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Effect of thermal stress on creep lifetime for a gas turbine combustion liner
Engineering Failure Analysis 47 (2015) 34–40
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Effect of thermal stress on creep lifetime for a gas turbine combustion liner Hokyu Moon a, Kyung Min Kim b, Yun Heung Jeon c, Sangwoo Shin a, Jun Su Park a, Hyung Hee Cho a,⇑ a
Department of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, Republic of Korea Korea District Heating Corporation, 781 Yangjae-daero, Gangnam-gu, Seoul 135-220, Republic of Korea c Korea Hydro & Nuclear Power-Central Research Institute, 1312 Gil, 70 Yuseongdaero, Yuseong-gu, Daejeon 305-343, Republic of Korea b
a r t i c l e
i n f o
Article history: Received 30 July 2013 Received in revised form 4 October 2014 Accepted 7 October 2014 Available online 16 October 2014 Keywords: Gas turbine Combustion liner Heat transfer Thermal stress Lifetime prediction
a b s t r a c t The present study investigates the effect of thermal stress on the creep lifetime for a combustion liner in a gas turbine. For the calculation of thermal stress of a combustion liner, 3D-numerical analyses are performed using an FEM commercial code. Actual operating conditions and material properties are also applied for the realistic calculation. As a result, high thermal stress is locally induced in the inlet of the rib-roughened region of the whole combustion liner. That is attributed to the high temperature gradients formed from the large temperature differences between the hot spots and the surrounding low temperature regions. The result is in a good agreement with the actually damaged combustion liner. Moreover, the hot gas side of the inlet of the rib-roughened region appeared vulnerable to creep and the minimum creep lifetime is estimated to be approximately 26,900 h. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction It is evident that the turbine inlet temperature (TIT) and the compressor discharge pressure should be increased to improve the performance of a gas turbine. In modern gas turbine engines, TIT has been steadily increased, thus novel base materials (such as super alloys), thermal barrier coatings (TBC), and/or advanced cooling methods have been extensively applied to improve the durability and the reliability of the hot components of gas turbine. As TIT is increased, hot components such as combustion liners, vanes, and blades should be protected from high temperature environment by using advanced cooling techniques. Especially, the gas turbine combustion liner is exposed to excessively high thermal load (1750 K) due to direct interaction with extremely hot combustion gas. For combustion liner cooling, various cooling methods such as impinging jet cooling, film cooling, and internal passage cooling are generally applied. Such cooling methods are usually applied in a combined fashion to maximize the cooling performance [1–9]. Nevertheless, hot components of gas turbines are still vulnerable under harsh thermal conditions thereby suffering from local thermal cracks and structural failure. Since the thermal stress is mainly induced by the temperature differences along the substrate which leads to the critical thermal damage of the hot components, there is a critical requirement to predict the thermal stress distributions of hot components under an actual operating condition [10–12].
⇑ Corresponding author. Tel.: +82 2 2123 2828; fax: +82 2 312 2159. E-mail address: [email protected] (H.H. Cho). http://dx.doi.org/10.1016/j.engfailanal.2014.10.004 1350-6307/Ó 2014 Elsevier Ltd. All rights reserved.
