Expansion Characteristics of Liquid-filled Cell on Hydrodynamic Ram Effect Subject to the Impact of High-speed Projectile

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(1.College of Naval Architecture and Ocean Engineering,Naval University of Engineering,Wuhan 430033,China;2.Unit 31202 of PLA,Guangzhou 510510,China)

Abstract: To investigate the effect of the expansion characteristics of the cell on the hydrodynamic ram(HRAM),several types of cell structures with different configurations are designed,numerical simulations of cell structures under high-speed projectile penetration are carried out,and the effect of the wall thickness is discussed.The concept of‘expansion impedance’is proposed to quantify the cell expansion characteristics.The attenuating effect of the cell expansion characteristics on the cavitation pressure caused by HRAM is also analyzed.The results show that the smaller the expansion impedance is, the easier the cell is to expand and deform.When the expansion impedance of the cell structure decreases,the bulging process of the cell will reduce the cavitation pressure load strength and attenuate the HRAM.Besides, the expansion impedance value shows a correlation with the thickness of the side walls when the cavitation pressure load is small and the expansion impedance value is related to the matching relationship of the thickness of each wall when the cavitation pressure load is large.

Key words:hydrodynamic ram;liquid-filled cell;expansion impedance;cavitation pressure load

0 Introduction

A strong pressure wave and liquid flow will be produced when a high-speed projectile penetrates a liquid-filled structure, which will induce catastrophic deformation and failure of the structure walls,and even lead to the burst of the overall structure[1-4].The pressure load caused by the hydrodynamic ram (HRAM) consists of the initial shock wave, the cavitation pressure load on the walls induced by radial liquid cavitation, and the localized high pressure in front of the projectile[5-6].Among them, the initial shock wave has a high peak value and short duration, and the strength of the projectile penetration point is very high, which attenuates rapidly with the increase of propagation distance[7].This mainly leads to the local reverse dish bending of the structure near the impact point.The localized high pressure in front of the projectile mainly leads to the local bending and perforation failure of the rear wall[8-9].The cavitation pressure load induced by the radial liquid motion and cavitation has a low peak value and long duration, so the specific impulse is relatively large[5,10].This mainly leads to the bulging deformation and corner tearing of the whole structure.When the size of the cavity formed in the liquid-filled cell subjected to projectile penetration is in the same order of magnitude as that of the cell itself, the pressure load induced by cavity expansion becomes the main load causing the deformation and failure of the overall structure[11].

At present, a large number of studies have been conducted on the influencing factors of the HRAM effect on the deformation and failure of liquid-filled containers[12-15].Chen et al[16]held that the deformation of the fuel tank mainly occurs in the cavitation and projectile exit phases.The deformation and failure modes of the structure are affected by many factors including the wall thickness, projectile velocity, projectile shape, container size and water filling ratio[17-20].Nishida et al[21]carried out impact tests on aluminum alloy thin-walled square tubes and the results showed that the strength of the wall material and the diameter of the bullet are the main influencing factors.The cavity formed due to HRAM is obviously affected by the shape of the liquid-filled structure, which could be observed in the 7.62 mm ballistic impact test by Deletombe et al[22].The volume and evolution law of the cavity largely depend on the geometry and stiffness of the container.Guo et al[23]studied the constraint effect of the container size on cavity evolution as the high-velocity projectile moved through water by a series of experiments.The results showed that compared to the small container,the cavity radius of the large container is bigger and the collapse occurs later.The maximum cavity radius increases linearly with the container radius.When the size of the container is reduced to the same size as the diameter of the cavity, the coefficient of drag is obviously larger than that of other large containers.Gao et al[24]analyzed the structural dynamic response and characteristics of loads on walls of the liquid-filled concave cells and cuboid cells under high-speed projectile penetration.Compared with the cuboid cell,the concave cell is more prone to expand and deform,which can effectively reduce the cavitation pressure load.Zhang et al[25]performed the numerical simulation for the spherical projectile impacting liquid-filled tanks with different configurations by taking the residual velocity of the projectile,pressure of the specific element and wall deformation as indicators.The fluid in the containers with different geometric configurations subjected to high-speed projectile penetration will produce different radial motions and cavitation,thus resulting in different pressure on the walls.In addition,studies have also shown that the geometric configuration,cell dimensions and strength of the wall material of the container etc.affect the pressure load and cavity produced by HRAM,while these factors are attributable to the different expansion characteristics of different structures[26-28].At present,the research on the influence of expansion characteristics of the structure on HRAM effect is yet to be initiated,which is of great significance to improve the defense performance of liquid-filled structures.

