Turbomachine and turbomachine rotor with free standing shrouded blades

Abstract

Disclosed herein is a turbomachine rotor comprising at least one annular array of shrouded blades (55) around a rotor axis. Each blade comprises an airfoil (55.1) having a leading edge, a trailing edge, a root, a tip, a concave pressure side and an opposite convex suction side, the pressure side and the suction side extending between the leading edge and the trailing edge. Each blade further comprises an inner platform (55.3), at the root of the airfoil, and an outer platform (55.4) at the tip of the airfoil. Each side edge (75) of the outer platform (55.4) of each blade is spaced apart from an opposite side edge (77) of an adjacent blade, such that in use a gap (G) separates the opposite side edges (75, 77) of adjacent blades and the opposite side edges are in a facing, non-contacting relationship to one another in any operating condition of the turbomachine.

Description

TURBOMACHINE AND TURBOMACHINE ROTOR WITH FREE STANDING SHROUDED BLADESDESCRIPTIONTECHNICAL FIELD

[0001] The present disclosure concerns turbomachines. Embodiments disclosed herein specifically refer to turbomachine rotors and power-generating turbomachines comprising said rotors.BACKGROUND ART

[0002] Power-generating turbomachines, such as turbines and expanders, include rotors having a plurality of annular arrays of rotor blades. Each annular array of rotor blades is positioned downstream of a corresponding annular array of stationary blades or nozzles. Each pair of annular arrays of stationary blades and respective annular array of rotor blades forms an expansion stage of the turbomachine. Process gas flows through sequentially arranged stages of the turbomachine and expands, such that enthalpy of the gas is converted into mechanical power which drives the rotor in rotation. Mechanical power generated by the expansion process is made available on the shaft of the turbine. The stationary blades and rotor blades of sequentially arranged annular arrays have a height which increases in a forward-to-aft direction, i.e., the height of the blades increases moving from the most upstream to the most downstream stage of the turbomachine, as the volume of the expanding process gas increases and requires a flow path with a increasing cross section.

[0003] In known turbomachines, the rotor blades of at least some of the more downstream turbomachine stages are shrouded. Each blade of an annular array has a shroud, or shroud section, at the tip thereof. In use, the shroud sections of the annularly arranged blades contact each other, thus forming a continuous annular shroud, which surrounds the entire annular array of rotor blades. The function of the annular shroud is two-fold.

[0004] On the one hand, the mutual contact between shroud sections increases the blade stiffness and reduces vibration of the blades during rotation. At the same timethe vibration frequency increases. An overall damping effect is obtained, which is beneficial from a mechanical viewpoint and increases the aeromechanics of the stage.

[0005] On the other hand, the continuous annular shroud has an important aerodynamic advantage. The shroud prevents the process gas from leaking above the rotor blades and around the blade tips, from the pressure side to the suction side of each blade. This significantly improves the aerodynamic efficiency of the expansion stage.

[0006] Shrouded blades are used in the more downstream stages of turbines, which include blades having a small chord compared to the blade height, resulting in a low blade stiffness. The stiffness of a blade is defined as the ratio between a momentum (Nm) applied to the tip of a blade and the relevant torsional deformation thereof, expressed in degrees. A low blade stiffness is mandatory for a shrouded turbine stage to operate correctly. Typically, the blades of shrouded turbine stages have a stiffness ranging between 12 and 20 Nm / deg.

[0007] Stiffer blades, typically the blades of the first, i.e., more upstream, stages of the turbine or expander, are typically unshrouded, since the high stiffness of the blades would lead to mechanical failure of the shroud during operation of the gas turbine or expander. This is particularly the case if the blades are mounted axially rather than tangentially.

[0008] While the greater torsional stiffness of the blades of the most upstream stages makes the use of shrouded blades superfluous with regard to the mechanical effect of blade stiffening, the favorable aerodynamic effect of shrouded blades would be beneficial also, and in particular, in the most upstream turbine or expander stages.

