Blade reverse-forward interactive modeling method based on geometric parameters of mean camber line

Abstract

The invention relates to the field of turbomachinery, and discloses a blade reverse-forward interactive modeling method based on geometric parameters of a mean camber line, and the method comprises the steps: extracting parameters, carrying out the geometric definition based on an inscribed circle of a source blade, solving to obtain the mean camber line, and extracting beta angle distribution and inscribed circle radius distribution; a forward mean camber line is generated, wherein the forward mean camber line is generated according to the extracted parameter integral; generating a forward blade molded line: constructing an inscribed circle along the forward mean camber line and solving an envelope line to generate the blade molded line; verification parameter extraction: performing parameter extraction on the positive blade profile; and deviation determination: comparing the original and verification parameters to determine the reproduction precision. The system comprises a parameter extraction module used for executing a parameter extraction function; the forward modeling module is used for executing a forward mean camber line generation function and a forward blade molded line generation function; and an interactive verification module for performing a deviation determination function. According to the method, through accurate geometric definition and a closed-loop verification mechanism, the blade design and manufacturing efficiency and precision are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of impeller machinery, in particular to a blade reverse-forward interactive modeling method based on camber line geometric parameters. BACKGROUND

[0002] As a key element of core components such as aero-engines and gas turbines, the precision of the geometric modeling of the blade directly affects the performance of the whole machine. In the field of blade design and reverse engineering, the camber line is a core element representing the geometric characteristics of the blade. However, the existing technology has significant defects in the extraction and forward modeling of the camber line of the blade.

[0003] Specifically, the mainstream blade reverse method usually interpolates and fits the pressure surface and suction surface profile, and then solves the midpoint by equal arc length to approximate the camber line. This reverse way is not based on the strict geometric definition of the camber line, that is, the trajectory of the points equidistant to the pressure surface and suction surface, so there is an inherent deviation from the true camber line. This deviation makes it difficult for the reverse-obtained parameters to accurately reflect the original geometric characteristics of the blade.

[0004] Further, in the process of blade forward modeling, the thickness is usually superimposed along the normal position of the camber line, that is, the thickness is superimposed along the normal position of the camber line. However, due to the large deviation between the camber line constructed by the beta angle used in forward modeling and the camber line obtained by reverse analysis, the blade modeled by forward modeling is difficult to accurately reproduce the design intent.

[0005] Currently, there is a lack of theory and program that can realize the interactive verification of reverse analysis and forward modeling. This means that when the results obtained by commercial reverse software analysis are applied to the blades generated by modeling software, they are often inconsistent with the reverse results. Conversely, the blades generated by modeling software cannot obtain results with small deviations from the input parameters when analyzed by reverse software. This non-interactive status not only makes it difficult for reverse engineering to obtain accurate design experience, but also makes it impossible to ensure that the modeled blade fully meets the design requirements in the design stage, which seriously restricts the efficiency and accuracy of blade design and manufacturing.

[0006] Therefore, the present application proposes a blade reverse-forward interactive modeling method based on camber line geometric parameters to solve the deficiencies of the prior art. SUMMARY

[0007] In view of the deficiencies of the prior art, the present application provides a blade reverse-forward interactive modeling method based on the geometric parameters of the mean camber line, which solves the problem of the inconsistency in definition and calculation logic between the geometric parameters extracted by the blade reverse engineering and the design parameters used in the forward modeling, resulting in uncontrollable deviation between the blade profile constructed based on the reverse parameters and the source blade, and vice versa, the original design parameters of the forward designed blade cannot be accurately restored by the reverse analysis, that is, the reverse and forward processes lack logical consistency and interactive verification.

[0008] To solve the above technical problems, the present application provides a blade reverse-forward interactive modeling method and system based on the geometric parameters of the mean camber line, which establishes a closed-loop verification modeling process by unifying the underlying geometric definition and calculation logic of the reverse parameter extraction and forward geometric modeling, thereby ensuring the accuracy of the model reconstruction and the faithful restoration of the design intent.

[0009] The present application provides a blade reverse-forward interactive modeling method based on the geometric parameters of the mean camber line, which comprises the following steps:

[0010] Firstly, a parameter extraction operation is performed. This operation takes the geometric profiles of the pressure surface and the suction surface of a given source blade as input. By solving the incircle of the pressure surface and the suction surface at a series of positions in the flow direction, the mean camber line of the source blade is obtained, and the beta angle distribution and the incircle radius distribution distributed along the mean camber line are extracted from the mean camber line.

[0011] Specifically, the process of solving the mean camber line of the source blade comprises:

[0012] A group of data points are selected in the leading edge region and the trailing edge region of the source blade, respectively, and the geometric centers of the leading edge and the trailing edge are obtained by quadratic curve fitting of these data points, and the two geometric centers are defined as the starting point and the ending point of the mean camber line, respectively. Between the starting point and the ending point, a series of solving stations are arranged along the predetermined flow direction of the source blade. At each solving station, a point is searched by iterative operation, which satisfies the condition that the shortest distance from the point to the pressure surface is equal to the shortest distance from the point to the suction surface, and this point is the mean camber line point at the station. Connecting all the mean camber line points obtained at the solving stations constitutes the mean camber line of the source blade. In the process of searching the mean camber line point, the equal shortest distances obtained are the incircle radii at the points, and the collection of all the incircle radii constitutes the incircle radius distribution.

