Mass transfer interaction of moving particles in a reactive dispersive system

Mass transfer from a system of particles moving linearly in a viscous fluid is considered. A chemical reaction on the particle surfaces is taken into account. The analysis is based on the investigation of concentration and velocity fields in a particle wake and of the distortion of these fields due to particles interaction. The values of both local and average Sherwood numbers are calculated.The results obtained are applied to the system of drops and solid spherical particles moving in line along the axis of uniform Stokes flow. It is shown, that if the distance 1 between the particles satisfies the condition (a is the sphere radius and P is the Peclet number) then the total diffusion flux to the surface of kth sphere is as follows

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. Here k is the particle number along the stream (for the leading particle k = 1), I₁ is the diffusion flux to the leading particle: n = 1 for drops, n = 2 for solid particles.     

Forecasting the velocity of quasi-stationary solar wind and the intensity of geomagnetic disturbances produced by it

A brief review is given of contemporary approaches to solving the problem of medium-term forecast of the velocity of quasi-stationary solar wind (SW) and of the intensity of geomagnetic disturbances caused by it. At the present time, two promising models of calculating the velocity of quasi-stationary SW at the Earth’s orbit are realized. One model is the semi-empirical model of Wang-Sheeley-Arge (WSA) which allows one to calculate the dependence V(t) of SW velocity at the Earth’s orbit using measured values of the photospheric magnetic field. This model is based on calculation of the local divergence f _S of magnetic field lines. The second model is semi-empirical model by Eselevich-Fainshtein-Rudenko (EFR). It is based on calculation in a potential approximation of the area of foot points on the solar surface of open magnetic tubes (sources of fast quasistationary SW). The new Bd-technology is used in these calculations, allowing one to calculate instantaneous distributions of the magnetic field above the entire visible surface of the Sun. Using predicted V(t) profiles, one can in EFR model calculate also the intensity of geomagnetic disturbances caused by quasi-stationary SW. This intensity is expressed through the K _p index. In this paper the EFR model is discussed in detail. Some examples of epignosis and real forecast of V(t) and K _p (t) are discussed. A comparison of the results of applying these two models for the SW velocity forecasting is presented.     

Directional Solidification Using a Baffle in Microgravity

Numerical simulations were performed to optimize the conditions and parameters for directional solidification of Te-doped GaSb in reduced gravity ranging from 10⁻³ to 10⁻⁵g₀. Our key goal was to quantify the velocity and concentration fields with and without a baffle present in the melt. The effect of the distance of the baffle from the solid–liquid interface was investigated. When the baffle is placed 0.5 cm from the solid–liquid interface, acceleration of 10⁻³g₀ does not cause significant interference with segregation. Furthermore, the flow between the baffle and the interface (low Reynolds number “creeping” flow) does not depend on fluid properties (viscosity).     

A diffusion model of radial distributions of plasma density from measurements on the Cassini spacecraft in the inner magnetosphere of Saturn

Equatorial radial distributions of plasma density in the 3 < L < 9 region of Saturn’s magnetosphere, obtained from measurements on the Cassini spacecraft, are considered on the basis of diffusion theory. The concentration of particles in the magnetic tubes is found to grow with L. The external source is located at L ? 9. The particles diffuse to Saturn. In the 5 < L < 9 interval the distribution is close to equilibrium. A relation between the diffusion coefficient and the densities of internal sources and losses is obtained in this interval. Prevalence of losses over sources is very probable. Estimates of the diffusion flux and its derivative are given. If the diffusion coefficient is expressed as D _LL = D _o L ³ and the contencentration of particles depends on L according to a power law, the diffusion rate is constant.     

