Impeller design method based on cylindrical projection

Abstract

The invention relates to the technical field of fluid machinery design, in particular to an impeller design method based on cylindrical projection, which comprises the following steps: firstly, three-dimensionally and geometrically decomposing an impeller into a layered structure of a hub layer, a central layer and a wheel cover layer, and representing the contour of each layer by adopting a three-dimensional space curve; projecting and equally dividing the space curve of each layer by taking the cylindrical surface of the outlet of the impeller as a projection reference surface; secondly, initial geometric parameters are determined according to actual working condition requirements, and geometric parameters of all stepping points are dynamically solved through collaborative iterative calculation of an axial molded line function and a radial molded line function; and finally, fitting to generate an optimized three-dimensional contour of the impeller. According to the method, through parameterized layered modeling and explicit function correlation, accurate matching of blade geometry and flow field characteristics is achieved, the problem of flow field distortion in traditional design is effectively solved, spanwise profile control is remarkably improved, secondary flow and separation loss are reduced, and the design efficiency is guaranteed while the design cost is reduced. And the aerodynamic performance and the structural reliability of the impeller under severe working conditions are greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of fluid machinery design, and in particular to a blade wheel design method based on cylindrical projection. BACKGROUND

[0002] As the key equipment for energy conversion and fluid transportation, the performance of turbomachinery (including expanders and compressors) is mainly determined by the design of blade wheels. As the component directly interacting with working fluid, the geometry of blade wheels determines the energy conversion efficiency, operation stability and energy consumption level of the equipment. Especially in the industrial applications such as hydrogen liquefaction and natural gas processing, the complex flow field characteristics and significant energy loss under low-temperature working conditions make the fine design of blade wheels the key to improving the performance of the whole machine.

[0003] The traditional blade wheel design method has obvious limitations. Based on the simplifying assumptions such as constant relative velocity of fluid and uniform pressure distribution along the blade height, these methods are difficult to accurately describe the real three-dimensional flow field characteristics in modern turbomachinery, especially the real gas effect and strong shear flow phenomenon under low-temperature and high-speed working conditions. More importantly, the existing methods mainly focus on the optimization of meridian flow passage shape and inlet and outlet angles, but ignore the systematic control of blade spanwise (from the hub to the shroud) profile variation. The smooth transition of spanwise profile plays a decisive role in suppressing secondary flow and reducing flow separation, and the lack of this key control strategy seriously restricts the further improvement of blade wheel performance.

[0004] In recent years, although improved methods using commercial CFD software combined with parameterized modeling have appeared, these methods still have defects in essence. They excessively rely on the "black box" optimization process of the software, making it difficult for designers to establish a direct correlation between blade geometric parameters and flow field physical characteristics (such as vortex structure, separation position, and energy loss distribution). The lack of this physical orientation leads to a lack of pertinence in parameter adjustment, and the relevance and controllability of the optimization process are also difficult to guarantee, ultimately limiting the improvement space of design effect. SUMMARY

[0005] The present application provides a blade wheel design method based on cylindrical projection, which solves the defects of the traditional blade wheel design method in the prior art based on simplifying assumptions and ignoring the variation of blade spanwise profile, realizes direct control of the correlation between blade geometry and flow field characteristics through parameterized means, and systematically optimizes the spanwise profile to suppress secondary flow.

[0006] The present application provides a blade wheel design method based on cylindrical projection, comprising the following steps: The three-dimensional solid geometry of the blade wheel is abstracted into a hub layer, a center layer and a shroud layer, and the outline of each layer is represented by a three-dimensional space curve.

[0007] A cylindrical surface corresponding to a circle where the impeller outlet radius is located is taken as a projection reference surface, and the three-dimensional space curves representing the hub layer, the center layer and the shroud layer are projected to the projection reference surface.

[0008] The projection of the three-dimensional space curves representing the hub layer, the center layer and the shroud layer on the projection reference surface is divided into n-1 segments by n iteration step points.

[0009] Based on the design requirements of the actual impeller working condition, performance index and size constraint, the axial length, the outlet radius, the circumferential projection length, the installation angle, the circumferential angle and the arc length of the hub layer, the center layer and the shroud layer of the impeller at the impeller outlet are determined, respectively, and are recorded as initial axial coordinates , initial radial coordinates , initial development coordinates , initial installation angles , initial circumferential angles and initial arc lengths .

[0010] Based on the axial profile function representing the relationship between the axial coordinates and the development coordinates and the radial profile function representing the relationship between the radial coordinates and the axial coordinates, the initial axial coordinates , the initial radial coordinates , the initial development coordinates , the initial installation angles , the initial circumferential angles and the initial arc lengths are iteratively calculated to obtain the axial coordinates, the radial coordinates, the installation angles, the circumferential angles and the arc lengths of all iteration step points.

