Immersed Boundary-lattice Boltzmann Method Research Articles

Enhancing tip vortices to improve the lift production through shear layers in flapping-wing flow control

Flow control of a low-aspect-ratio flat-plate heaving wing at an average angle of attack of $10^{\circ }$ by a steady-blowing jet is numerically studied by using a feedback immersed boundary–lattice Boltzmann method. Blowing jets at the leading edge, mid-chord and trailing edge are considered. The wing enjoys the highest lift production with the trailing-edge downstream blowing jet, which improves the average lift by 50.0 % at $Re = 1000$ and 22.9 % at $Re = 5000$ through the enhancement of the tip vortex circulation caused by the increase in the mass flux of the shear layer at the wing tips. This increase in mass flux decreases as $Re$ increases from 1000 to 5000 due to its self-limiting mechanism. A mid-chord vertical blowing jet induces a middle vortex which enhances the lift production but the enhancement is smaller than that of trailing-edge downstream blowing jet. Other jet arrangements do not significantly increase the lift coefficient, but the mid-chord upstream blowing jet experiences a significant reduction in the drag coefficient, leading to an increase of 50.6 % in the average lift-to-drag ratio. The effectiveness of the flow control is not significantly affected by the aspect ratio.

Addendum: Numerical simulation of heat transfer in particulate flows using a thermal immersed boundary lattice Boltzmann method

Addendum: Numerical simulation of heat transfer in particulate flows using a thermal immersed boundary lattice Boltzmann method

Impact of a compound droplet on a curved surface: Effects of Weber and Reynolds numbers

Droplet impact on curved surfaces is a common phenomenon in both industrial processes and the natural world. Prediction and design of advanced technologies, such as cell processing and biotechnology printing, require an in-depth understanding of the dynamics of compound droplet impacts. However, there is a significant scarcity of research concerning the dynamics of compound droplets impacting on curved surfaces. This study employs numerical simulations to investigate the impact dynamics of a compound droplet on a curved surface over a range of Weber number (We) and Reynolds number (Re). The numerical approach employed here is an immersed boundary lattice Boltzmann method. The numerical simulation results reveal that both the We and Re have a pronounced effect on the spreading, contraction, and rupturing, of compound droplets on a curved surface. An analysis, with We and Re as key factors, elucidates their influences on the impact behavior of compound droplets. Furthermore, based on the phase diagram of impact results on the We and Re coordinate axes, two split lines are introduced for the first time, delineated by inertia, viscosity, and surface tension forces. These split lines provide clear guidance on controlling the droplet impact pattern by changing either We or Re, thereby facilitating accurate predictions of compound droplet impact results.

Statistics and evolution of Reynolds shear stress structure in cylinder-wake/boundary-layer interaction

The three-dimensional structures based on the quadrant classification of the tangential Reynolds stress (Qs), are studied in direct numerical simulations of cylinder-wake/boundary-layer interaction with a moderate gap ratio (G/D=1.0) and low or middle Reynolds numbers. In this paper, direct numerical simulations are performed using the immersed boundary lattice Boltzmann method (LBM). We utilize a three-dimensional clustering method to identify Reynolds shear stress structures (Qs-structures) associated with intense events. The kinematic characteristics of coherent structures are discussed through the statistical properties of Qs-structures. The spatial relationship of between vortex clusters and Qs-structures (mainly Q2-structures as well as Q4-structures) is explained by their evolution characteristics. The spatial distribution of Qs-structures, determined by the volume distribution of the minimum and maximum wall distances (ymin and ymax), are found to be similar to that of vortex clusters in the cylinder/wall interaction. In the near-wall statistical region, the secondary vortex clusters are surrounded by the parallel Q2 and Q4 pairs, and mostly lodged within the Q2. During the evolution process of coherent structures, the Q2-structures and the secondary vortex clusters developed into hairpin-like structures, respectively. The conditional average results demonstrated that the generated hairpin vortex structures are attributed to the momentum transfers.

