A method for integrated evaluation of cross-medium static stability margin of supercavitating vehicles

Abstract

The application discloses a method for evaluating the static stability margin of a supercavitating vehicle in cross-medium, which comprises the following steps: (1) establishing a fluid domain and a solid domain model, and dividing the grid, the solid wall surface in contact with the fluid needs good matching, setting the initial and boundary conditions of the fluid domain, setting the material properties of the solid structure and giving the initial working condition; (2) monitoring the pitch moment in the air and the pitch force value, calculating the aerodynamic center of the supercavitating vehicle in the air, and obtaining the static stability margin of the vehicle in the flight state; (3) according to the experience bubble profile formula and the underwater characteristics of the supercavitating vehicle, the wetted volume of the vehicle and the equivalent float center position are obtained, and the static stability margin of the fully developed air bubble in water is calculated; (4) the static stability margin in the air and underwater is comprehensively weighted and averaged, so as to obtain a judgment of the static stability margin of the supercavitating vehicle in the cross-medium water entry process. The method can help to determine the static stability of the water entry of the navigation chart.

Description

Technical Field

[0001] This invention belongs to the field of cross-medium water entry, specifically relating to an integrated evaluation method for the cross-medium static stability margin of supercavitating vehicles. Background Technology

[0002] Research on cross-medium water entry originated from the analysis of water entry trajectories of weapons such as torpedoes and missiles. For example, submarine-launched missiles need to ensure attitude stability after emerging from the water, while torpedoes need to avoid deviation from their trajectory due to cavitation collapse or attitude instability upon entry. At this stage, research relied heavily on experiments and empirical formulas, such as water tunnel tests and scaled-down model tests.

[0003] Supercavitating vehicles generate gaseous cavitation bubbles that envelop the vehicle through a cavitation generator at the nose, significantly reducing underwater drag (drag reduction rate can reach over 90%) and enabling high-speed (>100 m / s) underwater movement. However, at the moment the vehicle enters the water from the air (the cross-medium stage), the cavitation morphology changes drastically, which may lead to attitude instability or even trajectory deviation.

[0004] Currently, there are relatively mature methods for judging the static stability margin of a vehicle in the air and underwater. However, there is no mature theoretical method for analyzing the static stability during the cross-medium water entry stage. The difficulty lies in: (1) Gas-liquid-solid multiphase transient coupling: At the moment of water entry, the impact of the vehicle's head on the water surface causes the generation, expansion and collapse of cavitation bubbles, involving phase change, turbulence and compressibility effects of gas-liquid two-phase flow. The interaction between cavitation bubbles and the free liquid surface may lead to asymmetry of the flow field around the vehicle, generating longitudinal torque and disrupting static equilibrium. (2) Nonlinear attitude dynamics: When the vehicle enters the water body (high density medium) from the air (low density medium), the parameters such as buoyancy and added mass change abruptly, resulting in strong nonlinearity in the dynamic equations. The pitch, roll and yaw motions are coupled, and a six-degree-of-freedom (6-DOF) model needs to be established to analyze the stable equilibrium point. (3) Fluid-structure interaction: The high-speed water entry impact load may cause vibration of the vehicle, change the cavitation morphology and fluid load distribution, and form a feedback loop. The localized high pressure (up to GPa level) generated by cavitation collapse may damage the surface of the aircraft, and structural resonance needs to be avoided through stability analysis.

[0005] Currently, there is no mature method for quantitatively evaluating the static stability of cross-medium vehicles, while static stability analysis during cross-medium water entry is of great significance for the performance evaluation of cross-medium vehicles. Summary of the Invention

[0006] The purpose of this invention is to provide an integrated evaluation method for the static stability margin of supercavitating vehicles across media, which can simultaneously and uniformly evaluate the static stability margin of supercavitating vehicles in the air, in water, and in complex cross-media water entry processes, thereby providing some assistance in determining the static stability of supercavitating vehicles entering water across media.

[0007] The technical solution to achieve the purpose of this invention is as follows:

[0008] A method for integrated evaluation of the cross-medium static stability margin of a supercavitating vehicle is characterized by confirming whether the supercavitating vehicle experiences bouncing upon water entry through the cross-medium static stability margin of the vehicle. for:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015]

[0016] when Within the specified range, it is assumed that the supercavitating vehicle will not ricochet upon entering the water.

