In this paper, a three-dimensional calculation of the formation and rising of double bubbles in a gas-liquid-solid flow system with two air-intake orifices is done through computational fluid dynamics. The coupled method of volume of fluid (VOF) and discrete element model (DEM) is used to capture the interface of bubbles and track the movement of particles. The numerical method is validated by comparing our numerical results to experimental data (from other literature) of the double-bubble rising process under the same conditions. Two cases of the bubble formation and rising, when particles are laid at the container bottom (case I) and when particles are settling freely (case II), are studied carefully. At first, for case I, the detachment time of the first bubble when there is a proper time difference of the air intake start of two orifices is less than that when the start time is the same. Secondly, for case I, the possible reason of the coalescence of two parallel bubbles and reason of the shift of the bubble queues to the left or right are discussed by analyzing the velocity vector diagrams. By comparing case I and case II, it is disclosed that the free settlement of particles could prevent bubbles from coalescence and weaken the deviation of the bubble queues. Finally, for case II, the suitable distance between two orifices for better particle entrainment under different air intaking velocities is also studied, and it will increase as the air intaking velocity increases. The results of this paper is helpful to the deep understanding of the gas-liquid-solid fluidized system.

An assumption common to many approaches to understanding and modeling turbulent mixing is that the statistics of a passive scalar at small length scales will approach the analogous statistics of the velocity field as the scale separation increases between the flow-specific outer scales and the small scales of interest. This assumption follows from the hypotheses of Kolmogorov, Oboukhov, Corrsin, and Batchelor, although it is well recognized that differences in the scalar and velocity dynamics prevent the overall statistics of the two being the same. Considerable research on the effect of Reynolds number and Schmidt number on the scalar statistics has shown that the assumption is not very good at either high Reynolds number or high Schmidt number individually. Because of limitations in laboratory measurements, direct numerical simulations (DNSs), and in situ measurements of the ocean and atmosphere, it is difficult to obtain data in which the Reynolds number is high enough for an unequivocal inertial-convective subrange, and the Schmidt number is simultaneously high enough for a clear viscous-convective subrange. Our hypothesis is that, when both subranges exist, then there is sufficient scale separation in the velocity field for its statistics to be approximately universal, and also sufficient additional scale separation for the scalar to relax so that its small-scale statistics approach those of the velocity. We explore this hypothesis with DNS resolved on up to $14256\times 14256\times 14256$ grid points, Taylor Reynolds number ${\mathrm{Re}}_{\lambda }=633$, and Schmidt number $\mathrm{Sc}=[0.1,0.7,1.0,7.0]$, with the aim of studying the validity of this hypothesis for mixing in air and water. When the Schmidt number is not greater than unity at high Reynolds number, a viscous-convective subrange does not exist and we find that small-scale isotropy, the intermittency exponent, and the probability density function of the scalar dissipation rate are all much different from the analogous velocity statistics, as reported widely in literature. However, when the Schmidt number is greater than unity at high Reynolds number, inertial-convective and viscous-convective subranges both exist, and the velocity and scalar statistics are similar. Since this similarity is a consequence of the presence of both inertial convective and viscous convective subranges, it is achieved only at both high Reynolds and Schmidt numbers, and the statistics show a sharp change when the Schmidt number is changed from from 1 to 7. This suggests that at high Reynolds numbers, the modeling assumption of similarity between velocity and scalar statistics is valid for mixing in water, but not in air.

