Turbine design and turbine manufacturing processes

Abstract

A turbine design method in connection with a material change of a runner disk (9a, 9b) of a turbine runner (102), characterized in that the time required for a temperature of the runner disk (9a, 9b) at the time of starting a turbine (3) to reach a second temperature from a first temperature is the temperature rise time, and that the distance between the surfaces on an inlet side and an outlet side of the runner disk (9a, 9b) is a distance between the surfaces, wherein the turbine design method comprises: determining a temperature rise time ratio, which is a desired ratio of the temperature rise time after the material change to the temperature rise time before the material change; determining the distance between the surfaces after the material change based on the determined temperature rise time ratio;Determining a shape of the impeller disk (9a, 9b) after the material change based on the determined distance between the surfaces; and designing the turbine (3) while the determined shape of the impeller disk (9a, 9b) is reflected in the turbine impeller (102), and wherein the temperature rise time is defined by the following formula: t = c⋅m⋅L / (k⋅S), where “c” is a specific heat of the impeller disk (9a, 9b), “m” is a weight of the impeller disk (9a, 9b), “L” is a distance between the surfaces, “k” is a thermal conductivity of the impeller disk (9a, 9b), and “S” is a cross-sectional area of ​​an annular section with a central axis of the impeller disk (9a, 9b) as its center point.

Description

BACKGROUND OF THE INVENTION 1. Field of the invention The present invention relates to a turbine design and a turbine manufacturing method. 2. Description of the related area In recent years, there have been calls to increase the temperature of combustion gases to improve the efficiency of gas turbines. However, as the combustion gas temperature increases, there is a tendency for the quality of the turbine components exposed to the combustion gas, such as the turbine runner, to decrease, potentially shortening their service life. As a method for preventing the deterioration of turbine runner quality, there is a method for applying a material with excellent high-temperature strength to the turbine runner (see, e.g., JP-2013-199680-A). WO 2019 / 016 352 A1 (see patent document 2) discloses a method for manufacturing gas turbine components, such as rotor or stator blades, wherein this method aims to streamline the development and testing process of gas turbine engine components in order to ultimately reduce costs and time while ensuring the quality and reliability of the final production components. US 2003 / 204 823 A1 (see patent document 3) discloses a method for optimizing component design using computer-aided design (CAD) and analysis tools, wherein the taught analysis and optimization techniques contribute to improved product quality and a shorter design time.Furthermore, the scientific publication "Optimization in Structural Mechanics" by Baier et al. provides specialist knowledge on the topic of finite element modeling. State of the art document Patent document Patent document 1: JP-2013-199680-A, Patent document 2: WO 2019 / 016 352 A1, Patent document 3: US 2003 / 204 823 A1 In the case of a change in the material applied to the turbine runner, as in JP-2013-199680-A, the thermal expansion of the turbine runner can change along with the values ​​of the material's physical properties. Therefore, it is necessary to re-understand the thermal expansion of the turbine runner after the material change and to redesign the turbine. A common method for understanding thermal expansion is analysis using a non-stationary finite element method (non-stationary FEM analysis). However, non-stationary FEM analysis requires a long run time, and the number of iterations required to obtain design data that meets the turbine's requirements is large. Thus, the design and manufacturing of a turbine in conjunction with a material change can be very time-consuming and labor-intensive. The present invention was made in light of the foregoing and it is an object of the present invention to reduce the time required for the design and manufacture of a turbine in connection with a change in material. SUMMARY OF THE INVENTION The problem is solved by the features of claims 1 and 8. Specific embodiments are described in the dependent claims. According to the present invention, the time required for the design and manufacture of a turbine in connection with a change in material can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 is a schematic representation showing a configuration example of a gas turbine to which a turbine according to a first embodiment of the present invention is applied; Fig. 2 is a sectional view showing the internal structure of the turbine according to the first embodiment of the present invention; Fig. 3 is a flow chart showing the design and manufacturing procedure of the turbine according to the first embodiment of the present invention; Fig. 4 is a sectional view showing the shape of an impeller disk before and after a material change; Fig. 5 is a table showing, by way of example, the ratios of elements before and after a material change of the impeller disk; Fig. 6 is a flow chart showing the design and manufacturing procedure of a turbine according to a second embodiment of the present invention; and Fig.Table 7 shows, by way of example, the ratio of elements before and after a material change of an impeller disc. DESCRIPTION