Construction method of trailing vortex mode and fluid force forecasting model of rudder wing structure

Abstract

The invention discloses a method for constructing a trailing vortex mode and fluid force forecasting model of a rudder wing structure. The method comprises the following steps: establishing a two-dimensional rudder wing physical model; defining boundary conditions of an external flow field of the model, determining a grid size and performing grid division; setting fluid parameters, boundary conditions and solving parameters, wherein the solving parameters comprise a turbulence model, solving precision, a time step length and a total grid number; comparing, analyzing and selecting an optimal turbulence model, and performing time step independence verification and grid independence check on the selected numerical value; calculating the optimal turbulence model, drawing a plurality of rudder wing trailing vortex shedding cloud charts and fluid force coefficient curve charts under different conditions, analyzing a trailing vortex shedding structure, carrying out vortex shedding mode definition on the trailing vortex structure, calculating lift-drag coefficient root-mean-square values of incoming flow velocities under different attack angles, and calculating the optimal turbulence model; and establishing a trailing vortex shedding mode forecasting model and a fluid force forecasting model of the rudder wing. According to the method, the rudder wing trailing vortex shedding mode and the fluid force under different incoming flow velocities and different attack angles can be quickly forecasted.

Description

Technical Field

[0001] The present invention relates to the technical field of rudder wing structure model prediction, and in particular to a method for constructing a rudder wing structure tail vortex mode and fluid force prediction model. Background Art

[0002] When the fluid flows around the rudder, the slight difference in fluid velocity on both sides of the rudder causes a pressure difference on both sides of the tail of the rudder, causing the two sides of the tail of the rudder to shed double-row vortices with opposite rotation directions and periodic arrangement. Different incoming flow speeds and rudder attack angles will affect the shedding frequency and intensity of the rudder tail vortex. At present, the research on the shedding of rudder tail vortex and fluid force prediction is relatively small and complex. In order to quickly predict the shedding of complex rudder tail vortex and the magnitude of fluid force under different incoming flow speeds and different attack angles, it is necessary to establish a method for constructing a rudder tail vortex pattern and fluid force prediction model. Summary of the invention

[0003] The main purpose of the present invention is to propose a method for constructing a rudder wing structure wake vortex pattern and fluid force prediction model. By establishing a two-dimensional rudder wing physical model, and then comparing and analyzing the selected turbulence model, time step value and grid independence, the laws of rudder wing wake vortex shedding and lift and drag coefficients under different working conditions are analyzed through simulation calculation. Finally, a model prediction of the rudder wing structure's wake vortex shedding and fluid force (including lift and drag) is obtained, so as to quickly predict the rudder wing wake vortex shedding pattern and fluid force size under different incoming flow velocities and different attack angles.

[0004] The technical solution adopted by the present invention is:

[0005] A method for constructing a rudder wing structure wake vortex mode and fluid force prediction model, comprising:

[0006] S1, establishing a two-dimensional rudder wing physical model to be calculated;

[0007] S2. Clarify the external flow field boundary conditions of the calculation model, determine the grid size and perform grid division; generate a grid file and import the grid into the fluid calculation software;

[0008] S3. Setting fluid parameters, boundary conditions and solution parameters in the fluid calculation software, wherein the setting of solution parameters includes: turbulence model, solution accuracy, time step and total number of grids. In order to ensure the accuracy of the calculation results, multiple different turbulence models are set;

[0009] S4. Solve the flow field, draw the rudder wing wake vortex shedding cloud diagram and the rudder wing lift and drag coefficient curve diagram under different turbulence models, and select the most suitable turbulence model by comparative analysis;

[0010] S5, respectively perform time step independence verification and grid independence check on the selected time step and total number of grids. If the results meet the calculation requirements, proceed to the next step of calculation; otherwise, return to step S3 and select a suitable time step or total number of grids to recalculate;

[0011] S6. Calculate the vortex shedding data and lift-drag coefficient data of the rudder wing at different incoming flow speeds and different attack angles in the fluid calculation software, and draw a vortex shedding cloud diagram of the rudder wing and a lift-drag coefficient curve diagram;