Vortex-induced vibration (VIV) is a major cause of structural damage in engineering, thus effective control methods need to be developed to suppress it. In the present work, the control effect on VIV by using a finite-span flexible splitter plate attached to the rear stagnation point of a circular cylinder is experimentally studied. The reduced velocity is in the range $2.43<U^{*}<12.46$, corresponding to the Reynolds numbers over the range $1910<\mathrm{Re}<9800$. The finite-span flexible splitter plate has a fixed streamwise length of 2.$5D$ based on the cylinder diameter and different widths (spanwise length) of $2.5\%L$ to $30\%L$ based on the submerged cylinder length, aiming to find a critical width where the desired control effect can be achieved. The results show that the suppression efficiency of the flexible splitter plate is gradually improved with an increase in its width. Though the difference in total lift fluctuation between the baseline and control cases is not obvious at the lower branch, the vortex lift fluctuation and the energy transfer from fluid to structure motion are reduced for the control cases, which is beneficial to the suppression of VIV. The phenomenon, that the flexible splitter plate of $20\%L$ increases the lift fluctuation of the stationary circular cylinder but suppresses VIV, inspires us that the reduction of lift fluctuation of a stationary circular cylinder may not necessarily lead to the suppression of VIV. In order to understand the spanwise effect of the finite-span flexible splitter plate, its dynamic motion as well as the flow field at different spanwise cross sections are measured for both the stationary and elastically mounted circular cylinders. When the width of the flexible splitter plate is small, such as $2.5\%L$, the plate vibrates synchronously with the circular cylinder with a good periodicity. The wake evolution at the plate region is efficiently controlled, however, the vibration characteristics of the entire cylinder are not changed. For the flexible splitter plate with a large width, such as $20\%L$, although the flow field, the force, and the vibration of the cylinder are coupled, the plate flapping is chaotic. Moreover, the wake evolution in the plate region is obviously changed, and the control effect can be transmitted to the cross section away from the plate, though the effect is weakened. This indicates the possibility that a finite-span flexible splitter plate can suppress VIV of a circular cylinder that has a much larger spanwise length.

The wake behind a bluff body in the presence of a density gradient is characterized by competing effects of buoyancy, momentum, and ultimately viscosity as the flow decays. Consequently, there are a number of distinct flow regimes into which the wakes can be placed, and there is some interest in whether any given wake can be traced back to its source through interrogation of selected fluid mechanical properties in the wake. Here we use dynamic mode decomposition (DMD) to find modes that can be used to characterize and automate such a process. A custom-designed algorithm is proposed that can sort and classify stratified wakes based on a selection of the most energetic DMD modes. The approach is very, or partially successful, depending on the quality and dimension of the input data. The success of these first steps may be used to develop similar methods for more challenging and fully turbulent wakes, and also can serve as a guide for data-driven methods that require no prior knowledge of the flow structure.

Classically, the rotation of ellipsoids in shear Stokes flow is captured by Jeffery's orbits. Here we demonstrate that Jeffery's orbits also describe high-frequency shape-deforming swimmers moving in the plane of a shear flow, employing only basic properties of Stokes flow and a multiple-scales asymptotic analysis. In doing so, we support the use of these simple models for capturing shape-changing swimmer dynamics in studies of active matter and highlight the ubiquity of ellipsoid-like dynamics in complex systems. This result is robust to weakly confounding effects, such as distant boundaries, and also applies in the low-frequency limit.

This study experimentally investigates the effect of structural damping on the transverse flow-induced vibration (FIV) of an elastically mounted circular cylinder under imposed axial rotation in a free stream. It has been shown by Wong et al. [K. W. L. Wong, J. Zhao, D. Lo Jacono, M. C. Thompson, and J. Sheridan, J. Fluid Mech. 829, 486 (2017)] that FIV of a circular cylinder can be enhanced or attenuated by imposing an axial rotation. Here, we demonstrate that the rotation-enhanced FIV response is more susceptible to the varying damping than the nonrotating cylinder. The rotation-enhanced response diminishes when the damping ratio is increased to a certain value for the fixed rotation rate of $\alpha =2.0$ ($\alpha =$ cylinder surface to free-stream velocity). We also analyze the forcing components, showing that the time-averaged lift coefficient is predominantly dependent on the rotation rate over the Reynolds number range ($1130⩽\mathrm{Re}⩽5260$) tested. Interestingly, it emerges that the FIV of a rotating cylinder is associated with harmonic force components and wake modes different than those of the nonrotating cylinder, despite the existence of a similar three-branch response. In terms of the implication for energy harvesting, we demonstrate a $33\%$ increase in the peak power output compared with the nonrotating cylinder, noting that enhancement occurs within the range $1.5⩽\alpha ⩽2.0$.