OF PREFERRED EXECUTION FORMS <Erste Ausführungsform> (Configuration) 1. Gas turbine Fig. 1 is a schematic representation showing a configuration example of a gas turbine to which a turbine according to the present embodiment is applied. The following describes a case in which the turbine according to the present embodiment is applied to the gas turbine, but the object to which the turbine according to the present embodiment is to be applied is not limited and the turbine can, for example, be applied to a steam turbine. As shown in Fig. 1, a gas turbine 100 comprises a compressor 1, a combustion chamber 2, and a turbine 3. The compressor 1 and the turbine 3 are coupled to each other via a shaft (not shown). The compressor 1 is driven by the turbine 3, compressing air 6, which is drawn in through an inlet section 5, to generate high-pressure air (combustion air), and supplies the high-pressure air to the combustion chamber 2. The combustion chamber 2 mixes the high-pressure air supplied by the compressor 1 with fuel supplied by a fuel system (not shown) to carry out combustion, producing a high-temperature combustion gas 7, and supplies it to the turbine 3. The turbine 3 is driven by the expansion of the combustion gas 7 supplied by the combustion chamber 2. A load device (not shown) is coupled to the turbine 3 or to the compressor 1.In the present embodiment, a generator is coupled to the turbine 3 as a load device, wherein the power obtained by subtracting the power for driving the compressor 1 from the rotational power of the turbine 3 is converted into electrical power by the generator. The combustion gas 7, which has driven the turbine 3, is expelled to the atmosphere as turbine exhaust. 2. Turbine Fig. 2 is a sectional view showing the internal structure of a part of the turbine according to the present embodiment. As shown in Fig. 2, the turbine 3 comprises a stationary body 101 and a turbine impeller 102, which forms a rotating body that is rotated relative to the stationary body 101. The stationary body 101 mainly contains a casing 8, an outer ring 18, stationary blades 11 (11a, 11b), an inner ring 15, an intermediate floor 14 and cover bands 32 (32a, 32b). The casing 8 is a cylindrical element that forms a circumferential wall of the turbine 3. The outer ring 18, the fixed blades 11 (11a, 11b), the inner ring 15, the intermediate plate 14 and the turbine impeller 102 are housed in the casing 8. An outer circumferential end wall 18 is supported by an inner circumferential wall 8a of the housing 8 via the cover band 32, which will be described later. The outer circumferential end wall 18 is a cylindrical element that runs in the circumferential direction of the turbine impeller 102. Several fixed blades 11b are provided at regular intervals along the circumferential direction of the turbine runner 102 on the inner circumferential surface of the outer circumferential end wall 18. The fixed blades 11b extend from the inner circumferential surface of the outer circumferential end wall 18 towards the radial inner side of the turbine runner 102. Hereinafter, the radial inner side and the radial outer side of the turbine runner 102 are simply referred to as "the radial inner side" and "the radial outer side". Furthermore, the fixed blades 11b are arranged in several rows along an axial direction of the turbine runner 102, with sets of these forming turbine stages together with runner blades 12. In the example from Fig. 1, the fixed blades 11a of the first stage and the fixed blades 11b of the second stage are shown, although the number of stages can be optional. An inner circumferential end wall 15b is provided on the radially inward side of the stationary blades 11b. The inner circumferential end wall 15b is a cylindrical element that extends in the circumferential direction of the turbine runner 102. The stationary blades 11b are connected to an outer circumferential surface of the inner circumferential end wall 15b. In other words, the stationary blades 11b are fixed between the outer end wall 18 and the inner circumferential end wall 15b. A space separated by the outer circumferential end wall 18 and the inner circumferential end wall 15b forms a gas path, a flow channel for the combustion gas within the turbine 3. The intermediate floor 14 is attached to the inner circumferential surface of the inner circumferential side end wall 15b and extends in the circumferential direction of the turbine impeller 102. The intermediate floor 14 is provided with lamellae (not shown) extending from an inner circumferential surface (a surface opposite an outer circumferential surface 30 of a spacer disk 10a, which will be described later) towards the radially inward side. Furthermore, the cover bands 32 (32a, 32b) are attached to the inner circumferential wall 8a of the casing 8 as elements that support the inner rings 18 of the stationary blades 11. The cover bands 32 are annular elements and are positioned opposite the leading ends of the impeller blades 12, which will be described later.In the illustrated example, the cover band 31a, which is opposite the impeller blade 12a of the first stage, supports the outlet side of the outer circumferential end wall 18 of the stationary blade 11a of the first stage and the inlet side of the outer circumferential end wall 18 of the stationary blade 11b of the second stage. The cover band 32b, which is opposite the stationary blade 12b of the second stage, supports the outlet side of the outer circumferential end wall 18b of the stationary blade 12a of the