Effects of Liquid Parameters on Liquid-Filled Compartment

materials

Article Eﬀects of Liquid Parameters on Liquid-Filled Compartment Structure Defense Against Metal Jet

Xudong Zu 1,* , Wei Dai 2, Zhengxiang Huang 1 and Xiaochun Yin 3

1 School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; [email protected] 2 Beijing Special Vehicle Research Institute, Beijing 100072, China; [email protected] 3 Department of Mechanics and Engineering Science, Nanjing University of Science and Technology, Nanjing 210094, China; [email protected] * Correspondence: [email protected]; Tel.: +86-25-84315649

Received: 14 April 2019; Accepted: 31 May 2019; Published: 4 June 2019

Abstract: The effect of liquid parameters on the defense capability of the liquid-filled compartment structure (LFCS) of a shaped charge jet (SCJ) is quantified using dimension analysis of experiments on the reduced depth of SCJ penetration, which is disturbed via the LFCS with different liquids. The effects of three parameters, namely, liquid density, sound velocity and dynamic viscosity, on LFCS defense for SCJ are discussed quantitatively. Dynamic viscosity exerts the most important effect on LFCS disturbance of SCJ penetration, followed by liquid density. Meanwhile, sound velocity causes a negligible effect on LFCS disturbance of SCJ when the hole diameter in LFCSs are short. LFCSs offer excellent protection as they can significantly reduce the penetration capability of SCJ. Thus, LFCSs can be used as a new kind of armor for defense against SCJ.

Keywords: liquid parameter; depth of penetration; shaped charge jet; liquid-ﬁlled structure

1. Introduction Liquid-filled compartment structure (LFCS) is an excellent structure that can be used on the side tanks of ships and as an additional liquid-filled cover armor of armored vehicles to resist incoming penetrative projectiles. As a kind of armor, LFCS can disturb the stability of high-speed projectiles during penetration. However, no reliable model can be used to accurately describe the interaction between a LFCS and projectiles and evaluate the effects of the former on the latter. High explosive anti-tank (HEAT) cartridges represent an important kind of ammunition that is widely used to attack armored target. A LFCS can reduce the penetration capability of shaped charge jet (SCJ) from HEAT cartridges. The properties of liquid materials (e.g., density, sound velocity and dynamic viscosity) play an important role in the way LFCSs disturb the stability of the SCJ and reduce their penetration capability [1]. Therefore, this study establishes a mode that includes the parameters of liquid materials in calculating the effects of the LFCS to the penetration capability of SCJ through dimensional analysis. In general, during projectile impact (fragments or bullets) in a liquid container, a cavity is formed by projectile drag, and a bubble is created by a hydrodynamic ram event induced by projectile penetration at ballistic speed in a confined geometry filled with liquid; this condition reduces the kinetic energy of the projectile and changes the motion trail. Most researchers pay considerable attention to expansion and collapse cavity and the deformation and destruction of containers. Lecysyn [2] analyzed shock wave propagation, cavity formation and energy loss of fluid-filled tanks under high-speed projectile impact through experimental work and theoretical modeling. The experimental phenomena can be described by a theoretical model. Disimile [3] undertook a detailed study on hydrodynamic ram and the destructive interference offered by a pressure mitigation system through firing a spherical

