A serpentine inlet design method based on shape-preserving piecewise cubic Hermites interpolation

Abstract

The present invention discloses a serpentine air inlet design method based on conformal segmented cubic Hermites interpolation. The conformal segmented cubic Hermites interpolation method uses the characteristics of given target points and curve conformal to avoid the "Runge phenomenon" caused by transitions between complex shapes in the design method based on curvature transformation, so that the surface of the serpentine air inlet is continuous and the transition is smooth. Compared with the traditional polynomial algorithm, the present invention effectively solves the problem that the traditional algorithm cannot be applied to the serpentine air inlet, and provides an active and flexible design method for the aerodynamic design of the serpentine air inlet.

Description

Technical Field

[0001] The invention relates to the technical field of aircraft air inlet ducts, and in particular to the technical field of a serpentine air inlet duct design method based on conformal segmented cubic Hermites interpolation. Background Art

[0002] For advanced fighters that perform missions, stealth and maneuverability are key design factors. The propulsion system is the main power source of air-breathing aircraft and the main source of the forward radar cross-section (RCS). It is one of the key components to achieve overall performance improvement. Ultra-compact serpentine inlet is a way to meet the above design requirements: through the twisting of the inner surface and the serpentine centerline design, the downstream fan can be shielded in all directions. However, the design of the overly compact and twisted inner surface leads to a sharp flow turn and reverse pressure gradient, which inevitably produces large-scale flow separation in the tube, resulting in a decrease in the maneuverability of the aircraft. Therefore, it is necessary to carry out parametric design of the serpentine inlet, comprehensively evaluate the influence of stealth and maneuverability, and obtain the optimal configuration of the two. Common design methods include constructing a three-dimensional surface mesh curve using superelliptic equations and NUBS curves, and then sweeping to generate smooth geometric surfaces in sequence, but both require a lot of calculations on the cross-sectional shape along the way. When the cross-sectional shape becomes more complicated, the parameters input by the superelliptic equation and NUBS curve will increase geometrically, and the efficiency of parametric design will decrease. The design method based on curvature transformation proposed in the document "A Design Method for Complex Variable Cross-Section Inlet" Journal of Aerospace Power, 2009, 24(06):1357-1363, uses the curvature distribution function to generate the cross-sectional shape according to the algorithm, which significantly improves the efficiency of parametric design.

[0003] For conventional S-curve inlets that only require inlet and outlet geometry design, the curvature distribution function can meet the smooth transition requirements through a polynomial curve. However, for ultra-compact serpentine inlets, the complex shape of the center control section causes the "Runge phenomenon" to appear in the change pattern along the way, and it is impossible to achieve continuous transition of the shapes of each section along the way. Therefore, it is necessary to design a new algorithm to solve the above technical problems. Summary of the invention

[0004] The purpose of the present invention is to address the shortcomings of the above-mentioned background technology and to propose a serpentine inlet design method based on conformal segmented cubic Hermites interpolation to solve the technical problems in the prior art of discontinuous cross-sectional shape transition under complex center control sections and the inlet surface cannot be smoothly swept.

[0005] In order to achieve the above object, the present invention may adopt the following technical solutions:

[0006] A serpentine inlet design method based on conformal piecewise cubic Hermites interpolation includes the following steps:

[0007] (1) Determine the curves of the serpentine inlet inlet shape, outlet shape, and center control section shape based on external geometric constraints;

[0008] (2) Discretize the curves of the inlet geometry, outlet shape, and center control section shape into a set of points with equal arc length and uniform distribution;

[0009] (3) Calculate the distribution law of the curve curvature of the inlet shape, outlet shape and central control section shape with arc length based on discrete points;

[0010] (4) The distribution law of the curve curvature along the serpentine inlet from the inlet to the outlet is calculated by using the shape-preserving piecewise cubic Hermites interpolation method;

[0011] (5) Reverse design to obtain the shape curves of each cross section;

[0012] (6) Scaling each cross section according to the cross-sectional area variation relationship along the serpentine inlet from the inlet to the outlet;

[0013] (7) According to the centerline of the air inlet, translate and rotate each section;

[0014] (8) The cross-sectional shape curves obtained by scaling, displacement and rotation are swept in sequence to generate a smooth inlet duct surface.

