- Email: [email protected]
Failure analysis in after shell section of gas turbine combustion liner under base-load operation
Engineering Failure Analysis 17 (2010) 848–856
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Failure analysis in after shell section of gas turbine combustion liner under base-load operation Kyung Min Kim, Namgeon Yun, Yun Heung Jeon, Dong Hyun Lee, Hyung Hee Cho * Department of Mechanical Engineering, Yonsei University, 134, Sinchon-dong, Seodaemun-gu, Seoul 120-749, Republic of Korea
a r t i c l e
i n f o
Article history: Received 13 July 2009 Accepted 11 October 2009 Available online 16 December 2009 Keywords: Failure analysis Gas turbine failures High temperature fatigue Thermal stress
a b s t r a c t The present study investigates the failure analysis and the lifetime prediction in the after shell section of gas turbine combustion liner with internal cooling passages called C-channel. To calculate distributions of temperature and stresses, 3D-numerical simulations using FVM and FEM commercial codes are performed. As a result, the discrepancy in thermal expansion between hot and coolant side walls induces high thermal stresses in the welding region and above the divider of the C-channel. Thus, these two regions are much weaker than the other regions. The locations match well to those of thermal cracks in actual gas turbine combustors in service. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In gas turbine systems, the achievement of high thermal efficiency is strongly related to the increase in the turbine inlet temperature, which is accompanied by the excess thermal load in the hot components of gas turbine. Thus, various cooling techniques [1–3] have been used to protect the main hot parts of the gas turbines. If unsuitable cooling method is used, the local thermal crack and structural failure are yielded due to the thermal stress and the reduction of the material strength in high temperature. Therefore, the failure analyses as well as the thermal analyses for temperature, deformation and stress are required for the effective thermal design and the lifetime prediction of hot components. It is noted that the failure analysis was investigated only in material point of view, but rarely with thermal analysis, by many researchers [4–8]. Furthermore, the temperature gradient in each hot component increases with the turbine inlet temperature increasing, and it generates thermal damages by high thermal stresses. It is necessary to estimate the temperature distributions in the materials of the system in an appropriate thermal environment to predict the life and safety of hot components such as combustors, vanes, and blades. In recent years, several investigators [9–12] have attempted a thermal analysis in hot components of gas turbines and the thermal damages were predicted. It has been shown that the computational results are useful for inspecting the thermal environment of the gas turbine and defining the factors that contribute to advanced maintenance and operation. In this paper, we can find the locations of high stresses under the steady state operation and the base-load operation using the thermal analysis of the after section of combustor liners. However, it is hard to decide whether the high stresses will cause fatigues induced by the transient operations such as unit start-up and shut-down. Therefore, the objective of the present research is to find major causes of thermal damages affecting the creep lifetime induced by the temperature and thermal stress distributions. As an example, we calculated the lifetime and the distributions of temperature and thermal stress which have often yielded the axial and weld cracks in an actual combustion liner in service as shown in Fig. 1, and then we find the causes of these cracks from the analysis results. * Corresponding author. Tel.: +82 2 2123 2828; fax: +82 2 312 2159. E-mail address: [email protected] (H.H. Cho). 1350-6307/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2009.10.018
K.M. Kim et al. / Engineering Failure Analysis 17 (2010) 848–856
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Nomenclature D E h K t T2 Tw Tm q UTS YS
hole diameter Young’s modulus heat transfer coefficients, q/(Tw Tm) thermal conductivity the lifetime in hours coolant flow temperature wall temperature main flow temperature heat flux per unit area ultimate tensile stress yield stress
Greek symbols thermal expansion coefficient v Poisson’s ratio rv von-Mises stress rn de-bonding stress or stress in the direction normal to the TBC bonded surface rc initial creep stress
a
2. Research methods The combustion liner [13] is divided into three parts such as forward shell section, center shell section, and after shell section as shown in Fig. 2a. Each section has different cooling methods. In other words, the forward shell, the center shell, and the after shell sections are cooled by rib-roughened passage, impingement jet, and C-channel, respectively. Among these sections, the after shell section is cooled using an internal passage cooling method because this section is inserted into transition piece. It is called C-channel and is invented by Intile et al. [14]. The C-channel consists of cooling holes, divider walls, hot side wall, coolant side wall, and spring seals as described in Fig. 2b. In the present study, one hole segment of the 88 cooling holes of which diameter (D) is 2.6 mm in this section is considered for analysis because the shape has a symmetric behavior as shown in Fig. 3a. The calculations of fluid flow and heat transfer are conducted using a computational fluid dynamics (CFD) code, CFX v11. The Reynold-averaged Navier–Stokes equations and the transport equations of the turbulent quantities are solved by the pressure correction algorithm SIMPLE. The fluid is considered to be compressible and fluid properties are assumed as a function of flow temperature. The turbulence model is the SST k–x model. The grid consists of approximately 1.5 million cells including flow and solid domains with TBC, of which thickness is 1.0 mm as shown in Fig. 3b. The external boundary conditions were set to constants in Table 1. A stress analysis was conducted using the calculated temperature data to find the causes of the thermal damage in the aforementioned geometries. The numerical stress analysis was performed using a finite element analysis (FEA) code, ANSYS v11. In the numerical calculations, the boundary conditions used the temperature and the heat transfer data calculated from the CFD analysis. To calculate the thermal stresses, symmetric conditions in both the side regions and constant forces of 1500 N into reverse z-axis direction at locations of spring seal were imposed. Constraints are very important because most stresses are caused by settlements of constraints and thermal effects (arising from temperature changes and differences). In other words, the thermal stress for structural materials is proportional to the material property, thermal expansion coeffi-
Fig. 1. Thermal damages observed in service.