Materials 2019, 12, 1809; doi:10.3390/ma12111809 www.mdpi.com/journal/materials Materials 2019, 12, 1809 2 of 14 projectile onto a water tank. The results showed that the hydrodynamic ram effect can be reduced with an appropriate assembly design. Charles [4] used numerical methods to model the expansion and collapse of cavities that develop in containers after impact and arrest by water with ballistic projectiles. A numerical model was used to evaluate the proportion of kinetic energy of the bullet that was converted into internal, fluid kinetic and latent energy of water, which can finally be transferred to a deformable fuel tank structure. Fourest et al. [5,6] analyzed bubble dynamics through a hydrodynamic ram in a pool and liquid-filled container by using the Rayleigh–Plesset equation. The results showed that liquid compressibility influences the dynamics of confined bubbles, and that the gas pressure in bubbles exerts minimal influence on bubble dynamics and the hydrodynamic loads applied to the structure. Varas [7] studied plastic deformation and the pressure of water-filled aluminum square tubes filled with fluid at different levels and subjected to the impact of a spherical steel projectile with various velocities. They observed that the momentum normal to the wall is the most important factor influencing tube deformation. Varas [8] investigated liquid pressure, wall displacement of a square tube and cavity evolution at different impact velocities created by a steel spherical projectile impacting a partially water-filled aluminum square tube through simulations and experiments. The results proved that the arbitrary Lagrange–Euler technique can reproduce the stages of a hydrodynamic ram in partially filled tubes and cavity evolution, which is the main cause of final tank deformations. Artero-Guerrero [9] analyzed pressure at different points and strains on the tube wall and cavity evolution under a projectile with different velocities to impact a liquid-filled woven carbon fiber-reinforced plastic tube through simulation and experimental methods. The numerical results showed that the relationship between the magnitude of pressure pulse and impact velocity quadratically increased, and that the maximum cavity size linearly increased. Deletombe [10] observed and measured the dynamic evolution of the geometry of the wake behind and the cavity around a projectile with a 7.62 mm bullet shot liquid-filled container by using high-speed digital image cameras. Kong [11] investigated the penetration of single and double fragments into a liquid-filled cabin. The simulation results showed that the peaks of shock wave pressure from the impact of double fragments are twice higher than those in single fragments. Several researchers also considered the effects on projectiles. Sauer [12] investigated the impact response of projectiles on fluid-filled containers through numerical modeling, in which container rupture, water spread, and residual velocity were studied through 2D axisymmetric hydrocode simulations. The results showed that the adaptive smoothed particle hydrodynamics approach can be accurately used to calculate deformation, water spread and residual velocity. Uhlig [13] examined the interplay of an eroded target material and the remaining projectile, wherein copper rods perforated the liquid-filled channels that were circumferentially confined by steel cylinders. Channel width was found to play a more important role during penetration in low-density materials than in high-density materials. Shaped charge warheads are the main warheads used to attack ships and armored vehicles. Researchers analyzed the effects of liquid-filled structures on SCJ. Held [14] modified Szendrei equations and obtained the reaming equations of jet penetration in water through high spatial and temporal resolutions and profile streak technology. Lee [15] explored the penetration of jet particles by using water in high-speed photography and X-ray experiments. The researchers observed that the contour of bubbles formed no smooth curve, but that wave packets and jet particles only arrived at the penetration bottom when the foregoing particles were consumed completely during penetration. Huang et al. [16,17] established a mechanical model of a diesel oil-filled hermetic structure that interferes with a jet and obtained the expressions of the interfered velocity range. They also verified the theoretical model via X-ray experiments. In the present study, liquid parameters, such as density, sound velocity, and dynamic viscosity, are considered. The relationship between the defense capability of LFCSs, directly shown as the reduced depth of penetration (DOP) by the LFCS and SCJ and target, is obtained through dimensional analysis. Coefficient values are fitted on the basis of the experimental results. The effects of each liquid parameter on reduced DOP is discussed. MaterialsMaterials 20192019,, 1212,, 1809x FOR PEER REVIEW 33 ofof 1414 Materials 2019, 12, x FOR PEER REVIEW 3 of 14

2. Physics Phenomena and Principles 2. 2.Physics Physics Phenomena Phenomena and and Principles Principles Take for example a HEAT attack on a tank with LFCS as additional armor. The effect of the LFCS TakeTake for for example example a HEAT a HEAT attack attack on a on tank a tankwith withLFCS LFCS as additional as additional armor. armor. The effect The of e theffect LFCS of the on the SCJ of the HEAT cartridge is shown in Figure 1. The LFCS as an additional armor is always onLFCS the SCJ on of the the SCJ HEAT of the cartridge HEAT cartridge is shown is in shown Figure in 1. FigureThe LFCS1. The as LFCSan additional as an additional armor is armoralways is fixed on the main armor by bolts which establishes a certain distance between the LFCS and the main fixedalways on the fixed main on armor the main by bolts armor which by bolts establishes which establishes a certain distance a certain between distance the between LFCS and the the LFCS main and armor (Figure 1ІІ). When the HEAT cartridge attacks the tank with LFCS as additional armor (Figure armorthe main (Figure armor 1ІІ). (Figure When1 theII). HEAT When thecartridge HEAT attacks cartridge the attacks tank with the tankLFCS with as additional LFCS as additional armor (Figure armor 1І), the fuse detonates the explosive in the HEAT cartridge, and SCJ is formed and penetrates the 1І),(Figure the fuse1I), detonates the fuse detonates the explosive the explosive in the HEAT in the cartridge, HEAT cartridge, and SCJ and is SCJformed is formed and penetrates and penetrates the LFCS after the node of the HEAT cartridge impacts the LFCS. In the process of the SCJ penetrating, LFCSthe LFCSafter the after node the nodeof the of HEAT the HEAT cartridge cartridge impacts impacts the LFCS. the LFCS. In the In theprocess process of the of the SCJ SCJ penetrating, penetrating, the disturbed jet drifts off from the penetrating axis (Figure 1ІІІ). thethe disturbed disturbed jet jet drifts drifts off o fffromfrom the the penetrating penetrating axis axis (Figure (Figure 11ІІІIII).).

