Method for analyzing interference of multiple projectiles entering water at high speed in parallel

Abstract

The invention provides a multi-projectile high-speed parallel water entry interference analysis method, which comprises the following steps: (S1) establishing two same projectile three-dimensional geometric models, and taking three times of the diameter of the distance between the two projectiles; and (S2) importing the model into a fluid solver, and carrying out grid division and boundary condition setting. Dividing boundary layer grids on the surface of the projectile body so as to capture the complex flow phenomenon of the near wall surface; (S3) importing the model into a structure solver for grid division and defining material attributes; (S4) setting a monitoring point, endowing the projectile with an initial working condition, and performing numerical solution; and (S5) analyzing the disturbing force suffered by each parallel water-entry projectile by using a formula, and analyzing whether the cavitation bubbles are continuously fused or separated according to the cavitation bubble contour formula calculation and the cavitation bubble fusion criterion model. And if the cavitation bubbles are fused, adding a fusion factor, correcting the model of the disturbance force borne by the projectile, and calculating and analyzing the disturbance force borne by the projectile under the cavitation bubble fusion condition.

Description

Technical Field

[0001] The present invention belongs to the field of multiphase flow calculation and projectile dynamics, and specifically relates to an analysis of three-dimensional fluid interference during the parallel entry of multiple projectiles into water, and is particularly suitable for the evaluation of inter-projectile interference in salvo weapons. Background Art

[0002] Research on high-speed water entry is often conducted through theoretical studies, numerical methods, and experimental investigations. The entire water entry process generally refers to the time span from the moment the head of a structure contacts the water to complete wetting. During this process, the structure undergoes four stages: impact with the water, flow formation, cavitation navigation, and complete wetting. Simultaneously, strong interactions occur between the air, water, and structure, accompanied by a series of complex physical phenomena. The water entry process is transient, highly dynamic, and complex, making theoretical analysis of certain water entry phenomena quite difficult. Therefore, it is essential to establish analytical models and methods for the disturbances experienced by projectiles during high-speed water entry.

[0003] In actual scenarios, to respond to crisis situations, it is usually necessary to launch multiple projectiles continuously in a short period of time to increase the launch density to improve the hit rate and lethality. The interaction between projectiles greatly increases the complexity of the physical phenomena when entering the water and the impact on each projectile. The traditional single-projectile model cannot handle the phenomenon of cavitation fusion between projectiles. Therefore, it is also necessary to consider the interference encountered by multiple projectiles when entering the water at high speed. Summary of the Invention

[0004] The object of the present invention is to provide a method for analyzing the interference received by multiple projectiles when they enter water in parallel at high speed, so as to analyze the interference received by each projectile when multiple projectiles enter water in parallel at the same time.

[0005] The technical solutions for achieving the purpose of the present invention are:

[0006] A method for analyzing the interference experienced by multiple projectiles entering water at high speed and in parallel is proposed. The interference force experienced by projectile i is calculated using the following interference force formula:

[0007]

[0008] Γ j ′=Γ j (1+k r φ)

[0009]

[0010] Where ρ represents the density of the liquid, Γ j ′ represents the circulation Γ induced by projectile j j The correction value of r ij | represents the distance between projectile i and projectile j, Ai represents the characteristic area of ​​projectile i, represents the effective area of ​​projectile i perpendicular to the interference flow, and n j ′ represents the unit normal vector n of the vortex ring of projectile j j Corrected value, V j represents the velocity vector of projectile j, k r is the vorticity enhancement coefficient, φ is the fusion factor, and δn is the direction offset

[0011] Compared with the prior art, the present invention has the following significant advantages:

[0012] (1) Compared with the traditional projectile model, considering the influence of cavitation fusion between projectiles when multiple projectiles enter the water at high speed and in parallel, an interference force calculation model considering cavitation fusion is established by introducing the fusion factor, circulation, and unit normal vector of the vortex ring, which can more accurately analyze the interference between projectiles.

[0013] (2) Cavitation fusion criterion: A cavitation fusion criterion based on the fusion Weber number and the critical Weber number is proposed. By comparing the sizes of the two, it is determined whether the cavitation has fused, which provides a quantitative standard for the analysis of the cavitation state when multiple projectiles enter water. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Schematic diagram of the overall process.

[0015] Figure 2 Schematic diagram of supercavitating projectile dimensions.

