Airflow can strongly modify droplet solidification by inducing deformation and altering the thermal transport around the droplet. Here, we investigate the solidification of two tandem droplets deposited on a substrate under transverse airflow, focusing on the effects of droplet spacing, Reynolds number (Re), and Prandtl number (Pr). We find that droplet spacing governs the strength of inter-droplet aerodynamic interactions and, consequently, the solidification dynamics. At small spacings, wake vortices shed by the upstream droplet interact strongly with the downstream droplet, limiting the streamwise shift of its liquid-phase centroid and resulting in a less deformed final solidified shape. With increasing spacing, this wake-mediated interaction progressively weakens, and the solidification behaviors of the two droplets converge. Increasing Re by increasing the inflow velocity enhances aerodynamic forcing, leading to stronger droplet deformation and faster contraction of the solidification front, while increasing the overall non-dimensional solidification time. In contrast, Pr has only a minor effect on both solidification morphology and non-dimensional solidification time. More importantly, the non-dimensional solidification time exhibits a systematic dependence on the inflow velocity. By incorporating a spacing-dependent coefficient, the non-dimensional solidification time data for the downstream droplet at different spacings collapse onto a unified empirical correlation. This correlation is applicable within the investigated two-dimensional configuration and parameter range.
The wake dynamics of a square cylinder under a prescribed large-amplitude, low-frequency sinusoidal inflow, characterized by û/u¯=1 and fuD/u¯=0.01, are investigated experimentally over 6.0×103≤Re≤1.7×104. A posteriori harmonic decomposition was employed to separate the deterministic first-harmonic response from the residual wake fluctuations. The deterministic harmonic energy was concentrated mainly along the separated shear layers, whereas the residual energy developed farther downstream and remained substantially higher and more spatially extensive than the fluctuation energy under smooth inflow. Two-point correlation analysis showed that the alternating wake organization was retained under sinusoidal inflow, but its spatial coherence was weakened. The streamwise coherence length and correlation-based wake width decreased, while the vortex formation length increased over the investigated Reynolds-number range. Spectral analysis identified a statistically robust, spatially organized higher-frequency component in the sinusoidal residual wake at Re=6.0×103. Together, the residual-velocity evolution, broadened two-dimensional Fourier spectra, spectral entropy, and non-primary-band energy fraction show the development of multi-scale flow structures under sinusoidal inflow. Proper orthogonal decomposition further reveals a redistribution of residual wake energy from the leading coherent mode pair to additional modes. A four-component decomposition successfully separates the mean, deterministic harmonic, phase-averaged coherent residual, and remaining non-phase-locked motions. Under the present large-amplitude, low-frequency forcing condition, these results show that sinusoidal inflow reorganizes the separated shear layers and residual wake dynamics rather than merely superposing a low-frequency velocity oscillation.
Inertial particle transport and deposition in helically forced wall-bounded turbulence are controlled by turbulent diffusion, near-wall shear, secondary motion, and finite particle inertia. The wire-wrapped rod bundle is treated as a representative configuration in which spacer wires generate cross-flow, local acceleration, and narrow-gap transport pathways. A discrete-phase model with two-way momentum coupling was established to simulate Fe3O4 particle migration and deposition in a 19-pin wire-wrapped rod-bundle flow with lead-bismuth eutectic as the carrier fluid. The continuous phase was resolved using the shear stress transport k–ω model, and a particle–wall collision and deposition criterion was used to distinguish rebound from deposition. Particles of 1–100 μm were tracked to analyze axial migration, transverse redistribution, near-wall enrichment, and wall deposition. Results show that inlet velocity gradients and wire-induced cross-flow drive particles away from streamlines and toward near-wall low-speed regions. For 1–10 μm particles, 61.8% of the area-integrated wall deposition occurred within the first 0.5 wire pitch. Deposition hotspots occur mainly on upstream-facing wire surfaces, box-wall edges, and narrow gaps among the wire, cladding, and box wall. Increasing particle diameter raises relaxation time and Stokes number, enhancing trajectory deviation and collision probability while shifting concentration and deposition-flux peaks downstream. As the particle size increases, the dimensionless deposition rate increased and showed a sublinear dependence on the Stokes number, while the deposition rate remained far below unity, indicating that deposition is governed by coupled turbulent diffusion, near-wall shear, wire-induced transverse migration and finite inertia rather than inertia alone.
The hydrodynamics of hemline-shaped thread formation in a co-flowing microchannel under periodic inlet perturbations are numerically investigated using the volume of fluid method. Two flow regimes, dome-shaped threads and hemline-shaped threads, are identified and mapped onto regime diagrams. The transition between these regimes is governed by a critical threshold of the waveform steepness, which captures the combined effects of perturbation frequency, amplitude, and flow rate ratio. The hemline formation process has protruding and folding stages. During the protruding stage, inertial momentum surplus at each velocity crest drives the protrusion formation. In the subsequent folding stage, differential advection arising from the core-annular axial velocity gradient progressively folds the protrusions into hemline structures. The generated hemline is stretched in the axial direction without significant radial deformation. Hemline length is governed by the waveform steepness. Increasing the frequency, amplitude, or flow rate ratio steepens the waveform, thereby enhancing folding dynamics and resulting in longer hemline length. Hemline pitch is primarily controlled by the generation frequency. Higher frequency compresses the temporal period of protrusion formation, generating more protrusions per unit time. Based on these mechanistic insights, predictive scaling laws are established and validated against numerical data. The dimensionless hemline pitch is inversely proportional to the dimensionless frequency, while the dimensionless hemline length follows a superlinear scaling with the amplitude and flow rate ratio. These scaling laws provide a quantitative basis for the design of hemline-shaped microfibers with tunable liquid-transport capabilities.
Near-bed confinement alters the spreading, velocity distribution, and turbulence of ship propeller jets, resulting in development distinct from that of a free jet. Flume experiments were conducted under different clearance-height and rotational-speed conditions, and instantaneous three-component velocities were measured using an acoustic Doppler velocimeter at locations in the centerline longitudinal plane. Three successive flow regimes were identified: free-jet spreading, jet impingement, and wall-jet development. Reducing the relative clearance height restricted downward jet spreading, shifted the representative regime boundaries upstream, and nearly eliminated the free-jet spreading regime at the lowest clearance. Increasing rotational speed primarily increased the jet velocity and turbulent kinetic energy (TKE), while exerting limited influence on the regime boundaries. Axial velocity dominated the downstream development, whereas decreasing clearance displaced the velocity and TKE peaks toward the bed. Within the resolvable 0.098–12.5 Hz frequency band, near-bed velocity-fluctuation energy and the relative energy contribution from the upper portion of the band decreased downstream, indicating progressive attenuation and redistribution of the resolved fluctuations. To quantify jet decay, the maximum resultant velocity extracted from the centerline longitudinal plane, Vp-max, was used as an approximation of the cross-sectional maximum under the approximately symmetric experimental conditions. At Zp/Dp = 1.00, normalized decay was gradual during free-jet spreading, rapid during impingement, and characterized by local recovery and slow adjustment during wall-jet development. Continuity-constrained linear, power-law, and quadratic functions described these regimes, respectively. These results provide a regime-based framework for characterizing near-bed propeller-jet development and velocity decay within the tested range.