[0015] Furthermore, the serpentine air inlet flow channel is designed as a double S-bend.

[0016] Furthermore, the inlet shape, outlet shape and center control section shape of the serpentine air inlet are respectively determined by the aircraft shape, the downstream engine inlet end face, the aircraft load distribution and the space inside the aircraft.

[0017] Furthermore, the inlet and outlet of the serpentine air inlet are respectively located at the head and tail of the air inlet, and the center control section is located between the inlet and outlet of the serpentine air inlet.

[0018] Furthermore, in step (2) and step (3), for the curve point set of the given inlet shape, outlet shape and center control section shape, the description form of the point set is respectively the inlet shape (x in,i )、(y in,i ); outlet shape (x out,i )、(y out,i ); Center console cross-sectional shape (x c,i )、(y c,i ), where i = 0, 1, ···, I, I is the number of each point set, (x in,i )、(y in,i) represents the point set of the inlet entrance shape, (x out,i )、(y out,i ) represents the point set of the inlet outlet shape, (x c,i )、(y c,i ) represents the point set of the central control section shape; connect the points in sequence with lines to obtain the curvature with the dimensionless arc length S i The expression is:

[0019]

[0020] Where θ is the angle between the points and the positive horizontal axis, in rad, SS i is the length of each line segment.

[0021] Furthermore, in step (4), the serial number of each section along the process is expressed as S j (j=0, 1, 2, ···, J), J is the total number of sections along the process; the dimensionless expression of the section position is t=j / J, and the center control section position is expressed as t c =c / J(0 <t c <1), for point i in each section, the distribution law of the curve curvature with arc length in each section is expressed by shape-preserving piecewise cubic Hermites interpolation:

[0022]

[0023] The dimensionless expression of the cross-section position is t = j / J, and the center control cross-section position is t c =c / J(0 <t c <1), k(t) is the distribution function of the curve curvature with the cross-sectional position, k'(t) is the derivative of k(t) at t; k(0) is the curvature at point i of the inlet, k(t c ) is the curvature at point i of the center control section, and k(1) is the curvature at point i of the inlet duct outlet.

[0024] Furthermore, in step (5), the shape curves of each section are obtained by inverse design based on the distribution law of the curvature of the curve along each section along the process with the arc length; starting from the base point of the curve, the specific steps are as follows:

[0025] (θ i -θ i-1 )=SS i-1 *k i-1

[0026] θ i =SS i-1 *k i-1 +θ i-1

[0027] x i =xi-1 +SS i-1 cosθ i

[0028] y i =y i-1 +SS i-1 sinθ i

[0029] Where i = 0, 1, ..., I, I is the number of each point set, θ is the angle between the line segment obtained by connecting the points in sequence and the positive horizontal axis, in rad, SS i is the length of each line segment; k i is the curvature of the curve at point i, x i ,y i are the coordinate values ​​of point i respectively.

[0030] Furthermore, in step (6), the area variation law of each cross section along the process can be set to f(t), f(0) = 0, f(1) = 1; the area variation law of the j-th cross section can be expressed as:

[0031] A j =A in +f(t j )*(A out -A in )

[0032] Close the curve obtained by the inverse design in the previous section. Take section j as an example. If the area of ​​the closed figure of the section is inconsistent with the change law of the cross-sectional area, then enlarge or reduce the figure proportionally to A. j .

[0033] Furthermore, in the difference calculation of the shape-preserving piecewise cubic Hermites interpolation, the centerline shape of the inlet duct is calculated by giving k(0), k(t c ) and k(1) are obtained and their derivatives are designed by conformal piecewise cubic Hermites interpolation.

[0034] Furthermore, in step (7), each scaled cross section is translated and rotated according to the center line shape to ensure that the centroid is located at the dimensionless position t of the center line shape and the cross section normal is parallel to the center line shape at this point.

[0035] Compared with the traditional design method, this method solves the technical problems that the shape transition of the middle section is discontinuous under the complex center control section and the inlet surface cannot be smoothly swept. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the three-dimensional modeling of the air intake duct and the shapes of each cross section in the design method of the present invention.

