Patent Publication Number: US-2022220856-A1

Title: Turbine rotor blade and gas turbine

Description:
TECHNICAL FIELD 
     The present disclosure relates to a turbine rotor blade and a cooling structure of a gas turbine. 
     BACKGROUND 
     Since a turbine rotor blade of a gas turbine is exposed to hot gas, the blade surface is film-cooled by injecting cooling air from a plurality of cooling holes formed in the leading edge portion. The cooling hole has an effect of cooling the leading edge portion through the inner surface of the cooling hole (heat sink effect) in addition to the film cooling effect. 
     For example, Patent Document 1 discloses a turbine rotor blade including a leading edge portion having three cooling hole rows linearly arranged along the blade height direction. 
     CITATION LIST 
     Patent Literature 
     Patent Document 1: JP5536001B 
     SUMMARY 
     Problems to be Solved 
     In a typical turbine rotor blade, the curvature radius of the blade surface at the leading edge decreases toward the blade tip (tip side). In this case, if the leading edge portion has a plurality of cooling holes arranged along the blade height direction as in the turbine rotor blade of Patent Document 1, the distance between adjacent cooling holes tends to decrease toward the blade tip. In such a case, at the leading edge portion, the blade tip side is more likely to be cooled than the blade root side (hub side). Accordingly, when a sufficient amount of cooling air is supplied to the cooling holes on the blade root side, an excessive amount of cooling air is supplied to the cooling holes on the blade tip side. 
     In view of the above, an object of at least one embodiment of the present invention is to provide a turbine rotor blade and a gas turbine whereby it is possible to cool the leading edge portion with a small amount of cooling air. 
     Solution to the Problems 
     (1) A turbine rotor blade according to at least one embodiment of the present invention comprises: a leading edge portion having a plurality of cooling holes. The plurality of cooling holes includes: m cooling holes arranged in a first range in a blade height direction, where m is an integer of 2 or more; and n cooling holes arranged in a second range on a blade tip side of the first range in the blade height direction, where n is an integer of 2 or more, and n/b&lt;m/a is satisfied, where a is a dimension of the first range in the blade height direction, and b is a dimension of the second range in the blade height direction. 
     With the turbine rotor blade described in the above (1), since n/b&lt;m/a is satisfied, it is possible to prevent that an excessive amount of cooling air is supplied to the cooling holes in the second range. Thus, the amount of cooling air supplied to the cooling holes in the first range and the amount of cooling air supplied to the cooling holes in the second range can be optimized, and the leading edge portion can be effectively cooled with a small amount of cooling air. 
     (2) In some embodiments, in the above configuration (1), a curvature radius of a blade surface of the leading edge portion in a cross-section perpendicular to the blade height direction decreases toward a blade tip. 
     When the curvature radius of the blade surface of the leading edge portion in a cross-section perpendicular to the blade height direction decreases toward the blade tip, the distance between adjacent cooling holes at the leading edge portion decreases toward the blade tip. Therefore, if n/b is equal to m/a, the blade tip side is more likely to be cooled than the blade root side. 
     In this regard, with the turbine rotor blade described in the above (2), since n/b&lt;m/a is satisfied, it is possible to prevent that an excessive amount of cooling air is supplied to the cooling holes in the second range. Thus, the amount of cooling air supplied to the cooling holes in the first range and the amount of cooling air supplied to the cooling holes in the second range can be optimized, and the leading edge portion can be effectively cooled with a small amount of cooling air. 
     (3) In some embodiments, in the above configuration (1), the second range is located between a position at one-half of a blade height and the blade tip. 
     With the turbine rotor blade described in the above (3), the amount of cooling air supplied to the cooling holes in a range in the vicinity of the blade tip, where the supply amount of cooling air tends to be excessive, can be reduced, and the leading edge portion can be effectively cooled with a small amount of cooling air. 
     (4) In some embodiments, in the above configuration (3), the second range includes a range from a position at two-thirds of the blade height to the blade tip. 
     With the turbine rotor blade described in the above (4), the amount of cooling air supplied to the cooling holes in the range in the vicinity of the blade tip, where the supply amount of cooling air tends to be excessive, can be reduced, and the leading edge portion can be effectively cooled with a small amount of cooling air. 
