Control of Jets in Crossflow using Direct Numerical Simulations A THESIS SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY

We use direct numerical simulations to study control of jets in crossflow by axial pulsing. Our main idea is that pulsing generates vortex rings; the effect of pulsing on jets in crossflow can therefore be explained by studying the behavior of vortex rings in crossflow. A method is proposed that allows optimal values of pulsation frequency, modulation and energy to be estimated a priori. This is accomplished in the following three stages. First, direct numerical simulation is used to study the mixing of a passive scalar by a vortex ring issuing from a nozzle into stationary fluid. The ‘formation number’ (Gharib et al 1998), is found to be 3.6. Simulations are performed for a range of stroke ratios encompassing the formation number, and the effect of stroke ratio on entrainment, and mixing is examined. When the stroke ratio is greater than the formation number, the resulting vortex ring with trailing column of fluid is shown to be less effective, at mixing and entrainment. As the ring forms, ambient fluid is entrained radially into the ring from the region outside the nozzle exit. This entrainment stops once the ring forms, and is absent in the trailing column. The rate of change of scalar containing fluid is studied for its dependence on stroke ratio. This rate varies linearly with stroke ratio until the formation number, and falls below the linear curve for stroke ratios greater than the formation number. This behavior is explained by considering the entrainment to be a combination of that due to the leading vortex ring, and that due to the trailing column. For stroke ratios less than the formation number, the trailing column is absent, and the size of the vortex ring