Blade parametric design method

Abstract

This invention discloses a parametric blade design method, which relates to the field of blade design. The method comprises the following steps: first, generating a 2D blade profile along the radial direction at each layer. The 2D blade profile is determined using an 11-parameter method to determine five points on the blade; second, converting the 2D profile into 3D and generating a 3D blade along the stacking line. First, radial equilibrium conditions are used to determine the metal angles at the blade inlet and outlet at different radial interfaces from the blade root to the blade tip. Second, 3D Bezier curves are used as the stacking line of the blade profile to generate possible forward and backward tilts. This parametric blade design method can efficiently generate smooth blade shapes.

Description

Technical Field

[0001] The present invention relates to the field of blade design, and in particular to a blade parameterized design method. Background Art

[0002] Currently, the methods for parameterizing the generation of blade surfaces include: Casey's Bezier-patches method (a baseline design and perturbation function superposition), the combined method proposed by Zhang and He combining the distribution of arc and thickness functions, the work of Arnone et al., and the general parameter airfoil function proposed by Kulfan. The main disadvantage of these methods is the lack of physical definition of the design variables. The main difference between Pritchard's 11-parameter method and the method used in this study is that curve 2 in Pritchard's method (the suction surface curve downstream of the throat is a circular curve) means that the trailing edge wedge angle value ε TE Depends on other design variables.

[0003] The main problem with existing methods is the lack of physically meaningful parameterization. While the Pritchard method can generate a blade shape, the fact that curve 2 is a circular arc significantly restricts the blade geometry, limiting the potential for performance improvement and preventing the creation of a smooth blade shape. Summary of the Invention

[0004] The object of the present invention is to provide a blade parameterized design method capable of efficiently generating a smooth blade shape.

[0005] To achieve the above object, the present invention adopts a technical solution: a blade parameterized design method, comprising:

[0006] Step 1: Generate a 2D blade profile at each layer along the radial direction, wherein the 2D blade profile is determined by an 11-parameter method using five points on the blade;

[0007] Step 2: Convert the 2D contour to 3D and generate a 3D blade along the stacking line. First, the radial equilibrium condition is used to determine the metal angle of the blade inlet and outlet at different radial interfaces from the blade root to the blade tip. Second, a 3D Bezier curve is used as the stacking line of the blade contour to generate possible forward and backward tilts.

[0008] Preferably, the 11 parameters in step 1 include the axial chord length C ax , pitch p, stagger angle α stagger , throat t, unguided steering δ unguided , blade leading edge radius r LE , trailing edge radius r TE , leading edge wedge angle ε LE , trailing edge wedge angle ε TE, leading edge metal angle β LE , trailing edge metal angle β TE .

[0009] Preferably, the radial balance equation SRE of the radial balance condition in step 2 is:

[0010]

[0011] Where r is the radius, u ax and u θ are the axial flow velocity and the circumferential velocity, respectively;

[0012] The radial equilibrium equation shows that at the same axial position, once the radial variation of the axial velocity u is defined ax , the circumferential velocity u can be calculated accordingly θ Corresponding changes, axial speed u ax It is set to be constant along the radial direction and a free vortex design is assumed.

[0013] Preferably, the radial balance equation is derived from the first law of thermodynamics, the Gibbs equation and the centrifugal force balance equation.

[0014] The first law of thermodynamics equation: dh = de + Pdv + vdP

[0015] The Gibbs equation is: Tds = de + Pdv

[0016] The centrifugal force balance equation is:

[0017] Where h is the flow enthalpy; e is the flow internal energy; P is the pressure; v is the specific volume, s is the entropy, d represents the total differential operation; T represents the temperature; ρ represents the temperature; u θ Represents the circumferential velocity.

