A method and system for determining a turbine throat area considering a sweep and a meridian runner contraction-expansion

Abstract

The present application relates to aerospace field, disclose a kind of turbine throat area determination method and system considering sweep and meridian flow passage convergence, method includes: obtaining geometric data to establish circumferential adjacent blade, form three-dimensional fluid passage;Extract meridian profile, establish flow direction position correspondence and interpolation to obtain intermediate meridian profile, rotation forms equal relative blade height section;The space intersection of section and blade profile is calculated, the local shortest distance is solved, and the throat endpoint candidate interval is established with this as center;With the parameter of endpoint in candidate interval to construct non-coplanar space area microelement, under the constraint condition, with the minimum total area as target to implement joint solution, determine continuous three-dimensional turbine throat surface and calculate total area.The system contains passage construction, section construction, candidate interval establishment and joint solution module.The present application solves the relative blade height mismatch and endpoint jump problem caused by traditional section, improves the calculation accuracy of complex cascade throat area.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, specifically to a method and system for determining the turbine throat area considering sweep profile and meridional channel contraction and expansion. Background Technology

[0002] The turbine throat area is a key parameter in the aerodynamic design of aero-engines and gas turbines. It determines the flow capacity of turbine components and directly affects the engine's flow matching and overall performance. Physically, the throat typically refers to the region with the smallest cross-sectional area of ​​the fluid passage between two adjacent turbine blades. Accurately calculating the area of ​​this region is fundamental to evaluating and validating turbine aerodynamic design schemes.

[0003] Existing methods for calculating turbine throat area typically involve taking multiple cylindrical surfaces of fixed radii along the blade height direction. At each cross-section, the minimum distance between adjacent blade surfaces is independently determined as the local throat width, and finally, the total area is obtained by radial integration of these widths. However, modern turbine blades commonly employ complex three-dimensional structures such as swept-forward, swept-back, and compound swept profiles, and their corresponding meridional channels often exhibit contraction or expansion characteristics. When the channel height varies along the axial direction, using cylindrical surfaces of fixed radii for cross-sections can lead to mismatches in the relative blade heights at different axial positions, making it difficult to maintain a consistent relative channel height relationship.

[0004] Meanwhile, the complex blade sweep and flow channel expansion and contraction result in the local throat segments at different blade heights being non-coplanar in space. Existing area integration methods often simplify the spatial distances or superimpose additional empirical correction formulas, leading to inherent geometric approximation errors. On the other hand, independently solving for the shortest distance on each cross-section lacks longitudinal spatial geometric constraints. When the blade surface curvature changes drastically, the calculated throat endpoints of adjacent cross-sections often exhibit discontinuous jumps. These endpoint jumps cause spatial computational element flipping and segment intersections, making it impossible to construct a continuous and smooth three-dimensional physical throat surface, resulting in deviations in the calculation results of complex turbine flow capacity. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method and system for determining the area of ​​a turbine throat that considers sweep profile and meridional channel contraction and expansion. This solves the problem that existing technologies, when calculating the area of ​​a turbine throat with sweep profile and meridional channel contraction and expansion characteristics, suffer from inaccurate calculations of the three-dimensional throat area due to mismatch between the blade height and the blade section and the lack of longitudinal geometric constraints causing endpoint jumps.

[0006] To achieve the above objectives, the present invention provides the following technical solution: The first aspect of this invention provides a method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion, comprising the following steps: Obtain geometric data to establish circumferentially adjacent blades, forming a three-dimensional turbine fluid channel; Extract the hub meridian profile and the casing meridian profile, establish the flow direction position correspondence and interpolate to obtain the intermediate meridian profile, and rotate the intermediate meridian profile around the engine axis to form a blade height bisector with equal relative height; Calculate the spatial intersection lines between each relative blade height cutting surface and the current blade profile and adjacent blade profiles. Solve for the local shortest distance between the intersection lines in the channel. Establish candidate intervals for the trailing edge throat endpoint and suction side throat endpoint with the corresponding initial point as the center. Using the endpoint positions within the candidate interval as joint parameters to be determined, a non-coplanar spatial area micro-element is constructed and its area is calculated. Under preset constraints, a joint solution is implemented with the goal of minimizing the total area, to determine the continuous three-dimensional turbine throat surface spanning the blade passage and to calculate the total throat area.

[0007] Preferably, the step of acquiring geometric data to establish circumferentially adjacent blades and form a three-dimensional turbine fluid channel specifically includes: Obtain the current three-dimensional profile of the blade, the hub flow channel surface, the casing flow channel surface, the number of blades in the entire ring, and the feature area identifiers on the blade surface; The circumferential pitch angle is calculated based on the number of blades in the ring, or circumferential adjacent blades are established based on a given grid pitch to form a three-dimensional turbine fluid channel.

[0008] Preferably, the step of establishing the correspondence between flow directions and positions and interpolating to obtain the intermediate meridian line specifically includes: Establish the geometric positional correspondence between the hub meridional profile and the casing meridional profile in the direction of fluid flow, and map the positional correspondence in the direction of flow into normalized flow direction parameters; The intermediate meridian profile is obtained by spatial interpolation calculation at the same flow direction position according to the preset relative leaf height ratio.

[0009] Preferably, the calculation of the spatial intersection lines between each relative blade height cutting surface and the current blade profile and adjacent blade profiles specifically includes: Calculate the spatial intersection lines between each of the aforementioned equal relative leaf height cutting surfaces and the current three-dimensional surface of the blade, as well as the three-dimensional surface of the adjacent circumferential blades; Based on the characteristic region markings on the blade surface, candidate curves on the trailing edge side are extracted from the current blade intersection line, and candidate curves on the suction side are extracted from the intersection line of adjacent blades, thus obtaining the candidate curves on the trailing edge side and the candidate curves on the suction side.

