Soft-sphere Discrete Element Method Research Articles

PhasicFlow: A parallel, multi-architecture open-source code for DEM simulations

PhasicFlow is an open-source code for DEM simulations developed in C++, licensed under GPL V-3.0 [www.github.com/PhasicFlow/phasicFlow]. It is parallelized based on shared-memory model and can be executed on multi-core CPUs or GPUs. The philosophy of its development is to provide an efficient, easy-to-use, and easy-to-extend tool for a wide range of hardware including cheap to high-end desktop computers. Here, the code structure, the most important features, its performance for simulating small to large problems (250,000 to 80,000,000 particles) on various hardware are presented. In all cases, the execution time varied linearly with number of particles that is ideal for DEM. The computation load per particle was almost constant for all problem sizes except for small simulations (higher). For CPU simulations, a good scaling was observed with number of cores, and scaling was closer to ideal state for larger simulations. The performance of PhasicFlow was compared with similar tools, wherever possible. It was shown that the performance of PhasicFlow is much higher than the similar tools in CPU execution mode and it is around 10–15% faster than similar tools in GPU execution mode. This new tool broadens the application of computer simulation to larger problems and allows researchers to perform DEM simulations on a wider range of hardware. Program summaryProgram title: PhasicFlowCPC Library link to program files:https://doi.org/10.17632/fs7w7jb8mr.1Developer's repository link:www.github.com/PhasicFlow/phasicFlowLicensing provisions: GNU General Public License 3Programming language: C++Nature of problem: The code covers the simulation of granular matter in powder, gas-solid and liquid-solid flows. The formulation is based on the soft-sphere discrete element method (DEM) which is a powerful tool for simulating solid powder flows. Solid particles are considered distinct bodies that may interact with solid surfaces, other particles and fluid around them.This method can be purely used for investigating various flow problems or can be coupled with proper fluid flow simulation code to be used in multiphase flow systems. The main goal here is to provide a powerful tool for researchers to perform large-scale powder and multiphase flows on cheaper and more accessible hardware.Solution method: The solution method is based on the high-order explicit integration of equations of motions for discrete particles over time to obtain their linear and rotational position and velocity. Triangulation is used for representing solid walls and various motion models are implemented, which cover a wide range of processing units in the real-life application. Particle-particle and particle-wall interactions are modeled using linear and non-linear models accompanied with friction models.The code is designed to be executed fast, to efficiently use computational resources, and to be easily understood, altered and extended for specific uses. It is multi-architecture and can be executed in parallel on both CPU and GPU, depending on the available hardware. It uses Kokkos as the backend code for managing memory resources and dispatching parallel work on computational resources. Accordingly, a single code can be compiled for various hardware types. The parallelization is performed on high-level and with negligible overhead costs, so the developers of the code are not facing hardware-specific programming models when parallelizing the computations workloads.Additional comments including restrictions and unusual features: The simulation setup in the code is based on human readable text-based files that are supplied by the user. To use the code, no knowledge of programming is required. The GitHub repository contains a wiki page that provides a full set of tutorials to show researchers how to simulate various granular flows. A step-by-step procedure for building the code is also provided in the repository that has been tested on various version of Ubuntu, including versions 18.04 LTS, 20.04 LTS and 22.04 LTS.

Discrete-element modeling of shear-induced particle migration during concrete pipe flow: Effect of size distribution and concentration of aggregate on formation of lubrication layer

The paper seeks to better understand the particulate mechanics giving rise to the lubrication layer (LL) in flows with wide particle-size distributions (PSD) typical of concrete pumping applications. The study uses a soft-sphere discrete element method (DEM) to simulate the shear-induced particle migration (SIPM) mechanism of formation of the LL. To provide realistic understanding of SIPM and rheological heterogeneity of concrete, three wide PSDs (fine, medium, and coarse) and three different concentrations (10 %–40 %) of five spherical-particle subclasses (1–17 mm diameter) were investigated. The radial evolution of concentration and particle distribution was simulated over time and the LL formation was successfully simulated. The predicted LL thicknesses compared well with experimental values. The coupled effect of PSD, concentration, and mean diameter of particles on wall effect, SIPM, and rheological heterogeneities across the pipe was evaluated. Higher rheological heterogeneity across the pipe was obtained for higher concentration and coarser particle size distributions.