[0018] Preferably, du ax / dr is equal to 0, based on the radial balance equation, d(ru θ )=0, indicating that θ The radial direction is constant, and the axial and circumferential speeds vary along the radial direction, i.e. u ax (r) and u θ (r) can pass through the axial u of the mid-span ax,m and circumferential speed u θ,m It is calculated by the following two formulas, where r m is the mid-span radius,

[0019] u ax (r)=u ax,m

[0020]

[0021] As the axial velocity changes along the radial direction u ax (r), circumferential velocity changes along the radial direction u θ (r), and the defined blade rotation speed, the absolute airflow angular distribution α of the stator can be derived r and the relative airflow angle distribution of the rotor β r , which are also the metal corners of the stator and rotor.

[0022] Preferably, the metal angle of the blade varies radially and is applied to all points on the blade profile. The radial distribution of the metal angle is only used at the leading edge and the trailing edge. The leading edge metal angle β LE and trailing edge metal angle β TE is the blade profile design variable mentioned above, and the radial balance equation can be applied to derive the radial variation of the angle along the span β LE (r) and β TE (r).

[0023] Preferably, the stacking line is generated by a non-uniform rational basis spline with four control points: A, B, C and D. The first control point A is the stationary point of the blade profile at the hub, and the coordinate origin is at point A along the half span extending radially.

[0024] Preferably, the sweep angle α x Calculated by the following formula:

[0025]

[0026] Preferably, the twist of the blade can be obtained by rotating the formulated 2D blade profile around a defined rotation center, with a taper δ taper The taper δ is obtained by reducing / expanding the blade profile to a certain taper length. taper Through the cone angle α taper The radius difference between the tapered section and the mid-span is calculated using the following formula:

[0027] δ taper =Δrtanα taper .

[0028] The beneficial effect of the blade parametric design method of the present invention is that the geometry of a complex blade shape can be determined by specifying only a dozen parameters. Parameterization is helpful in guiding the design of the blade shape and in guiding research on improving blade performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 are the 11 parameters used to parameterize the airfoil;

[0030] Figure 2Generate Curv1, curv2, and curv4 for the ninth-order Bezier curve formed by 10 control points;

[0031] Figure 3 is the local cylindrical coordinate system for 3D stacked NURBS;

[0032] Figure 4 The local cylindrical coordinate system for 3D stacked NURBS. DETAILED DESCRIPTION

[0033] The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solutions of the present invention, but the present invention is not limited to these embodiments.

[0034] Combined with attachment Figure 1-4 As shown in the embodiment, a parametric design method for blades is performed in a 2D-3D manner. First, a 2D blade profile is generated at each layer along the radial direction. Then, the 2D profile is converted to 3D and a 3D blade is generated along the stacking line.

[0035] 1. 11 parameter method for 2D blade contour

[0036] The 2D blade profile is determined by the 11-parameter method. The 11 parameters in this method all have physical meanings, so designers can easily identify design features and incorporate previous design experience into the parametric design system. The 11 parameters are axial chord length C ax , pitch p, stagger angle α stagger , throat t, unguided steering δ unguided , blade leading edge radius r LE , trailing edge radius r TE ,,Leading edge wedge angle ε LE , trailing edge wedge angle ε TE , leading edge metal angle β LE , trailing edge metal angle β TE ,like Figure 1 shown.

[0037] By assigning the values of these 11 parameters, the five points pt1, pt2, pt3, pt4 and pt5 on the leaf can be determined. Figure 1 The top shape of a single blade is shown in Figure a). The geometric relationship between two adjacent blades is shown in Figure b). These five points divide the blade into five parts: curve 1, curve 2, curve 3, curve 4, and curve 5. Figure 2 As shown in , among these curves, curve 5 and curve 3 are the leading edge curve and the trailing edge curve. Curve 1, curve 2, and curve 4 are ninth-order Saibel curves with 10 control points, as shown in Figure 2 In this application, curve 2 is a ninth-order Seibel curve, and ε TEis an independent design variable.

