With the emergence of advanced technologies like nanoprinting, the impact dynamics of nanodroplets have attracted growing attention. In practical printing processes, off-center impacts of droplets on curved surfaces are frequently encountered, yet the underlying mechanisms remain insufficiently understood. In this study, molecular dynamics simulations are employed to systematically investigate the off-center impact of nanodroplets on hydrophobic and hydrophilic spheres, with the aim of comprehensively elucidating the impact outcomes. Four outcomes are identified: deposition, bouncing, dripping, and separation. All outcomes are observed on hydrophobic surfaces, whereas bouncing is suppressed on hydrophilic surfaces due to the enhanced solid–liquid adhesion. Based on these outcomes, phase diagrams are constructed for impacts on the hydrophobic and hydrophilic spheres. The separation-dripping boundary shows that the critical Weber number (We) increases with the normalized off-center distance (B) on both hydrophilic and hydrophobic surfaces. Nonetheless, for the boundary between separation and other outcomes, on hydrophobic surfaces, the critical We increases with B, while it in turn decreases with B on hydrophilic surfaces. The observed boundary on hydrophobic surfaces challenges the conventional understanding that increasing B enhances the off-center kinetic energy to promote separation. This is because on hydrophobic surfaces, the head-on part bounces off spheres with significant rotational motion, followed by the occurrence of separation. For this situation, the bouncing kinetic energy drives the separation process, instead of the off-center kinetic energy. Based on different mechanisms of separation, two boundary equations are proposed by using distinct driving kinetic energy, which show good agreement with our simulation results.
To reveal the evolution of the cavitation field and the wall cavitation erosion response in a confined variable-cross section micro-hole under time-varying pressure generated by volume alternation, this study investigates an Al 1060 variable-cross section micro-hole with a diameter transition from 1 to 2 mm. A mathematical model of bidirectional volume-alternating cavitation (BVAC) and a three-dimensional numerical flow-field model were established. The evolution of the cavitation field and its flow characteristics were analyzed, the effects of alternating frequency and alternating stroke on the cavitation field were clarified; and cavitation erosion experiments were conducted to examine the correspondence between the numerical flow-field characteristics and the wall response. These results indicate that after five alternating cycles, the BVAC flow field reaches a dynamically stable state and exhibits periodic evolution. The abrupt cross-sectional change induces the formation of large-scale, symmetrically distributed vortex structures in the flow field. Both the vapor volume fraction and the flow velocity increase with increasing alternating frequency and alternating stroke. Cavitation erosion experiments at different alternating frequencies, with the alternating stroke fixed at 20 mm and the erosion time at 6 h, showed the best overall improvement at 40 Hz, with the surface roughness Ra of the large-diameter, small-diameter, and transition sections reduced by approximately 52.9%, 60.7%, and 30.5%, respectively. The differences in roughness improvement among different sections are generally consistent with the regional differences in cavitation action revealed by the numerical simulation.
The Rortex vector, also referred to as Liutex in part of the literature, provides a rotation-axis-based measure of local rigid-body rotation and supports Rortex–shear decomposition and derivative-based vortex dynamics analysis. However, the original Rortex field may exhibit non-smooth derivatives near vortex boundaries, leading to spurious spikes and oscillations in gradients, Laplacians, material derivatives, viscous terms, and Rortex–shear interaction terms. To improve derivative robustness, a regularized Rortex magnitude Rreg is introduced. The formulation preserves the rigid-body rotation limit and the principal vortical structures identified by the original Rortex while smoothing the transition near vortex boundaries. Its behavior is examined using the Lamb–Oseen vortex, two- and three-dimensional Taylor–Green vortices, the Burgers vortex, and a two-dimensional cylinder wake. The canonical cases show that Rreg substantially reduces boundary-induced artifacts in first- and second-order derivatives while retaining the main vortex topology. In the cylinder wake, the regularized formulation yields more robust finite-difference evaluations of temporal, convective, viscous, material-derivative, and Rortex–shear interaction terms. These results demonstrate that the proposed regularization improves the numerical robustness of Rortex-based differential diagnostics and provides a more reliable basis for vortex-boundary and vortex-dynamics analyses.
