Initial Horizontal Velocity Research Articles

Estimation Model of Rockfall Trajectory Lateral Dispersion on Slopes with Loose Granular Cushion Layer Based on Three-Dimensional Discrete Element Method Simulations

Rockfall is a typical successive hazard with a high incidence rate following primary geological disasters such as landslides, rock avalanches, and debris flows. The lateral dispersion of rockfall is significantly affected by the loose granular cushion layer deposited on slopes. This paper aims to develop a quick estimation model for this effect based on the 3D-DEM (discrete element method) numerical simulations. The DEM model employs particles with different bonding properties to create a modeling double-layer granular slope. The present model is also verified by comparing the data from the antecedent large-scale outdoor rockfall experiment with the numerical simulations. Accordingly, the influences of four factors: the initial horizontal release velocity, the size of the rock mass, the granular cushion thickness, and the slope angle on the lateral dispersion of the rockfall trajectory are analyzed, and the underlying physical mechanism is discussed thoroughly. Ultimately, we identify a nondimensional parameter that demonstrates a strong correlation with the evolution of the lateral dispersion ratio of the rockfall trajectory. Based on this insight, we propose an estimation model for predicting the lateral dispersion of the rockfall trajectory. This model can assist engineering and construction personnel in rapidly determining the lateral dispersion range of the rockfall.

Numerical investigation of free surface flow impact using an accelerated three-dimensional smoothed particle hydrodynamics

Water impact problems are inevitable in the realm of ocean engineering. The smoothed particle hydrodynamics method (SPH), as a meshless particle approach, can effectively reproduce the slamming process which involves large deformation of the free surface. In this study, an accelerated three-dimensional SPH model is constructed based on the graphic processing unit (GPU) with the speedup of up to 40. The six-degree-of-freedom motion equation is introduced to realize the responses of the solid. The fluid-solid interaction system is achieved by regarding the rigid body as the moving boundary of the fluid. The computational accuracy and efficiency of the developed model are respectively verified by the wedge water entry, dam breaking and inclined cylinder water entry. Finally, the developed model is applied to a complex flight vehicle landing problem, and the effect of the initial horizontal velocity, vertical velocity and pitch angle on the impact process are qualitatively and quantitively studied.

Global solutions to the three-dimensional inhomogeneous incompressible Phan-Thien–Tanner system with a class of large initial data

In this paper, we consider the global well-posedness of the three-dimensional inhomogeneous incompressible Phan-Thien–Tanner (PTT) system with general initial data in the critical Besov spaces. The question of whether or not PTT system is globally well posed for large data is still open. When the density ρ is away from zero, we denote by ϱ:=1ρ−1. More precisely, we prove that the PTT system admits a unique global solution, provided that the initial data ϱ 0, the initial horizontal velocity uh0 , the product ωu30 of the coupling parameter ω and the initial vertical velocity u 30, and the initial symmetric tensor of constraints τ 0 are sufficiently small. In particular, this result includes the global well-posedness of the PTT system for small initial data in the case where ω∈[0,1) and for large initial vertical velocity in the case where ω tends to zero. As a by-product, our results can be applied to the so-called Oldroyd-B system.

Improved local existence result of the Green–Naghdi equations with the Coriolis effect

The aim of this paper is to provide an alternative proof of the well-posedness of the Green–Naghdi equations with the Coriolis effect established by Chen et al. (2018). We showed that an additional assumption on the initial horizontal velocity is not necessary to obtain well-posedness. Indeed, with a refined symmetrizer and appropriately scaling the rotation parameter, we can derive a prior energy estimate based solely on the physically relevant depth-condition.

Optimizing and designing a leg shape to increase robustness of a running robot on rough terrain

The superior ability of dynamic legged locomotion in traversing rough terrain relative to wheeled or tracked mechanisms comes with the cost of fragile stability. Simple control methods that use only a few basic detection sensors and apply a single controller help robots keep their balance when traversing unforeseen rough terrain. Exploiting multiple controllers simultaneously, such as the free leg length and stiffness in our hopping monopod, can further improve robustness but is often mechanically hard to implement. This work demonstrates that a curved leg shape can improve the robustness of a robot to perturbations in both terrain levels and initial horizontal velocity without complicating the control scheme. Our work develops spring loaded inverted pendulum (SLIP) based models that manifest the coupling of the leg’s parameters and capture the rolling motion. We use these models to find an optimal combination of parameters that maximizes a measure for long-term stability−reaching a desired relative height above terrain. We demonstrate that when traversing unknown rough terrain, such optimal coupling can increase robustness to perturbations in the initial horizontal velocity by 93% relative to the optimal conventional SLIP model. We further demonstrate our results in experiments.

