Parametric blades for rotary machines

Description

State of the Art

In the state of the art the shape of the blade can be defined in different ways. The definitions assumed hereafter refer to "Staking", "Sweep" and "Lean" (or Dihedral) .

The Staking is generally the radial composition of Sweep and Lean.

The Sweep is: 1) either the radial distribution of the airfoils in direction parallel to the chord; 2) or the radial distribution of the airfoils in direction parallel to the spin axis of the machine.

The Lean or Dihedral is 1) either the radial distribution of the airfoils in direction perpendicular to the chord; 2) or the radial distribution of the airfoils perpendicularly to the spin axis of the machine .

The first definition is preferable to design rotor blades "33" and stator blades "44" with high twist and pitch; the second definition instead is advised for blades that have small aspect ratio, pitch and twist.

Fig.l refigure blades, according to definition 2), with sweep and lean, respectively, perpendicular and parallel to the spin axis of the machine.

Sweep and a lean define together the airfoil position' s and the shape of the blades and are strictly related to

aerodynamic & acoustic performances and to mechanical stress of rotary machines with axial or mix flows.

Till now, some ideas have been disclosed to design stator and rotor blades with various lean and sweep, but none of them considers the ideas proposed in this application. The author proposed sinusoidal swept rotor blades suitable to reduce aerodynamic torque and mechanical stresses, patent WO/02055845 Al. The General Electric introduced a sinusoidal swept design to reduce shock loses in the patent GB2431697. Examples of non linear distributions of the lean instead have been proposed in patent US2005008494 and EP1333181. A combination of lean and the sweep, based on polynomial curves of the fourth order, has been instead proposed in the patent US2006210395.

No reference have been instead found for aerodynamic airfoils realized with arc of ellipses and blades with variable geometries.

Currently, there are a number of different airfoils used to design rotor and stator blades; for instance:

• Airfoils type NACA, Clark etc, based on a continues distribution of the thickness along the centre line (e.g. the centre line may be realized with arcs of circumference, parabola, ellipse or a spline) .

• Airfoils DCA (Double Circular Arc) , MCA (Arches Multiple Circulars), employed for transonic flows.

• Airfoils designed with programs (e.g. based on the inverse design and the diffusion control) . The designer generate the airfoils with programs which elaborate

iteratively some inputs (e.g. the isentropic Mach distributions on both the pressure and suction sides of the airfoil, the diffusion factor, the flow angles, the solidity, the chord and the pitch) .

The novelty of the ideas introduced in this patent application, will became readily apparent in the description and in the relevant drawings, everyone of which means to represent rather than to limit the scope of the invention.

Short description of the patent

This patent concerns the optimization of rotor "33" and stator "44" parametric blade's for employment in axial and mix flow rotary machines.

The solutions proposed herewith are one or a combination of the following:

1. Blades with Sinusoidal Lean,-

2. Blades with Sinusoidal stacking (Lean plus Sweep) where the sinusoids are not necessarily similar and may both be in phase or not .

3. 3D parametric blades further characterized from (chord, curvature, thickness, etc) controlled with parametric curves in radial direction, not necessarily having a sinusoidal shape.

4. At least one succession of one rotor and one stator row with sinusoidal lean and sweep not necessarily similar.

5. Parametric airfoils, located on planar, axis-symmetric or stream surfaces, realized with arcs of ellipsis.

6. Blades generated with 3D parametric CAD software suitable to be controlled with programs (e.g.. Excel, Matlab, etc) . The blades herewith disclosed can be used also within a number of optimization systems. They can be integrated, automatically or semi- automaticalIy, within iterative designing cycles (e.g.. of the type based on neural networks and/or genetic algorithms) .

7. At least one stator or rotor rows with sinusoidal stacked blades, characterized from variable chord and/or pitch distributions.

8. Stator and rotor rows with sinusoidal stacked blades, designed with single and/or slotted airfoils.

9. Blades built with memory form material to increase the stability margins and reduce losses.

The advantages foresee from the proposed parametric airfoils & blades are:

• Reduction of the acoustic emissions and increment of the efficiency;

• Reduction of secondary vortices and leakage losses;

• Reduction of mechanical stresses, vibrations, deformations and possibility to use composite material to built complex shapes;

• Increment of the torsional rigidity of the blade,-

• Continuity of the curvature;

• Control of the gap between rotor blades and duct with either aero-elastic or centrifugal deformations;

• Flexibility and simplicity to create 3D parametric airfoils and blades;

• Integration of parametric blades in optimization process .

