JP2012052526A - Shrouded turbine blade with contoured platform and axial dovetail - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a shrouded turbine blade that can minimize vortex effects while still permitting simple assembly.SOLUTION: A turbine blade 26 includes an airfoil 34 having a root 38, a blade tip 40, a concave pressure side 46, and a laterally opposite convex suction side 48, the pressure and suction sides extending in chord between opposite a leading edge 56 and a trailing edge 58; an outer platform 36 disposed at the blade tip of the airfoil, the outer platform having spaced-apart lateral edges 60 which each define an interlocking element; an inner platform 32 with two spaced-apart curved lateral edges disposed at the blade root of the airfoil, the inner platform having a hot side facing the airfoil which is contoured in a non-axisymmetric shape; and a dovetail 28 extending radially inward from the opposite side of the inner platform, wherein the dovetail is axially straight.

Description

  The present invention relates generally to gas turbine engines, and more particularly to a turbine of a gas turbine engine. The US Government has certain rights in this invention pursuant to Contract Number W911W6-07-2-0002 awarded by the Department of Army.

  In a gas turbine engine, air is pressurized in a compressor and then mixed with fuel and burned in a combustor to produce combustion gases. One or more turbines downstream of the combustor extract energy from the combustion gases and drive a compressor, as well as a fan, shaft, propeller, or other mechanical load. Each turbine includes one or more rotors, each including a disk carrying a row of turbine blades or buckets. A stationary nozzle comprising a row of stator vanes with radially outer and inner endwalls in the form of an annular band is located upstream of each rotor and serves to optimally direct the flow of combustion gases to the rotor. Each nozzle and downstream rotor are collectively referred to as a “stage” of the turbine.

  The complex three-dimensional (3D) configuration of the vane and blade airfoil is tuned to maximize operational efficiency, radially along the airfoil and even between the leading and trailing edges The wing width varies in the axial direction along the chord of the airfoil. As a result, the velocity distribution and pressure distribution of the combustion gas on the airfoil surface vary, and the velocity distribution and pressure distribution of the combustion gas in the flow path also vary.

  As such, undesirable pressure losses in the combustion gas flow path lead to undesirable reductions in overall turbine efficiency. For example, combustion gas inevitably diverts at each leading edge of the airfoil as it enters the flow path between the corresponding row of vanes and blades.

  The locus of the stagnation point of the inflowing combustion gas extends along the front edge of each airfoil. Corresponding boundary layers are formed along the pressure and suction sides of each airfoil and along the radially outer and inner endwalls that together define the boundaries of the four sides of each flow path. Is done. In the boundary layer, the local flow rate of the combustion gas varies from zero along the endwall and airfoil surfaces to an unlimited flow rate of the combustion gas at the location where the boundary layer terminates.

  One common cause of turbine pressure loss is the formation of horseshoe vortices and channel vortices when combustion gas movement is diverted around the leading edge of the airfoil. The total pressure gradient occurs in the boundary layer flow at the junction between the leading edge of the airfoil and the end wall. This pressure gradient at the leading edge of the airfoil forms a pair of counter-rotating horseshoe vortices that move downstream on both sides of each airfoil near the end wall. Since the vertical vortex is generated by the rotation of the horseshoe vortex, the channel vortex also develops.

  These vortices move backward along the opposing pressure side and suction side of each airfoil and behave differently because the pressure and velocity distributions are different along the vortex. For example, according to computer analysis, the suction side vortex moves toward the trailing edge of the airfoil in a direction away from the end wall, and then follows the trailing edge of the airfoil and flows backward toward the trailing edge of the airfoil. It interacts with the vortex on the pressure side.

  The vortex interaction on the pressure side and suction side occurs near the airfoil intermediate region of the airfoil, causing a total pressure loss and correspondingly reducing turbine efficiency. These vortices also cause turbulence and increase unwanted heating of the endwall.

  Correspondingly, a horseshoe vortex and a channel vortex are formed at the junction of the turbine rotor blade and its integral root platform, and at the junction of the nozzle stator vane and its outer and inner bands. As the turbine efficiency is lost, the end wall components are further heated.

