Model design method and unsteady aerodynamic modeling method for folded rudder supersonic wind tunnel test under large obstruction conditions

Abstract

The invention relates to a model design method and an unsteady aerodynamic modeling method for a folding rudder under large blockage conditions in a supersonic wind tunnel test, and belongs to the technical field of wind tunnel test modeling. In order to improve the simulation accuracy of the unsteady aerodynamic force of the folding rudder deployment, the invention includes designing a folding rudder carrier model in a diamond-shaped area of ​​the test section; designing the head shock wave angle of the folding rudder carrier model; and controlling the local flow field of the folding rudder carrier model to be close to the local flow field of the original folding rudder carrier model. The invention can realize the equivalent scaling design of the model under large blockage conditions in a supersonic wind tunnel test of a folding rudder. By establishing a mathematical proxy model for the aerodynamic rolling moment of the folding rudder under the test conditions, an accurate test posture that meets the folding rudder assessment target is obtained, and the working law of the folding rudder under different angles of attack and sideslip angles is summarized. The invention solves the problem that it is difficult to quickly determine whether the assessment target has been achieved under test conditions, which is very likely to cause test failure, and ensures high calculation accuracy in the process.

Description

Technical Field

[0001] The present invention belongs to the technical field of wind tunnel test modeling, and in particular relates to a model design method and an unsteady aerodynamic modeling method under large blockage conditions for a folded rudder supersonic wind tunnel test. Background Art

[0002] To save space, the tail rudders of internally embedded missiles are generally designed to be foldable, also known as folding rudders. To assess the missile's ability to smoothly deploy and lock the folding rudders during launch, and to assess the impact resistance of the rudder surface material, deployment tests of the actual folding rudders are required. Currently, these tests are divided into two categories: flight tests and ground loading tests. Flight tests are expensive and risky and should be avoided as much as possible. Most ground loading tests utilize mass blocks or high-pressure gas to simulate the aerodynamic forces of deploying the folding rudders. These tests are low-cost, safe, and time-efficient, but the accuracy of the tests is insufficient, requiring a significant redundancy in the actuator design.

[0003] Wind tunnels are widely used for dynamic deployment testing of folding rudders. However, the main challenge is the difficulty of measuring the dynamic aerodynamic forces of the rudders without damaging the rudder surface. Using balance strain gauges to measure dynamic aerodynamic forces on folding rudders presents shortcomings such as poor signal measurement accuracy and the inability to conduct physical testing due to damage to the rudder surface. Currently, a more accurate method for determining the aerodynamic forces of a folding rudder is to accurately determine the distribution of the driving force within the rudder actuator as a function of deployment angle, which is largely unaffected by load variations. This internal driving force distribution is then determined through ground-based no-load testing. Wind-loaded deployment tests are then conducted in wind tunnels. The rudder angle and angular velocity parameters, obtained using high-speed photography during the tests, are used to determine the wind load distribution and work performed on the rudder. However, the use of CFD to design an equivalent scalable folding rudder model and model the unsteady aerodynamic forces under test conditions have become crucial for evaluating the unsteady aerodynamic forces of folding rudder deployment. Summary of the Invention

[0004] The problem to be solved by the present invention is to improve the simulation accuracy of the unsteady aerodynamic force of the folding rudder deployment, and propose a model design method and an unsteady aerodynamic modeling method under large blockage conditions of a folding rudder supersonic wind tunnel test.

[0005] To achieve the above object, the present invention is implemented through the following technical solutions:

[0006] A method for designing a model for a folding rudder supersonic wind tunnel test under high-blockage conditions comprises the following steps:

[0007] S1. Design the folding rudder carrier model to be located in the diamond-shaped area of ​​the test section;

[0008] S2. Design the head shock wave angle of the folding rudder carrier model;

[0009] S3. The local flow field of the controlled folding rudder carrier model is close to the local flow field of the original folding rudder carrier model.

[0010] Furthermore, in step S1, the total length of the folding rudder carrier model is controlled to be less than the length of the diamond-shaped area of ​​the test section. The length of the diamond-shaped area of ​​the test section is calculated as follows:

[0011]

[0012] Where L is the length of the diamond area, c is the safety factor, which is generally taken as 0.6, H is the height or width of the test section, and Ma is the Mach number.

