Patent Publication Number: US-9410432-B2

Title: Turbine

Description:
TECHNICAL FIELD 
     The present invention relates to a turbine, for example, that is used in power plants, chemical plants, gas plants, iron mills and marine vessels. Priority is claimed on Japanese Patent Application No. 2012-067893 filed Mar. 23, 2012, the content of which is incorporated by reference herein. 
     BACKGROUND ART 
     As a well-known type of steam turbine, one is known which is provided with a casing, a shaft body (rotor) installed inside the casing so as to be rotatable, a plurality of turbine vanes arranged by being fixed to an inner circumference portion of the casing and a plurality of turbine blades radially installed at the shaft body in the downstream side of the plurality of turbine vanes. Of these steam turbines, an impulse turbine converts pressure energy of steam (fluid) to velocity energy by turbine vanes and also converts the velocity energy to rotational energy (mechanical energy) by turbine blades. Further, in a reaction turbine, pressure energy is converted to velocity energy also inside turbine blades and the velocity energy is converted to rotational energy (mechanical energy) by reaction force derived from ejection of steam. 
     In the above-described types of steam turbines, normally, a clearance is formed in the radial direction between the tip portion of a turbine blade and a casing which surrounds the turbine blade to form a flow channel of steam. A clearance is also formed in the radial direction between the tip portion of a turbine vane and a shaft body. However, leakage steam passing to the downstream side through the clearance between the tip portion of the turbine blade and the casing does not impart torque to the turbine blade. Furthermore, in leakage steam which passes to the downstream side through the clearance between the tip portion of the turbine vane and the shaft body, pressure energy thereof is not converted to velocity energy by the turbine vane. Therefore, torque is hardly imparted to the turbine blade on the downstream side. Therefore, in order to improve the performance of a steam turbine, it is important to reduce the flow rate of the leakage steam (amount of leakage steam) which passes through the clearance. 
     As a related art, for example, Patent Document 1 proposes a structure in which a plurality of stepped parts are provided in the tip portion of the turbine blade in such a manner that the height thereof becomes gradually higher from the upstream side toward the downstream side in an axial direction; a plurality of seal fins extending toward each of the stepped parts are provided in the casing; and a small clearance is formed between each of the stepped parts and tip of each of the seal fins. 
     In the turbine, fluid which has flowed from the upstream side into the clearance collides with a step surface of a stepped part, thereby a main vortex is generated on the upstream side of the step surface and a separation vortex is generated on the downstream side (vicinity on the upstream side of the small clearance) of the step surface. Subsequently, the reduction of the leakage flow passing through the small clearance is achieved by the separation vortex generated in the vicinity on the upstream side of the small clearance. In other words, the reduction in the flow rate (amount of leakage steam) of the leakage fluid passing through a clearance between a tip portion of a turbine blade and a casing is achieved. 
     PRIOR ART DOCUMENT 
     Patent Document 
     
         
         [Patent Document 1] Japanese Unexamined Patent Application, First Publication No. 2011-080452 (see  FIG. 6 ) 
       
    
     SUMMARY OF INVENTION 
     Problem to be Solved by the Invention 
     Meanwhile, in the turbine provided with the plurality of stepped parts and seal fins as described above, the pressure (static pressure) or density of the fluid in the clearance between the tip of the turbine blade and the casing becomes reduced from the upstream side toward the downstream side in the axial direction. Thereby, the flow velocity of the fluid passing through the small clearance on the downstream side is faster than that of the fluid passing through the small clearance on the upstream side. 
     Therefore, the speed (rotational speed) of the main vortex generated in the stepped part positioned on the downstream side is faster than the speed (rotational speed) of the main vortex generated in the stepped part positioned on the upstream side. Particularly, in the main vortex closer to the downstream side, the flow velocity thereof flowing in the radial direction along the step surface is increased. Thereby, the shape of the separation vortex generated in the stepped part closer to the downstream side is more elongated in the radial direction. If the shape of the separation vortex is elongated, in the separation vortex, the maximum position of a velocity component of the flow flowing in the radial direction from the tip of the seal fin toward the stepped part is moved apart (apart from the small clearance in the radial direction) from the tip of the seal fin toward a base end side thereof. Therefore, the contraction flow effect of reducing the leakage flow passing through the small clearance on the downstream side of the separation vortex becomes reduced. Also, the static pressure reduction effect becomes reduced. As a result, the turbine in the related art has a problem in that the reduction of the amount of leakage steam is limited. 
     Means for Solving the Problem 
     An object of the present invention is to provide a turbine capable of further reducing the amount of leakage steam. 
     According to a first aspect of the present invention, a turbine includes a blade member; and a structural member located close to the blade member such that a clearance is provided between a tip portion of the blade member and the structural member, and fluid passes through the clearance. One of the blade member and the structural member is available to rotate relative to the other. One of the tip of the blade member and part of the structural member opposing the tip portion of the blade member is provided with stepped parts which have step surfaces facing the upstream side in a rotating axial direction of the structural member, and which protrude toward the other of the tip of the blade member and the part of the structural member, the stepped parts are aligned in the rotating axial direction. In the other of the tip of the blade member and the part of the structural member is provided with seal fins which extend toward the circumference surface of the stepped parts and form small clearances between the seal fins and the circumference surfaces corresponding to the stepped parts are provided. A first distance between a first one of the seal fins and the step surface corresponding to the first seal fin in the rotating axial direction is longer than a second distance between a second one of the seal fins adjacent to the first seal fin and the step surface corresponding to the second seal fin, wherein the step surface corresponding to the first seal fin is located at the downstream side with respect to the step surface corresponding to the second seal fin. 
     In the turbine described above, fluid which has flowed from the upstream side into the clearance collides with the step surface of each stepped part, thereby a main vortex is generated on the upstream side of the step surface, similar to the related art. Furthermore, at a corner section (edge) between the step surface and circumference surface of each stepped part, some flow is separated from the main vortex. Thereby, a separation vortex rotating in a reverse direction to the main vortex is generated on a circumference surface of each stepped part positioned on the downstream side of the step surface thereof. This separation vortex causes a downflow flowing from a tip of the seal fin toward the circumference surface of the stepped part, whereby the separation vortex exhibits a contraction flow effect against the fluid passing through the small clearance between the tip of the seal fin and the stepped part. 