[0011] Based on the axial coordinates, the radial coordinates, the installation angles, the circumferential angles and the arc lengths of all iteration step points, the hub layer, the center layer and the shroud layer of the impeller are fitted and generated, and the three-dimensional profile of the impeller is constructed by the hub layer, the center layer and the shroud layer.

[0012] According to the impeller design method based on cylindrical projection provided by the application, the axial profile function is characterized by the following formula: In the formula, z represents the axial coordinate, represents the axial length of the impeller, represents the twist of the blade outlet, represents the development coordinate, represents the sharpness of the turning section of the radial-to-axial transition, represents the total length of the circumferential development.

[0013] According to the impeller design method based on cylindrical projection provided by the present invention, the radial profile function is obtained by fitting existing impeller meridional data or by constructing a new meridional equation.

[0014] According to the impeller design method based on cylindrical projection provided by the present invention, after the step of constructing the three-dimensional profile of the impeller from the hub layer, the center layer, and the wheel cover layer, the method further includes: Based on the hub layer, the center layer and the wheel cover layer, a three-dimensional profile of the impeller is constructed. Computational fluid dynamics performance analysis and structural strength verification are performed. If the analysis results do not meet the design requirements, the torsion parameters of the blade outlet and the sharpness parameters of the turning section from radial to axial are adjusted in reverse, and iterative calculations are performed again until an impeller that meets the design requirements is obtained.

[0015] According to the impeller design method based on cylindrical projection provided by the present invention, the initial unfolded coordinates... The value is zero for the initial unfolded coordinates. The steps for performing iterative calculations include: Based on the initial radial coordinates and the maximum sweep angle of the blades from inlet to outlet From the formula Calculate the total length of the circumferential unfolding .

[0016] Based on the total length of the circumferential unfolding Divide into n-1 equal segments, according to the formula Iteration step size for calculating the expanded coordinates .

[0017] Based on formula For the initial radial coordinates By continuously performing iterative calculations, the expanded coordinates of all iterative step points are obtained.

[0018] According to the impeller design method based on cylindrical projection provided by the present invention, the initial axial coordinates This includes the axial lengths of the hub layer, center layer, and wheel cover layer at the impeller outlet.

[0019] The axial length of the hub layer at the impeller outlet The axial length of the central layer at the impeller outlet The axial length of the wheel cover layer at the impeller outlet ,in, Indicates the axial length of the impeller. This indicates the inlet height of the impeller blades.

[0020] For the initial axial coordinates The steps for performing iterative calculations include: calculating the axial coordinates corresponding to the unfolded coordinates of all iterative step points based on the axial profile function.

[0021] According to the impeller design method based on cylindrical projection provided by the present invention, the initial radial coordinates This includes the impeller outlet radii of the hub layer, center layer, and wheel cover layer at the impeller outlet; and the initial radial coordinates. The steps for performing iterative calculations include: calculating the radial coordinates corresponding to the axial coordinates of all iterative step points based on the radial profile function.

[0022] According to the impeller design method based on cylindrical projection provided by the present invention, the initial circumferential angle The value is zero for the initial circumferential angle. The steps for performing iterative calculations include: Iteration step size based on unfolded coordinates and initial radial coordinates Through formula Calculate the increment value of the circumferential angle .

[0023] Based on the initial circumferential angle and the increment value of the circumferential angle Through formula Calculate the circumferential angle at all iteration step points.

[0024] According to the impeller design method based on cylindrical projection provided by the present invention, the initial installation angle... The value is zero for the initial installation angle. The steps for performing iterative calculations include: Calculate the first derivative of the radial coordinates corresponding to the axial coordinates of the current iteration step point based on the radial profile function. and second derivative .

[0025] Based on the first derivative and the second derivative Through formula Calculate the radius of curvature at the current iteration step point. .

[0026] Calculate the axial coordinate increment based on the axial coordinate of the current iteration step point and the axial coordinate of the next iteration step point. .

[0027] Installation angle based on the current iteration step point and axial coordinate increment value Through formula Calculate the installation angle increment value of the current iteration step point. .

[0028] Based on initial installation angle Incremental value of installation angle Through formula Calculate the installation angle for all iteration step points.

[0029] According to the impeller design method based on cylindrical projection provided by the present invention, the initial arc length The value is zero for the initial arc length. The steps for performing iterative calculations include: Installation angle based on the current iteration step point and axial coordinate increment value Through formula Calculate the arc length increment value of the current iteration step point. .

[0030] Based on the initial arc length Arc length increment value Through formula Calculate the arc length of all iteration step points.

