Powerful Processing Tools
Powerful processing tools allow for sophisticated visualization of the computed particle trajectories. Particle trajectories can be represented by points, comet tails, lines, or tubes. Animations can easily be created and viewed directly in the graphical user interface (GUI) or exported to file. The particle trajectories can be colored with arbitrary expressions that can depend on the particles, the fields, or any combination of the two. In cases where the trajectory of many particles are simulated, it is possible to filter out specific particle trajectories according to a logical expression. The group behavior of the particles can be projected onto a lower dimension and visualized using Poincaré maps or phase portraits. It is also possible to perform operations on the particles to compute and plot the maximum, minimum, average, or integral of some quantity over all the particles. The particle trajectory data itself can be evaluated and written to the Results table or exported to a file. You can conveniently visualize the velocity and energy distributions of the particles, using 1D or 2D histograms.
Charged Particles in Electric and Magnetic Fields
Charged particles, such as electrons, individual ions, or small ion clusters, are affected by three primary forces in electric and magnetic fields:
- The electric force, which arises either due to a gradient in the electric potential or due to a time-varying magnetic vector potential. Particles with negative charge move in the opposite direction to the electric field, and particles with positive charge move in the same direction as the electric field. The electric force does work on these particles.
- The magnetic force, which does no work on the charged particles but can significantly alter their trajectory. The magnetic force often results in “banana” orbits for charged particles, causing them to orbit around magnetic field lines with a distance proportional to their mass.
- Collisional forces, which occur when charged particles collide with a background gas. The higher the background pressure, the more important the collisional forces.
If the number density of charged species is less than around 1013 1/m3, the effect of the particles on the fields can be neglected. This allows you to compute the fields independently from the particle trajectories. The fields are then used to compute the electric, magnetic, and collisional forces on the particles. The fact that the particle trajectories can be computed in their own study allows efficient and computationally inexpensive iterative solvers to be used.
Solving for Particle Tracing
For each particle, an ordinary differential equation is solved for each component of the position vector. This means that three ordinary differential equations are solved for each particle in 3D, and two in 2D. At each time step, the forces acting on each particle are queried from the computed fields at the current particle position. If particle-particle interaction forces are included in the model, they are added to the total force. The particle position is then updated, and the process repeats until the specified end time for the simulation is reached. Since the Particle Tracing Module uses a very general formulation for computing particle trajectories, the Particle Tracing interfaces can be used to model charged particle motion in electromagnetic fields, large scale planetary and galactic movement, and particle motion in laminar, turbulent, and two-phase fluid systems.
Studying Particle Tracking in a Fluid
The motion of microscopic- and macroscopic-sized particles is typically dominated by the drag force acting on particles immersed in a fluid. There are two phases in the system: a discrete phase consisting of bubbles, particles, or droplets, and a continuous phase in which the particles are immersed. In order for the particle tracking approach to be valid, the system should be a dilute or dispersed flow. This means that the volume fraction of the discrete phase should be much smaller than the volume fraction of the continuous phase (generally less than 1%). When the volume fraction of the particles is not small, the fluid system is categorized as a dense flow and you are required to take a different modeling approach. It is important to realize that, with the particle tracking approach, particles do not displace the fluid they occupy.
In a sparse flow, the continuous phase affects the motion of the particles, but not vice versa. This is often referred to as “one-way coupling”. When modeling such a system, it is usually most efficient to solve for the continuous phase first, then to compute the trajectories of the dispersed phases.
In a dilute flow, the continuous phase affects the motion of the particles, and the particle motion in turn disrupts the continuous phase. This is often referred to as “two-way coupling”. In order to model this effect, you must compute the continuous phase and disperse phase simultaneously. Thus, the computational demand is significantly higher when modeling dilute flows than when modeling sparse flows.