, 5th Floor, Prestige Tech Park, Sarjapur Marathahalli Outer Ring Road, Bangalore, Karnataka, 560103, India js.rao@altair.com Bhaskar Kishore Project Engineer, Altair ProductDesign Mercury 2B Block, 5th Floor, Prestige Tech Park, Sarjapur Marathahalli Outer Ring Road, Bangalore, Karnataka, 560103, India bhaska.chirravuri@altair.com Vasantha Kumar Project Manager, Altair ProductDesign Mercury 2B Block, 5th Floor, Prestige Tech Park, Sarjapur Marathahalli Outer Ring Road, Bangalore, Karnataka, 560103, India vasanthakumar.mahadevappa@altair.comwww.altairproductdesign.comcopyright Altair Engineering, Inc. 2011
  2. 2. www.altairproductdesign.comAbstractOptimization of aircraft structures and engines for minimum weight has become important inthe recent designs. Topology optimization of airframe structures, wings, and fuselage … isnow practiced since last 3-4 years to reduce weight considerably in ribbed members, rotatingstructures in engines is of much more recent origin.Advanced engine rotating components such as blades and disks operate as globally elasticbut locally plastic structures. The shape of the notch in these structures where yield occurscan be optimized to reduce peak strain levels considerably that can significantly increase lifeof the component.In addition, designers have been practicing to remove some material in the blade platformarea by analysis. This weight removal can be optimized to obtain maximum reduction withoutcompromising the structural integrity. This procedure is illustrated in this paper by using twooptimization codes, Altair OptiStruct for linear structures and Altair HyperStudy for nonlinearstructures using Ansys platform as the main solver. Using this procedure nearly 10% weightreduction is achieved.1.0 IntroductionBladed Disks are most flexible elements in steam and gas turbines used in land based andaerospace applications. While the average stress in the mating areas of these bladed disks isfully elastic and well below yield, the peak stress at singularities in the groove shape canreach yield values and into local plastic region. Last stage LP turbine blades and first stage LPcompressor blades are the most severely stressed blades in the system. Usually these are thelimiting cases of blade design allowing the peak stresses to reach yield or just above yieldconditions. Failures can occur with crack initiation at the stress raiser location andpropagation, two cases can be cited. The last stage blades in an Electricite de France B2 TGSet failed in Porcheville on August 22, 1977 during over speed testing Frank (1982). OnMarch 31,1993 Narora machine LP last stage blades suffered catastrophic failures, see Rao(1998). These blades have stresses well beyond yield. On Narora machine blade, initial fullyelastic analysis has shown a peak stress value 3253 MFa though the average stress is only318 MFa. An elasto plastic analysis for the same case showed that the peak stress is 1157MFa well beyond the yield. While it is not possible to eliminate the yield and keep the structurefully elastic to achieve the last stage blades in limiting cases, it will be advisable to achieve theyield conditions to be as low as possible. Invariably all the earlier long blade designs in laststage LP turbines or first stage LP compressors operate in local plastic regions.Until recently, the dynamic stress field under nonlinear conditions is determined using energymethods and one dimensional beam models as given by Rao and Vyas (1996). A seriousdisadvantage in this approach is the inability to model the stress field in the regions ofdiscontinuities or stress raisers. Todays commercial finite element codes can handle largemesh sizes and can be used as solvers not only for an accurate assessment of the stress andstrain field Rao et. al., (2000) but also for applicationsCopyright Altair Engineering, Inc., 2011 2
  3. 3. www.altairproductdesign.comin optimization.The shape optimization in recent years depended on determining strain energy density andbased on the location where it is high, different shapes were chosen and models aregenerated. Rao (2003) discussed these developments from an industry perspective. Becausethe problem is highly nonlinear due to centrifugal stiffening and spin softening, considerabletime is taken to achieve an optimized root.Optimization has become a necessity in the recent years to achieve an optimal design instress or strain, stiffness and weight etc. In earlier practices, dedicated codes are developedto achieve a specific optimization problem. For example, Bhat, Rao and Sankar (1982) usedthe method of feasibility directions to achieve optimum journal bearings for minimumunbalance response.OptiStruct (2003) has been developed recently to perform linear structural