Comparison between Lagrangian and Eulerian approaches in predicting motion of micron-sized particles in laminar flows

Abstract Modeling the behavior of suspended particles in gaseous phase is important for diverse reasons; e.g. aerosol is usually the main subject of CFD simulations in clean rooms. Additionally, to determine the rate and sites of deposition of particles suspended in inhaled air, the motion of the particles should be predicted in lung airways. Meanwhile there are two basically different approaches to simulate the behavior of particles suspension, Lagrangian and Eulerian approaches. This study compares the results of these two approaches on simulating the same problem. An in-house particle tracking code was developed to simulate the motion of particles with Lagrangian approach. In order to simulate the same problem with Eulerian approach, the solution to the transport equation with appropriate initial and boundary conditions was used. In the first case study, diffusion of particles, initially positioned homogeneously on an infinite plane was modeled with both approaches and the results were compared and the mismatch between Lagrangian and Eulerian approaches was analyzed for different concentrations. In the second case study, airflow with parabolic velocity profile moving between two parallel plates was modeled with two approaches. The airflow initially contained a homogeneous suspension of particles and the plates were maintained at zero concentration. The concentration along the plates was compared between the two approaches and the differences in the performance of each approach were investigated, again for different initial concentrations. The overall results confirm that as particle concentration falls below a minimum amount, approximately 105 m−2, the results of the two approaches deviate considerably from each other and hence the Eulerian approach cannot be taken as an alternative for Lagrangian approach for low concentrations. For the third problem, we investigated the 3D particle flow in an expanding lung alveolus. It is shown that when the number of total released particles increases, the results of Eulerian approach can be used as an alternative to Lagrangian simulation. Since the number of particles existing in the lung alveolus in normal condition is much lower than this value, we concluded that Eulerian method cannot be applied to problems involving low concentration of particles. Although, the results of the Lagrangian problem may converge to the Eulerian one by increasing simulation time, but it is a hypothetical situation which not really exist in short time scale problems such as third case study in this paper.