Advancements in the estimation of fluid flows from remote sensors have rapidly progressed through the emerging use of artificial neural networks (ANNs). However, further development of the robustness of estimation strategies warrants their validation on more complex benchmark cases. This work presents a family of challenge flow cases for the advancement of sparse sensor-based flow estimation techniques. The flows under investigation are the laminar wake development and wake interactions of two cylinders in proximity. Vortex shedding occurs from both the cylinders, and the flow regime is defined based on the nature of the interaction of the two wakes. Two flow regimes are studied: one where the wake interaction yields a low-frequency beating behavior, known as modulated-periodic (MP), and another where the wake is characterized by highly nonlinear interactions that result in irregular flow behavior, called flip-flop (FF). The estimation of the velocity flow fields is performed in a proper orthogonal decomposition (POD)-based low-dimensional subspace using sparsely placed pressure sensors. The estimation performance is assessed for modified linear and quadratic stochastic estimators (LSE/QSE-POD), shallow feedforward neural networks (FFNN), and long short-term memory (LSTM) networks. For the MP regime, the results show that both ANNs significantly outperform the LSE/QSE-POD approaches both instantaneously and in an average least-square sense. For the FF regime, the LSTM-based estimator significantly outperforms the other approaches in both the time and frequency domains. For both regimes, it is found that the trained LSTM-based estimators are far more robust to sensor noise and are relatively insensitive to sensor placements considered in this study. Unlike the single cylinder in cross-flow, the wake interactions in the two-cylinder flow regimes investigated are characterized by multiscale spatiotemporal phenomena, offering ample complexity for systematic development of techniques in sensor-based estimation, scale-extraction, and model prediction.

In reacting flows where chemical reactions occur within a flowing fluid, certain changes in the properties of the fluid, induced by the chemical reaction, can alter the flow dynamics. Generally, the most significant changes in the flow characteristics are associated with the largest changes in the fluid properties induced by the reaction. Specifically, the flow changes monotonically in response to the change in the physical properties induced by the reaction. However, this paper demonstrates a reacting liquid flow where the effect on the flow reverses in response to changes in the physical properties. We experimentally investigated viscous fingering (VF) in a reacting flow where the chemical reaction produces a gel. VF is a phenomenon wherein the interface of two fluids is fluid-dynamically unstable and forms a fingerlike pattern when the more-viscous fluid is displaced by the less-viscous one in porous media or Hele-Shaw cells. Rheological measurements of the gel produced at the liquid-liquid interface demonstrate that gel production affects the VF dynamics in completely opposing manners, depending on the strength of the gel. The VF pattern is approximately the same as the nonreactive case when the gel strength is weak, the fingers become narrower when the gel strength is medium, and the fingers become wider when the gel strength is strong. These opposing trends cannot be explained by standard linear stability analysis for a reactive system where only the viscosity effect is considered. In this paper, we propose a model that explains these opposite effects via a stability analysis of the VF that considers the strength and viscoelastic properties of the gel. In the proposed model, the VF becomes thinner when the shear thinning viscosity of the gel is effective, whereas the VF becomes wider when the gel behaves as an elastic or solid material and, thus, acts to reduce the permeability of the porous media. The aforementioned viscoelastic properties are based on actual viscosity measurements of the gel bulk itself. Combining the experimental results and theoretical considerations, we demonstrate that it is possible to achieve opposite VF effects depending on the gel strength. This is enabled by the fact that the rheological properties, which are primarily responsible for the flow dynamics, change depending on the gel strength.

