Influence of
thermal barrier coating and
cooling flow on turbine blades
Impact of manufacturing tolerances on life assessments
Amanda Eriksson Simon Reinberth
Link¨opings universitet Department of Management and Engineering (IEI)
Link¨opings universitet Department of Management and Engineering (IEI) Division of Solid Mechanics Thesis work 2020|LIU-IEI-TEK-A--20/03668–SE
Influence of
thermal barrier coating and
cooling flow on turbine blades
Impact of manufacturing tolerances on life assessments
Amanda Eriksson Simon Reinberth
Academic supervisor: Daniel Leidermark
Industrial supervisors: Jonas Gustafsson, Tove Hagstedt Palagyi Examiner: Robert Eriksson
Link¨oping universitet SE-581 83 Link¨oping, Sverige
Abstract
Industrial gas turbines play an important role in reducing energy shortage and will play a major role in transitioning to renewable energy sources in the future. This creates new demands from customers regarding faster start up times, longer life, increased number of start up cycles and higher efficiency. By increasing the turbine inlet temperature a higher efficiency can be reached. However, this also reduces the life of the turbine blades. In this thesis the influence of manufacturing tolerances regarding the thermal barrier coating (TBC) thickness and cooling mass flow rate on the first turbine stage were investigated to find out how the tolerances affect life of the turbine blades.
Five different turbine blades were investigated in regard of thermo-mechanical fa-tigue and creep. In this report results for only one blade are presented due to secrecy. Meshed models of turbine blades were altered to TBC thicknesses corresponding to manufacturing drawings. The minimum cooling flow tolerances were investigated for three of the five blades. Conjugate heat transfer analyses were made and the metal temperatures were extracted and used as input for the creep and crack initiation simulations. Creep and crack initiation were evaluated by finite element analysis.
Results for each blade were investigated to evaluate the influence of the TBC and cooling flow tolerances. An overall conclusion for all blades was that the TBC tolerances had small influence on the structural damages evaluated. However, for minimum TBC tolerance creep increased while crack initiation decreased. Reducing the cooling mass flow gave more local temperature differences and in most cases increased crack initiation life, while creep almost always increased. To fully under-stand the influence of TBC thickness, it is necessary to perform crack propagation analysis which was not included in this thesis.
Acknowledgements
First and foremost we would like to thank our supervisors at Siemens Energy, Jonas Gustafsson and Tove Hagstedt Palagyi for their support during this project. By al-ways taking the time to share their knowledge and offer guidance they have helped us become better engineers. During the months we have worked on our thesis we have received great assistance from Andreas H¨agg. By holding presentations, contribut-ing in discussions and sharcontribut-ing his own experience on workcontribut-ing with turbine blades he gave us valuable input to our thesis. We would also like to take the opportunity to thank Malin Berggren and Mats Annerfeldt and everyone else at Siemens Energy’s R&D department in Finsp˚ang that has helped us by offering ideas and providing feedback of how the project could become better.
During this thesis we have had great help from our academic supervisor Daniel Lei-dermark and examiner Robert Eriksson. They have both contributed with valuable feedback to improve the report and helped us keeping an academic focus to finalize our master’s degree. We have also had great help of our opponents Elin Persson and Nils Rignell. Thank you for offering valuable guidance and encourage us to take coffee breaks at 9 a.m. It helped us get through days when completing the thesis felt far away.
Contents
1 Introduction 1
1.1 Background . . . 1
1.2 Purpose and research questions . . . 1
1.3 Delimitations . . . 2
1.4 Outline . . . 2
1.5 Other considerations . . . 2
2 Theory 5 2.1 Gas turbine engines . . . 5
2.2 Heat transfer in airfoils and fluid flows . . . 6
2.2.1 Conduction . . . 6
2.2.2 Convection . . . 7
2.2.3 Radiation . . . 8
2.3 Thermal barrier coating . . . 8
2.4 Cooling flow . . . 10
2.4.1 Cooling by convection . . . 11
2.4.2 Film cooling . . . 13
2.5 Sources of turbine stresses . . . 14
2.5.1 Centrifugal stress . . . 14
2.5.2 Gas bending stress . . . 15
2.5.3 Thermal stress . . . 16
2.6 Damage mechanisms . . . 16
2.6.1 Low cycle fatigue . . . 16
2.6.2 Creep . . . 18
2.6.3 Oxidation and corrosion . . . 19
2.6.4 Thermo-mechanical fatigue . . . 20
3 Method 21 3.1 Manufacturing tolerances . . . 21
3.2 Geometries . . . 23
3.3 Computational heat transfer . . . 23
3.3.1 Computational set-up . . . 25
3.4 Mesh . . . 26
3.5 Finite element analysis . . . 27
3.5.1 Computational set-up . . . 28
3.5.2 Creep simulation . . . 28
3.5.3 TMF simulation . . . 29
4 Results 31 4.1 Cooling mass flow reduction - 750 . . . 36
4.1.1 Reduced mass flow- TMF results 750 . . . 38
5 Discussion 43 5.1 Evaluation of method . . . 46 5.2 Further work . . . 48
1
Introduction
The research was done by evaluating gas turbines developed by Siemens Energy in Finsp˚ang. Siemens Energy develops industrial gas turbines with an aim to create products with low environmental impact. There are three types of gas turbines eval-uated in the project, named SGT-700, SGT-750 and SGT-800.
1.1
Background
A gas turbine consist of three main components, compressor, combustion chamber and turbine [1]. Gas exiting a combustion chamber may have temperatures above 1300◦C. Gas with high temperature contains more energy which can increase the efficiency of a gas turbine. However, high temperatures put larger demand on heat resistance and cooling of turbine blades. Warm turbine blades are at risk for creep and thermo-mechanical fatigue (TMF), which also include low cycle fatigue and oxidation. When a material reach its ultimate limit or fatigue limit, a component fails in regard to company specifications, which reduces reliability and may have large consequences on the surrounding area. To reduce the risk of creep, blades are cooled with air which runs in channels within the blade. A blade’s surface can be protected with a ceramic thermal barrier coating (TBC). The thickness of TBC on blades differs due to manufacturing tolerances. As such, blade temperature and also creep rate differs. Cooling techniques using cooling flow can be used to increase convective and conductive cooling. The efficiency of the cooling flow can be in-creased with for example film cooling, turbulators or impingement. For the turbine blades analysed in this project some or all of the techniques were used on each blade.
Due to the high temperatures at the first turbine stage of gas turbines it is diffi-cult to measure the temperature at the turbine blade surfaces with high accuracy. Tests performed usually have high costs and are time consuming. Temperature dis-tribution is also very sensitive to the cooling techniques and can differ depending on type of combustion chamber. Validating the results would involve running a gas turbine for thousands of hours, which is not an option for a gas turbine manufacturer.
1.2
Purpose and research questions
To increase efficiency of gas turbines, and at the same time not reduce reliability, fur-ther research on how manufacturing differences influence temperature distributions have to be done. With larger knowledge of cooling effectiveness, turbine efficiency and reliability of a gas turbine may be increased. In this thesis the effects of man-ufacturing tolerances for TBC thickness and cooling flow were investigated, with focus on answering the following questions:
What influence does manufacturing tolerances due to TBC thickness have on the final temperature distribution and life of current turbine blades?
How does the cooling mass flow tolerances affect temperature and life of turbine blades?
Which locations on turbine blades are most sensitive in regard to manufacturing tolerances?
