Patent Publication Number: US-11643935-B2

Title: Turbine blade and gas turbine

Description:
TECHNICAL FIELD 
     The present disclosure relates to a turbine blade and a gas turbine. 
     BACKGROUND 
     It is known that, in a turbine blade for a gas turbine or the like, the turbine blade exposed to a high-temperature gas flow or the like is cooled by flowing a cooling fluid to a cooling passage formed inside the turbine blade. 
     For example, Patent Documents 1 to 3 each disclose a turbine blade having an airfoil portion inside of which a serpentine flow passage is formed by a plurality of cooling passages extending along a blade height direction. Rib-shaped turbulators are provided on inner wall surfaces of the cooling passages in the turbine blade. The turbulators are provided in order to improve a heat-transfer coefficient between the cooling fluid and the turbine blade by promoting turbulence in the flow of the cooling fluid in the cooling passages. 
     In addition, Patent Document 3 describes that the turbulators are provided such that an inclination angle formed between each of the turbulator (rib) and the direction of a cooling flow in each of the cooling passages is substantially constant. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Document 1: JPH11-229806A 
         Patent Document 2: JP2004-137958A 
         Patent Document 3: JP2015-214979A 
       
    
     SUMMARY 
     Technical Problem 
     However, depending on the shape or an operation state of a turbine blade, the selection of a turbulator having a high heat-transfer coefficient and high cooling performance may rather have a negative effect on the performance of the turbine blade. 
     Thus, an object of at least one embodiment of the present invention is to provide a turbine blade and a gas turbine capable of efficiently cooling a turbine by selecting an appropriate turbulator. 
     Solution to Problem 
     (1) A turbine blade according to at least one embodiment of the present invention includes an airfoil body, and a plurality of cooling passages extending along a blade height direction inside the airfoil body and communicating with each other to form a serpentine flow passage. The cooling passages include first turbulators disposed on an inner wall surface of an upstream side passage of the plurality of cooling passages, and second turbulators disposed on an inner wall surface of a downstream side passage of the plurality of cooling passages, the second turbulators being arranged on a downstream side of the upstream side passage. A second angle formed by the second turbulators with respect to a flow direction of a cooling fluid in the most downstream passage is smaller than a first angle formed by the first turbulators with respect to the flow direction of the cooling fluid in the upstream side passage. 
     (1′) Alternatively, a turbine blade according to at least one embodiment of the present invention includes an airfoil body, a plurality of cooling passages extending along a blade height direction inside the airfoil body and communicating with each other to form a serpentine flow passage, rib-shaped first turbulators disposed on an inner wall surface of an upstream side passage of the plurality of cooling passages, and rib-shaped second turbulators disposed on an inner wall surface of a downstream side passage of the plurality of cooling passages, the rib-shaped second turbulators being arranged on a downstream side of the upstream side passage. A second angle formed by the second turbulators with respect to a flow direction of a cooling fluid in the most downstream passage is smaller than a first angle formed by the first turbulators with respect to the flow direction of the cooling fluid in the upstream side passage. 
     In the cooling passages, in a range where an angle formed by the turbulators with respect to the flow direction of the cooling fluid (may also be referred to as an “inclination angle” hereinafter) is in the vicinity of 90 degrees, the heat-transfer coefficient between the cooling fluid and the turbine blade tends to high as the inclination angle is small. 
     In this regard, with the above configuration (1), the inclination angle (second angle) of the second turbulators in the most downstream passage is smaller than the inclination angle (first angle) of the first turbulators in the upstream side passage of the serpentine flow passage. Thus, the above-described heat-transfer coefficient is relatively low in the upstream side passage, and cooling of the turbine blade is suppressed, making it possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low, and the above-described heat-transfer coefficient is relatively high in the downstream side passage, and cooling of the turbine blade is promoted, making it possible to enhance cooling of the turbine blade in a downstream side region of the serpentine flow passage. Thus, it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage to cool the turbine blade, making it possible to improve thermal efficiency of the turbine including the gas turbine and the like. 
     (2) In some embodiments, in the above configuration (1), a second shape factor defined by a height and a pitch of the second turbulators with respect to the flow direction of the cooling fluid in the downstream side passage is smaller than a first shape factor defined by a height and a pitch of the first turbulators with respect to the flow direction of the cooling fluid in the upstream side passage. 
     (3) A turbine blade according to at least one embodiment of the present invention includes an airfoil body, and a plurality of cooling passages extending along a blade height direction inside the airfoil body and communicating with each other to form a serpentine flow passage. The cooling passages include first turbulators disposed on an inner wall surface of an upstream side passage of the plurality of cooling passages, and second turbulators disposed on an inner wall surface of a downstream side passage of the plurality of cooling passages, the second turbulators communicating with the upstream side passage and being positioned on a downstream side of the upstream side passage. A second shape factor defined by a height and a pitch of the second turbulators with respect to a flow direction of a cooling fluid in the downstream side passage is smaller than a first shape factor defined by a height and a pitch of the first turbulators with respect to the flow direction of the cooling fluid in the upstream side passage. 
     With the above configuration (3), the first shape factor in the upstream side passage is smaller than the second shape factor in the downstream passage. Thus, the above-described heat-transfer coefficient is relatively low in the upstream side passage, and cooling of the turbine blade is suppressed, making it possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low, and the above-described heat-transfer coefficient is relatively high in the downstream side passage, and cooling of the turbine blade is promoted, making it possible to enhance cooling of the turbine blade in the downstream side region of a folded flow passage. Thus, it is possible to reduce the amount of the cooling fluid supplied to the folded flow passage to cool the turbine blade, making it possible to improve thermal efficiency of the turbine including the gas turbine and the like. 
     (4) In some embodiments, in the above configuration (3), a second angle formed by the second turbulators with respect to the flow direction of the cooling fluid in the most downstream passage is smaller than a first angle formed by the first turbulators with respect to the flow direction of the cooling fluid in the upstream side passage. 
     In the cooling passages, in the range where the angle formed by the turbulators with respect to the flow direction of the cooling fluid (may also be referred to as the “inclination angle” hereinafter) is in the vicinity of 90 degrees, the heat-transfer coefficient between the cooling fluid and the turbine blade tends to high as the inclination angle is small. 
     In this regard, with the above configuration (4), the inclination angle (second angle) of the second turbulators in the most downstream passage is smaller than the inclination angle (first angle) of the first turbulators in the upstream side passage of the serpentine flow passage. Thus, the above-described heat-transfer coefficient is relatively low in the upstream side passage, and cooling of the turbine blade is suppressed, making it possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low, and the above-described heat-transfer coefficient is relatively high in the downstream side passage, and cooling of the turbine blade is promoted, making it possible to enhance cooling of the turbine blade in the downstream side region of the folded flow passage. Thus, it is possible to further reduce the amount of the cooling fluid supplied to the folded flow passage to cool the turbine blade, making it possible to further improve thermal efficiency of the turbine including the gas turbine and the like. 
     (5) In some embodiments, in any one of the above configuration (1), (2), or (4), the upstream side passage is provided with a plurality of first turbulators arranged along the blade height direction, the downstream side passage is provided with a plurality of second turbulators arranged along the blade height direction, and an average of second angles of the plurality of second turbulators is smaller than an average of first angles of the plurality of first turbulators. 
     With the above configuration (5), the average of the inclination angles (second angles) of the plurality of second turbulators in the most downstream passage is smaller than the average of the inclination angles (first angles) of the plurality of first turbulators in the upstream side passage of the serpentine flow passage. Thus, as described in the above configuration (1), it is possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low, and to enhance cooling of the turbine blade in the downstream side region of the serpentine flow passage. Thus, it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage to cool the turbine blade, making it possible to improve thermal efficiency of the turbine including the gas turbine and the like. 
     (6) In some embodiments, in any one of the above configurations (2) to (4), the upstream side passage is provided with a plurality of first turbulators arranged along the blade height direction, the downstream side passage is provided with a plurality of second turbulators arranged along the blade height direction, and an average of the second shape factors of the plurality of second turbulators is smaller than an average of the first shape factors of the plurality of first turbulators. 
     (7) In some embodiments, in any one of the above configurations (2) to (4) or (6), the first shape factors of some of the first turbulators are smaller than an average of the first shape factors of other of the first turbulators in the same passage. 
     With the above configuration (7), even if a hot spot occurs in the blade inner wall in the same passage, it is possible to enhance local cooling by making the first shape factors of the first turbulators in the part smaller than the first shape factors of the other first turbulators. 
     (8) In some embodiments, in any one of the above configurations (1) to (7), the turbine blade includes the first turbulators provided in the upstream side passage and having the first angle of 90 degrees. 
     As described above, in the range where the inclination angle of the turbulators in the cooling passages is in the vicinity of 90 degrees, the heat-transfer coefficient between the cooling fluid and the turbine blade tends to high as the inclination angle is small. In this regard, with the above configuration (8), since the inclination angle (first angle) of the first turbulators in the upstream side passage is 90 degrees, and the inclination angle (second angle) of the second turbulators in the most downstream passage is less than 90 degrees, it is possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low, and to enhance cooling of the turbine blade in the downstream side region of the serpentine flow passage. Thus, it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage to cool the turbine blade, making it possible to improve thermal efficiency of the turbine including the gas turbine and the like. 
     (9) In some embodiments, in any one of the above configurations (2) to (4), (6) or (7), the first shape factor is represented by a ratio P 1 /e 1  of a pitch P 1  of an adjacent pair of first turbulators of the plurality of first turbulators to a height e 1  of the pair of first turbulators with reference to the inner wall surface of the upstream side passage, and the second shape factor is represented by a ratio P 2 /e 2  of a pitch P 2  of an adjacent pair of second turbulators of the plurality of second turbulators to a height e 2  of the pair of second turbulators with reference to the inner wall surface of the downstream side passage. 
