A turbine disc plays a significant role in gas turbine. The disc on which blades are mounted transmitting this motion holds a key point to better efficiency of gas turbine. Thus more focus should be given to the design of turbine disc.
Gas turbine discs are normally operated at high temperatures. Hot gases contact the blades and the rim of the turbine rotor and thus maintain the rim at higher temperature. The temperature gradient at rim and central portion of rotor causes the sources for thermal stresses. The disc is expected to perform well in spite of all stringent conditions.
Also along with performing well, another requirement is weight reduction of disc. As we know increase of structural weight in aircraft costs very high both in terms of operation and maintenance. Also more weight causes more vibration and hence weight becomes a key parameter in design of turbine disc. Weight of the disc depends upon the volume and material of disc. If shape of disc is changed then there is change in material used and this can be used to reduce overall weight of disc.
In this project an attempt has been made to compare two cross-sections of turbine disc. One is the original that is used in jet-engines and another is of uniform thickness. It is obvious that the stresses withstand by uniform thickness disc is more compared to varying cross-section. But it is shown by ANSYS analysis about the significance of using disc with variable cross-section in terms of various stresses withstand by both disc and burst margin of both cross-sections.
LIST OF FIGURES
Fig. No. Name of Figure Page No.
1 Working Model of Gas Turbine Engine 5
2 Turbine Disc 7
3 section view of gas turbine disc model 13
4 Full gas turbine disc model 13
5 Quad Node Element Solid PLANET 182 14
6 Variable Thickness Disc Model with Thermal Boundary 15
7 Uniform Thickness Disc Model with Thermal Boundary 15
8 Temperature Distributions in Variable Thickness Disc 16
9 Temperature Distributions in Uniform Thickness Disc 16
10 Variable Thickness Disc Model With Structural Boundary 17
11 Uniform Thickness Disc Model With Structural Boundary 17
12 Hoop Stress at Speed of 22800 rpm 18
13 Radial Stress at Speed of 22800 rpm 18
14 Von Mises Stress at Speed of 22800 rpm 19
15 Hoop Stress at Speed of 22780 rpm 19
16 Radial Stress at Speed of 22780 rpm 19
17 Von Mises Stress at Speed of 22780 rpm 20
18 Max. Radial Stress Vs. Speed (rpm) Plot 20
19 Max. Von Mises Stress Vs. Speed(rpm) Plot 20
20 Max. Hoop Stress Vs. Speed(rpm) Plot 21
21 Deformation Vs. Speed Plot for Uniform Disc 21
22 Deformation Vs. Speed Plot for Variable Disc 21
23 Hoop Stress for Test Model 22
24 Radial Stress for Test Model 22
25 Burst Gas Turbine Disc 24
26 Burst Margin Vs. Speed (rpm) Plot 28
LIST OF TABLES
Table No. Name of Table Page No.
1 Burst Margin Result for Uniform Thickness Disc 26
2 Burst Margin Result for Variable Thickness Disc 27
INDEX :
SR.NO TITLE PG.NO
GAS TURBINE 8
TURBINE DISC 9
MATERIAL PROPERITIES 9
THERMAL ANALYSIS 10
STRESS ANALYSIS 11
MODELLING OF DISC 12
THERMAL BOUNDARY CONDITION 15
RESULT 16
STRESS ANALYSIS 17
BOUNDARY CONDITION 17
RESULT 18
THEORITICAL VALIDATION OF TEST 22
MODEL
BRUST MARGIN 24
AREA WEIGHTED MEAN HOOP STRESS 25
BRUST MARGIN RESULT 26
CONCLUSION 29
BIBLOGRAPHY 30
GAS TURBINE
.
Working Model of Gas Turbine Engine
Gas turbine, also called a combustion turbine, is a rotary engine that extracts energy from a flow of combustion gas.Gas turbines are described thermodynamically by the Braytoncycle, in which air is compressed is entropically, combustion occurs at constant pressure, and expansion over the turbine occurs is entropically back to the starting pressure.
In order to achieve maximum structural performance, all the critical components of an aircraft gas turbine engine must be operated as close to their optimum design limits as possible.
Because of very high temperature at the rotor disc, it makes the disc and blades very critical components for the mechanical design of the engine.
At normal operating condition, the disc behaves elastically, but circumstances may force pilot to exceed maximum operating speed. At certain speed plastic yielding will initiate at the bore. Further increase in speed causes the yield zone to spread rapidly outward due to lost material properties. This results in large plastic strain in the disc which grows in diameter until burst takes place.
