# Latest papers in fluid mechanics

### Quantifying the role of Darrieus–Landau instability in turbulent premixed flame speed determination at various burner sizes

To probe the impact of Darrieus–Landau (DL) instability on turbulent premixed flame propagation at various burner sizes, methane–air premixed flames from five Bunsen-type burners with different nozzle diameters (4 mm, 6 mm, 8 mm, 10 mm, and 12 mm) were investigated at Reynolds numbers ranging from 1000 to 8500. The flame curvatures used to identify DL instability were determined using Mie scatter images captured by a particle image velocimetry system. The flame speed was further derived by applying an asymmetric hypothesis to the images. The energy-frequency spectrum of the inflow disturbance was determined using a hot-wire anemometry system, and specific wavelet transform analysis was performed to investigate the dependence of DL instability on the proportion of effective disturbances (P ed ) and quantify the role of DL instability in determining the turbulent flame speed. The results showed that the burner diameter had an obvious effect on the presence of DL instability and its role in flame propagation. The ability of DL instability to enhance the flame curvature skewness and the turbulent flame speed was closely related to P ed . P ed increased when the burner diameter increased from 6 mm to 12 mm, thus enhancing the DL instability. Changing the burner diameter also affected the interplay between DL instability and turbulence. The above interactions and their effects on the flame speed during the change of inflow disturbances could be formulated by P ed . Finally, a P ed -based correlation was proposed to describe the dependence of the turbulent flame speed on the burner size.

### Motion and clustering of bonded particles in narrow solid–liquid fluidized beds

This paper presents an experimental and numerical investigation of solid–liquid fluidized beds consisting of bonded spheres in very narrow tubes, i.e., when the ratio between the tube and grain diameters is small. In narrow beds, high confinement effects have proved to induce crystallization, jamming, and different patterns, which can be intensified or modified if some grains are bonded together. In order to investigate that, we produced duos and trios of bonded aluminum spheres with a diameter of 4.8 mm and formed beds consisting either of 150–300 duos or 100–200 trios in a 25.4 mm-ID pipe, which were submitted to water velocities above those necessary for fluidization. For the experiments, we filmed the bed with high-speed and conventional cameras and processed the images, obtaining measurements at both the bed and grain scales. For the numerical part, we computed the bed evolution for the same conditions with a computational fluid dynamics–discrete element method code. Our results show distinct motions for individual duos and trios and different structures within the bed. We also found that jamming may occur suddenly for trios, where even the microscopic motion (fluctuation at the grain scale) stops, calling into question the fluidization conditions for those cases.

### Non-normal effect of the velocity gradient tensor and the relevant subgrid-scale model in compressible turbulent boundary layer

The non-normal effects of the velocity gradient tensor (VGT) in a compressible turbulent boundary layer are studied by means of the Schur decomposition of the VGT into its normal and non-normal parts. Based on the analysis of the relative importance of them, it is found that the non-normal part significantly affects the dynamics of the VGT in the wall-bounded turbulent flow and the relevant non-normal effect has a dominant influence on the enstrophy and dissipation. It is revealed that the deviatoric part of the pressure Hessian is associated with the non-normal effect and the isotropic part is associated with the normal effect. The pressure Hessian significantly influences the vortex stretching. The non-normal effect reinforces the preferences for the vorticity vector to align with the intermediate strain-rate eigenvector and to be perpendicular to the extensive and compressive strain-rate eigenvector in the near-wall region. The non-normal effect also reduces the intermediate eigenvalue of the strain-rate tensor. Furthermore, a subgrid scale (SGS) model that separately considers the normal and non-normal effects is proposed based on the above characters and is verified to give a better prediction of the SGS dissipations in the wall-bounded turbulent flow.

### Effects of size ratio and inter-cylinder spacing on wake transition in flow past finite inline circular cylinders mounted on plane surface

Three-dimensional numerical computations have been carried out in flow past two inline finite-height circular cylinders using Open Source Field Operation and Manipulation. Investigations have been carried out for the varying Reynolds number (Re) ranging from 150 to 300. The diameter of the upstream cylinder is varied in such a way that the size ratio (SR, ratio of the diameter of the upstream cylinder to that of the downstream cylinder) takes values of 0.25, 0.5, and 1.0. For each size of the upstream cylinder, the downstream cylinder is placed at different locations in the streamwise direction. Effects of Re, SR, and inter-cylinder spacing (S) on three-dimensional unsteady wake characteristics behind upstream and downstream cylinders have been examined using iso-Q surfaces. Unsteady wake oscillations in both the wakes are analyzed qualitatively and quantitatively in terms of Hilbert spectra and the degree of stationarity using the transverse velocity component in the wake. Different flow regimes for upstream and downstream wakes have been identified and discussed with the change in Re, SR, and S. Transitions in the wake flow are illustrated using vorticity contours, frequency spectra, and bifurcation diagram. The level of wake synchronization in the upstream wake, downstream wake, and between both the wakes has been identified with the help of the cross correlation function.

