Proximity to the water surface markedly enhances the force production on underwater flapping wings.

The potential application of flapping wings in micro-aerial vehicles is gaining interest due to their ability to generate high lift even in confined spaces. Most studies in the past have investigated hovering wings as well as those flapping near solid surfaces. However, the presence of surface tension at the water-air interface and the ability of the water surface to move might differentiate its response to the proximity of wings, compared to that of solid surfaces. Motivated by underwater, amphibian robots and several underwater experimental studies on flapping wings, our study investigated the effects of the proximity of flapping wings to the water surface at low Reynolds numbers (Re = 3400). Experiments were performed on a rectangular wing in a water tank with prescribed flapping kinematics and the aerodynamic forces were measured. The effects of surface proximity on the wing in its both upright and inverted orientations were studied. Broadly, the mean lift and drag coefficients in both orientations decreased significantly (by up to 60%) as the distance from the water surface was increased. In the case of the upright orientation, the mean lift coefficient was slightly decreased very close to the water surface with its peak being observed at the normalized clearance of [Formula: see text]. Overall, the study revealed an enhancement in the aerodynamic forces closer to the water surface.

Learning to school in dense configurations with multi-agent deep reinforcement learning.

Fish are observed to school in different configurations. However, how and why fish maintain a stable schooling formation still remains unclear. This work presents a numerical study of the dense schooling of two free swimmers by a hybrid method of the multi-agent deep reinforcement learning and the immersed boundary-lattice Boltzmann method. Active control policies are developed by synchronously training the leader to swim at a given speed and orientation and the follower to hold close proximity to the leader. After training, the swimmers could resist the strong hydrodynamic force to remain in stable formations and meantime swim in desired path, only by their tail-beat flapping. The tail movement of the swimmers in the stable formations are irregular and asymmetrical, indicating the swimmers are carefully adjusting their body-kinematics to balance the hydrodynamic force. In addition, a significant decrease in the mean amplitude and the cost of transport is found for the followers, indicating these swimmers could maintain the swimming speed with less efforts. The results also show that the side-by-side formation is hydrodynamically more stable but energetically less efficient than other configurations, while the full-body staggered formation is energetically more efficient as a whole.

Fast prediction of blood flow in stenosed arteries using machine learning and immersed boundary-lattice Boltzmann method.

A fast prediction of blood flow in stenosed arteries with a hybrid framework of machine learning and immersed boundary-lattice Boltzmann method (IB-LBM) is presented. The integrated framework incorporates the immersed boundary method for its excellent capability in handling complex boundaries, the multi-relaxation-time LBM for its efficient modelling for unsteady flows and the deep neural network (DNN) for its high efficiency in artificial learning. Specifically, the stenosed artery is modelled by a channel for two-dimensional (2D) cases or a tube for three-dimensional (3D) cases with a stenosis approximated by a fifth-order polynomial. An IB-LBM is adopted to obtain the training data for the DNN which is constructed to generate an approximate model for the fast flow prediction. In the DNN, the inputs are the characteristic parameters of the stenosis and fluid node coordinates, and the outputs are the mean velocity and pressure at each node. To characterise complex stenosis, a convolutional neural network (CNN) is built to extract the stenosis properties by using the data generated by the aforementioned polynomial. Both 2D and 3D cases (including 3D asymmetrical case) are constructed and examined to demonstrate the effectiveness of the proposed method. Once the DNN model is trained, the prediction efficiency of blood flow in stenosed arteries is much higher compared with the direct computational fluid dynamics simulations. The proposed method has a potential for applications in clinical diagnosis and treatment where the real-time modelling results are desired.

Effects of uniform vertical inflow perturbations on the performance of flapping wings.

