ISSN 2319-8885
Vol.03,Issue.10
May-2014,
Pages:2200-2004
www.semargroup.org,
www.ijsetr.com
Design and Stress Distribution of First Stage Gas Turbine Rotor Blade
M. WIN LAI HTWE1, DR. HTAY HTAY WIN2
1
Dept of Mechanical Engineering, Mandalay Technological University, Mandalay, Myanmar, Email:[email protected].
2
Dept of Mechanical Engineering, Mandalay Technological University, Mandalay, Myanmar.
Abstract: Gas turbines have an important role in power generation and propulsion unit. Gas turbine technology is used in a
variety of configurations for electric power generation. The gas turbine in its most common from is a rotary heat engine
operating by means of series of processes consisting of air taken from the atmosphere increase of gas temperature by constant
pressure combustion of the fuel the whole process being continuous. Turbine Blades are the most important components in a
gas turbine power plant. A blade can be defined as the medium of transfer of energy from the gases to the turbine rotor. The
turbine blades are mainly affected due to static loads. Also the temperature has significant effect on the blades. In this paper the
first stage rotor blade of the gas turbine is created in SolidWorks software and design calculation is computed by MATLAB
software. The material of the blade is NI-CR alloys. The gas forces namely tangential, axial were determined by constructing
velocity triangles at inlet and exist of rotor blades. The stress distribution due to the flow of gases and the impact of flow gases
are considered. The gas turbine rotor blade was performed to determine the regions of maximum stress and moment which
occur on a typical gas turbine engine at variable rotational speeds. The results document the effect of velocities, pressure,
temperatures and Mach numbers etc. on the blade profile and the distribution of stresses.
Keywords: Design, Gas Turbine Rotor Blade, Stresses, Solidworks, MATLAB.
I. INTRODUCTION
The purpose of turbine technology are to extract the
maximum quantity of energy from the working fluid to
convert it into useful work with maximum efficiency by
means of a plant having maximum reliability, minimum cost,
minimum supervision and minimum starting time. The gas
turbine obtains its power by utilizing the energy of burnt
gases and the air which is at high temperature and pressure
by expanding through the several rings of fixed and moving
blades. The outstanding characteristics of gas turbines, which
make them eminent of all turbines, are as follows:
1. It has a very simple mechanism.
2. It runs at higher speed.
3. It is very compact engine compared to other
requiring less weight and space.
4. It requires less maintenance cost.
5. Cheaper liquid fuel can be used, as phenomenon of
6. Detonation does not exist.
7. It is highly situated for peak load and standby power
generation and aircraft propulsion.
8. It works at high operating pressures.
9. It has greater power to weight ration than other
engines.
10. It requires less manpower.
A gas turbine, also called a combustion turbine, is a type
of internal combustion engine. It has an upstream rotating
compressor coupled to a downstream turbine, and a
combustion chamber in-between. The basic operation of the
gas turbine is similar to that of the steam power plant except
that air is used instead of water. Fresh atmospheric air flows
through a compressor that brings it to higher pressure.
Energy is then added by spraying fuel into the air and
igniting it so the combustion generates a high-temperature
flow. This high temperature high-pressure gas enters a
turbine, where it expands down to the exhaust pressure,
producing a shaft work output in the process. The turbine
shaft work is used to drive the compressor and other devices
such as an electric generator that may be coupled to the shaft.
The energy that is not used for shaft work comes out in the
exhaust gases, so these have either a high temperature or a
high velocity. The purpose of the gas turbine determines the
design so that the most desirable energy form is maximized.
Gas turbines are used to power aircraft, trains, ships,
electrical generators, or even tanks.
II. WORKING PRINCIPLES OF GAS TURBINE
A gas turbine is an engine where fuel is continuously
burnt with compressed air to produce a steam of hot, fast
moving gas. This gas stream is used to power the compressor
that supplies the air to the engine as well as providing excess
energy that may be used to do other work. Turbine
compressor usually sits at the front of the engine. There are
two main types of compressor, the centrifugal compressor
and the axial compressor. The compressor will draw in air
and compress it before it is fed into the combustion chamber.
In both types, the compressor rotates and it is driven by a
Copyright @ 2014 SEMAR GROUPS TECHNICAL SOCIETY. All rights reserved.
M. WIN LAI HTWE, DR. HTAY HTAY WIN
shaft that passes through the middle of the engine and is
TABLE I: Material Properties of Ni-Cr Alloys (10%
attached to the turbine as shown in figure 1.
Chromium and 90% Nickel)
Material Properties
