scholarly journals Granular jets and hydraulic jumps on an inclined plane

2011 ◽  
Vol 675 ◽  
pp. 87-116 ◽  
Author(s):  
C. G. JOHNSON ◽  
J. M. N. T. GRAY
Keyword(s):  
Granular Material ◽  
Numerical Solutions ◽  
Slope Angle ◽  
Three Dimensional ◽  
Breaking Wave ◽  
Hydraulic Jumps ◽  
Inclined Plane ◽  
Steady Regime ◽  
Diverse Range ◽  
The Impact

A jet of granular material impinging on an inclined plane produces a diverse range of flows, from steady hydraulic jumps to periodic avalanches, self-channelised flows and pile collapse behaviour. We describe the various flow regimes and study in detail a steady-state flow, in which the jet generates a closed teardrop-shaped hydraulic jump on the plane, enclosing a region of fast-moving radial flow. On shallower slopes, a second steady regime exists in which the shock is not teardrop-shaped, but exhibits a more complex ‘blunted’ shape with a steadily breaking wave. We explain these regimes by consideration of the supercritical or subcritical nature of the flow surrounding the shock. A model is developed in which the impact of the jet on the inclined plane is treated as an inviscid flow, which is then coupled to a depth-integrated model for the resulting thin granular avalanche on the inclined plane. Numerical simulations produce a flow regime diagram strikingly similar to that obtained in experiments, with the model correctly reproducing the regimes and their dependence on the jet velocity and slope angle. The size and shape of the steady experimental shocks and the location of sub- and supercritical flow regions are also both accurately predicted. We find that the physics underlying the rapid flow inside the shock is dominated by depth-averaged mass and momentum transport, with granular friction, pressure gradients and three-dimensional aspects of the flow having comparatively little effect. Further downstream, the flow is governed by a friction–gravity balance, and some flow features, such as a persistent indentation in the free surface, are not reproduced in the numerical solutions. On planes inclined at a shallow angle, the effect of stationary granular material becomes important in the flow evolution, and oscillatory and more general time-dependent flows are observed. The hysteretic transition between static and dynamic friction leads to two phenomena observed in the flows: unsteady avalanching behaviour, and the feedback from static grains on the flowing region, leading to levéed, self-channelised flows.

scholarly journals A Stochastic Rockfall Model Related to Random Ground Roughness Based on Three-Dimensional Discontinuous Deformation Analysis

2021 ◽  
Vol 9 ◽  
Author(s):  
Lu Zheng ◽  
Zhiyuan Zhu ◽  
Qi Wei ◽  
Kaihui Ren ◽  
Yihan Wu ◽  
...  
Keyword(s):  
Dynamic Behavior ◽  
Lateral Displacement ◽  
Grid Point ◽  
Slope Angle ◽  
Three Dimensional ◽  
Discontinuous Deformation Analysis ◽  
Cumulative Distribution ◽  
Deformation Analysis ◽  
Discontinuous Deformation ◽  
The Impact

The use of feasible 3-D numerical methods has become essential for addressing problems related to rockfall hazard. Although several models with various degrees of complexity are available, certain trajectories and impact dynamics related to some model inputs could fall in the rockfall observations area but are rarely calibrated against reflecting its range, especially the lateral deviations. A major difficulty exists in the lack of simulating the apparent randomness during the impact-rebound process leading to both ground roughness and block irregularities. The model presented here is based on three-dimensional discontinuous deformation analysis (3-D DDA). Despite similarities to previous simulations using 3-D DDA, the model presented here incorporates several novel concepts: (1) ground roughness is represented as a random change of slope angle by height perturbation at a grid point in DEM terrain; (2) block irregularities are modelled directly using polyhedron data; (3) a scaled velocity restitution relationship is introduced to consider incident velocity and its angle. Lateral deviations of rebound velocity, both direction and value, at impact are similarly accounted for by perturbing the ground orientation laterally, thus inducing scatter of run-out directions. With these features, the model is capable to describe the stochastic rockfall dynamics. In this study, 3-D DDA was then conducted to investigate the dynamic behavior of the rockfall and examine the role of sphericity of the rock block travelling on bench slopes with different ground roughness levels. Parametric analyses were carried out in terms of cumulative distribution function (CDF) to investigate for spatial distribution (both runout distance and lateral displacement), velocity and jumping height. The effects of block shape and ground roughness revealed by these factors were discussed. It suggests that ground roughness amplifies the randomness and plays important roles on the dynamic behavior of the system; irregularity from block sphericity will further amplify the randomness especially when the size of the rock is relatively small compared to the roughness level. Both irregularities should be taken into consideration in simulating rockfall problems. Further calibration of the new model against a range of field datasets is essential.

