We investigate how density stratification influences hydrodynamic interactions between a pair of settling particles. While numerical studies suggest that particle interactions in stratified fluids differ fundamentally from those in homogeneous fluids, experimental evidence and mechanistic understanding remain limited. We systematically examine the settling dynamics of isolated particles and side-by-side particle pairs in homogeneous and stratified environments, complemented by numerical simulations resolving the three-dimensional wake structures. The Galileo number is fixed at Ga approximate to 178, and the Froude number is varied from Fr=6.4 to 19.4. In a homogeneous fluid, particle-pair separation is governed by two mechanisms: a short-range inter-particle interaction that deterministically sets the inclination of the particle wakes, and a long-range wake-induced particle-fluid interaction that sustains continued separation. Although the direct interaction decays rapidly beyond s>2D (where D is the particle diameter), lateral wake-induced motion persists. Density stratification suppresses this process by maintaining near-axisymmetric wakes, thereby inhibiting horizontal particle motion and significantly reducing the total separation distance.

This study focuses on the design of the propeller layout for tilt-wing fixed-wing unmanned aerial vehicles (UAVs) with distributed electric propulsion (DEP). A numerical simulation method is used to analyze the effects of propeller diameter, quantity, and other parameters on aerodynamic performance under hover and cruise conditions. Meanwhile, aerodynamic mechanisms of propeller-wing interference are analyzed. Six sets of DEP layouts with different quantities and sizes of propellers are designed and studied. The results indicate that propeller quantity and size significantly affect the power loading, overall efficiency, and lift-to-drag ratio. In the hover state, a greater number of propellers increases the power loading, whereas employing a greater number of smaller propellers decreases the power loading. In the cruise state, a greater number of propellers enhances the overall efficiency of the DEP system, but reduces the lift-to-drag ratio of the aircraft. Comprehensive analysis shows that the Prop1–2 and Prop1–3 layouts exhibit superior overall performance in both hover and cruise conditions. This study provides crucial theoretical support for the design of tilt-wing vertical take-off and landing UAVs.

This study investigates the unsteady oscillation cycle of sheet and tip vortex cavitation over an elliptical NACA 66 Subscript 2 66 2 $66_2$ -415 hydrofoil using high-speed imaging and time-resolved tomographic particle image velocimetry. Synchronised measurements of radiated noise are conducted. The oscillation cycle consists of three phases, involving growth and collapse of the sheet and tip vortex cavitation, followed by intermittent rebounding of the tip vortex cavity. The collapse of the sheet cavity is triggered by a side-entrant jet, leading to the formation of the cloud and secondary vortex cavitation. The interaction between the secondary and tip vortex cavities further promotes the collapse of the latter. The three-dimensional instantaneous flow organisation indicates that the evolution of cavitation affects the centre displacement, deformation and breakdown of the tip vortex. Spanwise vortices emerge and interact with the tip vortex after the growth phase, causing violent fluctuations of the tip vortex during the collapse phase. The intense interaction between these vortices enhances the perturbation growth and promotes tip vortex breakdown. Proper orthogonal decomposition analysis reveals that the dominant unstable modes near the hydrofoil tip correspond to the displacement and deformation types. In addition to the suction-side shear layer, the vortex interaction region also exhibits intense production of turbulent kinetic energy. The temporal variation of sound pressure over an oscillation cycle indicates a strong correlation with the cavity morphology.