     Provided that a ratio P/e of a pitch P of an adjacent pair of turbulators of a plurality of turbulators provided in the cooling passages to an average height e of the these turbulators with reference to the inner wall surfaces of the cooling passages is the a shape factor, the heat-transfer coefficient between the cooling fluid and the turbine blade tends to high as the shape factor P/e is small. 
     In this regard, with the above configuration (9), the first shape factor P 1 /e 1  in the upstream side passage is smaller than the second shape factor P 2 /e 2  in the downstream side passage. Thus, the above-described heat-transfer coefficient is relatively low in the upstream side passage, and cooling of the turbine blade is suppressed, making it possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low, and the above-described heat-transfer coefficient is relatively high in the downstream side passage, and cooling of the turbine blade is promoted, making it possible to enhance cooling of the turbine blade in a downstream side region of the serpentine flow passage. Thus, it is possible to further reduce the amount of the cooling fluid supplied to the serpentine flow passage to cool the turbine blade, making it possible to further improve thermal efficiency of the turbine including the gas turbine and the like. 
     (10) In some embodiments, in any one of the above configurations (1) to (9), the downstream side passage includes the most downstream passage positioned on a most downstream side of the flow direction of the cooling fluid of the plurality of cooling passages, and the upstream side passage includes the cooling passage arranged adjacent to the most downstream passage. 
     The cooling fluid which flows through the plurality of cooling passages forming the serpentine flow passage increases downward in temperature by a heat exchange with the turbine blade to be cooled. The temperature of the cooling fluid is the highest in the most downstream passage positioned on the most downstream side of the flow of the cooling fluid. 
     In this regard, with the above configuration (10), in the downstream side passage including the most downstream passage, the inclination angle of the turbulators is smaller than in the upstream side passage arranged adjacent to the most downstream passage. Thus, the above-described heat-transfer coefficient is relatively low in the upstream side passage, and cooling of the turbine blade is suppressed, making it possible to relatively maintain the temperature of the cooling fluid from the upstream side passage toward the most downstream passage, and the above-described heat-transfer coefficient is relatively high in the most downstream passage, and cooling of the turbine blade is promoted, making it possible to enhance cooling of the turbine blade in the most downstream passage. Thus, it is possible to effectively reduce the amount of the cooling fluid supplied to the folded flow passage to cool the turbine blade, and to improve thermal efficiency of the turbine including the gas turbine and the like. 
     (11) In some embodiments, in any one of the above configurations (1) to (10), the plurality of cooling passages are a serpentine passage including at least the three cooling passages. 
     With the above configuration (11), it is possible to make the inclination angle (second angle) of the second turbulators in the most downstream passage of at least the three cooling passages smaller than the inclination angle (first angle) of the first turbulators in the upstream side passage of at least the three cooling passages forming the serpentine flow passage. Thus, as described in the above configuration (1), it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage to cool the turbine blade, making it possible to improve thermal efficiency of the turbine including the gas turbine and the like. 
     (12) In some embodiments, in the above configuration (11), the plurality of cooling passages include a most upstream passage positioned on a most upstream side of the flow direction of the cooling fluid of the plurality of cooling passages, and an inner wall surface of the most upstream passage is formed by a smooth surface which is not provided with any turbulators. 
     In a case in which the inner wall surface of the cooling passage is formed by the smooth surface which is not provided with any turbulators, the heat-transfer coefficient between the cooling fluid and the turbine blade is low, as compared with a case in which the turbulators are provided on the inner wall surface of the cooling passage. 
     In this regard, with the above configuration (12), since the inner wall surface of the most upstream passage positioned on the most upstream side of the plurality of cooling passages is formed by the smooth surface which is not provided with any turbulators, the above-described heat-transfer coefficient in the most upstream passage is lower than the above-described heat-transfer coefficient in the upstream side passage. That is, the above-described heat-transfer coefficient in the most upstream passage, the upstream side passage, and the downstream side passage forming the serpentine flow passage increases in this order. Thus, the heat-transfer coefficient is easily changed in stages in the serpentine flow passage, facilitating adjustment of the cooling performance in each of the cooling passages. 
     (13) In some embodiments, in any one of the above configurations (1) to (12), the downstream side passage includes the most downstream passage positioned on the most downstream side of a flow of the cooling fluid of the plurality of cooling passages, and the most downstream passage is formed such that a flow passage area thereof decreases toward the downstream side of the flow of the cooling fluid. 
     With the above configuration (13), since the most downstream passage is formed such that the flow passage area thereof decreases toward the downstream side of the flow of the cooling fluid, the flow velocity of the cooling fluid is increased toward downstream in the most downstream passage. Thus, it is possible to improve cooling efficiency in the most downstream passage where the temperature of the cooling fluid is relatively high. 
     (14) In some embodiments, in any one of the above configurations (1) to (13), the downstream side passage includes the most downstream passage positioned on the most downstream side of a flow of the cooling fluid of the plurality of cooling passages, and the turbine blade further includes a cooling fluid supply path disposed so as to communicate with an upstream part of the most downstream passage and configured to supply a cooling fluid from outside to the most downstream passage without via the upstream side passage. 
     With the above configuration (14), in addition to the inflow of the cooling fluid from the upstream side passage to the most downstream passage, the cooling fluid from outside is supplied to the most downstream passage via the cooling fluid supply path. Thus, it is possible to further enhance cooling in the most downstream passage where the temperature of the cooling fluid from the upstream side passage is relatively high. 
     (15) In some embodiments, in any one of the above configurations (1) to (14), the turbine blade is a rotor blade for a gas turbine. 
     With the above configuration (15), since the rotor blade for the gas turbine as the turbine blade has any one of the above configurations (1) to (14), it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage to cool the rotor blade, making it possible to improve thermal efficiency of the gas turbine. 
     (16) In some embodiments, in any one of the above configurations (1) to (14), the turbine blade is a stator vane for a gas turbine. 
     With the above configuration (16), since the stator vane for the gas turbine as the turbine blade has any one of the above configurations (1) to (14), it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage to cool the stator vane, making it possible to improve thermal efficiency of the gas turbine. 
     (17) A gas turbine according to at least one embodiment of the present invention includes the turbine blade according to any one of the above configurations (1) to (16), and a combustor for producing a combustion gas to flow through a combustion gas flow passage in which the turbine blade is disposed. 
     With the above configuration (17), since the turbine blade has any one of the above configurations (1) to (16), it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage to cool the turbine blade, making it possible to improve thermal efficiency of the gas turbine. 
     Advantageous Effects 
     According to at least one embodiment of the present invention, a turbine blade and a gas turbine are provided, which are capable of efficiently cooling a turbine. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a schematic configuration view of a gas turbine to which a turbine blade is applied according to an embodiment. 
         FIG.  2 A  is a partial cross-sectional view of a rotor blade (turbine blade) along a blade height direction according to an embodiment. 
         FIG.  2 B  is a view taken along line IIB-IIB of  FIG.  2 A . 
         FIG.  3 A  is a partial cross-sectional view of the rotor blade (turbine blade) along the blade height direction according to an embodiment. 
         FIG.  3 B  is a view taken along line IIIB-IIIB of  FIG.  3 A . 
         FIG.  4    is a schematic view for describing the configuration of turbulators according to an embodiment. 
         FIG.  5    is a schematic view for describing the configuration of the turbulators according to an embodiment. 
         FIG.  6    is a schematic cross-sectional view of the rotor blade (turbine blade) according to an embodiment. 
         FIG.  7    is a schematic cross-sectional view of the rotor blade (turbine blade) according to an embodiment. 
         FIG.  8    is a schematic cross-sectional view of the rotor blade (turbine blade) according to an embodiment. 
         FIG.  9    is a schematic cross-sectional view of the rotor blade (turbine blade) according to an embodiment. 
         FIG.  10    is a schematic cross-sectional view of the rotor blade (turbine blade) according to an embodiment. 
         FIG.  11    is a schematic cross-sectional view of a stator vane (turbine blade) according to an embodiment. 
         FIG.  12    is a schematic cross-sectional view of the rotor blade (turbine blade) according to an embodiment. 
         FIG.  13    is a graph showing an example of a correlation between a heat-transfer coefficient ratio α and an inclination angle θ of the turbulators. 
         FIG.  14    is a graph showing an example of a correlation between the heat-transfer coefficient ratio α and a shape factor P/e of the turbulators. 
     
    
    
     DETAILED DESCRIPTION 
     Some embodiments of the present invention will be described below with reference to the accompanying drawings. It is intended, however, that unless particularly identified, dimensions, materials, shapes, relative positions and the like of components described in the embodiments or shown in the drawings shall be interpreted as illustrative only and not intended to limit the scope of the present invention. 
     First, a gas turbine to which the turbine blade is applied according to some embodiments will be described. 
     The basic idea of the present invention common to some embodiments to be described later will be described below. 
     Since a representative turbine blade is arranged in an atmosphere of a high-temperature combustion gas, the interior of an airfoil body is cooled with a cooling fluid in order to prevent thermal damage from a combustion gas of the airfoil body. The airfoil body is cooled by flowing the cooling fluid into a serpentine flow passage formed in the airfoil body. In addition, in order to further enhance cooling performance by the cooling fluid of the airfoil body, a turbulence promoting member (turbulator) is arranged on a blade inner wall of a passage through which the cooling fluid flows. That is, an optimum turbulator is selected, and a heat-transfer coefficient between the cooling fluid and the blade inner wall is increased as much as possible, thereby implementing an optimum cooling structure of the airfoil body. 
