Numerical analysis of critical jet penetration

In this paper, a computational program for two dimensional unsteady compressible, elastic-plastic flow is used to study low speed jet penetration into a steel target. Based on the computational results, the dynamic process of penetration can be distinguished into two stages, cratering and steady penetrating. This is in agreement with the jet penetration mechanism developed by Cheng Che Min in 1972^[1,2]. The consumption of the jet energy is discussed and the value of the critical jet velocity, which represents the strength resistance of the target, is estimated.     

Analytical models for the penetration of semi-infinite targets by rigid, deformable and erosive long rods

A theoretical study is presented herein on the pen- etration of a semi-infinite target by a spherical-headed long rod for Yp 〉 S, where Yp is the penetrator strength and S is the static target resistance. For Yp 〉 S, depending upon initial impact velocity, there exist three types of penetration, namely, penetration by a rigid long rod, penetration by a deforming non-erosive long rod and penetration by an erosive long rod. If the impact velocity of the penetrator is higher than the hydrodynamic velocity （VH）, it will penetrate the target in an erosive mode; if the impact velocity lies between the hydrodynamic velocity （VH） and the rigid body velocity （VR）, it will penetrate the target in a deformable mode; if the impact velocity is less than the rigid body velocity （VR）, it will penetrate the target in a rigid mode. The critical conditions for the transition among these three penetration modes are proposed. It is demonstrated that the present model predictions correlate well with the experimental observations in terms of depth of penetration （DOP） and the critical transition conditions.     

Characterization of plunging liquid jets: A combined experimental and numerical investigation

This paper presents a combined experimental and numerical study of the flow characteristics of round vertical liquid jets plunging into a cylindrical liquid bath. The main objective of the experimental work consists in determining the plunging jet flow patterns, entrained air bubble sizes and the influence of the jet velocity and variations of jet falling lengths on the jet penetration depth. The instability of the jet influenced by the jet velocity and falling length is also probed. On the numerical side, two different approaches were used, namely the mixture model approach and interface-tracking approach using the level-set technique with the standard two-equation turbulence model. The numerical results are contrasted with the experimental data. Good agreements were found between experiments and the two modelling approaches on the jet penetration depth and entraining flow characteristics, with interface tracking rendering better predictions. However, visible differences are observed as to the jet instability, free surface deformation and subsequent air bubble entrainment, where interface tracking is seen to be more accurate. The CFD results support the notion that the jet with the higher flow rate thus more susceptible to surface instabilities, entrains more bubbles, reflecting in turn a smaller penetration depth as a result of momentum diffusion due to bubble concentration and generated fluctuations. The liquid average velocity field and air concentration under tank water surface were compared to existing semi-analytical correlations. Noticeable differences were revealed as to the maximum velocity at the jet centreline and associated bubble concentration. The mixture model predicts a higher velocity than the level-set and the theory at the early stage of jet penetration, due to a higher concentration of air that cannot rise to the surface and remain trapped around the jet head. The location of the maximum air content and the peak value of air holdup are also predicted differently.     

On the deep penetration of deforming long rods

A series of 2D numerical simulations was performed in order to follow various features in the penetration mechanics of deforming long rods. In particular, we were interested in the threshold velocity which marks the transition from rigid to deforming rod and the resulting depths of penetration around this transition velocity. We simulated various cases in which we varied the yield strengths of the rod and the target, as well as their densities and the nose shape of the rod. With the results of these simulations we constructed a rather simple model which accounts for the threshold velocity from rigid to deforming rod behavior. This model’s predictions are in good agreement with both our simulations and with experimental data for various rods and targets.     

A simplified approximate model of compressible hypervelocity penetration

A simplified approximate model considering rod/target material’s compressibility is proposed for hypervelocity penetration. We study the effect of shockwaves on hypervelocity penetration whenever the compressibility of the rod is much larger, analogously, and much less than that of the target, respectively. The results show that the effect of shockwaves is insignificant up to 12 km/s, so the shockwave is neglected in the present approximate model. The Murnaghan equation of state is adopted to simulate the material behaviors in penetration and its validity is proved. The approximate model is finally reduced to an equation depending only on the penetration velocity and a simple approximate solution is achieved. The solution of the approximate model is in agreement with the result of the complete compressible model. In addition, the effect of shockwaves on hypervelocity penetration is shown to weaken material’s compressibility and reduce the interface pressure of the rod/target, and thus the striking/protective performance of the rod/target is weakened, respectively. We also conduct an error analysis of the interface pressure and penetration efficiency. With a velocity change of 1.6 times the initial sound speed for the rod or target, the error of the approximate model is very small. For metallic rod–target combinations, the approximate model is applicable even at an impact velocity of 12 km/s.     