     Furthermore, the diameter of the separation vortex generated in this way shows a tendency to be proportional to the distance from the step surface of the stepped part to the small clearance on the downstream side thereof. In other words, the shorter the distance is, the smaller the diameter of the separation vortex is. Therefore, according to the turbine described above, even when the speed of flow separated at the corner section between the step surface and the circumference surface of the stepped part on the downstream side is faster than that of flow separated from the main vortex at the corner section between the step surface and the circumference surface of the stepped part on the upstream side, it is possible to reduce the diameter of the separation vortex on the downstream side. 
     The diameter of the separation vortex on the downstream side is reduced as described above, whereby it is possible to, in the separation vortex on the downstream side, set the maximum position of a velocity component of the flow flowing in the radial direction from the tip of the seal fin toward the downstream side of the stepped part upstream side moved close to the tip of the seal fin. Therefore, it is possible to strengthen the downflow due to the separation vortex on the downstream side. As a result, it is possible to reduce the leakage fluid which passes through the small clearance positioned on the downstream side of the separation vortex. In other words, it is possible to improve the contraction flow effect. 
     Moreover, the diameter of the separation vortex on the downstream side is reduced, whereby it is possible to reduce static pressure in the separation vortex. Thereby, it is possible to decrease a pressure difference between the upstream side and the downstream side of the small clearance positioned on the downstream side of the separation vortex. In other words, corresponding to the reduction of the pressure difference, it is possible to improve the static pressure reduction effect which causes the leakage flow passing through the small clearance positioned on the downstream side to be reduced. 
     According to a second aspect of the present invention, in the turbine, it is further preferable that the distance from the seal fins to the stepped parts are set such that one corresponding to the stepped parts positioned as close to the downstream side is shorter than the other. 
     According to the turbine described above, the separation vortex closer to the downstream side is further reduced in diameter. Thereby, in the small clearance closer to the downstream side, it is possible to effectively improve the contraction flow effect and the static pressure reduction effect due to the separation vortex described above. 
     Furthermore, according to the turbine described above, an inclined surface inclined from the upstream side toward the downstream side is formed on at least the step surface corresponding to the first seal fin located at the downstream side with respect to the step surface corresponding to the second seal fin, wherein the inclined surface communicates with the circumference surface. 
     According to the configuration, in the main vortex generated on the upstream side of the step surface in the stepped part on the downstream side, the direction of flow separated at the corner section between the step surface and the circumference surface of the stepped part on the downstream side is inclined, by the inclined surface, to the downstream side in an axial direction with respect to the radial direction. Thereby, it is possible to further reduce the diameter of the separation vortex generated on the circumference surface of the stepped part on the downstream side. Therefore, it is possible to further improve the contraction flow effect and the static pressure reduction effect due to the separation vortex described above. 
     According to a third aspect of the present invention, in the turbine, inclined surfaces are formed on the step surfaces corresponding to the first and second seal fins, and the inclination angles are set such that a first inclination angle of the step surface corresponding to the first seal fin is smaller than a second inclination angle of the step surface corresponding to the second seal fin. 
     According to the configuration, it is possible to reduce the diameter of the separation vortices generated on the circumference surfaces of the step surfaces of the two adjacent stepped parts. Furthermore, since the inclination angle of the inclined surface formed on the stepped part on the downstream side is greater than that of the stepped part on the upstream side, it is possible to strengthen a tendency of reducing the diameter of the separation vortex generated on the circumference surface of the stepped part on the downstream side so as to be smaller than that of the stepped part on the upstream side. Therefore, it is possible to further improve the contraction flow effect and the static pressure reduction effect due to the separation vortex described above. 
     According to the present invention, even in the turbine provided with the plurality of stepped parts and seal fins, it is possible to improve the contraction flow effect and the static pressure reduction effect due to the separation vortex generated in the stepped part positioned on the downstream side. Therefore, the reduction of the amount of leakage steam passing through the clearance between the tip of the blade member (blade) and the structural member can be further improved. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic configuration sectional view which shows a steam turbine according to the present invention. 
         FIG. 2  is a drawing which shows a first embodiment of the present invention and an enlarged sectional view showing a major part I in  FIG. 1 . 
         FIG. 3  is a drawing which describes actions of the steam turbine according to the first embodiment of the present invention. 
         FIG. 4A  is a graph which shows a relationship between an aspect ratio L/H of a distance L to a small clearance H and a flow rate coefficient Cd of steam passing through the small clearance H in the configuration shown in  FIG. 2 . 
         FIG. 4B  is a graph which shows a relationship between an aspect ratio L/H of a distance L to a small clearance H and a flow rate coefficient Cd of steam passing through the small clearance H in the configuration shown in  FIG. 2 . 
         FIG. 4C  is a graph which shows a relationship between an aspect ratio L/H of a distance L to a small clearance H and a flow rate coefficient Cd of steam passing through the small clearance H in the configuration shown in  FIG. 2 . 
         FIG. 5  is a drawing which shows a second embodiment of the present invention and an enlarged sectional view showing the major part I in  FIG. 1 . 
         FIG. 6  is a drawing which describes actions of the steam turbine according to the second embodiment of the present invention. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     First Embodiment 
     Hereinafter, a first embodiment of the present invention will be described referring to  FIGS. 1 to 4C . 
     As shown in  FIG. 1 , a steam turbine  1  according to the embodiment is schematically constituted to include a casing (structural member)  10 , a regulating valve  20  to regulate the amount and pressure of steam (fluid) S flowing into the casing  10 , a shaft body (rotor)  30  which is provided inside the casing  10  so as to rotate freely and transmits power to a machine such as a generator (not shown), turbine vanes  40  held in the casing  10 , turbine blades (blades)  50  provided in the shaft body  30 , and a bearing portion  60  which supports the shaft body  30  so as to be axially rotatable. 
