Distorted rudder guide edge design method and system

Abstract

The invention discloses a twisted rudder guide edge design method and system, and the method comprises the steps: obtaining flow field data of a propeller wake flow, carrying out the multi-scale decomposition of the flow field data to recognize a rotation direction dominant region, a kinetic energy concentration region and a shear sensitive region in the wake flow, and building a mapping relation between wake flow characteristic parameters and guide edge geometric parameters on this basis, thereby achieving the design of a twisted rudder guide edge. Generating spanwise discrete distribution of a guide edge target torsion angle and a leading edge curvature parameter, constructing a guide edge torsion angle distribution function and a leading edge curvature distribution function which continuously change along the spanwise direction of the rudder blade through an interpolation mode, and performing parameterized description on the guide edge according to the distribution functions, and determining the space torsion direction and the front edge geometric shape of the guide edge at different spanwise positions, so as to form the three-dimensional twisted rudder guide edge geometry. According to the method, propeller wake flow characteristics are converted into input variables of guide edge design, self-adaptive matching of guide edge geometry to a wake flow structure is achieved, the inflow condition in front of a rudder can be improved, the energy recovery effect is improved, and the unsteady load risk is reduced.

Description

Technical Field

[0001] This invention belongs to the field of ship propulsion system design, and particularly relates to a design method and system for a tortuous rudder guide edge. Background Technology

[0002] In ship propulsion systems, the propeller and rudder are typically located close to each other in space. When the propeller operates, it creates a wake field behind it with distinct rotational characteristics and strong non-uniformity. The rudder blades are constantly within this wake's influence region, and the hydrodynamic characteristics they experience differ significantly from those under open water conditions. The propeller wake not only exhibits a significant radial gradient in its axial velocity distribution but also possesses strong rotationally induced velocities in the circumferential direction, accompanied by complex turbulent fluctuations and shear structures. This complex wake environment significantly impacts the rudder's lift characteristics, drag characteristics, rudder shaft load, cavitation, and vibration performance, and is one of the key factors limiting further improvements in propulsion efficiency and maneuverability.

[0003] To mitigate adverse interference between the propeller and rudder and recover rotational energy from the propeller wake, rudder designs with twisted guide edges have gradually emerged in existing technologies. These designs typically alter the geometry of the rudder blade guide edges to align them to some extent with the propeller wake's rotational direction, thereby achieving wake rectification, reducing energy loss, and improving propulsion efficiency. However, existing twisted guide edge rudder design methods largely rely on engineering experience or a limited number of parametric forms, such as sinusoidal, polygonal, or curved guide edges, and compare and select different schemes through numerical calculations or model tests. While these methods have shown some effectiveness in practical engineering applications, their design philosophy essentially remains at the level of pre-setting the geometry and then verifying performance.

[0004] Because propeller wakes exhibit significant spatial non-uniformity and temporal fluctuations, their flow structure continuously changes with blade rotation, exhibiting differences at different radial positions, spanwise heights, and operating conditions. Existing torsion guide edge design methods based on fixed geometric types struggle to accurately reflect the true characteristics of the wake field. Especially under multi-condition operation, simply relying on a single or a few guide edge configurations often only achieves limited improvement under specific conditions, while potentially introducing additional drag, increased rudder shaft torque, or cavitation risks under other conditions. Furthermore, current technologies in torsion guide edge design typically treat the propeller wake as a result of performance evaluation, observing its impact on rudder performance through calculations or experiments, rather than analyzing and utilizing the wake field itself as a systematic design basis. The axial velocity distribution, circumferential rotational characteristics, and turbulent fluctuation information contained in the wake are not effectively extracted and transformed into parameters that can guide rudder blade guide edge geometry design. This results in a lack of unified theoretical basis for determining the guide edge torsion angle, its variation law, and its effective range, leading to a design process heavily reliant on experience and trial and error.

[0005] Against this backdrop, how to better understand the spatial and temporal characteristics of propeller wakes and avoid selecting guide edges based solely on experience or limited parameters, thereby achieving an effective match between the twisted guide edge geometry and the actual wake flow characteristics, has become an urgent technical problem to be solved in the existing marine twisted rudder design technology. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method and system for designing a twisted rudder guide edge.

[0007] Specifically, the technical solution provided by this invention is as follows: A method for designing a twisted rudder guide edge includes the following steps: S1. Under propeller self-propulsion conditions, acquire propeller wake flow field data at a predetermined reference plane. The flow field data includes at least axial velocity components, circumferential velocity components, and time variation information corresponding to the velocity components. S2. Perform multi-scale decomposition on the flow field data, identify the characteristic regions of the wake field, and parameterize each characteristic region to form a set of wake characteristic parameters. The characteristic regions include the rotation-dominant region, the kinetic energy concentration region, and the shear-sensitive region. S3. Based on the set of wake characteristic parameters, construct a mapping relationship between the wake characteristic parameters and the geometric parameters of the twisted rudder guide edge. The geometric parameters include at least the guide edge twist angle parameter and the guide edge leading edge curvature parameter, so that the geometric parameters can change continuously with the spanwise position of the rudder blade. S4. Based on the mapping relationship, generate the guide edge torsion angle distribution function and the guide edge leading edge curvature distribution function that continuously change along the span of the rudder blade, thereby determining the geometric state of the twisted rudder guide edge at different span positions. S5. Output the torsion angle distribution function and the curvature distribution function of the leading edge as the final design result to construct the three-dimensional geometry of the torsion rudder guide edge, so as to achieve the matching design between the guide edge geometry and the propeller wake characteristics.

[0008] Furthermore, step S1 includes: A reference surface is set at a predetermined axial position downstream of the propeller axis. Timing sampling of the propeller wake is performed on the reference plane to obtain the axial velocity components of the wake at different radial and circumferential positions. and circumferential velocity components ,in, This indicates the position of the reference surface in the axial direction. r Represents the radial coordinates relative to the propeller axis. Represents the circumferential angle coordinates. t Indicates the sampling time; Over a complete propeller rotation cycle, the axial velocity component and the circumferential velocity component are statistically analyzed over time, and their periodic average values ​​are calculated. The periodic average axial velocity... and periodic average circumferential velocity satisfy:

[0009]

[0010] in, t 0 represents the starting point of the periodic statistics. T p The rotation period of the propeller; Based on the fluctuation of the axial velocity component within one propeller rotation cycle, the pulsation intensity of the wake axial velocity is calculated. It satisfies:

[0011]

[0012]

[0013] in, A preset positive number used to avoid a denominator of zero; Thus on the reference plane The wake flow field data generated simultaneously includes the periodic average axial velocity, the periodic average circumferential velocity, and the intensity of axial velocity fluctuations.

[0014] Furthermore, the identification of the dominant rotation region in step S2 includes: Let the spanwise height of the rudder blade be H r Reference surface The spanwise coordinates within the rudder blade projection range are as follows: z And define the spanwise normalized coordinates as , The coordinates are the lower boundary coordinates of the rudder blade's spanwise range; on the reference plane. Establish a discrete sampling point set , Indicates radial sampling coordinates, This represents the circumferential sampling angle coordinates, and maps each sampling point to the rudder blade spanwise coordinates. z Corresponding normalized span coordinates This establishes a one-to-one correspondence between the reference surface sampling points and the spanwise position of the rudder blade; For any spanwise position Select the set of sampling points on the reference plane corresponding to the spanwise position. And calculate the periodic average circumferential velocity in the set of sampling points. The spanning statistical mean:

[0015] in, Represents the set of sampling points The arithmetic mean of all sampling points within the sample is calculated. Based on the aforementioned spanning statistical mean The sign determines the direction of rotation attribute, when When the spanwise position is determined to be in the positive rotation zone, The region is determined to be in the reverse rotation region; to avoid sign noise interference in the weak rotation region, a rotation intensity threshold coefficient is introduced. ,when Only then is the spanwise layer identified as the dominant spiral layer. This represents the maximum value of the global periodic average circumferential velocity amplitude over the reference surface. The spanwise positions that simultaneously satisfy both the spin direction determination condition and the spin intensity threshold condition are set together and defined as the spin dominance region. The upper and lower boundary intervals of the spin dominance region in the rudder blade spanwise direction are determined by the minimum and maximum spanwise coordinates corresponding to the set.

[0016] Furthermore, the identification of the kinetic energy concentration region in step S2 includes: For the radial position on the reference plane, the periodic average circumferential velocity By statistical averaging along the circumferential angular direction, the characteristic quantity of radial circumferential kinetic energy density is defined as:

[0017] in, Indicates a fixed radial coordinate r The circumferential arithmetic mean under the given conditions; For radially normalized coordinates, The radius of the propeller; The radial circumferential kinetic energy density characteristic quantity is applied across the entire radial position range. Compare and determine its maximum value. Introducing a proportional threshold coefficient ,when When this condition is met, the radial segment is determined to be the kinetic energy concentration radial zone. All radial positions that meet this condition are collected and formed into radially continuous or discrete kinetic energy concentration segments. The region corresponding to this radial segment on the reference plane is defined as the kinetic energy concentration region, which is used to characterize the main distribution location of recoverable circumferential kinetic energy in the propeller wake.