Transmission of a Seismic Wave Generated by Impacts on Granular Asteroids

In this paper, we use a soft-sphere discrete element method code to simulate the transmission and study the attenuation of a seismic wave. Then, we apply our findings to the different space missions that have had to touch the surface of different small bodies in the solar system. Additionally, we do the same in regard to the seismic wave generated by the hypervelocity impacts produced by the DART and Hayabusa2 missions once the shock wave transforms into a seismic wave. We find that even at very low pressures, such as those present in the interior of asteroids, the seismic wave speed can still be on the order of hundreds of meters per second depending on the velocity of the impact that produces the wave. As expected from experimental measurements, our results show that wave velocity is directly dependent on P 1/6, where P is the total pressure (confining pressure plus wave-induced pressure). Regardless of the pressure of the system and the velocity of the impact (in the investigated range), energy dissipation is extremely high. These results provide us with a way to anticipate the extent to which a seismic wave could have been capable of moving some small particles on the surface of a small body upon contact with a spacecraft. Additionally, this rapid energy dissipation would imply that even hypervelocity impacts should perturb only the external layer of a self-gravitating aggregate on which segregation and other phenomena could take place. This would, in turn, produce a layered structure of which some evidence has been observed.

Self-similar velocity and solid fraction profiles in silos with eccentrically located outlets

We examine the gravity-induced flow of dry and cohesionless granular media through an outlet placed eccentrically in a planar silo, employing computations based on a soft-sphere discrete element method. The vertical velocity profiles, measured at the outlet, are self-similar when the eccentric position of an outlet is given in terms of the smallest gap (s) between its corners and the lateral walls. On the other hand, the self-similarity of vertical velocity does not always hold for all eccentricities (e) given by the distance between the centers of an outlet and the silo base, which is a typical metric of eccentricity. For the former measure of the eccentric location, the flow conditions are observed to be similar for different outlet sizes. In contrast, we observe, the latter leads to differing flow patterns for the highest eccentricity wherein the largest outlet touches the sidewall and the rest are located at a distance. The effect of using s on the self-similarity of solid fraction profiles is observed to be minor in comparison to e. This study establishes the importance of s compared to e from the viewpoint of the self-similarity of the vertical velocity profiles at the outlet and generalizes the notion of the scaling of velocity and solid fraction reported by Janda et al. [“Flow rate of particles through apertures obtained from self-similar density and velocity profiles,” Phys. Rev. Lett. 108, 248001 (2012)] in a silo with a centric exit to the one with eccentric granular discharge. Finally, we propose expressions for the scaled vertical velocity and solid fraction in terms of s.

The influence of gravity on granular impacts

Context. Slow interactions on small body surfaces occur both naturally and through human intervention. The resettling of grains and boulders following a cratering event, as well as observations made during small body missions, can provide clues regarding the material properties and the physical evolution of a surface. In order to analyze such events, it is necessary to understand how gravity influences granular behavior. Aims. In this work, we study slow impacts into granular materials for different collision velocities and gravity levels. Our objectives are to develop a model that describes the penetration depth in terms of the dimensionless Froude number and to use this model to understand the relationship between collision behavior, collision velocity, and gravity. Methods. We used the soft-sphere discrete element method to simulate impacts into glass beads under gravitational accelerations ranging from 9.81 m s−2 to 0.001 m s−2. We quantified collision behavior using the peak acceleration, the penetration depth, and the collision duration of the projectile, and we compared the collision behavior for impacts within a Froude number range of 0–10. Results. The measured penetration depth and collision duration for low-velocity collisions are comparable when the impact parameters are scaled by the Froude number, and the presented model predicts the collision behavior well within the tested Froude number range. If the impact Froude number is low (0 < Fr < 1.5), the collision occurs in a regime that is dominated by a depth-dependent quasi-static friction force. If the impact Froude number is high enough (1.5 < Fr < 10), the collision enters a second regime that is dominated by inertial drag. Conclusions. The presented collision model can be used to constrain the properties of a granular surface material using the penetration depth measurement from a single impact event. If the projectile size, the collision velocity, the gravity level, and the final penetration depth are known and if the material density is estimated, then the internal friction angle of the material can be deduced.

