EP1798375A2 - Airfoil shape for variable stator vanes - Google Patents

Abstract

For the purposes of blade profile definition, a profile skeleton line extends along the meridional flow line, and the stator is divided into three radial zones (Z0, Z1, Z2). These zones, from the radially inner- to the radially-outer edge, have a profile skeleton line constructed to satisfy a set of equations. These relate angles of inclination at the stator leading edge (alpha 1) and trailing edge (alpha 2), the dimensionless reference angle of overall curvature (alpha star), dimensionless running length (S) (reference) and angles (alpha P) between the tangent and meridional flow line at each point, and other variables.

Description

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

In detail, the invention relates to at least one adjustable stator blade, possibly also an adjustable Vorleitrad, a fluid flow machine. The blading in question is within a housing, which limits the flow through at least one rotor and a stator with a fluid to the outside. While a rotor comprises a plurality of rotor blades attached to a rotating shaft and supplies energy to the working fluid, a stator consists of a plurality of stator blades usually mounted in the housing.

The aerodynamic load capacity and the efficiency of fluid flow machines, such as fans, compressors, pumps and fans, is limited in particular by the growth and separation of boundary layers in the region of the radial gap between the blading and the housing or hub, which is structurally necessary at the annular channel edge.

Rotary adjustable stators in particular, which are characterized by the necessary free cuts in front of and behind the rotary spindle, have a pronounced radial gap and cause considerable flow losses. In order to limit these losses, turntables as large as possible are usually provided at the inner and outer ends of the adjusting stators in order to keep the extent of the cutouts in the flow direction small. Preferably, the turntables are arranged so that they are located in the critically classified profile leading edge zone of the blade edge cuts.

However, due to failure guidelines and design restrictions, there are often configurations of adjustable stators that have only a small size and a position of the turntable that is not far enough forward. Then inevitably remains a considerable radial gap, both in front of and behind the turntable. The prior art does not provide aerodynamically favorable solutions to this fundamental problem. The general idea of edge control of radial run gaps by changing the skeleton line type along the blade height is included in the prior art, but the known solutions, in particular for the flow conditions at a blade end with turntable and two partial radial gaps are not suitable and therefore ineffective.

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. The presentation is limited to a mounted in hub as housing variable stator, a storage solely in housing or hub with a full radial gap at the other end of the blade but in some cases also occurs.

On the left side of the picture, a conventional variable stator without variation of the skeleton line type is shown. In this simplest standard case, the blade consists of only one block (ZO) in which the type of skeleton line is given according to uniform 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 of a conventional bucket with a reaching to the front edge turntable is shown. Instead of a completely uniform profiling, the blade according to the prior art can also be subjected over the entire height to a continuous change of the profile type. Then the whole bucket is not represented by a block (Z0) of uniform profiling but by a single large transition zone. These include concepts from prior art publications contemplating a transition from a CDA skeleton lineage type to a more profile-behind-loading skeleton lineage type in the outboard blade areas ( RF 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 ). None of the existing solutions relates to adjustable stators.

The present invention relates to stators, which are rotatably mounted on at least one blade end and can be adjusted via a spindle about a fixed axis of rotation. 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. Particularly in the case of adjustable stators, blade concepts with a skeleton line variation along the blade height, which lack a profile preliminary load that is favorable in the blade center region, are lacking appropriate way with a favorable for the edge areas type of load distribution.

The present invention has for its object to provide an adjustable stator blade of the type mentioned, which achieves a very effective influencing the edge flow through targeted and problematic, block-wise definition of the profile skeleton lines along the blade height while avoiding the prior art.

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 ausgeprägte aerodynamische Profilvorderlast im Schaufelmittenbereich auf vorteilhafte Weise mit einer speziellen Profillastverteilung 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, an adjustable stator blade is provided for use in a fluid flow machine, 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 skeletal line types along the blade height combines a pronounced aerodynamic profile front load in the blade center region in an advantageous manner with a specific profile load distribution in the edge regions,
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 a specially constrained skeleton line type is provided according to the definition given below.

