This study computes the optimal normal actuation on the surface of a NACA0012 airfoil at an angle of attack of 15° and a Reynolds number of Re = 1000, using costs defined for minimal drag and maximal lift. To allow for a general actuation profile, non-zero actuation is permissible on both the suction and pressure surfaces. This approach of optimal actuation along the full airfoil surface augments most other studies that have focused on parametrically varied open-loop control restricted to the suction surface. The gradient-based optimization procedure requires the gradient of the cost functional with respect to the design variables, which is determined using the adjoint of the governing equations. The optimal actuation profile for the two performance aims are compared. Where possible, similarities with commonly considered open-loop actuation in the form of backward traveling waves on the suction surface have been highlighted. In addition, the key spatial locations on the airfoil surface for the two optimal control strategies have been compared to earlier works where actuation has been limited to a sub-domain of the airfoil surface. The flow features emerging from the optimal actuation variations, and their consequent influence on the instantaneous aerodynamic coefficients, have been analyzed. To complement our findings with normal actuation, we also provide in the appendix: results for a more general form of actuation with independent x and y components, and for a different optimization window to assess the effect of this window parameter on the actuation profile and the flow features.
The current research focuses on modeling the lift response due to dynamic (time-varying) 'burst-type' actuation on a stalled airfoil. Dynamic `burst-type' actuation exhibits two different characteristic dynamic behaviors within the system, namely the high-frequency and low-frequency components. These characteristics introduce modeling challenges. In this paper, we propose a hybrid model composed of two individual sub-models, one for each of the two frequencies. The lift response due to high-frequency single burst actuation is captured using a convolution model. The low-frequency component due …
High-fidelity simulations are performed to study active flow control techniques for alleviating deep dynamic stall of a SD7003 airfoil in plunging motion. The flow Reynolds number is $Re=60{,}000$ and the freestream Mach number is $M=0.1$. Numerical simulations are performed with a finite difference based solver that incorporates high-order compact schemes for differentiation, interpolation and filtering on a staggered grid. A mesh convergence study is conducted and results show good agreement with available data in terms of aerodynamic coefficients. Different spanwise arrangements of actuator…
The separated flow response to single and multiple burst mode actuation over a 2-D airfoil at $12^o$ angle of attack was studied experimentally. For the single-burst actuation case, surface pressure signals were correlated with the flowfield observations of the roll-up and convection of a large-scale vortex structure that follows the actuator burst input. A spatially localized region of high pressure occurs below and slightly upstream of a "kink" that forms in the shear layer, which is responsible for the lift reversal that occurs within $2.0t^+$ after the burst signal was triggered. Proper or…
We establish the theoretical framework for adjoint-based phase reduction analysis for incompressible periodic flows. Through this adjoint-based method, we obtain spatiotemporal phase sensitivity fields through a single pair of forward and backward direct numerical simulations, as opposed to the impulse-based method that requires a very large number of simulations. Phase-based analysis involves perturbation analysis about a periodically varying base state and hence is tailored for the analysis of periodic flows. We formulate the phase description of periodic flows with respect to the potential …
Active Control of Turbulent Airfoil Flows Using Adjoint-based Deep Learning
Graduate Student, Department of Aerospace and Mechanical Engineering（航空航天与机械工程系）；Postdoctoral Research Associate, Mathematical Institute（数学学院）；Assistant Professor, Department of Aerospace and Mechanical Engineering（航空航天与机械工程系）
We present a systematic approach for determining the optimal actuator location for separation control from input-output response data, gathered from numerical simulations or physical experiments. The Eigensystem Realization Algorithm is used to extract state-space descriptions from the response data associated with a candidate set of actuator locations. These system realizations are then used to determine the actuator location among the set that can drive the system output to an arbitrary value with minimal control effort. The solution of the corresponding minimum energy optimal control proble…
