Kavli Affiliate: Morteza Gharib
| First 5 Authors: Alejandro A. Stefan-Zavala, Isabel Scherl, Ioannis Mandralis, Steven L. Brunton, Morteza Gharib
| Summary:
Fan-array wind tunnels are an emerging technology to design bespoke wind
fields through grids of individually controllable fans. This design is
especially suited for the turbulent, dynamic, non-uniform flow conditions found
close to the ground, and has enabled applications from entomology to flight on
Mars. However, due to the high dimensionality of fan-array actuation and the
complexity of unsteady fluid flow, the physics of fan arrays are not fully
characterized, making it difficult to prescribe arbitrary flow fields.
Accessing the full capability of fan arrays requires resolving the map from
time-varying grids of fan speeds to three-dimensional unsteady flow fields,
which remains an open problem. This map is unfeasible to span in a single
study, but it can be partitioned and studied in subsets. In this paper, we
study the special case of constant fan-speeds and time-averaged streamwise
velocities with one homogeneous spanwise axis. We produce a proof-of-concept
surrogate model by fitting a regularized linear map to a dataset of fan-array
measurements. We use this model as the basis for an open-loop control scheme to
design flow profiles subject to constraints on fan speeds. In experimental
validation, our model scored a mean prediction error of 1.02 m/s and our
control scheme a mean tracking error of 1.05 m/s in a fan array with velocities
up to 12 m/s. We empirically conclude that the physics relating constant fan
speeds to time-averaged streamwise velocities are dominated by linear dynamics,
and present our method as a foundational step to fully resolve fan-array wind
tunnel control.
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