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Numerical Approach for On-the-Fly Active Flow Control via Flow Map Learning Method

Xinyu Liu, Qifan Chen, Dongbin Xiu

TL;DR

A data-driven numerical approach is presented for on-the-fly active flow control and its effectiveness for drag reduction in two-dimensional incompressible flow past a cylinder is demonstrated and offers the potential for real-time optimal control in other systems.

Abstract

We present a data-driven numerical approach for on-the-fly active flow control and demonstrate its effectiveness for drag reduction in two-dimensional incompressible flow past a cylinder. The method is based on flow map learning (FML), a recently developed framework for modeling unknown dynamical systems that is particularly effective for partially observed systems. For active flow control, we construct an FML dynamical model for the quantities of interest (QoIs), namely the drag and lift forces. During offline learning, training data are generated for the responses of drag and lift to the control variable, and a deep neural network (DNN)-based FML model is constructed. The learned FML model enables online optimal flow control without requiring simulations of the flow field. We demonstrate that the FML-based approach can be integrated with existing optimal control strategies, including deep reinforcement learning (DRL) and model predictive control (MPC). Numerical results show that the proposed approach enables on-the-fly flow control and achieves more than $20\%$ drag reduction. By eliminating the need for forward simulations during control optimization, the approach offers the potential for real-time optimal control in other systems.

Numerical Approach for On-the-Fly Active Flow Control via Flow Map Learning Method

TL;DR

A data-driven numerical approach is presented for on-the-fly active flow control and its effectiveness for drag reduction in two-dimensional incompressible flow past a cylinder is demonstrated and offers the potential for real-time optimal control in other systems.

Abstract

We present a data-driven numerical approach for on-the-fly active flow control and demonstrate its effectiveness for drag reduction in two-dimensional incompressible flow past a cylinder. The method is based on flow map learning (FML), a recently developed framework for modeling unknown dynamical systems that is particularly effective for partially observed systems. For active flow control, we construct an FML dynamical model for the quantities of interest (QoIs), namely the drag and lift forces. During offline learning, training data are generated for the responses of drag and lift to the control variable, and a deep neural network (DNN)-based FML model is constructed. The learned FML model enables online optimal flow control without requiring simulations of the flow field. We demonstrate that the FML-based approach can be integrated with existing optimal control strategies, including deep reinforcement learning (DRL) and model predictive control (MPC). Numerical results show that the proposed approach enables on-the-fly flow control and achieves more than drag reduction. By eliminating the need for forward simulations during control optimization, the approach offers the potential for real-time optimal control in other systems.
Paper Structure (21 sections, 34 equations, 9 figures)

This paper contains 21 sections, 34 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Computational Setup and Numerical Solver
  4. Active Flow Control for Drag Reduction
  5. Preliminaries
  6. Flow Map Learning
  7. Reinforcement Learning
  8. Model Predictive Control
  9. FML Modeling for QoI Dynamics under Excitation
  10. FML Models
  11. Data Generation
  12. FML Model Construction
  13. FML based Optimal Control
  14. Deep Reinforcement Learning with FML
  15. Model Predictive Control with FML
  16. ...and 6 more sections

Figures (9)

  • Figure 2.1: Computational setup for the flow past cylinder simulation. Left: the computational domain; Right: the computational mesh.
  • Figure 2.2: Velocity boundary conditions for the two synthetic jets on the cylinder surface.
  • Figure 4.1: DNN structure for QoI FML model \ref{['eq:QoI_dynamic']}.
  • Figure 6.1: Open-loop validation for the trained FML-1 model at $Re=300$. Left: drag coefficient ($C_D$); Right: lift coefficient ($C_L$).
  • Figure 6.2: Open-loop validation of the trained FML-2 model. Left column: drag coefficient ($C_D$); Right column: lift coefficient ($C_L$). Top row: $Re = 118.62$; Middle row: $Re = 303.10$; Bottom row: $Re = 444.22$. The $Re$ numbers are randomly generated from $Re \in [100,500]$ and unknown to the FML-2 model.
  • ...and 4 more figures