     However, in order to further improve thermal efficiency of the gas turbine, the flow rate of the cooling fluid may need a further reduction. The reduction in the flow rate of the cooling fluid brings about a decrease in the flow velocity of the cooling fluid, resulting in a decrease in the cooling performance of the airfoil body and an increase in a metal temperature of the airfoil body. Thus, a measure to, for example, reduce the cross-sectional area of the passage and to increase the flow velocity is needed. 
     However, a cooling structure, in which the cross-sectional area of the passage is reduced, and a turbulator having the highest heat-transfer coefficient is applied, may not be an appropriate cooling structure for the blade, and a cooling structure suitable for the shape and an operation condition of the blade needs to be selected. For example, if a cooling structure having good cooling performance is applied to a blade with a blade shape having a high blade height (spanwise direction) relative to a blade length (a length in a chordwise direction) or blade aiming at improving thermal efficiency of the gas turbine by suppressing the flow rate of the cooling fluid relative to a heat load, the cooling fluid is heated up in the course whereby the cooling fluid flows through the serpentine flow passage, and a metal temperature of a final passage (most downstream passage) may exceed a service temperature limit. For such a blade, it is important to select an appropriate cooling structure in which heatup is suppressed, and the metal temperature of the final passage does not exceed the service temperature limit. 
     More specifically, it is desirable to select a turbulator which has a heat-transfer coefficient between the flow of the cooling fluid and the blade surface kept low for a turbulator of an upstream side passage on the upstream side of the final passage, and to select a turbulator having the highest heat-transfer coefficient for a turbulator of the final passage. With the above-described selection, heatup of a cooling fluid flowing through the upstream side passage is suppressed and in the course whereby the cooling fluid suppressed in heatup flows through the final passage, cooling performance by the cooling fluid with respect to the airfoil body is improved by applying a turbulator having a high heat-transfer coefficient. As a result, it is possible to keep the metal temperature of the final passage not more than the service temperature limit. In addition, as described above, keeping the heat-transfer coefficient low has an effect of reducing a pressure loss of the cooling fluid. Therefore, with multiple effects of the effect of suppressing the heatup and the effect of reducing the pressure loss of the cooling fluid, the cooling performance in the final passage is maximized. 
     As shown in  FIGS.  4  and  5   , turbulators are formed by protruding ribs which are disposed on a blade inner wall forming a cooling flow passage, the details of which are to be described later. The ribs are arranged at predetermined intervals in a flow direction of the cooling fluid. When the cooling fluid flows over the ribs, a swirl is generated on the downstream side of the flow direction, promoting heat transfer between the blade inner wall and the flow of the cooling fluid. Therefore, there is a large difference in heat-transfer coefficient between a blade inner wall having a smooth surface without any rib and a blade inner wall with the ribs. 
     Factors defining the performance and the specifications of the turbulators are inclination angles and shape factors of the turbulators. 
       FIG.  13    shows a relationship between the inclination angle of the turbulators and the heat-transfer coefficient between the cooling fluid and the blade inner wall, and  FIG.  14    shows a relationship between the shape factor of the turbulators and the heat-transfer coefficient between the cooling fluid and the blade inner wall, the details of which are to be described later. If the turbulators have the inclination angle which is an optimum angle (optimum value) and the shape factor which is also an optimum factor (optimum value), the highest heat-transfer coefficient and the best cooling performance are obtained. As a result, cooling of a blade inner wall surface is promoted, making it possible to decrease the metal temperature of the cooling flow passage. On the other hand, if turbulators are selected which have the inclination angle which is an intermediate angle (intermediate value) larger than the optimum value and have the shape factor which is also an intermediate factor (intermediate value) larger than the optimum value, the heat-transfer coefficient is lower, and the cooling performance is suppressed as compared with a case in which the optimum values of the inclination angle and the shape factor are applied. 
     As described above, depending on the blade shape and the operation condition, adopting a blade structure having a cooling structure, in which the cooling performance is suppressed in the upstream side passage and the cooling performance is maximized in the final passage, rather than selecting turbulators having the highest heat-transfer coefficient and good cooling performance may be appropriate as a cooling structure of an entire blade. A specific blade configuration along the above-descried idea will be described with reference to a blade configuration of each of the embodiments to be described later. In the cooling structure of each of the embodiments to be described below, the turbulator specifications of the upstream side passage have a configuration which varies according to the respective embodiments. However, the configuration is common to the respective embodiments in that the optimum values are selected for both the inclination angle and the shape factor of the turbulators in the final passage. 
     In the embodiment shown in  FIG.  6   , inclination angles are selected in which the inclination angles of the turbulators are optimum values for all passages. For the shape factor, the optimum value is selected in the final passage, and the intermediate value is selected in the upstream side passage on the upstream side of the final passage. With such a cooling structure, heatup of the cooling fluid in the upstream side passage is suppressed. On the other hand, since the airfoil body is sufficiently cooled in the course whereby the cooling fluid flows through the final passage having good cooling performance, the metal temperature of the blade inner wall is prevented from increasing and does not exceed the service temperature limit. 
     The embodiment shown in  FIG.  7    is an example in which the cooling performance of the upstream side passage is further suppressed relative to the cooling structure in  FIG.  6   . That is, the embodiment shown in  FIG.  7    is an example in which the intermediate angle (intermediate value) which is larger than the optimum angle (optimum value) is selected for the inclination angle of the turbulators in the upstream side passage, as compared with the cooling structure in  FIG.  6   . A margin is produced in a cooling capacity of the final passage in a case in which the metal temperature of the upstream side passage does not exceed the service temperature limit even if the heat-transfer coefficient of the upstream side passage is further suppressed as compared with the cooling structure in  FIG.  6   . Thus, the embodiment shown in  FIG.  7    has a further advantage over the cooling structure in  FIG.  6    in terms of the cooling capacity of the final passage. That is, in the cooling structure shown in  FIG.  7   , the intermediate value is selected at which inclination angles of the turbulators in all upstream side passages on the upstream side of the final passage are larger than the inclination angle (optimum value) of the turbulators in the final passage. However, different intermediate values are selected for the inclination angles in the respective passages. The selection is made such that the inclination angle of the turbulators in the most upstream passage of the upstream side passages is smaller than 90 degrees, and the inclination angles of the turbulators in the respective upstream side passages gradually decrease toward the final passage. Moreover, regarding the shape factor of the turbulators, the same intermediate value is selected in the upstream side passages, and the optimum value is selected in the final passage, as the same configuration as the cooling structure in  FIG.  6   . With such a cooling structure, as compared with the cooling structure shown in  FIG.  6   , cooling in the upstream side passage is suppressed, the temperature of the cooling fluid is decreased than in the structure shown in  FIG.  6   , and the margin is produced in the cooling capacity in the final passage. Therefore, it is possible to gradually enhance the cooling performance while suppressing the heatup of the cooling fluid in the upstream side passage, making it possible to compensate for deficiency in the cooling capacity in the final passage. 
     The embodiment shown in  FIG.  8    is an example in which the cooling performance of the upstream side passage is further suppressed relative to the cooling structure in  FIG.  7   . That is, with the cooling structure shown in  FIG.  8    as well, a further margin is produced in the cooling capacity of the final passage in the case in which the metal temperature of the upstream side passage does not exceed the service temperature limit. That is, in the cooling structure shown in  FIG.  8   , the inclination angle of the turbulators in the upstream side passage is 90 degrees across the board, and only the inclination angle of the turbulators in the final passage has the optimum value. Moreover, regarding the shape factor of the turbulators, the intermediate value is selected in the upstream side passage, and the optimum value is selected in the final passage, as the same configuration as the cooling structure in  FIG.  6   . With such a cooling structure, heatup of the cooling fluid in the upstream side passage is further suppressed as compared with the cooling structure shown in  FIG.  7   . Therefore, an inflow temperature of the cooling fluid supplied to the final passage is further lower than in the structure shown in  FIG.  7   . In the course whereby the cooling fluid flows through the final passage, as compared with the structure in  FIG.  7   , the final passage is cooled more easily, the increase in the metal temperature of the blade inner wall is suppressed, and the metal temperature of the final passage can be kept within the service temperature limit. 
     In the embodiment shown in  FIG.  9   , the cooling performance of the upstream side passage is further suppressed relative to the cooling structure in  FIG.  8   . That is, the blade configuration shown in the present embodiment is such that no turbulator is arranged in the most upstream passage in the upstream side passage, and a flow passage inner wall is formed by a smooth surface. Heatup of the cooling fluid is further suppressed, and a further margin is produced in the cooling capacity of the final passage, if the metal temperature of the most upstream passage is lower than the service temperature limit even in the case of the smooth surface without any turbulators. That is, in the structure shown in  FIG.  9   , the most upstream passage is formed by the smooth surface, the intermediate value is selected for the inclination angles of the turbulators in the other upstream side passages except the most upstream passage, and the intermediate value having the same configuration as  FIG.  8    is selected for the shape factor of the turbulators. The inclination angle and the shape factor of the turbulators in the final passage are the same as the configuration of  FIG.  6   . With such a cooling structure, it is possible to further suppress heatup of the cooling fluid in the upstream side passage as compared with the cooling structure shown in  FIG.  8   . Moreover, a margin is produced in the cooling capacity of the cooling fluid in the final passage, and the final passage is cooled more easily. 
