Increase In Relative Velocity Research Articles

Orbital Stability Study of the Taiji Space Gravitational Wave Detector

Space-based gravitational wave detection is extremely sensitive to disturbances. The Keplerian configuration cannot accurately reflect the variations in spacecraft configuration. Planetary gravitational disturbances are one of the main sources. Numerical simulation is an effective method to investigate the impact of perturbation on spacecraft orbits. This study shows that, in the context of the Taiji project, Earth’s gravity is an essential factor in the change in heliocentric formation configuration, contributing to the relative acceleration between spacecrafts in the order of O(10−6)m·s−2. Considering 00:00:00 on 27 October 2032 as the initial orbiting moment, under the influence of Earth’s gravitational perturbation, the maximum relative change in armlengths and variation rates of armlengths for Taiji is 1.6×105km, 32m·s−1, respectively, compared with the unperturbed Keplerian orbit. Additionally, by considering the gravitational perturbations of Venus and Jupiter, the armlength and relative velocity for Taiji are reduced by 16.01% and 17.45%, respectively, compared with when only considering that of Earth. The maximum amplitude of the formation motion indicator changes with the orbit entry time. Results show that the relative velocity increase between the spacecrafts is minimal when the initial orbital moment occurs in July. Moreover, the numerical simulation results are inconsistent when using different ephemerides. The differences between ephemerides DE440 and DE430 are smaller than those between DE440 and DE421.

Velocity dependence of barrel friction

A tribological model is presented that provides a correlation between bullet velocity and friction force in firearms. The model is based on the observation that higher velocities result in lower friction and assumes that the surfaces of the bullet and barrel consist of elastic asperities. The model predicts that as the relative velocity increases, the asperities are less likely to return to their neutral positions. The model was tested using experimental muzzle velocity and gas pressure measurements for caliber 5.56 × 45 bullets and the results were in good agreement with the model predictions. The coefficient of friction obtained with the model is also in line with literature values for very low sliding velocities.

Buoyancy-driven bubbly flows: scaling of velocities in bubble columns operated in the heterogeneous regime

The hydrodynamics of bubble columns in the heterogeneous regime is revisited. Focusing on air–water systems at large aspect ratio, we show from dimensional analysis that buoyancy equilibrates inertia, and that velocities scale as $(gD\varepsilon )^{1/2}$ , where $D$ is the bubble column diameter, $\varepsilon$ the void fraction and $g$ the gravitational acceleration. From new experiments in a $0.4$ m diameter column with ${{O}}(10^3)$ particle Reynolds number bubbles and from a detailed analysis of published data, we confirm the self-organization prevailing in the heterogeneous regime, and that the liquid flow rate is only set by the column diameter $D$ . Besides, direct liquid and gas velocity measurements demonstrate that the relative velocity increases above the terminal velocity $U_T$ in the heterogeneous regime, and that it tends to ${\sim }2.4 U_T$ at very large gas superficial velocities $V_{sg}$ . The proposed velocity scaling is shown to hold for liquid and gas mean velocities and for their standard deviations. Furthermore, it is found to be valid over a wide range of conditions, corresponding to Froude numbers $Fr=V_{sg}/(gD)^{1/2}$ from 0.02 to 0.5. Then, the relevance of this scaling for coalescing media is discussed. Moreover, following the successful prediction of the void fraction with a Zuber & Findlay approach at the beginning of the heterogeneous regime, we show how the void fraction is correlated with $Fr$ . Further investigations are finally suggested to connect the increase in relative velocity with meso-scale structures known to exist in the heterogeneous regime.

Study on flow characteristics of bidirectional sinusoidal liquid pulsed gas-liquid-solid multiphase fluidized bed

Gas-liquid-solid three-phase fluidized bed has been widely used in chemical, biotechnology and environmental industries for its advantages of large inter-phase contact area, high heat/mass transfer efficiency and intense reaction process. In this work, the bidirectional sinusoidal liquid pulsed GLS fluidized bed was proposed to improve the interphase relative velocity and reaction efficiency. The effects of particle properties and pulsed liquid amplitude/frequency on the flow characteristics were studied by numerical simulations and experiments. In a complete circulation period, the average axial solids holdup is larger near the middle region of the fluidized bed and gradually decreases along the upper and lower inlets. With the increase of pulsation amplitude or period, the axial average gas holdup distribution uniformity and the liquid-solid relative velocity increase significantly. Compared with the conventional upward gas-liquid-solid fluidized bed, the bidirectional fluidized bed can further improve the liquid-solid relative velocity and reaction efficiency. The obtained studies have important implications for better design, scale-up and operation of gas-liquid-solid multiphase fluidization systems.

