High Stokes Number Droplets in Homogeneous Isotropic Turbulent Flow

Abstract

Understanding sprays in turbulent flow is important to help improve the performance of gas turbine engines, and can be achieved by simulating liquid droplets in turbulent flow. Introduction of liquid droplets into homogeneous isotropic turbulent (HIT) flow requires forcing of the Navier- Stokes equations to counteract decay caused by energy dissipation. A source term (consisting of a forcing coefficient multiplied with the local velocity field) is added to the momentum equation in order to induce constant turbulent kinetic energy. We will study the effect of such a source in this work. In turbulent flow, vortices within the flow tend to affect the path of the droplet. Stokes number is used in determining these effects on a droplet’s motion. Smaller droplets (St < 0:5) may tend to follow the streamlines however the larger droplets (0:5 < St < 5) are subjected to centrifugal force generated by the turbulent eddies and will be pushed away from the vortex core. However droplets with significantly higher Stokes Number (~ 50) have high inertia and therefore do not deviate significantly in the presence of a vortex. In fact, the droplet response time may be longer than the life of the characteristic turbulent eddy, and as such special care must be exercised to study these types of flows in HIT. In this study, an Eulerian framework is used to solve the gas phase transport equations and Lagrangian equations are used to solve the liquid phase. We study high Stokes Number droplets in HIT using a triply periodic cubic domain. The forcing scheme combines the feedback control approach of Bassenne et. al. [1], with the filtered linear forcing technique of Palmore and Desjardins [2]. We study the effects of HIT forcing algorithm on high Stokes Number droplet sprays in turbulent flow.