Analysis of the Changes in Velocity of Balls Rolling off Edges using Chi-squared Model Testing

When a ball rolls over the edge of a table, its horizontal velocity is consistently observed to be higher than the initial horizontal velocity. While multiple studies have investigated this phenomenon, none of these studies provided data on the linear velocity of the ball, nor discussed the variance between the data and the model. This paper studied the motion of a ball rolling over the edge using chi-squared curve fitting and model testing. Video analysis was used to collect velocity data of the ball’s motion, and chi-square curve fitting and analysis was performed using a python script. The kick in velocity was observed to decrease as the initial velocity increased, consistent with previous studies. However, the best fit parameter values were not consistent with the derived theoretical model. Furthermore, chi-squared analysis indicated that the best fit model was not a good fit for the data, suggesting that revisions are necessary to the experiment and model.

Investigation on the Horizontal Landing Velocity and Pitch Angle Impact on the Soft-Landing Dynamic Characteristics

The dynamic analysis of the soft landing of the lunar probe is very important to the design of the probe. The initial movement and attitude parameters of the probe during landing have a direct influence on the landing impact. In order to investigate the lunar probe soft-landing dynamic impact by different initial horizontal velocities, pitch angles, and inclinations of the lunar slope, an inertial force-based 7-DOF soft-landing dynamic model is applied under two conditions: the upward and downward slope landing surfaces. The impact on the dynamic characteristics of soft landing is analyzed in terms of body displacement, body overload, and the forces of the primary and secondary buffer struts due to the change of initial horizontal velocity and initial pitch angle of the probe. The result shows that, in 2-2 landing mode, the stress conditions on the primary and secondary struts are obviously impacted by initial horizontal velocity, and the initial pitch angle affects the body overload and the loading state of the secondary buffer strut. The body overload and landing impact could be significantly mitigated if the lunar probe’s horizontal landing speed is limited within 1 m/s, the pitch angle is limited within 12°, and the landing is along the uphill terrain with the inclination of the lunar slope less and equal to 9°. The analysis can directly determine the range of the horizontal speed and pitch attitude angle to ensure the safety of landing, and provide a reference for the reasonable control design of the lander’s horizontal speed and pitch attitude.

Research on hull pressure distribution of amphibious landing on water based on RANS method

Aiming at the strength problem of amphibious landing on water, the pressure distribution of ship bottom is studied. RANS multi-phase flow method is used to solve the coupling problem of gas, liquid and solid in the process of amphibious landing on the water surface. Overlapping grid technology is used to simulate the landing under different initial horizontal velocity and vertical velocity. The influence of initial conditions on the motion response of amphibious is analyzed, and the variation law of pressure on each section of ship bottom with time is obtained, This paper analyzes the variation of pressure with time and position, and provides technical reference for the design and application of water loads in the development of amphibious.

The meshless numerical simulation of Kelvin–Helmholtz instability during the wave growth of liquid–liquid slug flow

Kelvin–Helmholtz instability (KHI) occurs at the interface of two fluids, in which the heavier fluid flows at the bottom. In the present numerical work, the KHI was analyzed by solving the modification of two-dimensional (2-D) incompressible Navier–Stokes equations. To capture the interface, the Cahn–Hilliard equation was implemented into the Navier–Stokes equations. The phenomena around the KHI of two and three-component fluids were investigated numerically by using radial basis function (RBF) combined with the domain decomposition method (DDM) in a primitive variable formulation. Here DDM is able to solve the large scale problem. On the other hand the calculation accuracy decreases with the increase of the number of the subdomains. For the above reason, in the present works, the domain was partitioned into 15 x 15 subdomains in order to reduce the decrease in accuracy due to the domain division. Next, fractional step method was used to solve the modification of the Navier–Stokes equations.The numerical results indicate that the procedure used in the present work can easily handle the KHI problem under the variations of the interface thickness, density ratios, and initial velocity differences. Moreover, the interface evolutions obtained from the present method agree well with those of the finite difference method. The effects of the interface thickness, density ratio and magnitude of velocity difference on the KHI were also investigated. The decrease of the interface thickness produces a non-smooth concentration profile, and the increase of the interface thickness produces too much surface diffusion. It was found also that the increase of the density ratio reduces the growth of KHI. The interface rolls up are strongly affected by the initial horizontal velocity difference. Finally, the present study also shows that the RBF method is a reliable method to solve the KHI on the complex domains.