[0010] Preferably, the step of solving for the local shortest distance between intersection lines within the channel, and establishing candidate intervals for the endpoints of the tail-side throat and the suction-side throat with the corresponding initial point as the center, specifically includes: Among the valid point pairs excluding those that pass through the blade or endwall solid boundary, the point pair with the smallest Euclidean distance is found as the initial point on the trailing edge side and the initial point on the suction side, thus obtaining the local shortest distance. Centered on the initial point on the trailing edge side and the initial point on the suction side, candidate intervals for the throat endpoints on the trailing edge side and the suction side are established within a pre-marked effective area based on local geometric features.

[0011] Preferably, finding the pair of points with the smallest Euclidean distance as the initial point on the trailing edge side and the initial point on the suction side specifically includes: When the trailing edge of the current blade has an arc-shaped profile at the corresponding cutting position, calculate the nearest point from the center of the trailing edge to the candidate curve of the suction side, and use it as the initial point of the suction side. Along the spatial vector direction pointing from the center of the trailing edge circle to the initial point on the suction side, determine a point on the corresponding trailing edge arc whose distance from the center is equal to the radius of the trailing edge arc, and use this point as the initial point on the trailing edge side. Preferably, the construction of non-coplanar spatial area micro-elements and the calculation of their areas specifically include: A spatial quadrilateral is defined by the four three-dimensional endpoints of the local throat segments corresponding to two adjacent cutting positions; Divide the spatial quadrilateral into two spatial triangles along the diagonal, and calculate the area of ​​each spatial triangle based on the cross product of the side vectors. The area of ​​the non-coplanar spatial area element is obtained by summing the areas of the two spatial triangles.

[0012] Preferably, the joint solution under preset constraints with the objective of minimizing the total area specifically includes: The geometric constraints include continuous and smooth endpoint trajectories, no flipping of the area micro-element and no penetration of the fluid channel, and the end being constrained by the flow channel surface. The candidate results that satisfy the geometric constraints are compared by area, and the result with the smallest total area of ​​each of the non-coplanar spatial area micro-elements is selected to determine the continuous three-dimensional turbine throat surface.

[0013] Preferably, after determining the continuous three-dimensional turbine throat surface spanning the blade passage and calculating the total throat area, the method further includes: Intermediate splitting points are added between adjacent splitting points, and local discretization errors are calculated; When the local discretization error exceeds the first preset threshold, the newly added intermediate cutting surface is retained and the joint solution is re-executed for all throat endpoints; When all local discretization errors are less than the first preset threshold, and the total area convergence of the two calculations is less than the second preset threshold, stop adding the cutting surface and output the total area of ​​the turbine throat obtained at the current calculation.

[0014] A second aspect of the present invention provides a turbine throat area determination system that takes into account sweep profile and meridional channel contraction and expansion, comprising: The data input and channel construction module is used to acquire geometric data to establish circumferentially adjacent blades and form a three-dimensional turbine fluid channel. The slicing surface construction module is used to extract the hub meridional profile and the casing meridional profile, establish the flow direction position correspondence and interpolate to obtain the intermediate meridional profile, and rotate the intermediate meridional profile around the engine axis to form a slicing surface with equal relative blade height; The candidate interval establishment module is used to calculate the spatial intersection lines between each relative blade height cutting surface and the current blade profile and adjacent blade profiles, solve the local shortest distance between the intersection lines in the channel, and establish the candidate intervals for the trailing edge throat endpoint and the suction side throat endpoint with the corresponding initial point as the center. The joint solution module is used to construct non-coplanar spatial area micro-elements with the endpoint positions in the candidate interval as joint parameters to be determined and to calculate the area. Under preset constraints, the joint solution is performed with the goal of minimizing the total area to determine the continuous three-dimensional turbine throat surface and calculate the total throat area.

[0015] This invention provides a method and system for determining the turbine throat area considering sweeping and meridional channel contraction and expansion. It has the following beneficial effects: 1. This invention constructs a constant relative blade height sectional surface that varies with the meridional flow channel by constructing a sectional surface with the same relative flow channel height according to the flow direction correspondence between the hub meridional profile and the casing meridional profile. This achieves the technical effect of keeping the relative flow channel height consistent at different axial positions of each sectional surface, and solves the technical problem of relative blade height mismatch that is easily generated in the traditional method of using a fixed radius cylindrical section in contraction, expansion and compound contraction and expansion flow channels.

[0016] 2. This invention constructs a non-coplanar spatial area micro-element by utilizing the four actual three-dimensional endpoints of adjacent local throat segments and directly calculates the area using the cross product of triangular side vectors. This achieves the technical effect of directly incorporating the blade sweep shape, the change in throat segment direction, and the asynchronous displacement of the trajectories of the two endpoints into the calculation. It solves the technical problems of traditional methods that require simplifying the spatial distance between adjacent throat segments to a single sheet thickness and require additional correction formulas, resulting in inaccurate calculations.

[0017] 3. This invention achieves the technical effect of obtaining a three-dimensional throat surface that extends continuously and smoothly from the hub to the casing by jointly determining the throat endpoints at each blade height position within the candidate interval and applying geometric constraints such as continuous endpoint trajectory, consistent micro-element direction, and end boundary restriction. This solves the technical problems of endpoint jumps, line segment intersections, and micro-element flips that easily occur when each dicing surface independently obtains the local shortest line. Attached Figure Description

[0018] Figure 1This is a system architecture diagram of the present invention; Figure 2 This is a flowchart of the method steps of the present invention; Figure 3 This is a schematic diagram of the three-dimensional turbine channel and the equal relative blade height segmentation that varies with the meridional flow channel according to the present invention; Figure 4 This is a schematic diagram of the local shortest distance and throat endpoint candidate interval corresponding to a single cut position in this invention; Figure 5 This is a schematic diagram of the spatial throat area micro-element structure corresponding to adjacent cutting positions in the present invention; Figure 6 This is a schematic diagram of a three-dimensional turbine throat surface formed by continuously splicing multiple spatial area micro-elements according to the present invention. Detailed Implementation

[0019] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] Please see the appendix Figure 1 This invention provides a turbine throat area determination system that considers sweeping and meridional channel contraction and expansion, including a data input and channel construction module, a sectional surface construction module, a candidate interval establishment module, and a joint solution module.