optimization andsuccessfully applied for topology, topography, gauge and shape optimizations of automotiveand airframe structures, e.g., Schuhmacher (2006), Taylor et. al., (2006) discussed the weightoptimization achieved in aircraft structures. HyperStudy (2003) is a multi-purpose DOE/Optimization/ Stochastic tool used to perform wide cross-section of optimizations in CFD, HeatTransfer, Structures or multi physics problems using available commercial code platforms.With additional advances in mesh morphing techniques, HyperMesh (2003), it has becomesomewhat easier in shape optimization.Advanced engine rotating components such as blades and disks operate as globally elasticbut locally plastic structures. The shape of the notch in these structures where yield occurscan be optimized to reduce peak strain levels considerably that can significantly increase lifeof the component. In advanced military aircraft engines the weight removal can be a majorobjective even if it is small. This paper illustrates shape and weight optimization in the bladeroot region.2.0 Shape Optimization of a Steam Turbine Blade Root NotchThe Bladed Disk considered has 60 pre-twisted blades each with a height of 290 mm placedon the disk with the bottom of the blade root at a radius of 248 mm from the axis of the rotor.Asector of rotor disc is modeled to make use of cyclic symmetry condition. Fig. 1 shows the 3-D finite element model having 8 noded brick elements with finer mesh in all the critical regionsaround the singularities in the dovetail root fillet regions with 2 to 3 layers of elements and sizeas low as 0.235 mm. The mesh shown in Fig. 1 consists of 305524 elements and 344129nodes.Baseline AnalysisBefore attempting a shape optimization of the given root, a base line stress analysis is firstcarried out. For this purpose the blade along with disk effect is considered by modeling a 1/60sector of the disk with one blade and using cyclic symmetry boundary conditions applied onboth the partition surfaces as shown in Fig. 1. The common nodes on the pressure faces atsix positions, shown in Fig. 1, where the load transfer between blade and disc takes place areCopyright Altair Engineering, Inc., 2011 3
  4. 4. www.altairproductdesign.comjoined together to make it as a single entity. The blade and disc are assumed to be made upof same material with Yield stress 585 MPa, Youngs Modulus 210 GPa, Density 7900 Kg/m 3and Poissons Ratio OJ. Figure 1: Bladed Disk Model Showing the FE MeshElastic AnalysisAn elastic stress analysis is conducted for a centrifugal load at full speed 8500 RPM, usingANSYS solver (2004). The Von Mises elastic stress field near the root region is shown in Fig.2. The root fillet in the first landing area experiences a severe stress of 1825 MPa at node153608 well beyond Yield 585 MPa, with an average sectional stress 256 MPa. Stresscontour beyond yield is shown to be spread across 3 elements over a depth of 1.22 mm. Figure 2: Von Mises Stress in Elastic domain at 8500 RPMElasto Plastic AnalysisCopyright Altair Engineering, Inc., 2011 4
  5. 5. www.altairproductdesign.comThe hardening property of the material in the plastic region is given in Fig. 3. The elasto-plastic analysis result for the von Mises stress is given in Fig. 4. The root fillet nowexperiences a peak Von Mises stress 768 MPa at a node 176017 in the same region which isbeyond the yield value 585 MPa. The peak stress value has dropped considerably from theelastic analysis result 1825 MPa to a value 768 MPa just above the yield.The peak strain observed at the node 153608 in the same region closer to peak stresslocation is 0.0153. Figure 4: Material hardening characteristic in the plastic region Figure 4: Results of Elasto-Plastic analysis at 8500 RPMCopyright Altair Engineering, Inc., 2011 5
  6. 6. www.altairproductdesign.com3.0 Shape OptimizationThe peak stress in the root region being plastic, the strain gets hardened while stress relaxesdue to yielding. An optimization for minimum peak stress is carried out that will substantiallydecrease plastic strain. With decreased local strain, life gets enhanced.HyperStudyHyperStudy can be applied in the multi-disciplinary optimization of a design combiningdifferent analysis types. Once the finite element model and shape variables are developed, anoptimization can be performed by linking HyperStudy to a particular solver of choice that caninclude nonlinear analyses.Global optimization methods used in HyperStudy use higher order polynomials to approximatethe original structural optimization problem over a wide range of design variables. Thepolynomial approximation techniques are referred to as Response Surface methods. Asequential response surface method approach is used in which, the objective