[0016] Figure 3 Schematic diagram of the aerial simulation of a supercavitating projectile. DETAILED DESCRIPTION

[0017] The following will clearly and completely describe the technical solutions in the invention examples in conjunction with the drawings in the invention examples. Obviously, the described examples are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0018] like Figure 1 As shown, the embodiment of the present invention discloses a method for analyzing interference caused by multiple projectiles entering water at high speed in parallel, taking two projectiles entering water in parallel as an example. The method includes the following steps:

[0019] Step 1: Create a projectile geometry model. The structure of the projectile is a rotational body, such as Figure 2 As shown. Its diameter D is 12.7mm, the total length is 142mm, and the diameter of the head cavitator is D c In this example, two projectiles are selected to enter the water in parallel, and the distance S between the two projectiles is 3 times the diameter;

[0020] Step 2: Import the geometric model created in step 1 into the fluid solver, and establish the flow field calculation domain to define the gas-liquid environment of the projectile entering the water, such as Figure 3 As shown. Carry out mesh division and boundary condition setting. Set a two-dimensional fluid domain, with the horizontal direction along the free liquid surface as the x direction and the normal as the y direction. Set the calculation domain length along the x direction to 50D, and the calculation domain height along the y direction to 40D. Use hexahedral meshing to divide the background grid as the flow field calculation domain. The overlapping grid method is used to mesh the projectile and background domain, and the projectile sub-grid and background domain grid both use three-dimensional hexahedral grids. Locally encrypt the areas with large flow gradients and near the wall, and divide the boundary layer grid on the projectile surface to capture the complex flow phenomena near the wall. The boundary conditions are to simulate infinite airspace, and are all set to pressure outlets.

[0021] The VOF model is preferably selected as the multiphase flow model, which can describe multiphase flow fields composed of mixtures of water, water vapor, and non-condensable gases. The SST k-ω turbulence model can more accurately simulate various flow conditions, especially flows involving boundary layers, flow separation, and reattachment. The Z-Wart cavitation model is selected as the cavitation model. This model uses the modified Rayleigh-Plesset equation to describe the volume change of cavitation bubbles and is suitable for calculating the unsteady process of cavitation flow.

[0022] Step 3: Set monitoring points for each projectile: the projectile's center of mass, velocity monitoring point P1, displacement monitoring point P2, and lateral displacement monitoring point P3. Assign the projectile an initial operating condition: vertical entry into the water at a velocity of 450 m / s. Numerical calculations are used to determine the projectile's velocity, the disturbance force, and displacement and lateral deflection to determine whether the projectile is unstable.

[0023] Step 4: Use the formula to analyze the interference force on each parallel water-entering projectile. The interference force F on projectile i is i The calculation formula is as follows:

[0024]

[0025] Where ρ represents the density of the liquid; Γ j represents the circulation induced by the projectile j. According to Kelvin's circulation theorem, the circulation of the vortex ring shed from the projectile surface is equal to the circulation change caused by the projectile; |r ij | represents the distance between projectile i and projectile j; A i represents the characteristic area of ​​projectile i, which represents the effective area of ​​projectile i perpendicular to the interference flow. The interference flow is the interference of the vortex ring of projectile j on projectile i, which is the characteristic area; V j represents the velocity vector of projectile j; n jrepresents the unit normal vector of the vortex ring of projectile j (direction perpendicular to the vortex ring plane). For cylindrical / projectile objects, the circulation can be derived from the boundary layer separation point Where V j is the velocity of projectile j, D is the characteristic diameter of the projectile, and Cr is the circulation coefficient. r =0.25(1+0.2·Re 0.5 ), where Re is the Reynolds number.

[0026] Furthermore, in order to determine the possible interference caused by the fusion phenomenon of cavitation when the projectiles enter the water in parallel, the cavitation profile formula is used for calculation. This formula describes the elliptical distribution of the cavitation cross-section radius along the axial direction, with the semi-major axis L and the semi-minor axis R0:

[0027]

[0028] Where R(x) is the radius of the cavity at a vertical distance x from the projectile tip; R0 is the maximum radius of the cavity, V i is the velocity of projectile i; L is the total length of the cavitation bubble. Where D is the characteristic diameter of the projectile, C d is the cavitation characteristic coefficient, usually taken as 1.2; Where σ is the cavitation number, Where P is the static pressure of the environment, which is 101325Pa. v The saturated vapor pressure of the fluid is 3170 Pa, which is the saturated vapor pressure of water at room temperature. i is the velocity of projectile i, ρ is the density of the liquid, which is approximately 1000 kg / m 3 When the sum of the cavitation radii of adjacent projectiles is greater than or equal to the projectile spacing, fusion obviously occurs, and 2max[R(x)]≥|r ij |.

[0029] When 2max[R(x)]≥|r ij When |, the cavitation fusion criterion model is introduced to analyze whether the cavitation continues to fuse or separate. The formula is as follows:

[0030]

[0031] We crit =15(1+0.2N 1.5 )

[0032] Where We f is the fusion Weber number, ρ is the fluid density, and the density of seawater is 1025 kg / m 3 ; V iis the velocity of projectile i; D is the characteristic diameter of the projectile; τ is the surface tension of the liquid, and the surface tension of seawater is 0.0728 N / m; We crit is the critical Weber number; N is the number of adjacent projectiles, such as N = 2 when two projectiles are arranged side by side in a single row, and N = 3 when they are arranged in a triangle. f ≥We crit When the cavitation is combined, the boundaries of the cavitation bubbles around the projectiles will connect with each other due to the dominant force of fluid inertia (the surface tension effect is weakened), forming a larger joint cavitation structure. The fused cavitation bubbles will significantly change the pressure distribution of the local flow field, resulting in an increase in three-dimensional asymmetric loads, which may cause the projectile to become unstable.