[0038] 2 3D blade parameterization

[0039] Stacking 2D blades to generate a 3D blade surface involves two steps: First, radial equilibrium conditions are used to determine the metal angles at the blade inlet and outlet at various radial interfaces from root to tip. During this step, the blade profile can be tapered and twisted to achieve the 2D-to-3D conversion. Second, 3D Bezier curves are used as the stacking lines of the blade profile to generate possible pitch and sweep.

[0040] 2.1 Radial equilibrium condition

[0041] The radial equilibrium condition defines the radial pressure gradient necessary to provide the centripetal force required to maintain circular motion. Assuming the flow is steady, inviscid, adiabatic, and axisymmetric, and that there is no radial displacement along the meridional streamlines, the simplified radial equilibrium equation SRE can be obtained:

[0042]

[0043] Where r is the radius, u ax and u θ are the axial flow velocity and the circumferential flow velocity, respectively.

[0044] This equation is derived from the first law of thermodynamics (Formula 2), the Gibbs equation (Formula 3) and the centrifugal force balance equation (Formula 4). Where h is the flow enthalpy; e is the flow internal energy; P is the pressure; v is the specific volume, s is the entropy, d represents the total differential operation; T represents the temperature; ρ represents the temperature; u θ Represents the circumferential velocity.

[0045] dh=de+Pdv+vdP (2)

[0046] Tds=de+Pdv (3)

[0047]

[0048] The simplified radial equilibrium equation shows that at the same axial position, once the radial variation of the axial velocity u is defined, ax , the circumferential velocity u can be calculated accordingly θ In this study, the axial speed u ax is set to be constant along the radial direction and a free vortex design is assumed. Therefore, du ax / dr is equal to 0. Based on the radial equilibrium equation, d(ru θ )=0 indicates that ru θ It is a constant value along the radial direction. Therefore, the change of axial and circumferential speed along the radial direction, that is, u ax(r) and u θ (r) can be obtained by the axial and circumferential speed u at the mid-span ax,m and u θ,m Calculated by formula 5 and formula 6, where r m is the mid-span radius.

[0049] u ax (r)=u ax,m (5)

[0050]

[0051] As the axial velocity changes along the radial direction u ax (r), circumferential velocity changes along the radial direction u θ (r), and the defined blade rotation speed, the absolute airflow angular distribution α of the stator can be derived r and the relative airflow angle distribution of the rotor β r , which are also the metal angles of the stator and rotor. Ideally, the radial variation of the blade metal angle should be applied to all points on the blade profile. Here, the radial distribution of the blade metal angle is only used at the leading and trailing edges, and the leading edge metal angle β LE and trailing edge metal angle β TE are the blade profile design variables shown above. Therefore, the radial balance equation can be applied to derive the radial variation of the angle along the span, β LE (r) and β TE (r).

[0052] 2.2 3D stacking lines

[0053] The stacking lines used in this study are generated by 3DNURBS (Non-Uniform Rational Basis Splines) with 4 control points A, B, C, and D, as shown in Figure 3 As shown. In the figure, x, θ and r represent axial, tangential and radial directions respectively. 3D stacking line, the control point is G. In the fixed coordinate system, the first control point A is the stationary point of the blade profile at the hub, and the coordinate origin is half the span extending radially from point A. Here h represents the span. r B ,r C and r D Calculate the values and make sure B, C, and D are at 0.2, 0.8, and 1 span of the blade.

[0054] The first control point A is fixed in the coordinate system. Due to the difference between the local coordinate system and the global coordinate system of the blade, the radial coordinates of the other three control points B, C and D are calculated to ensure that these three points are at 0.2, 0.8 and 1 span of the blade. In the local coordinate system, the tangent coordinate θ represents the blade tilt angle. The sweep angle α xIt is calculated by formula 7 (x in formula 7 is the x-axis coordinate). Therefore, the blade shape parameterization system can generate blades with specified characteristics (such as tilt and sweep).

[0055]

[0056] like Figure 4 As shown in Figure 2, the twist of the blade can be obtained by rotating the formulated 2D blade profile around a defined rotation center. taper Obtained by reducing / expanding the blade profile to a certain taper length. Taper δ taper Through the cone angle α taper The radius difference between the tapered section and the mid-span is calculated using Equation 8.

