Vladimir Vinnikov

Constraining the Pre-atmospheric Parameters of Large Meteoroids: Košice, a Case Study

Out of a total around 50,000 meteorites currently known to science, the atmospheric passage was recorded instrumentally in only 25 cases with the potential to derive their atmospheric trajectories and pre-impact heliocentric orbits. Similarly, while observations of meteors generate thousands of new entries per month to existing databases, it is extremely rare they lead to meteorite recovery (http://www.meteoriteorbits.info/). These 25 exceptional cases thus deserve a thorough re-examination by different techniques—not only to ensure that we are able to match the model with the observations, but also to enable the best possible interpretation scenario and facilitate the robust extraction of key characteristics of a meteoroid based on the available data. In this study, we evaluate the dynamic mass of the Kosice meteoroid using analysis of drag and mass-loss rate available from the observations. We estimate the dynamic pre-atmospheric meteoroid mass at 1850 kg. The pre-fragmentation size proportions of the Kosice meteoroid are estimated based on the statistical distribution of the recovered meteorite fragments. The heliocentric orbit of the Kosice meteoroid, derived using numerical integration of the equations of motion, is found to be in close agreement to earlier published results.

Shape estimation for Košice, Almahata Sitta and Bassikounou meteoroids

This paper is concerned with a meteoroid shape estimation technique based on statistical laws of distribution for fragment masses. The idea is derived from the experiments that show that brittle fracturing produces multiple fragments of size lesser than or equal to the least dimension of the body. The number of fragments depends on fragment masses as a power law with exponential cutoff. The scaling exponent essentially indicates the initial form of the fragmented body. We apply the technique of scaling analysis to the empirical data on the mass distributions for Kosice, Almahata Sitta and Bassikounou meteorites.

Two-phase shock layer in a supersonic dusty gas flow

The problems of the numerical simulation of a dusty supersonic flow past a blunt body is examined. The model of a two-phase shock layer is presented. The Euler description of the gas phase and the Lagrange description of the dispersed phase that is used in combination is the basis of the present model. The complete variant of a discrete-elemental method, i.e., the direct numerical simulation of a dynamic admixture, is used. The effect of collisional and collisionless foreign particles on to the carrying gas flow and heat transfer is studied, as well as the direct impact of a two-phase gas flow onto a streamlined surface, by considering particle collisions and the dispersed phase’s reverse impact on the gas phase.

Numerical Simulation of Heterogeneous Flows and Heat-Mass Transfer in Complex Domains on Rectangular Grids

This paper is concerned with numerical simulation of two-phase flows in complex computational regions. Both nozzle flow and jet-obstacle interaction are considered. The presence of dispersed phase (solid or liquid particles) may lead to specific thermal and erosional interaction of inertial particles with the nozzle walls and the obstacle material. The latter makes the conjugated problem much more complicated. Therefore, we consider the complete flow field in the nozzle-jet-obstacle system. The present work is a continuation of the recent study by the authors [1, 2]. A unified approach to the general problem of a two-phase nozzle-jet-obstacle flow is suggested. In this approach, both the continuous and dispersed phase behavior is calculated using the fixed rectangular grids. The solution of transient conduction equation in the solid is also carried out on rectangular grids. Both dynamics and heating/cooling of particles are calculated using the discrete-element method in Lagrangian variables. The computational model includes many mechanical effects such as collisions of particles with each other, reflection of particles from the wall surface and the feedback effect of the dispersed phase on the gas flow. The distinctive feature is the direct numerical simulation of dispersed phase dynamics, where each single real particle in the flow has its computational counterpart. All governing equations for continuous fields are solved on rectangular grids using a ghost-cell immersed boundary method. This method provides discretization of the appropriate boundary conditions via a procedure of polynomial approximation. Such approach works well for both the incompressible and compressible flows. Rectangular grids allow a straightforward implementation of high order TVD and ENO schemes for the numerical simulation of gas flows. The immersed boundary method is perfectly suited for the problems within a computational domain of varying geometry, since it doesn’t require rebuilding the grid after each boundary movement. This feature was successfully used in the numerical simulation of erosive destruction of the circular cylinder in the two-phase flow [2], where the mass carried away from the body resulted in moving boundaries. The current work incorporates the previous methods and algorithms into the software package allowing the numerical investigation of heterogeneous flows in more complex configurations.Copyright

Estimation of the initial shape of meteoroids based on statistical distributions of fragment masses

An approach to the estimation of the initial shape of a meteoroid based on the statistical distributions of masses of its recovered fragments is presented. The fragment distribution function is used to determine the corresponding scaling index of the power law with exponential cutoff. The scaling index is related empirically to the shape parameter of a fragmenting body by a quadratic equation, and the shape parameter is expressed through the proportions of the initial object. This technique is used to study a representative set of fragments of the Bassikounou meteorite and compare the obtained data with the results of statistical analysis of other meteorites.

Statistical approach to estimate initial meteoroid shape from empirical mass distribution of recovered fragments

We present a study on statistical approach to estimate initial meteoroid shape of the Sutter’s Mill meteorite, aiming to fit lognormal, Weibull and Grady statistical mass distributions to the recovered fragments. We show a good correspondence of the selected distribution functions to the experimental data, with the best fit obtained with exponential cumulative distribution function (as a special case of Weibull distribution). This allows us to implement a novel technique for meteoroid pre-entry shape estimation, based on the detailed data on surviving meteorite fragments recovered on the ground. In total, all the available 77 fragments of the Sutter’s Mill meteorite were analyzed. This recovered fragment set is proved statistically complete. From the results obtained in this study, we suggest that only one major fragmentation event occurred during the atmospheric passage of the Sutter’s Mill meteoroid. The scaling analysis reveals an elongated pre-fragmentation shape of the meteoroid, being an average bet...

Mathematical model for estimation of meteoroid dark flight trajectory

This paper is concerned with mathematical model for numerical simulation of meteoroid dynamics. The simulations of bolide ballistics are carried out via hard sphere approximation. System of differential equations for movement and heat transfer is solved in Lagrange variables via Runge-Kutta methods. The drag force of atmospheric air is computed via Henderson formula, valid for wide ranges of Reynolds and Mach numbers. The parameters of surrounding gas are obtained from standard atmosphere model. The impact pressure is computed taking into account entropy jump through bow head shockwave and consequent isentropic deceleration of the flow in the vicinity of streamlined sphere. Meteoroid fragmentation is modeled as sequential division of parent body into two parts using random weighting coefficient for parent mass. The condition for fragmentation event occur when the hemisphere-averaged value of impact pressure exceeds the threshold of relative body strength, which nonlinearly depends on ration of initial met...