Spectral-element simulations using Nek5000 are performed to compare three-dimensional lid-driven cavities with and without a central bottom-mounted cubic obstacle at Re = 1000, 3200, and 5000. The obstacle has a side length of 0.2L and occupies only 0.8% of the unobstructed cavity volume but directly intersects the near-bottom return branch of the primary circulation. The analysis considers the mean flow, second-order statistics, finite-time Q-criterion occupancy, and the spectra and coherence of an eight-probe network. All coordinates are normalized by the cavity side length L; z/L = 0.1 denotes a near-bottom horizontal section passing through the obstacle, and y/L = 0.5 denotes the spanwise mid-plane. The obstacle redistributes the return flow over its top and along its spanwise sides and modifies the primary-recirculation closure position. At Re = 5000, the total displacement of the primary-recirculation critical point reaches 0.2511L. At Re = 3200, the maximum fluctuation kinetic energy increases to 2.88 times that of the no-obstacle case, while the fluid-volume fractions containing 50% and 90% of the total fluctuation kinetic energy increase from 10.1% to 20.6% and from 49.8% to 67.8%, respectively. At Re = 5000, the local maximum decreases, whereas the corresponding volume fractions increase from 18.0% to 28.7% and from 67.2% to 74.0%, indicating broader spatial redistribution. High-occupancy strong rotational events are concentrated mainly in the right-side inflow, spanwise bypass, and obstacle-top regions. The nondimensional frequency is defined as f * = fL/U0, where f is the dimensional frequency, and U0 is the maximum lid velocity. At Re = 3200, the peak probe-network mean coherence increases from 0.657 to 0.883 and shifts to f * = 0.036. At Re = 5000, the local spectral responses are distributed among multiple frequency bands, and the peak coherence decreases from 0.494 to 0.266. These results demonstrate a clear Reynolds-number dependence in the effects of local bottom blockage on the mean recirculation and unsteady spatial organization of the closed cavity.
The present study investigates heat transfer behavior under steady and mechanically perturbed free-surface conditions in an open-channel flow using single- and two-heated test module configurations. The perturbation is generated using an Arduino-controlled rack-and-pinion mechanism driven by stepper motors. Heat transfer performance is evaluated using the Nusselt number (Nu), while the effects of imposed wave motion and module spacing are systematically examined. For a single module, Nu increases with increasing power input (Q) under both conditions; however, the relative enhancement decreases from approximately 36% at Q=347 W to 18% at Q=546 W. The influence of wave characteristics is further analyzed over a frequency range of 0.5–0.9 Hz and an amplitude range of 7–41.8 mm, where the variation in Nu remains within nearly 17%, indicating weak sensitivity of heat transfer within the investigated range. Particle image velocimetry analysis reveals that modulation of the separated shear layer and coherent vortical structures enhances near-wall mixing and thermal transport. A two-module investigation is subsequently performed by varying the normalized spacing distance between the modules. Under steady conditions, the upstream module exhibits a nearly invariant Nu, whereas the downstream module shows enhanced heat transfer as spacing increases. Under perturbed conditions, the upstream module exhibits a spacing-dependent modulation in Nu. This modulation is governed by the relative timing between wake convection and the imposed free-surface oscillation, with synchronization producing the heat-transfer maxima and desynchronization producing the minima. In contrast, the downstream module follows trends similar to those under steady conditions, indicating that its thermal transport remains predominantly governed by wake evolution.