     (5) In some embodiments, in the turbine rotor blade described in any one of the above (1) to (4), the plurality of cooling holes includes: a plurality of cooling hole rows each of which is arranged along the blade height direction in the first range; and at least one cooling hole row which or each of which is arranged along the blade height direction in the second range. The number of cooling hole rows in the second range is less than the number of cooling hole rows in the first range. 
     When the curvature radius of the blade surface of the leading edge portion in a cross-section perpendicular to the blade height direction decreases toward the blade tip, the distance between adjacent cooling hole rows at the leading edge portion decreases toward the blade tip. Therefore, if the number of cooling hole rows in the first range is equal to the number of cooling hole rows in the second range, the blade tip side is more likely to be cooled than the blade root side. 
     In this regard, with the turbine rotor blade described in the above (5), since the number of cooling hole rows in the second range is less than the number of cooling hole rows in the first range, it is possible to prevent that an excessive amount of cooling air is supplied to the cooling hole row(s) in the second range. Thus, the amount of cooling air supplied to the cooling holes in the first range and the amount of cooling air supplied to the cooling holes in the second range can be optimized, and the leading edge portion can be effectively cooled with a small amount of cooling air. 
     (6) In some embodiments, in the above configuration (5), the number of cooling hole rows in the first range is 3, and the number of cooling hole rows in the second range is 2. 
     With the turbine rotor blade described in the above (6), compared with the case where the number of cooling hole rows in the first range and the number of cooling hole rows in the second range are both 3, it is possible to prevent that an excessive amount of cooling air is supplied to the cooling hole rows in the second range. Thus, the leading edge portion can be effectively cooled with a small amount of cooling air. 
     (7) In some embodiments, in the above configuration (6), the plurality of cooling hole rows in the first range includes a pressure-side cooling hole row formed on a pressure surface, a suction-side cooling hole row formed on a suction surface, and a middle cooling hole row formed between the pressure-side cooling hole row and the suction-side cooling hole row. The at least one cooling hole row in the second range includes a pressure-side cooling hole row formed on the pressure surface, and a suction-side cooling hole row formed on the suction surface. 
     With the turbine rotor blade described in the above (7), the leading edge portion exposed to hot gas can be effectively cooled from the pressure surface to the suction surface with a small amount of cooling air. 
     (8) In some embodiments, in the above configuration (7), the pressure-side cooling hole row in the first range is arranged along a first virtual line which is linear, the suction-side cooling hole row in the first range is arranged along a second virtual line which is linear, the middle cooling hole row is arranged along a third virtual line which is linear, and when X is defined as a distance between the first virtual line and the second virtual line at a same position in the blade height direction on the blade surface, Y is defined as a distance between the second virtual line and the third virtual line at a same position in the blade height direction on the blade surface, Ymax is defined as a maximum value of the distance Y in the first range, and h 1  is defined as a position in the blade height direction such that the distance X is less than the distance Ymax, the second range is located between the position h 1  and the blade tip. 
     With the turbine rotor blade described in the above (8), even when the number of cooling hole rows in the second range is less than the number of cooling hole rows in the first range, since the second range is located between the position h 1  and the blade tip, the distance between cooling hole rows in the second range can be made less than the distance Ymax. Thus, it is possible to prevent the supply amount of cooling air to the cooling hole rows in the second range from being insufficient. Thus, the amount of cooling air supplied to the cooling holes in the first range and the amount of cooling air supplied to the cooling holes in the second range can be optimized, and the leading edge portion can be effectively cooled with a small amount of cooling air. 
     (9) In some embodiments, in the turbine rotor blade described in the above (7) or (8), each of the cooling holes of the pressure-side cooling hole row in the first range extends along a direction parallel to a first straight line intersecting the pressure surface, each of the cooling holes of the suction-side cooling hole row in the first range extends along a direction parallel to a second straight line intersecting the suction surface, each of the cooling holes of the pressure-side cooling hole row in the second range extends along a direction parallel to a third straight line intersecting the pressure surface, each of the cooling holes of the suction-side cooling hole row in the second range extends along a direction parallel to a fourth straight line intersecting the suction surface, and an angle between the third straight line and the fourth straight line is less than an angle between the first straight line and the second straight line. 