     In the embodiment shown in  FIG.  10   , the cooling performance of the upstream side passage is further suppressed relative to the cooling structure in  FIG.  9   . The embodiment in  FIG.  10    is common to the embodiment in  FIG.  9    in that the most upstream passage is formed by the smooth surface and does not include the turbulators. However, the embodiment in  FIG.  10    is different from the cooling structure shown in  FIG.  9    in that the inclination angles of the turbulators in other two adjacent upstream side passages following the most upstream passage are 90 degrees. The inclination angle of the turbulators in the upstream side passage adjacent to the final passage is the same as the structure shown in  FIG.  9   . In addition, the inclination angle and the shape factor of the turbulators in the final passage are the same as the configuration shown in  FIG.  6   . Even in the case of such a cooling structure, it is possible to suppress heatup of the cooling fluid in the upstream side passage, and a further margin is produced in the cooling capacity of the final passage, if the metal temperature of the upstream side passage does not exceed the service temperature limit. With the cooling structure shown in  FIG.  10   , the final passage is cooled more easily, the increase in the metal temperature of the blade inner wall of the final passage is suppressed, and the metal temperature can be kept within the service temperature limit. 
     The embodiment shown in  FIG.  11    is an example in which a basic idea of the present invention is applied to a stator vane. In the case of the stator vane, an inlet of the cooling fluid supplied to the serpentine flow passage is disposed radially outward of the airfoil body, and the radial flow direction of the cooling fluid flowing through the final passage is opposite to that of the rotor blade. However, the inclination angle and the shape factor of the turbulators have the same configuration as  FIG.  6   . Even with such a cooling structure, compared with the blade configuration in which the optimum values are selected as the inclination angle and the shape factor of the turbulators, heatup of the cooling fluid in the upstream side passage is suppressed and in the course whereby the cooling fluid flows through the final passage, the increase in the metal temperature of the blade inner wall is suppressed, and the metal temperature can be kept within the service temperature limit. 
     As described above, selecting the appropriate turbulator specifications suitable for the blade shape and the operation condition, heatup of the cooling fluid in the upstream side passage is suppressed, the increase in the metal temperature of the airfoil body in the final passage is suppressed, and the gas turbine can efficiently be cooled. Specific contents of the respective embodiments will be described in detail below. 
       FIG.  1    is a schematic configuration view of the gas turbine to which the turbine blade is applied according to an embodiment. As shown in  FIG.  1   , a gas turbine  1  includes a compressor  2  for generating compressed air, combustors  4  for each generating a combustion gas from the compressed air and fuel, and a turbine  6  configured to be rotationally driven by the combustion gas. In the case of the gas turbine  1  for power generation, a generator (not shown) is connected to the turbine  6 . 
     The compressor  2  includes a plurality of stator vanes  16  fixed to the side of a compressor casing  10  and a plurality of rotor blades  18  implanted on a rotor  8  so as to be arranged alternately with respect to the stator vanes  16 . 
     Intake air from an air inlet  12  is sent to the compressor  2 , and passes through the plurality of stator vanes  16  and the plurality of rotor blades  18  to be compressed, turning into compressed air having a high temperature and a high pressure. 
     Each of the combustors  4  is supplied with fuel and the compressed air generated by the compressor  2 . In each of the combustors  4 , the fuel and the compressed air are mixed and combusted to generate the combustion gas which serves as a working fluid of the turbine  6 . As shown in  FIG.  1   , a plurality of combustors  4  may circumferentially be arranged in the casing  20  centering around the rotor. 
     The turbine  6  includes a combustion gas flow passage  28  formed in a turbine casing  22 , and includes a plurality of stator vanes  24  and rotor blades  26  disposed in the combustion gas flow passage  28 . 
     Each of the stator vanes  24  is fixed to the side of the turbine casing  22 . The plurality of stator vanes  24  arranged along the circumferential direction of the rotor  8  form a stator vane row. Moreover, each of the rotor blades  26  is implanted on the rotor  8 . The plurality of rotor blades  26  arranged along the circumferential direction of the rotor  8  form a rotor blade row. The stator vane row and the rotor blade row are alternately arranged in the axial direction of the rotor  8 . 
     In the turbine  6 , the combustion gas flowing into the combustion gas flow passage  28  from the combustors  4  passes through the plurality of stator vanes  24  and the plurality of rotor blades  26 , rotary driving the rotor  8 . Consequently, the generator connected to the rotor  8  is driven to generate power. The combustion gas having driven the turbine  6  is discharged outside via an exhaust chamber  30 . 
     In some embodiments, at least either of the rotor blades  26  or the stator vanes  24  of the turbine  6  are turbine blades  40  to be described below. 
     A description will be given below mainly with reference to the drawings of the rotor blade  26  as the turbine blade  40 . However, the same description is basically applicable to the stator vane  24  as the turbine blade  40  as well. 
       FIGS.  2 A and  3 A  are partial cross-sectional views of the rotor blade  26  (turbine blade  40 ) along a blade height direction according to an embodiment.  FIGS.  2 B and  3 B  are views taken along line IIIA-IIIA of  FIG.  2 A  and taken along line IIIB-IIIB, respectively. Arrows in the views each indicate the flow direction of the cooling fluid. 
     As shown in  FIGS.  2 A to  3 B , the rotor blade  26  as the turbine blade  40  according to an embodiment includes an airfoil body  42 , a platform  80 , and a blade root portion  82 . The blade root portion  82  is embedded in the rotor  8  (see  FIG.  1   ). The rotor blade  26  rotates together with the rotor  8 . The platform  80  is formed integrally with the blade root portion  82 . 
     The airfoil body  42  is disposed so as to extend along the radial direction of the rotor  8  (may simply be referred to as a “radial direction” or a “spanwise direction” hereinafter), and has a base  50  (end part  1 ) fixed to the platform  80  and a tip  48  (end part  2 ) which is positioned on a side opposite to the base  50  (radially outward) in the blade height direction (the radial direction of the rotor  8 ) and is made of a top board  49  forming the top of the airfoil body  42 . 
     In addition, the airfoil body  42  of the rotor blade  26  has a leading edge  44  and a trailing edge  46  from the base  50  to the tip  48 . An airfoil surface of the airfoil body  42  has a pressure surface (concave surface)  56  and a suction surface (convex surface)  58  extending along the blade height direction between the base  50  and the tip  48 . 
     The airfoil body  42  internally includes a cooling flow passage for flowing a cooling fluid (for example, air) for cooling the turbine blade  40 . In the exemplary embodiments shown in  FIGS.  2 A to  3 B , in the airfoil body  42 , a serpentine flow passage  61  and a leading-edge side flow passage  36  positioned between the serpentine flow passage  61  and the leading edge  44  are formed as cooling flow passages. A cooling fluid from outside is supplied to the folded flow passage  61  and the leading-edge side flow passage  36  via interior flow passages  84 ,  35 , respectively. 
     By thus supplying the cooling fluid to the cooling flow passages such as the serpentine flow passage  61  and the leading-edge side flow passage  36 , the airfoil body  42  disposed in the combustion gas flow passage  28  of the turbine  6  and exposed to the high-temperature combustion gas is cooled. 
     In the turbine blade  40 , the serpentine flow passage  61  includes a plurality of cooling passages  60   a ,  60   b ,  60   c , . . . (may collectively be referred to as “cooling passages  60 ” hereinafter) each extending along the blade height direction. The airfoil body  42  of the turbine blade  40  internally includes a plurality of ribs  32  along the blade height direction. The adjacent cooling passages  60  are divided by a corresponding one of the ribs  32 . 
     In the exemplary embodiments shown in  FIGS.  2 A and  2 B , the serpentine flow passage  61  includes the three cooling passages  60   a  to  60   c . The cooling passages  60   a  to  60   c  are arranged in this order from the side of the leading edge  44  toward the side of the trailing edge  46 . Moreover, in the exemplary embodiments shown in  FIGS.  3 A and  3 B , the folded flow passage  61  includes the five cooling passages  60   a  to  60   e . The cooling passages  60   a  to  60   e  are arranged in this order from the side of the leading edge  44  toward the side of the trailing edge  46 . 
     The cooling passages adjacent to each other (for example, the cooling passage  60   a  and the cooling passage  60   b ) of the plurality of cooling passages  60  forming the serpentine flow passage  61  are connected to each other on the side of the tip  48  or the side of the base  50 . In the connection part, a return flow passage with the flow direction of the cooling fluid being reversely folded in the blade height direction is formed, and the serpentine flow passage  61  has a serpentine shape in the radial direction as a whole. That is, the plurality of cooling passages  60  communicate with each other to form the serpentine flow passage  61 . 
     The plurality of cooling passages  60  forming the serpentine flow passage  61  includes a most upstream passage positioned most upstream and a most downstream passage positioned on the most downstream side of the plurality of cooling passages  60 . In the exemplary embodiments shown in  FIGS.  2 A to  3 B , of the plurality of cooling passages  60 , the cooling passage  60   a  positioned closest to the leading edge  44  is a most upstream passage  65 , and the cooling passage  60   c  ( FIGS.  2 A and  2 B ) or the cooling passage  60   e  ( FIGS.  3 A and  3 B ) positioned closest to the trailing edge  46  is a most downstream passage  66 . 
     In the turbine blade  40  including the serpentine flow passage  61  described above, the cooling fluid is introduced into, for example, the most upstream passage  65  of the serpentine flow passage  61  via the interior flow passage  84  formed inside the blade root portion  82  and an inlet opening  62  disposed on the side of the base  50  of the airfoil body  42  (see  FIGS.  2 A and  4 A ), and sequentially flows through the plurality of cooling passages  60  downward. Then, the cooling fluid flowing through the most downstream passage  66  on the most downstream side of the flow direction of the cooling fluid of the plurality of cooling passages  60  flows out to the combustion gas flow passage  28  external to the turbine blade  40  via an outlet opening  64  disposed on the side of the tip  48  of the airfoil body  42 . The outlet opening  64  is an opening formed in the top board  49 . The cooling fluid flowing through the most downstream passage  66  is partially discharged from the outlet opening  64 . Providing the outlet opening  64 , a stagnation space of the cooling fluid is generated in a space in the vicinity of the top board  49  of the most downstream passage  66 , making it possible to prevent the inner wall surface  63  of the top board  49  from being heated. 
