Instantaneous Kinetic Energy Research Articles

Discussion on “ Characteristics of the Instantaneous Kinetic Energy and Agitating intensity Index for the Bath Flow Under Various Bottom Regiment Configurations” Published in the Transactions of IIM, 2024, pp. 2073–2081

Discussion on “ Characteristics of the Instantaneous Kinetic Energy and Agitating intensity Index for the Bath Flow Under Various Bottom Regiment Configurations” Published in the Transactions of IIM, 2024, pp. 2073–2081

From Newton's First Law to the Motion of Celestial Bodies

Newton's original work "Principles" was written in Latin. An English version translated two years after his death changed the first law from "in directum" to "in a right line." Later generations think that only static or uniform straight line motion is inertia, while excluding rotational motion. This article proposes that the gravitational potential energy of a planet's revolution is equal to its centrifugal kinetic energy (mυ2). The work done by an object is a process quantity, but kinetic energy is a state variable that can be divided into instantaneous kinetic energy and average kinetic energy. Uniform motion does not do work, and instantaneous kinetic energy in variable speed motion does not also do work, only the average kinetic energy of variable speed motion does work. Only the energy between work and the average kinetic energy of variable speed motion can be converted into each other. We have clarified the relationship between work and kinetic energy, completed the transition of the kinetic energy formula at low and high speeds, achieved the unification of the kinetic energy formula and the mass energy relationship formula, and explained the √2 factor in the escape velocity..

Research on key factors of pulsed CO2 laser annealing of Ge core fiber

The germanium (Ge) core fiber with a core diameter of 29–32 μm and a cladding diameter of 158–162 μm was annealed by pulsed CO2 laser, exploring the key factors determining the properties of annealed Ge core fiber. The experimental results shown that the single pulse energy and the laser scanning speed are key factors of pulsed CO2 laser annealing of Ge core fibers. The reasons for experimental results were preliminarily analyzed from the perspectives of Ge atomic instantaneous kinetic energy and temperature field of Ge core during annealing. For different frequencies of laser annealing, optimal samples with similar properties can be obtained by adjusting the single pulse energy and laser scanning speed. For the samples annealed by 30 kHz, 50 kHz, 60 kHz, and 70 kHz lasers, the optimal Raman frequency average value is 301.191 cm−1, 301.107 cm−1, 301.153 cm−1, and 301.174 cm−1; the lowest propagation loss is 2.174 dB/cm, 2.596 dB/cm, 2.387 dB/cm, and 2.312 dB/cm respectively, which were measured using a quantum cascade laser with the wavelength range from 4.7 to 4.9 μm.

Characteristics of the Instantaneous Kinetic Energy and Agitating Intensity Index for the Bath Flow under Various Bottom Regiment Configurations

Characteristics of the Instantaneous Kinetic Energy and Agitating Intensity Index for the Bath Flow under Various Bottom Regiment Configurations

Dynamics of run‐off hydraulic characteristics during gully headcut erosion driven by head height

AbstractIn the granitic red soil hills region of South China, gully headcut erosion is considered one of the main processes in the development of gullies. However, the dynamics of run‐off hydraulic characteristics such as hydrodynamics and energy consumption during erosion have not been clarified. We investigated the effects of five headcut heights (25 to 125 cm) on hydrodynamic and energy consumption characteristics using field in situ water discharge scouring experiments. The results demonstrated that the flow velocity (V), Froude number (Fr), Reynolds number (Re), run‐off shear (τ) and run‐off power (ω) all indicate the upstream area (UA) > gully bed (GB). Except for V and Fr, several other hydraulic parameters exhibited a trend of sandy soil layer > red soil layer, and a fluctuating increase with increasing headcut height was observed in the GB. The jet velocity at the edge of the headcut (Vb), jet shear stress (τj), potential energy conversion (∆EP) and bottoming instantaneous kinetic energy (EKbottom) all increased exponentially with increasing headcut height by factors of 1.10 to 1.37, 1.16 to 2.00, 1.07 to 2.06 and 1.22 to 1.86, respectively. Except for ∆EP, all others performed a trend of sandy soil layer > red soil layer. The energy consumption at the gully head (∆EH) and its contribution tended to significantly increase with increasing headcut height, and the ∆EH of sandy soil layer was 13.20% to 49.89% higher than that of red soil layer. When the headcut height was greater than 100 cm, the contribution of energy consumption exceeded 50%. In addition, the sediment deposition process throughout the system was significantly influenced by the hydraulic and jet characteristics, and energy consumption was positively correlated with soil loss. The study results contribute to a profound understanding of gully headcut erosion and its hydrodynamic mechanisms.