The motion of a finite mass of granular material down a rough incline

1989 ◽  
Vol 199 ◽  
pp. 177-215 ◽  
Author(s):  
S. B. Savage ◽  
K. Hutter
Keyword(s):  
Granular Material ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Similarity Solutions ◽  
The Other ◽  
Continuum Approximation ◽  
Finite Difference Schemes ◽  
Finite Mass ◽  
Inclined Plane ◽  
Numerical Predictions

Rock, snow and ice masses are often dislodged on steep slopes of mountainous regions. The masses, which typically are in the form of innumerable discrete blocks or granules, initially accelerate down the slope until the angle of inclination of the bed approaches the horizontal and bed friction eventually brings them to rest. The present paper describes an initial investigation which considers the idealized problem of a finite mass of material released from rest on a rough inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth-averaged equations of motion are derived; they bear a superficial resemblance to the nonlinear shallow-water wave equations. Two similarity solutions are found for the motion. They both are of surprisingly simple analytical form and show a rather unanticipated behaviour. One has the form of a pile of granular material in the shape of a parabolic cap and the other has the form of anM-wave with vertical faces at the leading and trailing edges. The linear stability of the similarity solutions is studied. A restricted stability analysis, in which the spread is left unperturbed shows them to be stable, suggesting that mathematically both are possible asymptotic wave forms. Two numerical finite-difference schemes, one of Lagrangian, the other of Eulerian type, are presented. While the Eulerian technique is able to reproduce theM-wave similarity solution, it appears to give spurious results for more general initial conditions and the Lagrangian technique is best suited for the present problem. The numerical predictions are compared with laboratory experiments of Huber (1980) involving the motion of gravel released from rest on a rough inclined plane. Although in these experiments the continuum approximation breaks down at large times when the gravel layer is only a few particle diameters thick, the general features of the development of the gravel mass are well predicted by the numerical solutions.

Dynamic Buckling of 50000m3 Vertical Storage Tanks under Seismic Excitation

2013 ◽  
Vol 353-356 ◽  
pp. 2039-2042
Author(s):  
Sun Ying ◽  
Jian Gang Sun ◽  
Li Fu Cui
Keyword(s):  
Storage Tank ◽  
Numerical Solutions ◽  
Base Isolation ◽  
Three Dimensional ◽  
Dynamic Buckling ◽  
Seismic Excitation ◽  
Storage Tanks ◽  
Isolation System ◽  
Base Isolation System ◽  
The Impact

To study the dynamic buckling characteristics of storage tank subjected to three-dimensional seismic excitation, selecting 50000m3 large vertical floating roof storage tanks as research object, the base isolation system was introduced and allowing for the impact of floating roof. The finite element models of non-isolation and base isolation storage tank were established respectively by ADINA. The seismic responses of these two types of storage tank were calculated and the numerical solutions were compared. The results indicate that the dynamic buckling modes of these two types of storage tank system belong to plastic buckling; base isolation measure can effectively increase the critical load value of dynamic buckling and plasticity yielding, the improve rates up to 38% and 60% respectively. The effectiveness of the base isolation can be verified from the angle of buckling.

scholarly journals BREAKING WAVE KINEMATICS, LOCAL PRESSURES, AND FORCES ON A TRIPOD STRUCTURE

