Outcome Of Collisions Research Articles

Collision and impact simulations including porosity

AbstractThe Smooth Particle Hydrodynamics (SPH) impact code (Benz & Asphaug 1994) has been developed for the simulation of impacts and collisions involving brittle solids in the strength-and gravity-dominated regime. In the latter regime, the gravitational overburden is used to increase the fracture threshold. In this paper, we extend our numerical approach to include the effect of porosity at a sub-resolution scale by adapting the so-called P -α model (Herrman 1969). Using our extended 3D SPH impact code, we investigated collisions between porous bodies to examine the sensitivity of collisional outcomes to the degree of porosity. Two applications that illustrate the capabilities of our approach are shown: 1) the modeling of a Deep Impact-like impact and 2) the computation of the amount of momentum transferred to an asteroid following the impact of a high velocity projectile.

Collision between immiscible drops with large surface tension difference: diesel oil and water

The collision outcomes of immiscible drops with large surface tension difference, namely, a water drop and a diesel oil drop, were observed experimentally. In a near head-on collision between immiscible drops with large surface tension difference, an “overlaying” action for the drop of the smaller surface tension, i.e., the diesel oil drop, to go around the surface of the drop of the larger surface tension, i.e., the water drop, occurs during the collision. This overlaying action reduces the reflex energy for head-on collisions, making reflex separation more difficult to occur. At the same time, due to the immiscibility, the liquid bridge during stretching separation becomes narrower, which makes stretching separation easier to happen. No coalescence could be observed for a collision of Weber number greater than 60. In addition, compound drops are produced frequently.

Geometric parametrization of binary elastic collisions

A geometric view of the possible outcomes of elastic collisions of two massive bodies is developed that integrates laboratory, center of mass, and relative body frames in a single diagram. From these diagrams all the scattering properties of binary collisions can be obtained. The particular case of gravitational scattering by a moving massive object corresponds to the slingshot maneuver, and its maximum velocity is obtained.

Rebound characteristics for 50-μm particles impacting a powdery deposit

The formation of powdery deposits on the tubes in a waste heat boiler reduces the heat transfer coefficient by about 25%. Because of these fouling layers, the efficiency with which energy can be recovered from flue gases is reduced. The growth of the layers by the deposition of fly ash particles onto the tubes is strongly dependent on the interaction of the incident particle with the bed of particles. In this study the interaction is modelled as the outcome of a 2-body collision between an incident fly-ash particle and a second particle that represents a developing fouling layer. The mass of this second particle is dependent on the characteristics of the layer. The present paper focuses on the applicability of the 2-body collision model to predict the rebound characteristics of 50-μm particles impacting a powdery deposit. This is studied by impaction experiments of glass particles on different types of glass layers (powdery vs. glued), under various impaction angles (ranging from 0° to 30°) and with different incident velocities (ranging from 0.5 to 1 m/s). The experiments are carried out in a vacuumed column and, using a digital camera system, individual impacts are recorded. With this set-up the normal coefficient of restitution, the Coulomb friction coefficient and the proportionality factor are determined for particles in the 50-μm range. Besides, a 2-body collision model is developed to simulate the rebound characteristics. From a comparison between the experimental results and the model, it is shown that the 2-body approach to model the rebound characteristics of particles impacting a powdery layer is valid and that the proportionality factor is dependent on the binding between the particles in the layer and the relative particle size of the particles in the layer compared to the size of the incident particles.

Collisions of a string of water drops on a water jet of equal diameter

The collision between a water drop and a water jet of equal diameter was experimentally studied. The collision outcome was found to depend on the impact parameter, the cross-jet Weber number, and the along-jet Weber number. Five collision outcomes; namely, segmenting coalescence, clinging coalescence, stretching separation, bouncing, and splashing were observed. The lower impact parameter limit for stretching separation to happen was found to decrease with increasing cross-jet Weber number. For a constant cross-jet Weber number, as the along-jet Weber number increases, the collision produces first segmenting coalescence, and then clinging coalescence with diminishing jet deformation. Bouncing happens for small cross-jet and along-jet Weber numbers, and small impact parameters. Simple energy models for segmenting coalescence and stretching separation were developed with their empirical constants determined from experimental data.