Turbine Disc
Gas Turbine Disc is the major component of the gas turbine engine. The disc is used to support the rotor blades through the fir-tree joint. Disc is one of the most highly stressed critical components in an aero-engine. The forces acting on the disc are the centrifugal force due to high rotational speed, centrifugal force due to blade attachment, thermal load due to varying temperature gradient along radius and axial force due to high velocity gas flow across it. The disc is also subjected to vibration due to non-uniform stress distribution which makes analysis further difficult. All these loads are cyclic in nature
The characteristics required for turbine disc material are high strength and high strength to weight ratio. As the component is in the hot section of the engine it should have good thermal conductivity in order to reduce thermal stress at bore, which is highly stressed region during actual mission. The material used in present day is austenitic nickel-chromium based super alloys.
MATERIALPROPERTIES
Material INCONEL 718
Young’s Modulus 2.09e5 N/mm
Poisson’s Ratio 0.3
Density 8.22e-9 tons/mm
Shear Modulus 8.173e4 N/mm
Thermal Conductivity 11.11e-3 W/mm ??C
THERMAL ANALYSIS
High temperature gradient exists in gas turbine disc, because of high temperature combustion products surrounds it. This affects the material properties considerably and hence temperature dependent material properties are used. Thus thermal analysis is carried out first. Thermal analysis gives the temperature at all locations throughout the disc. Finally these temperatures are used for structural analysis of the turbine disc.
Temperatureat differentlocations
Location Temperature (??C)
TurbineDiscBore
481.50
TurbineDiscRim
510.00
STRESSANALYSIS
Sources ofstress developmentin typicaldisc
Centrifugalload duetoblade attachment.
Thelive stressesduetothe bodycentrifugalforces inthe discitself.
The radialthermal gradient(eithersteadystate ortransient)
The first category ofstressesisdependentofany physicalproperties of the disc,the seconddependsdirectlyupon the densityofthe material and the third dependsupon the modulus ofelasticity and averagecoefficientofthe thermal expansion (both ofwhich vary with temperature) throughout the disc.
Young’s modulusand coefficientoflinearexpansion
Temperature (??C)
Property 20 100 400 500 600 700
Young Modulus (104N/-mm) 20.9 19.5 18.3 17.8 17.0 15.7
CoefficientofLinear expansion(106/ ??C) 12.2 12.8 13.9 14.0 14.5 15.0
Temperature (??C)
Property 21 93 204 316 427 538 649 750
Thermal Conductivity (103W/mm 0C) 11.11 12.41 14.14 16.02 17.95 19.48 21.21 23.09
TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY
STRESS STRAIN RELATIONSHIP
Strain Stress (N/-mm)
At 20??C At 650??C
0.0058 1157.58 863.28
0.01 1245.87 922.14
0.012 1285.11 941. 76
0.016 1314.54 1000.62
0.02 1334.16 1059.48
MODELING THE DISC
InANSYSthe discismodeledusing axis-symmetric method where the cross section onlyis designedinstead ofthe whole disc.The geometry of section is designed such that revolving it about an axis of symmetry produce the solid disc. Analysis ofthe disciscarried out forboth variable and uniformthickness ofthe disc.
Axis-symmetric method is used to analyze Gas Turbine Disc using FEM based analysis softwarepackageANSYSVII. Here onlycross section of the disc is modeled for analysis in both variable thickness and uniform thickness rotating disc. Solid PLANEI82 2-D element is used for meshing geometryofthe disc.Inthe analysis free mesh generation isdoneforvariable thickness disc and mapped mesh is done for uniform thickness disc. As a boundary condition,the discisconstrained in Ydirectionsuch that it isfree toexpand radially aswell ascontract in thickness. Foruniformthickness disc neutral fiber on the disc is constrained in Ydirection whereas, for variable thickness disc only mid node at both sides i.e. at bore and at rim is constrained inYdirection.
