For steady flow past a circular cylinder, analytical solutions can be obtained describing uniform flow and a stable pair of symmetric vortices. The latter approximates the viscous vortex flow at low Reynolds number, prior to the onset of vortex shedding. Herein, we employ the analytical Föppl vortex solution to model idealised steady and unsteady heat transfer from a cylinder, and explore connections with viscous theory for this problem. We use numerical methods based on the combination of a streamline-tracing technique with operator splitting to obtain fast, accurate solutions of the convection–diffusion equation. Comparison between results from our model with those for viscous flows, based on geometric similarity criteria, show significant similarity at low Reynolds numbers, but exhibit systematic discrepancies at higher Reynolds numbers. This paper showcases important differences between viscous and inviscid heat transfer, and suggests the use of the simple Föppl vortex case as a benchmark for numerical studies.
Friction drag reduction by delaying the laminar-turbulent transition has a huge potential in aerospace applications. Miniature vortex generators (MVGs) are a promising passive control method to attenuate the growth of Tollmien-Schlichting (TS) waves, the dominant instability mechanism that triggers transition in the presence of low sweep. MVGs dampen the TS wave growth by introducing streamwise-elongated spanwise-periodic slow-fast regions (streaks), which are generated by counter-rotating streamwise vortices through the lift-up mechanism.In the development of MVGs, it is important to assess the performance of the flow control method in the presence of changes in the nominal parameters, such as off-design conditions and uncertainties. Therefore, statistical uncertainty analysis of the MVGs is performed using the direction-adaptive sparse grid stochastic collocation method. Two uncertain parameters are considered: change in the free-stream velocity magnitude and change in the sweep angle. Two configurations are investigated in this study: one from previous wind-tunnel experiments (Sattarzadeh & Fransson, Exp. Fluids 56, 58 (2015)), and one based on a numerical study (Szabó et al. Comp. & Fluids, 269, 106123 (2024)), whose methodology was utilized in this work. The quantities of interest are the streak amplitude and the transition Reynolds number. It is shown that the presence of uncertainties can severely impact the MVG performance. Changes in the sweep angle are much more influential than changes in the velocity magnitude, and overall, a deteriorated MVG performance is expected. Moreover, the importance of appropriately choosing the input probability density distribution is also highlighted.
A fixed rectangular structure with two unequal thin plates protruding downward from the sides is considered in a free surface of water of finite depth to study wave scattering and the forces acting on it. The study is carried out by converting the boundary-value problem into a system of integral equations. A Galerkin method is employed to obtain a very accurate approximate solution of the integral equations. The findings indicate that the wider rectangular structure with unequal plates transmits less wave energy than either the equal-plate or single-plate structures. The structure with unequal plates experiences greater wave forces and overturning moments than those with equal plates and a single plate. However, increasing the structure width can mitigate wave forces and the resulting overturning moments. In addition, a comparison of the transmission coefficient with an empirical formula of heave motion reveals that the proposed structure in a fixed position transmits less incident wave energy. The fluid velocity is decreased when the unequal plates are interchanged. The findings help engineers estimate the wave-scattering performance of a new breakwater configuration integrating a rectangular structure and unequal thin plates.
Shock wave/boundary layer interactions (SWBLIs) play a significant role in aeronautics and aerospace engineering. In this study, the well-validated Spalart-Allmaras (S-A) model has been applied to investigate the ramp-induced SWBLIs, with a particular focus on the effects of Mach number on flow structure, wall pressure distribution, and interaction length scales. The results show that an increase in Mach number generally postpones the onset of separation and increases the pressure-plateau values. An inviscid model has been employed to elucidate the relationship between the pressure plateau values and the specific angles. Additionally, we found that the classical free-interaction theory (FIT) may not accurately predict post-separation pressure under certain strong-interaction conditions. Finally, the previously proposed scaling law for interaction length has been extended to the supersonic regime by integrating a large amount of classical experimental datasets and our Reynolds-averaged Navier-Stokes (RANS) results. Therefore, this study effectively fills the vacuum in the research of interaction length scales for strong supersonic SWBLIs.
