# Latest papers in fluid mechanics

### Study on a mesoscopic model of droplets freezing considering the recalescence process

There are many practical applications of droplets freezing, and in many cases, it is necessary to prevent the droplets freezing to reduce the loss caused by freezing. Based on the many-body dissipative particle dynamics with energy conservation method, this research proposes an icing model that considers the recalescence process and initial ice mass fraction of droplets for the first time, which obtains a complete simulation of the two-phase four-stage freezing process of droplets. The accuracy and applicability of this model are verified by studying the single-phase Stefan problem, the recalescence process of droplet, and whether the initial ice mass fraction is considered for freezing. Then, the freezing process of droplets under four surface temperatures and five types of surface wettability was studied, and it was found that the temperature of droplets in recalescence stage would jump from nucleation temperature to equilibrium temperature, and almost unaffected by external factors. Change of the temperature distribution with dimensionless height [math] before recalescence is only affected by the surface temperature and nucleation temperature. At the end of droplets recalescence, the initial ice mass fraction has little relationship with volume. As the contact angle, surface temperature, and droplet volume increase, temperature changes in the pre-cooling and solidification stages of droplets will slow down, and the solidification time will increase. Additionally, the temperature of the solid wall surface has almost no effect on the final ice shape, and the final ice tip phenomenon is more obvious on the surface with a larger contact angle.

### Study on a mesoscopic model of droplets freezing considering the recalescence process

There are many practical applications of droplets freezing, and in many cases, it is necessary to prevent the droplets freezing to reduce the loss caused by freezing. Based on the many-body dissipative particle dynamics with energy conservation method, this research proposes an icing model that considers the recalescence process and initial ice mass fraction of droplets for the first time, which obtains a complete simulation of the two-phase four-stage freezing process of droplets. The accuracy and applicability of this model are verified by studying the single-phase Stefan problem, the recalescence process of droplet, and whether the initial ice mass fraction is considered for freezing. Then, the freezing process of droplets under four surface temperatures and five types of surface wettability was studied, and it was found that the temperature of droplets in recalescence stage would jump from nucleation temperature to equilibrium temperature, and almost unaffected by external factors. Change of the temperature distribution with dimensionless height [math] before recalescence is only affected by the surface temperature and nucleation temperature. At the end of droplets recalescence, the initial ice mass fraction has little relationship with volume. As the contact angle, surface temperature, and droplet volume increase, temperature changes in the pre-cooling and solidification stages of droplets will slow down, and the solidification time will increase. Additionally, the temperature of the solid wall surface has almost no effect on the final ice shape, and the final ice tip phenomenon is more obvious on the surface with a larger contact angle.

### Effect of the aspect ratio on the dynamics of air bubbles within Rayleigh–Bénard convection

Laboratory experiments and numerical simulations were performed to quantify the effect of the aspect ratio, Γ, in the dynamics of air bubbles within turbulent Rayleigh–Bénard (RB) convection. We explored four scenarios defined by [math], 1.5, 2, and 2.5 under Rayleigh numbers ranging from [math] to [math]. Continuous 1-mm bubbles were released at two locations from the bottom along the roll path. Three-dimensional particle tracking velocimetry was used to track a large number of bubbles and determine features of the trajectories and pair dispersion, [math], for various initial separations, rp within [math]; here, H is the height. The [math] of the bubbles within a quiescent medium was included for reference. Characterization of the bubble streams, namely, the center of mass (Lc), mean deviation (Rc) to Lc, vertical (vz) and lateral (vL) velocities, and their ratios reveal the strong modulation of the roll structure and Γ. In particular, Lc exhibited an approximately symmetric distribution around the maximum, which occurred at the middle height only in the [math] case. Maximum Lc was near the wall top with the highest aspect ratio. However, Rc did not vary substantially among the cases. Bubbles' lateral pair dispersion [math] shows correlated trends with Γ, particularly at large initial separations and times, whereas the vertical pair dispersion is mainly dominated by buoyancy. The [math] decreased as Γ increased. It indicates the effect of different-sized roll structures modulated by Γ. In general, R2 embodies distinct features of [math]-modulated bubble dynamics in RB convection.