• Fig.1: eine schematische Darstellung von Verstellstatoren nach dem Stand der Technik,
• Fig.2: die Definition von Meridianstromlinien und Stromlinienprofilschnitten,
• Fig.3a: einen erfindungsgemäßen Verstellstator (Lagerung in Gehäuse und Nabe) "SGN",
• Fig.3b: einen erfindungsgemäßen Verstellstator (Lagerung im Gehäuse) "SG",
• Fig.3c: einen erfindungsgemäßen Verstellstator (Lagerung in der Nabe) "SN",
• Fig.3d: die erfindungsgemäße Zuordnung der Schaufelzonen Z1, Z0, Z2 und der definierten Skelettlinientypen PM und PR,
• Fig.4: die Definition des Höhenseitenverhältnisses HSV und der individuellen Zonenweiten (Blockweiten) WZ1, WT1, WZ0, WT2, WZ2,
• Fig.5: die Definition der Drehachsenposition an den Schaufelenden,
• Fig.6a: die Definition der Skelettlinie eines Stromlinienprofilschnitts,
• Fig.6b: die Definition des Profilskelettlinientyps "PM" für die Schaufelmittelzone,
• Fig.6c: die Definition des Profilskelettlinientyps "PR" für die Schaufelrandzone bei einer Drehachsenposition von D=0,3,
• Fig.6d: die Definition des Profilskelettlinientyps "PR" für die Schaufelrandzone bei einer Drehachsenposition von D=0,5.

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

• 1 shows a schematic representation of prior art Verstellstatoren,
• 2 shows the definition of meridional flow lines and streamline profile sections,
• 3a shows a variable stator according to the invention (storage in housing and hub) "SGN",
• 3 b shows a variable stator according to the invention (storage in the housing) "SG",
• 3 c shows an adjusting stator according to the invention (storage in the hub) "SN",
• 3d shows the assignment according to the invention of the blade zones Z1, Z0, Z2 and the defined skeleton line types PM and PR,
• 4 shows the definition of the height side ratio HSV and the individual zone widths (block widths) WZ1, WT1, WZ0, WT2, WZ2,
• 5: the definition of the rotational axis position at the blade ends,
• 6a: the definition of the skeleton line of a streamline profile section,
• 6b: the definition of the profile skeleton type "PM" for the vane center zone,
• FIG. 6c shows the definition of the profile skeleton type "PR" for the blade edge zone at a rotational axis position of D = 0.3, FIG.
• FIG. 6d shows the definition of the profile skeleton type "PR" for the blade edge zone at a rotational axis position of D = 0.5.

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 invention adjustable stator blade with storage in housing and hub "SGN" 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.

3b and 3c show the stator blade according to the invention with mounting in the housing "SG" and the stator blade according to the invention with mounting in the hub "SN".

• PM - Profilskelettlinientyp für die Schaufelmittelzone,
• PR - Profilskelettlinientyp für die Schaufelrandzone.

FIG. 3d shows in tabular form the assignment according to the invention of the three blade zones Z1, Z0, Z2 and the skeleton line types PM and PR specified in the following (FIG. 6b-d). For example, for the blade configuration "SGN", the type PR is provided in zone Z1, the type PM in zone Z0 and the type PR in zone Z2. Freely configurable is the zone Z1 in the case of the blade configuration "SG" and the zone Z2 in the case of the blade configuration "SN" due to the missing at the respective blade end turntable.

• PM - profile skeleton line type for the vane center zone,
• PR - profile skeleton line type for the blade edge zone.

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 determined as follows: $$\mathrm{HSV}=5\cdot \mathrm{H}/\left({\mathrm{L}}_{\mathrm{SL}10}+{\mathrm{L}}_{\mathrm{SL}30}+{\mathrm{L}}_{\mathrm{SL}50}+{\mathrm{L}}_{\mathrm{SL}70}+{\mathrm{L}}_{\mathrm{SL}90}\right)\mathrm{,}$$

$$\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WT}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{,}\mathrm{30}\mathrm{\cdot }{\mathrm{HSV}}^{\mathrm{0}\mathrm{,}\mathrm{80}}\right)\mathrm{/}\mathrm{HSV}$$

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

The zone widths are determined in relation to the vertical aspect ratio in relative form (relative to the Total channel width W determined according to the following calculation rule: $$\mathrm{WZ}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WZ}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{.}\mathrm{06}\mathrm{\cdot }{\mathrm{<figure-callout\; id="0"\; label="HSV"\; filenames="imgf0012.png"\; state="\{\{state\}\}">HSV</figure-callout>}}^{\mathrm{0}\mathrm{.}\mathrm{65}}\right)\mathrm{/}\mathrm{HSV}$$

$$\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WT}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{.}\mathrm{30}\mathrm{\cdot }{\mathrm{<figure-callout\; id="0"\; label="HSV"\; filenames="imgf0012.png"\; state="\{\{state\}\}">HSV</figure-callout>}}^{\mathrm{0}\mathrm{.}\mathrm{80}}\right)\mathrm{/}\mathrm{HSV}$$

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

5 shows the definition of the rotational axis position, which is co-determining for the invention according to the invention provided profile skeleton line type PR. The picture shows a schematic of the streamline section through the adjustable stator blade at 5% and 95% channel width, respectively. Shown is the puncture point of the axis of rotation in the plane of the streamline section, point D. This point does not necessarily have to lie within the profile, as shown here. The entire chord length is L. Determined by the perpendicular Lot of the point D on the chord, one obtains the measured distance d of the axis of rotation in the same direction from the front edge. The relative position of the axis of rotation in the direction of the chord is denoted by d * = d / L.

