A ring segment for gas turbine engine and computer-implemented method of designing ring segment

Abstract

A ring segment (150) for a gas turbine engine includes a base body (152) having a first inner surface (154) that may be subjected to a hot working medium (156) and a second outer surface (158) disposed opposite the first surface (154), the first surface (154) extends in an axial direction (X) from a first axial end (160) to a second axial end (162) and in a circumferential direction (T) from a first lateral end (164) to a second lateral end (166), and wherein the first surface (154) comprises a nominal region (168) extending along the two axial ends (160, 162) and the two lateral ends (164, 166). In order to reduce the average radial clearance between the airfoil tip and the first surface and to increase the efficiency of the gas turbine engine, it is proposed that the nominal region completely delimits a central region (170) of the first surface (154), the central region comprising a depression (172).

Description

Technical Field

[0001] The invention relates to a segment for a gas turbine, a method for operating a gas turbine and a computer-implemented method for designing and manufacturing such a segment according to the preamble of claim 1 . Background Art

[0002] Conventional ring segments, also known as blade outer air seals, are typically arranged within gas turbines to delimit the hot gas path of the turbine section. These ring segments are arranged circumferentially, such that all circumferential segments form an annular arrangement. Within this annular arrangement and during operation of the gas turbine, the tips of rotor blades mounted on the turbine rotor move along the hot gas path delimited by the ring segments.

[0003] The ring segments are typically carried by a vane carrier, which has a circular shape in a cross-section perpendicular to the gas turbine's axis of rotation. For stationary gas turbines, the vane carrier is divided into a lower and upper half. These contain circumferentially extending grooves into which the ring segments can be sequentially slid into their designated positions to form the aforementioned outer boundary of the hot gas path. To provide a concentric outer hot gas path boundary, the ring segments must be rigidly held in place by the vane carrier. This arrangement is known from EP 3 118 419 A1.

[0004] Furthermore, US Pat. No. 4,784,569 A discloses a shroud ring having a modified hot gas surface. This reverse curvature or concave surface allows the shroud ring to deform to a certain extent at high temperatures without any significant change in the original design clearance between the ring and the turbine blades, and without the risk of frictional contact between the turbine blades and the ring.

[0005] During gas turbine operation, the ring segments are exposed to the hot gas. The thermal effects of the hot gas induce internal stresses and tensions, ultimately causing the ring segments to elastically expand. This expansion creates uneven and unfavorable tip clearances for the rotor blades, extending along the boundaries of the hot gas path.

[0006] In the past, tip clearances had to be large enough to account for thermally driven displacement of the ring segments relative to the blade tip. Consequently, the tip-to-ring segment clearance was larger than desired because, as the clearance size increased, the fraction of hot gas that bypassed the airfoil without converting its thermal energy into mechanical energy increased. This bypass effect, also known as tip loss, reduced gas turbine efficiency.

[0007] Accordingly, a first object of the present invention is to provide a ring segment that, when assembled and operated in a gas turbine, reduces blade tip losses on rotor blades. A second object of the present invention is to provide a method of operating a gas turbine more efficiently, and a third object of the present invention is to provide a computer-implemented method of designing and / or manufacturing a ring segment that contributes to improved gas turbine performance. Summary of the Invention

[0008] In order to solve the above-mentioned problem, the ring segment according to the invention has the features of claim 1 .

[0009] The problem with respect to the operating method is solved by the method according to the features of claim 9 , and the problem with respect to the method for designing and / or producing the ring segment is solved by the features of claim 10 .

[0010] The invention is based on the idea of ​​reducing the average radial gap between the tip of the rotor blade and the oppositely arranged surface of the ring segment in the hot operating state.

