Inertial Effects Research Articles

Inertial issues in renewable energy integrated systems and virtual inertia techniques

The global proliferation of renewable energy drastically altered the characteristics of power systems. Integration of clean energy sources reduces the inherent rotational inertia, making the system precarious and susceptible to various disturbances. The major challenges encountered are fast frequency fluctuations, voltage fluctuations, high rate of change of frequency (RoCoF), and frequency nadir. In order to address and adapt to a future low-inertia scenario, it is crucial to understand the effect of inertia on various parameters. This paper introduces a comprehensive review of the fundamental aspects of inertia and challenges that arise due to the reduction in inertia. Researchers have tackled this issue by employing various virtual inertia (VI) emulation techniques, which also have been extensively reviewed in the literature along with their merits, limitations, and recent developments. The impact of RES penetration on system dynamics is analyzed by simulating an IEEE-9 bus system with renewable energy source (RES) in MATLAB/Simulink. Furthermore, a three-phase fault is also introduced, to emphasize the effect of reduced inertia by observing the rotor angle and frequency deviation. The results validate that RES integration and fault location are observed to have a significant impact on stability parameters, making them extremely unstable.

Numerical simulations of the sedimentation of soft particles in confined Newtonian liquids

The gravitational sedimentation of solid particles in liquids is important in several applications, many of which involve soft particles (e.g., microplastics, microgels, and biological cells). However, there is still little knowledge on the sedimentation of deformable beads. In this work, we employ fully three-dimensional finite-element numerical simulations to investigate the sedimentation of an initially spherical elastic bead in a Newtonian liquid contained inside a square-cross section vessel. In particular, we carry out a wide parametric analysis to understand the effects of inertia, particle deformability, and geometrical confinement on the particle sedimentation dynamics and settling velocity. In addition, the sedimentation of a particle in a Newtonian liquid close to a vertical wall is studied. When the particle sediments at the center of the vessel, the settling velocity increases at increasing inertia and decreases at increasing confinement and deformability. However, at intermediate inertia, the settling velocity passes through a minimum and then rises as the particle gets softer. Correspondingly, the equilibrium deformed shape of the particle shows the appearance of a concavity at the rear. When the sedimentation occurs close to a vertical wall, the closer the particle to the solid surface, the slower its sedimentation. On the other hand, the hydrodynamic interaction between the particle and the wall makes the particle move away from the wall.

The Approximate Analysis of Higher-Order Frequencies of Nonlinear Vibrations of a Cantilever Beam With the Extended Galerkin Method

Abstract The nonlinear vibrations of elastic beams with large amplitudes are frequently treated as a typical problem of an elastica. As the continuation of the analysis of the deformation of an elastica, the nonlinear vibration equation of the elastic beam in the rotation angle of the cross section has been established. Using the deformation function, the nonlinear equation with the inertia effect has been solved by the newly proposed extended Galerkin method (EGM). The solution to the vibration problem of the elastica is compared with earlier approximate solutions including the frequencies and mode shapes obtained by other methods, and the rotation angle and energy of each mode at the high-order frequency are also calculated. This solution procedure provides an alternative technique to the elastica problem by the EGM with possible applications to other nonlinear problems in many fields of science and technology.

한국 주택가격의 동태적 변화 연구

Housing is one of the essential goods that determine the conditions of life. However, housing prices fluctuate widely depending on macroeconomic conditions, making it an important research topic. This study analyzes the dynamic changes in quarterly housing prices from 2006 to 2023, using GARCH model, Granger causality test, and vector error correction model(VECM). The main finding are as follows. First, there are inertial feedback effects in house price changes. Second, there is clustering and long-run persistence in the dynamics of house price volatility. Third, we find significant effects of housing loans on the demand side and housing construction permits and unsold housing units on the supply side on house prices. Housing loans have a positive effect in the short run, while housing supply variables such as housing construction permits and the number of unsold housing units have a negative effect in the long run. These results of our analysis suggest that the housing market follows the market principle that the role of housing supply and demand works well, and that housing prices have inertial characteristics with spikes and crashes depending on the economic environment. Housing policy-makers need to take these findings into account when formulating housing policies.