     The casing  10  is formed such that an inner space thereof is sealed hermetically. The casing  10  includes a main body portion  11  which forms a flow channel of the steam S and a ring-shaped diaphragm outer ring  12  which is securely fixed on an inner wall surface of the main body portion  11 . 
     A plurality of the regulating valves  20  are installed inside the main body portion  11  of the casing  10 . Each of the regulating valves  20  includes a regulating valve chamber  21  into which steam S flows from a boiler (not shown), a valve body  22 , a valve seat  23  and a steam chamber  24 . In the regulating valve  20 , the valve body  22  thereof moves apart from the valve seat  23 , whereby a steam flow channel is opened. Subsequently, the steam S flows into the inner space of the casing  10  via the steam chamber  24 . 
     The shaft body  30  includes a shaft main body  31  and a plurality of disks  32  extending outward in the radial direction from an outer circumference of the shaft main body  31 . The shaft body  30  transmits rotational energy to a machine such as a generator (not shown). 
     Furthermore, the bearing portion  60  includes a journal-bearing part  61  and a thrust-bearing part  62 , and supports the shaft body  30  which inserted into the main body portion  11  of the casing  10  so as to be rotatable in the outer side of the main body portion  11 . 
     A large number of the turbine vanes  40  are arranged in a radial pattern so as to surround the shaft body  30 . The plurality of turbine vanes  40  which are thus arranged configure groups of annular turbine vanes. Also, the turbine vanes  40  are individually held in the diaphragm outer ring  12 . In other words, each of the turbine vanes  40  extends inward in the radial direction from the diaphragm outer ring  12 . 
     Hab shrouds  41  are constituted by the tip of the turbine vanes  40  in the extending direction thereof. The hub shrouds  41  are formed in a ring shape so as to connect the plurality of turbine vanes  40  constituting the same group of annular turbine vanes. The shaft body  30  inserts the hub shrouds  41 . Also, the hub shroud  41  is disposed with a clearance kept with respect to the shaft body  30  in the radial direction. 
     In addition, six groups of annular turbine vanes constituted by the plurality of turbine vanes  40  are formed so as to be spaced apart from each other in the rotating axial direction of the casing  10  and the shaft body  30  (hereinafter, referred to as an axial direction). The groups of annular turbine vanes convert pressure energy of steam S to velocity energy, thereby guiding the steam S to the turbine blades  50  side adjacent to each other on the downstream side in the axial direction. 
     The turbine blades  50  are securely installed on an outer circumference portion of the disk  32  constituting the shaft body  30  and extend outward in the radial direction from the shaft body  30 . On the downstream side of each annular turbine vane group, a large number of the turbine blades  50  are arranged in a radial pattern and configure groups of annular turbines. 
     One stage is configured with one set of a group of annular turbine vanes and a group of annular turbine blades. That is, the steam turbine  1  is configured in six stages. A tip shroud  51  extending in the circumferential direction is formed on a tip of the turbine blade  50 . 
     As shown in  FIG. 2 , the tip shroud  51  formed on the tip of the turbine blade  50  is arranged so as to face the diaphragm outer ring  12  or the casing  10 , with a clearance kept in the radial direction therebetween. On the tip shroud  51 , four stepped parts  52  ( 52 A to  52 D) which respectively have step surfaces  53  ( 53 A to  53 D) and protrude toward the diaphragm outer ring  12  are formed along the axial direction of the shaft body  30 . 
     The protrusion heights of the four stepped parts  52 A to  52 D, which mean the height from the turbine  50  to each of outer circumference surfaces (circumference surfaces)  54 A to  54 D ( 54 ) of the four stepped parts  52 A to  52 D, are set so as to become gradually higher from the upstream side toward the downstream side in the shaft direction. Therefore, the step surface  53  of each of the stepped parts  52  is formed to face the upstream side in the axial direction. Furthermore, in the embodiment, the step surface  53  of each of the stepped parts  52  is parallel in the radial direction. Also, the four step surfaces  53 A to  53 D are all equal in height. Still further, in the embodiment, the outer circumference surface  54  of each of the stepped parts  52  is parallel in the axial direction. 
     On the other hand, in the diaphragm outer ring  12 , an annular groove  121  extending in a circumferential direction is formed on the region corresponding to the tip shroud  51 . In the embodiment, the annular groove  121  is formed on an inner circumference surface of the diaphragm outer ring  12  so as to be recessed outward in the radial direction. The tip shroud  51  is disposed so as to be housed in the annular groove  121 . 
     Also, in a bottom portion of the annular groove  121  facing inward in the radial direction, five annular recessed portions  122  ( 122 A to  122 E) are formed along the axial direction so as to face the four stepped parts  52 A to  52 D. In addition, from the upstream side toward the downstream side, the diameters of the four annular recessed portions  122 A to  122 D positioned on the upstream side in the axial direction are gradually widened by means of the steps. On the other hand, the diameter of the annular recessed portion  122 E positioned on the most downstream side is smaller than that of the fourth-stage annular recessed portion  122 D adjacent in the upstream side. 
     Furthermore, seal fins  124  ( 124 A to  124 D) extending inward in the radial direction toward the tip shroud  51  are respectively provided in end edge portions (edge portions)  123  ( 123 A to  123 D) which are positioned at the boundary between two annular recessed portions  122  and  122  adjacent in the axial direction. The position of the end edge portions  123  and the seal fins  124  is set so as to face the outer circumference surface  54  of the each stepped parts  52 . More specifically, the four seal fins  124 A to  124 D are arranged spaced apart from each other in the axial direction, and provided so as to correspond to the four stepped parts  52 A to  52 D on a one-to-one basis. Also, in the embodiment, the four seal fins  124 A to  124 D are arranged at the same intervals in the axial direction. 
