Research on the characteristics of projectile penetration into water based on fluid-structure Interaction

To study the water entry characteristics such as fuze overload, projectile overload and water-gas interface change during the penetration of projectile from air to water at different angles. Using the HyperMesh/LS-Dyna joint simulation tool and the fluid-structure-Interaction algorithm, the relevant characteristics of the projectile penetrating water at different angles (30 °, 60 °, 90 °) are simulated numerically. The numerical simulation results show that the axial overload peak of the projectile is almost unchanged when the projectile penetrates the water at different angles, and the axial overload peak of the fuze decreases with the increase of the angle. Both the radial overload peak of the projectile and the fuze decrease with increasing water entry angle. The results show that the shock wave generated when the projectile penetrates into the water has a greater effect on the radial overload of the projectile and fuze than on the axial overload.


Introduction
In view of the research on the impact problem of projectile penetration into water, domestic and foreign researchers have carried out relevant research from different angles.For example, projectile penetration into water is a complex physical process, when the projectile penetrates into the water at a certain speed will produce cavitation effect, relevant studies have shown that when the projectile penetrates into the water at a lower speed will produce cavitation effect, the generation of cavitation effect will affect the motion characteristics and hydrodynamic characteristics of the projectile into the water [1], so there are many research literature on the empty cannon effect of low-speed projectile penetration into the water [2,3].Dong Shengpeng et al. conducted numerical simulation research on the process of entering the water at different speeds and different falling angles of a medium-caliber naval gun, and studied the change law of the pre-flush overload when the projectile penetrated into the water [4]; Liu Yu et al. used numerical simulation to study the overload response of bullet penetrating into water [5].
Fluid-Structure-Interaction (FSI) is used to describe the interaction and mutual influence between moving or deformed solids and the fluid's internal or external flow field, simply put, the various behaviors of deformed solids under the action of fluid (force, heat), involving the coupling calculation of flow field and structure, which essentially belongs to the coupling behavior of multiple physical fields, and its key point lies in the interaction between fluid and solid.In the simulation analysis using FSI algorithm, the influence of fluid on solid is generally ignored, but in some problems, solid deformation cannot be ignored, and the interaction between fluid and solid plays a key role in the result, and the FSI method needs to be used to analyze the problem.Therefore, for the simulation of projectile penetration by air into water, it is more appropriate to use the FSI algorithm for calculation.

Build 3D model
The projectile is composed of warhead and fuze.The warhead material is 30CrMnSi, the projectile diameter is 320mm, the two sets of fuzes are eccentrically and symmetrically installed at the bottom of the projectile, and the two sets of fuzes are redundant in parallel with each other.The schematic diagram of the projectile is shown in Figure 1.

Figure 1. Schematic diagram of projectile
The fuze in Figure 1 includes the fuze shell, pressure screw, test device and battery base, and the charge is replaced by counterweight.

Establish finite element model
The numerical calculation adopts HyperMesh/LS-DYNA finite element analysis software.When modeling warhead and fuze, the simplified treatment is carried out without affecting the calculation results.The details such as thread and chamfer are removed.The booster charge is only attached to the fuze shell as a mass counterweight.Considering the symmetry of non normal penetration, only half of the model is established, and the influence of sea waves is not considered in the simulation process.
The simulation model is mainly composed of warhead, fuze, air, water, etc. ALE algorithm is used for air and water, Larrange algorithm is used for warhead, fuze, etc., and contact penalty function coupling algorithm is used for the interface between warhead and air and water.Boundary conditions: apply transmission boundary conditions on the boundary of water and air models to simulate the effect of infinite fluid domain; At the boundary of water-structure and air-structure, the constraint equation is established by Euler/Lagrange penalty function coupling algorithm, coupling the structure and fluid, and realizing the transfer of mechanical parameters; At the water-air boundary, the material boundary is controlled by multiple material units.
According to the above analysis, the HyperMesh software is used for finite element modeling.The whole modeling process uses the cm-g -µ s unit system.The mesh unit is the hexahedral SOLID 164 unit, in which the air and water center grids are slightly dense (the part in contact with the warhead), and the transition to the surrounding part is from dense to sparse.The finite element model is shown in Figure 2. In Figure 2, the boundary between the water grid and the air domain grid is co-noded, and in the fluid-structure interaction algorithm, the projectile mesh should be completely contained in the air domain grid, and there is no co-node relationship between the projectile mesh and the air/water domain grid.

Constitutive parameter
The warhead material is 30CrMnSiA2, and the bilinear follow-up plastic material model is selected; The fuze shell and screw material are TC4, and the follow-up plastic material model is selected; The test device, counterweight and battery holder material are duralumin 2A12, and the follow-up plastic material model is selected; the NULL model is used for air and water, and the equation of state is GRUNEISEN.The basic material parameters are shown in Table 1.

Boundary condition setting
According to the symmetry of the model structure, in order to reduce the amount of calculation, a halfmodel is used, so symmetrical constraints are established at the symmetrical surfaces of the air domain, water domain and projectile, and non-reflective constraints are established at the rest of the boundary of the air domain and water domain.Automatic contact algorithm is adopted between the projectile body and the charge, and between the projectile body and the fuze shell, and the automatic contact and fixed contact algorithm are adopted between the fuze shell and the screw, the test device and the battery holder, and the projectile penetration speed is 850m/s, and the penetration angle is 30°, 60° and 90°, respectively.