[0011] Specifically, the present invention proposes a ring segment for a gas turbine, comprising a base body having a first surface which, when assembled in the gas turbine, is subjected to a working medium during operation of the gas turbine, and a second surface arranged opposite to the first surface, wherein, when the ring segment is assembled in the gas turbine relative to the rotation axis of the rotor of the gas turbine, the first surface and the second surface of the ring segment extend in the axial direction from the first axial end to the second axial end and in the circumferential direction from the first lateral end to the second lateral end, and wherein the first surface includes a nominal area which is curved along the two axial ends, the two axial ends being curved in the circumferential direction, and at a constant radius relative to the rotation axis of the gas turbine, and wherein the nominal area at least partially defines a central area of ​​the first surface, which includes a depression.

[0012] In other words: in the center of the first surface, a depression is arranged as a deviation from the nominal area of ​​the first surface, the nominal area surrounding the depression.

[0013] A "nominal area" or "nominal plane" is defined as an arcuate segment of the envelope of a right truncated cone or cylinder. A right truncated cone is also known as a frustum of a cone, where the envelope of the cone represents the outer flow path boundary with a non-zero opening angle. Conventional ring segments have a first surface that perfectly matches the arcuate segment or right truncated cone, resulting in a uniform radial clearance distribution for cold operating conditions when the corresponding angled airfoil tip of the rotor blade passes by during rotor rotation.

[0014] The radial distance between the hot gas surface of a ring segment and the tip of a rotor blade, or more precisely, the radial distance between the tip of the rotor blade's airfoil, is hereinafter referred to as the radial clearance and also referred to as the tip clearance. Because each airfoil and its tip are aerodynamically curved and extend in both the axial and circumferential directions, there is not just one radial clearance for a single blade. Instead, there are an infinite number of radial clearances for each airfoil tip, where the radial clearance for each considered position depends on the considered position, the local shape of the airfoil tip, the local circumferential position of the rotor blade during rotation about the gas turbine's axis of rotation, and the radial position of the first surface relative to the considered position. This spatially resolved dependence of the radial clearance can generally be understood as a "radial clearance distribution" and is associated with its "variance" and "mean radial clearance" values. The "mean radial clearance" is thus the average of a plurality or an indefinite number of distances between the first surface of a ring segment and the tip of the rotor blade, where this distance is determined or calculated, for example, by simulation, at different axial and / or circumferential positions of the relevant ring segment.

[0015] The terms "cold" and "hot" should be understood as "cold" referring to room temperature or ambient temperature, and "hot" referring to a temperature that has a certain level that causes relevant thermal growth and expansion, such as temperatures of several hundred degrees Celsius or higher, up to a temperature level before the ring segment is damaged.

[0016] The "opening angle" of the outer flow channel boundary is determined relative to the rotation axis of the gas turbine. If the opening angle is zero, then the outer flow channel boundary is parallel to the rotation axis in cross section.

[0017] Of course, the shape according to the invention of the first surface does not take into account manufacturing tolerances at all.

[0018] The invention is based on the knowledge that conventional segment segments are generally subject to thermally driven expansion. In particular, conventional segment segments are assembled into the stationary blade carrier under cold as well as hot conditions with the aid of a plurality of hooks, which are located at the upstream and downstream ends relative to the flow direction of the working medium and are located on concentric circles. As a result, expansion of the first surface is hardly possible in these positions. The base body therefore at least partially compensates for the thermal load by thermal expansion between the hooks, so that the first surface bends into the flow channel of the working medium. This thermal expansion ultimately gives the first surface an unsuitable shape, with the narrowest radial gap only in a small area at the point of the largest protrusion. The size of the radial gap depends on the position considered and has a large variance compared to the cold operating state. In other words: in the hot operating state, the radial gaps become very inhomogeneous and their sizes differ significantly.