[0018] Furthermore, the identification of the shear-sensitive region in step S2 includes: First, construct a shear / fluctuation sensitivity index:

[0019] in, Indicates the intensity of axial velocity fluctuations on the reference surface; This represents the periodic average axial velocity. This represents a two-dimensional gradient operator defined within the reference plane. ; Under discrete sampling conditions, the radial partial derivative of the periodically averaged axial velocity is approximated using the central difference method:

[0020] The circumferential partial derivative of the periodically average axial velocity is approximated using the angular central difference method:

[0021] in, Indicates the first i Coordinates of radial sampling points, Indicates the first j One circumferential sampling angle; Based on the aforementioned radial and circumferential partial derivatives, the magnitude of the periodic average axial velocity gradient within the reference plane is calculated as follows:

[0022] This leads to the shear / fluctuation sensitivity index corresponding to each sampling point on the reference surface. ; Within the entire sampling range of the reference surface, the statistical distribution of the shear / fluctuation sensitivity index is analyzed, and the values ​​corresponding to all sampling points are... Sort the values ​​and select the quantiles. q Statistical values Q q When a certain sampling point satisfies When the sampling point is determined to be a shear-sensitive point, all sampling points that meet this condition are aggregated on the reference surface and defined as shear-sensitive regions, which are used to characterize the regions in the propeller wake that are more sensitive to rudder pressure fluctuations, local cavitation and vibration response under the combined action of velocity fluctuations and velocity gradients.

[0023] Furthermore, step S3 includes: Normalized coordinates of rudder blade span As the independent variable, construct the guide twist angle parameter. The continuous mapping relationship of the extension direction, For the first m The spanwise coordinates of the rudder blades corresponding to each spanwise discrete layer To ensure that the direction of the guide edge twist is consistent with the directional attribute of the dominant rotation region, at each spanwise position... At this point, a rotation sign function is introduced. ,in, It is a sign function used to characterize the positive or negative property of a numerical value; For exhibition location The spanwise statistical mean of the periodic average circumferential velocity; when When indicates a positive reversal, when Time indicates reverse twisting; After determining the torsion direction, the amplitude of the guide torsion angle is designed to be determined by the rotational strength characteristic quantity. Kinetic energy coverage characteristic quantity and risk suppression characteristic quantity Driven by the same factors, the spanwise continuous mapping relationship of the guide edge target twist angle is constructed as follows:

[0024] in, For exhibition location The target twist angle at the guide edge, The maximum allowable torsional angle amplitude; exponential parameter p , q , sIt is a non-negative real number used to adjust the sensitivity of the rotation strength characteristic, kinetic energy coverage characteristic, and risk suppression characteristic to the guide twist angle; Let be the truncation function, indicating that when Time to take a ,when Time to take b Otherwise take x ; Through the above mapping relationship, the torsion angle of the guide edge is continuously varied in the spanwise direction of the rudder blade, and the torsion effect is enhanced in the region where the rotation direction is dominant and the kinetic energy is concentrated. In the region where the risk of shearing or pulsation is high, the torsion amplitude is suppressed, thereby obtaining a torsion distribution of the rudder guide edge that is adapted to the structural characteristics of the propeller wake.

[0025] Furthermore, step S3 includes: First, we construct an index for the degree of non-uniformity of spanwise inflow:

[0026] in, This is the global maximum value of the periodic average axial velocity gradient magnitude within the reference plane; To prevent extremely small positive numbers with a denominator of zero; Based on this, the target distribution of the leading edge curvature is designed to be determined by the inflow non-uniformity index. Risk suppression characteristic Adjust together, and use the leading edge curvature radius. As an intermediate variable, the spanwise continuous mapping relationship of the radius of curvature of the leading edge is defined as follows:

[0027] in, w 1. w 2 is a non-negative weighting coefficient used to characterize the relative contribution of inflow nonuniformity and shear sensitivity to the leading edge passivation requirement; Indicates the permissible range of leading edge curvature radius; Based on the aforementioned leading edge curvature radius The curvature parameter of the leading edge is determined as follows: ; This allows the leading edge curvature parameter to change continuously in the spanwise direction of the rudder blade, and automatically increases the degree of leading edge passivation in areas with strong inflow gradients or high risk of shear / pulsation, while maintaining a small curvature change in non-sensitive areas, so as to obtain a leading edge geometric distribution that is compatible with the propeller wake structure and local pressure distribution characteristics.

[0028] Furthermore, step S4 includes: In obtaining the spanwise discrete sequence of the target twist angle of the guide edge and the spanwise discrete sequence of the radius of curvature of the leading edge back, N z To determine the total number of spanwise discrete layers, the discrete sequence is converted into a continuously varying guide edge twist angle distribution function and a guide edge leading edge curvature distribution function along the span of the rudder blade. This process includes: Distribution function of twist angle of the guide side and the distribution function of the radius of curvature of the leading edge The interpolation is constructed using a piecewise cubic Hermite interpolation function, within each adjacent spanning node interval. Internally respectively to and Construct a piecewise cubic polynomial such that the function values ​​are continuous and the first derivative is continuous; In any adjacent node interval Define the normalized interval parameters.

[0029] Define Hermite basis functions as

[0030]

[0031] Therefore, the distribution function of the leading edge twist angle within the specified interval is expressed as:

[0032] in, , The discrete values ​​of the guide twist angle at adjacent spanwise nodes; and They are nodes and The first derivative of the twist angle of the leading edge with respect to the spanwise coordinates; Similarly, the discrete sequence of the leading edge curvature radius is processed. Construct a spanwise continuous radius of curvature distribution function and further by Determine the curvature distribution function of the leading edge. This represents the geometric curvature of the leading edge at the corresponding spanwise position.

[0033] Furthermore, step S5 includes: The guide twist angle distribution function that varies continuously along the rudder blade span is obtained. Distribution function of radius of curvature of the leading edge Then, a spatial description for constructing the 3D twisted rudder guide edge geometry is generated using a parametric approach: First, define the guide edge baseline under the condition of no torsion. The baseline is used to characterize the spatial position of the guide edge along the spanwise direction of the rudder blade in the untorsed state, and its parameterized expression is as follows: ,in, , Determined by the reference projection curve of the rudder blade shape at the guide edge; Subsequently, at any spanning position At this point, a local coordinate system is established within the local profile plane, and its normal unit vector is defined as follows: The tangential unit vector is defined as , Consistent with the chordal direction of the rudder blade profile, and and Orthogonal in the plane of the cross section; Using the aforementioned guide edge torsion angle distribution function The rotation angle representing the local direction of the guide edge relative to the reference direction is then the unit vector of the guide edge direction after the torsion is applied. Expressed as

[0034] Based on this, the distribution function of the radius of curvature of the leading edge is used. Define the geometric arc shape of the leading edge in a local section, where the curvature of the leading edge satisfies The curvature is used to control the degree of passivation of the leading edge at the corresponding spanwise position; in the local profile, the leading edge of the guide edge is approximately represented by a radius of... The circular arc curve is obtained, and the center position and the endpoint of the circular arc are determined according to the geometric continuity condition of the circular arc and the rest of the rudder blade section, so as to obtain the geometry of the leading edge section front edge at the spanwise position. By each orientation position Torsion direction vector Determine the direction, and determine it based on the radius of curvature of the leading edge. The leading edge curve of the guide edge profile with a local circular arc shape is determined and connected along the spanwise direction of the rudder blade to form a continuous three-dimensional twisted rudder guide edge surface, thereby determining the spatial geometry of the guide edge that matches the wake characteristics at different spanwise positions.

[0035] A twisted rudder guide edge design system based on the above method, the system includes the following modules: The flow field data acquisition and management module is used to acquire or import propeller wake flow field data under self-propelled conditions. The flow field data includes at least the axial velocity component, circumferential velocity component and related data characterizing the intensity of unsteady pulsations on the reference plane. It also manages flow field data from different sources or with different sampling densities in a unified manner to ensure that subsequent processing is carried out under a consistent spatial reference and coordinate definition. The data preprocessing and unification module is used to preprocess the flow field data, including denoising and outlier removal of the sampled data, interpolation unification or resampling of the spatial sampling grid, phase alignment of the time series, and reference system correction of the velocity components, so that the axial velocity components and the circumferential velocity components are expressed in the same coordinate system, thereby forming a spatiotemporally aligned wake dataset. The multi-scale decomposition and feature region identification module is used to perform radial scale decomposition, spanwise scale decomposition and time scale decomposition on the wake data after the uniformization process. It identifies the degree of axial inflow non-uniformity and circumferential kinetic energy distribution characteristics through radial statistics, identifies the wake vortex-dominant region and its boundary through spanwise statistics, and identifies the shear-sensitive region through the coupling of pulsation intensity and velocity gradient, thereby obtaining the vortex-dominant region, kinetic energy concentration region and shear-sensitive region. The wake feature parameter set construction module is used to parameterize the rotation-dominant region, kinetic energy concentration region and shear-sensitive region to form a wake feature parameter set that can be indexed by spanwise position, which can be used as input for generating guide edge geometry parameters; The geometric parameter mapping generation module is used to establish a mapping relationship between the wake characteristic parameters and the guide edge geometric parameters based on the wake characteristic parameter set, generate the spanwise discrete distribution of the guide edge target twist angle and the spanwise discrete distribution of the guide edge leading edge curvature or leading edge curvature radius, and apply allowable range constraints to the twist angle amplitude. The spanwise continuity and manufacturability assurance module is used to convert the spanwise discrete distribution of the target twist angle and leading edge curvature or leading edge curvature radius of the guide edge into a function expression that changes continuously along the spanwise direction of the rudder blade, so as to ensure the continuity and smoothness of the guide edge geometric parameters in the spanwise direction and avoid abrupt changes in geometric parameters. The three-dimensional guide edge geometry generation module is used to construct the guide edge baseline based on the continuous guide edge torsion angle distribution function and the leading edge curvature or leading edge curvature radius distribution function, and to determine the spatial torsion direction and leading edge geometry of the guide edge at each spanwise position. The guide edge profiles at each spanwise position are connected along the spanwise direction to generate a continuous three-dimensional twisted rudder guide edge geometry model.

