SBIR Phase I:A Flexion-Based Computational Fluid Dynamics Tool for the Fast Computation of Turbulent Flow over Complex Geometries

The broader impact of this Small Business Innovation Research (SBIR) Phase I project is the acceleration of the development of innovative industrial design concepts involving complex turbulent fluid flow using computational fluid dynamics (CFD) software. Although CFD software has broad applications in several industries, the company’s particular interest is in bodies with strong vortical wakes such as bio-inspired renewable energy extraction devices and electric vertical takeoff/landing (eVTOL) vehicles. It is anticipated that the project may lead to the timely and cost-effective design of energy extraction devices without the need to build and test prototypes during the design phase.The project may also enhance the safety and operating envelope of urban air mobility vehicles. The proposed cloud-based CFD software will provide startups and smaller companies (without access to high-performance computing resources) with the ability to perform CFD analysis in reasonable timeframes. The proposed novel reformulation of the Navier-Stokes equations will also have a lasting impact on the education of the next generation of engineers and scientists as they gain a better understanding of the advantages of the new set of equations for turbulent flows.This Small Business Innovation Research (SBIR) Phase I project seeks to develop a fast high-fidelity computational fluid dynamics (CFD) software for predicting unsteady flow separations over complex geometries at large Reynolds (Re) numbers without any heuristic turbulence modeling. The softwarewill build upon prior work by the proposer who developed a novel flexion-based Large Eddy Simulation (LES) method for high Re turbulent flows. The LES method uses the flexion (vorticity curl) vector as the primary dependent variable in the Navier-Stokes equations to better track sharp vorticity-gradient regions in high Re flows. The method also uses hyperviscous dissipation instead of a parameterized sub-grid model for unresolved small-scale turbulent motions. The flexion-based LES method will be extended to complex geometries by coupling it with a vortex panel method for the body surface. The vortex panel method leads to accurate predictions of the shear stress on wall boundaries from the wall vorticity without the computationally demanding requirement of a fine mesh to resolve the thin boundary layers that occur in high Re flows. The proposed approach represents a new technique of using panel methods, which have a rich history in aerodynamics, to provide boundary conditions for large eddy simulations of the vortical wake.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.