DEM simulations of spherical particle–particle collisions

AbstractThe randomness, diversity, and complexity of the high‐speed particle crushing process bring great difficulties to the theoretical analysis of powder engineering. In this paper, the discrete element method is used to simulate the collision of spherical particles, which provides a reference for studying the process and mechanism of crushing between particles under impact load. The Hertz–Mindlin with bonded contact model is used as the particle–particle contact model. The central collisions of particles with different diameter ratios under different high‐speed motions and the eccentric collisions with different eccentricities are discussed. The results show that the bond damage increases with the increase of relative velocity in both centre impact and eccentric impact. In centre collisions, particles of smaller objects are more fragmented than particles of larger objects. For smaller target particles, the larger the diameter ratio is, the more particle elements are detached from the target particles, and the greater the bond breakage rate. For larger target particles, the larger the diameter ratio is, the less the particle element falls off and the smaller the bond breakage rate. This provides guidance for the collision and crushing of particles with different particle size ratios and different eccentricities during high‐speed motion in engineering applications in the future.

Impact mechanism of gas temperature in metal powder production via gas atomization* *Project supported by the Open Fund of State Key Laboratory of Advanced Forming Technology and Equipment (Grant No. SKL2019006) and the National Natural Science Foundation of China (Grant No. 51975240).

This paper aims at studying the influence mechanism of gas temperatures (300 K, 400 K, 500 K, and 600 K) on gas atomization by simulating the integral atomization process of the close-coupled nozzle in vacuum induction gas atomization (VIGA). The primary atomization is simulated by the volume of fluid (VOF) approach, and the second atomization is studied by the discrete phase model (DPM) combined with the instability breakage model. The results show that, at an increased gas temperature, the influences of gas–liquid contact angle and gas temperature in the recirculation zone on the primary atomization are virtually negligible. However, increasing the gas temperature will increase the gas–liquid relative velocity near the recirculation zone and decrease the melt film thickness, which are the main reasons for the reduced mass median diameter (MMD, d 50) of primary atomized droplets. During the secondary atomization, increasing the gas temperature from 300 K to 600 K results in an increase in the droplet dispersion angle, which is beneficial to the formation of spherical metal powder. In addition, increasing the gas temperature, the positive effect of gas–liquid relative velocity increase on droplets refinement overweighs the negative influence of the GMR decrease, resulting in the reduced MMD and diameter distribution interval. From the analysis of the atomization mechanism, the increase in atomization efficiency caused by increasing the temperature of the atomizing gas, including primary atomization and secondary atomization, is mainly due to the increase in the gas drag force difference between the inner and outer sides of the annular liquid film.

Numerical Simulation of Liquid Droplet Coalescence and Breakup

Abstract This paper studied the evolution of binary droplet collision in liquid and also a mathematical calculation method of coalescence time. Binary droplet collisions occur in many engineering applications; however, the accurate models to predict the collision of droplets in the liquid are still lacking. In this work, the binary collision processes of droplets were simulated through computational fluid dynamic (CFD) method, where the interfaces between the two phases were tracked by the volume of fluid (VOF) approach. The results reveal that Weber number determines the results of the head-on collisions, and the cases with the same Weber number present similar evolution processes. If coalescence happens, the collision time decreases with increase in relative velocity, whereas the shape recovery time is independent with the relative velocity, but depends on droplet diameter. It is derived from this research that the collision time is proportional to the droplet diameter, and the shape recovery time is proportional to the 3/2 power of droplet diameter. The droplet moving directions play an important role in the collision results, and the case of two droplets moving toward each other with equal velocity is the easiest way to coalesce. When two droplets with different sizes collide, besides relative velocity, the coalescence and breakup are determined by the absolute velocities, the size, and size ratio of the two droplets. The increase in viscosity of continuous phase results an increase in collision time, but decrease in coalescence time.