     In addition, the three seal fins  124 A to  124 C positioned on the upstream side are disposed such that a surface of each seal fin  124  facing downstream side and inner surfaces  125  ( 125 B to  125 D) on the upstream side of the annular recessed portions  122  ( 122 B to  122 D) which are respectively positioned on the downstream side of the seal fins  124  form the same plane. On the other hand, the seal fin  124 D (fourth seal fin  124 D) positioned on the most downstream side is disposed such that a surface of the seal fin  124 D facing upstream side and an inner surface  125 E on the downstream side of the annular recessed portions  122 D which is positioned on the upstream side of the fourth seal fin  124 D form the same plane. 
     Still further, each of small clearances H (H 1  to H 4 ) is formed between the outer circumference surface  54  of each stepped part  52  and the tip of each seal fin  124 , in the radial direction. Each of the small clearances H is set to the minimum value within a safety range in which the casing  10  is not in contact with the turbine blades  50 , by taking into consideration on a thermal expansion amount of the casing  10  or the turbine blade  50 , a centrifugal expansion amount of the turbine blade  50 , or the like. In the embodiment, the four small clearances H 1  to H 4  are all equal in size. 
     Furthermore, in the embodiment, along the axial direction, a distance L (length L of the outer circumference surface  54  of each stepped part  52 , namely a distance from each small clearance H to the step surface  53  on the upstream side) from each small clearance H (each seal fin  124 ) to the step surface  53  of the stepped part  52  positioned on the downstream side is set to the smaller value in the stepped part  52  positioned closer to the downstream side, compared to the other ones. 
     That is, a relationship between a distance L 1  (first distance L 1 ) from a first small clearance H 1  on the outer circumference surface  54 A of the first-stage stepped part  52 A positioned on the most upstream side to the step surface  53 A of the first-stage stepped part  52 A, a distance L 2  (second distance L 2 ) from a second small clearance H 2  on the outer circumference surface  54 B of the second-stage stepped part  52 B to the step surface  53 B of the second-stage stepped part  52 B, a distance L 3  (third distance L 3 ) from a third small clearance H 3  on the outer circumference surface  54 C of the third-stage stepped part  52 C to the step surface  53 C of the third-stage stepped part  52 C, and a distance L 4  (fourth distance L 4 ) from a fourth small clearance H 4  on the outer circumference surface  54 D of the fourth-stage stepped part  52 D to the step surface  53 D of the fourth-stage stepped part  52 D in the axial direction satisfies the following Formula (1).
 
L1&gt;L2&gt;L3&gt;L4  (1)
 
     In other words, in the embodiment, an aspect ratio L/H of the distance L to the small clearance H is set such that the aspect ratio L/H of the stepped part  52  positioned closer to the downstream side is smaller than the other one. 
     In addition, the seal fins  124  are provided as described above, whereby four cavities C (C 1  to C 4 ) are formed between the tip shrouds  51  and the diaphragm outer ring  12  so as to be arranged in the axial direction. Each of the cavities C is formed between the seal fin  124  corresponding to each stepped part  52  and a partition wall opposing the seal fin  124  on the upstream side in the axial direction. 
     More specifically, a first cavity C 1  formed on the most upstream side in the axial direction is formed between the first seal fin  124 A corresponding to the first-stage stepped part  52 A and the inner surface  125 A on the upstream side of the first-stage annular recessed portion  122 A which opposes the first seal fin  124 A on the upstream side in the axial direction. 
     Furthermore, a second cavity C 2  adjacent the first cavity C 1  on the downstream side is formed between the second seal fin  124 B corresponding to the second-stage stepped part  52 B, and the first seal fin  124 A opposing the second seal fin  124 B on the upstream side in the axial direction and the inner surface  125 B on the upstream side of the second-stage annular recessed portion  122 B. 
     Still further, similar to the second cavity C 2 , a third cavity C 3  adjacent the second cavity C 2  on the downstream side is formed between the third seal fin  124 C corresponding to the third-stage stepped part  52 C, and the second seal fin  124 B and the inner surface  125 C on the upstream side of the third-stage annular recessed portion  122 C. 
     In addition, a fourth cavity C 4  adjacent the third cavity C 3  is formed between the third seal fin  124 D corresponding to the fourth-stage stepped part  52 D and the inner surface  125 E on the downstream side of the fourth-stage annular recessed portion  122 D, and the third seal fin  124 C opposing the seal fin  124 D on the upstream side in the axial direction and the inner surface  125 D on the upstream side of the fourth-stage annular recessed portion  122 D. 
     Moreover, according to the embodiment, in each of the cavities of C, a corner portion between a bottom surface (surface facing inward in the radial direction) of each annular recessed portion  122  and the inner surface  125  of each annular recessed portion  122  or each seal fin  124  is roundedly formed. Thereby, the bottom surface of each annular recessed portion  122  and the inner surface  125  of the annular recessed portion  122  are smoothly continued. Also, the bottom surface of each annular recessed portion  122  and the surface of the seal fin  124  on the upstream or downstream side in the axial direction are smoothly continued. Since the corner portion of the cavity C is roundedly formed as described above, the outline thereof becomes close to the shape of a main vortex MV generated in the cavity C, as described below. Therefore, it is possible to suppress energy losses of the main vortex MV in the corner portion of the cavity C (see  FIG. 3 ). 
     Furthermore, in the embodiment, each part of the four cavities C 1  to C 4  is set to the same size, except the distance L described above. For example, axial directional distances (axial directional widths W (W 1  to W 4 ) of the cavities C) from the seal fins  124  to the partition wall opposing the seal fins  124  on the upstream side in the axial direction, or radial directional distances (radial directional distances D (D 1  to D 4 ) of the cavities) from the bottom surfaces of the annular recessed portions  122  to lower ends (radial directional inner ends) of the step surfaces  53  of the stepped parts  52  are set to the same sizes in the four cavities C 1  to C 4 . In addition, it is preferable that, a ratio D/W (aspect ratio D/W in the cavity) of the radial directional distance D to the axial directional width W in each cavity C is approximately set to 1.0 such that the size of a separation vortex SV generated in the cavity C is smaller than that of the main vortex MV generated in the same cavity C, as described below (see  FIG. 3 ). 