  By using non-axisymmetric endwall contouring (EWC) in the turbine airfoil to reduce the effects of vortices, performance can be significantly improved. One known design includes a “ridge” on the leading edge, a “valley” on the suction side, and a “ridge” on the trailing edge. Usually, the blade dovetail and the platform edge are straight. With this straight dovetail / platform design, the trailing edge saddle straddles from one platform to an adjacent platform. Manufacturing tolerances and assembly tolerances can interrupt the saddle at the trailing edge, creating a forward step that adversely affects performance. It would be desirable to have an improved platform design that can maintain the benefits of EWC without suffering the disadvantages of trailing edge trough interruptions. An arcuate platform can be used to place the trailing edge saddle in a single platform without straddling adjacent platforms. However, this is only possible in the case of blades that do not have a tip shroud and are individually assembled to the rotor disk. In the case of shrouded turbine blades, the blade tip shrouds that mesh with each other, the curved platform, and the conventional curved dovetail block the assembly of the rotor.

  It is therefore desirable to minimize the effects of vortices on shrouded turbine blades and still allow simple assembly.

  The above needs are met by the present invention which provides a shrouded turbine blade having a 3D contoured inner band surface and an axially straight dovetail.

  According to one aspect of the present invention, the turbine blade is an airfoil having a root portion, a blade tip portion, a concave pressure surface side, and a convex suction surface side facing in the lateral direction, wherein the pressure surface and the suction surface side are: An airfoil extending in a chordwise direction between opposing leading and trailing edges and an outer platform disposed at a wing tip of the airfoil, each spaced apart lateral edge forming a mating element An inner platform having an outer platform with two spaced curved lateral edges disposed at the root of the airfoil, the non-axisymmetric contoured hot side facing the airfoil And an axially dovetail portion extending radially inward from the opposite side of the inner platform.

  According to another aspect of the present invention, a turbine blade assembly is an airfoil having a root portion, a blade tip portion, a concave pressure surface side, and a convex suction surface side facing in the lateral direction, the pressure surface side and the suction surface. Side is an airfoil extending in chord direction between opposing leading and trailing edges and an outer platform located at the wing tip of the airfoil and spaced apart and configured with mating elements An inner platform with an outer platform having a lateral edge and two spaced curved lateral edges disposed at the root of the airfoil, the airfoil being contoured in a non-axisymmetric shape A plurality of blades each having an inner platform having a hot side facing. The blades are annular to form a plurality of channels, each channel being defined between two inner platforms, two outer platforms, and adjacent first and second airfoils. Are arranged in parallel. The mating elements of adjacent outer platforms engage each other. The hot side of the inner platform in each flow path is a ridge having a relatively high radial height adjacent to the pressure side of the first airfoil adjacent to the leading edge of the first airfoil And a trough having a relatively low radial height, parallel to the suction surface side of the second airfoil and second in the rear of the front edge of the second airfoil. Are spaced apart from the suction side of the airfoil, and the peaks and troughs together form an arcuate groove extending axially along the inner platform between the first and second airfoils. Form.

  The invention may best be understood by referring to the following description in conjunction with the accompanying drawings.

1 is a schematic view of a gas turbine engine incorporating a turbine nozzle constructed in accordance with aspects of the present invention. FIG. It is a left perspective view of the turbine blade of the engine shown in FIG. FIG. 3 is a partially enlarged view of the turbine blade shown in FIG. 2. 2 is a cross-sectional view of several turbine blades assembled in parallel. FIG. FIG. 5 is a schematic view taken along line 5-5 of FIG. FIG. 6 is a view taken along line 6-6 of FIG. It is the disassembled perspective view which showed a part of turbine disk and several turbine blades together.

  Referring to the drawings, in which like elements are designated with like reference numerals throughout the various drawings, FIG. 1 shows a fan 12, with the flow arranged in an axial series relationship, both along the longitudinal central axis “A”. 1 is a schematic diagram illustrating elements of a typical gas turbine engine 10 having a high pressure compressor 14, a combustor 16, a high pressure turbine (“HPT”) 18, and a low pressure turbine 20. The high-pressure compressor 14, the combustor 16, and the high-pressure turbine 18 are collectively referred to as a “core portion”. The high-pressure compressor 14 supplies compressed air that is sent into the combustor 12, and fuel is introduced into the combustor and burns to generate high-temperature combustion gas. The high-temperature combustion gas is discharged to the high-pressure turbine 18, and at this time, the high-temperature combustion gas is expanded to extract energy. The high pressure turbine 18 drives the compressor 10 via the outer shaft 22. Pressurized air flowing out of the high pressure turbine 18 is discharged to a low pressure turbine (“LPT”) 20 where the pressurized air is further expanded to extract energy. The low pressure turbine 20 drives the fan 12 via the inner shaft 24. The fan 12 generates a pressurized air flow, a part of this pressurized air flow is supercharged to the intake port of the high-pressure compressor 14, and most of the pressurized air bypasses the "core part" It brings most of the thrust from the engine 10.