[0013] The process of extracting the beta angle distribution comprises:

[0014] The Cartesian coordinates of each point on the mean camber line of the source blade are converted into cylindrical coordinates, thereby obtaining the meridian direction coordinate m of each mean camber line point.k , radius r k , and position angle Θ k . Then based on these cylindrical coordinate values, the beta angle distribution β k is obtained by the following calculation:

[0015]

[0016] where β k is the beta angle of the centerline point at meridional coordinate m k ; r k is the radius of the centerline point at meridional coordinate m k ; and Θ is the derivative of the position angle with respect to the meridional coordinate at point k.

[0017] Secondly, a forward centerline generation operation is performed. This operation takes the beta angle distribution and the inscribed circle radius distribution extracted in the first step as inputs, and generates a new, forward centerline by an integration operation. To obtain the position angle distribution of this forward centerline, a numerical integration operation on a differential equation is performed. This integration operation obtains the beta angle tangent value from the input beta angle distribution, and obtains the radius value from the input centerline radius distribution. The differential equation is:

[0018]

[0019] where dΘ is the differential of the position angle of the forward centerline; tan(β) is the beta angle tangent value provided by the beta angle distribution; r is the radius value provided by the centerline radius distribution; and dm is the differential of the meridional coordinate.

[0020] Thirdly, a forward blade profile generation operation is performed. This operation constructs an inscribed circle with a radius corresponding to the inscribed circle radius distribution at each position point of the forward centerline generated in the previous step, thereby forming a series of inscribed circles along the forward centerline. Then, by solving the envelope of this series of inscribed circles, the final forward blade profile is generated.

[0021] The specific process of solving the envelope is as follows:

[0022] For each pair of adjacent inscribed circles, the common tangent line is solved; then the tangent points of the common tangent line on each inscribed circle are connected, and the curve formed by connecting all the tangent points constitutes the forward blade profile.

[0023] For the solution of the suction side tangent point of the common external tangent on the ithinset circle, the generated forward camber line (providing the coordinates of the center of the circle) and the inputted insetting circle radius distribution are taken as inputs. First, the coordinates of the center of the ithinset circle (x i ,y i ) and the radius R i , as well as the coordinates of the center of the adjacent (i+1)thinset circle (x i+1 ,y i+1 ) and the radius R i+1 , are determined according to the inputs. Second, based on these coordinates of the center of the circle and the radius, the azimuth angle φ of the line connecting the two centers of the circle and the deflection angle a of the common external tangent relative to the line connecting the two centers of the circle are calculated. Finally, the coordinates of the tangent point t i,ss on the suction side are calculated by the following formula:

[0024] t i,ss =(x i -R i sin(φ-α),y i +R i cos(φ-α));

[0025] where (x i ,y i ) is the coordinates of the center of the ithinset circle; R i is the radius of the ithinset circle; φ is the azimuth angle; and a is the deflection angle.

[0026] Subsequently, a verification parameter extraction operation is performed. This operation takes the generated forward blade profile as a new input, and again uses the same insetting circle geometric definition as in the first step to solve the camber line of the forward blade profile and extract the verification beta angle distribution and the verification insetting circle radius distribution from the camber line.

[0027] The process specifically includes:

[0028] A series of verification solving stations are arranged along the forward blade profile, and at each verification solving station, a verification camber line point is searched for, which has equal shortest distances to the pressure side and the suction side of the forward blade profile, and the shortest distance is defined as the verification insetting circle radius of the point, thereby obtaining the verification insetting circle radius distribution; and all the verification camber line points are connected to form the camber line of the forward blade profile. Subsequently, the camber line is converted into cylindrical coordinates to obtain the verification meridional direction coordinate m′ k , the verification radius r′ k and the verification position angle θ′ k at each verification camber line point. Based on these verification cylindrical coordinates, the verification beta angle distribution β′ k is calculated by the following formula:

[0029]

[0030] wherein β′ k is the verification beta angle at the verification meridian coordinate m′ k ; r′ k is the verification radius at the verification meridian coordinate m′ k ; is the derivative of the verification position angle with respect to the verification meridian coordinate at point k.

[0031] Finally, a deviation determination operation is performed. This operation determines whether the forward blade profile accurately reproduces the geometric features defined by the original parameters within a preset tolerance range, according to the deviation between the original beta angle distribution and the verification beta angle distribution, and the deviation between the original inscribed circle radius distribution and the verification inscribed circle radius distribution.

[0032] The specific determination process is as follows:

[0033] The first maximum absolute deviation between the beta angle distribution and the verification beta angle distribution, and the second maximum absolute deviation between the inscribed circle radius distribution and the verification inscribed circle radius distribution are calculated. When the first maximum absolute deviation is less than a first preset tolerance threshold, and the second maximum absolute deviation is less than a second preset tolerance threshold, it is determined that the forward blade profile accurately reproduces the geometric features within a preset tolerance range.

[0034] In an embodiment, the method further comprises parameter space blending. This process first performs the aforementioned parameter extraction operation on a first source blade and a second source blade respectively, to obtain a first parameter set and a second parameter set containing beta angle distribution and inscribed circle radius distribution. Then, according to a preset weight function, the first parameter set and the second parameter set are weighted and interpolated to generate a set of mixed parameter sets. Finally, the mixed parameter set is taken as input to perform the aforementioned forward camber line generation and forward blade profile generation operations to generate a mixed blade that combines the geometric features of the two source blades.

