Lagrangian Particle Tracking (LPT) is a powerful technique used in Computational Fluid Dynamics (CFD) to simulate the behavior of individual particles as they move through a fluid system. In LPT, each particle is treated as an individual entity that interacts with the surrounding fluid, and its motion is tracked over time. This technique can be used to model a wide range of phenomena in areas such as engineering applications: simulating the mixing of fuel droplets in the combustion chamber of propulsion systems; environmental applications: simulating the dispersion of pollutants emerging from factories formation and growth of raindrops, and transport of atmospheric aerosols; medical applications: simulating the drug delivery to pulmonary systems and deposition of blood cells in the human body [1-5].
To model the interaction between the particles and the fluid flow, different classes of coupling can be used. One-way coupling is the simplest and most commonly used approach, where the particles are assumed to have no effect on the fluid flow. Two-way coupling, on the other hand, considers the effect of the particles on the fluid flow (the particle's wake increases dissipation in the carrier fluid), as well as the fluid's effect on the particles. Three-way coupling takes into account the mutual interaction between the fluid flow and particles, also, the effect of the influent of a particle's motion through the fluid on another particle. Four-way coupling involves all that happens in the three-way plus particle-particle collision on top. Modeling each of these coupling classes has its own advantages and limitations, and the choice of coupling depends on the specific application and the level of detail required in the simulation.
One of the key advantages of Lagrangian particle tracking is its ability to provide detailed information about the behavior of individual particles. By tracking the position, velocity, and other properties of each particle over time, researchers can gain insights into the transport and dispersion of particles in complex fluid systems. Another important application of Lagrangian particle tracking is in the modeling of turbulent flows. Turbulence is a complex phenomenon that is difficult to simulate using traditional methods. However, by tracking large numbers of low-inertia (i.e. tracer particles) through a turbulent flow, researchers can gain a better understanding of the dynamics of turbulence and how it affects particle transport.
Using tracer particles is a widely used technique in CFD to study the behavior of complex turbulent flows under the well-mixed criterion. Tracer particles are typically small, non-reactive particles that are added to a fluid system to help visualize the flow patterns and transport mechanisms. By tracking the position and velocity of tracer particles as they move through a fluid system, researchers can gain insights into the turbulent mixing and dispersion of particles in the flow. This technique is particularly useful in applications where the well-mixed criterion is important, such as in chemical reactions or environmental transport modeling. By using tracer particles in CFD simulations, researchers can improve our understanding of the complex behavior of turbulent flows and develop more accurate models for a wide range of applications.
Lagrangian particle tracking is also useful in the modelling of multiphase flows, where two or more phases (e.g., liquid-gas or solid-liquid) are present. By tracking particles of different phases through the system, researchers can gain insights into the behavior of each phase and how they interact with each other. To accurately model particle motion in such flows, it is very important to solve the underlying fluid dynamics (carrier medium) equations with a high degree of accuracy. This involves simulating the complex interactions between the fluid and the particles, such as fluid-particle collisions, drag forces, and turbulence effects. By accurately capturing these interactions, Lagrangian particle tracking can provide insights into the behaviour of particle-laden flows that are difficult to obtain through experimental measurements alone.
To implement an LPT algorithm in a CFD code, a two-step procedure is usually performed; a search step and an interpolation step. In the search step, the computational domain is scanned to detect the closest cell center (e.g. in cell-centered codes) to the particle location. Then, from the cell index, the closest node to this particle can be identified. This is a necessary operation at the first time step where particles are just introduced into the domain. Once done, the algorithm locates the neighbouring cells encapsulating the particle’s closest node. In an optimized fashion, those very surrounding cells are to be scanned for the next time step after advancing the particle (i.e. instead of scanning the whole domain) and so on.
For advancing particles, one additional transport equation to fluid flow equations has to be solved for each individual particle, which is known as the Lagrangian Equation of Motion (LEM). This equation is simply the manifestation of Newton's second law - accounting for the sum of forces acting on the particle (see Ref. 11).
As mentioned above, simulating particle-laden flows in Computational Fluid Dynamics (CFD) requires careful consideration of several factors to ensure accurate and reliable results. Here are some of the best practices that should be followed when simulating particle-laden flows in CFD:
By following these best practices, accurate and reliable results of the particle-laden flows can be obtained.
In summary, Lagrangian particle tracking is a powerful tool that is transforming the way we model and understand fluid systems. As research continues in this area, we can expect to see even more exciting applications of this technique in a wide range of industries.
For more details about the implementation of LPT, a simple and easy-to-understand algorithm is implemented in the Open-Source code T-Flows. The code features a few test cases that are easy to run on a personal computer. The algorithm has been verified and validated through several benchmarks [6-11]. The latest version of the code is accessible through Github link above.
