Hemispherical Nose Research Articles

Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and conical noses : Part II: numerical simulations

In Part I of this paper, projectiles with three different nose shapes (blunt, hemispherical and conical) were used in gas gun experiments to penetrate 12 mm thick Weldox 460 E steel plates. It was found that the nose shape of the projectile severely affected both the energy absorption and the failure mode of the target structure during penetration. This part of the paper describes numerical simulations of the problem investigated experimentally. A constitutive model of viscoplasticity and ductile damage for projectile impact has earlier been developed and implemented in the explicit finite element code LS-DYNA. Numerical simulations involving this model have been carried out, and the results are compared with the experimental data. However, numerical problems associated with the element mesh were detected, and adaptive meshing was found necessary in order to obtain reliable results for conical projectiles. From the numerical simulations it is found that the LS-DYNA code is able to describe the different failure modes without any predefined defects in the element mesh if special care is taken, and good agreement is in general obtained between the numerical simulations and experimental results.

Perforation of 12 mm thick steel plates by 20 mm diameter projectiles with flat, hemispherical and conical noses : Part I: Experimental study

Projectiles with three different nose shapes (blunt, hemispherical and conical) have been used in gas gun experiments to penetrate 12 mm thick Weldox 460 E steel plates. Based on the experimental results, the residual velocity curves of the target material were constructed and compared. It was found that the nose shape of the projectile significantly affected both the energy absorption mechanism and the failure mode of the target during penetration. The ballistic limit velocities were about equal and close to 300 m/s for hemispherical and conical projectiles, while it was considerably lower for blunt projectiles. Blunt projectiles caused failure by plugging, which is dominated by shear banding, while hemispherical and conical projectiles penetrated the target mainly by pushing the material in front of the projectile aside. Also, the residual velocity curves were influenced by nose shape, partly due to the differences in projectile deformation at impact. The experimental study, given in this part of the paper forms the basis for explicit finite element analysis using the commercial code LS-DYNA presented in Part II of the paper.

Deep punching PMMA

The authors performed deep punching experiments on PMMA (polymethyl methacrylate) using cylindrical-shaped punches with conical and hemispherical noses. The test samples cracked when no lateral confinement was provided. Application of proper lateral confinement suppressed the cracks. The punching force recorded from the experiments correlates very well with cavity expansion theory. Because the use of a single friction coefficient gives excellent agreement between theory and experiments for two different-shaped punches, the authors propose deep punching as a new technique to measure the friction coefficient.

Experimental Study on Flow Noise Generated by Axi-symmetric Boundary Layer (II) - Forced Transition on an Axi-symmetric Nose and Radiated Sound -

The oscillatory excitation with a Strouhal number of 2.65 ncar the stagnation zone of hemispherical nose model was employed to control the laminar separation bubble and the transition to turbulence. The effects of oscillatory excitation upon the separation bubble and the transition were addressed in terms of kurtosis/skewness and time-frequency analyses. The measured noise spectrum of radiated sound from the turbulent boundary layer on the axi-symmetric infinite cylinder is compared with that by Sevik's wave-number white approximations. The noise sources in TBL on axi-symmetric cylinder and the caling of their far-field sound are also discussed.

Axisymmetric oscillations of an opposing jet from a hemispherical nose

The flowfield around a hemispherical nose with a sonic opposing jet in a freestream of Mach 2.5 is computed by a time-accurate algorithm using the axisymmetric Navier-Stokes equations. Five total pressure ratios of a jet to a freestream, 0.816 ∼ 1.633, are examined. The results obtained strongly depend on the total pressure ratio as the previous experimental results did. In some cases, the computed flowfield oscillates intensely in which the drastic change of the jet structure and the surrounding pressure takes place. The flowfield changes from the stable flow to the unstable flow for the same total pressure ratio as in the experiment The mechanism of the oscillations and the condition of transition between both types of flow are interpreted physically on the basis of unsteady numerical solutions here.

Application of wall functions to generalized nonorthogonal curvilinear coordinate systems

A method has been developed for the application of wall functions to generalized curvilinear coordinate systems with nonorthogonal grids. Two test cases have been computed using this method with the k-e turbulence model: flow over a flat plate at 0-deg angle of attack using a nonorthogonal grid at the wall and flow over a prolate hemispheroid with a hemispherical nose cap at 0-deg angle of attack. All results are compared with experimental data. In addition, the hemispheroid results are compared with computations using the Baldwin-Lomax algebraic turbulence model and the Chien low-Reynolds-number k-e turbulence model.

