EP1760321A2 - Blade for turbomachine - Google Patents

Abstract

The blade has a profile skeleton line and an extended meridian flow line, and is divided into three zones in radial direction. The profile skeleton line is set within the divided zones following predetermined conditions involving the a point of the profile skeleton line, the inclination angles of the front and rear edges of the blade, the dimensions and total curvature of the blade, the angles of the tangent at any point of the profile skeleton line to the middle of the meridian flow line, and the complete length of the profile skeleton line.

Description

The present invention relates to blades of fluid flow machines such as fans, compressors, pumps and fans in the axial, semi-axial or even radial design. The working medium (fluid) can be gaseous or liquid.

In detail, the invention relates to at least one blade of a fluid flow machine. The blading in question is within a housing which limits the flow of a rotor and, if present, a stator with a fluid to the outside. While a rotor comprises a plurality of rotor blades attached to a rotating shaft and emits energy to the working fluid, a stator consists of a plurality of fixed, mostly in the housing mounted stator blades.

The aerodynamic load capacity and efficiency of fluid flow machines, such as fans, compressors, pumps and fans, is limited particularly by the growth and separation of boundary layers in the area of rotor and stator radial gaps and fixed blade ends near the annular channel walls. The state of the art provides only limited solutions to this fundamental problem. The general idea of boundary effect by changing the skeleton line type along the blade height is included in the prior art, but the known solutions, especially for the flow conditions at a blade end with radial gap, not sufficiently targeted and thus only partially effective.

FIG. 1 shows a schematic representation of two blade configurations according to the prior art in the meridian plane given by the radial direction r and the axial direction x.

On the left side, a standard blade is shown without variation of the skeleton line type. In this simplest standard case, the blade consists of only one block (Z0) in which the type of skeleton line is given uniformly according to fixed rules. This category includes the so-called CDA (controlled diffusion aerofoils) US4431376 , From an aerodynamic point of view, the CDA aims for a moderate profile frontload.

On the right side, a standard blade is shown with unspecified but continuous variation of the skeleton line type along the blade height. Here, the entire blade is represented by a correspondingly large transition zone (T0). These include concepts from known publications contemplating a rapid transition from a CDA skeleton lineage type to a more profile-behind-target skeleton lineage type in the outboard blade areas (R.F. Behlke, Journal of Turbomachinery, Vol. 8, July 1986).

In addition, there are proposed solutions, in which the marginal zone flow is positively influenced by a particular shape of the blade axis, a bend, a sweep or a V-position (see EP0661413A1 . EP1106835A2 . EP1106836A2 ).

On the one hand, the invention relates to a rotor with a fixed connection to the hub and a free blade end with a radial gap on the housing. Analogously, the invention relates to a stator which has a fixed connection to the edge on the housing side and has a free blade end with a radial gap on the hub side. Finally, the invention relates to a rotor or stator, the hub side as well as the housing side has a firm connection to the edge (shroud configuration).

As in all representations shown here, the inflow of the relevant row of blades takes place, as indicated by the thick arrow, from left to right.

It is disadvantageous in the prior art that the corresponding blade shapes are often deliberately designed with little complexity with respect to the skeleton line shape. In the event that different types of skeleton lines are used along the blade height, there is no blockwise profiling of the profile skeleton lines that could have a greater impact on the profile pressure distribution near the wall to achieve the maximum possible crevice and edge flow settling. In addition, there are no blade concepts with skeleton line distributions along the blade height, which combine a favorable in the blade center region, extreme profile front load in an appropriate manner with a favorable for the edge regions, moderate profile rear load. Therefore, the increases in efficiency and stability of the fluid power machine associated with the prior art are present but comparatively small. Consequently, a corresponding reduction in the number of components is correspondingly small.

The present invention has for its object to provide a rotor or stator blade of the aforementioned type which, while avoiding the disadvantages of the prior art, effectively influencing the edge flow by targeted and problematic, block-wise definition of the profile skeleton lines along the blade height.

According to the invention the object is achieved by the feature combination of the main claim, the subclaims show further advantageous embodiments of the invention.

