Lagrangian Parcel Volume Method for Unsteady Particle Concentration

A new technique is proposed for computing particle concentrations and fluxes with Lagrangian trajectories. This method calculates particle concentrations based on the volume of a parcel element, or cloud, at the flux plane compared against the initial volume and is referred to as the Lagrangian Parcel Volume (LPV) method. This method combines the steady-state accuracy of area-based methods with the unsteady capabilities of bin-based methods. The LPV method results for one-dimensional (1D) unsteady flows and linear two-dimensional (2D) steady flows show that a quadrilateral element shape composed of a single parcel (with four edge particles) is capable of accurately predicting particle concentrations. However, nonlinear 2D flows can lead to concave or crossed quadrilaterals which produce significant numerical errors. This problem was solved by dividing the quadrilateral parcel into two triangular semi-parcels (each with three edge particles), such that triangular shapes are maintained regardless of trajectory crossing effects. Various schemes were used to understand the relationship between computational resolution and accuracy, the influence of particle timestep and parcel size and spacing. It was found that concentration interpolation can be used to reduce the number of parcels in the convection direction while maintaining high accuracy. For unsteady 2D flows, it is suggested that in order to correctly obtain the effective concentration, parcels must be released in succession; however, a larger distance between parcels is possible with the use of an interpolation at the cost of accuracy.