[0031] The impeller design method based on cylindrical projection provided by this invention achieves precise design of the impeller's three-dimensional geometry through layered modeling and parametric control technology. First, the three-dimensional geometry of the impeller is abstracted into a layered structure consisting of a hub layer, a center layer, and a shroud layer, with each layer's contour represented by a three-dimensional spatial curve. Then, using the cylindrical surface corresponding to the impeller outlet radius as the projection reference plane, the spatial curves of each layer are projected onto this projection reference plane, and the projected curves are divided into n-1 segments through n iterative step points. Next, the initial geometric parameters of each layer at the impeller outlet (including axial / radial coordinates, installation angle, etc.) are determined according to the actual design requirements. Then, through the coordinated iteration of the axial profile function (controlling blade twist and the sharpness of the turning section) and the radial profile function (describing the meridional shape), the geometric parameters of all step points are dynamically calculated. Finally, the three-dimensional contour of the impeller is fitted and generated. The impeller design method based on cylindrical projection of the present invention achieves precise matching between blade geometry and flow field characteristics through parametric hierarchical modeling and explicit function association. It solves the problem of flow field distortion caused by simplification assumptions in traditional design, as well as secondary flow and separation losses caused by insufficient spanwise profile control. It significantly improves the aerodynamic efficiency and structural reliability of the impeller under harsh conditions such as low temperature and high speed, while shortening the design cycle. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0033] Figure 1 This is a flowchart illustrating the impeller design method based on cylindrical projection provided by the present invention.

[0034] Figure 2 This is a schematic diagram provided by the present invention, which abstracts the three-dimensional solid geometry of the impeller into a structure consisting of a hub layer, a center layer, and a wheel cover layer.

[0035] Figure 3 This is a comparative schematic diagram of the hub layer, center layer, and wheel cover layer provided by the present invention with the projection reference plane.

[0036] Figure 4 This is a schematic diagram showing the projection of the three-dimensional spatial curve of the central layer provided by the present invention onto the impeller meridional plane, which is divided into n-1 segments.

[0037] Figure 5 This is a schematic diagram of the iterative calculation process of the impeller design method based on cylindrical projection provided by the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0039] The following is combined with Figures 1 to 5 The specific implementation process of the impeller design method based on cylindrical projection of the present invention is described.

[0040] One embodiment of the present invention provides an impeller design method based on cylindrical projection, see [link to relevant documentation]. Figure 1 As shown, the impeller design method based on cylindrical projection includes the following steps S1 to S6.

[0041] S1. The three-dimensional solid geometry of the impeller is abstracted into a hub layer, a center layer, and a wheel cover layer, with the outline of each layer represented by a three-dimensional spatial curve.

[0042] S2. Using the cylindrical surface corresponding to the circle where the impeller outlet radius is located as the projection reference plane, the three-dimensional spatial curves representing the hub layer, center layer and wheel cover layer are simulated and projected onto the projection reference plane.

[0043] S3. The projection of the three-dimensional spatial curves representing the hub layer, center layer and wheel cover layer onto the projection reference plane is divided into n-1 segments by n iterative step points.

[0044] S4. Based on the actual impeller's operating conditions, performance indicators, and dimensional constraints, determine the axial length, impeller outlet radius, circumferential projection length, installation angle, circumferential angle, and arc length of the impeller's hub layer, center layer, and shroud layer at the impeller outlet, respectively, and record them as the initial axial coordinates. Initial radial coordinates Initial expansion coordinates Initial installation angle Initial circumferential angle and initial arc length .

[0045] S5. Based on the axial profile function representing the relationship between axial coordinates and unfolded coordinates, and the radial profile function representing the relationship between radial coordinates and axial coordinates, the initial axial coordinates are... Initial radial coordinates Initial expansion coordinates Initial installation angle Initial circumferential angle and initial arc length Perform iterative calculations to obtain the axial coordinates, radial coordinates, mounting angle, circumferential angle, and arc length of all iterative step points.

[0046] S6. Based on the axial coordinates, radial coordinates, mounting angle, circumferential angle and arc length of all iterative step points, the hub layer, center layer and wheel cover layer of the impeller are fitted and generated, and the three-dimensional contour of the impeller is constructed from the hub layer, center layer and wheel cover layer.