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
35
Nomenclature E h k p t Tw DT
Young’s modulus convective heat transfer coefficients, q00 /(Tw Tm) thermal conductivity Larson–Miller parameter creep lifetime wall temperature temperature difference
Greek symbols a thermal expansion coefficient ev von Mises strain m Poisson’s ratio r stress rv von Mises equivalent stress
Under this circumstance, most of the studies on the gas turbine hot components are mainly focused on fluid dynamics or heat transfer measurement/enhancement. Likewise, for the combustion systems, there are also numerous studies such as combustion mechanism, combustion gas flow, and heat transfer in combustors [13–15]. There have been some efforts to predict failure and lifetime in combustors, but only for the local part of component or segments in archival journal papers [16,17]. In this study, therefore, we focus on the thermal failure analysis and lifetime prediction of the whole gas turbine combustion liner. For the analysis and prediction, we calculated the thermal stress of the whole combustion liner under the actual base-load operating conditions with real conditions and material properties. With this calculated result, we also predict the creep lifetime of whole combustion liner using Larson–Miller parameter. 2. Research methods The objective of the present study is to analyze the thermal stress and to predict the lifetime on a whole combustion liner. First, FEM analysis was performed to figure out the thermal stress distributions on the combustion liner. Then, the creep lifetime prediction was conducted for the combustion liner during the steady base-load operation using the calculated thermal stress results. 2.1. Geometry and cooling method The dry low NOx combustion liner that is typically applied to land-based gas turbine was modeled. A single combustion liner consists of six premixed burners and it is composed of the several additional components such as flow sleeve, combustion liner, impinging sleeve, and transition piece [10,12]. The impinging and flow sleeves surround the transition piece and combustion liner, and this combination creates a flow channel between the sleeves and combustion liner and transition piece for forced convective cooling. It should be noted that this combustion liner mainly adopts impinging jet cooling and rib-roughened passage cooling, instead of film cooling for lean premixed combustion. As Fig. 1 indicates, the combustion liner falls into three parts such
Fig. 1. Geometry of target combustion liner.
36
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
Table 1 Physical properties of super-alloy [10,18]. 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
as forward shell, center shell, and after shell. In detail, each part utilizes different cooling methods which are rib-roughened passage cooling, impingement jet cooling, and internal passage cooling, respectively as aforementioned order. 2.2. Material properties and operating conditions The substrate of the combustion liner was chosen as Nimonic 263 which is a nickel based super alloy. In general, the inner wall of the combustion liner, which is directly exposed to hot gas, is protected by TBC (Yttria-Stabilized Zirconia). However, in this study, we neglect the TBC layer and consider only for the substrate for the calculation because the critical failure events are occurred on the substrate. Moreover, in actual operation and maintenance process, the TBC layers are periodically recoated. Therefore, we primarily focus on the substrate failure only. Since the thermo-mechanical properties of the super alloy such as thermal conductivity, thermal expansion coefficient, Young’s modulus, and Poisson’s ratio are highly temperature-dependent, we applied temperature-varying properties for the calculation. The thermo-mechanical properties of the super alloy under the temperature range from 100 K to 1000 K are presented in Table 1 [10,18]. As for the operation mode, we simulated the base-load condition. Among the several steps in gas turbine operating (start/ stop) cycle, the base-load condition is regarded as the most harsh condition because the firing temperature is much higher than other steps, so the material easily gets damaged by the steady state thermal load. Thus, the steady state base-load condition is only simulated as an operating condition to calculate the thermal stress and lifetime under the most extreme condition. 2.3. Thermal stress analysis The FEM analyses were conducted to predict the thermal stress of the combustion liner system using a commercial code, ANSYS v11. The boundary conditions for calculating the thermal stress and strain distributions, such as substrate temperature distributions and environment gas temperature are adopted from our previous work [19]. The thermal stress on the objective materials is proportional to the thermal expansion coefficient and temperature difference as presented in the following equation.
r ¼ EaDT
ð1Þ
The von Mises equivalent stress and strain distributions of the whole combustion liner were obtained. A finite element mesh was created with ANSYS Design Modeler. We conducted grid independent test, and total number of elements was about 300,000. 2.4. Creep life prediction Creep is well-known as a dominant life-restricting factor of the gas turbine hot components during steady-state operation (base load). Under this operating condition, high temperature and stress are constantly imposed to the substrate thereby the creep lifetime becomes shortened due to the decrease of the creep resistance of the materials even if the substrate is a heatproof material. To calculate creep lifetime, calculated wall temperature and von Mises equivalent stress at each element were applied. Especially, f(r), which is the third-order polynomial function, is extracted from Larson–Miller rupture curves of the material. From this, the creep lifetime (t) is obtained using the following equation.
