The interaction between droplets of different scales and turbulent flow is investigated with numerical simulations. To capture the gas flow characteristics and interface evolution accurately, the large eddy simulation method is combined with adaptive mesh refinement. This numerical strategy is shown to be suitable for complex two-phase flow simulations at moderate costs. The initial sizes of droplets are the characteristic length scales in homogeneous isotropic turbulence. From large to small sizes, the finite-, inertial-, Hinze- and Taylor-scale droplets are set separately in each simulation. Results show that droplets of different initial sizes respond differently to the gas flow. Large droplets present periphery shedding at the initial stage of breakup and tend to be stretched into a disklike shape before final breakup. Small droplets are carried by the gas field and deform into cylindrical structures besides the disklike shape. Pressure perturbations are found in both phases, and the average pressure is increased on the whole. The breakup processes introduce more fine structures in the flow field, and oscillation of the energy spectra in the inertial subrange is observed. Most vorticity vectors are aligned with the second principal axis of strain rate tensor and perpendicular to the third principal axis. The distribution of vortical structures is modified by the existence of droplets, and the unstable flow patterns are found to be enhanced as droplets break up. The turbulence kinetic energy of the gas phase is suppressed more extensively with the decrease of droplet scale. The simulations provide more insights into the mechanisms of the two-phase interaction under realistic conditions.

The transition route from laminar to turbulent flow in a magnetohydrodynamic (MHD) duct with a square cross section is investigated in the limit of low magnetic Reynolds number. In the presence of a transverse magnetic field, Hartmann and Shercliff layers are present on the walls orthogonal and parallel to the field direction, respectively. We assume reflection symmetries in both transverse directions, and investigate the competition between transition mechanisms specific to each boundary layer using direct numerical simulations. Independently of the initial location of a finite perturbation, transition relies exclusively on a tripping of the Shercliff layer by perturbations, while the Hartmann layer plays a passive role. This is explained, using a dynamical systems interpretation, by the spatial localization of the edge states in the Shercliff layer at the expense of the Hartmann layer. The link between these nonlinear coherent structures and the linear optimal modes known from nonmodal stability and energy stability theory is pointed out.

The growth and manipulation of a heavy fluid layer with dual-mode perturbations imposed only at the downstream interface are investigated. To quantify the effects of reverberating waves, the processes of the disturbed reverberating waves interacting with the layer are theoretically modeled. When the compression waves hit the downstream interface, they will suppress (promote) the mode growth if the mode has (has not) completed the phase inversion. The relationship between the perturbation parameters and the layer width is obtained when the mode amplitude is zero at the arrival of the compression waves. Four different initial layer widths are then designed in experiments by fixing the perturbation parameters to manipulate the mode growth. For a large layer width, the growth of the downstream interface is suppressed relative to that of a dual-mode interface between semi-infinite domains, because both mode amplitudes are suppressed by compression waves. As the layer width reduces, the mixing width growth is enhanced, because the long-wavelength perturbation growth is promoted. In addition, the compression waves have more prominent effects on the short-wavelength perturbation than the long-wavelength perturbation. Through considering the reverberating waves effects in a classic model, the mode amplitude growth can generally be predicted. The reverberating waves play a more prominent role than interface coupling in the development of the dual-mode perturbations at the downstream interface during the time studied. The initially planar upstream interface also acquires perturbations via the rarefaction waves and interface coupling. However, interface coupling dominates the amplitude growth of the modes at the upstream interface, and it has a greater effect on the long-wavelength perturbation than the short-wavelength perturbation. This work might shed some light on how to manipulate the growth of the dual-mode perturbations via reverberating waves.

