High-order resolution Eulerian–Lagrangian simulations of particle dispersion in the accelerated flow behind a moving shock

Abstract

This paper presents a computational study of the two-dimensional particle-laden flow developments of bronze particle clouds in the accelerated flow behind a moving normal shock. Particle clouds with a particle volume concentration of 4% are arranged initially in a rectangular, triangular and circular shape. Simulations are performed with a recently developed high-order resolution Eulerian–Lagrangian method that approximates the Euler equations governing the gas dynamics with the improved high order weighted essentially non-oscillatory (WENO-Z) scheme, while individual particles are traced in the Lagrangian frame using high-order time integration schemes. Reflected shocks form ahead of all the cloud shapes. The detached shock in front of the triangular cloud is weakest. At later times, the wake behind the cloud becomes unstable, and a two-dimensional vortex-dominated wake forms. Separated shear layers at the edges of the clouds pull particles initially out of the clouds that are consequently transported along the shear layers. Since flows separated trivially at sharp corners, particles are mostly transported out of the cloud into the flow at the sharp front corner of the rectangular cloud and at the trailing corner of the triangular cloud. Particles are transported smoothly out of the circular cloud, since it lacks sharp corners. At late times, the accelerated flow behind the running shock disperses the particles in cross-stream direction the most for the circular cloud, followed by the rectangular cloud and the triangular cloud.