logðtÞ ¼ 103 f ðrÞ=T w 20
ð2Þ
3. Results and discussion 3.1. Review of the previous work In our previous study [19], we have dealt about the flow behavior of the combustion gas and coolant, convective heat transfer on the combustion liner, and temperature distributions of the whole combustion liner under the base-load operation. The present study employs these data in order to calculate the thermal stress and lifetime. Therefore, we briefly review
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
37
Fig. 2. (a) Flow and temperature distributions in cross section, (b) distributions of heat transfer coefficients by combustion, (c) distributions of heat transfer coefficients by cooling flow, and (d) contour plots of wall temperature distributions (Cooling side). (Part (a), (b), (c), and (d) reprinted with permission from [19]. Ó2010 Journal of Mechanical Science and Technology).
the previous results before discussing the thermal stress result in order to provide more insight to the in-depth analysis of the results. Fig. 2(a) shows the flow and temperature distributions of the combustion gas. The patterns of the combustion gas flow exhibits swirling flow due to the swirler which is set on the fuel injector. This swirling effect helps to the mixing of gas for the combustion. The maximum gas temperature of 1760 K is distributed at the core of the combustion gas flow. This flow behavior have affected on the convective heat transfer on the inside of the combustion liner. Fig. 2(b) indicates distribution of internal heat transfer coefficient. The maximum heat transfer coefficient is regularly dispersed on the inside of ribroughened region, which is located near the swirler, because of the development of the swirling flow near the inlet region. In other words, swirling flow induced high heat transfer region that should be suffer from relatively high thermal load. At the exit area of the combustion liner, the heat transfer distribution naturally diffuses and converges to an average value. Fig. 2(c) depicts the heat transfer distributions on the external surface. As mentioned earlier, this combustion liner simultaneously utilizes applied rib-roughened passage cooling and impinging jet cooling. The peak heat transfer coefficient appears on the impinging regions because much more amount of coolant flow is impinged on the surface compared to the other regions. At the rib-roughened region, the heat transfer distributions are relatively lower than other regions because impinged flow has been weakened by the cross flow from the impinging flow. Fig. 2(d) shows the temperature distributions on the substrate. The temperature distribution varies approximately from 700 K to 1200 K. The highest temperature, among the rib-roughened region of the substrate is about 1130 K. Whereas, the maximum temperature is distributed on the TBC surface which is about 1400 K. This is the most important reason why the highest thermal stress and the lowest lifetime appeared on this region. In other words, the rib-roughed region is exposed to the highest thermal load. 3.2. Thermal stress analysis Fig. 3(a) shows the distributions of von Mises equivalent stress on the surface of the combustion liner substrate. The highest stress is locally induced at the inlet of the rib-roughened region that exactly matches the highest temperature region
38
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
Fig. 3. Comparing the calculated results to actual pictures: (a) stress distributions on metal surface, (b) and (c) cracks on the combustion liner.
(Fig. 2(d)). The stress value ranges from 0.18 MPa to 27.1 MPa and these values are solely caused by the thermal effect. This is because high temperature gradient is caused by large temperature differences between the periodic hot spots. This prediction is in a good agreement with the actually damaged combustion liner (Fig. 3(b) and (c)), which is provided by Gas Turbine Technology Service Center, Korea Plant Service & Engineering (KPS). Fig. 4(a) and (b) depicts the quantitative distributions of von Mises equivalent stresses and strains along to the x-axis (longitudinal) of the combustion liner, respectively. The results show that there are three peaked regions of the thermal
Fig. 4. Stress and strain distributions: (a) stress distribution along x-axis and (b) strain distribution along x-axis.
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
39
Fig. 5. Creep-rupture data of super-alloy for prediction of the lifetime [10].
stress distributions on the combustion liner. The first peak, the maximum value, is the inlet of the rib-roughened region. This region exposed to large difference of temperature through the thickness direction locally, so concentrated-thermal stress is dispersed periodically. This intermittent distribution of thermal stress is also similar to the heat transfer distributions induced by swirling combustion gas (Fig. 2(b)). The second peak region is connecting part between center shell and after shell (x = 750). In the longitudinal direction, internal heat transfer distribution converges to the average value (Fig. 2(b)), unlike the inner side, the heat transfer distribution on the cooling side is sharply varied to circumferential direction due to coolant impingement by flow sleeve (Fig. 2(c)). To resemble, uneven heat transfer is also distributed through the thickness direction. From that, the difference of the cooling intensity makes difference of the temperature gradient along to the x-axis and thickness direction, so this temperature difference (100–150 K) leads to the high thermal stress concentration on the connecting region between center shell and after shell at x = 750 (Fig. 2(d)). Moreover, on the tip of combustion liner (x = 900), another peak value (actually the third peak) of the thermal stress appears. It is because fixed condition was applied to the tip area of combustion liner for thermal stress calculation.