Owing to its conceptual simplicity, computational efficiency, and ability to achieve high-order accuracy, the Finite Difference Method (FDM) has been widely employed in Computational Fluid Dynamics (CFD). Nevertheless, when applied to complex geometries or curvilinear grids, coordinate transformations may introduce geometrically induced errors (GIEs), which can degrade numerical accuracy. The Geometric Conservation Law (GCL) was introduced to eliminate such errors. However, conventional GCL algorithms are typically constructed under the freestream (uniform-flow) assumption, and their performance for non-uniform flows remains less understood. Our recent investigations reveal that even freestream preservation (FP) schemes that satisfy the GCL still suffer from GIEs when computing linear streams whose first derivatives remain constant, thereby leading to a loss of accuracy. To address this issue, this study proposes a numerical construction framework, termed the Straight-Stencil Paradigm (SSP), and further develops a Straight-Metric Linear-Preserving (SMLP) scheme based on this paradigm. This method constructs local straight-line stencils on curvilinear grids to evaluate geometric metrics and physical quantities at the half-nodes, thereby improving geometric consistency and reducing the impact of grid curvature and non-uniformity. Numerical tests indicate that the SMLP scheme improves accuracy preservation and robustness on curvilinear grids, particularly under grid distortion. The present work provides a useful approach for enhancing numerical performance on complex configurations.
Compact and efficient absorption refrigeration systems can effectively utilize industrial waste heat and renewable energy through microchannel membrane-based generator. Hydrophobic membrane plays a vital role within the generator. The effect of membrane hydrophobicity on the dynamic behavior of bubble was studied by numerical simulation. It was found that the bubble venting process can be divided into four stages: bubble growth, liquid film rupture and bubble deformation, alternating spreading and contracting movements, and stable bubble removal. In the second stage, after the bubble contacts the membrane, it primarily exhibits spreading behavior, with obvious venting behavior not occurring immediately. As membrane hydrophobicity increases, the fourth stage gradually disappears. During the venting process, an increase in bubble volume within the microchannel (such as due to higher wall superheat, increased wall hydrophobicity, or a greater number of bubbles) alters the frequency and amplitude of bubble movement within the above-mentioned stages. However, it does not significantly change the overall movement pattern. An increase in the inlet Reynolds number facilitates bubble removal but also reduces the bubble's residence time in the microchannel. Therefore, determining the optimal inlet Reynolds number is essential. Compared to hydrophobic membrane, superhydrophobic membrane exhibit higher exhaust efficiency.
The calibration of RANS turbulence models is essential for improving predictive accuracy. However, existing approaches are often limited to a single flow scenario that lacks generalizability, or they overfit closure coefficients to a selected set of flow configurations. This study introduces the Reinforced Holistic Calibration (RHC) framework that extends existing calibration strategies through an iterative reinforcement mechanism. RHC identifies cases with the largest prediction errors and recalibrates the RANS model within a multi-case loop, thereby systematically improving model generalizability while mitigating overfitting.The RHC framework was demonstrated by calibrating the k-ω Shear Stress Transport (SST) turbulence model for flows over wall-mounted rectangular prisms at various freestream velocities. Time-resolved particle image velocimetry (TR-PIV) measurements were carried out in a dedicated wind-tunnel campaign, where LEGO-based models enabled systematic and robust variations in prism geometry and spacing. The experimental campaign provided detailed turbulent flow fields for the calibration and validation phases.The optimized closure coefficients showed systematic changes: dissipation-related terms (β1, β2, β∗) were modified to adjust modeled dissipation of k and ω, while the production and stress limiter coefficients (γ1, γ2, a1, b1) were tuned to suppress excessive ω production and limit turbulent viscosity in separation regions. The calibration resulted in elevated turbulent kinetic energy levels within separation and wake zones, elongated reattachment lengths, and intensified after-body interactions in double-block configurations.The RHC framework delivers generalizable calibration, significantly enhancing the k-ω SST model’s predictive fidelity for flow over wall-mounted prisms. Its iterative procedure offers a cost-effective calibration for turbulence models.