### Effect of the aspect ratio on the dynamics of air bubbles within Rayleigh–Bénard convection

Laboratory experiments and numerical simulations were performed to quantify the effect of the aspect ratio, Γ, in the dynamics of air bubbles within turbulent Rayleigh–Bénard (RB) convection. We explored four scenarios defined by [math], 1.5, 2, and 2.5 under Rayleigh numbers ranging from [math] to [math]. Continuous 1-mm bubbles were released at two locations from the bottom along the roll path. Three-dimensional particle tracking velocimetry was used to track a large number of bubbles and determine features of the trajectories and pair dispersion, [math], for various initial separations, rp within [math]; here, H is the height. The [math] of the bubbles within a quiescent medium was included for reference. Characterization of the bubble streams, namely, the center of mass (Lc), mean deviation (Rc) to Lc, vertical (vz) and lateral (vL) velocities, and their ratios reveal the strong modulation of the roll structure and Γ. In particular, Lc exhibited an approximately symmetric distribution around the maximum, which occurred at the middle height only in the [math] case. Maximum Lc was near the wall top with the highest aspect ratio. However, Rc did not vary substantially among the cases. Bubbles' lateral pair dispersion [math] shows correlated trends with Γ, particularly at large initial separations and times, whereas the vertical pair dispersion is mainly dominated by buoyancy. The [math] decreased as Γ increased. It indicates the effect of different-sized roll structures modulated by Γ. In general, R2 embodies distinct features of [math]-modulated bubble dynamics in RB convection.

### Effect of the aspect ratio on the dynamics of air bubbles within Rayleigh–Bénard convection

Laboratory experiments and numerical simulations were performed to quantify the effect of the aspect ratio, Γ, in the dynamics of air bubbles within turbulent Rayleigh–Bénard (RB) convection. We explored four scenarios defined by [math], 1.5, 2, and 2.5 under Rayleigh numbers ranging from [math] to [math]. Continuous 1-mm bubbles were released at two locations from the bottom along the roll path. Three-dimensional particle tracking velocimetry was used to track a large number of bubbles and determine features of the trajectories and pair dispersion, [math], for various initial separations, rp within [math]; here, H is the height. The [math] of the bubbles within a quiescent medium was included for reference. Characterization of the bubble streams, namely, the center of mass (Lc), mean deviation (Rc) to Lc, vertical (vz) and lateral (vL) velocities, and their ratios reveal the strong modulation of the roll structure and Γ. In particular, Lc exhibited an approximately symmetric distribution around the maximum, which occurred at the middle height only in the [math] case. Maximum Lc was near the wall top with the highest aspect ratio. However, Rc did not vary substantially among the cases. Bubbles' lateral pair dispersion [math] shows correlated trends with Γ, particularly at large initial separations and times, whereas the vertical pair dispersion is mainly dominated by buoyancy. The [math] decreased as Γ increased. It indicates the effect of different-sized roll structures modulated by Γ. In general, R2 embodies distinct features of [math]-modulated bubble dynamics in RB convection.

### On two approaches to the third-order solution of surface gravity waves

A third-order approximate solution for surface gravity waves in the finite water depth is studied in the context of potential flow theory. This solution corresponds to the steady-state part of a multidirectional irregular wave field and provides explicit expressions for the surface elevation, free-surface velocity potential, and velocity potential. The amplitude dispersion relation is also provided. Two approaches are used to derive the third-order analytical solution, resulting in two types of approximate solutions: the perturbation solution and the Hamiltonian solution. The perturbation solution is obtained by a classical perturbation technique in which the time variable is expanded in multiscale to eliminate secular terms. The Hamiltonian solution is derived from the canonical transformation in the Hamiltonian theory of water waves. By comparing the two types of solutions, it is found that they are completely equivalent for the first- and second-order solutions and the nonlinear dispersion, but for the third-order part only the sum–sum terms are the same. Due to the canonical transformation that could completely separate the dynamic and bound harmonics, the Hamiltonian solutions break through the difficulty that the perturbation theory breaks down due to singularities in the transfer functions when the quartet resonance criterion is satisfied. Furthermore, it is also found that some time-averaged quantities based on the Hamiltonian solution, such as mean potential energy and mean kinetic energy, are equal to those in the initial state in which the sea surface is assumed to be a Gaussian random process. This is because there are associated conserved quantities in the Hamiltonian form. All of these show that the Hamiltonian solution is more reasonable and accurate to describe the third-order steady-state wave field. Finally, based on the Hamiltonian solution, some statistics are given such as the volume flux, skewness, excess kurtosis, and non-uniqueness of the induced mean flow and mean surface.

