Failue of Engineeing Mateials & Stuctues Code 12 UET TAXILA MECHNICAL ENGINEERING DEPARTMENT Stess Distibution of the Gas Tubine Blade Mohammad Javed Hyde 1 and Hafiz Laiq-u-Rehman 2 1 Pofesso and 2 JE Lectue, Depatment of Mechanical Engineeing, PIEAS, Islamabad ABSTRACT The vaiations of diffeent paametes such as Tempeatue (T), Pessue (P), Velocities (v), Mach No. (M a ), Degee of eaction (Λ), Flow coefficient (Φ) etc. on the blade passage has been pesented. These calculations wee done fo a pessue atio of 6 and at vey high velocities which ae usually associated with the gas tubines. The stess distibution due to the flow of gases was analyzed and the impact of flow gases is consideed. An analysis of gas tubine blade was pefomed to detemine the egions of maximum stess and moment which occu on a typical gas tubine engine at vaiable otational speeds. The esults document the effect of velocities, pessue, tempeatues and Mach numbes etc. on the blade pofile, the distibution of stesses and the moments. INTRODUCTION Ove the past hunded yeas, aicaft and powe geneation gas tubine designes have been tying to incease the pessue atio of gas tubine and to pemit woking at elevated tempeatues. High values of tempeatues not only incease the isentopic efficiency and thust, but also educe the specific fuel consumption. Unfotunately, this feedom is devastated by the mateial limitations and also diffeent design paametes like Flow coefficient (Φ), Degee of eaction (Λ), Blade loading coefficient (Ψ) and mass flow ate (m) etc [1]. To satisfy all the paametes and pevent failue of tubine blades fom disk bust phenomena caused mainly by the excessive otational speed (RPM), all these paametes need to be incopoated in the design phase of the blade. In gas tubines the ai fist comes into the compesso followed by the combustos and finally comes into the tubine in the fom of high tempeatue buned gases. A pat of the enteing ai into the compesso is used in the cooling of the blades to educe the themal stesses geneated in the blades, while the emaining pat of ai comes in tubine [2].
Mohammad Javed Hyde and Hafiz Laiq-u-Rehman FEMS (2007) 12 80 In addition to the high tempeatues, ecent measuements in actual gas tubine engines have shown the flow exiting the combusto to be highly tubulent. Thus in designing with film cooling, matching engine-epesentatives and fee-steam tubulence levels has become impeative. Selection of mateial and opeations to be pefomed on blade manufactuing has also become citical [2]. PRESENT STUDY Until now the pocedue adapted by the eseaches is to select a seies of NACA blade pofile accoding to thei equiement but in this case the emphasis will mainly be upon the fomation of blade pofile. Once all the paametes ae calculated satisfying the necessities, yet the big poblem is to daw the pofile optimally. Fo this a blade pofile is geneated fo simplicity a two dimensional pofile is consideed. The analytical calculations ae then compaed to the softwae TURBN [1] and they ae found in accodance with each othe. All the paametes have been calculated fo two stage axial flow gas tubine. The pofile consideed is fom fist stage oto section and analysis has been pefomed. Reason fo using two dimensional flow is the blade of fist stage is vey small and the twist in the blade is minimal. The esults may not be matching with the values calculated analytically mainly due to the consideation of two dimensional flow. Anothe eason fo not been able to pefom thee dimensional flows is the technology limitations. Even two dimensional flow needs numbe of elements to be in thousands fo meshing and poblem will be compounded dastically if thee dimensional flow is consideed. Thee dimensional flows may need to be pefomed on paallel computing as it demands moe pecise mesh and pocessing speed. The paametes which have been calculated ae listed in Table 1. Table 1. Geometical Data Rotational speed (RPM) 24,000 Mass flow ate (kg/sec) 10 Inlet tempeatue to blade (K) 1100 Outlet tempeatue to blade (K) 872.5 Inlet pessue to blade (kpa) 608 Outlet pessue fom blade (kpa) 199.3 Ai inlet angle of Tubine (Degee) 0 Ai outlet angle of Tubine (Degee) 43.9 Inlet velocity to blade (m/sec) 253 Outlet velocity fom blade (m/sec) 271 Degee of eaction 0.65 Flow coefficient 1.02 Blade loading coefficient 2 Mean adius (m) 0.15 This data is fo the two stages of the axial flow tubine. The analysis has been pefomed on the oto blade and data fo the second stage oto section is given in Table 2. The esults obtained fom TURBN [3] ae in accodance with the analytical esults as mentioned in Table 2 and hence countechecks the methodology. Fom these esults one can get some moe useful data which will be helpful in designing blade pofile includes chod length, pitch and height of the blade etc. All esults obtained ae mentioned in Figs.1 & 2.