Fig. 6. Creep lifetime on combustion liner: (a) creep lifetime contour on metal surface and (b) creep lifetime distribution along x-axis.
40
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
3.3. Creep lifetime analysis Fig. 5 shows creep-rupture data of nickel-base super alloy and its third-order polynomial fitting curve [10]. As mentioned above, third-order polynomial function, f(r), was used for creep lifetime calculation. Fig. 6 presents the distribution of the predicted creep lifetime along with stress distribution. The lifetime spans many orders of magnitude along the x-axis direction, ranging from 104 h to the 1022 h. The minimum lifetime is estimated at 26,900 h on the hot combustion gas side of the inlet of the rib-roughened region. This region exposed the maximum temperature and stress. Moreover, one minor region that exhibits relatively low lifetime is connecting part between center shell and after shell (x = 750) because of the thermal stress concentration. 4. Conclusions In this study, numerical analyses were conducted to figure out the distributions of thermal stress and strain using a commercial code, ANSYS 11.0. Creep lifetime was also calculated using the thermal stress results and Larson–miller parameter. As a result, we predicted thermally weak region at the inlet of the rib-roughened region of combustion liner. The maximum stress is imposed on the rib-roughened region due to high temperature gradients resulting from the large temperature differences between the hot spots and the surrounding low temperature regions. The maximum strain is also imposed on the same region where the maximum stress distributed. The creep lifetime distribution was widely ranged from order of 104 h to 1022 h. The minimum lifetime was estimated at 26,900 h on the inlet of the rib-roughened region. This prediction was reasonable comparing with the actual fracture case. From these results, we conclude that the thermal stress analysis was effective on predicting the most probable region for a failure to occur. Therefore, further research on thermal design such as thermal optimization is required to avoid such thermal failure on a combustion liner. Acknowledgments This work was supported by the Human Resources Development program (No. 20144030200560) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) Grant funded by the Korea Government Ministry of Trade, Industry and Energy. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
Goldstein RJ. Film cooling. Adv Heat Transf 1971;7:321–79. Lakshminarayana B. Frontmatter. Wiley Online Library; 1996. Han J-C, Dutta S, Ekkad S. Gas turbine heat transfer and cooling technology. Taylor & Francis; 2012. Han B, Goldstein R. Jet-impingement heat transfer in gas turbine systems. Ann N Y Acad Sci 2001;934:147–61. Lee DH, Rhee D-H, Kim KM, Cho HH, Moon HK. Detailed measurement of heat/mass transfer with continuous and multiple V-shaped ribs in rectangular channel. Energy 2009;34:1770–8. Kim KM, Kim BS, Lee DH, Moon H, Cho HH. Optimal design of transverse ribs in tubes for thermal performance enhancement. Energy 2010;35:2400–6. Hwang SD, Kwon HG, Cho HH. Local heat transfer and thermal performance on periodically dimple-protrusion patterned walls for compact heat exchangers. Energy 2010;35:5357–64. Kwon HG, Hwang SD, Cho HH. Measurement of local heat/mass transfer coefficients on a dimple using naphthalene sublimation. Int J Heat Mass Transf 2011;54:1071–80. Hong SK, Lee DH, Cho HH. Effect of jet direction on heat/mass transfer of rotating impingement jet. Appl Therm Eng 2009;29:2914–20. Kim KM, Yun N, Jeon YH, Lee DH, Cho HH. Failure analysis in after shell section of gas turbine combustion liner under base-load operation. Eng Failure Anal 2010;17:848–56. Kim KM, Park JS, Lee DH, Lee TW, Cho HH. Analysis of conjugated heat transfer, stress and failure in a gas turbine blade with circular cooling passages. Eng Failure Anal 2011;18:1212–22. Yun N, Jeon YH, Kim KM, Lee DH, Cho HH. Thermal and creep analysis in a gas turbine combustion liner. In: Proceedings of the 4th IASME/WSEAS international conference on energy & environment, World Scientific and Engineering Academy and Society (WSEAS); 2009. p. 315–20. Sivaramakrishna G, Muthuveerappan N, Shankar V. ISABE-2001-1089 Combustor geometry optimization studies using CFD technique. Ahsiracfésmggv ISABE; 2001. p. 62. Facchini