[0035] The second aspect of the present application provides a blade reverse-forward interactive modeling system based on camber line geometric parameters, which comprises:

[0036] A parameter extraction module, which is configured to solve the camber line of a source blade based on the inscribed circle geometry definition of the pressure surface and the suction surface of the source blade, and extract the beta angle distribution and the inscribed circle radius distribution along the camber line flow direction from the camber line of the source blade;

[0037] a forward modeling module, which is configured to generate a forward mean camber line by integral operation according to the beta angle distribution and the inscribed circle radius distribution, and to construct a series of inscribed circles along the forward mean camber line according to the inscribed circle radius distribution, and to generate a forward blade profile by solving an envelope of the series of inscribed circles;

[0038] an interactive verification module, which is configured to extract a verification beta angle distribution and a verification inscribed circle radius distribution based on the geometric definition of the inscribed circles of the pressure surface and the suction surface of the forward blade profile, and to determine whether the forward blade profile accurately reproduces the geometric features defined by the beta angle distribution and the inscribed circle radius distribution within a preset tolerance range according to deviations between the beta angle distribution and the verification beta angle distribution and between the inscribed circle radius distribution and the verification inscribed circle radius distribution.

[0039] The modules work cooperatively to realize a closed-loop verification process between blade reverse parameter extraction and forward geometry modeling.

[0040] The present application provides a blade reverse-forward interactive modeling method based on mean camber line geometric parameters.

[0041] 1. The present application establishes a logically self-consistent reverse-forward modeling closed loop. By using a unified inscribed circle geometric definition to solve the mean camber line and represent the blade thickness throughout the whole process of parameter extraction (reverse) and blade modeling (forward), the present application ensures that the beta angle distribution and the inscribed circle radius distribution obtained by reverse analysis are completely consistent with the geometric parameters on which the forward modeling is based in fundamental definition. This inherent logical unity enables the reverse and forward processes to verify each other, solves the problem that the model and the parameters cannot be accurately corresponded due to inconsistent definitions in the prior art, and realizes real interactive modeling.

[0042] 2. The technical solution of the present application can realize high-precision reproduction of the geometric features of a source blade. Unlike the traditional method of solving the mean camber line by using approximate methods such as equal arc length midpoint, the present application directly converges to solve the mean camber line according to the strict geometric definition of the inscribed circle, and generates the blade profile by solving the envelope of the series of inscribed circles. This non-approximate method based on geometric definition ensures that each step from parameter extraction to geometry modeling has a solid theoretical basis, so that the finally generated forward blade profile can restore the geometric shape defined by the beta angle distribution and the inscribed circle radius distribution with extremely high fidelity.

[0043] 3、The present application provides stronger controllability and flexibility for blade design by decomposing complex blade geometry into two key parameter sets: beta angle distribution and inscribed circle radius distribution. Designers can directly manipulate these two parameters with clear geometric meaning to achieve precise adjustment of blade profile. Furthermore, this parameterization method also supports parameter space hybrid modeling, allowing the creation of hybrid blades with new characteristics through weighted interpolation of different source blade parameter sets, greatly enriching design methods and improving design efficiency.

[0044] 4、The modeling method proposed by the present application has wide applicability and robustness. Since its core principle is rooted in the universal inscribed circle geometric definition, rather than relying on empirical models of specific blade types, this method can be widely applied to various two-dimensional blades, including but not limited to various compressor and turbine blades located on different revolution surfaces. This makes the reverse-forward interactive modeling framework constructed by the present application a general technical platform that can serve multiple industrial design and reverse engineering scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0045] Figure 1 is a general flowchart of the method of the present application;

[0046] Figure 2 is a leading edge / trailing edge geometry fitting diagram of the present application;

[0047] Figure 3 is a mid-chord line point iteration solution diagram of the present application;

[0048] Figure 4 is a reverse parameter extraction result diagram of the present application;

[0049] Figure 5 is a common external tangent line solution diagram of adjacent inscribed circles of the present application;

[0050] Figure 6 is a leading edge region construction method diagram of the present application;

[0051] Figure 7 is an effect verification comparison diagram of an application case of the present application;

[0052] Figure 8 is a system structure block diagram of the present application.

[0053] Among them, 10, parameter extraction module; 20, forward modeling module; 30, interactive verification module. DETAILED DESCRIPTION

[0054] With reference to the accompanying drawings, the technical solutions in the embodiments of the present application will be clearly and completely described below, obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work belong to the protection scope of the present application.

[0055] With reference to Figure 1 , Figure 1 is a flow chart of a blade reverse-forward interactive modeling method based on camber line geometric parameters according to an embodiment of the present application. The present application provides a blade reverse-forward interactive modeling method based on camber line geometric parameters, which solves the design and model deviation problem caused by inconsistent reverse and forward modeling logic in the prior art by establishing a set of logically unified and closed-loop verifiable processes. The method can include the following steps:

[0056] Step S1: parameter extraction. Based on the inscribed circle geometric definition of the pressure surface and the suction surface of a source blade, the camber line of the source blade is solved, and the beta angle distribution and the inscribed circle radius distribution distributed along the camber line flow direction are extracted from the camber line of the source blade.

[0057] Step S2: forward camber line generation. According to the beta angle distribution and the inscribed circle radius distribution extracted in step S1, a forward camber line is generated by integral operation.

[0058] Step S3: forward blade profile generation. Along the forward camber line generated in step S2, a series of inscribed circles are constructed according to the inscribed circle radius distribution, and then the envelope of the series of inscribed circles is solved to generate the final forward blade profile.

[0059] Step S4: verification parameter extraction. Again based on the inscribed circle geometric definition of the pressure surface and the suction surface of the forward blade profile generated in step S3, that is, using the same technical means as in step S1, the camber line of the forward blade profile is solved, and the verification beta angle distribution and the verification inscribed circle radius distribution are extracted from the camber line.