Effects of inlet-air temperature on the hot-spot dynamics in a dual-stage swirl spray combustor were investigated using large-eddy simulation with a flamelet-generated manifold combustion model. The mesh resolution was tested with the Pope criterion, and the predicted velocity was validated with particle image velocimetry measurements. Two kinds of flame conditions were designed with improved inlet-air temperature: the constant-velocity strategy from 403 to 473 K, and the constant-flow-rate strategy from 473 to 543 K, featured by increased inlet velocity. The results show that increased inlet-air temperature consistently improves the exit-temperature uniformity for the two strategies. The hot-spot formation is found to be sustained by diffusion-flame-dominated heat release. The formation and dissipation of the hot spots are systematically revealed. With a lower inlet temperature of 403 K, the primary recirculation zone (PRZ) is the weakest, which permits deep spray penetration and strong fuel accumulation, leading to aggregation-dominated hot spots. These hot spots are trapped within the PRZ and persist downstream, thereby deteriorating the exit temperature uniformity. With elevated inlet temperature for both strategies, the hot-spot dissipation is enhanced following a similar mechanism, i.e., with strengthened vortices and turbulent mixing promoting the hot-spot stretching and breakup, which lead to better temperature uniformity. Especially at 543 K, the hot spots dissipate over a short axial distance rapidly before reaching the exit. These findings provide new insights into the formation, evolution, and dissipation of hot spots in swirl spray combustors through detailed analysis of flow-flame dynamics.
Conventional turbulence models based on the linear eddy-viscosity hypothesis cannot adequately represent turbulence anisotropy, which limits their predictive accuracy for three-dimensional separated flows around the Ahmed body. Within the Reynolds-averaged Navier–Stokes framework, this study develops a nonlinear Reynolds-stress anisotropy correction model for Ahmed-body wakes based on a tensor-basis neural network (TBNN), with a newly introduced canonical-flow training dataset and a wall-distance-based blending treatment. A posteriori evaluations of the Ahmed body flow demonstrate that the enriched training dataset improves the predictive accuracy of the TBNN model. At the same time, the wall-distance-based blending enhances numerical convergence and robustness. Compared with the baseline RANS model, the proposed model more accurately reproduces the major wake structures, including the recirculation region and C-pillar vortices, and yields flow-field predictions closer to those obtained from detached-eddy simulation (DES). Across rear-slant angles from 0° to 40°, the model exhibits favorable generalization for configurations with wake regimes similar to those in the training dataset. For the 5° configuration, whose wake regime lies outside the range covered by the training data, the improvement is comparatively limited. The proposed model also reduces computational time by 42% relative to DES, indicating its potential as an efficient turbulence modeling approach for automotive aerodynamic simulations.
Tracheal stenosis significantly alters respiratory airflow and influences the transport and deposition of inhaled drug particles. The present study numerically investigates aerosol transport, particle deposition, and thin-film formation in disease-specific tracheobronchial airways with mild (15%), moderate (45%), and extreme (70%) stenosis under a realistic inhalation maneuver. The novelty of this study lies in its disease-specific assessment of aerosol drug delivery across different degrees of tracheal stenosis under physiological conditions. Furthermore, the combined Eulerian wall film and discrete phase model (DPM) captures both particle deposition and post-deposition liquid film behavior, providing a more realistic representation of inhaled drug transport than conventional DPM-based approaches. The investigation evaluates airflow characteristics, deposition efficiency, film thickness, and area coverage for aerosol particles of 1, 5, and 10 μm. The results indicate that increasing stenosis severity significantly alters airflow asymmetry, leading to directionally biased jet formation and distinct particle deposition behavior. The peak velocity magnitude along the stenosis increases from nearly 4.2 to 12 m/s, leading to an equally strong increase in vorticity generation (4000 to 12 000 s−1) as severity increases from mild to extreme. As a result, the drug deposition asymmetry also changes significantly, leading to a 7.51 times higher film thickness in the right lung for the extreme cases, compared to 2.49 and 0.07 times in the similar moderate and mild stenosis cases, respectively. Clinically, extreme stenosis promotes localized drug accumulation and non-uniform aerosol delivery due to jet-induced asymmetric particle transport, highlighting the need for patient-specific inhalation therapy optimization.