     Next, the operation of the steam turbine  1  configured as above will be described. 
     First, when the regulating valve  20  (see  FIG. 1 ) is in an opened state, steam S flows from a boiler (not shown) into the inner space of the casing  10 . 
     The steam S flowing into the inner space of the casing  10  sequentially passes the group of annular turbine vanes and the group of annular turbine blades in each stage. At this time, turbine vanes  40  convert pressure energy to velocity energy, and then almost all of the steam S which has passed the turbine vanes  40  flows into the turbine blades  50  constituting the same stage. Subsequently, the turbine blades  50  convert the velocity energy of the steam S to rotational energy, whereby torque is imparted to the shaft body  30 . Meanwhile, some of the steam S (for example, several percent) flows from the turbine vanes  40  into the annular groove  121  (clearance between the tip shroud  51  of the turbine blade  50  and the diaphragm outer ring  12  of the casing  10 ) as shown in  FIG. 3 . That is, some of the steam S becomes leakage steam. 
     In this case, the steam S flowing into the annular groove  121  collides with the step surface  53 A of the first-stage stepped part  52 A as soon as flowing into the first cavity C 1 , whereby the steam S flows so as to return to the upstream side. Thereby, a main vortex MV 1  rotating counterclockwise (first rotational direction) is generated in the first cavity C 1 . 
     At this time, particularly at the corner section (edge) between the step surface  53 A and the outer circumference surface  54 A in the first-stage stepped part  52 A, some flow is separated from the main vortex MV 1 . Therefore, a separation vortex SV 1  rotating clockwise (second rotational direction) which is a reverse direction to the main vortex MV 1  is generated on the outer circumference surface  54 A of the first-stage stepped part  52 A. 
     The separation vortex SV 1  is positioned in the vicinity on the upstream side of the first small clearance H 1  between the first-stage stepped part  52 A and the first seal fin  124 A. Particularly, in the separation vortex SV 1 , a downflow flowing inward in the radial direction is generated at the position immediately before the first step surface H 1 . Thereby, the separation vortex SV 1  exhibits a contraction flow effect which reduces the leakage flow flowing from the first cavity C 1  into the second cavity C 2  on the downstream side through the first small clearance H. 
     Subsequently, when the steam S flows from the first cavity C 1  into the second cavity C 2  through the first step surface H 1 , the steam S collides with the step surface  53 B of the second-stage stepped part  52 B, whereby flowing so as to return to the upstream side. Thereby, a main vortex MV 2  rotating in the first rotational direction, namely the same direction as the main vortex MV 1  generated in the first cavity C 1 , is generated in the second cavity C 2 . 
     Also, at the corner section between the step surface  53 B and the outer circumference surface  54 B in the second-stage stepped part  52 B, some flow is separated from the main vortex MV 2 . Therefore, a separation vortex SV 2  rotating in the reverse direction to the main vortex MV 2  (second rotational direction) is generated on the outer circumference surface MB of the second-stage stepped part  52 B. 
     Subsequently, when the steam S passes through the second small clearance H 2  and flows into the third cavity C 3 , similar to the case at the first and second cavities C 1  and C 2 , the steam S collides with the step surface  53 C of the third-stage stepped part  52 C, whereby flowing so as to return to the upstream side. Thereby, a main vortex MV 3  rotating in the first rotational direction is generated in the third cavity C 3 . Also, a separation vortex SV 3  rotating in the second rotational direction is generated on the outer circumference surface  54 C of the third stepped part  52 C. 
     In the same way as above, when the steam S passes through the third small clearance H 3  and flows into the fourth cavity C 4 , the steam S collides with the step surface  53 D of the fourth-stage stepped part  52 D, whereby a main vortex MV 4  rotating in the first rotational direction is generated in the fourth cavity C 4 . Also, a separation vortex SV 4  rotating in the second rotational direction is generated on the outer circumference surface  54 D of the fourth stepped part  52 D. 
     In this case, similar to the related art, the pressure (static pressure) or density of the steam S in the clearance between the tip shroud  51  and the diaphragm outer ring  112  becomes reduced from the upstream side toward the downstream side in the axial direction. Therefore, as approaching closer to the downstream side, the flow velocity of the steam S flowing from the each of the small clearances H (H 1  to H 3 ) into the each of the cavities C (C 2  to C 4 ) on the downstream side, or the speed (rotational speed) of the main vortices MV (MV 2  to MV 4 ) generated in the cavities C (C 2  to C 4 ) on the downstream side is increased. Particularly, in the main vortices MV (MV 2  to MV 4 ) closer to the downstream side, the flow velocity flowing outward in the radial direction along the step surface  53  is increased. Therefore, there is a possibility that the diameters of the separation vortices SV (separation vortices SV 2  to SV 4 , for example) generated on the outer circumference surface  54  of each stepped part  52  on the downstream side may be greater than that of the separation vortex SV (separation vortex SV 1 , for example) generated on the outer circumference surface  54  of the stepped part  52  on the upstream side. 
     However, in the embodiment, along the axial direction, the distances L (L 1  to L 4 ) from the small clearances H to the step surfaces  53  on the upstream side are set so as to satisfy Formula (1) described above. Therefore, it is possible to reduce the diameters of the separation vortices SV 2  to SV 4  on the downstream side, because the smaller the distance L (aspect ratio L/H) is, the smaller the diameter of the separation vortex SV produced on the outer circumference surface  54  of the stepped part  52  is. 
