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Description
This thesis presents a two dimensional Eulerian-Eulerian model with a first order Godunov scheme for a normal running shock interacting with a cloud of particles. This model treats both carrier phase and dispersed phase in Eulerian reference, which analyzes all fluid's and particles' characteristics in a specific location over time. The governing equations are Euler equations for the carrier phase, and Shotorban's model for the dispersed phase. Dr. Shotorban's model is a two-fluid model for the direct numerical simulation of particle-laden flows. The two dimensional reduced Euler equations and Shotorban's model, as well as their characteristic forms are derived. For the dispersed phase, the eigenvalues _ derived in x and y directions show their dependency on particle velocities __, __ and particle sub-grid-scale stresses ___, ___. Values of ___, ___ are set to a small value of _ where particles are not present to avoid singularity or imaginary values in eigenvector matrices. Both carrier and dispersed phases are numerically solved using dimensional splitting, to decompose the systems into two one-dimensional problems that are solved alternately in x and y directions. The decoupled carrier phase is verified with higher order Godunov based Eulerian model for a two dimensional cylindrical explosion case. The dispersed phase is verified against one dimensional Eulerian-Eulerian model, using a quasi-two-dimensional normal moving shock interacting with a cloud of particles. The Eulerian-Eulerian model for a two dimensional normal running shock interacting with a rectangular cloud of particles was then validated against higher order, WENO-3 and WENO-5 PSIC Eulerian-Lagragian models. The Eulerian-Lagragian model treats the carrier phase in an Eulerian reference, and the dispersed phase in a Lagragian framework where the particle characteristics are defined and updated along the particle path-lines.