[0047] This embodiment of the impeller design method based on cylindrical projection achieves precise design of the impeller's three-dimensional geometry through layered modeling and parametric control techniques. First, the impeller's three-dimensional geometry is abstracted into a layered structure consisting of a hub layer, a center layer, and a shroud layer, as follows: Figure 2 As shown, each contour layer is represented by a three-dimensional spatial curve; then see... Figure 3As shown, the cylindrical surface corresponding to the impeller outlet radius is used as the projection reference plane. The spatial curves of each layer are projected onto this projection reference plane, and the projected curves are divided into n-1 segments by n iterative step points. Then, the initial geometric parameters (including axial / radial coordinates, installation angle, etc.) of each layer at the impeller outlet are determined according to the actual design requirements. Then, the geometric parameters of all step points are dynamically calculated through the coordinated iteration of the axial profile function (controlling the blade twist and the sharpness of the turning section) and the radial profile function (describing the meridional shape). Finally, the three-dimensional profile of the impeller is fitted and generated. The impeller design method based on cylindrical projection in this embodiment achieves accurate matching between blade geometry and flow field characteristics through parametric layered modeling and explicit function association. It solves the flow field distortion problem caused by the simplification assumptions in traditional design, as well as the secondary flow and separation loss caused by insufficient spanwise profile control. It significantly improves the aerodynamic efficiency and structural reliability of the impeller under harsh conditions such as low temperature and high speed, while shortening the design cycle.

[0048] In some embodiments of the impeller design method based on cylindrical projection of the present invention, the axial profile function is characterized by the following formula: In the formula, z represents the axial coordinate. Indicates the axial length of the impeller. Indicates the direction of twist at the blade exit. Indicates the expanded coordinates, Indicates the sharpness of the turning segment where the radial direction transitions to the axial direction. This represents the total circumferential unfolded length. The radial profile function is obtained by fitting existing impeller meridional data or by constructing a new meridional equation.

[0049] It is understood that the axial profile function proposed in this embodiment precisely controls the geometric characteristics of the blade through mathematical formulas, wherein the axial coordinates From the axial length of the impeller Blade outlet twist Expand coordinates Sharpness of the turning section and total length of circumferential unfolding These key parameters collectively determine the axial profile of the blade, enabling parametric control. The radial profile function, on the other hand, is data-driven, supporting both fitting based on existing impeller meridional data and obtaining it by constructing new meridional equations, thus providing flexibility for radial profile design. This design method, combining axial and radial profile functions, achieves precise control of blade geometry through parametric means, providing a new technical approach for optimizing impeller performance.

[0050] In some embodiments of the impeller design method based on cylindrical projection of the present invention, after the step of constructing the three-dimensional profile of the impeller by the hub layer, the center layer and the wheel cover layer, the impeller design method based on cylindrical projection further includes the following step S7: performing computational fluid dynamics performance analysis and structural strength verification based on the three-dimensional profile of the impeller constructed by the hub layer, the center layer and the wheel cover layer; if the analysis results do not meet the design requirements, adjusting the torsional parameters of the blade outlet and the sharpness parameters of the turning section from radial to axial, and re-iteratio calculation until an impeller that meets the design requirements is obtained.

[0051] Understandably, in step S7 of this embodiment, after completing the three-dimensional profile construction of the impeller, a crucial step of performance verification and optimization iteration is added. The design results are verified through computational fluid dynamics (CFD) analysis and structural strength checks. If the requirements are not met, intelligent feedback is provided to adjust the blade outlet twist parameters and the sharpness parameters of the turning section, restarting the iterative calculation process. This closed-loop design method of "design-verification-feedback-optimization" achieves continuous optimization of impeller performance through dynamic adjustment of key parameters, ensuring both fluid dynamic performance and structural strength requirements, significantly improving design efficiency and product reliability.

[0052] This embodiment uses parameters (Control blade exit region curvature / slope) and parameters A dual-parameter coordinated control mechanism (controlling the abruptness of blade profile transition) enables targeted optimization of the impeller, with clearly defined physical meanings for the parameters, directly correlated to flow field loss mechanisms. It is important to understand the torsional parameters at the blade exit. The sharpness parameter of the turning segment transitioning from radial to axial direction These are two parameters that determine the shape of the blade. The main control is the slope (or curvature) of the outlet region. This slope directly and significantly affects the outlet flow field structure and energy conversion efficiency. It is the dominant parameter because the total axial length of the impeller is fixed, and a larger outlet slope (higher) is more important. This means that a larger portion of the blade's axial length is used to torsion the flow field near the exit, fundamentally altering the blade's torsional capability and flow guidance effect in this critical region. Parameters The main control is the sharpness of the transition from the radially dominant flow region to the axially dominant flow region, suppressing flow separation and secondary flow under different operating conditions. Higher values ​​result in a sharper transition (abrupt curvature change), while lower values ​​result in a smoother transition (gradual curvature change). For expansion impellers, increasing... Optimize the outlet flow field diffusion characteristics to reduce vortex losses; for the compressor impeller, reduce... Values ​​enhance airflow pressurization efficiency, while all are adjusted The value controls the smoothness of the transition zone between the radial and axial flow channels. Only two parameters need to be adjusted to achieve precise control of the three-dimensional shape of the expansion / compression impeller flow channel while keeping the key geometric features of the inlet and outlet (axial length, inlet and outlet diameter, blade height, etc.) unchanged.

