Rebound Model Research Articles

A neural network based framework to model particle rebound and fracture

The current state of the art approach in the simulation of particle-laden flow in turbomachinery is to handle particle–wall interactions via rebound and erosion models. Rebound models often require a priori parameter tuning to match experimental measurements. Moreover, the actual stochastic nature of the rebound is neglected, and the particle is assumed not to fracture upon impact. However, this affects the resulting particle trajectories and is particularly critical at high (normal) impact velocities, where particles in typical aero engine flow exhibit a high probability of fracture, as illustrated in our previous work. In this work, we propose a method to develop a generalized rebound model which is parameter-free for the user and considers the stochasticity of the rebound. To this end, state of the art methods from function approximation, more precisely, deep dense neural networks are employed. The networks are trained through a supervised learning approach, where the neural network maps the impacting particles’ characteristics to its new particle trajectory after rebound. For this, we present an efficient method to predict probability distributions in a supervised learning context without a priori parameter tuning of known PDFs. In a second step, we extend the network to account for particle fracture, where the particle breakage is based on a fracture probability distribution to determine whether a particle breaks. The performance of the proposed framework is illustrated by the use of experimental measurements of the statistical rebound of sand particles in an erosion test rig specifically designed to match flow and impact conditions (including particle fracture) as well as particle sizes in aero engine compressors.

Effects of particle size and liquid film viscosity on characteristics of particles colliding with dry and wet walls

Particle-wall collisions frequently occur in fluidized beds, granulation processes, and the transportation of gas–solid two-phase flows in pipelines. Exploring the rebound characteristics of particles after colliding with the wall will enable more accurate calculation models of collision rebound, enhanced control of the collision–rebound process, and improved efficiency of industrial production. This paper studies the relationship between the energy consumed by the liquid film and the energy consumed in the collision and investigates the effects of different particle sizes and liquid film viscosities on the liquid bridge morphology, coefficient of restitution (COR), and critical capture angle (CCA). The results show that the normal COR is affected by particle size, incident velocity, and viscosity, while the tangential COR is only related to the existence of the liquid film. Additionally, the maximum size of the liquid bridge and the growth rate of COR change suddenly in a transition region. The particle size and liquid film viscosity have significant effects on the CCA of the particle. The numerical results enable us to propose a general form of the normal wet collision model.

Evidence for a more extensive Greenland Ice Sheet in southwestern Greenland during the Last Glacial Maximum

Abstract The maximum extent and elevation of the Greenland Ice Sheet in southwestern Greenland during the Last Glacial Maximum (LGM, 26–19.5 ka) is poorly constrained. Yet, the size of the Greenland Ice Sheet during the LGM helps to inform estimates of past ice-sheet sensitivity to climate change and provides benchmarks for ice-sheet modeling. Reconstructions of LGM ice extents vary between an inner continental shelf minimum, a mid-shelf position, and a maximum extent at the shelf break. We use three approaches to resolve LGM ice extent in the Sisimiut sector of southwestern Greenland. First, we explore the likelihood of minimum versus maximum Greenland Ice Sheet reconstructions using existing relative sea-level data. We use an empirical relationship between marine limit elevation and distance to LGM terminus established from other Northern Hemisphere Pleistocene ice sheets as context for interpreting marine limit data in southwestern Greenland. Our analysis supports a maximum regional Greenland Ice Sheet extent to the shelf break during the LGM. Second, we apply a simple 1-D crustal rebound model to simulate relative sea-level curves for contrasting ice-sheet sizes and compare these simulated curves with existing relative sea-level data. The only realistic ice-sheet configuration resulting in relative sea-level model-data fit suggests that the Greenland Ice Sheet terminated at the shelf break during the LGM. Lastly, we constrain the LGM ice-sheet thickness using cosmogenic 10Be, 26Al, and 14C exposure dating from two summit areas, one at 381 m above sea level at the coast, and another at 798 m asl 32 km inland. Twenty-four cosmogenic radionuclide measurements, combined with results of our first two approaches, reveal that our targeted summits were likely ice-covered during the LGM and became deglaciated at ca. 11.6 ka. Inventories of in situ 14C in bedrock at one summit point to a small degree of inherited 14C and suggest that the Greenland Ice Sheet advanced to its maximum late Pleistocene extent at 17.1 ± 2.5 ka. Our results point to a configuration where the southwestern part of the Greenland Ice Sheet reached its maximum LGM extent at the continental shelf break.