Finite-Element Crash Test Simulation of New York Portable Concrete Barrier with I-Shaped Connector

Use of finite-element simulations in designing and analyzing roadside hardware has increased significantly over the past decade. Due to considerable progress in computer technology in conjunction with nonlinear finite-element software, outcome of complex vehicle-roadside hardware collisions can be accurately predicted using simulation programs. In this paper, the finite-element simulation program LS-DYNA was used to analyze and improve the crash test behavior of New York Department of Transportation Portable Concrete Barrier (NYPCB). A full-scale crash test demonstrated that the current NYPCB design was unable to meet national standards. Inspections after the test revealed that the welding at metal connectors forming the joint between the barrier segments was not properly fabricated. A finite-element representation of the crash-tested barrier was developed with a special fillet weld with failure model and subjected to crash testing using the nonlinear finite-element code LS-DYNA. This baseline model simulation was intended to replicate the failed crash test and validate the fidelity of the finite-element models. Qualitative and quantitative comparisons show that the baseline model simulation was successful in replicating the failed crash test. Upon validation, an improved NYPCB model was developed by using proper welding details and subjected to full-scale impact simulation to determine whether this design would satisfy the crash testing requirements. Results of the simulation were encouraging. It was predicted that the barrier would successfully contain and redirect the impacting vehicle in a stable manner. Subsequent full-scale crash testing on the NYPCB with proper welding details passed the NCHRP Report 350 requirements and substantiated LS-DYNA predictions.

Factors Affecting Common Vehicle-to-Vehicle Collision Types

The number of older drivers (65+ years old) is increasing as a result of the baby boom generation reaching retirement age and an increase in driver's license holders among the elderly. The types of collisions incurred by older drivers are compared with those of drivers 30 to 60 years old in vehicle-to-vehicle collisions using the General Estimates System 2002–2003 sampling of reported motor vehicle collisions compiled by the NHTSA National Center for Statistics and Analysis. Multinomial logit vehicle-to-vehicle collision outcome models that account for driver, vehicle, roadway, environmental, and temporal characteristics were created for drivers age 65 and older and a comparison group of drivers 30 to 60 years old. The older drivers are significantly more prone to collisions related to vehicle turning and intersecting paths—particularly at signalized intersections—than are 30-to-60-year-old drivers. As a factor, age is elastic for same-direction and vehicle-turning crashes. Probability decreases with age for same-direction collision types but increases with age for vehicle-turning collision types, this indicates that difficulty with intersections increases for older drivers. Within the 30-to-60-year-old group, age was not significant. The results support findings of previous studies that older drivers tend to avoid driving in suboptimal conditions. The conclusions provide insight into roadway improvements that require priority for research and funding to make driving easier and safer for road users in general and older drivers in particular.

Factors Affecting Common Vehicle-to-Vehicle Collision Types: Road Safety Priorities in an Aging Society

The number of older drivers (65+ years old) is increasing as a result of the baby boom generation reaching retirement age and an increase in driver's license holders among the elderly. The types of collisions incurred by older drivers are compared with those of drivers 30 to 60 years old in vehicle-to-vehicle collisions using the General Estimates System 2002-2003 sampling of reported motor vehicle collisions compiled by the NHTSA National Center for Statistics and Analysis. Multinomial logit vehicle-to-vehicle collision outcome models that account for driver, vehicle, roadway, environmental, and temporal characteristics were created for drivers age 65 and older and a comparison group of drivers 30 to 60 years old. The older drivers are significantly more prone to collisions related to vehicle turning and intersecting paths—particularly at signalized intersections—than are 30-to-60-year-old drivers. As a factor, age is elastic for same-direction and vehicle-turning crashes. Probability decreases with age ...