[0019] Now, the inventors propose to take into account and compensate for the thermal expansion of the segment in advance when designing the first surface. Therefore, the new first surface must have a structure in cold operation that is opposite to the first surface of the conventional segment in the hot operation state. That is, instead of having a convex first surface in the hot operation state, the reverse design of the segment of the present invention has a depression at the same position as the convex portion in the cold operation state. The thermal shock of the segment having a depression in its first surface in the cold operation state causes the segment to have a very flat first surface in the hot operation state, which, in theory, in the best case, is the same as the nominal area. The shape and form of the depression, such as its length, width and depth, depend on the overall design and size of the segment, such as its size, the aspect ratio of its length and width, the thickness of the substrate, the thermal load, etc.

[0020] The nominal area of ​​the ring segment also completely defines a depression in the central region of the first surface, extending along both lateral ends. Because the stiffness of the base body in the middle, between the two lateral ends, is less than that at the lateral ends themselves, it is advantageous to have a nominal area extending from the first axial end to the second axial end along each lateral end. Thus, the depression in the first surface is completely surrounded by an area of ​​the first surface that is also the same as the nominal area.

[0021] This measure results in a more uniform spatially resolved radial clearance in hot operation, with a smaller average radial clearance and smaller variance compared to the prior art. In this respect, the tip clearance is optimized. A more uniform radial clearance distribution reduces blade tip losses during gas turbine operation, which contributes to improved gas turbine efficiency. In other words, the use of the ring segment according to the present invention results in a smaller average radial clearance in hot operation than the average radial clearance of the prior art ring segment during hot operation.

[0022] The advantages described for the ring segments apply analogously to the method for operating a gas turbine and the method for designing and / or producing a ring segment.

[0023] In order to solve the problem relating to a method for operating a gas turbine, the method according to the invention has the features of claim 8 .

[0024] In particular, the method of operating a gas turbine comprising a ring segment according to the invention comprises the step of heating the ring segment in order to reduce the average radial clearance between the airfoil tip and the central region in a hot operating state compared to the average radial clearance between the airfoil tip and the central region in a cold operating state, without, of course, taking into account the effects of thermal shock and centrifugal forces on the rotor blades.

[0025] In order to solve the problem relating to a method for designing and / or manufacturing a ring segment, a computer-implemented method according to the invention has the features of claim 10 .

[0026] A computer-implemented method for designing and / or manufacturing a ring segment for a gas turbine, wherein the ring segment includes a base having a first surface that can be subjected to a working medium of the gas turbine and a second surface opposite the first surface, wherein fixing elements are located at different axial positions on the second surface, wherein a plurality of ring segments, when assembled in the gas turbine, form a portion of an annular outer flow channel boundary for the working medium of the gas turbine, the portion of the annular outer flow channel boundary being positioned opposite a row of airfoil tips of rotor blades, the method comprising the following steps:

[0027] - determining or providing a first surface by taking into account the axial position of the first surface in the flow channel, the radial distance of the first surface to the axis of rotation of the gas turbine and / or the opening angle of the annular outer flow channel boundary, the first surface being completely realized as a nominal region for the cold operating state of the gas turbine,

[0028] - determining or providing a segment operating temperature distribution for a thermal operating state, in particular a steady-state operating state, of the gas turbine,

[0029] - determining a thermal operating profile of the first surface based on the operating temperature distribution and preferably relative to a nominal plane by taking into account the thermal expansion of the ring segments, in particular the thermal expansion of a plurality of locations of the first surface, and

[0030] - Modifying the first surface in a cold operating state from a fully nominal area to a first surface including a depressed central area to reduce the average radial clearance compared to the average radial clearance based on a hot operating profile of the first surface.

[0031] The term "taking into account" should be understood as using the features listed after the term to determine and / or decide the corresponding feature of the sentence.

[0032] Further preferred embodiments are mentioned in the dependent claims, wherein their features can readily be combined in any manner.

[0033] Preferably, the design method is a computer-implemented method and is thus performed by a computer.The invention therefore also comprises a data processing device having means for performing the steps of the design method.

[0034] Furthermore, the present invention comprises a computer program product comprising instructions which, when the program is executed by a computer, cause the computer to perform the steps of the design method.