[0060] Step S5: deviation determination. According to the deviation between the original beta angle distribution obtained in step S1 and the verification beta angle distribution obtained in step S4, and the deviation between the original inscribed circle radius distribution and the verification inscribed circle radius distribution, it is determined whether the forward blade profile accurately reproduces the geometric characteristics defined by the original parameters within a preset tolerance range.

[0061] The specific steps in the embodiment method of the present application shown in FIG. 1 will be described in detail below. Figure 1

[0062] ​Step S1: Reverse extraction of source blade geometry parameters

[0063] The purpose of this step is to extract the parameter set used to characterize the core geometric features of the given source blade profile data, i.e. the beta angle distribution and the inscribed circle radius distribution. This step mainly includes determination of the solution range of the camber line, arrangement of the solution stations, iterative solution of the camber line points and their inscribed circle radii, and calculation of the beta angle distribution.

[0064] Referring to Figure 2 , Figure 2 is a leading edge or trailing edge geometric fitting schematic diagram used to determine the start and end points of the camber line in the reverse parameter extraction process according to an embodiment of the present application.

[0065] To determine the start and end points of the camber line, it is necessary to first perform geometric fitting on the leading edge and trailing edge regions of the source blade to determine their geometric centers. This process first selects a set of data points (e.g. five or more) in the leading edge region and the trailing edge region of the source blade. Subsequently, a quadratic curve fitting method is used for each selected set of data points. A general quadratic curve equation is:

[0066]

[0067] By substituting the coordinates (x i ,y i ) of each data point into the above equation, a linear equation set about the undetermined coefficients A, B, C, D, E, F can be constructed, and solved in matrix form.

[0068] After obtaining the equation coefficients, the value of the discriminant B 2 -4AC is calculated to determine the curve type. When the value of the discriminant is close to zero, the curve is determined to be circular; otherwise, it is determined to be elliptical. According to the equation of the fitted circular or elliptical curve, the geometric center coordinates are calculated. The obtained leading edge geometric center and trailing edge geometric center are defined as the start point and end point of the camber line of the source blade, respectively.

[0069] After determining the start and end points of the camber line, a series of discrete solution stations are arranged between them along the predetermined flow direction (e.g. meridional direction). These solution stations define the specific positions for subsequent camber line point solving.

[0070] The point arrangement strategy can use a global uniform distribution algorithm. If the flow direction coordinates of the start and end points of the camber line are m0 and m1, and the total number of points is p, then the flow direction coordinate m i of the i-th solution station can be calculated by:

[0071]

[0072] Alternatively, the distribution strategy can also adopt a two-end encryption algorithm to obtain higher solution accuracy in areas with sharp curvature changes such as leading and trailing edges. The algorithm divides the solution domain into an intermediate uniform distribution area and two end encryption areas. The point distribution in the encryption area follows the geometric progression law, so that the station closer to the end point is more dense. If the total length of the encryption area is l, the number of encryption points is n, and the length of the line closest to the uniform distribution area is a n , the sum equation of the geometric progression can be solved to obtain the expansion ratio q by iteration. The coordinates of the encryption station closest to the starting point can be calculated by , where a1 is the first term.

[0073] Referring to Figure 3 , Figure 3 is the iterative method for solving a single camber line point in the reverse parameter extraction process according to an embodiment of the present application. This is the core of the reverse extraction process.

[0074] At each solution station, an iterative process is used to search for a camber line point. This process strictly follows the geometric definition of the inscribed circle, that is, the shortest distance from the camber line point to the pressure surface and the shortest distance to the suction surface must be equal.

[0075] Specifically, for a given solution station with a streamwise coordinate, in a coordinate direction perpendicular to the streamwise direction, a bisection method is used for iterative search. In each iteration, the shortest distance d1 from the current iteration point to the pressure surface profile and the shortest distance d2 to the suction surface profile are calculated. If d1 is not equal to d2, the position of the point in the perpendicular coordinate direction is adjusted according to the size relationship between the two and the next iteration is entered. For example, when the point is closer to the suction surface (i.e., d1 > d2), the point is moved towards the pressure surface. This iterative process continues until the absolute value of the difference between the two distances is less than a predetermined accuracy threshold (i.e., |d1-d2| < ∈). At this time, the iteration point is determined as the camber line point at the solution station.

[0076] In the above iterative process, the method for calculating the shortest distance of the point to the profile is as follows:

[0077] First, the discrete pressure surface and suction surface profile data points are fitted with a cubic spline curve respectively to obtain a continuous and smooth curve equation. The spline fitting uses the not-a-knot boundary condition, that is, the third derivative of the curve is forced to be continuous at the boundaries of the first and second intervals and the boundaries of the second last and last intervals.

[0078] Then, a multi-round segmentation approximation algorithm is used to search for the point on the spline curve closest to the iteration point:

[0079] The spline curve is divided into a parts according to equal arc length, the distances from each division point to the target point are calculated, and the b closest points are recorded; then the arc length range formed by the b points is taken as a new search interval, and the above division and search process is repeated until the arc length of the search interval is less than a preset small amount δ. At this time, the distance from the midpoint of the search interval to the target point is the shortest distance to be solved.

[0080] After the iteration converges, the obtained equal shortest distance d1 (or d2) is defined as the radius of the inscribed circle at the midpoint of the camber line. The values of the radii of the inscribed circles obtained at all solving stations are collected, thereby forming the distribution of the radii of the inscribed circles along the camber line in the flow direction.