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(a)
Forward Shell Section
Center Shell Section
(b)
After Shell Section
Spring Seal
Coolant Side Wall
Cooling Hole
C-Channel Divider Wall
Hot Side Wall Fig. 2. Geometries and names in the combustion liner: (a) section names in the combustion liner [13] and (b) schematic of C-channel in after shell section [14].
cient (a) and temperature difference (DT) as presented as r = EaDT. The used mechanical properties such as thermal expansion coefficient (a), Young’s modulus (E), and Poisson’s ratio (v), are presented in Tables 2 and 3. The equivalent or von-Mises stress (rv) is obtained in the calculated results because it is a part of the maximum stress in failure theory used to predict yielding in a ductile material. The de-bonding stress (rn) in the direction normal to the interface is used in order to predict the TBC de-bonding force. The creep stress (rc) is additional strength induced by constraints except strain generated by thermal deformation in free constraints. In order to predict the creep lifetime (t) using these temperature and creep stress at each element, three-order polynomial function, f(rc) is induced from Larson–Miller rupture curves and creep stress (rc) in the material (supper-alloy), where Larson–Miller values are Tw(log t + 20)/1000. Then, from two functions, the lifetime (t) is induced as following equation.
log ðtÞ ¼ 103 f ðrc Þ=T w 20 where Tw is temperature in K, t is time in h, and rc is stress in MPa.
ð1Þ
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Fig. 3. Numerical domains and boundary conditions for thermal analysis: (a) boundary conditions of external surfaces and (b) flow and solid domains for calculating internal heat transfer coefficients.
Table 1 Boundary conditions imposed on the external surfaces. Boundary surface
Conditions
Values
Hot combustion gas side
Heat transfer coefficient Flow temperature Heat transfer coefficient Flow temperature Heat transfer coefficient Flow temperature Flow temperature Re based on hole diameter
1000 W/m2 K 1350 °C 150 W/m2 K 400 °C 2000 W/m2 K 400 °C 400 °C 40,000
Compressed coolant air side above spring seal Compressed coolant air side on the others Hole-inlet coolant flow
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Table 2 Physical properties of super-alloy. Temperature (°C)
Thermal conductivity (W/m °C)
Thermal expansion coefficient (lm/m °C)
Young’s modulus (GPa)
Poisson’s ratio
100 200 400 600 800 1000
13.0 14.7 18.0 21.4 24.7 28.5
11.0 12.1 13.0 13.9 15.3 17.4
217 212 198 185 168 143
0.382 0.384 0.387 0.391 0.397 0.402
Table 3 Physical properties of TBC. Temperature (°C)
Thermal conductivity (W/m °C)
Thermal expansion coefficient (lm/m °C)
Young’s modulus (GPa)
Poisson’s ratio
400 600 800 1000 1100 1200
2.1 2.13 2.2 2.3 2.35 2.4
10.2 10.3 10.4 10.5 10.4 10.3
30.5 31.3 32.0 32.5 31.3 30.1
0.265 0.268 0.270 0.275 0.278 0.280
3. Results and discussion Fig. 4 shows distributions of heat transfer coefficient and wall adjacent temperature in the internal passage called C-channel. The wall adjacent temperature (Fig. 4a) under the impinging hole is risen by 30 °C more than the flow inlet temperature of 400 °C due to the crossflow by the side wall nearby the welding region. The lowest wall adjacent temperature appears in the region between impingement jet hole and divider wall tip because the jet flow is deflected by the crossflow. The flow temperature increases as moving downstream from the hole and then it reaches up to 640 °C on the hot side wall of the flow outlet. The temperature on the hot side wall is approximately 30 °C higher than that on the coolant side wall. The reason is that the hot side wall is heated by hot combustion gas flow through conduction heat transfer, while the coolant side wall is cooled by coolant air flow. As shown in Fig. 4a–c, the heat transfer coefficients are changed largely in the whole domain. In this whole domain, the distributions f heat transfer coefficients are divided into four different regions: (1) in the region of impingement jet and nearby side welding wall, the lowest heat transfer is obtained because of the interaction of the crossflow and the impinging jet. The crossflow, created by the side welding wall, deflects the impinging jet flow; (2) in the region downstream of the impinging jet hole, heat transfer is enhanced significantly by the impingement of deflected jet flow. This flow yields the highest heat transfer coefficients in this region of the coolant side wall as presented in Fig. 4c. Also, the heat transfer increases on the coolant side wall as shown in Fig. 4b because the flow ascends toward the coolant side wall. The reason is that the gap distance between the hot and the coolant side walls is very short; (3) in the region after the tip of the divider wall, the impinged cooling flow is divided into two channels, and then the flow is accelerated because the flow area is reduced by the divider wall. Therefore, the