A coupled distributed Lagrange multiplier (DLM) and discrete element method (DEM) approach to simulate particulate flow with collisions

In this paper, a coupled DLM-DEM numerical approach is proposed to enable particle-particle and particle-wall interactions within the open-source IBAMR (Immersed Boundary Adaptive Mesh Refinement) framework. A soft-sphere DEM collision model is adopted and compared against the particle-particle repulsion force model suggested in the literature. It is demonstrated that the former collision model remains effective at both low and high particle-fluid density ratios, whereas the latter model can lead to unphysical particle-particle interaction dynamics at high density ratios. Moreover, the soft-sphere DEM collision model is based on physical material properties, which is in contrast to an artificial parameter-based repulsion force model. The proposed DLM-DEM approach is validated by simulating the particle-particle collision in drafting, kissing, and tumbling (DKT) phenomenon, and particle-wall collision at various Stokes numbers. Using this approach, we also simulate the interactions between a single colliding particle and a particle cluster and analyze the particles' motion and distribution. Additionally, sedimentation of polygon-shaped particles is also considered to demonstrate the versatility of the proposed approach.

The influence of gravity on granular impacts

Context. Impacts on small-body surfaces can occur naturally during cratering events or even strategically during carefully planned impact experiments, sampling maneuvers, and landing attempts. A proper interpretation of impact dynamics allows for a better understanding of the physical properties and the dynamical process of their regolith-covered surfaces and their general evolution. Aims. This work aims to first validate low-velocity, low-gravity impact simulations against experimental results, and then to discuss the observed collision behaviors in terms of a popular phenomenological collision model and a commonly referenced scaling relationship. Methods. We performed simulations using the soft-sphere discrete element method and two different codes, Chrono and pkdgrav. The simulations consist of a 10-cm-diameter spherical projectile impacting a bed of approximately 1-cm-diameter glass beads at collision velocities up to 1 m s−1. The impact simulations and experiments were conducted under terrestrial and low-gravity conditions, and the experimental results were used to calibrate the simulation parameters. Results. Both Chrono and pkdgrav succeed in replicating the terrestrial gravity impact experiments with high and comparable computational performance, allowing us to simulate impacts in other gravity conditions with confidence. Low-gravity impact simulations with Chrono show that the penetration depth and collision duration both increase when the gravity level decreases. However, the presented collision model and scaling relationship fail to describe the projectile’s behavior over the full range of impact cases. Conclusions. The impact simulations reveal that the penetration depth is a more reliable metric than the peak acceleration for assessing collision behavior in a coarse-grained material. This observation is important to consider when analyzing lander-regolith interactions using the accelerometer data from small-body missions. The objective of future work will be to determine the correct form and applicability of the cited collision models for different impact velocity and gravity regimes.

High fidelity, discrete element method simulation of magnetorheological fluids using accurate particle size distributions in LIGGGHTS extended with mutual dipole method

We simulate magnetorheological fluids (MRF) using open source LIGGGHTS soft sphere discrete element method code, extended by us to include a mutual dipole magnetic model. Our simulations take advantage of the many pair forces available in the LIGGGHTS framework, including SJKR cohesion, friction, and rolling resistance. In addition, we have included an uncoupled, Couette flow background carrier fluid. The simulated particles in this work are polydisperse, with distributions made to match the distributions used to produce magnetorheological fluids in literature, increasing the fidelity of the simulations. Using the accurate particle size distributions, high heritage contact models, and an uncoupled fluid model, we are able to match experimental MRF yield stress results more closely than with monodisperse simulations.

The divergence of nearby trajectories in soft-sphere DEM

The n-body instability is investigated with the soft-sphere discrete element method. The divergence of nearby trajectories is quantified by the dynamical memory time. Using the inverse proportionality between the dynamical memory time and the largest Lyapunov exponent, the soft-sphere discrete element method results are compared to previous hard-sphere molecular dynamics data for the first time. Good agreement is observed at low concentrations and the degree of instability is shown to increase asymptotically with increasing spring stiffness. At particle concentrations above 30%, the soft-sphere Lyapunov exponents increase faster than the corresponding hard-sphere data. This paper concludes with a demonstration of how this case study may be used in conjunction with regression testing and code verification activities.