A series of simulations with a circular cylinder of diameter $D$ placed in an open channel flow of depth $H$ are conducted in both purely oscillatory flow (one-mode forcing with maximum orbital velocity, $U_m$) and in combined oscillatory and current flow regime (mean velocity, $U_s$). The paper discusses how the phase-averaged flow, the coherent structures generated around the cylinder, and the forces induced on the cylinder change with the ratio between the steady current velocity and the oscillatory velocity ($0\le U_s/U_m\le 1.4$) and with the Keulegan-Carpenter number, $\mathrm{KC}=U_{m}T/D$ ($1.5\le \mathrm{KC}\le 30.8$), where $T$ is the period of the oscillatory flow. Results show that for constant $U_s/U_m$, the capacity of the horseshoe vortex to erode the bed increases with the KC number. For constant KC number, the overall coherence and lifespan of the main horseshoe vortex forming during each oscillatory cycle increase with $U_s/U_m$. The same is true for the number and initial circulation of the wake vortices shed on the downstream side of the cylinder in the simulations conducted with $\mathrm{KC}=15.4$ and 30.8. An instability in the form of large-scale hairpin-like vortices develops along the vertical cores of the wake vortices in the $\mathrm{KC}=1.5$ simulations with $U_s/U_m\ge 1.0$. For combined wave-current flows with $U_s/U_m\ge 0.4$, the regions of relatively high bed shear stress magnitude and the peak values inside these regions increase monotonically with the KC number for constant $U_s/U_m$. Results show that even for cases with a steady current, the oscillatory component of the phase-averaged in-line force is reasonably well described by Morisson's equation. A drag coefficient can be defined for the steady component of the in-line force with $U_s$ as the velocity scale. For high KC numbers and $U_s/U_m>1$ this drag coefficient is comparable to the standard drag coefficient in steady flow. The phase lag between the in-line force and the oscillatory velocity component decreases with increasing KC and is independent of $U_s/U_m$. For cases where the number of vortices shed in the wake is the same during all cycles, the phase-averaged spanwise force remains small. However, at times, the cylinder is subject to instantaneous forces of comparable magnitude along the streamwise and spanwise directions for $\mathrm{KC}\ge 15.4$, which has important consequences for the design of piles in combined wave-current flow.

Variations in liquid properties can significantly influence the terminal velocity and stabilized shape of the rising bubble, subsequently affecting its rebound motion from the free surface. In this study, the effects of liquid viscosity and surface tension on the bouncing behavior of a millimetric rising bubble upon impact with a free surface are studied numerically through axisymmetric simulations. The main objective of the paper is to investigate the trends in the kinematic properties of bubble motion as influenced by the Morton and Weber numbers, including terminal velocity, bounce period, amplitude, maximum rise height, along with the bubble's geometric configuration and the deformation of the liquid film. Furthermore, two critical parameters that dictate the bounce behavior of the bubble are identified. The simulation results reveal that the amplitude of the first bounce is primarily governed by the bubble's impact velocity, whereas the second rebound is mainly contingent on the shape of the bubble. Moreover, an analysis of the energy budget and conversions throughout the bouncing process is presented.

When a flat plate impacts upon the water surface, bubbles of different shapes can be entrapped depending on impact velocity. In this paper, the morphology of trapped air bubbles and the underlying physics are numerically investigated. Among the wide range of impact velocities, two typical air bubble patterns have been discovered: small-bubble pattern and large-bubble pattern. Specifically, as the plate descends, an air layer is initially entrapped underneath, and is then enclosed into a large air bubble upon initial contact of plate edge with water surface. Subsequently, this large bubble breaks into lots of small bubbles at low impact velocities, but remains intact at higher impact velocities, exhibiting two distinct patterns. The morphological evolution of air bubbles is found to be dictated by two physical factors: the compression-expansion intensity of trapped air during initial impact stages (before the contact of plate edge with water surface) and wind-driven waves on the water surface below plate. Particularly, the former determines the thickness and shape of the initially enclosed large bubble. At low impact velocities, due to the weak compression-expansion behavior of trapped air, the initially formed large bubble is thin and flat, in which the wind-driven waves can make direct contact with plate bottom easily, thereby splitting the large bubble into many small bubbles. At higher impact velocities, the compression-expansion intensity of trapped air becomes increasingly stronger, causing the initially formed large bubble to be considerably thicker and rounder, in which the wind-driven waves fail to wet the plate bottom; thus, the large bubble is preserved.