Assessing the Risk of Orbital Debris Impact

A Space Debris Impact Risk Analysis Tool (SDIRAT) was developed and implemented to assess the orbital debris impact risk on a specified target in Earth orbit, in terms of flux, relative velocity, impact velocity, direction of the incoming particles, debris mass and diameter. Based on a deterministic approach, SDIRAT uses a realistic orbital debris population where each representative particle is identified by its rectangular coordinates (position and velocity) at a reference epoch. Using this information, some geometrical algorithms were developed and implemented to evaluate the contribution of each particle to the incoming flux. The position of the particle with respect to a specified target drives the selection criteria to reject, or select, it as a possible projectile. On the other hand, the relative velocity vector can be used to estimate the impact direction of the incoming flux. SDIRAT was conceived as a general tool for a variety of scenarios, such as low circular and elliptical orbits, up to the geosynchronous ring. This paper presents some examples of possible applications, including the computation of the incoming debris flux on SAX (low Earth orbit), SIRIO (geosynchronous orbit) and the IRIS upper stage (elliptical orbit). Other applications assess the impact risk for the Soviet Radar Ocean Reconnaissance Satellites Cosmos 1900 and Cosmos 1932.     

Peculiarities of the formation of a thin current sheet in the Earth’s magnetosphere

We investigate the process of the self-consistent formation of a thin current sheet with a thickness close to the ion Larmor gyroradius in the presence of decreasing magnetic field’s normal component B_n. This behavior is typical of the current sheet of the Earth’s magnetospheric tail during geomagnetic substorms. It has been shown that, in a numerical model of the current sheet, based on the particle-in-cell method, the appearance of self-consistent electric field component E_y in the current sheet vicinity can lead to its significant thinning and, eventually, to the formation of a multiscale configuration with a thin current sheet (TCS) in the central region supported by transient particles. The structure of the resulting equilibrium is determined by the initial parameters of the model and by the particle dynamics during the sheet thinning. Under certain conditions, the particle drift in the crossed electric and magnetic fields leads to a significant portion of ions becoming trapped near the neutral sheet and, in this way, to the formation of a wider configuration with an embedded thin current sheet. The population of trapped particles produces diamagnetic negative currents that manifest in the form of negative wings at the periphery of the sheet. Correspondingly, in the direction perpendicular to the sheet, a nonmonotonic coordinate dependence of the magnetic field appears. The mechanisms of the evolution of the current sheet in the Earth’s magnetotail and the formation of a multiscale structure are discussed.     

Radial profile of pressure in a storm ring current as a function of D st

Using satellite data obtained near the equatorial plane during 12 magnetic storms with amplitudes from ?61 down to ?422 nT, the dependences of maximum in L-profile of pressure (L _m) of the ring current (RC) on the current value of D _st are constructed, and their analytical approximations are derived. It is established that function L _m(D _st ) is steeper on the phase of recovery than during the storm’s main phase. The form of the outer edge of experimental radial profiles of RC pressure is studied, and it is demonstrated to correspond to exponential growth of the total energy of RC particles on a given L shell with decreasing L. It is shown that during the storms’ main phase the ratio of plasma and magnetic field pressures at the RC maximum does not practically depend on the storm strength and L _m value. This fact reflects resistance of the Earth’s magnetic field to RC expansion, and testifies that during storms the possibilities of injection to small L are limited for RC particles. During the storms’ recovery phase this ratio quickly increases with increasing L _m, which reflects an increased fraction of plasma in the total pressure balance. It is demonstrated that function L _m(D _st ) is derived for the main phase of storms from the equations of drift motion of RC ions in electrical and magnetic fields, reflecting the dipole character of magnetic field and scale invariance of the pattern of particle convection near the RC maximum. For the recovery phase it is obtained from the Dessler-Parker-Sckopke relationship. The obtained regularities allow one to judge about the radial profile of RC pressure from ground-based magnetic measurements (data on the D _st variation).     

Illumination of the Earth’s ionosphere by the vacuum ultraviolet radiation reflected by the moon

The spectral curve of the flux density of the radiation, which is reflected by the full moon towards the Earth’s ionosphere within a wavelength range of 200–1700 Å, has been presented. This curve is obtained by the approximation of space experiment data available in the scientific literature on the lunar spectral albedo and solar spectrum. Estimates of maximum values of spectral densities of fluxes reflected by the full moon in the neighborhood of wavelengths of ionization of basic ionospheric particles (neutral atoms of H I, He I, N I, O I, and Ar I and ions of He II, N II, O II, Ar II, N III, O III, and Ar III, as well as molecules of H₂, N₂, and O₂) are given.     