Bottom-up butterfly model with thorax-pitch control and wing-pitch flexibility

The diversity in butterfly morphology has attracted many people around the world since ancient times. Despite morphological diversity, the wing and body kinematics of butterflies have several common features. In the present study, we constructed a bottom-up butterfly model, whose morphology and kinematics are simplified while preserving the important features of butterflies. The present bottom-up butterfly model is composed of two trapezoidal wings and a rod-shaped body with a thorax and abdomen. Its wings are flapped downward in the downstroke and backward in the upstroke by changing the geometric angle of attack (AOA). The geometric AOA is determined by the thorax-pitch and wing-pitch angles. The thorax-pitch angle is actively controlled by abdominal undulation, and the wing-pitch angle is passively determined because of a rotary spring representing the basalar and subalar muscles connecting the wings and thorax. We investigated the effectiveness of abdominal undulation for thorax-pitch control and how wing-pitch flexibility affects aerodynamic-force generation and thorax-pitch control, through numerical simulations using the immersed boundary–lattice Boltzmann method. As a result, the thorax-pitch angle perfectly follows the desired angle through abdominal undulation. In addition, there is an optimal wing-pitch flexibility that maximizes the flying speed in both the forward and upward directions, but the effect of wing-pitch flexibility on thorax-pitch control is not significant. Finally, we compared the flight behavior of the present bottom-up butterfly model with that of an actual butterfly. It was found that the present model does not reproduce reasonable body kinematics but can provide reasonable aerodynamics in butterfly flights.

Numerical analysis of an oscillating square and circular bluff body submerged in the wake of an identical static bluff body: A GPU Accelerated Immersed Boundary-Lattice Boltzmann Approach

Hydrodynamic forces acting on marine structures, tubes, and objects can trigger disruptive vibrations. This study is an effort to encapsulate the results of wake induced vibration among tandem bodies. Specifically, impact of a static upstream body on a downstream oscillating body at Reynolds number 100 and constant frequency ratio Fr=1.0. The effects of streamwise displacement are investigated in a tandem arrangement of 1.05≤Lx/D≤12.0. In this study an in-house developed code employed that combines an immersed boundary lattice Boltzmann method with a structural equation and is accelerated using a graphical processing unit. When comparing scenario 1 (both bodies oscillate) to scenario 2 (only the downstream body oscillates), the study finds that the upstream square body motion has little effect on the downstream square body oscillation. However, the upstream circular body motion significantly impacts the downstream body oscillation. In addition, the study observes that the maximum amplitude occurs after reaching the critical spacing in scenario 2, whereas it occurs at and after the critical spacing in scenario 1. The critical spacing ratio is similar in both scenarios but varies for square and circular bodies. Lastly, the study examines the flow physics and hydrodynamic force coefficients of the downstream oscillating body.

Dynamic modeling of a soft robotic fish driven by dielectric elastomer based on the ANCF and IB-LBM

Dielectric elastomer (DE) is an intelligent and pliable material that exhibits significant deformation when subjected to an electric field. It possesses attributes such as remarkable strain, exceptional energy density, rapid responsiveness, and minimal weight, making it uniquely advantageous in the propulsion of bionic fish. Due to the nonlinearity and large deformation characteristics of DEs, it is challenging to accurately describe their complex deformations. The absolute nodal coordinate formulation (ANCF) possesses notable advantages in precisely depicting phenomena entailing substantial deformation and displacement. This paper focuses on the study of a bionic robotic fish driven by dielectric elastomer actuators (DEAs) based on body/caudal fin (BCF) propulsion, wherein the fish body is delineated as a laminated beam structure. By combining the ANCF higher-order beam element with the DE constitutive model and the neo-Hookean hyperelastic constitutive model, the dynamic equations of the laminated beam are derived. The interaction between the bionic fish and the fluid is effectively handled through the implementation of the immersed boundary - lattice Boltzmann method (IB-LBM), and by combining ANCF with IB-LBM, the dynamic responses of the fish under voltage excitation and fluid resistance are simulated and analyzed. This study would contribute to the exploration of the intricate mechanism behind the substantial amplitude motion of bionic robotic fish driven by DEAs, yielding valuable insights for further research endeavors.

