Vortex Models for Data Assimilation
- Author(s): Darakananda, Darwin
- Advisor(s): Eldredge, Jeff D
- et al.
Inviscid vortex models have been used for decades to investigate unsteady aerodynamics. However, real-time use of these models has been hindered by the tradeoff between increasing a model's dynamical capability and reducing its dimensionality. In this work, we present two different solutions to this problem. First, we develop a hybrid model where vortex sheets represent shear layers that separate from the wing and point vortices represent the rolled-up cores of these shear layers and the other coherent vortices in the wake. Instead of rolling up, each vortex sheet feeds its circulation into a point vortex using a circulation transfer procedure we developed. This procedure eliminates the spurious force that manifests when transferring circulation between vortex elements. By tuning the rate at which the vortex sheets are siphoned into the point vortices, we can adjust the balance between the model's dimensionality and dynamical richness. This hybrid model can capture the development and subsequent shedding of the starting vortices in real time, and remain low-dimensional enough to simulate long time horizon events such as periodic bluff-body shedding. Our second solution augments a vortex blob model with surface pressure measurements using the ensemble Kalman filter (EnKF). We adapt our circulation transfer procedure to aggressively aggregate the vortex blobs in order to prevent the dimension of the system from increasing indefinitely. The reduced number of blobs, along with the parallel nature of the EnKF, allow this solution to also run in real time. We find that not only does the data assimilation process compensate for the severe reduction in dimension, it also seems to fill in some missing physics from our inviscid model.