  The illustrated engine 10 is a high bypass turbofan engine, but the principles described herein are based on turboprop engines, turbojet engines, turboshaft engines, and other turbine and stationary applications used in stationary applications. Is equally applicable. The principles described herein are also applicable to turbines such as steam turbines that use working fluids other than air. Also, although LPT blades are used as an example, the principles of the present invention are applicable to any turbine blade having an inner or outer shroud, or platform, including but not limited to HPT and intermediate pressure turbine (IPT). I want you to understand.

  Conventionally, the LPT 20 includes a series of stages with nozzles in each stage, including a row of airfoil type vanes and a downstream rotating disk carrying a row of turbine blades. 2 and 3 show the configuration of the turbine blade denoted by reference numeral 26 in more detail. The blade 26 is an integral part including a dovetail portion 28, a shank portion 30, an inner platform 32, an airfoil 34, and an outer platform 36. The airfoil includes a root 38, a wing tip 40, a leading edge 42, a trailing edge 44, and a concave pressure side 46 opposite the convex suction side 48. Inner and outer platforms 32 and 36 respectively define inner and outer radial boundaries of the gas flow through the airfoil 34.

  The dovetail portion 28 has a cross-sectional shape having a land portion and a groove portion configured in a conventional manner. The dovetail portion 28 is aligned in the axial direction with respect to the engine center line, and the shape thereof is “linear in the axial direction”. In other words, the shape of the dovetail is equivalent to the shape formed by translating the contour of the dovetail along a line “L” parallel to the longitudinal center axis of the engine, and has a curvature or warp. No.

  The outer platform 36 has a “hot side” 50 facing the hot gas flow path and a “cold side” 52 facing away from the hot gas flow path. One or more annular seal teeth 54 extend radially outward from the cold side 52 of the outer platform. Outer platform 36 is defined by opposing leading and trailing edges 56 and 58 and lateral edges 60 and 62 extending between leading edge 56 and trailing edge 58. The lateral edges 60 and 62 of the outer platform 36 have a non-linear shape. Each lateral edge 60 and 62 includes an engagement element that provides an axial engagement action when the two outer platforms 36 are assembled together. In the illustrated example, the lateral edges 60 and 62 have the same shape in plan view, but as a result, the right lateral edge 62 (when viewed from the rear to the front) is effective. A laterally extending tab 64 is formed, and the left lateral edge 60 forms a complementary recess 66.

  The inner platform also has a “hot side” 68 facing the hot gas flow path and a “cold side” 70 facing away from the hot gas flow path. Inner platform 32 is defined by opposing leading and trailing edges 72 and 74 and lateral edges 76 and 78 extending between leading and trailing edges 72 and 74. The lateral edges 76 and 78 of the inner platform 32 are curved (the arc may be arcuate or any other shape depending on the particular application). In the illustrated example, the lateral edges 76 and 78 have the same shape in plan view. As a result, one lateral side of the inner platform 32 is convex in the plan view, and the other lateral side is concave in the plan view. These curvatures correspond to the direction in which the airfoil 34 is warped. As will be described in more detail below, the arcuate lateral edges 76 and 78 do not require crossing over to the inner platform 32 of an adjacent turbine blade 26 and a 3D contouring mechanism for the inner platform 32 can be realized.

  During operation, the gas pressure gradient at the leading edge of the airfoil creates a pair of counter-rotating horseshoe vortices that move downstream on each side of each airfoil 34 near the inner platform 32. In the schematic diagram of FIG. 2, the movement directions of the vortices on the pressure side and the suction side are indicated by reference signs PS and SS, respectively. When the vertical vortex is generated by the rotation of the horseshoe vortex, the flow vortex develops, and the low momentum fluid in the end wall layer is biased by the lateral pressure gradient, and the flow path between the air foils 34 is positively moved. Cross from the pressure side to the suction side.