     With the turbine rotor blade described in the above (9), the leading edge portion exposed to hot gas can be effectively cooled from the pressure surface to the suction surface with a small amount of cooling air. 
     (10) A gas turbine according to at least one embodiment of the present invention comprises: a compressor for producing compressed air; a combustor for producing combustion gas using the compressed air and fuel; and a turbine configured to be driven by the combustion gas, and the turbine includes the turbine rotor blade described in any one of the above (1) to (9). 
     With the gas turbine described in the above (10), since the turbine rotor blade described in any one of the above (1) to (9) is included, the amount of cooling air supplied to the cooling holes in the first range and the amount of cooling air supplied to the cooling holes in the second range can be optimized, and the leading edge portion can be effectively cooled with a small amount of cooling air. Therefore, damage of the turbine rotor blade can be reduced with a small amount of cooling air, so that the gas turbine can be stably operated. 
     Advantageous Effects 
     At least one embodiment of the present invention provides a turbine rotor blade and a gas turbine whereby it is possible to cool the leading edge portion with a small amount of cooling air. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a schematic configuration diagram of a gas turbine  1  according to an embodiment. 
         FIG. 2  is a schematic configuration diagram of a turbine rotor blade  26  according to an embodiment. 
         FIG. 3  is a partial view of a cross-section of the turbine rotor blade  26  shown in  FIG. 2  in a first range S 1  taken perpendicular to the blade height direction. 
         FIG. 4  is a partial view of a cross-section of the turbine rotor blade  26  shown in  FIG. 2  in a second range S 2  taken perpendicular to the blade height direction. 
         FIG. 5  is a diagram showing a relationship between the blade height directional position h and the distance X, Y, when X is defined as a distance on the blade surface  50  between the first virtual line V 1  and the second virtual line V 2  shown in  FIG. 2 or 3  at the same position in the blade height direction, and Y is defined as a distance on the blade surface  50  between the second virtual line V 2  and the third virtual line V 3  at the same position in the blade height direction. 
         FIG. 6  is a schematic configuration diagram of a turbine rotor blade  26  according to an embodiment. 
         FIG. 7  is a partial view of a cross-section of the turbine rotor blade  26  shown in  FIG. 6  in a second range S 2  taken perpendicular to the blade height direction. 
         FIG. 8  is a diagram showing a relationship between the blade height directional position h and the distance X, Y, Z, when X is defined as a distance on the blade surface  50  between the first virtual line V 1  and the second virtual line V 2  shown in  FIG. 3, 6 , or  7  at the same position in the blade height direction, Y is defined as a distance on the blade surface  50  between the second virtual line V 2  and the third virtual line V 3  at the same position in the blade height direction, and Z is defined as a distance on the blade surface  50  between the fourth virtual line V 4  and the fifth virtual line V 5  at the same position in the blade height direction. 
         FIG. 9  is a diagram showing another example of the arrangement of the cooling holes  48  of the leading edge portion  46 . 
         FIG. 10  is a diagram showing another example of the arrangement of the cooling holes  48  of the leading edge portion  46 . 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments of the present invention will now be described in detail 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 shall be interpreted as illustrative only and not intended to limit the scope of the present invention. 
     For instance, 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, for instance, 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. 
     On the other hand, an expression such as “comprise”, “include”, “have”, “contain” and “constitute” are not intended to be exclusive of other components. 
       FIG. 1  is a schematic configuration diagram of a gas turbine  1  according to an embodiment. 
     As shown in  FIG. 1 , the gas turbine  1  includes a compressor  2  for producing compressed air, a combustor  4  for producing 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 compressor stator vanes  16  fixed to a compressor casing  10  and a plurality of compressor rotor blades  18  implanted on a rotor shaft  8  so as to be arranged alternately with the compressor stator vanes  16 . To the compressor  2 , air sucked in from an air inlet  12  is supplied. The air flows through the plurality of compressor stator vanes  16  and the plurality of compressor rotor blades  18  to be compressed into compressed air having a high temperature and a high pressure. 
     The combustor  4  is supplied with fuel and the compressed air produced in the compressor  2 . The combustor  4  combusts the fuel to produce combustion gas that serves as a working fluid of the turbine  6 . As shown in  FIG. 1 , the gas turbine  1  has a plurality of combustors  4  arranged along the circumferential direction around the rotor shaft  8  inside a casing  20 . 
