Multi-missile serial water entry interference assessment method based on wake vortex field

Abstract

The invention discloses a multi-missile serial water entry interference assessment method based on a wake vortex field, and belongs to the technical field of underwater vehicle water entry interference modeling. According to the method, a kinetic model of a preorder projectile body in the process of entering water is established, additional mass force, resistance, gravity, buoyancy and pitching restoring torque are combined, and the speed and posture changes of the projectile body are calculated based on a four-order Runge-Kutta numerical method; further describing vorticity distribution of a wake disturbance area by adopting a Lamb-Oseen vortex model, solving a vortex induced velocity field by utilizing a Biot-Savart law, and introducing the disturbance field into stress calculation of a subsequent projectile body to obtain velocity and attitude evolution of the disturbed projectile body; and finally calculating an axial speed attenuation degree and a pitch angle deflection degree as interference evaluation indexes. The model can represent the hydrodynamic coupling and interference effect in the multi-missile serial water entry process, and is suitable for underwater missile body layout optimization, control strategy design and interference suppression analysis.

Description

Technical Field

[0001] The invention belongs to the field of fluid mechanics and underwater weapon systems and is an evaluation method for the interference of multiple projectiles entering water in series based on wake vortex fields. Background Art

[0002] In the development of modern underwater weapon systems, to improve strike efficiency and penetration capabilities of combat platforms, an increasing number of combat scenarios are adopting a serial entry mode for multiple projectiles. This mode effectively enhances the density and saturation of attacks, thereby increasing the probability of successful target strikes. However, during the sequential entry of multiple projectiles, the complex disturbances caused by the preceding projectile will propagate through the water in a specific manner, causing significant dynamic interference to subsequent projectiles. These disturbances can adversely affect the entry attitude, entry angle, velocity variation, and even stability of the subsequent projectiles, potentially causing subsequent projectiles to deviate from the planned path, become unstable, and experience severe deceleration, thereby compromising the strike accuracy and robustness of the overall combat system.

[0003] Currently, research on the interference problem of multiple projectiles entering the water in series focuses primarily on experimental observations and large-scale numerical simulations based on CFD. While these methods can accurately characterize the flow field evolution and interference response, they generally suffer from the following limitations: First, the experimental setup is complex, with poor repeatability, and the inability to efficiently cover the entire parameter space, resulting in high experimental costs. Second, CFD simulations rely on high-precision meshes and time-stepping control, consuming significant computational resources and hindering rapid application in engineering design. Third, there is currently a lack of analytical or semi-analytical models with clear structure, explicit physical meaning, and the ability to describe the disturbance propagation and response mechanisms. Consequently, there is a lack of a universal and scalable theoretical framework to guide system design and parameter optimization.

[0004] Therefore, a modeling method with a scalable structure and the ability to quickly evaluate the interference effects of multiple missiles entering water is urgently needed to support the engineering design, layout optimization, and control algorithm development of related systems. Summary of the Invention

[0005] The purpose of the present invention is to provide a method for evaluating the interference of multiple missiles entering water in series based on wake vortex fields, so as to characterize the fluid mechanics coupling and interference effects during the process of multiple missiles entering water in series.

[0006] The technical solutions for achieving the purpose of the present invention are:

[0007] A method for evaluating the interference of multiple missiles entering water in series based on the wake vortex field is proposed. The disturbance degree of the subsequent missile dynamic parameters is quantitatively analyzed and the interference evaluation index is defined as follows:

[0008] Using dimensionless parameter K v Characterize the attenuation characteristics of the subsequent projectile in the axial velocity direction and define the axial velocity attenuation degree:

[0009]

[0010] Among them, v0 is the initial velocity of the preceding and following projectiles, K v The larger the value, the more significant the disturbance in the velocity attenuation of the subsequent projectile.

[0011] Introducing parameter K θ Quantify the degree of disturbance of the subsequent projectile pitch angle and define the pitch angle deflection as:

[0012] K θ =|θ2-θ|

[0013] K θ The larger the value, the more the projectile's pitch attitude angle deviates from the preset trajectory.

[0014] Where v and θ are the axial velocity and pitch angle of the preceding projectile obtained by using the fourth-order Runge–Kutta numerical integration method based on the dynamic model of the preceding projectile; v2 and θ2 are the axial velocity and pitch angle of the preceding projectile obtained by using the fourth-order Runge–Kutta numerical integration method based on the dynamic model of the subsequent projectile considering the wake disturbance of the preceding projectile.

