Low-Memory Reduced-Order Modelling With Dynamic Mode Decomposition Applied on Unsteady Wheel Aerodynamics

Wheel aerodynamics has a major impact on the overall aerodynamic performance of a vehicle. Different vortex excitation mechanisms are responsible for the induced forces on the geometry. Due to the high degree of complexity, it is difficult to gain further insight into the vortex structures at the rotating wheel. Therefore, wheel aerodynamics is usually investigated using temporally averaged flow fields. This work presents an approach to apply a recently introduced low-memory variant of Dynamic Mode Decomposition (DMD), namely Streaming Total DMD (STDMD), to investigate temporally resolved simulations in greater detail. The performance of STDMD is shown to be comparable to conventional DMD for a rotating generic closed wheel simulation test case. By creating a Reduced-Order Model (ROM) using a comparably small amount of DMD modes, the amount of complexity in the flow field can be drastically reduced. Orthonormal basis compression, amplitude ordering and a newly introduced amplitude weighting method are analyzed for creating a suitable ROM of DMD modes. A combination of compression and ordering by eigenvalue-weighted amplitude is concluded to be best suited and applied to the Delayed Detached Eddy Simulation (DDES) of the rotating generic closed wheel and a production vehicle rim wheel. The most dominant flow structures are captured at frequencies between 18Hz and 176Hz. Leading modes for both geometries are found close to the wheel rotation frequency and multiples of that frequency. The modes are identified as recirculation modes and vortex shedding.