     The turbine  6  has a combustion gas passage  28  formed by a turbine casing  22  and includes a plurality of turbine stator vanes  24  and a plurality of turbine rotor blades  26  disposed in the combustion gas passage  28 . The turbine stator vanes  24  are fixed to the turbine casing  22 , and a set of the turbine stator vanes  24  arranged along the circumferential direction of the rotor shaft  8  forms a stator vane array. Further, the turbine rotor blades  26  are implanted on the rotor shaft  8 , and a set of the turbine rotor blades  26  arranged along the circumferential direction of the rotor shaft  8  forms a rotor blade array. The stator vane arrays and the rotor blade arrays are arranged alternately in the axial direction of the rotor shaft  8 . 
     In the turbine  6 , as the combustion gas introduced from the combustor  4  into the combustion gas passage  28  passes through the plurality of turbine stator vanes  24  and the plurality of turbine rotor blades  26 , the rotor shaft  8  is rotationally driven. Thereby, the generator connected to the rotor shaft  8  is driven to generate power. The combustion gas having driven the turbine  6  is discharged outside via an exhaust chamber  30 . 
       FIG. 2  is a schematic configuration diagram of the turbine rotor blade  26  according to an embodiment.  FIG. 3  is a partial view of a cross-section of the turbine rotor blade  26  shown in  FIG. 2  in a first range S 1  taken perpendicular to the blade height direction (radial direction of rotor shaft  8 ).  FIG. 4  is a partial view of a cross-section of the turbine rotor blade  26  shown in  FIG. 2  in a second range S 2  taken perpendicular to the blade height direction. 
     As shown in  FIG. 2 , the turbine rotor blade  26  includes a root portion  32  fixed to the rotor shaft  8  (see  FIG. 1 ) and an airfoil portion  36  having an airfoil cross-section. A blade surface  50  of the airfoil portion  36  includes a leading edge  38 , a trailing edge  40 , a pressure surface  42 , and a suction surface  44 . The curvature radius R of the blade surface  50  at a leading edge portion  46  in a cross-section perpendicular to the blade height direction shown in  FIGS. 3 and 4  decreases toward a blade tip  56  (tip of the airfoil portion  36  in the blade height direction) shown in  FIG. 2 . 
     As shown in  FIG. 2 , the leading edge portion  46  of the airfoil portion  36  has a plurality of cooling holes  48 . The plurality of cooling holes  48  of the leading edge portion  46  includes a plurality of cooling hole rows  48 A,  48 B,  48 C each arranged linearly along the blade height direction in the first range S 1  in the blade height direction. 
     The plurality of cooling hole rows  48 A,  48 B,  48 C includes a pressure-side cooling hole row  48 A formed on the pressure surface  42 , a suction-side cooling hole row  48 B formed on the suction surface  44 , and a middle cooling hole row  48 C formed between the pressure-side cooling hole row  48 A and the suction-side cooling hole row  48 B. 
     The pressure-side cooling hole row  48 A is composed of a plurality of cooling holes  48  arranged along a first virtual line V 1  which linearly extends along the blade height direction. The suction-side cooling hole row  48 B is composed of a plurality of cooling holes  48  arranged along a second virtual line V 2  which linearly extends along the blade height direction. The middle cooling hole row  48 C is composed of a plurality of cooling holes  48  arranged along a third virtual line V 3  which linearly extends along the blade height direction. The cooling holes  48  formed in the first range S 1  of the leading edge portion  46  are staggeringly arranged. In the illustrated exemplary embodiment, a fillet portion  58  is formed at the boundary between a hub surface  54  of the turbine rotor blade  26  and the blade surface  50  of the airfoil portion  36 . The fillet portion  58  has no cooling holes  48 . The upper end of the fillet portion  58  corresponds to the lower end of the first range S 1 . 
     The plurality of cooling holes  48  of the leading edge portion  46  includes a plurality of cooling hole rows  48 D,  48 E each arranged linearly along the blade height direction in the second range S 2  on the blade tip  56  side of the first range S 1  in the blade height direction. The first range S 1  and the second range S 2  are adjacent to each other in the blade height direction. In the illustrated exemplary embodiment, the second range S 2  is located between the position at one-half of the blade height H and the blade tip  56 . For example, the second range S 2  is a range from the position at two-thirds of the blade height H to the blade tip  56 . Here, the blade height H means the height of the turbine rotor blade  26  along the radial direction of the rotor shaft  8  from the hub surface  54  to the blade tip  56 . 
