Deep reinforcement learning (DRL) algorithms are rapidly making inroads into fluid mechanics, following the remarkable achievements of these techniques in a wide range of science and engineering applications. In this paper, a deep reinforcement learning (DRL) agent has been employed to train an artificial neural network (ANN) using computational fluid dynamics (CFD) data to perform active flow control (AFC) around a 2-D circular cylinder. Flow control strategies are investigated at a diameter-based Reynolds number Re_D = 100 using advantage actor-critic (A2C) algorithm by means of two symmetric plasma actuators located on the surface of the cylinder near the separation point. The DRL agent interacts with the computational fluid dynamics (CFD) environment through manipulating the non-dimensional burst frequency (f^+) of the two plasma actuators, and the time-averaged surface pressure is used as a feedback observation to the deep neural networks (DNNs). The results show that a regular actuation using a constant non-dimensional burst frequency gives a maximum drag reduction of 21.8 %, while the DRL agent is able to learn a control strategy that achieves a drag reduction of 22.6%. By analyzing the flow-field, it is shown that the drag reduction is accompanied with a strong flow reattachment and a significant reduction in the mean velocity magnitude and velocity fluctuations at the wake region. These outcomes prove the great capabilities of the deep reinforcement learning (DRL) paradigm in performing active flow control (AFC), and pave the way toward developing robust flow control strategies for real-life applications.
The Betz limit expresses the maximum proportion of the kinetic energy flux incident on an energy conversion device that can be extracted from an unbounded flow. The derivation of the Betz limit requires an assumption of steady flow through a notional actuator disk that is stationary in the streamwise direction. The present derivation relaxes the assumptions of steady flow and streamwise actuator disk stationarity, which expands the physically realizable parameter space of flow conditions upstream and downstream of the actuator disk. A key consequence of this generalization is the existence of …
This paper considers single-sensor estimation of vortex shedding in cylinder wakes at $Re=100$ in simulations and at $Re=1036$ in experiments. A model based on harmonic decomposition is developed to capture the periodic dynamics of vortex shedding. Two model-based methods are proposed to estimate time-resolved flow fields. First, Linear Estimation (LE) which implements a Kalman Filter to estimate the flow. Second, Linear-Trigonometric Estimation (LTE), which utilizes the same Kalman Filter together with a nonlinear relationship between harmonics of the vortex shedding frequency. LTE shows good…
Unsteady flow fields over a circular cylinder are trained and predicted using four different deep learning networks: convolutional neural networks with and without consideration of conservation laws, generative adversarial networks with and without consideration of conservation laws. Flow fields at future occasions are predicted based on information of flow fields at previous occasions. Deep learning networks are trained first using flow fields at Reynolds numbers of 100, 200, 300, and 400, while flow fields at Reynolds numbers of 500 and 3000 are predicted using the trained deep learning netw…
The flow around a cylinder oscillating in the streamwise direction with a frequency, $f_f$, much lower than the shedding frequency, $f_s$, has been relatively less studied than the case when these frequencies have the same order of magnitude, or the transverse oscillation configuration. In this study, Particle Image Velocimetry and Koopman Mode Decomposition are used to investigate the streamwise-oscillating cylinder wake for forcing frequencies $f_f/f_s \sim 0.04-0.2$ and mean Reynolds number, $Re_0 = 900$. The amplitude of oscillation is such that the instantaneous Reynolds number remains ab…
Reduced-order modelling of parametrized unsteady Navier-Stokes equations and application to flow around cylinders with periodic changing boundary conditions
We study effects of both magnetic field and radiation on unsteady free convective magnetohydrodynamic (MHD) flow under the influence of heat and mass transfer. An implicit finite difference scheme of Crank-Nicolson method is used to analyze the results. The governing boundary layer equations along with the initial and boundary conditions are casted into a dimensionless form which results in a more precise solution. We determine the change in velocity under the influence of radiation and magnetic field with temperature and concentration taken into account. A code is constructed (FORTRAN 6.5) to…
A number of new closed-form fundamental solutions for the generalized unsteady Oseen and Stokes flows associated with arbitrary time-dependent translational and rotational motions have been developed. These solutions are decomposed into two parts corresponding to a longitudinal wave and a transversal wave. As examples of application, the hydrodynamic force acting on a sphere or on a circular cylinder translating in an unsteady flow field at low Reynolds numbers are calculated using the new generalized fundamental solutions. The results for a rotating viscous flow past an impulsively moving sph…
A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow structures and pointwise measurement to calibrate their amplitudes. A computationally-affordable time-stepping methodology to obtain resolvent modes in non-trivial flow domains is introduced and compared to previous existing matrix-free and matrix-forming strategies. The technique is applied to the unsteady flow around an inclined square cylinder at low Reynold…
Mass transfer from a composite cylinder - made of an inner core and an outer enveloping semipermeable shell - under channel crossflow is studied numerically using two-dimensional lattice-Boltzmann simulations. The core is initially loaded with a solute that diffuses passively through the shell towards the fluid. The cylinder internal structure and the initial condition considered in this study differ and thus complement the classical studies dealing with homogeneous uncoated cylinders whose surfaces are sustained at either constant concentration or constant mass flux. Here, the cylinder acts a…