### Thin-film evolution and fingering instability of self-rewetting films flowing down an inclined plane

This paper examines the evolution patterns and essential mechanisms of flow instability of a self-rewetting fluid (SRF) coating on an inclined plane. Considering that the self-rewetting liquid has an anomalous surface tension with temperature change, some interesting phenomena will be found and should be explained. Using the thin-film model, the evolution equation of the air–liquid interface is derived, and the thickness of the liquid film is determined by a fourth-order partial differential equation. Taking T 0 (temperature corresponding to the minimum of surface tension) as a cutoff point, two representative cases of the nonlinear flow are comprehensively discussed. One is the case of T i > T 0, and the other is T i < T 0 (interfacial temperature T i ). Based on traveling wave solutions, linear stability analysis (LSA) of the small perturbation applied to the initial condition is given, and the results of LSA are confirmed and explained by the numerical simulations. Results show that the inclined angle and the Weber number always stabilize the free surface, while the Marangoni effect and the Biot number play different roles for the two cases. As T i − T 0 varies from a negative value to a positive value, the Marangoni effect switches to the reverse Marangoni effect. With T i − T 0 < 0, the Marangoni effect enhances the fingering instability, while the Marangoni effect makes the flow more stable if T i − T 0 > 0. The Biot number Bi = 1 corresponds to the most unstable state for T i < T 0 and to the most stable state for T i > T 0.

### Magnified heat transfer from curved surfaces: A scaling prediction

We report the first definitive Nusselt number scale of thermal boundary layers from curved surfaces characterized by the proposed non-dimensional curvature parameter ξ = R 0/(H Ra −1/4), where R 0 denotes the radius of a curved surface, H denotes the corresponding finite height, and Ra denotes the global Rayleigh number of a virtual reference thermal boundary layer on a vertical flat surface. The Nusselt number scale is given by Nu ∼ ξ −1/5 Ra 1/4 in which Nu ∼ Ra 1/4 is the scale for the flat surface case, revealing that curved thermal boundary layers could present times-of-magnitude larger heat flux with the curvature parameter being ξ ≪ 1. The velocity and thickness scales are also given by [math] and [math].

### Slippage effect on interfacial destabilization driven by standing surface acoustic waves under hydrophilic conditions

Author(s): J. Muñoz, J. Arcos, I. Campos-Silva, O. Bautista, and F. Méndez

The influence of the slippage phenomenon over the interfacial dynamics of a millimeter-order fluid drop exposed to surface acoustic wave atomization is numerically studied under hydrophilic conditions. Implementation of the Navier-slip model into the governing hydrodynamic equations yields an interfacial evolution equation. The solution suggests that slippage at the wall constitutes a valuable phenomenon to manipulate the parent drop geometric aspect ratio and consequently the characteristic aerosol size during the atomization process.

[Phys. Rev. Fluids 6, 024002] Published Wed Feb 03, 2021

### Nanoflows induced by MEMS and NEMS: Limits of two-dimensional models

Author(s): Alyssa T. Liem, Atakan B. Ari, Chaoyang Ti, Mark J. Cops, James G. McDaniel, and Kamil L. Ekinci

The mechanical oscillations of a miniaturized resonator generate viscous oscillatory nanoflows in the surrounding fluid. As a result, the fluid presents an effective added mass and damping to the resonator, which is commonly predicted by a two-dimensional flow model. Here, the limitations to the two-dimensional model are examined when a substrate and axial flow are present. Results from experiments and three-dimensional finite element models are presented to illustrate where and why the two-dimensional flow models break down.