Systematic study of two proton radioactivity within the effective liquid drop model

In this study, we investigated two-proton radioactivity using the effective liquid drop model with varying mass asymmetry shapes and effective inertia coefficients (VMAS-EFF). Gaudin’s expression term for Coulomb potential energy is replaced in the current study’s calculation of potential energy. The VMAS-EFF combination predicts the half-life with the lowest standard deviation ( σ =1.03) compared to other models and previous constant mass asymmetry with Werner-inertial Wheeler’s coefficient combinations. The lowest standard deviation value indicates that the VMAS-EFF combination is suitable for reproducing the experimental data. We extended the half-life predictions to another 54 nuclei and compared them with six theoretical model predictions and two empirical formula predictions. The present work also investigated the decay possibilities using quantum tunnelling by computing the driving potential (V-Q) for various states of angular momentum l = 0, 2, 3, and 4. Found that 6Be, 6B, 8C, 12O,15,16Ne, 19Mg, 22Si, 26S, 30Ar 38,39Ti, 40V, 42Cr, 45Fe, 48,49Ni, 54Zn, 58,59,60Ge and 64Se nuclei have a high chance of emission for two protons, while 7B, 10N, 14F, 17Na, 24P, 28Cl,32K, 34Ca, 36,37Sc, 44Mn, 47Co, 52Cu, 56,57,58Ga, 61,62As nuclei have a lower chance for two proton than one proton decay. The computation of separation energy findings agree well with the driving potential findings.

An analytical investigation on nonlinear vibrations and stability of Timoshenko pipes conveying two-phase flow

The primary objective of this study is to conduct a comprehensive investigation on the nonlinear free vibration and stability analysis of the multilayer graphene reinforced pipe conveying liquid–gas two–phase flow based on the Timoshenko beam model. The Halpin–Tsai micromechanics model is employed which provides a means to evaluate and analyze the mechanical behavior and performance of the multilayer FG reinforced pipe. According to Von–Kármán strain relations and applying the Hamilton's principle, the governing equations of motion are derived. The Galerkin technique is operated to convert the partial differential equation (PDE) to the ordinary differential equation (ODE). The homotopy analysis method is employed to solve the fourth order nonlinear differential equation. Closed–form expressions for the nth nonlinear frequency and time history as well as the critical flow velocity based on the Timoshenko theory are achieved. The results demonstrate that neglecting the effects of rotary inertia and shear deformation may cause some errors by the increment of the initial amplitude. Furthermore, the critical flow velocity, depends not only on the mechanical and geometrical properties of the pipe but also on the initial mode shape excitation. The results indicate that by the increment of flow velocity, liquid density and slenderness ratio, the nonlinear frequency decreases, on the other hand, by the increment of the initial amplitude, the nonlinear frequency increases.

Two-temperature modeling of lamellar cathode arc

Abstract A three-dimensional, two-temperature (2T) model of a lamellar cathode arc is constructed, drawing upon the conservation equations for mass, momentum, electron energy, and heavy particle energy, in addition to Maxwell's equations. The model aims to elucidate how the physical properties of electrons and heavy particles affect heat transfer and fluid flow in a lamellar cathode arc. This is achieved by solving and comparing the fields of electron temperature, heavy particle temperature, fluid flow, current density, and Lorentz force distribution under varying welding currents. The results show that the guiding effect of the lamellar cathode on current density, the inertial drag effect of moving arc, and the attraction effect of Lorentz force at the lamellar cathode tip primarily govern the distribution of the arc's physical fields. The guiding effect localizes the current density to the front end of the lamellar cathode, particularly where the discharge gap is minimal. Both the inertial drag effect and the attraction effect of Lorentz force direct arc flow toward its periphery. Under the influence of the aforementioned factors, the physical fields of the lamellar cathode arc undergo expansion and shift counter to the arc's direction of motion. A reduction in welding current substantially weakens the guiding effect, causing the arc's physical fields to deviate further in the direction opposite to the arc motion. In comparison with a cylindrical cathode arc, the physical fields of the lamellar cathode arc are markedly expanded, leading to a reduction in current density, electron temperature, heavy particle temperature, cathode jet flow velocity, and Lorentz force.

Quantitative Evaluation of the Onset and Evolution for the Non‐Darcy Behavior of the Partially Filled Rough Fracture