Wall-modeled large eddy simulation in the immersed boundary-lattice Boltzmann method

This work presents the wall-modeled large eddy simulation (WMLES) in the immersed boundary-lattice Boltzmann method (IB-LBM). Here, the wall model with both diffusive- and sharp-interface immersed boundary methods (IBMs) is incorporated into the IB-LBM to handle the turbulent boundary layer in high Reynolds number turbulent flows. To maintain the numerical stability, two collision models, i.e., multiple-relaxation-time (MRT) and recursive regularized (RR), are implemented. The performance of these models in the WMLES is examined and compared in the simulation of internal and external flows by considering four benchmarks, i.e., turbulent flow in a channel, flow around a hull of submarine, flow around an Ahmed car model, and flow around a circular cylinder. It is found that a diffusive-interface IBM with wall model is capable to achieve excellent results for the simulation of external flows around bluff objects but fails in the simulation of internal flows of underestimating the wall shear stress due to its extra dissipation. The sharp-interface IBM with the wall model predicts the internal flow very well but fails in some simulations of external flow around bluff bodies due to the failure in the separation flow modeling. It is also found that the MRT-LBM is less dissipative than the RR-LBM, but it generates spurious nonphysical noise in the turbulent flows and tends to be unstable at high Reynolds numbers. Therefore, the diffusive-interface IBM with the wall model is more suitable for the external turbulent flow modeling, while its sharp-interface counterpart is more suitable for the internal turbulent flow modeling. The RR-LBM outperforms the MRT-LBM for the better stability and less nonphysical noise.

Vortex synchronization-enabled heat-transfer enhancement in a channel with backward- and forward-facing steps

A channel with one backward-facing step and one forward-facing step is a typical configuration in engineering applications. In the channel, good heat transfer performance is often required, and the enhancement is usually achieved by employing different passive control methods, such as modification of geometric configuration or application of nanofluid. However, the other control method, i.e., active flow control (AFC), which is likely more effective, has been rarely applied in such a scenario. This study aims to bridge this gap by exploring how a rigid plate affects the heat transfer of the channel. The plate either is stationary or actively rotates, corresponding to passive flow control or AFC. The influences of the horizontal position of the plate (S) and its orientation angle (θ) on the heat transfer performance are studied when the plate is stationary to provide a baseline. Compared to the baseline, the effects of S, θ, and the rotation frequency (fr) are revealed when the plate undergoes a sinusoidal rotation. Such a thermo-fluid dynamic problem is numerically simulated by the immersed-boundary lattice Boltzmann method. The results show that the plate can improve the heat transfer performance no matter whether it rotates or not, compared to the case without a plate. The rotating plate outperforms the stationary one when θ and fr are properly chosen at each S. Substantial improvement can be achieved when vortex synchronization or resonance occurs in the channel, i.e., when the natural vortex shedding frequency is close or equal to fr.

Artificial swim by undulating rigid flagellum with joint controllers

In this paper, we investigate the locomotion of artificial (robotic) swimmers by an undulating rigid flagellum, whose joints are controlled by actuators. The locomotion of a swimmer with an undulating rigid flagellum inside a two-dimensional channel sandwiched by two non-slip walls is numerically analyzed using the immersed boundary lattice Boltzmann method. Multi-relaxation-time scheme is applied to calculate the flow field under a high Reynolds number (Re). Our numerical results show that the optimal Re exists to maximize the locomotion distance, whereas the direction of locomotion can be reversed in the lower and higher Re limits.

A computational study of cell membrane damage and intracellular delivery in a cross-slot microchannel.

