Velocity Distribution Research Articles

Overlapping effect of detonation driving during multi-point initiation

Employing multi-point initiation in warhead structures produces a detonation wave aiming warhead. Numerous studies have concentrated on enhancing the velocity and analyzing its distribution in this type of warhead. Researchers have developed formulas for the velocity distribution of asymmetrically one-line initiated warheads; however, a reliable and complete calculation method for the velocity distribution in asymmetrically two-line initiated warheads is yet to be established. A new idea is proposed and verified in this work: the velocity distribution for the asymmetric two-line initiation can be derived from that of the one-line initiation. Initial efforts include conducting experimentally verified numerical modeling to examine the propagation and interaction of detonation waves in asymmetrically two-line initiated warheads. Subsequently, using the principle of independent propagation, a model is formulated to use the velocity distribution from asymmetric one-line initiation to predict that of asymmetric two-line initiations. Finally, arena tests are performed to corroborate the overlapping model. This research can provide valuable insights for lethality assessment, protection design, and security analysis.

Experimental study of the effects of a particle filter in front of automotive radiator on its cooling performances and cooling drag

According to the World Health Organization (WHO), air pollution is the single greatest worldwide health risk especially in urban environments. In these areas, the vehicle traffic significantly contributes to the fine dust concentration in the ambient air. While the current legislation focuses mainly on the exhaust emission of vehicles, 85% of the overall fine dust emissions originating from brakes, tires, and road abrasion are not yet regulated. In this context, an integrated particulate filter system fitted into previously unused installation spaces in frontend of a vehicle in front of the radiator allows to compensate a part of the particle emissions of a vehicle try to reach the neutral emission. Add filter is not without consequences for the cooling performances. This study aims to assess the impact of the particulate filter system on the radiator cooling performances and cooling drag coefficient. An experimental setup was developed to characterize an automotive radiator with and without particle filter in terms of power and velocity distribution. Cooling capacity of the radiator depends clearly of the airflow through the radiator. Filter increases the pressure drop and decreases airflow. Hence, the heat power exchange can be reduced up to 10% for a pressure drop level almost twice. The airflow inlet inside engine compartment is not beneficial for aerodynamic aspect. By increasing pressure drop, the cooling drag coefficient can be reduced up to 10% when a filter covers entirely the radiator surface. The results indicate that the filter affects the cooling capacity of the radiator, which can require modifications to the cooling system strategy.

Integrated modeling of anisotropic neutron yields of classical and spherical tokamaks

Estimations of counting rates of neutron spectrometers in experiments on controlled fusion with magnetic confinement, as well as calculations of energy resolved flux densities of fusion neutrons from plasma to the walls of a reactor require spatial integration of the local, usually anisotropic function of the neutron source. The integrated modeling consists of three main stages. First, sources of fast particles in beam- or wave-heated plasma are calculated. The next stage deals with spatial, energetic, and angular velocity distributions of plasma ions. Finally, double differential rate coefficients of nuclear fusion reactions are computed. This article describes calculations of spatial distributions of nuclear fusion reaction rates in classical and spherical tokamaks and the anisotropy of the neutron yield and spectra. The results are based on analytical formulas for energetic and angular distributions of the local source of fusion products in plasma. Examples of energetic spectral densities of neutron fluxes on first walls are presented, as well as energy resolved counting rates of collimated neutron spectrometers for perpendicular and tangential lines of sight.

ThunderBoltz: an open-source direct simulation Monte Carlo Boltzmann solver for plasma transport, chemical kinetics, and 0D modeling

Abstract Plasma-neutral interactions, including reactive kinetics, are often either studied in 0D using ODE-based descriptions, or in multi-dimensional fluid or particle-based plasma codes. The latter case involves a complex assembly of procedures that are not always necessary to test effects of underlying physical models and mechanisms for particle-based descriptions. Here we present ThunderBoltz, a lightweight, publicly available 0D direct simulation Monte Carlo code designed to accommodate a generalized combination of species and arbitrary cross sections without the overhead of expensive field solves. It can produce electron, ion, and neutral velocity distributions in applied AC/DC E-field and/or static B-field scenarios. The code is built in the C++ standard library and includes a convenient Python interface that allows for input file generation (including compatibility with cross section data from the LXCat database), electron transport and reaction rate constant post-processing, input parameter constraint satisfaction, calculation scheduling, and diagnostic plotting. These codes can be accessed at the repository: https://github.com/lanl/ThunderBoltz. In this work we compare ThunderBoltz transport calculations against Bolsig+ calculations, benchmark test problems, and swarm experiment data, finding good agreement with all three in the appropriate field regimes. In addition, we present example use cases where the electron, ion, and background neutral particle species are self-consistently evolved to model the background kinetics, a feature that is absent in fixed-background Monte Carlo and n-term Boltzmann solvers. The latter functionality allows for the possibility of particle-based chemical kinetics simulations of the plasma and neutral species as a new alternative to ODE-based approaches.

