Large Eddy Simulation and Analysis of Shear Flows in Complex Geometries

In the present work, large eddy simulation is used to numerically investigate two types of shear flows in complex geometries, (i) a novel momentum driven countercurrent shear flow in dump geometry and (ii) a film cooling flow (inclined jet in crossflow). Verification of subgrid scale model is done through comparisons with measurements for a turbulent flow over back step, present cases of counter current shear and film cooling flow. In the first part, a three dimensional stability analysis is conducted for countercurrent shear flow using Dynamic mode decomposition and spectral analysis. Kelvin-Helmholtz is identified as primary instability mechanism and observed as global mode at a specific parameter. Mechanism of global mode synchronization over distinct spatial location is studied. In the second part, the flow physics of film cooling flows is analysed. The origin, evolution of various coherent flow structures and their role in film cooling heat transfer is studied based on detailed flow visualization. Further, the contribution of coherent structures in film cooling heat transfer and mixing is studied through modal analysis. Low frequency modes are found to have large contribution in cooling surface adiabatic temperature fluctuation while high frequency modes play larger role in bulk mixing. Finally, a new contoured crater shape is developed and shown to have improved performance at shallow depth compared to earlier designs

On the state space geometry of the Kuramoto-Sivashinsky flow in a periodic domain

The continuous and discrete symmetries of the Kuramoto-Sivashinsky system restricted to a spatially periodic domain play a prominent role in shaping the invariant sets of its chaotic dynamics. The continuous spatial translation symmetry leads to relative equilibrium (traveling wave) and relative periodic orbit (modulated traveling wave) solutions. The discrete symmetries lead to existence of equilibrium and periodic orbit solutions, induce decomposition of state space into invariant subspaces, and enforce certain structurally stable heteroclinic connections between equilibria. We show, on the example of a particular small-cell Kuramoto-Sivashinsky system, how the geometry of its dynamical state space is organized by a rigid `cage' built by heteroclinic connections between equilibria, and demonstrate the preponderance of unstable relative periodic orbits and their likely role as the skeleton underpinning spatiotemporal turbulence in systems with continuous symmetries. We also offer novel visualizations of the high-dimensional Kuramoto-Sivashinsky state space flow through projections onto low-dimensional, PDE representation independent, dynamically invariant intrinsic coordinate frames, as well as in terms of the physical, symmetry invariant energy transfer rates.Comment: 31 pages, 17 figures; added references, corrected typos. Due to file size restrictions some figures in this preprint are of low quality. A high quality copy may be obtained from http://www.cns.gatech.edu/~predrag/papers/preprints.html#rp