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We investigate the effect of imposed kinematics on the self-propulsion of the NACA0015 symmetric airfoil section subject to sinusoidal pitching. We employ a rotary apparatus capable of achieving self-propulsion. A power-spring-based crank-rocker mechanism actuates the airfoil. Three distinct scaling relations emerge, which relate the self-propulsion Reynolds number $Re_s$ to the frequency Reynolds number $Re_f$, the amplitude of pitching $θ_0$, and the location of the pitching point, $p$. When pitched near the center, a \textit{linear} scaling emerges with $Re_s \sim Re_f θ_0$. When pitched near the leading edge, a \textit{power} scaling emerges with $Re_s \sim (1-2p)(Re_f θ_0)^{3/2}$ for low amplitude pitching and a \textit{separable} scaling emerges with $Re_s \sim (1-2p)^{1/2}Re_fθ_0^{1/2}$ for moderate to high amplitude pitching. These relations are consistent with the scaling relations derived from balancing inviscid thrust with viscous drag, pressure drag, and enhanced pressure drag for the \textit{power}, \textit{separable}, and \textit{linear} regimes, respectively. We find that different vortical patterns in the wake are directly correlated to the airfoil's self-propulsion

This study introduces a vortex gust generation method for isolated vortices impacting a downstream airfoil that is applicable to both numerical simulations and experiments. The vortex gust is generated by a symmetric airfoil undergoing a rapid pitching maneuver during a prescribed heaving motion. The resulting vortices propagate along trajectories nearly parallel to the incoming flow, while the associated wake extends obliquely from the vortex core. Despite differences in Reynolds number, rapid pitching duration and detailed vortex structure between simulations and experiments, consistent trends are observed in how the vortex rotation orientation, strength, and position vary with the prescribed motion parameters. Analysis of the lift response of the downstream airfoil shows that the aerodynamic influence associated with the wake does not persist over extended time scales. These results demonstrate that the proposed method enables the controlled generation of vortex gusts with prescribed characteristics, providing a flexible approach for systematic studies of vortex-airfoil interaction.

We present an experimental investigation examining how the complexity of pitching kinematics influences dynamic stall characteristics, including the stall delay and aerodynamic force response. The study examines whether the pitch rate defined at the static stall angle adequately characterises time-varying pitching kinematics for stall onset prediction. We then evaluate the performance of the generalised Goman-Khrabrov model in predicting force responses of nonlinear pitching motions and propose necessary modifications to extend the model's applicability to complex kinematics.

The Unmapped Tent Pitching (UTP) algorithm is a space--time domain decomposition method for the parallel solution of hyperbolic problems. It was originally introduced for the homogeneous one-dimensional wave equation in [Ciaramella, Gander, Mazzieri, 2024]. UTP is inspired by the Mapped Tent Pitching (MTP) algorithm [Gopalakrishnan, Sch{ö}berl, Wintersteiger, 2017], which constructs the solution by iteratively building polytopal space--time subdomains, referred to as tents. In MTP, each physical tent is mapped onto a space--time rectangle, where local problems are solved before being mapped back to the original domain. In contrast, UTP avoids the nonlinear and potentially singular mapping step by computing the solution directly on a physical space--time rectangle that contains the tent, at the expense of redundant computations in the region outside the tent. In this work, we investigate several strategies to extend UTP to heterogeneous media, where the wave propagation speed is piecewise constant over two subregions of the domain. Among the considered approaches, the most efficient in terms of computational time is the one employing space--time subdomains with identical spatial and

This study examines the center of pressure (CoP) movement of rigid pitching swept wings based on prior measurements by (Zhu, Breuer, 2023}. The wings analyzed feature sweep angles of $0^{\circ}$, $10^{\circ}$, and $20^{\circ}$, and are subjected to large amplitude sinusoidal pitching instabilities below a critical torsional spring stiffness. The CoP location is determined from time-resolved force and moment measurements, revealing minimal variation in the cross-chord direction but significant spanwise and chord-wise movement, varied by sweep angle. The trajectory of the CoP varies with sweep angle due to the evolving strength and dynamics of the leading edge and tip vortices. The Force Moment Partitioning Method (FMPM) is applied to stereo Particle Image Velocimetry (PIV) data to identify contributions from wing kinematics, vortex structures, and viscous effects. This approach elucidates the roles of leading edge and tip vortices, as well as the periodic and stochastic components of the flow field, in influencing the net forces and moments.