[0013] Furthermore, in step S2, the head shape of the folding rudder carrier model is designed to be a conical rotating body or a streamlined elliptical cone to limit the oblique shock wave angle of the model head;

[0014] For a streamlined elliptical cone, the calculation process of the oblique shock wave angle and the deflection angle is as follows:

[0015] First, calculate the oblique shock wave angle using the following formula:

[0016]

[0017] Among them, θ is the deflection angle, β is the oblique shock wave angle, and M1 is the wavefront Mach number. In aerodynamics, this formula can be plotted as a θ-β-M curve;

[0018] According to the Mach number formula of the oblique shock wave, the vertical Mach number and the Mach number behind the wave are obtained:

[0019]

[0020] Among them, M2 is the Mach number after the wave, γ is the specific heat ratio, which is 1.4 when air is the medium, M n,2 is the vertical Mach number behind the wave, M n,1 is the vertical Mach number of the wavefront;

[0021] Then, based on the obtained θ and M2, the oblique shock wave angle β2 is calculated according to the θ-β-M curve, and the oblique shock wave angle Φ reflected from the cave wall is calculated relative to the surrounding cave walls. The calculation formula is:

[0022] Φ = β2 - θ;

[0023] Based on the total length of the folding rudder carrier model and the angle of the oblique shock wave reflected from the cave wall obtained in step S1, the positional relationship between the reflected shock wave and the tail of the folding rudder carrier model in the flow direction is obtained.

[0024] Furthermore, in step S3, the folding rudder carrier model and the geometric model from the previous double root chord length position to the tail are kept unchanged, so as to achieve that the flow field around the folding rudder carrier model is close to the local flow field of the original folding rudder carrier model.

[0025] A method for modeling unsteady aerodynamic forces of a folded rudder supersonic wind tunnel test model under large obstruction conditions is provided, which is based on the model under large obstruction conditions of the folded rudder supersonic wind tunnel test, and includes the following steps:

[0026] Step 1. Assume that the folding rudder is a rigid body, and the translational motion equation of the object is as follows:

[0027]

[0028] in, is the resultant force vector, m is the mass of the folded rudder, is the acceleration vector;

[0029]

[0030] Where x, y, z are the x-axis coordinates, y-axis coordinates, and z-axis coordinates of the folding rudder's center of mass in the inertial coordinate system, and t is time;

[0031] Step 2. Design the vector expression of the 6-DOF rotational motion equation as follows:

[0032]

[0033] in, is the sum moment vector, is the angular acceleration vector, is the angular velocity vector, I is the moment of inertia vector; θ x ,θ y ,θ z are the angles of the object around the x, y, and z axes, respectively, and ω x =dθ x / dt,ω y =dθ y / dt,ω z =dθ z / dt;

[0034]

[0035] Among them, I xx , I yy , I zz are the moments of inertia of the folding rudder about the x, y, and z axes respectively;

[0036] Step 3. Since the folding rudder is hinged on the rudder shaft, the 6-DOF motion is simplified to a rotational motion about the x-axis. The simplified rotational motion equation is:

[0037] M x =Ixx ·d 2 θ x / dt 2 or d 2 θ x / dt 2 =M x / I xx ;

[0038] Based on M x The torque of the folding rudder around the x-axis is calculated by the combined force of gravity, aerodynamic force, mechanical friction, and actuator driving force. The calculation formula is:

[0039]

[0040] Among them, M G is the hinge moment due to gravity, M a is the hinge moment caused by aerodynamic forces, M f is the hinge torque caused by mechanical friction, M e The hinge torque caused by the actuator driving force;

[0041] Then design the angular velocity of the folding rudder The equation is as follows:

[0042]

[0043] Folding rudder rotation angle θ x The equation is as follows:

[0044]

[0045] Step 4. Add and combine the hinge torque caused by the mechanical friction of the folding rudder and the driving force of the actuator, collectively referred to as the internal driving torque. The value of the internal driving torque is measured by conducting a ground no-wind deployment test of the folding rudder in advance;

[0046] Step 5. After the internal driving torque is determined, CFD is used to simulate the deployment process under different incoming flow conditions to obtain a variety of relationship samples between the deployment aerodynamic hinge torque and the deployment angle. Then, based on the relationship samples between the various deployment aerodynamic hinge torque and the deployment angle, RBF modeling or polynomial modeling is established to obtain the hinge torque aerodynamic model of the folding rudder.

