Evaluation Tests of 1700 °C Class Turbine Cooled Blades for aHydrogen Fueled Combustion Turbine System

Takanari Okamura,1 Hiroyuki Kawagishi,2 Akinori Koga,2 and Shoko Itoh2

1Department of Energy Engineering, Hachinohe Institute of Technology, 031-8501 Japan2Power and Industrial Systems R&D Center, Toshiba Corporation, 230-0045 Japan

The development of 1700 °C class hydrogen fueled combustion turbine systemwith output of 500 MW and thermal efficiency of over 60% (HHV) has been conductedin the World Energy Network (WE-NET) program. This paper describes the develop-ment of the first-stage turbine cooled stator and rotor blades applied to the powergeneration system. The conceptual design of these cooling blades which were servedin hot steam flow was carried out. The hybrid cooling method combining recoverycooling with partial ejection cooling was chosen from several cooling systems from aviewpoint of plant efficiency, operational reliability, and durability of cooled blades.Also, the single crystal superalloy (SC) as a blade substrate and thermal barrier coating(TBC) were applied. The experiments of the scale model turbine cooled blades werecarried out using a hydrogen–oxygen combustion wind tunnel with practical steamconditions of 1700 °C and 2.5 MPa. The cooling effectiveness and metal temperatureat rated condition and the soundness of TBC and blade substrate of the first stage statorand rotor test blades were clarified. © 2003 Wiley Periodicals, Inc. Heat TransAsian Res, 32(3): 237–252, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.10088

Key words: turbine, hydrogen, cooling blade, thermal barrier coating, singlecrystal superalloy

1. Introduction

The International Clean Energy Network Using Hydrogen Conversion Program (WorldEnergy Network: WE-NET) was launched in 1993 as one of the national projects of Japan in orderto meet the growing energy demand with minimum possible pollution to the environment. Theprogram includes development of a turbine power generation system using hydrogen as fuel. Thesystem provides the turbine combusting hydrogen with oxygen directly and the target is to achieveplant thermal efficiency above 60% (HHV). This is a zero emission system whose exhaust gas is freefrom pollution such as CO2, NOx, and SOx because the working gas is steam. Mouri and colleagues[1] presented their work on the research and development of the turbine blade with cooling which is

© 2003 Wiley Periodicals, Inc.

Heat Transfer—Asian Research, 32 (3), 2003

Contract grant sponsors: Supported by the New Energy and Industrial Technology Development Organization (NEDO) as partof the WE-NET program, and was directly entrusted by the Japan Power Engineering and Inspection Corporation (JAPEIC).

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the key component in this turbine system. The authors participated in this program and have developedhigh-temperature turbine cooled blades. The turbine inlet gas temperature is the 1700 °C class whichis higher than the 1500 °C class advanced gas turbine which was expected to be used for future powergeneration system in early 2000. The first stage turbine blades were selected as the development objectas they serve under the most severe conditions.

In order to successfully develop these critical turbine cooled blades which serve in a very hotsteam environment, it is necessary to pay attention to the following issues: advanced coolingtechnologies, evaluation of blade substrate on the basis of strength and oxidation resistance in hightemperature steam environments, and application of TBC for reducing high heat flux generated byhot steam flow. In the present work, the cooling system is selected and cooling structures are shownin the course of developing the first stage turbine blades.

Then the results are described on the cascade evaluation tests which were conducted using awind tunnel with hot gas flow having a temperature of 1700 °C and pressure of 2.5 MPa generatedby hydrogen–oxygen combustion. The objective of the present study is to clarify the coolingeffectiveness, blade metal temperatures, and robustness of the first stage cooled stator and rotor bladesof turbine exposed to a practical hot steam flow environment.

Nomenclature

Gc supplied cooling steam mass flow per blade (Gc = Gc1 + Gc2)Gc1 recovery cooling steam mass flow per bladeGc2 ejection cooling steam mass flow per bladeGg hot gas mass flow per blade pathMa Mach numberPf pattern factorPg hot gas pressure at the cascade inletR gas constantRe Reynolds numbert timeTc supplied cooling steam temperatureTg hot gas temperature at the mean height of cooling bladeTgave averaged hot gas temperatureTgmax maximum hot gas temperatureTgth theoretical combustion temperatureTin combustor inlet steam temperatureTm metal temperatureXBS nondimensional blade surface locationηc cooling effectiveness