[0012] S7, defining the vortex shedding mode according to the vortex shedding structure of the rudder wing under different attack angles at various incoming flow speeds in the vortex shedding cloud map, integrating the vortex shedding mode of the rudder wing under different attack angles at various incoming flow speeds, and establishing a rudder wing vortex shedding prediction model with the attack angle as the x-axis and the incoming flow speed as the y-axis;

[0013] The lift and drag coefficients of a stable wake of the rudder wing at different attack angles at various incoming flow speeds are selected, the root mean square value of the lift and drag coefficient at various incoming flow speeds is calculated, and a fluid force prediction model with the attack angle as the x-axis and the root mean square value of the lift and drag coefficient as the y-axis is established.

[0014] In the above scheme, the ICEM CFD software is used to establish the two-dimensional rudder wing physical model to be calculated and to divide the mesh; a rudder wing with a chord length of b is placed in the incoming flow, and its surface is set as a no-slip wall; the left side of the rudder wing is the incoming flow boundary, the upper and lower boundaries of the flow field are symmetrical walls, and the right side of the rudder wing is the outlet boundary; the body-fitting grid part is generated using the "O-block" strategy in the ICEM software, and the outer flow field area uses a quadrilateral structured grid setting.

[0015] In the above scheme, in step S3, four turbulence models are selected, namely, LES model, DES model, Realizable ke model and SST k-Ω model, and the boundary conditions set for each turbulence model are the same.

[0016] In the above scheme, in step S4, a curve diagram of the change of lift-drag coefficient with time under different turbulence models is obtained by calculation, and the change of lift-drag coefficient curve of each turbulence model is compared and analyzed, and a turbulence model with obvious periodic change of lift-drag coefficient is selected; then, a rudder wing wake vortex shedding cloud diagram of the turbulence model is calculated and drawn, and the wake vortex shedding mode is compared and analyzed, and the vortex with regular and alternating arrangement at the wake shedding is selected as the most suitable turbulence model.

[0017] In the above scheme, in step S5, the time step independence of the selected time step is verified. The specific method is: multiple time steps under the same incoming flow velocity and angle of attack are selected for verification, and the vortex shedding frequency of the rudder at each time step is extracted. If the vortex shedding frequency shows a stable trend, the calculation requirements are met.

[0018] In the above scheme, in step S5, a grid independence check is performed on the total number of grids. The specific method is: use multiple rudder wing models with the same total number of grids under the same incoming flow velocity and angle of attack to perform calculations, analyze the relative errors between the Strouhal numbers St or the drag mean Cd of different rudder wing grid models, and if the relative error between the results of adjacent total number of grids is within 4%, the calculation requirements are met.

[0019] In the above scheme, in step S6, the vortex shedding data is plotted using Tecplot software to plot vortex shedding cloud diagrams for each incoming flow velocity at different attack angles.

[0020] In the above scheme, in step S6, Origin software is used to draw a lift-drag coefficient curve graph for the lift-drag coefficient data.

[0021] In the above scheme, in step S7, the defined wake vortex shedding modes include 2S mode, 2S+U mode, U+2S mode, T+S mode and 2P mode; the 2S mode is that the wake presents a positive and negative vortex structure that is periodically and alternately shed; the 2S+U mode is that the wake first has alternating positive and negative vortices, and as the vortices continue to develop, it finally turns into a stable wake structure; the U+2S mode is that the wake first maintains a stable wake structure for a period of time, and then alternately has positive and negative vortex structures; the T+S mode is that three vortices are shed from the upper side of the rudder wing, which are respectively negative positive and negative vortices, and then an alternating positive and negative vortex structure appears; the 2P mode is that two pairs of positive and negative vortices are shed from the upper side of the rudder wing.