Исследование постледниковых движений Фенноскандии по данным глобальных навигационных спутниковых систем

Based on the data from GNSS sites located in Fennoscandia, for the period from the mid-1990s to the present, an analysis of the region’s geodynamics was carried out. For the first time, an extended data set was used, including field observations of the Satellite Methods Laboratory for Studying Geophysical Processes of IPE RAS and sites of the fundamental astronomical geodetic network. It enabled expanding the area of post-glacial rebound modeling in the eastern part of Fennoscandia. As in many previous studies, a vertical velocity field was obtained with a maximum uplift rate of 10 mm/year, located in the northern part of the Gulf of Bothnia. In addition, for the eastern regions of Fennoscandia, a lane of compression deformations of the earth’s surface was revealed. The highlighted lane marks the transition zone from the vaulted uplift area to the East European platform.

Model of non-spherical particles' rebound and scattering at high speed interaction with a streamlined surface

A new model is proposed for a non-spherical solid particles' impact interaction with a surface as applied to gas-particle flows over surfaces. The range of a particle impact speed typical for a vehicle flight in a dusty atmosphere is considered. The model is based on the laws of mechanics and experimental data on the restitution coefficient of the particle normal velocity. The tangential force impulse during a particle-surface interaction is assumed to be proportional to both the normal impulse and the mean tangential velocity of the particle contact point. The space orientation of incident particles relative to the surface is considered as random. The rebound of particles of different shape with varying shape parameters and of a particle mixture is studied numerically. Statistical characteristics of particles' rebound and scattering are obtained. Comparison with the known experimental data of numerical results for the mean values of the normal and tangential velocities of the particles' gravity centers in the plane of impact after rebound showed their good agreement. Keywords: dispersed particles, 3D model of impact, numerical investigation, statistical characteristics of rebound and scattering, comparison with experimental data.

Large Eddy Simulation of Particle Transport and Deposition Over Multiple 2D Square Obstacles in a Turbulent Boundary Layer

AbstractPredicting solid particle transport in the lowest parts of the atmosphere is a major issue for man‐made obstacles in semi‐arid regions. Here, we investigate the effects on solid particle saltation, of square obstacles on the ground with different spacings. The aerodynamic field is determined by large eddy simulations coupled with an immersed boundary method for the obstacles. Solid particles are tracked by a Lagrangian approach. Take‐off and rebound models are introduced for the interaction of particles with the wall. Without particles, fluid velocity profiles are first compared with experiments (Simoens et al., 2007, https://doi.org/10.1016/j.atmosenv.2007.08.013) showing good agreement. Special focus is put on the recirculation zone that plays an important role in solid particle entrapment.Particle concentration fields are presented. Accumulation zones are studied regarding the different obstacle spacings as an extension of the aerodynamic scheme by Oke (1988, https://doi.org/10.1016/0378-7788(88)90026-6) to solid particle transport. A deposition peak appears before the first obstacle. When the spacing between the two obstacles is large enough, some particles are trapped within the recirculation and a second deposition peak arises. The streamwise evolution of the horizontal saltation flux shows that the lowest flux downstream of the obstacles is obtained for the highest separation. The deposition rate or the streamwise saltation flux are estimated globally as a function of obstacle spacing. These results illustrate how the numerical tool developed here can be used for assessing air quality in terms of solid particle concentration.

Rapid Formation of an Ice Doline on Amery Ice Shelf, East Antarctica.

Surface meltwater accumulating on Antarctic ice shelves can drive fractures through to the ocean and potentially cause their collapse, leading to increased ice discharge from the continent. Implications of increasing surface melt for future ice shelf stability are inadequately understood. The southern Amery Ice Shelf has an extensive surface hydrological system, and we present data from satellite imagery and ICESat‐2 showing a rapid surface disruption there in winter 2019, covering ∼60 km2. We interpret this as an ice‐covered lake draining through the ice shelf, forming an ice doline with a central depression reaching 80 m depth amidst over 36 m uplift. Flexural rebound modeling suggests 0.75 km3 of water was lost. We observed transient refilling of the doline the following summer with rapid incision of a narrow meltwater channel (20 m wide and 6 m deep). This study demonstrates how high‐resolution geodetic measurements can explore critical fine‐scale ice shelf processes.