Figure 1. Effects of the liquid-filled compartment structure (LFCS) on the shaped charge jet (SCJ) of FigureFigure 1. 1.EffectsEﬀects of ofthe the liquid-filled liquid-ﬁlled compartment compartment structur structuree (LFCS) (LFCS) on onthe the shaped shaped charge charge jet jet(SCJ) (SCJ) of of high explosive anti-tank (HEAT) cartridge. highhigh explosive explosive anti-tank anti-tank (HEAT) (HEAT) cartridge. cartridge. In the present research, the LFCS consists of a main target body and a front plate. The main InIn the the present present research, research, the the LFCS consistsconsists ofof a a main main target target body body and and a front a front plate. plate. The The main main target target body comprises bulk #45 steel drilled with matrix cylindrical blind holes. The materials of the targetbody body comprises comprises bulk bulk #45 steel#45 steel drilled drilled with with matrix matrix cylindrical cylindrical blind blind holes. holes. The The materials materials of the of the main main target body and front plate are #45 steel and Q235 steel, respectively. Figure 2 shows the target maintarget target body body and and front front plate plate are #45are #45 steel steel and and Q235 Q235 steel, steel, respectively. respectively. Figure Figure2 shows 2 shows the target the target size. size. size.

Figure 2. LFCS (all dimensions in mm). Figure 2. LFCS (all dimensions in mm). Figure 2. LFCS (all dimensions in mm). Materials 2019, 12, x; doi: FOR PEER REVIEW www.mdpi.com/journal/materials Materials 2019, 12, x; doi: FOR PEER REVIEW www.mdpi.com/journal/materials Materials 2019, 12, 1809 4 of 14 Materials 2019, 12, x FOR PEER REVIEW 4 of 14

TheThe schematicschematic ofof thethe interactioninteraction betweenbetween thethe SCJSCJ andand LFCSLFCS isis shownshown inin FigureFigure3 .3. The The basic basic principleprinciple [[16,17]16,17] betweenbetween thethe LFCSLFCS andand thethe SCJSCJ isis presentedpresented asas follows:follows:

FigureFigure 3.3. InteractionInteraction betweenbetween thethe SCJSCJ withwith thethe LFCS.LFCS.

WhenWhen the SCJ penetrates the the liquid liquid in in the the LFCS, LFCS, a ashock shock wave wave is assumed is assumed to be to beformed formed from from the thetip tipof the of theSCJ, SCJ, because because the thepenetration penetration velocity velocity is faster is faster than than the sound the sound velocity velocity of the of liquid the liquid (t1). (tThe1). Theshock shock wave wave is a isconically a conically diffused diffused spherical spherical wave, wave, and and its itspropagation propagation direction direction is perpendicular is perpendicular to tothe the wave wave front front along along its its normal normal direction direction (from (from A A to to B B along along line line ІI).). The The initial shock wave quicklyquickly reachesreaches thethe sidewallsidewall ofof thethe structurestructure thatthat reflectsreflects thethe shockshock wavewave (from(from BB toto CC alongalong lineline IIІІ).). ReflectedReflected wavewave propagationpropagation preventsprevents thethe reamingreaming processprocess ofof thethe subsequentsubsequent jet.jet. If thethe surfacesurface stressstress ofof thethe reflectedreflected shockshock wave wave is greateris greater than than the expansionthe expansio stress,n stress, then thethen liquid the entersliquid aenters convergence a convergence process. Theprocess. convergence The convergence liquid under liquid the under reflected the reflected wave disturbs wave thedisturbs SCJ (t the2) and SCJ makes(t2) and that makes part that of the part SCJ of driftthe SCJ off fromdrift off the from penetrating the penetrating axis. axis. InIn previousprevious research,research, onlyonly oneone kindkind ofof liquidliquid dieseldiesel usedused inin thethe LFCSLFCS andand thethe soundsound velocityvelocity ofof thethe liquidliquid werewere considered.considered. Moreover,Moreover, thethe densitydensity andand dynamicdynamic viscosityviscosity ofof thethe liquidliquid materialmaterial werewere ignored.ignored. However,However, densitydensity andand dynamicdynamic viscosityviscosity playplay importantimportant rolesroles inin thethe LFCSsLFCSs disturbancedisturbance ofof thethe stabilitystability ofof thethe SCJ.SCJ. InIn fact,fact, eeffectsffects areare complicatedcomplicated whenwhen thethe LFCSLFCS interactsinteracts withwith thethe SCJSCJ (high(high 9 10 temperaturetemperature ofof 800–1000800–1000◦ °C,C, highhigh pressurepressure ofof 10109–10–1010 Pa). However, However, the whole interaction is didifficultfficult toto describe.describe. Therefore,Therefore, dimensiondimension analysisanalysis isis suitablesuitable forfor thethe studystudy ofof thethe eeffectsffects ofof liquidliquid parametersparameters onon LFCSLFCS defensedefense againstagainst SCJ.SCJ.