Study on the formation and characteristics of unstable sheet cavitation on hydrofoils

Hydrofoils, as fundamental components of hydraulic machinery, directly influence the performance of such machinery. This study conducted an analysis of the cavitation characteristics of hydrofoils at a + 4° angle of attack under various cavitation numbers using numerical simulation and experimental research methods. The focus of the research was to explore the phenomenon of unstable sheet cavitation and its causes, as well as to reveal the characteristics of the re-entrant jet. The large eddy simulation method was employed to calculate the cavitation morphology under three different cavitation numbers. The method is highly consistent with the experimental results in simulating the small-scale detachment at the tail of unstable sheet cavitation and the large-scale shedding of cloud cavitation. The study found that the detachment of unstable sheet cavitation is closely related to the re-entrant jet, which exhibits transient and abrupt characteristics during the unstable sheet cavitation phase. Furthermore, by applying FFT processing to the distribution of maximum reverse velocity and the spatiotemporal changes of Ux on characteristic lines, eigenfrequency of the detachment of unstable sheet cavitation were identified. The research results indicate that cavitation mainly show as sheet cavitation when the cavitation closure point does not exceed the zero-slope point. Beyond this point, it transitions to cloud cavitation. This study provides new insights into the cavitation phenomenon of hydrofoils and offers quantitative research on the phenomenon of unstable sheet cavitation.

Seismic Modeling of Bedload Transport in a Gravel‐Bed Alluvial Channel

AbstractRecent theoretical models and field observations suggest that fluvial bedload flux can be estimated from seismic energy measured within appropriate frequency bands. We present an application of the Tsai et al. (2012, https://doi.org/10.1029/2011gl050255) bedload seismic model to an ephemeral channel located in the semi‐arid southwestern US and incorporate modifications to better estimate bedload flux in this environment. To test the model, we collected streambank seismic signals and directly measured bedload flux during four flash‐floods. Bedload predictions calculated by inversion from the Tsai model underestimated bedload flux observations by one‐to‐two orders of magnitude at low stages. However, model predictions were better for moderate flow depths (>50 cm), where saltation is expected to dominate bedload transport. We explored three differences between the model assumptions and our field conditions: (a) rolling and sliding particles have different impact frequencies than saltating particles; (b) the velocity and angle of impact of rolling particles onto the riverbed differ; and (c) the fine‐grained alluvial character of this and similar riverbeds leads to inelastic impacts, as opposed to the originally conceptualized elastic impacts onto rigid bedrock. We modified the original model to assume inelastic bed impacts and to incorporate rolling and sliding by adjusting the statistical distributions of bedload impact frequency, velocity, and angle. Our modified “multiple‐transport‐mode bedload seismic model” decreased error relative to observations to less than one order of magnitude across all measured flow conditions. Further investigations in other environmental settings are required to demonstrate the robustness and general applicability of the model.

Dynamic characteristics of the hydrogen injector-ejector unit in a PEM fuel cell system

The ejector, as a fluid-dynamics controlled passive component, is a promising hydrogen recirculation device in proton exchange membrane (PEM) fuel cell systems. Nevertheless, its performance is significantly affected by dynamic operating conditions and the behavior of the injector. This study investigates the dynamic performance of an ejector integrated with a hydrogen injector in a 100 kW PEM fuel cell system. A dynamic computational fluid dynamics (CFD) model of the integrated injector-ejector unit is developed using a dynamic mesh method and validated through theoretical analysis and experimental data. A thorough analysis of the global performance and local fluid flow characteristics of the injector-ejector unit is conducted. The results show that the hydrogen injector, with a throat diameter of 2.00 mm, exhibits an adjustable linear flow range from 0 to 1.62 g/s under an inlet pressure of 2.0 MPa. Additionally, the primary mass flow rate can be linearly regulated by adjusting the valve gap, while the secondary mass flow rate exhibits asynchronous behavior with the primary flow. The velocity and temperature distributions within the injector-ejector unit undergo significant changes under dynamic conditions. These findings contribute to optimizing the design and control strategies of hydrogen supply components in PEM fuel cell systems.