Direct numerical simulations (DNSs) of spatially evolving turbulent planar jets and wakes of viscoelastic polymer solutions are performed in order to study the small-scale mixing and large-scale stirring of passive scalars in free turbulent viscoelastic flows. The finitely extensible nonlinear elastic–Peterlin rheological model is adopted for the DNS. Viscoelasticity is found to suppress small-scale scalar mixing but it initially suppresses and later enhances large- and intermediate-scale stirring, provided viscoelasticity is sufficiently high. The normalized dissipation rate of scalar variance that is typically used to quantify the small-scale mixing is reduced by a factor larger than 4 in some cases, whereas the normalized turbulent flux, which is characteristic of the large-scale stirring, increases by a factor larger than 6 in the most significant case. The explanation is the suppression of small-scale perturbations caused by the polymers, suppressing the mixing, and allowing the appearance of larger coherent structures that promote the stirring at the large scales. In the high elasticity region, the transport of passive scalars is more strongly modified by viscoelasticity than the momentum transport, and the Reynolds analogy is not applicable.

This paper introduces a one-dimensional model for the response of a monodisperse nonevaporating spray injected into a laminar uniform gaseous stream when it is submitted to acoustic disturbances. The dynamics of both the continuous and dispersed phases of the spray are addressed using an Eulerian framework. Explicit analytical expressions are derived for the linearized balance equations governing particle velocity and particle number density responses to acoustic excitation in two scenarios: when particles are injected with the same velocity as the gaseous flow and when their injection velocities differ. It is shown that particle velocity disturbances can be decomposed into an evanescent convective wave and a propagating acoustic wave. The final amplitudes and phase lags of these waves with respect to acoustic disturbances depend on particle Stokes and flow Mach numbers. The expression for particle number density disturbances uncovers two distinct types of particle clustering. The first, termed acoustic particle clustering (APC), is controlled by the relative particle velocity fluctuations compared to the gas velocity fluctuations. The second, designated convective particle clustering (CPC), is linked to gas velocity fluctuations and operates independently of the acoustic particle velocity response. Particle clustering predominantly arises from CPC, whereas APC is only discernible at low Stokes numbers. The analysis further delves into the impact of differences between the particle injection velocity and gas mean velocity on the amplitude and phase lag of CPC wave. It is shown that the zone over which the particle velocity relaxes to the gas velocity fully controls CPC. Numerical simulations validate analytical predictions, with good agreement for relatively small Stokes numbers, and cases wherein the particle injection velocity exceeds the mean gas velocity. The expressions derived in this work represent a preliminary step toward modeling the acoustic response of spray flames.

In the ocean, submesoscale flows tend to undergo several hydrodynamic instabilities. In particular, inertial instability (InI) and Ekman-inertial instability (EII) are known to develop in geostrophically balanced barotropic flows whose lateral shear is larger in magnitude and opposite in sign to the Coriolis parameter. Although these instabilities share some elements, their dynamical nature can lead to fundamental differences. However, the current analytical description of EII is one-dimensional, which makes it difficult to compare against InI in a more realistic scenario. To overcome this limitation, we conduct two-dimensional numerical simulations of both InI and EII in a submesoscale jet and explore the induced vertical flow, the growth rate, and the energetics of each instability. Furthermore, we investigate the sensitivity of our results to variations in the minimum Rossby number of the jet. We find that EII grows faster than InI and induces stronger vertical flow, especially near the surface. Both instabilities radiate inertial waves away from the current, and these waves predominantly propagate across the anticyclonic side of the jet. Finally, when the instabilities weaken, the fluid reaches a stable state that is remarkably similar in both cases. This study highlights the similarities and differences between InI and EII and provides further insight into the mechanism behind EII that makes it capable of outcompeting other submesoscale instabilities.