Impact-Detection Algorithm That Uses Point Clouds as Topographic Inputs for 3D Rockfall Simulations

Numerous 3D rockfall simulation models use coarse gridded digital terrain model (DTM raster) as their topography input. Artificial surface roughness is often added to overcome the loss of details that occurs during the gridding process. Together with the use of sensitive energy damping parameters, they provide great freedom to the user at the expense of the objectivity of the method. To quantify and limit the range of such artificial values, we developed an impact-detection algorithm that can be used to extract the perceived surface roughness from detailed terrain samples in relation to the size of the impacting rocks. The algorithm can also be combined with a rebound model to perform rockfall simulations directly on detailed 3D point clouds. The abilities of the algorithm are demonstrated by objectively extracting different perceived surface roughnesses from detailed terrain samples and by simulating rockfalls on detailed terrain models as proof of concept. The results produced are also compared to that of rockfall simulation software CRSP 4, RocFall 8 and Rockyfor3D 5.2.15 as validation. Although differences were observed, the validation shows that the algorithm can produce similar results. With the presented approach not being limited to coarse terrain models, the need for adding artificial terrain roughness or for adjusting sensitive damping parameters on a per-site basis is reduced, thereby limiting the related biases and subjectivity.

Characterization of the Solid Particle Erosion of the Sealing Surface Materials of a Ball Valve

The ball valve is an essential piece of equipment in an oil and gas pipeline. The sand particles transported through the pipeline can cause erosion and wear to the ball valve, thus causing it to fail, leading to serious safety hazards. In this paper, the self-designed erosion experiment method was combined with computational fluid dynamics (CFD), while the Euler-Lagrange method was also introduced to optimize the Oka erosion model and Ford particle-wall rebound model. The erosion mechanism and characteristics of the ball valve sealing surface in gas-solid two-phase flow were simulated, while the erosion condition of the specimen was analyzed and compared when exposed to different factors, such as different particle velocities, impact angle, particle size, and specimen materials. The experimental data conformed well to the CFD erosion simulation data, verifying the accuracy of the CFD simulation analysis. The results indicated that the worn surface was caused by various wear mechanisms, while a “stagnation zone” was identified at the center of the specimen. The maximum erosion area, which was U-shaped, was also located at the center. The erosion rate increased in conjunction with an increase in the particle velocity and size, both of which failed to affect the erosion pattern. The erosion rate initially increased, after which it decreased with the impact angle, reaching the maximum value at an impact angle of 30°. This paper summarizes the erosion failure mechanism and characteristics in gas–solid two-phase flow and provides both technical support and a theoretical basis for the on-site maintenance of essential vulnerable parts in the pipeline, such as ball valves.

Analysis of the effect of particle-wall collision process in DPF on the spatial structure of smoke cake layer.

Based on the rebound model of particle-wall collision, the influence of adhesion force on the deposition process of particles on the smoke cake wall was studied by using atomic force microscopy (AFM) and automatic specific surface area (BET) and pore size distribution analyzer. The interaction between the deposition process and the spatial structure of smoke cake was analyzed. The results show that with the increase of diesel engine speed, Young's modulus of particles decreases and the average particle size increases; the kinetic energy of particles impacting on the surface of smoke cake layer in diesel particle filter (DPF) increases; when the velocity of particles with the same particle size entering the wall increases, the maximum compression distance between particles and the surface of the smoke cake layer increases; and the adhesion force and adhesion energy increase. With the increase of diesel engine speed, the box counting dimension of smoke cake layer in DPF increases from 1.9478 to 1.996, the characteristic radius of pores decreases from 15.32 nm to 7.53 nm, the average pore diameter decreases, and the average pore volume increases. When the fractal dimension increases from 2.633 to 2.732, the deformation degree of particles increases, the smoke cake layer becomes more compact and dense, the internal structure of pores becomes more complex, the surface of pores is rougher, and particle adhesion requires overcoming larger adhesion barriers when particles adhere.