  As shown in FIGS. 3-6, the hot side 68 of the inner platform 32 is preferably more undulating than a conventional axisymmetric or circumferential shape to reduce the adverse effects of flow path vortices and horseshoe vortices. Contoured. In particular, the contour of the inner platform is not axisymmetric and is contoured with undulations in the radial direction from a wide crest 80 adjacent to the pressure side 46 of each blade 26 to a recessed trough 82 that is recessed. The This contouring is generally referred to as “3D contouring”. The overall shape forming the aerodynamic “endwall” of the flow path between two adjacent airfoils 34 of the assembled rotor is such that the portions of the side-by-side inner platform 32 of the airfoils 34 are arranged side by side. It will be understood that they are formed together.

  A typical prior art inner band generally has a convexly curved surface shape that is similar to the top surface of the airfoil when viewed in longitudinal section (see FIG. 5). This shape is a symmetrical plane of rotation about the longitudinal axis of the engine 10. This shape is regarded as a baseline reference, and is indicated by a broken line indicated by “B”. The surface shape with the 3D contour formed is shown by a solid line. In the drawing, points having the same height or radial dimension are connected to each other by contour lines. As shown in FIG. 4, each airfoil 34 has a chord length “C” measured from its leading edge 42 to its trailing edge 44, and a direction parallel to this dimension is “blade”. It will be in the “string” direction. As indicated by an arrow labeled “T” in FIG. 4, a direction parallel to the front edge 72 or the rear edge 74 of the inner platform 32 is referred to as a tangential direction. As used herein, “positive bumps”, “mountains”, and similar terms are surface characteristics located radially outward, or when measured from the longitudinal axis A rather than the local baseline B. , Refers to surface properties with large radii, “valley”, “negative ridge”, and similar terms as surface properties located radially inward, or when measured from the longitudinal axis A rather than the local baseline B This refers to surface characteristics with a smaller radius.

  With reference to FIGS. 4 and 5, the trough 82 is on the hot side 68 of the inner platform 32 between the pairs of airfoils 34 and extends from approximately the leading edge 42 to the trailing edge 44 of the airfoil 34. To do. The deepest portion of the valley 82 extends along a line that is substantially parallel to the suction side 48 of the airfoil 34 that coincides with line 6-6 shown in FIG. In the illustrated embodiment, the deepest portion of the valley 82 is about 20% of the total radial height difference between the lowest and highest positions of the hot side 68, ie, the overall height difference is about 8.5. When it is a unit amount, it is lower than the baseline shape B by about 2 unit amounts. When measured from the suction side 48 of the airfoil 34 in the tangential direction, the line representing the deepest portion of the valley 82 is at a position about 10% of the distance to the pressure side 46 of the adjacent airfoil 34. In the chord direction, the deepest portion of the valley portion 82 is located at a position having a substantially maximum cross-sectional thickness of the airfoil 34 (generally referred to as a “high-C” position).

  As shown in FIGS. 4 and 5, the crest 80 extends along a line that is substantially parallel to the pressure side 46 of the adjacent airfoil 34. The hook-shaped portion 81 extends from the highest portion of the peak portion 80 and extends in a substantially tangential direction so as to be separated from the pressure surface side 46 of the adjacent airfoil 34. The height in the radial direction of the peak portion 80 is inclined toward both the front edge 42 and the rear edge 42 of the airfoil 34 in a direction away from the hook-shaped portion 81. The crest 80 increases behind the front edge 42 from the baseline height B to the maximum height with a large gradient from the front edge 42 over one third of the chord length. From the trailing edge 44 over the remaining two thirds of the chord length, the height is increased evenly from the trailing edge 44 with a substantially smaller slope or slope.

  In the illustrated example, the highest portion of the crest 80 is about 80% of the overall radial height difference between the lowest and highest positions of the hot side 68, ie, the overall difference is about 8.5 unit quantities. In some cases, it is higher than baseline shape B by about 7 unit quantities. In the chord direction, the highest portion of the crest 80 is located between the mid chord position and the leading edge 42 of the adjacent airfoil 34.