     The plurality of cooling hole rows  48 D,  48 E includes a pressure-side cooling hole row  48 D formed on the pressure surface  42 , and a suction-side cooling hole row  48 E formed on the suction surface  44 . The pressure-side cooling hole row  48 D is composed of a plurality of cooling holes  48  arranged along the first virtual line V 1 . The suction-side cooling hole row  48 E is composed of a plurality of cooling holes  48  arranged along the second virtual line V 2 . The cooling holes  48  formed in the second range S 2  of the leading edge portion  46  are staggeringly arranged. 
     In the illustrated exemplary embodiment, the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1  of the leading edge portion  46  is  3 , and the number of cooling hole rows  48 D,  48 E in the second range S 2  of the leading edge portion  46  is  2 . Thus, the number of cooling hole rows  48 D,  48 E in the second range S 2  of the leading edge portion  46  is set to be less than the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1 . Further, n/b&lt;m/a is satisfied, where m is the number of cooling holes  48  arranged in the first range S 1  among the plurality of cooling holes  48  of the leading edge portion  46  (provided that m is an integer of 2 or more), n is the number of cooling holes  48  arranged in the second range S 2  among the plurality of cooling holes  48  of the leading edge portion  46  (provided that n is an integer of 2 or more), a is the dimension of the first range S 1  in the blade height direction, and b is the dimension of the second range S 2  in the blade height direction. That is, a value obtained by dividing d by b is smaller than a value obtained by dividing m by a. 
     As shown in  FIGS. 3 and 4 , a cooling passage  52  extending along the blade height direction is formed inside the airfoil portion  36 , and each cooling hole  48  of the leading edge portion  46  communicates with the cooling passage  52 . The cooling passage  52  is supplied with a part of the compressed air produced by the compressor  2  (see  FIG. 1 ) as cooling air. The cooling air flows from the cooling passage  52  to each cooling hole  58  and is used for film cooling of the blade surface  50 . 
     As shown in  FIG. 3 , each cooling hole  48  of the pressure-side cooling hole row  48 A extends along a direction parallel to a first straight line L 1  intersecting the pressure surface  42 . Each cooling hole  48  of the suction-side cooling hole row  48 B extends along a direction parallel to a second straight line L 2  intersecting the suction surface  44 . 
     Further, as shown in  FIG. 4 , each cooling hole  48  of the pressure-side cooling hole row  48 D extends along a direction parallel to a third straight line L 3  intersecting the pressure surface  42 . Each cooling hole  48  of the suction-side cooling hole row  48 E extends along a direction parallel to a fourth straight line L 4  intersecting the suction surface  44 . Here, the angle θ 2  between the third straight line L 3  and the fourth straight line L 4  is equal to the angle θ 1  between the first straight line L 1  and the second straight line L 2 . 
     As shown in  FIG. 3 , when X is defined as a distance between the first virtual line V 1  and the second virtual line V 2  at the same position in the blade height direction on the blade surface  50 , and Y is defined as a distance between the second virtual line V 2  and the third virtual line V 3  at the same position in the blade height direction on the blade surface  50 , a relationship between the blade height directional position h and the distance X, Y is shown in  FIG. 5 . The blade height directional position h means a distance from the hub surface  54  in the blade height direction. 
     As shown in  FIG. 5 , when Ymax is defined as a maximum value of the distance Y in the first range S 1 , and h 1  is defined as a position in the blade height direction such that the distance X is less than the distance Ymax, the second range S 2  is located between the position h 1  and the blade tip  56 . 
     With the above configuration, even when the curvature radius R of the blade surface  50  of the leading edge portion  46  decreases toward the blade tip  56 , since the number of cooling hole rows  48 D,  48 E in the second range S 2  is set to be less than the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1 , n/b&lt;m/a is satisfied, so that it is possible to prevent that an excessive amount of cooling air is supplied to the cooling hole rows  48 D,  48 E in the second range S 2 . Thus, the amount of cooling air supplied to the cooling holes  48  in the first range S 1  and the amount of cooling air supplied to the cooling holes  48  in the second range S 2  can be optimized, and the leading edge portion  46  can be effectively cooled with a small amount of cooling air. 