[0017] in This represents the static stability margin in the air for a supercavitating vehicle. This represents the axial static stability margin of the airborne vehicle. This represents the radial static stability margin of the airborne vehicle. Here is the axial coordinate of the aerodynamic center of the aircraft. Here are the radial coordinates of the aerodynamic center of the vehicle. For the length of the hull, This represents the hydrostatic stability margin of a supercavitating vehicle in water. This represents the axial static stability margin of the vehicle in water. This represents the radial static stability margin of the vehicle body in water. The axial coordinate of the equivalent center of buoyancy of the ship is given. The coordinates of the ship's centroid axis are given. The radial coordinates of the center of mass of the ship are as follows: The diameter of the head cavitation unit; , The static stability margin value across the medium The linear weighting coefficients satisfy .

[0018] The significant advantages of this invention compared to existing technologies are:

[0019] (1) Compared with physical experiments and cross-medium water entry simulation, only 2D aerodynamic simulation of the vehicle in the air and analysis of the underwater characteristics of the supercavitating vehicle based on the empirical formula of supercavitation can effectively save computing power.

[0020] (2) By using the unified static stability margin (SSM) index, the aerodynamic and inertial forces are analyzed in a coordinated manner, which generally reflects the stability changes of the vehicle from water to air (or in the opposite direction). Attached Figure Description

[0021] Figure 1 Overall process diagram.

[0022] Figure 2 Schematic diagram of the dimensions of a supercavitating spacecraft.

[0023] Figure 3 Aerial simulation diagram of a supercavitating vehicle.

[0024] Figure 4 Schematic diagram of pitch moment and pitch force monitoring points.

[0025] Figure 5 Schematic diagram of the tail and shoulder positions of a supercavitating spacecraft.

[0026] Figure 6 Flowchart of simulation verification for the example.

[0027] Figure 7 Example simulation verification diagram. Detailed Implementation

[0028] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0029] The following provides specific implementation parameters and a supercavitating vehicle model for an integrated evaluation of its cross-medium static stability margin. A detailed flowchart is shown below. Figure 1 As shown, the method is further verified through cross-medium water ingress simulation calculations, specifically including the following steps:

[0030] Step 1: Establish fluid and solid domain models separately and mesh them. The solid walls in contact with the fluid need good matching, meaning the boundary receptor mesh of the overlapping mesh outside the solid domain should be roughly the same size as the background mesh (i.e., the fluid domain mesh). Set the initial and boundary conditions for the fluid domain, set the material properties of the solid structure, and assign initial operating conditions to the vehicle, such as velocity. Angle of attack and the water inlet corner wait.

[0031] Separate fluid and solid domain models were established and meshed. The solid walls in contact with the fluid required good compatibility; the movement of the vehicle was constrained. The directional degree of freedom refers to the left and right yaw directions of the vehicle. Therefore, the fluid domain only needs to consider... The directions are limited by scale, namely the roll and pitch directions of the vehicle about its axis. The initial boundaries of the fluid domain are set at... Directional Scale , Length of the aircraft ,set up , = The simulation domain employs a cut-volume mesh and prism layer mesh generation method, setting the fluid domain as the background mesh and nesting overlapping meshes around the solid domain. The size of the receptor mesh at the boundary of the overlapping mesh is comparable to that of the fluid domain mesh. Figure 2 As shown; in this example, the supercavitating vehicle, after being launched, has a speed of 300 m / s, angle of attack , into the water corner It flies in the air, its structure is a spiral body, with a sloping cone-shaped head and a cylindrical tail, and the length of the flying body is... It is 100 mm in diameter. Head cavitation diameter It is 3.5mm, with a taper of 𝜃 ,like Figure 3 As shown. A supercavitating spacecraft is configured. Directional velocity , Directional velocity The solid material of the aircraft body is #75 structural steel, and its specific physical properties are shown in Table 1. The boundary conditions are all set as pressure outlet to simulate an infinite airspace.

[0032] Table 1—Materials of Supercavitating Spacecraft

[0033]

[0034] Step 2: Monitor the pitch moment and pitch force of the supercavitating vehicle in the air, and calculate the aerodynamic center of the supercavitating vehicle in the air. Thus, the static stability margin under its flight state is obtained. .

[0035] Pitch force and torque monitoring points P1, P2, and P3 are respectively set at the nose, bottom of the cone, and bottom of the cylinder of the supercavitating vehicle. Figure 4 As shown, the pitch moment is measured. And pitch force values Using the formula ,in The coordinates of the focal point on the longitudinal plane of the supercavitating spacecraft, i.e., the XOZ plane. The reference point coordinates are: In this embodiment, the reference point is assumed to be the apex of the aircraft's head, with coordinates as follows: ,but Centroid coordinates According to the formula , , ,in This refers to the static stability margin along the airborne central axis of the aircraft. Let be the radial static stability margin of the airborne body. Since the airborne body in the embodiment is a rotating body with a uniform mass distribution in the Z direction, the aerodynamic center formula can be simplified to: The static stability margin of the airborne vehicle was obtained. .