[0036] Compared with the prior art, the present invention has at least the following beneficial effects: Existing methods for designing twisted rudders or guide edges typically rely on empirical formulas, predetermined geometric functions, or numerical comparisons under limited operating conditions. These methods often treat the propeller wake as a verification object after design completion, making it difficult to accurately reflect the non-uniform characteristics of the wake in time and space, and also hindering the establishment of a clear correspondence between the wake structure and the guide edge geometry. This invention, however, starts from the propeller's self-propelled operating conditions, using the wake velocity field as the core design input. Through systematic analysis of the wake's axial velocity, circumferential velocity, and pulsation characteristics, it quantitatively extracts the rotational features, energy distribution characteristics, and shear sensitivity characteristics originally implicit in the flow field results. This transforms the wake from a passive response object into an active driving variable, fundamentally improving the relevance and physical consistency of the guide edge geometry design.

[0037] Furthermore, this invention establishes a mapping relationship between wake characteristic parameters and lead-edge twist angle and leading-edge curvature. This allows the lead-edge geometry to no longer rely on a preset single function form or discrete angle settings, but rather adaptively generates a continuously changing geometric distribution based on the changes in wake characteristics at different spanwise positions. This method of generating geometry based on flow field characteristics can more effectively coordinate the matching relationship between the lead-edge and the propeller wake across the entire spanwise range, helping to improve the lead-edge headwind conditions, weaken the impact of unfavorable vortices on the control surface, and avoid additional flow losses caused by local excessive twisting or geometric abrupt changes. Attached Figure Description

[0038] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0039] Figure 1 This is a schematic diagram of the design method for the twisted rudder guide edge provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the twisted rudder guide edge design system framework provided in an embodiment of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of 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, other embodiments obtained by those skilled in the art without creative effort are all within the scope of protection of the present invention.

[0041] Example 1 This embodiment provides a method for designing a twisted rudder guide edge, applicable to the working conditions of propeller and rudder cooperation in ship propulsion systems. This method takes the wake flow field formed by the propeller in self-propelled mode as the research object. Through systematic analysis of the wake flow characteristics, it transforms the spatial distribution and temporal variation characteristics inherent in the wake into the basis for rudder guide edge geometry design, thereby achieving a match between the twisted guide edge geometry and the actual wake flow state.

[0042] like Figure 1 As shown, the method mainly includes the following steps: I. Determine the design operating conditions and establish a propeller-rudder coordinated reference system First, determine the design object of the twisted rudder guide edge, including the basic geometric and operational parameters of the ship's propulsion system and rudder system. The propulsion system parameters include at least the propeller diameter. D p Propeller rotation direction, propeller axis spatial position, and axial distance between the propeller and the rudder. L pr Among them, the propeller diameter D p The outer diameter of the propeller disk can be obtained from ship design data or actual ship measurements; the propeller rotation direction characterizes the direction of rotation of the propeller when viewed in the propulsion direction, and can be determined according to the propulsion system configuration; the propeller axis position is used to determine the origin and direction of the subsequent coordinate system; axial distance. L pr Defined as the axial distance from the geometric center of the propeller disk to the reference plane of the leading edge of the rudder blade, its value can be obtained directly from the propulsion system layout diagram.

[0043] At the same time, determine the relevant parameters of the rudder system, including at least the outer contour shape of the rudder blade and the spanwise height of the rudder blade. H r And the reference profile position of the rudder blade used for geometric description. The spanwise height of the rudder blade. H r Defined as the maximum geometric dimension of the rudder blade in the vertical direction, it is used to limit the spanwise range of subsequent wake sampling and guide edge design; the reference section position can be selected from the middle of the rudder blade or the design reference section, which is used as a reference starting point for the change of guide edge twist angle and curvature.

[0044] After determining the design object, the design conditions for the tortuous rudder guide edge are further determined, including at least the design speed. V s Design draft T And the corresponding self-propulsion status. Design speed V s The propulsion speed of a ship under target operating conditions can be given by the ship's technical specifications or design requirements; design draft. TThis refers to the static or operational draft of the vessel at this speed condition, used to determine the actual submerged positions of the propeller and rudder in the water. The self-propulsion state characterizes the actual operating state of the propeller under conditions of overcoming hull resistance, rather than the open-water state, thus ensuring that the subsequent wake field can accurately reflect the flow characteristics after the interaction between the propulsion system and the hull.

[0045] Based on the aforementioned design objects and operating conditions, a unified spatial reference system for the coordinated action of the propeller and rudder is established. This reference system is established with the propeller axis as the core reference, wherein the axial coordinate... x Direction is defined as the direction consistent with the ship's sailing direction, pointing from bow to stern; radial coordinates. r Defined as the radial distance centered on the propeller axis and perpendicular to the axial direction; circumferential coordinates. i Defined as an angular coordinate system about the propeller axis, its zero-angle position can be determined based on the direction above the propeller or a design-defined direction. This coordinate system allows the axial velocity components, circumferential velocity components, and their spatial distribution in the propeller wake to be expressed in a unified form.

[0046] Under the unified coordinate system, at least one wake sampling reference surface is set behind the propeller and upstream of the leading edge of the rudder blade. This reference surface is a plane perpendicular to the propeller axis, and its axial position is... x ref satisfy:

[0047] in, x ref The axial distance of the reference plane relative to the propeller disk surface should be chosen to ensure that the reference plane is located before the propeller wake significantly interferes with the rudder blades, while also characterizing the wake state about to enter the rudder blade's action zone. The radial range of the reference plane should at least cover the spanwise height of the rudder blades. H r The corresponding projection area ensures that the collected wake information corresponds one-to-one with the subsequent guide edge design area in space.

[0048] II. Obtaining propeller wake flow field data under self-propelled conditions The purpose of this step is to acquire and form a wake dataset based on the established propeller-rudder cooperative reference system and wake sampling reference surface. This wake dataset should at least include: the axial velocity field, the circumferential velocity field at the reference surface, and turbulent fluctuation information reflecting the intensity of unsteady fluctuations, and meet the requirements of spatial coverage of the rudder blade spanwise range and temporal coverage of at least one propeller rotation cycle.

[0049] 1. Unified expression of wake velocity components and sampling domain In the coordinate system established in the preceding steps, let the instantaneous velocity vector of the fluid be... .

[0050] Define the unit vectors in three orthogonal directions as follows: e x : Axial unit vector, along the direction of ship's navigation (propulsion direction); e r Radial unit vector, perpendicular to e x And it points away from the propeller shaft; e θ Circumferential unit vector, tangential direction about the propeller shaft, satisfying the right-hand rule (and) i (The direction of increase is consistent).

[0051] The velocity component is then defined as:

[0052]

[0053]

[0054] in, Output from a numerical solver or obtained from a measurement device. e x , e r , e θ It is calculated using the geometric definition of the coordinate system.

[0055] Wake sampling at the reference plane Onwards, Defined as a plane with constant axial coordinates:

[0056] The sampling domain's radial range on the reference plane should at least cover the range corresponding to the rudder blade's spanwise height. In engineering practice, the following values ​​are acceptable:

[0057] And in Sampling is performed across the entire circumference to avoid missing rotational features.

[0058] 2. Calculation of unsteady fluctuation (turbulence / wave) information To output the wake unsteadiness in a computable manner, this step outputs at least one pulsation intensity index. This embodiment uses a time-averaged + pulsation RMS approach, detailed below.

[0059] Let the propeller angular velocity be w(unit: rad / s), or rotational speed: n (Unit: rps) Then the propeller rotation period is:

[0060] in, w The propeller speed can be given by solving the self-propulsion problem. n It can be given by the propulsion system design values ​​or the self-propulsion balance solution.

[0061] For any point on the reference plane ( r , i The time average of axial velocity is defined as:

[0062] Similarly, it can be defined .in t 0 is the selected statistical starting time. In practical implementation, the integral can be approximated by discrete sampling and summation. If within one period... N t There are 1 time points, and the time step is 1. ,but:

[0063] Define the axial velocity pulsation component:

[0064] Its root mean square (RMS) is:

[0065] Circumferential velocity pulsation RMS Calculate similarly.

[0066] To output dimensionless turbulence intensity (or velocity fluctuation intensity), you can define:

[0067] in To prevent the denominator from approaching a very small positive number of zero, thus ensuring numerical stability.

[0068] In the implementation method of obtaining propeller wake flow field data using numerical calculation, an incompressible viscous fluid is used as the physical model basis. Coupled flow solutions are performed on the propulsion system consisting of the propeller, hull, and rudder under self-propelled conditions. This yields the axial velocity components, circumferential velocity components, and corresponding unsteady pulsation information at the reference plane determined in the preceding steps. Given the relatively low propulsion speed of the ship and the fact that the water can be approximated as incompressible under these conditions, the flow control equations are described using the incompressible continuity equation and the Reynolds time-averaged momentum equation. The continuity equation is...

