Arrangement of axial turbines blades

0001The invention relates to an axial turbine having at least one respective rotor blade grid and a stator blade grid of turbine blades arranged in series in an annular flow channel in turbine circumferential direction. For technical reasons, reference is made, for example, to DE 43 44 189 C1.

0002An axial turbine according to the invention can be used in particular in an aircraft gas turbine, but also generally in stationary gas and steam turbines. With regard to turbine blade design, the present invention primarily relates to thin full blades (both rotor and stator) for uncooled low pressure turbines in multi-shaft engines. However, it is also possible to use it on other types of axial turbines, such as cooled high-pressure turbines with hollow blades.

0003The application particularly relates to axial turbines having a degree of reaction of 50% or less. Therefore, in order to achieve an unambiguous assignment of the defined load parameters with the aerodynamic load of the blade grids, reference is also made to the staggering angle known to the person skilled in the art. The degree of reaction of an axial turbine, which is a measure of the breakdown of the pressure reduction on rotor and stator blades, correlates in a first approximation with the stagger angle of the blade profiles. Turbines with a degree of reaction of around 50% have grading angles of 30 ° or less in the middle section, ie at less than 55% of the total bucket height. The degree of reaction known to a person skilled in the art, which is used as the basis for the design of gas turbines as an average degree of reaction of 0.5, follows the ratio Δ<i>p</i>_<i>r</i> to Δ<i>p</i>_<i>0</i> where Δ<i>p</i>_<i>r</i> the pressure reduction, ie the expansion in the rotor, and Δ<i>p</i>_<i>0</i> the total reduction of the total pressure in the turbine stage is. Accordingly, the degree of reaction is a measure of the distribution of pressure reduction on rotor and stator blades.

0004Among other things, in the preferred application of a low-pressure turbine, the number of blades in the blade grid, ie per blade row primarily by aerodynamic criteria such as. determines the doubt number or other aerodynamic loading parameters. Taking into account such load parameters, the aim is to arrange as few blades as possible in a blade grid, since the number of blades has a direct effect on the module weight and on the production costs. Manufacturers of aircraft engines usually use an aerodynamic load criterion, which is the minimum of the number of blades per rotor and stator blade ring or -Steel lattice pretends.

0005The already mentioned doubt number, which is a measure of the aerodynamic loading of a single turbine blade, is a dimensionless parameter for characterizing the force acting circumferentially on the blade. The number of doubts is originally defined for a two-dimensional flow, for example in the plane lattice test. Here, the force acting on the two-dimensional blade section in the circumferential direction is related to a reference force, which by an imaginary<img file="EP0937862A2_D0001.tif" />The reference distribution has a constant pressure on the pressure side of the blade equal to the total pressure at the inlet and a constant pressure on the suction side of the blade equal to the static pressure at the outlet.

0006A comparable parameter is also used to design real three-dimensional blades. There, the design is usually carried out on quasi two-dimensional stream surfaces. Such variations vary in thickness and radius from the blade entrance to the blade exit, making the definition of a loading parameter somewhat more difficult. However, based on the two-dimensional flow, the principle is transferred to the design of several two-dimensional sections, in order subsequently to be able to assemble the real, three-dimensional blade from the essentially two-dimensional profile sections.

0007The larger the doubt number or Generally, the load parameter is the higher the aerodynamic load on the bucket. Large doubt figures mean that delayed flow areas tend to be tolerated on the suction side of the blade profile, although in most cases the flow in the turbine grid is accelerated on average. However, a delayed flow always carries the risk of separating the boundary layer. This is usually considered undesirable because it increases the flow losses. However, even without peeling phenomena, delaying the flow along the suction side of the airfoil causes the boundary layer thickness to increase, thereby increasing the flow losses.

0008On the other hand, blade vanes whose blades are designed for a relatively large number of doubts, under given aerodynamic boundary conditions (such as total mass flow, Mach number, degree of reaction, work or deflection) can reduce the number of blades, resulting in an increased split ratio ,

0009In practice, this now means that the increased losses and losses in efficiency resulting from greater deceleration on the airfoil suction sides must be weighed against increased blade numbers and the associated increased manufacturing costs and weight. In particular, in series-produced aircraft gas turbines cost and weight play a relatively large role, so that it may be useful to increase the number of doubts beyond a purely aerodynamically optimal level.