[0015] Compared with the prior art, the present invention has the following significant advantages:

[0016] (1) This paper proposes a model for analyzing the disturbance of projectiles entering water in series, which provides strong support for the calculation of disturbances caused by subsequent projectiles entering water;

[0017] (2) The present invention proposes a method for calculating the superimposed disturbance effect of the wake vortex field. By introducing the induced velocity of the wake vortex field of the preceding projectile into the force equation of the succeeding projectile, the additional force and torque of the succeeding projectile when it is subjected to the wake disturbance can be calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 A step diagram of an embodiment of the present invention.

[0019] Figure 2 Schematic diagram of the forces acting on the preceding projectile when entering water.

[0020] Figure 3 Schematic diagram of the forces acting on the subsequent projectile entering the water.

[0021] Figure 4 Schematic diagram of the vortex interference in the wake of a projectile during underwater serial motion. DETAILED DESCRIPTION

[0022] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0023] This embodiment provides a method for evaluating dynamic interference of multiple missiles entering water in series, which is particularly suitable for the scenario of multiple missiles entering water in succession. Figure 1 The flowchart of the method is shown. The core of the present invention is to establish a fully coupled interference assessment model of the preceding projectile motion-wake vortex field evolution-following projectile disturbance response, which specifically includes the following steps:

[0024] Step 1: Construct a dynamic model of the preceding projectile.

[0025] First, the spatial coordinate system O-xyz is established with the point where the preceding projectile enters the water as the origin, where the x-axis coincides with and is parallel to the water surface, pointing to the horizontal direction of the projectile entering the water; the y-axis is perpendicular to the projectile's axis and is located in the horizontal plane, pointing to the left side of the projectile; and the z-axis is perpendicular to the water surface and points above the water surface.

[0026] Then, analyze the forces acting on the preceding projectile during its entry into the water:

[0027] When the leading projectile is navigating underwater, the surrounding water will be accelerated due to viscosity and inertia, which manifests as an added mass effect. The additional force caused by the added mass effect can be calculated by the following formula:

[0028]

[0029] Among them, C ma is the additional mass coefficient, which is related to the shape of the projectile and the flow field characteristics, ρ is the density of water, V is the volume of water displaced by the projectile, v is the velocity of the preceding projectile at time t, m a is the additional mass of the preceding projectile.

[0030] During the movement of the preceding projectile, it is also subject to fluid resistance along the axial direction. The resistance it is subject to can be calculated by the following formula:

[0031]

[0032] Among them, C d is the drag coefficient of the preceding projectile, and A is the cross-sectional area of ​​the preceding projectile.

[0033] In addition, the preceding projectile is also subject to its own downward gravity:

[0034] G=mg

[0035] Where m is the mass of the preceding projectile and g is the acceleration due to gravity.

[0036] The leading projectile is also subject to the upward buoyancy force from the water:

[0037] F b =ρVg

[0038] Where V is the volume of water displaced by the preceding projectile.

[0039] Combining the above calculation formula and according to Figure 2 The force analysis of the preceding projectile shown in , when the preceding projectile enters the water at an angle θ with the water surface, the dynamic equation along the projectile axis can be expressed as follows:

[0040]

[0041] In addition, the projectile will generate a pitching restoring moment under the action of its geometric structure and the surrounding fluid medium, prompting it to return to its initial stable state. The pitching restoring moment M r It can be expressed as:

[0042]

[0043] Among them, C m0 is the pitching moment coefficient of the preceding projectile at zero angle of attack, which is related to the water entry angle θ and the projectile shape, and L is the length of the preceding projectile.

[0044] Then the pitch dynamic equation of the preceding projectile around the center of mass can be expressed as:

[0045]

[0046] Where I is the moment of inertia of the preceding projectile.

[0047] Step 2: Solve the motion parameters of the preceding projectile, including axial velocity and pitch angle.

[0048] The fourth-order Runge–Kutta numerical integration method is used to iteratively solve the changes in the velocity and pitch angle of the preceding projectile over time. The specific process is as follows:

[0049] According to the dynamic equation of the preceding projectile in step 1, the first-order ordinary differential equation of velocity change is obtained:

[0050]

[0051] Among them, f(t,v) represents the value of the acceleration function at the prediction point (t,v).

[0052] The Runge–Kutta numerical integration method calculates the slopes at four different points within each time step h and takes a weighted average of them to obtain an approximate solution for the next time step. For the first-order differential equation above, given the initial condition v(t0) = v0, multiple "slopes" (k values) are calculated within each time step to approximate the value of v at the next step.

[0053] Specifically, the initial time t0 and initial velocity v0 are known.

[0054] Assume that the current time is t n, the corresponding speed is v n , the time step of the integral calculation is h.