According to the generation principle of HRAM effect, the characteristics of loads on walls of the liquid-filled cell structure and the influence of cell expansion characteristics on the loads are firstly investigated, then several cell structures with different configurations are designed and the concept of‘expansion impedance’are put forward to quantify cell expansion characteristics.Finally numerical calculations for the high-speed projectile penetrating the liquid-filled cell using finite element analysis software are performed, and the relationship between the expansion impedance and cavitation pressure load is analyzed, so as to provide a reference for the design of liquid-filled structures.

1 Cell expansion characteristics

1.1 Definition of cell expansion impedance

The degree of the cell expansion depends on the internal pressure load and expansion characteristics of the structure.According to the definition of electric resistance,the expansion impedance of a cell is the ratio between the evenly-distributed pressure load on the inner surfaces of cell wallspand the increment of the relative volume of the cell under loading ΔV/V,expressed byδE,which is given by

wherepis the static or dynamic pressure load, and the obtained expansion impedance is correspondingly the static or dynamic expansion impedance.When the pressure load on the inner surfaces of the cell walls is constant,the larger the expansion impedance,the smaller the increment of the cell volume.The cell expansion impedance is influenced by the cell configuration, cell wall thickness and strength of the wall material.

The dynamic expansion impedance is also related to the dynamic characteristics of the structure.As the natural vibration period of each wall of the structure is different,they oscillate with different frequencies under dynamic loading.The dynamic expansion impedance is closely linked to the load spectrum characteristics that different load levels and durations will cause diversified dynamic deformations of the walls.Therefore, the dynamic expansion impedance is closely related to the natural vibration period of the wall and the load characteristics,which is not easy to calculate.

When the loading duration is much less than the natural vibration period of the structure wall,a subtransient impact expansion impedance can be defined.The expansion impedance is the ratio between the impulse of load per unit area and the increment of the relative volume of structure.During a HRAM event, the pressure load caused by radial liquid flow and cavitation usually does not meet the condition that the load duration is far less than the natural vibration period of the walls,so the static expansion impedance is used to characterize the expansion characteristics of the structure in this paper.

1.2 Expansion impedance of cells with different configurations

1.2.1 Cell configuration design

To study the expansion characteristics of cells with different configurations, four types of cell structures are designed: concave, cuboid, convex and cylindrical cell structures.The sizes of the concave and cuboid cells follow the design in Ref.[29],and those of the convex and cylindrical cells are determined according to the principle of equal volume and equal length of water region, as shown in Fig.1.The convex cell is 296 mm in height and 148 mm in width with 260 mm in length of water region.The cylindrical cell is 144.6 mm in radius with 260 mm in length of water region.The cell wall thickness is 2 mm,and the whole structure is filled with liquid.

1.2.2 Expansion impedance of cells with different configurations

Fig.1 Schematic diagram of the cell dimensions(mm)

To investigate the expansion impedance of cells with different configurations, finite element models of the concave,cuboid,convex and cylindrical cells are established using shell elements,related modeling methods can be found in Ref.[24].The cell structure consists of Q235 steel,and the bilinear elastic-plastic constitutive model is utilized to describe the steel material,with a density of 7850 kg/m3,an elastic modulus of 210 GPa,Poisson's ratio of 0.3,a hardening modulus of 250 MPa and a yield strength of 235 MPa.The dynamic finite element software LS-DYNA is used for numerical calculation to obtain the expansion impedance of cells with different configurations by applying uniform internal pressure load on the cell wall (Fig.2(a)).To reduce the vibration of cell wall deformation, the rise time of applied load is obviously longer than the first natural period of vibration of the largest cell wall and the load remains constant after the load reaches the target value (Fig.2(b)).