Adjoint method is widely used in aerodynamic design because only once solution of flow field is required for adjoint method to obtain the gradients of all design variables. However, the calculation cost of adjoint vector is approximately equal to that of flow computation. In order to accelerate the solution of adjoint vector and improve the adjoint-based optimization efficiency, machine learning for adjoint vector modeling is presented. Deep neural network (DNN) is employed to construct the mapping between the adjoint vector and the local flow variables. DNN can efficiently predict adjoint vec…
The Precessing Vortex Core (PVC) is a coherent structure that can arise in swirling jets from a global instability. In this work, the PVC is investigated under highly turbulent conditions. The goal is to characterize the receptivity of the PVC to active flow control, both theoretically and experimentally. Based on stereoscopic particle image velocimetry and surface pressure measurements, the experimental studies are facilitated by Fourier decomposition and proper orthogonal decomposition. The frequency and the mode shape of the PVC are extracted and a very good agreement with the theoretical p…
Dielectric barrier discharge (DBD) plasma actuators are an attractive option for separation control, lift enhancement, and drag reduction. Some plasma actuators feature optimized electrode shapes, electrical waveforms to maximize the aerodynamic forces at higher angles of attack. Here, we analyze the performance of a direct current augmented DBD (DBD - DCA) actuator with a sawtooth shape exposed electrode. The active electrode was positioned at 18% chord and the electrode at 48% chord of NACA 0012 airfoil. Wind tunnel experiments were conducted at wind speeds of 15 - 25 m/s, corresponding to R…
In the current work we numerically study the effect of traveling-wave surface morphing actuation on the suction surface of NACA0012 at Re = 1,000. Although this actuation strategy has been studied at higher Reynolds numbers for an airfoil and a rectangular flat plate, its effects at low Reynolds numbers have not yet been investigated. The kinematics of actuation are defined by wavenumber and wavespeed, both of which are varied over a wide range of values to include parameters that considerably change the lift dynamics as well as those that do not. We first study the effect of actuation at an a…
Ordinary Differential Equations are derived for the adjoint Euler equations firstly using the method of characteristics in 2D. For this system of partial-differential equations, the characteristic curves appear to be the streamtraces and the well-known C+ and C- curves of the theory applied to the flow. The differential equations satisfied along the streamtraces in 2D are then extended and demonstrated in 3D by linear combinations of the original adjoint equations. These findings extend their well-known counterparts for the direct system, and should serve analytical and possibly numerical stud…
Shocks Under Control: Taming Transonic Compressible Flow over an RAE2822 Airfoil with Deep Reinforcement Learning
Aerospace Engineering Department, Worcester Polytechnic Institute（航空航天工程系，沃斯特理工学院）；Department of Aerospace Engineering, University of Michigan（航空航天工程系，密歇根大学）
Accurate simulation of turbulent flow with separation is an important but challenging problem. In this paper, a data-driven Reynolds-averaged turbulence modeling approach, field inversion and machine learning is implemented to modify the Spalart-Allmaras model separately on three cases, namely, the S809 airfoil, a periodic hill and the GLC305 airfoil with ice shape 944. Field inversion based on a discrete adjoint method is used to quantify the model-form uncertainty with limited experimental data. An artificial neural network is trained to predict the model corrections with local flow features…
Two-dimensional (2D) flows are efficiently controlled with spanwise waviness, i.e. spanwise-periodic (SP) wall blowing/suction/deformation. We tackle the global linear stability of 2D flows subject to small-amplitude 3D SP control. Building on previous work for parallel flows (Boujo et al. 2015), an adjoint method is proposed for computing the 2nd-order eigenvalue sensitivity. Such control has a zero 1st-order linear effect, so the 2nd-order quadratic effect prevails. The sensitivity operator allows one (i) to predict the effect of any control without computing the controlled flow, (ii) to com…
Numerical simulations of plasma flow induced by dielectric barrier discharge plasma actuators (DBD-PA) are conducted with two different body-force models: Suzen-Huang (S-H) model and drift-diffusion (D-D) model. The induced flow generated in quiescent air over a flat plate in continuous actuation and the PA-based flow control effect with burst actuation in separated flow over NACA0015 is studied. In the comparative study, the body-force field and the induced velocity field are firstly investigated in the quiescent field to see the spatial difference and the temporal difference in a single disc…