2. Hydrogen Fueled Combustion Turbine System and Blade Cooling System

A schematic view of the hydrogen fueled combustion turbine system is presented in Fig. 1.This turbine system was based on a complex cycle composed of a closed Brayton cycle and a Rankinecycle. The Brayton cycle consists of compressor, combustor, and high temperature turbine. Compres-

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sor inlet and delivery pressures were 0.14 and 5.0 MPa, respectively, and pressure ratio was 35.7.Hydrogen and oxygen were supplied to the combustor as fuel and oxidant under stoichiometricconditions and burn in steam delivered from the compressor. The hot steam having a temperature of1700 °C and pressure of 4.75 MPa was fed to the high temperature turbine. The steam generator,which was installed in the high temperature turbine exhaust system, generated high pressure steamand this steam was introduced to the high pressure turbine to expand and then fed to the inlet of thecombustor. The low pressure steam branched at the outlet of the steam generator which led to the lowpressure turbine. The low temperature exhaust steam from the economizer was fed to the compressorinlet and the Brayton cycle was a closed one.

As the turbine blade cooling method strongly affects the plant thermal efficiency, its selectionis important. There are two cooling methods using steam: one is the ejection cooling such as fullcoverage film cooling, and the other is recovery cooling which recovers the steam after cooling. Inaddition, water cooling and water evaporation cooling were considered. The parameters to beevaluated were operational reliability and durability of turbine blade, in addition to plant thermalefficiency. Based on the results of evaluation, a hybrid cooling technique was chosen for cooling thefirst stage blades. In the present hybrid cooling, recovery cooling was combined with partial ejection

Fig. 1. Schematic diagram of hydrogen fueled combustion turbine system.

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such as film cooling. The ejection cooling was applied to the high heat load part such as the leadingedge and the trailing edge of the turbine blades. The recovery cooling method was used for coolingthe low pressure stage blades, in which the gas temperature drops under the 1500 °C level. The turbineblade cooling steam was obtained from the high pressure turbine outlet, cooled on its way by thecooler (CSC in Fig. 1), and the recovered steam was led to the combustor inlet.

The relation between the thermal efficiency and the cooling steam flow rate was investigatedand it was shown that increasing the ejection cooling flow greatly decreased the thermal efficiencyas compared to the recovery cooling. Under the rated condition, the flow rate of recovery cooling was24% and that of ejection cooling, inclusive of cooling the rotor disk and the casing, was 8.4% of theturbine inlet flow for the present conceptual design of the high temperature turbine. Plant thermalefficiency greater than 60% was obtained based on the calculated result of the plant heat balance.

3. High Temperature Turbine Cooled Blades

3.1 Turbine blades for a plant

Design of the first stage turbine blades was carried out on the basis of specifying the hightemperature turbine flow path. Since an aerodynamically high load design was considered in thedesign of cooled turbine blades, the number of blades and stages was decreased, resulting in reducedcoolant flow rate. In the design of the cooled blade as well as the calculation of plant heat balance,the steam table of the Japan Society of Mechanical Engineers (JSME) was used for temperature levelsbelow 800 °C and data from the National Bureau of Standards (NBS) [presently the National Instituteof Standards and Technology (NIST)] were used for temperature levels above 800 °C. Althoughallowable metal and TBC temperatures should be decided for blade cooling design, poor data areavailable for mechanical properties and oxidation resistance of blade substrate in high temperaturesteam environments and long duty stability of microstructure of TBC. Therefore, preliminary basictests were conducted to decide the allowable temperatures.

The specifications of the first stage stator and rotor blades are shown in Table 1 including thetest models. The mean gas temperatures and the maximum ones at the inlet are 1700 and 1809 °C forthe stator blade, respectively, and 1570 and 1641 °C for the rotor blade, respectively. Thosetemperature values correspond to combustor pattern factors of 10 and 7%, respectively, which aredefined as follows:

Pf = (Tgmax − Tgave) / (Tgave − Tin) (1)

Here combustor inlet steam temperature Tin is 625 °C. The ratio of mass flow rates of the coolant tothe inlet gas was 6.4% for stator blades and 6.9% for rotor blades. Exit Mach numbers were 0.68 and0.46 for stator and rotor blades, respectively. The Reynolds number based on chord length was 6.5 ×106 and 1.8 × 106 for stator and rotor blades, respectively. Top coat of ZrO2-8%Y2O3 and bond coatof NiCoCrAlY were adopted for TBC. The thickness of top coat in TBC was chosen as 0.2 and 0.15mm for stator and rotor blades, respectively, based on the endurance and high temperature resistibilityof TBC.