Effect of distance between two elbows in series on erosion for gas dominated conditions

Solid particle erosion is a potential problem in pipelines for the oil and gas processing industries. Solid particle erosion usually occurs in piping components or equipment when the direction of the flow changes, such as in elbows and tees. The distance between two elbows effects on the behavior of solid particle erosion on the second elbow has been investigated experimentally and computationally. Firstly, paint removal experiments were carried out to investigate the erosion pattern in a standard 3-inch (76.2 mm) elbow with a bend radius to pipe diameter (r/D) ratio equal to 1.5 for a gas-sand condition with different particle sizes. The investigated distances between the two elbows are 2D and 12D. Secondly, the erosion magnitudes in a standard 3-inch (76.2 mm) stainless steel elbow were measured using a state-of-the-art ultrasonic technique. These results have been compared with the previous experimental data in a 4-inch (101.6 mm) elbows to investigate the pipe size effect. Thirdly, a commercial CFD code was used to simulate the experimental conditions and compare erosion predictions with the experimental results. Different turbulence and particle rebound models were applied in the CFD simulations to examine their influence on the predicted erosion on the elbows. Finally, the effect of distance between the two elbows on the particle trajectories were investigated using the CFD approach.

CFD SIMULATION OF EROSION BY PARTICLE COLLISION IN U-BEND AND HELICAL TYPE PIPES

Erosion caused by solid particles in curve pipes is one of the major concerns in the oil and gas industries. Small solid particles flow with a carrier liquid fluid and impact the inner wall of the piping, valves, and other equipment. These components face a high risk of solid particle erosion due to the constant collision, which may result in equipment malfunctioning and even failure. In this study, the two-way coupled Eulerian-Lagrangian method with the Oka erosion and Grant and Tabakoff particle-wall rebound models approach is employed to simulate the liquid-solid flow in U-bend and helical pipes using computational fluid dynamics. The effects of operating parameters (inlet fluid velocity and temperature, particle density and diameter, and mass flow rate) and design parameters (mean curvature radius/pipe diameter ratio) are investigated on the erosion of these tubes walls. It is obtained that increasing the fluid velocity and temperature, particle mass flow and particle density increase the penetration rate, particle diameter affects the rate of penetration, and increasing mean curvature radius/pipe diameter ratio decreases the rate of penetration.

Neural activity during a simple reaching task in macaques is counter to gating and rebound in basal ganglia-thalamic communication.

Task-related activity in the ventral thalamus, a major target of basal ganglia output, is often assumed to be permitted or triggered by changes in basal ganglia activity through gating- or rebound-like mechanisms. To test those hypotheses, we sampled single-unit activity from connected basal ganglia output and thalamic nuclei (globus pallidus-internus [GPi] and ventrolateral anterior nucleus [VLa]) in monkeys performing a reaching task. Rate increases were the most common peri-movement change in both nuclei. Moreover, peri-movement changes generally began earlier in VLa than in GPi. Simultaneously recorded GPi-VLa pairs rarely showed short-time-scale spike-to-spike correlations or slow across-trials covariations, and both were equally positive and negative. Finally, spontaneous GPi bursts and pauses were both followed by small, slow reductions in VLa rate. These results appear incompatible with standard gating and rebound models. Still, gating or rebound may be possible in other physiological situations: simulations show how GPi-VLa communication can scale with GPi synchrony and GPi-to-VLa convergence, illuminating how synchrony of basal ganglia output during motor learning or in pathological conditions may render this pathway effective. Thus, in the healthy state, basal ganglia-thalamic communication during learned movement is more subtle than expected, with changes in firing rates possibly being dominated by a common external source.

Models of SIV rebound after treatment interruption that involve multiple reactivation events.