[Phys. Rev. Fluids 6, 024201] Published Tue Feb 02, 2021

### Flow structure and turbulence in the near field of an immiscible buoyant oil jet

Author(s): Xinzhi Xue, Lakshmana Dora Chandrala, and Joseph Katz

Simultaneous applications of particle image velocimetry and planar laser-induced fluorescence in a refractive index matched facility are used to visualize the phase distribution and measure velocity in an immiscible low Reynolds number buoyant oil jet injected into water. Initially, mixing involves entrainment of water ligaments inward and oil ligaments outward, followed by phase fragmentation into blobs and then droplets. Phase-based conditioning reveals spatially varying discrepancies between the velocity and all Reynolds stress components in the oil and water phases. Trends are attributed to intermittency and differences in turbulence production rate.

[Phys. Rev. Fluids 6, 024301] Published Tue Feb 02, 2021

### Inertial torque on a small spheroid in a stationary uniform flow

Author(s): F. Jiang, L. Zhao, H. I. Andersson, K. Gustavsson, A. Pumir, and B. Mehlig

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. The torque acting on a small spheroid in a uniform flow is computed by numerically solving the Navier-Stokes equations. Overall, the numerical results provide a justification of recent theories for the orientation statistics of ice crystals settling in cold clouds.

[Phys. Rev. Fluids 6, 024302] Published Tue Feb 02, 2021

### Laboratory model for plastic fragmentation in the turbulent ocean

Author(s): Christophe Brouzet, Raphaël Guiné, Marie-Julie Dalbe, Benjamin Favier, Nicolas Vandenberghe, Emmanuel Villermaux, and Gautier Verhille

We study the fragmentation of deformable and brittle fibers in the inertial range of turbulence using laboratory experiments and numerical simulations. The fragmentation process is shown to be limited at small scales by a physical cut-off length due to fluid-structure interactions of the object with turbulence, and thus independent of the fiber brittleness. This scenario, comprehensively modeled by an evolution equation, leads to the accumulation of fragments slightly longer than the cut-off scale, as smaller fragments are too short to be deformed and broken by the turbulence. This result may improve our understanding of microplastic formation in the ocean.

[Phys. Rev. Fluids 6, 024601] Published Tue Feb 02, 2021

### Fluid dynamics and epidemiology: Seasonality and transmission dynamics

Epidemic models do not account for the effects of climate conditions on the transmission dynamics of viruses. This study presents the vital relationship between weather seasonality, airborne virus transmission, and pandemic outbreaks over a whole year. Using the data obtained from high-fidelity multi-phase, fluid dynamics simulations, we calculate the concentration rate of Coronavirus particles in contaminated saliva droplets and use it to derive a new Airborne Infection Rate (AIR) index. Combining the simplest form of an epidemiological model, the susceptible–infected–recovered, and the AIR index, we show through data evidence how weather seasonality induces two outbreaks per year, as it is observed with the COVID-19 pandemic worldwide. We present the results for the number of cases and transmission rates for three cities, New York, Paris, and Rio de Janeiro. The results suggest that two pandemic outbreaks per year are inevitable because they are directly linked to what we call weather seasonality. The pandemic outbreaks are associated with changes in temperature, relative humidity, and wind speed independently of the particular season. We propose that epidemiological models must incorporate climate effects through the AIR index.

### On formation of dry spots in heated liquid films

Here, the phenomenon of food sticking when frying in a frying pan is experimentally explained. Thermocapillary convection causes a dry spot formation in the center of the frying pan upon heating of the sunflower oil film. It is shown that the speed of formation of a dry spot is similar to the speed of receding motion of the edge of a droplet upon impact and spreading on a solid surface. This allows theoretical determination of the speed of dewetting. For the thin liquid film flowing vertically over a solid surface, the critical volumetric flow rate qcr partitions two regimes: metastable or subcritical, when small perturbation of the film free surface results in the film rupture (q < qcr) and stable or supercritical at q > qcr. For the falling thin liquid film, the critical volumetric flow rate qcr partitions two regimes: metastable or subcritical (q < qcr) and stable or supercritical at q > qcr. At q < qcr, small deformations of the film free surface result in the film rupture. For the case of the temperature distribution in the form of a unit step function, the fundamental solution G1(x) describing the deformation of the film free surface has been derived by the perturbation technique. This solution is important by itself since it describes the most “dangerous” film surface profile at a prescribed value of the temperature drop. For an arbitrary surface temperature distribution θ (ξ), the convolution of G1(ξ) and θ ′(ξ) yields the film thickness profile.