[0037] Figure 2 It is a schematic diagram of the curvature calculation of each point on the cross section in the design method of the present invention.

[0038] Figure 3 This is the distribution law of the curvature of the shape of the air inlet entrance, the air inlet center control section and the air inlet outlet along with the arc length in the design method of the present invention.

[0039] Figure 4 It is a schematic diagram of the shape-preserving piecewise cubic Hermites interpolation method in the design method of the present invention.

[0040] Figure 5 The figure is a comparison between the shape-preserving piecewise cubic Hermites interpolation algorithm and the traditional polynomial algorithm for surface modeling in the design method of the present invention. DETAILED DESCRIPTION

[0041] See also Figure 1 As shown, Figure 1 It includes the inlet 1, the outlet 3 and the central control section 2 of the inlet. Each section 7 along the inlet is located between the inlet 1 and the central control section 2 and between the central control section 2 and the outlet 3. The centerline 5 of the inlet is the line connecting the geometric centers of each section 7 along the inlet, including the inlet 1, the outlet 3 and the central control section 2. The symmetry plane 6 of the inlet passes through the centerline 5 and is perpendicular to the profile 4 of the inlet. Since the profile 4 of the inlet is mirror-symmetrical about the symmetry plane 6 of the inlet, half of the shape curve of each section can be taken for analysis in the design step, such as P a -P e curve.

[0042] The detailed implementation steps of this embodiment of the method of the present invention are described below.

[0043] (1) According to the external geometric constraints, the curves of the serpentine inlet 1, the inlet outlet 3 and the inlet center control section 2 are determined. Figure 1 As shown, in the embodiment of the method of the present invention, the shape of the air inlet 1 is a chamfered rectangle, the shape of the air inlet outlet 3 is a circle, and the shape of the air inlet center control section 2 is concave.

[0044] (2) The curves of the intake duct inlet 1, the intake duct outlet 3 and the intake duct center control section 2 are discretized into a set of points with equal arc lengths, uniform distribution and the same number.

[0045] (3) Based on the discrete points, the distribution law of the curvature of the curves of the inlet duct inlet 1, the inlet duct outlet 3 and the inlet duct center control section 2 with arc length is calculated. The description form of the point set is (x in,i )、(y in,i ), (x out,i )、(y out,i ) and (x c,i), (y c,i ), where \(i = 0, 1, \cdots, I\), and \(I\) is the number of each point set. As Figure 2 shown, connecting each point with a line in sequence, the expression of the curvature with respect to the dimensionless arc length \(S\) can be obtained: i The expression is:

[0046]

[0047]

[0048] where \(\theta\) is the angle between each line segment and the positive horizontal axis, with the unit of rad, and \(SS\) i is the length of each line segment.

[0049] Figure 3 Illustrates the distribution law of the curvature with respect to the arc length at the inlet 1, outlet 3, and middle control section 2 of the intake duct in the embodiment of the present invention.

[0050] (4) Through conformal piecewise cubic Hermites interpolation, interpolate and calculate the distribution law of the curve curvature with respect to the arc length at each cross-section 7 along the way. The specific steps are as follows: Select the \(i\)-th point of the point sets at the inlet 1, outlet 3, and middle control section 2 of the intake duct, and obtain the curvature at this point, that is, \(k\) i_in , \(k\) i_out , \(k\) i_c . The serial numbers of each cross-section 7 along the way are expressed as \(S_j\) (\(j = 0, 1, 2, \cdots, J\)), and \(J\) is the total number of each cross-section 7 along the way. Therefore, the dimensionless of the cross-section position can be expressed as \(t = j / J\), and the position of the middle control section can be expressed as \(t_c = c / J\) (\(0 < t_c < 1\)); \(k(t)\) is the distribution function of the curve curvature with respect to the cross-section position, and \(k^\prime(t)\) is the derivative of \(k(t)\) at \(t\); \(k(0)\) is the curvature at the \(i\)-th point at the inlet of the intake duct, \(k(t\) c ) is the curvature at the \(i\)-th point at the middle control section, \(k(1)\) is the curvature at the \(i\)-th point at the outlet of the intake duct, and \(k^\prime(0)\), \(k^\prime(t\) c ) and \(k^\prime(1)\) are usually taken as 0 to ensure the smoothness of the curve. For conformal piecewise cubic Hermites interpolation, \(k\) i_in = \(k(0)\), \(k\) i_out = \(k(1)\), \(k\) i_c = \(k(t\) c ), and substitute them into the following equation. Among them, \(k^\prime(t)\) is the derivative of the curve at \(t\).