[0022] The beneficial effects produced by the present invention are:

[0023] The present invention is based on the commercial software Ansys / Fluent, takes the vortex shedding situation and fluid force size of the rudder wing at different incoming flow speeds and different angles of attack as the research background, and constructs the vortex shedding mode and fluid force prediction model of the rudder wing. A more suitable turbulence model is selected through comparative analysis, and the selected numerical value is verified for time step independence and grid independence to ensure the accuracy and reliability of the subsequent calculation results. Then the most suitable turbulence model is calculated, and the vortex shedding cloud map and fluid force coefficient curve map of the rudder wing under multiple different conditions are drawn, the vortex shedding structure under different conditions is analyzed, and the vortex shedding mode is defined for the vortex structure, and then the root mean square value of the lift and drag coefficient at different angles of attack of each incoming flow speed is calculated, and finally the vortex shedding mode prediction model and fluid force prediction model of the rudder wing are established. Compared with the prior art, the method for constructing a rudder-wing structure wake vortex pattern and fluid force prediction model provided by the present invention can quickly and accurately predict the rudder-wing wake vortex shedding and lift-drag coefficient size under different incoming flow velocities and different attack angles, providing a guiding basis for the analysis of the rudder-wing structure's wake vortex shedding and fluid force size under different conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0025] Figure 1 It is a flow chart of the method for constructing the tail vortex mode and fluid force prediction model of the rudder wing structure of the present invention;

[0026] Figure 2 Schematic diagram of the calculation domain and boundary conditions of a two-dimensional rudder wing in an embodiment of the present invention;

[0027] Figure 3 The cloud diagram of the vortex shedding of the rudder wing at different attack angles and different incoming flow velocities in the embodiment of the present invention;

[0028] Figure 4 The lift-drag coefficient curve diagram of the rudder wing at different incoming flow speeds at different attack angles in the embodiment of the present invention;

[0029] Figure 5 : The vortex shedding modes of the rudder wing at different attack angles when U=1m / s in the embodiment of the present invention;

[0030] Figure 6 This is a prediction diagram of the vortex shedding mode of the rudder wing at different attack angles and different incoming flow velocities in an embodiment of the present invention;

[0031] Figure 7 It is a prediction diagram of the lift and drag coefficient root mean square of the rudder wing at different attack angles and different incoming flow velocities in an embodiment of the present invention. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0033] It should be noted that the illustrations provided in the embodiments of the present invention are only used to illustrate the basic concept of the present invention in a schematic manner. Therefore, the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout type may also be more complicated.

[0034] In the present invention, it is also necessary to explain that, if the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. appear, the orientation or position relationship indicated is based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. In addition, if the terms "first" and "second" appear, they are only used for description and distinction purposes, and cannot be understood as indicating or implying relative importance.

[0035] like Figure 1 As shown, it is a flow chart of the method for constructing the vortex pattern and fluid force prediction model of the rudder wing structure proposed by the present invention. The specific implementation method of the present invention is described below by taking the two-dimensional rudder wing flow in a turbulent flow field as an example, which includes the following steps:

[0036] S1. Establish a two-dimensional rudder wing physical model. ICEM CFD software is used to establish a two-dimensional numerical model of the rudder wing at different attack angles α (0°, 0.5°, 1°, 1.5°, 2°), that is, a near-wall rudder wing flow model.

[0037] S2. Set the external flow field boundary conditions: Figure 2 As shown in the figure, the rudder wing surface is set as a non-slip wall; the left side of the rudder wing (Inlet) is the incoming flow boundary with a radius of 14b, b is the chord length of the rudder wing, and the upper and lower boundaries of the flow field (Wall) are symmetrical walls with a uniform distance of 14b from the rudder wing; the right side of the rudder wing (Outlet) is the outlet boundary with a distance of 21b from the rudder wing. The body-fitting mesh part is generated using the "O-block" strategy in the ICEM software, and the outer flow field area uses a quadrilateral structured mesh setting to determine the mesh size and perform mesh division. Generate a boundary layer mesh on the rudder wing wall; generate a mesh file and import it into the Fluent software.