Comparative numerical study featuring magnetized nanofluids configured by elongating sheet with thermophoresis and Brownian motion

This study investigates the heat and mass transfer characteristics of MHD rotating Fe₃O₄-Al₂O₃/H₂O hybrid nanofluid flow over a three-dimensional stretching surface. Comparative analysis was conducted among the base fluid H₂O, Al₂O₃-H₂O nanofluid, and Fe₃O₄-Al₂O₃/H₂O hybrid nanofluid, focusing on velocity, temperature, and concentration distributions influenced by thermophoresis, Brownian motion, Hall current, temperature ratio, magnetic parameter, rotation, and thermal radiation. The governing nonlinear partial differential equations were transformed into ordinary differential equations using similarity adaptations and solved numerically with the BVP-5C method in MATLAB. Results indicate that increasing the thermophoresis and Brownian motion parameters elevates the temperature profile while affecting the concentration distribution differently. The hybrid nanofluid exhibited a higher temperature distribution compared to the nanofluid and base fluid, whereas the base fluid showed a greater concentration gradient.

Entropy Analysis in Magnetized Blood-Based Hybrid Nanofluid Flow via Parallel Disks

Magnetized hybrid nanofluid combined with ferrite and silver in a blood-based liquid presents their vital role in several aspects such as artificial heart pumping system, drug delivery process, the flow of blood in the artery, etc. This is because the high heat transportation rate of the nanofluid is caused by the inclusion of nanoparticles. The current investigation is based on the characteristic of particle concentration comprised of Fe3O4 and Ag in the base liquid blood that passed in between two infinite parallel disks filled with porous matrix. The electrically conducting fluid associated to maximum of 1.5% of volume concentration from each of the solid particles affects the flow phenomena. However, the impact of thermal radiation vis-à-vis the heat dissipation provides efficient heat transport properties with the inclusion of the effective thermal conductivity assumed from the Hamilton-Crosser model. The proposed conductivity model describes the role of particle shapes on the enhanced thermal properties. Further, numerical treatment is obtained for the transformed designed problem following similarity rules that are used for the conversion of the governing equations into their non-dimensional form. The computation of various flow profiles leads to get the entropy generation due to the irreversibility processes. Along with the fluid velocity and temperature distributions, the study is carried out for the entropy as well as the computation of Bejan number and afterwards the simulation of the shear and heat transportation rate are also depicted graphically. The main finding of the proposed study is that solid particle concentrations have a substantial impact to increasing fluid velocity in magnitude, resulting in a narrower wall thickness at both channel walls. Thermal radiation was shown to be more effective at increasing entropy generation and Bejan value.

Three-dimensional numerical simulations and experimental studies on the viscoelastic rheological and deformation behavior of polymer catheter in gas-assisted extrusion processing

Gas-assisted extrusion is an effective method for improving the deformation behavior of polymer catheters during extrusion. However, the underlying mechanisms that dictate how geometrical and constitutive models influence the complex rheological behavior of the melt are not yet fully understood, which hinders further utilization and optimization. In this study, the three-dimensional (3D) gas–liquid–gas model for catheter gas-assisted extrusion was constructed. Subsequently, the Bird–Carreau model and the Phan–Thien–Tanner (PTT) model were employed in finite element numerical simulations to analyze the complex behavior. For comparative analysis, simplified two-dimensional (2D) model numerical simulations were also conducted. Additionally, experiments on catheter gas-assisted extrusion and parameterization studies of key constitutive model parameters were performed. The findings indicate that the 3D model, when integrated with the PTT constitutive model, demonstrates superior predictability and aligns more closely with experimental results. Furthermore, as the flow rate increases, discrepancies among different models diminish, and the distance required for the melt and gas to achieve motion equilibrium decreases. The internal mechanisms behind these phenomena are elucidated through the analysis of velocity and stress field distributions. This research enhances our understanding of the complex rheological behavior in polymer catheter gas-assisted extrusion, providing valuable insights for both academic research and industrial production in this field.

