ASSESSMENT OF NUMERICAL INTEGRATION SCHEMES APPLIED TO INERTIAL PARTICLE TRACKING IN CYCLONE SEPARATORS
Ricardo de Vasconcelos Salvo1; Francisco José de Souza1; Diego Alves de Moro Martins1
1 UFU
Resumo
Gas-solid flow is extremely important in many industrial branches, since it is found in various operations, which include pneumatic transport, fluidized beds and several industrial pollution control devices, such as cyclone separators. From a numerical point of view there are basically two treatments for gas-solid flow, namely the Eulerian-Eulerian and the EulerianLagrangian approaches. In the former, both the continuous phase (gas flow field) and the particulate phase (solid particles) are treated in an Eulerian reference frame, i.e., it is assumed that the particulate phase can also be treated as a continuum, being more recommended for dense flows. In the second approach, the particulate phase is treated in a Lagrangian reference frame. The individual particles trajectories are computed as ordinary differential equations based on Newton's second law. In order to compute particles velocity and position, these ODEs have to be integrated in time. In the present work, a comparative study between different numerical schemes for integrating these ODEs, namely the Euler scheme, the trapezoidal scheme and an analytical scheme, was performed. The assessment of these integration schemes was performed in an LES simulation (with the dynamic turbulence model) of the flow within a small laboratory cyclone separator, operating at a moderate Reynolds number. The grade efficiency curves are compared to experimental data for each scheme. The numerical code utilized is an in-house tool, UNSCYFL3D, based on the finite volume approach on unstructured grids with the SIMPLE algorithm for pressure-velocity coupling. The results shows that, regardless of the integration scheme, the usage of sub-time steps are mandatory for the integration of particle motion in order to improve results and reduce the cost of the simulations. Also, both the trapezoidal and analytical schemes provide quite similar results, whereas the Euler scheme requires a smaller particle substep to ensure accurate solutions.
Palavras-chave: Cyclone Separator; LES; Eulerian-Lagrangian; Grade efficiency; Numerical integration schemes