Transfer mechanism and criteria for static–dynamic failure of granite under true triaxial unloading test

In the construction procedure of infrastructure, the excavation disturbance significantly changes the initial stress state of rocks in deep geotechnical engineering, and a rock burst would occur accompanied by the ejection of rock block. In the present study, a true triaxial unloading test and its corresponding numerical analysis based on the three-dimensional particle flow code (PFC3D) are conducted on granite specimens to acquire characteristic information of static and dynamic failure during unloading and to explore the criteria for determining static and dynamic failure. The results indicate that the failure modes of granite under true triaxial unloading can be classified into three categories: ① no obvious coalesced crack, ② a main coalescence shear crack, and ③ a main coalescence shear crack with a V-shaped pit. The instantaneous kinetic energy in static failure is characterized by a sharp increase and sporadic sharp increases, while that in dynamic failure shows a sharp increase, a short quiet period, and a substantial increase. The critical stress combination for the transformation of static–dynamic failure of granite is proposed, which is consistent with the experimental results. The number of shear cracks gradually increases in static failure, while it suddenly increases in dynamic failure. During the transformation from static failure to dynamic failure, the ratio of a tensile crack number to that of shear crack number decreases. The proportion of shear cracks in particle bonding increases, while the trend of tensile failure weakens. However, tensile failure remains predominant in granite, accompanied by shear failure.

Inferring turbulent environments via machine learning.

The problem of classifying turbulent environments from partial observation is key for some theoretical and applied fields, from engineering to earth observation and astrophysics, e.g., to precondition searching of optimal control policies in different turbulent backgrounds, to predict the probability of rare events and/or to infer physical parameters labeling different turbulent setups. To achieve such goal one can use different tools depending on the system's knowledge and on the quality and quantity of the accessible data. In this context, we assume to work in a model-free setup completely blind to all dynamical laws, but with a large quantity of (good quality) data for training. As a prototype of complex flows with different attractors, and different multi-scale statistical properties we selected 10 turbulent 'ensembles' by changing the rotation frequency of the frame of reference of the 3d domain and we suppose to have access to a set of partial observations limited to the instantaneous kinetic energy distribution in a 2d plane, as it is often the case in geophysics and astrophysics. We compare results obtained by a machine learning (ML) approach consisting of a state-of-the-art deep convolutional neural network (DCNN) against Bayesian inference which exploits the information on velocity and entropy moments. First, we discuss the supremacy of the ML approach, presenting also results at changing the number of training data and of the hyper-parameters. Second, we present an ablation study on the input data aimed to perform a ranking on the importance of the flow features used by the DCNN, helping to identify the main physical contents used by the classifier. Finally, we discuss the main limitations of such data-driven methods and potential interesting applications.

The Impact of Non-constant Inertia and Nonlinear Damping on the Torsional Vibration Characteristics of Internal Combustion Engine Including External Forces

Failures of the crankshaft-slider mechanism are the most reasons that affect the durability and operational reliability of the internal combustion engine. An accurate and sophisticated nonlinear dynamic model overcomes the obvious simulation errors of linearized models. The present work studies the effect of the non-conservative forces and nonlinear damping on the torsional vibration of single-cylinder internal combustion engines. Comprehensive dynamic modeling based on a developed expression for the instantaneous kinetic energy of the reciprocating parts and a general model of the overall kinetic energy of the system in terms of the inertia parameters were derived. The effect of variable inertia and nonlinear damping on the damped forced response of slider-crank assembly of the engine was investigated using the numerical integration method. The numerical results show that the phenomenon of secondary rolling excitation torque is well activated and gives arises to variation of frequencies and their corresponding amplitudes. Also, the amplitude of the external excitation torque is strengthened by the secondary excitation inertia torque and introduces multi resonance amplitudes phenomenon and widening the critical range of engine speed which results in producing of dangerous vibrational stress amplitudes. Also, the damped forced results indicate that the presents of damping lead to a vital reduction in the amplitude of torsional displacement and excitation torques. The present work aims to enhance nonlinear dynamic modeling and introduces more reliable design for reciprocating engine crankshaft assembly.