1. i.) die Verteilung der Skelettlinientypen längs Schaufelhöhe eine extreme aerodynamische Profilvorderlast im Schaufelmittenbereich auf vorteilhafte Weise mit einer aerodynamischen Profilhinterlast in den Randbereichen kombiniert,
2. ii.) in den definierten Randzonen Z1 und Z2 durchgängig ein speziell eingegrenzter Skelettlinientyp gemäß der weiter unten gegebenen Definition vorgesehen ist,
3. iii.) die Wahl des Skelettlinientyps in den sich zur Schaufelmitte hin an Z1 und Z2 anschließenden Transitionszonen T1 und T2 frei ist,
4. iv.) in der definierten mittleren Schaufelzone Z0 durchgängig ein speziell eingegrenzter Skelettlinientyp gemäß der weiter unten gegebenen Definition vorgesehen ist.

According to the invention, for use in a turbomachine, a rotor or stator blade is provided which has different types of profile skeleton lines defined in different zones (blocks) of the blade height defined by meridional flow lines, with the proviso that

1. i) the distribution of the skeleton line types along the blade height combines an extreme aerodynamic profile front load in the blade center area in an advantageous manner with an aerodynamic profile rear load in the edge areas,
2. ii.) in the defined marginal zones Z1 and Z2 is provided throughout a specially limited skeleton line type according to the definition given below,
3. iii.) the selection of the skeleton line type in the transition zones T1 and T2 adjoining the blade center at Z1 and Z2 is free,
4. iv.) in the defined mean blade zone Z0 is provided throughout a specially limited skeleton line type according to the definition given below.

Fig.1:

eine schematische Darstellung zum Stand der Technik,

Fig.2:

die Definition von Meridianstromlinien und Stromlinienprofilschnitten,

Fig.3a:

die erfindungsgemäße Rotorschaufel mit Radialspalt am Gehäuse,

Fig. 3b:

die erfindungsgemäße Statorschaufel mit Radialspalt an der Nabe,

Fig.3c:

die erfindungsgemäße Schaufel ohne Radialspalt, Rotor oder Stator,

Fig.4:

die Definition des Höhenseitenverhältnisses HSV und der individuellen Zonenweiten (Blockweiten) WZ1, WT1, WZ0, WT2, WZ2,

Fig.5:

die erfindungsgemäße Zuordnung der Schaufelzonen (Z1), (Z0), (Z2) und der definierten Skelettlinientypen PF, PM, PR

Fig.6a:

die Definition der Skelettlinie eines Stromlinienprofilschnitts,

Fig.6b:

die Definition des Profilskelettlinientyps "PF" für die Schaufelzone am festen Ende,

Fig.6c:

die Definition des Profilskelettlinientyps "PM" für die Schaufelmittelzone,

Fig.6d:

die Definition des Profilskelettlinientyps "PR" für die Schaufelzone am Radialspalt.

In the following the invention will be described by means of embodiments in conjunction with the figures. Showing:

Fig.1:

a schematic representation of the prior art,

Figure 2:

the definition of meridian streamlines and streamline profile sections,

3a:

the rotor blade according to the invention with a radial gap on the housing,

3b:

the stator blade according to the invention with a radial gap at the hub,

3 c:

the blade according to the invention without a radial gap, rotor or stator,

Figure 4:

the definition of the height-side ratio HSV and the individual zone widths (block widths) WZ1, WT1, WZ0, WT2, WZ2,

Figure 5:

the assignment according to the invention of the blade zones (Z1), (Z0), (Z2) and the defined skeleton line types PF, PM, PR

6a:

the definition of the skeleton line of a streamline profile section,

Figure 6b:

the definition of the profile skeleton line type "PF" for the blade zone at the fixed end,

6C:

the definition of the profile skeleton type "PM" for the vane center zone,

Fig.6d:

the definition of the profile skeleton type "PR" for the blade zone at the radial gap.

Fig. 2 gives a precise definition of the meridional flow lines and the streamline profile sections. The middle meridional flow line is formed by the geometric center of the ring channel. If one establishes a normal at each location of the middle streamline, one obtains the course of the ring channel width W along the flow path and, on the other hand, a number of normals with whose help further meridional flow lines result with the same relative subdivision in the direction of the channel height. The intersection of a meridional streamline with a blade results in a streamline profile intersection.