Fig.2 Application mode of pressure load

When the applied pressure is greater than 1.0 MPa, the destruction appears on the concave cell wall due to excessive loading, and the volume of the deformed structure cannot be accurately measured.This means that the expansion impedance after cell damage is not considered in the calculation.Fig.3 shows the time-displacement curve of the central point on the upper wall of the concave cell under the load of 0.4 MPa.As shown in Fig.3, after the load is stabilized, the variation of displacement of the cell wall is small,which meets the requirement of calculating the expansion impedance.

The volume of the cell structures after their deformation and failure is calculated by Hypermesh.The relationship between the increment of the relative volume of cell and the applied internal pressure load on the wall is shown in Fig.4.

Fig.3 Time-displacement curve of the central point on the upper wall of the concave cell(0.4 MPa)

Fig.4 Relationship curves between the relative volume increment of cells and pressure load (t=2 mm)

Fig.5 Remaining sidewall spacing curve of the concave cell

As shown in Fig.4, when the internal pressure load is relatively small, all the walls of the cell are in the stage of elastic deformation.The growth rate of the relative increment of its volume gradually slows down with the increase of the internal pressure load.The reason for the above phenomenon is that each wall of cell is mainly in elastic bending deformation that is relatively easy to occur at first.When the internal pressure load is relatively large, the walls of cuboid cell (>0.2 MPa),convex cell and cylindrical cell (>0.3 MPa) begin to form plastic hinged lines at the boundary(Fig.4(b)), resulting in elastic-plastic membrane deformation.The increment of the relative volume of cell increases approximately linearly with the increase of the internal pressure load,and the expansion deformation of the concave cell also has the stage of elastic-plastic buckling deformation except for elastic and plastic deformation.When the internal pressure is between 0.2 MPa and 0.5 MPa,the relative volume increment of the concave cell is approximately linear with the internal pressure load,and the deformation of each wall is mainly elastic-plastic membrane deformation.When the pressure is greater than 0.5 MPa,the concave wall and edge begin to undergo buckling deformation(Fig.5),and the volume growth rate increases gradually.

In addition,as the cavitation pressure load generated by HRAM is relatively large,the walls of the cell will undergo large plastic deformation and the concave wall will undergo buckling.Therefore, the range of the internal pressure load considered in calculating the expansion impedance of the structure should be greater than 0.5 MPa,where the concave cell has the largest relative volume increment,followed by the cuboid cell,and finally the cylindrical cell.

The expansion impedance of the cells with different configurations is calculated by Eq.(1), whose results are shown in Fig.6.As shown in Fig.6, it can be observed that the expansion impedance of the cell changes with the increase of pressure load.When the pressure is less than 0.4 MPa, the expansion impedance of the concave cell is slightly larger than the cuboid cell.With the increase of the pressure, the expansion impedance of the concave cell decreases obviously, and its value is gradually lower than that of the cuboid cell, indicating the expansion of the concave cell is easier than that of the cuboid cell under the larger load.The expansion impedance of the convex cell and the cylindrical cell is large when the initial load is very small, showing the property of expanding difficulty.

The expansion impedance of the four cells all increase first and then decrease, and the cell is not easy to expand when load is small.When the pressure is added to a certain value,the cell walls change from elastic membrane deformation to elastic-plastic membrane deformation,and the expansion impedance decreases slightly.When the pressure is greater than 0.5 MPa,the concave cell has the smallest expansion impedance so that it is most prone to expand and deform among the four cell structures.In comparison,the cylindrical cell has the largest expansion impedance.