A first confirmation of the achievable results have been found numerically (with 3D CFD computations) and experimentally (testing and comparing few rotor prototypes) .

Description of the drawings

Fig. Ia defines a stator blade "44" with lean and sweep characterized from sinusoidal curves similar and in phase; Fig. Ib defines a rotor blade "33" with lean and sweep characterized from sinusoidal curves different and not in phase .

Fig.2 shows five different distributions of sinusoidal lean defined with periodic sinusoidal curves (2a & 2b) , with non periodic sinusoidal curves (2c & 2d) and with sinusoidal curves having a minimum to one tip (2e) .

Fig.3 schematizes a few examples of applications in which the blades herewith proposed can be employed. Fig.3a represents the front part of a turbofan with the fan, its relative stator and the first stage of the booster. In this and the following drawings, the "phantom" lines (line and points) represent the lean: the two phantom lines, present on the blades, indicate the concave part of the sinusoids; the example outlines blades with lean not in phase between rotor and stator rows.

Fig.3b shows the front part of a turbofan in which the rotor "33" and stator "44" blades are, partially or entirely, realized with multiple airfoils "22" (the sinusoidal lean is not represented, it can be similar or different to Fig.3a) . Fig.3ba, 3bb 3bc and 3bd illustrate a few combinations between the sections "p" (section where the multiple airfoils become single airfoil in radial direction of blades

"33" and "44") . The section of the downstream blade "P _v " can be located with an offset positive " +" , negative "- " or coincide with the section of the upstream blade "P _M " •

The sections "P _v " and "P _M " can be defined on orthogonal planes, streamsurfaces or axis-symmetric surfaces.

Fig.3c represent one of the possible applications with counter rotating rotors.

Fig.3d shows a ducted fan with stators upstream and downstream the rotor (only one stator row upstream or downstream may be used as well) .

Fig.3e schematize a stage of turbine with IGV (Inlet Guides

Vanes) . Not all the applications where those blades may be used are schematized in the drawings.

Fig.4 shows a few of the combinations between sinusoidal lean and sweep that can be used to design blades "33" and "44"

Fig.5 illustrates simple examples of three sinusoidal parametric distributions (e.g. lean, sweep and chord) connected each other to reduce number of parameters .

Fig.6 Fig.7 and Fig.8 show a few possible combinations of the lean between blades "44" and "33". Figures a are the top views and figures b are the side views. In these figures, and only for illustrative purposes, the rotor and stator blades are similar and are aligned; in practice those blades must be designed and rotated in agreement to their speed triangles .

In Fig.6 the rotor and stator blades have sweep and lean similar; in Fig.7 the sweep is similar but the lean it is not in phase; in Fig.8 the lean is similar and the sweep not in phase. Of course more combination may be used and not necessarily with both lean and sweep defined from sinusoidal shape .

Fig.9a and Fig.9b show a portion of a rotor, respectively with and without a shroud. The shroud is an axis -symmetric airfoil located around one of the tip of the blades. Also stators with one shroud may include one of the solution proposed in this patent application.

Fig.10 illustrates three similar blades designed so that the leading edge distribution "LE" is respectively forward, centred and backward, respect to a radial line "R" passing for the LE root of the blade.

Fig.11 shows some parametric distributions of the chord defined by means of continuous curves. The stacking in this case it is the same on each blade.

Fig.12 illustrates a few of the blade shapes that could be designed with a sinusoidal lean. Fig.l2g and 12h shows one example of blades built with airfoils "11" and "22" realized with arch of ellipses. Fig.l2i and Fig.121 represent blades obtained interpolating a different number of airfoils.

Fig.13 shows blades with the extremities defined by arc of ellipse, solution employed to realize also the blades of Fig.l2g, 12h, 14 and 15.

Fig.14 represents a fan with variable pitch rotor blades "33" . Also variable pitch propeller or stators can have one of the solution herewith described.

Fig.15 represent one example of propeller with sinusoidal lean; in this case the blades are realized with multiple airfoils "22" to the hub and single airfoils "11" to the tip.