We compare the flow behavior of several shear-thinning fluids of xanthan gum (XG) and polyethylene oxide (PEO) with a relatively similar shear-thinning index $(\sim 0.34\text{–}0.50)$ in a microfluidic planar contraction/expansion geometry. We explore vortex formation and growth near the abrupt constriction over a wide range of Re ($0.0046\lesssim \mathrm{Re}\lesssim 3.7$) and effective Weissenberg ($134\le {\mathrm{Wi}}_{\mathrm{eff}}\lesssim 9381$). An important aspect of the present study is careful rheological characterization to determine the relaxation time of aqueous solutions. From flow visualization experiments, we observed that corner vortices form in the weakly elastic aqueous solutions upstream of the constriction. In the PEO solution, a Newtonian-like behavior (with no corner vortex) was observed up to $\mathrm{Re}=0.0067$, and the vortex length remained relatively unchanged up to much higher flow rates $(\mathrm{Re}=0.4)$. The vortex growth mechanism was observed at higher flow rates. When $\mathrm{Re}\ge 1$ the flow became time dependent and chaotic. In xanthan gum solutions, the initial vortex appeared at Re as low as 0.0046, and the vortex length grew by increasing the Re, and ${\mathrm{Wi}}_{\mathrm{eff}}$. Interestingly, at similar Re, the vortex was much longer than the one in the PEO solution and the flow remained stable over the entire range of flow rates studied. We believe fluid elasticity is central in the vortex formation and growth. The onset of vortex formation and growth shifted to lower Re and Wi by increasing the elasticity number $\left(\mathrm{El}=\mathrm{Wi}/\mathrm{Re}\right)$, revealing the importance of fluid elasticity over inertia in the formation of upstream corner vortices. While chaotic flow instabilities can offer advantages in micromixing, heat, and mass transfer by employing elastic non-Newtonian fluids, instabilities have to be prevented in many other applications, including microrheometry, inkjet printing, and roll coating. Understanding the onset and mechanisms of flow instabilities can shed light on designing more efficient industrial processes and optimal products.

Cavitation has been extensively studied in Newtonian fluids and to a lesser yet significant degree in shear-thinning fluids. However, cavitation has not been previously investigated in shear-thickening fluids, of which a water-cornstarch suspension is perhaps the best-known example. An interesting property of such fluids is that, when subjected to an increase in strain rate, their viscosity increases until they exhibit solidlike behavior and can even fracture. As cavitation bubbles are capable of generating extreme strain rates, they could be affected by shear-thickening fluid behavior. As visual access is limited by opaque or non-index-matched particles present in such fluids, an experimental study of nominally cylindrical spark-induced cavitation bubbles is conducted in a 2 mm gap between two parallel flat and transparent plates, which allows visualization of the bubbles as they contact the boundary. They are theoretically studied through the cylindrical Keller-Miksis equation adapted to a shear-thickening fluid using a Cross model. For volume fractions starting from $\varphi =0.44$, the limit between continuous and discontinuous shear-thickening regime, cavitation bubbles deform increasingly until they are replaced by cavitation-induced fracture between $\varphi =0.46$ and $\varphi =0.52$. Fracture propagation speeds were found to be in the same range as fracture speeds previously reported for pressure-driven cavity expansion, albeit for estimated initial pressures that are now orders of magnitude higher.

We investigate resonant triad interactions (RTIs) in a two-dimensional stably stratified uniform shear flow confined between two infinite parallel walls in the absence of viscous and diffusive effects. RTIs occur when three interacting waves satisfy the spatial and temporal resonance conditions of the form $\pm {\mathit{k}}_m\pm {\mathit{k}}_n={\mathit{k}}_r$ and $\pm {\omega }_m\pm {\omega }_n={\omega }_r$ with ${\mathit{k}}_{m,n,r}$ and ${\omega }_{m,n,r}$ being the wave vectors and frequencies of the interacting waves, respectively. In two-dimensional flows, the interaction between two primary modes having the same frequency $\omega$ but different wave numbers $k_m$ and $k_n$ produces two different secondary terms: one time-dependent (superharmonic) mode having frequency $2\omega$ and wave number $k_m+k_n$, and the other time-independent mean flow with zero frequency and wave number $k_m-k_n$, where $k_m$ and $k_n$ are the horizontal components of the wave vectors ${\mathit{k}}_m$ and ${\mathit{k}}_n$, respectively. The linear stability problem is solved analytically, which gives the eigenfunctions in the form of modified Bessel functions. The differential equations governing the spatial amplitudes of the superharmonic mode and secondary mean flow are solved numerically as well as analytically using the spectral collocation method and the method of variation of parameters, respectively. It turns out that the linear operator associated with the differential equation of both secondary modes is the same as the linear stability operator and that the solvability condition of the differential equation is found to be associated with the existence of RTIs. We address two types of RTIs: self-resonances and different mode interactions. The self-resonating modes are identified using dispersion curves, but in different mode interactions the prediction of RTIs using dispersion curves is not so straightforward. Thus, to show the existence of RTIs for the different mode interaction case, we adopt a numerical method; in addition, we use the fact that the superharmonic mode diverges. Various cases of wave interactions in a stably stratified shear flow are analyzed in the presence of a resonant triad for various frequencies and mode numbers.

