Analysis of Turbulent Flows-From Chaos to Structure
The development of models for several phenomena occurring in turbulent single and multi-phase flows requires improved description and quantification of turbulent structures. Phenomena such as, for example, mixing, coalescence and break-up, are often fast and nonlinear. In many engineering applications, the time scale is equal to or smaller than the lifetime of turbulent vortices; thus, these phenomena are not adequately described by using average turbulence properties. The interaction is better described by the properties of single turbulent vortices. For this reason, turbulence has been modeled using LES and with the help of the dynamic Smagorinsky-Lilly SGS model for different Reynolds numbers. As a result, an efficient vortex-tracking algorithm to identify and quantify thousands of vortices and their turbulent properties has been developed.
This thesis presents the results of the analyses of a number of turbulent vortices. The results of these analyses of turbulent kinetic energy in turbulent structures, using the normalized Q criterion, showed that peak turbulent kinetic energy is located near the edge of the region identified as coherent, making the analysis challenging and model development difficult. Using the Biot-Savart law, it is possible to extend the region identified as coherent to capture the required amount of turbulent kinetic energy with the help of vortices. A detailed analysis of a small number of coherent vortices of turbulent pipe flow from LES revealed new information about the growth of these vortices (i.e. entrainment of the surrounding liquid), enstrophy and energy mechanisms over time.
Furthermore, this thesis investigates the statistical properties of turbulent vortices including the number density and distribution of associated enstrophy within the same size of coherent structures. The statistical analysis of thousands of vortices was performed at different Reynolds numbers. The number densities of turbulent vortices were described as a function of spatial positions. The number density computed was highly compatible with the models suggested by Batchelor and Martinez for vortices located in the inertial subrange and those that were larger. Moreover, it was discovered that the associated enstrophy within the same size of coherent structures had a similarly wide distribution function as turbulent kinetic energy.
Large Eddy Simulation