Magnitudes
Density
8900kg/m3
Modulus of elasticity
206.84GPa
Poisson’s ratio
0.33
Thermal expansion coefficient
1.340e-5/k
Heat capacity
444J/kg-K
Thermal conductivity
90.7W/m-K
Fig1. Indicator diagram of gas turbine.
Figure 2 shows the construction of turbine rotor blades
and their components. Knowing the fluid conditions at exit of
the gas generators, a value of static pressure was assumed at
the turbine outlet. From this, the corresponding enthalpy drop
required in the power turbine was calculated. The limitation
in fixing the velocity triangles come from the peripheral
speed of rotor and flow velocities. It is preferable to keep the
both in reasonable range so as to minimize the losses. After
the primary fixing of velocity triangles between the axial
gaps of the turbine blade rows, the blade profile is selected.
In blade section there are two approaches, the direct and
indirect approach. The blade profile selected should yield the
flow angle required to give the desirable enthalpy drop. Also
the pressure distribution at the end of stage should be
uniform. If it is not so the blade angles are changed to match
these requirements.
IV. MODELLING
With the dimensional parameters of the gas turbine rotor
blade is modeled using the SolidWorks software. Existing
data of the turbine first stage rotor blade is shown in table 2.
Figure 3 shows a conventional blade profile constructed from
circular arcs and straight lines. Gas turbines have until
recently used profiles closely resembling this, although
specified by aerofoil terminology. In this paper, the T6 base
profile which is symmetrical about the center line. It has a
thickness /chord ratio (t/c) of 0.2, a leading edge radius of
12%t and a trailing edge radius of 6%t. When scaled up to a
t/c of 0.2 and used in conjunction with a parabolic camber
line having the point of maximum camber a distance of about
40% chord from the leading edge, the T6 profile leads to a
blade section similar to that shown but with a trailing edge.
TABLE II: Existing Data for First Stage Gas Turbine
Rotor Blade
Rotational speed (rpm)
5100
Mass flow rate (kg/sec)
112.8889
Blade inlet temperature (K)
2073
Blade outlet temperature (K)
1803.8
Degree of reaction
0.5
Flow coefficient
0.8
Temperature drop coefficient
4.3
Blade tip radius (m)
1.3716
Blade mean radius (m)
1.2848
Blade root radius (m)
1.1980
Blade height (m)
0.0868
Mach number at the mean
0.4082
Fig2. Construction of turbine rotor blades and their
components.
III. MATERIAL OF TURBINE ROTOR BLADE
In this work, the stresses distribution of the first stage gas
turbine rotor blade made of Ni-Cr alloys was carried out.
Fig3. Conventional blade profile of rotor blade.
International Journal of Scientific Engineering and Technology Research
Volume.03, IssueNo.10, May-2014, Pages: 2200-2004
Design and Stress Distribution of First Stage Gas Turbine Rotor Blade
All such blade profiles may be referred to as conventional
V. EVALUATION OF GAS FORCES ON THE FIRST
blade profiles. Figure 4 shows the turbine first stage rotor
STAGE ROTOR BLADE
blade profile at root radius, figure 5 shows the turbine first
The velocity triangle for the first stage gas turbine rotor
stage rotor blade profile at mean radius, figure 6 shows the
blade is shown in figure 8. The gas forces namy tangential
turbine first stage rotor blade profile at tip radius and figure 7
and axial were determined by constructing velocity triangle
shows the turbine first stage rotor blade profile.
at the inlet and exit of the rotor blades. The number of first
stage gas turbine rotor blade nR1 is 92 blades. Total tangential
force on first stage rotor blade,
Fig4. Turbine 1st stage rotor blade profile (at root radius).
Fig8. Inlet and outlet velocities triangle for the first stage
rotor blade.
Ft1 total  m Ca 2  Ca 3 
Fig5. Turbine 1st stage rotor blade profile (at mean
radius).
Fig6. Turbine 1st stage rotor blade profile (at tip radius).
(1)
Tangential force on each rotor blade,
Ft1  Ft1 total n R1
(2)
Total axial force,
Fa1 total  m Cw2  C w3 
(3)
Axial force on each rotor blade,
Fa1  Fa1 total n R1
(4)
VI. STRESSES CALCULATION
Many kinds of stresses do come into play when it comes
to turbo machinery especially turbine where the temperature
changes have also become vital. The important stresses in the
designing of gas turbine include gas bending stress,
centrifugal tensile stress and radial stress.
A. Gas Bending Stress
The force arising from the change in angular momentum of
the gas in the tangential direction, which produces the useful
torque, also produces a gas bending moment about the axial
direction. Assuming the angle of incidence is zero at the
design operating condition, the blade camber is virtually
equal to the gas deflection, namely at the root,
β  β  108.5797
2r
3r
B = 400, n = 1.27,
n
z
Fig7. Turbine 1st stage rotor blade profile.
1 t
3
10   0.0060 mm /mm chord
B c
International Journal of Scientific Engineering and Technology Research
Volume.03, IssueNo.10, May-2014, Pages: 2200-2004
M. WIN LAI HTWE, DR. HTAY HTAY WIN
 C w2m  C w3m  h 1
m
σ gb max 
n
2 zc 3