弹体高速侵彻效率的实验和量纲分析

为了研究高速侵彻时弹体撞击速度、材料强度等对质量侵蚀特性和侵彻效率的影响规律,开展了不同材料强度和长径比的弹体高速侵彻半无限厚素混凝土靶实验,弹体撞击速度为880~1 900 m/s,弹头形状为尖卵型(半径口径比为3),口径为30 mm。由实验发现:弹体撞击速度对侵彻效率的影响呈抛物线分布,最大侵彻效率时的弹体特征撞击速度约1 400 m/s;高速侵彻时弹体的质量侵蚀主要发生在卵形头部,弹身及尾部损伤极少;速度超过特征撞击速度时,弹体侵蚀严重,甚至弯曲变形或解体;弹体强度提高至约2倍时,质量侵蚀率降低约80%。基于实验,利用量纲分析原则建立了量纲一侵彻效率和量纲一弹体撞击速度的函数关系式,可估算出最大侵彻效率对应的弹体撞靶速度,为高速侵彻效应模拟实验提供理论指导。     

Numerical modeling of multi micro jet impingement cooling of a three dimensional turbine vane

This paper reports a numerical investigation on the prediction of the thermal and hydrodynamic flow fields of multi micro jet impingement cooling of three dimensional turbine vanes. A three dimensional vane is modeled with an in-line array of impinging jets of diameters 0.5 and 0.25 mm. The numerical model consists of the steady, Reynolds-Averaged Navier–Stokes equations and the Kω SST Turbulence model. The governing equations are solved using a finite volume method. The crossflow mass velocity (G _c ) to jet mass velocity (G _j ) ratio, and the average and local heat transfer distributions are analyzed with varying mass velocity and jet-to-target spacing. It is found out that a significant decrease in crossflow ratio occurs with the smaller diameters. Due to the lower crossflow and higher exit velocities of the smaller jets, the penetration into the crossflow is much higher. Moreover, at a constant mass flow, the use of micro-jets enhanced the overall average heat transfer coefficient by 63%, while at a fixed pressure drop across the vane instead of the mass flow, the smaller diameters will still yield an enhancement of 34.3% in the overall average heat transfer coefficient.     

大气/钢靶板交界处对平行入射聚能射流干扰的数值模拟

利用非线性动力学软件LS-DYNA,对聚能射流平行入射大气/钢靶板交界处的侵彻过程进行了数值模拟.通过分析数值模拟过程和结果,讨论了聚能射流头部速度和碰撞出口处横向速度的变化规律.结果表明:大气/钢靶板交界处不仅降低了聚能射流头部的轴向速度,而且使射流头部产生横向偏移,最大速度达到约1.8 km/s;后续射流横向偏移速...     

Simulations of vertical jet penetration using a filtered two-fluid model in a gas–solid fluidized bed

The influence of a vertical jet located at the distributor in a cylindrical fluidized bed on the flow behavior of gas and particles was predicted using a filtered two-fluid model proposed by Sundaresan and coworkers. The distributions of volume fraction and the velocity of particles along the lateral direction were investigated for different jet velocities by analyzing the simulated results. The vertical jet penetration lengths at the different gas jet velocities have been obtained and compared with predictions derived from empirical correlations; the predicted air jet penetration length is discussed. Agreement between the numerical simulations and experimental results has been achieved.     

