Critical Kinetic Energy Research Articles

Multiple states of two-dimensional turbulence above topography

The recent work of Siegelman & Young (Proc. Natl Acad. Sci. USA, vol. 120, issue 44, 2023, e2308018120) revealed two extreme states reached by the evolution of unforced and weakly damped two-dimensional turbulence above random rough topography, separated by a critical kinetic energy $E_\#$ . The low- and high-energy solutions correspond to topographically locked and roaming vortices, surrounded by non-uniform and homogeneous background potential vorticity (PV), respectively. However, we found that these phenomena are restricted to the particular intermediate length scale where the energy was initially injected into the system. Through simulations initialized by injecting the energy at larger and smaller length scales, we found that the long-term state of topographic turbulence is also dependent on the initial length scale and thus the initial enstrophy. If the initial length scale is comparable to the domain size, the long-term flow field resembles the minimum-enstrophy state proposed by Bretherton & Haidvogel (J. Fluid Mech., vol. 78, issue 1, 1976, pp. 129–154), with very few topographically locked vortices; the long-term enstrophy is quite close to the minimum value, especially when the energy is no larger than $E_\#$ . As the initial length scale becomes smaller, more vortices nucleate and become more mobile; the long-term enstrophy increasingly deviates from the minimum value. Simultaneously, the background PV tends to homogenization, even if the energy is below $E_\#$ . These results complement the phenomenology of topographic turbulence documented by Siegelman & Young, by showing that the minimum-enstrophy and background PV homogenization states can be adequately approached by large- and small-scale initial fields, respectively, with relatively arbitrary energy.

Proposing an analytical model for predicting the dimensions of interfacial waves produced in the explosive welding of coaxial cylinders

There is an increasing interest in designing the explosive welding process and predicting its results. However, publications concerning explosive bonding have majorly focused on the welding of planar geometries. In this research, a novel analytical equation is presented for predicting the size of interfacial waves formed in the oblique collision of explosively-driven cylindrical surfaces. The experimental data from explosive welding of stainless-steel 316L to carbon steel CK22 tubes are used to validate the proposed model. In addition, the weldability window for this pair of metals is plotted. To calculate the impact angles, a series of numerical simulations are performed, considering three-dimensional (3-D) conditions. In these simulations, to reproduce the tubes’ impact and the detonation process, the Finite Element (FE) and Smoothed-Particle Hydrodynamics (SPH) methods are utilized, respectively. The findings of this research showed that the predictions of the proposed equation are consistent with the experimental data. However, by initiating the wavy-smooth transition, the corresponding values deviate from each other. Furthermore, examining the effects of the explosive load ratio on the collision velocity, it is observed that by reducing the load ratio from 0.552 to 0.14, the collision velocity decreased, linearly, by 77%. On the other hand, it is shown that the placement of design points within the allowable boundaries of the weldability window is the necessary condition for welding. However, to ensure the formation of a wavy interface, the kinetic energy lost per unit area should exceed a critical value. Compared with the conventional models, this critical kinetic energy can more accurately predict the initiation of the wavy-smooth transition process, for it considers the effects of varying thickness of the flyer tube. The value of the critical kinetic energy for the investigated pair of steel tubes, in this research, equals 515 J/cm2.

Simulation and experimental studies of debris penetrating skull

Studying the critical kinetic energy (CKE) and critical specific kinetic energy (CSKE) of the debris penetrating the human skull is of great importance for the development of head protection devices. In general, obtaining human skull specimens and conducting direct penetration experiments is difficult. Finite element simulation, on the other hand, is an effective method for determining critical values. However, it is necessary to validate the modeling and simulation method before conducting simulations on the human skull. To validate the method, this study first established a finite element model of a pig skull and performed simulations of debris penetrating the skull. The modeling and simulation methods were verified by comparing the corresponding penetration experimental results on pig skulls with those of the simulations. As the modeling and simulation methods were indirectly validated, an anatomical human skull finite element model was developed to conduct simulations of spherical and cubic debris penetrating the skull to iteratively obtain the CKE and CSKE of the two pieces of debris. Finally, the influence of different attitudes of cubic debris on the penetration energy of the human skull was investigated.

