Building a Turbulent Jet: Measuring/Modeling Lagrangian Dispersion, Particle Trajectory Dynamics and Intermittency

The mechanics of how particles diffuse, interact, eject, etc. within a fluid is applicable to numerous industrial and environmental applications. Unwanted products of combustion, dust contamination of solar panels, pathogen transport during a cough and ejections of particles during volcanic eruptions, are a few examples of flows in which increased knowledge of particle dynamics could result in substantial reduction of negative environmental and economic impacts. To better understand the tendencies of particles within shearing flows (such as jets), an extensive experimental campaign was conducted. Measurements of a turbulent round water jet were performed within an icosahedral tank. Particle tracking velocimetry was employed to create three-component, three-dimensional trajectories. Particles of varying size and weight were used to seed the flow in order to provide a range of inertial effects based on the particle interaction with the fluid. Numerous Eulerian and Lagrangian parameters were characterized and most notable, a trajectory stationarization technique was successfully implemented to address the inhomogeneity of the flow field. This approach could be extended to provide systematic methods to analyze complicated flow fields, enhancing knowledge of their dynamics. Alternatively, theoretical models of particle mechanics have been constructed, contributing to the baseline understanding of Lagrangian dynamics. Stochastic processes and phenomenological approaches are presented to accurately predict the low-order statistics of tracers, point particles which follow the motion of the fluid, for the idealized flow of homogeneous, isotropic and stationary turbulence (i.e. without the inclusions of external forces). In comparison to previous models, the proposed process is infinitely differentiable for finite Reynolds number and includes intermittent scaling properties. Furthermore, particle accelerations and velocities can be modeled based on the stochastic processes, providing full temporal information of the flow dynamics. The advancements made to homogeneous, isotropic and stationary turbulence are then exploited and used as an input to generate an inhomogeneous flow field based on self-similar relations within a jet to include, in a simple way, the intermittent behavior of the turbulence. Specifically, a model is proposed to compensate a stationary signal by the evolution of the Eulerian background properties of a jet to transform Lagrangian velocities in order to build up an ensemble of turbulent jet trajectories. The modeled jet, based on inputted signals from a stochastic process and direct numerical simulation are compared against the experimental data. Statistics show remarkable agreement for statistics of velocity increments and for higher-order moments, accurately capturing dissipative behavior within the non-homogeneous flow. With some additional study, the proposed model could be applied to modeling of particle velocity statistics during volcanic eruptions, pathogen transport during a cough and pollutant contamination from smokestacks