We investigate the synchronization properties of the two-dimensional periodic flow over a circular cylinder using the principles of phase-reduction theory. The influence of harmonic external forcings on the wake dynamics, and the possible synchronization of the vortex shedding behind the cylinder to these forcings, is determined by evaluating the phase response of the system to weak impulse perturbations. These horizontal and vertical perturbations are added at different phase values over a period, in order to develop a linear one-dimensional model with respect to the limit cycle that describes the high-dimensional and nonlinear dynamics of the fluid flow via only a single scalar phase variable. This model is then utilized to acquire the theoretical conditions for the synchronization between the cylinder wake and the harmonic forcings added in the global near-wake region. Valuable insights are gained by comparing the findings of the present research against those rendered by the dynamic mode decomposition and adjoint analysis of the wake dynamics in earlier works. The present analysis reveals regions in the flow which enable phase synchronization or desynchronization to periodic excitations for applications such as active flow control and fluid-structure interactions.
Phase synchronization between the vortex shedding behind a two-dimensional circular cylinder and its vibrations is investigated using the phase-reduction analysis. Leveraging this approach enables the development of a one-dimensional, linear model with respect to the limit-cycle attractor of the laminar wake, which accurately describes the phase dynamics of the high-dimensional, nonlinear fluid flow and its response to rotational, transverse and longitudinal vibrations of the cylinder. This phase-based model is derived by assessing the phase-response and sensitivity of the wake dynamics to imp…
A spatially confined stability analysis is reported for the cylinder wake at Reynolds numbers 190 and 260. The two three-dimensional instabilities at these Reynolds numbers are shown to be driven by the flow just behind the cylinder.
Flows over two side-by-side circular cylinders exhibit fascinating flow physics due to complex interactions between the coupled wakes. However, their mutual interference effects have not been elucidated in a quantitative manner thus far. In this paper, we create a mismatch between the two wakes by introducing a size difference in the cylinder pair, such that the effects of one wake on the other can be distinguished. Depending on the size and gap ratios between the two cylinders, the coupled wake exhibits distinct dynamical features including the quasi-periodic flow, synchronized flow, and chao…
A numerical study of the problem of laminar infinite flow of viscous incompressible fluid around a rotating circular cylinder at Reynolds number $ 50 \le {\rm Re} \le 500 $ and dimensionless rotation rate $ 0 \le α\le 7 $ has been carried out. The parametric map of flow regimes has been constructed, where two zones of steady and two zones of periodic solutions are signed out. The dependencies of the drag and lift coefficients on the rotation rate for $ {\rm Re} = 200 $ are studied in detail. Convergence of the numerical solution to the known asymptotic solution at large $ α$ is confirmed.
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…
Natural convection from a stack of isothermal solid horizontal cylinders has been investigated numerically in a three dimensional computational domain. Simulations were conducted in both laminar and turbulent flow regimes of Rayleigh number (Ra) spanning in the range (10^4 to 10^8) and (10^10 to 10^13), respectively. In the present study, the length to diameter ratio of the cylinders has been varied in the range 0.5 to 20. Three different stack arrangements were considered for the numerical simulations by arranging three, six and ten number of cylinders in a triangular manner. The present comp…
A dual-step cylinder is comprised of a large diameter cylinder (D) with low aspect ratio (L/D) attached co-axially to the mid-span of a small diameter cylinder (d). The fluid dynamics video presented in this investigation is used to illustrate the effect of aspect ratio on dual step cylinder wake development for Re = 2100, D/d = 2, and 0.2 < L/D < 3. In addition, the video provides visualization of such flow phenomena as interaction of spanwise vortices, development of streamwise vortex filaments, and formation of Kelvin-Helmholtz rollers. The experiments were performed in a water flume at the…
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…
An inclined gravity-driven soap film channel was used to study the wake patterns formed behind a transversely oscillating cylinder at $Re =235 \pm 14$. The natural frequency of vortex shedding from a stationary cylinder, $f_{\text{St}}$, was used to identify the oscillation frequencies of interest. The (dimensionless) frequency, $f^*=f/{f_{\text{St}}}$, and amplitude, $A^*=A/D$, of the cylinder's motion was varied over a large portion of the fundamental synchronization region (i.e., for $f^* \approx 1$), and a `map' of wake patterns was constructed in ${(f^*, A^*)}$ space. Lock-on between the …
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…