heat transfer coefficients are enhanced; (4) in the region downstream of the divider wall tip, the heat transfer rate is decreased slightly by the development of flow and thermal boundary layers. Fig. 5 shows the temperature distributions in the after section of the combustion liner. The figures consist of the overall domain (Fig. 5a), the segment coolant side wall (Fig. 5b), and top (Fig. 5c)/bottom (Fig. 5d) regions of the TBC. The characteristics of the temperature distributions are divided into four parts in the whole region. In region 1, the temperature gradient is generated by only conduction between hot and cold regions. The maximum temperature appears at the end of the segment on TBC bottom and its magnitude is 915.85 °C. Total temperature drop in z-axial direction is approximately 200 °C, where the temperature drop in each material is 150 °C at TBC and 50 °C at super-alloy. In region 2 (welding region), the temperature is ranged from 410 °C to 520 °C because the heat transfer is affected greatly by convection from region as well as conduction from region 1, but. The temperature in region 3 is decreased significantly up to 407.15 °C in the x-axial direction because this coolant side wall is separated from hot side wall by the internal cooling channel. However, in region 4, the contact between the two walls is made by the divider wall. Thus, the temperature reaches up to 630 °C, because this region is away from the impinging jet hole and the conduction occurs between two coolant and hot side walls. Fig. 6 presents the thermal stresses resulting from the temperature distributions. High thermal stresses on the coolant side wall appear in three local regions which are on the welding part of region 2, nearby the hole in region 3, and above the divider wall of region 4 as shown in Fig. 6a. The von-Mises stresses are distributed in ranges between 400 MPa and 500 MPa. The high thermal stresses are caused by following reasons: (1) in the welding part of region 2, the temperature gradient in the x-axial direction is decreased steeply by the cooling flow in the C-channel. The reason is that heat transfer rate of conduction is higher than that of convection in a super-alloy; (2) around the hole in region 3, the thermal expansion
K.M. Kim et al. / Engineering Failure Analysis 17 (2010) 848–856
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Fig. 4. Distributions of heat transfer coefficient and wall adjacent temperature in the internal C-channel: (a) 3D-view; (b) heat transfer coefficient on coolant side wall; and (c) heat transfer coefficient on hot side wall.
rate is the lowest due to the lowest temperature. However, the deformation in these regions is enforced due to high thermal expansion rate around high temperature metals, Thus, the thermal stress around the hole becomes bigger; (3) above the divider wall of region 4, the thermal expansion rate on the coolant side wall is lower than that on the hot side wall, and then the deformation of the coolant side wall region is also influenced by the divider wall. Therefore, the high thermal stress is generated above the divider wall. In addition, the high thermal stress on the hot side wall also appears in the vicinity of the divider of the other hot side wall as shown in Fig. 6b. The highest de-bonding stress (Fig. 6c), which can yield TBC delamination (normal stress, rn), appears at the location of divider tip on the interface between TBC and super-alloy. The magnitude of maximum thermal stress reaches to 10.8 MPa. Fig. 7 presents creep-rupture property data of nickel-base alloy supplied by special metals [15] and a third order polynomial fit of the values. The lifetime (t) as presented in Eq. (2) is induced from the Larson–Miller parameter, Eq. (1) and the third order polynomial fit in Fig. 7.
t ¼ 10P ; where P ¼ 103 =T w f ðrc Þ 20 and f ðrc Þ ¼ ajrc j3 þ bjrc j2 þ cjrc j þ d
ð2Þ
Fig. 8a shows the initial creep stress (rc) at each element for the lifetime prediction. The stress distributions of the negative on the hot side wall but the positive on the coolant side wall are caused by the thermal stresses. Fig. 8b presents the lifetime predicted from the creep stress and temperature using Eq. (2) at each element. The other short lifetime regions
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Fig. 5. Wall temperature distributions: (a) without spring seal; (b) without coolant side wall; (c) on interface between TBC and super-alloy; and (d) on hot gas flow surface.
among elements exist on the top of the welding part of region 2 and on the divider wall of region 4 in the coolant side wall. The minimum lifetime of the regions 2 and 4 is 19,000 h and 20,000 h, respectively. In hot side wall, the minimum lifetime is approximately 26,000 h in the elements in region 4 (R4). The locations of elements with the short lifetime agree well with locations of actual thermal damages, such as the weld and axial cracks in service as aforementioned in Fig. 1.