Numerical modeling of lander interaction with a low-gravity asteroid regolith surface

Context.The JAXA asteroid sample return mission Hayabusa2 reached its target (162173) Ryugu in June 2018 and released the European (CNES-DLR) lander MASCOT in October 2018. MASCOT successfully landed on the surface, and the Hayabusa2 Optical Navigation Camera system has been able to image parts of the MASCOT trajectory.Aims.This work builds on our previous study of interactions between a landing package and a granular material in the context of MASCOT on Ryugu. The purpose is to expand our knowledge on this topic and to help constrain physical properties of surfaces by considering the actual trajectory of MASCOT and observations of Ryugu from Hayabusa2.Methods.We ran a new campaign of numerical simulations using theN-body codepkdgravwith the soft-sphere discrete element method by expanding the parameter space to characterize the actual landing scenario of MASCOT on Ryugu. The surface was modeled as a granular medium, but we also considered a large boulder in the bed at various depths and a rigid wall representing a cliff. MASCOT was faithfully modeled as the actual lander, and we considered different impact angles, speeds, and surface slopes. We were particularly interested in the outgoing-to-incoming speed ratio of MASCOT during the landing process.Results.We found that a boulder in the bed generally increases both the stochasticity of the outcomes and the speed ratio, with larger increases when the boulder sits closer to the surface. We also found that the surface slope does not affect our previous results and that the impact speed does not affect the speed ratio for moderate-friction granular material. Finally, we found that a speed ratio as low as 0.3, as estimated in the actual scenario, can occur with a solid-rock surface, not only with a soft surface, because the geometry of the lander is nonspherical. This means that we must infer the physical properties of the surface from outcomes such as the speed ratio with caution: it depends on the lander geometry.

Critical spin periods of sub-km-sized cohesive rubble-pile asteroids: dependences on material parameters

ABSTRACT In this work, we employ a soft-sphere discrete element method with a cohesion implementation to model the dynamical process of sub-km-sized cohesive rubble piles under continuous spin-up. The dependences of the critical spin periods Tc on several material parameters for oblate rubble piles with different diameters were explored. Our simulations show that the interparticle cohesive force can strengthen the bodies as expected, especially for the smaller ones. The simulated results of Tc were fitted with the continuum theory developed by Holsapple, through which we find the interparticle cohesion is proportional to the best-fitting bulk cohesion and the ratio shows no dependence on the density. In addition, we find Tc decreases as the density increases in the compressive regime, while the trend reverses when transitioning to the tensile regime. Besides, though a higher friction angle can strengthen the bodies, its influence on Tc is minimized near the separation between the two regimes. Our numerical findings are generally consistent with the continuum theory, except that the latter predicts that Tc should increase as the friction angle increases in the tensile regime, which is contrary to the numerical results. This remarkable difference reminds us to take caution when applying the continuum theory to critically spinning cohesive rubble piles in the tensile regime, especially when dealing with the effect of the friction angle. Finally, we emphasize that the separation between the regimes can be specified by a characteristic period, which is only a function of density for a given shape.

Validating N-body code chrono for granular DEM simulations in reduced-gravity environments

ABSTRACT The Discrete Element Method (DEM) is frequently used to model complex granular systems and to augment the knowledge that we obtain through theory, experimentation, and real-world observations. Numerical simulations are a particularly powerful tool for studying the regolith-covered surfaces of asteroids, comets, and small moons, where reduced-gravity environments produce ill-defined flow behaviours. In this work, we present a method for validating soft-sphere DEM codes for both terrestrial and small-body granular environments. The open-source code chrono is modified and evaluated first with a series of simple two-body-collision tests, and then, with a set of piling and tumbler tests. In the piling tests, we vary the coefficient of rolling friction to calibrate the simulations against experiments with 1 mm glass beads. Then, we use the friction coefficient to model the flow of 1 mm glass beads in a rotating drum, using a drum configuration from a previous experimental study. We measure the dynamic angle of repose, the flowing layer thickness, and the flowing layer velocity for tests with different particle sizes, contact force models, coefficients of rolling friction, cohesion levels, drum rotation speeds, and gravity levels. The tests show that the same flow patterns can be observed at the Earth and reduced-gravity levels if the drum rotation speed and the gravity level are set according to the dimensionless parameter known as the Froude number. chrono is successfully validated against known flow behaviours at different gravity and cohesion levels, and will be used to study small-body regolith dynamics in future works.