Unsteady laminar vortex shedding over a circular cylinder is predicted using a deep learning technique, a generative adversarial network (GAN), with a particular emphasis on elucidating the potential of learning the solution of the Navier-Stokes equations. Numerical simulations at two different Reynolds numbers with different time-step sizes are conducted to produce training datasets of flow field variables. Unsteady flow fields in the future at a Reynolds number which is not in the training datasets are predicted using a GAN. Predicted flow fields are found to qualitatively and quantitatively…
Yaw control has proven to be promising in alleviating the wake effects that plague the efficiency of wind farms. In this work, the actuator line modeling (ALM) method is adopted to simulate the flows over two tandem turbines distanced by $3 - 7$ rotor diameters, with the yaw angle of the upstream rotor varying from $γ_1=0^{\circ}$ to $50^{\circ}$. The aim is to provide a comprehensive aerodynamic characterization of a simple wind farm under yaw misalignment. With increasing yaw angle, the power generated by the downstream rotor increases, compensating the power loss in the upstream rotor, and …
A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is constituted by the convolutional neural network (CNN), improved convolutional Long-Short Term Memory neural network (ConvLSTM) and deconvolutional neural network (DeCNN). Flow fields at future time step can be predicted through flow fields by previous time steps and boundary positions at those steps by the novel hybrid deep neural network. Unsteady wake flows ar…
A dual time-stepping strategy of gas-kinetic scheme for the simulation of unsteady flows is introduced in this work. The dual time-stepping strategy is always used in the approaches of unsteady flows, and the ability of dual time-stepping to accelerate the computation with acceptable error tolerance is evident. In our paper, we adopt the techniques of dual time-stepping methods for implicit gas-kinetic scheme to simulate the unsteady flows, which is very popular for the numerical methods based on the Navier-Stokes equations. It is carried out by (a) solving the gas-kinetic scheme in finite vol…
We investigate the prediction of the turbulent flow around a canonical square cylinder at Re= 22000 solving the unsteady Reynolds-averaged Navier-Stokes (URANS) equations. The limitations of URANS modelling are overcome through the application of a data assimilation technique involving a feedback control term, allowing to drive the URANS predictions towards reference data. Using regularly-spaced temporally-resolved reference data that are extracted from DNS, we assess the abilities of the data assimilation methodology in improving the unsteady URANS predictions. While improving the low-frequen…
We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most amplified stability eigenmode is readily identified by a power method, the technical challenge is the computation of more damped higher-order eigenmodes. This challenge is addressed by a novel method to compute unstable periodically forced solutions of the linearized Navier-Stokes solution. This method utilizes two key enablers. First, the linear dynamics is transf…
Numerical models of the flow and wakes due to turbines operating within a real-scale offshore wind farm can lead to a prohibitively large computational cost, particularly when considering blade-resolved simulations. With the introduction of turbine parametrizations such as the actuator disk (AD) or the actuator line (AL) models, this problem has been partially addressed, yet the computational cost associated with these simulations remains high. In this work, we present an implementation and validation of an AL model within the mesh-adaptive three-dimensional fluid dynamics solver, Fluidity, un…
We investigate the wake dynamics of an optimally designed wavy cylinder that completely suppresses the Kármán vortex shedding. Such a wavy cylinder is forced to oscillate with a sinusoidal motion in the crossflow direction. Examination of the lift force spectrum reveals that a critical forcing frequency exists, below which the flow control effectiveness of the wavy cylinder is retained, and beyond which the inherent vortex shedding resurrects. Moreover, the resurrected unsteady vortex shedding can persist even without sustained forcing, leading to the loss of control efficacy. This suggests th…
The paper gives experimental observations on the hypersonic flow past an axisymmetric flat-face cylinder with a protruding sharp-tip spike at a freestream Mach number of $M_\infty = 8.16$ at two different freestream Reynolds numbers based on the base body diameter ($Re_D = 0.76 \times 10^6$, and $3.05 \times 10^6$). Furthermore, modal analysis is done on schlieren images to understand the flow dynamics parallel with the unsteady pressure measurements. The protruding spike of length to base body diameter ratio of $[l/D]=1$ creates a familiar unsteady flowfield called 'pulsation.' Pressure loadi…
In this article, we propose a methodology to reconstruct, in a single step, the mean- and unsteady properties of a flow from very few time-resolved measurements. The procedure is based on the {\it a priori} alignement of Fourier- and Resolvent-modes over energetic frequencies, which is a common feature in shear-dominated transitional flows. Hence, the Reynolds-stresses, which determine the mean-flow, may be approximated from a series of Resolvent modes, which discretize the fluctuation field in the frequency space and whose amplitudes can be tuned thanks to few measurements. In practice, we so…
The present study investigates unsteady wake dynamics in flow past oscillating cylinder. Two-dimensional computational study is carried out for flow past sinusoidally oscillating cylinder. Operating parameters like Reynolds number, forcing frequency, amplitude and wavelength are systematically varied and their effect on wake dynamics is investigated. Lift and drag coefficients are plotted with cylinder position to characterize the flow. Further, flow field is investigated using Proper Orthogonal Decomposition (POD). Time-resolved vorticity contours are obtained. These results are then processe…