[0009] A novel blade design, which allows to achieve some of the aerodynamic advantages of shrouded blades in the most upstream stages of a power-generating turbomachine, would therefore be welcome in the art.SUMMARY

[0010] Disclosed herein is a turbomachine rotor comprising at least one annular array of shrouded blades around a rotor axis, wherein each shrouded blade comprises: an airfoil having a leading edge, a trailing edge, a root, a tip, a concave pressure side andan opposite convex suction side, the pressure side and the suction side extending between the leading edge and the trailing edge. Each blade further includes an inner platform, at the root of the airfoil and an outer platform at the tip of the airfoil. The outer platform has a leading edge, a trailing edge and two side edges extending between the leading edge and the trailing edge of the outer platform. Each side edge of the outer platform of each blade is spaced apart from an opposite side edge of an adjacent blade, such that, in use, a gap separates the opposite side edges of the outer platforms of adjacent blades; the opposite side edges are in a facing, non-contacting relationship to one another. The width of the gap is such that, when the turbomachine is in use, the outer platforms of adjacent blades do not touch each other even as a result of any movement due to blade vibration.

[0011] In embodiments disclosed herein, the blades are thus free-standing and without interaction between the outer platforms thereof. This implies that the blade arrangement is also free of damping elements or any other mechanical feature which may interact with the outer platforms of adjacent blades. When the turbomachine is in use, no mechanical force is exchanged between adjacent outer platforms of the annular array of rotor blades.

[0012] As used herein, “in use” means when the turbomachine, in which the rotor is rotatingly housed, rotates at a rated speed and temperature.

[0013] Disclosed herein is also a power-generating turbomachine comprising a casing, at least one array of stationary blades housed in the casing; and a turbomachine rotor as outlined above.

[0014] The outer platforms, i.e. the platforms arranged at the tip of the airfoils of the at least one annular array of blades, form a discontinuous shroud, wherein each outer platform remains separate from the adjacent outer platforms when the turbomachine is in use, i.e. at the rated temperature thereof. The platforms increase the efficiency of the rotor stage, without introducing the adverse effects of a continuous annular shroud.

[0015] Further features and embodiments of the rotor and of the turbomachine according to the present disclosure are described below and outlined in the attached claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Reference is now made briefly to the accompanying drawings, in which:Fig. l shows a sectional view of an expander, specifically an expander for an oxyfuel combustion cycle, according to an embodiment of the disclosure;Fig.2 is an axonometric view of a portion of an annular array of blades of the one of the most upstream expander stages;Fig.3 is a top axonometric view from the portion of the annular array of blades of Fig, 2;Fig.3 A is a schematic section of the flowpath according to a radial plane containing the rotation axis of the rotor, showing one blade and relevant outer platform and inner platform;Fig.4 is a side view of a rotor blade of Figs. 2 and 3; andFig.5 is a schematic cross-sectional view of an airfoil profile of a blade according to line V-V of Fig.4.DETAILED DESCRIPTION

[0017] To alleviate the above-outlined drawbacks and limitations of the current art, according to the present disclosure at least one or some of the most upstream stages of a power-generating turbomachine include an annular array of shrouded blades, wherein the blades have an outer platform at the tip of the respective airfoil. The outer platforms have each a leading edge and a trailing edge as well as two side edges extending between the leading edge and the trailing edge. The outer platforms of the rotor blades belonging to the same stage are designed such that each side edge of the outer platform of each blade is spaced apart from the adjacent side edge of an adjacent blade. The mutual distance between facing, i.e., opposite side edges of adjacent outer platforms is such that, in use, a gap or clearance separates the opposite side edges of adjacent blades.

[0018] The outer platforms prevent or limit leakages of process gas around the tip of the blades, from the pressure side towards the suction side of each blade, thus improving the aerodynamic efficiency of the expansion stage. Since adjacent outer platforms remain in a non-contact condition during operation, the drawbacks arising from the contact pressure between adjacent outer platforms, which prevent the use of shroudedblades in the most upstream stages, are avoided.

[0019] In the following description, reference is specifically made to an exemplary expander, and more specifically to a supercritical carbon dioxide (sCCh) expander, as a possible exemplary embodiment of a power-generating turbomachine according to the present disclosure. Those skilled in the art of turbomachinery will nevertheless understand that novel features disclosed herein can be used with advantage also in other power-generating turbomachines, such as expanders using a fluid different than carbon dioxide, or using carbon dioxide in a non-supercritical state, or such as a gas turbine, or in a gas turbine engine, including a compressor section, a combustor, and a turbine section.