Estimation of the soil composition by IR observation of the Earth by satellites

A number of missions are in progress for Earth resources satellites to perform soil diagnosis by observing the bare soil thermal response to the heat input from the surrounding atmosphere. Heat capacity missions (and similar missions) are accomplished by measuring the soil temperature at the times of the satellite passes over the soil site.The models which are usually adopted assume that, for atmospheric conditions periodically changing during the day, the surface temperature time dependence is a function of the soil thermal inertia alone (for a dry soil).The present author has shown elsewhere that a more appropriate, two dimensional finite element modelling of the thermal behaviour of the soil, exhibits a dependence of the surface temperature time evolution on both the thermal conductivity (k) and on the volume heat capacity (?c) (for no evaporation at the interface). At least two independent temperature measurements are necessary in order to get information about k and ?c. It is shown that, within the range of values of k and ?c of the usual soils, temperature measurements taken at two successive satellite passes may yield the necessary information on the soil thermophysical properties. Charts can be constructed which will provide information on k and ?c when two soil temperatures are measured at proper times.     

The influence of kinetics of neutral particles on near-surface glow of spacecraft

A technique for calculation of the glow around low-orbit spacecraft is developed, taking into consideration the kinetics of neutral particles. Using this technique, the altitude ranges are determined where molecular processes dominate over ion-electron mechanisms. The influence of the molecular composition of the Earth’s atmosphere on the production of excited radicals NO ₂ ^* near the surface of spacecraft is studied in some detail.     

Buoyancy effects on smoldering combustion

A theoretical and experimental study is carried out to determine the effect of buoyancy on the rate of spread of a cocurrent smolder reaction through a porous combustible material. Since buoyant forces are proportional to the product g(_gi − _g), they can be controlled experimentally by varying either the gravitational acceleration, g, or the density difference, _gi − _g. The latter approach was followed in the present work. Measurements are performed of the smolder spread rate through porous α-cellulose (0.83 void fraction) as a function of the ambient air pressure. The experiments are carried out in a pressure vessel for ambient pressures ranging from 0.5 to 1.2 atm. The rate of spread was obtained from the temperature histories of thermocouples placed at fixed intervals along the fuel centerline. The smolder velocity was found to increase as the ambient pressure was increased. Extinction was found to occur when the buoyancy forces could not overcome the drag forces, indicating that at least for the present experimental conditions transport by diffusion cannot, by itself, support the spread of a smolder reaction. This conclusion is particularly important for outer space conditions where gravity and consequently buoyancy could be negligible. In the analysis, which assumes one-dimensional processes, the transport equations are solved to give the smolder spread rate as a function of the inlet oxygen mass flux. This mass flux is then estimated by balancing buoyancy and drag forces. Assuming that the smolder chemical reaction is only weakly dependent on pressure, the analysis finally predicts a smolder velocity dependence of the form v Y_oig²_gi Pa², i.e. is proportional to the ambient pressure squared. Good qualitative agreement is found between the theoretical predictions and the experimental results.     

Gravitational Sensitivity of Solutions–Melts at the Crystallization of Two-Phase InSb–InBi Alloys under Space Conditions

Analyzing the results of space and ground-based experiments carried out in the Baikov Institute of Metallurgy and Materials Science to study the processes of the melting and crystallization of two-phase InSb–InBi alloys of an indium–antimony–bismuth (In–Sb– Bi) triple system, we have demonstrated the gravitational sensitivity of the InSb-based solution– melt. It manifests itself as a certain asymmetry of the boundary of the dissolution of the InSb ingot by the InSb–InBi melt and heterogeneity of the melt along this boundary depending on the magnitude and direction of the gravity force acceleration gin the range (1–10^–3–10^–5)g ₀, where g ₀is the acceleration of the gravity force on Earth. For the first time, it is established in the experiments under analysis that the homogeneity of melts of a complex composition with components of various densities can be reached only at magnitudes of quasistationary (residual) microaccelerations g< 10^–6 g ₀.     