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3.2 Turbine blades for testing

The present work carried out the design and manufacture of scaled model test blades of a sizeabout one half of that used in practical turbines. The hot gas temperatures for both the blade test caseswere the same as those used in practical turbines, whereas the inlet gas pressure was 2.44 MPa orabout one half of that used in practical turbines. The test sections for both the stator and the rotorblades consisted of linear cascade with a mean-section contour similar to that in the practical blades.

Figure 2 shows the distributions of calculated outer surface heat transfer coefficient of statorand rotor test blades, together with the calculated ones of turbine blades for the 500 MW plant. Theseresults were obtained on the basis of solving the two-dimensional Reynolds Averaged Navier–Stokesequations (RANS) [2]. The results indicate that the surface heat transfer coefficients of test blades arethree times as high as those of air cooled large gas turbine blades because of the difference inthermophysical properties between steam and air and also the high pressure level.

Figure 3 shows the cooling configuration of the stator blade. In the stator, steam used as thecoolant is divided in three flow paths: leading edge portion, trailing edge portion (ejection), and centralportion (recovery). The leading edge portion was cooled by combining impingement cooling andshower head film cooling. Diffuse shaped film cooling holes were provided on the pressure and thesuction surfaces near the leading edge region, which resulted in higher film cooling effectiveness ascompared to the conventional type of holes. Forty-five-degree skewed ribs arranged periodically werecast onto the wall of internal cooling passages in the central and the trailing edge portions to enhancethe heat transfer coefficient. End walls were cooled by impingement cooling. Part of cooling steamwas used for film cooling and the rest was recovered. In the rotor blade, serpentine cooling passages

Table 1. Specifications of Scale Model Test Blades and Machine Blades

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Fig. 3. Cooling structure of test turbine stator blade.

Fig. 2. Distribution of calculated outer heat transfer coefficient on the stator and the rotor blades.

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in the central and the trailing edge portions were provided with a periodic arrangement of 45° skewedribs. Figure 4 shows the cooling configuration of the rotor blade. Leading and trailing edge portionswere cooled by ejection cooling and the central one was cooled by recovery cooling with serpentinecooling paths the same as the stator blade. Forty-five-degree skewed ribs were provided in the centraland the trailing edge portions.

TBC thickness and materials were the same as those in the case of practical turbine for boththe stator and the rotor blades. Vacuum plasma spraying was used for a bond coat and a top coat ofZrO2-8%Y2O3 was built by means of electron beam physical vapor deposition (EB-PVD) method.

4. Cascade Evaluation Test

4.1 Test apparatus

The diagram of the hydrogen–oxygen combustion cascade test apparatus is shown in Fig. 5.The boiler supplies the steam for the combustor, for blade cooling and for sealing of the test section

Fig. 5. Diagram of hydrogen–oxygen combustion cascade test apparatus.

Fig. 4. Cooling structure of test turbine rotor blade.

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through control valves which adjust the flow rate and the pressure. Hydrogen fuel and oxygen aresupplied from each gas loader. The inlet and the outlet ducts having water cooled structures wereprovided with feed and recovery lines of cooling water. Each temperature, pressure, and mass flowrate was measured at respective lines for hydrogen, oxygen, steam, and water. Flow rate andtemperature of cooling steam for the measuring blade were measured at the feed and recovery lines,so that flow rate could be obtained for ejection and recovery cooling. Figure 6 shows the cascade testsection. Five thermocouples in spanwise direction of the inlet duct were installed to measure the mainsteam temperature distribution. Several thermocouples and pressure taps were installed in themeasuring blades in order to measure the metal temperatures and pressures. The number of thermo-couples chosen was 24 on the center blade for the stator blade: 14 at 50% height, 4 at 10% height,and 6 at the end walls. For the rotor blade, 27 thermocouples were provided: 17 at the 50% height, 4at the 90% height, 2 at the 10% height, and 4 at the platform. Inconel 600 standard Chromel–Alumelthermocouples having an outer diameter of 0.5 mm were embedded in the narrow grooves extendingin the spanwise direction, and thermocouples of 0.25 mm in diameter were used near the trailing edgehaving thin wall thickness.

The experimental uncertainties associated with the temperature measurements for the mainsteam were ±20 °C, those for the blade metal were ±10 °C, and those for the cooling flow rate were±3%. ASME code was used for the temperature and JIS was used for the flow rate. This accuracy isconsidered within an acceptable range for measuring the cooling efficiency and the metal temperature.