Study of collisions between particles and unloaded bubbles with point-particle model embedded in the direct numerical simulation of turbulent flows

Simulations of a particle-bubble collision system composed of monosized spherical solid particles and air bubbles in a quiescent liquid and homogeneous isotropic turbulence have been performed using the pseudo-spectral method for the fluid flow and Lagrangian tracking for particles and bubbles. Particle-bubble collisions in a quiescent liquid were first simulated and compared to the existing theoretical models of particle-bubble collisions. Both numerical results and theoretical models indicate that decreasing bubble size and increasing particle size can increase the particle-bubble collision efficiency. A DNS model for studying the effect of turbulence on the collisions between particles and unloaded bubbles was then developed. A nonuniform time-dependent stochastic forcing scheme was implemented to maintain turbulence intensity at targeted levels. A statistical analysis of a group of particles and bubbles in the forced turbulent flow was performed to probe the mechanism of particle-bubble collision in a turbulent flow. A simplifying assumption (motivated purely by computational limitations) has been made that bubbles and particles can be randomly relocated during the simulation, unlike what happens in reality, but the size of the effect that this simplifying assumption will have on our results is unknown. Reductions in particle-bubble collisions due to preferential concentrations of particles and bubbles in different flow regions were not found. Comparing respectively the contributions of radial relative velocity and radial distribution function to the collision kernel, the contribution of radial distribution function could be neglected because the radial relative velocity increases by about 1900% (from 1.55 cm/s to 28.87 cm/s) while the radial distribution function decreases by only 33% (from 1.33 to 1.00). Collisions between particles and bubbles increased with turbulent dissipation rate primarily due to the fact that radial relative velocities between particles and bubbles increased with the flow dissipation rate.

Improving Design of Rotary-Pulsation Apparatuses

Designs and principles of operation of new rotary-pulsation apparatuses are described. The essential technical feature of the developed designs consists in installation of additional dispersing elements in the apparatus chambers. Turbulent pulsations with randomly directed velocity vectors occur when the components of the treated medium interact with such elements. This causes increase of relative velocity of the flow around the particles of a heterogeneous medium, which ensures intensification of emulsification, dispersion, and mass transfer processes.

Near fields of annular slotted hoods measured via 2D-PIV

In order to improve the effectiveness of a local exhaust ventilation system, an attempt is the changed hood geometry by adding a plate. The near fields of a simple exhaust and the annular slotted hoods with different slot widths are measured by a 2D-particle image velocimetry (PIV) system. The time-averaged velocity fields show that the slotted-hood designs enhance the capture velocities beyond half a diameter (0.5D) downstream the hood. The relative velocity increase coefficient (IC) along the hypothetical boundaries in the near fields was proposed to compared with the simple exhaust and determine the effect of slot width on the capture velocity enhancement, the IC for different slot widths is approximately 109%–130%. To predict the velocity at downstream of the hood for a given slot width and velocity, a unimodal-skewed distribution model was developed with a correlation coefficient of approximately 94%. Regarding turbulence statistics, the influence of the plate only involves the near hood region. The higher-order statistics also show no obvious differences between slotted hoods with different slot widths. In general, this study not only motivates us to design and improve the performance of LEV systems for forced advection problems by adding a baffle plate, but also provides benchmark flow data for a follow-up numerical simulation study.

Geometric random walk of finite number of agents under constant variance

The characteristics of the 1D geometric random walk of a finite number of agents are investigated by assuming constant variance. Firstly, the characteristics of the steady state solution of the distribution function, which is obtained using the extended geometric Brownian motion (EGBM), are investigated in the framework of the 1D Fokker–Planck type equation. The uniqueness and existence of the steady state solution of the distribution function requires the number of particles to be finite. To avoid the divergence of the steady state solution of the distribution function at the mean value in the 1D Fokker–Planck type equation, the hybrid model, which is a combination of EGBM and normal BM, is proposed. Next, the steady state solution of the distribution function, which is obtained using the geometric Lévy flight, is investigated under constant variance in the framework of the space fractional 1D Fokker–Planck type equation. Additionally, we confirm that the solution of the distribution function obtained using the super-elastic and inelastic (SI-) Boltzmann equation under constant variance approaches the Cauchy distribution, when the power law number of the relative velocity increases. Finally, dissipation processes of the pressure deviator and heat flux are numerically investigated using the 2D space fractional Fokker–Planck type equations for Lévy flight and SI-Boltzmann equation by assuming their linear response relations.

Interaction and propagation characteristics of two counter and co-propagating Mach cones in a dusty plasma

We theoretically investigate the interaction and propagation characteristics of two co/counter propagating Mach cones triggered by two projectile particles moving with supersonic velocities in the same/opposite directions through a dusty plasma medium. The Mach cone solutions are obtained by solving a model set of fluid equations for a heavily charged dust fluid that includes the contributions of the projectile particles in the Poisson equation. The density profiles and velocity vector maps of the Mach wings show interesting structural changes when they interact with each other and form patterns similar to interference fringes. Compared to the co-propagating Mach cones, the wings of counter propagating Mach cones produce a larger number of maxima and minima in the pattern resulting from their mutual interaction. In addition, the time duration of the formation of two maxima or minima at a particular point decreases due to the interactions of Mach cones. Another notable feature is that the spacing between adjacent maxima increases, while the fringe angle decreases with the increase of relative velocity of the counter propagating projectile particles.