We study experimentally a symmetrical rigid foil performing pitching oscillations around a mean incidence angle ($α_{m}$) with respect to an incoming flow in a hydrodynamic channel at a constant velocity where the Reynolds number according to the chord of the foil is, $Re_{c} = ρU_{\infty} c / μ= 14400$. The problem is inspired from the pumping maneuver used by athletes on the new hydrofoil-based windsurf boards. The goal of the study is to quantify the forces on this configuration by varying the pitching kinematics characterized by the Strouhal number ($St_{A} = fA/U_{\infty}$), from 0 to 0.27, and the mean incidence angle $α_{m}$, from 0 to 30$^{\circ}$, of the foil. The force measurements show a high lift production and the delay of the stall angle according to $St_A$ which can be linked to previous studies about the generation of vortices at the trailing edge. A general trend of decrease is observed for the drag force coefficient in pitching compare to the static case. For the highest Strouhal numbers tested, drag coefficient can become negative (thrust) in a range of $α_{m}$ up to 15$^{\circ}$ in specific case. We present the various impacts of the amplitude of beating and the

Combined pitching-and-surging of an airfoil at the identical frequency (i.e., synchronously), at four different phase-differences, was investigated theoretically and experimentally. The most general unsteady theoretical formulation was adopted to calculate the lift coefficient, and then extended to explicitly compute the unsteady bound vortex sheet. This was used for comparison to experiments and facilitated the computation of both Joukowsky and impulsive-pressure lift contributions. Experiments were performed using a NACA 0018 airfoil in an unsteady wind tunnel at an average Reynolds number of $3.0 \times 10^5$, with a free-stream oscillation amplitude of 0.51, an angle-of-attack range of $2^\circ \pm 2^\circ$, and a reduced frequency of 0.097. In general, excellent correspondence was observed between theory and experiment, representing the first direct experimental validation of the general theory. It was shown, both theoretically and experimentally, that the lift coefficient was not accurately represented by independent superposition of surging and pitching effects, due to variations in the instantaneous effective reduced frequency not accounted for during pure pitching. Deviati

This study introduces novel physics-based scaling laws to estimate the propulsive performance of synchronously pitching foils in various schooling configurations at Re=4000. These relations are derived from quasi-steady lift-based and added mass forces. Hydrodynamic interactions among the schooling foils are considered through vortex-induced velocities imposed on them, constituting the ground effect. Generalized scaling equations are formulated for cycle-averaged coefficients of thrust and power. These equations encompass both the pure-pitching and induced velocity terms, capturing their combined effects. The equations are compared to computational results obtained from two-foils systems, exhibiting foil arrangements over a wide range of parameter space, including Strouhal number (0.15 \leq St \leq 0.4), pitching amplitude (5 deg \leq θ_0 \leq 14 deg), and phase difference (0 deg \leq φ\leq 180 deg). The individual contributions of pure-pitching and induced velocity terms to propulsive performance elucidate that solely relying on the pure-pitching terms leads to inadequate estimation, emphasizing the significance of the induced velocity terms. Validity of the approach is further as

Recent measurement technologies enable us to analyze baseball at higher levels. There are, however, still many unclear points around the pitching strategy. The two elements make it difficult to measure the effect of pitching strategy. First, most public datasets do not include location data where the catcher demands a ball, which is essential information to obtain the battery's intent. Second, there are many confounders associated with pitching/batting results when evaluating pitching strategy. We here clarify the effect of pitching attempts to a specific location, e.g., inside or outside. We employ a causal inference framework called stratified analysis using a propensity score to evaluate the effects while removing the effect of disturbing factors. We used a pitch-by-pitch dataset of Japanese professional baseball games held in 2014-2019, which includes location data where the catcher demands a ball. The results reveal that an outside pitching attempt is more effective than an inside one to minimize allowed run on average. Besides, the stratified analysis shows that the outside pitching attempt was always effective despite the magnitude of the estimated batter's ability, and the