1.3 Expansion impedance of cells with different wall thicknesses

In order to investigate the difference of the expansion characteristics of the cells under different wall thicknesses, the finite element models of the concave cell with different wall thicknesses are further developed.To ensure that the velocity of the projectile entering and exiting the water is not affected by the wall thickness,the thickness of the front and rear walls of the cells is 2 mm,and only the thickness of the rest of the walls is changed.A total of six types of cells are set up with the thicknesses of 1 mm, 2 mm, 3 mm, 4 mm, 6 mm and 8 mm, except for the front and rear walls (referred to as the side walls).A uniform pressure load is applied to simulate the HRAM effect on the walls, and the pressure application position and method are consistent with those shown in Fig.3.The maximum value of applied pressure is up to 1 MPa.

Fig.6 Expansion impedance of different cells under the pressure load

The calculated expansion impedance of the concave cell in each working condition is shown in Fig.7.For the cell with a wall thickness of 1 mm, a breakage occurs at the central point of the junction line between the front(rear) and left (right) walls of the cell after the pressure load reaches 0.2 MPa,thus the expansion impedance value after structural failure is not calculated.

In general, the increase of the thickness of the side walls raises the expansion impedance of the cell which makes it more difficult for the structure to undergo bulge deformation.The deformation process of each wall surface of the cell can be divided into two phases: bending deformation and membrane deformation.When the thickness of the side walls is smaller (2 mm, 3 mm), the two deformation phases of the front and rear walls and the side walls occur almost simultaneously,so the deformation of the whole structure can also be divided into two phases: bending deformation and membrane deformation, and the expansion impedance is expressed as rising-declining.When the thickness of the side walls surface is larger (4 mm, 6 mm, 8 mm), the structure deformation can be divided into three phases: the front and rear walls bending, the front and rear walls membrane deformation, and the side walls bending.Thus, the structural expansion impedance is also reflected as‘rising-declining-rising’.

In addition, for the cells with side walls with a thickness of 2 mm to 8 mm, all walls are in the bending deformation phase when the pressure is smaller (0.1 MPa to 0.5 MPa), and the expansion impedance difference is smaller for each cell with different side wall thicknesses.However, the bending/membrane deformation phase of each cell wall is different when the pressure is greater (0.5 MPa to 1 MPa), and the expansion impedance difference of each cell with different side wall thickness increases significantly.It can be seen that the thickness matching relationship of each wall can lead to different deformation patterns of the cell, which can affect the expansion impedance change process of the cell.This phenomenon is especially obvious at higher pressure values.

2 Influence of cell expansion characteristics on HRAM pressure load

Fig.7 Comparison of expansion impedances of concave cells with different wall thicknesses

2.1 Influence of cell configuration on HRAM pressure load

The numerical simulation and calculation of liquid-filled cells with four configurations under high-speed projectile penetration are conducted using the dynamics analysis software LS-DYNA.To save calculation time, 1/2 finite element models of the concave, cuboid, convex and cylindrical cells are established.Among them, eight groups of ballistic impact experiments are carried out,with both the concave cells and cuboid cells filled with liquid.The specific details are described in Ref.[24].Solid elements are adopted.The mesh generation,material model,contact setting and algorithm setting are designed according to Ref.[24].Cylindrical projectiles with a diameter of 14.5 mm and a length of 18 mm are selected for the experiments.In order to verify the reliability and accuracy of the simulation method,the simulation is performed according to the actual impact position and the initial velocities of the projectiles.The residual velocities and the maximum deformation of cell walls are calculated and compared with the experimental results.The relative deviation of the residual velocities is within 10%,which proves the numerical simulation method can simulate the velocity attenuation of projectiles accurately.