AbstractThe non‐Darcy flow behavior in unfilled and fully filled rough fractures has been investigated thoroughly for decades. Natural fractures usually be partially filled with porous media due to long‐term internal and external dynamic disturbances and water flow erosion. However, how to evaluate the nonlinear seepage characteristics of the partially filled rough fracture (PFRF) is never scrutinized. In the present study, 2D direct numerical simulations are conducted to investigate the non‐Darcy behavior for flow through 6 PFRF models under different filling conditions (i.e., filling degree, roughness, and hydraulic conductivity capability of the filling medium), which included coupling between the free and seepage flow in the unfilled and filled region, respectively. The results show that the critical non‐Darcy factor E = 0.02 can be used to judge the onset of the non‐Darcy regime in PFRF, which is also the critical point of eddy region (ER) volume mutation. The higher the filling degree and the weaker the hydraulic conductivity of the filled medium, the more significant the non‐Darcy behavior. Furthermore, the variation of ER volume can be divided into three stages with the increasing inertia effect, that is, stable stage (E < 0.02), slow nonlinear growth stage (0.02 ≤ E ≤ 0.1), and rapid linear growth stage (E > 0.1). In addition, a new model for quantitatively evaluating the non‐Darcy behavior of PFRF is developed via gene expression programming based on 735 simulation data set, which is further employed to establish the relationship between the friction factor.

The merger of co-rotating vortices in dusty flows

We investigate the effect of particle inertia on the merger of co-rotating dusty vortex pairs at semi-dilute concentrations. In a particle-free flow, the merger is triggered once the ratio of vortex core size to vortex separation reaches a critical value. The vortex pair separation then decreases monotonically until the two cores merge together. Using Eulerian–Lagrangian simulations of co-rotating particle-laden vortices, we show substantial departure from the vortex dynamics previously established in particle-free flows. Most strikingly, we find that disperse particles with moderate inertia cause the vortex pair to push apart to a separation nearly twice as large as the initial separation. During this stage, the drag force exerted by particles ejected out of the vortex cores on the fluid results in a net repulsive force that pushes the two cores apart. Eventually, the two dusty vortices merge into a single vortex with most particles accumulating outside the core, similar to the dusty Lamb–Oseen vortex described in Shuai & Kasbaoui (J. Fluid Mech., vol 936, 2022, p. A8). For weakly inertial particles, we find that the merger dynamics follows the same mechanics as that of a single-phase flow, albeit with a density that must be adjusted to match the mixture density. For highly inertial particles, the feedback force exerted by the particles on the fluid may stretch the two cores during the merger to a point where each core splits into two, resulting in inner and outer vortex pairs. In this case, the merger occurs in two stages where the inner vortices merge first, followed by the outer ones.

Grey wolf optimizer based-natural frequency optimization of laminated composite shells carrying distributed mass

In this study, a grey wolf optimizer is proposed to find the optimum stacking sequence to maximize the fundamental frequency of shells. The vibration analysis of the shells is done using first-order shear deformation theory and a nine-node isoparametric element with five degrees of freedom per node. A mass lumping scheme with rotary inertia is considered in the finite element formulation to include the rotary inertia effect. The design variable considered is the fiber angle orientation of the shells. The present approaches are compared with previously published results using layerwise optimization theory, the Ritz method, and classical lamination theory. A comparison study is also performed, comparing the GWO-based finite element model against six different metaheuristic approaches, and it demonstrates that the Grey Wolf Optimizer consistently outperforms these competing algorithms. The optimum fiber angle orientation of shells carrying distributed mass for various boundary conditions and shell types is analyzed for the first time, to the best of the author’s knowledge. This novel discovery will benefit future studies.

Strain rate effect of concrete based on split Hopkinson pressure bar (SHPB) test

Concrete is a strain rate sensitive material, which is widely used in protective structures, and its strain rate effect needs to be considered. This study aims to obtain the real strain rate effect of concrete material. Firstly, the dynamic compression test of concrete was carried out by using split Hopkinson pressure bar (SHPB). The classical Holmquist-Johnson-Cook (HJC) model of concrete is modified based on the test results and the test data of the static performance of concrete. Then the finite element model is established. The numerical simulation results and theoretical analysis show that the inertia effect leads to the error between the test value and the simulation value. To eliminate the influence of inertia effect, this study embeds the inertia effect term into the constitutive model for secondary modification. According to the results of numerical analysis, the specific form of this term and its related parameters are determined. The modified constitutive model can better predict the test results and reproduce the damage morphology of concrete under impact load.

Variable Time-Step Physics Engine with Continuous Compliance Contact Model for Optimal Robotic Grinding Trajectory Planning.