[0051]

[0052] Figure 4 Illustrates the formula obtained by the conformal piecewise cubic Hermites interpolation method for the \(i\)-th point in the embodiment of the present invention.

[0053] (5) The shape curve of each section 7 along the process is obtained by inverse design. The curvature value of each point along each section 7 can be obtained through the above interpolation, so the distribution law of the curve curvature with the arc length can be constructed. The position of each point can be inversely calculated by the following formula:

[0054] (θ i -θ i-1 )=SS i-1 *k i-1 (5)

[0055] θ i =SS i-1 *k i-1 +θ i-1 (6)

[0056] x i =x i-1 +SS i-1 cosθ i (7)

[0057] y i =y i-1 +SS i-1 sinθ i (8)

[0058] Where i = 0, 1, ..., I, I is the number of each point set, θ is the angle between the line segment obtained by connecting the points in sequence and the positive horizontal axis, in rad, SS i is the length of each line segment; k i is the curvature of the curve at point i, x i ,y i are the coordinate values ​​of point i respectively.

[0059] (6) According to the area change relationship of the cross section 7 along the process, scale each cross section 7 along the process. Close the curve obtained by the inverse design. Take the j section as an example. If the area of ​​the closed figure of the cross section is inconsistent with the change law of the cross section area, then the figure is enlarged or reduced in proportion to A. j . A j The expression is as follows:

[0060] A j =A in +f(t j )*(A out -A in )(9)

[0061] Where f(0) = 0, f(1) = 1. f(t) is not strictly limited and is a monotone continuous curve passing through two points.

[0062] (7) According to the centerline shape 5 of the inlet duct, each cross section 7 along the way is translated and rotated. Each cross section obtained after scaling is translated and rotated according to the centerline shape 5 to ensure that the geometric center is located at the dimensionless position t of the cross section and the cross section normal is parallel to the centerline shape 5 at this point.

[0063] (8) The curves obtained by scaling, displacement and rotation are swept in sequence to generate a smooth air inlet profile 4.

[0064] The air intake duct designed by the above method is as follows Figure 5 As shown in the figure, as a comparison, the same type of air intake is designed according to the traditional polynomial algorithm with the same geometric constraints. Comparing the difference between the two, under the traditional polynomial algorithm, due to the "Runge phenomenon" of polynomial interpolation, the geometric surface of the air intake is distorted and discontinuous, which violates the design requirement of smooth and continuous inner wall of the subsonic air intake. The conformal segmented cubic Hermites interpolation can solve the problem of avoiding the occurrence of this phenomenon. The designed air intake is smooth and continuous, which is competent for the design requirements of ultra-compact serpentine air intake under the constraints of complex center control section.