3a shows the rotor blade according to the invention with a radial gap on the housing "RmR" in the meridian plane determined by the axial coordinate x and the radial coordinate r. Therein, the blade edge zones Z1 and Z2, the transition zones T1 and T2 and the blade central zone Z0 are particularly marked and limited in each case by meridional flow lines as defined in FIG. Each of the five bucket zones is assigned a subset (WZ1, WT1, WZ0, WT2, WZ2) which is measured in the direction of the channel width W.

According to this representation, FIGS. 3 b and 3 c show the stator blade according to the invention with a radial gap at the hub "SmR" and the blade according to the invention (rotor or stator) without a radial gap "RSoR".

wobei

• H die Höhe entlang einer in einem Punkt G senkrecht auf einer mittleren Stromlinie stehenden Geraden,
• L die Länge der Profilsehne, und
• die einzelnen Längen L der Profilsehnen für fünf Stromlinien bei 10 %, 30 %, 50 %, 70 % und 90 % einer Weite W des Strömungskanals sind.

FIG. 4 shows the definition of the altitude aspect ratio, which is decisive for the determination of the respective zone widths. In the lower right half of the picture a blade configuration with a number of meridian flow lines is sketched. The middle streamline first gives the position for the determination of the total blade height H when halving the distance between the leading and trailing edges (point G). The height H is determined along a straight line at point G perpendicular to the middle streamline. Furthermore, five flow lines are specified at 10%, 30%, 50%, 70% and 90% of the channel width W (SL10, SL30, SL50, SL70, SL90), along which the respective chord length L is to be determined. The definition of L is shown for any meridian flow area (um level) in the upper left half of the picture. The chord length resulting at xy% of the channel width is denoted by LSLxy here and in the formulas of FIG. The height aspect ratio is finally to be determined as follows: $$\mathrm{HSV}\mathrm{=}\mathrm{5}\mathrm{\cdot }\mathrm{H}\mathrm{/}\left({\mathrm{L}}_{\mathrm{SL}\mathrm{10}}\mathrm{+}{\mathrm{L}}_{\mathrm{SL}\mathrm{30}}\mathrm{+}{\mathrm{L}}_{\mathrm{SL}\mathrm{50}}\mathrm{+}{\mathrm{L}}_{\mathrm{SL}\mathrm{70}}\mathrm{+}{\mathrm{L}}_{\mathrm{SL}\mathrm{90}}\right)$$

in which

• H is the height along a line perpendicular to a middle streamline at a point G,
• L is the length of the chord, and
• the individual lengths L of the chords for five streamlines at 10%, 30%, 50%, 70% and 90% of a width W of the flow channel are.

$$\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WT}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{,}25\mathrm{\cdot }{\mathrm{HSV}}^{\mathrm{0}\mathrm{,}\mathrm{85}}\right)\mathrm{/}\mathrm{HSV}$$

$$\mathrm{WZ}\mathrm{0}\mathrm{/}\mathrm{W}\mathrm{=}1-\mathrm{WZ}\mathrm{1}\mathrm{/}\mathrm{W}-\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}-\mathrm{WZT}\mathrm{2}\mathrm{/}\mathrm{W}-\mathrm{WZ}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{.}$$

The zone widths are determined as a function of the vertical aspect ratio in relative form (relative to the total channel width W) according to the following calculation rule: $$\mathrm{WZ}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WZ}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{.}\mathrm{10}\mathrm{\cdot }{\mathrm{HSV}}^{\mathrm{0}\mathrm{.}\mathrm{58}}\right)\mathrm{/}\mathrm{HSV}$$

$$\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WT}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{.}25\mathrm{\cdot }{\mathrm{HSV}}^{\mathrm{0}\mathrm{.}\mathrm{85}}\right)\mathrm{/}\mathrm{HSV}$$

$$\mathrm{WZ}\mathrm{0}\mathrm{/}\mathrm{W}\mathrm{=}1-\mathrm{WZ}\mathrm{1}\mathrm{/}\mathrm{W}-\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}-\mathrm{WZT}\mathrm{2}\mathrm{/}\mathrm{W}-\mathrm{WZ}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{,}$$

PF -

Profilskelettlinientyp für die Schaufelzone am festen Ende,

PM -

Profilskelettlinientyp für die Schaufelmittelzone,

PR -

Profilskelettlinientyp für die Schaufelzone am Radialspalt.