In the transition from virtual environments to real-world applications, the role of physics engines is crucial for accurately emulating and representing systems. To address the prevalent issue of inaccurate simulations, this paper introduces a novel physics engine uniquely designed with a compliant contact model designed for robotic grinding. It features continuous and variable time-step simulations, emphasizing accurate contact force calculations during object collision. Firstly, the engine derives dynamic equations considering spring stiffness, damping coefficients, coefficients of restitution, and external forces. This facilitates the effective determination of dynamic parameters such as contact force, acceleration, velocity, and position throughout penetration processes continuously. Secondly, the approach utilizes effective inertia in developing the contact model, which is designed for multi-jointed robots through pose transformation. The proposed physics engine effectively captures energy conversion in scenarios with convex contact surface shapes through the application of spring dampers during collisions. Finally, the reliability of the contact solver in the simulation was verified through bouncing ball experiments and robotic grinding experiments under different coefficients of restitution. These experiments effectively recorded the continuous variations in parameters, such as contact force, verifying the integral stability of the system. In summary, this article advances physics engine technology beyond current geometrically constrained contact solutions, enhancing the accuracy of simulations and modeling in virtual environments. This is particularly significant in scenarios wherein there are constant changes in the outside world, such as robotic grinding tasks.

Dynamical behavior of a spinning tapered Rayleigh beam subjected to an axial load

As a first attempt, the vibration and stability analysis of a spinning tapered beam subjected to an axial load are investigated. The radius of the cross-section of the beam is assumed to vary exponentially in the longitudinal direction. The tapered beam is modeled in Rayleigh beam assumption with rotary inertia, eccentricity, and gyroscopic effects. Based on the Hamilton principle, the governing equations of motion of the spinning tapered beam with an axial force are obtained. Also, a Galerkin discretization scheme is employed to obtain the natural frequency and critical divergence rotating speeds of the system. As a result, the instability thresholds and stability evolution of the system are acquired. Furthermore, a detailed parametric study is conducted to evaluate the effects of the slenderness ratio, taper parameter, axial load, and eccentricity ratio on the dynamical behavior of the system. The results show that the natural frequency and critical divergence rotating speed of the tapered beam are larger than those of the circular-section beam. In addition, the axial load, taper parameter, and eccentricity are the key factors that influence the stability of the system.

When an active bath behaves as an equilibrium one.

Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity v_{0}. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as ∼v_{0}^{α} with 1<α<2. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior.

Magnetization spiral structure and high domain wall velocity induced by inertial effect

In ultrafast magnetism, i.e., the short time scales such as picosecond and femtosecond, we report that the spiral structure of magnetization can be formed by the inertial effect. Comparing with the case of fast magnetism in nanosecond time scale, we can obtain a higher velocity of domain wall in ultrafast magnetism due to the driving of inertial moment. There is a critical value τc of angular momentum relaxation time τ for the inertial breakdown in uniaxial ferromagnet. Under the action of the inertial effect the domain wall width shows the characteristics of increases firstly as τ<τc, and then decreasing as τ>τc. It directly leads to the positive or negative mobility for the domain wall velocity as the inertia is less than or exceeds the critical value, respectively. In the high frequency mode (i.e., high field mode), we obtain the limit domain wall velocity, i.e., V→1/ατ. The smaller the inertia or damping, the faster the domain wall moves. For the case of biaxial anisotropic ferromagnets, the domain wall width and velocity decreases with the increasing inertia term, respectively. In the presence of inertia effect, there is an another critical magnetic field hc. The domain wall width decreases with the increase of the magnetic field as h<hc, while increases as h>hc. However, the domain wall velocity shows a nearly linear increase with the magnetic field. These results indicate that the ultrafast magnetism has more advantages than fast magnetism. It also provides a good control technique for rapid information processing in the future.

The influence of turbulence and inertia in radial fracture flow

Industrial applications of flow through fractures such as geothermal energy or hydraulic stimulation involve forcing large flow rates through small fractures, thereby inducing inertial fluid behaviours and turbulence. The most common fracture flow model, Poiseuille flow (the cubic law), is incapable of capturing these phenomena and thus the impact of inertial and turbulent forces in fracture flow has remained relatively unexplored. The GG22 flow model is a newly derived fracture flow model that is capable of capturing inertial, transient and turbulent forces. In this article, we apply the GG22 flow model to hydraulic stimulation of radial fractures for the first time to determine how these phenomena manifest. We show that inertia and turbulence only manifest near the wellbore (within 30 radii) and lead to changes in fracture shape and injection pressure but have little impact on tip behaviour. Turbulence increases wellbore pressure and aperture while inertia decreases wellbore pressure and aperture. The majority of the pressure loss along the fracture occurs near the wellbore and is captured by turbulence where entrance correction factors would otherwise be needed. Using water, turbulence is the dominant mechanism that causes departures from Poiseuille flow at high $Re$ . The solution departs immediately upon the manifestation of turbulence ( $Re\geq 2\times 10^3$ ), while inertial effects manifest at higher flow rates ( $Re\geq 2\times 10^4$ ). Using slickwater, the opposite trend is observed: inertial effects manifest first ( $Re\geq 5\times 10^3$ ), while turbulent effects are delayed ( $Re\geq 10^4$ ). In both cases, the threshold for departures from the Poiseuille flow solution are low and the differences are large.