[0036] Step 3: Based on the empirical cavitation profile formula and the fact that a supercavitating vehicle will generate supercavitation covering its entire body, with only the cavitation plane and tail flap getting wet, the wetted volume of the vehicle is calculated, thus determining the equivalent center of buoyancy position. The static stability margin after the cavitation bubbles in the water have fully developed was calculated. .

[0037] Based on the empirical formula for cavitation profile: ,in Distance from the head of the vehicle Location, Time The cavitation radius at time, where The coordinates of the apex at the center of the head along the axis of the aircraft body. From head to tail The coordinates gradually increase; The maximum radius of the cavitation bubble. , The maximum diameter of the hull. The characteristic coefficients of the cavitation ... In this embodiment, the value is 1.2; The speed of the moving body; This is the total length of the cavitation bubble. , For emptying, ,in For environmental static pressure, The saturated vapor pressure of the fluid. This is the density of water. Take atmospheric pressure 101325 , The saturated vapor pressure of water at room temperature is 3170. , Approximately 1000 , Take 0.0004 , to obtain cavitation number , 0.18 m, thus obtaining the tail cavitation radius. General angle of attack At an angle of attack of φ, the wetted area of ​​the supercavitating vehicle in the water is the tail. When the cone angle is 𝜃, the shoulder area is wet. A diagram of the tail shoulder area is shown below. Figure 5 As shown; define the wetted volume ratio: ,in The volume of a supercavitating spacecraft. For the effective wetted volume of a supercavitating spacecraft, The length of the non-conical section of the supercavitating vehicle. The length of the oblique cone section of the supercavitating vehicle. Then this embodiment Axial coordinates of the equivalent center of buoyancy of the ship Radial coordinates of the equivalent center of buoyancy of the ship In the formula To effectively display the discrete coordinates of the wetted volume, For the multiphase flow density, we approximate the density of water here. , This is the acceleration due to gravity; due to discrete coordinates In practical engineering, this is difficult to capture, so some simplification assumptions must be made, namely, assuming that the wetted area is along... The direction is uniform, and the wetted volume during one cycle of up-and-down oscillation at the tail is consistent. This allows the discrete coordinates of the wetted volume to be concentrated onto the axis of the supercavitating vehicle. ,at this time center of mass According to the formula , , ,in This refers to the axial static stability margin of the vehicle in water. To determine the radial static stability margin of the vehicle body in water, the static stability margin value of the vehicle body in water is obtained. Since the Z-coordinates on the axis of the vehicle are all 0, there is no need to consider them further. The direction of the center of mass, focus, and equivalent displacement of the center of buoyancy.

[0038] Step 4: Perform a first-order linear weighted algorithm to determine the static stability margin of the vehicle across the medium. ,in , The coefficients are linearly weighted and satisfy the following conditions: ,also The weight in ( ), corresponding The weight in ( In academia, the static stability margin of a flight vehicle in the air is generally required to be within a certain range. The static stability margin of a waterborne vehicle is in This is because in water, a supercavitating vehicle relies solely on its tail flap for balance. When the static stability margin is too small, the restoring torque generated by the tail flap is insufficient, and the vehicle's shaft remains stable within the cavitation. In cross-medium processes, the high density of the water phase dominates the static stability margin, but the role of the gas phase, including water vapor and air, cannot be ignored. Generally, it is considered that the static stability margin in cross-medium processes should be greater than the minimum allowable static stability margin in air but less than the maximum allowable static stability margin in water. exist Between these points, the cross-medium vehicle has sufficient static stability reserves upon entering the water, while also retaining maneuverability. At small angles of attack... To ensure that no bouncing occurs upon entry into water, in this embodiment, [the following is taken]. That is, the static stability margin of the carrier across the medium. ,Discover Therefore, it can be considered that the supercavitating vessel operates at a small angle of attack. No ricochet will occur upon entry into water. It is important to note that this invention has only been verified under low angles of attack, i.e. At high angles of attack, the axial symmetry of the vehicle is disrupted, and the forces and moments exerted by the water on the vehicle are difficult to be equivalent to those on the vehicle's axis, resulting in inaccurate calculation of the equivalent center of buoyancy and causing prediction errors.