4. Conclusions In the present study, the failure analysis and the lifetime prediction were investigated from distributions of temperature and thermal stress in after shell section of gas turbine combustion liner. 3D-numerical simulations using the FEM and FVM commercial codes, ANSYS and CFX, were conducted to calculate distributions of temperature and thermal stresses in the Cchannel, which protected this section connecting to a gas turbine transition piece. The calculated temperature on the coolant side wall was lower than that on the hot side wall. The thermal deformation of the hot side wall is larger than that of the coolant side wall by the thermal expansion difference. The high thermal stresses resulting from the difference in thermal expansion were presented at three regions such as the welding region, around the hole, and the divider wall of C-channel. Furthermore, the lifetimes of the welding region and the divider wall region were shorter than those of the other regions. The calculated locations were similar to those of actual thermal cracks in combustion liner after section of gas turbine. In summary, the thermal analysis including heat transfer and thermal stress calculations and the lifetime prediction using creep-rupture data are suitable for predicting thermal damage. Further studies on thermal design, including both thermal analysis and detailed cooling design, are required to reduce the large and dramatic temperature difference (thermal stress) in the materials.
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Fig. 6. Thermal results: (a) stress distribution without spring seal; (b) stress distribution without coolant side wall; and (c) de-bonding stress on interface between super-alloy and TBC.
28
Larson Miller Parameter (10
-3
)
Values on Data Sheet Polynomial Fit of the Values
26 24
22 20 18 16 0
100
200
300
400
500
600
700
Stress (MPa) Fig. 7. Creep-rupture data of super-alloy for prediction of the lifetime.
800
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Fig. 8. Predictions of the lifetime at each element: (a) creep stress at each element; and (b) lifetime by creep stress and temperature.
Acknowledgment This work was supported partially by the Electric Power Industry Technology Evaluation and Planning. References [1] Goldstein RJ. Film cooling. Adv Heat Trans 1971;7:321–79. [2] Han JC, Dutta S, Ekkad SV. Gas turbine heat transfer and cooling technology. New York: Taylor and Francis; 2000. [3] Kim KM, Kim YY, Lee DH, Rhee DH, Cho HH. Influence of duct aspect ratio on heat/mass transfer in coolant passages with rotation. Int J Heat Fluid Flow 2007;28(3):357–73. [4] Tryon RG, Cruse TA, Mahadevan S. Development of a reliability-based fatigue life model for gas turbine engine structures. Eng Fract Mech 1996;53(5):807–28. [5] Gallardo JM, Rodriguez JA, Herrera EJ. Failure of gas turbine blades. Wear 2002;252:264–8. [6] Chang JC, Yun YH, Choi C, Kim JC. Failure analysis of gas turbine buckets. Eng Fail Anal 2003;10:559–67. [7] Carter TJ. Common failures in gas turbine blades. Eng Fail Anal 2005;12:237–47. [8] Kawasaki A, Watanabe R. Thermal fracture behavior of metal/ceramic functionally graded materials. Eng Fract Mech 2002;69:1713–28. [9] Cunha FJ, Dahmer MT, Chyu MK. Thermal–mechanical life prediction system for anisotropic turbine components. ASME J Turbomach 2006;128:240–50. [10] Tinga T, Kampen JF, Jager B, Kok JBW. Gas turbine combustor liner life assessment using a combined fluid/structural approach. ASME J Eng Gas Turb Power 2007;129(1):69–79. [11] Hou NX, Wen ZX, Du ZX, Yue ZF. Crystallographic failure analysis of film near cooling hole under temperature gradient of nickel-based single crystal superalloys. Theor Appl Fract Mech 2007;47:164–70. [12] Kim KM, Lee DH, Cho HH. Thermal analysis of a film cooling system with normal injection holes using experimental data. Int J Fluid Mach Syst 2009;2(1):55–60. [13] Martling VC, Xiao Z. Combustion liner having improved cooling and sealing. United States Patent No. US7269957 B2; 2007. [14] Intile JC, West JA, Byrne W. Method and apparatus for cooling combustion liner and transition piece of a gas turbine. United States Patent No. US7010921 B2; 2007. [15] Special metals. Product handbook of high-performance alloys. Special Metals Corporation; 2007 [Publication No. SMC-054].