Off-design operation reorganizes centrifugal-pump pressure pulsations through interaction between the rotating impeller discharge and the stationary volute. To clarify how the non-uniform impeller-outlet pressure field is concentrated and modulated in the volute, unsteady computational fluid dynamics was performed at 0.8Qd, 1.0Qd, and 1.2Qd. Fast Fourier transform, proper orthogonal decomposition (POD), variational mode decomposition, sample entropy, permutation entropy, and Lempel–Ziv complexity were combined to characterize the frequency content, spatial organization, temporal scales, and complexity of the pressure response. The 1.2Qd condition produced the strongest pulsations. The impeller response was dominated by the shaft frequency fr = 29.17 Hz and its low-order harmonics, whereas the volute response was governed by the blade passing frequency fimp = 175 Hz and its harmonics. The first four POD modes captured 91% and 90% of the fluctuating-pressure energy in the impeller and volute, respectively. The impeller modes were spatially distributed and phase shifted, whereas the volute modes were localized near the tongue and impeller outlet. The dominant impeller intrinsic mode functions retained 96.2% and 96.5% of the decomposed energy and remained close to the shaft-frequency scale; the dominant volute components exceeded 85% and clustered near fimp and 2fimp. Complexity analysis revealed an ordered low-frequency backbone with low-energy high-frequency complexity in the impeller, but stronger complexity across the blade passing frequency, its harmonics, and higher-frequency scales in the volute. The volute tongue concentrates and modulates the non-uniform impeller-outlet pressure field in a region-dependent multiscale response.
Erosive wear of centrifugal pumps under solid–liquid two-phase flow critically limits long-term stable operation of fluid transport systems. Current studies lack an in-depth understanding of particle size–solid concentration synergistic effects on internal flow structures and the hydrodynamic link between flow characteristics and wall erosion. Using a single-stage closed-impeller centrifugal pump, this work performs computational fluid dynamics–discrete phase model coupled simulations and systematic erosion tests across three particle sizes (0.6, 0.9, and 1.5 mm) and three solid volume fractions (2.5%, 5%, and 7.5%). The wear resistance and failure mechanisms of atmospheric plasma-sprayed alumina and high-velocity oxygen-fuel-sprayed tungsten carbide–10 wt. % nickel coatings are comparatively analyzed via three-dimensional (3D) optical profilometry, scanning electron microscopy, and energy dispersive spectrometry. Key findings are threefold. First, the impeller outlet average velocity shows non-monotonic variation with rising particle size at high concentrations, arising from the competition between centrifugal particle inertial migration and clustering-induced flow passage blockage. Second, erosion hotspots (blade pressure side trailing edge and volute tongue) are determined by internal flow topology; higher solid concentration intensifies erosion but does not alter hotspot locations. Third, coating failure modes are strongly flow-dependent: Low-angle high-velocity impact at passage outlets causes plastic deformation and micro-cutting, while high-angle inlet impact dominates brittle spalling. This study clarifies the hydrodynamic formation mechanism of wear hotspots and establishes the intrinsic correspondence between local flow parameters and coating failure modes, providing physical guidance for targeted anti-wear design of centrifugal pumps. The coating performance conclusions are valid under the tested conditions.
Downburst events generate extreme near-surface winds over a considerable area, posing significant threats to structures. The existing empirical models usually model the vertical and radial steady-state profiles of the downburst separately based on empirical equations. However, these models are difficult to consider the effects of the nonlinear growth of boundary layer thickness, and a spatial wind velocity field encompassing the core region has yet to be established. This study proposes a novel empirical model based on a generalized modal decomposition. It features an improved vertical shaping function for the radial velocity and a set of data-based characteristic functions for the model parameters. Furthermore, the integral expression for the vertical velocity field is derived based on the mass continuity equation. Detailed computational fluid dynamics (CFD) simulations using large eddy simulation were conducted for model calibration and validation. The results demonstrate that the improved vertical shaping function significantly improves the accuracy of the simulated radial velocity, particularly in the near-wall region near the downburst center. By employing the empirical model alongside the CFD simulation data, continuous radial and vertical velocity fields in space of downbursts are constructed for the computational region. These fields show excellent agreement with the validated CFD simulations and available wind tunnel test data, indicating that the model can provide a valuable reference for wind load calculation and structural safety assessment of structures subjected to downburst winds.