[0033] Add the fusion factor to modify the interference force model of the projectile, calculate the influence of the cavitation fusion on the interference force of the projectile, and define the fusion factor:

[0034]

[0035] The vortex ring strength is enhanced due to the cavitation fusion, which affects the annular quantity Γ. j The correction is:

[0036] Γ j ′=Γ j (1+k r φ)

[0037] Where k r is the vorticity enhancement coefficient, k r ∈[0.3~0.4], the value in this example is 0.3.

[0038] After the cavitation fusion, the direction of the vortex ring changes accordingly. j The correction is:

[0039]

[0040]

[0041] Where r ji represents the vector from projectile j to projectile i. ji | is the distance between the two projectiles. The physical meaning of the directional offset vector δn is that after cavitation fusion, the direction of the vortex ring around projectile j is affected by the neighboring projectile i. The magnitude of this influence is proportional to the fusion factor, and the direction is the weighted average of the relative positions of the neighboring projectiles (the average of the unit direction vectors). When the degree of fusion is high and φ is large, the directional offset is large; the more projectiles there are, the more the influence of each projectile is averaged.

[0042] The corrected interference force formula on the projectile is listed as follows:

[0043]

[0044] It can be seen that in the liquid density ρ, A i represents the characteristic area of ​​projectile i, represents the effective area of ​​projectile i perpendicular to the interference flow, the interference flow is the interference of the vortex ring of projectile j on projectile i, and the speed of projectile j is V j , projectile distance|r ij |Unchanged, the amount of circulation Γ caused by cavitation fusion j ′ will directly lead to the increase of interference force, and the vortex ring unit normal vector n j The deflection of ' makes the projectile more likely to lose stability and rotate in the water. Therefore, the projectile spacing|r ij |, so that the interference force F i Reduce, or let 2max[R(x)]<|r ij |, the cavitation cannot contact and fuse to ensure the stability of the projectile. Or reduce the projectile speed, according to the cavitation radius formula It can be seen that when the projectile velocity decreases, the cavitation radius decreases. And ensuring the initial velocity of the projectiles is consistent when leaving the barrel, so that the velocity difference between the projectiles after entering the water is small, the interference force is small and the stability of the projectile is ensured.

Claims

1. A method for analyzing interference caused by multiple missiles entering water at high speed and in parallel, characterized in that: The interference force on projectile i is calculated using the following interference force formula: Where ρ represents the density of the liquid, Γ j ' represents the circulation Γ induced by projectile j j The correction value of r ij | represents the distance between projectile i and projectile j, A i represents the characteristic area of ​​projectile i, represents the effective area of ​​projectile i perpendicular to the interference flow, and n j ' represents the unit normal vector n of the vortex ring of projectile j j Corrected value, V j represents the velocity vector of projectile j, k r is the vorticity enhancement coefficient, φ is the fusion factor, and δn is the directional offset.

2. The interference analysis method for multiple missiles entering water at high speed and in parallel according to claim 1 is characterized in that: Where r ji represents the vector from projectile j to projectile i, |r ji | is the distance between two projectiles, and N is the number of adjacent projectiles.

3. The interference analysis method for multiple missiles entering water at high speed and in parallel according to claim 1 or 2 is characterized in that: The fusion factor value is: Among them, We f To integrate the Weber number, We crit is the critical Weber number.

4. The interference analysis method for multiple missiles entering water at high speed and in parallel according to claim 3 is characterized in that: We crit =15(1+0.2N 1.5 ) where D is the characteristic diameter of the projectile, τ is the surface tension of the liquid, and N is the number of adjacent projectiles.

5. The interference analysis method for multiple missiles entering water at high speed and in parallel according to claim 1 is characterized in that: Circulation Γ induced by projectile j j for: Where D is the characteristic diameter of the projectile, C r is the circulation coefficient.

6. The interference analysis method for multiple missiles entering water at high speed and in parallel according to claim 5 is characterized in that: Circulation coefficient C r for: C r =0.25(1+0.2·Re 0.5 ) Where Re is the Reynolds number.

7. The interference analysis method for multiple missiles entering water at high speed and in parallel according to claim 1 is characterized in that: By controlling the projectile spacing|r ij |, so that the interference force F i Reduce, or let 2max[R(x)]<|r ij |, cavitation bubbles cannot contact and fuse to ensure the stability of the projectile; in R(x) is the radius of the cavitation bubble at a vertical distance x from the projectile tip, R0 is the maximum radius of the cavitation bubble, V i is the velocity of projectile i; L is the total length of the cavitation bubble.

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