A method for analyzing the stability of high-speed water-entry vehicles

Abstract

This invention discloses a method for analyzing the stability of high-speed vehicles entering water in series, comprising: constructing a geometric model of the high-speed vehicle's series entry process, and meshing the vehicle and computational domain; establishing a multiphase flow control equation set, introducing cavitation and turbulence models, setting boundary conditions, and performing numerical calculations; defining a set of characteristic parameters to characterize the vehicle's motion stability, monitoring the evolution of each characteristic parameter in real time, and solving for its critical values; defining a dimensionless instability factor based on the characteristic parameters and critical values; and establishing a stability probability criterion based on the numerical simulation results, judging stability by comparing each instability factor with a threshold, and identifying the dominant instability mode or a compound instability mode. This invention can systematically evaluate the entry stability of vehicles under series conditions, providing a theoretical basis and engineering reference for the problem of high-speed vehicles entering water in series.

Description

Technical Field

[0001] This invention belongs to the fields of transmedium fluid mechanics and underwater weapon ballistics. Specifically, it relates to a method for analyzing the motion stability of a vehicle during its sequential entry into water under high-speed conditions. It is particularly suitable for constructing stability criteria and identifying multiple instability modes, providing a theoretical basis and engineering reference for the coordinated strike of supercavitating vehicles, transmedium aircraft, and other weapon systems. Background Technology

[0002] High-speed water entry refers to the process by which a vehicle enters the water at a speed exceeding the speed of sound in water (approximately 1500 m / s) across the free surface. This technique is widely used in weapon systems such as supercavitating vehicles and cross-medium aircraft. The cross-medium water entry process involves complex flow phenomena such as gas-liquid two-phase flow, cavitation flow, turbulence, and shock waves, exhibiting strong unsteady and nonlinear characteristics. With the development of underwater defense technologies and the concept of cluster strikes, continuous, sequential water entry of vehicles has become an important way to improve the effectiveness of striking underwater targets.

[0003] Current research primarily focuses on the load characteristics and ballistic stability of single-unit water entry, resulting in relatively mature theoretical models, numerical methods, and experimental techniques. However, the theories and methods for single-unit water entry are difficult to directly extend to sequential water entry scenarios. When a vehicle enters water sequentially, the cavitation and wake fields formed after the forebody's entry significantly alter the entry environment of the aftbody. This causes the incoming flow conditions for the aftbody to no longer be a still surface or uniform flow field, but rather a complex perturbed flow field containing unsteady cavitation interfaces, vortex structures, and velocity deficits. This flow field disturbance effect leads to asymmetrical pressure distribution on the aftbody surface, thereby triggering ballistic instability. Furthermore, the compressibility of water under high-speed conditions cannot be ignored, and a detached shock wave is generated at the vehicle's nose. The shock wave couples with the cavitation interface, forming complex multiphysics interactions, further increasing the difficulty of stability analysis. Currently, there is a lack of analytical methods to quantitatively assess the stability of the aftbody under forebody wake disturbances, making it difficult to provide a theoretical basis for parameter optimization in coordinated vehicle strikes. Therefore, it is urgent to establish a stability analysis method suitable for sequential water entry of high-speed vehicles. Summary of the Invention

[0004] The purpose of this invention is to provide a method for analyzing the sequential water entry stability of high-speed vehicles, enabling the analysis of water entry stability of high-speed vehicles under conditions of forebody wake disturbance, shock wave-cavitation coupling effect, and fluid-structure interaction.

[0005] The technical solution to achieve the purpose of this invention is as follows:

[0006] A method for analyzing the stability of high-speed vehicles entering water sequentially is characterized by determining the stability of the following vehicle under the wake disturbance of the preceding vehicle using the following stability probability criterion:

[0007] Stability probability criterion:

[0008]

[0009] like If it is determined to be stable; It is determined to be unstable. To stabilize the critical threshold; The sum of the overall instability indices is calculated using the following formula:

[0010]

[0011] in This represents the pressure pulsation coefficient at the head shock wave stagnation point. This refers to the non-uniformity of pressure within the cavitation bubble. It is an asymmetric wetting factor. This is the pitch moment coefficient. For the equivalent angle of attack, This is the wake interference intensity coefficient. , , , , They are respectively , , , , , The critical value.