We propose a three-dimensional computational framework to simulate the flow-induced cell membrane damage and the resulting enhanced intracellular mass transport in a cross-slot microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane and solve the cell deformation using a well-tested immersed-boundary lattice-Boltzmann method. The cell membrane damage, which is directly related to the membrane permeability, is considered using continuum damage mechanics. The transport of the diffusive solute into the cell is solved by a lattice-Boltzmann model. After validating the computational framework against several benchmark cases, we consider a cell flowing through a cross-slot microchannel, focusing on the effects of the flow strength, channel fluid viscosity and cell membrane viscosity on the membrane damage and enhanced intracellular transport. Interestingly, we find that under a comparable pressure drop across the device, for cells with low membrane viscosity, the inertial flow regime, which can be achieved by driving a low-viscosity liquid at a high speed, often leads to much larger membrane damage, compared with the high-viscosity low-speed viscous flow regime. However, the enhancement can be significantly reduced or even reversed by an increase of the cell membrane viscosity, which limits cell deformation, particularly in the inertial flow regime. Our computational framework and simulation results may guide the design and optimisation of microfluidic devices, which use cross-slot geometry to disrupt cell membranes to enhance intracellular delivery of solutes.

Effects of Different Motion Parameters on the Interaction of Fish School Subsystems.

For a long time, fish school swimming has attracted a great deal of attention in biological systems, as fish schools can have complex hydrodynamic effects on individuals. This work adopted a non-iterative, immersed boundary-lattice Boltzmann method (IB-LBM). A numerical simulation of two-dimensional three-degree-of-freedom self-propelled fish, in side-by-side, staggered, and triangle formations, was conducted by adjusting spacing and motion parameters. A comprehensive analysis of individual speed gains and energy efficiencies in these formations was carried out. Furthermore, an analysis of the hydrodynamic characteristics of fish schools was performed, using instantaneous vorticity profiles and pressure fields. Certain studies have shown that passive interactions between individuals cannot always bring hydrodynamic benefits. The swimming efficiency of side-by-side formations in the same phase gradually increases as the distance decreases, but it also brings certain burdens to individuals when the phases are different. This paper also shows that the roles of passive interactions, spacing, and deflections affect fish school subsystems differently. When the low-pressure areas created by a wake vortex act on one side of an individual's body, the tail-end fish are good at gaining hydrodynamic benefits from it. This effect is not universal, and the degree to which individuals benefit from changes in exercise parameters varies. This study provides a theoretical basis for bioinspired robots, as well as providing certain insights into the mechanism of collective biological movement.

Stability Improvement of the Immersed Boundary–Lattice Boltzmann Coupling Scheme by Semi-Implicit Weighting of External Force

The immersed boundary–lattice Boltzmann (IB-LB) coupling scheme is known as an efficient scheme for fluid–structure interactions (FSIs). However, the conventional IB-LB schemes suffer from instability because they involve a high-Reynolds-number flow or a larger stiffness structure. An averagely weighted iteration approach is presented to improve the stability restriction in this paper. This new approach, which improves the stability by mitigating the high-frequency fluctuations, is implemented by iteratively calculating the external force, and averagely weighting the force obtained at every iterative step. Five cases are simulated to verify the accuracy and effectiveness of the present approach. Under the premise of maintaining the accuracy of the conventional IB-LB method, the implementation of the present approach can significantly enhance the numerical stability. Compared with the conventional IB-LB method, the present approach can significantly expand the material parameter range for simulation; in particular, this approach qualitatively improves the upper limit of the bending rigidity coefficient by approximately 8000 times. To use the outstanding stability of the present approach, the IB inertia force can be directly incorporated into the simulation. In addition, under the low-viscosity condition, the present approach can effectively simulate the large-deformation FSI problem.

The effects of particle shape, orientation, and Reynolds number on particle-wall collisions