  The trailing edge collar 84 is on the hot side 68 of the inner platform 32 behind the airfoil 34 (see FIGS. 3 and 4). The trailing edge hook extends rearward from the trailing edge 44 of the airfoil 34 along a line that is substantially an extension of the chord line of the airfoil 34. The radial height of the trailing edge collar 84 is inclined toward both the leading edge 42 and trailing edge 44 of the airfoil 34 in a direction away from this line. In the illustrated embodiment, the trailing edge collar 84 is about 60% of the total radial height difference between the lowest and highest positions of the hot side 68, i.e., the overall difference is 8.5 units. The highest part of is about 5 units higher than the baseline shape B. The highest portion of the trailing edge collar 84 is directly adjacent to the trailing edge 44 of the airfoil 34 and is located at the root 38 thereof.

  Note that the specific numerical values described above are merely examples, and can be changed in order to obtain optimum performance for individual applications. For example, ± 20% of the radial height can be easily changed, and ± 15% of the tangential position can be changed.

  Although the crest 80 has locally different portions near its maximum height, the trough 82 has a substantially uniform shallowness over substantially the entire length in the longitudinal or axial direction. The raised crest 80, the recessed trough 82, and the trailing edge collar 84 together form the concave pressure side 46 of one airfoil 34 and the convex suction side of the adjacent airfoil 34. 48, an aerodynamically smooth chute groove or curved groove is formed in accordance with the arcuate shape of the flow path, whereby the combustion gas is guided smoothly. In particular, the peak portion 80 and the valley portion 82 together smoothly bend or change the direction of the combustion gas according to the inflow angle of the combustion gas, thereby reducing adverse effects due to the horseshoe vortex and the channel vortex. The arc-shaped inner platform 32 can be disposed in one inner platform 32 without the trailing edge hook portion 84 straddling the adjacent inner platform 32. Thus, the endwall boundary layer flow along the trailing edge saddle 84 does not “see” a radial break or “step”. In particular, the front step is eliminated. This feature helps to maintain and improve the aerodynamic performance of 3D contouring.

  In the example shown herein, there is no large fillet or other similar structure on the hot side 68 of the inner platform 32 between the trailing edge 44 and trailing edge collar 84 of the airfoil 34. In other words, there is a clearly defined intersection between the root 38 of the trailing edge 44 of the airfoil 34 and the trailing edge collar 84. For mechanical strength, it may be necessary to include any type of fillet at this location. For aerodynamic reasons, any fillet placement should be minimized.

  According to the computer analysis of the airfoil and inner platform configuration described above, it is expected that the aerodynamic pressure loss near the inner platform hot side 68 during engine operation will be significantly reduced. Since the improvement in pressure distribution extends from the hot side 68 to a substantial portion of the lower portion of the airfoil 34, the strength of the vortex is reduced and the horseshoe vortex is moved toward the airfoil suction side 48. The pressure gradient between the energized flow paths is greatly reduced. The 3D contoured hot side 68 further reduces total pressure loss while reducing vortex movement toward the airfoil 34 wing span center. These advantages increase the performance and efficiency of the LPT 20 and the engine 10.

  Referring to FIG. 7, the blade 26 is attached to the turbine disk 86 as follows. First, a set of blades 86 is assembled into a complete 360 degree array. Using a holding fixture or jig (not shown), the blade 26 is fixed in position. When assembled in this manner, the lateral edges 76 and 78 of the inner platform 32 are in contact or intimate contact, and the lateral edges 60 and 62 of the outer platform 36 are in contact or intimate contact. The tab 64 of each outer platform 36 is received in the recess 66 of the adjacent outer platform 36. This prevents the outer platform 36 from axially moving because the outer platform 36 effectively meshes with each other. The array of blades 26 is then inserted into the dovetail slot 88 of the disk 86 (only a portion is shown in FIG. 7). Thereafter, the blade 26 is held axially on the disk 86 using well-known components such as a bolted retainer, a disk plate, or an annular seal (not shown). After assembly, a flow path “P” is formed in the gap between the blades 26. Each flow path P is defined by two adjacent inner platforms 32, two adjacent outer platforms 36, and two adjacent airfoils 34.

  In the foregoing, a turbine blade with a shroud having a 3D contoured inner band has been described. While specific embodiments of the present invention have been described, it will be apparent to those skilled in the art that various modifications can be made without departing from the spirit and scope of the invention. Accordingly, the present invention is to be defined solely by the appended claims, and the preferred embodiments of the present invention described above and the best mode for carrying out the invention are not intended to be limiting but merely for illustrative purposes. ing.

