Wei-Xi Huang

Simulation of flexible filaments in a uniform flow by the immersed boundary method

An improved version of the immersed boundary (IB) method is developed for simulating flexible filaments in a uniform flow. The proposed IB method is based on an efficient Navier-Stokes solver adopting the fractional step method and a staggered Cartesian grid system. The fluid motion defined on an Eulerian grid and the filament motion defined on a Lagrangian grid are independently solved and their interaction force is explicitly calculated using a feedback law. A direct numerical method is developed to calculate the filament motion under the constraint of inextensibility. When applied to the case of a swinging filament analogous to a rope pendulum, the proposed method gave results very similar to those of the analytical solution derived using the perturbation method. For a flexible filament flapping in a uniform flow, the mechanism by which small vortex processions are produced was investigated. The bistable property of the system was observed by altering the filament length, and the effects of the boundary condition at the fixed end (simply supported or clamped) were studied. For two side-by-side filaments in a uniform flow, both in-phase flapping and out-of-phase flapping were reproduced in the present simulations. A repulsive force was included in the formulation to handle collisions between the free ends of side-by-side filaments undergoing out-of-phase flapping.

Three-dimensional simulation of a flapping flag in a uniform flow

A three-dimensional computational model is developed for simulating the flag motion in a uniform flow. The nonlinear dynamics of the coupled fluid–flag system after setting up of flapping is investigated by a series of numerical tests. At low Reynolds numbers, the flag flaps symmetrically about its centreline when gravity is excluded, and the bending in the spanwise direction is observed near the corners on the trailing edge. As the Reynolds number increases, the spanwise bending is flattened due to the decrease of the positive pressure near the side edges as well as the viscous force of the fluid. At a certain critical Reynolds number, the flag loses its symmetry about the centreline, which is shown to be related to the coupled fluid–flag instability. The three-dimensional vortical structures shed from the flag show a significant difference from the results of two-dimensional simulations. Hairpin or O-shaped vortical structures are formed behind the flag by connecting those generated at the flag side edges and the trailing edge. Such vortical structures have a stabilization effect on the flag by reducing the pressure difference across the flag. Moreover, the positive pressure near the side edges is significantly reduced as compared with that in the center region, causing the spanwise bending. The Strouhal number defined based on the flag length is slightly dependent on the Reynolds number and the flag width, but scales with the density ratio as St ~ ρ −1/2 ). On the other hand, the flapping-amplitude-based Strouhal number remains close to 0.2, consistent with the values reported for flying or swimming animals. A flag flapping under gravity is then simulated, which is directed along the negative spanwise direction. The sagging down of the flag and the rolling motion of the upper corner are observed. The dual effects of gravity are demonstrated, i.e. the destabilization effect like the flag inertia and the stabilization effect by increasing the longitudinal tension force.

Constructive and destructive interaction modes between two tandem flexible flags in viscous flow

Two tandem flexible flags in viscous flow were modelled by numerical simulation using an improved version of the immersed boundary method. The flexible flapping flag and the vortices produced by an upstream flag were found to interact via either a constructive or destructive mode. These interaction modes gave rise to significant differences in the drag force acting on the downstream flapping flag in viscous flow. The constructive mode increased the drag force, while the destructive mode decreased the drag force. Drag on the downstream flexible body was investigated as a function of the streamwise and spanwise gap distances, and the bending coefficient of the flexible flags at intermediate Reynolds numbers (200 ≤ Re ≤ 400).