Influence of flow-induced bend–twist coupling on the natural vibration responses of flexible hydrofoils

For flexible hydrofoils, the natural flow-induced bending and twisting deformations are coupled if the center of lift is away from the elastic axis; this coupling may be influenced by viscous effects due to movement in the center of lift. The objective of this work is to investigate the role of flow-induced bend–twist coupling effects, as well as their dependence on the reduced velocity and solid-to-fluid added mass ratio. A secondary objective is to compare inviscid and viscous fluid–structure interaction (FSI) simulations of the natural flow-induced vibration responses of flexible cantilevered hydrofoils in water. The focus is on attached flow conditions in fully turbulent regimes at low angles of attack, where inviscid FSI method should be relatively accurate, and the foil response should be dominated by the foil's natural frequencies. The viscous FSI model is formulated by coupling a two-dimensional (2D) unsteady Reynolds-averaged Navier–Stokes (URANS) model with a two-degrees-of-freedom (2-DOF) model representing the spanwise tip bending and twisting deformations. The results show that the flow-induced bend–twist coupling terms are important for accurate prediction of the natural vibration frequencies and damping characteristics, particularly for the twisting motion, and their relative importance grows when the relative velocity increases and the solid-to-fluid added mass ratio decreases.

Bimetallic Microswimmers Speed Up in Confining Channels.

Synthetic microswimmers are envisioned to be useful in numerous applications, many of which occur in tightly confined spaces. It is therefore important to understand how confinement influences swimmer dynamics. Here we study the motility of bimetallic microswimmers in linear and curved channels. Our experiments show swimmer velocities increase, up to 5 times, with the degree of confinement, and the relative velocity increase depends weakly on the fuel concentration and ionic strength in solution. Experimental results are reproduced in a numerical model which attributes the swimmer velocity increase to electrostatic and electrohydrodynamic boundary effects. Our work not only helps to elucidate the confinement effect of phoretic swimmers, but also suggests that spatial confinement may be used as an effective control method for them.

Analytical and numerical studies on a single-droplet evaporation and combustion under forced convection

Existing droplet evaporation/combustion models in computational fluid dynamics (CFD) simulation of spray combustion are based on simplified 1-D models. Both these models and recently developed 3-D models of single-droplet combustion do not give the conditions for the different existing droplet combustion modes. In this paper, droplet evaporation and combustion are studied both analytically and numerically. In the analytical solution, a 2-D axisymmetric flow surrounding an evaporating and combusting droplet was considered. The governing equations were solved using an integral method, similar to the Karman–Pohlhausen method for solving boundary-layer flows with pressure gradient. The results give a local evaporation rate and flame radius in agreement with experimental results. In numerical simulation, 3-D combusting gas flows surrounding an ethanol droplet were studied. The prediction results show three modes of droplet combustion under different relative velocities, explaining the change in the evaporation constant with an increase in relative velocity observed in experiments. This implies that different droplet combustion models should be developed in simulating spray combustion. The predicted local evaporation rate and flame radius by numerical simulation are in agreement with the analytical solution in the range of azimuthal angles $$0^{\circ }<\theta <90^{\circ }$$ . The numerical results indicate that the drag force of an evaporating and combusting droplet is much smaller than that of a cold solid particle, and thus the currently used drag models should be modified.

Sensitivity of the hearing system to the velocity of auditory motion: Discrimination thresholds and mismatch negativity

The parallel psychophysical and MMN study focused at the sensitivity of human hearing system to variations in velocity of sound image movement. The motion of sound stimuli with various velocities in the 450 deg/s to 732 deg/s range in increments of 6 deg/s to the left or to the right from the head midline was simulated by introducing linear changes of interaural delay into dichotic stimuli. The psychophysical experiments were designed according to the 2-alternative forced choice paradigm. The subjects were presented by pairs of moving stimuli and were asked to decide which moved faster. The stimuli created for the present study ensured that the subjects performed the discrimination task without relying on associated cues of sound displacement or duration. The psychophysical measures were compared with electrophysiological indexes of sound processing (auditory evoked responses (ERPs) and mismatch negativity (MMN)). Significant MMN was elicited by the difference of 170 deg/s between the reference and test velocity, which corresponded to the relative velocity increase of 38%. At the same time, the difference thresholds for velocity were much higher and exceeded 50%. The results suggest that MMN magnitude depended on the velocity difference between standard and deviant stimuli and was more sensitive to velocity difference than psychophysical measure.