The respective skeleton 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 picture shows a streamlined section of the blade on a meridian flow surface (u-m plane).

For this purpose, the inclination angle αP and the run length sP covered up to this point are determined in all points of the skeleton line. 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: $$\mathrm{\alpha }\mathrm{*}\left(\mathrm{\alpha }\mathrm{1}\mathrm{-}\mathrm{\alpha P}\right)\mathrm{/}\mathrm{(}\mathrm{\alpha }\mathrm{1}\mathrm{-}\mathrm{\alpha }\mathrm{2}\mathrm{)}\mathrm{and\; s}\mathrm{*}\mathrm{sP}\mathrm{/}\mathrm{S}\mathrm{,}$$

FIG. 6b shows in the known 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: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}\mathrm{3}\mathrm{.}\mathrm{8512520965}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{6}}\mathrm{+}\mathrm{14}\mathrm{.}\mathrm{6764714420}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{5}}\mathrm{-}\mathrm{21}\mathrm{.}\mathrm{6808727924}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{4}}\mathrm{+}\mathrm{16}\mathrm{.}\mathrm{3850592743}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{3}}\mathrm{-}\mathrm{6}\mathrm{.}\mathrm{9703863077}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{2}}\mathrm{+}\mathrm{2}\mathrm{.}\mathrm{4431236235}\left(\mathrm{s}\mathrm{*}\right)\mathrm{-}\mathrm{0}\mathrm{.}\mathrm{0060854622}$$

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. FIGS. 6c and 6d show in the known relative representation the definition of the skeletal line type "PR" for the rotational axis positions d * = 0.3 and d * = 0.5. Skeleton line courses according to the invention are located below the continuous upper limit line and run over the lower limit line given in a specific interval. Skeleton lines in the exclusion area above and on the upper boundary line are not according to the invention. Skeleton line courses below or on the lower boundary line are also not according to the invention.

Depending on the relative rotational axis positions d *, the boundary lines for the skeleton line type "PR" are given by the following definitions:

Upper limit line for d * = 0.3: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}15.1441661664\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{6}}\mathrm{+}52.8168915277\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{5}}\mathrm{-}67.2135203453\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{4}}\mathrm{+}35.9670881201\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{3}}\mathrm{-}6.8146566070\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{2}}\mathrm{+}1.3350483823\left(\mathrm{s}\mathrm{*}\right)+\mathrm{0}\mathrm{.}0535731815$$

Upper limit line for d * = 0.5: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}3.6478453237\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{6}}\mathrm{+}5.6044881912\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{5}}\mathrm{-}5.3211690262\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{4}}\mathrm{+}11.7583720270\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{3}}\mathrm{-}4.3361971934\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{2}}\mathrm{+}0.8062070974\left(\mathrm{s}\mathrm{*}\right)+\mathrm{0}\mathrm{.}0502599068$$

For axes of rotation positions d * other than 0.3 and 0.5, when determining the values of α *, linearly interpolate between those for d * = 0.3 and d * = 0.5: $$\mathrm{\alpha }\mathrm{*}\left(\mathrm{d}\mathrm{*}\right)\mathrm{=}\mathrm{\alpha }\mathrm{*}\left(\mathrm{d}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{5}\right)\mathrm{+}\left[\mathrm{\alpha }\mathrm{*}\left(\mathrm{d}\mathrm{*}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{3}\right)\mathrm{-}\mathrm{\alpha }\left(\mathrm{d}\mathrm{*}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{5}\right)\right]\mathrm{*}\left[\mathrm{0}\mathrm{.}\mathrm{5}\mathrm{-}\mathrm{d}\mathrm{*}\right]\mathrm{/}\mathrm{0}\mathrm{.}\mathrm{2}$$

Lower limit . $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{2}\mathrm{.}\mathrm{0}\left(\mathrm{s}\mathrm{*}\right)\mathrm{-}\mathrm{2}\mathrm{d}\mathrm{*}$$