[0047] Beneficial effects of the present invention:

[0048] The method for designing a model for a folding rudder under high-blockage conditions in supersonic wind tunnel testing, described in this invention, addresses the technical challenges posed to high-speed wind tunnel testing technology during the development of embedded weapons. It addresses the need to successfully conduct folding rudder testing on schedule, reduce expected testing costs, and compress testing cycles. This method enables equivalent scaling of models under high-blockage conditions in supersonic wind tunnel testing of folding rudders. By establishing a mathematical proxy model for the aerodynamic rolling moment of the folding rudder under these test conditions, an accurate test attitude that meets the folding rudder assessment objectives is obtained, and the working patterns of the folding rudder under different angles of attack and sideslip angles are summarized. Overall, this method saves project funds and ensures the successful implementation of the project.

[0049] The present invention describes a method for designing a model for a folding rudder under high-blockage conditions in a supersonic wind tunnel test. This method designs a well-designed, shock-wave-free folding rudder shape that conforms to supersonic and high-blockage conditions, accurately calculates the aerodynamic rolling moment during its deployment under test conditions, and then establishes a reasonable mathematical proxy model. This method effectively addresses the model design challenges encountered when CFD is unavailable, and the difficulty in quickly determining whether assessment objectives have been achieved under test conditions, which can easily lead to test failure. High computational accuracy is ensured during this process, ensuring that the difference between the proxy model and the final test results is within 10%. This method has been tested as a proven pilot verification method. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of the typical folding rudder distribution and carrier described in the present invention;

[0051] Figure 2 It is the design of the folding rudder aerodynamic assessment process and the link diagram of the invention in the red frame;

[0052] Figure 3 It is a schematic diagram of the model scaling design described in the present invention;

[0053] Figure 4 is a schematic diagram of the deployment of the folding rudder described in the present invention;

[0054] Figure 5 This is a schematic diagram of the aerodynamic rolling moment during the RBF fitting of a single folding rudder deployment process described in the present invention;

[0055] Figure 6 This is a schematic diagram of the RBF modeling and fitting of the aerodynamic rolling moment during the folding rudder deployment process as a function of the deployment angle and angular velocity described in the present invention;

[0056] Figure 7 This is a schematic diagram of the polynomial modeling and fitting of the aerodynamic rolling moment during the folding rudder deployment process as a function of the deployment angle, angle of attack, and sideslip angle described in the present invention;

[0057] Figure 8is a comparison chart of the aerodynamic rolling moment distribution estimated by the aerodynamic model described in the present invention and the test results;

[0058] Figure 9 is a graph showing how the aerodynamic rolling moment hindering work varies with angle of attack, as estimated by the aerodynamic model described in the present invention;

[0059] Figure 10 This is a diagram showing how the aerodynamic rolling torque promoting work changes with the angle of attack as predicted by the aerodynamic model described in the present invention. DETAILED DESCRIPTION

[0060] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the specific embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the specific embodiments of the present invention described and illustrated in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0061] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected specific embodiments of the present invention. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0062] In order to further understand the content, features and effects of the present invention, the following specific embodiments are given as examples, and the attached Figure 1 -Attached Figure 10 The detailed instructions are as follows:

[0063] Example 1:

[0064] A method for designing a model for a folding rudder supersonic wind tunnel test under high-blockage conditions comprises the following steps:

[0065] S1. Design the folding rudder carrier model to be located in the diamond-shaped area of ​​the test section;

[0066] Furthermore, in step S1, the total length of the folding rudder carrier model is controlled to be smaller than the length of the diamond-shaped area of ​​the test section. The length of the diamond-shaped area of ​​the test section is calculated as follows:

[0067]

[0068] Where L is the length of the diamond area, c is the safety factor, which is generally taken as 0.6, H is the height or width of the test section, and Ma is the Mach number;

[0069] Furthermore, when the wind tunnel is 1.6 meters and the wind tunnel width is 1.5 meters, 1.5 meters is taken to estimate the model length. If the Mach number is 1.5, the calculated L is approximately 1.006 meters.