[0020] Turning now to the drawings, Fig.1 illustrates an exemplary power-generating turbomachine, where the use of the novel blade design according to the present disclosure may be particularly beneficial. As mentioned, the turbomachine of Fig.1 is an expander specifically designed for a supercritical carbon dioxide thermodynamic cycle, for example an expander for an oxy-fuel combustion cycle, such as an Allam cycle, or the like.

[0021] As will be clear to those skilled in the field of turbomachinery, the constructive details of the expander can vary, without thereby departing from the scope of the present disclosure. The novel design of the rotor blades of the first stages disclosed herein can be advantageously employed also in expanders of different configurations, and can be beneficial whenever it may be useful to reduce the process fluid leakage from the pressure side to the suction side of the airfoils of the blades, the stiffness whereof would make the use of standard shrouded blades unsuitable.

[0022] Novel features disclosed herein are particularly beneficial in expanders operating at high pressure, for instance where the highest available pressure in the thermodynamic cycle is at or above 50 barA, for instance equal to or higher than 300 barA.

[0023] In some embodiments, the expander 3 comprises an outer casing 41, which houses a combustor 7, for example a can-type combustor, an annular combustor, a canannular combustor (aka cannular combustor). The combustor can include a plurality of combustion chambers 7A arranged around an axis A-A of the expander 3.

[0024] In other embodiments, not shown, the combustor can be arranged outside the expander. In yet further embodiments, the expander may not include a combustor and can be used in a closed thermodynamic cycle, wherein heat is transferred to the process fluid through a heat exchanger, for instance.

[0025] In some embodiments the outer casing 41 includes a main body 41.1, referred to herein as a high-pressure casing, and a closure 41.2, referred to herein as a low- pressure exhaust casing.

[0026] The low-pressure exhaust casing 41.2 can be positioned at the discharge side, i.e. the aft side, of the expander 3, i.e. opposite the combustor 7, which is located at the forward side of the expander 3.

[0027] The high-pressure casing 41.1 and the low-pressure exhaust casing 41.2 can be connected to one another along a plane P which is orthogonal to a rotation axis A- A of a rotor 43 supported for rotation in the outer casing 41. The expander 3 is therefore a vertically-split expander. In other embodiments, the expander can be a horizontally split expander, including a casing which comprises two casing portions connected to one another along a plane containing the rotation axis A-A of the rotor 43.

[0028] In some embodiments, the low-pressure exhaust casing 41.2 forms a discharge volute or discharge plenum 41.3, through which exhausted flue gas is discharged from the expander 3.

[0029] Reference numbers 45, 47 indicate bearing arrangements, which rotatingly support the rotor 43. For instance, the bearing arrangement 45 on the side opposite the combustor 7, i.e., on the aft side, may include an axial or thrust bearing in combination with a radial bearing, or a bearing having an axial-radial bearing capability. The bearing arrangement 47 on the combustor side, i.e., on the forward side, may include a radial bearing. A reversed arrangement is also possible, with a bearing having axial load capability arranged on the combustor side. The bearing arrangements 45, 47 can be housed in bearing casings, not shown in detail.

[0030] In some embodiments, the rotor 43 is housed in an inner casing 51, stationar- ily housed in the outer casing 41.

[0031] In the embodiment of Fig.1 the expander 3 includes a plurality of stages. Just by way of example, the expander of Fig. 1 includes eight stages. Those skilled in the art will, however, understand that novel features disclosed herein can be beneficial also in expanders having a different number of stages, specifically one, two, or three stages, or higher.

[0032] Each stage comprises an annular row of stationary vanes or stationary blades 53, which are stationarily arranged in the outer casing 41. In the exemplary embodiment of Fig.1, the annular rows of stationary blades 53 are housed in the inner casings 51. Each expansion stage further includes a respective annular row of rotor blades 55, arranged downstream the respective annular row of stationary blades 53 along the expansion flow path, which extends from the combustor 7 to the discharge plenum 41.3 in a forward-to-aft direction through the plurality of expansion stages of the expander.