second stage. The turbine impeller 102 contains impeller discs 9a and 9b, the spacer disc 10a and the impeller blades 12a and 12b. The impeller discs 9a and 9b and the spacer disc 10a are disc-shaped elements aligned in the direction of flow of the combustion gas 7. Hereinafter, the inlet side and the outlet side are simply referred to as "the inlet side" and the "outlet side" with respect to the direction of flow of the combustion gas 7. The impeller discs 9a and 9b and the spacer disc 10a are rigidly mounted by means of stacking bolts 13. The multiple stacking bolts 13 are arranged around the circumference of a circle with the central axis 1 of the turbine 3 as its center point. The impeller disc 9a comprises an inner circumferential part 21, an outer circumferential part 22, and a stacking butt part 23. Although the configuration of the impeller disc 9a is described below, the other impeller disc, including the impeller disc 9b, also has a similar configuration, except for the presence or absence of a central hole. The inner circumferential section 21 forms a portion on the radially inward side (the side of the central axis 1) of the impeller disk 9a. The inner circumferential section 21 is designed such that the distance D1 between the surfaces in the radially outward direction of a cross-sectional surface of the impeller disk 9a, cut along a plane containing the central axis 1 (hereinafter referred to as the cross-sectional surface of the impeller disk 9a), gradually decreases. In the present embodiment, the "distance between the surfaces" refers to the distance between the surfaces on the inlet side and the outlet side of the impeller disk 9a, more precisely, to the distance between two surfaces at optional radial orientation positions of the impeller disk 9a in the cross-sectional surface of the impeller disk 9a.The inner circumferential part 21 is opposite the spacer disc 10a, which is provided adjacent to the outlet side of the impeller disc 9a, with an intermediate space 28 between them. The stacking butt section 23 is a section located between the inner circumferential section 21 and the outer circumferential section 22. The stacking butt section 23 is formed with several hole sections (not shown) into and through which the stacking bolts 13 can be inserted and passed in the circumferential direction of the turbine impeller 102. The stacking butt section 23 has a surface on the inlet side and a surface on the outlet side that are parallel to a plane orthogonal to the central axis 1, these surfaces being formed such that the distance D3 between the surfaces in the radial direction of the turbine impeller 102 is constant in the cross-sectional surface of the impeller disk 9a.A surface on the outlet side of the stacking butt 23 is provided such that contact is established with a surface on the inlet side of the adjacent spacer disk 10 (a surface on the outlet side of the stacking butt 23 and a surface on the inlet side of an impact surface of the spacer disk 10a are in contact with each other). Several impeller disks overlap over the spacer disks and are fastened by the stacking bolts 13, which penetrate the stacking butt 23. The outer circumferential part 22 forms a portion on the radially outer side of the impeller disk 9a. The outer circumferential part 22 is shaped such that the distance D2 between the surfaces in the cut surface of the impeller disk 9a is shorter than the distance D3 between the surfaces of the stacking butt part 23. The outer circumferential part 22 is opposite the spacer disk 10a, with a gap 29 between them. An annular space formed between the impeller discs 9a and 9b, the inner ring 15, the inner circumferential wall 8b of the housing 8, and the outer ring 18, forms a flow channel (combustion gas flow channel) 31 through which the combustion gas 7 flows. The inner circumferential wall of the combustion gas flow channel 31 is formed by the outer circumferential surfaces of the impeller discs 9a and 9b and by the outer circumferential surface of the inner ring 15, while the outer circumferential wall is formed by the inner circumferential wall 8a of the housing 8 and by the inner circumferential surface of the outer ring 18. A spacer disc 10a is provided between the impeller discs 9a and 9b. The spacer disc 10a includes a projecting section 27 that extends from a surface (outer circumferential surface) 30 on the radially outer side in the direction of the radially outer side. The projecting section 27 of the spacer disc 10a interacts with the lamellae of the intermediate floor 14 to form a sealing section. On the outer circumferential surfaces of the impeller discs 9a and 9b, the multiple impeller blades 12a and 12b are provided at regular intervals along the circumferential direction of the turbine impeller 102. The impeller blades 12a and 12b extend from the outer circumferential surfaces of the impeller discs 9a and 9b towards the radially outer side (the side of the inner circumferential wall 8a of the housing 8). Gaps 19 and 20 are formed between the outer circumferential portions (the end portions on the radially outer side) of the impeller blades 12a and 12b and the cover bands 32a and 32b attached to the housing 8. The impeller blades 12a and 12b are rotated by the combustion gas 7 flowing through the combustion gas flow channel 31 with the central axis 1 as a center point, together with the impeller disks 9a and 9b and the spacer disk 10a. The impeller blades 12a and 12b and the fixed blades 11a and 11b are arranged alternately in the direction of flow