Mechanics of ballistic impact with non-axisymmetric projectiles on thin aluminium targets. Part II: Energy considerations

In Part I of this study, the ballistic performance and failure mechanisms of a thin aluminium target impacted by plate-like, non-axisymmetric projectiles with three different geometries, were considered using the gas-gun experiments. Failure mechanisms of the target material were found to depend strongly on the projectile’s geometrical features. Also, the local target’s response was not a reliable predictor of the critical kinetic energy for perforation or penetration. In order to improve the prediction of ballistic performance of thin targets, a nonlocal target behaviour should also be accounted for. In this part of the study, the global target response is examined, and a heuristic approach is introduced for the energy balance. The approach involves a new factor that represents additional energy-dissipating mechanisms between the projectile’s critical energy and the local work in target defeat. The methodology is based on the identified strong correlation of the normalised impact-induced peak kinetic energy in the target, KE¯Tmax, and the normalised target impact-induced nonlocal internal energy, U¯TPL+KE, associated with plastic deformation and increase in kinetic energy. A physically-based semi-analytical formulation for KE¯Tmax is developed by decomposition of the contributions by the inclined and blunt projectile sections, succeeding statistical analysis of key projectile’s geometrical and impact parameters. The developed approach was assessed for 17 projectile geometries implementing a total of 119 finite-element simulations with experimentally validated numerical models at subcritical (50) and critical/supercritical (69) projectile velocities. The obtained predictions had an average absolute error of less than 6.5% for impact velocities at and above the ballistic limit, while at subcritical velocities a higher scatter was observed as a result of secondary interaction effects between the projectile and the target. Overall, the methodology yielded results for the ballistic limit with an error below 5%, improving the otherwise derived results nearly twofold. The method was proven to be a practical and accurate way to improve the projectile’s critical energy prediction for thin targets, and, even though developed for non-axisymmetric projectile cases, its framework is directly transferable to axisymmetric projectiles.

Practical Considerations For The Application Of A Survival Probability Model For Rockfall

Rockfall fragmentation is a common and very complex phenomenon that is still inadequately understood and rarely modelled. When falling rock blocks break upon impact, their shape and size change and the kinetic energy is distributed amongst fragments. To efficiently design mitigation measures, it is necessary to adequately account for fragmentation when modelling rockfall trajectories. To do so, a better understanding of the fragmentation process, its occurrence and its likely outcomes is needed. The authors have recently proposed a novel model which can predict the survival probability (SP) of brittle spheres upon impact from the statistical distribution of material parameters, obtained by standard quasi- static tests (Brazilian tests and unconfined compression tests). The model predicts two Weibull parameters (shape parameter -m- and scale parameter – critical kinetic energy) that are used to define the SP. The model is based on theoretically-derived (from Hertzian contact theory) conversion factors used to transform the critical work required to fail disc samples in quasi-static indirect tension into the critical kinetic energy to cause failure of spheres at impact in vertical drop tests. The objective of this paper is to provide some practical insights into this model in relation of the analysis of the Brazilian test results and the number of Brazilian tests required to achieve an acceptable prediction. A first analysis highlights the importance of distribution of forces required to break the specimens in Brazilian tests and a common statistical based outlier removal methodology was applied to reduce the experimental error associated with the operator. After eliminating the outlier data, the quality of prediction is improved and, in particular, the influence of the specimen diameter used in Brazilian compressions to derive the model input parameter is significantly reduced. This latter point implies that the size effect is adequately captured. The second analysis reveals the highest variability for batches with low number of tests and a progressive reduction as the number of sampled test increases. Based on these results, it is suggested to use at least 30 Brazilian tests and remove outliers using the simple statistical approach presented in the paper.

Comprehensive adhesion model based on the surface characteristics of the coal particles

A comprehensive model for the adhesion of coal ash or char particle was established in this study, which includes the particles’ properties and slag layer. The physical properties of the particles include their kinetic parameters and surface characteristics. The particle surface characteristics, such as particle ash ratio and melting fraction, play an important role in particle adhesion. A sub-model of adhesion probability, constructed based on particle surface properties, was also introduced as a part of this comprehensive model. The particle adhesion propensity was determined by considering the kinetic energy criterion of the particles. The model was validated using two sets of particle deposition experiments at different temperatures. Discussion of the model shows that, when the particle kinetic energy is within the medium range, more significant than the critical velocity and less than the critical kinetic energy required to overcome viscosity or surface tension, the particle adhesion is determined by the probability corresponding to the surface characteristics. Furthermore, it is found that the adhesion probability increases with ash-carbon ratio and carbon conversion, and exhibits different trends above and below the flow temperature.