In order to explore the acting law of the pressure load for different cells filled with liquid under the penetration of a high-speed projectile, the projectile's incident velocityv=981 m/s is kept constant in the numerical calculation.The center of the cross section of the projectile and the centers of the front and rear walls of the cell are on a straight line.The total time of numerical calculation is 8 ms.Two Eulerian locations are selected for different cells to record the pressure time history, numbered E-1 and E-2 respectively.Their distance to the axis of symmetry is equal, and the distance between the same measuring point of the different cells and the front wall is also the same.At the typical positions near the side wall,three Eulerian locations are selected to record the pressure time history, numbered E-3, E-4 and E-5 respectively.The distances from E-3 and E-4 to the axis of symmetry are equal.At the corners of the cell, two Eulerian locations are selected to record the pressure time history,numbered E-6 and E-7 respectively.The specific layout of the selected Eulerian locations is shown in Fig.8.

Fig.8 Arrangement of selected locations to represent the pressure time history inside different cells

2.1.1 Comparative analysis of load characteristics of concave cell and cuboid cell

Fig.9 shows the pressure time history plots of the concave and cuboid cells at the typical positions on the side wall and inside the cell.From the figure, although the projectile is gradually far away from the pressure measuring point, the pressure at the measuring points will rise again after some time.The reason is that part of the kinetic energy of the projectile is transferred to the liquid in the drag stage which causes the liquid to move outwards in the radial direction[30].Due to the obstruction of the cell walls to the liquid motion,the liquid exert pressure on the walls[31]which results in pressure load rising.For the measuring points inside the cell,it can be seen in Figs.9(a)-(b)that there is little difference in the initial shock wave peak values in the early stage, especially at E-1 where the pressure peak values are almost the same.For the cavitation pressure load at E-1, the cuboid cell is remarkably greater than the concave cell in the range of 400-800 μs, and the same trend appears at E-2 in the range of 500-1400 μs.For the measure points near the cell side wall,the pressure time history plots in Figs.9(c)-(d)show that there is a significant difference in the cavitation pressure loads between the concave cell and the cuboid cell.Compared with that of the cuboid cell,the cavitation pressure load of the concave cell is smaller.

Fig.9 Pressure time history plots of typical positions of the concave cell and cuboid cell

By integrating the aforementioned pressure time history plots, the specific impulse of the cavitation pressure load on the typical positions on the cell side walls and inside the cell is obtained, as shown in Fig.10.From the figure, the cavitation pressure loads of the concave cell at all measuring points are less than those of the cuboid cell.Especially for the center of the side wall (E-5) of the concave cell, the specific impulse of the cavitation pressure load is far less than that of the cuboid cell due to the premature entry into the cavitation zone.As shown in Fig.9, the cavitation pressure load on the wall is generally greater than 0.3 MPa.In this case, the expansion impedance of the concave cell is smaller than that of the cuboid cell.

Fig.10 Specific impulses of cavitation pressure load at different positions of the concave cell and cuboid cell

2.1.2 Comparative analysis of load characteristics of cuboid cell and convex cell

Fig.11 Pressure time history plots of typical positions of the side walls of the cuboid cell and convex cell

Fig.11 shows the pressure time history plots of typical positions on the side walls of the cuboid cell and convex cell.It can be observed from the figure that for the typical positions near the side wall, the peak of the cavitation pressure load of the convex cell is greater than that of the cuboid cell,and the pressure loads on the convex cell walls are generally larger during the cavitation extrusion phase.Fig.12 presents the specific impulses of the cuboid cell and convex cell at typical positions of the side walls.From the figure, the specific impulse of the cavitation pressure load on the convex cell is greater than that on the cuboid cell,but their difference is not significant.According to the above calculation results, the expansion impedance of the cuboid cell is smaller than that of the convex cell, which makes it more prone to expand and deform under loading and effectively mitigates the pressure load exerted by the liquid on the wall.

2.1.3 Comparative analysis of load characteristics of convex cell and cylindrical cell

For the convex cell and cylindrical cell,the Eulerian locations in front of the center of the side wall are selected to record the pressure time history.The distance from the position to the front and rear walls is equal,and their distance to the axis of symmetry is also approximately equal.The pressure time history plots of the convex and cylindrical cells are obtained, as shown in Fig.13.From the figure,the cavitation pressure load on the convex cell walls is generally less than that on the cylindrical cell walls.