Effect of frictional force on the steady state axisymmetric deformations of a viscoplastic target

We study steady state axistmmetric deformations of a thick viscoplastic target being penetrated by a fast-moving long rigid cylindrical rod with a hemispherical nose. The deformations of the target appear steady to an observer situated on the penetrator nose tip and moving with it. The objective of this work is to investigate the effect of the frictional force acting on the target/penetrator interface upon the deformations of the target. It is postulated that the frictional force at a point on the target/penetrator interface is proportional to the normal traction there and depends upon the speed of the target particle relative to the penetrator. It is found that the frictional force affects significantly the variation of the tangential speed and the second invariant of the strain-rate tensor on the penetrator nose surface, but minimally the distribution of the normal stress there, since the dominant component of the normal stress is the hydrostatic pressure which is affected little by the consideration of friction forces.

Steady state axisymmetric penetration of a kinematically hardening thermoviscoplastic target

We study axisymmetric thermomechanical deformations of a thick target being penetrated by a fast-moving rigid cylindrical rod with a hemispherical nose, and presume that target deformations appear steady to an observer situated at the penetrator nose tip. Both isotropic and kinematic hardening of the target material are considered. It is found that kinematic hardening increases the normal stress acting on the penetrator nose surface and the temperature rise of target particles abutting the penetrator. However, the value of the hydrostatic pressure at a point in the deforming target region is affected very little by the consideration of kinematic hardening. For suitable values of material parameters appearing in the evolution equation of the back-stress, the computed values of the back-stress at target particles abutting the penetrator nose surface equal three times the yield stress of the target material in a quasistatic simple compression test.

Effect of constitutive models on steady state axisymmetric deformations of thermoelastic-viscoplastic targets

We study the steady state axisymmetric deformations of a thick target being penetrated by a rigid cylindrical penetrator with a hemispherical nose and use three different constitutive relations, namely, the Litonski-Batra flow rule, the Bodner-Partom flow rule, and the Brown-Kim-Anand flow rule, to model the thermoelastic-viscoplastic response of the target. Each of these constitutive relations uses an internal variable to account for the microstructural changes in the body. The three flow rules are calibrated to give virtually identical effective stress-logarithmic strain curves during the overall adiabatic plane strain compression of a block of the target material deformed at an average strain rate of 3300s −1 . It is found that the three constitutive relations give nearly the same value of the resisting force acting on the penetrator, temperature rise of material particles in the vicinity of the target-penetrator interface, and other macroscopic measures of deformation, such as the effective stress and logarithmic strain rate.

Impact Properties of Three-Dimensional Braided Graphite/Epoxy Composites

An experimental study of the response and damage of three-dimensional braided graphite/epoxy composite due to sub-perforation velocity impact was carried out in this research. Simply supported square plates were impacted with an instrumented impact pendulum and also a projectile fired by a gas gun. Hemispherical nose impactors of two different diameters, 12.7 mm and 25.4 mm, were used in the pendulum tests. In addition, static flexure tests were performed. Impact damage was assessed using X-radiography, and compression after impact tests. Damages involved in impacted braided panel are matrix cracking in resin pockets, separation of fiber tows, and fiber tow breakage, mostly in fiber bundle crimp areas. A quasi-isotropic laminate was impact tested with pendulum for comparison of impact tolerance between the two composite systems.

Impact damage on single interface GFRP laminates — An experimental study

Impact damage on single interface GFRP laminate impacted by a steel projectile with a hemispherical nose was studied. The delamination damage area was investigated by varying the depth of the interface from 1 ply to 7 plies. The impact caused delamination damage of an oblong shape with aspect ratios of 27·5 for an interface at one ply depth and 2·1 for an interface at 7 plies depth. In specimens with the interfaces at 1, 2 or 3 plies depth, the damage was mainly caused by generation of a transverse crack at the rear ply in each specimen. Damages on specimens with interfaces at 4, 5, 6 plies deep, were of ‘dumb-bell’ shapes generated by shear and tensile stresses. The specimen with the rearmost interface exhibited delamination damage caused mainly by the spread of several transverse cracks at the interface. The compressive stresses of flexural waves were also observed to generate transverse cracks on the impact face with associated delamination damage in specimens with interfaces 4–7 plies deep. However, the delamination damage of such a crack was of small width but lengths comparable to the dimensions of the overall damage. The specimens with interfaces 5 plies deep showed the maximum damage.