长杆弹撞击陶瓷靶的一种数值模拟方法

陶瓷材料具有高强度和低密度等特点，抗弹性能优越，被广泛用于各类装甲中。长杆弹撞击陶瓷靶时会发生径向流动、质量显著侵蚀而无明显侵彻的界面击溃现象，是陶瓷抗侵彻性能研究中具有重要研究价值的特殊现象。利用有限元软件AUTODYN建立了长杆弹撞击陶瓷靶的二维轴对称计算模型，采用Lagrange和光滑粒子流体动力学（smooth particle hydrodynamics, SPH）算法，模拟了柱形钨合金长杆弹撞击带盖板的碳化硅陶瓷，通过改变长杆弹的撞击速度，得到了界面击溃、驻留转侵彻和直接侵彻3个不同现象。讨论了不同建模算法、边界条件以及材料参数对模拟结果的影响。通过网格收敛性验证和与实验结果进行拟合，综合验证了计算模型中算法、边界条件和参数设定的可靠性。结果表明，在建模中若同时使用SPH算法和Lagrange算法，需要考虑粒子和网格大小对于模拟结果的影响。针对长杆弹撞击陶瓷靶的界面击溃模拟，不建议对陶瓷材料采用SPH粒子建模。相关建模和参数选择方法对后续陶瓷抗侵彻/界面击溃的数值模拟具有重要的指导意义。     

A CORRELATION EQUATION FOR CALCULATING INCLINED JET PENETRATION LENGTH IN A GAS-SOLID FLUIDIZED BED

Numerical simulation of gas-solid flow in a two-dimensional fluidized bed with an inclined jet was performed. The numerical model is based on the two-fluid model of gas and solids phase in which the solids constitutive equations are based on the kinetic theory of granular flow. The improved ICE algorithm, which can be used for both low and high-velocity fluid flow, were used to solve the model equations. The mechanism of jet formation was analyzed using both numerical simulations and experiments. The emergence and movement of gas bubbles were captured numerically and experimentally. The influences of jet velocity, nozzle diameter, nozzle inclination and jet position on jet penetration length were obtained. A semi-empirical expression was derived and the parameters were correlated from experimental data. The correlation equation, which can be easily used to obtain the inclined jet penetration length, was compared with our experimental data and published correlation equations.     

卵形头部刚性弹侵彻厚靶的半解析模型

基于确定靶体中速度势和速度场的方法分析刚性卵形头部弹体对有限厚靶的侵彻问题。推导了靶体中速度场与应力场的计算方法,利用据此编制的计算程序,计算了卵形头部钢弹体对铝靶的侵彻与穿透问题,给出了侵彻深度与剩余速度同初始碰撞速度的关系。结果表明,在对实验参数不经过任何调整的情况下,得到了同试验曲线相吻合的结果。可以看出该方法的有效性。     

Impinging sweeping jet and convective heat transfer on curved surfaces

The application of an impinging sweeping jet, which oscillates periodically with a large angle, to convective heat transfer has received attention owing to its capability to provide a more spatially uniform and enhanced heat removal rate when compared to a steady jet. Herein, we study how the surface curvature affects the heat transfer performance of a sweeping jet and couple it with the representative flow characteristics. Heat transfer measurement and quantitative flow visualization are conducted experimentally for concave and convex surfaces as well as a flat surface. Whereas concave surfaces have a better heat transfer rate than a flat surface, the enhancement of the heat transfer is relatively small for a convex surface. For both concave and convex surfaces, the Nusselt number does not increase monotonically with the curvature magnitude but has a peak for a moderate curvature. The variation in heat transfer performance with the surface curvature is correlated with the phase-averaged velocity profile of the wall jet deflected after an impingement and the turbulence kinetic energy inside the jet. For both concave and convex surfaces, the wall jet becomes thinner than a flat surface in general, which contributes to improved heat transfer. However, whereas the turbulence kinetic energy is significantly larger for a concave surface of a moderate curvature than that of a flat surface, the turbulence kinetic energy for a convex surface is reduced from that of a flat surface, resulting in degradation of the heat transfer performance.     

聚能射流侵彻径向扩孔的可压缩模型

聚能射流侵彻厚靶时,对靶材同时进行轴向和径向挤压进而发生轴向侵彻和径向扩孔。本文中基于聚能射流侵彻可压缩模型并结合Szendrei-Held扩孔方程,推导给出考虑弹/靶材料可压缩性的聚能射流扩孔方程。为简化完整可压缩模型繁琐的计算过程,又基于Murnaghan状态方程给出可压缩模型的近似解。与水中聚能射流扩孔的实验研究对比分析,表明该模型预测优于Szendrei-Held扩孔方程。模型分析表明,射流半径、驻点压力、靶材强度、驻点处靶材密度以及聚能射流速度是影响聚能射流扩孔的主要因素。本文模型可以更准确地预测聚能射流侵彻可压缩性较强的靶材的扩孔情况。相关工作可为含液密闭结构干扰聚能射流侵彻提供理论基础。     