[0055] Calculate the four slopes:

[0056] k1=f(t n ,v n )

[0057]

[0058] k4=f(t n +h,v n +hk3)

[0059] Among them, k i The slope is essentially the derivative of the velocity increment with respect to time. k1 represents the time at the current point (t n ,v n ), which is the one-step forecast used in the Euler method, is the midpoint of the current moment, indicating half a step long time, and k2 indicates the midpoint of the current moment The slope at the midpoint is used to correct the single-step prediction of the Euler method. k3 is the slope at another midpoint, which further corrects the predicted value. k4 is the slope at the next time point t n+1 The slope at the end of the interval is used to capture the changing trend.

[0060] Then the next moment t n+1 =t n +h speed v n+1 The calculation formula is:

[0061]

[0062] Among them, the weight of slope k1 is 1, the weights of slopes k2 and k3 are 2 each, and the weight of slope k4 is 1.

[0063] Repeat the above steps to get the velocity of the preceding projectile at each time step. n ,v n ))}Save or draw the image to obtain the change history of the preceding projectile velocity v with time t.

[0064] Similarly, the second-order differential equation for the pitch angle θ can be transformed into two first-order equations. Based on the initial angle θ0, the same Runge–Kutta method is used to solve it. By repeating the calculation, the time history of the pitch angle θ of the preceding projectile at each moment can be obtained.

[0065] Step 3: Model the vortex field in the wake disturbance zone of the preceding projectile.

[0066] After the leading projectile enters the water, a discrete vortex core system is formed in the wake region, and the Lamb-Oseen vortex model is used to describe the vorticity distribution.

[0067] Specifically, assume that the wake region contains N vortex cores, and the coordinates of the center of the i-th vortex core are x i =(x i ,y i ,z i ), the circulation is Γ i , then the superimposed vorticity field at any point x = (x, y, z) in space is:

[0068]

[0069] Where μ is the dynamic viscosity of water, ||xx i || is the radial distance between the spatial point and the i-th vortex core.

[0070] Therefore, according to the Biot-Savart law, the induced velocity of the vortex core system at the spatial point x is:

[0071]

[0072] Among them, the integration area V ' It is the wake disturbance area.

[0073] For a discrete vortex core system, the integral can be replaced by a finite sum to obtain the induced velocity:

[0074]

[0075] Among them, e θ is the tangential unit vector of the vortex core. This is the superposition induced velocity of the vortex core at a certain point in space, which can be used to calculate the velocity field when the subsequent projectile passes through the disturbance zone.

[0076] Step 4: Calculate the response of the subsequent projectile to the wake disturbance and solve the motion parameters of the subsequent projectile.

[0077] like Figure 3 As shown in the figure, the vortex core induced velocity field changes the originally symmetrical flow in the flow field, causing the flow field distribution to deviate, and inducing additional force and additional torque to be generated by the subsequent projectile.

[0078] The subsequent projectile is in the non-uniform wake, and the local velocity on the surface is determined by the velocity v2 of the subsequent projectile and the induced velocity u ind The superposition speed is:

[0079] ||v2-u ind || 2 =(v 2x -u ind,x ) 2 +(v2y -u ind,y ) 2 +(v 2z -u ind,z ) 2

[0080] Among them, v 2x 、v 2y 、v 2z are the velocity components of the subsequent projectile in the x, y, and z directions, u ind,x 、u ind,y 、u ind,z are the velocity components of the induced velocity in the x, y, and z directions.

[0081] Then, the resistance of the subsequent projectile is corrected as follows:

[0082]

[0083] Among them, C d2 is the drag coefficient of the subsequent projectile, and A2 is the cross-sectional area of ​​the subsequent projectile.

[0084] Therefore, for the subsequent projectile, its dynamic equation along the axial direction can be modified as follows:

[0085]

[0086] Among them, m2 is the mass of the subsequent projectile, m a2 is the additional mass of the subsequent projectile, v2 is the modulus of the velocity vector v2 of the subsequent projectile, θ2 is the pitch angle of the subsequent projectile, V2 is the displacement volume of the subsequent projectile, C d2 is the drag coefficient of the subsequent projectile. The lateral component of the induced velocity field will generate lateral flow on the cylinder wall, thereby generating additional lift. Based on the linear lift theory, the lift force on the subsequent projectile is:

[0087] F L =C L ρA2v2u ind

[0088] Among them, C L is the lift coefficient, u ind is the induced velocity vector u ind Model.

[0089] The force arm of this lift relative to the center of mass of the subsequent projectile is e, which forms an additional pitching moment on the subsequent projectile:

[0090] M add =F L e=C L ρAv2u ind e

[0091] Then the pitch dynamic equation of the subsequent projectile is corrected to:

[0092]

[0093] Among them, I2 is the moment of inertia of the subsequent projectile, C m02 is the pitching moment coefficient of the subsequent projectile at zero angle of attack, and L2 is the length of the subsequent projectile.