[0070] S2. Design the head shock wave angle of the folding rudder carrier model;

[0071] Furthermore, in step S2, the head shape of the folding rudder carrier model is designed to be a conical rotating body or a streamlined elliptical cone to limit the oblique shock wave angle of the model head;

[0072] For a streamlined elliptical cone, the calculation process of the oblique shock wave angle and the deflection angle is as follows:

[0073] First, calculate the oblique shock wave angle using the following formula:

[0074]

[0075] Among them, θ is the deflection angle, β is the oblique shock wave angle, and M1 is the wavefront Mach number. In aerodynamics, this formula can be plotted as a θ-β-M curve;

[0076] According to the Mach number formula of the oblique shock wave, the vertical Mach number and the Mach number behind the wave are obtained:

[0077]

[0078] Among them, M2 is the Mach number after the wave, γ is the specific heat ratio, which is 1.4 when air is the medium, M n,2 is the vertical Mach number behind the wave, M n,1 is the vertical Mach number of the wavefront;

[0079] Then, based on the obtained θ and M2, the oblique shock wave angle β2 is calculated according to the θ-β-M curve, and the oblique shock wave angle Φ reflected from the cave wall is calculated relative to the surrounding cave walls. The calculation formula is:

[0080] Φ=β2-θ

[0081] Based on the total length of the folding rudder carrier model and the angle of the oblique shock wave reflected from the cave wall obtained in step S1, the positional relationship between the reflected shock wave and the tail of the folding rudder carrier model in the flow direction is obtained;

[0082] Furthermore, when the model is a two-dimensional wedge, θ is the half angle of the wedge, that is, half of the full angle of the wedge, and the angle of the generated head oblique shock wave is limited to within about 45° as much as possible to reduce the influence of the head oblique shock wave and its reflected shock wave.

[0083] For wedge-shaped bodies;

[0084] The above method is used to determine the shape of the reflected shock wave from a wedge-shaped object in a wind tunnel. However, in three-dimensional experiments, the streamlined model's shape approaches a cone or elliptical cone. The shock wave angle decreases as it moves farther from the model surface. Therefore, the shock wave angle is smaller than that of the wedge-shaped object, and the uniform flow field within the shock wave is extended, making it less likely to interfere with the model's tail. To minimize shock wave interference during design, theoretical calculations should be performed based on the wedge-shaped object's shape, and the resulting wedge half-angle should be used as the model's head cone angle.

[0085] When establishing the geometric shape of the model head, it is necessary to establish a series of smooth bridging curves from the model head cusp to the model tail end. The curves are in the form of NURBS curves (non-uniform rational B-spline curves). The NURBS curves ensure a smooth transition between the bridging curves and other curves, meeting the requirements for curve smoothness and continuity in the design. If the model head is designed as a rotational body, only one NURBS curve needs to be established. If it is an elliptical cone, the model head half mold can be designed first. To establish the half mold part, at least 4 points must be selected on the edge of the half mold on the bottom surface of the elliptical cone, and smooth bridging curves must be established with these points using the model head cusp as the starting point. Then, a smooth surface is established in the form of a fill or a multi-section surface.

[0086] S3. The local flow field of the controlled folding rudder carrier model is close to the local flow field of the original folding rudder carrier model.

[0087] Furthermore, in step S3, the folding rudder carrier model and the geometric model from the previous double root chord length position to the tail are kept unchanged, so as to achieve that the flow field around the folding rudder carrier model is close to the local flow field of the original folding rudder carrier model.

[0088] Furthermore, a preliminary model was designed based on the implementation of the above three design requirements. By comparing the flow field near the folding rudder of the original shape and the test model through CFD calculation, the model design is considered qualified when the maximum difference in the surface pressure coefficient distribution of the rudder surface is within 10%. If the difference is greater than 10%, the model length is further reduced and the head cone angle is adjusted to obtain a shape that meets the surface pressure error requirements. However, excessive reduction of the model length should also be avoided, which will cause the head shock wave to directly sweep the folding rudder surface. The most obvious feature of the above method is to control the total length of the model, modify the head shape, and retain the carrier shape around the folding rudder to ensure the similarity of the flow field around the folding rudder before and after the model scaling design.