5 shows in tabular form the assignment according to the invention of the three blade zones (Z1), (Z0), (Z2) and the skeleton line types PF, PM, PR specified in the following (FIG. 6b-d). For example, for the blade configuration RmR, the type PF is provided in zone (Z1), the type PM in zone (Z0) and the type PR in zone (Z2).

PF -

Profile skeleton line type for the bucket zone at the fixed end,

PM -

Profile skeleton line type for the vane center zone,

PR -

Profile skeleton line type for the blade zone at the radial gap.

The respective skeletal line type is determined in relative representation with the help of the related inclination angle α * and the related run length S *, see Fig.6a. The image shows a streamline profile cut of the blade on a meridian flow surface (um-plane).

$$\mathrm{S}\mathrm{*}\mathrm{=}\frac{{\mathrm{S}}_{\mathrm{P}}}{\mathrm{S}}$$

For this purpose, in all points of the skeleton line of the inclination angle α _P and to go back down run length _P s be determined. As reference values, the inclination angles at leading and trailing edges α1 and α2 as well as the total running length of the skeleton line S are used. The following applies: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\frac{{\mathrm{\alpha }}_{\mathrm{1}}\mathrm{-}{\mathrm{\alpha }}_{\mathrm{P}}}{{\mathrm{\alpha }}_{\mathrm{1}}\mathrm{-}{\mathrm{\alpha }}_{\mathrm{2}}}$$

$$\mathrm{S}\mathrm{*}\mathrm{=}\frac{{\mathrm{S}}_{\mathrm{P}}}{\mathrm{S}}$$

FIG. 6b shows the definition of the skeleton line type "PF" in the above-derived relative representation. Skeleton lines according to the invention are located below a borderline. Skeleton lines in the exclusion area above and on the boundary line are not according to the invention. The skeleton line type "PF" boundary line is given by the following definition: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}\mathrm{3}\mathrm{.}\mathrm{3550017483}{\mathrm{S}\mathrm{*}}^{\mathrm{6}}\mathrm{+}\mathrm{12}\mathrm{.}\mathrm{8091744282}{\mathrm{S}\mathrm{*}}^{\mathrm{5}}\mathrm{-}\mathrm{19}\mathrm{.}\mathrm{1276527122}{\mathrm{S}\mathrm{*}}^{\mathrm{4}}\mathrm{+}\mathrm{14}\mathrm{.}\mathrm{1735887616}{\mathrm{S}\mathrm{*}}^{\mathrm{3}}\mathrm{-}\mathrm{5}\mathrm{.}\mathrm{4814126258}{\mathrm{S}\mathrm{*}}^{\mathrm{2}}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{9327011304}\mathrm{S}\mathrm{*}\mathrm{+}\mathrm{0}\mathrm{.}\mathrm{0513455055}$$

By way of example, a skeleton line distribution which can be provided according to the invention for the blade block at a fixed end is shown.

FIG. 6c shows in the relative representation the definition of the skeleton line type "PM". Skeleton lines according to the invention are located above a boundary line. Skeleton lines in the exclusion area below and on the boundary line are not according to the invention. The boundary line for the skeleton line type "PM" is given by the following definition: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}\mathrm{12}\mathrm{.}\mathrm{3534715888}{\mathrm{S}\mathrm{*}}^{\mathrm{6}}\mathrm{+}\mathrm{43}\mathrm{.}\mathrm{3609801205}{\mathrm{S}\mathrm{*}}^{\mathrm{5}}\mathrm{-}\mathrm{59}\mathrm{.}\mathrm{8902846910}{\mathrm{S}\mathrm{*}}^{\mathrm{4}}\mathrm{+}\mathrm{41}\mathrm{.}\mathrm{7663332787}{\mathrm{S}\mathrm{*}}^{\mathrm{3}}\mathrm{-}\mathrm{15}\mathrm{.}\mathrm{5211559470}{\mathrm{S}\mathrm{*}}^{\mathrm{2}}\mathrm{+}\mathrm{3}\mathrm{.}\mathrm{6376953490}\mathrm{S}\mathrm{*}-\mathrm{0}\mathrm{.}\mathrm{0064632100}$$

By way of example, a skeleton line distribution which can be provided according to the invention for the block in the center of the blade is shown.