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Failure analysis in after shell section of gas turbine combustion liner under base-load operation Kyung Min Kim, Namgeon Yun, Yun Heung Jeon, Dong Hyun Lee, Hyung Hee Cho * Department of Mechanical Engineering, Yonsei University, 134, Sinchon-dong, Seodaemun-gu, Seoul 120-749, Republic of Korea
a r t i c l e
i n f o
Article history: Received 13 July 2009 Accepted 11 October 2009 Available online 16 December 2009 Keywords: Failure analysis Gas turbine failures High temperature fatigue Thermal stress
a b s t r a c t The present study investigates the failure analysis and the lifetime prediction in the after shell section of gas turbine combustion liner with internal cooling passages called C-channel. To calculate distributions of temperature and stresses, 3D-numerical simulations using FVM and FEM commercial codes are performed. As a result, the discrepancy in thermal expansion between hot and coolant side walls induces high thermal stresses in the welding region and above the divider of the C-channel. Thus, these two regions are much weaker than the other regions. The locations match well to those of thermal cracks in actual gas turbine combustors in service. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction In gas turbine systems, the achievement of high thermal efficiency is strongly related to the increase in the turbine inlet temperature, which is accompanied by the excess thermal load in the hot components of gas turbine. Thus, various cooling techniques [1–3] have been used to protect the main hot parts of the gas turbines. If unsuitable cooling method is used, the local thermal crack and structural failure are yielded due to the thermal stress and the reduction of the material strength in high temperature. Therefore, the failure analyses as well as the thermal analyses for temperature, deformation and stress are required for the effective thermal design and the lifetime prediction of hot components. It is noted that the failure analysis was investigated only in material point of view, but rarely with thermal analysis, by many researchers [4–8]. Furthermore, the temperature gradient in each hot component increases with the turbine inlet temperature increasing, and it generates thermal damages by high thermal stresses. It is necessary to estimate the temperature distributions in the materials of the system in an appropriate thermal environment to predict the life and safety of hot components such as combustors, vanes, and blades. In recent years, several investigators [9–12] have attempted a thermal analysis in hot components of gas turbines and the thermal damages were predicted. It has been shown that the computational results are useful for inspecting the thermal environment of the gas turbine and defining the factors that contribute to advanced maintenance and operation. In this paper, we can find the locations of high stresses under the steady state operation and the base-load operation using the thermal analysis of the after section of combustor liners. However, it is hard to decide whether the high stresses will cause fatigues induced by the transient operations such as unit start-up and shut-down. Therefore, the objective of the present research is to find major causes of thermal damages affecting the creep lifetime induced by the temperature and thermal stress distributions. As an example, we calculated the lifetime and the distributions of temperature and thermal stress which have often yielded the axial and weld cracks in an actual combustion liner in service as shown in Fig. 1, and then we find the causes of these cracks from the analysis results. * Corresponding author. Tel.: +82 2 2123 2828; fax: +82 2 312 2159. E-mail address: [email protected] (H.H. Cho). 1350-6307/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.engfailanal.2009.10.018
K.M. Kim et al. / Engineering Failure Analysis 17 (2010) 848–856
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Nomenclature D E h K t T2 Tw Tm q UTS YS
hole diameter Young’s modulus heat transfer coefficients, q/(Tw Tm) thermal conductivity the lifetime in hours coolant flow temperature wall temperature main flow temperature heat flux per unit area ultimate tensile stress yield stress
Greek symbols thermal expansion coefficient v Poisson’s ratio rv von-Mises stress rn de-bonding stress or stress in the direction normal to the TBC bonded surface rc initial creep stress
a
2. Research methods The combustion liner [13] is divided into three parts such as forward shell section, center shell section, and after shell section as shown in Fig. 2a. Each section has different cooling methods. In other words, the forward shell, the center shell, and the after shell sections are cooled by rib-roughened passage, impingement jet, and C-channel, respectively. Among these sections, the after shell section is cooled using an internal passage cooling method because this section is inserted into transition piece. It is called C-channel and is invented by Intile et al. [14]. The C-channel consists of cooling holes, divider walls, hot side wall, coolant side wall, and spring seals as described in Fig. 2b. In the present study, one hole segment of the 88 cooling holes of which diameter (D) is 2.6 mm in this section is considered for analysis because the shape has a symmetric behavior as shown in Fig. 3a. The calculations of fluid flow and heat transfer are conducted using a computational fluid dynamics (CFD) code, CFX v11. The Reynold-averaged Navier–Stokes equations and the transport equations of the turbulent quantities are solved by the pressure correction algorithm SIMPLE. The fluid is considered to be compressible and fluid properties are assumed as a function of flow temperature. The turbulence model is the SST k–x model. The grid consists of approximately 1.5 million cells including flow and solid domains with TBC, of which thickness is 1.0 mm as shown in Fig. 3b. The external boundary conditions were set to constants in Table 1. A stress analysis was conducted using the calculated temperature data to find the causes of the thermal damage in the aforementioned geometries. The numerical stress analysis was performed using a finite element analysis (FEA) code, ANSYS v11. In the numerical calculations, the boundary conditions used the temperature and the heat transfer data calculated from the CFD analysis. To calculate the thermal stresses, symmetric conditions in both the side regions and constant forces of 1500 N into reverse z-axis direction at locations of spring seal were imposed. Constraints are very important because most stresses are caused by settlements of constraints and thermal effects (arising from temperature changes and differences). In other words, the thermal stress for structural materials is proportional to the material property, thermal expansion coeffi-
Fig. 1. Thermal damages observed in service.
