Trajectory tracers

When fired, a tracer bullet leaves a visible trace behind it so that the trajectory can be seen and the aim corrected if necessary (trajectory tracer). A tracer bullet has a cavity at the base which is filled with a mixture of substances that are ignited by the propellant. The bullets are available in a range of rifle, pistol, and revolver calibers, although they are more common in rifle calibers. 

Regular and high-speed movies were taken of the tracer particle movement around the jets at different velocities and different solid loadings. The tracer particles used are red plastic pellets of similar size and density to the bed material. The movies were then analyzed frame by frame using a motion analyzer to record the particle trajectories and the particle velocities. 

Typical particle trajectories observed in the movies are shown in Fig. 47 for a jet velocity of 62.5 m/s and a solid loading of 1.52. The time elapsed between dots shown in Fig. 47 was typically 5 movie frames, while the movie speed was 24 frames/s. The colored tracer particles were followed in the vicinity of the jet until they disappeared into the jet, as... 

Dispersion in packed tubes with wall effects was part of the CFD study by Magnico (2003), for N — 5.96 and N — 7.8, so the author was able to focus on mass transfer mechanisms near the tube wall. After establishing a steady-state flow, a Lagrangian approach was used in which particles were followed along the trajectories, with molecular diffusion suppressed, to single out the connection between flow and radial mass transport. The results showed the ratio of longitudinal to transverse dispersion coefficients to be smaller than in the literature, which may have been connected to the wall effects. The flow structure near the wall was probed by the tracer technique, and it was observed that there was a boundary layer near the wall of width about Jp/4 (at Ret — 7) in which there was no radial velocity component, so that mass transfer across the layer... 

Mixing was visualized by additional fluorescent 500 nm tracer particles (yellow-green carboxylate FluoSpheres), marking by their tracer trajectories the flow pattern... 

Tracer trajectories giving the flow field around a rotating microsphere... 

M 7 [P 6] By coupled electrorotation of a microsphere local circulation of the surrounding liquid can be induced, as proven by the trajectories of fluorescent particle tracers around the (larger) rotating microsphere [95], Hence the mixing effect was shown qualitatively. No details on quantitative results such as mixing time were given. 

P 62] A Lagrangian particle tracking technique, i.e. the computation of trajectories of massless tracer particles, which allows the computation of interfacial stretching factors, was coupled to CFD simulation [47]. Some calculations concerning the residence time distribution were also performed. A constant, uniform velocity and pressure were applied at the inlet and outlet, respectively. The existence of a fully developed flow without any noticeable effect of the inlet and outlet boundaries was assured by inspection of the computed flow fields obtained in the third mixer segment for all Reynolds numbers under study. 

If the tracer is composed of the same species as that of the solid host, then the diffusion coefficient is named the tracer self-diffusion coefficient, where DA is the tracer self-diffusion coefficient. It is necessary to clarify that self-diffusion is a particle transport process that takes place in the absence of a chemical potential gradient [13]. This process is described, as explained later, by following the molecular trajectories of a large number of molecules, and determining their mean square displacement (MSD). 

Maring, H., Settle, D. M., Buat-Meanard, P., Dulac, F., and Patterson, C. C. (1987). Stable lead isotope tracers of air mass trajectories in the Mediterranean region. Nature 330, 154—156. 

The problem of vacancy-mediated tracer diffusion in two dimensions has been investigated for a long time [40-44] and several different methods (simulation, analytical models, enumeration of trajectories, etc.) can be used to address it. The mathematics of this type of diffusion was solved first for the simplest case [41], when the diffusion of the vacancy is unbiased (all diffusion barriers are equal the tracer atom is identical to the other atoms), the lattice is two-dimensional and infinite. There is a single vacancy present that makes a nearest-neighbor move in a random direction at regular time intervals and has an infinite lifetime, as there are no traps. The solution is constructed by separating the motion of the tracer and that of the vacancy. The correlation between the moves of the tracer atom is calculated from the probability that the vacancy returns to the tracer from a direction, which is equal, perpendicular or opposite to its previous departure. The probability density distribution of the tracer atom spreads with... 

In practice, both the return probabilities of the vacancy and the displacement distribution of the tracer atom are obtained via direct evaluation of probabilities (enumeration of trajectories), which has better convergence properties than Monte-Carlo-type methods. 

Using this, the tracer atom is described as if it forms a pair with the vacancy on one of the bonds adjacent to its original site, it walks on the bond lattice, and at the end of the walk (which happens after each move with probability prec) it is released with equal probability at either end of the last visited bond. Results for the probabilities of the different jump lengths (beginning-to-end vectors of these trajectories) are shown in Fig. 9. Note, that the model calculations in Fig. 9 contain no adjustable parameters. 

Single-component diffusion under equilibrium conditions can be monitored either by labeling some of the molecules or by following their trajectories. Considering the diffusion flux of the labeled molecules, again a proportionality relation of the type of eq 2 may be established. The factor of proportionality is called the coefficient of self-diffusion (or tracer diffusion). In a completely equivalent way [2], the self-diffusion coefficient may be determined on the basis of Einstein s relation... 

In this study we have employed the simultaneous collection of atmospheric particles and gases followed by multielement analysis as an approach for the determination of source-receptor relationships. A number of particulate tracer elements have previously been linked to sources (e.g., V to identify oil-fired power plant emissions, Na for marine aerosols, and Pb for motor vehicle contribution). Receptor methods commonly used to assess the interregional impact of such emissions include chemical mass balances (CMBs) and factor analysis (FA), the latter often including wind trajectories. With CMBs, source-strengths are determined (1) from the relative concentrations of marker elements measured at emission sources. When enough sample analyses are available, correlation calculations from FA and knowledge of source-emission compositions may identify groups of species from a common source type and identify potential marker elements. The source composition patterns are not necessary as the elemental concentrations in each sample are normalized to the mean value of the element. Recently a hybrid receptor model was proposed by Lewis and Stevens (2) in which the dispersion, deposition, and conversion characteristics of sulfur species in power-plant emissions... 

In IFS tracer data assimilation mode, the IFS tracer forecast mode is applied in the outer loops of ECMWF data assimilation system, i.e. the calculation of the trajectories runs of the complete model of the 4D VAR (Mahfouf and Rabier 2000) The iimer loops used in the minimisation step with the tangent linear and adjoint model are currently run uncoupled, i.e. without the application of the source and sink tendencies from the CTM. 

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