Three-dimensional direct numerical simulations (DNS) are performed to uncover the effect of the horizontal aspect ratio ($\mathrm{\Gamma }=k_y/k_x$, $k_x$ and $k_y$ being the wave numbers along the $x$ and $y$ directions, respectively) on magnetoconvective instabilities using plane layer Rayleigh-Bénard geometry in the presence of an external uniform horizontal magnetic field. The fluid under consideration is an electrically conducting, Newtonian fluid (liquid metal) having a very small Prandtl number ($\mathrm{Pr}\sim {10}^{-2}$) and vanishingly small magnetic Prandtl number ($\mathrm{Pm}\sim {10}^{-6}$). Extensive DNS are conducted to explore the dynamics of the system by varying the control parameters, namely, the Chandrasekhar number ($Q$, strength of the magnetic field) and the Rayleigh number ($\mathrm{Ra}$, vigor of the buoyancy) together with $\mathrm{\Gamma }$ in the ranges of $0<Q\le {10}^3$, $0<\mathrm{Ra}\le 7\times {10}^3$, and $1/2\le \mathrm{\Gamma }\le 6$. It is found that both $Q$ and $\mathrm{\Gamma }$ have a similar effect on the system dynamics in the sense that an increment in either of them delays the oscillatory instability and enhances the stability regime of two-dimensional rolls. The onset of oscillatory instability is found to scale as $Q^{\alpha }$. Two different scaling exponents have been identified depending on the strength of the magnetic field and $\mathrm{\Gamma }$. For weak and moderate magnetic field ($Q<100$), the exponent $\alpha$ is found to be much higher compared to that of a stronger magnetic field ($Q\ge 100$) and gradually decreases with the increment in $\mathrm{\Gamma }$. Different routes to chaos are also observed depending on $\mathrm{\Gamma }$ and $Q$ including the well-known period doubling and quasiperiodic routes to chaos. The appearance of transient chaos (TC) in the system due to the presence of chaotic saddles is found to be a remarkable finding of the present study. It is found that TC eventually leads to persistent chaos and can be considered as a possible route to chaos in magnetoconvection. Chaotic flow reversals induced by an attractor-merging crisis are also observed for $\mathrm{\Gamma }\le 3$. Interestingly, we notice transient chaotic flow reversals in a wide parameter space which may be attributed to the presence of a merged chaotic saddle there. It is found that transient chaotic flow reversals also lead to persistent chaotic flow reversals as the Rayleigh number increases.

This work studies the effects of a through-flow on two-dimensional electrohydrodynamic (EHD) flows of a dielectric liquid confined between two plane plates, as a model problem to further our understanding of the fluid mechanics in the presence of an electric field. The liquid is subjected to a strong unipolar charge injection from the bottom plate and a pressure gradient along the streamwise direction (forming a Poiseuille flow). Highly accurate numerical simulations and weakly nonlinear stability analyses based on multiple-scale expansion and amplitude expansion methods are used to unravel the nonlinear spatiotemporal instability mechanisms in this combined flow. We found that the through-flow makes the hysteresis loop in the EHD flow narrower. In the numerical simulation of an impulse response, the leading and trailing edges of the wave packet within the nonlinear regime are consistent with the linear ones, a result which we also verified against that in natural convection. In addition, as the bifurcation in EHD-Poiseuille flows is of a subcritical nature, nonlinear finite-amplitude solutions exist in the subcritical regime, and our calculation indicates that they are convectively unstable (at least for the parameters investigated). The validity of the Ginzburg-Landau equation (GLE), derived from the weakly nonlinear expansion of Navier-Stokes equations and the Maxwell's equations in the quasielectrostatic limit, serving as a physical reduced-order model for probing the spatiotemporal dynamics in this flow, has also been investigated. We found that the coefficients in the GLE calculated using amplitude expansion method can predict the absolute growth rates even when the parameters are away from the linear critical conditions, compared favorably with the local dispersion relation, whereas the validity range of the GLE derived from the multiple-scale expansion method is confined to the vicinity of the linear critical conditions.