We perform interface-resolved direct numerical simulations of deformable bubble swarms in a high-Reynolds-number wobbling regime ( R-eb approximate to 434, Eo=3) to investigate the interplay between collective motion, bubble clustering, and bubble-induced turbulence over a wide range of void fractions ( phi=2%-16%). To overcome the challenge of numerical coalescence in the volume-of-fluid method, we extend a previously developed short-range repulsive force model to swarm simulations, enabling the robust simulation of long-duration, close-interaction dynamics. Our primary finding is a striking non-monotonic dependence of the mean swarm rise velocity on the void fraction. At low void fractions ( phi <= 4%), the swarm velocity is enhanced relative to an isolated bubble, driven by the formation of persistent, vertically-aligned chain-like structures. This clustering, sustained by the negative lift force on deformable bubbles in wake-induced shear, provides a low-drag configuration. In contrast, at higher void fractions ( phi >= 8%), intense multi-bubble interactions disrupt these coherent structures, leading to a collective hindrance effect that suppresses the rise velocity. This transition in dynamics is directly mirrored in the statistics of the liquid-phase pseudo-turbulence. At low void fractions, vertical clustering leads to a strong anisotropic suppression of velocity fluctuations, fundamentally altering the horizontal velocity probability density functions to a single-slope exponential decay. As the void fraction increases, the flow transitions toward a more isotropic, Gaussian-like state. Finally, across all void fractions, the kinetic energy spectra universally exhibit a k(-3) scaling law at sub-bubble scales, while the energy at large scales is dictated by the dominant collective structure. These results provide new fundamental insights into the structural and statistical properties of dense, high-Reynolds-number bubbly flows.

Tilt-wing vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) present significant modeling and control challenges due to their complex, multi-body dynamics and severe variations in control authority during the transition phase. This paper presents a comprehensive framework-spanning hardware design, modeling, trajectory optimization, and control-to enable safe and efficient altitude-hold transitions. First, the design of a novel tilt-wing VTOL platform is detailed, upon which a high-fidelity, multi-body dynamic model is developed. Based on this model, a Dynamic Transition Corridor (DTC) is numerically generated to fully characterize the dynamically feasible flight envelope. An optimal control problem is then formulated to generate multi-objective transition trajectories guaranteed to remain within the safe confines of this pre-computed DTC. To robustly track these trajectories, a hierarchical flight control system is designed, featuring a novel decoupled scheduling strategy for smooth handover between multi-copter and fixed-wing logics. The entire integrated framework was successfully validated through high-fidelity simulations and real-world flight tests, which demonstrated a satisfactory altitude-hold capability with a maximum one-sided deviation of <3.6 m during the complete forward and backward transitions. This research provides a systematic methodology for designing and implementing complex transition maneuvers, significantly bridging the sim-to-real gap for this challenging class of aircraft. Flight videos can be found at: https://youtu.be/YTU5gD94G6g.

Agile waypoint tracking for fixed-wing UAVs under full 6-DOF nonlinear dynamics poses a fundamental conflict between dynamic fidelity and real-time feasibility: classical geometric guidance methods sacrifice optimality, while offline optimal control methods incur prohibitive computational latency. This paper presents a reinforcement learning-based hybrid strategy that resolves this conflict through two key design choices. First, a Proximal Policy Optimization policy operates at the guidance level, outputting airspeed and load factor commands to a low-level gain-scheduled cascade controller rather than directly commanding actuators. Second, this gain-scheduled controller is embedded within the training environment, ensuring the policy learns over the true closed-loop dynamic response of the 6-DOF model. Coupled with random initialization, a composite reward function featuring heading alignment and dynamic decoupling enables a lightweight neural network to master agile maneuvers while maintaining low inference latency per step, thereby empowering the UAV for online agile planning. Multi-scale simulations demonstrate that the proposed strategy achieves a 90.90% tracking success rate while maintaining inference latency suitable for online planning, outperforming classical Line-of-Sight guidance in agility. In a single-waypoint benchmark, the proposed strategy achieves a completion time 8.6% longer than the controller-feasible optimal control solution, affirming its agile tracking capability.