and constraintfunctions are approximated in terms of design variables using a second order polynomial. Onecan create a sequential response surface update by linear steps or by quadratic responsesurfaces. The process can also be used for non-linear physics and experimental analysisusing wrap-around software, which can link with various solvers.Optimization through HyperStudyHere, HyperStudy is linked with ANSYS solver used in base line analysis. Shape optimizationis carried by using the baseline model, having the cyclic symmetry boundary conditionsimposed on the disc, with the objective to minimize the peak stresses. Shape variables aregiven in Table 1, as depicted in Fig. 5. These parameters are taken as the design variables inthe optimization problem. Table 1: Shape Variable DefinitionsCopyright Altair Engineering, Inc., 2011 6
  7. 7. www.altairproductdesign.com Figure 5: Parameters used for defining the shape variablesThe details of mesh are given in Fig. 6 which is morphed with the parameters as continuousvariables using HyperMesh. Figure 6: Morphed Mesh for the Design VariablesCopyright Altair Engineering, Inc., 2011 7
  8. 8. www.altairproductdesign.com Figure 7: Shape Optimization in 21 IterationsCopyright Altair Engineering, Inc., 2011 8
  9. 9. www.altairproductdesign.com Figure 8: Optimized ShapeThe objective function and shape variables during the optimization process are given in Fig. 7and the final optimized shape is shown in Fig. 8. Table 2 gives the optimized shape comparedwith the base line. Table 2: Comparison of Optimized Shape with BaselineMaximum stress has decreased marginally from 768 to 746 MPa by 22 MPa (2.86%) frombaseline elastoplastic analysis for 8500 RPM; however the peak plastic strains reduced from0.0153 to 0.01126 by 26.4%. This is the major advantage in optimization for a blade rootshape.4.0 Weight OptimizationShape optimization was discussed in the previous section where the main aim is to increaselife when the blades are subjected to local plastic conditions. If the local plastic conditions areto be avoided, one may have to sacrifice the blade length so as to decrease the centrifugalloads with a corresponding loss in extraction of power from the turbine. The case of militaryaircraft engines, on the other hand, is different; here the life can be limited, but weight is anCopyright Altair Engineering, Inc., 2011 9
  10. 10. www.altairproductdesign.comimportant criterion. Usually considerable material sits near the platform region taking very littleload and can be easily removed without endangering the structural integrity. Here, such aweight optimization problem is illustrated.LP Compressor Blade for Weight Optimization Fig. 9 shows the CAD model of a typicalaircraft engine LP compressor blade made of a Ti-alloy; Mass Density = 4.42x10-9N.sec2/mm4, Poissons ratio = 0.3, Youngs modulus = 102 GPa, Yield strength = 820 MPa. Figure 9: CAD Model ofA LP Compressor Bladed DiskThe blade separated from the disk is shown in Fig. 10. The FE model of the disk is shown inFig. 11. It has 106066 Solid 45 elements with 121948 nodes. The FE model of the blade isgiven in Fig. 12 with 46970 Solid 45 elements and 41811 nodes. Loads and boundaryconditions are given in Fig. 13.The nonlinear material property of the bladed-disk is shown in Fig. 14.Copyright Altair Engineering, Inc., 2011 10
  11. 11. www.altairproductdesign.com Figure 10: CAD Model of Blade Figure 11: FE Model of DiskCopyright Altair Engineering, Inc., 2011 11
  12. 12. www.altairproductdesign.com Figure 12: FE Model of Blade Figure 13: Loads and Boundary ConditionsCopyright Altair Engineering, Inc., 2011 12
  13. 13. www.altairproductdesign.com Figure 14: Material Stress-Strain CharacteristicsBaseline ResultsThe baseline results are given in Figs. 15 and 16 for the disk and blade respectively.The peak stress in the disk is 787 MPa below the yield strength of the material. The maximumvalue of stress in the blade is 721 MPa.OptimizationHyperStudy is used to optimize the blade for weight reduction by limiting the peak stress tothe yield value, 820 MPa in the blade-disk system. Ansys is the solver used to determine theelasto-plastic stress condition with HyperStudy calling Ansys for optimization.Copyright Altair Engineering, Inc., 2011 13
  14. 14. www.altairproductdesign.com Figure 15: Disk Baseline Stress Results Figure 16: Blade Baseline Stress ResultThe blade root and shank have considerable regions of stress well below yield and a baselinefor optimization is chosen as given in Fig. 17. As shown, 8 holes with radius R=1.75 nun areprovided in the blade root and two cutouts in the shank are allowed to reduce the weight. Fig.18 gives the cutout proposed in the shank. The blade root in Fig. 18 originally without anycutouts was 7890.34 mm3. The objective function is chosen to be this volume and it wasminimized subject to the condition that the peak stress is limited to the yield value, namely820MPa.Copyright Altair Engineering, Inc., 2011 14