Viscoelastic planar flow is explored numerically in simple geometries, namely, confined cylinders and T junctions, where an asymmetry is introduced and varied. The simulations illustrate that the flow asymmetry arising from the introduction of the geometric asymmetry is enhanced at Weissenberg numbers above unity, i.e., the flow in the nonpreferred pathway falls significantly, even for very small asymmetry. This phenomenon is studied in detail using the Oldroyd-B, White-Metzner, and FENE-P models. In the two last cases, the flow enhancement in the preferential path is reduced due to shear thinning. This enhancement is shown to be a purely elastic phenomenon and is proposed as one of the primary drivers of the emergence of preferential pathways in complex geometries.

Stationary velocity-perturbation streaks have recently been identified in laminar swept-wing boundary-layer flow interacting with a surface forward-facing step. Streaky structures at the step promote early laminar-turbulent transition under certain conditions. This work utilizes direct numerical simulations to explore the mechanisms of growth of stationary streaks at the step and provides insight into their origin, nature, and spatial organization. The analysis is mainly focused on, but not restricted to, incoming perturbations in the form of stationary crossflow instability. Stationary streaky structures are found to be universal to swept forward-facing-step flow subjected to three-dimensional perturbations in the incoming boundary layer. The streaks at the step are primarily ascribed to the lift-up effect. They appear as a linear perturbation response of the highly sheared step flow to the cross-stream pattern of incoming perturbations. A mechanism of base-flow deceleration additionally contributes to feeding growth to the streaks. Linear stability analysis carried out through the harmonic Navier-Stokes method confirms that the streaks are a linear perturbation phenomenon. Effects of spanwise perturbation wavelength and effective sweep angle on the mechanisms of the streaks are also assessed.

We have explored the contact line dynamics on superhydrophobic surfaces. Using two complementary geometries (a millimetric sessile drop and a centimetric capillary bridge), we have measured the dynamic receding contact angle of water on surfaces composed of micropillar arrays for velocities spanning over five decades. We have also studied the effect of pillar fraction and compared the results to smooth surfaces with the same chemical nature and also to similar systems reported in the literature. We show that introducing surface textures in the form of micropillar arrays significantly decreases the dependency of the contact angle on the contact line speed compared to a smooth surface, and this velocity dependency also decreases with decreasing surface fraction of micropillars. Interestingly, we show that the exact texturation of the surface does not play a fundamental role in the angle-velocity relationships as long as microtextures present the same type of periodic pattern (pillar arrays or microgrids). These results are interpreted in terms of viscous friction reduction on superhydrophobic surfaces, shedding light on the underlying mechanisms governing their unique dynamic behavior.

We study the pore-scale transport of a conservative scalar forming an advancing mixing front, which can be re-interpreted to predict instantaneous mixing-limited bimolecular reactions. We investigate this using a set of two-dimensional, high-resolution numerical simulations within a poly-disperse granular porous medium, covering a wide range of Péclet (Pe) numbers. The aim is to show and exploit the direct link between pore-scale concentration gradients and mixing interface (midpoint concentration isocontour). We believe that such a perspective provides a complementary new lens to better understand mixing and spreading in porous media. We develop and validate a theoretical model that quantifies the temporal elongation of the mixing interface and the upscaled reaction kinetics in mixing-limited systems accounting for pore-scale concentration fluctuations. Contrary to the classical belief that, given sufficient time, pore-scale fluctuations would eventually be washed out, we show that for $\text{Pe}>1$ advection generates pore-scale concentration fluctuations more rapidly than they can be fully dissipated. For such Péclet numbers, once incomplete mixing is established, it will persist indefinitely. We identify critical Péclet thresholds ($\text{Pe}=18$ for Poiseuille flow, $\text{Pe}=48$ for porous media) where reaction efficiency is minimized. Finally, our developed model accurately reproduces the reaction product mass in a three-dimensional porous media column over a wide range of Péclet numbers, demonstrating its applicability to more realistic systems.