[0089] Example 2:

[0090] A method for modeling unsteady aerodynamic forces of a folded rudder supersonic wind tunnel test model under large obstruction conditions is implemented based on the model of the folded rudder supersonic wind tunnel test model under large obstruction conditions described in Example 1, comprising the following steps:

[0091] Step 1. Assume that the folding rudder is a rigid body, and the translational motion equation of the object is as follows:

[0092]

[0093] in, is the resultant force vector, m is the mass of the folded rudder, is the acceleration vector;

[0094]

[0095] Where x, y, z are the x-axis coordinates, y-axis coordinates, and z-axis coordinates of the folding rudder's center of mass in the inertial coordinate system, and t is time;

[0096] Step 2. Design the vector expression of the 6-DOF rotational motion equation as follows:

[0097]

[0098] in, is the sum moment vector, is the angular acceleration vector, is the angular velocity vector, I is ***; θ x ,θ y ,θ z are the angles of the object around the x, y, and z axes, respectively, and ω x =dθ x / dt,ω y =dθ y / dt,ω z =dθ z / dt;

[0099]

[0100] Among them, I xx , I yy , I zz are the moments of inertia of the folding rudder about the x, y, and z axes respectively;

[0101] Step 3. Since the folding rudder is hinged on the rudder shaft, the 6-DOF motion is simplified to a rotational motion about the x-axis. The simplified rotational motion equation is:

[0102] M x =I xx ·d 2 θ x / dt 2 or d 2 θ x / dt 2 =M x / Ixx ;

[0103] Based on M x The torque of the folding rudder around the x-axis is calculated by the combined force of gravity, aerodynamic force, mechanical friction, and actuator driving force. The calculation formula is:

[0104]

[0105] Among them, M G is the hinge moment due to gravity, M a is the hinge moment caused by aerodynamic forces, M f is the hinge torque caused by mechanical friction, M e The hinge torque caused by the actuator driving force;

[0106] Then design the angular velocity of the folding rudder The equation is as follows:

[0107]

[0108] Folding rudder rotation angle θ x The equation is as follows:

[0109]

[0110] Furthermore, the hinge torque caused by the mechanical friction of the folding rudder and the actuator drive force can be numerically added and combined, collectively referred to as the internal driving torque. Determining its value requires prior measurement through a ground-based, windless deployment test of the folding rudder. This ground-based, windless deployment test utilizes gas as a power source and establishes a load-applying mechanism on the folding rudder surface that unfolds as the rudder surface unfolds, thereby determining the internal driving torque of the folding rudder mechanism. During ground testing of the folding rudder actuator, the internal driving torque is relatively easy to determine when the actuator is driven by a torsion spring. However, when the actuator is driven by a fire control device, the internal driving torque is more difficult to determine and is affected by the speed of movement. This requires multiple tests to obtain a number of samples, which can then be determined through mathematical modeling.

[0111] Step 4. Add and combine the hinge torque caused by the mechanical friction of the folding rudder and the driving force of the actuator, collectively referred to as the internal driving torque. The value of the internal driving torque is measured by conducting a ground no-wind deployment test of the folding rudder in advance;

[0112] Step 5. After the internal driving torque is determined, CFD is used to simulate the deployment process under different incoming flow conditions to obtain a variety of relationship samples between the deployment aerodynamic hinge torque and the deployment angle. Then, based on the relationship samples between the various deployment aerodynamic hinge torque and the deployment angle, RBF modeling or polynomial modeling is established to obtain the hinge torque aerodynamic model of the folding rudder.

[0113] The specific implementation process of this embodiment is as follows:

[0114] (1) Input conditions confirmation:

[0115] Before establishing the scaled design and unsteady aerodynamic modeling for the folded rudder supersonic wind tunnel test under high-blockage conditions, the following inputs are required:

[0116] 1. Assessment target: After obtaining clear assessment targets for the folding rudder, the assessment targets are divided into two categories: the hindering end and the promoting end. The initial torque and total work energy of the assessment targets are the key quantities.