4.2 Test items and evaluation procedure

The evaluation test items of the scale model cooled blades in hot cascade test are the following:

• Cooling effectiveness

• Cooling steam flow rate versus pressure loss characteristics

• Blade metal temperature at design condition

• Pressure characteristics around airfoil

Fig. 6. Appearance of stator blade cascade test section.

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• Robustness of TBC and blade substrate

These tests were carried out in five steps raising the gas temperature from 1000 °C to design condition.“Run Nos.” of these steps arc S1 to S5, respectively, in the case of the stator blade and R1 to R5 inthe case of the rotor blade. Measurements were carried out at gas temperature of 1000 °C in each runas one course to raise the gas temperature.

Estimation of these items was carried out for practical turbine blades based on the test resultsof the sealed model blades following the steps below.

1) Step 1 (scaled model turbine blades)

a) Measurement results of scaled model blades at test conditions

b) Correction for difference between test and design conditions (temperature, pressure, andflow rate of hot gas and cooling steam, TBC thickness, etc.)

c) Estimation of metal temperature, pressure loss, etc., for the scale model test blades at designconditions

2) Step 2 (practical turbine blades)

a) Correction from the scale model blade to the machine blade (scale factor, pressure, flowrate, etc.)

b) Estimation of metal temperature

5. Experimental Results and Discussion

The stator and rotor blade cascade tests were carried out in five runs respectively. Table 2shows the test conditions. Test time was about 1 h per run because of the limitation of hydrogen fuelloader capacity, and the total firing time and testing time at rated gas temperature were 378 and 24min for stator blade and 282 and 22 min for rotor blade, respectively. After each test run, the testblades in the test rig were observed using a bore scope.

Table 2. Cascade Test Conditions of Stator and Rotor Blades

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5.1 Hot gas temperature

For the temperature of the inlet gas measured at five thermocouples, the influence of radiationto inlet duct from thermocouple and heat conduction through itself was investigated. As a result, itwas shown that these had very little effect under ±5 °C at the rated test conditions for both blades.Therefore, the gas temperature measured by the thermocouple was directly used to evaluate thecooling effectiveness without correction. Figure 7 shows the spanwise distributions of the inlet gastemperature in the stator blade tests. The figure also shows the distribution of the gas temperature ina single combustor test and both show similar patterns at the same theoretical combustion temperature.The theoretical combustion temperature is the calculated temperature based on measured flow ratesof hydrogen, oxygen, and steam assuming perfect combustion. The mean gas temperature estimatedfrom the measured gas temperature distribution is about 100 °C lower than the theoretical value atthe design conditions. The same tendency is observed for the rotor blade test. As one reason for thisdiscrepancy, hydrogen–oxygen combustion in steam was supposed to be imperfect. The pattern factorestimated based on the measurements for the stator blade around the design condition was about 11%and was almost at the same level as that of 10% used for the design of the cooled blade.

5.2 Cooling effectiveness

The cooling effectiveness of a turbine blade is defined as

ηc = (Tg − Tm) / (Tg − Tc) (3)

where Tm is the blade outer surface metal temperature obtained from the measured temperaturecorrected by the depth of thermocouple location for thermocouples embedded in the grooves. Becausethere was a large temperature gradient in the direction of metal thickness caused by high heat fluxfrom the hot steam flow, the correction was necessary to obtain the outer surface metal temperaturefrom the measured one.

Fig. 7. Inlet gas temperature distribution at stator blade test.

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5.2.1 Stator blade

Figure 8 shows the distribution of cooling effectiveness at the 50% height of the stator bladefor the theoretical gas temperature of 1000 °C level in Run Nos. S1 to S5. The cooling steam flowrate is in the range of 6.2 to 6.9% which is almost the same as the designed one. The measured coolingeffectiveness agrees well with the prediction on the whole. On the suction side, the cooling effective-ness shows the tendency to decrease as the test progresses and becomes a little lower than theprediction. The prediction was obtained using the analysis code which considers the heat transfer onthe inner and outer surface of the blade and the heat conduction in the blade metal. The analysis codecan calculate the thermodynamic properties of the cooling fluid and the heat transfer coefficient ateach location of the cooling flow network along the cooling path and the film cooling effectivenesson the blade surface.