Matrix‐free crosshole elliptical‐anisotropy tomography: parametrization analysis and ground‐penetrating radar applications in carbonates

ABSTRACTA novel traveltime tomographic approach is applied to anisotropic media, limited to 2D geometry at present. A general anisotropic Eikonal solver based on a discontinuous Galerkin method is combined with an efficient adjoint formulation for multiparameter least‐squares inversion. This new approach is tested considering synthetic crosshole ground‐penetrating radar data. The configuration of the ground‐penetrating radar survey is inspired by a real experiment done on layered carbonate media disturbed by the presence of a deep gallery, which induces a localized high‐electromagnetic contrast. This made it possible to define a well‐adapted general workflow in this context. We notably show that, under the elliptical anisotropic assumption, the parametrization based on vertical and horizontal velocities provides less biased results than those obtained by considering the vertical velocity and the relevant Thomsen parameter . The initial vertical and horizontal velocity models are identical and built from an isotropic inversion. The presence of the high‐contrast gallery generates a weak diffraction pattern, which is taken into account in our tomography approach. It also creates potential artefacts due to the model discretization, which are mitigated by a model regularization term within the definition of the misfit function. This general workflow is then applied to the real experiment dataset. The vertical and horizontal velocity images provide similar structures as those previously obtained by isotropic full waveform inversion, complemented by an image of a rather weak elliptical anisotropy.

Global well-posedness of the 3D primitive equations with horizontal viscosity and vertical diffusivity

In this paper, we consider the 3D primitive equations of oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation. Global well-posedness of strong solutions is established for any initial data such that the initial horizontal velocity v0∈H2(Ω) and the initial temperature T0∈H1(Ω)∩L∞(Ω) with ∇HT0∈Lq(Ω), for some q∈(2,∞). Moreover, the strong solutions enjoy correspondingly more regularities if the initial temperature belongs to H2(Ω). The main difficulties are the absence of the vertical viscosity and the lack of the horizontal diffusivity, which, interact with each other, thus causing the “mismatching” of regularities between the horizontal momentum and temperature equations. To handle this “mismatching” of regularities, we introduce several auxiliary functions, i.e., η,θ,φ, and ψ in the paper, which are the horizontal curls or some appropriate combinations of the temperature with the horizontal divergences of the horizontal velocity v or its vertical derivative ∂zv. To overcome the difficulties caused by the absence of the horizontal diffusivity, which leads to the requirement of some Lt1(Wx1,∞)-type a priori estimates on v, we decompose the velocity into the “temperature-independent” and temperature-dependent parts and deal with them in different ways, by using the logarithmic Sobolev inequalities of the Brézis–Gallouet–Wainger and Beale–Kato–Majda types, respectively. Specifically, a logarithmic Sobolev inequality of the limiting type, introduced in our previous work (Cao et al., 2016), is used, and a new logarithmic type Gronwall inequality is exploited.

DYNAMIC MODELLING FOR THE SECOND FLIGHT PHASE OF THE YURCHENKO LAYOUT VAULT BASED ON MSC. ADAMS

Gymnasts attempt to increase the angles of rotation about transversal and longitudinal axes during the post-flight of vaulting, and these angles are related to different mechanical properties. The present study uses a 3D angle-driven computer simulation model of a gymnast who performs Yurchenko layout vault using ADAMS software. Simulation initial conditions are horizontal and vertical velocities of gymnast’s pelvis center and angular velocities about the transversal and longitudinal axes which can be easily measured. The initial linear and angular velocity conditions of the simulation model are each changed in certain increments from measurement data collected from an elite woman gymnast. Increasing initial horizontal velocity results in an increased horizontal flight distance, but has no connection with the duration of flight and angle of twists. The overall angle of twists is concerned with initial vertical velocity and angular velocities about the transversal and longitudinal axes. Also, increasing initial vertical velocity and angular velocity about transverse axis leads to increase in touchdown angle between ground’s horizontal axis and gymnast’s longitudinal axis.

Position detection method and hydrodynamic characteristics of the water entry of a cylinder with multidegree motion