3.3. Dimension AnalysisAnalysis InIn broadeningbroadening thethe rangerange ofof applications,applications, dimensionaldimensional analysisanalysis requiresrequires nono generalgeneral governinggoverning equations.equations. To To simplify the model and show thethe majormajor inﬂuencinginfluencing factors,factors, thisthis studystudy makesmakes thethe followingfollowing assumptions:assumptions: (1) 1)The The density density of of the the SCJ SCJ shows shows no no change; change; (2) 2)The The SCJ SCJ is continuous;is continuous; (3) 3)Liquid Liquid vaporization vaporization is ignoredis ignored as as the the whole whole penetration penetration process process is extremelyis extremely short. short. Hence, when the SCJ penetrates the liquid-filled structure, the independent factors that affect the penetration capability of the SCJ are as follows:

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Hence, when the SCJ penetrates the liquid-ﬁlled structure, the independent factors that aﬀect the penetration capability of the SCJ are as follows:

(1) Parameters of SCJ: density ρj, velocity of jet tip vj0, velocity of jet tail vjt, initial length of the jet l0 and reduced DOP owing to the disturbed SCJ Pdis; (2) Liquid parameters: density ρl, sound velocity Cl and dynamic viscosity µ; (3) Parameters of compartment structure: inner diameter D, height of compartment H, sound velocity of compartment material Ct and density of compartment material ρt.

Table1 provides the symbols, units and dimensions of the parameters used in this study.

Table 1. Main parameters of the liquid, SCJ and target structure.

Material Parameter Symbol Unit Dimension Density ρ kg/m3 M L 3 l · − Liquid Sound velocity C m/s L T 1 l · − Dynamic viscosity µ Pa s M L 1 T 1 · · − · − 1 Velocity of the jet tip vj0 m/s L T− · 1 Velocity of the jet tail vjt m/s L T · − Initial length of the jet l0 m L SCJ 3 3 Density ρj kg/m M L · − Reduced DOP Pdis m L 1 Sound velocity Cj m/s L T · − Inner diameter D m L Height of the compartment H m L Compartment structure target 1 Sound velocity Ct m/s L T− 3 · 3 Density ρt kg/m M L · −

The penetration capability of the disturbed SCJ (reduced DOP) can be determined as follows: Pdis = f ρl, Cl, µ, vj0, vjt, l0, ρj, Cj, D, H, Ct, ρt (1) where ρl, Cl and l0 are independent dimension parameters. On the basis of the π theorem, k = 3, Equation (1) becomes dimensionless. ! Pdis µ vj0 vjt ρj Cj D H Ct ρt = f 0 , , , , , , , , (2) l ρ C l C C ρ C l l C ρ 0 l· l· 0 l l l l 0 0 l l

µ vj0 vjt ρj Cj D H Ct ρt Let π1 = , π2 = , π3 = , π4 = , π5 = , π6 = , π7 = , π8 = , π9 = . ρl Cl l0 Cl Cl ρl Cl l0 l0 Cl ρl The variables· · are reversed as follows to simplify their relation and clarify their physical signiﬁcance: = = = = = π10 π1/π6, π30 π3/π2, π50 π2/π5, π80 π8/π5, π90 π9/π4. Then, Equation (2) is transformed into the following: ! Pdis µ vj0 vjt ρj vj0 D H Ct ρt = g0 , , , , , , , , (3) l ρ C D C v ρ C l l C ρ 0 l· l· l j0 l j 0 0 j j

vjt vj ρ Given that the shaped charge and target are confirmed, and that , 0 , D , H , Ct , t are constant, vj0 Cj l0 l0 Cj ρj Equation (3) can be simplified as follows: ! P µ vj0 ρj dis = Φ , , (4) l ρ C D C ρ 0 l· l· l l µ In Equation (4), is the ratio of dynamic viscosity to the inertia force of the moving liquid and ρl Cl · v it characterizes the flow characteristic of the liquid. j0 is the ratio of the velocity of jet tip to the sound Cl Materials 2019, 12, 1809 6 of 14

Materialsvelocity 2019 of the, 12, x liquid FOR PEER and REVIEW it characterizes the shock wave strength when the jet penetrates the liquid.6 of 14 ρ j is density ratio of the jet to the liquid. Equation (4) can be written as a power function. ρl