A networked oscillator based analysis is performed for periodic bluff body flows to examine and control the transfer of kinetic energy. Spatial modes extracted from the flow field with corresponding amplitudes form a set of oscillators describing unsteady fluctuations. These oscillators are connected through a network that captures the energy exchanges amongst them. To extract the network of interactions among oscillators, amplitude and phase perturbations are impulsively introduced to the oscillators and the ensuing dynamics are analyzed. Using linear regression techniques, a networked oscill…
The dynamics and stability of a fluid-filled hollow cylindrical shell rolling on an inclined plane are analyzed. We study the motion in two dimensions by analyzing the interaction between the fluid and the cylindrical shell. An analytical solution is presented to describe the unsteady fluid velocity field as well as the cylindrical shell motion. From this solution, we show that the terminal state is associated with a constant acceleration. We also show that this state is independent of the liquid viscosity and only depends on the ratio of the shell mass to the fluid mass. We then analyze the s…
The classical problem of suppressing vortex shedding in the wake of a circular cylinder by using body rotation is revisited in an adjoint-based optimal control framework. The cylinder's unsteady and fully unconstrained rotation rate is optimized at Reynolds numbers between 75 and 200 and over horizons that are longer than in previous studies, where they are typically of the order of a vortex shedding period or shorter. In the best configuration, the drag is reduced by 19%, the vortex shedding is effectively suppressed, and this low drag state is maintained with minimal cylinder rotation after …
This investigation aims to assess the effect of different types of actuator forcing on the feedback loop of an under-expanded Mach 1.27 planar impinging jet using a resolvent framework. To this end, we employ a Large Eddy Simulation database as a truth model. The time and spanwise-averaged mean flow is taken as an input to global stability and resolvent analyses with the purpose of examining both the intrinsic instability and input-output characteristics. The results show that the inherent instability and primary energy amplification are attributed to the Kelvin-Helmholtz (K-H) instability. Mo…
Turbulent flow around a swept back circular cylinder was investigated experimentally using one or two small sweeping jets emanating tangentially to the surface and orthogonal to the axis of the cylinder creating a yawing moment that overcomes the natural restoring force to the plane of symmetry. It appears from the integral force balance data that large yawing moment coefficients can be generated in this manner, and the results could be used in the orientation and attitude control of a refueling boom thus avoiding the H-shape control surfaces that are currently used on Air Force tankers. The i…
In this paper, we discuss whether the instability of viscoelastic flow around a circular cylinder is subcritical or supercritical by numerical simulation. The Oldroyd-B model is selected to describe the viscoelastic constitutive relationship. The Log-conformation reformulation is employed to stabilize numerical simulation. The parameter ranges investigated are the Reynolds numbers ($Re$) spanning from 5 to 100 and the Weissenberg number ($Wi$) spanning from 0 to 10, with a fixed viscosity ratio of $β= 0.9$. Simulations are performed under two paths, i.e., 1) increasing $Re$ (or $Wi$) and 2) de…
Topographic complexity on continental shelves is the catalyst that transforms the barotropic tide into the secondary and residual circulations that dominate vertical and cross-shelf mixing processes. Island wakes are one such example that are observed to significantly influence the transport and distribution of biological and physical scalars. Despite the importance of island wakes, to date, no sufficient, mechanistic description of the physical processes governing their development exists for the general case of unsteady tidal forcing. Controlled laboratory experiments are necessary for the u…
The fast and accurate prediction of unsteady flow becomes a serious challenge in fluid dynamics, due to the high-dimensional and nonlinear characteristics. A novel hybrid deep neural network (DNN) architecture was designed to capture the unsteady flow spatio-temporal features directly from the high-dimensional unsteady flow fields. The hybrid deep neural network is constituted by the convolutional neural network (CNN), convolutional Long Short Term Memory neural network (ConvLSTM) and deconvolutional neural network (DeCNN). The flow around a cylinder at various Reynolds numbers and the flow ar…
We consider linear feedback control of the two-dimensional flow past a cylinder at low Reynolds numbers, with a particular focus on the optimal placement of a single sensor and a single actuator. To accommodate the high dimensionality of the flow we compute its leading resolvent forcing and response modes to enable the design of H2-optimal estimators and controllers. We then investigate three control problems: i) optimal estimation (OE) in which we measure the flow at a single location and estimate the entire flow; ii) full-state information control (FIC) in which we measure the entire flow bu…
We develop a general theory of transport barriers for three-dimensional unsteady flows with arbitrary time-dependence. The barriers are obtained as two-dimensional Lagrangian Coherent Structures (LCSs) that create locally maximal deformation. Along hyperbolic LCSs, this deformation is induced by locally maximal normal repulsion or attraction. Along shear LCSs, the deformation is created by locally maximal tangential shear. Hyperbolic LCSs, therefore, play the role of generalized stable and unstable manifolds, while closed shear LCSs (elliptic LCSs) act as generalized KAM tori or KAM-type cylin…