[0021] The data input and channel construction module is used to obtain the current blade 3D profile, hub flow channel surface, casing flow channel surface, number of blades in the entire ring, and feature region identifiers on the blade surface. Based on the circumferential pitch angle or a given grid pitch, the data input and channel construction module establishes circumferentially adjacent blades, constructing a 3D turbine fluid channel for throat calculation.

[0022] The slicing surface construction module is used to extract the hub meridional profile and the casing meridional profile within the meridional plane, establishing the flow direction positional correspondence between the two meridional profiles. The module then interpolates the intermediate meridional profile at the same flow direction position according to a preset relative blade height ratio, and rotates the intermediate meridional profile around the engine axis to generate a slicing surface with equal relative blade height that varies with the meridional flow path.

[0023] The candidate interval establishment module is used to calculate the intersection lines of the equal relative blade height cutting surface with the current blade profile and adjacent blade profiles. After excluding connecting lines that pass through the blade or endwall entity, the candidate interval establishment module solves for the local shortest distance between the trailing edge side intersection line and the suction side intersection line.

[0024] The candidate interval establishment module establishes candidate intervals for the tail-side throat endpoint and suction-side throat endpoint within a preset effective area, based on the endpoints corresponding to the local shortest distance.

[0025] The joint solver module is used to construct a non-coplanar spatial area element by using the endpoints within the candidate interval as the variables to be solved and the four three-dimensional endpoints of the two local throat segments at adjacent cutting positions. The joint solver module divides the non-coplanar spatial area element into spatial triangles and calculates the area using the cross product of the edge vectors.

[0026] Under the conditions that the endpoint trajectories are continuous, the local throat segments are located within the fluid channel, the adjacent area micro-elements are oriented in the same direction, and the ends are constrained by the end walls, the joint solution module performs global optimization with the goal of minimizing the total area of ​​each non-coplanar spatial area micro-elements, determines the continuous three-dimensional turbine throat surface, and outputs the total area of ​​the turbine throat.

[0027] Please see the appendix Figure 2 This invention provides a method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion, comprising the following steps: S1: Obtain the current blade three-dimensional profile, hub flow channel surface, casing flow channel surface, number of blades in the ring, and characteristic area identifiers on the blade surface; calculate the circumferential pitch angle or establish circumferential adjacent blades according to the given grid pitch; form a three-dimensional turbine fluid channel composed of the current blade and circumferential adjacent blades. S2, extract the hub meridian profile and the casing meridian profile in the meridional plane, establish the flow direction position correspondence between the hub meridian profile and the casing meridian profile, and perform interpolation calculation at the same flow direction position according to the preset relative blade height ratio to obtain the intermediate meridian profile, and rotate the intermediate meridian profile around the engine axis to form an equal relative blade height dicing surface that changes with the contraction, expansion or compound change of the meridional flow channel; S3, calculate the spatial intersection lines of each relative blade height cutting surface with the current blade profile and adjacent blade profiles, solve the local shortest distance between the trailing edge side intersection line and the suction side intersection line in the effective point pairs within the limited fluid channel, and establish the trailing edge throat endpoint candidate interval and the suction side throat endpoint candidate interval in the pre-marked effective area with the initial point corresponding to the local shortest distance as the center. S4 uses the endpoint positions within each candidate interval of the segmentation position as the joint parameters to be determined. It constructs non-coplanar spatial area micro-elements using the four three-dimensional endpoints of two adjacent local throat segments. The non-coplanar spatial area micro-elements are divided into spatial triangles and the area is calculated based on the cross product of the edge vectors. Under the conditions that the endpoint trajectory is continuous and smooth, the area micro-elements do not flip and do not penetrate the fluid channel, and the ends are constrained by the flow channel surface, the joint solution is implemented with the goal of minimizing the total area. The continuous three-dimensional turbine throat surface spanning the blade channel is determined and the total throat area is calculated.

[0028] The following section will provide a detailed explanation of the technical details and specific principles of the aforementioned systems and methods.

[0029] Please see the appendix Figure 3 -Appendix Figure 6 Step S1 of the present invention can be specifically divided into the following sub-steps: S11, establish a three-dimensional coordinate system with the engine axis as the rotation axis, and obtain the current three-dimensional profile of the blade, hub flow channel surface, casing flow channel surface, number of blades in the entire ring, and feature area identifiers on the blade surface.

[0030] When establishing a three-dimensional coordinate system, the axial coordinates of the engine are marked as follows: Radial coordinates are The circumferential angle is denoted as This coordinate system is used to uniformly describe all spatial geometric elements within the turbine passage. The acquired current blade 3D profile data encompasses the blade's true spatial distortion morphology. The specific representation of the current blade 3D profile data includes computer-aided design surfaces, discrete meshes, measured point clouds, or data reconstructed from multiple 2D blade profile sections.

[0031] The synchronously acquired geometric data also includes hub flow channel surface data and casing flow channel surface data used to define the upper and lower boundaries of the fluid passage. The feature region identifiers on the blade surface specifically include blade pressure side region identifiers, suction side region identifiers, and trailing edge region identifiers. These region identifiers are pre-defined and marked on the blade geometric model, primarily used to accurately define the search range of the throat endpoint in subsequent spatial intersection and distance calculation steps, avoiding invalid calculations in non-critical areas.

[0032] S12 calculates the circumferential pitch angle based on the number of blades in the ring, or establishes circumferentially adjacent blades based on a given grid pitch, forming a three-dimensional turbine fluid channel composed of the current blade and circumferentially adjacent blades.

[0033] When constructing adjacent channels of annular turbine blade cascades, the circumferential pitch angle of adjacent blades is calculated using the obtained number of blades in the entire ring. The calculation formula is as follows: ; In the formula, It is the circumferential pitch angle; Pi; This represents the number of blades in the entire ring.