[0033] In some embodiments, the first, i.e., most upstream, annular row of stationary blades 53 can be arranged at the discharge end of the combustor 7 and forms an array of nozzles directing hot, high-pressure process fluid from the combustion chambers 7A of the combustor 7 to the first annular row of rotor blades. The first annular row of rotor blades 55 is arranged directly downstream of the first annular row of stationary blades 53. A last, i.e. most downstream, annular row of stationary blades 53 can be positioned near the discharge plenum 41.3, upstream of the last, i.e., most downstream, annular row of rotor blades 55.

[0034] The rotor blades 55 form part of the rotor 43, i.e., are connected thereto for co-rotation with the rotor shaft. In embodiments, each annular row of rotor blades 55 is mounted on a respective rotor disk 57.

[0035] The unit comprised of a rotor disk 57 and the respective annular row of rotor blades 55 is referred to herein also as rotor wheel.

[0036] The rotor blades 55 of each stage can be manufactured separately from the respective rotor disk 57 and mechanically mounted thereon, as schematically shown in Fig. 1. In other embodiments, the rotor blades 55 and the rotor disk 57 of each stage can be manufactured as a monolithic body, for instance by additive manufacturing. In yet further embodiments, the two design options can be combined. One or some stagesmay include respective monolithically manufactured components including rotor blades and disks, and one or some stages may include a rotor disk and separately manufactured rotor blades mechanically coupled to the rotor disk.

[0037] In some embodiments, the rotor disks 57 are stacked and connected to one another by tie rods. In the exemplary embodiment of Fig.1 the tie rods comprise a plurality of tie rods 61 arranged at a distance from the rotation axis A-A and a central tie rod 63, which is coaxial with the rotor 43.

[0038] In other embodiments, a different arrangement of tie rods can be provided, for instance only a central single tie rod coaxial to the rotor 43, or only a set of tie rods arranged around the axis A-A and at a radial distance therefrom. In yet further embodiments, tie rods at different distances from the rotation axis A-A can be provided.

[0039] In some embodiments, the rotor 43 further comprises a forward shaft portion 64 and an aft shaft portion 66. Each one of said forward shaft portion 64 and aft shaft portion 66 can include one or more sections, connected to one another, e.g. by means of tie rods, as shown by way of example for the forward shaft portion 64.

[0040] While in the embodiment shown in Fig 1 all rotor blades are mounted on respective rotor disks, one rotor disk being provided for each expander stage, and the rotor disks are stacked to one another between the forward shaft portion 64 and the aft shaft portion 66, in other embodiments, not shown, one or more annular rows of rotor blades can be mounted directly on (or manufactured as one piece with) the forward shaft portion and / or one or more annular rows of rotor blades can be mounted directly on (or manufactured as one piece with) the aft shaft portion. In some embodiments, the rotor may include a forward shaft portion and an aft shaft portion, connected to one another by tie rods or the like, wherein the rotor blades of all stages are mounted on (or manufactured as one piece with) either the forward shaft portion, or the aft shaft portion, or partly on the forward shaft portion and partly on the aft shaft portion, without rotor disks in-between.

[0041] In some embodiments, the combustor 7 extends around the forward shaft portion 65. In some embodiments, the discharge plenum 41.3 extends around the aft shaft portion 66.

[0042] In some embodiments, the forward shaft portion 4 and the aft shaft portion 66 are connected to the rotor disks 57 in a stacked configuration by the tie rod arrangement mentioned above.

[0043] In some embodiments, each rotor disk 57 comprises front teeth on both a forward-facing side and an aft-facing side thereof. The front teeth are provided for torsional engagement of adjacent components of the rotor 43. In the embodiment of Fig. 1, the forward-facing side of the most upstream rotor disk 57 engages the forward shaft portion 64 and the aft-facing side of the most downstream rotor disk 57 engages the aft shaft portion 66.

[0044] In some embodiments, a respective sealing disk 68, aka distancing disk or spacer, is positioned between each pair of consecutive (i.e., adjacent) rotor disks 57. If sealing disks 68 are interspersed between pairs of rotor disks 57, front teeth are provided on the opposite sides of each sealing disk 68, and consecutively arranged rotor disks 57 are torsionally connected to one another through the interposed sealing disk 68, Hirth joints being formed between opposing sides of each rotor disk 57 and respective sealing disk 68.

