Session G04: Flow Control: General (5:00pm - 5:45pm CST)

Second-order adjoint-based sensitivity for hydrodynamic stability and control

Adjoint-based sensitivity analysis is routinely used today to assess efficiently the effect of flow control on the linear stability properties of globally unstable flows. Sensitivity maps identify regions where small-amplitude control is the most effective, i.e. yields the largest first-order (linear) eigenvalue variation. In this study an adjoint method is proposed for computing a second-order (quadratic) sensitivity operator. The method is applied to the flow past a circular cylinder, controlled with a steady body force or with a model of passive control device. Maps of second-order eigenvalue variations are obtained, without computing controlled base flows and eigenmodes. For finite control amplitudes, the second-order analysis improves the accuracy of the first-order prediction, informs about its range of validity, and about whether it under/overestimates the actual eigenvalue variation. The second-order variation can be decomposed into two mechanisms: second-order base flow modification, and interaction between first-order base flow and eigenmode modifications. Finally, the optimal control for second-order stabilization is computed via a quadratic eigenvalue problem.   

Increasing the aerodynamic efficiency of a NACA4412 airfoil with blowing and suction

Uniform blowing and uniform suction have been studied for a long time as a possible control method in aerodynamic applications. We performed highly-resolved large-eddy simulations (LES) of the turbulent flow around a NACA4412 at Reynolds numbers based on chord length and incoming velocity of $200,000$ and $400,000$, considering multiple control configurations. We found that uniform blowing applied over the suction side of the airfoil reduces the skin friction, but it increases the pressure drag by a higher amount. Furthermore, it reduces lift, resulting in lower aerodynamic efficiency. On the contrary, uniform suction increases the skin friction, but it decreases the pressure drag and increases lift, resulting in higher aerodynamic efficiency (these results are in agreement with experiments carried out by other groups with similar control configurations). Our high-fidelity numerical simulations allow studying the interaction between uniform blowing and suction with the strong adverse pressure gradient, which affects the turbulent boundary layer on the suction side of the airfoil. In the conference contribution, we will summarize the control effect on the aerodynamic properties of the airfoil and the properties of the flow, including the FIK identity and spectral analysis.   

Prescribed surface deformation on low Re airfoil: Spatio-temporal variation of flow field and resulting aerodynamic performance

The need for more maneuverable and disturbance-robust craft has driven investigations into flow control on canonical aerodynamic bodies. Our focus is on control strategies which employ surface deformation for aerodynamic benefit. We perform high-fidelity simulations at a Reynolds number of 1000 of a stationary NACA0012 airfoil with traveling waves prescribed along its suction surface. We quantify the effect of wavenumber and wavespeed of these prescribed surface motions on aerodynamic performance, and explain aerodynamically beneficial parameters in terms of their spatio-temporal impact on the pressure field and the formation and interaction of key vortical structures. To systematically build in problem complexity, we first consider a steady-flow case with the airfoil at an angle of attack of 5 degrees. We then incorporate surface deformations into an unsteady flow scenario, with the airfoil at an angle of attack of 15 degrees. In this unsteady setting, we highlight three separate behavioral regimes and explain their impact on aerodynamic performance by the way they interact with the underlying vortex shedding processes associated with the baseline (unactuated) case.   

Dynamical model identification via a method combining data driven and data assimilation approaches

Model-based control strategies require a dynamical model that is sufficiently accurate and robust with respect to the variation of the control parameters. When this model can not be determined using first principle equations, then identification techniques are needed. In this work, we present a general framework for identifying the parameters of a POD reduced-order model. The model obtained directly by POD Galerkin projection of the N-S equations is, in general, not robust. Here, we obtain a scalable identification of the parameters by a combined implementation of machine learning and data assimilation (DA) approaches. Recent advances in data driven techniques have given the possibility to learn the driving partial differential equations by using neural networks. However, without a partial knowledge of the underlying dynamics, the learning time may increase prohibitively with the number of parameters. To circumvent this difficulty, this work combines: i) PDE discovery methods to identify the parameters in the model, by using the physics-informed neural network\footnote{Raissi et al., J. Comp. Phys. 378 (2019)}, and ii) Dual Ensemble Kalman filter\footnote{Moradkhani et al., Adv. Water Res. 28(2) (2005)}, a DA technique to correct both the predicted state and parameters.   