[0053] The following describes the parameter iterative calculation process of the impeller design method based on cylindrical projection of this application with reference to specific embodiments.

[0054] In some embodiments of the impeller design method based on cylindrical projection of the present invention, the initial unfolded coordinates... The value is zero for the initial expanded coordinates. The steps for iterative calculation include: based on the initial radial coordinates and the maximum sweep angle of the blades from inlet to outlet From the formula Calculate the total length of the circumferential unfolding Based on the total length of the circumferential unfolding. Divide into n-1 equal segments, according to the formula Iteration step size for calculating the expanded coordinates Based on the formula For the initial radial coordinates By continuously performing iterative calculations, the expanded coordinates of all iterative step points are obtained.

[0055] The expanded coordinate iterative calculation method in this embodiment adopts a step-by-step parameterization strategy: first, using the initial radial coordinates... and the maximum sweep angle of the blade Using geometric relationships as input, the total circumferential unfolded length is accurately calculated. ( , Corresponding to the maximum sweep angle of the blade, such as Figure 1 and Figure 2 As shown, the sweep angles of the hub layer, center layer, and wheel arch layer are all approximately 35°; subsequently, the total circumferential length is unfolded. The system is divided into n-1 segments, and the iteration step size for discretization is determined. Finally, the unfolded coordinates are calculated step by step using a recursive formula, and the system generates the unfolded coordinate sequence for each iteration step point. This geometrically constrained discretization iterative algorithm in this embodiment not only ensures the mathematical rigor of the blade profile unfolding process, but also provides a precise coordinate reference for subsequent 3D contour construction through parameter segmentation control, realizing the quantitative conversion from the overall sweep angle to local coordinate points.

[0056] In some embodiments of the impeller design method based on cylindrical projection of the present invention, the initial axial coordinates This includes the axial lengths of the hub layer, center layer, and wheel cover layer at the impeller outlet, where the axial length of the hub layer at the impeller outlet is... The axial length of the central layer at the impeller outlet The axial length of the wheel cover at the impeller outlet ,in, Indicates the axial length of the impeller. This indicates the impeller blade inlet height. (Regarding the initial axial coordinates...) The steps for iterative calculation include: calculating the axial coordinates corresponding to the unfolded coordinates of all iteration step points based on the axial profile function.

[0057] This embodiment employs a layered parameterization method to precisely control the impeller's axial coordinates. First, the characteristic axial lengths of the hub, center, and shroud layers at the impeller outlet are defined, with each layer's axial length determined by the total impeller axial length and blade inlet height, establishing a complete axial geometric reference system. Then, based on the axial profile function, the unfolded coordinate sequence is mapped to the corresponding axial coordinate distribution, achieving a mathematical transformation from two-dimensional unfolded parameters to three-dimensional axial position. This layered-mapping axial coordinate generation mechanism maintains the independence of each layer's geometric features while ensuring the continuity and consistency of the axial profile through a unified profile function, providing a precise axial coordinate foundation for the impeller's three-dimensional modeling.

[0058] It should be understood that the impeller design method based on cylindrical projection of the present invention abstracts the three-dimensional solid geometry into a three-layer outline consisting of a hub layer, a center layer, and a wheel cover layer. This is a typical abstract layered structure. In practice, it is not limited to a three-layer structure. The three-dimensional solid geometry can be abstracted into more layers. The more layers there are, the more precise the impeller entity will be in the final fit.

[0059] In some embodiments of the impeller design method based on cylindrical projection of the present invention, the initial radial coordinates This includes the impeller outlet radii of the hub layer, center layer, and wheel cover layer at the impeller outlet; for the initial radial coordinates The steps for iterative calculation include: calculating the radial coordinates corresponding to the axial coordinates of all iterative step points based on the radial profile function.

[0060] It is understood that this embodiment employs a hierarchical radial coordinate iterative algorithm. Through hierarchical initialization, function-driven iteration, and geometric correlation control, it achieves precise construction of the impeller's radial profile. Hierarchical initialization includes setting the characteristic radius values ​​at the impeller outlet for the hub layer, center layer, and shroud layer respectively, establishing a radial design benchmark. Function-driven iteration includes dynamically calculating the corresponding radial coordinate distribution based on the radial profile function, using the axial coordinate sequence as input parameters. Geometric correlation control includes ensuring the geometric compatibility between radial and axial coordinates through function mapping, achieving precise control of the meridional channel profile. This embodiment uses a hierarchical parameterization method to maintain the independence of the radial features of each layer, and establishes a mathematical correlation between axial and radial coordinates through the radial profile function, achieving a systematic transformation from axial distribution to radial profile, providing a precise radial coordinate benchmark for the impeller's three-dimensional modeling. This radial coordinate generation mechanism based on function mapping ensures design accuracy while improving the efficiency of impeller geometric modeling.