Fig. 6d shows in the relative representation the definition of the skeleton line type "PR". Skeleton lines according to the invention are located below a borderline. Skeleton lines in the exclusion area above and on the boundary line are not according to the invention. The boundary line for the skeleton line type "PR" is given by the following definition: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}\mathrm{10}\mathrm{.}\mathrm{5762327507}{\mathrm{S}\mathrm{*}}^{\mathrm{6}}\mathrm{+}\mathrm{40}\mathrm{.}\mathrm{2486019609}{\mathrm{S}\mathrm{*}}^{\mathrm{5}}\mathrm{-}\mathrm{59}\mathrm{.}\mathrm{8510217536}{\mathrm{S}\mathrm{*}}^{\mathrm{4}}\mathrm{+}\mathrm{45}\mathrm{.}\mathrm{2961721770}{\mathrm{S}\mathrm{*}}^{\mathrm{3}}\mathrm{-}\mathrm{18}\mathrm{.}\mathrm{6486044740}{\mathrm{S}\mathrm{*}}^{\mathrm{2}}\mathrm{+}\mathrm{4}\mathrm{.}\mathrm{4885201025}\mathrm{S}\mathrm{*}\mathrm{+}\mathrm{0}\mathrm{.}\mathrm{0480220659}$$

By way of example, a skeleton line distribution which can be provided according to the invention for the blade block at the radial gap is shown.

In the blade according to the invention for fluid flow machines such as fans, compressors, pumps and fans an edge flow control is achieved, which can increase the efficiency of each stage by about 1% with the same stability. In addition, a reduction in the number of blades of up to 20% is possible. The inventive concept is applicable to different types of turbomachines and, depending on the degree of utilization of the concept, leads to reductions in costs and weight for the turbomachine of 2% to 10%. In addition, there is an improvement in the overall efficiency of the fluid flow machine, depending on the application, of up to 1.5%.

Claims (6)

A turbomachine blade having a tread line extending along a meridional flow line, said blade being radially divided into at least three zones (Z0, Z1, Z2) and within each of said three zones from each radially inner to radially outer edge said tread lines each zone (Z0, Z1, Z2) is designed to satisfy the following equations: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\frac{{\mathrm{\alpha }}_{\mathrm{1}}\mathrm{-}{\mathrm{\alpha }}_{\mathrm{P}}}{{\mathrm{\alpha }}_{\mathrm{1}}\mathrm{-}{\mathrm{\alpha }}_{\mathrm{2}}}$$

$$\mathrm{S}\mathrm{*}\mathrm{=}\frac{{\mathrm{S}}_{\mathrm{P}}}{\mathrm{S}}$$

in which P is any point of the profile skeleton line, α _{1 is} the angle of inclination at the blade leading edge, α _{2 is} the angle of inclination at the blade trailing edge, - α * the dimensionless, related angle of the total curvature, - S * the dimensionless, related run length, - α _{P is} the angle of the tangent at any point P of the profile skeleton line to the central meridional flow line, - s _{P is} the run length of the profile skeleton line at any point P, and - S are the total running length of the profile skeleton line. A blade according to claim 1, having a profile skeleton line (PF) for a zone of the blade at its fixed end, which is formed according to the following equation: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}\mathrm{3}\mathrm{.}\mathrm{3550017483}{\mathrm{S}\mathrm{*}}^{\mathrm{6}}\mathrm{+}\mathrm{12}\mathrm{.}\mathrm{8091744282}{\mathrm{S}\mathrm{*}}^{\mathrm{5}}\mathrm{-}\mathrm{19}\mathrm{.}\mathrm{1276527122}{\mathrm{S}\mathrm{*}}^{\mathrm{4}}\mathrm{+}\mathrm{14}\mathrm{.}\mathrm{1735887616}{\mathrm{S}\mathrm{*}}^{\mathrm{3}}\mathrm{-}\mathrm{5}\mathrm{.}\mathrm{4814126258}{\mathrm{S}\mathrm{*}}^{\mathrm{2}}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{9327011304}\mathrm{S}\mathrm{*}\mathrm{+}\mathrm{0}\mathrm{.}\mathrm{0513455055}$$