Airfoil designs are crucial for the aerodynamic performance of airplanes. Multiple objectives under several flight conditions to satisfy engineering requirements, especially for wide-speed-range aircraft or morphing aircraft are always considered. Airfoil generative design method is an end-to-end method which inputs design objectives and outputs airfoil geometry directly. In this study, a novel airfoil generative design method using a conditional denoising diffusion probabilistic model was developed to solve the multi-objective design problem. Airfoil-DDPM can flexibly solve multi-objective design problems considering both geometric constraints and arbitrary number set of aerodynamic constraints. The classifier-free diffusion guidance and the multi-objective sampling method were combined in the diffusion model to realize the flexible multi-objective design. Trained on 50k airfoils across 200k flow cases(Ma = 0.75, Re = 7 x 106, alpha = 0-3 degrees), the model generated airfoils with median drag coefficient and moment coefficient error of 0.0008 and 0.0069 respectively in multi-objective design. The accuracy Testing showed that the method can generate airfoils under geometric or aerodynamic constraints, while the airfoils generated under both constraints were better in line with the reference airfoil than those with only one kinds of constraint. Robustness testing showed that although the unreasonable input significantly deviates from the normal value, the generations satisfy the reasonable constraints well. The comparison resulted with other two generation models show that Airfoil-DDPM has absolute advantages over CVAE and CGAN in terms of generation quality and flexibility.

This paper introduces a novel Contrastive-Aligned Diffusion model (CA Diff), a cross-modal latent-space alignment and diffusion-based generative framework for multi-objective shape design. The framework jointly embeds cross-modal constraints, the structural geometry and corresponding performance, into a unified latent space through a contrastive learning module. Based on this aligned representation, a two-stage diffusion model can produce shapes that satisfy multi-objective performance constraints while maintaining diversity. To validate this new framework, a case of airfoil generation is studied. The results demonstrate that, under multi-objective aerodynamic constraints, CA Diff significantly reduces the generation error compared with non-aligned conditional diffusion models, achieving a drag-coefficient MAE of 10-4. Meanwhile, it possesses the ability to generate diverse shapes.

Machine learning has demonstrated significant potential as a valuable tool for aerodynamic design. However, collecting an abundant training set is usually computationally expensive and time-consuming. To address this data scarcity, meta-learning and transfer learning offer viable strategies. Meta-learning enables models to learn efficiently from limited data by leveraging experience across related tasks, while transfer learning reduces data requirements by reusing knowledge from pre-trained models. In addition, integrating physics knowledge into the models provides a complementary path to enhance the reliability and generalizability under data-scarce conditions. This paper studies meta-learning and transfer learning strategies to realize the prediction of supercritical airfoil pressure distribution under multiple free stream conditions with a small-scale dataset. All the models are tested both in the source domain and the target domain. Then, a systematic comparative analysis of different models across different target domain training sample scales is studied. Results show that meta-learning and transfer learning both improve target-domain performance compared to the baseline model. Yet, meta-learning still achieves limited accuracy in the target domain, and data-driven transfer learning exhibits poor generalization. Compared with data-driven models, the Mach number weighted transfer learning model provides more generalized results and higher accuracy.

In this study, a multiscale Euler-Lagrange method is proposed, integrating anew wall nucleation model tailored for predicting sheet cavitation dynamics. Differentiating from the previous homogeneous wall nucleation model, our approach calculates nucleation diameter based on local flow conditions. Specifically, within the flow attachment region, the nucleation diameter is dependent on the flow shear rate, whereas in separation zones, it correlates with the thickness of the low-momentum region. Transition corrections are incorporated into the delayed detached eddy simulation (DDES) model to enhance accuracy in predicting flow separation. Rigorous validation is conducted, focusing on Lagrangian bubble dynamics and predicting laminar separation. The method is then applied to investigate cavitation flow induced by an axisymmetric headform body. Predicted cavitation scenarios are compared with experimental observations, Euler cavitation simulations, and multiscale simulations employing the wall nucleation model introduced by Hsiao et al., (2017). Results demonstrate that our model accurately predicts cavity morphology and inception index, closely matching experimental findings. Moreover, our model offers a coherent explanation for the detachment position and inception index of sheet cavitation, emphasizing the pivotal role of wall nucleation in precise prediction of sheet cavitation phenomena.