[0069] Reynolds' time-averaged momentum equation is expressed as:

[0070] in, The fluid density is determined by selecting either seawater or freshwater density based on the design conditions. Dynamic viscosity; Average pressure over time; This is the time-averaged velocity vector; For velocity fluctuation components; The Reynolds stress term characterizes the effect of turbulent fluctuations on the mean flow. This Reynolds stress term is closed using a turbulence model, which can be a two-equation model, such as the Realizable k-ε model, the specific mathematical form of which is implemented by a general fluid dynamics solver.

[0071] During the numerical calculation, the computational domain needs to cover the propeller, rudder, and the surrounding water area, and the inlet boundary condition is set to the incoming flow velocity. V s Its direction is along the axial unit vector defined in the preceding steps. e x The inlet turbulence intensity can be given based on empirical formulas or experimental data. The outlet boundary can be set as a constant pressure boundary or an open boundary condition to ensure smooth wake discharge and avoid numerical backflow interference. The hull surface and rudder surface are set as non-slip wall boundaries, and the treatment of the near-wall region should match the mesh resolution, which can be achieved using the wall function method or a low Reynolds number treatment method. The propeller rotational motion can be realized through the slip mesh method or the multi-reference frame method. When it is necessary to obtain the pulsating information of velocity change over time, the slip mesh method is preferred to obtain the velocity component at the reference surface. and The timing output.

[0072] To ensure that the acquired wake data reflects the periodic changes caused by propeller rotation, the numerical calculation time should cover at least one propeller rotation cycle. T p The computation time meets the requirements.

[0073] in, t steady The transition time required for the flow to reach a statistically stable state.

[0074] After completing the time domain calculations, at the reference plane Establish a sampling point set Axial velocity components are extracted at each sampling point. and circumferential velocity components Based on the aforementioned time series data, the time average value of the axial velocity is calculated according to the aforementioned time average and root mean square calculation formulas. Time average of circumferential velocity Root mean square of axial velocity pulsation Root mean square of circumferential velocity fluctuations And further calculate the velocity pulsation intensity index This results in a wake dataset:

[0075] This dataset serves as the direct input for subsequent wake multi-scale decomposition and feature region identification.

[0076] In another embodiment, propeller wake flow field data can also be obtained through experimental measurement. Specifically, in a model test tank or equivalent test environment, velocity measurement points can be arranged at coordinate systems and reference planes that are completely consistent with the aforementioned steps. Using equipment such as acoustic Doppler velocimeters, laser Doppler velocimeters, or particle image velocimetry systems, data on the change of velocity vectors over time at each sampling point can be acquired. The measured velocity vectors are then used to calculate the axial velocity component through projection. With circumferential velocity component And calculate using the same time-averaged and root-mean-square formulas as the numerical calculations. , and pulsation intensity The sampling duration should cover at least one propeller rotation cycle, and may cover multiple cycles to improve statistical stability.

[0077] Furthermore, when numerical calculations or experiments are not feasible, it is permissible to reconstruct the wake flow field based on existing self-propelled test data, propulsion system databases, or historical data from similar vessels. During the reconstruction process, it should be ensured that the final output data is consistently projected onto the reference plane. and with , and pulsation intensity As the core data format, reconstruction methods can employ spatial interpolation, similarity criterion scaling, or regression model-based reconstruction. The key is to maintain consistency between spatial resolution and the definition of physical quantities to meet the needs of subsequent feature decomposition.

[0078] Wake stream dataset obtained through any of the above methods W Covering the reference plane in space The region corresponding to the spanwise height of the rudder blade reflects the flow characteristics within at least one propeller rotation cycle in a temporal or statistical sense, and includes information on axial average velocity, circumferential average velocity, and unsteady pulsation intensity in terms of physical quantities.

[0079] III. Multiscale Decomposition of Wake Data Since wake data may come from different sources or have different sampling densities, in order to ensure the stability of subsequent decomposition calculations, the wake data must first be preprocessed and standardized. This includes denoising and removing outliers from the sampled data, unifying or resampling the spatial grid, aligning the phase of the time series, and correcting the reference frame of the velocity components. This ensures that the axial velocity components and the circumferential velocity components are expressed under the same coordinate definition, thereby forming a wake dataset with a consistent format and spatiotemporal alignment.

[0080] After completing the wake data unification, the wake is decomposed into multiple scales to identify the flow structures in the wake that have a dominant influence on the guide edge design. Specifically: First, normalize the geometric coordinates on the reference plane. Let the propeller radius be... Then the radially normalized coordinates are defined as Regarding the spanwise direction, since the spanwise height of the rudder blade is... H r The vertical coordinates (or equivalent spanwise coordinates) of the reference plane within the rudder blade projection range can be denoted as z, and the spanwise normalized coordinates can be defined as... , z 0 represents the lower boundary coordinate of the rudder blade's spanwise range. z It can be directly obtained from the spatial coordinates of the sampling points on the reference surface. By normalizing radial and spanwise directions, the characteristic quantities of different ship sizes and propeller diameters have a consistent calculation caliber.

[0081] 1. In radial scale decomposition, the focus is on characterizing the degree of non-uniform inflow and the intensity of circumferential induced changes in the wake at different radial positions. Therefore, at a fixed circumferential angle... i Or to i Calculate the axial average velocity under statistical averaging conditions. Regarding the radial gradient characteristics, specifically, a radial non-uniformity index is defined. The radial variation intensity of the axial average velocity on the reference plane can be given by the following formula:

[0082] in This represents the statistical average over θ ∈ [0, 2π). / r represents the partial derivative operation with respect to the radial direction. Under discrete sampling conditions, let the radial sampling point be... The adjacent radial spacing is Then at the sampling point The radial gradient at a point can be approximated by the central difference as:

[0083] Then for all We can get the average. .in, The axial average velocity is obtained from the previous step using the periodic averaging formula. , The coordinates of the sampling points on the reference surface; The value is given by the sampling grid. The physical meaning of this index is: the larger the radial gradient, the more non-uniform the axial inflow of the wake, and the more likely it is to affect the local angle of attack and separation trend of the control surface. Therefore, it should be used as one of the key input parameters in the subsequent guide edge geometry allocation.

[0084] To further characterize the radial distribution of recoverable circumferential kinetic energy in the wake, a circumferential kinetic energy density index can be defined. Under incompressible flow conditions, the circumferential kinetic energy per unit mass can be used to express the flow, and the circumferential angles can be statistically analyzed.

[0085] in The circumferential average velocity component originates from the previous step. The periodic average. This index is used to identify radial sections in the wake with large circumferential induced velocity amplitudes, so as to determine the main area of ​​action of the guide-side torsion in subsequent mapping.

[0086] 2. In spanwise decomposition, the focus is on identifying the sign and amplitude variations of the wake rotation within the spanwise range of the rudder blade to determine the dominant rotation region and its upper and lower distribution boundaries. Since the reference surface uses... When expressing the span of the rudder blade z The relationship can be obtained through spatial coordinate conversion, therefore, positions falling in each spanwise direction can be selected from the set of sampling points on the reference surface. The point set is used to perform spanwise statistics on its circumferential average velocity. Specifically, the spanwise rotational characteristic function is defined. Sign-weighted amplitude of the circumferential average velocity:

[0087] Among them, sgn( ) is a symbolic function; Indicates the spanwise position on the reference plane. The set of sampling points; This indicates a statistical average of the point set. The purpose of this definition is to indicate when the wake exhibits a stable circumferential induced velocity of the same sign at a certain spanwise position. Maintain a stable sign; when the circumferential induction directions of the upper and lower regions are opposite, A sign flip occurs, which can then be used as a boundary criterion for dividing the upward and downward reverse rotation regions. For ease of engineering implementation, those skilled in the art can apply this to discrete spanwise layers. Above calculation And through detection The zero-crossing or sign mutation position determines the rotation direction boundary.

[0088] 3. In the time-scale decomposition, the focus is on quantifying the unsteady intensity and periodic characteristics of the wake to identify shear-sensitive regions and provide input for subsequent constraints. If the pulsation intensity index has already been output in the previous step... Then you can directly use As a fundamental quantity of unsteady strength, and to define a shear / wave sensitivity index. This is the coupling amount between the pulsation intensity and the velocity gradient, for example:

[0089] in, Indicated on the reference plane The two-dimensional gradient operator within can be written as Under discrete conditions, It can be calculated using the aforementioned central difference. Then it can be calculated based on the difference between adjacent angle points:

[0090] Thus obtain The physical meaning of the index Q is: when a region has both strong velocity fluctuations and a large inflow gradient or shear structure, the region is more sensitive to rudder surface pressure fluctuations, local cavitation and vibration. In the subsequent generation of guide edge geometry, constraint or smoothing strategies should be used to avoid excessive geometric changes.

[0091] When further identification of the periodic dominant frequency characteristics of the wake is required, spectral analysis of the velocity pulsation sequence can be performed at a specific sampling point or region on the reference plane. (Using axial pulsation...) For example, for discrete time series Perform a discrete Fourier transform to obtain the frequency domain amplitude. Its expression is:

[0092] in, i The imaginary unit; N t This represents the number of sampling points within a statistical window. Discrete frequency; This is the time step. Through analysis... The main peak frequency can determine the main periodic components of the wake unsteadiness and be used in subsequent constraints to avoid frequency bands that are prone to cause rudder surface resonance or pressure pulsation amplification.

[0093] IV. Wake Feature Region Identification and Parametric Representation After completing the multi-scale decomposition, this step involves the reference surface. The wake field is used to identify characteristic regions and express each characteristic region in a parametric form, so as to convert the continuously distributed flow field results into a set of design input parameters that can be directly used for guide edge geometry generation.