[0117] 2. Test conditions: Based on the aircraft's flight altitude and speed when the folding rudder is detached from the aircraft, the aircraft's dynamic pressure and Mach number are calculated. These dynamic pressure and Mach number are the test dynamic pressure and Mach number, which also determine the wind tunnel test conditions.

[0118] 3. Folding rudder mechanism: The distribution of the driving torque provided by the folding rudder structure as a function of the deployment angle. Rudder surface structural mass parameters, including the folding rudder's mass and moment of inertia about the axis of rotation.

[0119] 4. Folding rudder deployment time: Once the assessment objectives and folding rudder mechanism information are determined in the above inputs, the deployment time scale for the folding rudder under different assessment objectives should also be determined. Generally, the folding rudder deployment time ranges from 20ms to 200ms, with 20ms being considered a faster deployment and 200ms being considered a slower deployment. This deployment time significantly affects the magnitude of the dynamic aerodynamic force increment of the folding rudder, thus allowing the approximate range of angle of attack and sideslip angle combinations to be determined during the calculation.

[0120] (2) Model scaling design:

[0121] After the input conditions are confirmed, the model is scaled down according to the input conditions. The scale down is carried out according to three principles: ensure that the model is in the diamond area of ​​the test section, streamline the head of the model to reasonably control the head shock wave, and keep the shape near the folded rudder unchanged so that the local flow field is close to the original shape. The model scaling design results are shown in the attached figure. Figure 3 shown.

[0122] (3) Unsteady aerodynamic modeling of folding rudder:

[0123] The aerodynamic rolling moment of the rudder surface during unsteady deployment is of primary concern. Therefore, a comprehensive simulation method for the dynamic deployment of a folding rudder in a supersonic wind tunnel must be established. This method requires accurate and realistic representation of the rudder surface deployment process and unsteady aerodynamic forces. A single-degree-of-freedom aerodynamic equation of motion for the rudder surface deployment is established to simulate the motion process. This equation of motion includes gravity, aerodynamic forces, mechanical friction, and the actuator drive force during the folding rudder deployment process, including the rudder's mass and moment of inertia about the axis of rotation. The mechanical friction and actuator drive forces can be combined and collectively referred to as internal drive forces. Their values ​​require reference to the rudder actuator design specifications and windless deployment test results. When the actuator is driven by a torsion spring, its drive torque is relatively easy to determine using ground windless tests. When the actuator is driven by a fire control device, its drive torque is more difficult to determine and significantly interacts with the deployment speed, requiring multiple ground load tests to determine its value. At this time, the distribution results of driving torque with different loads are obtained. For different assessment targets, the driving torque results should be clarified. For example, the driving torque of the folding rudder during obstruction should be different from the driving torque during promotion.

[0124] CFD is used to calculate the unsteady motion of a folding rudder with a single degree of freedom. The CFD simulation process is set up as follows:

[0125] A URANS or DES-type method is used, with the fluid medium being a compressible ideal gas. Spatial discretization utilizes a finite volume method based on a grid-centered scheme, and time marching employs multi-level Runge-Kutta explicit time marching, with results for each physical time step obtained by dual time marching. Multigrids and dynamic CFL number adjustment are used to accelerate computational convergence. The folded rudder rotates relative to the carrier, with the area near the rudder surface nested as a subdomain within the carrier background domain. The computational mesh utilizes a hybrid unstructured mesh of three-dimensional prismatic layers and tetrahedrons, divided into the carrier background domain and the folded rudder subdomain. The interpolation accuracy of the nested boundaries is second-order. The meshes of the subdomains and background domains must be verified for mesh independence to ensure a reasonable density and distribution. A dense mesh is particularly important in the space surrounding the head shock and reflected shock waves. The mesh near the folded rudder surface should be denser. Due to the nesting, a gap exists between the moving and static rudder surfaces, typically no larger than 5 mm. In most cases, a 2 mm gap is maintained between the static and moving rudder surfaces. After the folded rudder is moved to a new position in each physical time step, it is re-nested to obtain the solution grid. The time step convergence analysis is performed at 1 / 10 to 1 / 200 of the dimensionless unsteady physical time step. At the same time, the angle swept by the tip of the rudder surface in each physical time step should be considered, and this angle should be kept within 1° as much as possible, or even increased to within 0.5°.