In this study, we investigate the coupling effects of roughness and wall shear in an annular centrifugal Rayleigh-Bénard convection system, where two cylinders rotate with different angular velocities. Two-dimensional direct numerical simulations are conducted within a Rayleigh number range of ${10}^6\le \mathrm{Ra}\le {10}^8$, and the nondimensional angular velocity difference ($\mathrm{\Omega }$), representing wall shear, varied from 0 to 1. The Prandtl number is fixed at $\mathrm{Pr}=4.3$, the inverse Rossby number at ${\mathrm{Ro}}^{-1}=20$, and the radius ratio at $\eta =0.5$. The interaction between wall shear and roughness leads to distinct heat transfer behavior in different regimes. In the buoyancy-dominant regime, an increase in the nondimensional angular velocity difference ($\mathrm{\Omega }$) significantly enhances heat transfer. However, as $\mathrm{\Omega }$ continues to rise, a sharp reduction in heat transfer is observed in the transitional regime. Beyond a critical value of $\mathrm{\Omega }$, the flow enters a shear-dominant regime, where heat transfer remains unchanged despite further increases in $\mathrm{\Omega }$. The underlying mechanisms behind these distinct heat transfer behaviors are then elucidated. The enhancement of heat transport in the buoyancy-dominant regime is attributed to the introduction of external shear by the rotating rough walls, which reinforces convection and secondary flows within the cavities. Additionally, these secondary flows improve the efficiency of transporting the trapped hot and cold fluids outside the cavities, further enhancing heat transfer. However, in the transitional regime, the number of convection rolls rapidly decreases with increasing shear, eventually reaching a point where sustaining them becomes challenging. Consequently, a sharp reduction in heat transfer occurs. In the shear-dominant regime, heat transfer is primarily governed by diffusion, leading to a constant heat transport rate.

Oscillatory flow past an elliptic cylinder with an aspect ratio of 0.4 has been investigated for Keulegan-Carpenter numbers ($KC$) ranging from 1 to 10 and Reynolds numbers ($Re$) ranging from 60 to 150 by conducting two-dimensional numerical simulations. The physics mechanisms underpinning the identified flow regimes (A, C, ${\mathrm{F}}^{\prime }$, and F), including the alternating top- and bottom-dominated vortex shedding in regime C, as well as the one-sided vortex pair shedding in a new flow regime ${\mathrm{F}}^{\prime }$, and the diagonal two-sided vortex pairs shedding in flow regime F, have been investigated in detail. The transition between the top- and bottom-dominated vortex shedding within a secondary period in regime C is explained in terms of the cycle-by-cycle merging and diffusion processes of the remaining vortices within each oscillation period. It appears that the formation of the vortex pair shed from the cylinder in regimes ${\mathrm{F}}^{\prime }$ and F depends on the strength of the vortex remaining from the previous half of the oscillation period. The resulting hydrodynamic forces acting on the cylinder are explained in light of the vortex dynamics around the cylinder; this includes the occurrence of two crests and two troughs of the lift coefficient within one oscillation period in the flow regime ${\mathrm{F}}^{\prime }$, and an additional crest and trough of the lift coefficient in the flow regime F.

We consider the propagation of linear gravity waves on the free surface of steady, axisymmetric flows with purely azimuthal velocity. We propose a two-dimensional set of governing equations for surface waves valid in the deep-water limit. These equations come from a closure condition at the free surface that reduces the three-dimensional Euler equations in the bulk of the fluid to a set of two-dimensional equations applied only at the free surface. Since the closure condition is not obtained rigorously, it is validated numerically through comparisons with full three-dimensional calculations for vortex flows, including for a Lamb-Oseen vortex. The model presented here overcomes three limitations of existing models: namely, it is not restricted to potential base flows, it does not assume the base flow to have a flat free surface, and it does not require the use of infinite-order differential operators [such as $tanh\left(\nabla \right)]$ in the governing equations. The model can be applied in the case of rapid swirl (large Froude number) where the base free surface is substantially deformed. Since the model contains only derivatives of finite order, it is readily amenable to standard numerical study.