0010In the known state of the art, the aerodynamic blade load is essentially limited to relatively low doubt numbers in order not to increase the aerodynamic losses too much. The permissible doubt number (resp. the permissible flow delay on the suction side of the blade profile) is the lower, the lower the Reynolds number. At low Reynolds numbers, the risk of non-reassigning detachment bubbles is particularly high. Also, the boundary layer grows faster.

0011Recent results, however, show that the flow losses and thus the efficiency of a turbine depends very much on the state of the boundary layer. In particular, it has been found that the transient interaction with upstream blade rows plays a major role. The suction-side boundary layer is periodically brought to the envelope by the wake flow of the upstream blade row and it forms a very complex but advantageous boundary layer development. This is characterized by alternating laminar, transitional, turbulent and so-called. laminar calmed zones. The laminar calmed zones only occur in unsteady boundary layers, but are advantageous for their loss behavior.

0012This applies in particular to low-pressure turbines in aircraft gas turbines, where the Reynolds numbers are very low and the predominantly laminar boundary layers tend to detach. While conventional doubt-number criteria, especially at low Reynolds numbers, are often obtained from studies in idealized trials (eg a flat lattice test with stationary homogeneous inflow), new doubly-number criteria can be developed by recognizing that the unsteady flow plays a non-negligible role, which are above the previous criteria, especially at very low Reynolds numbers without causing an increase in losses.

0013In addition to the doubt number is the course of the pressure distribution (the so-called. <img file="EP0937862A2_D0002.tif" />lift-style "), in particular on the suction side of a blade profile, determines the height of the aerodynamic losses. By an advantageous choice of the pressure distribution in connection with a high number of doubts, the number of blades per row of blades can be reduced compared to the conventional state of the art. without at the same time increasing the flow losses and thus lowering the efficiency.

0014The number of doubts as such, as well as the course of the pressure distribution (<img file="EP0937862A2_D0003.tif" />lift-style ") are aerodynamic criteria that can not easily be transferred into the design features of a turbine blade, and depending on the aerodynamic boundary conditions (eg mass flow, work conversion per stage, Mach numbers, degree of reaction, deflection, etc.) the application of the same doubts Number and same <img file="EP0937862A2_D0004.tif" />lift-styles "in design nevertheless lead to different Schelselprofilformen.

0015The mentioned new criteria for the doubt number and the course of the pressure distribution (<img file="EP0937862A2_D0005.tif" />Lift-style "), which are the basis of the present invention, are translated in the context of this invention into constructive features of turbine blade and turbine blade profiles or profile sections.

0016This is therefore the object of the present invention, namely the indication of reproducible criteria, with the help of which ultimately using higher doubt numbers and a changed course of the pressure distribution, the number of blades per blade ring or Bucket lattice compared to the usual number can be significantly reduced. The latter has - as already mentioned - extremely advantageous in terms of weight and the manufacturing costs of an axial turbine.

0017To solve this problem specified in the characterizing part of claim 1 features are provided, wherein two alternative measures are proposed. Advantageous developments are content of the dependent claims.

0018Before these features of the invention are explained in more detail with reference to the attached schematic diagrams, it should first be pointed out that the doubt number, which is initially defined only in a two-dimensional flow, can be approximately transferred, at least at a constant degree of reaction, into the division ratio known to those skilled in the art , An increased division ratio thus corresponds to an increased doubt number. Although this is strictly speaking only under the condition that the Mach numbers and the diversion or the degree of reaction remain constant. However, since in practice low pressure turbines are designed in a relatively small advantageous range of step loads (pressure ratio and kinematic load) as well as degrees of reactivity, the split ratio characterizes as a constructive feature the aerodynamic criterion of the doubt number.