[0057] δ taper =Δrtanα taper (8)

[0058] The specific embodiments described herein are merely illustrative of the spirit of the present invention. Persons skilled in the art may make various modifications, additions, or substitutions to the described specific embodiments without departing from the spirit of the present invention or exceeding the scope of the appended claims.

Claims

1. A blade parameter design method, characterized by: include Step 1: Generate a 2D blade profile at each layer along the radial direction, wherein the 2D blade profile is determined by an 11-parameter method using five points on the blade; Step 2: Convert the 2D profile to 3D and generate a 3D blade along the stacking line. First, the radial equilibrium condition is used to determine the metal angle of the blade inlet and outlet at different radial interfaces from the blade root to the blade tip. Second, a 3D Bezier curve is used as the stacking line of the blade profile to generate possible forward and backward sweeps. The 11 parameters in step 1 include the axial chord length C ax , pitch p, stagger angle α stagger , throat t, unguided steering δ unguided , blade leading edge radius r LE , trailing edge radius r TE , leading edge wedge angle ε LE , trailing edge wedge angle ε TE , leading edge metal angle β LE , trailing edge metal angle β TE ; The radial equilibrium equation SRE of the radial equilibrium condition in step 2 is: Where r is the radius, u ax and u θ are the axial flow velocity and the circumferential velocity, respectively; The radial equilibrium equation shows that at the same axial position, once the radial variation of the axial velocity u is defined ax , the circumferential velocity u can be calculated accordingly θ Corresponding changes, axial speed u ax It is set to be constant along the radial direction and a free vortex design is assumed; The stacking line is generated by a non-uniform rational basis spline with four control points: A, B, C and D. The first control point A is the stationary point of the blade profile at the hub, and the coordinate origin is half the span extending radially from point A. Sweep angle α x Calculated by the following formula: The twist of the blade can be obtained by rotating the formulated 2D blade profile around a defined rotation center, with a taper δ taper The taper δ is obtained by reducing / expanding the blade profile to a certain taper length. taper Through the cone angle α taper The radius difference between the tapered section and the mid-span is calculated using the following formula: d taper =Drtana taper 。 2. The blade parameter design method according to claim 1, characterized in that: The radial balance equation is derived from the first law of thermodynamics, the Gibbs equation and the centrifugal force balance equation. The first law of thermodynamics equation: dh = de + Pdv + vdP The Gibbs equation is: Tds = de + Pdv The centrifugal force balance equation is: Where h is the flow enthalpy; e is the flow internal energy; P is the pressure; v is the specific volume, s is the entropy, d represents the total differential operation; T represents the temperature; ρ represents the temperature; u θ Represents the circumferential velocity.

3. The blade parameter design method according to claim 1, characterized in that: du ax / dr is equal to 0, based on the radial balance equation, d(ru θ )=0, indicating that θ The radial direction is constant, and the axial and circumferential speeds vary along the radial direction, i.e. u ax (r) and u θ (r) can pass through the axial u of the mid-span ax,m and circumferential speed u θ,m It is calculated by the following two formulas, where r m is the mid-span radius, u ax (r)=u ax,m As the axial velocity changes along the radial direction u ax (r), circumferential velocity changes along the radial direction u θ (r), and the defined blade rotation speed, the absolute airflow angular distribution α of the stator can be derived r and the relative airflow angle distribution of the rotor β r , which are also the metal corners of the stator and rotor.

4. The blade parameter design method according to claim 3, characterized in that: The metal angle of the blade varies radially and is applied to all points on the blade profile. The radial distribution of the metal angle is only used at the leading edge and the trailing edge. The leading edge metal angle β LE and trailing edge metal angle β TE is the blade profile design variable mentioned above, and the radial balance equation can be applied to derive the radial variation of the angle along the span β LE (r) and β TE (r).

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