𝑃 𝜇 !α 𝑣!β !γ𝜌 Pdis= 𝐴 ∙ µ v∙j0 ρ∙j (5) 𝑙 = A 𝜌 ∙𝐶 ∙𝐷 𝐶 𝜌 (5) l · ρ C D · C · ρ 0 l· l· l l Referring to the 1D hydrodynamic penetration model, the DOP is equal to the length of the jet multipliedReferring by the to thesquare 1D hydrodynamicroot of the density penetration ratio of the model, jet to the the DOP targ iset. equal Thus, to the the number length of theγ may jet multiplied by the square root of the density ratio of the jet to the target. Thus, the number of γ may be be 1/2. So 𝑃 can be written as follows: 1/2. So Pdis can be written as follows: 𝜇 𝑣 𝜌 𝑃 = 𝐴 ∙ !α ∙!β r∙𝑙 µ vj0 ρj (6) P = A 𝜌 ∙𝐶 ∙𝐷 𝐶l 𝜌 (6) dis · ρ C D · C · 0 ρ l· l· l l where A, α and β represent the coefficients to be confirmed by experimental results. 𝑙q refers to ρj where A, α and β represent the coeﬃcients to be conﬁrmed by experimental results. l0 refers to the 1D hydrodynamic penetration jet model. ρl the 1D hydrodynamic penetration jet model.

4. Experimental Experimental Research Research

4.1. Shaped Shaped Charge Charge and Liquid For general research, the standard Φ56 mm shaped charge is adopted (Figure4 4).). TheThe jetjet tiptip velocity is 6453 m/s, m/s, and that of the tail is 1179 m/s. m/s. The length of the jet at 80 80 mm mm standoff standoﬀ is equal to 111.5 mm [[18].18].

Figure 4. StandardStandard shaped charge.

In the experiments, five ﬁve kinds of liquid are selected:selected: water, #0 diesel, polyethylene glycol with molecular weights of 200 and 400 (PEG 200 and PEG 400, respectively) and polypropylene glycol with molecular weight of 6000 (PPG 6000). The test method and conditions are the same as those of Newtonian fluid ﬂuid in reference [[19].19]. Table 2 2 displays displays thethe mainmain materialmaterial parameters. parameters.

Table 2. Main parameters of the liquid.

𝟑 𝟑 Material 𝛍 (𝐏𝐚 ∙𝐬) 𝛒 (𝒌𝒈⁄ 𝒎 ×𝟏𝟎 ) 𝑪𝒍 (𝒎𝒔⁄ ) Water 0.06 1.0 1480 #0 diesel 0.25 0.875 1775 PEG 200 0.37 1.21 1535 PEG 400 0.16 1.196 1602 PPG 6000 1.13 1.01 1278

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Table 2. Main parameters of the liquid.

Material µ (Pa s) ρ (kg/m3 103) C (m/s) · × l Water 0.06 1.0 1480 #0 diesel 0.25 0.875 1775 PEG 200 0.37 1.21 1535 Materials 2019, 12, x FOR PEER REVIEWPEG 400 0.16 1.196 1602 7 of 14 PPG 6000 1.13 1.01 1278 4.2. Experimental Setup and Results 4.2. Experimental Setup and Results The compartments of the LFCS were filled with liquid and sealed by the front plate through boltsThe before compartments experiments. of The the LFCSliquid were in the filled LFCS with could liquid not and flow sealed out. by The the DOP front experiments plate through on bolts the beforestandard experiments. shaped charge The liquid were in performed the LFCS couldinitiall noty flowto ensure out. The the DOP reduced experiments penetration on the capability standard shaped(reduced charge DOP) were of the performed SCJ. Then, initially the residual to ensure DOP the reducedexperiments penetration on SCJ capability penetration (reduced involving DOP) the of theLFCS SCJ. with Then, different the residual liquid materials DOP experiments were carried on SCJ out. penetration In all the experiments, involving the the LFCS distance with from different the liquidbottom materials of the shaped were charge carried to out. the In surface all the of experiments, the target was the the distance same. from the bottom of the shaped chargeThe to setup the surface of the of DOP the targetexperiment was the on same. the shaped charge at a standoff of 254 mm is shown in FigureThe 5. The setup setup of the of the DOP residual experiment DOP experiment on the shaped is shown charge in Figure at a stando 6. Theff standardof 254 mm shaped is shown charge in Figureconnects5. Theto the setup target of the liquid-filled residual DOP structure experiment through is shown an 80 inmm Figure standoff6. The cylinder, standard whereas shaped chargethe #45 connectssteel target to theconnects target to liquid-filled a 90 mm interval structure cylinder. through The an 80DOP mm experiment standoff cylinder, in which whereas the standoff the #45 is steel 254 targetmm (80 connects mm + 84 to mm a 90 + mm90 mm) interval is carried cylinder. out to The obtain DOP the experiment penetration in whichcapability the standoof the SCJff is with 254 mm the (80same mm distance+ 84 mm as that+ 90 when mm) the is carriedfront of out the tosteel obtain target the lacks penetration a liquid capabilitycomposite ofarmor. the SCJ Every with DOP the sameexperiment distance is repeated as that when twice. the front of the steel target lacks a liquid composite armor. Every DOP experimentThe results is repeated of the DOP twice. experiment were 254 and 258 mm. Therefore, the average result is 256 mm. TheOne results of the witness of the DOP targets experiment was cut wereinto two 254 piec andes 258 via mm. wire Therefore, electrode the cutting, average as shown result is in 256 Figure mm. One7. of the witness targets was cut into two pieces via wire electrode cutting, as shown in Figure7.