m C am1 tanα 2m  tanα 3m h 1

n
2 zc 3
 
σ ct max
(5)
B. Radial Stress
These stresses have considerable impact during the
transient phase when the machine is turned on. The
temperature gradient is enormous and one can easily
understand that the temperatures in turbine are quite
significant than compressor. So the radial stresses play a vital
role when it comes to the turbine to withstand such
conditions.
r
 1 rr1

1

σ r  αE 2 Tr  dr  2 Tr  dr 
 rr1

r 0
0


(6)
Radial stress distribution is shown in figure 9 and table IV.


1.4
Radial Stress (MPa)
ρ bω2
ar
rt1
 ar dr
rr1
(7)
This equation is used for this which shows Ar as its area of
interest at the required radius from the center, ρ shows the
density of the material, Ar shows the area at the root and ω
represents the angular speed. This stress is directly
proportional to the ρAω2 and if the blade is tapered linearly
then the magnitude of the stress can be reduced considerably.
The value of stress can be calculated for ‘Ni-Cr Alloys’
which are used for turbine blades. The distribution of
centrifugal stress is shown in figure and table V.
VII. RESULTS AND DISCUSSIONS
TABLE III: Results of Forces on Rotor Blade
Tangential force on each rotor
686.4119N
blade
Axial force on each rotor blade
Rotor disc radius '0.6858m'
Rotor disc radius '0.6026m'
Rotor disc radius '0.5194m'
1.2