Radial propagation velocity of energetic particle injections according to measurements onboard the <Emphasis Type="Italic">Cluster</Emphasis> satellites

Injections of energetic electrons with a dispersion over energies were observed during the February 23, 2004 (at about 03:20 UT) substorm onboard the Cluster satellites in the vicinity of perigee near the midnight meridian. The delays in the particle observation caused by the energy dependence of the magnetic drift velocities made it possible to determine the position and time of the beginning of the drift, tracing the trajectories of the leading center of particles back in time in the magnetospheric model. The comparisons of the measurements of four satellites allowed us to determine the radial propagation of the injection front with a velocity of 100–150 km/s at a distance of 7–9 R _E. The comparison with a few previous measurements shows a substantial slowing down of injections as they approached the Earth, and this confirms the prospects of this method for more detailed study of propagation of plasma injection into the inner magnetosphere.     

Low-energy Earth–Moon transfers involving manifolds through isomorphic mapping

Analysis and design of low-energy transfers to the Moon has been a subject of great interest for decades. Exterior and interior transfers, based on the transit through the regions where the collinear libration points are located, have been studied for a long time and some space missions have already taken advantage of the results of these studies. This paper is concerned with a geometrical approach for low-energy Earth-to-Moon mission analysis, based on isomorphic mapping. The isomorphic mapping of trajectories allows a visual, intuitive representation of periodic orbits and of the related invariant manifolds, which correspond to tubes that emanate from the curve associated with the periodic orbit. Two types of Earth-to-Moon missions are considered. The first mission is composed of the following arcs: (i) transfer trajectory from a circular low Earth orbit to the stable invariant manifold associated with the Lyapunov orbit at L₁ (corresponding to a specified energy level) and (ii) transfer trajectory along the unstable manifold associated with the Lyapunov orbit at L₁, with final injection in a periodic orbit around the Moon. The second mission is composed of the following arcs: (i) transfer trajectory from a circular low Earth orbit to the stable invariant manifold associated with the Lyapunov orbit at L₁ (corresponding to a specified energy level) and (ii) transfer trajectory along the unstable manifold associated with the Lyapunov orbit at L₁, with final injection in a capture (non-periodic) orbit around the Moon. In both cases three velocity impulses are needed to perform the transfer: the first at an unknown initial point along the low Earth orbit, the second at injection on the stable manifold, the third at injection in the final (periodic or capture) orbit. The final goal is in finding the optimization parameters, which are represented by the locations, directions, and magnitudes of the velocity impulses such that the overall delta-v of the transfer is minimized. This work proves how isomorphic mapping (in two distinct forms) can be profitably employed to optimize such transfers, by determining in a geometrical fashion the desired optimization parameters that minimize the delta-v budget required to perform the transfer.     

Applications of multi-body dynamical environments: The ARTEMIS transfer trajectory design

The application of forces in multi-body dynamical environments to permit the transfer of spacecraft from Earth orbit to Sun–Earth weak stability regions and then return to the Earth–Moon libration (L₁ and L₂) orbits has been successfully accomplished for the first time. This demonstrated that transfer is a positive step in the realization of a design process that can be used to transfer spacecraft with minimal Delta-V expenditures. Initialized using gravity assists to overcome fuel constraints; the ARTEMIS trajectory design has successfully placed two spacecrafts into Earth–Moon libration orbits by means of these applications.     

Order of magnitude analysis of convective effects in dendritic solidification

The different types of convective phenomena which may occur during the dendritic solidification of metallic alloys are discussed from an order of magnitude analysis. Bulk thermal convection and/or interdendritic solutal convection have to be considered according to the values of the experimental data. Scaling laws for the solute boundary layer resulting from bulk thermal convection have already been derived. It is shown here that the interdendritic flow depends on a solutal Grashof number Gr based on the horizontal density gradient and a characteristic length L_s which is of the order of the liquid channels width. For Gr < 1, which is generally verified in practical cases, the interdendritic flow velocity U_r is proportional to the Grashof number. This a priori law compares favorably with the results of horizontal solidification experiments where the mean interdendritic flow velocity has been estimated from the resulting measured macrosegregation. In these experiments, as well as for most horizontal dendritic solidifications of metallic alloys at 1 g, the ratio $\text{U}{}_{\mathrm{r}}\text{R}$ (R is the growth rate) is of order one. In order to cancel the interdendritic flow effects, this ratio has to be lowered by one order of magnitude. According to our analysis, this can be obtained by performing the experiments either at a slightly reduced g level (～10^?1 g), or at 1 g in a vertical stable configuration with a sufficiently low residual horizontal thermal gradient.     