Tidal turbines are deployed in sites which have elevated levels of free stream turbulence (FST). Accounting for elevated FST on their operation become vital from a design standpoint. Detailed experimental measurements of the dynamic near-wake of a tidal turbine model in elevated FST environments is presented; an active grid turbulence generator developed by our group was used to seed in the elevated FST and evaluate the influence of turbulence intensity (Ti) and inflow integral length scale (L) on the near-wake of the turbine. Three inflow conditions are tested: a quasi-laminar flow with Ti ~ …
We analyze the primitive variables of fluid flow and scalar fields through fast Fourier transform (FFT) in the near and far wake of an elliptic cylinder. Numerical simulation of flow and scalar fields behind an elliptic cylinder of axis ratio 0.4 at a Reynolds number of 130 is performed. The semi-major axis of the elliptic cylinder is kept perpendicular to the incoming flow, where the fluid flow is two-dimensional and the Prandtl number is 0.71. The scalar is injected into the flow field by means of heating the cylinder continuously. The simulation is run for a long time to show that the secon…
We perform direct numerical simulations of laminar separated flows over finite-aspect-ratio swept wings at a chord-base Reynolds number of $Re = 400$ to reveal a variety of wake structures generated for a range of aspect ratios ($sAR=0.5-4$), angles of attack ($α=16^{\circ}-30^{\circ}$), and sweep angles ($Λ=0^{\circ}-45^{\circ}$). Flows behind swept wings exhibit increased complexity in their dynamical features compared to unswept-wing wakes. For unswept wings, the wake dynamics are predominantly influenced by the tip effects. Steady wakes are mainly limited to low-aspect-ratio wings. Unstead…
The effect of freestream turbulence on the spreading of the near wake of a circular cylinder is investigated through particle image velocimetry (PIV) data. Different ``flavours'' of freestream turbulence, in which the turbulence intensity and integral length scale are independently varied, are subjected to the cylinder. The time-averaged spreading of the near wake is decoupled into the growth through entrainment and the envelope of the spatial extent of the instantaneous wake due to wake ``meandering'', induced by the presence of large-scale coherent structures, i.e. the von Karman vortex stre…
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…
The wake of a circular cylinder performing rotary oscillations is studied using hydrodynamic tunnel experiments at $Re=100$. Two-dimensional particle image velocimetry on the mid-plane perpendicular to the axis of cylinder is used to characterize the spatial development of the flow and its stability properties. The lock-in phenomenon that determines the boundaries between regions of the forcing parameter space were the wake is globally unstable or convectively unstable is scrutinized using the experimental data. A novel method based on the analysis of power density spectra of the flow allows u…
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 …
We reveal the effects of sweep on the wake dynamics around NACA 0015 wings at high angles of attack using direct numerical simulations and resolvent analysis. The influence of sweep on the wake dynamics is considered for sweep angles from $0^\circ$ to $45^\circ$ and angles of attack from $16^\circ$ to $30^\circ$ for a spanwise periodic wing at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Wing sweep affects the wake dynamics, especially in terms of stability and spanwise fluctuations with implications on the development of three-dimensional wakes. We observe that wing swee…
Reduced-order representations of an ensemble of cylinder wake transients are investigated. Locally linear embedding identifies a two-dimensional manifold with a maximum error of 1% from new snapshot data. This representation outperforms a 50-dimensional POD expansion from the same data and is not obtainable with cluster-based coarse graining of similar order. This manifold resolves the steady solution, the stability eigenmodes, the first post-transient POD modes, the intermediate vortex shedding structure as well as higher harmonics. The snapshot data are generated by a direct numerical simula…
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…
We study experimentally the impulse response of a cylinder wake below the critical Reynolds number of the Bénard-von Kármán instability. In this subcritical regime, a localized inhomogeneous region of convective instability exists which causes initial perturbations to be transiently amplified. The aim of this work is to quantify the evolution resulting from this convective instability using two-dimensional particle image velocimetry in a hydrodynamic tunnel experiment. The velocity fields allow us to describe the evolution of wave packets in terms of two control parameters: the Reynolds number…
We study numerically the two-dimensional flow past a circular cylinder as a prototypical transitional flow, and investigate the influence of a generic slip boundary condition on the wake dynamics. We show that slip significantly delays the onset of recirculation and shedding in the wake behind the cylinder. As expected, the drag on the cylinder decreases with slip, with an increased drag sensitivity for large Reynolds numbers. We also show that past the critical shedding Reynolds number, slip decreases the vorticity intensity in the wake, as well as the lift forces on the cylinder, but increas…
