Data-driven modelling for on-demand flow prescription in fan-array wind tunnels

Fan-array wind tunnels are an emerging technology to prescribe 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 flow, the physics of fan arrays are not fully characterised, 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. In this paper, we study the 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 regularised linear map to a dataset of fan-array measurements. We use this model as basis for an open-loop control scheme to prescribe flow profiles subject to constraints on fan speeds. We experimentally validate our model and control scheme, provide a physical interpretation of our model as a superposition of self-similar jet profiles and conclude that the physics relating constant fan-array speeds to time-averaged streamwise velocities are dominantly linear.