of the combustion gas 7. In other words, the impeller blades and the fixed blades are arranged alternately such that, from the inlet of the combustion gas flow channel 31 towards the outlet side, the fixed blade 11a of the first stage, the impeller blade 12a of the first stage, the fixed blade 11b of the second stage, the impeller blade 12b of the second stage, and so on, are present. The multiple fixed blades 11a of the first stage are arranged at regular intervals on the inlet side of the first-stage impeller blade 12a in the circumferential direction of the turbine impeller 102. The fixed blades 11a of the first stage are connected to an inner circumferential support section 26 provided on the inlet side of the impeller disk 9a and to an outer circumferential support section 25, which is provided opposite the inner circumferential support section 26, with the combustion gas flow channel 31 located between them. 3. Design and manufacture of the turbine Figure 3 is a flowchart illustrating a turbine design and manufacturing process according to the present embodiment. In this embodiment, a turbine design and manufacturing process involving a material change of the turbine impeller disc is described by showing, as an example, a case of changing to a material with higher thermal resistance. Impeller disc 9a is shown below as an example, but other impeller discs, including impeller disc 9b, can be configured similarly. • Step S1 A temperature rise time ratio is determined, which is a desired ratio of the temperature rise time after a material change to the temperature rise time before the material change. In the present embodiment, "the temperature rise time" is the time required for the temperature of the impeller disk to reach a second temperature from a first temperature at the time of turbine start-up. The first temperature and the second temperature are both target temperatures; the first temperature is, for example, a normal temperature (e.g., 20 °C ± 15 °C), while the second temperature is an average temperature of an optionally selected part or all parts of the impeller disk at the time of rated operation (e.g., 500 °C). Although a case is described in the present embodiment where the temperature rise time ratio is 1.0, the temperature rise time ratio can, for example, be in the range of 0.9 to 1.1.The temperature rise time is described below. In the present embodiment, specific heat formulas and heat conduction formulas are defined as formulas (1) and (2): where Q is the heat capacity of the impeller disk 9a, c is the specific heat of the impeller disk 9a, m is the weight of the impeller disk 9a and ΔT is the temperature change of an optionally selected part of the impeller disk 9a.where k is the thermal conductivity of the impeller disc 9a, S is the cross-sectional area of ​​a cutting surface in the case of cutting the impeller disc 9a in a plane orthogonal to the central axis 1 of the impeller disc 9a at an optional position in the direction of the central axis of the impeller disc 9a (the cross-sectional area of ​​an annular cutting surface with the central axis 1 of the impeller disc 9a as a center point), t is the temperature rise time at an optionally selected part of a cutting surface of the impeller disc 9a, T1 and T2 are temperatures (T1 > T2) of surfaces on the inlet side and on the outlet side in an optional radial direction position of a cutting surface of the impeller disc 9a, and L is the distance between the surfaces at the optional radial direction position. In the present embodiment, it is assumed that ΔT = T1 - T2. From formulas (1) and (2), the temperature rise time t can then be expressed as formula (3). If the temperature rise times are the same before and after the material change, it can be said that the ease with which the impeller disc heats up is the same both before and after the material change. If the temperature rise time after the material change is shorter than before (temperature rise time ratio < 1), the impeller disc is easier to heat after the material change than before, and if the temperature rise time after the material change is longer than before (temperature rise time ratio > 1), the impeller disc is harder to heat after the material change than before.It is noted that in the present embodiment a method for calculating the temperature rise time t from the formula for specific heat and from the formula for heat conduction has been described, but the method for calculating the temperature rise time t is not limited to this. • Step S2 The distance between the surfaces after the material change is determined based on the temperature rise time ratio determined in step S1. From formula (3) the temperature rise times t1 and t2 before and after the material change can be expressed as formulas (4) and (5) respectively. In the present embodiment, the temperature rise time ratio is 1.0 (t2 / t1= 1.0), so that formula (6) is obtained from formulas (4) and (5). For convenience, the cross-sectional area of ​​the impeller disc 9a is treated as unchanged (S1 = S2) before and after the material change in the present embodiment, and the weight ratio (m2 / m1), which is the ratio of the weight after the material change to the weight before the material change, and the ratio of the distance between the surfaces (L2 / L1), which is the ratio of the distance between the surfaces after the material change to the distance between the surfaces before the material change, are treated as equal. Thus, formula (6) becomes formula (7). In general, the specific heats c1 