966.2692N
Table III shows the results of forces on rotor blade. The
gas forces are calculated from the distributed unsteady forces
on the blade surface. The gas bending stress is
24.7840MN/m2 that will be tensile in the leading and trailing
edges. The maximum value of gas bending stress usually
occurs at either the leading or trailing edge of the root
section.
TABLE IV: Radial Stress Distribution of Disc at
Different Value
1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Rotor disc radius (m)
Radius, r (m)
Radial Stress Distribution (MPa)
0
1.3858
0.0232
1.3838
120
0.0464
1.3766
110
0.0695
1.3674
0.0927
1.3530
0.1159
1.3346
70
0.1391
1.3120
60
0.1622
1.2854
0.1854
1.2546
Fig10. Relation of rotor blade area changes from root to
tip and centrifugal stress.
0.2086
1.2198
0.2318
1.1808
C. Centrifugal Tensile stress
Centrifugal tensile stresses depend upon the size of the
rotor and the rotational speed of the rotor. When the
rotational speed is specified, the allowable centrifugal tensile
stress places a limit on the annulus area but does not affect
the choice of blade chord. The maximum value of this stress
occurs at the root and is readily seen to be given by,
0.2549
1.1379
0.2781
1.0907
0.3013
1.0394
0.3245
0.9840
Fig9. Relation of rotor disc radius and radial stress.
140
Nickel alloy
Beryllium copper
Alloy steel
Centrifugal stress (MPa)
130
100
90
80
50
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Ratio of rotor blade tip area and root area
International Journal of Scientific Engineering and Technology Research
Volume.03, IssueNo.10, May-2014, Pages: 2200-2004
0.3477
Design and Stress Distribution of First Stage Gas Turbine Rotor Blade
0.4
93.60
0.9245
0.3708
0.8611
0.3940
0.7934
0.4172
0.7216
0.4404
0.6456
0.4635
0.5660
0.4867
0.4818
0.5099
0.3936
0.5331
0.3012
0.5562
0.2052
0.5794
0.1047
0.6026
0
Figure 9 shows the relation of various rotor disc radius
and radial stress. The maximum radial stress occurs at the
rotor disc center point and minimum radial stress occurs at
the largest rotor disc radius. The values of radial stress are
changed in different rotor disc radius. Table IV shows the
radial stress distribution of rotor disc at different radius. The
value of maximum radial stress is 1.3858MPa at rotor disc
radius at center point and the minimum value of radial stress
is 0MPa at rotor disc radius ‘0.6026m’. In steady state
condition, turbine blade stresses are the highest at the root
section and failing along the span. Blade temperature is the
lowest at the root section and increasing along the span.
Figure 10 shows the relation of rotor blade area changes from
root to tip and centrifugal stress for different material types.
When the rotational speed is specified, the allowable
centrifugal tensile places a limit on the annulus area but does
not affect the choice of blade chord. The values of centrifugal
stress are changed in different values of the ratio of rotor
blade tip area and root area. Table V shows the centrifugal
stress distribution with rotor blade tip area and rotor blade
root area. The maximum value of centrifugal tensile stress
occurs at the blade root section.
TABLE V: Centrifugal Stress Distribution With Area
Change
At /Ar Centrifugal Stress Distribution (MPa)
1
134.94
0.9
128.05
0.8
121.16
0.7
114.27
0.6
107.38
0.5
100.49
0.3
86.71
0.2
79.81
0.1
72.92
0
66.03
VIII. CONCLUSION
In open cycle gas turbine power plant, axial-flow turbine is
one of the most important parts to generate electricity. The
output power of the turbine depends upon the flow rate. And
also, to get the required turbine output power, the turbine
rotor blade design is the most important parts. In this paper,
the detailed design of first stage rotor blade that is divided in
three sections is presented. Then SolidWorks software is used
to draw blade profile data. All the calculations show that the
trends of the results are in accordance qualitatively with the
results obtained from the MATLAB software.
VIII. REFERENCES
[1] Criteria for Accrediting Engineering Programs, 2012 –
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from http://www.abet.org/engineeringcriteria-2012-201
[2] SolidWorks 2011 Software, 1995-2011, Dassault
Systèmes SolidWorks Corporation.
[3] ANSYS Release 13 (2010), ANSYS Inc..
[4] Hill, P., & Peterson, C. (1992). Mechanics and
Thermodynamics of Propulsion, (2nd ed.). Addison Wesley.
[5] Saravanamutto, H. I. H., Rogers, G. F. C., Cohen, H., &
Straznicky, P. V. (2008). Gas Turbine Theory, (6th ed.).,
Prentice Hall.
[6] Mattingly, J. (1995). Engine Performance Cycle Analysis
(PERF). Software Ver. 3.10.
[7] Mattingly, J. (1996) Elements of Gas Turbine Propulsion,
McGraw Hill Inc.
[8] Mattingly, J. (1999). Turbine Preliminary Analysis
Program (TURBN). Ver. 4.3.
[9] John.V, T.Ramakrishna. “The Design Andanalysis of Gas
Turbine Blade”, International Journal of Advanced Research
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[10] V.Raga Deepu, R.P.Kumar Ropichrla. “Design and
Coupled Field Analysis Of First Stage Gas Turbine Rotor
Blades”, International journal of Mathematics and
Engineering, Vol 13, No.2, Pages: 1603-1612.
International Journal of Scientific Engineering and Technology Research
Volume.03, IssueNo.10, May-2014, Pages: 2200-2004