The root systems of mangroves, a tree species found in intertidal tropical and sub-tropical coastal zones, provide a natural barrier that dissipates wave energy effectively and reduces sediment erosion. In this work, we use a combination of experiments and numerical simulations to examine the wake and drag characteristics of porous arrays of cylinders, which serve as simplified models of mangrove root networks. Optimal arrangements of the arrays are obtained by coupling Navier-Stokes simulations with a multi-objective optimization algorithm, which seeks configurations that minimize wake enstrophy and maximize drag acting on the porous structure. These optimal configurations are investigated using Particle Image Velocimetry, and the internal and external flow around the porous arrays are analyzed using a combination of Proper Orthogonal Decomposition and Lagrangian particle tracking. Large variations in drag and enstrophy are observed by varying the relative positions of the cylinders, which indicates that the geometrical arrangement of porous arrays plays a prominent role in determining wake and drag characteristics. A sensitivity analysis suggests that enstrophy is more sensitive than drag to specific cylinder placement, and depends on distinctive flow patterns that develop in the interior due to interactions among individual cylinders. Arrays with higher drag are found to have higher average flow speeds in the wake and give rise to time-varying Lagrangian Coherent Structures, making them unfavorable for particle deposition and erosion. Overall, the results indicate that high-level metrics such as array porosity may not be sufficient on their own for predicting wake and drag characteristics.
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…
In this research article we study the wake formation behind 3-Dimensional Multi-scale Porous Obstacles (3DMPOs). Particle Imaging Velocimetry (PIV) is used in a non-shallow ($B/h =1.5$) water flume, with measurements carried out across the $x$ - $y$ plane (at $z$ = 130 mm) and with $Re=70,000$ based on the free-stream velocity ($U_{\infty}$). To characterise the downstream wake characteristics of 3DMPOs the obstacles are split into 3 regimes; (1) non-porous, (2) porous with a single internal scale and (3) porous fractals (based on the Sierpinski carpet). The void fraction ($ϕ=0.7$) and externa…
Reversed von Kármán streets are responsible for a velocity surplus in the wake of flapping foils, indicating the onset of thrust generation. However, the wake pattern cannot be predicted based solely on the flapping peak-to-peak amplitude $A$ and frequency $f$ because the transition also depends sensitively on other details of the kinematics. In this work we replace $A$ with the cycle-averaged swept trajectory $\mathcal{T}$ of the foil chord-line. Two dimensional simulations are performed for pure heave, pure pitch and a variety of heave-to-pitch coupling. In a phase space of dimensionless $\m…
The impact of fluidic actuation on the wake and drag of a three-dimensional blunt body is investigated experimentally. Jets blowing tangentially to the main flow allow to force the wake with variable frequency and amplitude. Depending on the forcing conditions, two flow regimes can be distinguished. First, in case of broadband actuation with frequencies comprising the natural wake time scale, the convection of the jet structures enhances wake entrainment, shortens the length of the recirculating flow and increases drag. Secondly, at higher actuation frequencies, shear-layer deviation leads to …
The effect of the variations of the permeability tensor on the close-to-the-wall behaviour of a turbulent channel flow bounded by porous walls is explored using a set of direct numerical simulations. It is found that the total drag can be either reduced or increased by more than $20\%$ by adjusting the permeability directional properties. Drag reduction is achieved for the case of materials with permeability in the vertical direction lower than the one in the wall-parallel planes. This configuration limits the wall normal velocity at the interface while promoting an increase of the tangential …
In this Letter, the falling of super-hydrophobic spheres is investigated experimentally at low Reynolds numbers. In particular, we show that super-hydrophobic coatings become ineffective at reducing drag unlike predicted by theoretical and numerical approaches. A time scale analysis describing both Marangoni-induced stresses and air/liquid interface deformation shows that these mechanisms are unlikely to account for the slippage effect disappearance observed in our study. Instead, we propose a simple model based on an isotropic porous medium approach, derived to account for losses induced by t…
We study by means of an Eulerian-Lagrangian model the statistical properties of velocity and acceleration of a neutrally-buoyant finite-sized particle in a turbulent flow statistically homogeneous and isotropic. The particle equation of motion, beside added mass and steady Stokes drag, keeps into account the unsteady Stokes drag force - known as Basset-Boussinesq history force - and the non-Stokesian drag based on Schiller-Naumann parametrization, together with the finite-size Faxen corrections. We focus on the case of flow at low Taylor-Reynolds number, Re_lambda ~ 31, for which fully resolve…
Wing flapping is one of the most widespread propulsion methods found in nature; however, the current understanding of the aerodynamics in bird wakes is incomplete. The role of the unsteady motion in the flow and its contribution to the aerodynamics is still an open question. In the current study, the wake of a freely flying European starling has been investigated using long-duration high-speed Particle Image Velocimetry (PIV) in the near wake. Kinematic analysis of the wings and body of the bird has been performed using additional high-speed cameras that recorded the bird movement simultaneous…
Fractal-based variable drag model for porous-media tree representations
Faculty of Engineering, Institute of Science Tokyo（东京科学大学工学院）；Supercomputing Research Center, Institute of Integrated Research, Institute of Science Tokyo（东京科学大学综合研究院超级计算研究中心）
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…