and c2 and the thermal conductivities k1 and k2 of the impeller disc 9a before and after the material change are determined by values ​​of the material's physical properties. Thus, the distance L2 between the surfaces after the material change can be determined from formula (7). • Step S3 Based on the distance between the surfaces determined in step S2, the shape of the impeller disc 9a is determined after the material change. In the present embodiment, the distance between the surfaces is changed for an optional radial orientation position of the impeller disk 9a based on the distance between the surfaces determined in step S2, and the shape of the impeller disk 9a after the material change is determined by a formula for disks under equal load. In the present embodiment, "formula for disks under equal load" refers to a formula for determining the shape of the impeller disk such that the load acting on each part of the impeller disk, taking into account the centrifugal force, is the same regardless of the radial orientation position of the turbine impeller. Fig. 4 is a sectional view showing the shapes of the impeller disc 9a before and after the material change. In Fig. 4, the dashed line indicates the shape of the impeller disc 9a after the material change, and the solid line indicates the shape of the impeller disc 9a before the material change. As shown in Fig. 4, the distances between the surfaces of the inner circumferential part 21 and the outer circumferential part 22 of the impeller disc 9a are changed before the material change in the present embodiment; more precisely, the distance D1 between the surfaces of the inner circumferential part 21 is set to D1' (< D1) before the material change and the distance D2 between the surfaces of the outer circumferential part 22 is set to D2' (< D2). In Fig. 4, the distances between the surfaces of the inner circumferential part 21 and the outer circumferential part 22 are changed uniformly such that the change ratio (D1' / D1) of the distance between the surfaces of the inner circumferential part 21 before and after the material change and the change ratio (D2' / D2) of the distance between the surfaces of the outer circumferential part 22 are equal, and that the distance between the surfaces of the outer circumferential part 22 of the planes C1 and C2 (dashed line), which define the surfaces A1' and C2 respectively, is equal.A2' on the inlet and outlet sides of the inner circumferential part 21 after the material change is equal to the distance D2' between the surfaces of the outer circumferential part 22 after the material change. In other words, the surfaces on the inlet (outlet) side of the inner circumferential part 21 and the outer circumferential part before and after the material change are contained in the same plane. It should be noted that the shape of the impeller disc 9a after the material change is not limited to that described above.For example, the distance between the surfaces of the outer circumferential part 22 after the material change can be set greater than the distance D2' between the surfaces of the outer circumferential part 22 in the case of a uniform change in the distances between the surfaces of the inner circumferential part 21 and the outer circumferential part 22, and the distance between the surfaces of the inner circumferential part 21 after the material change can be set less than the distance D1' between the surfaces of the inner circumferential part 21 in the case of a uniform change in the distances between the surfaces of the inner circumferential part 21 and the outer circumferential part 22, so that the distance between the surfaces of the outer circumferential part 22, if the distance between the surfaces of the inner circumferential part 21 has been increased after the material change, is greater than the distance between the surfaces of the outer circumferential part 22 after the material change.Since the outer circumferential part 22 of the impeller disk 9a is located further on the radially oriented outer side (the side of the combustion gas flow channel 31) than the inner circumferential part 21, the outer circumferential part 22 tends to be brought to a higher temperature than the inner circumferential part 21 due to the transfer of heat from the combustion gas 7; however, by ensuring that the distance between the surfaces of the outer circumferential part 22 becomes larger (thicker) after the material change, it is possible to improve the thermal resistance of the outer circumferential part 22 and to ensure the reliability of the turbine 3. • Step S4 The turbine 3 is designed while the shape of the impeller disk 9a determined in step S3 is reflected in the turbine impeller 102. In the present embodiment, the turbine impeller 102 is designed by adjusting the impeller disk 9a to the shape determined in step S3 and adjusting the spacer disk 10a and the impeller disk 12a to their shapes prior to the material change. The turbine 3 is then designed using the designed turbine impeller 102 and adjusting the components of the stationary body 101 (the casing 8, the outer circumferential end wall 18, the fixed blades 11b, the inner circumferential end wall 15a, the intermediate floor 14, and the like) to their shapes prior to the material change. • Step S5 The turbine 3 designed in step S4 is subjected to a non-stationary FEM analysis. In the present embodiment, "the non-stationary FEM analysis" is an analysis method for conceptually dividing the turbine into finite elements and for confirming, in an