[0035] According to a first preferred embodiment of the ring segment, the base body has a width and a length, the width being determined as the straight-line distance between the two axial ends and the length being determined as the curvilinear distance between the two lateral ends, and wherein the aspect ratio of the width to the length is in the range between 0.15 and 4, in particular in the range between 0.2 and 0.5

[0036] Typically, heavy-duty gas turbines include ring segments with an aspect ratio between 0.15 and 4, with the ring segments being used in all turbine stages. Because the radial clearance dimensions, relative to the span dimensions of the associated rotor blade airfoils, are larger for the leading turbine stages than for the trailing stages, the gain in turbine efficiency due to reduced blade tip losses is greater for the leading stages than for the trailing stages. Therefore, the use of the ring segments according to the present invention is most beneficial in the leading stages of turbines, where the ring segment dimensions typically have an aspect ratio between 0.2 and 0.5.

[0037] According to another preferred embodiment of the present invention, the depression has a maximum depth that is less than 25% of the central thickness of the base body, or less than 1.5 mm relative to the nominal area. Simulations and FEM calculations have shown that the best results in reducing the average radial gap are achieved when the maximum depth of the depression is approximately the aforementioned dimensions.

[0038] In order to avoid aerodynamic losses in the working medium due to steps in the first surface and to take into account different local expansions and thermal growth of the base body, according to a further preferred embodiment it is advantageous if the central region comprises a transition between the nominal area and the maximum depth of the depression.

[0039] According to another preferred embodiment, the area of ​​maximum depth has a racetrack profile.This design is particularly advantageous for ring segments whose aspect ratio of width to length differs significantly from 1.

[0040] Preferably, the depression has a maximum depth compared to the nominal area, the maximum depth of the depression being located axially 40% to 60% of the width from the first axial end and circumferentially 25% to 75% of the length from the first circumferential end.

[0041] In another preferred embodiment of the ring segment according to the present invention, the first surface comprises a coating system having one or more coating layers, preferably metallic and / or ceramic coating layers, and / or the substrate comprises channels. Thus, the present invention is not only applicable to uncoated and / or uncooled ring segments. The present invention can also be advantageously used with coated and / or cooled ring segments.

[0042] In another preferred embodiment of the method for designing and / or manufacturing a ring segment, after the modified first area has been determined, the radial length of the ring segment's securing elements (particularly implemented as hooks or rails) is adjusted. Because the bulging effect of the base of a conventional ring segment is no longer taken into account when specifying the radial clearance, increasing the radial length of the hooks or rails shifts the nominal area of ​​the first surface toward the tip of the rotor blade. This measure also helps reduce the average radial clearance, thereby improving the efficiency of the gas turbine.

[0043] Preferably, after the ring segments are designed, they are manufactured, more specifically by casting and / or machining or by additive manufacturing processes, particularly laser-powder bed fusion (LPBF). The latter manufacturing method is best suited for manufacturing components with complex, low-lying shapes and other shapes described herein. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Further advantages and features of the present invention will become apparent from the following description based on the accompanying drawings. The accompanying drawings show:

[0045] Figure 1 A gas turbine is schematically shown,

[0046] Figure 2 shows a perspective view of a conventional ring segment,

[0047] Figure 3 Shown through Figure 2 The cross section of a conventional ring segment,

[0048] Figure 4 shows a perspective view of an exemplary embodiment of a ring segment according to the invention,

[0049] Figure 5 Shown through Figure 4 A cross section of an exemplary embodiment of a ring segment,

[0050] Figure 6 shows a schematic cross section through a coated, cooled ring segment, and

[0051] Figure 7 A flow chart showing the design and manufacturing stages. DETAILED DESCRIPTION

[0052] The embodiments according to the present invention are described below with reference to the accompanying drawings. In all the drawings, the same features are marked with the same reference numerals.