[0038] S3. In Fluent software, set each boundary condition as follows: the left boundary condition is velocity-inlet; the right boundary condition is pressure-out; the upper and lower side (wall) boundary conditions are symmetry boundaries; the rudder wing surface is a no-slip wall. The fluid medium in the flow field is water. At room temperature, the density of water is ρ=998.2kg / m3, and the kinematic viscosity of water is υ=1.004×10-6m2 / s. In order to ensure the accuracy of the calculation results, a more appropriate turbulence model needs to be selected. This embodiment sets four turbulence models, namely LES model, DES model, Realizable ke model and SST k-Ω model, and the boundary conditions set for each turbulence model are the same. The solution accuracy is set to 0.00001; the time step is set to 0.0005s; and the total number of grids is set to 150,000.

[0039] S4. In order to obtain a more suitable turbulence model, a comparative analysis is performed by numerical simulation calculations of four models, namely, the LES model, the DES model, the Realizable ke model and the SST k-Ω model. The incoming flow velocity of the four turbulence models is uniformly set to U=1m / s, and the angle of attack is set to α=0°. In this embodiment, the lift coefficient curve time history diagram of different turbulence models is first calculated, and it is found that the lift coefficient calculated by the rudder wing using the SST k-Ω model and the Realizable ke model does not change significantly, so it does not meet the calculation requirements, and when the DES model and the LES model are used for calculation, the lift coefficient has obvious periodic changes; then the tail vortex shedding cloud map of the DES model and the LES model is calculated, and it is found that the DES model is used to shed regular, alternating vortices in the wake, while the LES model is used to shed complex and fragmented small vortices, so the DES model is the most suitable turbulence model.

[0040] S5. In order to determine a more appropriate time step, the incoming flow velocity is set to 1m / s, the angle of attack is set to α=0°, and four time steps of 0.005s, 0.001s, 0.0005s, and 0.0002s are selected for verification. The vortex shedding frequency of the rudder wing at each time step is extracted for comparison. The results show that starting from the time step of 0.001s, the vortex shedding frequency gradually becomes stable. To ensure the accuracy of the results, 0.0005s is finally selected as the time step for this calculation.

[0041] In order to verify the rationality of the total number of grids, multiple first-layer grid heights are selected near the first-layer boundary layer grid height of 0.02mm, namely (0.005mm, 0.01mm, 0.02mm, 0.03mm, and 0.035mm), so that rudder-wing grid models with different total numbers of grids appear. The incoming flow velocity is set to 1m / s, and the angle of attack is set to α=0°. The difference between the Strouhal number St or the mean drag Cd of different rudder-wing grid models is calculated and analyzed. The relative errors of the Strouhal number St and the mean drag Cd between the adjacent grid total number results of 0.02mm and 0.03mm in the first-layer boundary layer grid are 1% and 2%, respectively. Therefore, the rudder-wing grid model with a first-layer boundary layer grid height of 0.02mm and a total number of grids of 150,000 meets the calculation requirements.

[0042] S6. In order to study the vortex shedding of the rudder wake under different incoming flow velocities U and different attack angles α, this embodiment sets 4 incoming flow velocities U (0.5m / s, 1m / s, 1.5m / s, 2m / s) and 5 attack angles α (0°, 0.5°, 1°, 1.5°, 2°) for calculation. Then, according to the vortex shedding data calculated by the rudder under various conditions, the vortex shedding cloud diagram of each incoming flow velocity at different attack angles is drawn using Tecplot software, as shown in FIG. Figure 3 As shown, in the tail vortex shedding cloud diagram, the blue vortex is a positive vortex and the red vortex is a negative vortex.

[0043] In order to study the fluid force of the rudder wing under different incoming flow velocities U and different attack angles α, the lift-drag coefficient curve was drawn using Origin software based on the lift-drag coefficient data calculated under various conditions, as shown in Figure 2. Figure 4 As shown, Cl is the lift coefficient and Cd is the drag coefficient.