Three-dimensional simulation of elastic capsules in shear flow by the penalty immersed boundary method

An improved penalty immersed boundary method (pIBM) has been proposed for simulation of flow-induced deformation of three-dimensional (3D) elastic capsules. The motion of the capsule membrane is described in the Lagrangian coordinates. The membrane deformation takes account of the bending and twisting effects as well as the stretching and shearing effects. The method of subdivision surfaces is adopted to generate the mesh of membrane and the corresponding shape functions, which are required to be C^1 continuous. The membrane motion is then solved by the subdivision-surface based finite element method on the triangular unstructured mesh. On the other hand, the fluid motion is defined on the Eulerian domain, and is advanced by the fractional step method on a staggered Cartesian grid. Coupling of the fluid motion and the membrane motion is realized in the framework of the pIBM. Using the proposed method, deformation of 3D elastic capsules in a linear shear flow is studied in detail, and validations are examined by comparing with previous studies. Both the neo-Hookean membrane and the Skalak membrane are tested. For an initially spherical capsule the tank-treading motion is formed under various dimensionless shear rates and reduced bending moduli. It is found that buckling occurs near the equator of the capsule for small shear rates but near the tips for large shear rates, which is suppressed by including the bending rigidity of the membrane. Effects of the Reynolds number and the membrane density are investigated for an initially spherical capsule. For a non-spherical capsule, with the initial shape of the oblate spheroid or the biconcave circular disk as a model of the red blood cell, the swinging motion is observed due to the shape memory effect. By decreasing the dimensionless shear rate or increasing the reduced bending modulus, the swinging motion is transited into the tumbling motion.

An improved penalty immersed boundary method for fluid-flexible body interaction

An improved penalty immersed boundary (pIB) method has been proposed for simulation of fluid-flexible body interaction problems. In the proposed method, the fluid motion is defined on the Eulerian domain, while the solid motion is described by the Lagrangian variables. To account for the interaction, the flexible body is assumed to be composed of two parts: massive material points and massless material points, which are assumed to be linked closely by a stiff spring with damping. The massive material points are subjected to the elastic force of solid deformation but do not interact with the fluid directly, while the massless material points interact with the fluid by moving with the local fluid velocity. The flow solver and the solid solver are coupled in this framework and are developed separately by different methods. The fractional step method is adopted to solve the incompressible fluid motion on a staggered Cartesian grid, while the finite element method is developed to simulate the solid motion using an unstructured triangular mesh. The interaction force is just the restoring force of the stiff spring with damping, and is spread from the Lagrangian coordinates to the Eulerian grids by a smoothed approximation of the Dirac delta function. In the numerical simulations, we first validate the solid solver by using a vibrating circular ring in vacuum, and a second-order spatial accuracy is observed. Then both two- and three-dimensional simulations of fluid-flexible body interaction are carried out, including a circular disk in a linear shear flow, an elastic circular disk moving through a constricted channel, a spherical capsule in a linear shear flow, and a windsock in a uniform flow. The spatial accuracy is shown to be between first-order and second-order for both the fluid velocities and the solid positions. Comparisons between the numerical results and the theoretical solutions are also presented.

Transient response of Reynolds stress transport to spanwise wall oscillation in a turbulent channel flow

Turbulent channel flow at low Reynolds number subjected to spanwise wall oscillation is studied by direct numerical simulation. The Reynolds stress budgets under the influence of the oscillating wall are analyzed in the first two oscillation periods. It is found that the spanwise velocity fluctuations are enhanced at the very beginning of the wall oscillation, and the subsequent global turbulence suppression is caused by the sustained attenuation of the pressure-strain terms. The hindrance of intercomponent transfer of turbulent kinetic energy by the oscillating wall is a mechanism of the skin-friction reduction.

Optical levitation of a non-spherical particle in a loosely focused Gaussian beam

The optical force on a non-spherical particle subjected to a loosely focused laser beam was calculated using the dynamic ray tracing method. Ellipsoidal particles with different aspect ratios, inclination angles, and positions were modeled, and the effects of these parameters on the optical force were examined. The vertical component of the optical force parallel to the laser beam axis decreased as the aspect ratio decreased, whereas the ellipsoid with a small aspect ratio and a large inclination angle experienced a large vertical optical force. The ellipsoids were pulled toward or repelled away from the laser beam axis, depending on the inclination angle, and they experienced a torque near the focal point. The behavior of the ellipsoids in a viscous fluid was examined by analyzing a dynamic simulation based on the penalty immersed boundary method. As the ellipsoids levitated along the direction of the laser beam propagation, they moved horizontally with rotation. Except for the ellipsoid with a small aspect ratio and a zero inclination angle near the focal point, the ellipsoids rotated until the major axis aligned with the laser beam axis.