[0061] It's important to understand that, ignoring the thickness of a single blade on the impeller, the three-dimensional geometry is represented by three spatial curves: the hub layer, the center layer, and the wheel cover layer. Each spatial curve can be considered as being composed of countless scattered points, and each point is assumed to have known axial coordinates. radial coordinates Circumferential angle Theoretically, this 3D blade can be designed, but due to limitations of commercial software, generating a solid 3D impeller in the software requires point information from two files. The first is... A scatter dataset of iterative step points, containing coordinates along different axes. The corresponding radial coordinates below The other one is Scattered dataset of iterative step points Representing streamline coordinates, the length traversed along the streamline direction, it can represent the arc length at any iteration step point. It refers to the corresponding streamline coordinates. An angle, which can represent a circumferential angle. Compared to simple... , , Compared to the previous one, there is one more. The coordinates need to be obtained.

[0062] In some embodiments of the impeller design method based on cylindrical projection of the present invention, the initial circumferential angle The value is zero for the initial circumferential angle. The steps for iterative calculation include: the iteration step size based on the expanded coordinates. and initial radial coordinates Through formula Calculate the increment value of the circumferential angle Based on the initial circumferential angle and the increment value of the circumferential angle Through formula Calculate the circumferential angle at all iteration step points.

[0063] It is understood that the circumferential angle iterative calculation method proposed in this embodiment adopts a progressive geometric unfolding strategy, specifically including initial condition determination, incremental calculation mechanism, and cumulative iteration process. Initial condition determination involves initializing the circumferential angle parameters to zero values ​​to establish an angle calculation benchmark. The incremental calculation mechanism includes dynamically calculating the circumferential angle increment based on the unfolded coordinate iteration step size and the current radial coordinate using geometric relationship formulas, achieving a precise correlation between angle changes and radial / unfolding parameters. The cumulative iteration process includes using recursive formulas to gradually accumulate the circumferential angle, ensuring the continuity of angles at each iteration step point and forming a complete circumferential angle distribution sequence. This circumferential angle iterative calculation method in this embodiment achieves precise control of angle increments through parameterized formulas, uses an accumulation algorithm to ensure the continuity of angle evolution, and establishes a direct mathematical relationship between unfolded coordinates and circumferential angles, providing an angle benchmark for the three-dimensional twisted shape of the blade. This circumferential angle calculation method based on the principle of geometric unfolding effectively solves the problem of inaccurate angle control in traditional designs, providing reliable angle parameters for the spatial positioning of impeller blades.

[0064] In some embodiments of the impeller design method based on cylindrical projection of the present invention, the initial installation angle... The value is zero for the initial installation angle. The steps for iterative calculation include: calculating the first derivative of the radial coordinates corresponding to the axial coordinates of the current iteration step point based on the radial profile function. and second derivative Based on the first derivative and second derivative Through formula Calculate the radius of curvature at the current iteration step point. The axial coordinate increment is calculated based on the axial coordinates of the current iteration step point and the axial coordinates of the next iteration step point. Installation angle based on the current iteration step point and axial coordinate increment value Through formula Calculate the installation angle increment value of the current iteration step point. Based on the initial installation angle Incremental value of installation angle Through formula Calculate the installation angle for all iteration step points.

[0065] It is understood that the installation angle iterative calculation method proposed in this embodiment adopts a strategy combining differential geometry and recursive algorithms. The specific process includes a high-order geometric analysis stage and a dynamic recursive calculation stage. In the high-order geometric analysis stage, the first derivative of the current position is calculated analytically through the radial profile function. and second derivative Based on the radius of curvature formula For accurate solutions to local curvature features, see [link to relevant documentation]. Figure 4 As shown, express The radius of curvature at any iterative step point on the meridional plane; during the dynamic recursive calculation phase, the incremental value is calculated through axial coordinate difference. Establish an incremental installation angle algorithm: ,use The recursive formula enables the step-by-step generation of the installation angle sequence. This embodiment's iterative installation angle calculation method captures the curvature characteristics of the meridional channel through the second derivative, automatically adjusts the angle change rate based on the axial step size, and ensures the continuity of angle evolution through a recursive algorithm. This installation angle calculation method, which integrates differential geometry theory and recursive algorithms, overcomes the limitations of simplified blade installation angle processing in traditional designs. It achieves curvature-sensitive installation angle distribution, a torsional law that meets aerodynamic requirements, precise matching with radial / axial coordinates, and smooth transition characteristics that meet strength requirements, providing key geometric control parameters for the three-dimensional aerodynamic optimization of impeller blades.