0019For the consideration of the three-dimensional flow conditions in turbine blade passages, the definition of an aerodynamic load parameter, which should be similar to the doubter number in two-dimensional flow, is not easy. However, a division parameter which represents a measure of the aerodynamic loading of the blade is also defined here in analogy to the procedure for two-dimensional flow. This division parameter, which is defined taking into account three-dimensional flow conditions, is referred to below as 3D division parameter Y and characterizes (analogously to the known two-dimensional division parameter) the aerodynamic loading of a blade in a blade grid.

0020The present invention specifies preferred values ​​for this 3D division parameter. Another characteristic variable in a turbine blade grid is the split ratio in its usual definition, for which preferred values ​​are also given by the present invention. These two characteristic variables are to be considered for turbine reaction rates of the order of 50% or less. This corresponds to a stagger angle of less than 30 ° below a blade height of 55% of the total blade height and covers the main field of application of modern low-pressure turbines in aircraft gas turbines.

0021The invention will be explained in more detail with reference to the accompanying schematic diagrams, wherein<ul id="ul0001" list-style="none" compact="compact"><li>A longitudinal half-section of an axial turbine and</li><li>2 shows the development of a blade grid (or blade ring) in a conventional representation.</li></ul>

0022In the representation of an axial turbine 1 shown in Figure 1 in a radial-axial section, the usual cylindrical coordinate system is used, wherein the axial direction with the axial (or longitudinal) coordinate x and the radial direction with the radial coordinate r is designated , The third coordinate is the circumferential coordinate φ. In the illustration according to FIG. 1, an arbitrary point can thus be described by its location coordinates X (this is the axial coordinate) and R (this is the radial coordinate).

0023As usual, the axial turbine 1 shown also has alternately arranged guide vane grille 2 and running vane grille 3. In each case one guide vane grille 2 or stator vane grille 2 and one running vane grille 3 or rotor vane grille 3 form a step. FIG. 1 thus shows a two-stage axial turbine 1.

0024Each stator blade grid 2 consists of similar stator blades 4, which in the circumferential direction of the turbine φ in succession or arranged in series. In the same way, each rotor blade grid 3 consists of a plurality of similar rotor blades 5. The blades or blades 4, 5 of the blade grids 2, 3 extend in the radial direction r in a concentric with the machine axis 14 extending annular flow channel 7, in which according to the flow direction S, a working fluid is passed through the blade grid 2, 3.

0025This flow channel 7 is bounded in the radial direction r on the inside by the stator in the form of a stator 6 and further by the unspecified platforms at the bottom of the rotor blades 5, said elements called the so-called. inner channel boundary 8 form. In the radial direction r on the outside, the flow channel 7 is bounded by a housing wall 13, however, hereinafter referred to as the outer channel boundary 9 in the region of the rotor blades 9 either their blade tips or a (not shown here) shroud of the rotor blade grid 3. For the stator blades 4 thus the inner side of the housing wall 13 represents the outer channel boundary 9, for the rotor blades 5, however, the outer channel boundary 9 with respect to the inside of the housing wall 13 by the gap of course required peak gap between the rotor blades. 3 and the housing wall 13 is pulled radially inward.

0026The inner channel boundary 8 and the outer channel boundary 9 each extend concentrically with the machine axis 14 and have a divergent profile with respect to the flow direction S of the working fluid passed through the blade grids 2, 3 in the flow channel 7, so that the flow channel 7 widens in the flow direction S.

0027With regard to the rotor blade grid 3, it should be mentioned that these are designed here in disk construction, ie the rotor blades 5 are mounted in a grid shape on a running disk 10 rotating about the machine axis 14.

0028The definition of the above-mentioned 3D division parameter first requires the definition of vane vertices and of a quasi-stream surface <i>QS</i> with respect to a blade lattice 2 or 3.