     Therefore, in the steam turbine  1  according to the embodiment, it is possible to reduce the diameters of the separation vortices SV 2  to SV 4  on the downstream side. Thereby, in the separation vortices SV 2  to SV 4  on the downstream side, the maximum position of a velocity component of the flow which flows inward in the radial direction from the tip side of each of the seal fins  124 B to  124 D toward each of the outer circumference surfaces  54 B to  54 D of the stepped parts  52 B to  52 D can be moved closer to the tip of each of the seal fins  124 B to  124 D. Consequently, it is possible to, in each of the separation vortices SV 2  to SV 4  on the downstream side, strengthen the downflow generated immediately before each of the small clearances H 2  to H 4 . As a result, it is possible to reduce the leakage flow of the steam S which passes through each of the small clearances H 2  to H 4 . In other words, it is possible to improve the contraction flow effect. 
     Furthermore, since the diameters of the separation vortices SV 2  to SV 4  on the downstream side are reduced, it is possible to reduce the static pressures in the separation vortices SV 2  to SV 4 . Thereby, it is possible to reduce the pressure difference between the upstream side and the downstream side of the small clearances H 2  to H 4  positioned on the downstream side of the separation vortices SV 2  to SV 4 . For example, the diameter of the separation vortex SV 3  in the third cavity C 3  is reduced, whereby the static pressure difference between the static pressure in the third cavity C 3  on the upstream side and the static pressure in the fourth cavity C 4  on the downstream side can be reduced. Therefore, corresponding to the reduction of the pressure difference, it is possible to improve the static pressure reduction effect which causes the leakage flow passing through the small clearances H 2  to H 4  positioned on the downstream side to be reduced. 
     Particularly, in the embodiment, the distances L (L 1  to L 4 ) are set so as to satisfy Formula (1) described above. Therefore, the separation vortex SV closer to the downstream side is further reduced in diameter. As a result, in the small clearance H closer to the downstream side, the contraction flow effect and the static pressure reduction effect due to the separation vortex SV described above can be more effectively improved. 
     Consequently, according to the steam turbine  1  of the embodiment, it is possible to reduce the amount of leakage steam passing through the clearance between the tip shroud  51  of the turbine blade  50  and the diaphragm outer ring  12  of the casing  10 . 
     Furthermore, as shown in  FIGS. 4A to 4C , the effects described above are confirmed by the results of simulations conducted by the inventor. 
     Each of the graphs shown in  FIGS. 4A to 4C  shows the result of the simulation which was run with regard to a relationship between, in the same stepped part  52 , the aspect ratio L/H and the flow rate coefficient Cd of the steam S passing through the small clearance H, with respect to the second small clearance H 2  (second-stage stepped part  52 B), the third small clearance H 3  (third-stage stepped part  52 C) and the fourth small clearance H 4  (fourth-stage stepped part  52 D). In this graph, the smaller flow rate coefficient Cd, the smaller the flow rate of the steam S passing through the small clearance H. 
     According to the graph, in each of the small clearances H 2  to H 4 , the optimal value of the aspect ratio L/H to minimize the flow rate coefficient Cd is present. Specifically, the optimal value of the aspect ratio L/H in the second small clearance H 2  is 3.0 (see  FIG. 4A ), and the optimal value of the aspect ratio L/H in the third small clearance H 3  is 2.5 (see  FIG. 4B ). Also, the optimal value of the aspect ratio L/H in the fourth small clearance H 4  is 2.2 (see  FIG. 4C ). That is, the small clearance H positioned closer to the downward is small in the optimal value of the aspect ratio L/H to minimize the flow rate coefficient Cd. In other words, the optimal distance L thereof becomes shorter. 
     In addition, in the first embodiment described above, the five annular recessed portions  122 A to  122 E (particularly, the four annular recessed portions  122 A to  122 D on the upstream side) corresponding to the four stepped parts  52 A to  52 D are formed on the diaphragm outer ring  12  such that the sizes of the four cavities C do not become smaller from the upstream side to the downstream side. Therefore, even if the distance L of the cavity C (third cavity C 3  or fourth cavity C 4 , for example), especially on the downstream side, is not set finely and precisely, it is possible to simply set the size of the separation vortex SV generated in the cavity C to be smaller than the size of the main vortex MV generated in the same cavity C. 
     Furthermore, in the first embodiment, the step surface  53  of each of the stepped parts  52  is parallel in the radial direction. That is, the step surfaces  53  of the first embodiment are not inclined, as being inclined in the case of a second embodiment. Therefore, it is possible to simply reduce the size of the tip shroud  51  in the axial direction. 
     Second Embodiment 
     Next, the second embodiment of the present invention will be described referring to  FIGS. 5 and 6 . 
     Upon comparison with the steam turbine  1  of the first embodiment, the second embodiment has a difference in that only the shape of each stepped part  52  is different from that of the first embodiment, and other configurations are the same as those in the first embodiment. In the second embodiment, the same reference numerals and signs are given to the same constituent elements as those of the first element, and the description thereof will be omitted. 
     As shown in  FIG. 5 , inclined surfaces  56  ( 56 A to  56 D) inclined from the upstream side to the downstream side are respectively formed on the step surfaces  53  ( 53 A to  53 D) of the stepped parts  52  ( 52 A to  52 D) so as to be continuous with each of the outer circumference surfaces  54  ( 54 A to  54 D) of the same stepped parts  52 . 
     Furthermore, in the four inclined surfaces  56 A to  56 D, inclination angles θ 1  to θ 4  with respect to the radial direction become greater from the upstream side toward the downstream side. 
     That is, in the four stepped parts  52  ( 52 A to  52 D), the inclination angle θ 1  of the inclined surface  56 A formed on the step surface  53 A of the first-stage stepped part  52 A positioned on the most upstream side, the inclination angle θ 2  of the inclined surface  56 B formed on the step surface  53 B of the second-stage stepped part  52 B, the inclination angle θ 3  of the inclined surface  56 C formed on the step surface  53 C of the third-stage stepped part  52 C, and the inclination angle θ 4  of the inclined surface  56 D formed on the step surface  53 D of the fourth-stage stepped part  52 D satisfy the following Formula (2).