[0039] Verification: Using Figure 6 The calculation process described above simulates the cross-medium water entry of the supercavitating vehicle under the operating conditions of the embodiment. The simulation results further confirm that the method has a certain accuracy in estimating the static stability margin of the supercavitating vehicle during cross-medium water entry. The simulation results are as follows: Figure 7 As shown: the vehicle makes contact with the water surface at 0.01ms, the shoulder of the vehicle is completely submerged at 0.5ms, the vehicle is completely submerged at 1.5ms, and the vehicle is nearly twice its length submerged at 2.0ms. At this point, it was believed that the vehicle had safely entered the water across the medium.

[0040] Clearly, compared to physical experiments and cross-medium water entry simulations, this invention only performs 2D aerodynamic simulation of the vehicle in the air and analyzes the underwater characteristics of the supercavitating vehicle based on empirical formulas for supercavitation. This effectively saves computational resources. By unifying the static stability margin (SSM) index, it achieves coordinated analysis of aerodynamics, buoyancy, and inertia, broadly reflecting the stability changes of the vehicle from water to air (or vice versa).

[0041] Obviously, the above embodiments of the present invention are merely examples to clearly illustrate the present invention, and are not intended to limit the implementation of the present invention. For those skilled in the art, other variations or modifications can be made based on the above description. It is impossible to exhaustively list all the implementation methods here. All obvious variations or modifications derived from the technical solutions of the present invention are still within the protection scope of the present invention.

Claims

1. A method for integrated evaluation of the static stability margin of a supercavitating vehicle across a medium, characterized in that, The static stability margin of the supercavitating vehicle across the medium is used to determine whether a bounce occurs upon water entry, including: Establish fluid domain and solid domain models separately, and mesh them accordingly; By monitoring the pitching moment and pitching force of the supercavitating vehicle in the air, the aerodynamic center of the supercavitating vehicle in the air is calculated, thereby obtaining its static stability margin in flight. The static stability margin after the cavitation bubbles in the water have fully developed was calculated. A first-order linear weighted algorithm is used to calculate the cross-medium static stability margin of the supercavitating vehicle. The cross-medium static stability margin of supercavitating vehicles for: when Within the specified range, it is assumed that the supercavitating vehicle will not ricochet upon entering the water. in This represents the static stability margin in the air for a supercavitating vehicle. This represents the axial static stability margin of the airborne vehicle. This represents the radial static stability margin of the airborne vehicle. Here is the axial coordinate of the aerodynamic center of the aircraft. The radial coordinates of the aerodynamic center of the aircraft are given. For the length of the hull, This represents the hydrostatic stability margin of a supercavitating vehicle in water. This represents the axial static stability margin of the vehicle in water. This represents the radial static stability margin of the vehicle body in water. The axial coordinate of the equivalent center of buoyancy of the ship is given. The coordinates of the ship's centroid axis are given. The radial coordinates of the center of mass of the ship are as follows: The diameter of the head cavitation unit; , The static stability margin value across the medium The linear weighting coefficients satisfy , The value of is in ( ), The value of is in ( ).

2. The integrated evaluation method for the static stability margin of a supercavitating vehicle across media according to claim 1, characterized in that, in The coordinates are for the reference point, which is the top of the aircraft's head. For the pitching moment of a supercavitating vehicle, This represents the pitching force value for a supercavitating vehicle.

3. The integrated evaluation method for the static stability margin of a supercavitating vehicle across media according to claim 1, characterized in that, ； in For the effective wetted volume of a supercavitating spacecraft, The volume of the supercavitating spacecraft.

4. The integrated evaluation method for the static stability margin of a supercavitating vehicle across media according to claim 3, characterized in that, Effective wetted volume of supercavitating spacecraft The following formula is used to calculate: The length of the non-conical section of the supercavitating vehicle. The length of the oblique cone section of the supercavitating vehicle. Let be the angle of attack of the supercavitating vehicle, and let be the taper of the supercavitating vehicle. The radius of the cavitation at the tail of the supercavitating vehicle.

5. The integrated evaluation method for the static stability margin of a supercavitating vehicle across media according to claim 4, characterized in that, Cavitation radius at the tail of a supercavitating vehicle The following formula is used to calculate: = in For distance from the head of the supercavitating vehicle Location, Time Cavitation radius at time The maximum radius of the cavitation bubble. The total length of the cavitation bubble. Speed ​​of a supercavitating vehicle.

6. The integrated evaluation method for the static stability margin of a supercavitating vehicle across media according to claim 5, characterized in that, Maximum radius of cavitation The maximum diameter of the hull. These are the characteristic coefficients of the cavitation device; , It is an empty number.

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