### Squirt flow in porous media saturated by Maxwell-type non-Newtonian fluids

Author(s): Santiago G. Solazzi, Beatriz Quintal, and Klaus Holliger

Mechanical waves, which are commonly employed for the noninvasive characterization of fluid-saturated porous media, tend to induce pore-scale fluid pressure gradients. The corresponding fluid pressure relaxation process is commonly referred to as squirt flow and the associated viscous dissipation ca...

[Phys. Rev. E 103, 023101] Published Mon Feb 01, 2021

### Delaying leading edge vortex detachment by plasma flow control at topologically critical locations

Author(s): Johannes Kissing, Bastian Stumpf, Jochen Kriegseis, Jeanette Hussong, and Cameron Tropea

Leading edge vortices on flapping wings induce high transient lift during their growth phase and increase maneuverability at low flight speeds. A hypothesis is developed and experimentally validated that the vortex growth phase on a pitching and plunging airfoil can be prolonged with dielectric barrier discharge plasma actuators. This is demonstrated for various airfoils and for different motion dynamics and kinematics.

[Phys. Rev. Fluids 6, 023101] Published Mon Feb 01, 2021

### Control of viscous fingering: From the perspective of energy evolution

Author(s): Hongzhi Ma and Quanzi Yuan

An energy model is developed to describe the linear viscous fingering (VF) phenomena from the perspective of evolution paths of energy dissipation rate. By means of the variational method, rate-altering control schemes with different scaling laws are constructed in the energy model to control whether the VF instability develops or is suppressed. Furthermore, a stable and continuous forward movement of the fluid-fluid interface is achieved through a periodic suppression scheme. The effectiveness of the energy model and all control schemes are well verified by our experiments.

[Phys. Rev. Fluids 6, 023901] Published Mon Feb 01, 2021

### Phase separation of an ionic liquid mixture assisted by a temperature gradient

Author(s): Marc Pascual, Arthur Poquet, Alexandre Vilquin, and Marie-Caroline Jullien

To aid in the recycling of ionic liquids, a method that takes advantage of capillary phenomena at small scales is presented. The phase separation is performed in a temperature gradient by the joint effects of sedimentation and thermocapillary actuation. This gives rise to a complex three-dimensional flow structure, which is quantitatively captured by our model.

[Phys. Rev. Fluids 6, 024001] Published Mon Feb 01, 2021

### Computational fluid-structure interaction of a restrained ogive-cylindrical body with a blunt elliptical base at a high incidence

Author(s): Mark Ishay, Oded Gottlieb, and David Degani

The fluid-structure interaction of an elastically restrained inclined tangent ogive-cylindrical body with a blunt elliptical base is investigated numerically. The flow is three-dimensional, compressible, and laminar, and the slender body is allowed to yaw at high incidence. The resulting response exhibits an intricate bifurcation structure that includes bistable periodic (finite amplitude) and nonstationary (small amplitude) limit cycles for moderate angles of attack, and nonstationary (finite amplitude) oscillations for high angles of attack.

[Phys. Rev. Fluids 6, 014401] Published Fri Jan 29, 2021

### Roughness, inertia, and diffusion effects on anomalous transport in rough channel flows

Author(s): Seonkyoo Yoon and Peter K. Kang

Fluid flow and mass transport in rough channels are ubiquitous phenomena occurring in numerous engineering applications and natural processes. Comprehensive numerical simulations and stochastic upscaling elucidate how the complex interplay between channel roughness, inertia, and diffusion controls solute transport in channel flows. A mechanistic link between the complex interplay and anomalous transport in rough channel flows is successfully established.

[Phys. Rev. Fluids 6, 014502] Published Fri Jan 29, 2021

### Semi-conditional variational auto-encoder for flow reconstruction and uncertainty quantification from limited observations

We present a new data-driven model to reconstruct nonlinear flow from spatially sparse observations. The proposed model is a version of a Conditional Variational Auto-Encoder (CVAE), which allows for probabilistic reconstruction and thus uncertainty quantification of the prediction. We show that in our model, conditioning on measurements from the complete flow data leads to a CVAE where only the decoder depends on the measurements. For this reason, we call the model semi-conditional variational autoencoder. The method, reconstructions, and associated uncertainty estimates are illustrated on the velocity data from simulations of 2D flow around a cylinder and bottom currents from a simulation of the southern North Sea by the Bergen Ocean Model. The reconstruction errors are compared to those of the Gappy proper orthogonal decomposition method.