[0094] Finally, the fourth-order Runge-Kutta method in step 2 is used to solve step by step to obtain the velocity v2 and deflection angle θ2 of the subsequent projectile at each time step.

[0095] Step 5: Quantitatively analyze the disturbance degree of subsequent missile body dynamic parameters and define the disturbance evaluation index.

[0096] Using dimensionless parameter K v Characterize the attenuation characteristics of the subsequent projectile in the axial velocity direction and define the axial velocity attenuation degree:

[0097]

[0098] Among them, v0 is the initial velocity of the preceding and following projectiles, K v The larger the value, the more significant the disturbance in the velocity attenuation of the subsequent projectile.

[0099] Introducing parameter K θ Quantify the degree of disturbance of the subsequent projectile pitch angle and define the pitch angle deflection as:

[0100] K θ =|θ2-θ|

[0101] K θ The larger the value, the more the projectile's pitch angle deviates from the preset trajectory.

[0102] By combining the above-mentioned index system with the temporal and spatial distribution characteristics of the preceding projectile motion and the wake vortex field, it is possible to solve the velocity attenuation and attitude deflection of the subsequent projectile at any time, thereby evaluating the disturbance of the subsequent projectile during its underwater motion, and further providing a quantitative basis for evaluating the interference characteristics of the coordinated motion of clustered ammunition. The above description is an embodiment of the present invention. For those skilled in the art, based on the teachings of the present invention, all equivalent changes, modifications, substitutions and variations made within the scope of the patent application of the present invention without departing from the principles and spirit of the present invention should be covered by the scope of the present invention.

Claims

1. A method for evaluating the interference of multiple missiles entering water serially based on wake vortex field, characterized in that: Quantitatively analyze the disturbance degree of subsequent missile body dynamic parameters and define the disturbance evaluation index: Using dimensionless parameter K v Characterize the attenuation characteristics of the subsequent projectile in the axial velocity direction and define the axial velocity attenuation degree: Among them, v0 is the initial velocity of the preceding and following projectiles, K v The larger the value, the more significant the disturbance in the velocity attenuation of the subsequent projectile. Introducing parameter K θ Quantify the degree of disturbance of the subsequent projectile pitch angle and define the pitch angle deflection as: K θ =|θ2-θ| K θ The larger the value, the more the projectile's pitch attitude angle deviates from the preset trajectory. Where v and θ are the axial velocity and pitch angle of the preceding projectile obtained by using the fourth-order Runge–Kutta numerical integration method based on the dynamic model of the preceding projectile; v2 and θ2 are the axial velocity and pitch angle of the preceding projectile obtained by using the fourth-order Runge–Kutta numerical integration method based on the dynamic model of the subsequent projectile considering the wake disturbance of the preceding projectile.

2. The method for evaluating the interference of multiple missiles entering water serially based on wake vortex field according to claim 1 is characterized in that: The dynamic model of the preceding projectile is: Among them, m is the mass of the preceding projectile, m a is the additional mass of the preceding projectile, v is the velocity of the projectile at time t, g is the acceleration due to gravity, ρ is the water density, V is the volume of water displaced by the projectile, C d is the drag coefficient of the preceding projectile, A is the cross-sectional area of ​​the preceding projectile, and I is the moment of inertia of the preceding projectile.

3. The method for evaluating the interference of multiple missiles entering water in series based on wake vortex field according to claim 1 is characterized in that: The dynamic model of the subsequent projectile is: Among them, m2 is the mass of the subsequent projectile, m a2 is the additional mass of the subsequent projectile, g is the acceleration of gravity, V2 is the displacement volume of the subsequent projectile, C d2 is the resistance coefficient of the subsequent projectile, ρ is the water density, A2 is the cross-sectional area of ​​the subsequent projectile, v 2x 、v 2y 、v 2z are the velocity components of the subsequent projectile in the x, y, and z directions, u ind,x 、u ind,y 、u ind,z is the induced velocity u ind The velocity components in the x, y, and z directions, I2 is the moment of inertia of the subsequent projectile, C m02 is the zero-attack angle pitching moment coefficient of the subsequent projectile, L2 is the length of the subsequent projectile, C L is the lift coefficient, u ind is the induced velocity vector u ind The modulus of the lift, e is the force arm of the lift relative to the center of mass of the subsequent projectile.

4. The method for evaluating the interference of multiple missiles entering water in series based on wake vortex field according to claim 3 is characterized in that: The induced velocity vector u at the spatial point x ind for: Among them, e θ is the tangential unit vector of the vortex core, x i is the coordinate of the center of the i-th vortex core, N is the number of vortex cores, x is any point in space, ||xx i || is the radial distance between the spatial point and the i-th vortex core.

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