Maximum decrease of the cooling effectiveness is about 0.078 between Run Nos. S1 and S5,which corresponds to the increase of +110 °C converted in the blade metal temperature at designconditions. Observation of the test blades by bore scope was carried out after each run and it wasrecognized that the pressure side became brown as the test proceeded and sticky materials weredeposited. This suggests that the decrease of the cooling effectiveness on the blade pressure side duringtest progress is influenced by the variation of the blade surface condition.

Figure 9 shows the relation between the cooling effectiveness around the stator blade and thecooling steam flow rate at the theoretical combustion temperature of 1000 °C. In this case, the ratioof ejection cooling flow rate to the recovery one was kept the same as in design conditions. The rateof cooling effectiveness increase due to the cooling flow rate increase agrees well with the predictedtendency.

5.2.2 Rotor blade

Figure 10 shows the distribution of cooling effectiveness at the 50% height of the rotor bladefor the theoretical gas temperature of 1000 °C in Run Nos. R1 to R5. The cooling steam flow rate is

Fig. 8. Cooling effectiveness distribution instator blade.

Fig. 9. Variation of cooling effectivenesswith cooling flow rate in stator blade.

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in the range of 6.8 to 7.0% which is almost the same as the designed one. The measured coolingeffectiveness agrees well with the prediction on the whole. However, a little decrease in the coolingeffectiveness during the test progress is observed as a tendency on the pressure side. Observation bybore scope showed some color change and deposition accompanying the test progress, which werelighter than those for the stator blade. Predictions were obtained in the same way as for the statorblade.

5.3 Blade metal temperature

The measured metal temperature is shown below for turbine cooled blades at design condi-tions. First, composition analysis of the deposition on the blades was carried out, because the decreasein the cooling effectiveness was observed as the test proceeded especially on the pressure side of thestator blade and some deposition was observed on the pressure side by visual inspection after theevaluation test. As a result, it was revealed that the deposition was a metallic powder flying from thetest apparatus located upstream of the test blades. It was confirmed that the surface roughnessincreased especially on the pressure side compared to that before the test, as a result of surfaceroughness measurement. Maximum increase of heat transfer coefficient on the blade is estimated tobe about 40% by calculation including the effect of roughness [3]. It is supposed that the metallicpowder flying occurred due to insufficient preflushing for the piping and other parts of the testapparatus.

Therefore, the measured metal temperature at design conditions is supposed to include theeffect of roughness, although the stator blade test was carried out at conditions near the design ones.Thus, it was decided to obtain the metal temperature for design conditions correcting the test resultat design cooling flow rate in the “cooling effectiveness test” at gas temperature of 1000 °C andpressure level of 1.8 MPa in Run No. S1 conducted at the first stage of the test. The calculation showedthat the variation of gas temperature and pressure had little effect on the distribution of blade surfacecooling effectiveness, and therefore this method is considered to be appropriate. Figure 11 shows thesurface metal temperature corrected to that at design test conditions at 50% height of the stator blade.The figure also shows the distribution of metal temperature and TBC surface temperature obtainedby prediction calculation. The corrected metal temperature on the blade suction side is a little lower

Fig. 10. Cooling effectiveness distribution in rotor blade.

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than prediction and that on the pressure side shows the same level, so the measurement agrees wellwith our prediction.

Figure 12 shows the measured metal temperature at the end walls of the stator blade in Run

No. S5 together with the prediction. The outer end wall showed lower temperature than the prediction

so it is better cooled. On the other hand, the inner end wall showed fairly higher temperature than the

prediction. In order to clarify the reason, the stator blade was cross-examined by disassembly afterthe test and a gap was found between the cast blade and the impingement plate on the inner end wall.

It turned out that half of the cooling steam bypassed the impingement cooling plate in this situation;

therefore, metal temperature was calculated following this condition and produced nearly the same

value as the measurement. As a result of this investigation, it was confirmed that the end wall would

be cooled the same as the first prediction if the bypass was avoided.

Figure 13 shows the test result at 10, 50, and 90% heights of the rotor blade. The metal

temperatures of the three sections remain on the same level and agree well with the prediction as a

Fig. 11. Corrected metal temperature distribution in stator blade at the design test conditions.

Fig. 12. Metal temperatures of end wall in stator blade.

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whole. The test result shows that the measured temperature is acceptable although it is somewhathigher than predicted on the pressure side.