Section view of gas turbine disc model
Full gas turbine disc model
ELEMENT USED FOR ANALYSIS
Quad Node Element Solid PLANET 182
PLANE 182 elements were used for meshing the geometry of the disc. It is used for 2-D modeling of solid structures. The element can be used as either a plane element (plane stress, plane strain or generalized plane strain) or an axisymmetric element. It is defined by four nodes having two degrees of freedom at each node translations in the nodal x and y directions. The element has plasticity, hyper elasticity, stress stiffening, large deflection, and large strain capabilities. It also has mixed formulation capability for simulating deformations of nearly incompressible elastic-plastic materials, and fully incompressible hyper elastic materials. The element input data includes four nodes, a thickness (for the plane stress option only), and the orthotropic material properties. The default element coordinate system is along global directions. Element loads are described in Node and Element Loads. Pressures may be input as surface loads on the element faces as shown by the circled numbers on Figure Positive pressures act into the element. The outputs from the elements are nodal stresses, elemental area, nodal temperature etc. The restrictions of these elements are, the area of the element must be non-zero, the element must lie in global x-y plane, and y axis is the axis of symmetry for axis symmetry models. Also axis symmetry model or structure must be created in positive x-y plane.
Temperature Boundary conditions
Here respective temperatures at bore and rim surfaces are applied as mentioned in definition of problem. Other outer faces are assumed to be insulated and hence no heat convection.
Variable Thickness Disc Model with Thermal Boundary Condition
Uniform Thickness Disc Model with Thermal Boundary Condition
Results
As temperature varies throughout the disc due to temperature difference between bore region and outer rim surface thermal analysis will give the temperature distribution along the radius of the disc. This temperature is responsible for thermal stress which makes the structures weak. Hence this effect should be taken in to consideration for structural analysis. This temperature distribution is utilized along with ultimate tensile strength to accommodate for thermal stress in the structural analysis.
Temperature Distributions in Variable Thickness Disc
Temperature Distributions in Uniform Thickness Disc
STRESS ANALYSIS
Loads
‘ Body force due to rotation
‘ Centrifugal force due to blades attachment is 1256.6 KN
‘ Thermal load due to high temperature gradient
Boundary Conditions
Only the cross section of the disc is modeled, using axis symmetric modeling which takes care of whole solid disc. Mid node at bore and rim is restricted in y direction which represents neutral fiber of the disc.
Variable Thickness Disc Model With Structural Boundary Condition
Uniform Thickness Disc Model With Structural Boundary Condition
Results
In this analysis stress distribution throughout the disc is obtained. Hoop Stress and Von-Mises Stress are determined. These values are used for further calculations related to burst margin.
Hoop Stress at Speed of 22800 rpm
Radial Stress at Speed of 22800 rpm
Von Mises Stress at Speed of 22800 rpm
Hoop Stress at Speed of 22800 rpm
Radial Stress at Speed of 22780 rpm
Von Mises Stress at Speed of 22780 rpm
Max. Radial Stress Vs. Speed(rpm) Plot
Von Mises Stress Vs. Speed(rpm) Plot
Max. Hoop Stress Vs. Speed(rpm) Plot
Deformation Vs. Speed Plot for Uniform Disc
Deformation Vs. Speed Plot for Variable Disc
Theoretical Validation of Test Model
Hoop Stress for Test Model
Radial Stress for Test Model
Theoretical Maximum Hoop Stress Formula:
‘(??_??)’_max=1/4 (3+??)’?^2 [b^2+((1-??))/((3+??) ) a^2]
Theoretical Maximum Hoop Stress Formula:
‘(??_r)’_max=1/8 (3+??)’?^2 (‘b-a)’^2
Where,
?? = Poisson’s Ratio =0.3
?? = Density =8.23x’10’^(-9) tons/’mm’^3
?? = Angular Velocity = 1047.1976 rad/sec
a = Inner Radius of the Disc = 50 mm
b = Outer Radius of the Disc = 100 mm
‘(??_??)’_max = Maximum Hoop Stress
‘(??_r)’_max = Maximum Radial Stress
Hoop Stress Calculation
‘(??_??)’_max=1/4 (3+0.3)?? 8.23′??10’^(-9)’??(1047.1976)’^2 [‘100’^2+((1-0.3))/((3+0.3) )’??50’^2]
‘(??_??)’_max=77.89 Mpa
Radial Stress Calculation
‘(??_r)’_max=1/8 (3+0.3)?? 8.23′??10’^(-9)’??(1047.1976)’^2??(100-50)
‘(??_r)’_max=9.28 Mpa
Stress Theoretical Result ANSYS Result
Hoop Stress 77.89 MPa 77.84 MPa
Radial Stress 9.28 MPa 9.31 MPa
BURST MARGIN
Gas turbine disc generally operates at very high rotational speed. The disc possesses enormous energy during its operation. This leads to high hoop stress formation in the disc, which is responsible for the failure. Hence is treated as the most catastrophic mode of failure and no failure up to 122% of maximum operating speed have to be ensured during design of the disc.
