A globally Eulerian locally Lagrangian particle concentration scheme

•Globally Eulerian Locally Lagrangian (GELL) discretization technique was used.•GELL for Lagrangian Concentration Differential Equation (LCDE) was introduced.•LCDE was compared with other methods to test accuracy in different flow-fields.•LCDE and area methods need good trajectory computation for good accuracy.•Other bin methods need high number of particles to remain accurate.

For gas flows, a Lagrangian Concentration Differential Equation (LCDE) was solved along a particle path using Eulerian derivatives for the particle velocity divergence field. This equation is solved by a Globally Eulerian Locally Lagrangian (GELL) discretization technique which avoids the computationally intensive Jacobian calculations of the Full Lagrangian method, the steady-state assumption of the area method, and the computational inefficiency of the box-counting methods. The LCDE–GELL method was compared to such methods using a high-order temporal integration technique and evaluated for two fundamental flowfields: flow past a corner and past a cylinder. In the dilute limit, the particle concentration fields were predicted for various particle inertias (characterized by a range of Stokes numbers) including the zero-mass (tracer) limit for which an exact particle concentration solution exists. Both the weighted-average and ensemble-average methods required far more parcels to achieve the same accuracy demonstrated by the LCDE–GELL method. It is recommended that future work investigates the LCDE approach for three-dimensional, complex flows with particle–particle interaction to investigate its robustness.

Graphical abstractTrajectory and Normalized concentration with Δy/D = 0.05, Np = 50 at x/D = 1.5 at t = 0.01 for St = 0.Figure optionsDownload full-size imageDownload as PowerPoint slide