Unsteady effects in dense, high speed, particle laden flows

• A shock wave impacting a frozen particle cloud is simulated and modeled.
• The 1-D model captures the major flow features of the 2-D simulation.
• The turbulent and streamwise kinetic energy magnitudes are comparable.
• The pressure gradient of the 1-D model is shallower than in the 2-D simulation.
• Models are needed for the Reynolds stress and turbulent kinetic energy.

Dense high speed non-compacted multiphase flows exist in variable phase turbines, explosions, and ejector nozzles, where the particle volume fraction is in the range 0.001<αd<0.50.001<αd<0.5. A canonical problem that can be used to study modeling issues related to these types of flows is a shock wave impacting a planar particle cloud. Thus far, prior work has modeled the flow using a 1-D volume-averaged point particle approach and developed momentum and energy coupling terms that reproduce accurately the trajectory of particles in the experiments. Although these early results are promising, it is appropriate to question whether all aspects of the experimental flow can be captured using a one-dimensional model that is traditionally only used for dilute flows. Thus the objective of this work is to set-up a two-dimensional configuration that captures qualitatively the multidimensional behavior of a real three-dimensional particle cloud, but can be used as an exact solution to compare with an equivalent volume-averaged model. The 2-D data is phase-averaged to reduce it to one dimension, and x–t diagrams are used to characterize the flow behavior. These results show the importance of the Reynolds stress term inside the particle cloud and in its turbulent wake. A one-dimensional (1-D) model is developed for direct comparison with the 2-D simulation. While the 1-D model characterizes the overall steady-state flow behavior well, it fails to capture aspects of the unsteady behavior inside and behind the particle cloud because it neglects important unclosed terms.