[0053] Figure 1A gas turbine 100 is schematically shown, comprising a compressor 110, a combustion chamber 120, and a turbine unit 130. According to this exemplary embodiment, a generator 150 for generating electricity is coupled to the gas turbine's rotor 140. During operation, ambient air AA is drawn into the axial compressor 110. The ambient air is conveyed through the compressor, being compressed along the way. The compressed air VL is then mixed with fuel F and combusted in the combustion chamber 120, forming hot gas HG. The hot gas HG expands in the turbine unit 130 and exits the turbine unit as exhaust gas RG. In the turbine unit 130, the expansion of the hot gas HG generates torque on the rotor 140, which in turn drives the compressor 110 and the generator 142.

[0054] Figure 2 A perspective view of a conventional ring segment 149 for cold operation is shown. The ring segment 149 includes a generally rectangular base 152. When the ring segment 149 is assembled in the gas turbine 100, its base 152 extends from a first axial end 160 to a second axial end 162 in the axial direction A. The two axial ends 160, 162 can also be understood as the ring segment 149 relative to the flow direction of the working medium 165 (e.g., Figure 3 and Figure 5 The base 152 has an upstream leading edge and a downstream leading edge (shown in FIG. ). Furthermore, the base 152 extends in a circumferential direction T from a first lateral end 164 and a second lateral end 166. Both the axial direction A and the circumferential direction T are relative to the rotation axis 188 of the gas turbine 100, about which the rotor 140 rotates during operation. Therefore, the two edges of the base 152 extending in the circumferential direction T between the two lateral ends 164, 166 are arc-shaped. The other two edges of the base 152 extending in the axial direction A from one axial end 160, 162 to the other axial end 162, 160 are straight.

[0055] Typically, the conventional ring segment 149 includes a first surface 151 that faces and delimits a flow channel (not shown) of the gas turbine. During operation of the gas turbine 100, the first surface 154 is acted upon by a working medium 156. The base 152 includes a second surface 158 that is opposite to the first surface 151. First, in the radial direction R( Figure 3 ) extending from the second surface are two rows of hooks as fixing elements 194. These hooks can engage in correspondingly shaped grooves of the stationary blade carrier (not shown).

[0056] Ignoring manufacturing tolerances, if the outer boundary of the flow channel increases or decreases along its axial direction, first surface 151 is the same as a segment of a right truncated cone. However, if ring segment 149 is used in a flow channel with a zero-degree opening angle at the outer boundary, the first surface has a cylindrical shape rather than a right truncated cone shape.

[0057] Figure 3 The cross section III-III shows Figure 2 The conventional ring segment 149 and the airfoil tip 190 of the rotor blade 192 are positioned opposite the first surface 154. The airfoil tip 190 is angled accordingly with respect to the opening angle of the outer flow channel boundary, i.e., the airfoil tip 190 is parallel to the outer flow channel boundary. Figure 3 The solid line shows the shape of the ring segment 149 in the cold operating state, while the dashed lines 157 , 159 show the hot operating profiles of the first and second surfaces 151 , 158 as a result of the thermal growth and expansion that occurs during the hot operating state.

[0058] After the gas turbine has been cold started, the cold operating profile of the base body 152 changes to a convex shape, such as Figure 4 157 and 159. In the hot operating state, the second surface 158 includes depressions, while the first surface 151 includes convex portions or peaks that protrude into the flow channel. An average radial gap 198 can be determined between the airfoil tip 190 and the first surface 151, and has a large variation due to its shape.

[0059] Figure 4 An exemplary embodiment of a ring segment 150 according to the present invention is shown in a perspective view. A characteristic feature of ring segment 150, namely a cold-running profile 159 devoid of any thermal growth and expansion, is described below. Unlike conventional ring segments 149, ring segment 150 according to the present invention includes a depression 172 in its first surface 154, located in a central region 170. Central region 170 of first surface 154 is at least partially defined by a nominal region 168 of first surface 154, which extends at least along circumferential direction T between the two lateral ends 164, 166 along first axial end 160 and second axial end 162. Central region 170 and nominal region 168 of first surface 154 merge into one another without any steps.