Valid in the interval of s *: (d * + 0.1, d * + 0.3) By way of example, in FIGS. 6c and 6d, a skeleton line distribution which can be provided according to the invention for the blade edge block 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 (7)

A fluid flow machine displacement stator having a tine line extending along a meridional flowline, said stator being radially divided into at least three zones (Z0, Z1, Z2) and within each of said three zones from said radially inner to radially outer edges the profile skeleton lines of each zone (Z0, Z1, Z2) are 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, α1 the angle of inclination at the stator leading edge, α ₂ the inclination angle at the stator 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. Stator according to claim 1, having a profile skeleton line (PM) for a zone of the stator in the blade center region, which is formed according to the following equation: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}\mathrm{3}\mathrm{.}\mathrm{8512520965}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{6}}\mathrm{+}\mathrm{14}\mathrm{.}\mathrm{6764714420}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{5}}\mathrm{-}\mathrm{21}\mathrm{.}\mathrm{6808727924}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{4}}\mathrm{+}\mathrm{16}\mathrm{.}\mathrm{3850592743}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{3}}\mathrm{-}\mathrm{6}\mathrm{.}\mathrm{9703863077}\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{2}}\mathrm{+}\mathrm{2}\mathrm{.}\mathrm{4431236235}\left(\mathrm{s}\mathrm{*}\right)\mathrm{-}\mathrm{0}\mathrm{.}\mathrm{0060854622}$$

Stator according to claim 1 or 2, having a profile skeleton line (PR) at its fixed end for a relative rotational axis position d * = 0.3, which is formed according to the following equation: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}\mathrm{-}15.1441661664\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{6}}\mathrm{+}52.8168915277\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{5}}\mathrm{-}67.2135203453\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{4}}\mathrm{+}35.9670881201\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{3}}\mathrm{-}6.8146566070\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{2}}\mathrm{+}1.3350483823\left(\mathrm{s}\mathrm{*}\right)+\mathrm{0}\mathrm{.}0535731815$$

Stator according to claim 1 or 2, having a profile skeleton line (PR) at its fixed end for a relative rotational axis position d * = 0.5, which is formed according to the following equation: $$\mathrm{\alpha }\mathrm{*}\mathrm{=}3.6478453237\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{6}}\mathrm{+}5.6044881912\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{5}}\mathrm{-}5.3211690262\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{4}}\mathrm{+}11.7583720270\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{3}}\mathrm{-}4.3361971934\mathrm{(}\mathrm{s}\mathrm{*}{\mathrm{)}}^{\mathrm{2}}\mathrm{+}0.8062070974\left(\mathrm{s}\mathrm{*}\right)+\mathrm{0}\mathrm{.}0502599068$$

Stator according to Claim 1 or 2, having a profile skeleton line (PR) for a relative rotational axis position d * not equal to 0.3 and 0.5, which is formed according to the following equation: $$\mathrm{\alpha }\mathrm{*}\left(\mathrm{d}\mathrm{*}\right)\mathrm{=}\mathrm{\alpha }\mathrm{*}\left(\mathrm{d}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{5}\right)\mathrm{+}\left[\mathrm{\alpha }\mathrm{*}\left(\mathrm{d}\mathrm{*}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{3}\right)\mathrm{-}\mathrm{\alpha }\left(\mathrm{d}\mathrm{*}\mathrm{=}\mathrm{0}\mathrm{.}\mathrm{5}\right)\right]\mathrm{*}\left[\mathrm{0}\mathrm{.}\mathrm{5}\mathrm{-}\mathrm{d}\mathrm{*}\right]\mathrm{/}\mathrm{0}\mathrm{.}\mathrm{2}$$

Stator according to one of claims 1 to 5, 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. Stator according to claim 6, wherein zone widths as a function of the height side ratio (HSV) in relative form, relative to a total channel width (W), are determined according to the following calculation rule: $$\mathrm{WZ}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WZ}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{.}\mathrm{06}\mathrm{\cdot }{\mathrm{HSV}}^{\mathrm{0}\mathrm{.}\mathrm{65}}\right)\mathrm{/}\mathrm{HSV}$$

$$\mathrm{WT}\mathrm{1}\mathrm{/}\mathrm{W}\mathrm{=}\mathrm{WT}\mathrm{2}\mathrm{/}\mathrm{W}\mathrm{=}\left(\mathrm{0}\mathrm{.}\mathrm{30}\mathrm{\cdot }{\mathrm{HSV}}^{\mathrm{0}\mathrm{.}\mathrm{80}}\right)\mathrm{/}\mathrm{HSV}$$

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

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.

Images