[0094] First, on the reference plane Establish a discrete sampling grid or point set on top ,in For radial sampling points, It is a circumferential sampling angle point, and the sampling domain covers , Simultaneously, each sampling point is mapped to the rudder blade spanwise coordinate z and the normalized spanwise coordinate z. Through the above mapping, a one-to-one correspondence is established between the reference surface sampling points and the spanwise range of the rudder blade, ensuring a traceable spatial correlation between subsequent region identification and guide edge spanwise allocation.

[0095] To regionalize the wake, this step employs a standardization-then-discrimination approach to establish unified criteria for different physical quantities. Specifically, this applies to the entire reference surface. The statistics for circumferential velocity amplitude, axial velocity, and pulsation intensity are calculated and converted into dimensionless or relative quantities to avoid the influence of absolute value differences under different ship types and propeller diameters on stability assessment. Let the global maximum value of the circumferential velocity amplitude be...

[0096] The global average value of the axial average velocity is

[0097] in This represents the arithmetic mean of the sampling points over the reference surface. The global statistical quantile of the pulsation intensity can be denoted as... It is defined as: at all sampling points on the reference surface Take the quantile from the set as q (For example q The value of 0.9 is used as a threshold for the high volatility region.

[0098] In identifying regions of spin direction and intensity, the directional and intensity attributes of the dominant spin region are first determined. The directional attribute is used to distinguish the upward and downward opposing rotational trends of the wake along the rudder blade span. For any spanwise position... The sampling point set corresponding to this spanning layer Calculate the spanwise statistical mean of the circumferential average velocity:

[0099] And its sign determines the direction of rotation: when The time is recorded as the positive rotation zone, when This is designated as the reverse rotation region. To further avoid the influence of symbolic noise in the weak rotation region, a minimum intensity threshold can be set. ,when Only then is the spanwise layer identified as the dominant spiral layer. This is a scaling factor, set by the implementer based on accuracy requirements. Subsequently, all spanwise layers satisfying the above conditions are aggregated to obtain the rotation-dominant region. R swirl And record its upper and lower boundaries. The interval is used to determine the effective range of the subsequent guide-side torsion function.

[0100] In identifying energy concentration regions, this step uses the circumferential kinetic energy density characteristics defined above. As a basis, the sampling points on the reference surface are statistically analyzed radially to obtain...

[0101] in Indicates a fixed r (or fixed) The circumferential average under the given condition. Let its maximum value be... Similarly, a proportional threshold is introduced. ,when When this occurs, the radial segment is identified as a kinetic energy concentration radial zone, and the region corresponding to this radial zone is denoted as... R energy .in The value of is used to control the width of the concentrated zone and can be set as needed. This identification process clarifies the main source of the recoverable circumferential kinetic energy in the wake, providing input for subsequent guide-side torsional amplitude allocation; that is, the main torsional force of the guide side should be concentrated and covered. R energy The corresponding radial-stretching projection area.

[0102] In the identification of shear-sensitive regions, this step couples the intensity of unsteady pulsations with the velocity gradient to more stably identify regions more sensitive to pressure pulsations, cavitation, and vibration. The shear / fluctuation sensitivity index defined above is used.

[0103] in For the in-plane two-dimensional gradient operator, it is written as In discrete implementation, for Using central difference:

[0104] right Using angular difference:

[0105] Thus obtain

[0106] Recalculate This step applies to the entire domain. Q Take quantile threshold Q q (For example, take) q = 0.9 (the upper quantile value), when At that time, the corresponding area is identified as a shear-sensitive area. R shear .in Q q The calculation method is as follows: for all sampling points on the reference surface Q After sorting the set of values, take the quantile. q The value, q Set by the implementer. The advantage of using quantile thresholds instead of absolute thresholds is that the relative stability of area identification can be maintained under different ship types and different speed conditions.

[0107] After identifying the three regions mentioned above, this step parameterizes the regions to form a set of design input parameters that can be directly used for geometric mapping. Specifically, representative parameters are extracted for each type of region. For rotation-dominant regions... R swirl Output rotation sign function Rotational intensity distribution and the spanwise boundary of the dominance region of the spin For regions where kinetic energy is concentrated R energy Output concentrated radial band boundary and the corresponding Distribution, used to characterize the radial coverage area where the guide edge primarily functions. For shear-sensitive areas. R shear Output mask function for highly sensitive regions (Take 1 when the point belongs to the shear-sensitive region, otherwise take 0), and the statistics of this region are as follows: and It is used to constrain or smooth the torsional gradient and curvature changes in the subsequent geometry generation stage.

[0108] Finally, this step outputs a set of wake features. F With feature region identification map M .in F At least include , , , , , Q q , and the statistical threshold parameters on which its calculation is based. , , q ; M At least included in the reference plane The internal region mask result is used to label the region type to which each sampling point belongs.

[0109] V. Constructing the mapping rules from wake characteristic parameters to guide edge geometric parameters After completing the wake feature region identification and parameterized representation, this step establishes a mapping rule from wake feature parameters to guide edge geometric parameters to ensure that the geometric design of the twisted guide edge is driven by wake features rather than relying on a preset type. The input to the mapping rule is the wake feature set formed in the previous step. F With area identification map M The output is the target torsion angle distribution along the span of the guide edge rudder blade. and the target curvature distribution of the leading edge. (or equivalent leading edge radius of curvature) To ensure the mapping is reproducible and corresponds one-to-one with the wake data, the reference plane is first... sampling point set on Grouping by spanwise affiliation, constructing a set of sampling points for each spanwise layer. .in Indicates the first m Discrete spanwise layers (e.g., uniformly dividing the spanwise direction of the rudder blade) N z layer, (Or obtained by binning according to the z-value of the actual sampling points). The construction method is as follows: all sampling points are arranged according to their corresponding The value falls within the interval Classify them, among which The spanwise bin width is determined by the sampling density. Through this grouping, every value of any subsequent spanwise function can be calculated from a specific set of sampling points.

[0110] To reflect the differences in wake cyclonic intensity, recoverable circumferential kinetic energy, and shear / wave risk in the mapping, this step is performed at each spanwise layer. Three normalized feature quantities are constructed above: rotation intensity index Energy coverage index Risk suppression indicators Rotational strength index It is obtained by normalizing the statistical values ​​of the circumferential average velocity amplitude within the spanwise layer, and is defined as follows:

[0111] in, Represents a set of points The arithmetic mean; The maximum value of the global circumferential average velocity amplitude over the reference surface; To avoid extremely small positive numbers with a denominator of zero (as mentioned above) The functions are consistent, and the same order of magnitude can be used (as specified in the examples). From the previous step In one propeller cycle T p The discretization method is as follows: (The text abruptly ends here, suggesting an incomplete sentence or a missing section.)

[0112] in N t The number of sampling points within the period. t k For discrete sampling times. This index It characterizes the relative level of the rotational intensity of the wake at that spanwise position, and is subsequently used to determine the magnitude and trend of the guide-side torsion demand.

[0113] Energy Coverage Index This is used to indicate what proportion of the sampling points in the spanwise layer fall into the radial band of concentrated kinetic energy. This reflects the extent to which the leading-edge torsion acts on the critical energy region in the spanwise layer. Let the radially normalized coordinates be... Then define

[0114] in This is an indicator function; it takes the value 1 if the condition is true, and 0 otherwise. The number of sampling points within the point set; This comes from the automatic centralized area identification step. This indicator... The larger the value, the more sampling points the spanwise layer covers within the critical radial band where circumferential kinetic energy can be recovered, typically requiring a more defined leading-edge torsional response.

[0115] Risk suppression indicators This is used to represent the proportion of shear-sensitive regions in the spanwise layer, thereby applying adaptive suppression to torsional amplitude and curvature changes in the mapping. The shear-sensitive mask output from the previous step is then used. (Value 1 if it belongs to the shear-sensitive region, otherwise value 0), Definition:

[0116] This indicator The larger the value, the higher the proportion of highly sensitive points to shear / fluctuation in the spanwise layer. Subsequent mapping should reduce the intensity of geometric changes to suppress the amplification of adverse pressure pulsations or cavitation risks. If a mask is not output but a shear sensitivity scalar is output instead... It can also be used beyond the threshold. Q q To construct equivalents based on the proportions. ,in Q q The threshold for global quantiles (e.g., 0.9 quantile) is calculated in the same way as described above.

[0117] Based on the three normalized characteristic quantities mentioned above, this step establishes the distribution of the torsion angle of the target along the guide edge. The mapping expression. First, to be consistent with the directional properties of the rotation-dominant region, a rotation sign function is adopted. As a sign determinant of the twist angle, where

[0118] and according to = +1 or -1 determines the torsional direction of the guide edge in the spanwise layer. Subsequently, the torsional angle magnitude is designed to be determined by the rotational intensity. With energy coverage Driven by both factors and subject to risk mitigation Adjustment, providing the target torsion angle mapping formula:

[0119] in, The maximum allowable torsional angle amplitude can be determined by design experience, manufacturability, or other constraints. p , q , s It is a non-negative exponent used to adjust the sensitivity of different characteristic quantities to the torsion angle, for example, taking p=1, q=1, s=1 as a linear mapping, or adjusting it according to the target response). Let be the truncation function, indicating that when Time to take a ,when Time to take b Otherwise take x .