Figure 5. Depth of penetration (D (DOP)OP) experimental setup.

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Figure 6. Experimental setup. Figure 6. Experimental setup.

Figure 7. SplitSplit image image of of witness witness target target obtained by linear cutting. Figure 7. Split image of witness target obtained by linear cutting.

Table 22 illustrates illustrates thethe residualresidual DOPDOP (P (Presres)) results. results. Figures Figures 88–12–12 displaydisplay thethe DOPDOP inin thethe witnesswitness Table 2 illustrates the residual DOP (Pres) results. Figures 8–12 display the DOP in the witness targetTable with 2different di illustratesﬀerent liquids. the residual DOP (Pres) results. Figures 8–12 display the DOP in the witness target with different liquids.

Figure 8. DOPDOP with with water as liquid liquid.. Figure 8. DOP with water as liquid.

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Figure 9. DOP with #0 diesel as liquid. Figure 9. DOP with #0 diesel as liquid. Figure 9. DOP with #0 diesel as liquid. Figure 9. DOP with #0 diesel as liquid.

Figure 10. DOP with PEG200 (polyethylene glycol wi withth molecular weights of 200) as liquid.liquid. Figure 10. DOP with PEG200 (polyethylene glycol with molecular weights of 200) as liquid. Figure 10. DOP with PEG200 (polyethylene glycol with molecular weights of 200) as liquid.

Figure 11. DOP with PEG400 (polyethylene glycol wi withth molecular weights of 400) as liquid. Figure 11. DOP with PEG400 (polyethylene glycol with molecular weights of 400) as liquid. Figure 11. DOP with PEG400 (polyethylene glycol with molecular weights of 400) as liquid.

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Figure 12. DOP with PPG6000 (polypropylene glycol with molecular weight of 6000) as liquid. Figure 12. DOP with PPG6000 (polypropylene glycol with molecular weight of 6000) as liquid. Table3 and Figures8–12 show that the LFCS can considerably decrease the DOP of the SCJ. Table 3 and Figures 8–12 show that the LFCS can considerably decrease the DOP of the SCJ. However, comparison results in Tables2 and3 reveal that the LFCS can reduce the penetration However, comparison results in Tables 2 and 3 reveal that the LFCS can reduce the penetration capability of the SCJ obviously. Comparing the single parameter of the liquid with Pdis, shows that Pdis capability of the SCJ obviously. Comparing the single parameter of the liquid with Pdis, shows that increases with the dynamic viscosity of the liquid, except for PPG6000. Moreover, Pdis increases with Pdis increases with the dynamic viscosity of the liquid, except for PPG6000. Moreover, Pdis increases the density of the liquid, except for diesel. No relationship exists between Pdis and the sound velocity with the density of the liquid, except for diesel. No relationship exists between Pdis and the sound of the liquid. Thus, the parameters of the liquid in the LFCS show no notable relation with P . velocity of the liquid. Thus, the parameters of the liquid in the LFCS show no notable relationdis with Pdis. Table 3. Residual penetration in the witness target of SCJ penetrating the LFSC with diﬀerent liquids.