 
θ1&lt;θ2&lt;θ3&lt;θ4  (2)
 
     Furthermore, in the example shown in the drawings, each of the inclined surfaces  56  is formed on each of the step surfaces  53 . However, without being limited thereto, the inclined surface may be formed, for example, only on an upper end part (outward end part in the radial direction) of the step surface  53  continuous with the outer circumference surface  54  on the same stepped part  52 , and a lower end part (inward end part in the radial direction) of the step surface  53  may be parallel to the radial direction. 
     In the steam turbine of the second embodiment configured as above, as shown in  FIG. 6 , when the steam S flows into the annular groove  121 , each of the main vortices MV (MV 1  to MV 4 ) rotating in the first rotational direction and each of the separation vortices SV (SV 1  to SV 4 ) rotating in the second rotational direction are generated in each of the cavities C (C 1  to C 4 ), similar to the case of the first embodiment. 
     Therefore, according to the steam turbine  1  of the second embodiment, it is possible to achieve the same effect as the first embodiment. 
     Furthermore, in the second embodiment, the inclined surface  56  is formed on the step surface  53  of each stepped part  52 . Thereby, in the main vortex MV generated in each cavity C, the direction of flow separated at the corner section between the step surface  53  and the outer circumference surface  54  of each stepped part  52  is inclined, by the inclined surface  56 , to the downstream side in the axial direction with respect to the radial direction. Consequently, it is possible to reduce the diameter of the separation vortex SV generated on the outer circumference surface  54  of each stepped part  52 . 
     Furthermore, in the embodiment, the inclination angles θ 2  to θ 4  of the inclined surfaces  56 B to  56 D formed on the stepped parts  52 B to  52 D on the downstream side are greater than the inclination angle θ 1  of the inclined surface  56 A formed on the stepped part  52 A on the upstream side. Therefore, it is possible to strengthen the tendency to reduce the diameters of the separation vortices SV 2  to SV 4  generated on the outer circumference surfaces  54 B to  54 D of the stepped parts  52 B to  52 D on the downstream side smaller than the diameter of the separation vortex SV 1  generated on the outer circumference surface  54 A of the stepped part  52 A on the upstream side. 
     Consequently, it is possible to improve the contraction flow effect and the static pressure reduction effect due to the separation vortices SV 2  to SV 4  on the downstream side. 
     Particularly, in the second embodiment, since the inclination angles θ 1  to θ 4  are set to satisfy Formula (2) described above, the separation vortex SV closer to the downstream side is further reduced in diameter. As a result, in the small clearance H closer to the downstream side, the contraction flow effect and the static pressure reduction effect due to the separation vortex SV described above are much more effectively improved. 
     Consequently, according to the steam turbine  1  of the second embodiment, it is possible to further reduce the amount of leakage steam passing through the clearance between the tip shroud  51  of the turbine blade  50  and the diaphragm outer ring  12  of the casing  10  than in the case of the first embodiment. 
     In addition, in the second embodiment, each of the inclined surfaces  56  is formed in a linear cross-section shape having a constant inclination angle. However, without being limited thereto, each of the inclined surfaces  56  may be formed in a circular cross-section shape of which the inclination angle with respect to the radial direction is changed as approaching closer to the outer circumference surface  54  of each stepped part  52 , for example. Also, each of the inclined surfaces  56  may be formed in the appropriately combined shape having the linear cross-section shaped part and the circular cross-section shaped part. 
     As described above, if a part or the entire inclined surface  56  is formed in a circular cross-section shape, the flow of the main vortex MV along the step surface  53  becomes smooth. Therefore, it is possible to suppress energy losses of the main vortex MV. 
     Furthermore, in such a configuration where the inclined surface  56  has a circular cross-section shaped part, when the circular cross-section shaped part is continuous with the outer circumference surface  54 , a relative angle between the radial direction and the circular cross-section shaped part in the corner section between the circular cross-section shaped part and the outer circumference surface  54  may be set as an inclination angle of the inclined surface  56  with respect to the radial direction. Also, when the linear cross-section shaped part of the inclined surface  56  is continuous with the outer circumference surface  54 , similar to the case of the second embodiment described above, a relative angle between the radial direction and the linear cross-section shaped part may be set as an inclination angle of the inclined surface  56  with respect to the radial direction. 
     In addition, when a part or the entire inclined surface  56  is formed in a circular cross-section shape, the circular cross-section shape of which the inclination angle with respect to the radial direction is gradually decreased is preferable to the circular cross-section shape of which the inclination angle is gradually increased, from the standpoint of preventing the fluid flowing along the inclined surface  56 . 
     Still further, the inclination angles of the four inclined surfaces  56 A to  56 D are not limited to the values of the second embodiment which satisfy Formula (2). In at least two adjacent stepped parts  52  and  52 , the inclination angles of the inclined surfaces  56  thereof may be set so that one of the stepped part  52  on the upstream side is greater than the other one of the stepped part  52  on the downstream side. 
     For example, when the inclination angle θ 3  (third inclination angle θ 3 ) of the inclined surface  56 C of the third-stage stepped part  52 C is set to be smaller than the inclination angle θ 2  (second inclination angle θ 2 ) of the inclined surface  56 B of the second-stage stepped part  52 B, the second inclination angle θ 2  may be set to be equal to or more than the first inclination angle θ 1  of the inclined surface  56 A of the first-stage stepped part  52 A, or the fourth inclination angle θ 4  of the inclined surface  56 D of the fourth-stage stepped part  52 D may be set to be equal to or more than the third inclination angle θ 3 . 
     Furthermore, in the second embodiment, the inclined surfaces  56  are formed on all of the step surfaces  53 . However, in two adjacent stepped parts  52  and  52 , the inclined surface  56  may be formed at least on the step surface  53  of the stepped part  52  on the downstream side. 
     For example, the inclined surface  56 C may be only formed on the step surface  53 C of the third-stage stepped part  52 C, and the inclined surfaces  56 C may be not formed on the step surfaces  53 A,  53 B and  53 D of the other stepped parts  52 A,  52 B and  52 D. Also, for example, the inclined surfaces  56 A and  56 C may be only formed on the step surfaces  53 A and  53 C of the first-stage and third-stage stepped parts  52 A and  52 C, and the inclined surfaces  56 B and  56 D may be not formed on the step surfaces  53 B and  53 D of the second-stage and fourth-stage stepped parts  52 B and  52 D. 