Some natural wind-borne plants spread their seeds in a mode of autorotation, for example, maple, pterocarya stenoptera, and tristellateia. However, these wind-borne seeds have different numbers of wings. The current work focuses on the effects of wings number on the flight performance of autorotating seeds. Experiment and numerical simulation are used to analyze the aerodynamic performance of tristellateia seeds with different numbers of wings. In the free fall experiments, it is found that reducing the wings number leads to larger wing loadings, larger stable descending velocities, and larger spinning rates. The growth rate of descending velocity and spinning rate are related to the wings number. However, as the number of clipped wings increases, the seeds are more likely to fall into unsteady rotation even free fall. Numerical simulations are used to analyze the flow field around the rotating tristellateia seeds. It finds that seeds with clipped wings have larger pressure difference between the upper and lower wing surfaces, which contributes to larger lift. Three kinds of vortex systems occur on the rotating seeds: the leading-edge vortex, the wing tip vortex, and the separated vortex. Seeds with different clipped wings present various vortex morphology and structure. A stable separated vortex ring dominates the stable autorotation of tristellateia seeds. However, an unstable separated vortex emerges on the seeds with less wings, which makes these seeds difficult to achieve stability.

The present study investigates the control effect of a vane-shaped micro vortex generator (VG) on the inception and development of tip vortex cavitation. Five different arrangements were tested by varying the position and installation angle near the tip of a NACA (National Advisory Committee for Aeronautics) 662-415 hydrofoil. The spatial and temporal evolution of the tip vortex cavity was captured using high-speed imaging. The result shows that VG can induce both streamwise vortices and bubbles that affect the cavitation inception. When the VGs are aligned parallel to the incoming flow direction, the generated bubble content is relatively small. Meanwhile, due to the interaction between the tip vortex and the streamwise vortex induced by the VG, the vortex cavity in these cases exhibits notable deformation and diameter fluctuations compared with the smooth case. As a result, the inception of cavitation is significantly delayed, resulting in a notable reduction in the sound pressure level. The optimal control is achieved when the VG is placed at the tip. Conversely, the VG mounted at a larger alignment angle generates bubbles at a high cavitation number, which causes the premature onset of vortex cavitation and results in a detrimental effect.

This paper aims to address the nonlinear optimal guidance problem with impact-time and impact-angle constraints, which is fundamentally important for multiple pursuers to collaboratively achieve a target. Addressing such a guidance problem is equivalent to solving a nonlinear minimum-effort control problem in real time. To this end, the Pontryagain's maximum principle is employed to convert extremal trajectories as the solutions of a parameterized differential system. The geometric property for the solution of the parameterized system is analyzed, leading to an additional optimality condition. By incorporating this optimality condition and the usual disconjugacy condition into the parameterized system, the dataset for optimal trajectories can be generated by propagating the parameterized system without using any optimization methods. In addition, a scaling invariance property is found for the solutions of the parameterized system. As a consequence of this scaling invariance property, a simple feedforward neural network trained by the solution of the parameterized system, selected at any fixed time, can be used to generate the nonlinear optimal guidance within milliseconds. Finally, numerical examples are presented, showing that the nonlinear optimal guidance command generated by the trained network can not only ensure the expected impact angle and impact time are precisely met but also requires less control effort compared with existing guidance methods.

With the emergence of Distributed Electric Propulsion (DEP) configurations, efficient and accurate numerical analysis methods have become crucial. This study employs the meshless reformulated Vortex Particle Method (rVPM) model to explore the complex aerodynamic interactions between multi-propeller and a downstream wing in typical DEP configurations. The rVPM model is validated against experimental and numerical data under different operating conditions. Key findings indicate that the spanwise lift coefficient distribution on the downstream wing is significantly altered by the multi-propeller wakes, which displays distinct flow patterns at different angles of attack. In the co-rotating case, the sectional lift coefficient is higher at alpha=4 degrees, whereas the downwash effect on the sectional lift distribution is more pronounced in the counter-rotating case. The key difference between the CO-R and COU-R configurations is the opposing rotation directions of the middle propeller. This difference significantly affects the wing lift distribution by altering the upwash and downwash effects, as well as the swirl recovery mechanisms. The slipstream geometry is shaped by the interaction between propeller-induced spanwise velocity and wingtip-induced crossflow velocity, leading to distinct slipstream distortion at different spanwise positions. Additionally, the tip vortex tube of the multi-propeller undergoes significant deformation near the downstream wing. In the case of co-rotating, the wing drag coefficient fluctuates more than in the case of a mid-mounted propeller. These results provide critical insights into the aerodynamic characteristics of the multi-propeller/wing system, offering valuable implications for the design and optimization of DEP aircraft.