[0034] After obtaining the circumferential pitch angle, the current blade's three-dimensional geometry is rotated around the engine axis by either the forward or reverse circumferential pitch angle. When determining the specific rotation direction, a rotation direction is selected based on the characteristic region markings on the blade surface, causing the suction side of adjacent blades to face the trailing edge region of the current blade. This rotation operation generates the circumferentially adjacent blades for actual throat calculations.

[0035] When this invention is applied to a computational scenario involving straight blade cascades, since there is no annular pitch, the current blade is directly translated along the pitch direction according to the given physical pitch to establish an equivalent adjacent blade channel.

[0036] For rotation and translation transformations of three-dimensional geometric models, those skilled in the art can use conventional three-dimensional geometric transformation matrices and homogeneous coordinate operations to achieve them. The specific spatial array transformation is a well-known technique in the field and will not be described in detail here.

[0037] After the above rotation or translation operation, the current blade, the newly generated circumferential adjacent blade, the bottom hub flow channel surface and the top casing flow channel surface together form a confined fluid region, that is, a three-dimensional turbine fluid channel is formed.

[0038] The data input and channel construction module in this system is used to fully perform the functions of establishing a coordinate system, acquiring model data, and constructing fluid channels. The three-dimensional turbine fluid channels output by the data input and channel construction module can realistically reflect the forward sweep, backward sweep, or combined sweep characteristics of the blades, while also preserving the geometric features of the meridional channel that contract, expand, or undergo combined changes along the axial direction. This provides a complete basic geometric boundary for the subsequent construction of non-cylindrical sectional surfaces that vary with the meridional channel.

[0039] Step S2 of this invention is executed by the equal relative leaf height tangent surface construction module, and is specifically divided into the following sub-steps: S21. Extract the hub meridian profile and the casing meridian profile within the meridional plane, and establish the flow direction position correspondence between the hub meridian profile and the casing meridian profile.

[0040] The flow channel region formed by the turbine passage within the meridional plane containing the engine axis is called the meridional flow channel. The radial boundaries of this flow channel region are defined by the physical hub meridional profile and casing meridional profile, respectively. The spatial geometric contours of the hub and casing are obtained within the meridional plane, and the hub meridional profile and casing meridional profile are extracted to characterize the endwall morphology. A geometrical correspondence between the hub meridional profile and casing meridional profile in the flow direction is established according to the fluid flow direction from inlet to outlet. This correspondence can be established by using the same axial position, the same normalized meridional arc length, a preset quasi-orthogonal line, or a corresponding station specified in the flow channel design data. Using any of these correspondence methods, the relative progress of the hub and casing in the flow direction can be uniformly mapped to a normalized flow direction parameter.

[0041] The parametric coordinate representations of the hub meridian profile and the casing meridian profile are as follows: ; ; In the formula, The normalized flow direction position parameter has a value range of [0,1]. For flow direction position parameters Two-dimensional coordinates of the hub meridian line at the location; For the hub meridional profile in parameters The axial coordinate at the location; For the hub meridional profile in parameters The radial coordinate at the location; For flow direction position parameters Two-dimensional coordinates of the casing meridian line at the location; For the casing meridional profile in parameters The axial coordinate at the location; For the casing meridional profile in parameters The radial coordinates at that location.

[0042] S22, spatial interpolation calculation is performed at the same flow direction position according to the preset relative blade height ratio to obtain the intermediate meridian profile.

[0043] Multiple relative blade height positions are pre-set between the hub and the casing to divide the flow path. Specific settings... The relative leaf height position numerically satisfies For any given relative blade height ratio, at the same flow direction position parameters, linear interpolation is performed based on the spatial span between the hub and the casing to calculate the coordinates of the intermediate meridian corresponding to that relative height. The interpolation formula is as follows: ; In the formula, The relative leaf height ratio is a preset value, with a range of [0,1]. To achieve a relatively high leaf height ratio and flow direction location parameters Two-dimensional coordinates of the central meridian at the location; For flow direction position parameters Two-dimensional coordinates of the hub meridian line at the location; For flow direction position parameters Two-dimensional coordinates of the meridional line of the casing at the location.

[0044] In the setting of relative leaf height ratio, The relative height of the bottom of the wheel hub The relative height of the top of the corresponding casing, This corresponds to the height of the internal flow channel located between the hub and the casing. Among the N+1 relative blade height positions set, and These two extreme positions, corresponding to the original hub flow channel surface and casing flow channel surface respectively, are used to define the radial physical boundary of the final generated three-dimensional throat surface. to This corresponds to each intermediate meridian profile within the flow channel. Based on this interpolation relationship, for a given relative blade height ratio, the generated intermediate meridian profile maintains a fixed relative flow channel height at any flow direction position throughout the entire flow channel.

[0045] S23 rotates each of the generated intermediate meridional lines around the engine axis to form a constant relative blade height cutting surface that varies with the meridional flow channel.

[0046] After obtaining the intermediate meridional profile, it is rotated and swept around the engine axis within a circumferential pitch range of the blade cascade. The radial coordinates of the intermediate meridional profile fluctuate with the axial coordinates along the flow direction, and its rotated spatial surface exhibits a non-cylindrical surface of revolution. This surface of revolution constitutes a constant relative blade height sectional surface with specific relative blade height attributes. As the meridional channel contracts, expands, or undergoes combined contraction and expansion along the flow direction, the geometry of the constant relative blade height sectional surface adaptively adjusts.

[0047] This slicing surface construction mechanism overcomes the relative blade height mismatch defect caused by the traditional fixed-radius cylindrical slicing surface when the meridional channel height changes, so that the relative blade height relationship of each slicing surface remains consistent at different axial positions.

[0048] For the geometric operation of generating a three-dimensional surface by rotating a two-dimensional generatrix around a fixed axis, those skilled in the art can complete it using a basic three-dimensional surface of revolution modeling matrix. The numerical expression of its rotational forming is a well-known technique in the field and will not be elaborated here. The equal relative blade height cleaving surface construction module outputs this set of cleaving surface data with consistent relative height characteristics, providing a surface basis for subsequent three-dimensional spatial intersection extraction and throat endpoint search.