The flow phenomena around a rotating elliptic cylinder in a channel is studied numerically. The value of the confinement parameter βis varied as \frac{1}{k}, where k = 2, 4, 6, and 8 respectively, to demonstrate the vortex-shedding patterns around the cylinder in the downstream wake. The non-dimensional rotation rate αtakes up 0.5, 1, and 2 as its value. Additionally, the Reynolds number (\textit{Re}) based on the cylinder diameter is taken to be 50, 100, and 150 respectively. A parametric study is performed to explain the changes in drag coefficient \textit{(C_{D})}, lift coefficient \textit{…
We perform direct numerical simulations to characterize the three-dimensional wake dynamics of long inclined circular cylinders with inhomogeneous end boundary conditions. Three Reynolds numbers, $\Rey=100$, 200 and 300 are considered to reveal the roles of the intrinsic secondary instabilities and the extrinsic end boundary effects in shaping the three-dimensional flows. At $\Rey=100$, the end boundary effects are felt over the entire cylinder span by inducing oblique vortex shedding, which is associated with stronger spanwise flow in the wake than a parallel shedding. The Strouhal number of …
A numerical study of two-dimensional flow past a confined circular cylinder with slip wall is performed. A dimensionless number, Knudsen number ($Kn$) is used to describe the slip length of cylinder wall. The Reynolds number ($Re$) and Knudsen number ($Kn$) ranges considered are $Re = [1, 180]$ and $Kn = [0, \infty)$, respectively. Time-averaged flow separation angle ($\bar{θ_s}$), dimensionless recirculation length ($\bar{L_s}$) and the tangential velocity ($\bar{u_τ}$) distributed on the cylinder's wall, drag coefficient ($\bar{C_d}$) and drag reduction ($DR$) are investigated. The time-aver…
The wake of wavy cylinder has been shown to exhibit bistability. Depending on the initial condition, the final state of the wake can either develop into a steady flow (state I), or periodic shedding (state II). In this paper, we perform direct numerical simulations to reveal the Reynolds number effects on these two wake states. With increasing Reynolds number, the steady vortical structures in state I wake sways back and forth in the spanwise direction, resulting in low-frequency fluctuations in drag forces, but not in lift. For state II, the increase in Reynolds number is associated with the …
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…
We investigate the laminar shedding of hairpin vortices in the wake of a truncated square cylinder placed in a duct, for Reynolds numbers around the critical threshold of the onset of vortex shedding. We single out the formation mechanism of the hairpin vortices by means of a detailed analysis of the flow patterns in the steady regime. We show that unlike in previous studies of similar structures, the dynamics of the hairpin vortices is entwined with that of the counter-rotating pair of streamwise vortices, which we found to be generated in the bottom part of the near wake (these are usually r…
A novel nonlinear feedback control design methodology for incompressible fluid flows aiming at the optimisation of long-time averages of flow quantities is presented. It applies to reduced-order finite-dimensional models of fluid flows, expressed as a set of first-order nonlinear ordinary differential equations with the right-hand side being a polynomial function in the state variables and in the controls. The key idea, first discussed in Chernyshenko et al. 2014, Philos. T. Roy. Soc. 372(2020), is that the difficulties of treating and optimising long-time averages of a cost are relaxed by usi…
In this Letter, we study the motion and wake-patterns of freely rising and falling cylinders in quiescent fluid. We show that the amplitude of oscillation and the overall system-dynamics are intricately linked to two parameters: the particle's mass-density relative to the fluid $m^* \equiv ρ_p/ρ_f$ and its relative moment-of-inertia $I^* \equiv {I}_p/{I}_f$. This supersedes the current understanding that a critical mass density ($m^*\approx$ 0.54) alone triggers the sudden onset of vigorous vibrations. Using over 144 combinations of ${m}^*$ and $I^*$, we comprehensively map out the parameter s…
Direct numerical simulations are used to study the interaction of a stream of small heavy inertial particles with the laminar and turbulent wakes of an immobile sphere facing an incompressible uniform inflow. Particles that do not collide with the obstacle but move past it, are found to form preferential concentrations both in the sphere boundary layer and in its wake. In the laminar case, the upstream diverging flow pattern is responsible for particle clustering on a cylinder that extends far downstream the sphere. The interior of this surface contains no particles and can be seen as a shadow…
Experimental results are used to validate a 2D phenomenological model of the near wake based on Van Der Pol wake oscillators, which is the first one which describes the 2D motion of a cylinder in its transversal plan. In the case of a single cylinder, experimental and numerical results are in relatively good agreement. Those first results show that the proposed model can be used as a simple computation tool in the prediction of 2D VIV effects.
