Fan cascade aerodynamic design method based on bezeir suction surface superposition passage

Abstract

The application belongs to the field of aero-engine fan and compressor aerodynamic design, and discloses a fan cascade aerodynamic design method based on a Bezier suction surface superposition channel. The fan cascade aerodynamic design method comprises the following steps: determining cascade geometric parameters; calculating suction surface inlet and outlet angles; defining a suction surface axial length; setting a dimensionless suction surface control point; calculating a minimum included angle and a maximum included angle of the dimensionless suction surface control point; calculating a dimensioned suction surface control point; drawing the dimensioned suction surface control point; calculating suction surface curve coordinates; calculating a cascade channel pitch; calculating a cascade channel inlet width; calculating a cascade channel outlet width; calculating a cascade channel width distribution law; generating a pressure surface front section curve; generating a pressure surface rear section curve; and completing two-dimensional cascade design. The fan cascade aerodynamic design method can directly control the suction surface curve change law of the blade profile and the cascade channel size change law, and the control is direct, effective and convenient, and has engineering practical value.

Description

Technical Field

[0001] This invention belongs to the field of aerodynamic design of aero-engine fans and compressors, and specifically relates to an aerodynamic design method for fan blade cascades based on Bessel suction surface superimposed channels. Background Technology

[0002] In the field of aerodynamic design of aircraft engine fans and compressors, the method of superimposing thickness distribution along the mid-arc line is commonly used to generate two-dimensional airfoils. This method first gives the tangential coordinates of each point on the mid-arc line. Along the axial direction The pattern of change For example, higher-order polynomials or multi-circular curves; then give the blade thickness. Along the axial direction The pattern of change For example, higher-order polynomials; then, the first on the middle arc. Points Based on this point, the blade thickness is superimposed on both sides along the normal direction. The suction side points were obtained respectively. and pressure side point Connect all suction points to obtain the coordinates of the suction surface curve. Connect all pressure points to obtain the pressure surface curve coordinates. Finally, using the first and last points on the mid-arc line as a reference, the leading and trailing edges are supplemented with specific types of curves (such as circular arcs or elliptical arcs) to form the leading and trailing edge curves, thus completing the two-dimensional airfoil aerodynamic design.

[0003] The method of generating two-dimensional airfoils using the mid-arc superposition thickness distribution method has two main drawbacks: First, it is not intuitive; the suction surface curve is derived from the mid-arc superposition thickness distribution, and the variation law of the suction surface curve cannot be directly specified during the design; for the flow in the cascade channel, the suction surface, not the mid-arc, is in direct contact with the fluid, so the variation law of the suction surface curve cannot be directly controlled, which will make it difficult to directly control the flow characteristics of the cascade surface; Second, it lacks design convenience; since the variation law of the cascade channel size along the flow direction cannot be directly determined, there is a lack of direct means to control the overall flow characteristics of the cascade channel, and multiple matchings are often required to obtain a suitable cascade channel.

[0004] Currently, there is an urgent need to develop an aerodynamic design method for fan blade cascades based on the superposition of Bessel suction surfaces and channels. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a fan blade aerodynamic design method based on the superimposed channels of Bessel suction surfaces, so as to overcome the defects of the prior art.

[0006] The aerodynamic design method for fan blades based on superimposed channels of Bessel suction surfaces of the present invention includes the following steps:

[0007] S10. Determine the cascade geometry parameters;

[0008] Blade cascade geometry parameters include chord length Consistency Geometric inlet angle Geometric exit angle Radius of the leading edge small circle Radius of the small circle at the trailing edge Leading edge semi-wedge angle Tail margin semi-cune angle Compared with the expansion of import and export channels ;

[0009] S20. Calculate the inlet and outlet angles of the suction surface;

[0010] The angle between the tangent at the first point (not the leading edge) of the suction surface curve and the axial direction is... The angle between the tangent at the last point of the suction surface curve (excluding the tail edge) and the axial direction is... The calculation formula is as follows:

[0011] ;

[0012] S30. Define the axial length of the suction surface;

[0013] The axial projection length of the suction surface curve is Defined as the axial length of the suction surface The calculation formula is as follows:

[0014] ;

[0015] S40. Set the dimensionless suction surface control point;

[0016] The angular distribution of the dimensionless suction surface curve is controlled by a 14th-order Bézier curve, with a total of 15 control points. The horizontal axis represents the dimensionless axial position. The vertical axis represents the dimensionless angles at the tangents of the control points on the suction surface curve. Dimensionless angle The angle between the tangent at each control point of the suction surface curve and the positive axial half-axis; subscript Indicates dimensionless;