[0126] By applying the CFD method several times to simulate the deployment process of the folding rudder in the wind tunnel, the aerodynamic force sample of the folding rudder under test conditions is obtained. Check whether the aerodynamic rolling moment distribution and energy in the sample cover the assessment target, and whether its distribution trend is close to the roll moment distribution of the assessment target. If it deviates from the assessment target distribution, the angle of attack and sideslip angle of the model should be modified, so that the sample results finally cover the assessment target and the distribution trend is close. After the calculation of multiple groups of angle of attack and sideslip angle samples is completed, the aerodynamic rolling moment proxy model is established using RBF function or 4th-order polynomial. The independent variables of the model are the deployment angle of the folding rudder, the deployment angular velocity, the carrier angle of attack, and the carrier sideslip angle, and the dependent variable is the aerodynamic rolling moment of the folding rudder dynamic surface. The aerodynamic rolling moment distribution of the single deployment and multiple deployment processes established by RBF correspondence is shown in the attached figure. Figure 6 , Attachment Figure 7 As shown in the attached figure, the mathematical proxy model established by polynomial modeling and the aerodynamic rolling moment distribution calculated by CFD are shown in the attached figure. Figure 8 As shown, it can be seen that both have good fitting characteristics.

[0127] (4) Agent model assessment

[0128] The present invention selects either an RBF function (RBF function formulas are generally known; the Gaussian function form is used here) or a fourth-order polynomial to establish an aerodynamic roll torque proxy model, depending on the situation. When the internal driving torque at each deployment angle does not change with external aerodynamic forces, a fourth-order polynomial is used to establish the aerodynamic roll torque proxy model; otherwise, an RBF function is used. The independent variables of the fourth-order polynomial are the angle of attack, sideslip angle, deployment angle, and deployment angular velocity, and the dependent variable is the aerodynamic hinge torque.

[0129] Set the aerodynamic work as the assessment target, calculate the root mean square deviation of the aerodynamic hinge torque of the "assessment target-aerodynamic model" at the same deployment angle, use the genetic algorithm for optimization iteration, select the state corresponding to the minimum deviation, and obtain the optimal angle of attack and sideslip angle combination. Figure 2 After the wind tunnel test was carried out according to the process shown in the figure, the comparison results between the test and the aerodynamic model were obtained, as shown in the attached figure. Figure 8 As shown in the figure, the aerodynamic proxy model accurately predicts the model aerodynamic force distribution and the final total energy during the test. The optimal total energy error is less than 4%, and in general it can be within 10%, demonstrating the high accuracy of the aerodynamic proxy model.

[0130] (5) Distribution of work energy

[0131] In recent years, statistics on the calculation and test results of different folding rudders have shown that the total energy of the aerodynamic rolling torque during the folding rudder deployment process varies with the angle of attack or sideslip angle, and its slope is related to parameters such as the rudder surface area, the incoming flow Mach number, and the dynamic pressure. A typical example is shown in the attached figure. Figure 9 , Attachment Figure 10 As shown in the figure, the aerodynamic rolling moment of the folding rudder during the deployment process both hinders the work and promotes the work and presents an approximately linear inertia with the angle of attack.

[0132] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0133] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and components may be substituted with equivalents without departing from the scope of the present application. In particular, as long as there are no structural conflicts, the various features of the embodiments disclosed herein may be combined with each other in any manner, and the omission of an exhaustive description of these combinations in this specification is solely for the sake of space and resource conservation. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions within the scope of the claims.

