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The stability of the inverted flexible plate with non-uniform stiffness distribution in a free stream is studied by numerical simulation and mathematical theory. In our study, the bending stiffness distribution is expressed as the function of the leading edge's bending stiffness [Formula: see text] and the polynomial of the plate's coordinate. Based on the former theoretical work on the stability of inverted plates with uniform stiffness distribution, we derive the upper limit value of [Formula: see text] at which the zero-deflection equilibrium loses its stability for the plate with non-uniform stiffness distribution. The critical [Formula: see text] derived from the mathematical theory agrees well with that obtained from the numerical simulation. An effective bending stiffness is defined, which can be used to unify the regimes of the motion modes between uniform plates and non-uniform plates. Moreover, three orders of mass ratio [[Formula: see text], and [Formula: see text]] are investigated, and the underlying mechanism for large amplitude flapping is clarified for the inverted plate with different mass ratios. An appropriate bending stiffness distribution can greatly improve the deformation of the plate. The findings shed some light on the energy harvesting of the inverted plate.

Inertia may significantly influence the transient deformation process and the steady-state structure of a deformable capsule. The behavior of a two-dimensional deformable capsule in shear flow at finite Reynolds numbers ( Re) is studied numerically. By simulating numerous cases with different Re and frequencies ( f), we observed persistent oscillation, asymmetric oscillation, deflected oscillation, and stable modes. The phase diagram in the Re–f plane is presented. At low frequencies, a capsule shows a phase-lag phenomenon between the deformation and the applied shear. At moderate frequencies, the anomaly of decreasing maximum deformation with increasing Re is observed. The anomaly is attributed to the mode shift. In addition, a scaling law of the maximum deformation of the capsule as a function of Re and f is proposed. This study may shed some light on the identification and screening of cells in vitro as well as the transport and breakup of cells in vivo.

The locomotion of a flapping flexible plate with different shapes and non-uniform chordwise stiffness distribution in a stationary fluid is studied numerically. The normalized effective bending stiffness K∗ for three-dimensional plates with arbitrary stiffness distribution and shape parameters is proposed, and the overall bending stiffness of non-uniform plates with different shapes is reasonably characterized. It is found that the propulsion performance in terms of cruising speed and efficiency of the self-propelled flapping plate mainly depends on the effective bending stiffness. Plates with moderate flexibility K∗ show better propulsion performance. Meanwhile, both a large area moment of the plate and a flexible anterior are favorable to significantly improve their propulsive performance. The evolution of vortical structures and the pressure distribution on the upper and lower surfaces of the plate are analyzed, and the inherent mechanism is revealed. These findings are of great significance to the optimal design of propulsion systems with different fins or wings.

The effect of non-uniform chordwise stiffness distribution on the self-propulsive performance of three-dimensional flexible plates is studied numerically. Some typical stiffness distributions, including uniform, declining, and growing distribution, are considered. First, the normalized bending stiffness K is derived, which can well represent the overall bending stiffness of the non-uniform plates. For different non-uniformly distributed plates with the same K, the maximum displacement difference between the trailing and leading edges of the plate during the flapping is almost identical. There exists a common optimal K at which all the plates achieve their optimal performance, i.e., the highest cruising speed and efficiency. Second, we reveal what kind of non-uniform distribution could be the best at a specific K in terms of the propulsive performance. The force analysis indicates that a larger bending deformation in the anterior part for the growing distribution leads to a larger thrust. Hence, the large local slope along the anterior flexible plate is preferred to enhance the propulsive performance. The results obtained in this study may shed some light on a better understanding of the hydrodynamic effect on the self-propulsion of the non-uniform stiffness wings or fins of animals.

Two deep learning (DL) models addressing the super-resolution (SR) reconstruction of turbulent flows from low-resolution coarse flow field data are developed. One is the static convolutional neural network (SCNN), and the other is the novel multiple temporal paths convolutional neural network (MTPC). The SCNN model takes instantaneous snapshots as an input, while the MTPC model takes a time series of velocity fields as an input, and it includes spatial and temporal information simultaneously. Three temporal paths are designed in the MTPC to fully capture features in different time ranges. A weight path is added to generate pixel-level weight maps of each temporal path. These models were first applied to forced isotropic turbulence. The corresponding high-resolution flow fields were reconstructed with high accuracy. The MTPC seems to be able to reproduce many important features as well, such as kinetic energy spectra and the joint probability density function of the second and third invariants of the velocity gradient tensor. As a further evaluation, the SR reconstruction of anisotropic channel flow with the DL models was performed. The SCNN and MTPC remarkably improve the spatial resolution in various wall regions and potentially grasp all the anisotropic turbulent properties. It is also shown that the MTPC supplements more under-resolved details than the SCNN. The success is attributed to the fact that the MTPC can extract extra temporal information from consecutive fluid fields. The present work may contribute to the development of the subgrid-scale model in computational fluid dynamics and enrich the application of SR technology in fluid mechanics.

