In this paper, we study the fluid–structure interaction of a three-dimensional (3-D) flexible membrane immersed in an unsteady separated flow at moderate Reynolds numbers. We employ a body-conforming variational fluid–structure interaction solver based on the recently developed partitioned iterative scheme for the coupling of turbulent fluid flow with nonlinear structural dynamics. Of particular interest is to understand the flow-excited instability of a 3-D flexible membrane as a function of the non-dimensional mass ratio ( $m^{*}$ ), Reynolds number ( $Re$ ) and aeroelastic number ( $Ae$ ). For a wide range of parameters, we examine two distinct stability regimes of the fluid–membrane interaction: deformed steady state (DSS) and dynamic balance state (DBS). We propose stability phase diagrams to demarcate the DSS and DBS regimes for the parameter space of mass ratio versus Reynolds number ( $m^{*}$ - $Re$ ) and mass ratio versus aeroelastic number ( $m^{*}$ - $Ae$ ). With the aid of the global Fourier mode decomposition technique, the distinct dominant vibrational modes are identified from the intertwined membrane responses in the parameter space of $m^{*}$ - $Re$ and $m^{*}$ - $Ae$ . Compared to the deformed steady membrane, the flow-excited vibration produces relatively longer attached leading-edge vortices which improve the aerodynamic performance when the coupled system is near the flow-excited instability boundary. The optimal aerodynamic performance is achieved for lighter membranes with higher $Re$ and larger flexibility. Based on the global aeroelastic mode analysis, we observe a frequency lock-in phenomenon between the vortex-shedding frequency and the membrane vibration frequency causing self-sustained vibrations in the dynamic balance state. To characterize the origin of the frequency lock-in, we propose an approximate analytical formula for the nonlinear natural frequency by considering the added mass effect and employing a large deflection theory for a simply supported rectangular membrane. Through our systematic high-fidelity numerical investigation, we find that the onset of the membrane vibration and the mode transition has a direct dependence on the frequency lock-in between the natural frequency of the tensioned membrane and the vortex-shedding frequency or its harmonics. These findings on the fluid-elastic instability of membranes have implications for the design and development of control strategies for membrane wing-based unmanned systems and drones.

In this paper, we numerically investigate the propulsive performance of three-dimensional pitching flexible plates with varying flexibility and trailing edge shapes. We employ our recently developed body-conforming fluid-structure interaction solver for our high-fidelity numerical study. To eliminate the effect of other geometric parameters, only the trailing edge angle is varied from $45°$ (concave plate), $90°$ (rectangular plate) to $135°$ (convex plate) while maintaining the constant area of the flexible plate. For a wide range of flexibility, three distinctive flapping motion regimes are classified based on the variation of the flapping dynamics: (i) low bending stiffness $K_B^{\mathit{low}}$ , (ii) moderate bending stiffness $K_B^{\mathit{moderate}}$ near resonance, and (iii) high bending stiffness $K_B^{\mathit{high}}$ . We examine the impact of the frequency ratio $f^{*}$ defined as the ratio of the natural frequency of the flexible plate to the actuated pitching frequency. Through our numerical simulations, we find that the global maximum mean thrust occurs near $f^{*}\approx 1$ corresponding to the resonance condition. However, the optimal propulsive efficiency is achieved around $f^{*}$ = 1.54 instead of the resonance condition. While the convex plate with low and high bending stiffness values shows the best performance, the rectangular plate with moderate $K_B^{\mathit{moderate}}$ is the most efficient propulsion configuration. To examine the flow features and the correlated structural motions, we employ the sparsity-promoting dynamic mode decomposition. We find that the passive deformation induced by the flexibility effect can help in redistributing the pressure gradient, thus, improving the efficiency and the thrust production. A momentum-based thrust evaluation approach is adopted to link the temporal and spatial evolution of the vortical structures with the time-dependent thrust. When the vortices detach from the trailing edge, the instantaneous thrust shows the largest values due to the strong momentum change and convection process. Moderate flexibility and convex shape help to transfer momentum to the fluid, thereby improving the thrust generation and promoting the transition from drag to thrust. The increase in the trailing edge angle can broaden the range of flexibility that produces positive mean thrust. The role of added mass effect on the thrust generation is quantified for different pitching plates and the bending stiffness. These findings are of great significance to the optimal design of propulsion systems with flexible wings.