Explorative gradient method for active drag reduction of the fluidic pinball and slanted Ahmed body

We address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding suboptimal local minima. This challenge is addressed by a new optimizer, called explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hypercube sampling iteration. Thus, the convergence rate of a gradient based method is guaranteed while, at the same time, better minima are explored. For an analytical multi-modal test function, EGM is shown to significantly outperform the downhill simplex method, the random restart variant, Latin hypercube sampling, Monte Carlo iterations and the genetic algorithm. EGM is applied to minimize the net drag power of the two-dimensional fluidic pinball benchmark with three cylinder rotations as actuation parameters. The net drag power is reduced by 42 \%, owing to Coanda forcing for boat-tailing and partial stabilization of vortex shedding. EGM is also used to minimize drag of the slanted Ahmed body employing distributed steady blowing with 10 inputs. 17 \% drag reduction is achieved by inward-directed blowing at all trailing edges emulating boat tailing.   

An input-output approach to the robustness analysis of transverse wall oscillations in channel flows

Transverse wall oscillations have been shown to reduce the receptivity of wall-bounded shear flows to exogenous disturbances, suppress turbulence, and reduce skin-friction drag by as much as 40{\%}. However, the success of wall oscillations is tied to the appropriate selection of their amplitude and frequency. We analyze the robustness of this flow control strategy to imperfections in the amplitude and phase of oscillations. Design imperfections are modeled as parametric uncertainties in the time-periodic base flow and result in multiplicative changes to the coefficients of the linearized Navier-Stokes equations. We use an input-output analysis of the linearized equations to quantify the effect of additive and multiplicative sources of stochastic uncertainty on the fluctuation dynamics in a simulation-free manner and to specify conditions for the robust performance of the control strategy.   

Investigation of an Optimal Control Approach in the Context of Compressible Boundary Region Equations.

High-amplitude freestream disturbances, as well as surface roughness elements, trigger streamwise oriented vortices and streaks of varying amplitudes in laminar boundary layers, which can lead to secondary instabilities and ultimately to transition to turbulence. In the present work, we aim at deriving and numerically testing an optimal control algorithm in an attempt to reduce the growth of these streamwise vortices and eventually mitigate the frictional drag in a compressible boundary layer. We analytically reduce the compressible Navier-Stokes equations to the boundary region equations (BRE) in a high Reynolds number asymptotic framework, based on the assumption that the streamwise wavenumber of the streaks is much smaller than the cross-flow wavenumbers. Then, we utilize the method of Lagrange multipliers to derive the adjoint compressible boundary region equations, and the associated optimality conditions. The wall transpiration velocity represents the control variable, whereas the wall shear stress or the vortex energy designates the cost functional. We report and discuss results for different Mach numbers, wall conditions, and spanwise separations.   

Adaptable Fluidic Control of Round Inlet Flow in Cross Flow

Asymmetries in the suction flow into a round inlet are investigated in wind tunnel experiments in the presence of lateral flow across its entrance plane. For a given inlet flow, the presence of supercritical cross flow leads to the formation of a three-dimensional, horseshoe-like azimuthal separation domain having its tip near the center of the windward inlet surface. The evolution of the separation topology and its response to fluidic actuation using distributed arrays of surface-embedded fluidically-oscillating jets are investigated over a range of inlet flow rates and supercritical cross flow speeds. Because the azimuthal orientation and extent of the separation domain change with the inlet flow rate, azimuthally-varying control approaches are devised for optimal suppression of the separation at different inlet flow rates using spatially-varying fluidic actuation patterns. It is shown that this control approach yields significant broadband reduction of the total pressure distortions that are induced by the azimuthal separation and that switching between the azimuthal distributed actuation domains can effect optimal suppression of these distortion.   

Control of Unstable Slender Axisymmetric Bodies at High Incidence.

The unsteady flow over and aerodynamic loads on a wire-mounted slender axisymmetric body ($L$/$D=$ 9) fitted with an upstream forebody ($l$/$D=$ 2) are investigated at high angles of incidence (up to 65\textdegree ) in wind tunnel experiments. At high incidence, the vortex pair which forms over the forebody interacts with the hierarchy of vortical structures that form as a result of streamwise-successive separation off the cylinder. Time-varying asymmetries of these vortex-wake interactions about the model's vertical center plane result in unbalanced side forces and yawing moment that are coupled to motion of the wire-mounted model. Although the model is nominally stable to such time-varying loads, under certain conditions it can become unstable to angular oscillations. The present investigations utilize the receptivity of the forebody flow to small perturbations for controlling the evolution of the forebody vortices and thereby their aerodynamically-unstable coupling to the cylinder's wake. Upwind actuation is effected by surface synthetic jet actuators mounted at the juncture between the forebody and the cylinder. It is shown that the flow is extremely receptive to actuation at high incidence and the model's angular stability can be restored.   