[0045] As used herein, “torsionally connected” means a connection adapted to transmit a torque between the torsionally connected components, such that the torsionally connected components rotate as a single body around the rotation axis A-A of the rotor.

[0046] While in Fig. 1, sealing disks or spacers 68 extend radially inwardly between adjacent rotor discs 57, in other embodiments the rotor disks 57 can be stacked in direct mutual contact with one another, and may be provided with front teeth of respective Hirth joints, which transmit torque directly from one rotor disk 57 to the adjacent rotor disk 57. In this case, annular seals can engage between adjacent rotor wheels near the feet of the respective rotor blades 55 in co-acting arrangement with the ends of the stationary blades 53 facing radially inwardly.

[0047] In both cases, the annular seals, or the sealing disks 68 provide a seal against the radially inwardly facing ends of the stationary blades, to prevent expanding process fluid from leaking from the expansion flow path defined by interspersed rows of stationary blades and rotor blades towards the rotor axis, with the risk of thermal damagesto the rotor disks.

[0048] In operation, pressurized process fluid, e.g. a mixture of oxygen and carbon dioxide (if the expander 3 is operating in an oxy-fuel cycle) is delivered to the combustor 7, mixed with fuel and burned to produce hot, pressurized process fluid, i.e., hot and pressurized flue gas, which expands along the expansion flow path formed by the sequentially arranged annular rows of stationary vanes or blades, and annular rows of rotor blades, to generate mechanical power which is made available on the rotor shaft either at the aft end, at the forward end, or both at the aft end and forward end. The mechanical power can be converted into electric power by an electric generator driv- ingly coupled to the shaft of the rotor 43 and / or used to drive a load, such as a compressor, a pump or other rotating equipment. A gearbox can be provided along the shaft line, between the expander and the load connected thereto, such that the load can rotate at a speed different from the expander rotary speed.

[0049] If the expander does not include a combustor and is arranged in a closed thermodynamic cycle, the compressed process fluid can be heated, e.g., by heat exchange in a heat exchanger before expansion, and subsequently cooled in a cooler.

[0050] As shown in the sectional view of Fig.1, the height of both the stationary blades 53 and of the rotor blades 55 increases in the forward-to-aft direction, i.e., from upstream to downstream along the flow path of the process fluid, in the direction of flow of the process fluid. The most upstream blades, e.g., those of the first one to four stages, have a high stiffness and a low aspect ratio.

[0051] According to one aspect of the present disclosure, at least one and preferably some of the first annular arrays of rotor blades are provided with respective outer platforms at the tips of the rotor blades, forming a discontinuous shroud, i.e., a shroud wherein a gap is provided between each pair of adjacent outer platforms, belonging to adjacent blades. The gap or clearance between neighboring outer platforms is such that the adjacent, i.e., consecutively arranged outer platforms are out-of-contact in any operating condition of the expander 3. For instance, the gap or clearance is sufficiently large such that under any operating conditions the outer platforms of adjacent blades do not contact each other due to vibration of the blades.

[0052] A better understanding of the concept of discontinuous shroud is obtained from the following description of an embodiment of a rotor blades array.

[0053] With continuing reference to Fig.1, Figs 2, 3 and 4 illustrate axonometric views of a portion of an annular array of rotor blades, which can be part of any one of the more upstream expansion stages of the expander 3, for example any one of the first one, two, three or four stages of the expander 3. A larger number of stages can be provided with blades designed as shown in Figs. 2, 3 and 4.

[0054] More specifically, Figs 2 and 3 illustrate a portion of an annular array of rotor blades comprising three rotor blades 55 and Fig. 4 illustrates a side view of a rotor blade of the annular array. In the exemplary embodiment of Figs 2 to 4, each rotor blade 55 comprises an airfoil 55.1, which extends from an inner platform 55.3 to an outer platform 55.4. Each inner platform 55.3 can comprise a dovetail 55.6 extending radially inwardly from the inner platform 55.3 toward the rotation axis A-A of the rotor 43 and engaging in a complementarily shaped slots 60 formed in the rotor disk. The blade can be mounted on the relevant disk by introducing the dovetail 55.6 axially in the slot 60. The radially inward end of the airfoil 55.1 is referred to as the root of the blade and is labeled 55.2 in the drawing. The radially outward end of the airfoil 55.1 is referred to as the tip of the blade and is labeled 55.5.