     Further, even when the number of cooling hole rows  48 D,  48 E in the second range S 2  is less than the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1 , since the second range S 2  is located between the position h 1  and the blade tip  56 , the distance between the cooling hole row  48 D and the cooling hole row  48 E in the second range S 2  can be made less than the distance Ymax. Thus, it is possible to prevent the supply amount of cooling air to the cooling hole rows  48 D,  48 E in the second range S 2  from being insufficient. Thus, the amount of cooling air supplied to the cooling holes  48  in the first range S 1  and the amount of cooling air supplied to the cooling holes  48  in the second range S 2  can be optimized, and the leading edge portion  46  can be effectively cooled with a small amount of cooling air. 
     Other embodiments will now be described. 
       FIG. 6  is a schematic configuration diagram of the turbine rotor blade  26  according to an embodiment. The embodiment shown in  FIG. 6  differs from the embodiment shown in  FIG. 2  only in the configuration of the pressure-side cooling hole row  48 D and the suction-side cooling hole row  48 E; specifically, the distance between the pressure-side cooling hole row  48 D and the suction-side cooling hole row  48 E in the second range S 2  is set narrower than that of the embodiment shown in  FIG. 2 . Since other configurations are the same as those in the above-described embodiment, the configuration different from the above-described embodiment will be described below. 
     In the embodiment shown in  FIG. 6 , the pressure-side cooling hole row  48 D is composed of a plurality of cooling holes  48  arranged along a fourth virtual line V 4  which linearly extends along the blade height direction. The suction-side cooling hole row  48 B is composed of a plurality of cooling holes  48  arranged along a fifth virtual line V 5  which linearly extends along the blade height direction. Here, in the second range S 2 , the fourth virtual line V 4  is located closer to the leading edge  38  than the first virtual line V 1 , and the fifth virtual line V 5  is located closer to the leading edge  38  than the second virtual line V 2 . 
       FIG. 7  is a partial view of a cross-section of the turbine rotor blade  26  shown in  FIG. 6  in the second range S 2  taken perpendicular to the blade height direction. The configuration of the cross-section of the turbine rotor blade  26  shown in  FIG. 6  in the first range S 1  taken perpendicular to the blade height direction will not be described, since it is the same as the configuration shown in  FIG. 3 . 
     As shown in  FIG. 7 , each cooling hole  48  of the pressure-side cooling hole row  48 D extends along a direction parallel to a third straight line L 3  intersecting the pressure surface  42 . Each cooling hole  48  of the suction-side cooling hole row  48 E extends along a direction parallel to a fourth straight line L 4  intersecting the suction surface  44 . Here, the angle θ 2  between the third straight line L 3  and the fourth straight line L 4  in the second range S 2  is less than the angle θ 1  (see  FIG. 3 ) between the first straight line L 1  and the second straight line L 2  in the first range S 1 . 
     As shown in  FIGS. 3 and 7 , when X is defined as a distance between the first virtual line V 1  and the second virtual line V 2  at the same position in the blade height direction on the blade surface  50 , Y is defined as a distance between the second virtual line V 2  and the third virtual line V 3  at the same position in the blade height direction on the blade surface  50 , and Z is defined as a distance between the fourth virtual line V 4  and the fifth virtual line V 5  at the same position in the blade height direction on the blade surface  50 , a relationship between the blade height directional position h and the distance X, Y, Z is shown in  FIG. 8 . 
     In the configuration shown in  FIG. 8 , when Ymax is defined as a maximum value of the distance Y in the first range S 1 , and h 1  is defined as a position in the blade height direction such that the distance X is less than the distance Ymax, the second range S 2  is located between the position h 1  and the blade tip  56 . 
     As shown in  FIG. 8 , in the second range S 2 , the distance Z between the fourth virtual line V 4  and the fifth virtual line V 5  at the same position in the blade height direction on the blade surface  50  is set to be less than the distance X between the first virtual line V 1  and the second virtual line V 2  at the same position in the blade height direction on the blade surface  50 . 