B, Maiuolo F, Tarchi L, Coutandin D. Combined effect of slot injection, effusion array and dilution hole on the heat transfer coefficient of a real combustor liner: part 1—Experimental analysis. ASME 2010. Patil S, Abraham S, Tafti D, Ekkad S, Kim Y, Dutta P, et al. Experimental and numerical investigation of convective heat transfer in a gas turbine can combustor. J. Turbomachinery 2011;133. Tinoa T, Van Kampen J, de Jager B, Kok J. Gas turbine combustor liner life assessment using a combined fluid/structural approach. J Eng Gas Turbines Power 2007;129:69–79. Kim KM, Jeon YH, Yun N, Lee DH, Cho HH. Thermo-mechanical life prediction for material lifetime improvement of an internal cooling system in a combustion liner. Energy 2011;36:942–9. Special metals. Product hand book of high-performance alloys. Metals Corporation Publication; 2007. SMC-054. Kim KM, Yun N, Jeon YH, Lee DH, Cho HH, Kang S-H. Conjugated heat transfer and temperature distributions in a gas turbine combustion liner under base-load operation. J Mech Sci Technol 2010;24:1939–46.
Contents lists available at ScienceDirect
Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Effect of thermal stress on creep lifetime for a gas turbine combustion liner Hokyu Moon a, Kyung Min Kim b, Yun Heung Jeon c, Sangwoo Shin a, Jun Su Park a, Hyung Hee Cho a,⇑ a
Department of Mechanical Engineering, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, Republic of Korea Korea District Heating Corporation, 781 Yangjae-daero, Gangnam-gu, Seoul 135-220, Republic of Korea c Korea Hydro & Nuclear Power-Central Research Institute, 1312 Gil, 70 Yuseongdaero, Yuseong-gu, Daejeon 305-343, Republic of Korea b
a r t i c l e
i n f o
Article history: Received 30 July 2013 Received in revised form 4 October 2014 Accepted 7 October 2014 Available online 16 October 2014 Keywords: Gas turbine Combustion liner Heat transfer Thermal stress Lifetime prediction
a b s t r a c t The present study investigates the effect of thermal stress on the creep lifetime for a combustion liner in a gas turbine. For the calculation of thermal stress of a combustion liner, 3D-numerical analyses are performed using an FEM commercial code. Actual operating conditions and material properties are also applied for the realistic calculation. As a result, high thermal stress is locally induced in the inlet of the rib-roughened region of the whole combustion liner. That is attributed to the high temperature gradients formed from the large temperature differences between the hot spots and the surrounding low temperature regions. The result is in a good agreement with the actually damaged combustion liner. Moreover, the hot gas side of the inlet of the rib-roughened region appeared vulnerable to creep and the minimum creep lifetime is estimated to be approximately 26,900 h. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction It is evident that the turbine inlet temperature (TIT) and the compressor discharge pressure should be increased to improve the performance of a gas turbine. In modern gas turbine engines, TIT has been steadily increased, thus novel base materials (such as super alloys), thermal barrier coatings (TBC), and/or advanced cooling methods have been extensively applied to improve the durability and the reliability of the hot components of gas turbine. As TIT is increased, hot components such as combustion liners, vanes, and blades should be protected from high temperature environment by using advanced cooling techniques. Especially, the gas turbine combustion liner is exposed to excessively high thermal load (1750 K) due to direct interaction with extremely hot combustion gas. For combustion liner cooling, various cooling methods such as impinging jet cooling, film cooling, and internal passage cooling are generally applied. Such cooling methods are usually applied in a combined fashion to maximize the cooling performance [1–9]. Nevertheless, hot components of gas turbines are still vulnerable under harsh thermal conditions thereby suffering from local thermal cracks and structural failure. Since the thermal stress is mainly induced by the temperature differences along the substrate which leads to the critical thermal damage of the hot components, there is a critical requirement to predict the thermal stress distributions of hot components under an actual operating condition [10–12].