### On two approaches to the third-order solution of surface gravity waves

A third-order approximate solution for surface gravity waves in the finite water depth is studied in the context of potential flow theory. This solution corresponds to the steady-state part of a multidirectional irregular wave field and provides explicit expressions for the surface elevation, free-surface velocity potential, and velocity potential. The amplitude dispersion relation is also provided. Two approaches are used to derive the third-order analytical solution, resulting in two types of approximate solutions: the perturbation solution and the Hamiltonian solution. The perturbation solution is obtained by a classical perturbation technique in which the time variable is expanded in multiscale to eliminate secular terms. The Hamiltonian solution is derived from the canonical transformation in the Hamiltonian theory of water waves. By comparing the two types of solutions, it is found that they are completely equivalent for the first- and second-order solutions and the nonlinear dispersion, but for the third-order part only the sum–sum terms are the same. Due to the canonical transformation that could completely separate the dynamic and bound harmonics, the Hamiltonian solutions break through the difficulty that the perturbation theory breaks down due to singularities in the transfer functions when the quartet resonance criterion is satisfied. Furthermore, it is also found that some time-averaged quantities based on the Hamiltonian solution, such as mean potential energy and mean kinetic energy, are equal to those in the initial state in which the sea surface is assumed to be a Gaussian random process. This is because there are associated conserved quantities in the Hamiltonian form. All of these show that the Hamiltonian solution is more reasonable and accurate to describe the third-order steady-state wave field. Finally, based on the Hamiltonian solution, some statistics are given such as the volume flux, skewness, excess kurtosis, and non-uniqueness of the induced mean flow and mean surface.

### Elasto-inertial microparticle focusing in straight microchannels: A numerical parametric investigation

Elasto-inertial microfluidic particle separation has attracted attention in biotechnological applications due to its passive nature and enhanced versatility compared to inertial systems. Developing a robust elasto-inertial sorting device can be facilitated with numerical simulation. In this study, a numerical parametric investigation was undertaken to study elasto-inertial focusing of microparticles in a straight microchannel. Our goal was to develop an approach that could be both accurate and easily implementable on the commercial solvers. We simulated the flow field using the Carreau model. The resulting elastic lift force was implemented based on an approximation of the Oldroyd-B model. Results were verified and validated against experimental measurements by us and others. A parametric study was conducted to investigate elasto-inertial particle focusing considering the important non-dimensional numbers such as the Reynolds number (Re), the Deborah number (De), dimensionless channel length (L), and blockage ratio ([math]). Based on this investigation, the commonly used design threshold, that is, [math], for particle focusing was modified and a new threshold was proposed [math]. This reduced particle dispersion throughout the width of the channel from [math] to [math]. Based on this analysis and the new thresholding scheme, an empirical non-dimensional correlation was developed to predict elasto-inertial particle dispersion in straight square cross-sectional microchannels. Using this new correlation, variation in predicted dispersion was reduced from [math] to less than [math]. Our model can be used to optimize the design of elasto-inertial microfluidic particle sorters to improve experimental outcomes.