串联随进战斗部垂直侵彻装甲钢板实验研究

设计了一种串联随进战斗部,作用时前级聚能装药形成聚能杆式侵彻体对靶板进行侵彻开孔,随后后级随进子弹依靠动能嵌入到开孔的靶板中,实现对目标的毁伤与封锁。在着靶速度为220～330m/s范围内,开展了对该串联战斗部垂直作用于不同厚度装甲钢板的侵彻实验研究。实验结果表明,在230～300m/s范围内,此种结构的串联随进战斗部可以有效作用,随进子弹的嵌入深度总体上随着撞击速度的提高而增大,随进子弹保持完整且嵌入牢固,能够有效实现对目标的毁伤与封锁。     

Penetration into a granular bed in the presence of upward gas flows

We present a numerical study on the penetration of spherical projectiles into a granular bed in the presence of upward gas flows. Due to the presence of interstitial fluid, the force chains between particles in the granular bed are weakened significantly, and this distinguishes the penetration behavior from that in the absence of fluid. An interesting phenomenon, namely granular jet, is observed during the penetration, and the mechanism for its formation and growth is attributed to the merging of granular vortices generated by the interaction between the intruder and primary particles. Moreover, both the final penetration depth and the maximum diameter of the crater are found to follow a power-law dependence with the impact velocity, and the maximum height reached by the granular jet tends to increase linearly as the impact velocity increases, agreeing well with the experimental results reported in the literature.     

Spallation in cylinder-plate impact

A combined theoretical-experimental study has been made of spall-type fracture induced in steel plates impacted by blunt cylinders whose diameter is comparable to the plate thickness. Since attention is restricted to normal impact, the problem is two dimensional, involving rotational symmetry. Analysis of shock-wave patterns induced by impact is achieved by employing a two-dimensional computer program, HEMP, in which the equations of motion are combined with realistic constitutive relations appropriate for the dynamic high-pressure regimes encountered. Experimentally, a series of tests was conducted in which the impact velocity was increased incrementally until penetration occurred. Recovered targets were sectioned and examined for evidence of incipient internal fracture as well as extensive plastic deformation. Correlation with theoretical predictions is considered good.     

Application of a Synthetic Jet to Control Boundary Layer Separation under Ultra-High-Lift Turbine Pressure Distribution

The transition and separation processes of the boundary layer developing on a flat plate under a prescribed adverse pressure gradient typical of Ultra-High-Lift low-pressure turbine profiles have been investigated, with and without the application of a synthetic jet (zero net mass flow rate jet). A mechanical piston has been adopted to produce an intermittent flow with zero net mass flow rate. The capability of the device to suppress or reduce the large laminar separation bubble occurring under steady inflow condition at low Reynolds numbers has been experimentally investigated by means of hot-wire measurements. Wall static pressure measurements complement the hot-wire time-resolved velocity results. The paper reports the investigations performed for both steady and controlled conditions. The active device is able to control the laminar separation bubble induced at low Reynolds number conditions by the strong adverse pressure gradient. An overall view of the time-dependent evolution of the controlled boundary layer is provided by the phase-locked ensemble averaging technique, triggered at the synthetic jet frequency. The separated flow transition process, which is detected for the uncontrolled condition, is modified by the synthetic jet in different ways during the blowing and suction phases. Overall, the phase-locked velocity distributions show a reduced separated flow region for the whole jet cycle as compared to the uncontrolled condition. The phase-locked distributions of the random unsteadiness allow the identification of vortical structures growing along the shear layer mainly during the blowing phase.     

On the Failure and Dynamic Performance of Materials

Waves induced by impact initiate deformation mechanisms within a material that precede later flow. An impulse excites a cascade of deformation mechanisms starting with ultrafast and concluding with slower ones. In metals, brittle glasses and polycrystalline ceramics there are a combination of mechanisms with differing relaxation times that condition a loaded target. In the case of ballistic impact, once failure has occurred, long rod penetration can occur and the depth achieved within each target can be scaled with the deformation strengths recorded during the initial high pressure impulse. A review of material shock response and target preconditioning shows a correlation with the ballistic penetration of the target after loading. This indicates that the effect of an initial loading impulse upon material behaviour is a strong feature of the effects observed in many dynamic phenomena.