     The shape of the folded flow passage  61  is not limited to shapes shown in  FIGS.  2 A to  3 B . For example, a plurality of folded flow passages may be formed inside the airfoil body  42  of the one turbine blade  40 . Alternatively, the serpentine flow passage  61  may be branched into a plurality of flow passages at a branch point on the serpentine flow passage  61 . 
     In some embodiments, as shown in  FIGS.  2 A and  3 A , in a trailing edge part  47  (a part including the trailing edge  46 ) of the airfoil body  42 , a plurality of cooling holes  70  are formed to be arranged along the blade height direction. The plurality of cooling holes  70  communicate with the cooling passage (the most downstream passage  66  of the serpentine flow passage  61  in the illustrated example) formed inside the airfoil body  42  and open to a surface in the trailing edge part  47  of the airfoil body  42 . 
     The cooling fluid flowing through the cooling passage (the most downstream passage  66  of the serpentine flow passage  61  in the illustrated example) partially passes through the cooling holes  70  and flows out to the combustion gas flow passage  28  external to the turbine blade  40  from the opening in the trailing edge part  47  of the airfoil body  42 . Since the cooling fluid thus passes through the cooling holes  70 , convection-cooling of the trailing edge part  47  of the airfoil body  42  is performed. 
     The rib-shaped turbulators  34  are provided on at least some inner wall surfaces  63  of the plurality of cooling passages  60 . In the exemplary embodiments shown in  FIGS.  2 A to  3 B , the plurality of turbulators  34  are provided on the respective inner wall surfaces  63  of the plurality of cooling passages  60 . 
       FIGS.  4  and  5    are schematic views for each describing the configuration of the turbulators  34  according to an embodiment.  FIG.  4    is the schematic view of a partial cross-section along a plane including the blade height direction and a blade thickness direction (the circumferential direction of the rotor  8 ) of the turbine blade  40  shown in  FIGS.  2 A to  3 B .  FIG.  4    is the schematic view of a partial cross-section along a plane including the blade height direction and a blade width direction (the axial direction of the rotor  8 ) of the turbine blade  40  shown in  FIGS.  2 A to  3 B . 
     As shown in  FIG.  4   , each of the turbulators  34  is disposed on the inner wall surface  63  of the cooling passage  60 , and reference character “e” indicates a height of each of the turbulators  34  with reference to the inner wall surface  63 . Moreover, as shown in  FIGS.  4  and  5   , in the cooling passage  60 , the plurality of turbulators  34  are disposed at the interval of a pitch P. Furthermore, as shown in  FIG.  5   , an angle forming an acute angle (may also be referred to as an “inclination angle” hereinafter) between each of the turbulators  34  and a flow direction of the cooling fluid in the cooling passage  60  (an arrow LF in  FIG.  5   ) is an inclination angle θ. 
     Providing the above-described turbulators  34  in the cooling passage  60 , turbulence in the flow such as generation of vortex is promoted in the vicinity of the turbulators  34 . That is, the cooling fluid flowing over the turbulators  34  forms a swirl between the adjacent turbulators  34  arranged downstream. Thus, in the vicinity of an intermediate position between the turbulators  34  adjacent to each other in the flow direction of the cooling fluid, the swirl of the cooling fluid adheres to the inner wall surface  63  of the cooling passage  60 , making it possible to increase the heat-transfer coefficient between the cooling fluid and the airfoil body  42 , and to effectively cool the turbine blade  40 . However, a generation state of the swirl of the cooling fluid changes depending on the inclination angle of the turbulators  34 , influencing the heat-transfer coefficient with the blade inner wall. Moreover, if the height of the turbulators is extremely high as compared with the pitch of the turbulators, the swirl may not adhere to the inner wall surface  63 . Therefore, appropriate ranges exist between the heat-transfer coefficient and the inclination angle of the turbulators, and the heat-transfer coefficient and the ratio of the pitch and the height, as will be described later. Furthermore, extremely high turbulators may be the cause of an increase in pressure loss of the cooling fluid. 
     Each of  FIGS.  6  to  10  and  12    is a schematic cross-sectional views of the rotor blade  26  (turbine blade  40 ) according to an embodiment. In addition,  FIG.  11    is a schematic cross-sectional view of the stator vane  24  (turbine blade  40 ) according to an embodiment. Arrows in the drawings each indicate the flow direction of the cooling fluid. 
     The rotor blade  26  shown in  FIGS.  6  to  10  and  12    has the same configuration as the above-described rotor blade  26 . 
     Moreover, the serpentine flow passage  61  formed in the turbine blade  40  shown in  FIGS.  6  to  12    is formed by the five cooling passages  60   a  to  60   e . Of these cooling passages  60   a  to  60   e , the cooling passage  60   a  positioned closest to the leading edge  44  is the most upstream passage  65 , and the cooling passage  60   e  positioned closest to the trailing edge  46  is the most downstream passage  66 . 
     Hereinafter, the configuration of the stator vane  24  (turbine blade  40 ) according to an embodiment will be described with reference to  FIG.  11    before describing the characteristics of the turbulators  34  in the turbine blade  40  according to some embodiments with reference to  FIGS.  2 A to  3 B  and  FIGS.  6  to  12   . 
     As shown in  FIG.  11   , the stator vane  24  (turbine blade  40 ) according to an embodiment includes the airfoil body  42 , an inner shroud  86  positioned radially inward with respect to the airfoil body  42 , and an outer shroud  88  positioned radially outward with respect to the airfoil body  42 . The outer shroud  88  is supported by the turbine casing  22  (see  FIG.  1   ), and the stator vane  24  is supported by the turbine casing  22  via the outer shroud  88 . The airfoil body  42  has an outer end  52  positioned on the side of the outer shroud  88  (that is, radially outward) and an inner end  54  positioned on the side of the inner shroud  86  (that is, radially inward). 
     The airfoil body  42  of the stator vane  24  has the leading edge  44  and the trailing edge  46  from the outer end  52  to the inner end  54 . An airfoil surface of the airfoil body  42  has the pressure surface (concave surface)  56  and the suction surface (convex surface)  58  extending along the blade height direction between the outer end  52  and the inner end  54 . 
     The serpentine flow passage  61  formed by the plurality of cooling passages  60  is formed inside the airfoil body  42  of the stator vane  24 . The serpentine flow passage  61  has the same configuration as the serpentine flow passage  61  in the rotor blade  26  described above. In the exemplary embodiment shown in  FIG.  11   , the serpentine flow passage  61  is formed by the five cooling passages  60   a  to  60   e.    
     In the stator vane  24  (turbine blade  40 ) shown in  FIG.  11   , the cooling fluid is introduced into the serpentine flow passage  61  via an interior flow passage (not shown) formed inside the outer shroud  88  and the inlet opening  62  disposed on the side of the outer end  52  of the airfoil body  42 , and sequentially flows through the plurality of cooling passages  60  downward. Then, the cooling fluid flowing through the most downstream passage  66  on the most downstream side of the flow direction of the cooling fluid of the plurality of cooling passages  60  flows out to the combustion gas flow passage  28  external to the stator vane  24  (turbine blade  40 ) via the outlet opening  64  disposed on the side of the inner end  54  (on the side of the inner shroud  86 ) of the airfoil body  42 , or discharged into the combustion gas from the cooling holes  70  of the trailing edge part  47  to be described later. 
     In the stator vane  24 , the above-described turbulators  34  are provided on at least some inner wall surfaces of the plurality of cooling passages  60 . In the exemplary embodiment shown in  FIG.  11   , the plurality of turbulators  34  are provided on the respective inner wall surfaces of the plurality of cooling passages  60 . 
     In the stator vane  24 , in the trailing edge part  47  of the airfoil body  42 , the plurality of cooling holes  70  may be formed to be arranged in the blade height direction. 
     The characteristics of the turbulators  34  in the turbine blade  40  according to some embodiments will now be described with reference to  FIGS.  2 A to  3 B  and  FIGS.  6  to  12   . 
     In the turbine blade  40  shown in  FIGS.  6  to  12   , θa, θb, θc, θd, and θe are inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e , respectively, Pa, Pb, Pc, Pd, and Pe are pitches of the adjacent turbulators  34  in the respective passages, namely, the cooling passages  60   a  to  60   e , and ea, eb, ec, ed, and ee are heights (or average heights) of the adjacent turbulators  34  in the respective passages, respectively. 
     In the rotor blade  26  shown in  FIG.  6   , the inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy θa=θb=θc=θd=θe (&lt;90 degrees), and the pitches of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy Pa=Pb=Pc=Pd&gt;Pe. 
     In the rotor blade  26  shown in  FIG.  7   , the inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy θa (=90 degrees)&gt;θb&gt;θc&gt;θd&gt;θe, and the pitches of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy Pa=Pb=Pc=Pd&gt;Pe. 
     In the rotor blade  26  shown in  FIG.  8    and the stator vane  24  shown in  FIG.  11   , the inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy θa=θb=θc=θd (=90 degrees)&gt;θe, and the pitches of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy Pa=Pb=Pc=Pd&gt;Pe. 
     In the rotor blade  26  shown in  FIG.  9   , the inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy (90 degrees&gt;) θb=θc&gt;θd&gt;θe, and the pitches of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy Pb=Pc=Pd&gt;Pe. 