Fig.16 sketches some of either the stator or rotor row's configurations where the solutions herewith proposed may be used. Indeed, apart standard rows, type 16a, in which the distance between the blade "t" is constant and the airfoils have the same chord, the following configurations may be employed: rows with non constant "t" (e.g.. Fig.16b); rows with non constant chord (e.g.. Fig.16c, 16d, 16e) ; rows with constant chord and "t" with the airfoils disposed on continuous curves (e.g.. Fig.l6f shows a sinusoidal path); a combination of the previous,- moreover rotor and stator rows could have chords distributions in agreement to Fig.16 but not necessarily similar each radial section.

Fig.17 illustrates a few of the parametric airfoil that may be realized with arc of ellipses and defines some of the parameters used in the following description.

Fig.18 and Fig.19 show a few of the possibilities available to generate airfoils using at least two ellipses.

Fig.20a and Fig.20b show simple examples of airfoils "11" with either the suction ore the pressure side designed with more than one ellipses.

Fig.21 illustrates few examples of multiple airfoils "22" realized with arches of ellipse. Such airfoils are composed from at least one main airfoil "1" and one other "2", placed downstream of the first one, that can be partially overlapped (Fig.21a and 2Id), aligned (Fig.21b) or not overlapped (Fig.21c) . Airfoils "1" and "2" may be contained inside one main airfoil ^« pp" either defined from arches of ellipses or not.

Fig.22 represents a fan with variable Intake" and "Nozzle" realized moving axially the spinner "Og" and/or the exhaust cone "Cs" .

Detailed description of the patent

The blades with sinusoidal lean and sweep discussed in this patent, are generated both with periodic or non periodic waves made either with continuous curves type spline, Bezier curve, or with arches of (circumference, ellipse, parabola & hyperbola) themselves tangent and with opposite orientation, or with a combination of the above curves with or without lines in between.

Fig.2 shows a few example of one blade designed with different sinusoidal lean. Between the possible cases, not all shown in the figures, one of the best compromise between the aerodynamics, the mechanics and the acoustics of the blades, especially for rotor application, is the solution shown in Fig.2d. In fact this lean distribution (and similar) allows having blades stiff to the hub (zone subject to the greatest mechanical stresses) ; it allows to reduce the secondary vortices, the leakage losses and the shock losses to the tip (consequently reducing acoustic emissions and increasing both efficiency and the stability) ; it is useful to compensate the centrifugal force with the bending of the tip; it may increase the torsional rigidity on the top of the blade (where a little change in stagger modify sensibly mass flow and back pressure) .

The sinusoids defined for the lean can be used to define the sweep in analogous way, even if the optimal distribution can differ from the optimal distribution of the lean.

The sweep and lean curves can be generally oriented in three different ways. Fig.10 illustrates these three orientation referred to the sweep: the leading edge distribution "LE" is respectively forward, centred and backward, respect to a radial line "R" passing for the LE root of the blade. For the lean there are analogues definition referred to the pressure or suction side of the blade. Several combinations between forward and/or backward and/or centred lean & sweep are available. The best blade compromise depends from a specific application.

One other idea of this application is that rotor and stator rows have sinusoidal sweep and lean not necessarily similar or in phase . Stator and rotor blades may be designed in such a way that the sinusoidal lean and sweep are identical (Fig.6) or not (Fig.7 and 8) for all the blades. This allow to optimize the acoustic and aerodynamic interaction between rotary and static blades for a given application. The optimal solution depends at least from the kind of machine, the flow, the thermodynamic state, number of rotor and stator blades, from the solidity, the pitch, the aspect-ratio, the presence and the type of ducts and/or shroud, and from the number of revolution of the rotor.

One of the reasons to use different lean & sweep, is to defer the interaction between the vortices generated at the trailing edges of the upstream row with the leading edges of the downstream row. For example, the noises due to the impact between the turbulent air of the first row with the

successive one, could be modulated in space and time to widen the emitted frequencies and decrease the single intensities.

The blades foresee in this application could also be realized with materials with form memory. This means that the blade can have at least two forms, with different lean, that are changed according to the operation point of the machine. The deformation may be either active or passive. This might allows to increase the stability margins of the rotor blades, to control the secondary vortices and to reduce acoustic emissions.

Parametric blades can be used to design rotor and stator rows characterized from a constant or variable pitch "t" (Fig.16) (basically different type of blades in the row), having a constant or variable chord "C" and employing either single airfoils "11" or multiples ones "22"; or a combination of the previous.