Hybrid Modeling of Miniaturized 50 W Annular Hall Thruster

A 50-W-class annular Hall thruster is studied with a hybrid axial–radial two-dimensional model. Ions are described by a kinetic approach, whereas fluid conservation equations are solved for electrons. In such models, additional (anomalous) contributions must be added to the momentum-transfer electron collision frequency to obtain realistic values of the cross-field electron mobility. First, a parametric study is performed, where anomalous transport is described with a simple two-region model based on constant empirical parameters. The simulated global performance is subsequently compared with experimental measurements. Then, laser-induced fluorescence ion velocity measurements are employed to infer a continuous profile of the anomalous electron collision frequency along the channel centerline. The model reproduces the performance, the acceleration structure, the current oscillations, and the doubly charged ion fraction of the laboratory thruster. Measurements of the ion velocity distribution function highlight the presence of a slow ion population in the near plume. The production of the slow ions and their growth for increasing distances from the thruster channel exit is qualitatively reproduced by the model. The results obtained suggest that the generation and dynamics of the observed slow ions can be attributed to the presence of energetic electrons in the plume.

Explaining the Evolution of Ion Velocity Distributions at a Low Activity Comet

AbstractAt a low activity comet the plasma is distributed in an asymmetric way. The hybrid simulation code Amitis is used to look at the spatial evolution of ion velocity distribution functions (VDFs), from the upstream solar wind (SW) to within the comet magnetosphere where the SW is heavily mass‐loaded by the cometary plasma. We find that the spatial structures of the ions and fields form a highly asymmetric induced magnetosphere. The VDFs of SW and cometary ions vary drastically for different locations in the comet magnetosphere. The shape of the VDFs differ for different species. The SW protons show high anisotropies that occasionally resemble partial rings, in particular at small cometocentric distances. A second, decoupled, proton population is also found. Solar wind alpha particles show similar anisotropies, although less pronounced and at different spatial scales. The VDFs of cometary ions are mostly determined by the structure of the electric field. We perform supplementary dynamic particle backtracing to understand the flow patterns of SW ions that lead to these anisotropic distributions. This tracing is needed to understand the origin of cometary ions in a given part of the comet magnetosphere. The particle tracing also aids in interpreting observed VDFs and relating them to spatial features in the electric and magnetic fields of the comet environment.

Characterizing Solar Center-to-limb Radial-velocity Variability with SDO

Stellar photospheric inhomogeneities are a significant source of noise, which currently precludes the discovery of Earth-mass planets orbiting Sun-like stars with the radial-velocity (RV) method. To complement several previous studies that have used ground- and spaced-based facilities to characterize the RV of the Sun, here we characterize the center-to-limb variability (CLV) of solar RVs arising from various solar-surface inhomogeneities observed by the Solar Dynamics Observatory (SDO)/Helioseismic Magnetic Imager and SDO/Atmospheric Imaging Assembly. By using various SDO observables to classify pixels and calculate line-of-sight velocities as a function of pixel classification and limb angle, we show that each identified feature type, including the umbrae and penumbrae of sunspots, quiet-Sun magnetoconvective cells, magnetic network, and plage, exhibit distinct and complex CLV signatures, including a notable limb-angle dependence in the observed suppression of convective blueshift for magnetically active regions. We discuss the observed distributions of velocities by identified region type and limb angle, offer interpretations of the physical phenomena that shape these distributions, and emphasize the need to understand the RV signatures of these regions as astrophysical signals, rather than simple (un)correlated noise processes.

CloudFlex: A Flexible Parametric Model for the Small-scale Structure of the Circumgalactic Medium

We present CloudFlex, an open-source tool for predicting absorption-line signatures of cool gas in galaxy halos with small-scale structure. Motivated by analyses of ∼104 K material in hydrodynamical simulations of turbulent, multiphase media, we model cool gas structures as complexes of cloudlets sampled from a power-law distribution of mass ∝mcl−α with velocities drawn from a turbulent velocity field. The user may specify α, the lower limit of the cloudlet mass distribution ( mcl,min ), and several other parameters that set the mass, size, and velocity distribution of the complex. This permits investigation of the relation between these parameters and absorption-line observables. As a proof-of-concept, we calculate the Mg ii λ2796 absorption induced by the cloudlets in background quasi-stellar object (QSO) spectra. We demonstrate that, at fixed metallicity, the covering fraction of sight lines with equivalent widths W 2796 < 0.3 Å increases significantly with decreasing mcl,min , cloudlet number density (n cl), and complex size. We then use this framework to predict the halo-scale W 2796 distribution around ∼L * galaxies. We show that the observed incidences of W 2796 > 0.3 Å sight lines with impact parameters 10 kpc < R ⊥ < 50 kpc in projected QSO–galaxy studies are consistent with our model over much of parameter space. However, they are underpredicted by models with mcl,min≥100M⊙ and n cl ≥ 0.03 cm−3, in keeping with a picture in which the inner cool circumgalactic medium (CGM) is dominated by numerous low-mass cloudlets (m cl ≲ 100M ⊙) with a volume filling factor ≲1%. When used to model absorption-line data sets built from multi-sight line and/or spatially extended background probes, CloudFlex enables detailed constraints on the size and velocity distributions of structures comprising the photoionized CGM.