Birds employ rapid pitch-up motions for different purposes: perching birds use this motion to decelerate and come to a complete stop while hunting birds, like bald eagles, employ it to catch prey and swiftly fly away. Motivated by these observations, our study investigates how natural flyers accomplish diverse flying objectives by rapidly pitching their wings during deceleration. We conducted experimental and analytical investigations focusing on rapidly pitching plates during deceleration in close proximity to the ground to explore the impact of ground proximity on unsteady dynamics. Initially, we executed simultaneous deceleration and pitch-up motion close to the ground. Experimental results demonstrate that as the pitching wing approaches the ground, the instantaneous lift increases while the initial peak drag force remains relatively unchanged. Our analytical model confirms this trend, predicting an increase in lift force as the wing approaches the ground, indicating enhanced added mass and circulatory lift force due to the ground effect. Next, we examined asynchronous motion cases, where rapid pitching motions were initiated at different stages of deceleration. The results rev

We propose and validate a data-driven approach for modeling large-amplitude flow-induced oscillations of elastically mounted pitching wings. We first train a neural networks regression model for the nonlinear aerodynamic moment using data obtained from experimental measurements during prescribed pitching oscillations and at fixed angles of attack. We then embed this model into an ordinary differential equation solver to solve the governing equation of the passive aeroelastic system with desired structural parameters. The system dynamics predicted by the proposed data-driven approach are characterized and compared with those obtained from physical experiments. The predicted and experimental pitching amplitude, frequency and aerodynamic moment responses are found to be in excellent agreement. Both the inertia-dominated mode and the hydrodynamic-dominated mode are successfully predicted. The transient growth and saturation of the pitching oscillation amplitude and the aerodynamic moment are also faithfully captured by the proposed approach. Additional test cases demonstrate the broad applicability and good scalability potential of this approach.

The actuator line method (ALM) is an approach commonly used to represent lifting and dragging devices like wings and blades in large-eddy simulations (LES). The crux of the ALM is the projection of the actuator point forces onto the LES grid by means of a Gaussian regularisation kernel. The minimum width of the kernel is constrained by the grid size; however, for most practical applications like LES of wind turbines, this value is an order of magnitude larger than the optimal value which maximises accuracy. This discrepancy motivated the development of corrections for the actuator line, which, however, neglect the effect of unsteady spanwise shed vorticity. In this work, we develop a model for the impact of spanwise shed vorticity on the unsteady loading of an airfoil modelled as a Gaussian body force. The model solution is derived both in the time and frequency domain and features an explicit dependence on the Gaussian kernel width. We validate the model with LES within the linear regime of the lift curve for both pitch steps and periodic pitching with reduced frequencies of k=0.1, 0.2 and 0.3. The Gaussian kernel width affects, in particular, the amplitude of the unsteady lift, w

We experimentally study the dynamics and strength of vortices shed from a NACA 0012 wing undergoing sinusoidal pitching in quiescent water. We characterize the temporal evolution of the vortex trajectory and circulation over a range of pitching frequencies, amplitudes and pivot locations. By employing a physics-based force and moment partitioning method (FMPM), we estimate the vortex-induced aerodynamic moment from the velocity fields measured using particle image velocimetry. The vortex circulation, formation time and vorticity-induced moment are shown to follow scaling laws based on the feeding shear-layer velocity. The vortex dynamics, together with the spatial distribution of the vorticity-induced moment, provide quantitative explanations for the nonlinear behaviors observed in the fluid damping (Zhu et al., J. Fluid Mech., vol. 923, 2021, R2). The FMPM-estimated moment and damping are shown to match well in trend with direct force measurements, despite a discrepancy in magnitude. Our results demonstrate the powerful capability of the FMPM in dissecting experimental flow field data and providing valuable insights into the underlying flow physics.