[0049] Step S3 of this invention is executed by the local shortest distance and candidate interval determination module, and is specifically divided into the following sub-steps: S31, calculate the spatial intersection lines between each equal relative leaf height cutting surface and the current three-dimensional surface of the blade and the three-dimensional surface of the adjacent circumferential blades, and extract the corresponding candidate curves.

[0050] For the Given equal relative blade height sectional surfaces, solve for the geometric intersection lines between this spatial surface and the current blade's 3D surface, as well as the adjacent blade's 3D surfaces. On the obtained intersection lines of the current blade, based on pre-acquired blade surface feature region identifiers, extract curve segments located in the trailing edge region as candidate trailing edge curves, and parameterize them as follows: Similarly, on the intersection line of adjacent blades, the curve segment located in the suction side region is selected as the candidate curve for the suction side, and its parameterized representation is as follows: For specific algorithms regarding the intersection of spatial surfaces and the parameterization of curves, those skilled in the art can employ mature computer-aided design geometric intersection calculation methods. The surface intersection calculation and curve extraction are well-known techniques in this field and will not be elaborated upon here.

[0051] S32, search among the effective point pairs within the limited fluid channel to find the local shortest distance between the candidate curves on the trailing edge and the candidate curves on the suction side, and obtain the corresponding initial point.

[0052] The point pairs on the candidate curves on the trailing edge and suction sides are examined, and the three-dimensional connecting line segments formed between the two points are considered. Point pairs whose connecting line segments pass through the blade body or endwall boundary are excluded, retaining only valid point pairs whose connecting line segments are completely located within the fluid channel defined by the adjacent blades and endwalls. Within the search space formed by these valid point pairs, the combination of point pair parameters with the minimum Euclidean distance is sought. ; In the formula, The normalization parameters are used for the candidate curves on the trailing edge corresponding to the local shortest distance; Normalization parameters for candidate suction side curves corresponding to the local shortest distance; Normalization parameters Spatial coordinates of the candidate curve on the trailing edge side; Normalization parameters Spatial coordinates of the candidate curve on the suction side at the location; This represents the three-dimensional Euclidean distance between two points in space.

[0053] Based on the extreme value parameters obtained from the solution, determine the initial point on the trailing edge side, the initial point on the suction side, and the local shortest distance between them: ; ; ; In the formula, For the first The initial point on the trailing edge side corresponding to each cutting surface; For the first The initial point of the suction side corresponding to each cutting surface; This is the local shortest distance between the two initial points mentioned above.

[0054] As a specific implementation method, if the trailing edge of the current blade exhibits an arc-shaped profile at the corresponding cutting position, the geometric properties of a circle can be used to determine the initial point, thereby reducing the iterative search amount between the two candidate curves. Let the first... The center of the trailing edge at each cutting position is , radius is Calculate the closest point from the center of the trailing edge to the candidate curve on the suction side of the adjacent blade, and denote this as the initial point on the suction side. Along the spatial vector direction pointing from the center of the trailing edge to the initial point on the suction side, determine the distance from the center on the corresponding trailing edge arc. The point is used as the initial point on the trailing edge. .

[0055] The corresponding initial local throat width is calculated as follows: ; In the formula, For the first Spatial coordinates of the center of the trailing edge at each cutting point; This is the radius of the trailing edge arc corresponding to this position.

[0056] When performing the above calculations, it should be verified whether the initial point on the trailing edge side, determined by the direction of the center, is within the specified effective trailing edge arc range, and whether the connecting line segment between the initial point on the trailing edge side and the initial point on the suction side is within the blade cascade fluid channel. If the initial point on the trailing edge side exceeds the effective trailing edge arc range, the initial connecting line segment passes through the blade or endwall, or the trailing edge profile does not have an arc-shaped feature, then the aforementioned general shortest distance search method between curves should be used to determine the initial point.

[0057] S33. Using the initial point on the trailing edge and the initial point on the suction side obtained by the solution as the center, establish the candidate intervals for the endpoints of the throat on the trailing edge and the throat on the suction side within the pre-marked effective area.

[0058] The initial point corresponding to the local shortest distance is not directly used as the final endpoint representing the 3D throat surface. On the candidate curve on the tail edge side... Establish candidate parameter ranges for the trailing edge side centered on the center. On the candidate curve of the suction side, with Establish the candidate parameter range for the suction side centered on the center. .

[0059] The size of the candidate interval is set based on the local geometric features at the corresponding blade height, specifically referring to the trailing edge radius, local curvature, local blade chord length, and the endpoint distribution at adjacent blade height positions. The spatial extent of the candidate interval is strictly limited by the pre-defined effective region boundaries on the trailing edge side and suction side.

[0060] If, during the subsequent joint solution process, it is found that the optimized endpoint touches the boundary of the candidate interval, and the total throat area calculated after expanding the candidate interval decreases significantly, the local shortest distance and candidate interval determination module will trigger interval adaptive adjustment, gradually expand the corresponding candidate interval boundary and resubmit the solution request until the finally determined endpoint stably falls inside the candidate interval, or the candidate interval has expanded to the rigid boundary of the pre-identified effective area.

[0061] Step S4 of this invention is executed by the three-dimensional throat surface joint determination module, and is specifically divided into the following sub-steps: S41, the endpoint positions within the candidate intervals corresponding to the cut-off positions of each relative leaf height are used as joint parameters to be determined.

[0062] For the The throat endpoint was determined by dividing the leaf height into equal segments and using candidate regions on the trailing and suction sides, respectively. ; ; In the formula, For the first The trailing edge end points corresponding to the equal relative leaf height cutting positions; For the first The suction side endpoints corresponding to the equal relative blade height cutting positions; For having normalized parameters Candidate curves on the trailing edge side; For having normalized parameters Candidate curves for the suction side; , The candidate parameter range is for the trailing edge side. This represents the candidate parameter range for the suction side.

[0063] The initial point parameters corresponding to the local shortest distances are used as the initial values ​​for the joint solution, and the candidate parameter intervals on the trailing edge and the suction side are used as the value ranges of the corresponding optimization variables.