1.3
Delimitations
Turbine blades for three gas turbines, SGT-700, SGT-800 and SGT-750, were re-searched in this project. For the first two mentioned, two different versions of turbine blades were investigated. Due to time limitations, the research only covers three dif-ferent set-ups with TBC thicknesses where the whole blade had either minimum, nominal or maximum tolerance. Models used for heat transfer analysis and struc-tural simulations are provided by the company. Further delimitations are:
• Manufacturing tolerances only include TBC-thickness and cooling flow of first stage turbine blades.
• For cooling mass flow, only minimum tolerance was investigated for three selected turbine blades.
• Simulations of structural damages were only investigated in regard to creep and TMF.
• Only damages related to TBC thickness and cooling flow were considered. As such, damages to dove tails and discs are considered to be related to the design and not coating or cooling flow.
1.4
Outline
The research consists of both theoretical and practical work, with more focus on theory during the first half. The theory includes both turbine blades and cooling techniques as well as reasons of failure. Brief introductions and tutorials to pro-grams used in the project were attended at the start of the research. Practical work includes heat transfer simulations in C3D and stress simulations in the finite element software Abaqus. Results were later analyzed with the research questions in mind.
1.5
Other considerations
Industrial gas turbines can play a major role in the transition from traditional energy sources to more renewable alternatives. Since wind and solar power is dependent on
weather, limited to certain hours per day, the grid must be supplemented to create stability. Gas turbines can be used for this purpose since start and ramp up can be done in minutes [2]. This fact increases the demand on both start up time and cyclic life. For all gas turbines, including use for cyclic operations, the demand for higher efficiency is always important. One way to increase efficiency is to increase the turbine inlet temperatures (TIT). Increasing TIT has a negative impact on life regarding the first turbine stage, which beside from high temperatures are subjected to centrifugal loads. To optimize efficiency, knowledge of how manufacturing toler-ances affect turbine life is essential. No ethical or gender-related issues are aroused by the work.
2
Theory
A brief introduction of gas turbines in general and main differences between models are given here. To cool turbine blades both conduction and convection are used. Blades of the first turbine stage can be insulated by coverage of TBC. The efficiency and properties of the coating depends on application method, thickness and material properties. Centrifugal and heat loads increase the risk of failure due to TMF and creep.
2.1
Gas turbine engines
There are three main components in a gas turbine, compressor, combustion chamber and turbine. Air enters a compressor through an inlet. While air moves through the compressor, its velocity is reduced gradually by the rotating compressor blades for each compressor stage and is converted to a higher pressure. Before entering a combustion chamber approximately 60 % of the total airflow is led in a bypass to be used for cooling, where around 30 % of the air in the bypass is used to cool the turbine blades [3]. The rest of the bypass air (70 %) is used for cooling of other com-ponents. In a combustion chamber, air is mixed with fuel and ignited. Hot air from the combustion chamber enters the turbine, where energy is extracted. Depending on which type of gas turbine is used, exiting air may be used in a steam turbine (combined cycle) or released to the surroundings (simple cycle).
Gas turbines can have one to three shafts. A gas turbine with one shaft has the same rotational velocity for the compressor and turbine (Figure 1). Which means that the compressor has a constant rotational velocity, independent of the work load. For gas turbines with more than one shaft the compressor and turbine are divided into high and low pressure (Figure 2). As such, the the compressor’s rotational veloc-ity can be altered depending on the load. The compressor and the turbine driving the compressor is mounted on the same axis and has the same rotational velocity. Another option is to use a free-power turbine to drive a load which is mounted on a separate shaft. The rotational velocity can then be controlled independent of the compressor/turbine, (Figure 3).
Figure 2: Two-shaft gas turbine engine. Where the low pressure compressor (LPC) is connected to the low pressure turbine (LPT) and the load. The high pressure compressor (HPC) is connected to the low pressure turbine (HPT).
Figure 3: Single-shaft gas turbine engine with a free-power turbine.
2.2
Heat transfer in airfoils and fluid flows
In gas turbines, heat transfer is an important subject since hot gas with high pres-sure expands and increases its velocity. This is due to deflection of the high velocity gas stream in the turbine, where the kinetic energy is converted to mechanical work on blades and shaft. Since gases passed form a gas turbine’s combustion chamber are well above the melting temperature for the material of turbine blades, cooling flow must be guided from the cold section of the engine and forced through channels in the turbine blades to absorb heat and decrease temperature of the material. The cooling flow is supplemented by TBC to decrease the heat load transmitted to the metal. Heat can be transported by three different modes, conduction, convection and radiation. These modes are briefly covered in the following sections.
2.2.1
Conduction
If a body is subjected to a temperature gradient, a flow of heat must exist. Accord-ing to the second law of thermodynamics, heat flows from a hot area to a colder. This is said to be energy transportation by conduction, where the temperature gra-dient is proportional to the heat flux or heat transfer rate per unit area. The heat transfer rate by conduction can therefore be calculated by inserting a proportional-ity constant k, which is called the thermal conductivproportional-ity (Equation 1).
q = −kA∂T
This relation is called Fourier’s law, where ∂T∂x is the temperature gradient in the heat flow direction and A is the area. This equation can be used in steady heat transfer problems where no heat sources or sinks are present [4]. The equation is only suitable for problems where the heat conduction is assumed neglectable in y and z direction since this is a one-dimensional relation. However, the equation can be developed further to include two or three dimensions. TBC layers investigated in this thesis are thin, conduction can therefore be assumed one dimensional.
2.2.2
Convection
Convection is of great interest in gas turbine applications since it involves fluids both on the outside and inside of the turbine blades, i.e. the hot gases and cooling flow. Consider a flat plate exposed to a stream of air passing over it. Here, a bound-ary layer will form on top of the plate due to the viscosity in the fluid. According to boundary layer theory the velocity in contact with the plate will be zero and increase to the streamwise velocity in the free stream (u∞). This induces a
veloc-ity profile in the boundary layer, which is a function of the y-coordinate, see Figure 4.
Figure 4: Boundary layer formation over a flat plate.
Since the velocity is zero close to the plate, heat transfer will only occur through conduction between the stationary air and the plate. However, since the heat trans-fer is a function of the temperature diftrans-ference, Equation 1 is not specific enough to explain the heat transfer through convection between a solid and a moving fluid. The moving air in this example is transporting heat just above the stationary air, therefore the heat transfer is dependent on the rate at which the moving fluid is transporting the heat away. A larger flow velocity will therefore create a higher temperature gradient, which in turn results in a higher heat transfer rate [4].
Convection can either be natural or forced, where the latter is explained in the flat plate example. Natural convection occurs due to temperature differences, which in-duces a difference in density in a fluid. A density difference creates movement, since heated gas is lighter and wants to rise, while cooler gas is heavier and therefore de-scends. Heat transfer through convection can be calculated by the use of Equation 2.
Where Twis the plate’s temperature, T∞is the temperature of the fluid and Awis the
surface area of the plate. Convection heat transfer coefficient (h) can be determined from experiments and is dependent on conduction taking place in the stationary part of the boundary layer. It can also be found by convective correlations, but only for simpler geometries. Another approach is to use conjugate simulations to find the coefficient numerically [5].