Velocity field of a cylinder in the wake of a rotor in forward flight

The rotor and the airframe of a rotorcraft can have severe effects on each other because of flowfield interactions. Data on flowfield characteristics have been obtained using laser velocimetry in an attempt to identify and interpret the features of such interactions. This paper summarizes previous results on the flowfield of the rotor and then describes the effects of the rotor wake on the flowfield around an airframe model. A circular cylinder with a hemispherical nose is used as the airframe model and is instrumented with static pressure taps and flush-mounted microphones. A two-bladed teetering rotor is suspended above it in a wind tunnel. The periodic and time-averaged velocity fields are measured along lines parallel to the airframe axis at a rotor advance ratio of 0.1 and a rotor tip Mach number of 0.29. The dominant features in the velocity distribution over the airframe are seen to be linked to vortex interactions with the airframe surface. The tip vortex and the trailing vortex sheet are seen to be displaced in opposite directions by the airframe. Secondary vortex generation phenomena are observed near the airframe surface during vortex interaction.

An approximate analysis of steady state axisymmetric deformations of viscoplastic targets

Steady state axisymmetric deformations of a viscoplastic target being penetrated by a rigid cylindrical penetrator with a hemispherical nose are analyzed. The presumed kinematically admissible velocity field satisfies all of the boundary conditions on the target/penetrator interface, and also the balance of mass. The unknown parameters appearing in the admissible velocity field are found by minimizing the error in satisfying the balance of linear momentum. The solution so obtained is found to be very close to the finite element solution of the problem. An advantage of the present technique is the enormous savings in the computational effort and resources required to analyze the problem.

Results from laser sheet visualization of a periodic rotor wake

A laser sheet has been applied to the visualization of a periodic rotor wake produced by a model rotorcraft in forward flight. A stiff, two-bladed teetering rotor is mounted independently of an idealized airframe consisting of an instrumented circular cylinder with a hemispherical nose. The model was installed in a wind tunnel, and tests were carried out at three different advance ratios (forward flight speeds) at one value of rotor collective pitch angle. The laser sheet technique enables detailed flow visualization to be carried out. Quantitative data regarding the location of the rotor tip vortex can be obtained. Results from the flow visualization confirm that the rotor wake is a complex flowfield not amenable to simple analysis. However, the details of the tip vortex geometry are both periodic and repeatable. The motion of the rotor wake in close proximity to the airframe is examined. The behavior of the tip vortex is strongly affected by the presence of the airframe. In particular, the interaction of the rotor tip vortex with the airframe results in the destruction of the vortex core; apparently the vorticity is diffused, and the vortex loses its definition. No vortex filaments appear below the airframe as identifiable flow features. Examples of airframe surface pressure data are presented and are seen to correlate well with the results from the flow visualization.

Steady state penetration of compressible rigid perfectly plastic targets

Steady state axisymmetric deformations of a homogeneous, isotropic, compressible and rigid perfectly plastic target being penetrated by a rigid cylindrical penetrator with a hemispherical nose are studied by the finite element method. The steady state is reached with respect to an observer situated on the penetrator nose and moving with it. Tillotson's equation, restricted to mechanical deformations, is used to express the pressure as a function of the mass density. Contact between the penetrator and the target is assumed to be smooth. The effect of compressibility of the material is delineated by comparing results for compressible and incompressible materials. Also studied is the effect of the penetrator speed on target deformations.

Steady state penetration of rigid perfectly plastic targets

The problem of steady penetration by a semi-infinite, rigid penetrator into an infinite, rigid/perfectly plastic target has been studied. The rod is assumed to be cylindrical, with a hemispherical nose, and the target is assumed to obey the Von-Mises yield criterion with the associated flow rule. Contact between target and penetrator has been assumed to be smooth and frictionless. Results computed and presented graphically include the velocity field in the target, the tangential velocity of target particles on the penetrator nose, normal pressure over the penetrator nose, and the dependence of the axial resisting force on penetrator speed and target strength.

Scale effects on cavitating flows due to surface roughness and laminar separation

Roughness and viscous scale effects are an important consideration when using model data to predict limited cavitation on a prototype, since in many cases the limited cavitation number of a model is different from that of the prototype. In this paper it is shown that fixed patch cavitation, which is observed on axisymmetric headforms and sheet cavitation observed on hydrofoils, may be controlled by surface roughness. An analysis predicts the same general characteristics as that shown by the experimental data; namely, the cavitation number increases with Reynolds number Re for a given size and increases with decreasing size for a given value of Re. The results of a theoretical analysis of bubble-ring cavitation on a hemispherical nose are also presented. The analysis, which indicates that both Reynolds number and Weber number are important scaling parameters, is employed in an attempt to correlate extensive experimental data.