The Effect of Amplitude of Traveling Wave Actuations on Flow Control over an Airfoil

This study numerically investigates the effect of amplitude of surface morphing over the suction side of an airfoil on flow control. A NACA-0018 airfoil at an angle of attack 15 degrees, with a low Reynolds number (Re$=$50,000), is simulated using large eddy simulations (LES) curvilinear immersed boundary method (CURVIB). The numerical simulations are performed for low amplitude backward traveling waves with the focus on both a low varying amplitude starting from the leading edge and a low constant amplitude. In addition, an investigation of how the location of the oscillations of the backward traveling wave on the suction side of the airfoil could influence its aerodynamic performance is carried out. This work is supported by National Science Foundation (NSF) grant CBET 1905355, and the computational resources are provided by High Performance Computing (HPRC) group at Texas A{\&}M University.   

Using ROM and adjoint-ROM for an optimal control

Adjoint-based optimization allows to simultaneously optimize a large number of control parameters of a fluid problem without additional cost as the control parameters increases. The adjoint-based approaches make it possible to optimize fluid problems in a large control space where parametric study and other optimization approaches become computationally infeasible. However, typical adjoint-based approaches still involve computations as heavy as their forward computations (e.g. direct numerical simulation), the tens or hundreds of forward and adjoint computations involved in an optimization process will add up the cost quickly. Reduced order model (ROM), on the other hand, largely reduces the computational cost at the cost of lower fidelity. Though parametric study becomes possible in some cases with the much lower cost of ROMs, for a large group of problems, it is still too expensive due to the exponential increase of cost to the number of control parameters. The current study applies ROM and adjoint-ROM to provide a low-fidelity fast optimization which benefits from both the ROM's fast speed and the adjoint method's cost independence of the number of control parameters. The derivation and methodology will be first described, and then the benchmark and applications will be shown.   

Theoretical and data-driven models for the lift on an airfoil due to idealized synthetic jet actuation

The response to burst-type momentum-injection actuation near the leading edge of an airfoil in stall can be decomposed into two components: a short-time response that is characterized by an initial decrease followed by an increase in the lift, and a long-time response that can be sensitive to the instantaneous wake state at the onset of actuation. In this work, we develop both theoretical and data-driven models for these dynamics. We develop a theoretical model following classical unsteady aerodynamic theory, where the effect of actuation is modeled through a combination of sources/sinks, doublets, and vortex elements to capture the short-time response to actuation. We find that the lift response consists of a component directly proportional to the rate of change of actuation strength, and a circulatory contribution that persists after the actuation burst. Comparisons are presented between the theoretical results and direct numerical simulations for flow over a NACA0009 airfoil. We additionally demonstrate the capabilities of data-driven reduced-order models to model both the short- and long-time behavior of the system, utilizing insight from the theoretical model to specify and interpret the form that this model takes.   

Symmetry Reduction for Deep Reinforcement Learning Active Flow Control

Deep reinforcement learning (DRL), a data-driven model-free method to approximate optimal control policies with neural networks (NN), has become a prospective avenue for developing high dimensional active flow control solutions. Many geometries of interest for flow control exhibit continuous and discrete symmetries, which, when combined with spatially fixed actuators, implicitly requires the NN to learn sub-policies to account for each symmetry, leading to hampered performance. We describe a method for circumventing this issue by framing the DRL problem in a discrete-symmetry invariant subspace and test it in minimizing the dissipation for solutions of the Kuramoto-Sivashinsky equation, a system with translational and reflection symmetries that exhibits self-sustained spatiotemporal chaos. We accomplish this by reducing the symmetries of state observations prior to input into the NN, followed by a reintroduction of those respective symmetries to the output actuations. We demonstrate that our method yields substantial improvement in training data efficiency, policy robustness, and policy efficacy compared to the naive implementation of DRL. Finally, we observe the learned policy quickly drives the system to a low dissipation state and maintains it indefinitely.   

Aerodynamically-Adaptive Aerostructures using Flow-Interactive Control by Distributed Bleed Actuation

Controlled interactions between a 3-D flexible wing model and the embedding cross flow are explored in wind tunnel investigations for modification of its aeroelastic characteristics using variable aerodynamic loads effected by active flow control. The aerodynamic loads are regulated using distributed air bleed that is driven through surface ports and the wing's structure by flow-induced pressure differences between its pressure and suction surfaces and is varied by surface louvers on the pressure surface of the wing. The present investigations have explored both quasi-static and transitory coupling between bleed-induced aerodynamic loads and wing's aeroelastic properties with several bleed configurations using direct load measurements, surface motion analysis, and distributed accelerometers. In addition, stereo particle image velocimetry (PIV) in the spanwise cross-stream (y-z) plane in the near wake reveal the topology of the wake flow and the tip vortex and concentrations of streamwise vorticity are used for assessing spanwise distribution of sectional lift (using Prandtl's Lifting Line Theory). A constitutive, multiscale structural model for the bleed-actuated wing shows that the bleed-controlled aerodynamic loads effectively vary the wing's apparent stiffness.