Wire-to-two-drop plasma thruster: Experimental and numerical investigation of electroaerodynamic jet flow for micro aerial vehicle propulsion

Conventional micro aerial vehicles (MAVs) have primarily relied on complex, flapping-wing mechanisms for propulsion, often exhibiting limitations in terms of reliability and efficiency. To overcome these challenges, this study explores the potential of electroaerodynamic (EAD) thrusters as a novel propulsion system. By accelerating air molecules through ion collisions, EAD jet flow generates thrust, offering advantages such as noiseless operation and zero emissions due to its moving-part-free design. This research presents a comprehensive experimental and numerical investigation of a wire-to-two-drop thruster configuration to elucidate its electromechanical performance, plasma flow dynamics, and EAD jet characteristics. Experimental measurements of key parameters, including current, thrust, power, and effectiveness, were correlated with numerical simulations, demonstrating excellent agreement with a maximum error below 5%. These findings align strongly with established theoretical frameworks, revealing an inverse square root relationship between effectiveness and thrust. To optimize thruster performance, optimal operating voltages were identified at approximately 8.2, 9.4, and 11.6 kV for inter-electrode gap distances of 10, 15, and 20 mm, respectively, achieving a balanced trade-off between thrust and effectiveness. Detailed numerical visualizations of the plasma flow field, including velocity distribution, jet morphology, potential distribution, and electric field lines, provided valuable insights into the thruster's operation. Building upon these insights, a proof-of-concept EAD flier was constructed and tested, incorporating a serrated emitter electrode and lightweight materials. This flier achieved a mass of 0.5 g and generated a thrust of 0.77 g at 15 kV, resulting in a thrust-to-weight ratio of 1.54 and successful liftoff. This demonstration highlights the potential of EAD propulsion for practical MAV applications.

A novel Gauss–Jacobi quadrature for multiscale Boltzmann solvers

In this paper, we introduce a novel Gauss–Jacobi quadrature rule designed for infinite intervals, which is specifically applied to the velocity discretization in multi-scale Boltzmann solvers. Our method utilizes a newly formulated bell-shaped weight function for numerical integration. We establish the relationship between this new quadrature and the classical Gauss–Jacobi, as well as the Gauss–Hermite quadrature rules, and we compare the resulting discrete velocity distributions with several commonly used methods. Additionally, we validate the performance of our method through numerical simulations of flows with various Knudsen numbers. The proposed quadrature provides fresh insights into velocity space discretization.

Thermally induced oscillatory rarefied gas flow inside a rectangular cavity

Thermally induced oscillatory rarefied gas flow inside a two-dimensional rectangular cavity is investigated based on the hybrid macro-/mesoscopic scheme. The effects of the Knudsen (Kn) numbers and the oscillation frequency of lid temperature on the flow parameters are analyzed. The Shakhov model equation is solved numerically based on the mesoscopic approach in the near-wall region, and the macroscopic approach is adopted in the bulk flow region to reduce the computational cost. To close the numerical iteration procedure, the velocity distribution functions serving as the pseudo boundary between macroscopic and mesoscopic methods are reconstructed using the high-order Hermite polynomials. Numerical simulations demonstrate that the temperature profile at the central vertical of the cavity predicted by the hybrid method is in good agreement with results from the mesoscopic method, with a maximum error of 0.23%. In addition, the computational memory cost can be saved up to about 69.91%. The hybrid approach is able to capture the nonlinear phenomenon in the thermally induced oscillatory rarefied gas flow under high Kn numbers, where the horizontal velocity no longer obeys the law of periodic oscillating cosine function, and the rise time of the horizontal velocity is much longer than the fall time. The thickness of the viscous penetration layer and the disturbed region increases as the Kn number increases and decreases as the Strouhal number increases.

