Data-Driven Modeling for On-Demand Flow Prescription in Fan-Array Wind Tunnels

TL;DR

This paper develops a surrogate linear model to predict and control flow profiles in fan-array wind tunnels, enabling more precise and constrained flow design in complex turbulent environments.

Contribution

It introduces a linear surrogate model for fan-array flow prediction and demonstrates its use in an open-loop control scheme for flow profile design.

Findings

Model achieved a mean prediction error of 1.02 m/s.

Control scheme had a mean tracking error of 1.05 m/s.

Physics are dominated by linear dynamics for constant fan speeds.

Abstract

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.