Central vertical stabilizers are widely employed to enhance the aerodynamic stability of long-span bridges with streamlined box girders, yet the fundamental mechanisms underlying their effectiveness, particularly regarding the critical role of solidity ratio, remain incompletely understood and debated. This study comprehensively investigates the flutter control mechanisms of central vertical stabilizers, explicitly evaluating the impact of solidity ratio. By integrating the bimodal flutter analysis with surface pressure measurements, the research provides novel insights into the spatiotemporal distribution of self-excited forces during coupled deck motion. The results demonstrate that central vertical stabilizers increase the uncoupled torsional aerodynamic damping significantly, effectively suppressing coupled flutter. However, an insufficient solidity ratio (below 50% in this case) drastically diminishes this stabilizing effect. Pressure distribution analysis demonstrates that self-excited forces are mainly generated by the windward edge of the deck section, and the properties of self-excited forces generated by heaving and torsional motions differ primarily in their phase relative to the motion. Further, it is found that central vertical stabilizers fundamentally alter the flow pattern over the deck: they disrupt the large-scale separation bubble, splitting it and delaying reattachment downstream. This vortex restructuring induces a critical phase shift (30°–40° lag in this case) in self-excited forces behind the central vertical stabilizers. This phase shift is identified as the primary mechanism driving the observed increase in local aerodynamic damping and reduction in stiffness within that region, thereby enhancing the overall flutter stability.
To investigate the nonlinear flutter of bridge girder under non-uniform wind fields, a twin-box girder was studied via three-dimensional computational fluid dynamics free-vibration numerical simulations under four typical wind fields: uniform wind field (A1), non-uniform wind speed with uniform wind angle of attack (A2), uniform wind speed with non-uniform wind angle of attack (A3), and both non-uniform (A4). Within the investigated cases, the steady-state flutter amplitude and fluctuating aerodynamic forces exhibit the same trend, following A3 > A1 > A4 > A2. The spanwise correlation of fluctuating aerodynamic forces is strongest in A1 and A3, followed by A4, and weakest in A2. Surface pressure analysis identifies the leading edge of the upper surface as the critical region affecting correlation variations. Flow field analysis reveals that non-uniform wind speed weakens spanwise vortex synchronization and reduces aerodynamic correlation, whereas non-uniform wind angle of attack promotes vortex development and may enhance nonlinear aerodynamic characteristics. The vortex shedding frequency of the large-scale dominant vortices (DVs) is close to the structural vibration frequency, and thus, they are primarily associated with the fundamental component of the fluctuating aerodynamic forces. The smaller-scale subordinate vortices (SVs) are generated within the DVs and only exhibit periodic shedding when the DV scale is sufficiently large, resulting in higher shedding frequencies associated with higher-order harmonic components. In case A3, the enhanced DV scale promotes the development and shedding of SVs, thereby inducing more pronounced higher-order harmonic characteristics in the aerodynamic forces.
The interaction between marine propellers and sediment-laden seabeds is of significant importance for navigation safety, environmental protection, and the hydrodynamic performance of marine vehicles operating in shallow waters. In this study, wake evolution and mud entrainment of the National Research Council of Italy-Institute of Marine Engineering (CNR-INM) E779A propeller in a water–mud stratified environment are studied via improved delayed detached eddy simulation combined with the volume of fluid. The numerical methodology is first validated against available experimental data for propeller open-water performance and wake flow characteristics. The effects of the water–mud interface on propeller hydrodynamic loads, vortex evolution, turbulence transition, and sediment transport are subsequently analyzed. The results show that the presence of the mud layer induces pronounced periodic fluctuations in thrust, torque, and lateral forces due to the asymmetric interaction between the propeller wake and the water–mud interface. Compared with open-water conditions, the mud environment reshapes propeller wake evolution by suppressing secondary tip-vortex pairing, triggering earlier vortex instability and faster wake breakdown. Correspondingly, Reynolds stress redistribution is enhanced, and the turbulence structure transitions more rapidly from anisotropic to isotropic states, promoting momentum exchange across the interface. These modifications of wake dynamics substantially increase sediment entrainment and transport, resulting in intensified mud diffusion within the propeller slipstream. The present study reveals the fundamental role of wake instability in governing sediment entrainment processes in water–mud stratified environments and provides new insights into propeller-induced seabed interactions in shallow waters.