Deposition of dry particles on a fin-and-tube heat exchanger by a coupled soft-sphere DEM and CFD

In this study, a novel computational model is utilized for investigating fouling of two commonly encountered heat exchanger fin shapes in an air-conditioning application. The computational method utilizes the discrete element method (DEM) coupled with a large-eddy simulation (LES) framework. The fin-and-tube heat exchangers (FTHE) are investigated for three different Reynolds numbers (ReDh=243, 528, 793), three different particle sizes (Dp= 5, 10, 20 µm) and two different adhesive particle types based on the experimental values in the literature. The code is first benchmarked from the CFD and DEM viewpoints. A comprehensive fouling study of the FTHE’s, consisting of altogether 36 simulations, is then carried out. The major numerical findings of the paper consist of the following four features. First, with low adhesive particles, the plain fin shape has a 3.45 higher volume fouling rate with ReDh=793 than at ReDh=264. With the herringbone fin shape, and the low adhesive particles, the volume fouling rate is 1.76 higher with ReDh=793 than at ReDh=264. Second, for the high adhesive particles, the plain fin has a 5.4 times higher volume fouling rate at ReDh=793 than for ReDh=264. The herringbone fin shape has a 3.92 times higher volume fouling rate with the highest Reynolds number of ReDh=793 compared to ReDh=264. Third, high adhesive particles have 3.0 times higher volume fouling rate than low adhesive particles for both fin shapes, all particle sizes and all Reynolds numbers combined. And finally, herringbone fins have 1.74 times higher volume fouling rate than plain fins for low adhesive particles. For high adhesive particles, herringbone has 1.8 times higher volume fouling rate and when both particle types are summed together, herringbone has a 1.78 times higher volume fouling rate than the plain fin shape. As a major finding of the study, the high adhesive particle collection efficiency increases monotonously with the Stokes and Reynolds numbers while low adhesive particle collection efficiency poses a non-monotonous trend.

Impact and stick-slip dynamics in the soft-landing on minor celestial bodies

The soft-landing on the surface of minor celestial bodies has been investigated with considering the impact and stick-slip effect. The polyhedron model is used to analyze the irregular shape and topography and geomorphology of minor celestial bodies. The soft-sphere discrete element method is used to fill the irregular minor celestial body’s polyhedron model and cover the surface of the body; and then the irregular shape, the gravitational environment, as well as the impact and hopping with the surface can be calculated precisely. The dynamical parameters of failed soft-landing and successful soft-landing are calculated and analyzed. In the cases of successful soft-landing, there are two obviously different kinds: firstly, the final position of the lander is near the target position; secondly, the final position of the lander is far from the target position. The difference of these two kinds of results is discussed. This research shows the major dynamical behavior of soft-landing on minor celestial bodies includes impact, hopping, as well as stick-slip effect. If the initial positions of soft-landing are improper chosen, the lander may become orbital motion around minor celestial body after one or more impact and hopping, or turn to quasi-periodic motion around equilibrium points without impact, or perhaps be static far from the initial position after several times of impact and hopping and leads to the failure of the deep space mission. For the successful soft-landing process, after several times of landings on the surface during the soft-landing process, the lander will finally settle on the surface of the minor celestial body. The results show that the soft-landing region should be selected as a flat area or concave region, which is far from the equatorial plane of the minor celestial bodies.

Numerical simulations of the controlled motion of a hopping asteroid lander on the regolith surface

Previous missions have revealed that small Solar system bodies are topographically diverse, which raises an immense challenge to a lander that aims to perform scientific measurements at different locations on the surface of the target. In recent years, hopping mechanism has attracted considerable attention due to its adaptability to the granular regolith and the low-gravity environment. However, the hopping dynamics related to granular materials remains to be explored, which will contribute not only to future space missions but also to the understanding of the dynamical behaviour of granular systems under low gravity. In this paper, we studied the hopping locomotion of a cuboid lander on the regolith surface of an asteroid. Numerical simulations are performed based on the soft-sphere discrete element method. We systematically explored the effects of the controlled parameter and physical properties of the regolith particles. The results show that the hopping outcomes (velocity, angle, and morphology of the cavity left in the regolith) are strongly dependent on these parameters. The high resistance improves the robustness of granular force networks, therefore the lander hops farther in gravel-like media than less frictional media. When the cohesion between regolith particles is included, the cavity left after the hop becomes a mild indentation, differing from the non-cohesive cases, that give distinct crater-like cavities.