5.4 Flow characteristics of cooling steam

As the cooled blades are subjected to the hybrid cooling scheme combining recovery coolingwith ejection cooling, it is particularly important to maintain the exact flow balance in the coolingflow passages. Flow balance tests were conducted for the stator and the rotor blades using air and theflow rate was adjusted partly. During the cascade test, the flow rates and the pressure differences weremeasured for the feed and the recovery cooling steam, respectively. Figure 14 shows the relationbetween the cooling flow rate and the pressure difference for the rotor blade as an example. Themeasurements agree well with the prediction and the same relation was obtained for the stator blade.

Fig. 14. Cooling steam flow characteristics of rotor blade.

Fig. 13. Measured metal temperature distribution in rotor blade.

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5.5 Blade inspections after the test

Figure 15 shows the views of the stator and rotor blades after the cascade evaluation test,respectively. These blades showed no failure or deformation. Dark brown deposits were observed onthe pressure surface for the stator blade, while the suction surface was clean. For the rotor blade,similar deposits were observed but they were comparatively clean. TBC showed no visible spallingexcept at a part of the rotor blade platform where coating process conditions were not so favorable.TBC on the stator blade and rotor blade was inspected by an infrared ray inspection system, whichcan detect invisible separation in TBC. Soundness was confirmed as a result. Minimum resolutioncapability is 3 mm with this method for the inner separation of TBC.

Next, thickness of top coat in TBC was measured after the test, and it was the same as that ofas-coat blade. No erosion of TBC on both blades was found by the inspection. Microstructure of TBCwas observed by a secondary electron microscope and no change was found. Observation by X-raydiffraction was also carried out. X-ray wavelength is 1.54 Å and scan speed is 2°/min. X-ray peakdiffraction angles corresponding to the crystal axes were the same as those for as-coat material;therefore, a top coat of ZrO2-8wt%Y2O3 having dense columnar crystal structure was confirmed notto have changed after the cascade test. Bond coat showed no abnormal oxidation.

The metal temperature and cooling flow characteristics of the first stage cooled turbine bladesfor the practical turbine were estimated using the results of the scale model cascade tests and wereconfirmed to satisfy the allowable level for both stator and rotor blades.

The following issues are needed for improvement of the reliability of the turbine blades inoperation.

• Accurate estimation of outer and internal heat transfer and improvement of internal heat transfercoefficient

Fig. 15. View of stator and rotor blades after evaluation test.

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• Improvement of thermal cycle separation life and high temperature resistance for TBC

• Evaluation of strength and oxidation resistance for substrate in high temperature steam envi-ronment for long term

6. Conclusions

Hydrogen–oxygen combustion hot steam wind tunnel tests were carried out for the 1700 °Cclass turbine cooled blades and the conclusions are as follows.

(1) The cooling effectiveness obtained by the cascade test agrees well with the result ofanalysis on the suction and pressure sides for the stator and rotor blades, respectively.

(2) The measured metal temperatures of stator and rotor blades agree well with predictions atthe design test conditions and are within the allowable level. Based on these results, it was confirmedthat the metal temperature of the machine turbine cooled blades will be within the allowable level.

(3) It was confirmed that the hybrid cooling method was the effective cooling method underthe high heat flux conditions, using recovery cooling basically and combining ejection cooling forthe high heat loading part.

(4) TBCs showed no separation by visual and internal layer inspection and it was confirmedby micro structural inspection for TBC to have kept sound conditions the same as the blade substrate.

Acknowledgments

This work was supported by the New Energy and Industrial Technology DevelopmentOrganization (NEDO) as part of the WE-NET program, and was directly entrusted by the Japan PowerEngineering and Inspection Corporation (JAPEIC). The authors thank both organizations for theirsupport of this research.

Literature Cited

1. Mouri K, Arai N, Taniguchi H, Maekawa H. Research and development of hydrogen combus-tion turbine and very hot heat exchanger in WE-NET Project. IJPGC’98, Vol. 1, p 433–437.

2. Biswas D, Fukuyama Y. Calculation of transitional boundary layer with an improved lowReynolds number version of the k–ε turbulence model. ASME paper 93-GT-73, 1993.

3. Dippery DF, Sabersky RH. Heat and momentum transfer in smooth and rough tubes at variousPrandtl numbers. Int J Heat Mass Transfer 1963;6:329–353.

"F F F"

Originally, published in Trans JSME Ser B 66, 2000, 845–852.Translated by Akinori Koga, Power and Industrial Systems R&D Center, Toshiba Corporation, 2-4,

Suehiro-cho, Tsurumi-ku, Yokohama, 230-0045 Japan.

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