[0081] Connecting all the camber line points obtained at the solving stations forms the camber line of the source blade. Referring to Figure 4 , Figure 4 An example of a result after the above reverse parameter extraction process is shown, which clearly shows the source blade profile, the final camber line obtained by solving, and a series of inscribed circles on the camber line.

[0082] After obtaining the complete camber line, the beta angle distribution is calculated. First, the Cartesian coordinates (x k ,y k ) of each point on the camber line are converted into cylindrical coordinates to obtain the meridional direction coordinate m k , the radius r k and the position angle θ k at each camber line point.

[0083] Then, based on the obtained cylindrical coordinates, the beta angle distribution is calculated by differentiating the position angle θ k with respect to the meridional direction coordinate m k .

[0084]

[0085] In the formula, β k is the beta angle of the camber line point at the meridional direction coordinate m k ; r k is the radius of the camber line point at the meridional direction coordinate m k ; and is the derivative of the position angle with respect to the meridional direction coordinate at point k.

[0086] The specific steps in the method of the embodiment of the application shown in Figure 1 will be described in detail below.

[0087] This section describes in detail how to use the beta angle distribution and the inscribed circle radius distribution extracted in step S1 to construct the blade geometry profile through a forward, reproducible process.

[0088] Step S2: Forward camber line generation:

[0089] The input of this step is the beta angle distribution and the inscribed circle radius distribution obtained in step S1. The purpose is to solve the spatial coordinates of the forward camber line by integrating the given parameter distribution.

[0090] This process is achieved by numerically integrating the following differential equation:

[0091]

[0092] In the formula, dθ is the differential of the position angle of the forward camber line; tan(β) is the tangent value of the beta angle provided by the beta angle distribution; r is the radius value provided by the camber line radius distribution; dm is the differential of the meridian direction coordinate.

[0093] By using a numerical integration method (for example, the central difference method) and giving an initial condition (for example, at the starting position m=0 in the meridian direction, let the position angle θ=0), the distribution of the position angle θ can be solved point by point along the entire meridian direction. Combined with the known distributions of the radius r and the meridian coordinate m, the spatial coordinates of each point on the entire forward camber line can be determined.

[0094] Step S3: Forward blade profile generation:

[0095] This step uses the envelope principle, that is, by constructing a series of inscribed circles and solving their common tangent lines, the final blade pressure surface and suction surface profiles are generated.

[0096] Reference Figure 5 , Figure 5 is a schematic diagram of a method for solving the common tangent line based on adjacent inscribed circles in the forward geometric modeling process according to an embodiment of the present application. First, along the forward camber line generated in step S2, and according to the input inscribed circle radius distribution, an inscribed circle corresponding to each camber line point is constructed.

[0097] Subsequently, for the main body of the blade, the blade profile is constructed by solving the common tangent line of each pair of adjacent inscribed circles. For two adjacent inscribed circles with center coordinates (x1, y1) and (x2, y2) and radii r1 and r2, the coordinates of the tangent point on the common tangent line are calculated by analytical geometry method. In the calculation, it is ensured that r2>r1, and the included angle α of the tangent line relative to the line connecting the two centers is determined by the following formula:

[0098]

[0099] where d is the distance between the two circle centers.

[0100] The angle between the line connecting the two circle centers and the positive direction of the X-axis of the rectangular coordinate system is The coordinates of the four tangent points (t 11 ,t 12 and t 21 ,t 22 ) on the pressure surface and the suction surface are calculated by the following equations:

[0101] The coordinates of the tangent points in the counterclockwise direction of the line connecting the circle centers are:

[0102]

[0103] The coordinates of the tangent points in the clockwise direction of the line connecting the circle centers are:

[0104]

[0105] In one specific embodiment, based on the coordinates of the circle center, the radius of the ith inscribed circle, and the azimuth angle φ and the deflection angle α calculated, the coordinates of the tangent point t i,ss on the suction surface side are calculated by the following equation:

[0106] t i,ss = (x i -R i sin(φ-α), y i +R i cos(φ-α));

[0107] where (x i , y i ) is the coordinate of the circle center of the ith inscribed circle; R i is the radius of the ith inscribed circle; φ is the azimuth angle; and α is the deflection angle.

[0108] By repeating the above calculation for all adjacent inscribed circle pairs, a series of tangent points can be obtained. For each inscribed circle except the first and the last, there are two tangent points on it. The midpoint of the circular arc connecting the two tangent points is taken as a control point of the blade profile at this position. Finally, the complete blade pressure surface and suction surface are formed by all these control points and the leading edge profile and the trailing edge profile described below.

[0109] Referring to Figure 6 , Figure 6Fig. 1 is a schematic diagram of a method for constructing a leading edge region according to an embodiment of the present application. The leading edge and trailing edge regions of a blade are treated specially to ensure the closure and smoothness of the profile. Take the leading edge as an example. On the incircle of the leading edge, there are two known tangent points (obtained by tangency with a second incircle) and a given leading edge point. By constructing a circular arc that smoothly connects one tangent point, the leading edge point, and the other tangent point, a complete leading edge profile is formed.

[0110] The specific steps of the method are as follows:

[0111] First, the phase angles φ t1 ,φ t2 ,φ le of the two tangent points and the leading edge point on the first incircle are calculated. Then, the three phase angles are sorted. According to the sorting result, the leading edge profile is constructed by segmenting the angle domain of the parametric equation of the circle. For example, if φ t1 <φ le <φ t2 , then the leading edge line on one side is constructed by setting the angle domain of the parametric equation of the circle as φ t1 ,φ le , and the leading edge line on the other side is constructed by setting the angle domain as φ le ,φ t2 . The trailing edge region is treated in a similar manner to the leading edge region.