     With the configuration shown in  FIGS. 6 to 8 , in the same way as described above, even when the curvature radius R of the blade surface  50  of the leading edge portion  46  decreases toward the blade tip  56 , since the number of cooling hole rows  48 D,  48 E in the second range S 2  is set to be less than the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1 , n/b&lt;m/a is satisfied, so that it is possible to prevent that an excessive amount of cooling air is supplied to the cooling hole rows  48 D,  48 E in the second range S 2 . Thus, the amount of cooling air supplied to the cooling holes  48  in the first range S 1  and the amount of cooling air supplied to the cooling holes  48  in the second range S 2  can be optimized, and the leading edge portion  46  can be effectively cooled with a small amount of cooling air. 
     Further, even when the number of cooling hole rows  48 D,  48 E in the second range S 2  is less than the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1 , since the second range S 2  is located between the position h 1  and the blade tip  56 , the distance between the cooling hole row  48 D and the cooling hole row  48 E in the second range S 2  can be made less than the distance Ymax. Thus, it is possible to prevent the supply amount of cooling air to the cooling hole rows  48 D,  48 E in the second range S 2  from being insufficient. Thus, the amount of cooling air supplied to the cooling holes  48  in the first range S 1  and the amount of cooling air supplied to the cooling holes  48  in the second range S 2  can be optimized, and the leading edge portion  46  can be effectively cooled with a small amount of cooling air. 
     In addition, since the angle θ 2  between the third straight line L 3  and the fourth straight line L 4  is less than the angle θ 1  between the first straight line L 1  and the second straight line L 2 , the leading edge portion  46  exposed to hot gas can be effectively cooled from the pressure surface  42  to the suction surface  44  with a small amount of cooling air. 
     The present invention is not limited to the embodiments described above, but includes modifications to the embodiments described above, and embodiments composed of combinations of those embodiments. 
     For example, in the above-described embodiments, the number of cooling hole rows  48 D,  48 E in the second range S 2  is less than the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1 . However, the relationship between the number of cooling hole rows in the second range S 2  and the number of cooling hole rows in the first range is not limited, as long as the plurality of cooling holes  48  of the leading edge portion  46  satisfies n/b&lt;m/a. For example, as shown in  FIG. 9 , the number of cooling hole rows  48 D,  48 E,  48 F in the second range S 2  may be equal to the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1 , or as shown in  FIG. 10 , the number of cooling hole rows  48 D,  48 E,  48 F,  48 G in the second range S 2  may be more than the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1   
     In the embodiment shown in  FIG. 9 , while the number of cooling hole rows  48 D,  48 E,  48 F in the second range S 2  is equal to the number of cooling hole rows  48 A,  48 B,  48 C in the first range S 1 , the distance between the cooling holes  48  of the cooling hole row  48 F in the second range S 2  is more than the distance between the cooling holes  48  of the cooling hole row  48 C in the first range S 1 , so that n/b&lt;m/a is satisfied. 
     Alternatively, in the embodiment shown in  FIG. 10 , while the number of cooling hole rows  48 D,  48 E,  48 F,  48 G in the second range S 2  is more than the number of cooling hole rows  48 A,  48 B,  48 C in the first range S  1 , the distance (distance in blade height direction) between the cooling holes  48  of each cooling hole row  48 D,  48 E,  48 F,  48 G in the second range S 2  is more than the distance (distance in blade height direction) between the cooling holes  48  of each cooling hole row  48 A,  48 B,  48 C in the first range S 1 , so that n/b&lt;m/a is satisfied. 
     Thus, when n/b&lt;m/a is satisfied, the amount of cooling air supplied to the cooling holes in the first range and the amount of cooling air supplied to the cooling holes in the second range can be optimized, and the leading edge portion can be effectively cooled with a small amount of cooling air. 
     REFERENCE SIGNS LIST 
     
         
           1  Gas turbine 
           2  Compressor 
           4  Combustor 
           6  Turbine 
           26  Turbine rotor blade 
           38  Leading edge 
           42  Pressure surface 
           44  Suction surface 
           46  Leading edge portion 
           48  Cooling hole 
           48 A,  48 D Pressure-side cooling hole row 
           48 B,  48 E Suction-side cooling hole row 
           48 C Middle cooling hole row 
           50  Blade surface 
           56  Blade tip