     In the rotor blade  26  shown in  FIG.  10   , the inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy θb=θc (=90 degrees)&gt;θd=θe, and the pitches of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy Pb=Pc=Pd&gt;Pe. 
     In the rotor blade  26  shown in  FIG.  12   , the inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy θa=θb=θc=θd=θe (&lt;90 degrees). The pitches of the turbulators  34  in the cooling passages  60   a  to  60   e  of the rotor blade  26  shown in  FIG.  12    will be described later. 
     The cooling passage  60   a  of the rotor blade  26  shown in  FIGS.  9  and  10    is not provided with the turbulator  34 , and the inner wall surface of the cooling passage  60   a  is formed by the smooth surface. 
     In some embodiments, the rib-shaped first turbulators (turbulators  34 ) and the rib-shaped second turbulators (turbulators  34 ) are provided. The rib-shaped first turbulators (turbulators  34 ) are disposed on the inner wall surface of the upstream side passage of the plurality of cooling passages  60 . The rib-shaped second turbulators (turbulators  34 ) are disposed on the inner wall surface of a downstream side passage of the plurality of cooling passages  60 , the rib-shaped second turbulators (turbulators  34 ) being positioned on the downstream side of the upstream side passage in the serpentine flow passage  61 . Then, second angles θ 2  (inclination angles) formed by the second turbulators with respect to the flow direction of the cooling fluid in the downstream side passage are smaller than first angles θ 1  (inclination angles) formed by the first turbulators with respect to the flow direction of the cooling fluid in the upstream side passage. 
     That is, the plurality of cooling passages  60  include the upstream side passage provided with the first turbulators having the inclination angles of the first angles θ 1 , and the downstream side passage provided with the second turbulators having the inclination angles of the second angles θ 2  smaller than the first angles θ 1 . 
     The turbine blade  40  (the rotor blade  26  or the stator vane  24 ) shown in each of  FIGS.  7  and  8   , and  FIGS.  9  to  11    is the turbine blade according to the present embodiment. 
     For example, in the rotor blade  26  shown in  FIG.  8    and the stator vane  24  shown in  FIG.  11   , the inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy θa=θb=θc=θd&gt;θe. Thus, the cooling passages  60   a  to  60   d  in which the inclination angles of the turbulators  34  are θa to θd (first angles θ 1 ) are the above-described upstream side passages, and the cooling passage  60   e  (that is, the most downstream passage  66 ) in which the inclination angle of the turbulators  34  is θe (second angle θ 2 ) smaller than the first angles θ 1  is the above-described downstream side passage. 
     Moreover, for example, in the rotor blade  26  shown in  FIG.  9   , the inclination angles of the turbulators  34  in the cooling passages  60   a  to  60   e  satisfy θb=θc&gt;θd&gt;θe. Thus, the cooling passage  60   b  in which the inclination angle of the turbulators  34  is θb (first angle θ 1 ) is the above-described upstream side passage, and the cooling passages  60   d  and  60   e  in which the inclination angles of the turbulators  34  are θd and θe (second angles θ 2 ) smaller than the first angle θ 1  are the above-described downstream side passages. Likewise, provided that the cooling passage  60   c  is the upstream side passage with the inclination angle being the first angle θ 1  (θc), the cooling passages  60   d  and  60   e  are the downstream side passages with the inclination angles being the second angles θ 2  (&lt;θ 1 ). Moreover, likewise, provided that the cooling passage  60   d  is the upstream side passage in which the inclination angle is the first angle θ 1  (θd), the cooling passage  60   e  is the downstream side passages in which the inclination angles are the second angles θ 2  (&lt;θ 1 ). 
     Thus, the “upstream side passage” and the “downstream side passage” are to indicate the relative positional relationship between the two cooling passages  60  of the plurality of cooling passages  60 . 
       FIG.  13    is a graph showing an example of a correlation between a heat-transfer coefficient ratio α and the inclination angle θ of the turbulators. Note that the heat-transfer coefficient ratio α is a ratio h/h0 of a heat-transfer coefficient h between the turbine blade and the cooling fluid in the cooling passage including the turbulators on the inner wall surface thereof to a heat-transfer coefficient h0 between the turbine blade and cooling fluid in the cooling passage without any turbulators therein and the inner wall surface thereof is formed by the smooth surface. 
     As shown in  FIG.  13   , in a range where the inclination angle θ of the turbulators  34  in the cooling passage  60  is less than 90 degrees, the heat-transfer coefficient ratio α between the cooling fluid and the turbine blade  40  tends to high as the inclination angle θ is small. The heat-transfer coefficient h0 when the inner wall surface of the cooling passage is formed by the smooth surface does not depend on the inclination angle of the turbulators  34  but is a constant. Therefore, the high heat-transfer coefficient ratio α (=h/h0) means that the heat-transfer coefficient h between the cooling fluid and the turbine blade  40  is high. That is, in the range where the inclination angle θ of the turbulators  34  in the cooling passage  60  is less than 90 degrees, the heat-transfer coefficient h between the cooling fluid and the turbine blade  40  tends to high as the inclination angle θ is small. On the other hand, as the inclination angle θ of the turbulators  34  increases, the pressure loss of the cooling fluid flowing through the passage decreases. Therefore, it is important to select the inclination angle θ of the turbulators  34  while balancing between the increase in the heat-transfer coefficient and the increase in the pressure loss obtained by decreasing the inclination angle θ. As shown in  FIG.  13   , in the inclination angle θ, an optimum angle at which the heat-transfer coefficient ratio α is the highest exists. The above-described inclination angle θ is referred to as an optimum angle (optimum value), for the sake of convenience. One example of the optimum angle is 60 degrees. Moreover, an inclination angle which is larger than the optimum angle and smaller than 90 degrees, and at which the heat-transfer coefficient is lower than the heat-transfer coefficient ratio α at the optimum angle is referred to as an intermediate angle (intermediate value). 
     In this regard, in the above-described embodiments, the inclination angles (second angles θ 2 ) of the second turbulators in the downstream side passage are smaller than the inclination angles (first angles θ 1 ) of the first turbulators in the upstream side passage of the serpentine flow passage  61 . In this case, the optimum angle (optimum value) is selected for the inclination angles (second angles θ 2 ) of the second turbulators, and the intermediate angle (intermediate value) is selected for the inclination angles (first angles θ 1 ) of the first turbulators. Thus, the above-described heat-transfer coefficient h (or the heat-transfer coefficient ratio α) is relatively low in the upstream side passage, and cooling of the turbine blade  40  is suppressed, making it possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low. On the other hand, the above-described heat-transfer coefficient h (or the heat-transfer coefficient ratio α) is relatively high in the downstream side passage, and cooling of the turbine blade  40  is promoted, making it possible to enhance cooling of the turbine blade  40  in a downstream side region of the serpentine flow passage  61 . Thus, it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage  61  to cool the turbine blade  40 , making it possible to improve thermal efficiency of the turbine  6 . 
     In some embodiments, the average of the second angles θ 2  of the plurality of second turbulators (turbulators  34 ) is smaller than the average of the first angles θ 1  of the plurality of first turbulators (turbulators  34 ). 
     In this case as well, with the same reason described above, it is possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low, and to enhance cooling of the turbine blade  40  in the downstream side region of the serpentine flow passage  61 . Thus, it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage  61  to cool the turbine blade  40 , making it possible to improve thermal efficiency of the turbine  6 . 
     In some embodiments, for example, as shown in  FIGS.  7 ,  8 ,  10 , and  11   , the turbine blade  40  includes the first turbulators (turbulators  34 ) disposed on the upstream side passage and having the first angle θ 1  of 90 degrees. 
     That is, the cooling passage  60   a  in  FIG.  7   , one of the cooling passages  60   a  to  60   d  in  FIG.  8   , the cooling passage  60   b  or  60   c  in  FIG.  10   , or one of  60   a  to  60   d  in  FIG.  11    may be the upstream side passage which includes the first turbulators (turbulators  34 ) having the first angle θ 1  of 90 degrees, and at least the one cooling passage  60  positioned on the downstream side of the respective upstream side passages may be the downstream side passage. 
     As described above, in the range where the inclination angle θ of the turbulators  34  in the cooling passages  60  is 90 degrees or less than 90 degrees, the heat-transfer coefficient h (or the heat-transfer coefficient ratio α) between the cooling fluid and the turbine blade  40  tends to high as the inclination angle θ is small. In this regard, in the above-described embodiments, the inclination angles (first angles θ 1 ) of the first turbulators in the upstream side passage is 90 degrees, and the inclination angles (second angles θ 2 ) of the second turbulators in the downstream side passage is less than 90 degrees. Therefore, it is possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low, and to enhance cooling of the turbine blade  40  in the downstream side region of the serpentine flow passage  61 . Thus, it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage  61  to cool the turbine blade  40 , making it possible to improve thermal efficiency of the gas turbine  1 . 
     Herein, in the cooling passage  60 , a ratio P/e of the pitch P of the adjacent pair of turbulators  34  (see  FIGS.  4  and  5   ) to the height e of the turbulators  34  (or the average height e of the pair of turbulators  34 ) with reference to the inner wall surface  63  of the cooling passage  60  is defined as the shape factor. 
     In some embodiments, a second shape factor P 2 /e 2  of the plurality of second turbulators (turbulators  34 ) disposed in the downstream side passage is smaller than a first shape factor P 1 /e 1  of the plurality of first turbulators (turbulators  34 ) disposed in the upstream side passage. 