Mohammad Javed Hyde and Hafiz Laiq-u-Rehman FEMS (2007) 12 81 Table 2. Geometical Data fo Fist Stage Roto Blade Hub Radius (m) 0.138 Mean Radius (m) 0.15 Tip Radius (m) 0.162 Tempeatue at the mean adius of the blade (K) 892 Pessue at the mean adius of the blade (kpa) 228.7 Mach Numbe at the mean adius of the blade 0.666 Ai inlet angle of Tubine (Degee) 0 Velocity at the mean adius of blade (m/sec) 384 Flow Aea at the mean adius (m 2 ) 0.0227 Height of the blade (cm) 2.4 Flow coefficient 1.02 Blade loading coefficient 2 Degee of Reaction 0.23 Figue 1. Stage data fo two stages Axial flow tubine [3] Figue 2. Results obtained fom the softwae [3]
Mohammad Javed Hyde and Hafiz Laiq-u-Rehman FEMS (2007) 12 82 Figue 3. Coss-sectional view of two stage Axial flow tubine [3] The blade has also been geneated in the softwae and all of its equied paametes have also been calculated. The poblem is that to daw the pofile moe pecisely and accuately. The liteatue fo dawing a blade pofile is not available. Yet an attempt has been made to daw it in designing softwae on the basis of calculated values and then analyze it in softwae. Fig 4. shows the blade pofile which is dawn into the softwae and all the paametes have also been listed. Stess Calculations Figue 4. Blade pofile [3] Many kinds of stesses do come into play when it comes to tubo machiney especially tubine whee the tempeatue changes have also become vital. The impotant stesses in the designing of gas tubine include Themal stesses, Centifugal stesses and Ceep phenomena. Pime concen of this pape is to calculate the stess distibution in gas tubine.
Mohammad Javed Hyde and Hafiz Laiq-u-Rehman FEMS (2007) 12 83 Themal Stesses These stesses have consideable impact duing the tansient phase when the machine is tuned on. The tempeatue gadient is enomous at the stat like duing the take off of flight. One can easily undestand that the tempeatues in tubine ae quite significant than compesso. So the themal stesses play a vital ole when it comes to the tubine to withstand h σ 1 1 t = α E Td () Td () 2 2 h 0 0 (1) h 1 1 σt θ = αe Td () + Td () T 2 2 h 0 0 (2) Table 3. Themal Stess distibution of disk at diffeent values of adii Radius (m) Radial Stess Distibution (MPa) Tangential Stess Distibution (MPa) 0 286.16 286.16 0.005 274.43 262.70 0.01 262.70 239.25 0.015 250.98 215.79 0.02 239.25 192.34 0.025 227.52 168.88 0.03 215.79 145.43 0.035 204.06 121.97 0.04 192.34 98.51 0.045 180.61 75.06 0.05 168.88 51.60 0.055 157.15 28.15 0.06 145.43 4.69 0.065 133.70-18.76 0.07 121.97-42.22 0.075 110.24-65.68 0.08 98.51-89.13 0.085 86.79-112.59 0.09 75.06-136.04 0.095 63.33-159.50 0.1 51.60-182.95 0.105 39.87-206.41 0.11 28.15-229.87 0.115 16.42-253.32 0.12 4.69-276.78 0.122 0.00-286.16 such dastic conditions. One assumption is made while calculating the themal stesses is that the tempeatue is changing linealy i.e. T=T o +ΔT(/ h ). Eqs. 1 and 2 [4] ae used to calculate the adial and tangential stess distibution in the disk. E and α show the Modulus of