This research examines the aerodynamic behavior of a commercial electric UAV propeller featuring an S-shaped blade geometry induced by varying blade deflection angles, using both experimental measurements and CFD simulations. The SST k-ω turbulence model was employed to capture the turbulent flow behavior, and the numerical predictions showed good agreement with the experimental data, with a maximum deviation of 5.57%. Eight propeller configurations, with deflection angles ranging from 0° to 105° in 15° increments, were analyzed. Results indicate that increasing the deflection angle leads to a reduction in aerodynamic performance, power demand, and efficiency. The optimum performance was observed at different advance ratios (J), with the baseline propeller (0° deflection) providing the best balance between thrust and efficiency, achieving a maximum efficiency of 0.67 at J = 0.9 and maintaining good performance over a wide range of J. Propellers with higher blade deflection angles exhibited degraded performance with lower thrust and efficiency, and the optimal efficiency point shifted toward different J values. Although larger deflection angles resulted in lower efficiency, they also reduced power consumption. These findings highlight the importance of optimizing both the blade deflection angle and sectional angle of attack to balance energy efficiency and mission-specific performance, offering valuable guidance for designing electric UAV propulsion systems with improved endurance and reliability.
In high-pressure fuel injection systems, the rapid opening of the outlet valve induces sudden depressurization, generating transient pressure waves and flow rate oscillations that significantly affect engine power output and pollutant emissions. Nevertheless, the underlying mechanisms coupling the pressure surge and flow rate oscillation remain elusive. In this study, by constructing a simplified model of a high-pressure diesel fuel flow pipe, we elucidate the coupling mechanisms between pressure wave propagation and flow rate oscillations following sudden depressurization initiated by valve opening. Our computational fluid dynamics results reveal how transient pressure waves form and propagate back and forth within the pipe, inducing a segmental acceleration pattern in the local flow rate. We identify fluid compressibility as the source of flow rate oscillation and demonstrate the critical influence of pipe length on the periods of both pressure and flow rate oscillations. To interpret the intricate relationship between pressure wave attenuation and flow rate oscillations, we propose a multi-cycle segmental acceleration mechanism, highlighting the critical role of pressure wave propagation in flow rate oscillation.
This study investigates the migration of particles with different geometries in a two-dimensional channel flow of power-law fluid. The particle shapes considered include equilateral triangles, squares, regular pentagons, regular hexagons, and circles. The immersed boundary-lattice Boltzmann method (IB-LBM) is employed to analyze variations in equilibrium positions, total radian value (θ), and trajectory wavelength (λ) during particle migration. The results demonstrate that in power-law fluids, the equilibrium position of equilateral triangular particles is closer to the channel center than that of other shapes. As the number of sides N increases, the equilibrium position shifts gradually toward the channel wall, eventually approaching that of circular particles. In Newtonian fluids, the trajectory wavelength (λ) is the longest, while the total radian value is the smallest. For a given particle, an increase in the power-law index (n) moves the equilibrium position closer to the channel center. Additionally, the equilibrium position increases with decreasing Reynolds number, and particles with a larger blockage ratio (k) exhibit equilibrium positions nearer to the channel center in power-law fluids.
Most existing studies have investigated dissolution in shear flow without considering a first-order heterogeneous reaction. This study introduces a coupled lattice Boltzmann smoothed profile method (LBM-SPM) framework to simulate the dissolution of moving reactive cylindrical particles in a shear flow under a first-order heterogeneous reaction. Unlike previous approaches that primarily focus on Dirichlet boundary conditions, our method employs extrapolation techniques to impose a reaction boundary condition on moving solid-fluid interfaces. The accuracy of this mesoscopic-scale model is validated against macroscopic models numerically solved using COMSOL. Excellent agreement with COMSOL results confirms the successful implementation of a reaction boundary condition. Although it is common in LBM-SPM studies to assume that particles maintain their cylindrical shape during boundary reactions, this work demonstrates that this assumption is not always valid. Accordingly, we investigate the ranges of Damköhler numbers over which this assumption is violated. Results show that as the Damköhler number increases (especially for Da > 1), non-uniform dissolution leads to loss of circularity, indicating that the standard LBM-SPM model should be applied with caution.