Crystallisation is an important unit operation used in the production of Active Pharmaceutical Ingredients (APIs). Crystallisation is typically carried out using seed crystals in a process called secondary nucleation that allows for greater control of crystal quality attributes. The mechanism of secondary nucleation is still not well understood. Particle attrition is one proposed mechanism. This work examines the conditions under which particle-wall collisions occur. This is done through the simulation of free-moving particles in an impinging jet flow using an immersed-boundary lattice Boltzmann method (IB-LBM) CFD solver. Particle Reynolds numbers from 100 to 400 are examined. Particle shapes with aspect ratios from 1:1 to 8:1 are used to represent the crystal habits of APIs.Particles that start in their low-drag or high-drag orientation maintain this orientation on approach to the target surface. All other intermediate initial orientations examined cause particles to rotate toward and overshoot their high-drag form before adopting their high-drag form in proximity to the target surface. Particles in their low-drag form remain in their initial orientation due to the symmetry of the computational domain. In this orientation, a collision is most likely to occur, and the minimum critical Reynolds number at which a particle-wall collision will occur can be determined. This value is shown to increase with increasing particle frontal length. Pointed or rounded leading edges are shown to improve a particle's ability to pierce the boundary layer adjacent to the target surface and reduce this value. In cases where a Reynolds number of 400 is insufficient to cause a particle-wall collision, the particles’ minimum distances from the target surface are reported. Using the minimum critical Reynolds number values obtained, the approach velocities required for particles to collide with a wall are shown to be larger than the impeller tip speeds typically used during crystallisation operations. This work provides for the first time the conditions under which particle-wall collisions occur for varying shape and orientation, their behaviour on approach, and the associated impact velocities.

Aerodynamic performance of low aspect-ratio flapping wing with active wing-chord adjustment

In daily life, excellent aerodynamic performance of birds and bats has been widely observed during their flying and propulsion. In the present research, a low aspect-ratio wing flapping in uniform flow with a combined heaving-pitching motion has been adopted to mimic such aerodynamic process of flapping-wing-based propulsors. Inspired by the changeable skeleton of natural bio-livings, a bio-inspired flow controlling strategy based on active wing-chord adjustment has been raised to achieve aerodynamic enhancement. Adopting an Immersed Boundary-Lattice Boltzmann Method (IB-LBM) to resolve relating fluid flow with moving boundary, the effects of stretching pattern, i.e., the amplitude and the phase of the wing-chord adjustment, on the aerodynamic performance of the wing, and the role of Aspect-Ratio (Ar) have been confirmed and investigated in detail. With the Direct Numerical Simulation to achieve the vortical flow identification, detachment delaying of Leading Edge Vortex (LEV) and enhancement of Trailing Edge Vortex (TEV) have been observed for cases with in-phase active controlling, and it has been revealed that such phenomenons correlate well with the aerodynamic enhancement of the wing. On the other hand, it has been observed that, the out-phase wing-chord adjustment dominates the LEV detachment, and further the flow separation around the leading edge of the wing. It is believed that such flow detachment, together with the TEV weakening caused by the anti-phase wing-chord controlling, leads to the performance deterioration of the wing, compared with the in-phase case. Meanwhile, the present numerical results show that, with the increase of stretching ratio, the aerodynamic performance of the flapping wing becomes susceptible with respect to the stretching phase of wing-chord. Compared with the bounded thrust enhancement caused by the LEV bursting, the lifting enhancement of the flapping wing during the reinforced wing-chord adjustment shows consistent dependency on the stretching ratio.

Study on the Movement of Pulverized Coal Particles in Fractal Fracture Network.

Coalbed methane (CBM) exploitation is a complex multiphase flow process. With the development of CBM extraction technology, it is recognized that the migration of reservoir fluid in the fracture network is affected by the matrix fracture structure, fracture width, and pulverized coal particles plugging, therefore the fluid-particle coupling problem has received increasing attention. In this paper, six groups of fracture models with different fractal dimensions are established using the Weierstrass-Mandelbrot function, and the fluid-particle coupling phenomena in fractures with different roughness and aperture are simulated using an immersed boundary-lattice Boltzmann method (IB-LBM), by comparing the numerical simulation results with the theoretical analysis, it is proved that the IB-LBM numerical method has high accuracy and effectiveness. The effects of fractal dimension, particle size, and particle concentration on the plugging effect were investigated. The results show that the plugging effect on the fracture is enhanced with the increase of the pulverized coal particles content. When the concentration and size of pulverized coal particles are the same, the migration path of pulverized coal particles in complex fractures is more tortuous and more likely to be plugged. It may lead to a shift in the main seepage network of the fracture and the formation of new seepage channels. The research in this paper provides a data basis for the formation and plugging pattern of pulverized coal particles in coal seam fractures, which can provide a basis for the control of pulverized coal particles concentration in CBM drainage.