[0044] S7. In the wake vortex shedding cloud diagram, the wake vortex shedding mode is defined according to the wake vortex shedding structure of the rudder blade under different attack angle conditions at various incoming flow speeds, such as Figure 5 As shown in the figure, the blue is the positive vortex, and the red is the negative vortex. The defined wake vortex shedding modes include 2S mode, 2S+U mode, U+2S mode, T+S mode and 2P mode. Among them: 2S mode is a wake flow that presents a positive and negative vortex structure that sheds periodically and alternately; 2S+U mode is a wake flow that first alternately appears positive and negative vortices, and with the continuous development of the vortex, it finally transforms into a stable wake structure; U+2S mode is a wake flow that first maintains a stable wake structure, and then alternately appears positive and negative vortex structures; T+S mode is a wake flow that sheds three vortices on the upper side of the rudder wing, which are respectively negative positive and negative vortices, and then an alternating positive and negative vortex structure appears; 2P mode is a wake flow that sheds two pairs of positive and negative vortices on the upper side of the rudder wing. Based on the wake vortex shedding modes of the rudder wing at different attack angles at various incoming flow velocities, a rudder wing wake vortex shedding prediction model with the attack angle as the x-axis and the incoming flow velocity as the y-axis is established, as shown in Figure 6As shown, the tail vortex shedding mode of the rudder wing is predicted when the incoming flow velocity is 0-2m / s and the attack angle is 0-20°.

[0045] The lift and drag coefficients of a stable wake of the rudder wing at different attack angles at various incoming flow speeds are selected, the root mean square value of the lift and drag coefficients at various incoming flow speeds is calculated, and a fluid force prediction model with the attack angle as the x-axis and the root mean square value of the lift and drag coefficient as the y-axis is established, as shown in Figure 7 As shown in the figure, Cl RMS is the root mean square of the lift coefficient, Cd RMS The root mean square value of the lift and drag coefficient of the rudder wing is predicted when the incoming flow velocity is 0-2m / s and the attack angle is 0-20°.

[0046] In this embodiment, four turbulence models are compared and analyzed. To ensure the accuracy and reliability of the calculation results, the time step and the total number of grids are verified and checked. Then, a more suitable turbulence model is selected from the four turbulence models for calculation, and cloud maps of rudder wing wake vortex shedding and fluid force coefficient curves under multiple different conditions are plotted. The wake vortex shedding structure under different conditions is analyzed, and the vortex shedding mode of the wake vortex structure is defined. Then, the root mean square value of the lift and drag coefficient at each incoming flow velocity at different angles of attack is calculated. Finally, a wake vortex shedding mode prediction model and a fluid force prediction model of the rudder wing are established.

[0047] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, and two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0048] The order of execution of each step in the above embodiment does not mean the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment of the present application.

[0049] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A method for constructing a rudder wing structure wake vortex mode and fluid force prediction model, characterized in that: include: S1, establishing a two-dimensional rudder wing physical model to be calculated; S2. Clarify the external flow field boundary conditions of the calculation model, determine the grid size and perform grid division; Generate a mesh file and import the mesh into the fluid calculation software; S3. Setting fluid parameters, boundary conditions and solution parameters in the fluid calculation software, wherein the setting of solution parameters includes: turbulence model, solution accuracy, time step and total number of grids. In order to ensure the accuracy of the calculation results, multiple different turbulence models are set; S4. Solve the flow field, draw the rudder wing wake vortex shedding cloud diagram and rudder wing lift and drag coefficient curve diagram under different turbulence models, and select the most suitable turbulence model by comparative analysis; S5, respectively perform time step independence verification and grid independence check on the selected time step and total number of grids. If the results meet the calculation requirements, proceed to the next step of calculation; otherwise, return to step S3 and select a suitable time step or total number of grids to recalculate; S6. Calculate the vortex shedding data and lift-drag coefficient data of the rudder wing at different incoming flow speeds and different attack angles in the fluid calculation software, and draw a vortex shedding cloud diagram of the rudder wing and a lift-drag coefficient curve diagram; S7, defining the vortex shedding mode according to the vortex shedding structure of the rudder wing under different attack angles at various incoming flow speeds in the vortex shedding cloud map, integrating the vortex shedding mode of the rudder wing under different attack angles at various incoming flow speeds, and establishing a rudder wing vortex shedding prediction model with the attack angle as the x-axis and the incoming flow speed as the y-axis; The lift and drag coefficients of a stable wake of the rudder wing at different attack angles at various incoming flow speeds are selected, the root mean square value of the lift and drag coefficient at various incoming flow speeds is calculated, and a fluid force prediction model with the attack angle as the x-axis and the root mean square value of the lift and drag coefficient as the y-axis is established.