Particle Simulation Study of Obliquely Propagating Whistler Waves in Low‐Beta Plasmas

AbstractWhistler mode waves, which are electromagnetic emissions commonly observed in various space plasma environments, play critical roles in electron dynamics. While most whistler waves are driven by temperature anisotropy and propagate parallel to the background magnetic field, these waves can also be excited in the oblique direction when electron plasma beta is very low (&lt;0.025). Although linear theory accounts for the excitation processes of obliquely propagating whistler waves, the subsequent evolution and saturation processes remain inadequately understood. This study utilizes two‐dimensional self‐consistent simulations to investigate the complete wave‐particle interaction process. By scanning a broad parameter range, we derive scaling laws for the wave intensity, linking the wave properties to initial and final plasma conditions. The saturated temperature anisotropy from simulations can explain the upper bound anisotropy constraint observed by spacecraft well. Additional phase space analysis shows that both Landau and cyclotron resonance play critical roles in the evolution of electron velocity distribution, albeit in different energy ranges. Oblique whistler waves can effectively heat electrons through Landau resonance, creating a plateau distribution in the parallel direction. This research advances our understanding of the mechanisms behind obliquely propagating whistler waves in low‐beta plasmas and their impact on electron dynamics.

Quasi-one-dimensional non-equilibrium method for shock tube and stagnation line flows

Shock tube experiments are used to investigate non-equilibrium thermochemistry and radiative processes in reacting gas hypersonic flows. Boundary layer and shock structure are known to influence the spatial variation of the test slug state properties. This work derives and validates a novel method for viscous, quasi-one-dimensional, non-equilibrium flow in a shock tube assuming constant shock speed. The proposed method fully resolves the shock structure. Mirels' estimate for boundary layer growth around the test slug determines the dilation rate at the centerline. This, along with relevant boundary conditions, appropriately models core flow in a shock tube. The flow equations are discretized by finite differences on a staggered grid. The resulting highly non-linear set of algebraic equations is solved by Newton iterations. The Jacobian matrix is block tridiagonal with a Schur complement, allowing efficient inversion. This culminates in a unique and computationally efficient quasi-one-dimensional method offering improved modeling of the physical characteristics of shock tube experiments. Results of a 3 km/s, 66.6 Pa argon test case solved by a viscous, axisymmetric Navier–Stokes solution had agreement with the proposed method in temperature and pressure profiles to within 2% and post-shock velocity to within 15%. Reacting gas shock tube experiments in synthetic air and synthetic Titan atmospheres were analyzed. Radiance values in the non-equilibrium and equilibrium regions were compared under various assumptions for the shock structure and radial velocity distribution. These results highlight the necessity of a dedicated shock tube solver when analyzing shock tube thermochemistry, particularly when determining reaction rates and relaxation parameters.

Influence of Black Hole Kick Velocity on Microlensing Distributions

The natal kick velocity distribution for black holes (BHs) is unknown regardless of its importance for understanding the BH formation process. Gravitational microlensing is a unique tool for studying the distribution of BHs in our Galaxy, and the first isolated stellar-mass BH event, OGLE-2011-BLG-0462/MOA-2011-BLG-191 (OB110462), was recently identified by astrometric microlensing. This study investigates how the natal kick velocity for Galactic BHs affects the microlensing event rate distribution. We consider a Maxwell distribution with various average kick velocities, as well as the consequent variation of the spatial distribution of BHs. We find that the event rate for the BH lenses toward the Galactic bulge decreases as v avg increases, mainly due to the scale height inflation. We focus on the unique microlensing parameters measured for OB110462, with microlens parallax π E larger than 0.06 for its long timescale of t E > 200 days. We calculate the expected number of BH events occurring with parameters similar to OB110462 during the OGLE-IV survey by Mróz et al. and compare it with the actual number that occurred, at least one. Our fiducial model predicts 0.52, 0.38, 0.18, 0.042, and 4.0 × 10−3 events occurring for v avg = 25, 50, 100, 200, and 400 km s−1, respectively, which suggests that the average kick velocity is likely to be v avg ≲ 100 km s−1. The expected number smaller than unity even at maximum might indicate our luck in finding OB110462, which can be tested with future surveys by, e.g., the Roman Space Telescope.