A new kinetic theory model of granular flows that incorporates particle stiffness

Granular materials of practical interest in general have finite stiffness; therefore, the particle collision is a process that takes finite time to complete. Soft-sphere Discrete Element Method (DEM) simulations suggest that there are three regimes for granular shear flows: inertial regime (or rapid flow regime), elastic regime (or quasistatic regime), and the transition regime (or elastic-inertial regime). If we use tf to represent the mean free flight time for a particle between two consecutive collisions and tc to represent the binary collision duration, these regimes are implicitly related to the ratio tc/tf. Granular flows can be successfully predicted by the classical Kinetic Theory (KT) when they are in the inertial regime of low particle-particle collision frequencies and short time contacts (tc/tf ≈ 0). However, we find that KT becomes less accurate in the transition regime where the collision duration tc is no longer small compared with the collision interval tf (tc/tf > 0.05). To address this issue, we develop a soft-sphere KT (SSKT) model that takes particle stiffness k as an input parameter since tc/tf is mainly determined by k. This is achieved by proposing a modified expression for the collision frequency and introducing an elastic granular temperature Te. Compared with the classical KT that only considers the kinetic granular temperature Tk, a redefined total granular temperature (Tg = Tk + Te/3) that takes both kinetic fluctuation energy and elastic potential energy into consideration is used in the SSKT model. The model is developed for identical frictionless particles with the linear-spring-dashpot collision scheme; however, it can be extended to frictional systems as well after the modification of constitutive equations. We show that the proposed SSKT extends the applicability of the KT framework to the transition regime without losing significant accuracy. The rheological crossover has been explained physically, and the regime boundaries that separate the inertial regime and the elastic regime are quantitatively determined, showing good agreement with the previous regime map that was based on the DEM simulations. Our SSKT predictions also show that for unsteady flows such as homogeneous cooling, the particle stiffness could have a large impact on the granular flow behavior due to the energy transfer between Te and Tk.

Atmospheric humidity and particle charging state on agglomeration of aerosol particles

Formation of haze is a phenomenon dependent on the relative atmospheric humidity and concentration of aerosol particles. The physical and chemical reactions on particle surfaces would lead to variations in particle sizes. This paper focuses on the physical behaviour of aerosol particles under the influence of atmospheric humidity, which produces liquid bridging forces and electrostatic interactions among particles. By water absorption experiment, a correlation between relative humidity (RH) and water content on particles was obtained. Through theoretical derivation, a relationship between the relative humidity and humidity ratio was established for calculating liquid bridging forces. The findings from experiments on atmospheric particles charging, showed most aerosols were negatively or positively charged and the average charges on these particles was more than one. An extended soft-sphere discrete element method (DEM) was used to simulate the evolution of aerosol particles, encapsulated in water vapour by considering liquid bridging forces, electrostatic interactions and Brownian forces. Results suggest that the agglomeration rate of particles would increase with a rise in the atmospheric humidity due to the increased liquid bridging forces that enhance the agglomeration velocity. The higher humidity would enhance the ionization on particle surfaces, which could affect electrostatic interactions. This paper provides an insight of a mechanism for formation of haze in atmosphere.

