Experimental and numerical investigation of inertial particles in underexpanded jets

Experiments and numerical simulations of inertial particles in underexpanded jets are performed. The structure of the jet is controlled by varying the nozzle pressure ratio, while the influence of particles on emerging shocks and rarefaction patterns is controlled by varying the particle size and mass loading. Ultra-high-speed schlieren and Lagrangian particle tracking are used to experimentally determine the two-phase flow quantities. Three-dimensional simulations are performed using a high-order, low dissipative discretization of the gas phase while particles are tracked individually in a Lagrangian manner. A simple two-way coupling strategy is proposed to handle interphase exchange in the vicinity of shocks. Velocity statistics of each phase are reported for a wide range of pressure ratios, particle sizes, and volume fractions. The extent to which particles affect the location of the Mach disk are quantified and compared to previous work from the literature. Furthermore, a semi-analytic model is presented based on a one-dimensional Fanno flow that takes into account volume displacement by particles and interphase exchange due to drag and heat transfer. The percent shift in Mach disk is found to scale with the mass loading, nozzle pressure ratio, interphase slip velocity, and inversely with the particle diameter.