     Note that the first shape factor P 1 /e 1  is the ratio P 1 /e 1  of a pitch P 1  of the adjacent pair of plurality of first turbulators (turbulators  34 ) to a height e 1  of the first turbulators (or the average height e 1  of the pair of first turbulators). Furthermore, the second shape factor P 2 /e 2  is the ratio P 2 /e 2  of a pitch P 2  of the adjacent pair of plurality of second turbulators (turbulators  34 ) to a height e 2  of the second turbulators (or the average height e 2  of the pair of second turbulators). 
     The turbine blade  40  (the rotor blade  26  or the stator vane  24 ) shown in each of  FIGS.  6  to  12    is the turbine blade according to the present embodiment. 
     For example, in the rotor blade  26  or the stator vane  24  shown in  FIGS.  6  to  8    and  FIG.  11   , a shape factor Pe/ee in the cooling passage  60   e  is smaller than shape factors (Pa/ea to Pd/ed) in the cooling passages  60   a  to  60   d  positioned on the upstream side of the cooling passage  60   e.    
     Alternatively, in the rotor blade  26  shown in  FIGS.  9  and  10   , the shape factor Pe/ee in the cooling passage  60   e  is smaller than the shape factors (Pb/eb to Pd/ed) in the cooling passages  60   b  to  60   d  positioned on the upstream side of the cooling passage  60   e.    
     That is, the cooling passage  60   e  is the downstream side passage in which the shape factor of the turbulators  34  is the small second shape factor P 2 /e 2  (Pe/ee), and the cooling passages  60   a  to  60   d  or the cooling passages  60   b  to  60   d  positioned on the upstream side of the downstream side passage (cooling passage  60   e ) and in which the shape factor of the turbulators  34  is the first shape factor P 1 /e 1  (Pa/ea to Pd/ed or Pb/eb to Pd/ed) larger than the second shape factor P 1 /e 2  are the upstream side passages. 
       FIG.  14    is a graph showing an example of a correlation between the heat-transfer coefficient ratio α and the shape factor P/e of the turbulators. Note that the heat-transfer coefficient ratio α is the ratio h/h0 of the heat-transfer coefficient h to the heat-transfer coefficient h0 described above. 
     As shown in  FIG.  14   , the heat-transfer coefficient ratio α between the cooling fluid and the turbine blade  40  is high, and the heat-transfer coefficient h between the cooling fluid and the turbine blade  40  tends to high, as the shape factor P/e of the turbulators  34  in the cooling passage  60  is small. On the other hand, the pressure loss of the cooling fluid flowing through the passage tends to increase as the shape factor P/e of the turbulators  34  is decreased. For example, if the pitch P is decreased without changing the height e of the turbulators, the shape factor P/e is decreased, but the pressure loss of the cooling fluid increases. Therefore, it is important to select the shape factor P/e of the turbulators  34  while balancing between the increase in the heat-transfer coefficient and the increase in the pressure loss obtained by decreasing the shape factor P/e. However, as shown in  FIG.  14   , the increase in the heat-transfer coefficient ratio α is limited, even if the shape factor P/e is decreased. An optimum shape factor having the highest heat-transfer coefficient ratio α is referred to as an optimum factor (optimum value), for the sake of convenience. Moreover, the shape factor P/e which is larger than the optimum factor and where the heat-transfer coefficient ratio α is lower than that of the shape factor P/e of the optimum factor is referred to as an intermediate factor (intermediate value). 
     In this regard, in the above-described embodiments, the first shape factor P 1 /e 1  in the upstream side passage is larger than the second shape factor P 2 /e 2  in the downstream passage. In this case, the optimum factor is selected for the shape factor (second shape factor) of the second turbulators, and the intermediate factor is selected for the shape factor (first shape factor) of the first turbulators. Thus, the above-described heat-transfer coefficient h (or the heat-transfer coefficient ratio α) is relatively low in the upstream side passage, and cooling of the turbine blade  40  is suppressed, making it possible to maintain the temperature of the cooling fluid from the upstream side passage toward the downstream side passage relatively low. On the other hand, the above-described heat-transfer coefficient h (or the heat-transfer coefficient ratio α) is relatively high in the downstream side passage, and cooling of the turbine blade  40  is promoted, making it possible to enhance cooling of the turbine blade  40  in a downstream side region of the serpentine flow passage  61 . Thus, it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage  61  to cool the turbine blade  40 , making it possible to improve thermal efficiency of the gas turbine  1 . 
     As described above, the shape factor P/e of the turbulators  34  is represented by the ratio P/e of the pitch P of the adjacent pair of turbulators  34  to the height e of the turbulators  34 . Moreover, as shown in  FIG.  14   , the heat-transfer coefficient h (heat-transfer coefficient ratio α) changes if the shape factor P/e is changed. For example, the shape factor P/e is changed by changing the height e or the pitch P of the turbulators  34 , making it possible to select the targeted heat-transfer coefficient h. The height e of the turbulators is related to the shape factor P/e, and is also related to a width D of the passage in the concave-convex direction (see  FIG.  4   ). That is, the pressure loss of the cooling fluid flowing through the passage increases, if the height e of the turbulators  34  is extremely high relative to the width D in the concave-convex direction. In particular, the final passage (most downstream passage  66 ) has the small width D in the concave-convex direction, it is desirable that the height e of the turbulators  34  is less (lower) than the height e of the turbulators  34  in the upstream side passage. Selecting the appropriate height e of the turbulators  34 , it is possible to reduce the pressure loss of the cooling fluid while maintaining the heat-transfer coefficient h. 
     In some embodiments, the downstream side passage includes the most downstream passage  66  positioned on the most downstream side of the flow of the cooling fluid of the plurality of cooling passages  60 , and the upstream side passage includes the cooling passage  60  arranged adjacent to the most downstream passage  66 . 
     For example, in the exemplary embodiments shown in  FIGS.  6  to  10   , the cooling passage  60   e  (most downstream passage  66 ) positioned on the most downstream side of the plurality of cooling passages  60  is the downstream side passage, and the upstream side passage includes the cooling passage  60   d  arranged adjacent to the cooling passage  60   e  (most downstream passage  66 ). 
     The cooling fluid which flows through the plurality of cooling passages  60  forming the serpentine flow passage  61  is heated up by a heat exchange with the turbine blade  40  to be cooled. The temperature of the cooling fluid increases downward and is the highest in the most downstream passage  66  positioned on the most downstream side of the flow direction of the cooling fluid. 
     In this regard, in the above-described embodiments, in the downstream side passage including the most downstream passage  66 , the inclination angle of the turbulators  34  is smaller than in the upstream side passage, or the shape factor P/e of the turbulators  34  is smaller than in the upstream side passage. Thus, the above-described heat-transfer coefficient h (or the heat-transfer coefficient ratio α) is relatively low in the upstream side passage, and cooling of the turbine blade  40  is suppressed, making it possible to maintain the temperature of the cooling fluid from the upstream side passage toward the most downstream passage relatively low. On the other hand, the above-described heat-transfer coefficient h (or the heat-transfer coefficient ratio α) is relatively high in the most downstream passage, and cooling of the turbine blade  40  is promoted, making it possible to enhance cooling of the turbine blade  40  in the most downstream passage. Thus, it is possible to effectively reduce the amount of the cooling fluid supplied to the serpentine flow passage  61  to cool the turbine blade  40 , and to improve thermal efficiency of the gas turbine  1 . 
     For example, as shown in  FIGS.  2 A to  3 B  and  FIGS.  6  to  12   , the plurality of cooling passages  60  may include at least the three cooling passages  60 . 
     Alternatively, for example, as shown in  FIGS.  3 A and  3 B , and  FIGS.  6  to  12   , the plurality of cooling passages  60  may include at least the five cooling passages  60 . 
     In this case, it is possible to make the inclination angles (second angles θ 2 ) of the second turbulators in the downstream side passage of at least the three or five cooling passages  60  smaller than the inclination angles (first angles θ 1 ) of the first turbulators in the upstream side passage of at least the three or five cooling passages  60  forming the serpentine flow passage  61 . Alternatively, it is possible to make the shape factor P 2 /e 2  of the second turbulators in the downstream side passage of at least the three or five cooling passages  60  smaller than the shape factor P 1 /e 1  of the first turbulators in the upstream side passage. 
     Thus, it is possible to reduce the amount of the cooling fluid supplied to the serpentine flow passage  61  to cool the turbine blade  40 , making it possible to improve thermal efficiency of the gas turbine  1 . 
     Moreover, provided that at least the three or five cooling passages  60  form the serpentine flow passage  61 , increasing the number of cooling passages  60 , the cross-sectional areas of the respective cooling passages  60  are decreased. Thus, it is possible to increase the flow velocity of the cooling fluid, and to promote cooling of the turbine blade  40 . 
     Moreover, provided that at least the three or five cooling passages  60  form the serpentine flow passage  61 , increasing the number of cooling passages  60 , the number of ribs  32  disposed between the adjacent cooling passages  60  is also increased. Thus, the surface area of the turbine blade  40  contacting the cooling fluid increases. Thus, it is possible to effectively decrease the average temperature in the cross-section of the turbine blade  40 , and to reduce the amount of the cooling fluid since the tolerance of an average creep strength in the cross-section increases. 
     In some embodiments, for example, as shown in  FIGS.  9  and  10   , the inner wall surface of the most upstream passage  65  positioned on the most upstream side of the flow direction of the cooling fluid of the plurality of cooling passages  60  is formed by a smooth surface  67  which is not provided with any turbulators. 
     In a case in which the inner wall surface of the cooling passage  60  is formed by the smooth surface  67  which is not provided with any turbulators, the heat-transfer coefficient h=h0 (or the heat-transfer coefficient ratio α=1) between the cooling fluid and the turbine blade  40  is low, as compared with a case in which the turbulators are provided on the inner wall surface of the cooling passage  60 . 