Acceleration and particle transport in collisionless plasma in the process of dipolarization and nonstationary turbulence

This work is devoted to studying the processes of the acceleration of plasma particles in thin current sheets that appear during magnetospheric substorms in the Earth’s magnetosphere tail. A numerical model of magnetic dipolarization accompanied by plasma turbulence has been constructed and studied. The model allows one to investigate the particle acceleration due to the action of three principal mechanisms: (1) plasma turbulence; (2) magnetic dipolarization; (3) their simultaneous action. For the given velocity kappa-distributions, we obtained energy spectra of three types of accelerated particles, i.e., protons p⁺, ions of oxygen O⁺, and electrons e^–. It has been shown that the combined mechanism of dipolarization with turbulence (3) makes the largest contribution to the increase in the energy of protons and heavy ions as compared with a separate action of each of mechanisms (1) and (2); in this case, electrons accelerate less. The consideration of the joint action of acceleration mechanisms (1) and (2) can explain the apparition of particles with energies on the order of magnitude equal to hundreds keV in the Earth’s magnetosphere tail.     

Peculiarities of long-wave radio bursts from solar flares preceding strong geomagnetic storms

Radio bursts in the frequency range of 100–1500 kHz, recorded in 1997–2000 on the INTERBALL-1 satellite during the solar flares preceding the strong geomagnetic storms with D _st < ?100 nT, are analyzed in this paper. The observed long-wave III-type radio bursts of solar origin at frequencies of 1460 and 780 kHz were characterized by large values of the flux S _f = 10^?15 ?10^?17 W/m² Hz and duration longer than 10 min. The rapid frequency drift of a modulated radio burst continued up to a frequency of 250 kHz, which testified that the exciting agent (a beam of energetic electrons) propagated from the Sun to the Earth. All such flares were characterized by the appearance of halo coronal mass ejections, observed by the LASCO/SOHO, and by the presence of a southward B_z-component of the IMF, measured on the ACE and WIND spacecraft. In addition, shortly after radio bursts, the INTERBALL-1 satellite has recorded the fluxes of energetic electrons with E > 40 keV.     

Estimating the accuracy of the technique of reconstructing the rotational motion of a satellite based on the measurements of its angular velocity and the magnetic field of the Earth

The paper has studied the accuracy of the technique that allows the rotational motion of the Earth artificial satellites (AES) to be reconstructed based on the data of onboard measurements of angular velocity vectors and the strength of the Earth magnetic field (EMF). The technique is based on kinematic equations of the rotational motion of a rigid body. Both types of measurement data collected over some time interval have been processed jointly. The angular velocity measurements have been approximated using convenient formulas, which are substituted into the kinematic differential equations for the quaternion that specifies the transition from the body-fixed coordinate system of a satellite to the inertial coordinate system. Thus obtained equations represent a kinematic model of the rotational motion of a satellite. The solution of these equations, which approximate real motion, has been found by the least-square method from the condition of best fitting between the data of measurements of the EMF strength vector and its calculated values. The accuracy of the technique has been estimated by processing the data obtained from the board of the service module of the International Space Station (ISS). The reconstruction of station motion using the aforementioned technique has been compared with the telemetry data on the actual motion of the station. The technique has allowed us to reconstruct the station motion in the orbital orientation mode with a maximum error less than 0.6° and the turns with a maximal error of less than 1.2°.     

Evolution of the out-of-plane amplitude for quasi-periodic trajectories in the Earth–Moon system

The out-of-plane amplitude along quasi-periodic trajectories in the Earth–Moon system is highly sensitive to perturbations in position and/or velocity as underscored recently by the ARTEMIS spacecraft. Controlling the evolution of the out-of-plane amplitude is non-trivial, but can be critical to satisfying mission requirements. The sensitivity of the out-of-plane amplitude evolution to perturbations due to lunar eccentricity, solar gravity, and solar radiation pressure is explored and a strategy for designing low-cost deterministic maneuvers to control the amplitude history is also examined. The method is sufficiently general and is applied to the L₁ quasi-periodic orbit that serves as a baseline for the ARTEMIS P2 trajectory.