A novel data-driven modal decomposition of fluid flow is proposed comprising key features of POD and DMD. The first mode is the normalized real or imaginary part of the DMD mode which minimizes the time-averaged residual. The N-th mode is defined recursively in an analogous manner based on the residual of an expansion using the first N-1 modes. The resulting recursive DMD (RDMD) modes are orthogonal by construction, retain pure frequency content and aim at low residual. RDMD is applied to transient cylinder wake data and is benchmarked against POD and optimized DMD (Chen et al. 2012) for the s…
The flow-induced deformation of a thin, elastic splitter plate attached to the rear of a circular cylinder and subjected to laminar pulsatile inflow is investigated. The cylinder and elastic splitter plate are contained within a narrow channel and the Reynolds number is mostly restricted to Re = 100, primarily covering the two-dimensional flow regime. An in-house fluid-structure interaction code is employed for simulations, which couples a sharp-interface immersed boundary method for the fluid dynamics with a finite-element method to treat the structural dynamics. The structural solver is impl…
Annular Couette flow is the flow between two coaxial cylinders driven by the axial translation of the inner cylinder. It is investigated using direct numerical simulation in long domains, with an emphasis on the laminar-turbulent coexistence regime found for marginally low values of the Reynolds number. Three distinct flow regimes are demonstrated as the radius ratio $η$ is decreased from 0.8 to 0.5 and finally to 0.1. The high-$η$ regime features helically-shaped turbulent patches coexisting with laminar flow, as in planar shear flows. The moderate-$η$ regime does not feature any marked lamin…
This work studies the application of a reinforcement-learning-based (RL) flow control strategy to the flow past a cylinder confined between two walls in order to suppress vortex shedding. The control action is blowing and suction of two synthetic jets on the cylinder. The theme of this study is to investigate how to use and embed physical information of the flow in the RL-based control. First, global linear stability and sensitivity analyses based on the time-mean flow and the steady flow (which is a solution to the Navier-Stokes equations) are conducted in a range of blockage ratios and Reyno…
In this study, the wake flow around a circular nano-cylinder is numerically investigated with molecular dynamics simulation to reveal the micro/nano size effect on the wake flow. The cavitation occurring when Reynolds number (Re) > 101 can effectively influence the wake flow. The Strouhal number (St) of the wake flow increases with the Re at low Re, but steadily decreases with the Re after the cavitation appears. The dominant frequency of the lift force fluctuation can be higher than that of the velocity fluctuation, and be drowned in the chaotic fluctuating background of the Brownian forces w…
The turbulent flow past a wall-mounted square cylinder with an aspect ratio of four was investigated with the aid of Spalart-Allmaras improved delayed detached-eddy simulation (S-A IDDES) and proper orthogonal decomposition (POD). The Reynolds number was equal to 12,000 (based on the free-stream velocity and obstacle width). This study focused on analysing the vortical structure of the wake and vortex shedding process along the obstacle height. A quantitative comparison of the first and second-order flow statistics with the available experimental and direct numerical simulation data was used t…
In this paper I consider the self-excited rotation of an elliptical cylinder towed in a viscous fluid as a canonical model of nonlinear fluid structure interactions with possible applications in the design of sensors and energy extraction devices. First, the self-excited ellipse system is shown to be analogous to the forced bistable oscillators studied in classic chaos theory. A single variable, the distance between the pivot and the centroid, governs the system bifurcation into bi-stability. Next, fully coupled computational fluid dynamics simulations of the motion of the cylinder demonstrate…
The combined effect of fluid elasticity and yield-stress on the flow past a circular cylinder is studied by two-dimensional direct numerical simulation. We analyze the effects of yield-stress, elasticity, shear-thinning, and shear-thickening on the wake characteristics using the Saramito constitutive model. The elastoviscoplastic (EVP) wake flow is studied at a moderate Reynolds number (Re = 100) where two-dimensional vortex shedding occurs in the Newtonian case. We find that in the shear-thinning elastoviscoplastic flow, when yield stress increases, the drag coefficient and root mean square o…