[0066] In some embodiments of the impeller design method based on cylindrical projection of the present invention, the initial arc length The value is zero for the initial arc length. The steps for iterative calculation include: the installation angle based on the current iteration step point. and axial coordinate increment value Through formula Calculate the arc length increment value of the current iteration step point. Based on the initial arc length Arc length increment value Through formula Calculate the arc length of all iteration step points.

[0067] It is understood that the arc length iterative calculation method in this embodiment combines differential geometry and kinematic analysis, including an arc length differential calculation stage and a cumulative iterative calculation stage. The arc length differential calculation stage includes: based on the installation angle of the current iteration step point... Establish geometric relationships using the arc length differential formula Calculate the axial coordinate increment value The corresponding actual streamline length (arc length increment value) This considers the projection correction of the installation angle onto the actual flow channel length. The cumulative iterative calculation phase includes: using... The recursive algorithm achieves a precise conversion from axial coordinate increments to the actual arc length, constructing a complete streamline arc length distribution sequence. The arc length iterative calculation method in this embodiment eliminates axial projection errors through installation angle cosine correction, accurately reflecting the true trajectory length of fluid particles; it achieves efficient iteration through a simple recursive formula, co-optimizing with the installation angle calculation process; the arc length increment strictly corresponds to the flow channel geometry, providing accurate streamline parameters for subsequent CFD analysis; the precise arc length data provides a basis for blade strength calculation, supports refined aerodynamic performance evaluation, and facilitates flow channel loss analysis. This arc length calculation method based on installation angle correction overcomes the deficiency of ignoring the actual flow channel length in traditional designs, providing a key arc length parameter benchmark for refined impeller design.

[0068] Based on the description of the methods and processes in the above embodiments, a specific embodiment of the present invention provides an impeller design method based on cylindrical projection, including a design preparation stage, a parameterized iterative calculation stage, a three-dimensional contour generation stage, and a verification and optimization stage.

[0069] Specifically, the design preparation phase includes geometric abstraction and the definition of projection reference planes. Geometric abstraction includes: decomposing the three-dimensional structure of the impeller into a hub layer, a center layer, and a wheel cover layer, with the contour of each layer represented by a three-dimensional spatial curve; and determining the axial length. Blade inlet height Export radius and maximum sweep angle Key impeller parameters. The projection reference plane is defined by using the cylindrical surface containing the impeller outlet radius as the projection reference plane, and projecting the three-layer spatial curves onto this cylindrical surface.

[0070] See the parameterized iterative calculation stage. Figure 5 As shown, the process includes initial parameter setting, coordinate expansion iteration, axial coordinate calculation, radial coordinate calculation, circumferential angle iteration, installation angle iteration, and arc length calculation. For specific details, please refer to the above iterative calculation process embodiment.

[0071] The 3D contour generation stage includes a layered fitting step and a surface construction step. The layered fitting step iteratively generates the coordinates (radial coordinates) of each iteration step point. axial coordinates Circumferential angle ) and installation angle and arc length Three-dimensional spatial curves were fitted to the hub layer, center layer, and wheel cover layer, respectively. The surface construction step was to generate the blade surface by lofting the three-layer contour lines, and then combine the hub and wheel cover to construct a complete three-dimensional impeller model.

[0072] The verification and optimization phase employs CFD performance analysis to simulate the flow field of the 3D model, evaluating aerodynamic efficiency, pressure distribution, and other indicators. Structural strength is also checked to identify stress concentration areas and verify blade strength. If design requirements are not met, the blade exit twist is adjusted in the opposite direction. and the sharpness of the turning section Then, recalculate iteratively until the design requirements are met.

[0073] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A cylindrical projection based impeller design method, characterized by, The method comprises the steps that: The three-dimensional entity geometry of the impeller is abstracted into a hub layer, a center layer and a shroud layer, and the outline of each layer is represented by a three-dimensional space curve; A cylindrical surface corresponding to a circle where the outlet radius of the impeller is located is taken as a projection reference surface, and the three-dimensional space curves representing the hub layer, the center layer and the shroud layer are projected onto the projection reference surface; The projection of the three-dimensional space curves representing the hub layer, the center layer and the shroud layer on the projection reference surface is divided into n-1 segments by n iteration step points; Based on the design requirements of actual impeller working conditions, performance indicators and size constraints, the axial length, the impeller outlet radius, the circumferential projection length, the installation angle, the circumferential angle and the arc length of the hub layer, the center layer and the shroud layer of the impeller corresponding to the impeller outlet are determined, respectively, which are recorded as initial axial coordinates , initial radial coordinates , initial development coordinates , initial installation angles , initial circumferential angles and initial arc lengths ; Based on the axial line function representing the relationship between the axial coordinate and the developed coordinate and the radial line function representing the relationship between the radial coordinate and the axial coordinate, the initial axial coordinate , the initial radial coordinate , the initial developed coordinate , the initial installation angle , the initial circumferential angle and the initial arc length are iteratively calculated to obtain the axial coordinate, the radial coordinate, the installation angle, the circumferential angle and the arc length of all the iteration step points. Based on the axial coordinates, radial coordinates, installation angles, circumferential angles and arc lengths of all iteration step points, the hub layer, the center layer and the shroud layer of the impeller are fitted and generated, and the three-dimensional outline of the impeller is constructed by the hub layer, the center layer and the shroud layer.

