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 impulse perturbations of the cylinder, which can be performed in simulations and experiments. The resulting model in turn yields the theoretical conditions required for phase-locking between the cylinder vibrations and the wake. We furthermore show that this synchronization mechanism can be employed to stabilize the wake and subsequently reduce drag. We also uncover the circumstances under which the concurrent occurrence of different vibrational motions can be used to promote or impede synchronization. These findings provide valuable insights for the study of vortex-induced body oscillations, the enhancement of aerodynamic performance of flyers, or the mitigation of structural vibrations by synchronizing or desynchronizing the oscillatory motions of body to the periodic wake.
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 describe…
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…
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…
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…
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…
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…
An integral quantity is presented that relates the wake of a body in nominally two-dimensional flow to its drag, for Reynolds numbers ranging from 9,000 to 144,000. It is defined as the ratio of the kinetic energy to the vorticity in the fluid boundary and, for the special case of laminar flow, is proportional to the angular momentum in the wake bubble. The new quantity is useful for correlating drag data for circular and rectangular cylinders, wedges, v-gutters, and normal flat plates with and without splitter plates. The correlation indicates that the drag force is proportional to the flow s…
The interaction between turbulent axisymmetric wakes plays an important role in many industrial applications, notably in the modelling of wind farms. While the non-equilibrium high Reynolds number scalings present in the wake of axisymmetric plates has been shown to modify the averaged streamwise scalings of individual wakes, little attention has been paid to their consequences in terms of wake interactions. We propose an experimental setup that tests the presence of non-equilibrium turbulence using the streamwise variation of velocity fluctuations between two bluff bodies facing a laminar flo…
The flow transformation and the generation of vortex structures by a strong magnetic dipole field in a liquid metal duct flow is studied by means of three-dimensional direct numerical simulations. The dipole is considered as the paradigm for a magnetic obstacle which will deviate the streamlines due to Lorentz forces acting on the fluid elements. The duct is of square cross-section. The dipole is located above the top wall and is centered in spanwise direction. Our model uses the quasi-static approximation which is applicable in the limit of small magnetic Reynolds numbers. The analysis covers…
We present a dynamic decomposition analysis of the wake flow in fluid-structure interaction (FSI) systems under both laminar and turbulent flow conditions. Of particular interest is to provide the significance of low-dimensional wake flow features and their interaction dynamics to sustain the free vibration of a square cylinder at a relatively low mass ratio. To obtain the high-dimensional data, we employ a body-conforming variational fluid-structure interaction solver based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model for a moderate Rey…
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…
Viscoelasticity weakens the asymmetry of laminar shedding flow behind a blunt body in a free domain. In the present study, this finding is confirmed by four unsteady viscoelastic flows with asymmetric flow configuration, i.e., flow over an inclined flat plate with various angles of incidence, flow over a rotating circular cylinder, flow over a circular cylinder with asymmetric slip boundary distribution, and flow over an inclined row of eight equally closely spaced circular cylinders (which can be considered as a single large blunt body) through direct numerical simulation combined with the Pe…
The present study performs a numerical simulation of the interference and heat transfer between hairpin vortices formed in wakes behind staggered hills in a laminar boundary layer. Hairpin vortices are periodically shed in the wake of a row of hills, causing interference between the hairpin vortices. As the spanwise distance between the hills decreases, interference increases and the hairpin vortices become strong. At that time, because the interference between the legs of the hairpin vortex and the Q2 ejection becomes strong, the head of each hairpin vortex rises sharply. When the hill spacin…
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{…
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…