Strengthened opposition control for skin-friction reduction in wall-bounded turbulent flows

An opposition control scheme with strengthened control input is proposed and tested in turbulent channel flows at friction Reynolds number Reτ = 180 by direct numerical simulations. When the detection plane is located at less than 20 wall units, the drag reduction rate can be greatly enhanced by increasing the control amplitude parameter. The maximum drag reduction rate achieved in the present study is around 33%, which is much higher than the best value of 25% reported in literature. The strengthened control can be more efficient to attain a given drag reduction rate. Based on the total shear stress at the virtual wall established between the real wall and the detection plane by the control, a new friction velocity is proposed and the corresponding coordinate transform is made. Scaled by the proposed friction velocity, the wall-normal velocity fluctuation and the Reynolds shear stress of the controlled flows are collapsed well with those of the uncontrolled flow in the new coordinate. Based on the similarity, a relation between drag reduction rate and the effectiveness of the virtual wall is deduced, which disclosed that the elevation and residual Reynolds shear stress at the virtual wall are the key parameters to determine the drag reduction rate. The conclusion are also validated at Reτ = 395 and 590. The decrease of the drag reduction rate with the increase of the Reynolds number is attributed to the enhanced residual Reynolds shear stress at the virtual wall.

Synergistic Effects of Chiral Morphology and Reconfiguration in Cattail Leaves

Cattail, a type of herbaceous emergent aquatic macrophyte, has upright-standing leaves with a large slenderness ratio and a chiral morphology. With the aim of understanding the effect of chiral morphology on their mechanical behavior, we investigated, both experimentally and theoretically, the twisting chiral morphologies and wind-adaptive reconfigurations of cattail leaves. Their multiscale structures were observed by using optical microscope and scanning electron microscopy. Their mechanical properties were measured by uniaxial tension and three-point bending tests. By modeling a chiral leaf as a pre-twisted cantilever-free beam, fluid dynamics simulations were performed to elucidate the synergistic effects of the leaf’s chiral morphology and reconfiguration in wind. It was observed that the leaves have evolved multiscale structures and superior mechanical properties, both of which feature functionally gradient variations in the height direction, to improve their ability to resist lodging failure by reducing the maximal stress. The synergistic effect of chiral morphology and reconfiguration can greatly improve the survivability of cattail plants in wind.

Direct numerical simulation of spatially developing turbulent boundary layers with opposition control

Opposition control of spatially developing turbulent boundary layers for skin friction drag reduction is studied by direct numerical simulations. The boundary layer extends 800?0 in the streamwise (x) direction, with ?0 denoting the momentum thickness at the flow inlet. The Reynolds number, based on the external flow velocity and the momentum thickness, ranges from 300 to 860. Opposition control applied in different streamwise ranges, i.e. and as well as the uncontrolled case, are simulated. Statistical results and instantaneous flow fields are presented, with special attention paid to the spatial evolution properties of the boundary layer flow with control and the underlying mechanism. It is observed that a long spatial transient region after the control start and a long recovery region after the control end are present in the streamwise direction. A maximum drag reduction rate of about 22% is obtained as the transient region is passed, and an overshoot in the local skin friction coefficient (Cf) occurs in the recovery region. A new identity is derived for dynamical decomposition of Cf. Reduction of Cf by opposition control and overshoot of Cf in the recovery region are explained by quantifying the contributions from the viscous shear stress term, the Reynolds shear stress term, the mean convection term and other terms.