Experimental Study on Rockfall Mechanism of Platy Rock on a Complex Slope

The rock fall trajectory and its mechanisms are the most difficult to predict, owing to the complexity of the slope and the Irregular shape of falling rocks. To acquire a better knowledge of the rock fall mechanism of platy rock and to investigate the influence of various impact parameters, a comprehensive physical model experimental study was undertaken based on 3D printing technology using a high-speed camera and specially developed block release system. Based on the experimental results, the effects of the slope angle on the stopping position, the instantaneous kinetic energy and collision position of platy rock block were analyzed. Meanwhile, the effects of movement forms of platy rock before and after collision on the normal coefficient of restitution and the tangent coefficient of restitution were discussed. It is observed that rock fall trajectory depends not only on slope material characteristics, slope angle but also on factors related to the platy block (weight, size and shape). The experimental results showed the value of restitution coefficient exceeding 1 has an important relation with the combination of various movement forms (including the flip motion) and the change of movement forms of platy rock before and after the collision. A new feasible experimental method for research and prevention of rock fall disaster was put forward. It would be important and helpful to the geo-hazard control work.

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

The quantitative measure of dissipative properties of different numerical schemes is crucial to computational methods in the field of aerospace applications. Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme with three different slope limiters: one second-order and two third-order used within the framework of Implicit Large Eddy Simulations (ILES). The performance of the dynamic Smagorinsky subgrid-scale model used in the classical Large Eddy Simulation (LES) approach is examined. The assessment of these schemes is of significant importance to understand the numerical dissipation that could affect the accuracy of the numerical solution. A modified equation analysis has been employed to the convective term of the fully-compressible Navier–Stokes equations to formulate an analytical expression of truncation error for the second-order upwind scheme. The contribution of second-order partial derivatives in the expression of truncation error showed that the effect of this numerical error could not be neglected compared to the total kinetic energy dissipation rate. Transitions from laminar to turbulent flow are visualized considering the inviscid Taylor–Green Vortex (TGV) test-case. The evolution in time of volumetrically-averaged kinetic energy and kinetic energy dissipation rate have been monitored for all numerical schemes and all grid levels. The dissipation mechanism has been compared to Direct Numerical Simulation (DNS) data found in the literature at different Reynolds numbers. We found that the resolving power and the symmetry breaking property are enhanced with finer grid resolutions. The production of vorticity has been observed in terms of enstrophy and effective viscosity. The instantaneous kinetic energy spectrum has been computed using a three-dimensional Fast Fourier Transform (FFT). All combinations of numerical methods produce a k − 4 spectrum at t * = 4 , and near the dissipation peak, all methods were capable of predicting the k − 5 / 3 slope accurately when refining the mesh.

Mulching effects on erosion from steep slopes and sediment particle size distributions of gully colluvial deposits

Mulching is an effective soil conservation practice for permanent gullies in southern China. Knowledge of the sediment characteristics that occur in mulched soils of colluvial deposits could improve the utility of mulching for soil conservation. A rainfall simulation experiment was designed to evaluate the effects of mulch on the runoff, erosion, and particle size distribution of eroded sediments. Straw mulch coverage of 0, 25, 50, 75, and 95% was tested with simulated rainfall. The effective particle size distribution of the sediment was compared with the ultimate particle size distribution to investigate the detachment and transport mechanisms involved in sediment mobilization. Mulching delayed the runoff initiation time and reduced the average runoff rate. Compared with bare soil, the increased mulch coverage decreased the soil loss rate by 13.0 to 90.3%. Moreover, the peak sediment concentration decreased from 80 to 200gL−1 under the different mulch coverage conditions. The optimal straw application rate was 1.5 to 3.0Mgha−1 in the permanent gully's deposits. The relationship between instantaneous kinetic energy of rainfall and the proportion of effective clay- and sand-sized particles was well represented using an exponential equation. The effective clay-sized sediments under the different mulch coverage conditions were 2 to 4 times more common than those of the original soil, although there were only 13.9% sand-sized particles in the sediment when the mulch coverage was 95%. The silt-sized sediment was transported as primary particles under the different mulch coverage conditions. The effective to ultimate ratio of silt-sized particles fluctuated around 1. There were depletions of clay and silt in the colluvial deposit soil with mulch cover, and the enrichment ratios of clay and silt were larger than 1 while most of the enrichment ratios for sand were <1.