[0055] In other embodiments, each inner plate of the rotor blades may comprise a different feature for mechanical coupling to the rotor disk.

[0056] The shape of each airfoil 55.1 is best shown in the cross-sectional view of Fig.5. The airfoil 55.1 comprises a leading edge 61, a trailing edge 63, a suction side 65 and a pressure side 67. Reference C indicates the chord of the airfoil 55.1, also referred to as the chord of the blade as such, i.e., the distance between the leading edge 61 and the trailing edge 63. Cax is the so-called axial chord of the blade, i.e., the projection of the chord C on the axial direction of the rotor.

[0057] In the embodiment of Figs. 2 to 4, each outer platform 55.4 comprises seal teeth 69 projecting radially outwardly from the outer surface of the outer platform 55.4

[0058] Each outer platform 55.4 further includes a forward edge 71, also referred to herein as leading edge, which is oriented toward the forward end of the expander 3,i.e. towards the combustor 7. Opposite the forward edge 71, each outer platform 55.4 comprises an aft edge 73, also referred to herein as trailing edge, which is oriented towards the discharge plenum 41.3. Side edges 75, 77 extend on each side of each outer platform 55.4 from the leading edge 71 to the trailing edge 73 thereof.

[0059] Each outer platform 55.4 is configured such that each side edge 75 and the adjacent side edge 77 of the neighboring blade 55 are distanced from one another forming a gap or clearance G. Therefore, each outer platform 55.4 is in a non-contacting relationship with the outer platforms 55.4 of the neighboring blades 55. The blades are therefore free-standing, i.e., independent from one another. Specifically, neither additional damping element (separate from the outer platforms), nor intermediate elements are provided in contact with the outer platforms of neighboring blades, such that each outer platform of each blade is independent from the neighboring platform and no force is exchanged between neighboring, i.e. adjacent or consecutive, outer platforms.

[0060] The outer platforms 55.4 are dimensioned such that the gap G is maintained in any operating condition of the expander 3. In other words, the gap G has a tangential dimension such that the non-contacting relationship between the adjacent or neighboring outer platforms 55.4 is maintained also when the expander 3 is operating at maximum temperature conditions, i.e., when the outer platforms reach their maximum thermal expansion in tangential direction.

[0061] As shown in Figs. 2 and 3, the gap G can have a constant width along the full extension thereof, from the leading edge 71 to the trailing edge 73 outer platform 55.4. Additionally, the gap G can have a rectilinear shape. However, in other embodiments, not shown, the width of the gap can be variable along the extension thereof. In some embodiments, moreover, the gap can be non-rectilinear.

[0062] In some embodiments, as shown, the side edges 75, 77 can be rectilinear, such that the gap G has a straight shape.

[0063] In the embodiment of Figs 2 to 4, the leading edges 71 and the trailing edges 73 of the outer platforms 55.4 are positioned on respective planes orthogonal to the rotor axis A-A. Each side edge 75, 77 of the outer platforms 55.4 can be positioned on a radial plane containing the rotation axis A-A of the rotor, such that the gaps G extendparallel to the axial direction, i.e. each side edge 75, 77 of the outer platforms 55.4 is inclined by 90° with respect to a radial plane containing the rotor axis of the rotor. More generally, the gaps G can develop in a direction which is inclined over the tangential direction by an angle comprised between 10 and 90°, for example.

[0064] In some embodiments, mutually opposite side edges 75, 77 of outer platforms 55.4 of adjacent rotor blades 55 can form a gap which, in use, i.e., at steady-state operating temperature and rotational speed of the expander 3, is comprised between 0.5 mm and 10 mm, preferably between 1.1 mm and 5.0 mm.