Simulation Results of Condition 1
The finite element model that has been set up is imported into the display dynamics calculation program LS-DYNA to solve and calculate three working conditions, among which the working condition 1 is the projectile 30° drop angle penetration into the water, the working condition 2 is the projectile 60° drop angle penetration into the water, and the working condition 3 is the projectile 90° drop angle penetration into the water.The process of projectile penetrating water at 30 ° angle of impact is shown in Figure 3.It can be seen from Figure 3 that when the projectile penetrates into water, the projectile deflects slightly under the effect of water resistance, so that the shock wave generated by the projectile penetrates into water has an impact on the radial overload of the projectile and fuze.Due to the small penetration angle (30 °), the impact of shock wave on radial overload is large.
The velocity change curve of projectile penetrating water at 30 ° angle is shown in Figure 4.It can be seen from Figure 4 that when the projectile penetrates into water for 2000 μs, the velocity decreases from 850m/s to 835m/s.
The axial overload change curve of projectile penetrating water at 30 ° angle of impact is shown in Figure 5.It can be seen from Figure 5 that when the penetration angle is 30 °, the peak axial overload of the projectile body is about 1280g, and the peak axial overload of the fuze is about 6200g.
The radial overload change curve of projectile penetrating water at 30 ° angle of impact is shown in Figure 6.It can be seen from Figure 6 that when the penetration angle is 30 °, the peak radial overload of the projectile body is about 1650g, and the peak radial overload of the fuze is about 5000g.
The axial and the radial overload change curve of projectile penetrating water at 30 ° angle of impact is shown in Figure 7.It can be seen from Figure 7 that the contact problem between the fuze and the missile body leads to the superposition of the stress waves between the two.Therefore, the peak value of the fuze overload is far greater than the peak value of the missile body overload, whether it is radial or axial.

Simulation Results of Condition 2
The process of projectile penetrating water at 60 ° angle of impact is shown in Figure 8.It can be seen from Figure 8 that when the projectile penetrates into water, the projectile deflects slightly under the effect of water resistance, so that the shock wave generated by the projectile penetrates into water has an impact on the radial overload of the projectile and fuze.As the penetration angle of the projectile increases to 60 °, the gap between the shock wave pressure on both sides of the projectile decreases, and the shock wave pressure on the radial direction of the projectile and the fuze decreases gradually.
The velocity change curve of projectile penetrating water at 60 ° angle is shown in Figure 9.

Figure 9. Velocity curve
It can be seen from Figure 9 that when the projectile penetrates into water for 2000 μs, the velocity decreases from 850m/s to 834m/s.
The axial overload change curve of projectile penetrating water at 60 ° angle of impact is shown in Figure 10.It can be seen from Figure 10 that when the penetration angle is 60 °, the peak axial overload of the projectile body is about 1280g, and the peak axial overload of the fuze is about 4800g.
The radial overload change curve of projectile penetrating water at 60 ° angle of impact is shown in Figure 11.It can be seen from Figure 12 that the contact problem between the fuze and the missile body leads to the superposition of the stress waves between the two.Therefore, the peak value of the fuze overload is far greater than the peak value of the missile body overload, whether it is radial or axial.

Simulation Results of Condition 3
The process of projectile penetrating water at 90 ° angle of impact is shown in Figure 13.It can be seen from Figure 13 that when the projectile penetrates into water, the projectile deflects slightly under the effect of water resistance, so that the shock wave generated by the projectile penetrates into water has an impact on the radial overload of the projectile and fuze.As the penetration angle of the projectile continues to increase to 90 ° (the projectile penetrates the water vertically), the shock wave pressure on both sides of the projectile gradually tends to be balanced, at this time, the shock wave pressure on the projectile and the fuze radially is the smallest.
The velocity curve of projectile penetrating water at 90 ° angle is shown in Figure 14.It can be seen from Figure 15 that when the penetration angle is 90 °, the peak axial overload of the projectile body is about 1280g, and the peak axial overload of the fuze is about 3800g.
The radial overload change curve of projectile penetrating water at 90 ° angle of impact is shown in Figure 16.It can be seen from Figure 16 that when the penetration angle is 90 °, the peak radial overload of the projectile body is about 32g, and the peak radial overload of the fuze is about 160g.
The axial and the radial overload change curve of projectile penetrating water at 90 ° angle of impact is shown in Figure 17.It can be seen from Figure 17 that the contact problem between the fuze and the missile body leads to the superposition of the stress waves between the two.Therefore, the peak value of the fuze overload is far greater than the peak value of the missile body overload, whether it is radial or axial.

Conclusion
The following conclusions can be drawn from the analysis of the numerical simulation results of the projectile penetrating into water at a speed of 850 m/s and at different angles: (1) With the increase of penetration angle (from 30 °, 60 ° to 90 °), the axial overload peak of the projectile is almost constant, while the radial overload peak is 1650g, 580g and 32g respectively, and the radial overload peak of the projectile gradually decreases to 32g.
(2) With the increase of penetration angle (from 30 °, 60 ° to 90 °), the axial overload peak of the fuze is 6200g, 4800g and 3800g respectively, while the radial overload peak is 5000g, 2700g and 160g respectively, and the radial overload peak of the fuze gradually decreases to 160g.
(3) It can be seen from ( 1) and ( 2) that the impact of the shock wave generated when the projectile penetrates into the water at the same speed and at different angles on the axial overload of the projectile and fuze is less than that on the radial overload.

Figure 11 .
Figure 11.Radial overload curveIt can be seen from Figure11that when the penetration angle is 60 °, the peak radial overload of the projectile body is about 580g, and the peak radial overload of the fuze is about 2700g.

Figure 14 .Figure 15 .
Figure 14.Velocity curveIt can be seen from Figure14that when the projectile penetrates into water for 2000 μs, the velocity decreases from 850m/s to 833m/s.The axial overload change curve of projectile penetrating water at 90 ° angle of impact is shown in Figure15.