Airfoils "22" have at least two adjacent airfoils disposed in such way that the upstream one "1" is placed either over the suction side or under the pressure side of the successive airfoil "2" . In case that both single airfoils "11" and multiples "22" are employed between two blade rows, the passage section "pv" among single and multiple airfoils of the downstream row has a radial offset positive "+", negative "-" or coincide with the passage

section "p _M " of the upstream row (Fig.3b, 3ba, 3bb, 3bc and 3bd) .

Parametric blades are composed from at least one fin. If airfoils "22" are used, the blades are formed from more fins that can be: adjacent and not connected, adjacent and connected toward the tip, adjacent and connected toward the hub, adjacent and connected both to the hub and to the tip. In the parametric blades object of this patent, the parameters vary in continuous way, or have constant values, from the hub to the tip. This is necessary in order to generate geometrically continuous blades. The fact is that 3D CAD software can interpolate continuously a number of airfoils but, to obtain a good blade, it is necessary that those airfoils are guided from parameters defined on continuous curves (chosen in compliance with either structural, aerodynamic, acoustic or constructive considerations) . In case more curves are used (e.g. two arcs of circumference) to simulate a sinusoidal curve, those curves has to be preferably tangent .

The curves used to design the blade can be of the linear or curvilinear type. For example, Fig.11 illustrates a few different curves that defines the chord from hub to tip while keeping the other parameter distribution unvaried (e.g. staking) . Similar and different curves define and control the airfoils of a blade and the blade itself. Fig.11 indicates one of the solutions useful to design the planar shape of a blade: a combination of the distributions of sweep and chord from the hub to the tip (in this example

the sweep is not modified) . An other method to design the shape of the blade (shown in Fig.12) is to define directly the shapes of the blades defining the leading and trailing edge path (LE & TE) among hub and tip. In general, can be demonstrated that if either the leading or trailing edges have sinusoidal path, also the sweep will be of the sinusoidal type.

Similar solutions and considerations are applicable to the lean: it is first possible to define the lean and then the distribution of the thickness from hub to tip (Fig.2); or to model two curves that represent the distribution of the thickness between the pressure and suction sides of the blade consequently obtaining the distribution of the lean.

From a design point of view, the higher the number of parameters used to define one blade, the higher the quality of the blades and the flexibility to optimize it. However increasing the number of independent parameters, increases the difficulty to handle 3D parametric model and increases the time required for optimization process.

Therefore it is important to reflect on controlling, in an efficient way, all the various curves with a reduced number of parameters. A simple example in Fig.5 shows how to control simultaneously three sinusoidal curves (e.g. the lean, the sweep and the chord) , realized by arc of circumferences, with only six parameters. These parameters are :

• Dl _t i _p (distance between two curves to the tip) in this case the curves are equidistant;

• Dl _mozzo (distance between two curves to the hub) in this case the curves are equidistant;

• R _n , (radius of the middle curve) in this case the middle sinusoid is defined with two arc of circumference with equal radius; the other curves can be restrained with concentricity, proportionality or equivalence conditions regarding the middle reference curve;

• H (percentage of the maximum height of the blade where occurs the change of curvature) ;

• Sfasatura (angle that controls the phase difference between the curves) ; the sfasatura could be defined in other ways, as an example moving vertically the curves;

• D (horizontal distance between the tip and the bottom ends of the sinusoids) defines curves ahead, behind or cantered.

The segment "P" (defined in Fig.5a) that join the points where the sinusoids changes the chamber (associated to the parameter sfasatura) , could also be replaced from a curve.

In practise, according to the available resource, the number of parameters can be increased to have a greater number of possible configurations. The sinusoids could be defined also with opposite phases. Geometric, mechanical and aerodynamic analysis are necessary to define the better combination to design suitable rotor and stator rows for a given application.

The procedure to reduce the number of parameters is valid employing at least two curves and offers at least the following advantages: 1. It help to manage a reduced number of parameters;

2. It keep a proportionality between the curves, with consequent geometric continuity of the blade surfaces.

3. It allows simple 3D manipulations.

The blades object of this patent, are obtained interpolating several airfoils among hub and tip. Increasing the number of airfoils allow to control the flow in more sections and may increase the quality of the blades. This depends in turns from the ability to chose an airfoils that reproduce the required performances, and from the possibility to control smoothly and continuously the change of the airfoils shape. Figures 12i and 121 show two different blade, designed with the same number of main airfoils but having a different number of interpolated airfoils. In these cases airfoils change continuously.