2. The camber projection based impeller design method of claim 1, wherein, The axial profile function is represented by the following formula: wherein z represents an axial coordinate, represents an axial length of the impeller, represents a twist at the outlet of the blade, represents a development coordinate, represents a sharpness of a turning section that transitions from the radial direction to the axial direction, represents a total length of the circumferential development.

3. The camber projection based impeller design method of claim 1, wherein, The radial profile function is obtained based on existing impeller meridian surface data fitting or by constructing a new meridian surface equation.

4. The camber projection based impeller design method of claim 1, wherein, After the step of constructing the three-dimensional outline of the impeller by the hub layer, the center layer and the shroud layer, the method further comprises the steps that: Based on the three-dimensional outline of the impeller constructed by the hub layer, the center layer and the shroud layer, computational fluid dynamics performance analysis and structural strength checking are performed, when the analysis result does not meet the design requirement, the twist parameter of the blade outlet and the sharpness parameter of the turning section of the radial-to-axial transition are adjusted reversely, and iterative calculation is performed again until the impeller meeting the design requirement is obtained.

5. The cylindrical projection based impeller design method of any one of claims 1 to 4, wherein, the initial unfolded coordinate zero, the step of iteratively calculating the initial unfolded coordinate zero, the step of iteratively calculating the initial unfolded coordinate Based on initial radial coordinate and maximum sweep angle of the blade from the inlet to the outlet The circumferential developed total length L is calculated by the formula L = 2 * pi * R ; based on the total length of the circumferential development is divided into n-1 equal parts by the formula the iteration step size for calculating the development coordinates ; Based on the formula For the initial radial coordinate The iteration calculation is continuously carried out to obtain the unfolded coordinates of all iteration step points.

6. The camber projection based impeller design method of claim 5, wherein, the initial axial coordinate The hub layer, the center layer and the shroud layer respectively correspond to the axial length at the impeller outlet. the hub layer corresponds to an axial length of the impeller at the impeller outlet the center layer corresponds to an axial length of the impeller at the impeller outlet the shroud layer corresponds to an axial length of the impeller at the impeller outlet wherein, L represents an axial length of the impeller, H represents an impeller blade inlet height; to the initial axial coordinate The step of performing an iterative calculation includes calculating the axial coordinate corresponding to the developed coordinate of all iteration step points based on the axial curve function.

7. The cylindrical projection based impeller design method of claim 6, wherein, the initial radial coordinate The hub layer, the center layer and the shroud layer respectively correspond to an impeller outlet radius corresponding to the impeller outlet; the initial radial coordinate The step of iterative calculation comprises: calculating the radial coordinate corresponding to the axial coordinate of all iteration step points based on the radial profile function.

8. The cylindrical projection based impeller design method of claim 5, wherein, the initial circumferential angle zero, the step of iteratively calculating the initial circumferential angle includes Iteration step size based on unfolded coordinates and initial radial coordinates Through formula Calculate the increment value of the circumferential angle ; based on the initial circumferential angle and the incremental value of the circumferential angle , the circumferential angle of all iteration steps is calculated by the formula ​ 9. The cylindrical projection based impeller design method of claim 6, wherein, said initial installation angle zero, the step of iteratively calculating said initial installation angle zero, the step of iteratively calculating said initial installation angle calculating a first derivative of the radial coordinate corresponding to the axial coordinate of the current iteration step point based on the radial profile function and a second derivative ; based on the first derivative and the second derivative by the formula calculating the radius of curvature of the current iteration step ; calculating an axial coordinate increment value based on the axial coordinate of the current iteration step and the axial coordinate of the next iteration step ; An installation angle based on a current iteration step point and an axial coordinate increment value , calculates an installation angle increment value of the current iteration step point by a formula ; Based on the initial installation angle and the incremental value of the installation angle , the installation angle of all iteration steps is calculated by the formula ​ 10. The camber projection based impeller design method of claim 9, wherein, the initial arc length zero, the step of iteratively calculating the initial arc length includes Installation angle based on the current iteration step point and axial coordinate increment value Through formula Calculate the arc length increment value of the current iteration step point. ; based on the initial arc length and the arc length increment value , the arc length of all iteration steps is calculated by the formula ​

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