We present a numerical study to analyze the aeroelastic characteristics of two-dimensional flexible membrane wings subjected to the ceiling effect. A body-fitted variational aeroelastic solver based on the fully coupled Navier–Stokes and nonlinear structural equations is employed to model the coupled fluid-membrane system. The coupled dynamics and the aerodynamic performance of flexible membrane wings with ceiling effect are investigated in a parameter space of angle of attack and ceiling distance. The effect of ceiling distance on the aeroelastic characteristics is examined at pre-stall, near-stall, and stall conditions. The role of flexibility in the coupled system under near-ceiling conditions is investigated by comparing with its rigid flat and cambered counterparts. The effect of no-slip and perfect slip boundary conditions of the ceiling wall is compared to quantify the momentum transport influenced by the ceiling effect. The connection between the aerodynamic loads and the membrane deformation is constructed by two scaling relations presented in our previous studies. The results indicate that the aeroelastic characteristics of the flexible membrane wings under near-ceiling conditions are adjusted from three aspects, namely, (i) the gap to the ceiling, (ii) the wing flexibility, and (iii) the ceiling boundary condition. This study represents a step toward an improved understanding of the aeroelastic characteristics of flexible membrane wings under ceiling conditions with different boundary layer flows. These findings can facilitate the development of high-efficiency bio-inspired micro-air vehicles that have robust flight stability and can perform missions in confined spaces.

A liquid deposited on a solid surface exhibits various wetting properties, primarily influenced by solid–liquid intermolecular interactions. Achieving a well-estimation of wetting behaviors on textured surfaces remains challenging because the influence of surface textures on intermolecular interactions is unclear. Here, an equivalent surface model is proposed to unify the wettability of both plane and textured substrates through intermolecular interactions. We show that by incorporating intermolecular interactions, lattice structures, and surface topographies, the substrate wettability can be tailored in an equivalent plane with the same average Lennard–Jones potential energy field E. The wettability of one substrate (plane or patterned) is transferred from non-wetting, partial wetting to complete wetting by adjusting the potential well depth of E, εa. With enhancing εa, complete wetting is achieved under the critical potential well depth of E, εac. Before εac, the spreading radius grows as R ∼ t1/1.47 until reaches equilibrium. In this scenario, the equilibrium contact angle θ and spreading factor β are strongly dependent on εa, and cos θ is linear to εa. When exceeding εac, complete wetting is achieved, and droplets spread with a precursor film as R ∼ t1/2.3 latterly. This model builds a bridge to link intermolecular interactions and substrate wettability normalization. This strategy offers a framework for substrate surface design and wettability manipulation, catering to applications such as photoresist-drop dispensing in nanoimprint lithography, surface design for grating antifouling, and anti-icing on aircraft surfaces.

This work investigates the effect of wake interference on the nonlinear coupled dynamics and aerodynamic performance of flexible membrane wings at a moderate Reynolds number. A high-fidelity computational aeroelastic framework is employed to simulate the flow-induced vibration of flexible membrane wings in response to unsteady vortex wake flows produced by an upstream stationary circular cylinder. The coupled dynamics of the downstream membrane are investigated at different gap ratios, aeroelastic numbers, and offset distances. The variations in flow features, membrane responses, and frequency characteristics are analyzed to understand the wake interference effect on membrane aeroelasticity. The results indicate that the aerodynamic performance and flight stability of the downstream membrane are degraded under the wake interference effect. Four distinct flow regimes are classified for the cylinder–membrane configuration, namely (i) single body flow, (ii) co-shedding I, (iii) co-shedding II, and (iv) detached vortex-dominated vibration, respectively. The mode transition is found to build new frequency synchronization between the flexible membrane and its own surrounding flows, or the wake flows of the cylinder, to adjust the aerodynamic performance and membrane vibration. This study sheds new light on membrane aeroelasticity in response to wake flows and enhances understanding of the fluid–membrane coupling mechanism. These findings can facilitate the development of next-generation bio-inspired drones that have high flight efficiency and robust flight stability in gusty flows.