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K.M. Kim et al. / Engineering Failure Analysis 17 (2010) 848–856
(a)
Forward Shell Section
Center Shell Section
(b)
After Shell Section
Spring Seal
Coolant Side Wall
Cooling Hole
C-Channel Divider Wall
Hot Side Wall Fig. 2. Geometries and names in the combustion liner: (a) section names in the combustion liner [13] and (b) schematic of C-channel in after shell section [14].
cient (a) and temperature difference (DT) as presented as r = EaDT. The used mechanical properties such as thermal expansion coefficient (a), Young’s modulus (E), and Poisson’s ratio (v), are presented in Tables 2 and 3. The equivalent or von-Mises stress (rv) is obtained in the calculated results because it is a part of the maximum stress in failure theory used to predict yielding in a ductile material. The de-bonding stress (rn) in the direction normal to the interface is used in order to predict the TBC de-bonding force. The creep stress (rc) is additional strength induced by constraints except strain generated by thermal deformation in free constraints. In order to predict the creep lifetime (t) using these temperature and creep stress at each element, three-order polynomial function, f(rc) is induced from Larson–Miller rupture curves and creep stress (rc) in the material (supper-alloy), where Larson–Miller values are Tw(log t + 20)/1000. Then, from two functions, the lifetime (t) is induced as following equation.
log ðtÞ ¼ 103 f ðrc Þ=T w 20 where Tw is temperature in K, t is time in h, and rc is stress in MPa.
ð1Þ
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Fig. 3. Numerical domains and boundary conditions for thermal analysis: (a) boundary conditions of external surfaces and (b) flow and solid domains for calculating internal heat transfer coefficients.
Table 1 Boundary conditions imposed on the external surfaces. Boundary surface
Conditions
Values
Hot combustion gas side
Heat transfer coefficient Flow temperature Heat transfer coefficient Flow temperature Heat transfer coefficient Flow temperature Flow temperature Re based on hole diameter
1000 W/m2 K 1350 °C 150 W/m2 K 400 °C 2000 W/m2 K 400 °C 400 °C 40,000
Compressed coolant air side above spring seal Compressed coolant air side on the others Hole-inlet coolant flow
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Table 2 Physical properties of super-alloy. Temperature (°C)
Thermal conductivity (W/m °C)
Thermal expansion coefficient (lm/m °C)
Young’s modulus (GPa)
Poisson’s ratio
100 200 400 600 800 1000
13.0 14.7 18.0 21.4 24.7 28.5
11.0 12.1 13.0 13.9 15.3 17.4
217 212 198 185 168 143
0.382 0.384 0.387 0.391 0.397 0.402
Table 3 Physical properties of TBC. Temperature (°C)
Thermal conductivity (W/m °C)
Thermal expansion coefficient (lm/m °C)
Young’s modulus (GPa)
Poisson’s ratio
400 600 800 1000 1100 1200
2.1 2.13 2.2 2.3 2.35 2.4
10.2 10.3 10.4 10.5 10.4 10.3
30.5 31.3 32.0 32.5 31.3 30.1
0.265 0.268 0.270 0.275 0.278 0.280
3. Results and discussion Fig. 4 shows distributions of heat transfer coefficient and wall adjacent temperature in the internal passage called C-channel. The wall adjacent temperature (Fig. 4a) under the impinging hole is risen by 30 °C more than the flow inlet temperature of 400 °C due to the crossflow by the side wall nearby the welding region. The lowest wall adjacent temperature appears in the region between impingement jet hole and divider wall tip because the jet flow is deflected by the crossflow. The flow temperature increases as moving downstream from the hole and then it reaches up to 640 °C on the hot side wall of the flow outlet. The temperature on the hot side wall is approximately 30 °C higher than that on the coolant side wall. The reason is that the hot side wall is heated by hot combustion gas flow through conduction heat transfer, while the coolant side wall is cooled by coolant air flow. As shown in Fig. 4a–c, the heat transfer coefficients are changed largely in the whole domain. In this whole domain, the distributions f heat transfer coefficients are divided into four different regions: (1) in the region of impingement jet and nearby side welding wall, the lowest heat transfer is obtained because of the interaction of the crossflow and the impinging jet. The crossflow, created by the side welding wall, deflects the impinging jet flow; (2) in the region downstream of the impinging jet hole, heat transfer is enhanced significantly by the impingement of deflected jet flow. This flow yields the highest heat transfer coefficients in this region of the coolant side wall as presented in Fig. 4c. Also, the heat transfer increases on the coolant side wall as shown in Fig. 4b because the flow ascends toward the coolant side wall. The reason is that the gap distance between the hot and the coolant side walls is very short; (3) in the region after the tip of the divider wall, the impinged cooling flow is divided into two channels, and then the flow is accelerated because