2.2.3
Radiation
Heat transfer can also take place by electromagnetic radiation. For a perfect black body in perfect vacuum the rate of heat transfer can be calculated with Equation 3, which is called Stefan-Boltzmann law.
q = sAT4 (3)
Where s is a proportional constant, A the surface area of the black body and T the temperature of the black body. If radiation between a body placed within an enclosed surface is of interest, the heat transfer rate can be calculated by replacing T4with the difference of the fourth power between the temperatures of the body and the enclosing surface. If a body is not a perfect black body, emissivity is introduced (e). The emissivity is a factor used to relate radiation from a perfect black body to a grey body. Heat transfer in such a case can then be calculated by Equation 4 [4].
q = e1sA(T14− T24) (4)
Where T1 is the temperature of the body enclosed by a larger surface with
temper-ature T2. e1 represent the emissivity of the enclosed body.
2.3
Thermal barrier coating
By insulating a superalloy turbine blade with a ceramic material the heat resistance can be increased due to the insulating effects. With thermal barrier coating (TBC) the turbine inlet temperature may be increased since the bearing structure within the blade remains cooler. TBC can also decrease risk of failure of blades since it protect load bearing superalloy blades from high thermal gradients. A coating con-sists of two layers. Closest to a blade a metal bond coat creates an adhesive surface between blade and top coat. A metal bond coat reduces differences in thermal ex-pansion coefficients, which is beneficial since metal expand more under heat than top coats do. Between the blade and bond coat an interdiffusion zone is formed. On a bond coat, a top coat is added which main feature is to insulate the blade from hot gas. It does not add any strength to a component and on a downside it adds weight to a blade. A top coat fails when it has been damaged so it no longer can insulate a blade. Damage can be cracks in the layer or that parts of the top coat spalls off. Failure decreases operating hours of a turbine since it increases the need
for maintenance. Low thermal conduction of a top coat increases the temperature gradient through the thickness (Figure 5) [1]. Surface temperature of a top coat varies between gas turbines but can be around 1200◦C and bond coat temperatures are approximately 1000◦C [6]. Between bond coat and top coat a thermally grown oxidation layer (TGO) grows. The layer is heat sensitive and grows gradually. There are usually lots of tensions in the layer, which may give internal cracks and weaken the structure [7]. Thermal barrier coating is only efficient if used together with other cooling techniques of a blade since it only insulate the blade and not actively cool it. Thicker TBC provides better insulation but maximum thickness may be limited by influence of aerodynamic properties, weight and abilities to ensure the top coat sticks to the bond coat without risk of spallation.
Figure 5: Temperature gradients from the cooling flow to the hot ambient temperature. The temperature decrease faster through the top coat than the other materials [1].
There are several methods to apply TBC to a turbine blade. Only the two which are used on the blades investigated in this thesis are presented. One option is to use Atmospheric Plasma Spray (APS) where ceramic powder is melted and then shot on the surface of a blade. The ceramic layer then covers the surface in splats. Depend-ing on the temperature and spray angle of the ceramics the surface may differ [6]. TBC can also be implemented by using Electron Beam Physical Vapor Deposition (EB-PVD), which is a more expensive application option [8]. A bond coat and top coat are then sprayed on a turbine blade’s surface. The main difference between the application models are that EB-PVD has a more even surface which improves aerodynamic properties and has a better bonding between bond coat and top coat. However, APS has better thermal insulation since it does not have gaps parallel to the heat flow like the EB-PVD has [9]. The gaps in APS applied TBC also give lower thermal conductivity compared to EB-PVD due to its microstructure. When APS is applied many microcracks are formed. When the TBC is heated larger cracks forms which reduces stress resistance [8]. Relation between thicknesses of TBC layers are shown in Figure 6.
Figure 6: Material layers and approximate thicknesses of the layers from the metal surface of a turbine blade to the top coat of applied TBC [1]. For TBC applied with EB-PVD the top coat has gaps parallel to the heat flow while APS applied TBC is formed of unevenly shaped splats.
Depending on which composition of TBC is used, characteristics may vary. Com-paring two silicon ceramics, a silicon-nitride with higher density also has higher strength limits (Table 1) [10]. However, a material’s thermal conductivity also in-creases as the Young’s modulus increase. Thermal expansion coefficient, which is also an important parameter for turbine blade materials, remains constant since it is dependent on the energy of the bond.
Table 1: Comparison of material properties of two silicon ceramics.
Properties Si3N4 Si3N4-ZT
Density [g/cm3] 3.14 2.45 Young’s Modulus [GPa] 280 165 Strength [MPa] 500 200 Thermal expansion coefficient [◦C−1] 3e−6 3e−6
Thermal conductivity [W/m*K] 15 1.5
2.4
Cooling flow
Cold air used to cool turbine blades originates from the compressor and are led into the turbine blades to cool them from within. With efficient cooling, blade temperatures can be decreased by 200-300 ◦C [3]. There are different methods to extract heat from a blade’s surface to the air, and most turbine blades use several methods. Cooling methods do come with some losses. There is a reduction in turbine work since air used for cooling does not go through the combustion chamber. Since the cooling air moves within the blade it limits the design options of blades and usually decreases the aerodynamic performance. When air is ejected from a blade into the main gas stream there is a pressure loss. Air can either be injected through one or several inlets [1]. Cooling effectiveness (Φ) can be evaluated by comparing the gas temperature (TG), metal surface temperature (TM) and cooling gas (TC,inlet)
(Equation 5). The effectiveness factor is used to determine which cooling technique is suitable. However, this factor is not the only criteria used for selecting cooling method, other important aspects are for example manufacturing and cost.
Φ = TG− TM TG− TC,inlet
(5)
Cooling efficiency (η) can be evaluated by comparing the temperature of the cooling air at the inlet and outlet (TC,outlet) of an airfoil (Equation 6). Cooling efficiency
can be used to determine how well the cooling air is used before ejection.
η = TC,outlet− TC,inlet TM − TC,inlet
(6)
The amount of heat transferred from the cold and hot side of a blade can also be calculated (Equation 7 and Equation 8).
Qc= hcAc(TM− TC) (7)
Qh = hgAh(TG− TM) (8)
The magnitude of heat transferred from a cold side (Qc) should be equal to the
heat transfer from a hot side, (Qh), Figure 7. Parameters most easy to influence on
the cold side of the flow, without making larger changes to the turbine design, are the heat transfer coefficient of the cold air (hc) and the area on the cold side (Ac).
From the warm side, the gas temperature can be decreased (TG) by lowering the
tur-bine inlet temperature or with film cooling. Another option could be to reduce the heat transfer coefficient (hg) on the outside, which can be done by introducing TBC.
Figure 7: Variables calculating heat transfer rate. The metal temperature is measured on the hot side of the wall.
2.4.1
Cooling by convection
Cold air is led in channels within airfoils to extract heat from the inside surface with convection. Depending on cooling channel area and amount of airflow, effectiveness may vary. To use convective cooling turbine blades have to be thicker, which means
that it may be difficult to use in leading and trailing edges. Often a tradeoff between aerodynamic properties and cooling effectiveness affect the final design.
To increase efficiency of convective cooling, turbulators can be used within cooling channels. Increased turbulence in a flow does not only enhance momentum but also the heat transfer between flow and enclosing surface. A rib turbulator can be either straight, parallel or v-shaped. Another cooling design is to use a matrix within the blade instead of channels (Figure 8). A matrix consists of parallel ribs which form two flow channels, one upper and one lower. One drawback with this cooling method is that it does not significantly increase heat transfer coefficients in the blade. A better way to increase the heat transfer coefficient is to use Pin-Fins (Figure 9). Pin-Fins are usually placed at trailing edges where they add structure to thin parts of an airfoil and at the same time increase turbulence.