This study employs a coupled multiscale method to simulate and analyze cloud cavitation flow around a twisted hydrofoil under varying water quality conditions, focusing on cavitation erosion risk. The volume of fluid method captures the vapor–liquid interface of large-scale cavitation structures, while a discrete bubble model is adopted to track microscale bubbles. A Lagrangian erosion model, accounting for asymmetric bubble collapse, is employed to predict cavitation erosion risk. The results show that the multiscale approach effectively captures both the overall evolution of cloud cavitation and the generation, growth, and collapse behavior of small-scale bubbles. The spatial distribution of microbubbles exhibits periodic variation driven by the unsteady cloud cavitation, with most bubbles originating from the main detached cavity. Two distinct power–law size distributions characterize these bubbles, reflecting multiscale bubble dynamics. The predicted cavitation erosion risk aligns closely with experimental paint tests, revealing three regions with varying erosion intensity on the hydrofoil surface, with the highest erosion risk near the sheet cavity closure line. Further analysis indicates that, under nuclei-abundant (weak water) conditions, prolonged collapse of the U-shaped cavity increases cavitation erosion near the hydrofoil's trailing edge.

Tip vortex cavitation (TVC) is a critical phenomenon in propeller and turbine machinery. While much of the existing research on TVC has focused on its inception, the mechanisms driving its continuous growth remain under-explored. In this study, we propose a comprehensive theoretical model that integrates both gas diffusion and free nuclei entrainment to better understand the slow growth of tip vortex cavity. The efficacy of this model is validated by comparing its predicted temporal evolution of cavity size with experimental data, under both nuclei-depleted and large nuclei-injection conditions. Additionally, the model is used to further examine the individual effects of nuclei content and size on tip vortex cavity growth. Results reveal that, in sub-saturated nuclei flow, two critical equilibrium values for cavity size are identified: one determined by the balance of dissolved gases inside the cavity and the surrounding fluid, and the other by the balance between dissolved gases inside the cavity and the surrounding gas nuclei. The cavity stability size gradually shifts from the first to the second critical value as the gas nuclei content increases. However, since the model does not consider the destabilization mechanism of the cavity, the cavity may destabilize before reaching the second critical value. Meanwhile, the cavity growth rate increases significantly with increasing gas nuclei size. This work not only provides a comprehensive explanation for the experimental observations, but also provides new insights into the hysteresis phenomenon observed in TVC.

Freestream nuclei, also referred to as water quality, are known to significantly affect cavitation inception. However, their effects on fully developed cavitation and the corresponding noise characteristics remain inadequately understood. In this study, a multiscale hydroacoustic model based on the Euler–Lagrangian framework is used to investigate the impact of water quality on monopole noise characteristics of sheet and tip-leakage vortex (TLV) cavitating flow. Cavitating flows over the National Advisory Committee for Aeronautics 0009 hydrofoil under varying water qualities are simulated, and the results are compared with those from the conventional Eulerian cavitation model and experimental observations. The findings indicate that the sound pressure radiated by sheet cavitation exhibits the same baseline signature across different water qualities, but more intense peaks are observed in nuclei-depleted flow. For TLV cavitation, a higher baseline acoustic signature is predicted in “weak” water, while a lower baseline signature with more extreme loud events is predicted in “strong” water, consistent with experimental observations. The corresponding cavity evolution shows that strong acoustic pressure pulses generated by sheet cavitation in strong water result from the more intense collapse and rebound of the sheet cavity. Additionally, the smaller baseline acoustic signature of TLV cavitation in strong water arises from the absence of tip-separation cavitation and the intermittency of TLV cavitation, while the stronger acoustic pressure pulse originates from the complete collapse of the TLV cavity, a phenomenon not observed in weak water. For both cavitation types, frequency-domain analysis reveals that monopole noise is amplified in the high-frequency range as water is degassed, likely linked to the dynamic behavior of the local cavities.