⇑ Corresponding author. Tel.: +82 2 2123 2828; fax: +82 2 312 2159. E-mail address: [email protected] (H.H. Cho). http://dx.doi.org/10.1016/j.engfailanal.2014.10.004 1350-6307/Ó 2014 Elsevier Ltd. All rights reserved.
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
35
Nomenclature E h k p t Tw DT
Young’s modulus convective heat transfer coefficients, q00 /(Tw Tm) thermal conductivity Larson–Miller parameter creep lifetime wall temperature temperature difference
Greek symbols a thermal expansion coefficient ev von Mises strain m Poisson’s ratio r stress rv von Mises equivalent stress
Under this circumstance, most of the studies on the gas turbine hot components are mainly focused on fluid dynamics or heat transfer measurement/enhancement. Likewise, for the combustion systems, there are also numerous studies such as combustion mechanism, combustion gas flow, and heat transfer in combustors [13–15]. There have been some efforts to predict failure and lifetime in combustors, but only for the local part of component or segments in archival journal papers [16,17]. In this study, therefore, we focus on the thermal failure analysis and lifetime prediction of the whole gas turbine combustion liner. For the analysis and prediction, we calculated the thermal stress of the whole combustion liner under the actual base-load operating conditions with real conditions and material properties. With this calculated result, we also predict the creep lifetime of whole combustion liner using Larson–Miller parameter. 2. Research methods The objective of the present study is to analyze the thermal stress and to predict the lifetime on a whole combustion liner. First, FEM analysis was performed to figure out the thermal stress distributions on the combustion liner. Then, the creep lifetime prediction was conducted for the combustion liner during the steady base-load operation using the calculated thermal stress results. 2.1. Geometry and cooling method The dry low NOx combustion liner that is typically applied to land-based gas turbine was modeled. A single combustion liner consists of six premixed burners and it is composed of the several additional components such as flow sleeve, combustion liner, impinging sleeve, and transition piece [10,12]. The impinging and flow sleeves surround the transition piece and combustion liner, and this combination creates a flow channel between the sleeves and combustion liner and transition piece for forced convective cooling. It should be noted that this combustion liner mainly adopts impinging jet cooling and rib-roughened passage cooling, instead of film cooling for lean premixed combustion. As Fig. 1 indicates, the combustion liner falls into three parts such
Fig. 1. Geometry of target combustion liner.
36
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
Table 1 Physical properties of super-alloy [10,18]. 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
as forward shell, center shell, and after shell. In detail, each part utilizes different cooling methods which are rib-roughened passage cooling, impingement jet cooling, and internal passage cooling, respectively as aforementioned order. 2.2. Material properties and operating conditions The substrate of the combustion liner was chosen as Nimonic 263 which is a nickel based super alloy. In general, the inner wall of the combustion liner, which is directly exposed to hot gas, is protected by TBC (Yttria-Stabilized Zirconia). However, in this study, we neglect the TBC layer and consider only for the substrate for the calculation because the critical failure events are occurred on the substrate. Moreover, in actual operation and maintenance process, the TBC layers are periodically recoated. Therefore, we primarily focus on the substrate failure only. Since the thermo-mechanical properties of the super alloy such as thermal conductivity, thermal expansion coefficient, Young’s modulus, and Poisson’s ratio are highly temperature-dependent, we applied temperature-varying properties for the calculation. The thermo-mechanical properties of the super alloy under the temperature range from 100 K to 1000 K are presented in Table 1 [10,18]. As for the operation mode, we simulated the base-load condition. Among the several steps in gas turbine operating (start/ stop) cycle, the base-load condition is regarded as the most harsh condition because the firing temperature is much higher than other steps, so the material easily gets damaged by the steady state thermal load. Thus, the steady state base-load condition is only simulated as an operating condition to calculate the thermal stress and lifetime under the most extreme condition. 2.3. Thermal stress analysis The FEM analyses were conducted to predict the thermal stress of the combustion liner system using a commercial code, ANSYS v11. The boundary conditions for calculating the thermal stress and strain distributions, such as substrate temperature distributions and environment gas temperature are adopted from our previous work [19]. The thermal stress on the objective materials is proportional to the thermal expansion coefficient and temperature difference as presented in the following equation.