Burst Gas Turbine Disc
Generally maximum operating speed is restricted within the elastic limit of the disc material. But it is not necessary that disc will fail as soon as it crosses elastic limit. This means that even in plastic region disc will not fail up to its ultimate tensile stress is reached.
While creep and fatigue are major factors influencing the life of a turbine disc an important first step is to determine a safe maximum operating speed is the precise estimation of the short term burst strength. Experience in aero-engine has proven that smooth operation results when the average tangential stress is restricted by half the burst value. Area Weighted Mean Hoop Stress (AWMHS) is the criterion used to determine burst margin, which presuppose that regardless of rotor shape and material burst will occur when average tangential stress in the rotor becomes equal to ultimate tensile strength of the material. Here other criterions are also proposed to determine burst margin. These are based on the deformation taking place in the disc and the amount of the disc area undergoing plastic state. In the following paragraph we will discuss AWMHS criterion for determining burst.
AREA WEIGHTED MEAN HOOP STRESS
According to this criterion the disc will burst whenever average hoop stress becomes equal to ultimate tensile stress. Here burst margin is nothing but the margin of safety beyond maximum operating speed within which the disc will not fail. Mathematically it is presented by following formula.
BURST MARGIN= ‘(Avg.UTS)/(Avg.HOOP STRESS)
The average hoop stress is calculated from non-linear analysis of turbine disc while considering centrifugal and thermal loads. Here average hoop stress of the disc is determined using followingformula. Here hoop stress for each element is obtained from analysis and is multiplied with respective area of that element to obtain the numerator of the flowingformula.
Average Hoop Stress = (‘_(Element=i)^n”Area*Hoop Stress’)/(‘_(Element=i)^n’Area)
The above formulae are based on AWMHS method. Now as ultimate tensile stress is temperature dependent, temperature for each element is determined and is multiplied with respective area ofthat element to obtain the numerator of the following formula. Denominator is nothing but thesummation ofarea ofallelement commontoboth formulas.
Average UTS= (‘_(Element=i)^n”Area*UTS’)/(‘_(Element=i)^n’Area)
Where,
UTS=[‘UTS’_20-((‘UTS’_20-‘UTS’_650)/630)* (T_i-20) ]
‘UTS’_20 = 1361.628 N/’mm’^2 , ‘UTS’_650 = 1108.53 N/’mm’^2
T_i = Temperature of i^th Element
After finding the average hoop stress and average ultimate tensile stress burst margin can becalculated.Here asmentioned above area, average temperature and averagehoop stress ofeach element must be known. Alsoas speed changes value ofhoop stress changes, sodata must befound and stored for all range ofspeeds. A C++ program is written to find burst margin by making use ofallthese files.
RESULTS AND DISCUSSION
BURST MARGIN RESULT
Burst Margin Result for Uniform Thickness Disc
Sr.No. Speed MaxHS AvgHS AvgUTS MaxRS MaxVS BM
1 10000 440.09 278.10 1169.87 60.32 437.44 205.10
2 11000 505.17 322.69 1169.87 67.16 502.55 190.41
3 12000 576.45 371.52 1169.87 74.69 573.85 177.45
4 13000 653.92 424.59 1169.87 82.92 651.35 165.99
5 14000 737.60 481.92 1169.87 91.80 735.05 155.81
6 15000 827.47 543.49 1169.87 101.41 824.95 146.71
7 16000 923.54 609.30 1169.87 111.69 921.06 138.56
8 17000 959.49 679.37 1169.87 121.88 949.80 131.23
9 18000 979.28 753.67 1169.87 129.55 963.07 124.59
10 19000 992.86 832.23 1169.87 134.08 980.45 118.56
11 20000 1009.00 915.03 1169.87 137.44 1005.00 113.07
12 21000 1046.00 1002.08 1169.87 120.91 1042.00 108.05
13 22000 1155.00 1093.37 1169.87 130.74 1133.00 103.44
14 22750 1184.00 1164.62 1169.87 126.86 1133.00 100.22
15 22760 1184.00 1165.58 1169.87 126.61 1133.00 100.18
16 22780 1184.00 1167.52 1169.87 126.10 1133.00 100.10
Burst Margin Result for Variable Thickness Disc
Sr.No. Speed MaxHS AvgHS AvgUTS MaxRS MaxVS BM
1
10000
435.56
316.04
1171.34
262.75
437.98
192.52
2
11000
491.71
358.59
1171.34
283.52
494.82
180.73
3
12000
553.20
405.20
1171.34
306.27
557.08
170.02
4
13000
620.04
455.86
1171.34
331.00
624.76
160.30
5
14000
692.23