In order to assess the efficacy of novel HIV-1 treatments leading to a functional cure, the time to viral rebound is frequently used as a surrogate endpoint. The longer the time to viral rebound, the more efficacious the therapy. In support of such an approach, mathematical models serve as a connection between the size of the latent reservoir and the time to HIV-1 rebound after treatment interruption. The simplest of such models assumes that a single successful latent cell reactivation event leads to observable viremia after a period of exponential viral growth. Here we consider a generalization developed by Pinkevych et al. and Hill et al. of this simple model in which multiple reactivation events can occur, each contributing to the exponential growth of the viral load. We formalize and improve the previous derivation of the dynamics predicted by this model, and use the model to estimate relevant biological parameters from SIV rebound data. We confirm a previously described effect of very early antiretroviral therapy (ART) initiation on the rate of recrudescence and the viral load growth rate after treatment interruption. We find that every day ART initiation is delayed results in a 39% increase in the recrudescence rate (95% credible interval: [18%, 62%]), and a 11% decrease of the viral growth rate (95% credible interval: [4%, 20%]). We show that when viral rebound occurs early relative to the viral load doubling time, a model with multiple successful reactivation events fits the data better than a model with only a single successful reactivation event.

Analytical model of the deformation response of bedding slopes to excavation on the basis of Mindlin’s strain solution

To reveal the deformation law and mechanism of bedding slopes under excavation unloading, an unloading rebound model of slope deformation is established on the basis of Mindlin’s strain solution, and a bedding-slip model of slope deformation is deduced on the basis of the Kalhaway constitutive model. Combining the two models, this study presents a computational model for the deformation response of bedding slope excavation. This model can reflect the mechanism of excavation unloading and the characteristics of rock mass structure. The reliability of the model is verified by comparing the calculated results of the analytical model with the experimental results in the laboratory. On this basis, the influences of excavation angle, excavation depth, and stratum thickness are analyzed by using several calculation examples. The calculation results show that the deformation induced by excavation increases with the increase in excavation angle or depth and decreases with the increase in stratum thickness. The excavation response of bedding slopes is mainly affected by the effect of unloading and the slip of the structural plane. Moreover, the unloading effect is controlled by the amount of excavation, and the rebound deformation of slopes is approximately linearly correlated with excavation volume. Bedding slip is affected by many factors because the increase in excavation angle or the amount of rock stratum leads to the increase in slip deformation. The proposed model can provide a basis for the deformation mechanism of bedding slopes under excavation.

Deposition characteristics of particles in inclined heat exchange channel with surface ribs

Ash particles in flue gas flow would deposit on the heat recovery exchanger in the waste heat recovery system (WHRS), which may lead to the reduction of heat transfer efficiency and service life. Understanding of ash particle deposition in the heat exchange channel is crucial for the safe operation of WHRS. In this study, deposition characteristics of ash particles in an inclined heat exchange channel with surface ribs were investigated by using Reynolds stress model combined with discrete phase model. The turbulent fluctuation correction and particle rebound model were developed by using UDF program to improve the prediction accuracy. After grid sensitivity analysis and numerical verification, the flue gas thermal-fluid fields, the 3D particle deposition patterns and deposition efficiency on each ribbed channel surface were obtained and analyzed. Parameter study on the deposition characteristics was conducted by considering flue gas flow velocity, particle size and inclination angle of the ribbed channel. The results showed that significant secondary flow eddies can be observed near the rib windward surfaces and high-value turbulent intensity area appears near the rib crest. The windward surfaces and the crests of the ribs are the main deposition locations in the inclined heat exchange channel. The deposition efficiency in the ribbed channel is obviously changed by the particle diameter and flue gas flow velocity. The inclination angle has little influence on deposition efficiency for small particles (dp<5μm) but great effect on deposition efficiency for large particles (dp>10μm).