### A novel framework for cost-effectively reconstructing the global flow field by super-resolution

Fluid data are of great significance for analyzing the fluid structure and understanding the law of fluid movement. Apart from the experimental test, the computational fluid dynamics (CFD) method has been widely applied in the field of fluid dynamics over the past few decades. However, due to the high computational costs of CFD method and the limitation of computational resources, it is still challenging to accurately calculate and obtain the high-resolution (HR) flow fields. To this end, a novel framework based on the super-resolution (SR) algorithm, namely, new enhanced down-sampled skip-connection and multi-scale (E-DSC/MS), is reported to achieve the HR global flow reconstruction from low-resolution data. Through the new SR flow reconstruction method, the HR flow fields of two benchmark 2D cases (i.e., cylinder and hydrofoil) are precisely and efficiently predicted using a universal SR model. The effectiveness of the new E-DSC/MS algorithm is tested by comparing it with the traditional super-resolution convolution neural network and U-net in terms of the velocity field prediction of the self-region (training region) and other-region (untrained region). The result shows that the universal SR flow reconstruction framework is able to increase the spatial resolution of velocity field by 16 times, and flow fields reconstructed by E-DSC/MS are in good agreement with the ground-truth data. In addition, the E-DSC/MS model could reconstruct the global flow field with a correlation coefficient of more than 99% regardless of the selection of the arbitrary region/window for SR training. The present method overcomes the limitation of the existing techniques in efficiently reconstructing HR flow field, which helps to reduce the requirement for expensive experimental equipment and to accelerate the CFD simulation process.

### Elasto-inertial microparticle focusing in straight microchannels: A numerical parametric investigation

Elasto-inertial microfluidic particle separation has attracted attention in biotechnological applications due to its passive nature and enhanced versatility compared to inertial systems. Developing a robust elasto-inertial sorting device can be facilitated with numerical simulation. In this study, a numerical parametric investigation was undertaken to study elasto-inertial focusing of microparticles in a straight microchannel. Our goal was to develop an approach that could be both accurate and easily implementable on the commercial solvers. We simulated the flow field using the Carreau model. The resulting elastic lift force was implemented based on an approximation of the Oldroyd-B model. Results were verified and validated against experimental measurements by us and others. A parametric study was conducted to investigate elasto-inertial particle focusing considering the important non-dimensional numbers such as the Reynolds number (Re), the Deborah number (De), dimensionless channel length (L), and blockage ratio ([math]). Based on this investigation, the commonly used design threshold, that is, [math], for particle focusing was modified and a new threshold was proposed [math]. This reduced particle dispersion throughout the width of the channel from [math] to [math]. Based on this analysis and the new thresholding scheme, an empirical non-dimensional correlation was developed to predict elasto-inertial particle dispersion in straight square cross-sectional microchannels. Using this new correlation, variation in predicted dispersion was reduced from [math] to less than [math]. Our model can be used to optimize the design of elasto-inertial microfluidic particle sorters to improve experimental outcomes.

### A novel framework for cost-effectively reconstructing the global flow field by super-resolution

Fluid data are of great significance for analyzing the fluid structure and understanding the law of fluid movement. Apart from the experimental test, the computational fluid dynamics (CFD) method has been widely applied in the field of fluid dynamics over the past few decades. However, due to the high computational costs of CFD method and the limitation of computational resources, it is still challenging to accurately calculate and obtain the high-resolution (HR) flow fields. To this end, a novel framework based on the super-resolution (SR) algorithm, namely, new enhanced down-sampled skip-connection and multi-scale (E-DSC/MS), is reported to achieve the HR global flow reconstruction from low-resolution data. Through the new SR flow reconstruction method, the HR flow fields of two benchmark 2D cases (i.e., cylinder and hydrofoil) are precisely and efficiently predicted using a universal SR model. The effectiveness of the new E-DSC/MS algorithm is tested by comparing it with the traditional super-resolution convolution neural network and U-net in terms of the velocity field prediction of the self-region (training region) and other-region (untrained region). The result shows that the universal SR flow reconstruction framework is able to increase the spatial resolution of velocity field by 16 times, and flow fields reconstructed by E-DSC/MS are in good agreement with the ground-truth data. In addition, the E-DSC/MS model could reconstruct the global flow field with a correlation coefficient of more than 99% regardless of the selection of the arbitrary region/window for SR training. The present method overcomes the limitation of the existing techniques in efficiently reconstructing HR flow field, which helps to reduce the requirement for expensive experimental equipment and to accelerate the CFD simulation process.

