An alternative two-way coupled Euler-Lagrange scheme to model the performance of finite-size particle in supersonic flow

In Euler-Lagrange (EL) framework, the Gauss kernel (GK) is usually introduced to avoid Dirac source disturbance of traditional particle-in-cell (PIC) method in subsonic regime. This work investigates the applicability and limitations of PIC-two-way coupling and GK for finite-size particles subjected to supersonic and dilute regime. Results indicate that the source disturbance of GK always peaks at the symmetric center of GK causing a sub-optimal shock and ignoring wake in supersonic regime. Meanwhile, classical PIC-interpolation underestimates the drag force on particles due to shock and finite-size effects. To circumvent those issues, a modified coupling method utilizing upstream weighting averaged method and mix-gaussian kernel is proposed to optimize Euler-to -Lagrange coupling and Lagrange-to-Euler coupling, respectively. The modified method not only allows for accurate tracking of arbitrary finite-size particles in supersonic flows but also restores the undisturbed laden flow quantities exerting on particles. Shock and wake zone are reproduced before and after the particle based on recommended parameters. Furthermore, the modified method is validated using a particle-pair exposed to supersonic flow referred from Utkin's experiment(Utkin et al., 2021), and shows excellent agreement.