Mohammad Javed Hyde and Hafiz Laiq-u-Rehman FEMS (2007) 12 84 Elasticity and coefficient of linea themal expansion fo high stength Nickel alloys at coesponding tempeatues. Table 3 shows the themal stess distibution of disk at diffeent values of adii which clealy indicates that both have maximum magnitude at = 0. Centifugal Stesses Centifugal stesses depend upon the size of the oto and the otational speed of the oto. Equation 3 [4] is used fo this which shows A b as its aea of inteest at the equied adius fom the cente, ρ shows the density of the mateial, A h shows the aea at the hub and ω epesents the angula speed. Equation 4 [4] shows the moe simplified fom of the equation 3 in which all the paametes ae aleady calculated. This shows that stess is diectly popotional to the ρaω 2 and if the blade is tapeed linealy then the magnitude of the stess can be educed consideably. Coss-sectional aea of flow is shown by A. σ t Fc 2 Ab c = d A = ρω (3) h A h h 2 ρω A 2 A t 1 σ c = 2 1 1+ (4) 4π 3 A h h 1+ t Afte simplifying the expession the atio of σ c /ρ is calculated in tems of A N 2 and then fom gaph [4] the values of stess can be calculated fo Nickel based alloys which ae used fo the tubine blades. The distibution of centifugal stess is given in the Table 4 which clealy indicates that the magnitude of centifugal stesses ae educed to half of its oiginal value if thee is no tapeing (i.e. A t = 0 athe than A h = A t ). Table 4. Centifugal Stess distibution with aea change A t /A h Centifugal Stess Distibution (MPa) 1 199.09 0.9 189.14 0.8 179.18 0.7 169.23 0.6 159.28 0.5 149.32 0.4 139.37 0.3 129.41 0.2 119.46 0.1 109.50 0 99.55
Mohammad Javed Hyde and Hafiz Laiq-u-Rehman FEMS (2007) 12 85 Stength to Weight Ratio Stength has also been calculated fo 1% ceep fo 100 hous fom gaph [4] and is found to be 48.26 MPa. Similaly the stength to weight atio is found to be 58.6 MPa which is also found fo 1% ceep fo 100 hous fom gaph [4]. These two values ae the maximum possible values below which the tubine can un without any fea of disk bust phenomena. CONCLUSIONS All the calculations show that the tends of the esults ae in accodance qualitatively with the esults obtained fom the softwae. Howeve same may not be tue when it comes to quantitative analysis. One of the pime easons fo this is the assumption of two dimensional flow athe than thee dimensional flow. The othe pime facto which has ceated hindance is the technology limitations. It is quite obvious that the equiement fo thee dimensional flow will be much moe than simple two dimensional flow. Yet two dimensional flow gives good appoximations. This wok also eveals that the value of centifugal stess can be contolled by just simply tapeing the blades and the twist in the blade can incopoate the moments which ae developed in the blade. One main thing is that the path fo satisfying all the paametes within a given specified egion is also vey difficult to contol. Since all the paametes ae intedependent so a small change in one paamete may spoil all the calculations. So gaphs have been dawn to see the intedependencies of these and then to finalize the values. REFERENCES 1. Hafiz Laiq-u-Rehman, Design and Analysis of Tubine Blade, Thesis, Depatment of Chemical and Mateials Engineeing, PIEAS, 2006. 2. Hyde, M. J., Rehman H. L.U., (2007) Design and Analysis of Tubine Blade using ANSYS-10, IBCAST, Islamabad. Pakistan. 3. Mattingly, J.D., Heise, W.H. (2002) Ai Caft Engine Design, 2 nd edition, AIAA Education Seies 4. Mattingly, J.D. (1996) Elements of Gas Tubine Populsion, Intenational edition, McGaw Hill.