### Passage of surfactant-laden and particle-laden drops through a contraction

Author(s): Franz De Soete, Léa Delance, Nicolas Passade-Boupat, Michael Levant, Emilie Verneuil, François Lequeux, and Laurence Talini

The flow of either particle-laden or surfactant-laden drops through a contraction under an imposed pressure has been investigated in a microfluidic setup. The drop deformation generates surface concentration gradients in adsorbed species, which results in surface tension gradients. Crossing of the contraction is driven by the coupling between the drop flow and surface tension gradients and can result in larger passage times for surfactant-laden drops.

[Phys. Rev. Fluids 6, 093601] Published Thu Sep 02, 2021

### Armstrong liquid bridge: Formation, evolution and breakup

Author(s): Xueqin Pan, Man Hu, Bingrui Xu, Feng Wang, Peng Huo, Fangqi Chen, Zhibo Gu, and Daosheng Deng

This work revisits the liquid bridge, which was observed by Lord William G. Armstrong in 1893, from a fresh perspective of its stability and final fate in terms of its lifetime. Remarkably, a water fall and the associated effective length are strongly correlated with the breakup of the liquid bridge. The linear stability analysis of an electrified jet agrees with experiments well. These results shed light on the underlying physical mechanism and on promising technological applications via active regulation and control of a liquid bridge.

[Phys. Rev. Fluids 6, 093901] Published Thu Sep 02, 2021

### A numerical study on water entry of cylindrical projectiles

A series of numerical experiments carried out on the water entry of circular cylinders are presented in this study. A cylinder was entering into the water with a prescribed inclined angle and velocity. The interface between water and air is tracked by the piecewise linear interface calculation schemes in conjunction with the volume of fluid method. Overset meshes, which have been widely used for problems with relative motions, are applied to handle the moving cylinder. The numerical model is built on the framework of OpenFOAM, which is an open-source C++ toolbox. The results of the numerical model, such as the transient positions and inclined angles of the moving circular cylinder, have been validated with experimental data in the literature. The fluid physics of the oblique water entry problem has been examined. The formation and development of the air entrapment have been explored. Parametric studies on the hydrodynamics of the water entry problem have been performed. It has been revealed that the head geometry, entry impact velocity, entry inclined angle, liquid density, and object density are of considerable significance for the penetration depth and inclination of the diving cylinder. Surface wetness, which affects the detachment of the air channel, has also been studied.

### A numerical study on water entry of cylindrical projectiles

A series of numerical experiments carried out on the water entry of circular cylinders are presented in this study. A cylinder was entering into the water with a prescribed inclined angle and velocity. The interface between water and air is tracked by the piecewise linear interface calculation schemes in conjunction with the volume of fluid method. Overset meshes, which have been widely used for problems with relative motions, are applied to handle the moving cylinder. The numerical model is built on the framework of OpenFOAM, which is an open-source C++ toolbox. The results of the numerical model, such as the transient positions and inclined angles of the moving circular cylinder, have been validated with experimental data in the literature. The fluid physics of the oblique water entry problem has been examined. The formation and development of the air entrapment have been explored. Parametric studies on the hydrodynamics of the water entry problem have been performed. It has been revealed that the head geometry, entry impact velocity, entry inclined angle, liquid density, and object density are of considerable significance for the penetration depth and inclination of the diving cylinder. Surface wetness, which affects the detachment of the air channel, has also been studied.

### Diffusion of gravity waves by random space inhomogeneities in pancake-ice fields. Theory and validation with wave buoys and synthetic aperture radar

We study the diffusion of ocean waves by ice bodies much smaller than a wavelength, such as pancakes and small ice floes. We argue that inhomogeneities in the ice cover at scales comparable to that of the wavelength significantly increase diffusion, producing a contribution to wave attenuation comparable to what is observed in the field and usually explained by viscous effects. The resulting attenuation spectrum is characterized by a peak at the scale of the inhomogeneities in the ice cover, which could explain the rollover of the attenuation profile at small wavelengths observed in field experiments. The proposed attenuation mechanism leads to the same behaviors that would be produced by a viscous wave model with effective viscosity linearly dependent on the ice thickness. This may explain recent findings that viscous wave models require a thickness-dependent viscosity to fit experimental attenuation data. Experimental validation is carried out using wave buoy attenuation data and synthetic aperture radar image analysis.