This study experimentally investigates the hydrodynamic characteristics of a cylinder with multidegree motion during water entry with different initial horizontal velocities and inclined angles. A mechanical device is designed to provide certain initial conditions for the cylinder, and the cavity evolution and cylinder position are recorded with a high-speed camera. To obtain precise hydrodynamic forces, a new image-processing method is established to detect the center and attitude angle of the cylinder based on a step edge model and the Grubbs criterion. Additionally, an algorithm is employed to correct the refraction effects in the raw data. Using the above methods, the phenomena of asymmetric cavities, cavity pinch-off, double cavities and cavity ripples are observed in the wake region of the cylinder. Before the cavity pinches off, the hydrodynamic force driving the cylinder motion is generated from the pressure difference between the wet and dry parts. After pinch-off, the hydrodynamic force is mainly dominated by the induced lift, which depends on the angular speed, and a high-pressure region created by the pinch-off cavity causes an instantaneous impulse force that causes quick decreases in the cylinder accelerations. In addition, for the cylinder lift coefficient, the average rate of change increases almost linearly with an increasing initial angle of attack during water entry. For the drag coefficient, the average rate of increase rises nearly linearly with increasing absolute value of the initial angle of attack before pinch-off. After cavity pinch-off, this rate increases almost linearly with increasing |v0|/α0L.

Earth-Gravity Congruent Motion Facilitates Ocular Control for Pursuit of Parabolic Trajectories

There is evidence that humans rely on an earth gravity (9.81 m/s²) prior for a series of tasks involving perception and action, the reason being that gravity helps predict future positions of moving objects. Eye-movements in turn are partially guided by predictions about observed motion. Thus, the question arises whether knowledge about gravity is also used to guide eye-movements: If humans rely on a representation of earth gravity for the control of eye movements, earth-gravity-congruent motion should elicit improved visual pursuit. In a pre-registered experiment, we presented participants (n = 10) with parabolic motion governed by six different gravities (−1/0.7/0.85/1/1.15/1.3 g), two initial vertical velocities and two initial horizontal velocities in a 3D environment. Participants were instructed to follow the target with their eyes. We tracked their gaze and computed the visual gain (velocity of the eyes divided by velocity of the target) as proxy for the quality of pursuit. An LMM analysis with gravity condition as fixed effect and intercepts varying per subject showed that the gain was lower for −1 g than for 1 g (by −0.13, SE = 0.005). This model was significantly better than a null model without gravity as fixed effect (p < 0.001), supporting our hypothesis. A comparison of 1 g and the remaining gravity conditions revealed that 1.15 g (by 0.043, SE = 0.005) and 1.3 g (by 0.065, SE = 0.005) were associated with lower gains, while 0.7 g (by 0.054, SE = 0.005) and 0.85 g (by 0.029, SE = 0.005) were associated with higher gains. This model was again significantly better than a null model (p < 0.001), contradicting our hypothesis. Post-hoc analyses reveal that confounds in the 0.7/0.85/1/1.15/1.3 g condition may be responsible for these contradicting results. Despite these discrepancies, our data thus provide some support for the hypothesis that internalized knowledge about earth gravity guides eye movements.

Experimental study on water entry of inclined circular cylinders with horizontal velocities

The complex impact cavities and motion behaviours of water entry by a multi-degree-of-freedom motion cylinder are investigated experimentally for different initial horizontal velocities and inclined angles. The cylinder is released above the free surface with controlled component velocities and inclined angles by a newly designed mechanism. A high-speed photography technique is employed to reveal the unique cavity flow phenomena that vary with horizontal velocity and inclined angle and to record the corresponding position of the cylinder in water. The cavity dynamics, including the initial jet, open cavity, surface seal, cavity break, break jet, side cavity and pinch-off, are investigated for different initial impact conditions. Moreover, the effects of horizontal velocity, inclined angle and angle of attack on the motion characteristics are studied. The experimental results demonstrate a special cavity flow phenomenon, a suction airchannel, that is due to the closure of the splash dome prior to the growth of the cavity volume. For cases of violent cavity break, a water wedge is formed as the break jet penetrates into the fore end cavity. The hydrodynamics of impact force, pressure drop and spin-induced lift acting on the descending cylinder cause obvious curvature in the trajectory. In particular, when the absolute value of the angle of attack is greater than 22°, a circuitous phenomenon is found, and the inclined angle decreases rapidly as the cylinder descends.

Students’ conclusions from measurement data: The more decimal places, the better?

In this study with 153 middle school students, we investigate the influence of the number of decimal places from the reading of a measurement device on students’ decisions to change or keep an initial hypothesis about falling objects. Participants were divided into three groups, introduced to two experiments—the time it takes a free falling object with a zero, and a nonzero initial horizontal velocity to fall a certain distance—and asked to state a hypothesis that compares the falling times of the two experiments. We asked the participants whether they wanted to change or keep their initial hypothesis after they were provided with data sets. Members of each group were given the same number of measurements but with a different number of decimal places. Results show that for an increase in the number of decimal places, the number of participants switching from a false to a correct hypothesis decreases, and at the same time the number of students switching from a correct to a false hypothesis increases. These results indicate that showing more exact data to students—given through different resolutions of the measurement device—may hinder students’ ability to compare data sets and may lead them to incorrect conclusions. We argue that this is due to students’ lack of knowledge about measurement uncertainties and the concept of variance.Received 17 October 2018DOI:https://doi.org/10.1103/PhysRevPhysEducRes.15.010103Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEpistemology, attitudes, & beliefsScientific reasoning & problem solvingPhysics Education Research