[0112] Step S4: verification of the extraction of parameters:

[0113] The input of this step is the forward blade profile generated in step S3. The purpose is to obtain a set of geometric parameters for verification by applying the aforementioned step S1 (reverse extraction of geometric parameters of the source blade) completely and without modification to the forward blade profile.

[0114] Specifically, this step regards the forward blade profile as a new source blade and completely repeats all sub-steps in step S1, including:

[0115] Geometric fitting of the leading edge and trailing edge of the forward blade profile to determine the start and end points of the verification camber line.

[0116] Arranging solving stations within the solving range of the verification camber line.

[0117] At each solving station, the verification camber line point and its verification incircle radius are obtained by iterative solving, and finally the verification incircle radius distribution is formed.

[0118] After obtaining the complete verification camber line, its verification beta angle distribution is calculated.

[0119] The principle and formula for calculating the verification beta angle distribution in this step are completely consistent with those in step S1, but the operation object is the verification arc. The verification beta angle β' k is calculated as follows:

[0120]

[0121] where β' k is the verification beta angle at the verification meridian coordinate m' k ; r' k is the verification radius at the verification meridian coordinate m' k ; and is the derivative of the verification position angle with respect to the verification meridian coordinate at point k.

[0122] The final output of this step is a set of verification parameters, i.e., the verification beta angle distribution and the verification inscribed circle radius distribution.

[0123] Step S5: Deviation judgment:

[0124] Referring to Figure 7 , Figure 7 is a schematic diagram according to a specific application case of the present application, showing the comparison between the original parameter distribution and the verification parameter distribution. The purpose of this step is to quantitatively compare the original parameter set obtained in step S1 with the verification parameter set obtained in step S4, to determine the accuracy of model reproduction.

[0125] This process compares the two sets of parameter distributions point by point or as a whole. For example, at each corresponding meridian coordinate position m k , the deviation between the original beta angle β k and the verification beta angle β' k is calculated, as well as the deviation between the original inscribed circle radius R k and the verification inscribed circle radius R' k .

[0126] The specific judgment criteria include calculating the maximum absolute deviation, the relative deviation, or the root mean square deviation. For example, the maximum absolute deviation Δβ max of the beta angle distribution is calculated:

[0127]

[0128] and the maximum relative deviation ΔR rel,max of the inscribed circle radius distribution is calculated:

[0129]

[0130] Subsequently, the calculated deviation values (such as Δβ max and ΔRrel,max ) are compared with one or more preset tolerance thresholds. If all the calculated deviations are smaller than their corresponding tolerance thresholds, it is determined that the forward blade profile accurately reproduces the geometric features defined by the original parameters within the preset tolerance range, thereby proving the logical consistency and high fidelity of the reverse-forward interactive modeling method proposed in the present application.

[0131] Referring to Figure 7 , Figure 7 is a schematic diagram according to a specific application case of the present application. The embodiment takes a specific source blade as an example to completely describe the entire process of executing the method of the present application and demonstrate its technical effects.

[0132] First, the profile data of a source blade (labeled as ori in Figure 7 (a)) is provided, and the reverse parameter extraction process of step S100 is executed. By processing the source blade profile, the original beta angle distribution (labeled as ori in Figure 7 (b)) and the original inscribed circle radius distribution (labeled as ori in Figure 7 (c)) are extracted.

[0133] Second, the extracted original beta angle distribution and the original inscribed circle radius distribution are taken as inputs, and the forward geometric modeling process of steps S2 and S3 is executed. The process generates a reconstructed blade (labeled as reshape in Figure 7 (a)). As shown in Figure 7 (a), the geometric profile of the reconstructed blade is highly coincident with the geometric profile of the source blade, and through calculation, the geometric deviation between the two is within a very small range, for example, the geometric deviation in the middle region of the blade can be less than 0.003%.

[0134] Third, the reconstructed blade is taken as new input, and the verification parameter extraction process of step S4 is executed. The process uses the same technical means as step S1 to extract a set of verification beta angle distribution (labeled as Reshape in Figure 7 (b)) and verification inscribed circle radius distribution (labeled as Reshape in Figure 7 (c)) from the reconstructed blade.

[0135] Finally, the deviation determination process of step S5 is executed. As shown in Figure 8 (b) and Figure 8 (c), the original parameter distribution is compared with the verification parameter distribution. The calculation result shows that the deviation between the two sets of parameter distributions is extremely small, for example, the local beta angle deviation can reach 0.005°.

[0136] The results of the present embodiment show that the blade constructed by the forward method of the present application has highly consistent geometric profiles with the source blade; at the same time, the parameters obtained by the reverse construction of the forward constructed blade are also highly consistent with the original parameters. This proves that the reverse and forward modeling methods proposed by the present application have strict logical unity and high precision verifiability.

[0137] The method of the present application can also be applied to hybrid modeling in the parameter space to systematically generate blades with completely new characteristics. The specific steps are as follows:

[0138] At least two different source blades are provided, such as blade A and blade B.

[0139] The parameter extraction process of step S1 is independently performed for each source blade, thereby obtaining two independent sets of parameters: the beta angle distribution β A (m) and the inscribed circle radius distribution R A (m) of blade A, and the beta angle distribution β B (m) and the inscribed circle radius distribution R B (m) of blade B.