[0012] The significant advantages of this invention compared to existing technologies are:

[0013] (1) Existing technologies are mainly designed for single-body entry scenarios and are difficult to extend to sequential conditions of aircraft carriers. They also lack the ability to comprehensively characterize the multi-physics coupling effects such as forebody wake disturbance, shock wave-cavitation coupling, and asymmetric wetting. This invention establishes for the first time a complete analysis process from forebody flow field calculation to aftbody stability assessment. By constructing a computational domain covering the complete motion space of the forebody and aftbody, adopting a time-coupled numerical method, extracting six key feature parameters, and defining corresponding dimensionless instability factors, it achieves a quantitative characterization of the entire process of sequential entry stability of aircraft carriers, solving the problem that existing technologies cannot quantitatively assess aftbody stability under forebody wake disturbance.

[0014] (2) Existing technologies typically only provide qualitative assessments or single-parameter analyses of the stability of a single vessel entering the water, lacking quantitative prediction capabilities under the coupled effects of multiple factors, and are unable to identify multiple instability modes and their dominant mechanisms. This invention establishes a stability criterion based on an exponential probability function. By setting a critical threshold, it combines rapid determination of a single instability mode with comprehensive assessment under the coupling of multiple factors, accurately identifying six types of instability modes and distinguishing between dominant or compound instability modes. This provides a systematic quantitative tool for the stability assessment and instability mechanism analysis of high-speed vessels entering the water sequentially, filling a technological gap in this field. Attached Figure Description

[0015] Figure 1 A schematic diagram of the overall process for analyzing the stability of high-speed vehicles entering the water.

[0016] Figure 2 Schematic diagram of the aircraft carrier model.

[0017] Figure 3 Schematic diagram of the computational model.

[0018] Figure 4 Schematic diagram of cavitation and arc length coordinates of the axis of the spacecraft Detailed Implementation

[0019] The technical solutions in the invention examples will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described examples are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] This invention discloses a method for analyzing the sequential water entry stability of high-speed vehicles, the specific process of which is as follows: Figure 1 As shown, two spacecraft travel at a time interval ΔT * Taking the water entry with a distance of ΔX from the launch vehicle as an example, the following steps are included:

[0021] Step 1: The geometric model of the two tandem water-entry vehicles and the corresponding flow field computational domain were established. The structure of the vehicles is as follows: Figure 2 As shown. The vehicle body and flow field model are as follows. Figure 3As shown, to accurately capture the unique fore-and-aft interference effect of tandem entry into the water, the two vehicles are arranged sequentially along the same ballistic axis. The computational domain covers the unsteady supercavitation and tail flow field region formed after the fore-and-aft vehicle enters the water, as well as the complete space of the continuous motion of the aft-and-aft vehicle within this disturbed flow field. Mesh generation is performed on the vehicle and flow field models. An overlapping mesh method is introduced to decompose the flow field into a background region and a sub-region containing moving boundaries. Interpolation is used to transfer data and handle the moving boundary problem of the vehicle entering the water. Mesh refinement is applied to the vehicle in the flow field motion region, the gas-liquid interface, and the overlapping mesh region to reduce computational cost while maintaining accuracy.

[0022] Step 2: Import the geometric model established in Step 1 into the fluid solver. The multiphase flow field is captured using the VOF model, which can effectively track the evolution of the multiphase interface composed of water, water vapor, and non-condensable gases. To simulate the cavitation phenomenon induced by the high-speed entry of the vehicle into the water, the Schnerr-Sauer cavitation model and... A turbulence model is used to capture cavitation generation and accurately simulate the development of the boundary layer at the tail of the forebody and the wake flow field structure. In the numerical calculation, a time-coupled computation method is adopted. First, the entire process of the forebody crossing the free liquid surface under given operating conditions is calculated to obtain the evolution data of the unsteady flow field at its tail. Then, this data is used as the dynamic inflow boundary condition for the subsequent body entering the water, thereby simulating the entry process of the subsequent body into the water under the disturbance of the forebody's wake.