[0017] S50. Calculate the minimum and maximum included angles of the control points of the dimensional suction surface;

[0018] The minimum angle between the tangent at each control point of the dimensional suction surface and the positive axial half-axis. equal The maximum included angle is Maximum included angle The calculation formula is as follows:

[0019] ;

[0020] S60. Calculate the control points of the dimensional suction surface;

[0021] The axial position 0.000 represents the first point on the suction surface curve, and the dimensionless angle of the first point on the suction surface curve is... Dimensional angle is The axial position 1.000 represents the last point on the suction surface curve, and the dimensionless angle of the last point on the suction surface curve is... Dimensional angle is The dimensionless x-coordinate of the control points of a 14th-order Bézier curve is... The dimensionless vertical axis is The calculation formula is as follows:

[0022] ;

[0023] S70. Draw the control points of the dimensional suction surface;

[0024] by For a dimensionless x-axis, Given a dimensional ordinate, generate a dimensional Bézier curve;

[0025] S80. Draw the angle distribution curve of the suction surface;

[0026] S90. Calculate the coordinates of the suction surface curve;

[0027] Based on the position of the suction surface The angle between the tangent and the axis at the point The fourth-order Runge-Kutta method was used to calculate the coordinates of the suction surface curve.

[0028] S100. Calculate the cascade channel pitch;

[0029] According to the chord length Consistency Calculate the gate pitch :

[0030] ;

[0031] S110. Calculate the inlet width of the cascade passage;

[0032] Given the radius of the leading edge small circle Leading edge semi-wedge angle The suction surface curve is shifted one grid pitch in the negative tangential direction to obtain the offset suction surface curve; taking the first point of the suction surface inlet as the reference, a small leading circle is drawn, and the diameter of the common tangent circle between the small leading circle and the offset suction surface curve is... This refers to the inlet width of the blade cascade passage.

[0033] S120. Calculate the exit width of the cascade passage;

[0034] Known inlet width of the blade cascade channel Channel expansion ratio Calculate the outlet width of the cascade channel. Blade cascade channel exit width The calculation formula is as follows:

[0035] ;

[0036] S130. Calculate the width distribution of the cascade passageway;

[0037] The variation of the blade cascade passage width with the flow direction position was generated using a 5th-order Bézier curve through a total of 6 control points. The horizontal axis represents the flow direction position, and the vertical axis represents half of the blade cascade passage width.

[0038] S140. Generate the front section curve of the pressure front;

[0039] Superimposed on the cascade passage exit width on the bias suction surface curve The obtained envelope is the front section curve of the pressure front; the exit width through the blade passage Draw the leading and trailing edge curves;

[0040] S150. Generate the pressure surface rear section curve;

[0041] The pressure surface profile was generated using a third-order Bézier curve through four control points.

[0042] S160. Complete the two-dimensional blade cascade design.

[0043] Furthermore, S160 includes the following steps:

[0044] The complete airfoil curve is obtained by merging the suction surface curve, the leading and trailing edge curve, the front section curve of the pressure surface, and the trailing section curve of the pressure surface. The airfoil curve is then moved so that the leading edge point is located at the origin (0, 0). The formula for calculating the coordinates of the moved airfoil curve is as follows:

[0045] ;

[0046] in, These represent the axial and tangential coordinate displacements. The initial coordinates of the leading edge point of the airfoil before movement. These are the coordinates of the moved leaf profile curve.

[0047] The aerodynamic design method for fan blades based on superimposed channels of Bessel suction surfaces of the present invention has the following characteristics:

[0048] a. It can directly control the variation law of the blade suction surface curve; it uses Bézier curves to control the suction surface curve, which has a high degree of freedom and is easy to implement in controlling the blade suction surface curve;

[0049] b. It can directly control the size variation of the blade cascade channel; by using Bezier curves to control the width variation of the blade cascade channel along the flow direction, the geometric control of the blade cascade channel is direct and effective, and the expanded blade cascade channel can be constructed in one go during the design stage, making the design more convenient.