Flapping wings have attracted significant interest for use in miniature unmanned flying vehicles. Although numerous studies have investigated the performance of flapping wings under quiescent conditions, effects of freestream disturbances on their performance remain under-explored. In this study, we experimentally investigated the effects of uniform vertical inflows on flapping wings using a Reynolds-scaled apparatus operating in water at Reynolds number ≈ 3600. The overall lift and drag produced by a flapping wing were measured by varying the magnitude of inflow perturbation from J Vert = -1 (downward inflow) to J Vert = 1 (upward inflow), where J Vert is the ratio of the inflow velocity to the wing's velocity. The interaction between flapping wing and downward-oriented inflows resulted in a steady linear reduction in mean lift and drag coefficients, C ¯ L and C ¯ D , with increasing inflow magnitude. While a steady linear increase in C ¯ L and C ¯ D was noted for upward-oriented inflows between 0 < J Vert < 0.3 and J Vert > 0.7, a significant unsteady wing-wake interaction occurred when 0.3 ≤ J Vert < 0.7, which caused large variations in instantaneous forces over the wing and led to a reduction in mean performance. These findings highlight asymmetrical effects of vertically oriented perturbations on the performance of flapping wings and pave the way for development of suitable control strategies.

Performance of passively pitching flapping wings in the presence of vertical inflows.

The successful implementation of passively pitching flapping wings strongly depends on their ability to operate efficiently in wind disturbances. In this study, we experimentally investigated the interaction between a uniform vertical inflow perturbation and a passive-pitching flapping wing using a Reynolds-scaled apparatus operating in water at Reynolds number ≈3600. A parametric study was performed by systematically varying the Cauchy number (Ch) of the wings from 0.09 to 11.52. The overall lift and drag, and pitch angle of the wing were measured by varying the magnitude of perturbation fromJVert= -0.6 (downward inflow) toJVert= 0.6 (upward inflow) at eachCh, whereJVertis the ratio of the inflow velocity to the wing's velocity. We found that the lift and drag had remarkably different characteristics in response to bothChandJVert. Across allCh, while mean lift tended to increase as the inflow perturbation varied from -0.6 to 0.6, drag was significantly less sensitive to the perturbation. However effect of the vertical inflow on drag was dependent onCh, where it tended to vary from an increasing to a decreasing trend asChwas changed from 0.09 to 11.52. The differences in the lift and drag with perturbation magnitude could be attributed to the reorientation of the net force over the wing as a result of the interaction with the perturbation. These results highlight the complex interactions between passively pitching flapping wings and freestream perturbations and will guide the design of miniature flying crafts with such architectures.

A numerical study of fish adaption behaviors in complex environments with a deep reinforcement learning and immersed boundary-lattice Boltzmann method.

Fish adaption behaviors in complex environments are of great importance in improving the performance of underwater vehicles. This work presents a numerical study of the adaption behaviors of self-propelled fish in complex environments by developing a numerical framework of deep learning and immersed boundary-lattice Boltzmann method (IB-LBM). In this framework, the fish swimming in a viscous incompressible flow is simulated with an IB-LBM which is validated by conducting two benchmark problems including a uniform flow over a stationary cylinder and a self-propelled anguilliform swimming in a quiescent flow. Furthermore, a deep recurrent Q-network (DRQN) is incorporated with the IB-LBM to train the fish model to adapt its motion to optimally achieve a specific task, such as prey capture, rheotaxis and Kármán gaiting. Compared to existing learning models for fish, this work incorporates the fish position, velocity and acceleration into the state space in the DRQN; and it considers the amplitude and frequency action spaces as well as the historical effects. This framework makes use of the high computational efficiency of the IB-LBM which is of crucial importance for the effective coupling with learning algorithms. Applications of the proposed numerical framework in point-to-point swimming in quiescent flow and position holding both in a uniform stream and a Kármán vortex street demonstrate the strategies used to adapt to different situations.

Numerical simulation of flow over a parallel cantilevered flag in the vicinity of a rigid wall.