[0065] Referring to Figs 3 and 3 A, the gap G forms a passage between an inner surface Si (Fig.3A) of the outer platforms 55.4, which faces the rotation axis A-A of the rotor, and an outer surface So of the outer platforms 55.4, which faces radially opposite the rotation axis of the rotor. The area of the passage formed by the gap G can be measured on the inner surface Si of the outer platforms 55.4. This surface is usually conical, as can be appreciated from the schematic representation in Fig.3A. Angle a is the slope angle at the tip of the blade. As the radius of the surfaces Si and So is large compared to the tangential extension of each outer platform 55.4, the surface Si can be approximated to a planar surface. If the gap G has a constant width, i.e., if the gap G is defined between rectilinear and parallel edges 75, 77, the area of the gap G is given by the distance A (see Fig.3) between the trailing edge 73 and the leading edge 71 of the platform 55.4, and the distance between the facing edges 75 and 77, between which the gap G is formed. The distance A is measured on a plane containing the rotation axis A-A of the turbomachine and is plotted in Figs.3 and 3A. In some embodiments, in use (i.e., at steady state rotary speed and temperature of the turbine) the area of the passage formed by each gap G is greater than 0% and equal to or smaller than 20% of the area given by the product of the distance A and the pitch P (see Fig.3) of the blades, i.e. equal to or smaller than 0.2*A*P.

[0066] The non-contacting outer platforms 55.4 form a non-continuous outer shroud. The absence of contact between adjacent outer platforms 55.4, due to the gap or clearance G, in any operating condition of the expander 3, avoids mechanical overload and stresses which would arise if the outer platforms 55.4 were in mutual contact, as in shrouded blades of the current art. At the same time, the discontinuous shroud formedby the annularly arranged outer platforms 55.4 reduces the aerodynamic losses, which typically affect unshrouded blades, since the process gas leakage through the gaps G from the pressure sides to the suction sides of each blade is substantially reduced, compared to an unshrouded impeller.

[0067] While discontinuous shrouds formed by sequentially arranged and mutually non-contacting outer platforms 55.4 beneficially reduce process gas leakages around the blade tips 55.5, the overall aerodynamic advantage thereof vis-a-vis an unshrouded rotor wheel may be balanced and finally overcome by windage losses introduced by the outer platforms. Depending upon the design of the flow path, in some embodiments, it may be more advantageous to have at least a first expansion stage with unshrouded blades, i.e., blades 55 devoid of an outer platform 55.4 and having a freestanding blade tip 55.5, followed by one or more stages including a discontinuous shroud formed by annularly arranged outer platforms 55.4. The more downstream expansion stages of the expander 3 may include a shrouded design according to the current art, i.e., with a continuous rather than discontinuous shroud formed by mutually contacting outer platforms of sequentially arranged rotor blades of the respective annular array of blades.

[0068] A discontinuous shroud as described above can be particularly advantageous for blades having a low aspect ratio lower than 3, preferably lower than 2, more preferably equal to or lower than 1.5: The aspect ratio is the ratio between the length of the chord C (Fig.5) and the blade height. As understood herein, the blade height is the distance between an inwardly facing surface of the outer platform, i.e., the surface of the outer platform facing the inner platform, and the outwardly facing surface of the inner platform, i.e., the surface of the inner platform facing the outer platform. In other words, the height of the blade is the distance between blade root 55.2 and blade tip 55.5, i.e. the length in radial direction of the airfoil profile of the blade.

[0069] Such blades having a low aspect ratio may have a high stiffness, which makes the use of a state-of-the-art continuous shroud (formed by outer platforms in mutual contact with one another) unfeasible. A discontinuous shroud design as disclosed herein can be particularly beneficial, when in combination with blades having an aspect ratio as indicated above and a stiffness equal to or higher than 90 Nm / deg, forinstance equal to or higher than 100 Nm / deg, or equal to or higher than 110 Nm / deg. As mentioned in the introductory part of the disclosure, the blade stiffness is defined as the ratio between a torsional moment applied to the tip of the blade and the torsional twist around the longitudinal axis of the blade caused by the applied moment. Thus, a stiffness of “100 Nm / deg” means that the blade deforms torsionally by 1 degree if a moment of 100 Nm is applied across the tip and root thereof.

[0070] Exemplary embodiments have been disclosed above and illustrated in the accompanying drawings. It will be understood by those skilled in the art that various changes, omissions and additions may be made to that which is specifically disclosed herein without departing from the scope of the invention as defined in the following claims.