[0140] One or more mixing weight factors w are defined, where 0≤w≤1. By linearly weighted interpolation of the two sets of parameters, one or more new sets of hybrid parameters are generated. The hybrid beta angle distribution β C (m) and the hybrid inscribed circle radius distribution R C (m) can be calculated by the following formula:

[0141] β C (m)=w·β A (m)+(1-w)·β B (m);

[0142] R C (m)=w·R A (m)+(1-w)·R B (m);

[0143] The hybrid parameter set is input to perform the forward geometric modeling process of steps S2 and S3, thereby generating a completely new blade C whose geometric characteristics are a weighted mixture of the geometric characteristics of source blades A and B.

[0144] Referring to ​ , ​ is a structural block diagram of a blade reverse-forward interactive modeling system based on camber line geometric parameters according to an embodiment of the present application. The above method of the present application can be realized by a computer system or a software program. The system comprises a parameter extraction module 10, a forward modeling module 20 and an interactive verification module 30.

[0145] A parameter extraction module 10 is configured to perform the functions of steps S1 and S4, which receives the blade profile data as input and outputs the corresponding beta angle distribution and the inscribed circle radius distribution.

[0146] A forward modeling module 20 is configured to perform the functions of steps S2 and S3, which receives the parameter distribution generated by the parameter extraction module 10 as input and outputs the finally generated forward blade profile.

[0147] An interactive verification module 30 is configured to perform the function of step S5, which receives the original parameter distribution and the verification parameter distribution output by the parameter extraction module 10, performs deviation calculation and judgment, and outputs the judgment result.

[0148] The three modules work together to completely realize the reverse-forward interactive modeling and verification technical process proposed in the present application.

[0149] Although embodiments of the present application have been shown and described, it is to be understood that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the present application, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for inverse-forward interactive modeling of a blade based on mid-chord line geometric parameters, characterized in that, The method comprises the following steps: S1, based on the incircle geometry definition of the pressure surface and the suction surface of the source blade, the mean camber line of the source blade is solved, and the beta angle distribution and the incircle radius distribution along the mean camber line flow direction are extracted from the mean camber line of the source blade; S2, according to the beta angle distribution and the incircle radius distribution, the forward mean camber line is generated through integral operation; S3, a series of incircles are constructed along the forward mean camber line and according to the incircle radius distribution, and the forward blade profile is generated by solving the envelope of the series of incircles; S4, based on the incircle geometry definition of the pressure surface and the suction surface of the forward blade profile again, the mean camber line of the forward blade profile is solved, and the verification beta angle distribution and the verification incircle radius distribution are extracted from the mean camber line of the forward blade profile; S5, according to the deviation between the beta angle distribution and the verification beta angle distribution and the deviation between the incircle radius distribution and the verification incircle radius distribution, it is determined whether the forward blade profile accurately reproduces the geometric characteristics defined by the beta angle distribution and the incircle radius distribution within a preset tolerance range.

2. The inverse-forward interactive modeling method of a blade based on middle camber line geometric parameters according to claim 1, characterized in that, In step S1, based on the incircle geometry definition of the pressure surface and the suction surface of the source blade, the mean camber line of the source blade is solved, and the beta angle distribution and the incircle radius distribution along the mean camber line flow direction are extracted from the mean camber line of the source blade, which comprises: A group of data points are selected in the leading edge region and the trailing edge region of the source blade respectively, the geometric centers of the leading edge and the trailing edge are obtained by quadratic curve fitting on the data points, and the geometric centers are defined as the start and end points of the mean camber line of the source blade; A series of solving stations are arranged between the start and end points along the preset flow direction of the source blade; At each solving station, a mean camber line point is searched through iterative operation, so that the shortest distance from the mean camber line point to the pressure surface is equal to the shortest distance to the suction surface; All the mean camber line points obtained at the solving stations are connected to form the mean camber line of the source blade.

3. The inverse-forward interactive modeling method of a blade based on middle camber line geometric parameters according to claim 2, characterized in that, In step S1, based on the incircle geometry definition of the pressure surface and the suction surface of the source blade, the mean camber line of the source blade is solved, and the beta angle distribution and the incircle radius distribution along the mean camber line flow direction are extracted from the mean camber line of the source blade, which further comprises: Converting the Cartesian coordinates of each point on the mean camber line of the source blade into cylindrical coordinates to obtain a meridional direction coordinate m at each point on the mean camber line k , a radius r k , and a position angle θ k ; The beta angle distribution β is then calculated based on the obtained meridional coordinates, radius and position angle by the following formula k : where β k is the beta angle of the point of the mean curve at the meridional coordinate m k ; r k is the radius of the point of the mean curve at the meridional coordinate m k ; and is the derivative of the position angle with respect to the meridional coordinate at the point k.

4. The inverse-forward interactive modeling method of a blade based on middle camber line geometry parameters according to claim 1, characterized in that, In step S2, according to the beta angle distribution and the incircle radius distribution, the forward mean camber line is generated through integral operation, which comprises: A differential equation is used for numerical integral operation to obtain the position angle distribution of the forward mean camber line; The integral operation obtains the tangent value of the beta angle according to the input beta angle distribution, and obtains the radius value according to the input mean camber line radius distribution; The differential equation is: In the formula, dθ is the position angle differential of the forward mean camber line; tan(β) is the tangent value of the beta angle provided by the beta angle distribution; r is the radius value provided by the mean camber line radius distribution; and dm is the meridian direction coordinate differential.

5. The inverse-forward interactive modeling method of a blade based on middle camber line geometry parameters according to claim 1, characterized in that, In step S3, the step of constructing a series of inscribed circles along the forward camber line and according to the inscribed circle radius distribution, and then generating the forward blade profile by solving the envelope of the series of inscribed circles, comprises: solving the common external tangent line of each pair of adjacent inscribed circles; connecting the tangent points of the common external tangent line on each inscribed circle to form the forward blade profile.