An unsteady three-dimensional boundary element method is developed to provide fast calculations of biological and bio-inspired self-propelled locomotion. The approach uniquely combines an unsteady three-dimensional boundary element method, a boundary layer solver and self-propelled equations of motion. This novel implementation allows for the self-propelled speed, power, efficiency and economy to be accurately calculated. A Dirichlet formulation is used with a combination of constant strength source and doublet elements to represent a deforming body with a nonlinearly deforming wake. The wake …
This study investigates the linear stability of a laminar premixed flame, anchored on a square cylinder and confined inside a channel. Many modern linear analysis concepts have been developed and validated around non-reacting bluff-body wake flows, and the objective of this paper is to explore whether those tools can be applied with the same success to the study of reacting flows in similar configurations. It is found that linear instability analysis of steady reacting flow states accurately predicts critical flow parameters for the onset of limit-cycle oscillations, when compared to direct nu…
We present a numerical study to investigate the fluid-structure interaction of a flexible circular cantilever cylinder in a uniform cross-flow. We employ a fully-coupled fluid-structure solver based on the three-dimensional Navier-Stokes equations and the Euler-Bernoulli beam theory. We examine the dynamics of the cylinder for a wide range of reduced velocities ($U^*$), mass ratios ($m^*$), and Reynolds numbers ($Re$). Of particular interest is to explore the possibility of flow-induced vibrations in a slender cantilever cylinder of aspect ratio $AR=100$ at laminar subcritical $Re$ regime (i.e…
The study numerically investigates the three-dimensionality in the flow and two-degree-of-freedom (2 DOF) vortex-induced-vibrations (VIV) characteristics of an elastically mounted circular cylinder. The cylinder is allowed to vibrate in both streamwise and transverse directions. A low value of mass-ratio with the zero damping coefficient is taken for the simulations. The primary aim is to understand the vortex shedding behind the cylinder and the transition characteristics of the wake-flow from two-dimensional (2D) to three-dimensional (3D). The Reynolds number (Re) is varied from 150 (fully 2…
Cavitating flow over a circular cylinder is investigated over a range of cavitation numbers for both laminar and turbulent regimes. We observe non-cavitating, cyclic and transitional cavitation regimes with reduction in freestream $σ$. The cavitation inside the Karman vortices in the cyclic regime, is significantly altered by the onset of "condensation front" propagation in the transitional regime. At the transition, an order of magnitude jump in shedding Strouhal number is observed as the dominant frequency shifts from periodic vortex shedding in the cyclic regime, to irregular-regular vortex…
Information-theoretic machine learning for time-varying mode decomposition of separated aerodynamic flows
Department of Aerospace Engineering, Tohoku University（东京东京大学航空工程系）；Department of Mechanical and Aerospace Engineering, Tokyo University of Science（东京科学大学机械与航空航天工程系）
Fluid flows play a central role in scientific and technological development, and many of these flows are characterized by a dominant oscillation, such as the vortex shedding in the wake of nearly all transportation vehicles. The ability to control vortex shedding is critical to improve the aerodynamic performance of these unsteady fluid flow systems. This goal requires precise characterization of how perturbations affect the long-time phase of the oscillatory flow, as well as the ability to control transient behaviors. In this work, we develop an energy-efficient flow control strategy to rapid…
The present study investigates the passive flow control phenomena over a two-dimensional circular cylinder using numerical simulations in the laminar regime. The aim is to explore one of the passive control techniques, which involves the introduction of a slit to the geometry of the cylinder. The two parameters, slit width ratio S/D (slit width/diameter) and slit angle (measured with respect to the incoming flow direction), play an essential role in determining the trend of critical Reynolds number (Rec). Most of the analysis invokes flow visualization and saturation amplitude methods to obtai…
Flow around two rotating side-by-side circular cylinders of equal diameter D is numerically studied at the Reynolds number Re=40-200 and various rotation rate theta_i. The incoming flow is assumed to be two-dimensional laminar flow. The governing equations are the incompressible Navier-Stokes equations and solved by the finite volume method (FVM). The ratio of the center-to-center spacing to the cylinder diameter is T/D=2. The objective of the present work is to investigate the effect of rotational speed and Reynolds number on the stability of the flow. The simulation results are compared with…