The dynamics of a liquid drop impact on a liquid surface is studied experimentally. The drop diameter, the impact velocity, and the depth of the target liquid in the reservoir are parameters that are varied. The crown and the jet characteristics are mostly affected by the water depth and the size of the first secondary drop. The number of secondary drops strongly depends on the Weber number and the jet characteristics. The interplay between the inertia forces and surface tension forces during the expansion and contraction of the cavity determines the shape of the cavity. In shallow water, the cavity expansion and retraction is dominated by the surface tension forces, but in deep water the inertia forces and the gravity forces dominate the cavity dynamics. The crown evolution and the cavity evolution are almost simultaneous in deep water, but in the case of shallow water, it is not the same due to the hindrance caused by the reservoir bottom on the cavity retraction. Physical insights of the energy models for a drop impact on the deep pool are provided. These models incorporate the effects of surface tension, Bond number, and drop oscillations. The effects of the Weber number and the Froude number on the jet characteristics are found to be distinct on shallow and deep water. It is found that the jet velocity, Weber number, and water depth can form the boundary limits for the prediction of number of secondary drops. The expansion of cavity resembles a source of the potential flow below the surface of the liquid. Time resolved particle image velocimetry measurements enable estimates of time variation of the source strength. The source strength or the maximum discharge flow rate is found to be directly proportional to the momentum of the impacting drop and is negligible for low Froude numbers.

The present work investigates the fluid-structure interaction of a flexible cylindrical cantilever in a tandem configuration. A fully coupled fluid-structure solver based on the three-dimensional incompressible Navier-Stokes equations and Euler-Bernoulli beam equation is employed to numerically examine the coupled dynamics of the cantilever. We assess the extent to which such a flexible cylindrical structure could sustain oscillations in both subcritical and postcritical regimes of a Reynolds number ($\text{Re}$). Spatiotemporal power transfer patterns, response amplitudes, and vorticity dynamics are quantified and compared between isolated and tandem configurations. The results of our analysis indicate that the cantilever in tandem configuration is prone to sustained oscillations dependent on the Reynolds number and the reduced velocity parameter ($U^{*}$). In the subcritical $\text{Re}$ regime, the cantilever exhibits sustained oscillations with peak transverse oscillation amplitudes occurring within a specific range of $U^{*}$. Within this range, the transverse oscillations demonstrate lock-in behavior and synchronization with the vortex-shedding frequency. The vorticity dynamics in the subcritical $\text{Re}$ regime reveal that in the tandem configuration, the presence of the upstream cylinder significantly modifies the wake structure, delaying vortex formation and extending the near-wake region. In the postcritical regime of $\text{Re}$, the cantilever shows a wider range of sustained oscillations in terms of $U^{*}$, with single- and multifrequency response dynamics driven by vortex-body interactions. Power transfer analysis shows cyclic energy exchange patterns between the fluid and flexible structure, with significant variations in the hydrodynamic loading along the length of the cantilever. The findings of this work aim to broaden the understanding of sustained oscillations in flexible cantilevers and provide physical insights into the design of artificial cantilever flow sensors.

This work presents a feature-consistent field inversion and machine learning framework to enhance the capability of the Reynolds-averaged Navier-Stokes (RANS) turbulence model in predicting complex flows with separations. It effectively assimilates direct numerical simulation solutions and sparse experimental data, including velocity profiles, pressure distribution, and aerodynamic forces, into the improved k-ω shear stress transport (SST) closure model using the regularized ensemble Kalman inversion method. An artificial neural network (ANN) model is built to reconstruct the destruction term by considering local flow features. A modified analytical scheme with a prior mean-based regularization constraint is used to facilitate the model's exploration of the most influential regions for correction. The training process of the ANN model not only integrates the solution of the RANS equations but also minimizes the loss function by considering multiple flow conditions simultaneously so that feature inconsistency is avoided, resulting in a more effective model that delivers more accurate RANS results. Typical turbulent flow problems are simulated to validate the proposed method, including the separation flows over slopes and steps with low Reynolds numbers and the separation flows over airfoils with high Reynolds numbers. It is demonstrated that the proposed framework is capable of training a robust and consistent ANN-improved k-ω SST turbulence model for predicting turbulent flows with separations at both low and high Reynolds numbers. It also shows that the present ANN-improved k-ω SST turbulence model achieves generalization for separated flows with unforeseen geometries and Reynolds numbers.