Analysis of freezing process about falling droplet using the lattice Boltzmann method

PurposeThe freezing phenomenon of a falling droplet is a frequently encountered phenomenon in various applications, such as spray crystallization, hail formation and artificial snowmaking. Therefore, this paper aims to understand the freezing processes of a falling droplet without and with initial horizontal velocity in a cold space.Design/methodology/approachThe freezing processes of a falling droplet were characterized using a modified enthalpy-based lattice Boltzmann method.FindingsThe temperature field, streamlines and freezing process of the falling droplet were investigated and analyzed. The lower part of the droplet was frozen earlier than the upper part. The freezing trend slowed down in the later stage of the freezing process. The droplet shape was related to the initial vertical velocity, nucleation temperature and initial horizontal velocity.Originality/valueA modified enthalpy-based lattice Boltzmann method is proposed. In the model, the improved pseudo-potential model is used and the radiation is considered. This method was firstly used to simulate the freezing process of a falling droplet. By examining these freezing processes in detail, the freezing trend and the effect factors of droplet deformation and freezing time were obtained, respectively.

Effect of intermediate fluid layer on Kelvin–Helmholtz instability

Two-dimensional K-H (Kelvin–Helmholtz) instability of the three-component immiscible fluids with an intermediate fluid layer is numerically studied using the front-tracking method (FTM). The instability is governed by the Navier–Stokes equations and the conservation of mass equation for incompressible flow. A finite difference method is used to discretize the governing system. This study focuses on the influence of flow configuration, the thickness of intermediate fluid layer and the distribution of intermediate fluid layer on K-H instability. It is shown that the larger the initial horizontal velocity difference is, the faster the internal disturbance increases, and the characteristic form of K-H instability becomes more obvious for different flow configuration. It is also observed that the thickness of the intermediate fluid layer is negatively correlated to the billow height and the numerical growth rate. In addition, when the intermediate fluid layer is thicker than 0.4 times the disturbance wavelength, the billow height and the numerical growth rate for the K-H instability of the upper and lower interfaces change over time synchronously. The higher the initial height of the lower interface is, the greater the growth rate and billow height of the upper interface are. Besides, the upper and lower interfaces are rolled up synchronously over time when the intermediate fluid layer is symmetrically distributed with y = 0.5 in the fluid system.

Bidirectional Whitham equations as models of waves on shallow water

Hammack & Segur (1978) conducted a series of surface water-wave experiments in which the evolution of long waves of depression was measured and studied. This present work compares time series from these experiments with predictions from numerical simulations of the KdV, Serre, and five unidirectional and bidirectional Whitham-type equations. These comparisons show that the most accurate predictions come from models that contain accurate reproductions of the Euler phase velocity, sufficient nonlinearity, and surface tension effects. The main goal of this paper is to determine how accurately the bidirectional Whitham equations can model data from real-world experiments of waves on shallow water. Most interestingly, the unidirectional Whitham equation including surface tension provides the most accurate predictions for these experiments. If the initial horizontal velocities are assumed to be zero (the velocities were not measured in the experiments), the three bidirectional Whitham systems examined herein provide approximations that are significantly more accurate than the KdV and Serre equations. However, they are not as accurate as predictions obtained from the unidirectional Whitham equation.

Simulating Kelvin–Helmholtz instability using dissipative particle dynamics

Kelvin–Helmholtz (KH) instability is simulated using dissipative particle dynamics (DPD) at the mesoscopic particle level. To model two-phase flow, the ‘color’ repulsion model is introduced to describe binary fluids according to the Rothman–Keller method. The simulated results are compared with similar experiment and simulation using other techniques, and the work concludes that DPD is a promising method for simulating these systems. Furthermore, through the model and numerical simulation, the effects of intermiscibility, temperature, magnitude of velocity difference, and density ratio on the KH instability are investigated, respectively. It is shown that the poor intermiscibility reduces the mixing of two fluids and weakens the eddy currents. It is also found that as the temperature increases, the turbulence feature, i.e. plume-like structures, is more obvious. It is also revealed that as the initial horizontal velocity difference increases, the interface rolls up faster and higher. And it is also observed that as the density ratio increases, the KH instability becomes more suppressed.