Droplet collision and coalescence model

A new droplet collision and coalescence model was presented, a quick-sort method for locating collision partners was also devised and based on theoretical and experimental results, further advancement was made to the droplet collision outcome. The advantages of the two implementations of smoothed particle hydrodynamics (SPH) method were used to limit the collision of droplets to a given number of nearest droplets and define the probability of coalescence, numerical simulations were carried out for model validation. Results show that the model presented is mesh-independent and less time consuming, it can not only maintains the system momentum conservation perfectly, but not susceptible to initial droplet size distribution as well.

Simulations of binary drop collisions with a multiple-relaxation-time lattice-Boltzmann model

In this paper, we report simulations of drop-drop collisions using a multi-relaxation-time multiphase flow lattice Boltzmann model. Employing a multi-relaxation-time (MRT) model in lieu of the Bhatnagar-Gross-Krook (BGK) model used in the standard lattice-Boltzmann equation enables realization of stable computations of drop collisions at relatively lower fluid viscosities without increasing the lattice resolution to prohibitive levels. Head-on and off-center computations of collisions are carried out using axisymmetric and three-dimensional (3D) versions of the MRT model, respectively. Time-resolved results showing the interactions of the interfaces of drops for different characteristic nondimensional parameters are presented. Computations show that at low Weber numbers, We, coalescence with relatively smaller deformation occurs, sometimes entrapping a stable microbubble. At higher We, head-on collisions lead to reflexive separation with or without the formation of satellite droplets. The size of the satellite droplets appears to increase with increase in the We. The Ohnesorge number, Oh, seems to modulate the transient characteristics and the outcome of collisions. It is found that the greater the Oh, the smaller is the size of the satellite droplets formed. For off-center collisions at a given We, at lower values of the impact parameter permanent coalescence is observed, while higher values result in separation by stretching action. These findings are in satisfactory agreement with experimental observations.

Effects of tangential speed on low-normal-speed liquid drop impact on a non-wettable solid surface

A stream of water drops colliding on a rotating cylindrical Teflon surface was observed. The collision resulted in partial rebound, deposition, and split deposition. The collision outcome was found to depend on the normal Weber number and the tangential Weber number, which represent the collision momentum in the normal and the tangential direction, respectively. The extent of influence of the centrifugal acceleration induced by the rotation was kept negligibly under 2% compared with the impact momentum change. Through careful measurements on the elongation of the liquid drop after impact, the impact regime boundaries are seen to be governed by the long and short axes of the elliptical-disk shape at the maximal spread. Partial rebound first changes to deposition when the long axis is 1.1 times the short axis; and then changes to split deposition when the long axis is 1.46 times the short axis. Furthermore, the dimensionless excess spread area was found to be directly proportional to the tangential Weber number.

Reconnection of non-abelian cosmic strings

Cosmic strings in non-abelian gauge theories naturally gain a spectrum of massless, orlight, excitations arising from their embedding in colour and flavour space. This opens upthe possibility that colliding strings miss each other in the internal space, reducing theprobability of reconnection. We study the topology of the non-abelian vortex moduli spaceto determine the outcome of string collision. Surprisingly we find that the probability ofclassical reconnection in this system remains unity, with strings passing through each otheronly for finely tuned initial conditions. We proceed to show how this conclusion can bechanged by symmetry breaking effects, or by quantum effects associated to fermioniczero modes, and present examples where the probability of reconnection in aU(N) gauge theoryranges from 1/N for low-energy collisions to one at higher energies.

Alignment effects in charge transfer and excitation forH+andHe2+collisions withH2+