Assessing hazard and potential impact associated with volcanic ballistic projectiles: The example of La Soufrière de Guadeloupe volcano (Lesser Antilles)

The fallout of ballistic blocks and bombs ejected from eruptive vents has the potential to produce severe injuries to people and damage to infrastructure in areas proximal to volcanoes. The dimensions and dispersions of ballistic ejecta from explosive eruptions are pivotal parameters to forecast the potential impact associated with future eruptions based on the compilation of probabilistic hazard maps.In this study, we propose a new probabilistic hazard quantification strategy to provide the probability of Volcanic Ballistic Projectiles (VBPs) to exceed some critical kinetic energy thresholds, considering a variability on the site of the eruptive vents and the effect of wind. La Soufrière de Guadeloupe (Lesser Antilles) is chosen as a test case, focussing on the most likely explosive scenario associated with the eruption of an active lava dome (including phreatic, Vulcanian and Strombolian eruptions). Sensitivity analyses have guided the optimization of input parameters to balance the results stability and computational costs, showing that the topography is a pivotal factor when accounting for the spatial uncertainty on vent locations in the proximity of the dome area. Given an eruption within the adopted scenario, we provide maps showing the probability to exceed different energy reference thresholds for roof's perforation if at least one VBP falls in a target area. These maps are then combined with exposed elements to produce a qualitative exposure-based risk map. We compute the overall probability, conditional on the selected scenario, for roof perforation in a given area when a VBP is ejected. Results show probabilities varying from ca. 2% up to 40% within a few km from the volcano, quickly dropping away from the dome. However, when the probability to exceed the energy reference threshold is only conditional on falling of VBPs in a target area, most of Basse-Terre island would be affected by the 20–60% probability of roof perforation. This work confirms how the choice of a probabilistic approach is key to estimate the likelihood of occurrence of VBPs impacts as a first step towards the development and implementation of pro–active risk reduction strategies in volcanic areas.

High-Velocity Impacts of Pyrophoric Alloy Fragments on Thin Armour Steel Plates.

The terminal ballistics effects of Intermetallic Reactive Materials (IRM) fragments have been the object of intense research in recent years. IRM fragments flying at velocities up to 2000 m/s represent a realistic threat in modern warfare scenarios as these materials are substituting conventional solutions in defense applications. The IRM add Impact Induced Energy Release (IIER) to the mechanical interaction with a target. Therefore, the necessity of investigations on IIER to quantify potential threats to existing protection systems. In this study, Mixed Rare Earths (MRE) fragments were used due to the mechanical and pyrophoric affinity with IRM, the commercial availability and cost-effectiveness. High-Velocity Impacts (HVI) of MRE were performed at velocities ranging from 800 to 1600 m/s and recorded using a high-speed camera. 70 MREs cylindrical fragments and 24 steel fragments were shot on armour steel plates with thicknesses ranging from 2 mm to 3 mm. The influence of the impact pitch angle (α) on HVI outcomes was assessed, defining a threshold value at α of 20°. The influence of the failure modes of MRE and steel fragments on the critical impact velocities (CIV) and critical kinetic energy () was evaluated. An energy-based model was developed and fitted with sufficient accuracy the Normalised () determined from the experiments. IIER was observed in all the experiments involving MRE. From the analyses, it was observed that the IIER spreads behind the targets with velocities comparable to the residual velocities of plugs and shattered fragment.

Sensitivity analysis of a new model to predict the survival probability of artificial rock blocks upon dynamic impact

Rockfall fragmentation is a very complex phenomenon that is still poorly understood and modelled. Being able to adequately model fragmentation of impacting blocks, including change of shape, size, and energy after breakage, is essential to be able to predict realistic trajectories and design effective mitigation measures. In order to develop an accurate predictive model for rockfall fragmentation, it is necessary to better understand the fragmentation process and its likely outcomes. A novel model was recently proposed by the authors which can predict the survival probability (SP) of brittle spheres upon impact from the statistical distribution of material parameters, obtained by standard quasi-static tests (Brazilian tests and unconfined compression tests). The survival probability is described as a Weibull function whose two parameters (shape parameter-m-and scale parameter - critical kinetic energy) are predicted by the model. The model is based on theoretically-derived (from Hertzian contact theory) conversion factors used to transform the critical work required to fail disc samples in quasi-static indirect tension into the critical kinetic energy to cause failure of spheres at impact in vertical drop tests. This paper presents a sensitivity analysis on the parameters which influence the prediction of the critical kinetic energy.