The present investigation revisits the linear stability of Poiseuille channel flow interacting with compliant walls. The results obtained include the dynamics of Tollmien-Schlichting (TS) modes as well as flow-induced surface-instability (FSI) modes, in the form of both traveling-wave flutter (TWF) and divergence modes. The compliant wall model consists of a spring-backed plate with a viscous substrate deformable in the vertical direction [C. Davies and P. W. Carpenter, J. Fluid Mech. 352, 205 (1997)]. At the interface between the fluid and the walls, the continuity of velocities and stresses, including both viscous and pressure contributions, are taken into account. The FSI modes (both varicose and sinuous) and TS modes are then reinterpreted in the light of the two principal nondimensional control parameters: the Reynolds number (Re), which characterizes the base flow, and the reduced velocity ($V_R$), which measures the response of the flexible wall to hydrodynamic loading [E. De Langre, La Houille Blanche, 3, 14 (2000)]. The characteristics of TS and FSI modes are systematically investigated over a large control-parameter space, including wall dissipation, spring stiffness, and flexural rigidity. We observe that TWF modes are primarily governed by $V_R$ and largely independent of the Reynolds number. It is found that the instability is generally dominated by the TWF mode of varicose symmetry. Divergence and TS modes are both affected by $V_R$ and Re, confirming that these modes belong to a different class. The onset of the divergence mode is mainly observed for the sinuous motion, when increasing the dissipation. To provide physical insight into the mechanisms driving these instabilities, the perturbative energy equations for both FSI and TS modes are analyzed for a wide range of wall parameters and wavenumbers.

Rayleigh-Bénard convection in a rectangular enclosure of aspect ratio 2:1 filled by a class of nonlinear viscoelastic fluids represented by the Phan-Thien–Tanner (PTT) constitutive equation is investigated numerically. Governing equations are discretized by finite-difference methods in space and time. The momentum and PTT constitutive equations are written in a quasilinear formulation. Quasilinear terms are treated with the high-order upwind central (HOUC) method and velocity-pressure coupling is handled through the projection method. The developed model is validated for Oldroyd-B types of working fluids. The onset of time-dependent convection is observed and the critical Rayleigh number is determined for PTT types of fluids. The time-dependent flow pattern transition is investigated and explained. A transition from time-dependent flow to steady-state flow is observed at a higher Rayleigh number and the corresponding critical Rayleigh number is computed. The effect of the rheological parameters on heat transfer is investigated.

We report a critical assessment on the applicability of the large eddy simulation (LES) technique in predicting turbulence modulation due to the presence of particles with high Stokes numbers. The simulations have been performed for two Reynolds numbers of 3300 and 5600 based on average gas velocity and channel width. An increase in particle loading decreases the turbulence intensity, and at a particular volume fraction, the turbulence collapses due to the catastrophic reduction of turbulence production. It is observed that at low volume fractions, LES models predict the turbulence modulation with high accuracy ($>80\%$) but fail to predict the volume fraction [critical particle volume loading (CPVL)] at which turbulence collapse happens. A detailed analysis shows that an inaccurate prediction of the turbulent energy production is the source of error in CPVL prediction. This is contrary to the usual understanding of the limitation of the LES models in predicting accurate energy dissipation.

We quantify and model the airfoil response to its pitching flap using a comprehensive experimentally acquired database at chord-based Reynolds number $1.8\times {10}^6$. This quantification relies on two proposed metrics that characterize the dynamic lift hysteresis and allow describing its evolution under different pitching conditions. The analysis reveals a saturation of the relative lift hysteresis that is independent of the angle of attack. Moreover, the hysteresis loop is shown to reach phase opposition at the same reduced frequency as when its tilt slope begins to change direction. The two-pronged characterization of the lift hysteresis is a promising approach to quantify the unsteady aerodynamic behavior beyond the reported conditions and of other immersed bodies. The modeling strategy yields one nonlinear model and a set of linear models. The models' performance is examined under a range of flow and pitching conditions. Despite their reduced accuracy compared to the nonlinear model, the linear models are chosen to be incorporated in the closed-loop control strategy that we detail in Part II of this series [Phys. Rev. Fluids 7, 024706 (2022)].