The study of ion-atom collisions has a long history for both experimental and theoretical techniques. There has been much less effort for ion-molecule collisions. Computationally, the ion-molecule collisions are much more difficult than ion-atom collisions. This is partly due to the multicenter nature of the problem instead of the two centers for ion-atom collisions. Perhaps more importantly, the cross sections may depend on several other coordinates. Thus, there is a dramatic increase in the number of calculations needed to explore the physically relevant parameters. There is also the possibility that interference due to the extended size of the electron orbitals will cause the results to depend sensitively on the accuracy of the calculation. Finally, molecules have a larger number of low-lying excited states compared to similar atoms which may sensitively affect the outcome of collisions. To see where some of the difficulties lie, we examine what is needed for ions scattering from a diatomic molecule that has no initial angular momentum about the internuclear axis. We simplify the picture further by assuming the ion may be treated as a classical particle traveling in a straight line and the nuclei in the molecule may be treated as fixed in space during the collision. In the comparable case for ionatom collisions, one only needs to calculate the probability for a process as a function of the impact parameter. For the ion-molecule collision, the probability for a process needs to be calculated as a function of the impact parameter in a plane i.e., two dimensions, as a function of the separation of the nuclei, and as a function of the angle between the ion’s velocity and the internuclear axis. Thus, we have gone from one parameter to four; assuming we need 5–10 examples of each parameter for an adequate exploration of ion-molecule collision we find there are approximately 100–1000 times more trajectories that are needed for ion-molecule calculations than for a comparable ion-atom calculation. The simplest ion-molecule system is when there is only one electron present. References 1,2 studied the collision of He 2+ with the D 2 + molecular ion. Reference 1 measured the total charge transfer cross section and compared the results to calculations using a model for the electronic orbital for the molecule. The model used a linear combination of atomic orbitals and the transition amplitudes are approximated as a linear superposition of the amplitudes for each atomic orbital 3. The calculated and measured total charge transfer cross sections were in good agreement. Reference 2 measured the dependence of the total charge transfer cross section on the angle between the velocity of the atomic ion and the internuclear axis and compared the measurement to the results of a model calculation again based on Ref. 3. Although the agreement was not as good, the general trends were the same: the cross section is much larger for perpendicular geometry than when the velocity is parallel to the internuclear axis. At velocity 0.4 a.u., the measurement gives a cross section 3–4 times larger at 90° than at 0° while the calculation gives a factor of 7–8. At velocity 0.5 a.u., the measurement gives a cross section 3–6 times larger at 90° compared to 1.5–2 for the calculation. Reference 4 presents calculations for total charge transfer for this system using both classical methods and a 2+1 -center close-coupling approximation. The total charge transfer cross section was 20–30 % lower than the previous measurement and calculation. In this paper, we present the results of calculations for charge transfer from the H 2 + molecular ion to He 2+ ions and to H + ions. Because the protons of the molecular ion are fixed during the collision, our results apply equally well to D2 + . The focus of this paper is the dependence of the cross section on the angle between the ion’s velocity vector and the internuclear axis and the dependence on the internuclear separation. Our method of calculation consists of direct numerical solution of Schrodinger’s equation on a grid of points; grid methods can be thought of as a basis set method with the number of basis functions equal to the number of grid points 10 7 in our case but with a momentum cutoff roughly equal to the inverse of the separation of grid points.

Modeling Injection of Dense Liquid Sprays in Radio Frequency Inductively Coupled Plasmas

A spray model and a droplet collision model are implemented into a radio frequency inductively coupled plasma model. The discrete parcel technique combined with the stochastic Monte Carlo method is used to solve the spray equation and determine the outcomes of droplet collisions in dense sprays. Plasma--spray interactions are considered by adding source terms to the conservation equations of mass, momentum and energy of the plasma phase. Two types of the outcomes of water droplets collisions, coalescence and grazing, are predicted and compared to the experimental and analytical results. The agreement is quite good. The effects of droplet collisions on droplet size distribution of the spray and the spray evaporation are investigated. It is found that the droplet collisions can increase the average droplets size of the spray. For the mono-disperse spray, the collisions can lead to a delay on the spray evaporation. However, for the poly-disperse spray, the effect of droplet collisions on the spray evaporation could not be predicted before the calculation due to the randomness of droplet collisions.