2012 ◽  
Vol 1 (33) ◽  
pp. 71 ◽  
Author(s):  
Arndt Hildebrandt ◽  
Torsten Schlurmann
Keyword(s):  
Wave Front ◽  
Wave Breaking ◽  
Large Scale ◽  
Three Dimensional ◽  
Model Tests ◽  
Scale Model ◽  
Breaking Wave ◽  
Wave Loads ◽  
Large Wave ◽  
The Impact

This paper presents breaking wave loads on a tripod structure from physical model tests and numerical simulations. The large scale model tests (1:12) are described as well as the validation of the three dimensional numerical model by comparison of CFD wave gauge data and pressures with measurements in the large wave flume inside and outside the impact area. Subsequently, the impact areas due to a broken wave, a curled wave front as well as for wave breaking directly at the structure with a partly vertical wave front are compared to each other. Line forces in terms of slamming coefficients with variation in time and space are derived from CFD results and the velocity distribution is presented at the onset of wave breaking. Finally, the results are briefly discussed in comparison to other slamming studies.

Velocity, Pressure, and Dam-Break Similarity of Green Water Flow on a 3D Structure

2011 ◽  
Author(s):  
Kuang-An Chang ◽  
Kusalika Ariyarathne ◽  
Richard Mercier
Keyword(s):  
Vertical Wall ◽  
Three Dimensional ◽  
Dam Break ◽  
Green Water ◽  
Breaking Wave ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Wave Condition ◽  
Wall Impingement ◽  
The Impact

Flow dynamics of green water due to plunging breaking waves interacting with a simplified, three-dimensional model structure was investigated in laboratory. Two breaking wave conditions were tested: one with waves impinging and breaking on the vertical wall of the model at the still water level (referred as wall impingement) and the other with waves impinging and breaking on the horizontal deck surface (referred as deck impingement). The bubble image velocimetry (BIV) technique was used to measure the flow velocity. Measurements were taken on a vertical plane located at the center of the deck surface and a horizontal plane located slightly above the deck surface. The applicability of dam-break theory on green water velocity prediction for the three-dimensional model was also investigated. Furthermore, pressure measurements were performed at several locations above the horizontal deck surface for the wall impingement wave condition. Predictions of maximum impact pressure based on the measured pressure and flow velocities were investigated using the impact coefficient approach that links pressure with kinetic energy.

Nonlinear Feedback in a Five-Dimensional Lorenz Model

2014 ◽  
Vol 71 (5) ◽  
pp. 1701-1723 ◽  
Author(s):  
Bo-Wen Shen
Keyword(s):  
Numerical Solutions ◽  
Three Dimensional ◽  
Solution Stability ◽  
Nonlinear Feedback ◽  
Lorenz Model ◽  
Dissipative Term ◽  
Higher Dimensional ◽  
The Impact ◽  
Underlying Processes

Abstract In this study, based on the number of modes, the original three-dimensional Lorenz model (3DLM) is generalized with two additional modes [five-dimensional Lorenz model (5DLM)] to examine their role in the predictability of the numerical solutions and to understand the underlying processes that increase the solution stability. As a result of the simplicity of the 5DLM with respect to existing generalized Lorenz models (LMs), the author is able to obtain the analytical solutions of its critical points and identify the role of the major nonlinear term in the solution’s stability, which have previously not been documented in the literature. The nonlinear Jacobian terms of the governing equations are analyzed to highlight the importance of selecting new modes for extending the nonlinear feedback loop of the 3DLM and thus effectively increasing the degree of nonlinearity (i.e., the nonlinear mode–mode interactions) in the 5DLM. It is then shown that numerical solutions in the 5DLM require a larger normalized Rayleigh number r for the onset of chaos and are more predictable than those in the 3DLM when r is between 25 and 40 and the Prandtl number σ is 10. The improved predictability is attributable to the negative nonlinear feedback enabled by the new modes. The role of the (negative) nonlinear feedback is further verified using a revised 3DLM with a parameterized nonlinear eddy dissipative term. The finding of the increased stability in the 5DLM and revised 3DLM with respect to the 3DLM is confirmed with the linear stability analysis and the analysis of the Lyapunov exponents using different values of r and σ. To further understand the impact of an additional heating term, results from the 5DLM and a higher-dimensional LM [e.g., the six-dimensional LM (6DLM)] are analyzed and compared.

