Abstract

We apply deep reinforcement learning to active closed-loop control of a two-dimensional flow over a cylinder oscillating around its axis with a time-dependent angular velocity representing the only control parameter. Experimenting with the angular velocity, the neural network is able to devise a control strategy based on low frequency harmonic oscillations with some additional modulations to stabilize the Kármán vortex street at a low Reynolds number Re=100. We examine the convergence issue for two reward functions showing that later epoch number does not always guarantee a better result. The performance of the controller provide the drag reduction of 14% or 16% depending on the employed reward function. The additional efforts are very low as the maximum amplitude of the angular velocity is equal to 8% of the incoming flow in the first case while the latter reward function returns an impressive 0.8% rotation amplitude which is comparable with the state-of-the-art adjoint optimization results. A detailed comparison with a flow controlled by harmonic oscillations with fixed amplitude and frequency is presented, highlighting the benefits of a feedback loop.

Highlights

  • A well-known Kármán vortex street is typically formed in the wake of the flow over a bluff body exerting an oscillating value of the force [1]

  • We apply deep reinforcement learning to active closed-loop control of a two-dimensional flow over a cylinder oscillating around its axis with a time-dependent angular velocity representing the only control parameter

  • The performance of the controller provide the drag reduction of 14% or 16% depending on the employed reward function

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Summary

Introduction

A well-known Kármán vortex street is typically formed in the wake of the flow over a bluff body exerting an oscillating value of the force [1]. The control method based on sinusoidal wall oscillations around the axis of the cylinder is known to dramatically suppress the drag coefficient up to 85% for a certain parameters of the amplitude and frequency for Re = 1.5 × 104 [34] This experimental result has been qualitatively confirmed by a series of numerical simulations extending the study to even higher Re = 1.4 × 105 demonstrating that high-frequency and rather high-amplitude rotary oscillations lead to even larger decrease of the drag [35,36,37,38,39]. One way to improve this performance and neutralize the effect of the fluid viscosity is to reduce the amplitude of oscillations avoiding high-frequency rotary motion This fact indicates that the harmonic control signal at low Re is far from optimal. The results of optimal control theory may serve as a verification point for the fully data-driven DRL method with a reduced complexity of implementation

Problem Formulation and Computational Details
Flow Computations
Results and Discussion
1.50 CD unforced
Conclusions
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