A blade according to claim 1 or 2, having a sectional skeleton line (PM) for a blade central zone, which is formed according to the following equation: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}\mathrm{12}\mathrm{.}\mathrm{3534715888}{\mathrm{S}\mathrm{*}}^{\mathrm{6}}\mathrm{+}\mathrm{43}\mathrm{.}\mathrm{3609801205}{\mathrm{S}\mathrm{*}}^{\mathrm{5}}\mathrm{-}\mathrm{59}\mathrm{.}\mathrm{8902846910}{\mathrm{S}\mathrm{*}}^{\mathrm{4}}\mathrm{+}\mathrm{41}\mathrm{.}\mathrm{7663332787}{\mathrm{S}\mathrm{*}}^{\mathrm{3}}\mathrm{-}\mathrm{15}\mathrm{.}\mathrm{5211559470}{\mathrm{S}\mathrm{*}}^{\mathrm{2}}\mathrm{+}\mathrm{3}\mathrm{.}\mathrm{6376953490}\mathrm{S}\mathrm{*}-\mathrm{0}\mathrm{.}\mathrm{0064632100}$$

A blade according to any one of claims 1 to 3, having a profile skeleton line (PR) for a zone of the blade at the radial gap formed according to the following equation: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}\mathrm{10}\mathrm{.}\mathrm{5762327507}{\mathrm{S}\mathrm{*}}^{\mathrm{6}}\mathrm{+}\mathrm{40}\mathrm{.}\mathrm{2486019609}{\mathrm{S}\mathrm{*}}^{\mathrm{5}}\mathrm{-}\mathrm{59}\mathrm{.}\mathrm{8510217536}{\mathrm{S}\mathrm{*}}^{\mathrm{4}}\mathrm{+}\mathrm{45}\mathrm{.}\mathrm{2961721770}{\mathrm{S}\mathrm{*}}^{\mathrm{3}}\mathrm{-}\mathrm{18}\mathrm{.}\mathrm{6486044740}{\mathrm{S}\mathrm{*}}^{\mathrm{2}}\mathrm{+}\mathrm{4}\mathrm{.}\mathrm{4885201025}\mathrm{S}\mathrm{*}\mathrm{+}\mathrm{0}\mathrm{.}\mathrm{0480220659}$$

A blade according to any one of claims 1 to 4, wherein a height side ratio (HSV) is determined according to the following equation: $$\mathrm{HSV}\mathrm{=}\mathrm{5}\mathrm{\cdot }\mathrm{H}\mathrm{/}\left({\mathrm{L}}_{\mathrm{SL}\mathrm{10}}\mathrm{+}{\mathrm{L}}_{\mathrm{SL}\mathrm{30}}\mathrm{+}{\mathrm{L}}_{\mathrm{SL}\mathrm{50}}\mathrm{+}{\mathrm{L}}_{\mathrm{SL}\mathrm{70}}\mathrm{+}{\mathrm{L}}_{\mathrm{SL}\mathrm{90}}\right)\mathrm{,}$$

in which H is the height along a line perpendicular to a middle streamline at a point G, - L the length of the chord, and - The individual lengths L of the chords for five streamlines at 10%, 30%, 50%, 70% and 90% of a width W of the flow channel are. A blade according to claim 5, wherein zone widths are relative to the height side ratio (HSV) in relative terms to a total channel width (W) according to the following calculation rule: $$\mathrm{WZ}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WZ}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{.}\mathrm{10}\mathrm{\cdot }{\mathrm{HSV}}^{\mathrm{0}\mathrm{.}\mathrm{58}}\right)\mathrm{/}\mathrm{HSV}$$

$$\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WT}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{.}25\mathrm{\cdot }{\mathrm{HSV}}^{\mathrm{0}\mathrm{.}\mathrm{85}}\right)\mathrm{/}\mathrm{HSV}$$

$$\mathrm{WZ}\mathrm{0}\mathrm{/}\mathrm{W}\mathrm{=}1-\mathrm{WZ}\mathrm{1}\mathrm{/}\mathrm{W}-\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}-\mathrm{WZT}\mathrm{2}\mathrm{/}\mathrm{W}-\mathrm{WZ}\mathrm{2}\mathrm{/}\mathrm{W}.$$

in which W is the channel width, WZ1 the channel width in a zone 1, WZ2 the channel width in a zone 2, WZ0 the channel width in a middle zone, WT1 the channel width in a transitional area between the zone Z1 and the zone Z0, and - WT2 are the channel width in a transitional area between the zones Z0 and Z2.

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