Planetesimals to Protoplanets. I. Effect of Fragmentation on Terrestrial Planet Formation

We present results from a dozen direct N-body simulations of terrestrial planet formation with various initial conditions. In order to increase the realism of our simulations and investigate the effect of fragmentation on protoplanetary growth, we have developed a self-consistent planetesimal collision model that includes fragmentation and accretion of debris. In our model we treat all planetesimals as gravitational aggregates so that gravity is the dominant mechanism determining the collision outcome. We compare our results to those of Kokubo & Ida in which no fragmentation is allowed; perfect merging is the only collision outcome. After 400,000 yr of integration our results are virtually indistinguishable from those of Kokubo & Ida. We find that the number and masses of protoplanets and the time required to grow a protoplanet depend strongly on the initial conditions of the disk and are consistent with oligarchic theory. We have found that the elasticity of the collisions, which is controlled by the normal component of the coefficient of restitution, does not significantly affect planetesimal growth over a long timescale. In addition, it appears that there is a negligible amount of remaining at the end of oligarchic growth, where debris is defined as particles too small to be resolved in our method, although we caution that these results are for an initial mass fraction of 1%. The component is not massive enough to alter the dynamics of the protoplanets.

A comprehensive set of simulations of high-velocity collisions between main-sequence stars

We report on a very large set of simulations of collisions between two main-sequence (MS) stars. These computations were carried out with the smoothed particle hydrodynamics method. Realistic stellar structure models for evolved MS stars were used. In order to sample an extended domain of initial parameters space (masses of the stars, relative velocity and impact parameter), more than 14 000 simulations were carried out. We considered stellar masses ranging between 0.1 and 75 M⊙ and relative velocities up to a few thousand km s−1. To limit the computational burden, a resolution of 1000–32 000 particles per star was used. The primary goal of this study was to build a complete data base from which the result of any collision can be interpolated. This allows us to incorporate the effects of stellar collisions with an unprecedented level of realism into dynamical simulations of galactic nuclei and other dense stellar clusters. We make the data describing the initial condition and outcome (mass and energy loss, angle of deflection) of all our simulations available on the Internet. We find that the outcome of collisions depends sensitively on the stellar structure and that, in most cases, using polytropic models is inappropriate. Published fitting formulae for the collision outcomes, established from a limited set of collisions, prove of limited use because they do not allow robust extrapolation to other stellar structures or relative velocities.

Evolution of a Keplerian disk of colliding and fragmenting particles: a kinetic model with application to the Edgeworth–Kuiper belt

We present a kinetic model of a disk of solid particles, orbiting a primary and experiencing inelastic collisions. In distinction to other collisional models that use a 2D (mass–semimajor axis) binning and perform a separate analysis of the velocity (eccentricity, inclination) evolution, we choose mass and orbital elements as independent variables of a phase space. The distribution function in this space contains full information on the combined mass, spatial, and velocity distributions of particles. A general kinetic equation for the distribution function is derived, valid for any set of orbital elements and for any collisional outcome, specified by a single kernel function. The first implementation of the model utilizes a 3D phase space (mass–semimajor axis–eccentricity) and involves averages over the inclination and all angular elements. We assume collisions to be destructive, simulate them with available material- and size-dependent scaling laws, and include collisional damping. A closed set of kinetic equations for a mass–semimajor axis–eccentricity distribution is written and transformation rules to usual mass and spatial distributions of the disk material are obtained. The kinetic “core” of our approach is generic. It is possible to add inclination as an additional phase space variable, to include cratering collisions and agglomeration, dynamical friction and viscous stirring, gravity of large perturbers, drag forces, and other effects into the model. As a specific application, we address the collisional evolution of the classical population in the Edgeworth–Kuiper belt (EKB). We run the model for different initial disk's masses and radial profiles and different impact strengths of objects. Our results for the size distribution, collisional timescales, and mass loss are in agreement with previous studies. In particular, collisional evolution is found to be most substantial in the inner part of the EKB, where the separation size between the survivors over EKB's age and fragments of earlier collisions lies between a few and several tens of km. The size distribution in the EKB is not a single Dohnanyi-type power law, reflecting the size dependence of the critical specific energy in both strength and gravity regimes. The net mass loss rate of an evolved disk is nearly constant and is dominated by disruption of larger objects. Finally, assuming an initially uniform distribution of orbital eccentricities, we show that an evolved disk contains more objects in orbits with intermediate eccentricities than in nearly circular or more eccentric orbits. This property holds for objects of any size and is explained in terms of collisional probabilities. The effect should modulate the eccentricity distribution shaped by dynamical mechanisms, such as resonances and truncation of perihelia by Neptune.