Influence of the corner radii on the flow characteristics of three square-like cylinders in an equilateral-triangular arrangement using IB-LBM

A two-dimensional momentum exchange-based immersed boundary–lattice Boltzmann method (IB-LBM) is used to scrutinize the influence of the corner radii on the characteristics of laminar flow around square-like cylinders arranged in an equilateral-triangular configuration, with each cylinder represented by 300 discrete elements. Numerical simulations were carried out in Newtonian flow with viscous, incompressible, and constant properties, by simultaneously changing the corner ratio λ from 0.0 (square) to 1.0 (circular), Reynolds number Re from 40 to 160, and gap ratio δ from 0.5 to 5.0. The wake flow patterns, force coefficients, and Strouhal number St were calculated and discussed. The numerical outcomes demonstrate that the corner ratio, Re, and gap ratio have a prominent influence on the flow characteristics. The wake flow patterns in the λ-Re plane can be divided into steady-state, flip-flopping, anti-phase, and in-phase modes for δ = 3.0. The drag Cd and lift Cl coefficients exhibit a decreasing trend with increasing corner radius except for Clc1; as δ is increased, the Cl of all three cylinders for λ ranging from 0 to 1.0 gradually approached zero. The St of the steady state flow pattern is significantly lower than that of other flow states, the relationship between St and λ is complex and irregular; as δ increases, the St and λ show a positive correlation.

Transient deformation of a viscoelastic capsule in a cross-slot microchannel: effects of inertia and membrane viscosity

With an immersed-boundary lattice-Boltzmann method, we consider the transit of a three-dimensional initially spherical capsule with a viscoelastic membrane through a cross-slot microchannel. The capsule is released with a small initial off-centre distance in the feeding channel, to mimic experiments where capsules or cells are not perfectly aligned with the centreline. Our main objective is to establish the phase diagram of the capsule's deformation modes as a function of the flow inertia and capsule membrane viscosity. We mainly find three deformation modes in the channel cross-slot. For a capsule with low membrane viscosity, a quasi-steady mode occurs at low Reynolds numbers ( $Re$ ), in which the capsule can reach and maintain a steady ellipsoidal shape near the stagnation point, for a considerable time period. With $Re$ increasing to 20, an overshoot–retract mode is observed. The capsule deformation oscillates on an inertial–elastic time scale, suggesting that the dynamics is mainly driven by the balance of the inertial and membrane elastic forces. The membrane viscosity slows down the capsule deformation and suppresses the overshoot–retract mode. A capsule with high membrane viscosity undergoes a continuous-elongation mode, in which its deformation keeps increasing during most of its journey in the channel cross-slot. We summarise the results in phase diagrams, and propose a scaling model which can predict the deformation modes of a viscoelastic capsule in the inertial flow regime. We also discuss implications of the present findings for practical experiments for mechanical characterisation of capsules or cells.

A Non-Equilibrium Interpolation Scheme for IB-LBM Optimized by Approximate Force

A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies.

Numerical study on heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion

Janus particle is a research hotspot due to its novelty and settlement in acid liquid during wastewater treatment. Heat and mass transfer mechanisms of Janus particle sedimentation considering corrosion are numerically investigated based on immersed boundary lattice Boltzmann method. Chemical reaction heat ratio, Damkohler number, Peclet number, and particle number effects on temperature field, concentration field, Janus particle mass reduction, position, and velocity are investigated. The uniform particle has an equilibrium position of about 1/4 times the channel width for two corroded uniform particle settlement processes. The Janus particle horizontal position deviates from the uniform particle equilibrium position due to the force caused by nonuniform buoyancy and particle rotation. When the chemical reaction heat ratio is more than 1, the Janus particle horizontal position is closer to the channel centerline and has a positive deviation. However, the converse trend happens when the chemical reaction heat ratio is less than 1, and the Janus particle horizontal position has a negative deviation. The Janus particle horizontal position deviation magnitude increases with increasing Damkohler number and decreasing Peclet number. The horizontal position deviation phenomenon exists for the single corroded Janus particle and two corroded Janus particle settlement processes.