[0064] S42, establish the local throat segment and handle the end wall boundary.

[0065] Connection endpoints and The three-dimensional line segment is defined as the first... The length of a local throat segment is calculated as follows: ; In the formula, For the first The length of a local throat segment; It represents the three-dimensional Euclidean distance in space.

[0066] The relative blade height bisector is used to define the relative blade height positions of the two throat endpoints. The local throat width is calculated using the three-dimensional Euclidean distance between the two endpoints, not the arc length of the curve on the bisector. The local throat segment does not need to be completely located on the non-cylindrical bisector; the entire straight segment lies within the fluid channel defined by the adjacent blades and endwalls.

[0067] The throat boundaries at the hub and casing are connected along the actual endwall surface. The endwall boundary curve is determined within a preset candidate region on the hub or casing flow channel surface. The endwall boundary curve can be obtained using endwall parameter line interpolation, endwall discrete grid path search, or the shortest connection path on the endwall surface. The determined endwall boundary curve maintains continuous connection with adjacent internal local throat segments.

[0068] If the endwall boundary is curved, the endwall boundary curve is discretized into several short line segments in the order from the trailing edge end point to the suction end point. Adjacent internal local throat segments are then divided into an equal number of line segments according to their relative positions. Connecting the corresponding discrete points on both sides forms several spatial quadrilaterals, which are then divided into two spatial triangles using a uniform diagonal connection method. The area of ​​the blade height interval at the hub end and casing end is the sum of the areas of the sub-elemental triangles.

[0069] S43, construct a non-coplanar spatial area element and calculate its area.

[0070] The local throat segments corresponding to two adjacent cutting positions are respectively from the endpoints , and , Limited. Due to the presence of forward sweep, backward sweep, or combined sweep shapes in the blades, and the contraction or expansion of the meridional channel, the four three-dimensional endpoints mentioned above are in a non-coplanar state.

[0071] Divide the spatial quadrilateral formed by the four endpoints along the diagonal into two spatial triangles. Calculate the sum of the areas of these two triangles, and use this sum as the area of ​​the corresponding spatial area element: ; In the formula, For the first The area of ​​a spatial micro-element; It is the cross product of spatial vectors; For the first The tail edge end point of each cutting position; For the first The suction end point of each cutting position; For the first The tail edge end point of each cutting position; For the first The suction end point of each cutting position.

[0072] All spatial area elements are connected sequentially along the blade height to form a three-dimensional throat surface spanning the blade passage. The total area of ​​the turbine throat is calculated as follows: ; In the formula, This represents the total area of ​​the turbine throat; a total of [number] sections are provided. A relative leaf height position, forming One adjacent leaf height interval; For the first The sum of the areas of one or more triangular sub-elements within a leaf height interval. All spatial area elements in the same calculation use the same diagonal connection order to maintain consistent connectivity of the discrete throat surface. When the relative difference between the areas obtained by the two diagonal divisions exceeds a preset diagonal division difference threshold, a cutting surface is added within the corresponding leaf height interval to reduce the impact of quadrilateral distortion on the area result.

[0073] S44, under geometric constraints, performs a joint solution to determine the continuous three-dimensional turbine throat surface.

[0074] During the joint solution calculation, the following constraints are set: The local throat segment and the spatial area micro-element are all located within the fluid channel; The trailing edge end point and the suction edge end point form a continuous and smooth trajectory along the blade height direction; Adjacent area elements are connected by a consistent endpoint sequence without any orientation reversal. The curved surface of the larynx does not pass through the blade or end wall and does not cross or self-intersect; The throat surface boundaries at the hub and casing are located on the corresponding end wall surfaces.

[0075] The solution aims to minimize the total area of ​​all spatial area elements.

[0076] For optimization problems with spatial geometric constraints, those skilled in the art can employ numerical optimization algorithms such as sequential quadratic programming or interior point methods. The specific iterative solution process is well-known in the field and will not be elaborated upon here. During the iterative solution, candidate results where local throat segments cross blades or endwalls, area elements flip, or surfaces intersect are deemed infeasible and not included in the area comparison. Among the candidate results that satisfy the constraints, the result with the smallest total area is selected as the final three-dimensional throat surface. The final endpoints corresponding to each segmentation position form the trailing edge side endpoint trajectory and the suction side endpoint trajectory, respectively.

[0077] S45, perform adaptive partitioning and area convergence determination.

[0078] This step is a preferred treatment to improve the discretization stability in the blade height direction. Initial calculations are performed using a smaller number of equal-relative blade height segmentation surfaces, and the blade height intervals are adaptively refined based on local area changes. Intermediate segmentation positions are added between adjacent segmentation positions, and candidate curves for the trailing edge and suction sides are extracted for each new position. Spatial interpolation is performed on the throat endpoints of adjacent segmentation positions, and the interpolation points are projected onto the candidate curves corresponding to the new positions. These projection points serve as the initial values ​​for the new throat endpoints. The local discretization error after fine-grained segmentation is calculated. ; In the formula, This is a local discrete error; The area of ​​the spatial element before encryption; To increase the sum of the areas of the two area micro-elements after the intermediate cutting position; A preset positive number is used to avoid the denominator being zero.

[0079] When the local discretization error exceeds the first preset threshold, the newly added cutting surface is retained. After adding the cutting surfaces for the region requiring refinement, the joint solution is re-executed for all throat endpoints. The total area convergence of the global solution is calculated: ; In the formula, For the first The total area convergence of the joint solution; The number of times to solve for global encryption; For the first The total area of ​​the turbine throat obtained by the joint solution; For the first The total area of ​​the turbine throat obtained by the joint solution.

[0080] When the local discrete errors are all less than the first preset threshold and the total area convergence of the two calculations is less than the second preset threshold, the addition of the cutting surface is stopped, and the total area of ​​the turbine throat, the local throat width, the endpoint trajectory and the continuous three-dimensional throat surface calculated at the current time are output, so as to realize the geometric evaluation of the flow capacity of the turbine channel with complex sweeping shape and flow channel expansion and contraction characteristics.