### Diffusion of gravity waves by random space inhomogeneities in pancake-ice fields. Theory and validation with wave buoys and synthetic aperture radar

We study the diffusion of ocean waves by ice bodies much smaller than a wavelength, such as pancakes and small ice floes. We argue that inhomogeneities in the ice cover at scales comparable to that of the wavelength significantly increase diffusion, producing a contribution to wave attenuation comparable to what is observed in the field and usually explained by viscous effects. The resulting attenuation spectrum is characterized by a peak at the scale of the inhomogeneities in the ice cover, which could explain the rollover of the attenuation profile at small wavelengths observed in field experiments. The proposed attenuation mechanism leads to the same behaviors that would be produced by a viscous wave model with effective viscosity linearly dependent on the ice thickness. This may explain recent findings that viscous wave models require a thickness-dependent viscosity to fit experimental attenuation data. Experimental validation is carried out using wave buoy attenuation data and synthetic aperture radar image analysis.

### Frictional granular flows of rod and disk mixtures with particle shape distributions

Three-dimensional simulations of polydisperse shear flows of rod and disk mixtures are performed using the discrete element method. The effects of particle shape distribution on flow behaviors are investigated assuming that all particles have the same volume and density but different shapes in the simulations. The solid phase stresses and bulk friction coefficients show a strong dependence on the particle alignment and the structural anisotropy of interparticle contacts. The combined effects of interparticle friction and particle shape difference lead to larger stresses for mixtures of different particle shapes than the pure particle species in dense shear flows. For frictionless and frictional flows with particle shape distributions, it is observed that the particle fluctuating velocities follow non-Maxwellian distributions and the fluctuating kinetic energies are unequally partitioned among the different particle species.

### Frictional granular flows of rod and disk mixtures with particle shape distributions

Three-dimensional simulations of polydisperse shear flows of rod and disk mixtures are performed using the discrete element method. The effects of particle shape distribution on flow behaviors are investigated assuming that all particles have the same volume and density but different shapes in the simulations. The solid phase stresses and bulk friction coefficients show a strong dependence on the particle alignment and the structural anisotropy of interparticle contacts. The combined effects of interparticle friction and particle shape difference lead to larger stresses for mixtures of different particle shapes than the pure particle species in dense shear flows. For frictionless and frictional flows with particle shape distributions, it is observed that the particle fluctuating velocities follow non-Maxwellian distributions and the fluctuating kinetic energies are unequally partitioned among the different particle species.

### Experimental observation of flow-induced vibrations of a transversely oscillating D-section prism

Fluid–structure interactions of non-circular prisms are of significance from a scientific and practical viewpoint. In this paper, we present a new experimental observation of flow-induced vibrations and associated spectral characteristics of a transversely oscillating D-section prism at an angle of attack α varying from 0° to 180°, where α = 0° and 180° represent the configuration with the upstream curved and flat part, respectively. The Reynolds number range is 530–9620, and the reduced velocity range is 1–32, based on the projected prism width in the crossflow direction. The mass ratio of the prism is 11.35, and the structural damping ratio in still water is 0.0036. Based on the response amplitudes and spectral traits, the D-prism exhibits the typical vortex-induced vibration (VIV) at α = 0°–30°, the first transition response at α = 45°–60°, the small-amplitude VIV response at α = 105°–135°, the second transition response at α = 150°–165°, the combined VIV-galloping response at α = 90°, and the pure galloping at α = 75° and 180°. The second transition response between low- and high-amplitude branches is found to be hysteretic and intermittent. Flow physics behind the D-prism responses are further elucidated by the wake patterns based on a high-speed camera and the flow velocity spectra downstream of the prism.