environment where the temperature can be changed depending on time and position, whether there is a part in the impeller disk 9a where, in the process of a temperature increase, a high load exceeding a setpoint or the like is generated. If the result of the non-stationary FEM analysis is "Yes", the control system proceeds from step S5 to step S6. In the present embodiment, the fact that the result of the non-stationary FEM analysis is "Yes" refers to the absence of a section in the impeller disk 9a in the non-stationary FEM analysis where a high load exceeding a setpoint is generated during the temperature rise from a first temperature to a second temperature at the time of turbine start-up. Conversely, the control system returns to step S2 if the result of the non-stationary FEM analysis is "No".In the present embodiment, the fact that the result of the non-stationary FEM analysis for the impeller disc 9a is "No" refers to the presence of a section in the non-stationary FEM analysis where, during the temperature rise from the first temperature to the second temperature at the time of turbine start-up, a high load exceeding a setpoint is generated. If the result of the non-stationary FEM analysis in step S2 is "No", the distance between the surfaces determined at the previous time is adjusted (e.g., the distances between the surfaces of the inner circumferential part 21 and the outer circumferential part 22 are changed based on the result of the non-stationary FEM analysis) to recalculate the distance between the surfaces.Subsequently, in step S3 the shape of the impeller disc 9a is determined, in step S4 the turbine 3 is redesigned, and in step S5 the non-stationary FEM analysis is performed. Then steps S2 to S5 are repeated until the result of the non-stationary FEM analysis is "Yes". • Step S6 A turbine is manufactured based on the design in step S4. In the present embodiment, the impeller disk 9a is manufactured from the material after the material modification in the shape determined in step S3, while the components of the impeller disk 10a, the impeller blade 12a, and the stationary body 101 are manufactured from the material before the material modification, thereby producing the turbine 3. In the case of manufacturing (remodeling) a turbine based on an existing turbine, for example, the impeller disk 9a is manufactured from the material after the material modification in the shape determined in step S3, while the components of the spacer disk 10a, the impeller blade 12a, and the stationary body 101 are provided by substituting those of an existing turbine, thereby producing the turbine 3. (Beneficial effects) (1) In the present embodiment, the turbine 3 is designed by determining the temperature rise time ratio and by determining the distances between the surfaces after a material change based on the determined temperature rise time ratio. By determining the distances between the surfaces after the material change based on the temperature rise time ratio, it is possible to easily determine the shape of the impeller disk 9a such that the temperature rise time of the impeller disk 9a before and after the material change, or the ease with which the impeller disk 9a heats up, is a desired value determined by the temperature rise time ratio. Thus, it can be ensured that the impeller disk 9a is a thermodynamically suitable design from the outset after the material change, so that the result of the non-stationary FEM analysis tends to be "yes".As a result, the number of repetitions of the non-stationary FEM analysis during the design of a turbine 3 accompanying a material change can be reduced, and consequently, the time required for the design and manufacture of the turbine 3 can be shortened. In particular, in the present embodiment, the ease with which the impeller disk 9a heats up can be the same before and after the material change, since the temperature rise time ratio is set to 1.0, and the time required for the design and manufacture of the turbine 3 can be further reduced. (2) In the present embodiment, the shape of the impeller disk 9a after the material change is determined by changing the distances between the surfaces of the inner circumferential part 21 and the outer circumferential part 22 of the impeller disk 9a. Since the spaces 28 and 29 are formed between the inner circumferential part 21 and the outer circumferential part 22 of the impeller disk 9a and the spacer disk 10a, it is unnecessary to change the shape of the spacer disk 10a when changing the distances between the surfaces of the inner circumferential part 21 and the outer circumferential part 22. Thus, the work required for the design and manufacture of the turbine 3 in conjunction with the material change can be simplified. Furthermore, the shape of the spacer disk 10a can be used before the material change, and therefore an increase in the time required for the design and manufacture of the turbine 3 in conjunction with a material change can be avoided. Example 1 Fig. 5 is a table that shows, by way of example, the ratios of elements before and after a change in the material of the impeller disc. In the present embodiment, an example is shown in which the material of the impeller disc 9a is changed from a high-chromium steel (steel with high Cr content) to a nickel-based alloy (alloy on a Ni base). As shown in Fig. 5, in the present embodiment the ratio cr of specific heats, which is the ratio of the specific heat after the material change to the specific heat before the material change of the impeller disc 9a, is 