Session J17: Flow Control: Theory & Actuator Design

Optimal Control tools to minimize dispersion in turbulent flows

We develop optimal and quasi-optimal strategies to control Lagrangian objects navigating in 3d turbulent flows. We consider the problem of minimizing the dispersion rate of a couple of autonomous explorers moving into the complex fluid environment. Starting from the optimal solutions derived in control theory, we find approximated solutions that could be applied also under less restrictive conditions as, e.g., in the presence of partial observability. We are going to compare hard-wired policies resulting from different approximated solutions of the optimal control theory against strategies obtained by data-driven tools based on Reinforcement Learning.   

The inference of an incompressible flow from limited pressure data

In a variety of situations in fluid dynamics, we have data from a limited number of sensors and we wish to use these data to deduce more about the flow field. This problem can be posed as an example of elliptic inference: we seek to infer the source field (e.g., vorticity, an obstacle) from an observation field (e.g., pressure, velocity) that depends elliptically on the source. In this talk, we discuss the solution of this problem in a Bayesian ensemble-based setting: we draw a finite number of samples from a prior distribution (our initial guess) and then perform a Kalman update across the ensemble to develop our posterior, with a corresponding improved estimate of the state. We will discuss a new low-rank form of this update, in which the retained modes serve are the most informative directions in the map from the sensor data to the state update. We will demonstrate the low-rank inference in a variety of flow problems.   

A fundamental limit on the balance of power in shear- and pressure-driven channel flow

When suction/blowing control is applied at a wall, it can reduce the drag to even a sub-laminar level; however, there is an energetic cost to apply such control. Is the reduction of drag worth the cost of control? This presentation extends the results of Bewley (J. Fluid Mech., vol. 632, 443-446) and Fukagata et al. (Physica D, vol. 238, 1082-1086) to show that, in pressure- and shear-driven channel flows, the power consumed by the control at the wall is always greater than the power saved due to drag reduction below the laminar level, for any control distribution. In other words, the energetically optimal control solution is to relaminarize the flow.   

Automated Adjoint-Looping Optimization with Pseudospectral Simulations

Physics-constrained optimization can be used to study fluids systems in the context of science and engineering. In both cases, we aim to study flows which exhibit specific behaviors. We combine adjoint-looping with the Dedalus pseudospectral PDE solver to perform nonlinear optimization of initial conditions and spatially-dependent parameters. We describe how Dedalus' features (such as functional differentiation, implicit/explicit timestepping, and domain decomposition) are well-suited for adjoint-looping. Using this framework in future, we aim to study a diverse set of problems related to time-inversion, turbulence, solar physics, and shape optimization.   

Relax, then Punch: Recovering the body force from partial observations of the velocity field.

Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number of observed data points is at least an order of magnitude less than the number of modes that describes the forcing function indicating that the method introduced here is capable of identifying complicated forcing mechanisms from very simple observations. Not only is this method demonstrated on simulations of turbulent 2D Navier-Stokes equations, but we also rigorously justify convergence of the derived algorithm.   

Real-time estimation and control of flow over a NACA0012 airfoil using resolvent-based tools

This study aims to estimate and attenuate unsteady fluctuations in the near wake of a NACA 0012 airfoil at Ma = 0.3, Re=5,000, and α = 6^○ using the resolvent-based estimation and control tools recently developed by Martini et al. (J. Fluid Mech. 937:A19, 2022). The mean flow for the linearized compressible Navier-Stokes operator is obtained using direct numerical simulation, and resolvent analysis is performed as a preliminary step to validate our implementation and to gain insight into the flow physics and appropriate sensor and actuator placement. The resolvent-based estimation and control kernels are computed using a matrix-free approach, resulting in low computational cost without the need for a priori model reduction. A Wiener-Hopf formalism is used to optimally enforce causality for the estimation and control kernels. We show that our method can reduce the unsteady fluctuations in the near wake, and we investigate how this affects the aerodynamic performance of the airfoil.   

Effects of transient actuation on shear-layer oscillation dynamics in open-cavity flow

Active control of the shear-layer oscillation in a compressible open-cavity flow through an energy-based actuator remains an attractive technique. However, an efficient design of an unsteady actuation strategy is a great challenge due to our limited understanding of the transient dynamics of the interaction between the shear-layer oscillation and the actuation. In this work, we examine the response of cavity flow oscillations modified by various transient actuation introduced upstream of the cavity leading edge. The free stream Mach number is 0.5. Single- and multiple-cycle actuation with different duty cycles and wall-normal velocity amplitude are studied. The response captured from the probes in the shear layer and aftwall of the cavity exhibit significant transient dynamics, which amplifies or suppresses flow oscillation. The phase and the frequency of the oscillation change due to the actuation. Moreover, we perform modal analysis of the flow fields to gain insights into the dynamics of the dominant modes over a range of time periods during this transient process. The findings highlight the role of different actuation strategies on the dynamics of the shear-layer oscillation, which can serve as a foundation to develop more efficient unsteady active flow control strategies.

    

Design and testing of an acoustic-to-flow energy conversion device

A unique concept for the direct conversion of acoustic energy to kinetic energy in a boundary layer was developed and demonstrated. The device used a cavity with the upper surface constructed from a stretched membrane that was exposed to an incident sound field. A pitched orifice was located downstream of the membrane, which functioned as a synthetic jet. The membrane was acoustically excited in order to energize the periodic jet flow. A 2-degree-of-freedom design calculation was used to predict the natural frequencies of the device. Hot-wire measurements in an anechoic wind tunnel facility indicated a significant increase in mean and RMS velocity in the region downstream of the orifice when the device was exposed to an incident tonal acoustic pressure. The device has potential application as an aircraft engine acoustic liner that can improve internal aerodynamic performance.   

An oscillating air-water interface produces a fast-speed and energy-efficient streaming jet

Steady streaming motion induced by the oscillation of an air bubble is a powerful mechanism in many applications. Recently, it is found that the dynamic oscillation of an axisymmetric air-water interface induces various streaming patterns, e.g., a low-speed streaming vortex or a fast-speed streaming jet, when the non-dimensional oscillation amplitude d/D is large (d is the oscillation amplitude and D is the diameter of the interface). In particular, the streaming jet has many extraordinary characters, such as fast speed and high energy efficiency, which can be employed in many application areas, such as in turbulent boundary layer control and microfluidics devices.

    

Characterization of Sweeping Jet Actuator Flow Field using DMD analysis

The dynamic mode decomposition (DMD) algorithm captures the oscillating behavior of complex non-linear flow structures by identifying the low-rank coherent structures and superimposing the dominant modes to reconstruct the system. The basis vectors (modes) are determined using the Koopman theory. They are applied to develop an accurate shallow rank structure from a non-linear complex sweeping jet actuator flow field in the present study. With spectral decomposition, DMD can identify the dominant patterns in the oscillating flow structure - making it a valuable tool for spatio-temporal data extraction. Since the algorithm has no hyperparameter, it is flexible to implement in any periodic flow distribution to determine the temporal behavior. We have modified the classical DMD algorithm using amplitude-based data filtration for better accuracy and flexibility on computationally obtained raw data. For analysis, we considered velocity and pressure data series from two different sampling windows in a 2D sweeping jet actuator flow field for time step sensitivity and dominant mode requirement for reconstructing and predicting the coherent structure for a single mass flow rate. Finally, we demonstrated the model's effectiveness in data interpretation by combining two other sampling windows, which indicate its compatibility for working as a local tool to stitch the flow topology.