[0120] Unlike the twist angle, the curvature distribution of the leading edge... The mapping needs to simultaneously consider the effects of oncoming impact, separation tendency, and shear / wave sensitivity on local pressure distribution. Therefore, this step first constructs an index characterizing the degree of non-uniformity of the spanwise inflow. This can be obtained statistically from the gradient of the axial average velocity within the reference plane. Using the aforementioned reference plane gradient operator... ,definition

[0121] in The maximum gradient magnitude across the entire domain. It is a very small positive number; Discrete calculations can be performed according to

[0122] in and This is achieved using central difference and angular difference, and the difference formula is consistent with that given previously. Therefore, we obtain... The larger the value, the stronger the inflow gradient of the spanwise layer and the more significant the non-uniformity of the flow.

[0123] Based on this, the target distribution of the leading edge curvature is designed to be determined by the degree of inflow non-uniformity. Shear sensitivity ratio The curvature is adjusted together while maintaining it within a manufacturable range. To ensure consistency between the notation and geometric meaning, the radius of curvature is used here. The mapping is easier to implement in engineering (a larger radius of curvature indicates a more blunt and rounded leading edge, while a smaller radius indicates a sharper leading edge). Let the allowable range of radii of curvature be... (Unit length, consistent with rudder dimensions, value can be set according to rudder blade dimensions), definition

[0124] in w 1, w 2≥0 is a weighting coefficient used to characterize the relative contribution of inflow nonuniformity and shear sensitivity to the leading edge rounding passivation requirement, and can be taken as... w 1+ w 2 = 1. From this, we obtain the curvature.

[0125] If you prefer to output the curvature directly rather than the radius of curvature, you can also maintain... The units are consistent (e.g., m). -1 ), and It is used as an intermediate quantity in the calculation.

[0126] VI. Generating the torsional and curvature functions of the leading edge that vary continuously along the span. Obtaining the discrete sequence of the torsion angle of the guide edge target and discrete sequence of leading edge curvature radius Then, this step converts the above discrete nodes into a function expression that changes continuously along the span of the rudder blade, so as to ensure that the guide edge geometry remains smooth and continuous in the span direction, and avoid local separation, pressure concentration or processing discontinuity caused by abrupt changes in the torsion angle or leading edge curvature.

[0127] To ensure function continuity and manufacturability, this step preferably constructs at least a first-order continuous (C) function. 1 The interpolation or fitting function is used. Piecewise cubic Hermite interpolation (similar to the PCHIP method) is employed, with each piecewise cubic Hermite interpolation applied to different parts of the instrument. and Construct a piecewise cubic polynomial to ensure continuous function values ​​and continuous first derivatives, while avoiding overshoot caused by ordinary higher-order splines. For any interval between adjacent nodes... Define the normalized interval parameter

[0128] Define Hermite basis functions

[0129]

[0130] The continuous expression for the twist angle can then be written as:

[0131] in , The discrete node values ​​output by the preceding steps; and The twist angle at the node is about The derivative (slope) of the slope, and its calculation method, determines the smoothness of the interpolation and whether it overshoots. This embodiment provides a clear method for slope calculation: for internal nodes... First, calculate the slope of the secant line between adjacent intervals.

[0132] when and When all nodes have the same sign and are not zero, the slope of each node is used as the weighted harmonic mean to suppress overshoot:

[0133] when and When the sign is opposite or either is zero, to avoid local oscillations, the slope of this node is taken as...

[0134] The endpoint slope can be expressed using a first-order forward / backward difference: ,

[0135] The above slope rule can maintain smoothness in the monotonic variation range of nodes, and automatically flatten out nodes where there are inflection points or sign changes to avoid non-physical overshoot of the torsion angle.

[0136] The leading edge curvature radius sequence was processed in exactly the same way. Constructing continuous functions In the interval Inside, there is

[0137] in , for R LE about The nodal slope, calculated in the same way as Completely identical, just need to Replace with R LE If curvature is used in subsequent steps Expression, then, is obtained Then you can press Calculated.

[0138] To ensure the manufacturability of the continuous function, this step also involves explicit checking of the function's first rate of change and, optionally, amplitude limiting. Taking the torsion angle as an example, the torsional gradient along the lead edge in the spanwise direction can be obtained by differentiating the continuous function:

[0139] In the Hermite piecewise polynomial, this derivative can be obtained by applying the above equation... The derivative is obtained, or a numerical difference approximation is performed in a discrete implementation using subdivided sampling points. This is given if the maximum allowable torsional gradient is predetermined. (Units are degrees / normalized span or radians / normalized span, and...) (Units consistent), when a certain interval satisfies

[0140] This can be achieved by increasing the number of nodes. New Zealand For discrete nodes Slight smoothing (e.g., local moving average) is applied to satisfy the gradient constraint. The rate of change of the leading edge radius of curvature can be defined and checked similarly:

[0141] in The maximum allowable rate of change of radius of curvature can be set according to machining capabilities. Through the above checks, the continuous function is not only mathematically continuous, but also meets the machinability characteristics of not changing too drastically in engineering.

[0142] In obtaining continuous and Next, this step further describes the parameterization method for using it to generate the three-dimensional guide edge geometry. Specifically, the baseline of the rudder guide edge (the center line of the guide edge in the un-twisted state) is first defined as... ,in ; It can be given by the reference projection curve of the rudder blade shape at the guide edge, or taken in simplified implementation. , ( (This is the axial position constant at the guide plane), and the specific representation of this baseline is determined by the rudder blade shape. Subsequently, for each spanwise position... Define a local coordinate system for the guide edge within the local profile plane, with its normal along the axial direction. Tangential direction along the circumferential direction (or in the direction consistent with the chord direction of the rudder section). and with The rotation angle of the local direction of the guide edge relative to the reference direction represents the rotation angle of the guide edge. Then, the unit vector of the guide edge direction after twisting can be expressed as:

[0143] in To and An orthogonal unit vector within the profile plane (also determined by the rudder profile geometry). This direction vector allows the reference guide edge to be rotated in the spanwise direction to obtain the spatial orientation of the tortuous guide edge. Leading edge radius of curvature. The radius of the circle used to define the local leading edge arc controls the degree of roundness of the leading edge. Taking a local profile as an example, the curve of the leading edge on that profile can be approximated by a circular arc, whose curvature satisfies... The center position and endpoints of the arc are determined by the tangency condition between the arc and the rest of the rudder section, thus obtaining the leading edge profile geometry at that spanwise position. The leading edge curves of all spanwise positions are then... By connecting directions, a continuous three-dimensional guide surface can be formed.

[0144] Example 2 Based on the above method, this embodiment provides a corresponding twisted rudder guide edge design system. This system takes propeller wake flow field data as the core input and guide edge twist angle distribution function and leading edge curvature distribution function as the core output. It can complete wake feature identification, feature parameterization, geometric mapping, spanwise continuity and three-dimensional geometry generation under a unified data caliber, thereby obtaining a twisted rudder guide edge geometry scheme that matches the wake structure. It can be deployed as an independent software system at the design end, or used as a functional plug-in of a computational fluid dynamics platform or ship design platform.

[0145] like Figure 2As shown, the system includes a flow field data acquisition and management module, a data preprocessing and unification module, a multi-scale decomposition and feature region identification module, a wake feature parameter set construction module, a geometric parameter mapping generation module, a spanwise continuity and manufacturability assurance module, and a three-dimensional guide edge geometry generation and output module. The flow field data acquisition and management module receives or imports wake data from a reference plane under autonomous driving conditions. This data includes at least axial velocity components, circumferential velocity components, and related quantities reflecting unsteady fluctuations. It also manages and indexes data from different sources, with different sampling densities, or in different formats in a unified manner, ensuring that subsequent calculations can be performed under the same reference plane and the same coordinate definition. The data preprocessing and unification module performs denoising and outlier removal on the sampled data, interpolates and unifies or resamples the spatial grid, and performs phase alignment and reference frame correction on the time series, so that the axial and circumferential velocities are expressed in a consistent coordinate system, thereby forming a spatiotemporally aligned wake dataset, providing a stable data foundation for subsequent decomposition and identification.

[0146] The multi-scale decomposition and feature region identification module is used to decompose and analyze the wake data at radial, spanwise, and temporal scales to identify key feature regions in the wake field. At the radial scale, the module characterizes the non-uniformity of the axial inflow through radial statistics of the periodic average velocity field and identifies kinetic energy concentration sections based on the radial distribution of circumferential kinetic energy density, thus locking down the radial range where the leading-edge torsion amplitude should primarily play a role. At the spanwise scale, the module determines the dominant cyclonic region and its upper and lower boundaries based on the statistical mean of the circumferential average velocity in the spanwise layer and its sign variation, ensuring that the leading-edge torsion direction is consistent with the wake cyclonic properties. At the temporal scale, the module couples the pulsation intensity with the velocity gradient in the reference plane to construct a shear / wave sensitivity index and uses quantile thresholds to identify shear-sensitive regions, thereby suppressing or smoothing high-risk regions during the geometry generation stage. Based on the above identification results, the wake feature parameter set construction module parameterizes the rotation-dominant region, kinetic energy concentration region, and shear-sensitive region, forming a wake feature parameter set indexable by spanwise position. This provides a unified input interface for geometric mapping, avoiding the uninterpretability and instability caused by relying solely on empirical functions or single-index optimization.