0.8, the thermal conductivity ratio kr, which is the ratio of the thermal conductivity after the material change to the thermal conductivity before the material change of the impeller disc 9a, is 0.6, and the temperature rise time ratio tr is 1.0. Furthermore, similar to the first embodiment, for the sake of convenience, the cross-sectional area of ​​the impeller disc 9a is treated as unchanged before and after the material change (the cross-sectional area ratio Sr, which is the ratio of the cross-sectional area after the material change to the cross-sectional area before the material change, is 1.0), and the weight ratio mr and the ratio Ir of the distances between the surfaces of the impeller disc 9a are treated as equal. According to the conditions mentioned above, the ratio Lr of the distances between the surfaces from formula (7) is 0.87. Thus, after the material change in the present embodiment, the shape of the impeller disk is determined such that the ratio Lr of the distances between the surfaces is 0.87, and the turbine is designed and manufactured, thereby obtaining the advantageous effects mentioned above. <Zweite Ausführungsform> The present embodiment differs from the first embodiment in that the temperature rise time ratio is determined based on the gap between the turbine impeller and the housing. The other aspects are similar to those of the first embodiment. Generally, a gap is provided between the turbine runner (a rotating body) and the casing (a stationary body) to ensure the runner's rotation is not impeded. To guarantee a sufficient flow of combustion gas to drive the runner, it is desirable to reduce this gap. However, when the turbine starts, the runner is heated by high-temperature combustion gas and expands radially due to thermal expansion. If this expansion exceeds the aforementioned gap, the runner and casing can come into contact. Therefore, when designing and manufacturing a turbine, especially when changing the runner material, it is advisable to consider the gap between the runner and casing. Fig. 6 is a flowchart showing the design and manufacturing procedure of a turbine according to the present embodiment. • Step S200 The gap ratio is determined, which is a desired ratio of the gap after the material change to the gap before the material change of the impeller disk 9a at the time of turbine start-up. In the present embodiment, "the gap" refers to the opposite distance in the radial direction between the turbine impeller 102 (the impeller disk 9a) and the inner circumferential wall of the housing 8. In the present embodiment, the space D is defined as formula (8): where α is the linear expansion coefficient of the impeller disk 9a. Although the gap ratio in the present embodiment is 1.0, the gap ratio can be in the range of 0.9 to 1.1. • Step S201 The temperature rise time ratio is determined based on the gap ratio determined in step S200. The procedure for determining the temperature rise time ratio based on the gap ratio is described below. From formula (8) the spaces D1 and D2 before and after material changes can be expressed as formulas (9) and (10). Since the gap ratio in the present embodiment is 1.0 (D2 / D1= 1.0), formula (11) is obtained from formulas (9) and (10). The temperature rise time ratio (t2 / t1) can be determined from formula (11). • Steps S202 to S206 Steps S202 to S206 are similar to steps S2 to S6 in the first embodiment. More precisely, in step S202, the distance between the surfaces after the material change is determined using the temperature rise-time ratio determined in step S201. In step S203, the shape of the impeller disk 9a after the material change is determined based on the distance between the surfaces determined in step S202. In step S204, the turbine 3 is designed, reflecting the shape of the impeller disk 9a determined in step S203 on the turbine impeller. In step S205, the turbine 3 designed in step S204 is subjected to a non-stationary FEM analysis. If the result of the non-stationary FEM analysis is "Yes," the control system proceeds from step S205 to step S206. Conversely, the control system returns to step S202 if the result of the non-stationary FEM analysis is "No."In step S206, the turbine is manufactured based on the design in step S204. (Beneficial effects) In the present embodiment, the turbine 3 is designed by determining the gap ratio and, based on this gap ratio, determining the temperature rise time ratio. Furthermore, in this embodiment, the distance between the surfaces after the material change is determined based on the temperature rise time ratio, so that the shape of the impeller disk 9a can be easily determined such that the temperature rise time of the impeller disk 9a before and after the material change, or the ease with which the impeller disk 9a heats up, is achieved at a desired value determined by the temperature rise time ratio, thereby obtaining effects similar to those in the first embodiment.Furthermore, in the present embodiment, the shape of the impeller disk 9a can be easily determined such that the gap before and after the material change becomes a specific value, determined by the gap ratio, since the temperature rise time ratio is based on the gap ratio. Thus, contact between the turbine impeller 102 and the housing 8 after the material change can be avoided in the turbine 3, and the reliability of the turbine 3 can be ensured. In particular, the gap before and after the material change can be made the same in the present embodiment, since the gap ratio is 1.0, and the