6. The inverse-forward interactive modeling method of a blade based on middle camber line geometric parameters according to claim 5, characterized in that, The step of solving the suction side tangent point of the common external tangent line on the i-th inscribed circle, taking the forward camber line and the inscribed circle radius distribution as inputs, comprises: determines the center coordinate (x i ,y i ) and the radius R i of the i-th inscribed circle, and the center coordinate (x i+1 ,y i+1 ) and the radius R i+1 of the adjacent (i+1)-th inscribed circle; based on the coordinates of the circle centers and the radius, calculating the azimuth angle φ of the line connecting the two circle centers and the deflection angle α of the common external tangent line relative to the line connecting the two circle centers; Based on the center coordinate, the radius of the ith inscribed circle, and the azimuth angle φ and the deflection angle α obtained by calculation, the coordinates of the suction surface side tangent point t are calculated by the following equation: i,ss t = (R - r) cos φ + r cos (φ + α) t i,ss = (x i -R i sin(φ-α),y i +R i cos(φ-α)) where (x i ,y i ) is the center coordinate of the ith inscribed circle; R i is the radius of the ith inscribed circle; φ is the azimuth angle; and α is the deflection angle.

7. The inverse-forward interactive modeling method of a blade based on middle camber line geometry parameters according to claim 1, characterized in that, In step S4, the step of solving the camber line of the forward blade profile again based on the geometric definition of the inscribed circles of the pressure side and the suction side of the forward blade profile, and extracting the verification beta angle distribution and the verification inscribed circle radius distribution from the camber line of the forward blade profile, comprises: arranging a series of verification solving stations along the preset flow direction of the forward blade profile, searching for a point at each verification solving station as a verification camber line point of the verification solving station, so that the shortest distance from the verification camber line point to the pressure side of the forward blade profile is equal to the shortest distance to the suction side, and defining this shortest distance as the verification inscribed circle radius of the verification camber line point, thereby obtaining the verification inscribed circle radius distribution, and connecting all the obtained verification camber line points to form the camber line of the forward blade profile; converting the mean camber line of the forward blade profile into a cylindrical coordinate representation to obtain a verification meridional direction coordinate m' at each verification mean camber line point k , a verification radius r' k , and a verification position angle θ' k ; Based on the obtained verification column coordinates, the verification beta angle distribution β' is calculated by the following equation k : where β' = verification beta angle at verification meridian coordinate m' k k r' = verification radius at verification meridian coordinate m' k k where β' = verification beta angle at verification meridian coordinate m' where β' = verification beta angle at verification meridian coordinate m'​​ 8. The inverse-positive interactive modeling method of blade based on middle camber line geometry parameters according to claim 1, characterized in that, In step S5, the step of determining whether the forward blade profile accurately reproduces the geometric characteristics defined by the beta angle distribution and the inscribed circle radius distribution within a preset tolerance range according to the deviation between the beta angle distribution and the verification beta angle distribution and the deviation between the inscribed circle radius distribution and the verification inscribed circle radius distribution, comprises: calculating the first maximum absolute deviation between the beta angle distribution and the verification beta angle distribution, and the second maximum absolute deviation between the inscribed circle radius distribution and the verification inscribed circle radius distribution; and when the first maximum absolute deviation is less than a first preset tolerance threshold and the second maximum absolute deviation is less than a second preset tolerance threshold, determining that the forward blade profile accurately reproduces the geometric characteristics within the preset tolerance range.

9. The inverse-positive interactive modeling method of blade based on middle camber line geometry parameters according to claim 1, characterized in that, The method further comprises: performing a parameter extraction operation on the first source blade and the second source blade respectively, the parameter extraction operation being based on the geometric definition of the inscribed circles of the pressure side and the suction side of the blade, solving the camber line of the blade, and extracting the beta angle distribution and the inscribed circle radius distribution distributed along the camber line from the camber line, thereby obtaining a first parameter set and a second parameter set; performing weighted interpolation on the first parameter set and the second parameter set according to a preset weight function to generate a set of mixed parameter sets; taking the mixed parameter set as input, generating a forward camber line through integral operation, and constructing a series of inscribed circles along the forward camber line and according to the inscribed circle radius distribution in the mixed parameter set, and then generating a mixed blade by solving the envelope of the series of inscribed circles.

10. A blade inverse - direct interactive modeling system based on mid-arc geometric parameters, applied to the method of any one of claims 1-9, characterized in that, The system comprises: a parameter extraction module configured to solve a mean camber line of the source blade based on an inscribed circle geometry definition of a pressure surface and a suction surface of the source blade, and extract a beta angle distribution and an inscribed circle radius distribution along the mean camber line flow direction distribution from the mean camber line of the source blade; a forward modeling module configured to generate a forward mean camber line by integral operation according to the beta angle distribution and the inscribed circle radius distribution, and construct a series of inscribed circles along the forward mean camber line according to the inscribed circle radius distribution, and further generate a forward blade profile by solving an envelope line of the series of inscribed circles; an interactive verification module configured to extract a verification beta angle distribution and a verification inscribed circle radius distribution based on an inscribed circle geometry definition of a pressure surface and a suction surface of the forward blade profile, and determine whether the forward blade profile accurately reproduces the geometric features defined by the beta angle distribution and the inscribed circle radius distribution within a preset tolerance range according to a deviation between the beta angle distribution and the verification beta angle distribution and a deviation between the inscribed circle radius distribution and the verification inscribed circle radius distribution.

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