Flow over a parallel cantilevered flag in the vicinity of a rigid wall is numerically studied using an immersed boundary-lattice Boltzmann method (IB-LBM) in two-dimensional domain, where the dynamics of the fluid and structure are, respectively, solved by the LBM and a finite-element method (FEM), with a penalty IB to handle the fluid-structure interaction (FSI). Specifically, a benchmark case considering a plate attached to the downstream of a stationary cylinder is first conducted to validate the current solver. Then, the wall effects on the flag are systemically studied, considering the effects of off-wall distance, structure-to-fluid mass ratio, bending rigidity, and Reynolds number. Three flapping modes, including symmetrical flapping, asymmetrical flapping, and chaotic flapping, along with a steady state are observed in the simulations. It is found that the flag is vibrating or stable with a mean angle inclined in the fluid when it is mounted in the vicinity of a rigid wall. The mean inclined angle first increases in the steady state and then decreases in the unsteady state with the off-wall distance. In the unsteady regime, the dependency of the inclined angle on the off-wall distance is similar to that of the gradient of the fluid velocity. In addition, the rigid wall near the flag decreases the lift and drag generation and further stabilizes the flag-fluid system. Contrarily, the flag inertia destabilizes the flag, and large flag inertia induces chaotic vibrating modes.

Dynamic characteristics of a deformable capsule in a simple shear flow.

The dynamic characteristics of a two-dimensional deformable capsule in a simple shear flow are studied with an immersed boundary-lattice Boltzmann method. Simulations are conducted by varying the Reynolds number (Re) from 0.0125 to 2000 and the dimensionless shear rate (G) from 0.001 to 0.5. The G-Re plane can be divided into four regions according to the deformation dependence on the parameters considered: viscous dominant, inertia dominant, transitional, and anomalous regions. There are four typical dynamic behaviors over the G-Re plane: steady deformation, prerupture state, quasisteady deformation, and continuous elongation. Analysis indicates that the pressure distribution and its variations due to the interplay of the fluid inertia force, the viscous shear stress, and the membrane elastic force determines the complex behaviors of the capsule. The effects of the bending rigidity and the internal-to-external viscosity ratio on the dynamics of the capsule are further studied. It is found that the capsule experiences smaller deformation when the higher bending rigidity is included, and the low bending rigidity does not have a remarkable influence on the capsule deformation. The capsule normally experiences smaller deformation due to the increase of the internal-to-external viscosity ratio.

Deformation of a Capsule in a Power-Law Shear Flow.

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

Refuging rainbow trout selectively exploit flows behind tandem cylinders.

Fishes may exploit environmental vortices to save in the cost of locomotion. Previous work has investigated fish refuging behind a single cylinder in current, a behavior termed the Kármán gait. However, current-swept habitats often contain aggregations of physical objects, and it is unclear how the complex hydrodynamics shed from multiple structures affect refuging in fish. To begin to address this, we investigated how the flow fields produced by two D-shaped cylinders arranged in tandem affect the ability of rainbow trout (Oncorhynchus mykiss) to Kármán gait. We altered the spacing of the two cylinders from l/D of 0.7 to 2.7 (where l=downstream spacing of cylinders and D=cylinder diameter) and recorded the kinematics of trout swimming behind the cylinders with high-speed video at Re=10,000-55,000. Digital particle image velocimetry showed that increasing l/D decreased the strength of the vortex street by an average of 53% and decreased the frequency that vortices were shed by ∼20% for all speeds. Trout were able to Kármán gait behind all cylinder treatments despite these differences in the downstream wake; however, they Kármán gaited over twice as often behind closely spaced cylinders (l/D=0.7, 1.1, and 1.5). Computational fluid dynamics simulations show that when cylinders are widely spaced, the upstream cylinder generates a vortex street that interacts destructively with the downstream cylinder, producing weaker, more widely spaced and less-organized vortices that discourage Kármán gaiting. These findings are poised to help predict when fish may seek refuge in natural habitats based on the position and arrangement of stationary objects.