Fig.12 Specific impulses of cavitation pressure load at typical positions of side walls of cuboid cell and convex cell

The specific impulses of the cavitation pressure load in the center of the side walls of the convex cell and cylindrical cell are 442.4 and 836.6, respectively.The cavitation pressure load is generally greater than 0.1 MPa,and the specific impulse of the cavitation pressure load on the cylindrical cell is approximately twice that on the convex cell.In this case,the expansion impedance of the convex cell is less than that of the cylindrical cell.The convex cell is more prone to expand and deform than the cylindrical cell.

Fig.13 Pressure time history plots at the center of side walls of the convex cell and cylindrical cell

Fig.14 Specific impulses of cavitation pressure load at the corners of the cells with different configurations

Fig.14 presents the specific impulse of cavitation pressure load at corners of cells with different configurations.The specific impulse of the convex cell is very small because of the premature entry into the cavitation zone at the corners.The specific impulse of cavitation pressure load on the concave cell wall is the smallest, followed by the cuboid cell while that on the cylindrical cell wall is the biggest, which is consistent with the findings in the above research.The cell configuration will affect the pressure load on the walls and inside the water.The concave cell has the smallest expansion impedance, making it more prone to expand and deform after being penetrated by a highspeed projectile and mitigating the pressure load exerted by liquid motion on the walls caused by HRAM event to some extent.The above results indicate that the cavitation pressure load on the walls is affected by the expansion impedance of the cell.The smaller the expansion impedance of the cell is, the easier it is to expand and deform, which helps mitigate the pressure load exerted by the liquid on the walls and thus reduces the cavitation pressure load.

2.2 Influence of cell wall thickness on hydrodynamic ram pressure

The liquid-filled concave cells with wall thicknesses of 1 mm, 2 mm, 3 mm, 4 mm, 6 mm and 8 mm are modelled with solid elements.The numerical calculation is performed for a high-speed projectile penetrating the liquid-filled cells with different wall thicknesses.No changes are made for the six types of cells except for varying wall thickness.To ensure that the impact and exit velocities of the projectile are not affected by the wall thickness,the front and rear wall thicknesses of all the cells are set to 2 mm.In the numerical calculation,the incident velocityv=981 m/s is kept constant, and the center of the cross section of the projectile and the centers of the front and rear walls of the cell are on a straight line.The principle of selecting Eulerian locations to record the pressure time history is the same as the above(Fig.8).

Fig.15 Specific impulses-time histories of cells with different wall thicknesses(P-1)

2.2.1 Cell interior

In Fig.15, the specific impulse of pressure load at P-1 inside the cell is plotted against time.

The specific impulse of pressure load increases rapidly as the projectile moves through water at the initial moment, and the specific impulses of the six types of cells are almost equal.At around 120 μs, the specific impulse growth rate changes.The cell with a wall thickness of 8 mm has the fastest growth and the cell with a wall thickness of 1 mm has the slowest growth.At around 1300 μs, the specific impulse growth rate further decreases and finally the specific impulse tends to be stable.It can be seen from the figure that there is almost no difference in the effect of initial shock wave pressure on different cells.As the projectile exits the rear wall at about 650 μs,the difference of specific impulses of the cells with different wall thicknesses increases gradually.At this time, the HRAM event has entered the cavitation extrusion phase, and the walls are mainly subjected to the pressure load exerted by the liquid, indicating that the varying wall thickness affects the cavitation pressure load.

Figs.16-17 show the relationship between the initial shock wave peak pressure and wall thickness.When the projectile penetrates through the front wall and enters into the cell,the initial shock wave generated by the projectile impacting the liquid is first captured at P-1.As the front wall thickness remains unchanged, the peak pressures of initial shock wave on each cell are almost the same.Then the initial shock wave propagates around.When it reaches P-2, the peak pressure of cells with different wall thicknesses changes,but the difference is small.