Airfoils pitching in the stalled regime have been of keen interest in recent years due to their desirable aerodynamic force characteristics. In this study, we are numerically investigating the unsteady flow past a NACA 0012 airfoil under sinusoidally pitching motion, using a finite volume based sharp interface immersed boundary solver. The flow is investigated in the low Reynolds number regime (Re=3000) for reduced frequencies of 0.1 and 0.5, at three different pivot locations (c/3, c/2 and 2c/3 from the leading edge). The airfoil is subjected to sinusoidal oscillations with its incidence angle varying from 15o to 45o. Leading edge vortices (LEVs) that are formed during the pitching motion dictate the transient aerodynamic characteristics. The flow field data is used to identify individual LEVs in the flow field. The spatio-temporal evolution of LEVs in terms of their strengths are traced throughout the pitching cycle to obtain a quantitative estimate of its evolution. The effect of pivot location and pitching frequency on the vortex evolution and aerodynamic forces is investigated. Change in pitching frequency is found to have a drastic effect on the vortex dynamics. LEV formation

A classic lift decomposition (von Kármán & Sears 1938) is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift doesn't play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behavior provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for AR < 1.5 occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for

The experiment of separated flow response to a single-burst actuation over a 2-D NACA-0009 airfoil at $12^o$ angle of attack was conducted. The mechanism of the lift and pitching moment reversal following the single-burst actuation was studied. A spatially localized region of high pressure caused by a vortices-induced downwash is responsible for the lift and pitching moment reversal. Proper orthogonal decomposition (POD) of the flowfield shows that mode 2 shares a similar structure that produces the downwash and is responsible for the lift and pitching moment reversal. On the other hand, POD mode 1, which represents the direction and strength of the reverse flow on the suction side of the airfoil is responsible for the lift enhancement.

An adjoint-based optimization is applied to study the thrust performance of a pitching-rolling ellipsoidal plate in a uniform stream at Reynolds number 100. To achieve the highest thrust, the optimal kinematics of pitching-rolling motion is sought in a large control space including the pitching amplitude, the rolling amplitude, and the phase delay between the pitching and rolling motion. A continuous adjoint approach with boundary motion being handled by non-cylindrical calculous is developed as a computationally efficient optimization algorithm to deal with the large control space with morphing domain. The comparison between the optimal motion and other reference motions shows a significant improvement of thrust from the increase of rolling amplitude and an optimal phase delay of $122.6^\circ$ between the pitching and the rolling motion. The combination of these two factors impacts the overall thrust performance through their strong effects on the angle of attack, circulation, and the pressure distribution on the plate. Further wake structure analysis suggests that the optimal control improves its propulsive performance by generating a stronger leading-edge vortex (LEV) and straig

We present new scaling laws for the thrust production and power consumption of three-dimensional combined heaving and pitching hydrofoils by extending the three-dimensional pitching scaling laws introduced by Ayancik et al. (2019). New self-propelled inviscid simulations and previously published experimental data are used to validate the scaling laws over a wide range of motion amplitudes, Strouhal numbers, heave ratios, aspect ratios, and pitching axis locations. The developed scaling laws are shown to predict inviscid numerical data and experimental data well, within $\pm$ 25% and $\pm$ 16% of the thrust and power data, respectively. The scaling laws reveal that both the circulatory and added mass forces are important when considering a wide range of motion amplitudes and that nonlinear corrections to the classic linear theory are essential to modeling the performance across this wide amplitude range. By using the scaling laws as a guide, it is determined that peak efficiencies occur when $A^*$ > 1 and for these large-amplitude motions, there is an optimal $h^*$ that maximizes the efficiency in the narrow range of 0.75 < $h^*$ < 0.94. Finally, the scaling laws show that