Figure 8: Rib cooling and matrix cooling. Air in a matrix moves in upper and lower channels. When flow hits a wall it changes direction and level.
Figure 9: To the left: cold air moves into the area with Pin-Fins, usually at the trailing edge. Behind the Pin-Fins separation occurs which increase turbulence. To the right: cross section of a turbine blade trailing edge. The Pin-Fins add structure since they separate pressure and suction side.
Impingement cooling is a type of convection cooling, where the flow hits a surface normal to the radial direction. Air changes direction by a series of holes within the blade (Figure 10). Impingement is often used in leading edges combined with film cooling to lower the temperature at stagnation regions. A stagnation line is not constant on a turbine blade which makes it necessary to cool a larger region at leading edges [11].
Figure 10: To the left convective cooling with the flow in the radial direction of the blade. The cold air in the channels extracts heat from the warm outer surface which lowers the metal temperature. To the right impingement cooling, cold air turned normal to the surface by a series of holes.
2.4.2
Film cooling
Film cooling protects a turbine blade from hot gases by ejecting cold air through small holes in the blade. Cold air then disrupts the boundary layer and cools the surface with a layer of cold air closest to the blade surface. The cooling method demands careful design since holes weaken the structure and cooling air should not penetrate the boundary layer. Air which is injected with too high momentum will mix with the hot air in the turbine and as such not be able to protect the blade. Turbine blades with film cooling often have hot streaks due to non uniformly dis-tributed film on the surface. Design variables that can be changed are distances between holes, diameters of holes and the length cold air travels through the blade. It is vital for the cooling flow to have high enough pressure to ensure positive back flow margin, so the warm air is not sucked into a blade through the cooling holes (Figure 11). Film cooling is an efficient cooling method since air absorb heat within the airfoil, with convection, and is then ejected to form film cooling on the outer surface [3]. As such, holes are often diagonal through blade walls to increase convec-tion. A risk with film cooling is that potential particles of debris in the air covers the holes which reduces cooling efficiency. This is a design limitation for film cooling since it restricts the size of holes.
Figure 11: A cut in a plate with film cooling. Air moves in channels through a blade’s wall and cold air is pushed out through holes. On the outer surface a thin layer of cold air covers a the blade.
Another way to achieve film cooling is to use a porous material, so the cold air can trickle through the wall of a blade and form film cooling on the outer surface. This
method is called transpiration cooling and is in theory the most effective. However, the method increases production costs and decreases the reliability of the turbine due to the risk of blockage of the cooling holes. Since gas turbines mostly are used in tough environments there is a large possibility that particles are sucked into a turbine that may cover the pores in the material. As such there are no turbine blades with this cooling on the market at this time.
2.5
Sources of turbine stresses
A turbine blade in an industrial gas turbine application is a trade-off between aero-dynamic efficiency and structural design. Two major stress sources are of interest, steady and unsteady stresses. Failure due to steady stress is usually coupled to creep from inelastic deformation, while unsteady failure is coupled to cracks forming due to material fatigue. Cyclic stress can arise from transient effects, which here is related to start and stop cycles of the engine. It can also arise from dynamic effects related to cycles with higher frequencies (often one or more cycles per revolution of the shaft). Steady state stress in a gas turbine emerges from thermal sources, centrifu-gal forces and pressure loading arising from pressure difference between the pressure and suction side of a turbine blade. Unsteady stress arises from cycling loads such as interactions between rotating turbine blades and stationary guide vanes. Thermal cycling gives rise to thermal stresses which can cause low cycle fatigue. Combustion instabilities or blade/vane passage are related to dynamic effects that can result in high cycle fatigue and in the case of resonance, fast blade failures [3].
2.5.1
Centrifugal stress
Centrifugal stress is a tensile stress which is composed as a function of the radial position of a blade, rotational speed of the shaft and mass of the component (Equa-tion 9).
Fc= mω2r (9)
Where m is the mass, ω is the angular velocity and r the radius. If one small element in the blade is considered, a force balance can be written according to Equation 10.
d
dr(σrAb) = −ρbAbω
2r (10)
Where dr is the thickness, σr is the radial stress, Ab is the blade area and ρb the
blade density. Integration of both sides and assuming that the blade area is constant gives an expression for the radial stress according to Equation 11.
σr = ρb
ω2 2 (r
2
Here, rt represents the tip radius while r represents any radius along a blade.
Ac-cording to the equation, maximum radial stress will occur at the root of the blade. To counteract root stresses, turbine blades are designed with a greater thickness at the root, which decreases in the direction towards the tip [3].
2.5.2
Gas bending stress
Gas bending stress is a result of moments created by pressure and high velocity flow arising from the combustion chamber, placed forward of the turbine. Two forces are generated on rotor blades, an axial force (Fa) and a tangential force (Ft). An axial
force is a combination of momentum changes arising from axial velocity and pressure differences between the pressure and suction side of a blade. Tangential forces are related to power generated from a turbine stage divided on the number of blades making up the stage. The axial force creates a gas bending moment (Ma) around
the tangential direction axis while the tangential force creates moments around the axial direction (Mt) (Figure 12). The angle α represent the angle between the
orig-inal axes (axial and tangential axis) and the neutral axis of the blade. The neutral axis is used to create a new coordinate system (X,Y ) for the purpose of resolving the axial and tangential moments according to Equation 12 and Equation 13. The coordinate system originates at the blade’s centre of gravity [3].
Figure 12: Correlation between axial direction, tangential direction and the neutral axis. The neutral axis is inclined at an angle α from the tangential axis. The coordi-nates x and y represent the distance from the origin to the leading edge [3].
By introducing the moment of inertia in X- and Y -direction (IXX and IY Y), the
gas bending stress can be expressed according to Equation 14. Tensile stress can be found at the leading edge of a blade and compression at the trailing edge. For
example, inserting the coordinates x and y from Figure 12, in Equation 14, gives the gas bending stress for the leading edge.
MX = Mtcosα + Masinα (12) MY = Macosα − Mtsinα (13) σgb= MYX IY Y −MXY IXX (14)
2.5.3
Thermal stress
Thermal stress arises from temperature gradients in turbine blades. Gradients are temperature deviations in a blade compared to the average temperature. Temper-ature gradients are non-uniformed, both along blade height and through a cross-section. This is due to the non perfect match between external heat load and inter-nal cooling between different locations of the component [3]. Local relative hotspots expand a component, which create stresses in the material. The stresses are propor-tional to the product of the Young’s modulus, coefficient of thermal expansion and temperature difference in a material. Only a temperature difference of 50 ◦C can result in a local stress increase of 70 MPa.
2.6
Damage mechanisms
As previously discussed, the first stage in a turbine is exposed to harsh environment due to the high temperatures arising from the combustion chamber. High stresses are also caused by centrifugal loads. These factors are all affecting the life cycle of turbine blades and therefore the whole engine.