Fluid-structure interaction involving large deformations: 3D simulations and applications to biological systems.

Three-dimensional fluid-structure interaction (FSI) involving large deformations of flexible bodies is common in biological systems, but accurate and efficient numerical approaches for modeling such systems are still scarce. In this work, we report a successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations. This method represents a significant enhancement from the similar methods that are previously available. Based on the Cartesian grid, the viscous incompressible flow solver can handle boundaries of large displacements with simple mesh generation. The solid-mechanics solver has separate subroutines for analyzing general three-dimensional bodies and thin-walled structures composed of frames, membranes, and plates. Both geometric nonlinearity associated with large displacements and material nonlinearity associated with large strains are incorporated in the solver. The FSI is achieved through a strong coupling and partitioned approach. We perform several validation cases, and the results may be used to expand the currently limited database of FSI benchmark study. Finally, we demonstrate the versatility of the present method by applying it to the aerodynamics of elastic wings of insects and the flow-induced vocal fold vibration.

IB-LBM simulation on blood cell sorting with a micro-fence structure.

A size-based blood cell sorting model with a micro-fence structure is proposed in the frame of immersed boundary and lattice Boltzmann method (IB-LBM). The fluid dynamics is obtained by solving the discrete lattice Boltzmann equation, and the cells motion and deformation are handled by the immersed boundary method. A micro-fence consists of two parallel slope post rows which are adopted to separate red blood cells (RBCs) from white blood cells (WBCs), in which the cells to be separated are transported one after another by the flow into the passageway between the two post rows. Effected by the cross flow, RBCs are schemed to get through the pores of the nether post row since they are smaller and more deformable compared with WBCs. WBCs are required to move along the nether post row till they get out the micro-fence. Simulation results indicate that for a fix width of pores, the slope angle of the post row plays an important role in cell sorting. The cells mixture can not be separated properly in a small slope angle, while obvious blockages by WBCs will take place to disturb the continuous cell sorting in a big slope angle. As an optimal result, an adaptive slope angle is found to sort RBCs form WBCs correctly and continuously.

The role of finite displacements in vocal fold modeling.

Human vocal folds experience flow-induced vibrations during phonation. In previous computational models, the vocal fold dynamics has been treated with linear elasticity theory in which both the strain and the displacement of the tissue are assumed to be infinitesimal (referred to as model I). The effect of the nonlinear strain, or geometric nonlinearity, caused by finite displacements is yet not clear. In this work, a two-dimensional model is used to study the effect of geometric nonlinearity (referred to as model II) on the vocal fold and the airflow. The result shows that even though the deformation is under 1 mm, i.e., less than 10% of the size of the vocal fold, the geometric nonlinear effect is still significant. Specifically, model I underpredicts the gap width, the flow rate, and the impact stress on the medial surfaces as compared to model II. The study further shows that the differences are caused by the contact mechanics and, more importantly, the fluid-structure interaction that magnifies the error from the small-displacement assumption. The results suggest that using the large-displacement formulation in a computational model would be more appropriate for accurate simulations of the vocal fold dynamics.

Simulation of a pulsatile non-Newtonian flow past a stenosed 2D artery with atherosclerosis.

Atherosclerotic plaque can cause severe stenosis in the artery lumen. Blood flow through a substantially narrowed artery may have different flow characteristics and produce different forces acting on the plaque surface and artery wall. The disturbed flow and force fields in the lumen may have serious implications on vascular endothelial cells, smooth muscle cells, and circulating blood cells. In this work a simplified model is used to simulate a pulsatile non-Newtonian blood flow past a stenosed artery caused by atherosclerotic plaques of different severity. The focus is on a systematic parameter study of the effects of plaque size/geometry, flow Reynolds number, shear-rate dependent viscosity and flow pulsatility on the fluid wall shear stress and its gradient, fluid wall normal stress, and flow shear rate. The computational results obtained from this idealized model may shed light on the flow and force characteristics of more realistic blood flow through an atherosclerotic vessel.