[0065] In addition, there are many specific implementation methods and approaches of the present invention, and the above is only a preferred implementation of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A serpentine inlet design method based on conformal piecewise cubic Hermites interpolation, characterized in that: The following steps are involved: (1) Determine the curves of the serpentine inlet inlet shape, outlet shape and center control section shape according to external geometric constraints; the serpentine inlet inlet shape, outlet shape and center control section shape are determined by the aircraft shape, the downstream engine inlet end face, the aircraft load distribution and the internal space; (2) Discretize the curves of the inlet geometry, outlet shape, and center control section shape into a set of points with equal arc length and uniform distribution; (3) Calculate the distribution law of the curve curvature of the inlet shape, outlet shape and central control section shape with arc length based on discrete points; (4) The distribution law of the curve curvature along the serpentine inlet from the inlet to the outlet is calculated by using the shape-preserving piecewise cubic Hermites interpolation method; (5) The shape curves of each section are obtained by reverse design; the shape curves of each section are obtained by reverse design based on the distribution law of the curvature of the curve along the section along the arc length; starting from the base point of the curve, the specific steps are as follows: (θ i -θ i-1 )=SS i-1 *k i-1 θ i =SS i-1 *k i-1 +θ i-1 x i =x i-1 +SS i-1 cosθ i and i =and i-1 +SS i-1 sinθ i Where i = 0, 1, ..., I, I is the number of each point set, θ is the angle between the line segment connecting each point in sequence and the positive horizontal axis, the unit is rad, SS i is the length of each line segment; k i is the curvature of the curve at point i, x i ,y i are the coordinate values ​​of point i respectively; (6) Scaling each cross section according to the cross-sectional area variation relationship along the serpentine inlet from the inlet to the outlet; (7) According to the centerline of the air inlet, translate and rotate each section; (8) The cross-sectional shape curves obtained by scaling, displacement and rotation are swept in sequence to generate a smooth inlet duct surface.

2. The serpentine air inlet design method according to claim 1, characterized in that: The serpentine air inlet flow channel is designed as a double S-bend.

3. The serpentine air inlet design method according to claim 1, characterized in that: The inlet and outlet of the serpentine air inlet are respectively located at the head and tail of the air inlet, and the center control section is located between the inlet and outlet of the serpentine air inlet.

4. The method for designing a serpentine air inlet according to any one of claims 1 to 3, characterized in that: In step (2) and step (3), for the given curve point set of the inlet entrance shape, outlet shape and center control section shape, the description form of the point set is respectively the inlet shape (x in,i )、(y in,i ); outlet shape (x out,i )、(y out , i ); Center console cross-sectional shape (x c,i )、(y c,i ), where i = 0, 1, ···, I, I is the number of each point set, (x in,i )、(y in,i ) represents the point set of the inlet entrance shape, (x out,i )、(y out,i ) represents the point set of the inlet outlet shape, (x c,i )、(y c,i ) represents the point set of the central control section shape; connect the points in sequence with lines to obtain the curvature with the dimensionless arc length S i The expression is: Where θ is the angle between the points and the positive horizontal axis, in rad, SS i is the length of each line segment.

5. The serpentine air inlet design method according to claim 4, characterized in that: In step (4), the serial number of each section along the process is expressed as S j , j = 0, 1, 2, ···, J, J is the total number of sections along the process; the dimensionless expression of the section position is t = j / J, and the center control section position is expressed as t c =c / J,0 <t c <1, for each point i in each section, the distribution law of the curve curvature with arc length in each section is expressed by shape-preserving piecewise cubic Hermites interpolation: The dimensionless expression of the cross-section position is t = j / J, and the center control cross-section position is t c =c / J,0 <t c <1, k(t) is the distribution function of the curve curvature with the cross-sectional position, k'(t) is the derivative of k(t) at t; k(0) is the curvature at point i of the inlet, k(t c ) is the curvature at point i of the center control section, and k(1) is the curvature at point i of the inlet duct outlet.

6. The serpentine air inlet design method according to claim 5, characterized in that: In step (6), the area variation law of each section along the process is set to f(t), f(0) = 0, f(1) = 1; the area variation law of the j-th section is expressed as: A j =A in +f(t j )*(A out -A in ) Close the curve obtained by the inverse design in the previous section. Take section j as an example. If the area of ​​the closed figure of the section is inconsistent with the change law of the cross-sectional area, then enlarge or reduce the figure proportionally to A. j .

7. The serpentine air intake design method according to claim 6 is characterized in that: In the difference calculation of shape-preserving piecewise cubic Hermites interpolation, the centerline shape of the inlet duct is calculated by giving k(0), k(t c ) and k(1) are obtained and their derivatives are designed by conformal piecewise cubic Hermites interpolation.

8. The serpentine air inlet design method according to claim 7, characterized in that: In step (7), each scaled cross section is translated and rotated according to the center line shape to ensure that the centroid is located at the dimensionless position t of the center line shape and the cross section normal is parallel to the center line shape at this point.

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