Predicting the fragmentation survival probability of brittle spheres upon impact from statistical distribution of material properties

Fragmentation of rocks upon impact during rockfall is a phenomenon that is poorly understood, scarcely researched and difficult to predict. However, to adequately predict the outcomes of rockfall events, it is essential to know whether a given block is likely to fragment given the impact conditions and what will be the outcome of the fragmentation process; that is, the number, size and trajectory of fragments. To date, there is no model or data that can be used to fully answer these questions. This paper presents the first theoretical model that can predict the fragmentation survival probability of brittle spherical blocks upon dynamic impact (i.e. drop tests) from the statistical distribution of material properties, determined from a range of standard quasi-static tests. Considering that survival probabilities tend to follow a Weibull distribution, the model focuses on predicting the two Weibull parameters, commonly known as the shape parameter (m) and the scale parameter (here, the critical kinetic energy). The model is based on theoretically-derived conversion factors used to turn the critical work required to fail disc samples in quasi-static indirect tension into the critical kinetic energy to cause failure of spheres at impact in drop tests. The mechanistic conversion factors specifically account for the shape and size of the specimens tested and the increase of strength under dynamic loading (strain rate effect). Three series of drop tests were conducted (on spheres of three different diameters) and complemented by extensive material characterisation testing in order to validate the novel predictive model. The variability of material properties was characterised, and it was found that the material strength found by the characterisation tests generally follows a Weibull form, but the survival probability distribution of the drop tests seems to be linear. The predicted conversion factors were first compared against their experimental counterparts before validating the prediction of survival probability of the spheres upon dynamic impact (in drop tests). It was found that it is possible to predict the survival probability of artificial rock of three different diameters (50 mm, 75 mm, 100 mm) and two different strengths upon impact solely from the statistical information coming from Brazilian tests and with an average relative error of less than 9%.

Enhancing Transient Stability of Distribution Networks With Massive Proliferation of Converter-Interfaced Distributed Generators

High penetration of renewable energy sources and energy storage systems has considerably increased the flexibility in power distribution networks operation. However, employing converter-interfaced energy and storage sources may significantly reduce the mechanical inertia and as a result, the power grids may confront serious stability challenges during transient conditions. This article introduces a strategy for enhancing transient stability margin of active distribution networks with high penetration of electric vehicles (EVs). The proposed optimization strategy intends to control EVs contributions during transient stability conditions. The EVs contributions are controlled through a new index proposed based on the system's total corrected critical kinetic energy (TCCKE). The proposed procedure for TCCKE calculation is driven by a hybrid algorithm taking into account the equal area criterion and sensitivity analysis. The suggested procedure for TCCKE only depends on the during fault data and as a result, the proposed optimization strategy is useful to prevent transient instability in the case of first swing instability. The proposed optimization is applied and evaluated on the IEEE test systems. The results clearly demonstrate the applicability and efficacy during a multitude of fault and emergency conditions.

Optimal allocation of inverter connected DGs: An objective function to minimize deterioration of transient stability of power system

While renewable energy resources have provided more flexibility in operation of power system, it may threaten the security of the power system during transient phenomena. Previous investigation on the power system with high penetration of inverter based connected (IBC) distributed generations (DG) reveal that this type of DG has negative influence on the transient stability margin of the power system (Seungchan et al., 2018). An optimization framework is proposed in this paper, in which the negative effects of IBC type of DGs on the transient stability margin of the power system is minimized. More specifically, this paper proposes a new objective function (OF) to distribute the IBC type of DGs that have minimum deterioration of transient stability margin. To such aim, an improved index based on the kinetic energy is introduced which considers IBC type of DGs based on virtual synchronous generator concept. To calculate index, equal area criterion (EAC) and sensitivity analysis are respectively used for extracted critical kinetic energy (CKE) and consequently to take into account the effect of fault trajectory. The IBC type of DGs in this investigation includes photovoltaic and electrical vehicles. The proposed framework is applied on the IEEE 14-bus and 30-bus test system and further discussed during several contingencies and fault conditions.