[0147] The geometric parameter mapping generation module establishes a deterministic mapping relationship between wake characteristic parameters and guide edge geometric parameters, outputting a spanwise discrete sequence of the target twist angle and a spanwise discrete sequence of the leading edge curvature (or leading edge curvature radius). During the mapping process, this module simultaneously considers the determining effect of rotational properties on the twist direction, the driving effect of kinetic energy coverage on the twist amplitude, and the suppressive effect of shear / fluctuation risk on the amplitude. It also limits the twist angle within an allowable range through a truncation mechanism, ensuring that the guide edge twist effectively matches the wake structure while meeting design and manufacturing constraints. For the leading edge curvature, the module integrates the influence of inflow non-uniformity and shear sensitivity on local pressure distribution and separation tendency, outputting a leading edge curvature radius distribution that satisfies the manufacturable range, and further obtaining the leading edge curvature distribution to ensure a more robust geometry for the guide edge leading edge in high-gradient or high-risk regions.

[0148] The spanwise continuity and manufacturability assurance module is used to convert the aforementioned spanwise discrete sequence into a function expression that varies continuously along the spanwise direction of the rudder blade. This avoids local separation, pressure concentration, or processing discontinuities caused by abrupt changes in the twist angle or leading edge curvature in the spanwise direction. Based on the piecewise cubic Hermite interpolation concept, this module can construct at least one-order continuous interpolation curves, forming continuous distribution functions for the twist angle and leading edge curvature radius respectively. Overshoot is suppressed through controlled calculation of nodal derivatives, ensuring that the resulting continuous function is numerically smooth and engineering-feasible, thus guaranteeing the stable generation of the subsequent three-dimensional guide edge surface.

[0149] The 3D guide edge geometry generation and output module transforms the continuous torsion angle distribution function and leading edge curvature (or radius of curvature) distribution function into a parametric geometric description that can be used to generate 3D guide edge surfaces. This module first defines the spatial representation of the guide edge baseline in the untorsed state, establishes a local profile coordinate system at each spanwise position, and determines the rotation of the local guide edge direction relative to the baseline direction using the torsion angle, thus obtaining the spatial orientation of the torsioned guide edge. Simultaneously, the leading edge radius of curvature is used as the geometric control quantity for the local leading edge arc to determine the leading edge profile shape at that spanwise position. Then, the leading edge curves of the profiles at each spanwise position are connected along the spanwise direction to form a continuous 3D guide edge surface. The output can be a 3D geometric model, key parameter curves, or a geometric data file that can be used for subsequent CFD / structural evaluation, enabling the system to directly serve design closure and engineering delivery.

[0150] Through the collaborative work of the aforementioned modules, the system of this invention can transform the propeller wake from simulation results into input for guide edge design. Based on multi-scale feature recognition and parameterization, it generates the twist angle and leading edge curvature using a defined mapping function, and ensures geometric smoothness and manufacturability through spanwise continuity and parametric geometry generation, thereby achieving adaptive matching of the guide edge geometry to the wake structure. Compared to design methods that rely on experience-based selection or simple comparison, this system helps improve the interpretability and stability of design results, enhances the effectiveness of energy recovery, and suppresses geometric changes in regions with high shear / fluctuation risk, thereby reducing unsteady loads and local cavitation risks, and overall improving the engineering usability and reproducibility of the twisted rudder guide edge design.

[0151] The above system can execute the twisted rudder guide edge design method described in Embodiment 1, and has the corresponding functional modules and beneficial effects of the method. For technical details not described in detail in this embodiment, please refer to the twisted rudder guide edge design method provided in Embodiment 1 of the present invention.

[0152] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented using software plus a general-purpose hardware platform, or of course, using hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the related technology, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0153] 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; under the concept of the present invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the present invention as described above, which are not provided in detail for the sake of brevity; 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 scope of the technical solutions of the embodiments of this application.

Claims

1. A method for designing a twisted rudder guide edge, characterized in that, Includes the following steps: S1. Under propeller self-propulsion conditions, acquire propeller wake flow field data at a predetermined reference plane. The flow field data includes at least axial velocity components, circumferential velocity components, and time variation information corresponding to the velocity components. S2. Perform multi-scale decomposition on the flow field data, identify the characteristic regions of the wake field, and parameterize each characteristic region to form a set of wake characteristic parameters. The characteristic regions include the rotation-dominant region, the kinetic energy concentration region, and the shear-sensitive region. S3. Based on the set of wake characteristic parameters, construct a mapping relationship between the wake characteristic parameters and the geometric parameters of the twisted rudder guide edge. The geometric parameters include at least the guide edge twist angle parameter and the guide edge leading edge curvature parameter, so that the geometric parameters can change continuously with the spanwise position of the rudder blade. S4. Based on the mapping relationship, generate the guide edge torsion angle distribution function and the guide edge leading edge curvature distribution function that continuously change along the span of the rudder blade, thereby determining the geometric state of the twisted rudder guide edge at different span positions. S5. Output the torsion angle distribution function and the curvature distribution function of the leading edge as the final design result to construct the three-dimensional geometry of the torsion rudder guide edge, so as to achieve the matching design between the guide edge geometry and the propeller wake characteristics.

2. The twisted rudder guide edge design method as described in claim 1, characterized in that, Step S1 includes: A reference surface is set at a predetermined axial position downstream of the propeller axis. Timing sampling of the propeller wake is performed on the reference plane to obtain the axial velocity components of the wake at different radial and circumferential positions. and circumferential velocity components ,in, This indicates the position of the reference surface in the axial direction. r Represents the radial coordinates relative to the propeller axis. Represents the circumferential angle coordinates. t Indicates the sampling time; Over a complete propeller rotation cycle, the axial velocity component and the circumferential velocity component are statistically analyzed over time, and their periodic average values ​​are calculated. The periodic average axial velocity... and periodic average circumferential velocity satisfy: in, t 0 represents the starting point of the periodic statistics. T p The rotation period of the propeller; Based on the fluctuation of the axial velocity component within one propeller rotation cycle, the pulsation intensity of the wake axial velocity is calculated. It satisfies: in, A preset positive number used to avoid a denominator of zero; Thus on the reference plane The wake flow field data generated simultaneously includes the periodic average axial velocity, the periodic average circumferential velocity, and the intensity of axial velocity fluctuations.

3. The tortuous rudder guide edge design method as described in claim 2, characterized in that, The identification of the dominant rotation region in step S2 includes: Let the spanwise height of the rudder blade be H r Reference surface The spanwise coordinates within the rudder blade projection range are as follows: z And define the spanwise normalized coordinates as , The coordinates are the lower boundary coordinates of the rudder blade's spanwise range; on the reference plane. Establish a discrete sampling point set , Indicates radial sampling coordinates, This represents the circumferential sampling angle coordinates, and maps each sampling point to the rudder blade spanwise coordinates. z Corresponding normalized span coordinates This establishes a one-to-one correspondence between the reference surface sampling points and the spanwise position of the rudder blade; For any spanwise position Select the set of sampling points on the reference plane corresponding to the spanwise position. And calculate the periodic average circumferential velocity in the set of sampling points. The spanning statistical mean: in, Represents the set of sampling points The arithmetic mean of all sampling points within the sample is calculated. Based on the aforementioned spanning statistical mean The sign determines the direction of rotation attribute, when When the spanwise position is determined to be in the positive rotation zone, The region is determined to be in the reverse rotation region; to avoid sign noise interference in the weak rotation region, a rotation intensity threshold coefficient is introduced. ,when Only then is the spanwise layer identified as the dominant spiral layer. This represents the maximum value of the global periodic average circumferential velocity amplitude over the reference surface. The spanwise positions that simultaneously satisfy both the spin direction determination condition and the spin intensity threshold condition are set together and defined as the spin dominance region. The upper and lower boundary intervals of the spin dominance region in the rudder blade spanwise direction are determined by the minimum and maximum spanwise coordinates corresponding to the set.

4. The twisted rudder guide edge design method as described in claim 3, characterized in that, The identification of the kinetic energy concentration region in step S2 includes: For the radial position on the reference plane, the periodic average circumferential velocity By statistical averaging along the circumferential angular direction, the characteristic quantity of radial circumferential kinetic energy density is defined as: in, Indicates a fixed radial coordinate r The circumferential arithmetic mean under the given conditions; For radially normalized coordinates, The radius of the propeller; The radial circumferential kinetic energy density characteristic quantity is applied across the entire radial position range. Compare and determine its maximum value. Introducing a proportional threshold coefficient ,when When this condition is met, the radial segment is determined to be the kinetic energy concentration radial zone. All radial positions that meet this condition are collected and formed into radially continuous or discrete kinetic energy concentration segments. The region corresponding to this radial segment on the reference plane is defined as the kinetic energy concentration region, which is used to characterize the main distribution location of recoverable circumferential kinetic energy in the propeller wake.

5. The tortuous rudder guide edge design method as described in claim 4, characterized in that, The identification of the shear-sensitive region in step S2 includes: First, construct a shear / fluctuation sensitivity index: in, Indicates the intensity of axial velocity fluctuations on the reference surface; This represents the periodic average axial velocity. This represents a two-dimensional gradient operator defined within the reference plane. ; Under discrete sampling conditions, the radial partial derivative of the periodically averaged axial velocity is approximated using the central difference method: The circumferential partial derivative of the periodically average axial velocity is approximated using the angular central difference method: in, Indicates the first i Coordinates of radial sampling points, Indicates the first j One circumferential sampling angle; Based on the aforementioned radial and circumferential partial derivatives, the magnitude of the periodic average axial velocity gradient within the reference plane is calculated as follows: This leads to the shear / fluctuation sensitivity index corresponding to each sampling point on the reference surface. ; Within the entire sampling range of the reference surface, the statistical distribution of the shear / fluctuation sensitivity index is analyzed, and the values ​​corresponding to all sampling points are... Sort the values ​​and select the quantiles. q Statistical values Q q When a certain sampling point satisfies When the sampling point is determined to be a shear-sensitive point, all sampling points that meet this condition are aggregated on the reference surface and defined as shear-sensitive regions, which are used to characterize the regions in the propeller wake that are more sensitive to rudder pressure fluctuations, local cavitation and vibration response under the combined action of velocity fluctuations and velocity gradients.