Fig.17 Pressure time histories of selected locations inside the concave cells with different wall thicknesses

Fig.16 Relationship curves between initial shock wave pressure peak of concave cells and wall thickness

Fig.18 Specific impulses of cavitation pressure load inside concave cells with different wall thicknesses

By integrating the pressure time histories of cells with different wall thicknesses during the cavitation extrusion phase, the specific impulse of cavitation pressure load is obtained (Fig.18).From the figure, the action of the cavitation pressure load on the walls is affected by the wall thickness.When the wall thickness rises from 2 mm to 3 mm,the specific impulse of cavitation pressure load has the largest increase,which is consistent with the change law of expansion impedance.The expansion impedance also has the largest increase when the wall thickness rises from 2 mm to 3 mm.When the wall thickness exceeds 4 mm,the rise rate of specific impulse of cavitation pressure load reduces and the specific impulse tends to be stable.

2.2.2 Rear wall of cell

The transverse of the rear wall is defined asx.Seven Eulerian locations are selected at the positions in front of the rear wall 1 cm,3 cm,5cm,7 cm,9 cm,11 cm and 13 cm away from the center point of the wall in thexdirection.By integrating the pressure time history at different positions in the cavitation extrusion phase,graphs showing the relationship between the specific impulse of cavitation pressure load on the rear wall and the positions are obtained,as shown in Fig.19.

From the figure, the specific impulse at positions near the center of the wall is small, which may be due to the premature entry into the cavitation zone at these positions and the short duration of cavitation pressure load.After a comparison of the specific impulses of cavitation pressure load on the rear walls of the cells with different wall thicknesses,it can be found that the specific impulse increases with the increase of wall thickness.When the wall thickness rises from 2 mm to 3 mm, the specific impulse of the cavitation pressure load increases significantly, which is consistent with the law reflected by the pressure time history plots for the inside of the cell and the side wall.As the cell with thicker walls is more difficult to undergo expansion and deformation under the pressure load, the liquid motion caused by HRAM exerts a strong pressure load on the walls when the liquid-filled cell is impacted by the projectile,so the specific impulse of the cavitation pressure load is greater.

Fig.19 Specific impulses of cavitation pressure load of the cell rear walls

The above results show that the cavitation pressure load acting on the cell walls is influenced by the expansion impedance of the cell.With the increase of cell wall thickness, its expansion impedance gradually increases,resulting in the reduction of the expansion deformation ability and the enhancement of the cavitation pressure load inside the cell.But the wall thickness has limited impacts on the cavitation pressure load.When the wall thickness increases to a certain extent, the expansion impedance of the cell rises by a certain value, and the influence of the expansion impedance on the cavitation pressure load decreases.

3 Conclusions

According to the generation principle of HRAM, the concept of‘expansion impedance’by changing the cell configuration and wall thickness is presented in this paper.The expansion characteristics of the cell are quantified, and the influence of the cell configuration and wall thickness on cavitation pressure load caused by HRAM is researched.The main conclusions are as follows:

(1) The liquid-filled cell undergoes expansion deformation of the walls due to the cavitation under high-speed projectile penetration.The degree of expansion and deformation of the cell can be effectively reflected by the expansion impedance.The smaller the expansion impedance is, the easier the cell is to deform and expand.

(2) The hydrodynamic ram (HRAM) effect will lead to the cavitation pressure load under the high-speed projectile penetration.The strength of the cavitation pressure load is significantly influenced by the expansion impedance of the cell structure.When the expansion impedance of the cell structure is reduced, the bulging and deformation process of the cell will make the cavitation pressure load strength effectively reduced.

(3)The expansion impedance of the liquid-filled cell is related to the cavitation pressure load,the shape of the structure,the wall thickness and the deformation mode of cell.When the cavitation pressure load is small,the expansion of cell is dominated by wall bending deformation.As the pressure increases,the wall will undergo membrane deformation with the expansion impedance increasing dramatically.