[0060] In the exemplary embodiment, the depression 172 is racetrack-shaped and includes a flat region 178 (maximum depth 174) of 1 mm. Figure 5 At each merging location, the transition portion 176 connects the region 178 of the maximum depth 174 to the nominal region 168 of the first surface 154 in the form of a ramp without any step.

[0061] The width W of the ring segment 150 is determined as the straight-line distance between the two axial ends 160, 162, and the length L is determined as the curvilinear distance between the two lateral ends 164, 166. In the exemplary embodiment, the width-to-length ratio W / L of the ring segment 150 is 0.3 and, in this regard, is within a range between 0.15 and 4.0, and more particularly, within a range between 0.2 and 0.5.

[0062] Figure 5 Shown Figure 4 1 and 2. An exemplary embodiment of a ring segment 150 in cross section VV and an airfoil tip 190 of a rotor blade 192 is shown, which is located opposite the first surface 154. The airfoil tip 190 is angled accordingly with respect to the opening angle of the outer flow channel boundary, i.e., the airfoil tip 190 is parallel to the outer flow channel boundary. Figure 5 The solid line shows the shape of the ring segment 150 in the cold operating state, while the dashed lines 155 , 159 show the contours of the first surface 154 and the second surface 158 as they change due to thermal growth and expansion in the hot operating state.

[0063] Due to the depressed shape of the first surface 154 of the ring segment 150 in the cold operating state (i.e., at room temperature), the influence of heat in the range of several hundred degrees Celsius or up to 1200°C causes the base 152 to expand, which is shown by the dashed lines 155 and 159 as described above. As with the conventional ring segment 149, the cold, straight second surface 158 of the ring segment 150 becomes a depression when heated. However, when the ring segment 150 is subjected to heat and thermal loads, the first surface 154 including the depression 172 deforms into a shape that is significantly flatter than in the cold operating state. When perfectly simulated, calculated, manufactured, and depending on the actual thermal load, the first surface 154 may change its shape to a completely flat thermal profile 155.

[0064] When first surface 154 is in new shape 155 in a hot operating state, average radial clearance 200 is smaller than average radial clearance 198 of conventional ring segment 149. This results in reduced blade tip losses in working medium 156 and improved efficiency of gas turbine 100.

[0065] These thermal characteristics of the ring segment 150 allow gas turbine designers to reduce the cold radial clearance between the airfoil tip 190 and the ring segment 150. This is most easily achieved by increasing the radial length of the securing elements 194 (e.g., hooks) disposed on the second surface 158 of the ring segment 150. This measure also helps to further reduce blade tip losses in the working medium 156.

[0066] Figure 6A schematic cross section through the base body 152 of a coated and cooled ring segment 150 is shown. Figure 6 The depressions and other features are omitted. Three cooling channels 186 are located within the interior of the base 152. Other cooling schemes, such as impingement cooling schemes, may be applied as an alternative or in addition to internal convection cooling.

[0067] In addition, or in lieu of cooling the ring segments, substrate 152 can serve as a base for a coating system 180, which in this example includes two coating layers, such as a metallic coating 182 and a ceramic coating 184. Other coating systems are also possible. In each case, the first surface 154 of the coated ring segment 150 must still include a central region 170 having a depression 172.

[0068] Figure 7 is a flow chart of a method for designing and manufacturing a ring segment according to the present invention. The method 300 for designing and / or manufacturing a ring segment, in particular a ring segment, according to the present invention comprises a plurality of steps.

[0069] In a first step 302 for the cold operating state of the gas turbine 100, the first surface 151 is determined to be identical to a nominal area as part of the annular outer flow channel boundary, taking into account the radial distance of the first surface 151 from the axis of rotation 188 of the gas turbine 100 and the opening angle of the annular outer flow channel boundary. The opening angle of the outer flow channel boundary is identical to the angle of the aforementioned truncated cone.