0029The so-called vane corner points <i>VA, HA, VI, HI</i> are exemplary in Fig.1 for that in the flow direction <i>S</i> considered second rotor blade grid 3 shown. In the view shown, the four blade vertices result<i>VA, HA, VI, HI</i> each as intersections of the blade leading edge 11 and the blade trailing edge 12 with the inner channel boundary 8 and the outer channel boundary 9:

0030The vane corner point <i>VA</i> is thus the point of intersection between the blade leading edge 11 with the outer channel boundary 9 and lies in the flow direction S viewed in front and in the radial direction r considered outside. In an analogous manner, it is with<i>HA</i> around the flow direction <i>S</i> Viewing the rear and radial direction r outer blade corner point, which is defined by the intersection of the outer channel boundary 9 with the blade trailing edge 12. The vane corner point <i>VI</i> results from the intersection of the blade leading edge 11 with the inner channel boundary 8, ie <i>VI</i> is the flow direction <i>S</i> viewed front and radial direction r inner vane vertex while <i>HI</i> finally, in the flow direction <i>S</i> considered rear and viewed in the radial direction r inner vane corner point, which can also be described by the intersection of the blade trailing edge 12 with the inner channel boundary 8.

0031As a quasi-stream surface <i>QS</i> a blade lattice 2 or 3, a rotationally symmetrical surface is defined here, which results from an arbitrary rotationally symmetrical section in the form of a concentric surface through the associated row of blades 4 or 5, with the condition that this section through the same percentage height of the blade leading edge 11 and the blade trailing edge 12 extends. Here is the height<i>H</i>_<i>sv</i> the blade leading edge 11 - shown in Figure 1 on the example of the second rotor blade grid 3 - defined by:<maths id="math0001" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">H</mtext></mrow><mrow><mtext mathvariant="italic">sv</mtext></mrow></msub><mtext> = </mtext><mtext mathvariant="italic">R (VA)</mtext><mtext> - </mtext><mtext mathvariant="italic">R (VI)</mtext></mrow></math><img file="EP0937862A2_D0006.tif" /></maths> Analog is the height <i>H</i>_<i>sh</i> the blade trailing edge 12 defined by:<maths id="math0002" num=""><math display="block"><mrow><msub><mrow><mtext mathvariant="italic">H</mtext></mrow><mrow><mtext mathvariant="italic">sh</mtext></mrow></msub><mtext> = </mtext><mtext mathvariant="italic">R (HA)</mtext><mtext> - </mtext><mtext mathvariant="italic">R (HI)</mtext></mrow></math><img file="EP0937862A2_D0007.tif" /></maths>

0032Fig.1 exemplifies such a section <i>QS</i> through the second rotor grid 3. But also the cut <i>QS '</i> is considered a quasi-flow area in the sense of the above definition, since it has the same intersection points VQ and HQ with the blade leading edge 11 and the blade trailing edge 12 and therefore also the following condition with regard to the percentage blade heights <i>H</i>_<i>sv</i> or. <i>H</i>_<i>sh</i> Fulfills.

0033For the two cuts or quasi-current surfaces <i>QS</i> and <i>QS '</i> namely:<maths id="math0003" num=""><math display="block"><mrow><mfrac><mrow><mtext mathvariant="italic">Radius (VQ) -radius (VI)</mtext></mrow><mrow><mtext mathvariant="italic">Radius (VA) -radius (VI)</mtext></mrow></mfrac><mfenced open="|" close="|"><mrow><mtext>=</mtext><mfrac><mrow><mtext mathvariant="italic">Radius (HQ) -radius (HI)</mtext></mrow><mrow><mtext mathvariant="italic">Radius (HA) -radius (HI)</mtext></mrow></mfrac></mrow></mfenced><mtext> .</mtext></mrow></math><img file="EP0937862A2_D0008.tif" /></maths> in which <i>Radius (VQ)</i> and <i>Radius (HQ)</i> the radii of the intersections of the quasi-current surface marked VQ and HQ, respectively <i>QS</i> with the blade leading edge 11 and the blade trailing edge 12 of the second rotor blade grid 3.