An enhanced approach for probabilistic evaluation of transient stability

Due to the high penetration of renewable energy resources leading to the enhancement of uncertainty, the probabilistic assessment of the transient stability has become more important than deterministic assessment. In a previous method published by the authors, an algorithm to find the probability density function of the transient stability margin of the power system was published. This present paper presents a modified algorithm to find the probability density function of critical clearing time for each generator for the whole power grid for a certain contingency and during the fault-on period. First, the critical corrected kinetic energy is calculated based on a modified sensitivity-based algorithm at each step of the simulation during the fault-on period. Since the total kinetic energy of the generators does not contribute in the critical kinetic energy of the whole system, a new criterion - based on the rate of change of kinetic energy - is utilized to classify severely disturbed generators from less disturbed generators. Utilizing critical corrected kinetic energy of the whole power grid, an index based on the critical clearing time, so-called network critical clearing time, is calculated. Eventually, the proposed algorithm is applied on the optimal placement of a superconducting magnetic energy storage unit. It is shown that utilizing the proposed objective function for locating superconducting magnetic energy storage units effectively results in the improvement of the transient stability margin of the power system.

Influence of the softening stress path on crack development around underground excavations: Insights from 2D-FDEM modelling

Core material softening method has been widely used in two-dimensional tunnel excavation simulation by the combined finite-discrete element method (FDEM). In numerical studies, softening stress paths (generally described by critical kinetic energy (CKE), softening time step (STS) and softening curve (SC)) usually have a significant influence on simulation results and computational efficiency. There is not a direct way to determine these three parameters. In the present study, a series of numerical studies by the FDEM are performed to discuss the effects of these three parameters on the simulation results and calculation efficiency in a circular tunnel excavation project with a 4 m diameter. The results show that the CKE is closely related to the model size and rock density. The CKE can be obtained from the model kinetic energy curve, and a selection method is proposed. The STS value of 50 000 steps is optimal. To obtain a uniform and stable propagation process of the surrounding rock crack, the SC should be in an exponential function. The engineering case shows that the simulation results are consistent well with the field observations as the softening stress paths are calibrated by the proposed method.

Clamped sandwich beams with thick weak cores from central impact: A theoretical study

A theoretical model is obtained to predict the dynamic response of a clamped sandwich beam with thick weak core impacted centrally by a projectile. The core is weak and thick enough that only part or all of the front face sheet and the core undergo permanent plastic deformations, while the back face sheet undergoes an elastic vibration. The core is taken to be rigid-plastic and the front face sheet is treated as an individual rigid-plastic beam resting on a foundation. The back face sheet is modeled as an Euler–Bernoulli beam. Based on the rigid-perfectly theory and Galerkin method, two types of the sandwich beam response are given, i.e., intermediate strength and low strength core type responses. The critical kinetic energy of the projectile as the back face sheet reaches its elastic limit is studied. The localized indentation and response history of the sandwich beam are presented. It is found that the dynamic response of the sandwich beam is sensitive to the core strength, mass ratio, breadth and impact velocity of the projectile. The finite element (FE) simulation is also carried out to verify the analytical predictions and a good agreement is achieved.

A Study on the Ricochet of Concrete Debris Against Soil

In this study, the impact responses of concrete debris against soil are investigated. Three types of concrete debris are shot at soil with different incident conditions in experiments. A numerical modeling for the impact process is established and calibrated by the experimental results. A further study on the effect of debris size is then carried out based on the calibrated numerical modeling. A set of formulation is presented to predict the outgoing velocity and the outgoing angle in terms of the incident velocity and the incident angle. Critical lethality curves are derived based on the assumption of a critical kinetic energy of 79 J.