[0081] Specific application examples: To further illustrate the technical solution of the present invention, the following detailed explanation of the throat area calculation process under the conditions of forward sweep and meridional channel expansion is provided in conjunction with a specific application embodiment.

[0082] A set of three-dimensional turbine blades, along with their hub and casing flow channels, is selected as the calculation object. The positive axial direction of the engine is defined as downstream. The three-dimensional profile of the blade is formed by stacking three sets of two-dimensional sections—root, mid-section, and tip—according to their centroids. The centroid of the mid-section is offset by 8 mm downstream relative to the centroids of the root and tip sections, causing the root and tip to be offset upstream relative to the mid-section, forming a forward-swept blade. The meridional flow channel expands from the inlet to the outlet.

[0083] The key geometric parameters of the blade and flow channel are shown in Table 1: Table 1

[0084] The circumferential pitch angle is calculated by obtaining the number of blades in the entire ring. The current blade is then rotated around the engine axis by one circumferential pitch angle to obtain adjacent circumferential blades, thus forming a three-dimensional turbine fluid channel. Eleven equal relative blade height segments are initially set between the hub and the casing, with relative blade heights ranging from 0, 0.1 to 1.0. Based on the geometric correspondence between the hub meridian profile and the casing meridian profile at stations in the same flow direction, intermediate meridian profiles are constructed at each segmentation position according to the set relative blade height ratios. Each intermediate meridian profile is rotated around the engine axis to generate equal relative blade height segments that adaptively change with the expansion of the meridional channel.

[0085] Within each equal relative blade height sectional plane, candidate curves for the trailing edge side of the current blade and candidate curves for the suction side of the adjacent blade are calculated and extracted. The effective point pairs within the fluid channel are traversed, and the local shortest distance between the two candidate curves is obtained, yielding the initial point on the trailing edge side, the initial point on the suction side, and the corresponding local shortest distance.

[0086] Using the initial point on the trailing edge as a reference, extend the candidate curve on the trailing edge by 0.5% of the chord length of the mid-section of the blade to establish the candidate interval of the throat endpoint on the trailing edge. Using the initial point on the suction side as a reference, candidate intervals for the suction side throat endpoints are established by extending the candidate curve on both sides by 1% of the blade midsection chord length. All of these candidate intervals are strictly limited to the pre-defined trailing edge and effective suction side regions.

[0087] The candidate curve parameters on the trailing edge and the candidate curve parameters on the suction side corresponding to each cutting position are used as the joint parameters to be determined, and the initial point parameters corresponding to each local shortest distance are used as the initial values ​​for joint solution.

[0088] Within the specified candidate interval, local throat segments are determined, and spatial area elements are constructed using the four three-dimensional endpoints of two adjacent local throat segments. Each spatial area element is divided into two spatial triangles according to the diagonal connection method with uniform full leaf height. The areas of the two triangles are calculated based on the cross product of the side vectors, and the sum of the two is taken as the total area of ​​the non-coplanar spatial area element.

[0089] In the joint solution process, a sequential quadratic programming algorithm is used to jointly adjust the positions of each throat endpoint. The candidate intervals on the tail edge side and the suction side are used as the range of values ​​for the optimization variables, and the continuity and smoothness of the endpoint trajectories and the consistency of the connection direction of the area micro-elements are used as constraints.

[0090] After each iteration, the positional relationships between the local throat segments, spatial area elements, and the blade and endwall are rigorously checked. Candidates where segments or area elements pass through the blade or endwall, or where the throat surface intersects or flips, are deemed infeasible. The search continues by increasing the penalty value, reducing the search step size, or reselecting initial search values. Only feasible results that satisfy all geometric constraints are compared, with the minimum total throat area as the objective.

[0091] When the relative change of the objective function in two consecutive iterations is less than 1×10 6 And the maximum normalization constraint violation is less than 1×10 6 When the time is reached, the optimization iteration is terminated. Each constraint residual is normalized according to the corresponding allowable value, and the maximum value among all normalized constraint residuals is taken as the maximum normalized constraint violation.

[0092] When 11 dividing planes were initially used, the calculated total area of ​​the three-dimensional throat was 173.295 mm². 2 During the solution process, both the trailing edge end point trajectory and the suction side end point trajectory extended continuously from the hub to the casing, without any throat segment intersections, area element flips, or surface self-intersections. Subsequently, adaptive segmentation was performed, increasing the number of equal relative blade height segmentation surfaces to 21, and a joint solution was re-performed, yielding a total throat area of ​​173.383 mm². 2 The relative change between the two calculation results is 0.051%, which is lower than the preset area convergence threshold of 0.1%, and the final continuous three-dimensional turbine throat surface and its area are output.

[0093] As can be seen from the above application examples, the use of a constant relative blade height segmentation method that varies with the meridional channel can establish a consistent relative blade height segmentation relationship within a three-dimensional turbine cascade passage with both forward sweep and meridional channel expansion characteristics. By jointly determining the throat endpoints corresponding to each segmentation position and using the area micro-element of the non-coplanar space at the four endpoints for area calculation, a three-dimensional throat surface continuously extending from the hub to the casing is effectively obtained, meeting the requirements for geometric evaluation of the flow capacity of complex turbine passages.

[0094] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for determining the turbine throat area considering sweeping profile and meridional channel contraction and expansion, characterized in that, Includes the following steps: Obtain geometric data to establish circumferentially adjacent blades, forming a three-dimensional turbine fluid channel; Extract the hub meridian profile and the casing meridian profile, establish the flow direction position correspondence and interpolate to obtain the intermediate meridian profile, and rotate the intermediate meridian profile around the engine axis to form a blade height bisector with equal relative height; Calculate the spatial intersection lines between each relative blade height cutting surface and the current blade profile and adjacent blade profiles. Solve for the local shortest distance between the intersection lines in the channel. Establish candidate intervals for the trailing edge throat endpoint and suction side throat endpoint with the corresponding initial point as the center. Using the endpoint positions within the candidate interval as joint parameters to be determined, a non-coplanar spatial area micro-element is constructed and its area is calculated. Under preset constraints, a joint solution is implemented with the goal of minimizing the total area, to determine the continuous three-dimensional turbine throat surface spanning the blade passage and to calculate the total throat area.