0034Based on these definitions, a 3D division parameter Y of a blade grid 2, 3 is defined as follows:<maths id="math0004" num=""><math display="block"><mrow><mtext mathvariant="italic">Y</mtext><mtext> = </mtext><mfrac><mrow><mtext>2π</mtext><mover accent="true"><mrow><mtext mathvariant="italic">r</mtext></mrow><mo>¯</mo></mover></mrow><mrow><msub><mrow><mtext mathvariant="italic">N</mtext></mrow><mrow><mtext mathvariant="italic">off</mtext></mrow></msub><msub><mrow><mover accent="true"><mrow><mtext mathvariant="italic">C</mtext></mrow><mo>¯</mo></mover></mrow><mrow><mtext mathvariant="italic">ax</mtext></mrow></msub></mrow></mfrac></mrow></math><img file="EP0937862A2_D0009.tif" /></maths>

0035With<maths id="math0005" num=""><math display="block"><mrow><mtable><mtr><mtd><mrow><mtable><mtr><mtd><mrow><mover accent="true"><mrow><mtext>r</mtext></mrow><mo>¯</mo></mover><mtext> = </mtext><mfrac><mrow><mtext mathvariant="italic">R</mtext><mtext>(</mtext><mtext mathvariant="italic">VA</mtext><mtext>) +</mtext><mtext mathvariant="italic">R</mtext><mtext>(</mtext><mtext mathvariant="italic">VI</mtext><mtext>) +</mtext><mtext mathvariant="italic">R</mtext><mtext>(</mtext><mtext mathvariant="italic">HA</mtext><mtext>) +</mtext><mtext mathvariant="italic">R</mtext><mtext>(</mtext><mtext mathvariant="italic">HI</mtext><mtext>)</mtext></mrow><mrow><mtext>4</mtext></mrow></mfrac><mtext>.</mtext></mrow></mtd></mtr></mtable></mrow></mtd></mtr></mtable></mrow></math><img file="EP0937862A2_D0010.tif" /></maths><i>N</i>_<i>off</i> is the number of blades 4, 5 of the blade grid 2, 3, and<maths id="math0006" num=""><math display="block"><mrow><msub><mrow><mover accent="true"><mrow><mtext mathvariant="italic">C</mtext></mrow><mo>¯</mo></mover></mrow><mrow><mtext mathvariant="italic">ax</mtext></mrow></msub><mtext> = </mtext><mfrac><mrow><msqrt><mtext>(</mtext><mtext mathvariant="italic">X</mtext><mtext>(</mtext><mtext mathvariant="italic">HA</mtext><mtext>) -</mtext><mtext mathvariant="italic">X</mtext><mtext>(</mtext><mtext mathvariant="italic">VA</mtext><msup><mrow><mtext>))</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><mtext>+ (</mtext><mtext mathvariant="italic">R</mtext><mtext>(</mtext><mtext mathvariant="italic">HA</mtext><mtext>) -</mtext><mtext mathvariant="italic">R</mtext><mtext>(</mtext><mtext mathvariant="italic">VA</mtext><msup><mrow><mtext>))</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></msqrt><mtext> + </mtext><msqrt><mtext>(</mtext><mtext mathvariant="italic">X</mtext><mtext>(</mtext><mtext mathvariant="italic">HI</mtext><mtext>) -</mtext><mtext mathvariant="italic">X</mtext><mtext>(</mtext><mtext mathvariant="italic">VI</mtext><msup><mrow><mtext>))</mtext></mrow><mrow><mtext>2</mtext></mrow></msup><mtext>+ (</mtext><mtext mathvariant="italic">R</mtext><mtext>(</mtext><mtext mathvariant="italic">HI</mtext><mtext>) -</mtext><mtext mathvariant="italic">R</mtext><mtext>(</mtext><mtext mathvariant="italic">VI</mtext><msup><mrow><mtext>))</mtext></mrow><mrow><mtext>2</mtext></mrow></msup></msqrt></mrow><mrow><mtext>2</mtext></mrow></mfrac></mrow></math><img file="EP0937862A2_D0011.tif" /></maths>

0036Will now be such a number of blades for a blade grid 2 and 3, respectively <i>N</i>_<i>off</i> selected, that with the specified definitions the value of the described 3D graduation parameter is greater than 1.0 (<img file="EP0937862A2_D0012.tif" />one "), we obtain a blade grid 2, 3, in which using higher doubt numbers and a changed course of the pressure distribution, the number <i>N</i>_<i>off</i> the blades 4, 5 per blade ring or per blade grid compared to the usual number is significantly reduced. This criterion<i>Y</i> > 1.0 holds for β_s <30 ° for all quasi-flow areas QS below 55% blade height <i>H</i>_<i>sv</i> or. <i>H</i>_<i>sh</i> and represents the specified in the characterizing part of claim first condition (A).