[0050] In summary, the aerodynamic design method for fan blade cascades based on the superimposed channels of the Bessel suction surface of the present invention can directly control the variation law of the suction surface curve of the blade shape and the variation law of the size of the blade cascade channel. The control is direct and effective, the design is convenient, and it has practical engineering value. Attached Figure Description

[0051] Figure 1 Implementation steps for the aerodynamic design method of fan blades;

[0052] Figure 2 Bezier control points and curves for the angle distribution of the suction surface (dimensionless).

[0053] Figure 3 Bezier control points and curves (dimensioned) for the angle distribution of the suction surface.

[0054] Figure 4 The distribution pattern of the suction surface angle;

[0055] Figure 5 The suction surface curve;

[0056] Figure 6 This refers to the inlet width of the blade cascade passage.

[0057] Figure 7 The Bezier curve for the width distribution of the cascade channel;

[0058] Figure 8 The front section curve of the pressure front;

[0059] Figure 9 This is the curve of the latter part of the pressure surface;

[0060] Figure 10 For the leaf shape and leaf passage. Detailed Implementation

[0061] The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0062] Example: Figure 1 As shown, the aerodynamic design method for fan blades based on Bezier suction surface superimposed channels in this embodiment includes the following steps:

[0063] S10. Determine the cascade geometry parameters;

[0064] Blade cascade geometry parameters include chord length Consistency Geometric inlet angle Geometric exit angle Radius of the leading edge small circle Radius of the small circle at the trailing edge Leading edge semi-wedge angle Tail margin semi-cune angle Compared with the expansion of import and export channels ;

[0065] Among them, chord length Consistency Geometric inlet angle Geometric exit angle Radius of the leading edge small circle Radius of the small circle at the trailing edge Leading edge semi-wedge angle Tail margin semi-cune angle The expansion of import and export channels .

[0066] S20. Calculate the inlet and outlet angles of the suction surface;

[0067] The angle between the tangent at the first point (not the leading edge) of the suction surface curve and the axial direction is... The angle between the tangent at the last point of the suction surface curve (excluding the tail edge) and the axial direction is... The calculation formula is as follows:

[0068] ;

[0069] get , .

[0070] S30. Define the axial length of the suction surface;

[0071] The axial projection length of the suction surface curve is Defined as the axial length of the suction surface The calculation formula is as follows:

[0072] ;

[0073] get .

[0074] S40. Set the dimensionless suction surface control point;

[0075] The angular distribution of the dimensionless suction surface curve is controlled by a 14th-order Bézier curve, with a total of 15 control points. The horizontal axis represents the dimensionless axial position. The vertical axis represents the dimensionless angles at the tangents of the control points on the suction surface curve. Dimensionless angle The angle between the tangent at each control point of the suction surface curve and the positive axial half-axis; subscript Indicates dimensionless;

[0076] like Figure 2 As shown, each control point is marked with a black box, and the generated Bézier curve is shown as a smooth black curve without any markings. The coordinates of each control point are shown in Table 1.

[0077] Table 1. Angle distribution of suction surface. Bezier control points (dimensionless).

[0078] ;

[0079] S50. Calculate the minimum and maximum included angles of the control points of the dimensional suction surface;

[0080] The minimum angle between the tangent at each control point of the dimensional suction surface and the positive axial half-axis. equal The maximum included angle is Maximum included angle The calculation formula is as follows:

[0081] ;

[0082] get .

[0083] S60. Calculate the control points of the dimensional suction surface;

[0084] In the dimensionless data in Table 1, the axial position 0.000 represents the first point of the suction surface curve, and the dimensionless angle of the first point of the suction surface curve is... , Dimensional angle is The axial position 1.000 represents the last point on the suction surface curve, and the dimensionless angle of the last point on the suction surface curve is... , Dimensional angle is The dimensionless x-coordinate of the control points of a 14th-order Bézier curve is... The dimensionless vertical axis is The calculation formula is as follows:

[0085] ;

[0086] S70. Draw the control points of the dimensional suction surface;

[0087] by For a dimensionless x-axis, Given a dimensional ordinate, generate a dimensional Bézier curve; for example... Figure 3 As shown, each control point is marked with a black box, and the generated Bézier curve is shown as a smooth black curve without any markings. The coordinates of each control point are shown in Table 2.

[0088] Table 2. Bezier control points for suction surface angle distribution (dimensions provided)

[0089] ;

[0090] S80. Draw the angle distribution curve of the suction surface;

[0091] like Figure 4 As shown, the angle distribution of the suction surface is represented by the black curve, with a total of 111 points. The coordinates of each point are shown in Table 3.