Collisional Simulations of Cometary Nuclei

AbstractCollisional simulations of cometary nuclei (icy dust aggregates) are conducted. Conditions for sticking are determined as a function of the impact velocity and mechanical properties of nuclei. Possible collisional outcomes in three evolutionary stages of icy-dust aggregates are discussed.

Modeling droplet collision and coalescence in an icing wind tunnel and the influence of these processes on droplet size distribution

A theoretical model of a two-phase air/dispersed water spray flow in an icing wind tunnel is presented here. The mutual interactions taking place within the dispersed phase known as binary droplet collisions, as well as gravitational sedimentation are considered. Where large droplets and low air stream velocities are concerned, the effect of gravity on droplet dynamics is considerable. Gravity causes the vertical deflection of droplet trajectories and an increase in liquid water content (LWC) in the bottom half of the wind tunnel. Droplet collision tends to influence the size, trajectory and velocity of droplets thus affecting the characteristics of the flow and, thereby, the formation of ice on the object placed in the wind tunnel. The present model simulates droplet motion and droplet collision in an icing wind tunnel, where it may be observed that bouncing, stable coalescence, or coalescence followed by separation are the possible outcomes of collision. In the theoretical examination, firstly, the effect of gravity on the vertical deflection of droplet trajectories and on the vertical distribution of the LWC near the icing object are taken into account, while droplet collision is disregarded. Then both factors are considered and collision outcome is determined together with the size and velocity of post-collision droplets. The initial droplet size distribution (DSD), as it occurs at the nozzle outlet, is estimated by a curve in accordance with previous experimental results. The DSD is determined theoretically near the icing object, which makes it possible to calculate the median volume diameter and the LWC of the aerosol cloud. The simulation results with regard to the LWC are compared to the experimental results obtained in this research and a satisfactory qualitative coincidence is to be found between them.

Catastrophic disruption of pre-shattered parent bodies

In this paper, we analyze the effect of the internal structure of a parent body on its fragment properties following its disruption in different impact energy regimes. To simulate an asteroid breakup, we use the same numerical procedure as in our previous studies, i.e., a 3D SPH hydrocode to compute the fragmentation phase and the parallel N-body code pkdgrav to compute the subsequent gravitational re-accumulation phase. To explore the importance of the internal structure in determining the collisional outcome, we consider two different parent body models: (1) a purely monolithic one and (2) a pre-shattered one which consists of several fragments separated by damaged zones and small voids. We present here simulations spanning two different impact energy regimes—barely disruptive and highly catastrophic—corresponding to the formation of the Eunomia and Koronis families, respectively. As we already found for the intermediate energy regime represented by the Karin family, pre-shattered parent bodies always lead to outcome properties in better agreement with those of real families. In particular, the fragment size distribution obtained by disrupting a monolithic body always contains a large gap between the largest fragment and the next largest ones, whereas it is much more continuous in the case of a pre-shattered parent body. In the latter case, the ejection speeds of large fragments are also higher and a smaller impact energy is generally required to achieve a similar degree of disruption. Hence, unless the internal structure of bodies involved in a collision is known, predicting accurately the outcome is impossible. Interestingly, disrupting a pre-shattered parent body to reproduce the Koronis family yields a fragment size distribution characterized by four almost identical largest objects, as observed in the real family. This peculiar outcome has been found before in laboratory experiments but is obtained for the first time following gravitational re-accumulation. Finally, we show that material belonging to the largest fragments of a family originates from well-defined regions inside the parent body (the extent and location of which are dependent upon internal structure), despite the many gravitational interactions that occur during the re-accumulation process. Hence fragment formation does not proceed stochastically but results directly from the velocity field imparted during the impact.