Claims (12)

An airfoil having a root portion, a blade tip portion, a concave pressure surface side, and a convex suction surface side opposed in the lateral direction, the pressure surface and the suction surface side between the front edge and the rear edge facing each other An airfoil extending in the chord direction;
An outer platform disposed at the wing tip of the airfoil, the outer platforms each having spaced lateral edges that form mating elements;
A high temperature facing the airfoil, wherein the inner platform is provided with two spaced curved lateral edges disposed at the root of the airfoil and is contoured in a non-axisymmetric shape An inner platform having sides,
A turbine blade including an axially straight dovetail portion extending radially inward from an opposite side of the inner platform.   The turbine blade according to claim 1, wherein one lateral edge of the outer platform forms a protruding tab and the other lateral edge forms a recess having a shape complementary to the tab. . The hot side of the inner platform is
A peak portion adjacent to the front edge of the airfoil and adjacent to the pressure surface side of the airfoil and having a relatively high radial height;
Parallel to the suction surface side of the airfoil, spaced from the suction surface side of the airfoil and disposed behind the leading edge of the airfoil, a trough having a relatively low radial height,
The turbine blade of claim 1, wherein the turbine blade is contoured in a non-axisymmetric shape.   The turbine blade of claim 1, wherein the hot side of the inner platform includes a trailing edge ridge that extends behind the trailing edge of the airfoil and has a relatively high radial height. The crest has a center between the front edge and the chord middle position on the pressure surface side of the airfoil, and the height decreases forward, backward, and laterally from the center,
The trough has a center in the vicinity of the maximum thickness of the airfoil on the suction surface side of the airfoil, and the depth decreases from the center in the forward direction, the backward direction, and the lateral direction. The turbine blade described in 1.   The turbine blade of claim 1, wherein one of the lateral edges of the inner platform is convex and the other of the lateral edges is concave. An airfoil having a root portion, a blade tip portion, a concave pressure surface side, and a convex suction surface side facing in the lateral direction, wherein the pressure surface side and the suction surface side are between the front and rear edges facing each other. And an airfoil extending in the chord direction,
An outer platform disposed at the wing tip of the airfoil, the outer platform having spaced apart lateral edges configured with mating elements;
An inner platform having two spaced curved lateral edges disposed at the root of the airfoil, the hot side facing the airfoil being contoured in a non-axisymmetric shape An inner platform having,
Each having a plurality of blades,
The plurality of blades are annularly formed to form a plurality of flow paths each defined between the two inner platforms, the two outer platforms, and the adjacent first and second airfoils. Arranged in parallel,
The meshing elements of adjacent outer platforms engage each other;
The hot side of the inner platform in each of the flow paths has a relative radial height adjacent to the leading edge of the first airfoil and adjacent to the pressure side of the first airfoil. A trough that is contoured in a non-axisymmetric shape including a relatively high peak and has a relatively low radial height parallel to the second airfoil and behind the leading edge of the second airfoil Are spaced apart from the suction surface side of the second airfoil,
The turbine blade assembly, wherein the peaks and valleys together form an arcuate groove extending axially along the inner platform between the first and second airfoils. The crest is connected to the trough along the suction surface side of the second airfoil while reducing the height around the front edge of each of the first airfoil,
The turbine blade assembly of claim 7, wherein the valley extends along the suction surface side of the second airfoil to a trailing edge of the second airfoil.   The line defining the deepest portion of the valley is at a position about 10% of the tangential distance from the suction surface side of the second airfoil to the pressure surface side of the first airfoil. Item 8. The turbine blade assembly according to Item 7.   The turbine of claim 7, wherein the hot side of each inner platform includes a relatively high radial edge trailing edge that extends behind the trailing edge of the airfoil. Blade assembly. The crest has a center between the front edge and the chord intermediate position on the pressure surface side of each airfoil, and the height from the center toward the front, rear, and side is increased. Decreased,
The said valley part has a center near the maximum thickness of the airfoil on the suction surface side, and the depth decreases from the center toward the front direction, the rear direction, and the lateral direction. Turbine blade assembly.   The turbine blade assembly of claim 7, wherein one of the lateral edges of each inner platform is convex and the other of the lateral edges is concave.

Images