The role of the hydrodynamic effect in the collective locomotion of several birds or fish is an interesting topic. Taking a model of a self-propelled flapping plate, we numerically investigated the collective locomotion of a pair of plates with comparable but different propulsive capacities, e.g., one long and one short plates. The longer plate is supposed to have a stronger propulsive capacity. It is found that two typical equilibrium configurations, i.e., compact and sparse configurations, may emerge, which depend mainly on initial lateral and longitudinal gap spacing, i.e., H and G0, respectively. In the compact cases, when H is small, e.g., H < 0.6, in terms of cruising speed and efficiency, hydrodynamic advantages are found for both plates. In all sparse configurations, the propulsive performance of the leading plate is identical to that of the corresponding isolated one. The following short plate in the “long-short” (the longer in the front) sparse cases always takes hydrodynamic advantages in terms of cruising speed and efficiency. In the “short-long” (the shorter in the front) sparse cases, the follower’s propulsive capacity is suppressed because the cruising speed and input power decrease significantly compared to its isolated case. The analyses of hydrodynamic force and corresponding potential energy show that the staggered sparse configuration with H ∈ (0.4, 1.0) is more stable than that with other H. The “hydrodynamic drafting” analyzed here may shed some light on understanding the coordinated collective behaviors in biological and natural systems.

The free locomotion of a two-dimensional flapping flexible plate near the flat ground is studied by the lattice Boltzmann method for fluid flow and a finite-element method for the plate motion. The fluid flow and plate deformation are coupled through the immersed boundary scheme. When the leading edge of the plate is forced to oscillate sinusoidally near the ground, the plate may move freely in the horizontal direction due to the fluid-structure interaction. The mechanisms underlying the ground effect are elucidated. Besides a moderate rigidity, it is found that an appropriate density ratio between the plate and surrounding fluid (M) can improve the propulsive efficiency of the plate. When M is relatively small, the lateral force is enhanced, and the input work is increased when the plate is near the ground; when M is large, the deformation of the plate is inhibited and the input work is decreased when the plate is close to the ground. Usually the closer the plate flapping is to the wall, the more efficie...

Interaction between two tandem flexible loops with tension and bending stiffness in a viscous flow is investigated by numerical simulations. In most cases, the heads of the loops facing the oncoming flow are fixed but flapping around the head is allowed. The effect of the gap distance between the two passive flapping loops (G) on the drag coefficient is investigated in detail. Here, for the first time, the sudden drag force reduction at a specific G, i.e., Gc for the downstream loop has been found in the two tandem flexible loops system. It is different from the drag “jump” behavior in the two tandem rigid cylinder system. Although the drag is partially associated with the flapping amplitude, the drag force reduction of the downstream loop may be mainly attributed to flow regimes transition or vortices merging mode transition. The vortices merging is also analysed from a Lagrangian viewpoint, which gives insight into the mechanism. The effects of Reynolds number (20≤ Re ≤100), bending coefficient (10−4≤K≤...

Sedimentation behaviours of an ellipsoidal particle in narrow and infinitely long tubes are studied by a multi-relaxation-time lattice Boltzmann method (LBM). In the present study, both circular and square tubes with 12/13 ⩽ D/A ⩽ 2.5 are considered with the Galileo number (Ga) up to 150, where D and A are the width of the tube and the length of major axis of the ellipsoid, respectively. Besides three modes of motion mentioned in the literature, two novel modes are found for the narrow tubes in the higher Ga regime: the spiral mode and the vertically inclined mode. Near a transitional regime, in terms of average settling velocity, it is found that a lighter ellipsoid may settle faster than a heavier one. The relevant mechanism is revealed. The behaviour of sedimentation inside the square tubes is similar to that in the circular tubes. One significant difference is that the translation and rotation of ellipsoid are finally constrained to a diagonal plane in the square tubes. The other difference is that the anomalous rolling mode occurs in the square tubes. In this mode, the ellipsoid rotates as if it is contacting and rolling up one corner of the square tube when it settles down. Two critical factors that induce this mode are identified: the geometry of the tube and the inertia of the ellipsoid.

In this paper, the viscous coupling effects for immiscible two-phase (gas-liquid) flow in porous media were studied using the Shan–Chen-type single-component multiphase lattice Boltzmann model. Using the model, the two-phase flows in porous media with density ratio as high as 56 could be simulated and the contact angle of the gas-liquid interface at a solid wall is adjustable. To investigate viscous coupling effects, the co- and countercurrent steady-state two-phase flow patterns and relative permeabilities as a function of wetting saturation were obtained for different capillary numbers, wettabilities, and viscosity ratios. The cocurrent relative permeabilities seem usually larger than the countercurrent ones. The opposing drag-force effect and different pore-level saturation distributions in co- and countercurrent flows may contribute to this difference. It is found that for both co- and countercurrent flows, for strongly wet cases and viscosity ratio M>1, knw increase with the driving force and the vis...