reliability of the turbine 3 can be further ensured. Example 2 Fig. 7 is a table showing, by way of example, the ratios of elements before and after a change in the material of the impeller disc. The present example illustrates the case where the material of the impeller disc 9a is changed from a steel with a high chromium content to a nickel-based alloy. As shown in Fig. 7, in the present example the ratio αr of the linear expansion coefficients, which is the ratio of the linear expansion coefficient after the material change to the linear expansion coefficient before the material change, is 1.2, and the gap ratio Dr is 1.0. Thus, the temperature rise time ratio from formula (8) is 0.8. In the present example, the ratio of specific heats cr is 0.8 and the thermal conductivity ratio kr is 0.6. Furthermore, for the sake of convenience, the cross-sectional area of ​​the impeller disc 9a is treated as unchanged before and after the material change, and the weight ratio mr and the ratio Lr of the distances between the surfaces of the impeller disc 9a are treated as equal. Under the conditions mentioned above, the ratio Lr of the distances between the surfaces from formula (7) is 0.79. Accordingly, in the present example, by determining the shape of the impeller disk after the material change, it is determined that the ratio Lr of the distances between the surfaces is 0.79, and the effects mentioned above can be obtained in the design and manufacture of the turbine. DESCRIPTION OF REFERENCE MARK 3 Turbine 9a, 9b Impeller disc 21 Inner circumferential part 22 Outer circumferential part 23 Stacking butt part

Claims

A turbine design method in connection with a material change of a runner disk (9a, 9b) of a turbine runner (102), characterized in that the time required for a temperature of the runner disk (9a, 9b) at the time of starting a turbine (3) to reach a second temperature from a first temperature is the temperature rise time, and that the distance between the surfaces on an inlet side and an outlet side of the runner disk (9a, 9b) is a distance between the surfaces, wherein the turbine design method comprises: determining a temperature rise time ratio, which is a desired ratio of the temperature rise time after the material change to the temperature rise time before the material change; determining the distance between the surfaces after the material change based on the determined temperature rise time ratio;Determining a shape of the impeller disk (9a, 9b) after the material change on the basis of the determined distance between the surfaces; and designing the turbine (3) while the determined shape of the impeller disk (9a, 9b) is reflected on the turbine impeller (102), and wherein the temperature rise time is defined by the following formula: t = c ⋅ m ⋅ L / ( k ⋅ S ) ,; where “c” is a specific heat of the impeller disc (9a, 9b), “m” is a weight of the impeller disc (9a, 9b), “L” is a distance between the surfaces, “k” is a thermal conductivity of the impeller disc (9a, 9b) and “S” is a cross-sectional area of ​​an annular section with a central axis of the impeller disc (9a, 9b) as a center point. Turbine design method according to claim 1, wherein the impeller disk (9a, 9b) comprises an inner circumferential part (21) which is a part on a radially oriented inner side of the turbine impeller (102), an outer circumferential part (22) which is a part on a radially oriented outer side of the turbine impeller (102), and a stack butt part (23) which is located between the inner circumferential part (21) and the outer circumferential part (22), and the shape of the impeller disk (9a, 9b) is determined after the material change by changing the distances between the surfaces of the inner circumferential part (21) and the outer circumferential part (22). Turbine design method according to claim 1, wherein the distances between the surfaces of the inner circumferential part (21) and the outer circumferential part are changed in such a way that the distance between the surfaces of the outer circumferential part (22) after the material change is longer than the distance between the surfaces when the surfaces on the inlet side and on the outlet side of the inner circumferential part (21) are extended to the outer circumferential part (22) after the material change. Turbine design method according to claim 1, wherein the temperature rise time ratio is 1.

0. Turbine design method according to claim 1, wherein, if an opposing distance in a radial direction between the turbine impeller (102) and an inner circumferential wall of a housing accommodating the turbine impeller (102) is a space of the impeller disk (9a, 9b), the temperature rise time ratio is determined on the basis of a space ratio which is a desired ratio of the space after the material change to the space of the impeller disk (9a, 9b) before the material change when the temperature of the impeller disk (9a, 9b) reaches the second temperature. Turbine design method according to claim 5, wherein the gap is defined by the following formula: D = α ⋅ t , where “α” is a linear expansion coefficient of the impeller disk (9a, 9b) and “t” is a temperature rise time of the impeller disk (9a, 9b). Turbine design method according to claim 5, wherein the gap ratio is 1.

0. Turbine manufacturing method, wherein a turbine (3) is manufactured by designing the turbine by the turbine design method according to claim 1, wherein a rotor disk (9a, 9b) is manufactured from a material after a material change.

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