[0092] Table 3 Coordinates of Suction Surface Angle Distribution

[0093] ;

[0094] S90. Calculate the coordinates of the suction surface curve;

[0095] Based on the position of the suction surface The angle between the tangent and the axis at the point The fourth-order Runge-Kutta method was used to calculate the coordinates of the suction surface curve.

[0096] Figure 5 The red curve shows the suction surface curve, and the coordinates of each point on the suction surface curve are shown. Specific values ​​are shown in Table 4.

[0097] Table 4 Coordinates of Suction Surface Curve

[0098] ;

[0099] S100. Calculate the cascade channel pitch;

[0100] According to the chord length Consistency Calculate the gate pitch :

[0101] ;

[0102] Obtain the grid pitch .

[0103] S110. Calculate the inlet width of the cascade passage;

[0104] Given the radius of the leading edge small circle Leading edge semi-wedge angle ,like Figure 6 As shown, the suction surface curve is shifted tangentially in the negative direction by a grid pitch of 50mm to obtain the offset suction surface curve; taking the first point of the suction surface inlet as the reference, a small leading-edge circle is drawn, and the projection of the common tangent circle diameter of the small leading-edge circle and the offset suction surface curve onto the flow normal is obtained. The inlet width of the blade passage. ;

[0105] S120. Calculate the exit width of the cascade passage;

[0106] Known inlet width of the blade cascade channel Channel expansion ratio Calculate the outlet width of the cascade channel. Blade cascade channel exit width The calculation formula is as follows:

[0107] ;

[0108] Obtain the outlet width of the cascade channel .

[0109] S130. Calculate the width distribution of the cascade passageway;

[0110] like Figure 7 As shown, a 5th-order Bézier curve was used to generate the variation law of the blade cascade channel width with the flow direction position through a total of 6 control points. The horizontal axis is the flow direction position, and the vertical axis is half of the blade cascade channel width. The coordinates of each control point are shown in Table 5, and the coordinates of each point on the curve are shown in Table 6.

[0111] Table 5. Blade cascade channel width distribution (Bessel control points)

[0112]

[0113] Table 6. Distribution of Blade Cascade Channel Width

[0114] ;

[0115] S140. Generate the front section curve of the pressure front;

[0116] like Figure 8 As shown, the envelope obtained by superimposing the blade passage width distribution pattern on the bias suction surface curve is the front section curve of the pressure front; the bias suction surface curve is represented by a red line, and the front section curve of the pressure front is represented by a red-framed line; the width of the blade passage exit is shown. Draw the leading and trailing edge curves, using orange lines to represent them;

[0117] S150. Generate the pressure surface rear section curve;

[0118] like Figure 9 As shown, a third-order Bézier curve is used to generate the pressure surface curve through four control points; Figure 9 In the middle red section, the suction surface curve is shown; in the black section, the leading and trailing edge curve is shown; in the blue section, the pressure surface curve is shown; and in the orange section, the common tangent circle of the channel outlet is shown. The coordinates of the control points of the Bezier curves are shown in Table 7 and Table 8, respectively.

[0119] Table 7 Coordinates of control points for the rear section of the pressure surface curve

[0120]

[0121] Table 8. Coordinates of the curve of the rear section of the pressure surface

[0122] ;

[0123] S150. Complete the two-dimensional blade cascade design;

[0124] like Figure 10 As shown, a complete airfoil curve is obtained by merging the suction surface curve, the leading and trailing edge curve, the front section curve of the pressure surface, and the rear section curve of the pressure surface. The airfoil curve is then moved so that the leading edge point is located at the origin (0, 0). The formula for calculating the coordinates of the moved airfoil curve is as follows:

[0125] ;

[0126] in, For axial and tangential coordinate displacement; The initial coordinates of the leading edge point of the blade before movement are (-0.0438, -0.6571). The coordinates of the moved airfoil curve; Figure 10 The black curve in the figure represents the suction surface (including the suction side of the front and rear edges), and the red curve represents the pressure surface (including the pressure side of the front and rear edges). The specific coordinates are shown in Tables 9 and 10.