Propulsive performance of a body with a traveling-wave surface.

A body with a traveling-wave surface (TWS) is investigated by solving the incompressible Navier-Stokes equation numerically to understand the mechanisms of a novel propulsive strategy. In this study, a virtual model of a foil with a flexible surface which performs a traveling-wave movement is used as a free swimming body. Based on the simulations by varying the traveling-wave Reynolds number and the amplitude and wave number of the TWS, some propulsive properties including the forward speed, the swimming efficiency, and the flow field are analyzed in detail. It is found that the mean forward velocity increases with the traveling-wave Reynolds number, the amplitude, and the wave number of the TWS. A weak wake behind the free swimming body is identified and the propulsive mechanisms are discussed. Moreover, the TWS is a "quiet" propulsive approach, which is an advantage when preying. The results obtained in this study provide a novel propulsion concept, which may also lead to an important design capability for underwater vehicles.

An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments.

We have introduced a modified penalty approach into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass. The effect of the solid structure is handled by the IBM in which the stress exerted by the structure on the fluid is spread onto the collocated grid points near the boundary. The fluid motion is obtained by solving the discrete lattice Boltzmann equation. The inertial force of the thin solid structure is incorporated by connecting this structure through virtual springs to a ghost structure with the equivalent mass. This treatment ameliorates the numerical instability issue encountered in this type of problems. Thanks to the superior efficiency of the IBM and LBM, the overall method is extremely fast for a class of flow-structure interaction problems where details of flow patterns need to be resolved. Numerical examples, including those involving multiple solid bodies, are presented to verify the method and illustrate its efficiency. As an application of the present method, an elastic filament flapping in the Kármán gait and the entrainment regions near a cylinder is studied to model fish swimming in these regions. Significant drag reduction is found for the filament, and the result is consistent with the metabolic cost measured experimentally for the live fish.

Interaction between a flexible filament and a downstream rigid body.

A filament flapping in the bow wake of a rigid body is considered in order to study the hydrodynamic interaction between flexible and rigid bodies in tandem arrangement. Both numerical and experimental methods are adopted to analyze the motion of the filament, and the drag force on both bodies is computed. It is shown that the results largely depend on the gap between the two objects and the Reynolds number. The flexible body may have larger vibration amplitude but meanwhile experience a reduced drag force. On the other hand, the trailing rigid body enjoys a drag reduction. The qualitative behavior of the filament is independent of the filament's length and mass ratio or the shape of the rigid body for the parameter regime considered. The result is in contrast with the interaction between two rigid or two flexible objects in tandem arrangement, and it may provide a physical insight into the understanding of the aquatic animals swimming in the bow wake of ships or staying in the bow wake of stationary structures.

Secondary vortex street in the wake of two tandem circular cylinders at low Reynolds number.

The experiments on two tandem circular cylinders were conducted in a horizontal soap film tunnel for the Reynolds number Re=60 , 80, and 100 and the nondimensional center-to-center spacing Gamma ranging in 1 approximately 12. The flow patterns were recorded by a high-speed camera and the vortex shedding frequency was obtained by a spatiotemporal evolution method. The secondary vortex formation (SVF) mode characterized by the formation of a secondary vortex street in the wake of the downstream cylinder was found at large gamma. Moreover, some typical modes predicted by previous investigations, including the single bluff-body, shear layer reattachment, and synchronization of vortex shedding modes, were also revisited in our experiments. Further, numerical simulations were carried out using a space-time finite-element method and the results confirmed the existence of the SVF mode. The mechanism of SVF mode was analyzed in terms of the numerical results. The dependence of the Strouhal number Sr on Gamma was given and the flow characteristics relevant to the critical spacing values and the hysteretic mode transitions were investigated.