Table 3. Residual penetration in the witness targetPres/mm of SCJ penetrating the LFSC with different liquids. Liquid Pdis/mm First SecondPres/mm Average Liquid Pdis/mm Datum 254.0First Second 258.0 Average 256.0 WaterDatum 78.0254.0 258.0 81.0 256.0 79.5 176.5 Diesel 75.0 - 75.0 181 PEG200Water 62.078.0 81.0 66.0 79.5 64.0 176.5 192 PEG400Diesel 68.075.0 71.0 - 75.0 69.5 181 186.5 PPG6000PEG200 72.062.0 66.0 79.0 64.0 75.5 192 180.5 PEG400 68.0 71.0 69.5 186.5 PPG6000 72.0 79.0 75.5 180.5 Comparing Figures8–12 with Figure7 reveals that P res sharply drops by 68% after the SCJ penetrates the LFCS. The penetration holes on the witness target are not as straight as that when SCJ penetratesComparing the target Figures directly. 8–12 with In addition, Figure the7 reveals material that of P theres sharply jet was drops observed by on68% the after wall the of SCJ the penetrationpenetrates the hole LFCS. of the The witness penetration target. holes These on resultsthe witn areess mainly target are explained not as straight as follows. as that The when stability SCJ penetratesof the SCJ isthe disturbed target directly. when it In pierces addition, the LFCS.the material Parts ofof thethe SCJ jet segmentswas observed veer on off thethe wall axis beforeof the penetrationreaching the hole bottom of the of thewitness penetration target. These hole penetrated results are by mainly segments. explained These as parts follows. of the The SCJ stability segments of the SCJ is disturbed when it pierces the LFCS. Parts of the SCJ segments veer off the axis before cause the reduction of Pres. Although parts of the SCJ segments drift off the axis, they can still reach reachingthe bottom the of bottom the penetration of the penetrat hole penetratedion hole penetrated by previous by segments. These parts of the SCJ segments causehave penetrationthe reduction capability, of Pres. Although but they causeparts theof the penetration SCJ segments holes drift to bend. off the axis, they can still reach the bottomAccording of the to penetration the liquid parameters hole penetrated in Table by2 pr andevious the reducedsegments. DOP These in Tableparts3 of, the the experimental SCJ segments haveresult penetration involves five capability, groups, and but Equationthey cause (6) the only penetration comprises holes three to coe bend.fficients. Thus, the coefficient of EquationAccording (6) can to be the obtained liquid parameters by Origin 8.5. in Table Equation 2 and (6) the can reduced be computed DOP in as Table follows: 3, the experimental result involves five groups, and Equation (6) only comprises three coefficients. Thus, the coefficient !5.77e 3 ! 3.07e 3 r of Equation (6) can be obtained by Origin 8.µ5. Equation− (6)vj0 can− be− computedρj as follows: P = 0.62192 l . (7) dis . .0 · ρl Cl D · Cl · ρl 𝑃 = 0.62192 ∙ · · ∙ ∙𝑙 . (7) ∙∙

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5. Remarks 5. Remarks In the analysis of the effects of liquid parameters, one parameter is changed, and another two are fixed.In the By analysis considering of the eaﬀ parameterects of liquid change, parameters, the change one parameterin the disturbed is changed, DOP and Pdis anotheris obtained two (Figuresare ﬁxed. 13–15). By considering a parameter change, the change in the disturbed DOP Pdis is obtained (Figures 13–15).

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Figure 13. Eﬀects of liquid density on reduced DOP. Figure 13. Effects of liquid density on reduced DOP.

Figure 13 shows that with an increase in liquid density, the Pdis also decreases. For the five kinds of liquid, when the liquid density increases from 800 kg/m3 to 1500 kg/m3, and when the reduced ratio of Pdis gradually decreases, Pdis drops by 27.2%. This result means that at a low liquid density in the compartment structure, the structure can disturb a wide jet velocity range, thus the Pdis increases. The density characterizes the inertia of the liquid. The inertia increases with a rise in density. The state of motion does not easily change with an increase in density under the same stress. Thus, with an increase in density, the difficulty of liquid reflow in the LFCS rises; hence, the effect of the LFCS on the SCJ decreases, which indicates that liquid density increases with a decrease in Pdis.

Figure 14. Eﬀects of liquid sound velocity on reduced DOP. Figure 14. Effects of liquid sound velocity on reduced DOP.

Figure 14 shows that with increased sound velocity of the liquid, the Pdis slightly changes. For the five kinds of liquid, when the sound velocity of the liquid increases from 1000 m/s to 3000 m/s, Pdis reduction does not exceed 0.5%, indicating that the effect of sound velocity of the liquid on reduced DOP can be ignored. When the sound velocity of the liquid increases, the time between shock wave formation and

Materialsthe reflection 2019, 12, of x; doi:the FOR shock PEER wave REVIEW on the SCJ is reduced. In this way, the LFwww.mdpi.com/journal/materialsCS can disturb the high velocity range jet. However, in the current research, the diameter of the hole in the LFCS is considerably short, hence, the effect of the sound velocity of the liquid is minimal. Figure 15 shows that the Pdis exhibits a linearly increasing relation with the logarithm of dynamic viscosity of the liquid. Therefore, the high liquid viscosity in the compartment structure can substantially affect the SCJ and effectively reduce the penetration capability of the jet. The dynamic viscosity of the liquid characterizes the viscosity of such liquid. Under zero sliding condition, an increase in the dynamic viscosity of the liquid boosts the effect of liquid reflow in the LFCS to the SCJ; that is Pdis increases with a rise in the dynamic viscosity of the liquid.

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FigureFigure 15. 15.E ﬀEffectsects of of dynamic dynamic viscosity viscosity of of liquid liquid on on reduced reduced DOP. DOP.