2.6.1
Low cycle fatigue
Low cycle fatigue (LCF) is a damage mechanism arising from cyclic load amplitudes which can lead to rupture in less than 105 cycles. Plastic strain is the main cause
for LCF which is connected to the repeated cyclic load on a structure. High cycle fatigue (HCF) is another cause of fatigue failure in a structure. However, compared to LCF, HCF is characterized by high frequency elastic loadings with low amplitude, which also is present in gas turbine applications. For example, when a rotor blade passes a stator blade in a turbine. If these frequencies, coupled to the rotational velocity of an engine, matches the eigenfrequency of a blade, resonance can occur which may increase the amplitude further. LCF on the other hand is characterized by high amplitude and low frequency plastic strain, which implies that every cycle is subjected to stress greater than the yield point for the material. As such, rupture will occur after less cycles compared to HCF. In a turbine the effects of LCF can
usually be seen in areas where stress concentrations are high. Typical areas can be holes or at the dove tail, where there are flow systems for cooling air. A dove tail is the structure beneath the turbine blade platform used to attach the blade to the turbine disc. Stress arises from centrifugal loads, connected to the rotational speed of a turbine shaft [12].
Long fatigue lives are explained by Basquin’s relation and visualized by a stress-life curve, also known as W¨ohler-digram. Basquin’s relation can be rewritten to include elastic strain instead of stress (Equation 15). Short lives are characterised by plastic deformation and can be described by the Coffin-Manson relation given in Equation 16. Putting these two relations into one equation gives an expression for strain based LCF, called Morrow’s relation (Equation 17), used to describe fatigue for a component. The first term arising from Basquin’s relation is usually referred to as the elastic part, while the second term is referred as the plastic term, which together make up the total strain (Figure 13) [13].
logelastica = (σ 0 f E)(2Nf) b (15) plastica = 0f(2Nf)c (16) totala = (σ 0 f E)(2Nf) b+ 0 f(2Nf)c (17)
Figure 13: Fatigue failure as a function of strain (log-log) curve describing the relation between Basquin, Coffin-Manson and Morrow’s relation (Equation 15-17).
Here, σf0 represent the strength coefficient, E young’s modulus, Nf number of
cy-cles to failure, the exponent b stands for the strength exponent, c for the ductility exponent and 0f for the ductility coefficient.
2.6.2
Creep
Creep is a time dependent deformation process, which can occur in a material during an applied load. If a material is exposed to high temperatures the risk of creep is increased further and it is therefore a common problem in high thermal load appli-cations. Creep is a permanent inelastic deformation which occurs under a material’s specified yield point where strain increases over time with a constant stress. Creep deformation is coupled to the microstructure of a material and occurs when disloca-tions move adjacent to each other. The movement is due to diffusion, where empty voids in the lattice create a transport of material, which is due to a gradient of free energy. This free energy comes from applied stresses [14].
Since diffusion plays a crucial role in creep, it is assumed that the creep rate is partly proportional to the temperature by use of an Arrhenius term. The creep rate is also assumed to be partly proportional to the stress, which put together gives the creep rate according to Norton’s creep law (Equation 18).
D = Bσne−QRT (18)
Where B is a constant and n is the stress exponent which is dependent on the dominant creep mode. Q represent the activation energy, T the temperature and R the universal gas constant. The activation energy can be determined experimen-tally [14]. The relation between creep strain and time can be plotted (Figure 14). At time t=0 the instantaneous strain occurs due to the load applied to the model. Section one is primary creep where strain increases fast over time until stage two (2) is reached. At this time the rate of deformation is decreased and shows an al-most linear relation, called secondary creep. Stage three (3), called tertiary creep, is recognised by an increase in rate of deformation. This behaviour can be seen until the material ruptures (4) due to an increase in formation of grain boundary voids [15]. Stage 1 does not leave visible evidence of creep deformation. At stage 2, which increases linearly, the first voids can usually be seen. When voids in the microstructure grow larger and link together to form cracks it decrease the effective thickness. The applied load might then be enough to lead to rupture. One way to decrease risk for creep is to use a material with less grains, since formation of voids are dependent on grain boundary area. In gas turbine applications single crystal materials are often used since they only contain one single grain.
Another way to decrease the effects of creep is to keep the loaded material in a safe temperature range where creep is minimized. A rule of thumb is that a material exposed to a load should be located in an environment colder than a factor of 0.4 of the melting temperature for the material. The effects of increased temperature can be seen schematically in Figure 15.
Figure 14: The creep strain () plotted as a function of time can be used to explain the behaviour of creep, where the first stage (1) is called the primary creep, the second stage (2) the secondary stage, the third (3), tertiary stage and rupture at (4) [15]
Figure 15: Materials exposed to higher temperatures (T) will have higher creep rate [15].
2.6.3
Oxidation and corrosion
The harsh environment for turbine blades leads to another life reducing factor, oxi-dation and corrosion. Oxioxi-dation is considered as an attack on a material produced by oxygen while corrosion is considered as an attack of any other substance. Since most metals are unstable in presence of oxygen and other reactive substances this becomes an issue. In gas turbines, nickel-based superalloys have limited resistance to oxidation and corrosion due to the elevated temperature. TBC can protect a blade from damages arising from the reactive gases discharged from the combustion chamber. However, since TBC only protects a blade against oxidation and corrosion if it is completely free of cracks, it is very uncertain how much protection it adds against oxidation and corrosion. As such, it is often not included in those analysis.
Corrosion and oxidation can interact with other failure modes and enhance the ef-fects of the involved modes. One typical interaction in gas turbine applications is a
combination of mechanical crack propagation and oxidation/corrosion, where corro-sion pitting can initiate cracks or loss of load-bearing material in the structure. Gas turbine blades can be exposed to temperatures around 1100-1200 ◦C, as such they require heat resistant material which also reduce creep. Nickel-based superalloys are common materials used in these applications due to their favorable high tempera-ture properties. Since creep is one of the major concerns regarding turbine failure, superalloy materials emphasis creep reduction properties which affects resistance of oxidation/corrosion in a negative manner. This is due to the amount of chromium (Cr) which is present in the material. Cr is commonly used in steel to reduce effects of oxidation but reduced in superalloys to enhance creep resistance and strength at high temperatures. This induces a trade off between the risk off creep and oxidation in a turbine blade [16].
2.6.4
Thermo-mechanical fatigue
Thermo-mechanical fatigue is a damage mechanism used to describe the interaction of creep, fatigue and oxidation in a structure. All three components contribute to the total damage (Equation 19).
1 Nf = 1 Nff atigue + 1 Nfoxidation+ 1 Nfcreep (19) Where Nf represent the fatigue life in number of cycles. Loadings in TMF are
usually described as in-phase (IP) or out-of-phase (OP). In IP the maximum tem-perature and maximum tensile strain occurs at the same time, while in OP the maximum temperature occurs at minimum strain (compression). In gas turbine TMF simulations, the hydrostatic pressure in a blade can be used to evaluate if an area is subjected to IP or OP.
The components included in TMF dominate at different conditions. Fatigue domi-nates at high strain levels and low temperatures, while oxidation increase at higher temperatures. Oxidation damage often occurs in OP since oxide film forms dur-ing high temperature compression and then rupture durdur-ing the colder tensile strain since the material becomes more brittle. However, oxide damage can also occur during IP loading when the material undergoes buckling in the brittle compression state of the cycle. As mentioned before, the risk for creep damage is highest at high temperatures and high stress states [17].