Vortices are fundamental coherent structures whose statistical characteristics reveal essential properties of turbulence. Previous studies on open-channel flows (OCF) have predominantly focused on the characteristics of spanwise vortices within two-dimensional planes, whereas the behaviors of streamwise and vertical vortices, as well as the true three-dimensional scale characteristics of vortices, remain largely unexplored. This study employs direct numerical simulation (DNS) to compare the two-dimensional and three-dimensional spatial statistical characteristics of vortices in OCF and closed-channel flow (CCF) at a friction Reynolds number of Reτ= 500, revealing the influence of the free surface on vortex characteristics in OCF. Prograde and retrograde vortices (i.e., spanwise vortices whose rotation is aligned with or opposite to the mean-shear-induced rotation), together with streamwise and vertical vortices, are identified via the λci criterion. Vortex radii and circulations are extracted based on the intrinsic properties of the vortices, and the VATIP algorithm is utilized to reconstruct three-dimensional vortex topologies for scale analysis. The results show that the vortex statistics exhibit distinct depth-dependent variations. In the region 0 <y/h< 0.10, the radius trends differ among vortex types. Meanwhile, the circulations of prograde and vertical vortices decrease rapidly, whereas the circulation of streamwise vortices increases. This increase is consistent with the interaction between near-wall streaks and quasi-streamwise vortices. The radius-circulation relationship of prograde vortices and the spanwise energy-flux distribution further suggest that vortex-intensity enhancement associated with an inverse-energy-cascade-like process may occur under strong mean shear. In the region 0.10 <y/h< 0.80, the mean radii of different vortex types gradually increase, which may be associated with interactions or merging among neighboring rotating structures away from the wall; however, their mean circulations generally decrease. In the region 0.80 <y/h< 1.0, compared with CCF, the radii and circulations of spanwise and streamwise vortices in OCF decrease more rapidly, which is consistent with the wall-normal constraint imposed by the free surface, whereas vertical vortices exhibit an increase in radius. The three-dimensional scale analysis further shows that, in the region 0.70 <y/h< 0.95, vortices exhibit a tendency toward flattening, characterized by a decrease in the wall-normal scale and increases in the streamwise and spanwise scales. Pressure-strain redistribution near the free surface provides a possible statistical explanation for this anisotropic deformation.
The energy absorption characteristics of three-row traveling wave plates are studied by two-dimensional numerical simulation. The influence of flow direction spacing, lateral spacing, and phase difference on the energy absorption efficiency of the traveling wave plates is analyzed. The results show that the energy absorption efficiency of the traveling wave plates is significantly related to spacing and phase difference. Specifically, for the plate1, the efficiency initially increases and then declines with an increase in flow direction spacing at a phase difference of 0°, suggesting an optimal spacing for peak efficiency. At a phase difference of 90°, efficiency consistently rises with greater flow direction spacing. At 180°, efficiency trends are more complex, exhibiting fluctuations. Similar trends are observed for other plates. Within the scope of this study, plate4 achieves the highest efficiency of 52.86% under the condition of flow direction spacing of −0.5, lateral spacing of 0.6, and phase difference of 0°. In this paper, the energy absorption characteristics of three-row traveling wave plates are studied systematically for the first time, and the coupling mechanism of phase difference and spacing is revealed.