2. The method for constructing the rudder wing structure wake vortex mode and fluid force prediction model according to claim 1, characterized in that: The ICEM CFD software is used to establish the two-dimensional rudder wing physical model to be calculated and to divide the mesh. A rudder wing with a chord length of b is placed in the incoming flow, and its surface is set as a no-slip wall. The left side of the rudder wing is the incoming flow boundary, the upper and lower boundaries of the flow field are symmetrical walls, and the right side of the rudder wing is the outlet boundary. The body-fitting grid part is generated using the "O-block" strategy in the ICEM software, and the outer flow field area adopts a quadrilateral structured grid setting.

3. The method for constructing a rudder wing structure wake vortex mode and fluid force prediction model according to claim 1, characterized in that: In step S3, four turbulence models are selected, namely, LES model, DES model, Realizable ke model and SSTk-Ω model, and the boundary conditions set for each turbulence model are the same.

4. The method for constructing a rudder wing structure wake vortex mode and fluid force prediction model according to claim 1, characterized in that: In step S4, a curve diagram of the lift-drag coefficient variation with time under different turbulence models is obtained by calculation, and the lift-drag coefficient curve variation of each turbulence model is compared and analyzed, and a turbulence model with obvious periodic variation of the lift-drag coefficient is selected; then, a rudder wing wake vortex shedding cloud diagram of the turbulence model is calculated and drawn, and the wake vortex shedding mode is compared and analyzed, and the vortex with regular and alternating arrangement at the wake shedding is selected as the most suitable turbulence model.

5. The method for constructing a rudder wing structure wake vortex mode and fluid force prediction model according to claim 1, characterized in that: In step S5, the time step independence of the selected time step is verified. The specific method is: multiple time steps under the same incoming flow velocity and angle of attack are selected for verification, and the vortex shedding frequency of the rudder at each time step is extracted. If the vortex shedding frequency shows a stable trend, the calculation requirements are met.

6. The method for constructing a rudder wing structure wake vortex mode and fluid force prediction model according to claim 1, characterized in that: In step S5, a grid independence check is performed on the total number of grids. The specific method is: use multiple rudder wing models with the same total number of grids under the same incoming flow velocity and angle of attack to perform calculations, analyze the relative errors between the Strouhal numbers St or the drag mean Cd of different rudder wing grid models, and if the relative errors between the results of adjacent total number of grids are within 4%, the calculation requirements are met.

7. The method for constructing a rudder wing structure wake vortex mode and fluid force prediction model according to claim 1, characterized in that: In step S6, the vortex shedding data is plotted using Tecplot software to plot vortex shedding cloud diagrams for each incoming flow velocity at different attack angles.

8. The method for constructing a rudder wing structure wake vortex mode and fluid force prediction model according to claim 1, characterized in that: In step S6, the lift-drag coefficient curve is drawn based on the lift-drag coefficient data using Origin software.

9. The method for constructing a rudder wing structure wake vortex mode and fluid force prediction model according to claim 1, characterized in that: In step S7, the defined wake vortex shedding modes include 2S mode, 2S+U mode, U+2S mode, T+S mode and 2P mode; the 2S mode is a wake flow presenting a positive and negative vortex structure that is periodically and alternately shed; the 2S+U mode is a wake flow in which positive and negative vortices first appear alternately, and as the vortices continue to develop, they are finally transformed into a stable wake flow structure; the U+2S mode is a wake flow that first maintains a stable wake flow structure, and then positive and negative vortex structures appear alternately; the T+S mode is a wake flow in which three vortices are shed from the upper side of the rudder wing, which are respectively negative positive and negative vortices, and then an alternating positive and negative vortex structure appears; the 2P mode is a wake flow in which two pairs of positive and negative vortices are shed from the upper side of the rudder wing.

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