Wing-gust encounters arising from flight over complex terrain or adverse weather are unavoidable and cause large lift transients that may result in structural damage due to extreme loads and or fatigue. Gust mitigation through control has the potential to extend the lifetime of air vehicles and wind turbines, although it is challenged by sensor noise, time delays, and low latency requirements. In this study, we report on the successful design and deployment of a closed-loop controller to regulate the lift coefficient of an airfoil equipped with an actuated trailing-edge flap against vortical gust disturbances. The approach is served by a feedforward-feedback control strategy and dedicated hardware. The control strategy relies on the characterization and modeling of the lift response to flap deflections and gust disturbances. In Part $\mathrm{I}$ of this series [Phys. Rev. Fluids 7, 024705 (2022)], we quantify and model the lift response to flap deflections. In this second part, we examine and model the gust disturbances on the airfoil lift and combine the models within the control architecture. Gust characterization reveals previously unknown synergy between concurrent gusts with opposite rotation direction, yielding large bursts of lift. The lift response model to gust disturbances is compared to Küssner's and validated against experimental results. The model-based feedforward loop detects the onset and magnitude of gust disturbances, which are generated upstream by a pitching airfoil, through a two-component X-wire located upstream of the DLR-F15 research airfoil. The combined controller proves to be effective for lift regulation during gust encounters, with feedforward rejecting large disturbances, and feedback attenuating high-frequency sensor noise and compensating for model uncertainty.

Forward-swept wings offer unique advantages in the aerodynamic performance of air vehicles. However, the low-Reynolds-number characteristics of such wings have not been explored. In this work, we numerically study laminar separated flows over forward-swept wings ($\mathrm{\Lambda }=0^{\circ }$ to $-{45}^{\circ }$) with semi aspect ratios $\text{sAR}=0.5–2$ at a chord-based Reynolds number of 400. Forward-swept wings generate wakes that are significantly different from those of backward-swept wings. For low-aspect-ratio forward wings, the wakes remain steady due to the strong downwash effects induced by the tip vortices. For a larger aspect ratio, the downwash effects weaken over the inboard region of the wing, allowing unsteady vortex shedding to occur. A higher aspect ratio allows for the formation of streamwise vortices for highly swept wings, stabilizing the flow. Forward-swept wings can generate enhanced lift at high angles of attack compared to the unswept and backward-swept wings, with the cost of high drag. We show through force element analysis that the tip-vortex-induced downwash plays a favorable role in enhancing lift by maintaining a steady vortical structure near the tip region. With the additional vortex lift generated toward the tip of the forward-swept wing, the sectional lift is higher near the outboard region than at the inboard. This is opposite from the elliptical lift distribution for high-Reynolds-number attached flows, in which the downwash has an adverse effect on lift by reducing the effective angle of attack. The current findings offer a detailed understanding of the sweep effects on laminar separated flows over forward-swept wings, and they may pave the way for innovative designs of high-lift devices at low Reynolds numbers.

Ciliates are ubiquitous in the marine environment and important consumers of phytoplankton and flagellates. The feeding on suspended food particles in ciliates is complex and relies typically on coordinated motion in bands of transversal rows of cilia known as membranelles. Many ciliates are upstream collectors that use a single membranelle band to generate feeding flow, retain food particles, and transport them to the mouth region. To explore a representative upstream collector, we consider the ciliate Euplotes vannus. We determine the clearance rate using particle tracking and estimate the flow-generating force by fitting a point force model to the observed flow. To obtain a mechanistic understanding of feeding flow and particle retention, we use high-speed video microscopy. The cilia move parallel to the membranelle band towards the mouth region in the power strokes, and a metachronal wave propagates away from the mouth region parallel to the band and outwards along the membranelles. A gap, therefore, opens between neighboring membranelles from the inner side of the band where the mouth region is located, and while food particles are retained, water is drawn in and pushed outwards across the membranelle band as the gap closes from the inner side. We suggest a model that rationalizes our observations and quantifies the mechanism by which the membranelle band can both generate feeding flow and retain food particles. The model compares favorably with our observations and suggests a trade-off between the clearance rate and the membranelle gap that determines the lower cutoff in the prey size spectrum. We quantify the trade-off and discuss the ecological significance of our findings.