On the Averaging of Equations of Change for Mass, Species Mass, Momentum and Energy – One-Dimensional Pipe Flows

The single-phase and multiphase Eulerian equations of change are derived by applying a suitable averaging procedure to the local instantaneous equations of change. In the present work, the local instantaneous equations of change for mass, species mass, momentum and energy are gross-scale averaged over the cross-sectional area. In particular, the internal energy equation is achieved by subtracting the kinetic energy equation from the total energy balance. Thus, two paths are to our disposal for deriving the cross-sectional averaged internal energy balance: (i) the averaged kinetic energy equation is subtracted from the averaged total energy equation, or (ii) the local instantaneous kinetic energy equation is subtracted from the local instantaneous energy equation and the resulting equation is averaged. The resulting Euler equations of change for internal energy are not identical for these two approaches. Approach (ii) is recommended because of its simplicity.

Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel

This paper analyses the turbulent kinetic energy budget for bubble swarms in a turbulent channel flow configuration with realistic density difference. The data employed result from Euler–Lagrange Direct Numerical Simulations of vertical turbulent channel flow laden with finite-size bubbles and enable the individual evaluation of each term of the budget equation. Two monodisperse swarms are addressed with the same bubble diameter but with different total void fraction. For the parameter range investigated bubbles enhance the liquid turbulence, and this is quantified in the terms of the budget. The turbulence enhancement is generated by the interfacial term which is balanced by the dissipation term in the core region. In the near-wall region, also the production term and the transport term contribute to the budget in a significant manner. Furthermore, the local turbulence modification induced by the bubbles is investigated by means of the transport equation of the local instantaneous kinetic energy and its contributions. Finally, existing closures for the modelling of the interfacial term are assessed and an improvement of these closures is proposed. The data provided may constitute a reference for model development in the framework of Euler–Euler approaches to bubbly flows.

Local and instantaneous turbulence modification induced by small spherical bubbles

AbstractThe paper provides insight into the local and instantaneous turbulence modification induced by small spherical bubbles in an upward directed turbulent channel flow. This is accomplished by analyzing each term of the transport equation of the local and instantaneous kinetic energy for bubbly flows and dedicated flow visualizations are provided to address the mechanisms involved in the turbulence modification. (© 2015 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Approach to theoretical estimation of the activation energy of particle aggregation taking ionic nonclassic polarization into account

The activation energy of particle aggregation in suspensions is a very important kinetic parameter in a wide range of science and engineering applications. At present, however, there is no theory that can theoretically predict the activation energy. Because the activation energy is often less than 10 kT (where k is the Boltzmann constant and T is the temperature), it is difficult to experimentally measure. In this study, a theory for calculating the activation energy is established. Experimental measurements of the activation energy of montmorillonite aggregation were performed with different electrolyte and particle concentrations using the dynamic light scattering (DLS) technique. The validity of the theory was verified by the experiments. This study confirmed that both the method for activation energy measurements by DLS and the theory for its calculation can be applied to suspensions of polydisperse nonspherical particles. The average kinetic energy at the moment of particle collision in the aggregation process was found to be 0.2 kT, which is less than the instantaneous kinetic energy of a Brownian particle (0.5 kT) because of the viscous resistance of the water medium. This study also shows that adsorbed Na+ is strongly polarized in the electric field near the particle surface, and the polarization increases the effective charge of Na+ from +1 to +1.18.

Non-linear torsional vibration characteristics of an internal combustion engine crankshaft assembly

Crankshaft assembly failure is one of the main factors that affects the reliability and service life of engines. The linear lumped mass method, which has been universally applied to the dynamic modeling of engine crankshaft assembly, reveals obvious simulation errors. The nonlinear dynamic characteristics of a crankshaft assembly are instructionally significant to the improvement of modeling correctness. In this paper, a general expression for the non-constant inertia of a crankshaft assembly is derived based on the instantaneous kinetic energy equivalence method. The nonlinear dynamic equations of a multi-cylinder crankshaft assembly are established using the Lagrange rule considering nonlinear factors such as the non-constant inertia of reciprocating components and the structural damping of shaft segments. The natural frequency and mode shapes of a crankshaft assembly are investigated employing the eigenvector method. The forced vibration response of a diesel engine crankshaft assembly taking into account the non-constant inertia is studied using the numerical integral method. The simulation results are compared with a lumped mass model and a detailed model using the system matrix method. Results of non-linear torsional vibration analysis indicate that the additional excitation torque created by non-constant inertia activates the 2nd order rolling vibration, and the additional damping torque resulting from the non-constant inertia is the main nonlinear factor. The increased torsional angular displacement evoked by the high order excitation torque relates to the non-constant inertia. This research project is aimed at improving nonlinear dynamics theory, and the confirmed nonlinear parameters can be used for the structure design of a crankshaft assembly.