Low-Degree Tibial Slope Angle Prevents Component Overhang by Enlarging the Lateral Plateau Surface Area in Total Knee Arthroplasty

2020 ◽  
Author(s):  
Mehmet Emin Simsek ◽  
Mustafa Akkaya ◽  
Safa Gursoy ◽  
Özgür Kaya ◽  
Murat Bozkurt
Keyword(s):  
Total Knee Arthroplasty ◽  
Surface Area ◽  
Knee Arthroplasty ◽  
Tibial Plateau ◽  
Slope Angle ◽  
Three Dimensional ◽  
Tibial Slope ◽  
Total Knee ◽  
Lateral Plateau ◽  
Gender Groups

AbstractThis study aimed to investigate whether overhang or underhang around the tibial component that occurs during the placement of tibial baseplates was affected by different slope angles of the tibial plateau and determine the changes in the lateral and medial plateau diameters while changing the slope angle in total knee arthroplasty. Three-dimensional tibia models were reconstructed using the computed tomography scans of 120 tibial dry bones. Tibial plateau slope cuts were performed with 9, 7, 5, 3, and 0 degrees of slope angles 2-mm below the subchondral bone in the deepest point of the medial plateau. Total, lateral, and medial tibial plateau areas and overhang/underhang rates were measured at each cut level. Digital implantations of the asymmetric and symmetric tibial baseplates were made on the tibial plateau with each slope angles. Following the implantations, the slope angle that prevents overhang or underhang at the bone border and the slope angle that has more surface area was identified. A significant increase was noted in the total tibial surface area, lateral plateau surface area, and lateral anteroposterior distance, whereas the slope cut angles were changed from 9 to 0 degrees in both gender groups. It was found that the amount of posteromedial underhang and posterolateral overhang increased in both the asymmetric and symmetric tibial baseplates when the slope angle was changed from 0 to 9 degrees. Although the mediolateral diameter did not change after the proximal tibia cuts at different slope angles, the surface area and anteroposterior diameter of the lateral plateau could change, leading to increased lateral plateau area. Although prosthesis designs are highly compatible with the tibial surface area, it should be noted that the component overhangs, especially beyond the posterolateral edge, it can be prevented by changing the slope cut angle in males and females.

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

Analyzing the Impact of X-Ray Tomography on the Reliability of Integrated Circuits

2015 ◽  
Author(s):  
Halit Dogan ◽  
Md Mahbub Alam ◽  
Navid Asadizanjani ◽  
Sina Shahbazmohamadi ◽  
Domenic Forte ◽  
...  
Keyword(s):  
Integrated Circuits ◽  
Integrated Circuit ◽  
3D Imaging ◽  
Three Dimensional ◽  
Serial Sectioning ◽  
Promising Technique ◽  
Flash Memories ◽  
X Ray ◽  
3D Information ◽  
The Impact

Abstract X-ray tomography is a promising technique that can provide micron level, internal structure, and three dimensional (3D) information of an integrated circuit (IC) component without the need for serial sectioning or decapsulation. This is especially useful for counterfeit IC detection as demonstrated by recent work. Although the components remain physically intact during tomography, the effect of radiation on the electrical functionality is not yet fully investigated. In this paper we analyze the impact of X-ray tomography on the reliability of ICs with different fabrication technologies. We perform a 3D imaging using an advanced X-ray machine on Intel flash memories, Macronix flash memories, Xilinx Spartan 3 and Spartan 6 FPGAs. Electrical functionalities are then tested in a systematic procedure after each round of tomography to estimate the impact of X-ray on Flash erase time, read margin, and program operation, and the frequencies of ring oscillators in the FPGAs. A major finding is that erase times for flash memories of older technology are significantly degraded when exposed to tomography, eventually resulting in failure. However, the flash and Xilinx FPGAs of newer technologies seem less sensitive to tomography, as only minor degradations are observed. Further, we did not identify permanent failures for any chips in the time needed to perform tomography for counterfeit detection (approximately 2 hours).

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