Claims

CLAIMS1. A turbomachine rotor comprising at least one annular array of shrouded blades around a rotor axis, wherein each blade comprises: an airfoil having a leading edge, a trailing edge, a root, a tip, a concave pressure side and an opposite convex suction side, the pressure side and the suction side extending between the leading edge and the trailing edge; an inner platform, at the root of the airfoil; an outer platform at the tip of the airfoil, the outer platform having a leading edge, a trailing edge and two side edges extending between the leading edge and the trailing edge of the outer platform; wherein each side edge of the outer platform of each blade is spaced apart from an opposite side edge of an adjacent blade, such that in use a gap separates the opposite side edges of adjacent blades and the opposite side edges are in a facing, non-contacting relationship to one another in any operating condition of the turbomachine.

2. The turbomachine rotor of claim 1, wherein the outer platforms of the blades are freestanding and independent of each other.

3. The turbomachine rotor of claim 1 or 2, wherein the outer platforms of the blades are and without a damping element or intermediate element therebetween.

4. The turbomachine rotor of any one of the preceding claims, wherein the rotor comprises at least one rotor disk, around a periphery whereof the shrouded blades of said annular array are mounted.

5. The turbomachine rotor of any one of the preceding claims, wherein each inner platform has a mechanical connecting feature adapted to mechanically couple the blade to the rotor.

6. The turbomachine rotor of claim 5, wherein the inner platform of each blade is provided with a respective mechanical connecting feature, separate fromthe mechanical connecting feature of the adjacent blades.

7. The turbomachine rotor of claim 6, wherein a plurality of blade mounting slots are formed in the periphery of the rotor; wherein each blade has an inner platform locked in a respective one of said plurality of blade mounting slots.

8. The turbomachine rotor of claim 7, wherein the mechanical connecting feature is a dovetail extending radially inwardly from the inner platform toward the rotation axis of the rotor and engaging in a complementarily shaped slot formed in the rotor.

9. The turbomachine rotor of any one of the preceding claims, wherein the blades have an aspect ratio equal to or smaller than 3.5, preferably equal to or smaller than 3, even more preferably equal to or smaller than 2, or equal to or smaller than 1.5.

10. The turbomachine rotor of any one of the preceding claims, wherein the blades have a stiffness equal to or higher than 90 Nm / deg, preferably equal to or higher than 100 Nm / deg, more preferably equal to or higher than 110 Nm / deg.

11. The turbomachine rotor of any one of the preceding claims, comprising a plurality of annular arrays of blades arranged in a forward-to-aft direction along the rotor axis, and wherein said at least one annular array of shrouded blades is the most upstream of said plurality of annular arrays of blades.

12. The turbomachine rotor of any one of the preceding claims, wherein each gap has a constant width from the leading edge to the trailing edge of the outer platforms.

13. The turbomachine rotor of any one of the preceding claims, wherein the leading edges and the trailing edges of the outer platforms are positioned on respective planes orthogonal to the rotor axis, and wherein each side edge of the outer platforms is inclined by an angle comprised between 0 and 75° with respect to a radial plane containing the rotor axis of the rotor.

14. The turbomachine rotor of any one of the preceding claims, wherein the mutually opposite side edges of adjacent outer platforms form a gap which in use is greater than 0 mm and equal to or less than 10 mm.

15. The turbomachine rotor of any one of the preceding claims, wherein the mutually opposite side edges of the adjacent outer platforms form a gap which, in use, has an area which is greater than zero and equal to or smaller than 0.2*A*P, wherein A is the distance between the trailing edge and the leading edge of the platform and P is the pitch of the blades.

16. A power-generating turbomachine comprising: a casing; at least one array of stationary blades housed in the casing; a turbomachine rotor according to one or more of the preceding claims housed for rotation in the casing.

17. The turbomachine of claim 16, wherein the turbomachine is an expander.

18. The turbomachine of claim 17, wherein the expander is a supercritical carbon dioxide expander.

19. The turbomachine of any one of claims 16 to 18, comprising at least four expansion stages, preferably at least six expansion stages, each expansion stage including an annular array of stationary blades and an annular array of rotor blades, the annular array of rotor blades being downstream of the annular array of stationary blades in a forward-to-aft; and wherein at least the first and the second expansion stages comprise shrouded blades with outer platforms including spaced apart side edges.

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