[0023] Step 3: Based on the numerical simulation results, extract the basic variables such as flow field pressure, velocity, phase volume fraction, pitching moment, velocity components, and wetted area of ​​the vehicle, and calculate the stability characteristic parameters of six typical high-speed vehicles entering the water in sequence, namely: the pressure fluctuation coefficient at the head shock stagnation point. Non-uniformity of internal pressure of cavitation Pitch moment coefficient Equivalent angle of attack Asymmetric wetting factor and wake interference intensity coefficient The detailed calculation formula is as follows:

[0024]

[0025] The parameters on the right-hand side of all six equations above can be obtained through numerical calculations. This represents the instantaneous stagnation point pressure in the flow field. This represents the stagnation point pressure in the flow field. Let be the density of the liquid water. This indicates that the two vehicles have the same entry velocity into the water. This represents the pressure parameter along the cavitation axis within the cavitation bubble, where s is the arc length measured from the starting end of the cavitation bubble (near the head of the vehicle) along the centerline of the cavitation bubble, as shown in the figure. Figure 4 As shown in (a). For the pitching moment of the aircraft body, For reference area, the maximum cross-sectional area of ​​the aircraft carrier is often selected. (where D is the diameter of the hull), For reference length, the total length of the aircraft carrier is usually chosen. and These represent the horizontal and vertical velocity components of the vehicle, respectively. This represents the area of ​​the surface of the vehicle facing the current that is in direct contact with the water. This represents the area of ​​the surface of the vehicle on the opposite side of the current that is in direct contact with the water. The total surface area of ​​the navigating surface. Indicates the actual velocity of the precursor. Indicates the distance of the fluid from the tail of the forebody The actual flow field velocity at the centerline of the wake is denoted as , where is the volume fraction of gas in the supercavitation and wake field formed after the precursor enters the water, and c is the wake interference proportionality coefficient, ranging from 0.10 to 0.25.

[0026] The physical validity of the calculated raw data is verified. If any parameter exceeds the physically reasonable range, the numerical simulation result is deemed invalid, and the calculation result or numerical model settings must be re-examined.

[0027] Stability characteristic parameters Physically reasonable range Head shock stagnation point pressure Non-uniformity of internal pressure of cavitation Pitch moment coefficient Equivalent angle of attack Asymmetric wetting factor wake interference intensity coefficient

[0028] Step 4: Calculate separately , , , , and Six characteristic parameter critical values:

[0029]

[0030] The critical angle of attack is an empirical value, related to the slenderness ratio of the vehicle. For most high-speed vehicles, the equivalent critical angle of attack is... The range is between 5° and 10°. In the above formula... Mach number, The radius of curvature of the aircraft's nose is given. The number of empty bubbles. , The reference pressure is the undisturbed environmental pressure. This is the saturated vapor pressure of water. The maximum lateral force coefficient is for an uncontrolled sailing body. k is the proportionality coefficient, which is approximately 2 for slender bodies; m is the critical proportionality coefficient for wake interference, ranging from 0.10 to 0.25; and n is the sensitivity index for the moment of inertia of the aircraft, ranging from 0.30 to 0.55. The moment of inertia of the rear body during pitch rotation. For pitch static stability derivatives, for an axisymmetric slender body, , This represents the distribution function of the cross-sectional area of ​​the aircraft along the x-axis, where the x-coordinate origin is O. p Take the apex of the bow of the aircraft carrier and point it towards the tail along the axial direction of the aircraft carrier. The position of the center of mass of the spacecraft along the axial x-direction (e.g.) Figure 4 (b) is shown.

[0031] Based on the aforementioned characteristic parameters, six instability modes of the aircraft are summarized, including: nose shock wave oscillation instability, cavitation pressure non-uniformity instability, asymmetric wetting instability, pitch divergence instability, angle-of-attack instability, and wake-induced instability. Based on these six instability modes, dimensionless instability factors are defined for each:

[0032] , , , , ,

[0033] Step 5: Set a stable critical threshold The critical value corresponding to the sum of instability factors:

[0034]

[0035] First calculate to If any If so, it is directly determined that the vehicle body is unstable when entering the water in sequence under this working condition, and the dominant instability mode is recorded as follows. The corresponding mode;

[0036] If all This indicates that none of the instability modes individually dominated the instability process, and the multi-factor coupling effect needs to be further considered. Therefore, the sum of the overall instability indices is calculated:

[0037]

[0038] This leads to the stability probability criterion:

[0039]

[0040] like (Right now The condition was determined to be stable, indicating that the vehicle was able to maintain a stable entry attitude under the disturbance of the wake of the forebody.