510.58
1171.34
357.71
697.85
151.46
6
15000
769.76
569.34
1171.34
386.39
776.36
143.43
7
16000
852.64
632.17
1171.34
417.06
860.29
136.12
8
17000
940.87
699.04
1171.34
449.70
947.48
129.45
9
18000
955.01
769.96
1171.34
487.35
952.16
123.34
10
19000
1009.00
844.94
1171.34
519.58
968.63
117.74
11
20000
1083.00
923.98
1171.34
520.14
993.74
112.59
12
21000
1107.00
1007.07
1171.34
456.39
1030.00
107.85
13
22000
1192.00
1094.22
1171.34
487.82
1120.00
103.46
14
22800
1300.00
1166.85
1171.34
500.37
1133.00
100.19
Static non-linear analysis is carried out on the two discs to estimate over speed and burst margin based on Area Weighted Mean Hoop Stress Method (AWMHS). Here average hoop stress and average ultimate tensile stress values are used to determine Burst Margin and Over Speed. Values of Burst Margin at different Speeds are tabulated below for both Variable and Uniform thickness disc. Image of hoop stress distribution at bursting speed in both the case is shown below.
Burst Margin Vs. Speed (rpm) Plot
DISCUSSION
From above results we can observe that as speed increases Burst Margin decreases. The technical reason behind this is, as rotational speed of the disc increases, the centrifugal force due to weight of the disc also increases and loads due to blades attachment increase at high speed. This leads to development of high Hoop Stress at bore of the disc. As Hoop Stress increases at bore, it decreases the strength of the disc which leads to the decrease in Burst Margin. From the analysis it is concluded that variable thickness disc possess higher bursting speed than that of uniform thickness disc. As we know increases of structural weight in aircraft costs very high both in terms of operation and maintenance. Here it is to be noted that variable thickness of disc not only reduces overall weight of the disc but also reduces weight of other supporting components of aero-engine. It also helps to reduce vibration effects in aircraft. As the blades are attached to the disc rim we need to provide adequate support for it, which increases mass of disc at rim. This excessive mass at rim slightly decreases the value of burst margin in variable thickness disc. Also it has been observed that at higher speed levels maximum hoop stress shifts from bore to mid portion in the disc which is due to externally applied load on outer rim portion of the disc.
CONCLUSION
From the results of analysis it is found that Hoop Stress and Von-Mises Stress in the disc increases rapidly beyond the speed of 17,000 rpm where, burst margin is found to be 129% of maximum operating speed. Also it is found that disc fails beyond the speed of 22,000 rpm. As per MIL-STD-5007E, it is mandatory to ensure that gas turbine disc should have burst margin not less than 122% of maximum operating speed.
The gas turbine disc, which is critical component of aero-engine, analysed in both variable thickness and uniform thickness of disc in elastic and elastic-plastic states. Loads due to mass of the disc i.e. centrifugal force, due to blades attachment at rim and due to temperature variations are considered. From analysis stress distribution in the turbine disc at different speeds is obtained and is found to be approximately same for both the cases of variable thickness and uniform thickness. Even burst margin calculated by AWMHS for variable thickness disc is also found to be closer to that of uniform thickness disc. Thus the geometry of the disc with varying thickness is found to be optimum as results are compared with disc of uniform thickness. Burst margin and Fatigue life is found to be almost same for both the discs.
BIBLIOGRAPHY
‘"Advanced Mechanics ofSolids",byLSSrinath
‘"Theory ofelasticity", secondeditionbyTimoshenkoand Goodier
‘ "Gas Turbine Theory",fourtheditionbyHenryCohen,GFCRogers and HIHSaravanamuttoo.
‘ "Determination of Elastic stresses in gas turbine disc", by SSMenson
‘"Centrifugal and thermal stress in rotating disc", Journal of
AppliedMechanics
‘"Stresses in rotating disks at high temperature", ASME.Applied
Mechanics,byStanleyThompson
‘"Burst strength ofrotating Disc",byNEWaldren,MJ Percyand
PBMellor
‘ "The Gas Turbine Handbook: Principles and Practices", second editionbyTonyGiampaolo,MSME,PE.