[0070] In a next step 304 , an operating temperature distribution of the ring segment 150 is determined for a thermal operating state (in particular a steady-state operating state) of the gas turbine 100 .

[0071] In a following step 306 , a thermal operating profile 157 of the first surface 151 is determined based on the operating temperature distribution and relative to the nominal area by considering the thermal growth of the ring segments (particularly the thermally induced expansion of the first surface) for a plurality of points of the first surface 151 .

[0072] In a final step 308, the first surface 151 in the cold operating state is modified from a fully nominal area to a shape that includes a depressed central area 170. This depressed central area of ​​the modified first surface 154 reduces the average radial clearance 200 between the first surface 154 and the airfoil tip 190 in the hot operating state as compared to the average radial clearance between the first surface 154 and the airfoil tip 190 in the cold operating state. Preferably, the first surface is designed so that its hot operating profile 155 matches the profile of a portion of a right frustum or cylinder to at least 90% or greater.

[0073] When specifying the radial clearance between the first surface and the airfoil tip 190 during the design phase of the gas turbine to prevent the airfoil 190 from contacting the substrate, the thermal growth of the ring segment, and in particular its substrate 152, must be considered. When using an abradable coating on the ring segment, not all contact is to be avoided, but rather contact that would damage the airfoil tip 190, the substrate, and / or the abradable coating more severely than intended.

[0074] Preferably, after the ring segment 150 has been designed and the radial length of the fixing element 194 has been adjusted in an optional or supplementary step 310 , the ring segment 150 can be manufactured in a final step 312 .

[0075] The manufacturing may be by casting and / or machining. Alternatively, the manufacturing step may include manufacturing by additive manufacturing, for example by selective laser-powder bed fusion (LPBF).

[0076] It should be noted that the term "comprising" does not exclude other elements or steps, and "a" or "an" does not exclude a plurality. In addition, elements described in conjunction with different embodiments may be combined. It should also be noted that the reference numerals in the claims should not be interpreted as limiting the scope of the claims. Although the present invention has been described in detail and by preferred embodiments, the present invention is not limited to the disclosed examples, and other variations may be derived therefrom by those skilled in the art without departing from the scope of the present invention.

Claims

1. A ring segment (150) for a gas turbine (100), The invention comprises a substrate (152) having a first surface (154) capable of withstanding a working medium (156) of the gas turbine (100) and a second surface (158) arranged opposite the first surface (154). in, When the ring segment (150) is assembled in the gas turbine (100) relative to the rotation axis (188) of the rotor (140) of the gas turbine (100), the first surface (158) of the ring segment (150) extends in the axial direction (X) from the first axial end (160) to the second axial end (162) and in the circumferential direction (T) from the first lateral end (164) to the second lateral end (166), and wherein the first surface (154) includes a nominal area (168) extending along two axial ends (160, 162) and curving at a constant radius along the circumferential direction (T) relative to the axis of rotation (188) of the gas turbine (100), wherein the nominal area (168) at least partially defines a central region (170) of the first surface (154), the central region including a depression (172), It is characterized in that The nominal area (168) completely defines the depression in the central area (170) of the first surface (154) by extending along both lateral ends (164, 166).

2. The ring segment (150) according to claim 1, in, The base (152) has a width (W) and a length (L), The width is determined as the straight line distance between the two axial ends, and The length is determined as the curvilinear distance between the two lateral ends (164, 166), and Therein, the aspect ratio of width to length (W / L) is in the range between 0.15 and 4, in particular in the range between 0.2 and 0.

5.

3. The ring segment (150) according to claim 1 or 2, in, The depression (172) has a maximum depth (174) that is less than 25% of the central thickness of the base (152), or less than 1.5 mm relative to the nominal area.

