SBIR Phase I: A Fast Parallel Grid-Free Method for Simulating Turbulent Incompressible Flow In/Around Time-Varying Geometries

This Small Business Innovation Research (SBIR) Phase I project prepares the ground-work for the development of the first commercially available Computational Fluid Dynamics package for a truly grid-free Large Eddy Simulation (LES) of turbulent incompressible vortex dominated flow in complex time-varying geometries. The computational engine is based on the parallel, fast multi-pole implementation of a Lagrangian vortex-boundary element method. Turbulence is accounted for via LES, using a Lagrangian dynamic Smagorinsky sub-grid scale model. The method is: (1) fully grid-free in the fluid domain, (2) free of numerical diffusion, (3) inherently solution-adaptive, and (4) capable of modeling inhomogeneous unsteady wall-bounded turbulent flow. To this end, two new ideas will be developed during Phase I: A grid-free method for predicting diffusion with variable-viscosity, which is a pre-requisite for LES modeling; and a non-diffusive vortex merging strategy to curb the proliferation of particles and maintain long-time accuracy. These will then be incorporated into the Lagrangian vortex element method to demonstrate the salient features of grid-free vortex-based LES modeling of turbulent flows, using the prototypical example of the evolution of an initially perturbed infinite-Reynolds-number vortex ring in free space. The software is ideal for simulation and analysis of complex turbulent flow phenomena. This includes vortex breakdown, (massive) flow separation, vortex shedding, transient jets in cross-stream, wake-body interaction, high-swirl flow, etc. All are associated with the design of advanced flow control mechanisms used, for example, to reduce flow-induced noise and vibration, and to improve lift/drag performance at reduced energy consumption rates. Examples are flow over bluff bodies such as ground or under-water vehicles; in engines; in/around rotating machinery such as pumps and fans; helicopters; or in data storage units with rotating and moving parts.