3
Method
An overall simulation plan, describing the main steps in heat transfer and structural simulations, was created to get an overview of the method (Figure 16). A supplied meshed CAD model was loaded into the in-house heat transfer software C3D. The model was then altered by applying a TBC thickness or reducing the cooling mass flow in the model. The TBC thickness was altered in regard to manufacturing tol-erances on drawings and the mass flow was reduced with support of flow toltol-erances used when testing blades at production. A conjugate steady state heat transfer sim-ulation was then performed to evaluate the temperature distribution of the metal surface. From C3D, metal temperature, pressure and mesh were extracted. Some of the blades had first order elements in the C3D mesh, and as such were run through a python script to map the temperatures to the mesh and output a Abaqus read-able file used to interpolate middle node values in the second order mesh. The files from the heat transfer simulations were then loaded into Abaqus for structural simulations. Two different types of structural simulations were performed in the project, creep and TMF. Output from the TMF simulations were then imported to an in-house software (EVAL) which evaluated the entire model for minimum life expectancy. Note that oxidation is a contributing factor to TMF. However, no ad-ditional calculations regarding only oxidation were performed on the models beyond the TMF analysis. Abaqus viewer was used for post processing. The number of estimated cycles for the different models and creep strains were compared to com-pany compliance and the effect of varying TBC thicknesses and mass flow rate were compared for all cases to evaluate the influence of manufacturing tolerances on life.
3.1
Manufacturing tolerances
The first part of the project was aimed to investigate the influence of TBC thickness on life for the first stage turbine blades. Three different thicknesses were investigated, maximum tolerance (max), nominal tolerance (nom) and minimum tolerance (min). The thickness tolerances were linear on the majority of the blades. The specifics of the thicknesses were taken from production drawings provided by Siemens Energy.
The second part of the project was aimed to investigate the influence of reducing the cooling mass flow rate. All turbine blades are tested once during the manufacturing processes and once when they are coated and ready to be installed in a gas turbine to ensure that the mass flow is within the allowed margins. A worst case scenario, which implied minimum TBC tolerance combined with minimum cooling mass flow rate was investigated. The cooling mass flow rate was reduced by setting up the models according to test procedures, reduce the flow by two different configurations for each blade and apply the internal flow settings to a warm model (including gas temperatures).
Figure 16: Simulation process for the blades. The first parts marked in red were in C3D and the second green part were structural simulations in Abaqus.
Figure 17: Simulation set-up for the different gas turbines investigated. For SGT-700 and SGT-800 two blade versions for each gas turbine were evaluated. All five blades were tested with min, nom and max TBC. But only three blades were tested with min flow tolerance.
3.2
Geometries
A CAD model was provided for each turbine blade. Apart from the airfoil, the model also contained a platform, dovetail and a slice of the disk. The size of the disk slice was dependent on the number of turbine blades on the first stage. Includ-ing a disk slice in the simulations gave more realistic boundary conditions and made it possible to simulate the channels for cooling air. Depending on which gas turbine serie the blade belonged to, some parameters differed. Turbine blades for SGT-700 and SGT-750 are made of a poly-crystalline material. Gas turbines of the mentioned models also have in common that they have two shafts, which allow a more optimal rotational speed for the turbine. Turbine blades for a 750 are designed for a higher turbine inlet temperature and with a lower rotational speed than the SGT-700. A SGT-800 has only one shaft and the turbine blades are made of a single-crystal nickel-based superalloy of face-centred cubic structure. Compared to the SGT-700 and SGT-750 the rotational speed is lower, but the turbine inlet temperature is higher. A major difference between the materials is the crystal structures. As such, the 800 has larger resistance against fatigue, which is due to its lower Young’s modu-lus [18], since LCF is strain based. The single-crystalline microstructure also delays the onset of tertiary creep and gives higher creep ductility.
3.3
Computational heat transfer
C3D is an in-house software developed by Siemens Energy used for computational heat transfer and structural analysis. Models are meshed in a mesh software and imported to C3D where cooling channels get coupled to the model. A blade’s in-ternal cooling structure is represented as a 1D flow network constructed by nodes and connecting branches. The nodes store information about i.e. pressure and gas temperature while the branches among others store velocity, mass flow and Reynolds number. In the branches, cross-sectional area, hydraulic diameter and pressure loss coefficient (PLC) are user inputs. The flow solver can be used independently or, if a conjugate simulation is performed, together with the thermal solver. For a conju-gate simulation the flow branches need to be coupled to the surface mesh inside the cooling channels of the model. This enables an exchange of information between the flow and thermal solver. External gas properties, flow fields and pressure fields are imported from CFD-simulations and mapped to the model. TBC-layers can either be included in incoming mesh or added by a virtual paint tool in C3D. After solving the temperature distribution for a model, the results can for example be exported as a boundary condition to a FE-solver for stress-life analysis.
Meshed CAD models of turbine blades were loaded into C3D and the TBC thick-nesses were altered according to drawings. Two methods can be used to add the TBC thickness in C3D. The first method is to mesh TBC and assign appropriate material properties. The drawback of this method is that areas with linearly de-creasing thicknesses, which is common on leading edges are hard to mesh. Also, the blades must be re-meshed between each simulation, which is time consuming. The second method for applying TBC is to use a painting feature in C3D, where
the thickness is added to the surface mesh of the blade. This method makes it possible to decrease the thickness evenly in required areas and keep the same mesh in all simulations (Figure 18). The density of the TBC properties could then be altered to represent the accurate weight of the TBC in the FEA (finite element analysis) solver. Painted thicknesses applied in C3D are used to calculate new lo-cal heat transfer coefficients (HTC) to artificially represent real TBC thicknesses (Equation 20). The second method was used in this project. To run simulations a conjugate solver was used. From each simulation pressure, temperature and mesh were extracted. The blade was covered with TBC at the airfoil surface and platform.
HT C = 1 1
htc +
T BCthickness
T BCconductivity
(20)
Where htc is the heat transfer coefficient on the surface of the blade without TBC. By adding TBC properties a new HTC can be calculated which better represent blade properties.
To reduce cooling mass flow rate, a cold model was created for each blade to corre-spond to test procedures performed on manufactured blades, which implied without heat and rotational loads. All outlet parameters were altered to room temperature, 20◦C, and atmospheric pressure. The inlet nodes of the cooling flow were altered to a higher pressure, 1.5 bar, to ensure that the flow direction corresponded to opera-tion. A quasi-one-dimensional internal flow simulation was performed and the nom mass flow rate was measured. Depending on model design, either cross-sectional area and hydraulic diameter or PLC was altered in one or several branches to reach min flow. Contributing factors to the decision on how to reduce the flow were known manufacturing differences, knowledge on damages on the product and heat sensitive areas on the blade. As a last step before running the simulation, the new properties in the cold model flow network was transferred to a warm model with min TBC.
Figure 18: Distribution of TBC thickness on SGT-750. Parts of the airfoil and tip surface of the platform were covered with TBC. The different colors on the blade represent different thicknesses. Note that this figure only serves as an example on how the TBC can be applied.
3.3.1
Computational set-up
All boundary conditions for the heat transfer simulations were applied to the pre-pared models, except for TBC thicknesses and outlet area of the cooling channels. Applied boundary conditions were imported and mapped to a model from CFD sim-ulation output data. The CFD data included streamlines of the gas flow, velocity profiles, HTC values on the aero faces, pressure and gas temperature. The internal cooling channels for each blade were prepared in advance. Cooling channels were represented as a 1D flow network which was prepared in a CAD software and posi-tioned within the cooling channels in the C3D model (Figure 19). The flow network was then connected with nearby mesh.