Numerical modeling of lander interaction with a low-gravity asteroid regolith surface

Context. Landing on the surface of small bodies is particularly challenging, as the physical properties of the surface material are not well known and the mechanical response of this material in a low-gravity environment is not well understood. Aims. In order to improve our understanding of low-speed impact processes on granular media and their outcome in low-gravity environments, we consider the landing of the package MASCOT, to be released by the JAXA asteroid sample return mission Hayabusa2 on (162173) Ryugu in October 2018. Beyond addressing the theoretical aspects of the mechanical response of granular media in low gravity, this study also supports both engineering and scientific teams of Hayabusa2 in the search for the lander and in the determination of Ryugu’s surface properties. Methods. A campaign of hundreds of numerical simulations using the soft-sphere discrete element method implemented in the N-body code pkdgrav were performed to study the interaction between the lander and the low-gravity surface of the asteroid made of a granular medium representing the regolith. Assuming a broad range of regolith properties, and the lander’s trajectory and motion, we analyzed the outcomes of the landing (distance traveled by the lander, penetration depth, and shape of the traces left in the regolith surface) to determine the influence of the many parameters defining the properties of MASCOT and of the grains, and the ingoing motion of the lander. Results. We identify well-marked trends for the fate of the lander and the traces left in the granular material. Distances traveled by the lander are greater and penetrations are shallower for gravel-like media than for less frictional material. A similar trend is found for grazing impacts as opposed to vertical ones. Different regolith properties also generate different traces on the ground after the impact.

Early stages of agglomeration of adhesive particles in fully-developed turbulent pipe flows

We study how changes in particle response time and adhesiveness affect particles agglomeration in fully-developed turbulent pipe flows. For this purpose, particle-particle and particle-wall interactions are fully-resolved using the soft-sphere Discrete Element Method (DEM) modified to include adhesiveness due to van der Waals forces and electrostatic forces through JKR theory. The particulate phase is two-way coupled to the turbulent fluid phase, which is partly resolved using Large Eddy Simulations (LES). First, we validate the simulations by grid refinement and by comparing the statistics of the flow field to experiments in literature. Secondly, we vary the particle response time τp=ρpdp2/(18μ) and observe the largest agglomerates in terms of average number of particles per agglomerate to be formed by primary particles with intermediate Stokes numbers, e.g. Ste=τp/τe≈6.4 where τe=D/U is the eddy-turn over time or StL=τp/τL≈46.4 in terms of the integral time scale of the turbulent flow τL. Then we show how the total fraction of particles contained in agglomerates is almost constant up to Ste=6.4 after which there is a sudden drop in the fraction of particles contained in agglomerates. To investigate the transition from non-adhesive particles to highly adhesive particles, we vary the adhesiveness parameter Ad=γ/(ρpU2dp) to obtain particles that vary from non-adhesive particles where no agglomerates are formed to highly adhesive particles where more than 70% are contained in agglomerates. While varying the adhesiveness of the primary particles for a fixed particle response time, we observe three distinct regimes. For almost non-adhesive particles, the agglomerate number density is highest towards the centre of the pipe with a maximum at 0.2 < r/R < 0.3. Slightly more adhesive particles form an almost uniform agglomerate number density profile, while for highly adhesive particles there is a distinct peak in agglomerate number density at the wall where particles and agglomerates deposit.

The formation mechanism of 4179 Toutatis’ elongated bilobed structure in a close Earth encounter scenario

The optical images of near-Earth asteroid 4179 Toutatis acquired by Chang'e-2 spacecraft show that Toutatis has an elongated contact binary configuration, with the contact point located along the long axis. We speculate that such configuration may have resulted from a low-speed impact between two components. In this work, we performed a series of numerical simulations and compared the results with the optical images, to examine the mechanism and better understand the formation of Toutatis. Herein we propose an scenario that an assumed separated binary precursor could undergo a close encounter with Earth, leading to an impact between the primary and secondary, and the elongation is caused by Earth's tide. The precursor is assumed to be a doubly synchronous binary with a semi-major axis of 4 $R_p$ (radius of primary) and the two components are represented as spherical cohesionless self-gravitating granular aggregates. The mutual orbits are simulated in a Monte Carlo routine to provide appropriate parameters for our \emph{N}-body simulations of impact and tidal distortion. We employ the \emph{pkdgrav} package with a soft-sphere discrete element method (SSDEM) to explore the entire scenarios. The results show that contact binary configurations are natural outcomes under this scenario, whereas the shape of the primary is almost not affected by the impact of the secondary. However, our simulations further provide an elongated contact binary configuration best-matching to the shape of Toutatis at an approaching distance $r_p$ = 1.4 $\sim$ 1.5 $R_e$ (Earth radius), indicative of a likely formation scenario for configurations of Toutatis-like elongated contact binaries.