This study investigates the influence of pressure variation on droplet characteristics (count, size) and dynamics (velocity) in upward atomised full-cone sprays. The challenges of understanding the fundamental droplet behaviour in spray-flash desalination systems further imposes a need to explore methodologies such as directional conditional filtering in better resolving droplet behaviour. Directional filtering distinguishes upward-moving droplets (driven by momentum) from downward-moving droplets (entrained by gravity) thereby considering the differing residence times (downward falling droplets have a longer history). Particle Image Velocimetry (PIV) and Shadowgraph were applied to 75° full-cone nozzle at 1.75 L/min. Large Eddy Simulations (LES) were performed in two flash-environments (-0.50 bar gauge and −0.75 bar gauge) and compared to atmospheric pressure (1.01 bar absolute) sprays. Firstly, and in non-conditionally filtered droplets (raw data), droplet counts significantly increase with decreasing spray chamber pressure, with the highest counts observed under −0.75 bar gauge chamber pressure; attributed to enhanced flash-induced atomisation and secondary breakup associated with the larger pressure differentials. Along the spray centreline, unfiltered droplet counts at −0.75 bar gauge increase by 17.26%, 10.61%, 7.43%, and 6.40% at further downstream locations of Y = 0.1, 0.2, 0.3, and 0.4 m, respectively, relative to the −0.5 bar gauge chamber pressure. Counts at −0.75 bar gauge are also substantially much larger compared with atmospheric pressure sprays, with increases of 57.92%, 73.06%, 73.05%, and 78.17% at the same locations. Secondly, and with regard to droplet size relative to unfiltered droplet sizes in an atmospheric pressure environment, droplet size decreased much more appreciably at pressure reductions, reflecting intensified atomisation and flash-assisted breakup. At −0.50 bar gauge, the upward-filtered droplet size decreased by 21.3%, while at −0.75 bar gauge, it decreased by 30.55% compared to unfiltered droplet size at 1.01 bar. In case of downward-filtered droplet size and in comparison to unfiltered droplet size at 1.01 bar, it was reduced by 23.74% at −0.50 bar gauge and reduced by 29.92% at −0.75 bar gauge. Thirdly, and relative to unfiltered droplet velocity at 1.01 bar chamber pressure, upward droplet velocity increased at lower pressures. Initial upward-filtered droplet velocities rose by up to 32% at −0.50 bar gauge and 54% at −0.75 bar gauge compared with unfiltered droplet velocity at 1.01 bar. Upward-filtered droplets retained higher positive velocities near the spray core, whereas downward-filtered droplets exhibited stronger negative velocities under vacuum, indicating intensified gravitational recirculation. The results show that flash pressure and conditional filtering strongly impact the interpretation of results and so affect droplet count, size and velocity.
Accurate prediction of wake dynamics downstream hydrofoils is critical for mitigating vortex-induced vibrations and improving the performance of hydraulic machinery. Conventional turbulence modeling approaches often struggle to capture the unsteady, coherent structures governing wake behavior, particularly for slender hydrofoils operating at high Reynolds numbers. This study addresses this limitation by combining scale-resolving numerical simulations, including high-resolution Large Eddy Simulation (LES), with Particle Image Velocimetry (PIV) measurements to investigate the turbulent wake of a symmetric, blunt trailing edge hydrofoil operating at zero angle of attack. The flow was analyzed at a Reynolds number of approximately 7.5 × 10^5, i.e. close to the onset of wake–structure interaction effects. LES was performed using a fine mesh of approximately 500 million nodes to resolve near-wall and wake dynamics beyond the experimental field of view, while PIV measurements provided time-resolved velocity fields in the region downstream of the trailing edge. Proper Orthogonal Decomposition (POD) was applied to the PIV data to extract dominant coherent structures and quantify their contribution to the turbulent kinetic energy. POD analysis reveals that energy is distributed across many modes, with the leading mode capturing the primary wake dynamics, while other higher modes are forming coupled oscillatory pairs associated with Von Kármán vortex shedding. The agreement between PIV and LES results shows that wake measurements combined with numerical simulations enables full wake reconstruction and validates modeling for vibration-relevant hydrofoil dynamics.
Understanding ultrathin liquid-film dynamics is crucial for unraveling complex interfacial phenomena, yet deriving governing equations directly from experimental observations remains challenging. This study proposes a data-driven approach to model droplet dynamics, capturing liquid-film thickness on the nanometer scale in the form of a partial differential equation. As a challenging test case, we examine the superspreading wetting of surfactant-free nanofluids, a phenomenon whose physical mechanism defies standard theoretical explanations. We apply a sparse identification algorithm to spatiotemporal film-thickness profiles resolved at the nanometer scale using phase-shifting imaging ellipsometry. For a pure solvent, the discovered governing equation recovers classical lubrication physics driven by disjoining pressure and evaporation. In contrast, the nanofluid dynamics necessitates an additional, unique transport term scaling with the gradient of the inverse film thickness. Theoretical scaling analysis suggests this term represents a nanoparticle-induced bias flux, consistent with a hypothesized capillary wicking mechanism within the precursor film. The identification of the current nanofluid-specific term underscores the efficacy of integrating high-precision experimental measurements with data-driven modeling to discover hidden physics and generate testable hypotheses in complex wetting dynamics.