  15. 15. www.altairproductdesign.comFig. 19 gives the design variables chosen; the front shank has Dl=1.1, Wla=4.75, Wlb=13.94nun, while the rear shank D2-1.1, W2a=4.44, W2b=13.64 nun. Table 3 gives the range ofdesign variables allowed in optimization. Figure 17: Baseline for Weight Optimization Figure 18: Baseline Root Region of the BladeCopyright Altair Engineering, Inc., 2011 15
  16. 16. www.altairproductdesign.com Figure 19: Design Variables on the Front Shank Table 3: Range of Design VariablesFig. 20 gives the objective function for minimum volume during optimization; In 16 steps theresult was achieved. The objective function value decreased from 7890.34 to 7098.93 mm3,i.e., a reduction of 10.03%.The progress of the design variables in this process is shown in Fig. 21. Optimum designvariables are given in Table 4.Fig. 21 and 22 give the optimized stress results for the disk and blade respectively. In the disk,the peak stress increased from 787 to 810 MPa, while in the blade, the stress increased from721 to 798 MPa.Copyright Altair Engineering, Inc., 2011 16
  17. 17. www.altairproductdesign.com Figure 20: Objective Function, Volume of Blade Root Figure 21: Design Variables in OptimizationCopyright Altair Engineering, Inc., 2011 17
  18. 18. www.altairproductdesign.com Table 4: Optimized Design Variables Figure 22: Optimized Disk Stress ResultCopyright Altair Engineering, Inc., 2011 18
  19. 19. www.altairproductdesign.com Figure 23: Optimized Blade Stress ResultThe weight reduction in the root region achieved is 10.03%. This will be considerablereduction in the bladeddisk stage of this compressor. Such a reduction can be achieved in allcompressor and turbine stages for minimum weight objective.5.0 ConclusionsIn this paper turbomachinery blade optimization is performed to increase life and minimizeweight.Shape optimization is carried out in the peak stress regions to determine the most appropriateshape of the blade root in the stress raiser location. Peak stress was the objective functionand the shape was varied with several variables in the region. This optimization showed thatthe local strain can be reduced considerably by as much as 26%. This reduction will havesignificant influence on the life of the bladed disk.Next a case of weight optimization of the blades is considered. In the root region where thereis a considerable material with less stress load distribution, several holes and cutouts in theshank region are used as design variables. The weight of the blade root region where thecutouts are made is taken as the objective function. The shank cutouts and the holes in theCopyright Altair Engineering, Inc., 2011 19
  20. 20. www.altairproductdesign.comroot are used as design variables. The root region could be optimized to reduce weight by asmuch as 10%.6.0 AcknowledgementsThe authors are thankful to Altair Engineering India for their support.7.0 ReferencesANSYS, (2004) Release 9.0 Documentation, Ansys Inc., USABhat, R B., Rao, J S and Sankar, T S, (1982), Optimum Journal Bearing Parameters forMinimum Rotor Unbalance Response in Synchronous Whirl, Journal of Mechanical Design,TransASME, v.104, p.339Frank, W (1982), Schaden Speigel, 25, No.1, 20HyperMesh, (2003) Users Manual v7.0, AltairEngineering Inc., Troy, MI, USAHyperStudy, (2003) Users Manual v7.0, AltairEngineering Inc., Troy, MI, USAOptiStruct, (2003) Users Manual v7. 0, Altair Engineering Inc., Troy, MI, USARao, J S. (1998), Application of Fracture Mechanics in the Failure Analysis of A Last StageSteam Turbine Blade, Mechanism and Machine Theory, vol. 33, No.5, p. 9Rao, J S. (2003), Recent Advanced in India for Airframe & Aeroengine Design and Scope forGlobal Cooperation, Society of Indian Aerospace Technologies & Industries, 11th AnniversarySeminar, February 8, 2003, BangaloreRao, J. S. and vyas, N. S (1996), Determination of Blade Stresses under Constant Speed andTransient Conditions with Nonlinear Damping, J of Engng. for Gas Turbines and Power, TransASME, voL 116, p. 424Rao, J S., et. al. (2000), Elastic Plastic Fracture Mechanics of a LP Last Stage Steam TurbineBlade Root, ASME-2000-GT-0569Schuhmacher, G (2006), Optimizing Aircraft Structures, Concept to Reality, Winter Issue, p.12Taylor, R. M, et. al.(2006), Detail Part Optimization on the F-35 Joint Strike Fighter, AIAA2006-1868, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and MaterialConference, Newport, Rhode Island.Copyright Altair Engineering, Inc., 2011 20

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