We propose a multiscale Euler-Lagrange method to simulate tip vortex cavitation (TVC), accurately modelling bubble dynamics at the macroscopic Eulerian scale. The method employs mapping strategies using a Gaussian kernel function and topological relationships to represent momentum and mass transfer between the Eulerian and Lagrangian frames. We investigate the effects of nuclei content and spatial distribution on TVC inception induced by an elliptical foil, comparing the predicted cavitation inception indices with experimental data, wetted flow simulations, and conventional Euler cavitation simulations. Our results demonstrate that the model yields cavitation inception indices that closely align with experimental observations. Additionally, our simulations reveal a direct correlation between the index and location of TVC inception with both the content and spatial distribution of nuclei. We also examine the temporal evolution of a single nucleus injected at the same position under different cavitation numbers to elucidate the mechanism of TVC inception. We observe two distinct outcomes for nucleus evolution. At higher ambient pressures, only localised elongated cavities move downstream and eventually collapse, a phenomenon not captured by traditional Euler simulations or hybrid Euler-Lagrange methods. When pressure is sufficiently low, a nucleus captured downstream of the minimum pressure location can progress upstream and trigger sustained TVC by connecting to the downstream cavity. This research offers a promising methodology fora deeper understanding of TVC inception and highlights the significant role of nuclei in this process.

Cavitation performance is a critical hydrodynamic characteristic of ship propellers, and it has been a key focus in naval architecture research. This study introduces a hybrid multiscale Euler-Lagrange model for unsteady propeller cavitation simulations, incorporating the effects of water quality. A uniform mixture model is used for macroscopic cavity simulation. Under the Lagrangian framework, the dynamics and motion of nuclei and bubbles are resolved. Comparisons with experimental data and numerical results from traditional cavitation models show that the multiscale model accurately predicts cavitation on propeller blades and reproduces certain tip vortex cavitation phenomena. The model’s applicability is validated across different advance coefficients and cavitation numbers, further confirming its robustness in simulating propeller cavitation. Additionally, the study explores the distribution of nuclei and emphasizes the advantages of the multiscale approach in capturing tip vortex cavitation. This research provides a strong foundation for investigating the comprehensive effects of water quality on propeller cavitation and offers promising avenues for future studies in this area.

Physical monotonicity is a pervasive phenomenon in the aerodynamic characteristics of aircraft, where the aerodynamic lift consistently increases with the angle of attack within the stalling range. Existing machine learning models for aerodynamic predictions often overlook this monotonicity, resulting in poor interpretability and credibility. To address this issue, we introduce a monotonic model, the Deep Lattice Network, which integrates the monotonicity constraint of the lift coefficient into machine learning based aerodynamic prediction framework. In this paper, we propose a novel deep learning model, Deep Lattice Cross Network, which aims to rapidly predict aerodynamic forces with high precision while ensuring monotonic constraints. Multi-Task Learning method is utilized to simultaneously predict both lift and drag coefficients, thereby enhancing the efficiency of the model. To optimize the training process and minimize costs, we adopt a unique two-phase deep network training strategy. Based on computational fluid dynamics simulation datasets of a morphing aircraft, the model is trained, and the efficacy of the model is tested by two interpolation and two extrapolation datasets. The results show a remarkable alignment with computational fluid dynamics outcomes across all test scenarios. Extended testing across a wider range of attack angles further highlights the superiority of the Deep Lattice Cross Network in upholding monotonicity. Incorporating monotonicity constraints not only improves predictive accuracy of the model but also greatly enhances its physical interpretability, which is crucial for advancing the development of more dependable aerodynamic prediction models.