High-fidelity eulerian-lagrangian methods for simulation of three dimensional, unsteady, high-speed, two-phase flows in high-speed combustors

A preliminary study of a three-dimensional numerical model for determining the flow and particle developments through a shock tube containing 10⁸ bronze particles is presented here. The numerical experiment is initialized as a hexahedral cloud of particles immediately adjacent to a right running normal shock. Flow characteristics are computed using a three-dimensional high-order Eulerian-Lagrangian method, which solves the Euler equations governing the gas dynamics with an improved high order weighted essentially non-oscillatory (WENO-Z) scheme, while individual particle trajectories are traced in the Lagrangian frame using high-order time integration schemes. Two way coupling between the carrier gas and the particles is modeled, using a high-order ENO interpolation, via the exchange of the momentum and energy at the particle positions through the use of an additional source term in the Euler equations. A high-order central weighing deposits the particle influence on the carrier phase. The preliminary solution as computed in the 3D model is then compared to similar experiments analyzed with 2D models.