r ¼ EaDT
ð1Þ
The von Mises equivalent stress and strain distributions of the whole combustion liner were obtained. A finite element mesh was created with ANSYS Design Modeler. We conducted grid independent test, and total number of elements was about 300,000. 2.4. Creep life prediction Creep is well-known as a dominant life-restricting factor of the gas turbine hot components during steady-state operation (base load). Under this operating condition, high temperature and stress are constantly imposed to the substrate thereby the creep lifetime becomes shortened due to the decrease of the creep resistance of the materials even if the substrate is a heatproof material. To calculate creep lifetime, calculated wall temperature and von Mises equivalent stress at each element were applied. Especially, f(r), which is the third-order polynomial function, is extracted from Larson–Miller rupture curves of the material. From this, the creep lifetime (t) is obtained using the following equation.
logðtÞ ¼ 103 f ðrÞ=T w 20
ð2Þ
3. Results and discussion 3.1. Review of the previous work In our previous study [19], we have dealt about the flow behavior of the combustion gas and coolant, convective heat transfer on the combustion liner, and temperature distributions of the whole combustion liner under the base-load operation. The present study employs these data in order to calculate the thermal stress and lifetime. Therefore, we briefly review
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
37
Fig. 2. (a) Flow and temperature distributions in cross section, (b) distributions of heat transfer coefficients by combustion, (c) distributions of heat transfer coefficients by cooling flow, and (d) contour plots of wall temperature distributions (Cooling side). (Part (a), (b), (c), and (d) reprinted with permission from [19]. Ó2010 Journal of Mechanical Science and Technology).
the previous results before discussing the thermal stress result in order to provide more insight to the in-depth analysis of the results. Fig. 2(a) shows the flow and temperature distributions of the combustion gas. The patterns of the combustion gas flow exhibits swirling flow due to the swirler which is set on the fuel injector. This swirling effect helps to the mixing of gas for the combustion. The maximum gas temperature of 1760 K is distributed at the core of the combustion gas flow. This flow behavior have affected on the convective heat transfer on the inside of the combustion liner. Fig. 2(b) indicates distribution of internal heat transfer coefficient. The maximum heat transfer coefficient is regularly dispersed on the inside of ribroughened region, which is located near the swirler, because of the development of the swirling flow near the inlet region. In other words, swirling flow induced high heat transfer region that should be suffer from relatively high thermal load. At the exit area of the combustion liner, the heat transfer distribution naturally diffuses and converges to an average value. Fig. 2(c) depicts the heat transfer distributions on the external surface. As mentioned earlier, this combustion liner simultaneously utilizes applied rib-roughened passage cooling and impinging jet cooling. The peak heat transfer coefficient appears on the impinging regions because much more amount of coolant flow is impinged on the surface compared to the other regions. At the rib-roughened region, the heat transfer distributions are relatively lower than other regions because impinged flow has been weakened by the cross flow from the impinging flow. Fig. 2(d) shows the temperature distributions on the substrate. The temperature distribution varies approximately from 700 K to 1200 K. The highest temperature, among the rib-roughened region of the substrate is about 1130 K. Whereas, the maximum temperature is distributed on the TBC surface which is about 1400 K. This is the most important reason why the highest thermal stress and the lowest lifetime appeared on this region. In other words, the rib-roughed region is exposed to the highest thermal load. 3.2. Thermal stress analysis Fig. 3(a) shows the distributions of von Mises equivalent stress on the surface of the combustion liner substrate. The highest stress is locally induced at the inlet of the rib-roughened region that exactly matches the highest temperature region
38
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
Fig. 3. Comparing the calculated results to actual pictures: (a) stress distributions on metal surface, (b) and (c) cracks on the combustion liner.