Large eddy simulation of inertial particles dispersion in a turbulent gas-particle channel flow bounded by rough walls

The purpose of this paper is to understand the capability and consistency of large eddy simulation (LES) in Eulerian–Lagrangian studies aimed at predicting inertial particle dispersion in turbulent wall-bounded flows, in the absence of ad hoc closure models in the Lagrangian equations of particle motion. The degree of improvement granted by LES models is object of debate, in terms of both accurate prediction of particle accumulation and local particle segregation; therefore, we assessed the accuracy in the prediction of the particle velocity statistics by comparison against direct numerical simulation (DNS) of a finer computational mesh, under both one-way and two-way coupling regimes. We performed DNS and LES at friction Reynolds number $$\hbox {Re}_{\tau }=180$$ in smooth and rough channels, tracking particles with different inertia, with the aim to conduct a parametric study that examines the accuracy of particle statistics obtained from LES computations. The issue has been widely analysed in turbulent flow bounded by smooth walls, whereas the effect of rough boundaries on momentum coupled two-phase flows has been much less investigated until now. The action of the roughness of the wall is studied in terms of both turbulence modification and particle interaction with the wall surface due to particle rebounding off the solid boundary, without the introduction of a virtual rebound model. Results show that resolved LES adequately predicts particle-induced changes in both fluid and particle statistics in rough channels, at least for the range of parameters considered here.

Research on energy absorption effect of double damping system of high-power hydraulic rock drill

ABSTRACT The high-power hydraulic rock drill is the key to the development of modern hydraulic drill rig. With the increase of power and frequency of new type rock drill, the rebound of drill tool will be obvious during drilling, which will seriously affect the structural safety and operation efficiency. For this phenomenon, it is necessary to research the characteristics of double damping system to absorb the rebound energy of drill tool. A new model of incident stress wave is revised on the basis of rectangular wave. By combining the reflected stress wave with the model of damping system, the pressure fluctuation of damping system is analysed. Based on the theory of stress wave transmission, the rebound model of drill tool is established, and the transmission law of incident wave and reflection wave in drilling process is analysed. The stress wave experiment was designed and the incident wave shape was obtained by testing. Based on the experimental results, the incident wave in the rebound model is corrected by Fourier transform principle. The accumulator model and the double damping internal structure model are established. The two parameters that can independently change the energy absorption effect of the double damping system are summarised.

Are normal fault earthquakes due to elastic rebound or gravitational collapse?

We discuss two competing models for explaining the ground deformation associated with normal faulting earthquake in the brittle elastic upper crust. The classic elastic rebound theory is usually applied for all tectonic settings. In normal fault earthquakes, this model would predict a horizontal stretching eventually responsible for the elastic rebound at the earthquake. However, volumes mostly subside vertically during an extensional earthquake and the collapsed ground in the hanging wall is about one order of magnitude larger than the uplifted volumes of the surrounding hanging wall and footwall. The elastic rebound model would explain this asymmetry with a high horizontal elastic compressibility of the hanging wall and footwall absorbing the coseismic push. We rather suggest that the force activating normal fault earthquakes is mostly dictated by the sliding of the hanging wall, owing gravitational potential. The much larger coseismic subsidence with respect to the uplift can be explained by the closure at depth of a diffuse network of microfractures developed during the interseismic period. Since the horizontal stretching does not exist below ~1 km of depth, with the minimum horizontal stress tensor becoming positive below that depth, the development of a normal fault can be activated only by the vertical maximum stress tensor, i.e., the lithostatic load. The common fluids expulsion at the coseismic stage requires diffuse secondary permeability in the upper crust, in agreement with the presence of a diffuse network of microfractures.

Complex Temporal Patterns of Large Earthquakes: Devil’s Staircases

ABSTRACTPeriodic or quasiperiodic earthquake recurrence on individual faults, as predicted by the elastic rebound model, is not common in nature. Instead, most earthquake sequences are complex and variable, and often show clusters of events separated by long but irregular intervals of quiescence. Such temporal patterns are especially common for large earthquakes in complex fault zones or regional and global fault networks. Mathematically described as the Devil’s Staircase, such temporal patterns are a fractal property of nonlinear complex systems, in which a change of any part (e.g., rupture of a fault or fault segment) could affect the behavior of the whole system. We found that the lengths of the quiescent intervals between clusters are inversely related to tectonic-loading rates, whereas earthquake clustering can be attributed to many factors, including earthquake-induced viscoelastic relaxation and fault interaction. Whereas the underlying causes of the characteristics of earthquake sequences are not fully known, we attempted to statistically characterize these sequences. We found that most earthquake sequences are burstier than the Poisson model commonly used in probabilistic seismic hazard analysis, implying a higher probability of repeating events soon after a large earthquake.