Investigation of dissipation elements in a fully developed turbulent channel flow by tomographic particle-image velocimetry

A new method to describe statistical information from passive scalar fields has been proposed by Wang and Peters [“The length-scale distribution function of the distance between extremal points in passive scalar turbulence,” J. Fluid Mech. 554, 457 (2006)]. They used direct numerical simulations (DNS) of homogeneous shear flow to introduce the innovative concept. This novel method determines the local minimum and maximum points of the fluctuating scalar field via gradient trajectories, starting from every grid point in the direction of the steepest ascending and descending scalar gradients. Relying on gradient trajectories, a dissipation element is defined as the region of all the grid points, the trajectories of which share the same pair of maximum and minimum points. The procedure has also been successfully applied to various DNS fields of homogeneous shear turbulence using the three velocity components and the kinetic energy as scalar fields [L. Wang and N. Peters, “Length-scale distribution functions and conditional means for various fields in turbulence,” J. Fluid Mech. 608, 113 (2008)]. In this spirit, dissipation elements are, for the first time, determined from experimental data of a fully developed turbulent channel flow. The dissipation elements are deduced from the gradients of the instantaneous fluctuation of the three velocity components u′, v′, and w′ and the instantaneous kinetic energy k′, respectively. The measurements are conducted at a Reynolds number of 1.7×104 based on the channel half-height δ and the bulk velocity U. The required three-dimensional velocity data are obtained investigating a 17.75×17.75×6 mm3 (0.355δ×0.355δ×0.12δ) test volume using tomographic particle-image velocimetry. Detection and analysis of dissipation elements from the experimental velocity data are discussed in detail. The statistical results are compared to the DNS data from Wang and Peters [“The length-scale distribution function of the distance between extremal points in passive scalar turbulence,” J. Fluid Mech. 554, 457 (2006); “Length-scale distribution functions and conditional means for various fields in turbulence,” J. Fluid Mech. 608, 113 (2008)]. Similar characteristics have been found especially for the pdf’s of the large dissipation element length regarding the exponential decay. In agreement with the DNS results, over 99% of the experimental dissipation elements possess a length that is smaller than three times the average element length.

Doppler widths in electron quasielastic scattering from molecular gases

Recent quasielastic electron scattering experiments on some molecular gases at E(e) > or = 1.8 keV have shown that the scattering is from single isotopes of the atomic components of the gas. The scattered electron lines at definite angles are Doppler broadened by the instantaneous kinetic energy (KE) of the scattering atoms. We calculated the KE of the scattering atoms by accounting for translation, rotation, and all normal modes of vibrations of the molecule. The results reveal some large and fundamental differences from literature estimates.

Normalized kinetic energy as a hydrodynamical global quantity for inhomogeneous anisotropic turbulence

We introduce a hydrodynamical global quantity δ that characterizes turbulent fluctuations in inhomogeneous anisotropic flows. This time dependent quantity is constructed as the ratio of the instantaneous kinetic energy of the flow to the kinetic energy of the time-averaged flow. Such a normalization based on the dynamics of the flow makes this quantity comparable from one turbulent flow to any other. We show that δ(t) provides a useful quantitative characterization of any turbulent flow through generally only two parameters, its time average δ¯ and its variance δ2. These two quantities present topological and thermodynamical properties since they are connected, respectively, to the distance between the instantaneous and the time-averaged flow and to the number of degrees of freedom of the flow. Properties of δ¯ and δ2 are experimentally studied in the typical case of the von Kármán flow and used to characterize the scale by scale energy budget as a function of the forcing mode as well as the transition between two flow topologies.

Second-generation wave-function thermostat forab initiomolecular dynamics

A rigorous two-thermostat formulation for ab-initio molecular dynamics using the fictitious Lagrangian approach is presented. It integrates the concepts of mass renormalization and temperature control for the wave functions. The new thermostat adapts to the instantaneous kinetic energy of the nuclei and thus minimizes its influence on the dynamics. Deviations from the canonical ensemble, which are possible in the previous two-thermostat formulation, are avoided. The method uses a model for the effective mass of the wave functions, which is open to systematic improvement.