This patent application further concerns parametric airfoils designed with arcs of ellipses. Those airfoils are defined by a series of parameters (each one defined from a continuous curve from hub to tip) that generate a family of similar airfoils which vary continuously from hub to tip. The airfoils can be either defined or projected on axis- symmetric surfaces (curvilinear, circulars, conic, etc.), on planes or on streamsurfaces .

Preferably one airfoil should be parameterized using: chord, thickness, shape of the leading/trailing edges, flow angles, stagger angle, etc..., since those parameters define the main characteristic of an airfoils. To obtain a stable airfoil generator, it is recommended to suppress either all or as much as possible the degrees of freedom of the

ellipses (6 each one) (e.g. reducing the number of parameters using tangent condition or linking the dimensions which control axes and angles of the ellipses) .

The technique, to generate parametric airfoils discussed in this application, is compatible with any distribution of the lean, the sweep or other parameters and offers the possibility to control continuously the variations of the parameters from the hub to the tip of one blade and according to design inputs. A wide combination of airfoils may be obtained combining a number of ellipses.

Fig.17 to 21 show some example of airfoils designed with arch of ellipses. The ellipses, are geometric figures having two focus and defined from a greater axis and a minor axis. One property of the ellipses is that that the sum of the distances between every point of the ellipse and the focus is constant; consequently the chamber of the ellipse varies in continuous way. This property is perfect to design airfoils. In fact, the pressure and suction sides of an airfoils should not contain discontinuity points that may involve boundary layer transition and/or flow separation.

Ellipses are suitable to design parametric airfoils "11" & "22" for the following reasons:

1) are curves with constant second derivatives;

2) can be used to shape either the pressure or suction side of an airfoil so that, in any application, allow to control the point of max speed and the speed gradient;

3) a combination of arc of ellipses facilitate to design efficient parametric airfoils for subsonic, transonic and supersonic flows;

4) the dimensions and the orientation of ellipses, the distances and the angles of the tangent contact points between the ellipses can be parameterized and controlled according to a specific application;

5) minimize the losses accelerating/decelerating flow path.

As simplified in Figs .17 to 21, a number of airfoils may be designed. Those may differ both for application (e.g. axial & mix flow compressor, fan, blower, pump and turbine) , for mach number (subsonic, transonic and supersonic flows) and for type (rotor and stator) .

The ellipses can be connected each other with a wide combination of orientation to create either the leading edge or the pressure or the suction side of an airfoil. In some cases (e.g. when the fluid does not risk transition or separations of the boundary layer BL, or to manipulate the transition points of the BL) , the perimeter of the airfoil may have a discontinuity in either the 1 ^st or higher derivatives; however, it is recommendable to avoid at least discontinuity of the 1 ^st order (it means that the ellipses should be at least tangent) .

The ellipses can be reciprocally different, equal or linked by means of proportionality relations.

Fig.18, 19 and 20 show a few of the combinations of ellipses obtainable to generate subsonic, transonic and supersonic airfoils.

The suction and pressure sides can lay either on the side of the ellipses where the curvature decrease or increase or in between.

The proposed airfoils allow to reduce the losses due to the Prandalt & Mayer expansion in transonic/supersonic flow, to reduce the losses (mainly diffusion losses) in subsonic flow, to decrease noise emission and increase efficiency. A first confirmation have been found numerically (simulating and comparing, with CFD solver, 2D airfoil row's) .

Fig.21 shows a few multiple airfoils (also known as "slotted airfoil" or "tandem airfoil") realized with arches of ellipses. Airfoils "1" and "2" can be reciprocally disposed so that the trailing edge of the airfoil upstream "1" has a positive offset "+" (Fig.21a), is aligned "0" (Fig.21b), or has an offset negative "-" (Fig.21c) in respect to the leading edge of the airfoil downstream "2" .

One other solution proposed in this application are either the leading or the trailing edges of the tip portion of the blades designed with arc of ellipses. With reference to Fig.13, 14 and 15, arch of ellipse are employed to chamber the leading and trailing edges extremities of the blade. Such technique allows to control the speed gradient, between the tip and root of the blade to reduce discontinuities and vorticity in the flow patterns. This solution may be particularly indicated for variable pitch blade embodiments.