(Fig. 2(d)). The stress value ranges from 0.18 MPa to 27.1 MPa and these values are solely caused by the thermal effect. This is because high temperature gradient is caused by large temperature differences between the periodic hot spots. This prediction is in a good agreement with the actually damaged combustion liner (Fig. 3(b) and (c)), which is provided by Gas Turbine Technology Service Center, Korea Plant Service & Engineering (KPS). Fig. 4(a) and (b) depicts the quantitative distributions of von Mises equivalent stresses and strains along to the x-axis (longitudinal) of the combustion liner, respectively. The results show that there are three peaked regions of the thermal
Fig. 4. Stress and strain distributions: (a) stress distribution along x-axis and (b) strain distribution along x-axis.
H. Moon et al. / Engineering Failure Analysis 47 (2015) 34–40
39
Fig. 5. Creep-rupture data of super-alloy for prediction of the lifetime [10].
stress distributions on the combustion liner. The first peak, the maximum value, is the inlet of the rib-roughened region. This region exposed to large difference of temperature through the thickness direction locally, so concentrated-thermal stress is dispersed periodically. This intermittent distribution of thermal stress is also similar to the heat transfer distributions induced by swirling combustion gas (Fig. 2(b)). The second peak region is connecting part between center shell and after shell (x = 750). In the longitudinal direction, internal heat transfer distribution converges to the average value (Fig. 2(b)), unlike the inner side, the heat transfer distribution on the cooling side is sharply varied to circumferential direction due to coolant impingement by flow sleeve (Fig. 2(c)). To resemble, uneven heat transfer is also distributed through the thickness direction. From that, the difference of the cooling intensity makes difference of the temperature gradient along to the x-axis and thickness direction, so this temperature difference (100–150 K) leads to the high thermal stress concentration on the connecting region between center shell and after shell at x = 750 (Fig. 2(d)). Moreover, on the tip of combustion liner (x = 900), another peak value (actually the third peak) of the thermal stress appears. It is because fixed condition was applied to the tip area of combustion liner for thermal stress calculation.
Fig. 6. Creep lifetime on combustion liner: (a) creep lifetime contour on metal surface and (b) creep lifetime distribution along x-axis.
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3.3. Creep lifetime analysis Fig. 5 shows creep-rupture data of nickel-base super alloy and its third-order polynomial fitting curve [10]. As mentioned above, third-order polynomial function, f(r), was used for creep lifetime calculation. Fig. 6 presents the distribution of the predicted creep lifetime along with stress distribution. The lifetime spans many orders of magnitude along the x-axis direction, ranging from 104 h to the 1022 h. The minimum lifetime is estimated at 26,900 h on the hot combustion gas side of the inlet of the rib-roughened region. This region exposed the maximum temperature and stress. Moreover, one minor region that exhibits relatively low lifetime is connecting part between center shell and after shell (x = 750) because of the thermal stress concentration. 4. Conclusions In this study, numerical analyses were conducted to figure out the distributions of thermal stress and strain using a commercial code, ANSYS 11.0. Creep lifetime was also calculated using the thermal stress results and Larson–miller parameter. As a result, we predicted thermally weak region at the inlet of the rib-roughened region of combustion liner. The maximum stress is imposed on the rib-roughened region due to high temperature gradients resulting from the large temperature differences between the hot spots and the surrounding low temperature regions. The maximum strain is also imposed on the same region where the maximum stress distributed. The creep lifetime distribution was widely ranged from order of 104 h to 1022 h. The minimum lifetime was estimated at 26,900 h on the inlet of the rib-roughened region. This prediction was reasonable comparing with the actual fracture case. From these results, we conclude that the thermal stress analysis was effective on predicting the most probable region for a failure to occur. Therefore, further research on thermal design such as thermal optimization is required to avoid such thermal failure on a combustion liner. Acknowledgments This work was supported by the Human Resources Development program (No. 20144030200560) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) Grant funded by the Korea Government Ministry of Trade, Industry and Energy. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19]
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