0037However, another criterion or a second condition (B) was found, which leads to a comparable result. In this condition (B) is the geometry of the blades 4, 5 and the blade profile section 21 with, including the axial chord length<i>b</i>, For further explanation, reference is made to FIG. 2, in which essential variables for the two-dimensional design of blade profile sections 21 in quasi-flow surfaces<i>QS</i> are defined in more detail below.

00382 shows two blade profile sections 21 made of a rotor blade grid 3 or a stator blade grid 2, wherein all the profile sections 21 of a blade grid 2, 3 are identical and around the generally homogeneous division <i>t</i> are offset from each other in the circumferential direction φ. In this case, a coordinate system is selected which has a peripheral coordinate φ extending in the circumferential direction φ and one along the quasi-current surface<i>QS</i> in the axial direction x extending coordinate x ', on the percent axial chord length <i>b</i> is applied.

0039As usual, a blade profile section 21 consists essentially of a leading edge pitch circle 22 (which may also be part of an ellipse), a predominantly convex suction face 23, a trailing edge pitch circle 24 (which may also be part of an ellipse) and a predominantly concave pressure face 25 , In this connection, Fig. 2 further shows a so-called. Bi-tangent u_b, This is a simultaneous tangent to the leading edge pitch circle 22 and the trailing edge pitch circle 24, which with the parallels to the axial direction (chord length b) the already mentioned staggering angle β_<i>s</i> includes.

0040Between two adjacent blade profile sections 21 there is a constriction e, which is defined as the smallest distance from the pressure side 25 of the one blade profile section 21 to the suction side 23 of the other blade profile section 21. This smallest distance results from the well-known in the Schaufelgittertheorie method of<img file="EP0937862A2_D0013.tif" />In turbine blades 2, 3, the bottleneck e is usually (and thus also here) the smallest distance from the transition point of the pressure side 25 into the trailing edge pitch circle 24 of one blade profile section 21 to the suction side 23 of the other blade profile section 21.

0041The division <i>t</i> is defined according to Figure 2 as the distance between two adjacent blade profiles 21 in the circumferential direction or in the direction of the circumferential coordinate in cylindrical coordinates rφ. The axial chord length <i>b</i> is defined as the run length from the blade leading edge 11 to the blade trailing edge 12 along an axial section on the quasi-flow surface <i>QS</i>which, as already mentioned, is plotted on the coordinate x 'in FIG.

0042Are now for a blade grid 2 and 3, the blade profile cuts 21 formed such that for all quasi-current surfaces <i>QS</i> below 55% bucket height <i>H</i>_<i>sv</i> or. <i>H</i>_<i>sh</i> the quotient <i>t / b</i> greater than 1.0 (<img file="EP0937862A2_D0014.tif" />one "), we obtain a blade grid 2, 3, in which using higher doubt numbers and a changed course of the pressure distribution, the number <i>N</i>_<i>off</i> the blades 4, 5 per blade ring or each blade grid 2, 3 is significantly reduced compared to the usual number. This criterion<i>t / b</i> > 1.0 applies to <i>β</i>_<i>s</i> <30 ° for all quasi-flow areas QS below 55% blade height <i>H</i>_<i>sv</i> or. <i>H</i>_<i>sh</i> and represents the specified in the characterizing part of claim alternative condition (B).

0043The achievable effect and hence the overall efficiency of the axial turbine 1 can be further increased by the additional measures described below with regard to the blade profile cuts 21, to the explanation of which reference is again made to FIG.

