A method to find optimal 2nd-order perturbations is presented, and applied to find the optimal spanwise-wavy surface for suppression of cylinder wake instability. Second-order perturbations are required to capture the stabilizing effect of spanwise waviness, which is ignored by standard adjoint-based sensitivity analyses. Here, previous methods are extended so that (i) 2nd-order sensitivity is formulated for base flow changes satisfying linearised Navier-Stokes, and (ii) the resulting method is applicable to a 2D global instability problem. This makes it possible to formulate 2nd-order sensitivity to shape modifications. Using this formulation, we find the optimal shape to suppress the a cylinder wake instability. The optimal shape is then perturbed by random distributions in full 3D stability analysis to confirm that it is a local optimal at the given amplitude and wavelength. Furthermore, it is shown that none of the 10 random wavy shapes alone stabilize the wake flow at Re=50, while the optimal shape does. At Re=100, surface waviness of maximum height 1% of the cylinder diameter is sufficient to stabilize the flow. The optimal surface creates streaks by passively extracting energy from the base flow derivatives and effectively altering the tangential velocity component at the wall, as opposed to spanwise-wavy suction which inputs energy to the normal velocity component at the wall. This paper presents a fully two-dimensional and computationally affordable method to find optimal 2nd-order perturbations of generic flow instability problems and any boundary control (such as boundary forcing, shape modulation or suction).
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 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 …
The present article aims to study the suppression of vortex shedding using a passive flow control technique (slit through a circular cylinder) in the laminar regime (Re=100-500). The slit width ratio S/D (slit width/diameter) on the modified cylinder plays an essential role to control the vortex shedding. The additional flow through the slit leads to the suppression of the global instability and vortex shedding, whereas a large amount of flow through the slit drastically alters the behavior of vortex shedding. The nature of vortex shedding remains periodic for all S/D, and the root mean square…
Sensing the flow of water or air disturbance is critical for the survival of many animals: flow information helps them localize food, mates, and prey and to escape predators. Across species, many flow sensors take the form of long, flexible cantilevers. These cantilevers are known to exhibit sustained oscillations when interacting with fluid flow. In the presence of vortex shedding, the oscillations occur through mechanisms such as wake- or vortex-induced vibrations. There is, however, no clear explanation for the mechanisms governing the sustained oscillation of flexible cantilevers without v…
An alternative step in understanding the flows of near wall drag-reducing turbulence can be examining the flow in a well-organized streamwise vortex with a laminar background. Herein, we studied the flow behaviors of the Giesekus viscoelastic fluid in a rotating plane Couette flow system, which is accompanied by steady roll cell structures. By fixing the Reynolds and rotation numbers at values that provide as steady wavy roll cell, i.e., an array of meandering streamwise vortices, the Weissenberg number was increased up to 2000 (where the relaxation time was normalized by the wall speed and th…
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 …
The effect of uniform magnetic field applied along a fixed horizontal direction in Rayleigh-Bénard convection in low-Prandtl-number fluids has been studied using a low dimensional model. The model shows the onset of convection (primary instability) in the form of two dimensional stationary rolls in the absence of magnetic field, when the Rayleigh number $R$ is raised above a critical value $R_c$. The flow becomes three dimensional at slightly higher values of Rayleigh number via wavy instability. These wavy rolls become chaotic for slightly higher values of $R$ in low-Prandtl-number ($P_r$) fl…
We study the large-scale helical vortex shedding regime in the wake of an axisymmetric body with a blunt trailing edge at high Reynolds numbers, both experimentally and by means of local, linear, spatiotemporal stability analysis. In the instability analysis we take into account the detailed downstream evolution of the basic flow behind the body base. The study confirms the existence of a finite region of absolute instability for the first azimuthal number in the near field of the wake. Such instability is believed to trigger the large scale helical vortex shedding downstream of the recirculat…
An investigation of optimal feedback controllers' performance and robustness is carried out for vortex shedding behind a 2D cylinder at low Reynolds numbers. To facilitate controller design, we present an efficient modelling approach in which we utilise the resolvent operator to recast the linearised Navier-Stokes equations into an input-output form from which frequency responses can be computed. The difficulty of applying modern control design techniques to complex, high-dimensional flow systems is thus overcome by using low-order models identified from these frequency responses. The low-orde…
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…
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{…
An elastic foil interacting with a uniform flow with its trailing edge clamped, also known as the inverted foil, exhibits a wide range of complex self-induced flapping regimes such as large amplitude flapping (LAF), deformed and flipped flapping. Here, we perform three-dimensional numerical experiments to examine the role of vortex shedding and the vortex-vortex interaction on the LAF response at Reynolds number Re=30,000. Here we investigate the dynamics of the inverted foil for a novel configuration wherein we introduce a fixed splitter plate at the trailing edge to suppress the vortex shedd…
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…
Although the stability properties of the wake past impervious bluff bodies have been widely examined in the literature, similar analyses regarding the flow around and through porous ones are still lacking. In this work, the effect of the porosity and permeability on the wake patterns of porous rectangular cylinders is numerically investigated at low to moderate Reynolds numbers in the framework of direct numerical simulation combined with local and global stability analyses. A modified Darcy-Brinkman formulation is employed here so as to describe the flow behavior inside the porous media, wher…
Global instabilities in swirling flows can significantly alter the flame and flow dynamics of swirl-stabilized flames, such as those in modern power generation gas turbine engines. In this study, we characterize the interaction between the precessing vortex core (PVC), which is the consequence of a global hydrodynamic instability, and thermoacoustic instabilities, which are the result of a resonant coupling between combustor acoustics and the unsteady heat release rate of combustion. This characterization is performed using experimental data obtained from a model gas turbine combustor system e…
Molecular dynamics (MD) and continuum simulations are carried out to investigate the influence of shear rate and surface roughness on slip flow of a Newtonian fluid. For weak wall-fluid interaction energy, the nonlinear shear-rate dependence of the intrinsic slip length in the flow over an atomically flat surface is computed by MD simulations. We describe laminar flow away from a curved boundary by means of the effective slip length defined with respect to the mean height of the surface roughness. Both the magnitude of the effective slip length and the slope of its rate-dependence are signific…