Observations of the Various Types of Limited Cavitation on Axisymmetric Bodies

Observations are presented of various types of limited cavitation on 5.1 cm diameter Schiebe, hemispherical, and DTNSRDC noses. These three noses were selected to give various flow states over the range of test speeds 6.1–21.3 m/s ranging from laminar separation for all speeds (hemispherical nose) to nonseparated flow for all speeds (Schiebe nose) with the DTNSRDC nose experiencing both separated and nonseparated flow over the speed range. The types of cavitation observed fall into two broad classes, namely transient and attached. Transient cavitation was observed in three forms, namely travelling-bubble, travelling-patch and bubble-ring. Three types of attached cavitation were observed, namely band, fixed-patch and developed. Bubble-ring and band cavitation are observed only on a body with laminar separation as noted previously by Arakeri and Acosta. Bubble-ring cavitation has been observed only on hemispherical and eighth caliber ogive noses. The desinent cavitation numbers for band and bubble-ring cavitation on the hemispherical nose are related to measured mean and fluctuating pressure data. Travelling cavitation was the most prevalent type of cavitation and the cavitation number decreased with speed and increased with air content. An analysis of travelling cavitation data from several investigations is presented. The cavitation number for fixed-patch cavitation increases with speed which suggests that surface roughness effects are involved.

Inception of Cavitation From a Backward Facing Step

Cavitation inception measurements are reported for flow past a downstream facing step with the height of the step varying from about 0.4 to 5 percent of the forebody diameter. The forebody was a 49 mm hemispherical nose and σi values were found to be very strong function of the height of the step. In addition, σi values were found to depend on whether the boundary layer approaching the step was laminar or turbulent. Generally σi values for turbulent case were lower.

Transonic viscid-inviscid flow interaction about a hemisphere-cylinder

A wind-tunnel investigation was conducted of the viscous-inviscid interaction flowfield about a hemisphere- cylinder at zero incidence in the Mach number range 0.6-0.9. A nose separation bubble is revealed from analysis of shadowgraphs and surface pressure distributions between Mach numbers 0.7 and 0.9. A multiple shock system consisting of a lambda shape shock and two normal shocks prevails in the flowfield as a result of the viscous-inviscid flow interaction which is strongest at M^ =0.85. Velocity field measurements utilizing a laser velocimeter were obtained and analyzed by using the concept of an effective body and the particle dynamics for M =0.85. N Refs. 1 and 2, a theoretical and experimental in- vestigation of the flowfield about a hemisphere-cyl inder at zero incidence in the transonic and low supersonic freestream Mach number Mx from 0.7 to 1.3 is presented. It was found that a strong viscid-inviscid flow interaction with boundary- layer separation at the hemispherical nose occurs at M^ —0.8, yet for M^ >0.9 no flow separation was observed. A similar separation phenomenon is also presented in the data of Ref. 3. Since a hemisphere-cyl inder is one of the basic nose con- figurations for blunt nose bodies of revolution, a detailed study of the phenomena of transonic viscid-inviscid flow interaction with boundary-layer separation shall reveal the physical features of transonic axisymmetrical flow over blunt nose bodies in general. In this paper, an experimental investigation of the viscous- inviscid flow interaction phenomena for a hemisphere- cylinder at Mach numbers from 0.6 to 0.9 is presented. First, a nose separation bubble is revealed from analysis of shadowgraphs and surface pressure distribution between Mach numbers from 0.7 to 0.9. This result indicates a basic difference in the mechanism of separation between the present nose separation and the leading-edge separation of blunt nose airfoils and will be discussed herein. Second, a multiple shock system, consisting of a lambda shape shock and two normal shocks, prevails in the flowfield as a result of the viscid- inviscid flow interaction. The observed nose separation bubble and the multiple normal shocks are also analyzed through inviscid calculation utilizing the concept of an ef- fective body and shown to be physically sound. Third, a velocity field survey was conducted using a laser velocimeter. The influence of the nose separation on the velocity field is presented by comparison of the measured velocity com- ponents with the inviscid solutions for the hemisphere- cylinder and the effective body. A particle dynamic analysis to account for the particle lag in LV measurements is also presented. tinuous flow, nonreturn wind tunnel capable of being operated at Mach numbers from 0.2 to 1.5. The test section is 1 ft square and 37.5 in. long with 6% porous walls at the top and bottom and two plexiglas side walls for flow visualization. The model used in the test is a hemisphere- cylinder 1 in. in diameter and 10 in. long and is made of stainless steel. Eighteen pressure orifices are located along a single plane. The model is sting mounted with a sting diameter of 0.75 in. B. Flow Visualization