the flow area is reduced by the divider wall. Therefore, the heat transfer coefficients are enhanced; (4) in the region downstream of the divider wall tip, the heat transfer rate is decreased slightly by the development of flow and thermal boundary layers. Fig. 5 shows the temperature distributions in the after section of the combustion liner. The figures consist of the overall domain (Fig. 5a), the segment coolant side wall (Fig. 5b), and top (Fig. 5c)/bottom (Fig. 5d) regions of the TBC. The characteristics of the temperature distributions are divided into four parts in the whole region. In region 1, the temperature gradient is generated by only conduction between hot and cold regions. The maximum temperature appears at the end of the segment on TBC bottom and its magnitude is 915.85 °C. Total temperature drop in z-axial direction is approximately 200 °C, where the temperature drop in each material is 150 °C at TBC and 50 °C at super-alloy. In region 2 (welding region), the temperature is ranged from 410 °C to 520 °C because the heat transfer is affected greatly by convection from region as well as conduction from region 1, but. The temperature in region 3 is decreased significantly up to 407.15 °C in the x-axial direction because this coolant side wall is separated from hot side wall by the internal cooling channel. However, in region 4, the contact between the two walls is made by the divider wall. Thus, the temperature reaches up to 630 °C, because this region is away from the impinging jet hole and the conduction occurs between two coolant and hot side walls. Fig. 6 presents the thermal stresses resulting from the temperature distributions. High thermal stresses on the coolant side wall appear in three local regions which are on the welding part of region 2, nearby the hole in region 3, and above the divider wall of region 4 as shown in Fig. 6a. The von-Mises stresses are distributed in ranges between 400 MPa and 500 MPa. The high thermal stresses are caused by following reasons: (1) in the welding part of region 2, the temperature gradient in the x-axial direction is decreased steeply by the cooling flow in the C-channel. The reason is that heat transfer rate of conduction is higher than that of convection in a super-alloy; (2) around the hole in region 3, the thermal expansion
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Fig. 4. Distributions of heat transfer coefficient and wall adjacent temperature in the internal C-channel: (a) 3D-view; (b) heat transfer coefficient on coolant side wall; and (c) heat transfer coefficient on hot side wall.
rate is the lowest due to the lowest temperature. However, the deformation in these regions is enforced due to high thermal expansion rate around high temperature metals, Thus, the thermal stress around the hole becomes bigger; (3) above the divider wall of region 4, the thermal expansion rate on the coolant side wall is lower than that on the hot side wall, and then the deformation of the coolant side wall region is also influenced by the divider wall. Therefore, the high thermal stress is generated above the divider wall. In addition, the high thermal stress on the hot side wall also appears in the vicinity of the divider of the other hot side wall as shown in Fig. 6b. The highest de-bonding stress (Fig. 6c), which can yield TBC delamination (normal stress, rn), appears at the location of divider tip on the interface between TBC and super-alloy. The magnitude of maximum thermal stress reaches to 10.8 MPa. Fig. 7 presents creep-rupture property data of nickel-base alloy supplied by special metals [15] and a third order polynomial fit of the values. The lifetime (t) as presented in Eq. (2) is induced from the Larson–Miller parameter, Eq. (1) and the third order polynomial fit in Fig. 7.
t ¼ 10P ; where P ¼ 103 =T w f ðrc Þ 20 and f ðrc Þ ¼ ajrc j3 þ bjrc j2 þ cjrc j þ d
ð2Þ
Fig. 8a shows the initial creep stress (rc) at each element for the lifetime prediction. The stress distributions of the negative on the hot side wall but the positive on the coolant side wall are caused by the thermal stresses. Fig. 8b presents the lifetime predicted from the creep stress and temperature using Eq. (2) at each element. The other short lifetime regions
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Fig. 5. Wall temperature distributions: (a) without spring seal; (b) without coolant side wall; (c) on interface between TBC and super-alloy; and (d) on hot gas flow surface.
among elements exist on the top of the welding part of region 2 and on the divider wall of region 4 in the coolant side wall. The minimum lifetime of the regions 2 and 4 is 19,000 h and 20,000 h, respectively. In hot side wall, the minimum lifetime is approximately 26,000 h in the elements in region 4 (R4). The locations of elements with the short lifetime agree well with locations of actual thermal damages, such as the weld and axial cracks in service as aforementioned in Fig. 1.