Kinetic Energy Method for Predicting Initiation of Backward Erosion in Earthen Dams and Levees

Current methods to evaluate the potential risk of earthen dam and levee failures by internal erosion fail to consider appropriate failure criteria for the initiation, continuation, and progression phases and are often based on subjective assessment. Six different internal erosion failure modes may occur within a dam or levee, its abutments, or the foundation that are triggered or facilitated by different mechanisms and therefore have different failure criteria. In non-cohesive soils, suffusion, backward erosion, heave, or concentrated leak erosion (scour) are possible, although the physical mechanisms driving the failure criterion for each of these are very different. Currently, no credible failure criteria exist for evaluation of the initiation of backward erosion. This article presents derivation of a specific failure criterion for initiation of backward erosion in non-cohesive soils using the critical kinetic energy ( Ekcrit ) of initiation. Laboratory experiments conducted with different soils showed that Ekcrit is affected by the physical characteristics of the soil, effective stress conditions, and angle of the seepage path. In internally stable, non-cohesive soils (e.g., uniform medium sands) with up to 6 percent non-plastic fines, backward erosion initiated when the Ekcrit of seepage exceeded 0.075 Joules. In non-cohesive soils with 10 percent non-plastic fines, which are also prone to suffusion, the Ekcrit for backward erosion is reduced by a factor of as much as 100. Moreover, in soil with 20 percent plastic fines, initiation of backward erosion did not occur. Concentrated leak erosion along hydraulic-induced fractures was the dominant process of internal erosion in soils with plastic fines. A new backward erosion assessment methodology based on the factor of safety is proposed for initiation of backward erosion that relates the laboratory-derived Ekcrit and the anticipated maximum actual kinetic energy, as measured in the field or estimated during design. The advantage of this method is that laboratory-derived Ekcrit can take into account the natural factors that affect initiation of backward erosion. Several examples are presented to demonstrate the application of the factor of safety methodology under typical field conditions.

Completely Inelastic Collision to Confirm Maximum Punch Pressure Force of Cold Pressure Welding

The maximum punch pressure force (TMPPF) of cold welding pressure affects not only the performance of the welding bonding but also the amount of the area of welding bonding. If punch force is more bigger, it may be take place cracks, stress concentration and welding concave pits, which affect application of materials and increase incidence of faults. The process that punch pressure of cold welding pressure applied on sheet materials to attain welding bonding is simplified beam in cold pressure welding. Under normal circumstances it is an important method to TMPPF by the manner of experiment, but the method to attain TMPPF is limited. In the paper completely inelastic collision theory is applied to explain the process of cold welding pressure, the theory of completely inelastic collision offers principle theory to attain TMPPF. In this paper, two supposes are put forward, on the basis of two supposes the critical velocity is attained. At the same time, critical kinetic momentum or critical kinetic energy will be attained. On the basis of the law of conservation of energy, energy balance equation is attained, which will drop in calculating difficulty of the non-linear process of cold pressure welding and decrease calculated amount. In this paper on the basis of the process of collision all phases are analyzed. Indeed elastic-plastic deformation phase is completely inelastic collision phase, and from point of view of collision to calculate energy loss. At the same time, to suppose other plate is utter stiff can attain critical velocity, thus, to achieve the equation of TMPPF.

Reflection and Splitting of Channel-Guided Solitons in Two-Dimensional Nonlinear Schrödinger Equation

Solitons confined in a channel are studied in the two-dimensional nonlinear Schrödinger equation. When a channel branches into two channels, a soliton is split into two solitons, if the initial kinetic energy exceeds a critical value. The branching point works as a pulse splitter. If it is below the critical value, the soliton is reflected. The critical kinetic energy for splitting is evaluated by a variational method. The variational method can be applied in the design of channel systems with reduced reflection.

Size modification of Au nanoparticles induced by slow highly charged ions 40Arq+ irradiation

Abstract Size modification of Au nanoparticles (NPs), deposited on the Au-thick film surface and irradiated by slow highly charged ions (SHCI) 40Arq+ (3 ⩽ q ⩽ 12) with fixed low dose of 4.3 × 1011 ions/cm2 and various energy ranging from 74.64 to 290.64 keV at room temperature (293.15 K), was investigated by atomic force microscopy (AFM) and transmission electron microscopy (TEM). The effect of projectile kinetic energy on the modified size of NPs was explored by an appropriate choice of the fixed process parameters such as ion flux, irradiation temperature, incident angle, irradiation time, etc. The morphological changes of NPs were interpreted by models involving collisional mixing, Ostwald ripening (OR) and inverse Ostwald ripening (IOR) of spherical NPs on a substrate. A critical kinetic energy as well as a critical potential energy of the projectile in the Au NPs size modification process were observed.