4. The ring segment (150) according to any one of the preceding claims, in, The central region (170) includes a transition portion (176) between the nominal region (168) and the maximum depth of the depression (172).

5. The ring segment (150) according to claim 4, in, The region of maximum depth (178) has a racetrack profile.

6. The ring segment (150) according to any one of claims 2 to 5, in, The depression (172) has a maximum depth relative to the nominal area, The maximum depth of the depression is - axially at a distance of 40% to 60% of said width (W) from said first axial end (160), and - circumferentially at a distance from said first circumferential end (164) of 25% to 75% of said length (L).

7. The ring segment (150) according to any one of the preceding claims, A coating system (180) is included on the first surface (154) and / or one or more cooling channels (186) are included in the substrate (152), the coating system having one or more coating layers (182, 184), preferably metallic coating layers and / or ceramic coating layers.

8. A gas turbine (100) comprising a plurality of ring segments (150) according to any one of the preceding claims, said ring segments being arranged to establish a portion of an annular outer flow channel boundary for a working medium (156) of said gas turbine (100), said portion of said annular outer flow channel boundary being positioned opposite a row of airfoil tips (190) of rotor blades (192).

9. A method for operating a gas turbine (100) according to claim 8, characterized in that Due to heating of the ring segment (150), the actual depth of the depression decreases, thereby reducing the average radial clearance (200) between the airfoil tip (190) and the first surface (154) in the hot operating state compared to the average radial clearance (198) between the airfoil tip (190) and the first surface (154) in the cold operating state.

10. A computer-implemented method (300) for designing and / or manufacturing a ring segment (150) for a gas turbine engine, in, The ring segment (150) includes a base having a first surface (154) capable of withstanding a working medium (156) of the gas turbine (100) and a second surface (158) opposite the first surface (154), wherein fixing elements (194) are located at different axial positions on the second surface. wherein a plurality of ring segments (150) form a portion of an annular outer flow channel boundary for a working medium (156) of the gas turbine (100) when assembled in the gas turbine (100), the portion of the annular outer flow channel boundary surrounding a row of airfoil tips (190) of rotor blades (192) and forming radial gaps therebetween, The method comprises the following steps: The first surface is determined or provided (302) by taking into account the axial position of the first surface in the flow channel, the radial distance of the first surface from the axis of rotation (188) of the gas turbine (100) and / or the opening angle of the annular outer flow channel boundary, the first surface being fully embodied as a nominal area for a cold operating state of the gas turbine (100), determining or providing (304) the segment operating temperature distribution for a thermal operating state, in particular a steady operating state, of the gas turbine (100), determining (306) a thermal operating profile of the first surface based on the operating temperature distribution and preferably relative to the nominal plane by taking into account thermal growth of the ring segments, in particular thermal expansion of a plurality of locations of the first surface, and The first surface in a cold operating state is modified (308) from a fully nominal area to a first surface (154) including a depressed central area (170) to reduce an average radial clearance compared to an average radial clearance based on a hot operating profile of the first surface.

11. The method (300) according to claim 10, in, After the modified first area has been determined, the radial length of the fixing element of the ring segment (150), in particular a hook or a rail, is adjusted (310).

12. The method (300) according to claim 10 or 11, in, After designing the ring segment (150), The ring segment (150), in particular the ring segment (150) according to any one of claims 1 to 6, is manufactured (312).

13. The method (300) according to claim 12, in, The ring segments (150) are manufactured by casting and / or machining, or by an additive manufacturing process, in particular by laser-powder bed fusion (LPBF).

14. A data processing device comprising means for performing the steps of the method (300) according to any one of claims 10 or 11.

15. A computer program product comprising instructions which, when the program is executed by a computer, cause the computer to perform the steps of the method (300) according to any one of claims 10 or 11.

16. A computer-readable storage medium comprising instructions which, when executed by a computer, cause the computer to perform the steps of the method (300) according to any one of claims 10 or 11.

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