2. The method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion according to claim 1, characterized in that, The process of acquiring geometric data to establish circumferentially adjacent blades and form a three-dimensional turbine fluid channel specifically includes: Obtain the current three-dimensional profile of the blade, the hub flow channel surface, the casing flow channel surface, the number of blades in the entire ring, and the feature area identifiers on the blade surface; The circumferential pitch angle is calculated based on the number of blades in the ring, or circumferential adjacent blades are established based on a given grid pitch to form a three-dimensional turbine fluid channel.

3. The method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion according to claim 1, characterized in that, The process of establishing the correspondence between flow direction and location and interpolating to obtain the intermediate meridian line specifically includes: Establish the geometric positional correspondence between the hub meridional profile and the casing meridional profile in the direction of fluid flow, and map the positional correspondence in the direction of flow into normalized flow direction parameters; The intermediate meridian profile is obtained by spatial interpolation calculation at the same flow direction position according to the preset relative leaf height ratio.

4. The method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion according to claim 1, characterized in that, The calculation of the spatial intersection lines between each relative blade height cutting surface and the current blade profile and adjacent blade profiles specifically includes: Calculate the spatial intersection lines between each of the aforementioned equal relative leaf height cutting surfaces and the current three-dimensional surface of the blade, as well as the three-dimensional surface of the adjacent circumferential blades; Based on the characteristic region markings on the blade surface, candidate curves on the trailing edge side are extracted from the current blade intersection line, and candidate curves on the suction side are extracted from the intersection line of adjacent blades, thus obtaining the candidate curves on the trailing edge side and the candidate curves on the suction side.

5. The method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion according to claim 4, characterized in that, The process of solving for the local shortest distance between intersection lines within the channel, and establishing candidate intervals for the endpoints of the tail-side throat and the suction-side throat with the corresponding initial point as the center, specifically includes: Among the valid point pairs excluding those that pass through the blade or endwall solid boundary, the point pair with the smallest Euclidean distance is found as the initial point on the trailing edge side and the initial point on the suction side, thus obtaining the local shortest distance. Centered on the initial point on the trailing edge side and the initial point on the suction side, candidate intervals for the throat endpoints on the trailing edge side and the suction side are established within a pre-marked effective area based on local geometric features.

6. The method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion according to claim 5, characterized in that, The process of finding the pair of points with the minimum Euclidean distance as the initial points on the trailing edge and the suction side specifically includes: When the trailing edge of the current blade has an arc-shaped profile at the corresponding cutting position, calculate the nearest point from the center of the trailing edge to the candidate curve of the suction side, and use it as the initial point of the suction side. Along the spatial vector direction from the center of the trailing edge circle to the initial point of the suction side, a point on the corresponding trailing edge arc is determined at a distance from the center equal to the radius of the trailing edge arc, and is taken as the initial point of the trailing edge side.

7. The method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion according to claim 1, characterized in that, The construction of non-coplanar spatial area micro-elements and the calculation of their areas specifically include: A spatial quadrilateral is defined by the four three-dimensional endpoints of the local throat segments corresponding to two adjacent cutting positions; Divide the spatial quadrilateral into two spatial triangles along the diagonal, and calculate the area of ​​each spatial triangle based on the cross product of the side vectors. The area of ​​the non-coplanar spatial area element is obtained by summing the areas of the two spatial triangles.

8. The method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion according to claim 1, characterized in that, The joint solution method, which aims to minimize the total area under preset constraints, specifically includes: The geometric constraints include continuous and smooth endpoint trajectories, no flipping of the area micro-element and no penetration of the fluid channel, and the end being constrained by the flow channel surface. The candidate results that satisfy the geometric constraints are compared by area, and the result with the smallest total area of ​​each of the non-coplanar spatial area micro-elements is selected to determine the continuous three-dimensional turbine throat surface.

9. The method for determining the turbine throat area considering sweeping and meridional channel contraction and expansion according to claim 1, characterized in that, After determining the continuous three-dimensional turbine throat surface spanning the blade passage and calculating the total throat area, the process further includes: Intermediate splitting points are added between adjacent splitting points, and local discretization errors are calculated; When the local discretization error exceeds the first preset threshold, the newly added intermediate cutting surface is retained and the joint solution is re-executed for all throat endpoints; When all local discretization errors are less than the first preset threshold, and the total area convergence of the two calculations is less than the second preset threshold, stop adding the cutting surface and output the total area of ​​the turbine throat obtained at the current calculation.

10. A turbine throat area determination system considering sweeping profile and meridional channel contraction / expansion, applied to the turbine throat area determination method considering sweeping profile and meridional channel contraction / expansion as described in any one of claims 1-9, characterized in that, include: The data input and channel construction module is used to acquire geometric data to establish circumferentially adjacent blades and form a three-dimensional turbine fluid channel. The slicing surface construction module is used to extract the hub meridional profile and the casing meridional profile, establish the flow direction position correspondence and interpolate to obtain the intermediate meridional profile, and rotate the intermediate meridional profile around the engine axis to form a slicing surface with equal relative blade height; The candidate interval establishment module is used to calculate the spatial intersection lines between each relative blade height cutting surface and the current blade profile and adjacent blade profiles, solve the local shortest distance between the intersection lines in the channel, and establish the candidate intervals for the trailing edge throat endpoint and the suction side throat endpoint with the corresponding initial point as the center. The joint solution module is used to construct non-coplanar spatial area micro-elements with the endpoint positions in the candidate interval as joint parameters to be determined and to calculate the area. Under preset constraints, the joint solution is performed with the goal of minimizing the total area to determine the continuous three-dimensional turbine throat surface and calculate the total throat area.

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