Figure 13 shows that with an increase in liquid density, the Pdis also decreases. For the five kinds of6 liquid, Conclusions when the liquid density increases from 800 kg/m3 to 1500 kg/m3, and when the reduced ratio of Pdis Ingradually this study, decreases, the effects Pdis ofdrops liquidby parameters 27.2%. This and result Pdis are means studied. that Conclusions at a low liquid can density be formulated in the compartmentas follows: structure, the structure can disturb a wide jet velocity range, thus the Pdis increases. The density characterizes the inertia of the liquid. The inertia increases with a rise in density. 1) The reduced DOP of the SCJ can be described by Equation (6) when the liquid in the LFCS is The state of motion does not easily change with an increase in density under the same stress. Thus, Newtonian liquid. In addition, when the parameters of the SCJ and LFCS are fixed, the coefficient is with an increase in density, the difficulty of liquid reflow in the LFCS rises; hence, the effect of the LFCS easily confirmed by experimental results. on the SCJ decreases, which indicates that liquid density increases with a decrease in Pdis. 2) Based on Equation (7), the calculated results point out that the dynamic viscosity of liquid Figure 14 shows that with increased sound velocity of the liquid, the Pdis slightly changes. For the exerts the most important effect on LFCS disturbance of SCJ, with liquid density having the second five kinds of liquid, when the sound velocity of the liquid increases from 1000 m/s to 3000 m/s, Pdis most important impact. Moreover, sound velocity causes a negligible effect on LFCS disturbance of reduction does not exceed 0.5%, indicating that the effect of sound velocity of the liquid on reduced SCJ when the holes’ diameter in the LFCS are short. DOP can be ignored. In obtaining an LFCS with high defence capability, that is, the LFCS can further reduce the DOP When the sound velocity of the liquid increases, the time between shock wave formation and the of the SCJ, the liquid in the structure should feature high dynamic viscosity and low density. reflection of the shock wave on the SCJ is reduced. In this way, the LFCS can disturb the high velocity 3) LFCSs can disturb the stability of SCJ and reduce their DOP. These structures can thus be used range jet. However, in the current research, the diameter of the hole in the LFCS is considerably short, as a new kind of armor. hence, the effect of the sound velocity of the liquid is minimal. Figure 15 shows that the P exhibits a linearly increasing relation with the logarithm of dynamic Author Contributions: Conceptualizationdis and Writing—Review Draft, X.Z.; Data Curation, W.D.; Writing— viscosityReview ofand the Editing, liquid. Z.H. Therefore, and X.Y. the high liquid viscosity in the compartment structure can substantially affect the SCJ and effectively reduce the penetration capability of the jet. Funding: This research was supported by the National Natural Science Foundation of China (Grant No. The dynamic viscosity of the liquid characterizes the viscosity of such liquid. Under zero sliding 11402122) and the China Scholarship Council (201706845026). condition, an increase in the dynamic viscosity of the liquid boosts the effect of liquid reflow in the LFCSConflicts to the of SCJ; Interest: that The is P disauthorsincreases declare with no conflict a rise in of the interest. dynamic viscosity of the liquid.

6.References Conclusions

1. InFrano, this study, R.L.; theForasassi, effects ofG. liquidExperimental parameters evidence and Pofdis imperfectionare studied. influence Conclusions on the can buckling be formulated of thin as follows:cylindrical shell under uniform external pressure. Nucl. Eng. Des. 2009, 239, 193–200. 2. (1)Lecysyn, The reduced N.; Bony-Dandrieux, DOP of the SCJ A.; canAprin, be L.; described Heymes, by F.; EquationSlangen, P.; (6) Dusserre, when the G.; liquidMunier, in L.; the Le LFCS Gallic, is C. NewtonianExperimental liquid. Instudy addition, of hydraulic when theram parameterseffects on a of liquid the SCJ storage and LFCStank: Analys are fixed,is of the overpressure coefficient and is easily confirmedcavitation induced by experimental by a high-speed results. projectile. J. Hazard. Mater. 2010, 178, 635–643.

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(2) Based on Equation (7), the calculated results point out that the dynamic viscosity of liquid exerts the most important eﬀect on LFCS disturbance of SCJ, with liquid density having the second most important impact. Moreover, sound velocity causes a negligible eﬀect on LFCS disturbance of SCJ when the holes’ diameter in the LFCS are short. In obtaining an LFCS with high defence capability, that is, the LFCS can further reduce the DOP of the SCJ, the liquid in the structure should feature high dynamic viscosity and low density. (3) LFCSs can disturb the stability of SCJ and reduce their DOP. These structures can thus be used as a new kind of armor.

Author Contributions: Conceptualization and Writing—Review Draft, X.Z.; Data Curation, W.D.; Writing—Review and Editing, Z.H. and X.Y. Funding: This research was supported by the National Natural Science Foundation of China (Grant No. 11402122) and the China Scholarship Council (201706845026). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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