6. The twisted rudder guide edge design method as described in claim 5, characterized in that, Step S3 includes: Normalized coordinates of rudder blade span As the independent variable, construct the guide twist angle parameter. The continuous mapping relationship of the extension direction, For the first m The spanwise coordinates of the rudder blades corresponding to each spanwise discrete layer To ensure that the direction of the guide edge twist is consistent with the directional attribute of the dominant rotation region, at each spanwise position... At this point, a rotation sign function is introduced. ,in, It is a sign function used to characterize the positive or negative property of a numerical value; For exhibition location The spanwise statistical mean of the periodic average circumferential velocity; when When indicates a positive reversal, when Time indicates reverse twisting; After determining the torsion direction, the amplitude of the guide torsion angle is designed to be determined by the rotational strength characteristic quantity. Kinetic energy coverage characteristic quantity and risk suppression characteristic quantity Driven by the same factors, the spanwise continuous mapping relationship of the guide edge target twist angle is constructed as follows: in, For exhibition location The target twist angle at the guide edge, The maximum allowable torsional angle amplitude; exponential parameter p , q , s It is a non-negative real number used to adjust the sensitivity of the rotation strength characteristic, kinetic energy coverage characteristic, and risk suppression characteristic to the guide twist angle; Let be the truncation function, indicating that when Time to take a ,when Time to take b Otherwise take x ; Through the above mapping relationship, the torsion angle of the guide edge is continuously varied in the spanwise direction of the rudder blade, and the torsion effect is enhanced in the region where the rotation direction is dominant and the kinetic energy is concentrated. In the region where the risk of shearing or pulsation is high, the torsion amplitude is suppressed, thereby obtaining a torsion distribution of the rudder guide edge that is adapted to the structural characteristics of the propeller wake.

7. The tortuous rudder guide edge design method as described in claim 6, characterized in that, Step S3 includes: First, we construct an index for the degree of non-uniformity of spanwise inflow: in, This is the global maximum value of the periodic average axial velocity gradient magnitude within the reference plane; To prevent extremely small positive numbers with a denominator of zero; Based on this, the target distribution of the leading edge curvature is designed to be determined by the inflow non-uniformity index. Risk suppression characteristic Adjust together, and use the leading edge curvature radius. As an intermediate variable, the spanwise continuous mapping relationship of the radius of curvature of the leading edge is defined as follows: in, w 1. w 2 is a non-negative weighting coefficient used to characterize the relative contribution of inflow nonuniformity and shear sensitivity to the leading edge passivation requirement; Indicates the permissible range of leading edge curvature radius; Based on the aforementioned leading edge curvature radius The curvature parameter of the leading edge is determined as follows: ; This allows the leading edge curvature parameter to change continuously in the spanwise direction of the rudder blade, and automatically increases the degree of leading edge passivation in areas with strong inflow gradients or high risk of shear / pulsation, while maintaining a small curvature change in non-sensitive areas, so as to obtain a leading edge geometric distribution that is compatible with the propeller wake structure and local pressure distribution characteristics.

8. The tortuous rudder guide edge design method as described in claim 7, characterized in that, Step S4 includes: In obtaining the spanwise discrete sequence of the target twist angle of the guide edge and the spanwise discrete sequence of the radius of curvature of the leading edge back, N z To determine the total number of spanwise discrete layers, the discrete sequence is converted into a continuously varying guide edge twist angle distribution function and a guide edge leading edge curvature distribution function along the span of the rudder blade. This process includes: Distribution function of twist angle of the guide side and the distribution function of the radius of curvature of the leading edge The interpolation is constructed using a piecewise cubic Hermite interpolation function, within each adjacent spanning node interval. Internally respectively to and Construct a piecewise cubic polynomial such that the function values ​​are continuous and the first derivative is continuous; In any adjacent node interval Define the normalized interval parameters. Define Hermite basis functions as Therefore, the distribution function of the leading edge twist angle within the specified interval is expressed as: in, , The discrete values ​​of the guide twist angle at adjacent spanwise nodes; and They are nodes and The first derivative of the twist angle of the leading edge with respect to the spanwise coordinates; Similarly, the discrete sequence of the leading edge curvature radius is processed. Construct a spanwise continuous radius of curvature distribution function and further by Determine the curvature distribution function of the leading edge. This represents the geometric curvature of the leading edge at the corresponding spanwise position.

9. The tortuous rudder guide edge design method as described in claim 8, characterized in that, Step S5 includes: The guide twist angle distribution function that varies continuously along the rudder blade span is obtained. Distribution function of radius of curvature of the leading edge Then, a spatial description for constructing the 3D twisted rudder guide edge geometry is generated using a parametric approach: First, define the guide edge baseline under the condition of no torsion. The baseline is used to characterize the spatial position of the guide edge along the spanwise direction of the rudder blade in the untorsed state, and its parameterized expression is as follows: ,in, , Determined by the reference projection curve of the rudder blade shape at the guide edge; Subsequently, at any spanning position At this point, a local coordinate system is established within the local profile plane, and its normal unit vector is defined as follows: The tangential unit vector is defined as , Consistent with the chordal direction of the rudder blade profile, and and Orthogonal in the plane of the cross section; Using the aforementioned guide edge torsion angle distribution function The rotation angle representing the local direction of the guide edge relative to the reference direction is then the unit vector of the guide edge direction after the torsion is applied. Expressed as Based on this, the distribution function of the radius of curvature of the leading edge is used. Define the geometric arc shape of the leading edge in a local section, where the curvature of the leading edge satisfies The curvature is used to control the degree of passivation of the leading edge at the corresponding spanwise position; in the local profile, the leading edge of the guide edge is approximately represented by a radius of... The circular arc curve is obtained, and the center position and the endpoint of the circular arc are determined according to the geometric continuity condition of the circular arc and the rest of the rudder blade section, so as to obtain the geometry of the leading edge section front edge at the spanwise position. By each orientation position Torsion direction vector Determine the direction, and determine it based on the radius of curvature of the leading edge. The leading edge curve of the guide edge profile with a local circular arc shape is determined and connected along the spanwise direction of the rudder blade to form a continuous three-dimensional twisted rudder guide edge surface, thereby determining the spatial geometry of the guide edge that matches the wake characteristics at different spanwise positions.

10. A twisted rudder guide edge design system based on the method of any one of claims 1 to 9, characterized in that, The system includes the following modules: The flow field data acquisition and management module is used to acquire or import propeller wake flow field data under self-propelled conditions. The flow field data includes at least the axial velocity component, circumferential velocity component and related data characterizing the intensity of unsteady pulsations on the reference plane. It also manages flow field data from different sources or with different sampling densities in a unified manner to ensure that subsequent processing is carried out under a consistent spatial reference and coordinate definition. The data preprocessing and unification module is used to preprocess the flow field data, including denoising and outlier removal of the sampled data, interpolation unification or resampling of the spatial sampling grid, phase alignment of the time series, and reference system correction of the velocity components, so that the axial velocity components and the circumferential velocity components are expressed in the same coordinate system, thereby forming a spatiotemporally aligned wake dataset. The multi-scale decomposition and feature region identification module is used to perform radial scale decomposition, spanwise scale decomposition and time scale decomposition on the wake data after the uniformization process. It identifies the degree of axial inflow non-uniformity and circumferential kinetic energy distribution characteristics through radial statistics, identifies the wake vortex-dominant region and its boundary through spanwise statistics, and identifies the shear-sensitive region through the coupling of pulsation intensity and velocity gradient, thereby obtaining the vortex-dominant region, kinetic energy concentration region and shear-sensitive region. The wake feature parameter set construction module is used to parameterize the rotation-dominant region, kinetic energy concentration region and shear-sensitive region to form a wake feature parameter set that can be indexed by spanwise position, which can be used as input for generating guide edge geometry parameters; The geometric parameter mapping generation module is used to establish a mapping relationship between the wake characteristic parameters and the guide edge geometric parameters based on the wake characteristic parameter set, generate the spanwise discrete distribution of the guide edge target twist angle and the spanwise discrete distribution of the guide edge leading edge curvature or leading edge curvature radius, and apply allowable range constraints to the twist angle amplitude. The spanwise continuity and manufacturability assurance module is used to convert the spanwise discrete distribution of the target twist angle and leading edge curvature or leading edge curvature radius of the guide edge into a function expression that changes continuously along the spanwise direction of the rudder blade, so as to ensure the continuity and smoothness of the guide edge geometric parameters in the spanwise direction and avoid abrupt changes in geometric parameters. The three-dimensional guide edge geometry generation module is used to construct the guide edge baseline based on the continuous guide edge torsion angle distribution function and the leading edge curvature or leading edge curvature radius distribution function, and to determine the spatial torsion direction and leading edge geometry of the guide edge at each spanwise position. The guide edge profiles at each spanwise position are connected along the spanwise direction to generate a continuous three-dimensional twisted rudder guide edge geometry model.

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