     Thus, the details of the present invention are described, the present invention is not limited to the embodiments described above, and various modifications can be added to the embodiments without departing from the scope of the technical idea of the invention. 
     For example, it is preferable that the sizes of the four small clearances H 1  to H 4  are set to the same minimal values as the embodiments described above, but it is also possible to be set to sizes different from each other. Moreover, in this case, it is preferable that the four distances L 1  to L 4  are set such that the aspect ratios L/H of the distances L to the small clearances H become smaller from the upstream side to the downstream side. 
     Still further, the distances L from each of the small clearances H (each seal fin  124 ) to the step surface  53  of the stepped part  52  positioned on the upstream side thereof along the axial direction are not limited to the values satisfying Formula I described above. In at least two adjacent stepped parts  52  and  52 , the distances L may be set so that one of the stepped part  52  on the downstream side is shorter than the other one of the stepped part  52  on the upstream side. 
     Specifically, for example, when the third distance L 3  from the third small clearance H 3  to the step surface  53 C of the third-stage stepped part  52 C is set to be shorter than the second distance L 2  from the second small clearance H 2  to the step surface  53 B of the second-stage stepped part  52 B, the second distance L 2  may be set to be equal to or more than the first distance L 1  from the first small clearance H 1  to the step surface  53 A of the first-stage stepped part  52 A, or the fourth distance L 4  from the fourth small clearance H 4  to the step surface  53 D of the fourth-stage stepped part  52 D may be set to be equal to or more than the third distance L 3 . 
     Furthermore, in the embodiments, the heights of the four step surfaces  53 A to  53 D are set to the same, but it is also possible for them to be set differently. 
     Also, in the embodiments, the four seal fins  124 A to  124 D are arranged at the same intervals in the axial direction, but it is also possible for them to be arranged not at the same intervals. 
     Still further, in the embodiments, a part of the corner portion of each cavity C is roundedly formed. However, for example, all of the corner portion may be formed roundedly, or the corner portion may be not formed roundedly. 
     In addition, in the embodiments, the four annular recessed portion  122 A to  122 D of which the diameters are gradually widened by means of the steps, and the fifth-stage annular recessed portion  122 E of which the diameter is smaller than that of the fourth-stage annular recessed portion  122 D are respectively formed in the bottom portions of the annular grooves  121 . However, without being limited thereto, it is also possible to set the diameters of the bottom portions of the annular grooves  121  to approximately the same value, for example. In this case, the sizes of the four cavities C 1  to C 4  become smaller from the upstream side toward downstream side. 
     Also, in the embodiments, each part of the four cavities C 1  to C 4  is set to the same size, except the distance L, but it is also possible to be set not to the same values. 
     Still further, in the embodiments, the four stepped parts  52  are formed on the tip shroud  51 , whereby the four cavities C are formed corresponding thereto. However, at least a plurality of the stepped parts  52  and the cavities C corresponding thereto may be provided, such as two, three or five or more. 
     Furthermore, the seal fins  124  and the annular recessed portions  122  are formed on the diaphragm outer ring  12  of the casing  10 , but it is also possible for them to not be formed on the diaphragm outer ring  12  but directly on the main body portion  11  of the casing  10 , for example. 
     Still further, in the embodiment, the plurality of stepped parts  52  are provided on the tip shroud  51 , and the seal fins  124  are provided on the casing  10 . However, it is also possible to provide the plurality of stepped parts  52  on the casing  10  and to provide the seal fins  124  on the tip shroud  51 , for example. 
     Furthermore, the configuration which realizes the contraction flow effect and the static pressure reduction effect as in the embodiments described above is not limited to the configuration of being formed in the clearance between the tip shroud  51  constituting the tip of the turbine blade  50  and the casing  10 , and may be formed in the clearance between the hub shroud  41  constituting the tip of the turbine vane  40  and the shaft body  30 . In other words, the turbine vane  40  may be used as a “blade member (blade)” of the present invention, and the shaft body  30  may be used as a “structural member” of the present invention. In this case, it is possible to achieve the same effects as the embodiments described above. 
     In the embodiments described above, the present invention has been applied to a condensing steam turbine. However, the present invention may be applicable to other types of steam turbines, for example, a two-stage extraction turbine, an extraction turbine, and a mixed pressure turbine. 
     Furthermore, in the embodiments described above, the present invention is applied to a steam turbine. However, the present invention is also applicable to a gas turbine. Still further, the present invention is applicable to all machines with rotating blades. 
     Hereinbefore, a description has been so far made of preferred examples of the present invention. However, without being limited thereto, the present invention may be subjected to addition, omission, replacement and other modifications of the configuration within a scope not departing from the gist of the present invention. The present invention is not limited to the description described above, but is only limited by the scope of the attached claims. 
     DESCRIPTION OF REFERENCE NUMERALS 
       1 : steam turbine (turbine),  10 : casing (structural member),  11 : main body portion,  12 : diaphragm outer ring,  30 : shaft body,  40 : turbine vane,  41 : hub shroud,  50 : turbine blade (blade),  51 : tip shroud,  52 ,  52 A,  52 B,  52 C,  52 D: stepped part,  53 ,  53 A,  53 B,  53 C,  53 D: step surface,  54 ,  54 A,  54 B,  54 C,  54 D: outer circumference surface,  56 ,  56 A,  56 B,  56 C,  56 D: inclined surface,  121 : annular groove,  124 ,  124 A,  124 B,  124 C,  124 D: seal fin, C, C 1 , C 2 , C 3 , C 4 : cavity, H, H 1 , H 2 , H 3 , H 4 : small clearance, L, L 1 , L 2 , L 3 , L 4 : distance, S: steam (fluid), θ 1 , θ 2 , θ 3 , θ 4 : inclination angle