In this study, Large Eddy Simulations (LES) are employed to investigate the fundamental interplay between magnetic fields and thermal convection in a vertical, turbulent, liquid metal channel flow. The primary focus is on understanding the modifications to mean flow characteristics and higher-order statistical properties. This interaction leads to significant modifications to the turbulent flow structures, resulting in directional dependencies in the flow properties. The calculations are conducted at a friction Reynolds number of Reτ≈395, Hartmann number (Ha) in the range of 0≤Ha≤15, and Richardson number (Ri) varying between 0 and 0.05. We reveal that the presence of a wall-normal magnetic field in this particular setup suppresses turbulent kinetic energy, while buoyancy forces counteract this effect, promoting turbulence and introducing asymmetry into the statistical properties of the flow. Moreover, the magnetic field induces a preferential alignment of both vortical structures and near-wall streaks. The correlation analysis discovers a stretch of the longitudinal scales, while the spectral analysis indicates that both the magnetic field and buoyancy forces affect the distribution of turbulent kinetic energy at different scales. Notably, at Ha=15, the two-dimensional (2D) energy spectrum function has a slope similar to that predicted by the κ−3 law in the inertial range. This deviation of mechanism from “classical” turbulence scaling suggests that the applied magnetic field alters the energy cascade, primarily due to enhanced Joule dissipation.
Traditionally, studies of bluff body aerodynamics under blocking conditions have focused only on drag and small blockage ratios (<0.10). However, in practical engineering applications, bluff bodies often experience larger blockage ratios and nonzero angles of attack. To address this gap, this study investigates the hydrodynamic coefficients of bluff bodies across a range of Reynolds numbers (2×10⁴–2×10⁵), blockage ratios (0.16–0.49), and angles of attack (−6°–6°), using both wind tunnel experiments and numerical simulations. The hydrodynamic mechanisms are analyzed in conjunction with the vortex structures. The results show that the Reynolds number has a minimal effect under turbulent conditions, with a maximum variation coefficient of less than 10%. Among the hydrodynamic coefficients, drag is least affected, while torque is most sensitive. An enhancement effect of blockage on hydrodynamic coefficients is identified: as blockage ratio increases, both lift and drag coefficients increase nonlinearly. The slope of this increase grows with either higher blockage or larger attack angle. In terms of flow structure, a spatial vortex system is observed within the wake of the bluff body, induced by the attack angle. Changes in attack angle disrupt the rotational symmetry of the flow field, giving rise to multiple symmetrically distributed free vortices at either end of the meridional plane aligned with the attack angle. This transition breaks the rotational symmetry of the wake, reducing it to planar symmetry. Additionally, the increasing attack angle alters the blockage ratio and pressure distribution, which in turn leads to a nonlinear increase in drag coefficient amplitude.
The cryogenic Venturi tube is a specialized device that is employed to measure and control cryogenic fluid flow and is regarded as a critical component for stabilizing propellant flow prior to its entry into the rocket combustion chamber. Cavitation is induced when cryogenic fluids pass through the throat of the Venturi tube at high velocity. Such cavitation may result in severe vibration, noise, and surface erosion, ultimately causing damage to the Venturi tube and reducing its performance. The influence of throat length on cryogenic cavitation in Venturi tubes is examined in this study. A modified Zwart cavitation model applicable to cryogenic fluids was employed to account for their high thermal sensitivity and pronounced thermodynamic effects. The results indicate that cavitation development is intensified and the formation of large-scale cloud cavitation is promoted by a shorter throat length. As the throat length increases, cloud cavitation is gradually transformed into a more discrete pattern, accompanied by reduced intensity. The application of the Q-criterion, which links vortex structure to the pressure field, provides clearer insights into the effects of throat length variations on flow-field instability. Moreover, the mechanisms of cavitation bubble development, separation, and collapse are analyzed through the pressure shock waves generated within the flow field. Additionally, the distributions of turbulent kinetic energy and the entropy characterization method are employed to elucidate the energy transfer process during cryogenic cavitation, thereby demonstrating that shorter throat conditions lead to greater and more complex fluid energy loss.