4. Conclusions In the present study, the failure analysis and the lifetime prediction were investigated from distributions of temperature and thermal stress in after shell section of gas turbine combustion liner. 3D-numerical simulations using the FEM and FVM commercial codes, ANSYS and CFX, were conducted to calculate distributions of temperature and thermal stresses in the Cchannel, which protected this section connecting to a gas turbine transition piece. The calculated temperature on the coolant side wall was lower than that on the hot side wall. The thermal deformation of the hot side wall is larger than that of the coolant side wall by the thermal expansion difference. The high thermal stresses resulting from the difference in thermal expansion were presented at three regions such as the welding region, around the hole, and the divider wall of C-channel. Furthermore, the lifetimes of the welding region and the divider wall region were shorter than those of the other regions. The calculated locations were similar to those of actual thermal cracks in combustion liner after section of gas turbine. In summary, the thermal analysis including heat transfer and thermal stress calculations and the lifetime prediction using creep-rupture data are suitable for predicting thermal damage. Further studies on thermal design, including both thermal analysis and detailed cooling design, are required to reduce the large and dramatic temperature difference (thermal stress) in the materials.
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Fig. 6. Thermal results: (a) stress distribution without spring seal; (b) stress distribution without coolant side wall; and (c) de-bonding stress on interface between super-alloy and TBC.
28
Larson Miller Parameter (10
-3
)
Values on Data Sheet Polynomial Fit of the Values
26 24
22 20 18 16 0
100
200
300
400
500
600
700
Stress (MPa) Fig. 7. Creep-rupture data of super-alloy for prediction of the lifetime.
800
856
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Fig. 8. Predictions of the lifetime at each element: (a) creep stress at each element; and (b) lifetime by creep stress and temperature.
Acknowledgment This work was supported partially by the Electric Power Industry Technology Evaluation and Planning. References [1] Goldstein RJ. Film cooling. Adv Heat Trans 1971;7:321–79. [2] Han JC, Dutta S, Ekkad SV. Gas turbine heat transfer and cooling technology. New York: Taylor and Francis; 2000. [3] Kim KM, Kim YY, Lee DH, Rhee DH, Cho HH. Influence of duct aspect ratio on heat/mass transfer in coolant passages with rotation. Int J Heat Fluid Flow 2007;28(3):357–73. [4] Tryon RG, Cruse TA, Mahadevan S. Development of a reliability-based fatigue life model for gas turbine engine structures. Eng Fract Mech 1996;53(5):807–28. [5] Gallardo JM, Rodriguez JA, Herrera EJ. Failure of gas turbine blades. Wear 2002;252:264–8. [6] Chang JC, Yun YH, Choi C, Kim JC. Failure analysis of gas turbine buckets. Eng Fail Anal 2003;10:559–67. [7] Carter TJ. Common failures in gas turbine blades. Eng Fail Anal 2005;12:237–47. [8] Kawasaki A, Watanabe R. Thermal fracture behavior of metal/ceramic functionally graded materials. Eng Fract Mech 2002;69:1713–28. [9] Cunha FJ, Dahmer MT, Chyu MK. Thermal–mechanical life prediction system for anisotropic turbine components. ASME J Turbomach 2006;128:240–50. [10] Tinga T, Kampen JF, Jager B, Kok JBW. Gas turbine combustor liner life assessment using a combined fluid/structural approach. ASME J Eng Gas Turb Power 2007;129(1):69–79. [11] Hou NX, Wen ZX, Du ZX, Yue ZF. Crystallographic failure analysis of film near cooling hole under temperature gradient of nickel-based single crystal superalloys. Theor Appl Fract Mech 2007;47:164–70. [12] Kim KM, Lee DH, Cho HH. Thermal analysis of a film cooling system with normal injection holes using experimental data. Int J Fluid Mach Syst 2009;2(1):55–60. [13] Martling VC, Xiao Z. Combustion liner having improved cooling and sealing. United States Patent No. US7269957 B2; 2007. [14] Intile JC, West JA, Byrne W. Method and apparatus for cooling combustion liner and transition piece of a gas turbine. United States Patent No. US7010921 B2; 2007. [15] Special metals. Product handbook of high-performance alloys. Special Metals Corporation; 2007 [Publication No. SMC-054].