Transient shock evolution, pressure-wave dynamics, and shock-wave/boundary-layer interactions (SBLI) induced by moving boundaries are investigated during the opening process of a supersonic inlet. A dynamic-mesh-based numerical framework is developed to couple the rotational motion of the inlet cover with the unsteady compressible flow field. Using an integral solid rocket ramjet as a representative application, the effects of rotational inertia, spring preload, and incoming Mach number are systematically examined. The results show that inlet-cover motion is governed primarily by aerodynamic loading, with aerodynamic torque remaining substantially larger than both the spring-preload torque and gravitational moment throughout the opening process. Rotational inertia is identified as the dominant structural parameter. Although it does not alter the sequence of transient shock evolution, it changes the characteristic timescale of moving-boundary evolution and regulates the synchronization among geometric opening, shock evolution, pressure-wave propagation, and SBLI development. In contrast, spring preload only slightly modifies the opening history and has little influence on the subsequent transient flow evolution. Within the investigated range of Ma = 2.8–3.2, the incoming Mach number exhibits the strongest influence on transient shock evolution among the parameters considered. Increasing Mach number enhances aerodynamic loading and flow compressibility, accelerating moving-boundary evolution, pressure-wave propagation, and SBLI development, thereby promoting earlier shock displacement and stronger flow separation. The results further demonstrate that SBLI acts as the key intermediary mechanism linking pressure-wave propagation to transient shock evolution. Overall, transient flow evolution is governed by the coupled interaction between moving-boundary evolution and internal compressible-flow dynamics, providing new physical insight into moving-boundary compressible flows under time-varying geometric constraints.
Microfabrication techniques for rectangular microchannels typically produce heterogeneous surface textures, leading to distinct roughness and slip properties at lateral and top/bottom walls. This anisotropy in surface properties modifies fluid–wall interactions and has important consequences for flow dynamics, particularly in the determination of effective slip lengths and channel permeability. In practice, slip lengths inferred from velocity measurements along a single confinement direction often fail to reconcile with observed flow rates, suggesting the presence of unresolved multidimensional effects. In this work, an exact analytical solution is derived for oscillatory Newtonian flow in a rectangular microchannel with anisotropic slip boundary conditions. Different slip lengths are prescribed at the lateral and top/bottom walls in order to quantify their coupled influence on both the velocity field and the volumetric flow rate. The solution reveals a masking effect in which the flow rate caused by the primary slip length could be effectively reduced even by an order of magnitude, or magnified twofold, by the presence of a discrepant slip at the secondary walls. Based on this analysis, explicit correlations are obtained for an effective slip length that accounts for the interaction between local wall-dependent slip lengths. These results provide a practical framework to reconcile discrepancies between local velocity measurements and global flow rates and enable indirect estimation of slip properties along the secondary confinement direction, which are typically inaccessible experimentally. The proposed formulation offers a tractable route to incorporate heterogeneous surface effects into the characterization and design of microfluidic and porous systems under oscillatory forcing.
Free-surface waves strongly modify the near-airfoil flow field in close proximity to wavy surfaces. This paper investigates the aerodynamic, wake, and modal characteristics of the National Advisory Committee for Aeronautics 6412 airfoil near a wavy surface at different water-surface clearances and angles of attack using numerical simulations based on the volume of fluid method. The results show that larger angles of attack and smaller water-surface clearances lead to higher mean lift and stronger lift fluctuations, indicating more pronounced unsteady aerodynamic characteristics. Affected by the periodic motion of the wave free surface, the lift coefficient varies periodically with the wave phase. Moreover, the dominant frequency of the lift signal is nearly identical to the wave frequency, indicating that wave motion is the primary source of unsteady aerodynamic forces. As the wave surface rises and approaches the underside of the airfoil, the flow passage beneath the airfoil narrows, leading to a redistribution of the surface pressure and a corresponding phase-dependent variation in lift. Further higher-order dynamic mode decomposition analysis indicates that the wave frequency captures the fundamental frequency of the dominant mode, causing the near-wake structure to exhibit a periodic evolution consistent with the wave motion. An increase in the angle of attack expands the high-amplitude distribution of the dominant mode in the trailing edge and near-wake regions, indicating an enlargement of the area influenced by wave-induced coherent structures. These results provide useful guidance for aerodynamic-load evaluation and flow-mechanism analysis of near-surface ground-effect aircraft in wave environments.