     In this regard, in the above-described embodiments, since the inner wall surface of the most upstream passage  65  is formed by the smooth surface  67  which is not provided with any turbulators, the above-described heat-transfer coefficient h=h0 (or the heat-transfer coefficient ratio α=1) in the most upstream passage  65  is lower than the above-described heat-transfer coefficient h (or the heat-transfer coefficient ratio α) in the upstream side passage. That is, the above-described heat-transfer coefficient h (or the heat-transfer coefficient ratio α) in the most upstream passage  65 , the upstream side passage, and the downstream side passage forming the serpentine flow passage  61  increases in this order. Thus, the heat-transfer coefficient h (or the heat-transfer coefficient ratio α) is easily changed in stages in the serpentine flow passage  61 , facilitating adjustment of the cooling performance in each of the cooling passages  60 . 
     In some embodiments, the downstream side passage includes the most downstream passage  66  positioned on the most downstream side of the flow direction of the cooling fluid of the plurality of cooling passages  60 , and the most downstream passage  66  is formed such that the flow passage cross-sectional area thereof decreases toward the downstream side of the flow direction of the cooling fluid. 
     For example, in the exemplary embodiments shown in  FIGS.  2 A and  3 A , the most downstream passage  66  is a downstream side passage having the smaller inclination angle θ or shape factor P/e of the turbulators  34  than the cooling passage  60  positioned on the upstream side of the most downstream passage  66 . Then, the most downstream passage  66  is formed such that the flow passage cross-sectional area thereof decreases from upstream (the side of the base  50  (end part  1 ) of the airfoil body  42 ) toward downstream (the side of the tip  48  (end part  2 ) of the airfoil body  42 ) of the flow direction of the cooling fluid in the most downstream passage  66 . Moreover, the cooling passage  60   d  which is an upstream side passage adjacent to the most downstream passage  66  and communicating with the most downstream passage  66  is formed such that the flow passage cross-sectional area thereof decreases from upstream (the side of the tip  48  of the airfoil body  42 ) toward downstream (the side of the base  50  of the airfoil body  42 ) of the flow direction of the cooling fluid. 
     In this case, since the most downstream passage  66  is formed such that the flow passage cross-sectional area thereof decreases toward the downstream side of the flow direction of the cooling fluid, the flow velocity of the cooling fluid increases toward downstream in the most downstream passage  66 . Moreover, as with the most downstream passage  66 , since the cooling passage  60   d  is formed such that the flow passage cross-sectional area thereof decreases toward the downstream side of the flow direction of the cooling fluid, the flow velocity of the cooling fluid increases toward downstream in the cooling passage  60   d . Thus, it is possible to suppress an increase in the metal temperature of the blade inner wall on the side of the base  50  which is on the downstream side of the cooling passage  66   d . Furthermore, since the most downstream passage  66  is formed such that the flow passage cross-sectional area thereof decreases toward the side of the tip  48  which is on the downstream side of the flow direction of the cooling fluid, the flow velocity of the cooling fluid increases, making it possible to efficiently cool the blade inner wall. As a result, the increase in the metal temperature of the blade inner wall of the most downstream passage  66  is suppressed, making it possible to improve cooling efficiency in the most downstream passage  66  where the temperature of the cooling fluid is relatively high. The above description is applied to the case of the blade configuration of  FIG.  3 A . However, the same description is also applicable to changes in the flow passage cross-sectional areas of the most downstream passage  66  and the cooling passage  60   b  in the blade configuration shown in  FIG.  2 A . Moreover, even in the case of the stator vane  26  shown in the schematic view of  FIG.  11   , the most downstream passage  66  may be formed such that the flow passage cross-sectional area thereof decreases from the outer end  52  (end part  1 ) thereof toward the inner end  54  (end part  2 ) thereof on the downstream side of the flow direction of the cooling fluid. As a result, the flow velocity of the cooling fluid increases, making it possible to suppress the increase in the metal temperature of the blade inner wall of the most downstream passage  66 . 
     In some embodiments, the downstream side passage includes the most downstream passage  66  positioned on the most downstream side of the flow direction of the cooling fluid of the plurality of cooling passages  60 , and the turbine blade  40  further includes a cooling fluid supply path  92  disposed so as to communicate with the upstream part of the most downstream passage  66  and configured to supply the cooling fluid from outside to the most downstream passage  66  (downstream side passage) without via the upstream side passage. 
     For example, in the exemplary embodiments shown in  FIGS.  2 A and  3 A , the cooling fluid supply path  92  is disposed inside the blade root portion  82  so as to communicate with the upstream part (the side of the base  50  of the airfoil body  42 ) of the most downstream passage  66  which is the downstream side passage. Then, the cooling fluid from outside can be supplied to the most downstream passage  66  via the cooling fluid supply path  92  without via the upstream side passage (at least one of the cooling passages  60   a  to  60   d ) positioned on the upstream side of the most downstream passage  66 . 
     In this case, in addition to the inflow of the cooling fluid from the upstream side passage of the serpentine flow passage  61  to the most downstream passage  66 , the cooling fluid from outside is supplied to the most downstream passage  66  via the cooling fluid supply path  92 , increasing the flow velocity of the cooling fluid flowing through the most downstream passage. Thus, it is possible to further enhance cooling in the most downstream passage  66  where the temperature of the cooling fluid from the upstream side passage of the serpentine flow passage  61  is relatively high. 
     The stator vane  24  (turbine blade  40 ) shown in  FIG.  11    has the configuration (such as a magnitude relationship of the inclination angles θ or the shape factors P/e in the respective cooling passages  60 ) of the turbulators  34 , which corresponds to that of the rotor blade  26  (turbine blade  40 ) shown in  FIG.  8   . However, the stator vane  24  (turbine blade  40 ) according to some embodiments may have the configuration corresponding to that of one of the rotor blades  26  (turbine blades  40 ) shown in  FIGS.  6 ,  7 ,  9 ,  10 , and  12   . 
     In some embodiments, in the upstream side passage including the first turbulators, the first shape factors of some of the first turbulators are smaller than an average of the first shape factors of other of the first turbulators in the same passage. 
     As shown in  FIG.  12   , for the first shape factors of the first turbulators provided in the cooling passage  60   d  on the most downstream side of the upstream side passages, a factor which is smaller than an average value of the first shape factors of the other first turbulators in the same passage or the first shape factors of a plurality of other first turbulators is selected. For example, a hot spot occurs in a part in the same passage as the cooling passage  60   d  most downstream, and the metal temperature of the blade inner wall may locally be higher than that of another blade inner wall. In this case, for example, the pitch P is decreased without changing the height e of a turbulator  34   a  on the corresponding inner wall, decreasing the first shape factors P/e of the turbulators  34 . That is, the first shape factors of the first turbulators on the inner wall of the passage where the hot spot occurs is made smaller than those in another part to increase the heat-transfer coefficient h, making it possible to partially enhance cooling. The example shown in  FIG.  12    shows the example of the cooling passage  66   d . However, the present invention is not limited to the present embodiment, and the example shown in  FIG.  12    is also applicable to the other upstream side passage. 
     Embodiments of the present invention were described above, but the present invention is not limited thereto, and also includes an embodiment obtained by modifying the above-described embodiment and an embodiment obtained by combining these embodiments as appropriate. 
     Further, in the present specification, an expression of relative or absolute arrangement such as “in a direction”, “along a direction”, “parallel”, “orthogonal”, “centered”, “concentric” and “coaxial” shall not be construed as indicating only the arrangement in a strict literal sense, but also includes a state where the arrangement is relatively displaced by a tolerance, or by an angle or a distance whereby it is possible to achieve the same function. 
     For instance, an expression of an equal state such as “same” “equal” and “uniform” shall not be construed as indicating only the state in which the feature is strictly equal, but also includes a state in which there is a tolerance or a difference that can still achieve the same function. 
     Further, an expression of a shape such as a rectangular shape or a cylindrical shape shall not be construed as only the geometrically strict shape, but also includes a shape with unevenness or chamfered corners within the range in which the same effect can be achieved. 
     As used herein, the expressions “comprising”, “containing” or “having” one constitutional element is not an exclusive expression that excludes the presence of other constitutional elements. 
     REFERENCE SIGNS LIST 
     
         
           1  Gas turbine 
           2  Compressor 
           4  Combustor 
           6  Turbine 
           8  Rotor 
           10  Compressor casing 
           12  Air inlet 
           16  Stator vane 
           18  Rotor blade 
           20  Casing 
           22  Turbine casing 
           24  Stator vane 
           26  Rotor blade 
           28  Combustion gas flow passage 
           30  Exhaust chamber 
           32  Rib 
           34  Turbulator 
           35  Interior flow passage 
           36  Leading-edge side flow passage 
           40  Turbine blade 
           42  Airfoil body 
           44  Leading edge 
           46  Trailing edge 
           47  Trailing edge part 
           48  Tip 
           49  Top board 
           50  Base 
           52  Outer end 
           54  Inner end 
           60 ,  60   a  to  60   e  Cooling passage 
           61  serpentine flow passage 
           62  Inlet opening 
           63  Inner wall surface 
           64  Outlet opening 
           65  Most upstream passage 
           66  Most downstream passage (final passage) 
           67  Smooth surface 
           70  Cooling hole 
           80  Platform 
           82  Blade root portion 
           84  Interior flow passage 
           86  Inner shroud 
           88  Outer shroud 
           92  Cooling fluid supply path 
         P Pitch 
         e Height 
         θ Inclination angle