[0041] like (Right now ), was determined to be unstable, and further comparisons were made with each The size of the value is used to determine the dominant instability mode; if multiple The values ​​are close and all exceed If so, it is determined to be a complex instability mode.

Claims

1. A method for analyzing the stability of a high-speed vehicle entering water sequentially, characterized in that, First, calculate various instability factors: ， ， ， ， ， in This represents the pressure pulsation coefficient at the head shock wave stagnation point. This refers to the non-uniformity of pressure within the cavitation bubble. It is an asymmetric wetting factor. This is the pitch moment coefficient. For the equivalent angle of attack, This is the wake interference intensity coefficient. , , , , They are respectively , , , , , The critical value; If any If i=1~6, then it is directly determined that the water inlet of the vehicle is unstable under this working condition. , To stabilize the critical threshold; If all Further calculate the sum of the overall instability indices: This leads to the stability probability criterion: like If it is determined to be stable; It is determined to be unstable.

2. The method for analyzing the stability of a high-speed vehicle entering water sequentially according to claim 1, characterized in that, Dangruo This also includes further comparisons of various The size of the value is used to determine the dominant instability mode; - The corresponding instability modes are head shock oscillation instability, cavitation pressure non-uniform instability, asymmetric wetting instability, pitch divergence instability, angle of attack instability, and wake-induced instability.

3. The method for analyzing the stability of a high-speed vehicle entering water sequentially according to claim 1, characterized in that, in: in This represents the instantaneous stagnation point pressure in the flow field. This represents the stagnation point pressure in the flow field. Let be the density of the liquid water. This indicates that the two vehicles have the same entry velocity into the water. This represents the pressure parameter along the axis of the cavitation bubble. For the pitching moment of the aircraft, The maximum cross-sectional area of ​​the vehicle. The total length of the vehicle. and These represent the horizontal and vertical velocity components of the vehicle, respectively. This represents the area of ​​the surface of the vehicle facing the current that is in direct contact with the water. This represents the area of ​​the surface of the vehicle on the opposite side of the current that is in direct contact with the water. The total surface area of ​​the navigating surface. Indicates the actual velocity of the precursor. Indicates the distance of the fluid from the tail of the forebody The actual flow field velocity at the centerline of the wake is denoted as , where represents the volume fraction of gas in the supercavitation and wake field formed after the precursor enters the water, and c represents the wake interference proportionality coefficient.

4. The method for analyzing the stability of a high-speed vehicle entering water sequentially according to claim 1, characterized in that, The critical values ​​are as follows: in Mach number, D is the radius of curvature of the aircraft's nose, and D is the diameter of the aircraft. The number of empty bubbles. The reference pressure is the undisturbed environmental pressure. Let be the density of the liquid water. This indicates that the two vehicles have the same entry velocity into the water. For pitch static stability derivative, The maximum lateral force coefficient is k, and the proportionality coefficient is k. denoted as λ, where m is the critical proportionality coefficient for wake interference, and n is the sensitivity index of the vehicle's rotational inertia.

5. The method for analyzing the stability of a high-speed vehicle entering water sequentially according to claim 4, characterized in that, Empty bubble count for: in The reference pressure is the undisturbed environmental pressure. This is the saturated vapor pressure of water.

6. The method for analyzing the stability of a high-speed vehicle entering water sequentially according to claim 4, characterized in that, in The distribution function of the cross-sectional area of ​​the vehicle along the x-axis is given, where the origin of the x-coordinate is the vertex of the head of the vehicle and points towards the tail along the axial direction of the vehicle. Let x be the position of the center of mass of the spacecraft along the axial x-direction. The maximum cross-sectional area of ​​the ship. The total length of the vehicle.

7. The method for analyzing the stability of a high-speed vehicle entering water sequentially according to claim 1, characterized in that, The value of is between 5° and 10°.

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