Claims

1. A method for designing a model for a folding rudder supersonic wind tunnel test under high-blockage conditions, characterized in that: The steps include: S1. Design the folding rudder carrier model to be located in the diamond-shaped area of ​​the test section; In step S1, the total length of the folding rudder carrier model is controlled to be less than the length of the diamond-shaped area of ​​the test section. The length of the diamond-shaped area of ​​the test section is calculated as follows: Where L is the length of the diamond area, c is the safety factor, which is generally taken as 0.6, H is the height or width of the test section, and Ma is the Mach number; S2. Design the head shock wave angle of the folding rudder carrier model; Step S2: The head of the folding rudder carrier model is designed to be a conical rotating body or a streamlined elliptical cone to limit the angle of the oblique shock wave at the head of the model; For a streamlined elliptical cone, the calculation process of the oblique shock wave angle and the deflection angle is as follows: First, calculate the oblique shock wave angle using the following formula: Among them, θ is the deflection angle, β is the oblique shock wave angle, and M1 is the wavefront Mach number. In aerodynamics, this formula can be plotted as a θ-β-M curve; According to the Mach number formula of the oblique shock wave, the vertical Mach number and the Mach number behind the wave are obtained: Among them, M2 is the Mach number after the wave, γ is the specific heat ratio, which is 1.4 when air is the medium, and M n,2 is the vertical Mach number behind the wave, M n,1 is the vertical Mach number of the wavefront; Then, based on the obtained θ and M2, the oblique shock wave angle β2 is calculated according to the θ-β-M curve, and the oblique shock wave angle Φ reflected from the cave wall is calculated relative to the surrounding cave walls. The calculation formula is: Φ=β2-θ Based on the total length of the folding rudder carrier model and the angle of the oblique shock wave reflected from the cave wall obtained in step S1, the positional relationship between the reflected shock wave and the tail of the folding rudder carrier model in the flow direction is obtained; S3. The local flow field of the controlled folding rudder carrier model is close to the local flow field of the original folding rudder carrier model.

2. The method for designing a model for a folding rudder supersonic wind tunnel test under high-blockage conditions according to claim 1, characterized in that: In step S3, the folding rudder carrier model and the geometric model from the previous double root chord length position to the tail are kept unchanged, so as to achieve that the flow field around the folding rudder carrier model is close to the local flow field of the original folding rudder carrier model.

3. A method for modeling the unsteady aerodynamic forces of a folded rudder under high-blockage conditions in a supersonic wind tunnel test, based on the method for designing a folded rudder under high-blockage conditions in a supersonic wind tunnel test according to any one of claims 1-2, characterized in that: The steps include: Step 1. Assume that the folding rudder is a rigid body, and the translational motion equation of the object is as follows: in, is the resultant force vector, m is the mass of the folded rudder, is the acceleration vector; Where x, y, z are the x-axis coordinates, y-axis coordinates, and z-axis coordinates of the folding rudder's center of mass in the inertial coordinate system, and t is time; Step 2. Design the vector expression of the 6-DOF rotational motion equation as follows: in, is the sum moment vector, is the angular acceleration vector, is the angular velocity vector; θ x ,θ y ,θ z are the angles of the object around the x, y, and z axes, respectively, and ω x =dθ x / dt,ω y =dθ y / dt,ω z =dθ z / dt; Among them, I xx , I yy , I zz are the moments of inertia of the folding rudder about the x, y, and z axes respectively; Step 3. Since the folding rudder is hinged on the rudder shaft, the 6-DOF motion is simplified to a rotational motion about the x-axis. The simplified rotational motion equation is: M x = I xx · d 2 θ x / dt 2 or d 2 θ x / dt 2 = M x / I xx ; Based on M x The torque of the folding rudder around the x-axis is calculated by the combined force of gravity, aerodynamic force, mechanical friction, and actuator driving force. The calculation formula is: Among them, M G is the hinge moment due to gravity, M a is the hinge moment caused by aerodynamic forces, M f is the hinge torque caused by mechanical friction, M e The hinge torque caused by the actuator driving force; Then design the angular velocity of the folding rudder The equation is as follows: Folding rudder rotation angle θ x The equation is as follows: Step 4. Add and combine the hinge torque caused by the mechanical friction of the folding rudder and the driving force of the actuator, collectively referred to as the internal driving torque. The value of the internal driving torque is measured by conducting a ground no-wind deployment test of the folding rudder in advance; Step 5. After the internal driving torque is determined, CFD is used to simulate the deployment process under different incoming flow conditions to obtain a variety of relationship samples between the deployment aerodynamic hinge torque and the deployment angle. Then, based on the relationship samples between the various deployment aerodynamic hinge torque and the deployment angle, RBF modeling or polynomial modeling is established to obtain the hinge torque aerodynamic model of the folding rudder.

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