Figure 19: Part of a 1D flow network at the trailing edge of the SGT-750 first stage turbine blade in C3D. The network consisted of branches and nodes used to evaluate the cooling flow properties.
To study the influence of TBC thicknesses, the cooling flow was set according to the nominal values for the different blades. A symmetry boundary condition was used on the disc. The rotational velocity was constant and set according to operational conditions. Steady state simulations were used in C3D. A conjugate solver was used to loop all sub-solvers until convergence was reached for the metal temperature. Thermal tolerance of the conjugate solver was set to 0.1 ◦C, which was the maxi-mum allowed root mean square (RMS) value for one simulation. Maximaxi-mum number of iterations was set to 10.
3.4
Mesh
All models were meshed ahead of the project’s start. Two different types of meshes were used, one for the heat transfer analysis and one for the FEA. In C3D, mostly first order elements were used for heat transfer simulations, since it up until recently was the only supported element in C3D. In Abaqus, second order elements were used to better capture damages on the blades. Since the temperature field from C3D was exported as node values for the first order mesh, the temperatures had to be interpolated into the nodes and added in the second order elements. As such, the first order mesh nodes were used to interpolate the temperatures for the second order mesh nodes. This was done by the Abaqus input file. The mesh used for SGT-750 can be seen in Figure 20-21. The blade contained 509,000 elements and the disc approximately 36,000. In total around 1.1 million nodes were used for the full model.
To include the TBC’s weight, a meshed TBC layer was used in the FEA with ap-propriate material density. The Young’s modulus for the TBC was decreased by a factor 100,000 to make the calculations more conservative and remove any added creep strength from the TBC.
Figure 20: Mesh of the SGT-750 turbine blade for the FE-simulations with the TBC mesh excluded. Sensitive areas on the airfoil, such as leading and trailing edge have finer mesh.
Figure 21: Mesh of the SGT-750 turbine disc sector. The mesh is coarse since the disc mainly is simulated for improved boundary conditions.
3.5
Finite element analysis
The calculated metal temperatures of the blades together with the surface pressure were exported from C3D and applied to the FE-model for creep and TMF life anal-ysis in Abaqus. For both cases a ”cold” start up of the engine was performed in a simplified ramp step followed by steady state step simulating normal operating con-ditions. International standard atmosphere (ISA) was assumed with an exception regarding start up temperature, which was set to 30 ◦C. Equivalent creep strain was extracted from the creep simulations after 34,000 hours of operational time. The residual von Mises stress was extracted from the TMF simulations and used as an input for the in-house program EVAL, where life was analysed and compared between the different cases.
3.5.1
Computational set-up
The boundary conditions applied to the FEA models consisted of a cyclic symmetry on the disc’s two larger surfaces (tangential direction). The discs were restrained axially in the upstream directions and a point on the symmetry surface of the disc was restrained in the circumferential direction to avoid rigid body motion. Contacts were used between the disc and turbine blade with a specified friction coefficient of 0.3. To lock the axial direction of the turbine blade to the disc, an equation input was utilized. The equation input stated that movement along the grove for both disc and blade must remain equal. This was done by specifying input nodes on the surface of the dove tail and disc to tie the two parts in axial direction. The boundary conditions used in the model are summarized in Table 2, where the first column is linked to Figure 22. A centrifugal load was applied according to the steady state revolutions per minute (RPM) for each engine-serie. Metal temperatures and sur-face pressures exported from C3D were mapped onto the models.
Table 2: The boundary conditions used for the structural simulations, see figure 22.
Number Boundary condition
1 Cyclic symmetry
2 Contact between disc and foot. Blade axially tied to disc by equation. 3 Disc restrained in one point tangential direction.
4 Disc restrained in axial direction, upstream side.
Figure 22: Boundary conditions used for the structural simulations. The numbers correspond to the condition in Table 2.
3.5.2
Creep simulation
For creep simulations, a ramp up of both rotational velocity and temperature was done linearly from ISA start conditions. During the ramp up, plasticity models and creep models were activated to capture redistribution of stress and strain through
inelastic deformation. Step two consisted of 34,000 hours to capture the accumula-tion of creep (Figure 23). During the second step, steady state rotaaccumula-tional velocities were used together with steady state temperatures (Table 3). The constitutive model used in the simulations consisted of an elastic-ideal-plastic model and a ba-sic non-hardening creep model which utilizes creep strain to detect when tertiary creep begins. Tertiary creep is calculated by introducing a factor (g(in, T )), which is multiplied to the non-hardening creep model. The factor is chosen according to Equation 21.
g(in, T ) = (
1 if in< ter(T )
1 + c(in− ter(T )) if in≥ ter(T ) (21) Where in is the current creep, ter(T ) represent the onset to tertiary creep for the
material and c is a constant calibrated such that a specified ductility limit is reached at creep rupture time. T represent temperature.
Table 3: Steps for creep simulation. The simulations are divide into two steps, ramp up and steady state.
Step Duration Explanation 1 1 h Linear ramp up from ISA. 2 34,000 h Steady state temperature and RPM.
Figure 23: The creep simulation process seen over time for the two steps.
3.5.3
TMF simulation
A TMF simulation consisted of three steps, where the first step was a ramp up iden-tical to the creep simulation. The second step was similar to the second step in the creep simulations but with a duration of 5000 hours. The third step was a shut down ramp which linearly ramped both the rotational velocity and metal temperature of the blade (Table 4). The ramp down was done elastic with the plasticity model shut off (Figure 24). After Step 3, von Mises stress was extracted from calculated residual stresses, which served as an input to EVAL to calculate expected life in number of cycles.
Table 4: Steps for TMF simulations. Three steps were used, ramp-up, steady state and ramp-down.
Step Duration Explanation 1 1 h Linear ramp up from ISA. 2 5,000 h Steady state temperature and RPM. 3 1 h Linear ramp down.
Figure 24: The applied TMF simulation process seen over time. The simulations consisted of three steps, ramp up, steady state and ramp down.
EVAL
Input parameters to EVAL consisted of geometrical data, temperatures, stresses and strains. To conduct calculations, time points from TMF simulations were used. As initial condition, parameters at the last increment of Step 1 (point A) were used (Figure 25). All increments in Step 2 (point B) to Step 3 (point C) were then used in the evaluation.
Figure 25: Relation between the steps from the FEM calculations and stress.
Maximum Von Mises stress between point B and C were used to estimate the number of cycles required for crack initiation. Two different models were used to evaluate the Pseudo Elastic Residual Stress, which depended on if a node was evaluated as in-phase or out-of-phase. The hydrostatic pressure was used to determine if the node was considered as IP or OP.
4
Results
This chapter shows results from the SGT-750 simulations. The first part of the chapter is devoted the influence of TBC thickness tolerances.
Metal temperature plots of SGT-750 nom TBC from C3D showed high temperatures on both the pressure and suction side of the airfoil (Figure 26). The highest tem-perature was measured at the tip of the trailing edge, for both nom and max TBC thickness. However, for min TBC the maximum temperature location moved to the top edge at the suction side. On the pressure side the temperature field is approx-imately linear comparing the temperature difference between the TBC thicknesses (Figure 27). The tip of the airfoil is most sensitive to TBC thicknesses. Highest temperature difference was measured to 18◦C between min and nom at the tip of the blade close to the leading edge. Considering the suction side, the greatest temper-ature difference could be found close to the tip and on the airfoil surface (Figure 28).