[0127] Table 9 Coordinates of Suction Surface Curve

[0128]

[0129] Table 10 Coordinates of Pressure Surface Curve

[0130]

[0131] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. For those skilled in the art, all features disclosed in the present invention, or all steps in all methods or processes disclosed, except for mutually exclusive features and / or steps, can be combined in any way without departing from the principles of the present invention. The present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. An aerodynamic design method for fan blade cascades based on superimposed channels of Bezier suction surfaces, characterized in that, The aforementioned aerodynamic design method for fan blades includes the following steps: S10. Determine the cascade geometry parameters; Blade cascade geometry parameters include chord length Consistency Geometric inlet angle Geometric exit angle Radius of the leading edge small circle Radius of the small circle at the trailing edge Leading edge semi-wedge angle Tail margin semi-cune angle Compared with the expansion of import and export channels ; S20. Calculate the inlet and outlet angles of the suction surface; The angle between the tangent at the first point (not the leading edge) of the suction surface curve and the axial direction is... The angle between the tangent at the last point of the suction surface curve (excluding the tail edge) and the axial direction is... The calculation formula is as follows: ； S30. Define the axial length of the suction surface; The axial projection length of the suction surface curve is Defined as the axial length of the suction surface The calculation formula is as follows: ； S40. Set the dimensionless suction surface control point; The angular distribution of the dimensionless suction surface curve is controlled by a 14th-order Bézier curve, with a total of 15 control points. The horizontal axis represents the dimensionless axial position. The vertical axis represents the dimensionless angles at the tangents of the control points on the suction surface curve. Dimensionless angle The angle between the tangent at each control point of the suction surface curve and the positive axial half-axis; subscript Indicates dimensionless; S50. Calculate the minimum and maximum included angles of the control points of the dimensional suction surface; The minimum angle between the tangent at each control point of the dimensional suction surface and the positive axial half-axis. equal The maximum included angle is Maximum included angle The calculation formula is as follows: ； S60. Calculate the control points of the dimensional suction surface; The axial position 0.000 represents the first point on the suction surface curve, and the dimensionless angle of the first point on the suction surface curve is... Dimensional angle is The axial position 1.000 represents the last point on the suction surface curve, and the dimensionless angle of the last point on the suction surface curve is... Dimensional angle is The dimensionless x-coordinate of the control points of a 14th-order Bézier curve is... The dimensionless vertical axis is The calculation formula is as follows: ； S70. Draw the control points of the dimensional suction surface; by For a dimensionless x-axis, Given a dimensional ordinate, generate a dimensional Bézier curve; S80. Draw the angle distribution curve of the suction surface; S90. Calculate the coordinates of the suction surface curve; Based on the position of the suction surface The angle between the tangent and the axis at the point The fourth-order Runge-Kutta method was used to calculate the coordinates of the suction surface curve. S100. Calculate the cascade channel pitch; According to the chord length Consistency Calculate the gate pitch : ； S110. Calculate the inlet width of the cascade passage; Given the radius of the leading edge small circle Leading edge semi-wedge angle The suction surface curve is shifted one grid pitch in the negative tangential direction to obtain the offset suction surface curve; taking the first point of the suction surface inlet as the reference, a small leading circle is drawn, and the diameter of the common tangent circle between the small leading circle and the offset suction surface curve is... This refers to the inlet width of the blade cascade passage. S120. Calculate the exit width of the cascade passage; Known inlet width of the cascade channel Channel expansion ratio Calculate the outlet width of the cascade channel. Blade cascade channel exit width The calculation formula is as follows: ； S130. Calculate the width distribution of the cascade passageway; The variation of the blade cascade passage width with the flow direction position was generated using a 5th-order Bézier curve through a total of 6 control points. The horizontal axis represents the flow direction position, and the vertical axis represents half of the blade cascade passage width. S140. Generate the front section curve of the pressure front; Superimposed on the cascade passage exit width on the bias suction surface curve The obtained envelope is the front section curve of the pressure front; the exit width through the blade passage Draw the leading and trailing edge curves; S150. Generate the pressure surface rear section curve; The pressure surface profile was generated using a third-order Bézier curve through four control points. S160. Complete the two-dimensional blade cascade design.

2. The aerodynamic design method for fan blade cascades based on superimposed channels of Bezier suction surfaces according to claim 1, characterized in that, S160 includes the following steps: The complete airfoil curve is obtained by merging the suction surface curve, the leading and trailing edge curve, the front section curve of the pressure surface, and the trailing section curve of the pressure surface. The airfoil curve is then moved so that the leading edge point is located at the origin (0, 0). The formula for calculating the coordinates of the moved airfoil curve is as follows: ； in, For axial and tangential coordinate displacements, The initial coordinates of the leading edge point of the airfoil before movement. These are the coordinates of the moved leaf profile curve.

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