Large eddy simulations (LES) are employed to investigate the role of time-varying currents on the form drag and vortex dynamics of submerged 3D topography in a stratified rotating environment. The current is of the form $U_c+U_t \sin(2πf_t t)$, where $U_c$ is the mean, $U_t$ is the tidal component and $f_t$ is its frequency. A conical obstacle is considered in the regime of low Froude number. When tides are absent, eddies are shed at the natural shedding frequency $f_{s,c}$. The relative frequency $f^*=f_{s,c}/f_t$ is varied in a parametric study which reveals states of high time-averaged form…
The multiphase flow mechanism in miscible displacement through porous media is an important topic in various applications, such as petroleum engineering, low Reynolds number suspension flows, dusty gas dynamics, and fluidized beds. To simulate such flows, volume averaging spatial operators are considered to incorporate pressure drag and skin friction experienced by a porous medium. In this work, a streamline-based Lagrangian methodology is extended for an efficient numerical approach to handle dispersion and diffusion of solvent saturation during a miscible flow. Overall pressure drag on the d…
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 performances of an original passive control system based on a biomimetic approach are assessed by investigating the flow over a bluff-body. This control device consists in a couple of flaps made from the combination of a rigid plastic skeleton coated with a porous fabric mimicking the shaft and the vane of the bird's feathers, respectively. The sides of a square cylinder have been fitted with this system so as to enable the flaps to freely rotate around their leading edge. This feature allows the movable flaps to self-adapt to the flow conditions. Comparing both the uncontrolled and the co…
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 paper analyzes the adjoint solution of the Navier-Stokes equation. We focus on flow across a circular cylinder at three Reynolds numbers, Re_D=20, 100 and 500. The quantity of interest in the adjoint formulation is the drag on the cylinder. We use classical fluid mechanics approaches to analyze the adjoint solution, which is a vector field similar to a flow field. Production and dissipation of kinetic energy of the adjoint field is discussed. We also derive the evolution of circulation of the adjoint field along a closed material contour. These analytical results are used to explain three…
The appearance of detached recirculation regions in wakes with base bleed determines the aerodynamic properties of many natural organisms and technological applications. In this work we introduce an analytical model which captures certain key dimensions of the recirculation region in the wake of porous plates of infinite aspect ratio, along with the porosity range \ks{over which} it exists, when vortex shedding is absent or suppressed. The model is used to interpret why the recirculation region (i) emerges, (ii) migrates away from the body with increasing base bleed, (iii) disappears at a crit…
The development of nuclear reactors that utilize pebble fuel has drastically increased the demand for improving the capabilities to simulate the packed beds found in these reactors. The complex flow fields found in a pebble bed make computational fluid dynamics (CFD) simulations time consuming and costly. Intermediate fidelity porous media models, however, are capable of approximating these flow fields in a much more computationally efficient manner. These models require the use of closures to capture the effects of complex flow phenomena without modeling them explicitly. This research employs…
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 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…
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…
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…
Wind turbine wakes negatively impact downwind turbines in wind farms reducing their global efficiency. The reduction of wake-turbine interactions by actuating control on yaw angles and induction factors is an active area of research. In this study, the capability of spanwise-periodic wind turbine arrays with tilted rotors to reduce negative turbine-wakes interaction is investigated by means of large-eddy simulations. It is shown that by means of rotor tilt it is possible to replace turbine far wakes with high-speed streaks where the streamwise velocity exceeds the freestream velocity at hub he…
The influence of body anisotropy on wake characteristics and enstrophy production for prolate ellipsoids at $ \mathrm{Re}_{D} = 10,000 $
Harbor Branch Oceanographic Institute, Florida Atlantic University（佛罗里达大西洋大学哈勃分支海洋研究所）；Department of Ocean and Mechanical Engineering, Florida Atlantic University（佛罗里达大西洋大学海洋与机械工程系）
The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$; the deformability of the bubbles is controlled through the Weber n…
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…
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 …
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…
A comparative assessment of machine learning (ML) methods for active flow control is performed. The chosen benchmark problem is the drag reduction of a two-dimensional Kármán vortex street past a circular cylinder at a low Reynolds number ($Re=100$). The flow is manipulated with two blowing/suction actuators on the upper and lower side of a cylinder. The feedback employs several velocity sensors. Two probe configurations are evaluated: 5 and 11 velocity probes located at different points around the cylinder and in the wake. The control laws are optimized with Deep Reinforcement Learning (DRL) …
We examine the characteristics of mean flow and scalar concentration characteristics of a turbulent boundary layer flow impinging on a cluster of tall obstacles (which can also be interpreted as a porous obstruction). The cluster is created with a group of cylinders of diameter $d$ and height $h$ arranged in a circular patch of diameter $D$.The solidity of the patch/obstruction is defined by $ϕ$ (the total planar area covered by cylinders), which is systematically varied ($0.098 \leq ϕ\leq 1$) by increasing the number of cylinders in a patch ($N_c$). A point source is placed at ground level up…