Defect turbulence in a dense suspension of polar, active swimmers.

We study the effects of inertia in dense suspensions of polar swimmers. The hydrodynamic velocity field and the polar order parameter field describe the dynamics of the suspension. We show that a dimensionless parameter R (ratio of the swimmer self-advection speed to the active stress invasion speed [Phys. Rev. X 11, 031063 (2021)2160-330810.1103/PhysRevX.11.031063]) controls the stability of an ordered swimmer suspension. For R smaller than a threshold R_{1}, perturbations grow at a rate proportional to their wave number q. Beyond R_{1} we show that the growth rate is O(q^{2}) until a second threshold R=R_{2} is reached. The suspension is stable for R>R_{2}. We perform direct numerical simulations to characterize the steady-state properties and observe defect turbulence for R<R_{2}. An investigation of the spatial organization of defects unravels a hidden transition: for small R≈0 defects are uniformly distributed and cluster as R→R_{1}. Beyond R_{1}, clustering saturates and defects are arranged in nearly stringlike structures.

Excitation of nonlinear longitudinal structures in spin‐1/2 quantum plasma in the presence of ion beam

AbstractThe formation of longitudinal, nonlinear structures in an interacting ion beam, spin‐1/2 quantum, electron‐ion plasma is reported by employing a separate spin evolution quantum hydrodynamic model (SSE‐QHD). The reductive perturbation method is followed to develop the KdV equations. In the presence of an ion beam and keeping the finite electron inertial effects, ion acoustic (IA) soliton and spin electron acoustic (SEA) soliton are found. The critical values of beam speed and spin polarization, required for the existence of solitary structures, are highlighted. It is prescribed that the present model supports rarefactive and compressive SEA soliton and compressive IA soliton. It is shown that the ion beam is essential for the existence of a compressive SEA solitary structure. We have also calculated and compared the energy densities of both solitons. Furthermore, the dependence of the nonlinear structures on the beam parameters and spin polarization are also examined. Our findings would be useful to understand the new spin‐dependent nonlinear structures as well as the features of nonlinear IA waves in ion beam–plasma interactions.

Efficient calculation of higher order time history response derivatives by substructuring method

Time history response derivatives with respect to the design variables are frequently used in optimization design, damage detection, structural control, etc. This paper proposes a substructuring method for efficient calculation of higher order time history response derivatives of large-scale structures. First, the global structure is disassembled into several small substructures and the substructural displacement is projected onto the range space of a few substructural master eigenvectors. Afterwards, the derivative of substructural master eigenvectors of a few substructures containing the design variables are assembled to form the reduced first, second, and higher order sensitivity equations with a size of the number of master eigenvectors. The equivalent eigenvector which relates the slave and master eigenvectors is derived to compensate for the inertial effect of discarded slave eigenvectors. Finally, the first, second, and higher order time history response derivatives of global large-scale structure are efficiently solved from the reduced sensitivity equations by using Newmark- β method. A numerical one-bay plane frame and a numerical highway bridge are applied to verify the accuracy and efficiency of proposed substructuring method.

Influence of Non-Parallelism on the Micro-Interface Lubrication Mechanism of Water-Lubricated Bearings

Water-lubricated bearings can effectively solve the pollution problem caused by lubricant leakage and are used in offshore engineering equipment for this reason. Aiming at the problems of unclear and undefined micro-interface lubrication mechanisms of water-lubricated bearings, this paper investigates the influence of non-parallel micro-cavities on the micro-interface lubrication mechanism of bearings. Based on a single micro-cavity model, the lubrication mechanism of micro-cavities is studied in this paper. Lubrication models of the non-parallel contact friction pairs model are built, and the effect of the non-parallelism on the lubrication performance of the micro-cavities is obtained using the computational fluid dynamics method. The results show that, under the same Reynolds number and cavitation pressure, the wedge effect caused by the non-parallelism causes the pressure at the inlet to rise, thus increasing the load-carrying capacity. The existence of non-parallelism limits the rise of the high pressure of the inertia effect on the micro-cavities and reduces the load-carrying capacity. The presence of non-parallelism decreases the area of the negative pressure proportion and increases the proportion of the positive pressure zone inside the micro-cavities, thus increasing the load-carrying capacity.