0044As usual, a profile deflection γ of the blade profile section 21 downstream of the constriction e is defined as the maximum angle γ between a tangent u_e to the suction side 23 in the position of the constriction e and any tangent u_s to the profile on the suction side 23 between the position of the constriction e and the transition point of the suction side 23 in the trailing edge pitch circle 24th

0045Will now for all quasi-current surfaces <i>QS</i> below 55% bucket height <i>H</i>_<i>sv</i> or. <i>H</i>_<i>sh</i> downstream of the constriction e between adjacent blade profile sections 21, the suction-side profile deflection γ greater than 27 ° selected, it results with the according to the above conditions (A) and / or (B) significantly reduced number of blades <i>N</i>_<i>off</i> a particularly high efficiency of the axial turbine 1.

0046The same applies to such a shaped blade profile section 21, wherein in the profile profile of the suction side 23 between 3% and 15% axial chord length <i>b</i> a turning point W is present (see Fig.2), where 0% axial chord length <i>b</i> the blade leading edge 11 and 100% axial vision length <i>b</i> the blade trailing edge 12 denotes.

0047Not only by calculation, but also in an experiment was on an axial turbine 1 with the measures described a nearly 20% reduction in the number of blades <i>N</i>_<i>off</i> achieved over a standard design. A corresponding reduction of the module weight and the manufacturing costs follows from this. Furthermore, the efficiency improved by 0.3%. At full exhaustion of the potential of the invention (eg by using a completely novel blading) is a nearly 40% reduction in the number of blades and thus the weight and manufacturing costs possible, the efficiency of the axial turbine 1 can be kept constant.

<b>LIST OF REFERENCE NUMBERS</b>

0048<dl id="dl0001" compact="compact"><dt>1</dt><dd>axial turbine</dd><dt>2</dt><dd>Guide or stator vane grille</dd><dt>3</dt><dd>Running or rotor blade grid</dd><dt>4</dt><dd>Stator vane (s)</dd><dt>5</dt><dd>Rotor blade (s)</dd><dt>6</dt><dd>Stator wall (inside)</dd><dt>7</dt><dd>flow channel</dd><dt>8th</dt><dd>radially inner channel limitation (from 7)</dd><dt>9</dt><dd>radially outer channel boundary (from 7)</dd><dt>10</dt><dd>sheave</dd><dt>11</dt><dd>Blade leading edge</dd><dt>12</dt><dd>Blade trailing edge</dd><dt>13</dt><dd>Housing wall (outside)</dd><dt>14</dt><dd>machine axis</dd><dt>S</dt><dd>flow direction</dd><dt>x</dt><dd>Axial direction Axial coordinate of a point: X</dd><dt>r</dt><dd>Radial direction Radial coordinate of a point: R</dd><dt>φ</dt><dd>circumferentially</dd><dt><i>QS</i></dt><dd>Quasi-flow area</dd><dt><i>QS</i>'</dt><dd>Quasi-flow area</dd><dt><i>H</i>_<i>sv</i></dt><dd>Height of the blade leading edge 11</dd><dt><i>H</i>_<i>sh</i></dt><dd>Height of the blade trailing edge 12</dd><dt>21</dt><dd>Aerofoil section</dd><dt>22</dt><dd>Leading edge pitch circle (from 21)</dd><dt>23</dt><dd>Suction side (from 21)</dd><dt>24</dt><dd>Trailing edge circle (from 21)</dd><dt>25</dt><dd>Printing side (from 21)</dd><dt>t</dt><dd>division</dd><dt>b</dt><dd>axial chord length</dd><dt>e</dt><dd>Bottleneck (between adjacent blade profile cuts 21)</dd><dt>u_b</dt><dd>Bi-tangent at 22 and 24</dd><dt>u_e</dt><dd>Tangent to the suction side 23 in the position of the bottleneck e</dd><dt>u_s</dt><dd>Tangent to the suction side 23 of the blade profile section 21st</dd><dt>W</dt><dd>turning point</dd><dt>β_s</dt><dd>stagger angle</dd></dl>