Rainfall-induced soil erosion (SE) involves a hydrodynamic transition from distributed sheet flow to concentrated rill flow over an evolving mobile bed. To quantify the hydrodynamic mechanisms and flow–sediment interactions governing the interrill–rill transition in soils with contrasting particle-size distributions, 50 rainfall simulation experiments were conducted using sandy and loamy sand soils under five rainfall intensities (40–90 mm h−1) and five slope gradients (7.5%–17.5%). The sandy soil exhibited a transport-controlled response, with limited SE despite increasing hydrodynamic forcing, whereas the loamy sand soil developed hydraulically connected rills, resulting in an energy-controlled erosion regime. Flow remained laminar throughout all experiments, and supercritical flow occurred only under the highest rainfall intensity–slope combinations in the loamy sand soil. These findings suggest that supercritical flow accompanies advanced rill development but is not required for rill formation. Rainfall intensity dominated SE when all erosion regimes were analyzed together, whereas slope gradient became the dominant control in regime-specific analyses. Moreover, separating the interrill and rill regimes improved model performance for both soils, particularly for the loamy sand soil, where Nash–Sutcliffe efficiency increased from 0.59 to 0.97. Among the hydrodynamic parameters, unit stream power (P) emerged as the most effective predictor of SE. Receiver operating characteristic analysis identified critical P thresholds of 0.003 284 and 0.004 609 m s−1 for the sandy and loamy sand soils, respectively. Unlike the sandy soil, where particle motion and rill formation were separated by a broad energy interval, these processes occurred over a much narrower energy range in the loamy sand soil.
Shock–bubble interaction constitutes a canonical problem in compressible turbulence, governed by the interplay of compressive and vortical dynamics. Numerical simulations are employed to examine light (He) and heavy (R22) bubbles using dynamic mode decomposition and Favre-weighted turbulent kinetic energy spectra. The flow initially displays steep, shock-dominated spectra consistent with Burgers-type scaling. Following shock passage, the light bubble generates coherent jet-driven vortices and a hierarchical energy cascade, producing departures from k−2 scaling. In contrast, the heavy bubble suppresses large-scale coherence and dissipates energy rapidly. These findings highlight that spectral evolution is dictated by the competition among baroclinic vorticity generation, compressibility, and shear-driven turbulence. Although the numerical analysis clarifies the persistence of k−2 spectral scaling in shock–bubble interactions, its applicability is limited by the two-dimensional inviscid framework adopted for incident shocks at Mach 1.22 and Mach 1.8. Extrapolation to fully three-dimensional flows requires caution, as additional dissipative and vortical mechanisms may modify the scaling behavior.
Flow-induced noise, as an acoustic phenomenon generated by fluid motion, mainly originates from unsteady pressure fluctuations exerted by turbulent flow on solid surfaces, with the resulting acoustic energy radiating outward through the fluid medium. For underwater vehicles, stealth is one of the most critical performance indicators. As the structural complexity of such vehicles increases, various appendages inevitably alter the local flow field during navigation, thereby intensifying the generation of flow-induced noise. Among these, protruding structures, such as the sail and stern rudders, as well as recessed structures, such as flood holes, are particularly significant contributors to flow-induced noise because of their pronounced effects on flow separation, vortex evolution, and pressure fluctuations. A review of existing domestic and international studies on hydrodynamic noise indicates that systematic investigations into the influence of different appendage geometries on flow-induced noise remain relatively insufficient. Accordingly, this study focuses on the mechanism of flow-induced noise and selects typical protruding structures and recessed structures as research objects. Their effects on flow-induced noise are systematically analyzed, and the relative intensity of flow-induced noise generated by underwater vehicles under different structural configurations is revealed. The results show that the sail fillet, stern rudder configuration, flood-hole shape, flood-hole depth, and flood-hole layout all significantly affect the flow-induced noise. The sail fillet reduces the total sound pressure level (Total SPL) by approximately 10 dB, with local reductions reaching about 15 dB, while flood-hole shape and layout can lead to larger SPL variations. Furthermore, this study provides theoretical and methodological support for the optimization and noise reduction of underwater vehicles.