An investigation into the deformation, movement and coalescence characteristics of water-in-oil droplets in an AC electric field

Drop-drop coalescence is important in electric dehydrators used for oil-water separation in the oil industry. The deformation degree, angle between the electric field and the center line of two drops, effects of intensities and frequencies of the electric field have been studied by analyzing droplet images. However, seldom have people investigated the movement and the relative velocity in the process of drop-drop coalescence. In this paper forces acting on a single droplet and horizontal water droplets in an AC electric field were analyzed, and experiments were carried out to investigate the deformation, movement and coalescence characteristics of droplets with white oil and water. With a micro high-speed camera system and image processing technology, the droplet images were collected and analyzed. The results indicate that the deformation is mainly affected by the electric field intensity, frequency, droplet diameter and the oil viscosity. High field strength and large diameter facilitate deformation of drops in the electric field. The effect of frequency and oil viscosity is not obvious. Higher frequency and higher oil viscosity will lead to smaller oscillation amplitude. The effect of electric field intensity and droplet diameter on oscillation amplitude is not obvious. When the center-to-center distance between droplets is large, the forces acting on droplets in the horizontal direction are mainly dipole-dipole attraction and drag forces. There is also the film-thinning force when droplets get closer. The forces are simplified and derived. Based on force analysis and Newton’s second law, the relative movement is analyzed in different parts, and the relationship of center-to-center distance and time is in accordance with an explinear function at different stages. According to experimental data, the movement of 145 μm double droplets before coalescence can be fitted well with an explinear function at two stages. In addition, the whole movement process is investigated and can be estimated with a fourth order polynomial curve, from which the relative velocity of droplet movement can also be obtained. With an increases in electric field intensity and droplet diameter and a decrease in oil viscosity, the relative velocity increases. Only when the oil-water interfacial tension is obviously high, can it influence the relative movement significantly. The coalescence is mainly dipole coalescence and chain coalescence under influence of the AC electric field.

Study of sacrificial cathodic protection on marine structures in sea and fresh water in relation to flow conditions

The extent of corrosion between a miniature steel ship model at different relative velocities of sea water fitted with commercial sacrificial anodes of aluminium (Al) in sea water and magnesium (Mg) in fresh water is studied. The experimental results show that the degree of cathodic protection represented by the cathode potential at a given distance from different types of sacrificial anodes decreases slightly with an increase in the relative velocity. The results also show that the amount of Al or Mg required to protect the ship cathodically increases as the relative velocity increases.

Eccentricity effects of microhole arrays on drag reduction efficiency of microchannels with a hydrophobic wall

This paper experimentally investigates the effects of microhole eccentricity on the slip lengths of Stokes flow in microchannels with the bottom wall made of microhole arrays. The wettability of such microhole structures fabricated by the replica molding of polydimethylsiloxane is first analyzed measuring both static and dynamic contact angles. Subsequently, the drag reduction performance of the microchannels with such hydrophobic microhole surfaces is evaluated. The results indicate that the impact of microhole eccentricity on drag reduction performance correlates well with the contact angle hysteresis rather than with the static contact angle. Furthermore, microhole arrays with large normalized width and zero eccentricity show the minimum contact angle hysteresis of 18.7°. In these microchannels, the maximum percentage increase in the relative velocity is 39% corresponding to a slip length of 2.49 μm. For the same normalized width, increasing the normalized eccentricity to 2.6 increases the contact angle hysteresis to 36.5° that eventually reduces the percentage increase in relative velocity and slip length down to 16% and 0.91 μm, respectively. The obtained results are in qualitative agreement with the existing theoretical and numerical models. These findings provide additional insights in the design and fabrication of efficient micropatterned channels for reducing the flow resistance, and leave open questions for theoreticians to further investigate in this field.

Calculations of laser induced quadrupole–quadrupole collisional energy transfer in Xe–Kr

A laser induced quadrupole–quadrupole collisional energy transfer system of Xe–Kr is proposed, and the three-level laser induced collisional energy transfer (LICET) model is presented. Calculating results show that the peak of the LICET profile moves to the red and the FWHM becomes narrower, obviously with the laser field intensity increasing, while the resulting spectra is shifted in frequency toward the blue and the full width at half peak of the profile becomes larger as the relative velocity increases. The spectrum of the quadrupole–quadrupole LICET in the Xe–Kr system has a wider tunable range in an order of magnitude than the dipole–dipole LICET spectra. A cross section of 3.36×10−15 cm2 is obtained, which indicates that the quadrupole–quadrupole LICET process also can be an effective way to transfer energy selectively from a storage state to a target state.