Figure 26: Metal temperature field of SGT-750 nom TBC, where the legend has been normalised with the highest metal temperature. Highest values were measured at the tip of the blade, leading edge and platform.
Figure 27: Temperature difference of SGT-750 on the pressure side. To the left differ-ence between min and nom and to the right differdiffer-ence between nom and max TBC.
Figure 28: On the left metal temperature difference between min and nom TBC on the suction side of the SGT-750. On the right temperature difference between nom and max TBC.
Estimation of cycles from the TMF simulations are based on oxidation, fatigue and creep (Equation 19). Since only crack initiation, and not crack propagation has been evaluated, the study has not included any estimation on the total amount of cycles to failure. Most of the areas at risk for TMF were located at the platform (Figure 29). There was also an area spreading below the platform with low cycles (Figure 30). The airfoil surface, on both the inside and outside, do not have any areas with low cycles. Critical areas (Figure 31) estimated on the platform and air-foil were summarized (Table 5). According to the table, the tip of the airair-foil showed small differences between the TBC thicknesses. The temperature plots from C3D also showed that this area was relatively warm (Figure 29).
Figure 29: Result of TMF for SGT-750 with min TBC to the left, nom TBC in the middle and max TBC to the right. Values are normalised.
Figure 30: Life in number of cycles for SGT-750 including min, nom and max TBC from left to right seen from below. Both the area close to the leading edge and the area close to the trailing edge are reduced with thicker TBC, but is not completely removed. Values are normalised.
Table 5: TBC thickness influence on life in number of cycles for the SGT-750 turbine. Temperatures and stresses are presented as differences from nom TBC. Last column shows change in percentage from nom TBC.
MIN TBC Position ∆ Temp [◦C] ∆ σresv.M [MPa] IP/OP N, change rel. nom TBC [%] 1 5 24 OP -26 2 9 11 OP -1.6 3 9 15 IP -19 4 13 27 OP -8.5 5 11 33 OP -35 MAX TBC Position ∆ Temp [◦C] ∆ σresv.M [MPa] IP/OP N, change rel. nom TBC [%] 1 -5 -15 OP 23 2 -8 -7 OP -1.6 3 -7 -12 IP 20 4 -13 -23 OP 13 5 -10 -31 OP 49
Results from creep simulations after 34,000 hours showed a large area on the plat-form with larger creep strain than the majority of the blade (Figure 32-33). An area which also proved to be sensitive to the TBC thickness was the trailing edge. Apart from the trailing edge, the airfoil has close to zero creep on both the outside and inside of the airfoil for all TBC thicknesses. The results showed a decrease of stress and an increase of temperature at the trailing edge for min TBC thickness compared to max TBC thickness.
Figure 32: Results from SGT-750 creep simulations. To the left min TBC, middle nom TBC and to the right max TBC thickness. All values area normalized.
Figure 33: Creep on a SGT-750 turbine blade after 34,000 hours with different TBC thicknesses. Min TBC to the left, and max to the right with nom TBC in the middle. All values area normalized.
Areas which had a visible large difference of creep on the blade were evaluated (Fig-ure 34, Table 6). The most significant difference in creep can be seen at the trailing edge. Position P2 has a 61% increase in creep comparing nom to min TBC. Posi-tion P3, located on the sucPosi-tion side have the most significant creep increase of 76%, this is also the location with the highest stress relaxation. At the leading edge the displacement seems to be unaffected by the TBC thicknesses (Table 7). However, at the trailing edge a linear behavior of the difference in displacement was noted.
Table 6: TBC thickness influence on creep strain for some positions on SGT-750. All values are presented in comparison to nom TBC.
MIN TBC Position ∆ Temp [◦C] ∆ σv.M [MPa] Creep, change rel. nom TBC [%] 1 8 -3 35 2 11 -17 61 3 11 -29 76 4 9 -6.5 18 MAX TBC Position ∆ Temp [◦C] ∆ σv.M [MPa] Creep, change rel. nom TBC [%] 1 -8 4.3 -19 2 -9 18 -33 3 -9 16 -27 4 -8 1.5 -11
Table 7: TBC thickness influence on radial displacement for SGT-750 turbine blade, measured on the blade tip. The values are the difference in displacement compared to nom TBC.
Radial tip displacement
TBC tolerance ∆ LE displacement [mm] ∆ TE displacement [mm] MIN 0.00 0.06 MAX 0.01 -0.05
4.1
Cooling mass flow reduction - 750
Mass flow reduction of the SGT-750 blade was performed by setting up the cold model according to test procedures performed after casting. The film cooling holes on the leading edge together with the tip cooling holes were blocked. Two cases were considered for the blade. Mass flow rate for configuration 1 was reduced by increasing the PLC in the branch row between the last Pin-Fin row at the trailing edge (Figure 35 left). In configuration 2, a slightly different set-up was tested by not including the bottom branch of the pin-fin row (Figure 35 right). Both config-urations represents a deviation in casting for the aft part of the airfoil, resulting in a local pressure drop. For both configurations the total mass flow was decreased by 3.42% from the nominal value, which according to test procedures represent the minimum flow. For configuration 1 the PLC was increased by 62% for the selected branches and for configuration 2, a 74% increase of PLC was necessary since the
lower branch no longer was included in the set. Both configurations were applied to the hot model. The resulting temperature field was overall similar for both configu-rations (Figure 36) with the biggest difference compared to nom flow at the trailing edge and aft part of the airfoil. However, one major difference can be seen at the trailing edge root if the two configurations are compared. In configuration 1, a local hot spot can be seen, while this is not the case for configuration 2. When investi-gating the inside of the blade (Figure 35) it is obvious that the lower branch in the Pin-Fin row plays a major role for the temperature field, especially regarding the metal temperature on the inside of the blade. Configuration 1 creates a local hot area close to the lower branch while configuration 2 creates a much more distributed temperature rise in the whole matrix. The lower branch in configuration 1 lost 16% of the original flow velocity with the increased PLC, the neighbouring branch (radial direction) in the used set lost only 2.9% for comparison.
Figure 35: Metal temperature difference compared to nom flow of the pressure side seen from the inside, together with the flow network. Left: Configuration 1. Right: Configuration 2. The black boxes on the figure represent the area of branches which were used for the mass flow reduction. Note that configuration 2 does not include the lower horizontal branch of the selected branch row.
Figure 36: Temperature difference plot between nom mass flow rate with min TBC and min mass flow rate with min TBC thickness. Top: Configuration 1. Bottom: Configuration 2.
4.1.1
Reduced mass flow- TMF results 750
Results from TMF simulations with min flow tolerance showed small differences compared to nom flow. No visible differences could be seen when contour plots of life were compared between the cases and to a baseline case with min TBC and nom cooling flow (Figure 37). However, when looking at the positions regarding TMF used throughout this chapter, a difference can be seen for each position (Table 8). Note that the number of cycles to failure have increased for each position investi-gated. The greatest increase can be found in position P2 for configuration 1. Here the increase in life is over 8%. The same location on configuration 2 has an increase of 4.8%. For configuration 2 the highest increase can instead be found in position P3, also located on the platform close to the trailing edge. When looking at the temperature difference compared to the baseline case with nom flow, it is possible to see that the difference in the selected positions are very small. For configuration 2, the biggest difference is only 1 ◦C. For both configurations the residual stresses have decreased in each position compared to the baseline case.
