# Latest papers in fluid mechanics

### Asymmetric vortexes induced traveling drop on an oscillatory liquid bath

The traveling and dancing behaviors of the bouncing drops on the oscillating liquid bath have been reported in several investigations. It was shown that the normal force during the impact of the drop on an inclined liquid surface is responsible for the traveling of a 0.8 mm-sized drop. Here, we report that a pair of vortexes can be induced by the repeated impact of a 2 mm-sized drop on an oscillatory liquid bath. The traveling of a large drop on the oscillatory liquid bath with an inclined bottom is found to be associated with the induced asymmetric vortex flow underneath the liquid surface. The effect of the vortex flow becomes significant for the size of a drop larger than 1.8 mm. Two-coupled drops with different sizes are found to be self-propelled on the oscillatory liquid bath with a flat bottom. The coupled drops propagate toward the direction of the small-sized drop. The distribution of the vortex flow is investigated by the particle image velocimetry (PIV) technique and the numerical simulation of the acoustic streaming model. PIV measurement and numerical simulation of the speed distribution of the vortex flows induced by the single bouncing drop and two-coupled drops show consistent results. It is suspected that the traveling of two-coupled drops is associated with the motion of the small drop and the liquid flow near the liquid surface.

### Air-water meniscus shape in superhydrophobic triangular microgroove is dictated by a critical pressure under dynamic conditions

We bring out a critical force for shape transition of air-water meniscus in superhydrophobic triangular microgrooves under dynamic conditions, considering an intricate interplay of the viscous and capillary forces. A closed form theoretical expression for the critical force depicts its explicit dependence on the groove geometry and relevant physical properties. A negative value of this critical force denotes a convex meniscus shape, whereas a positive value signifies a concave meniscus shape. Considering the shape transition, the critical pressure is further interpreted to denote a physical condition under which the meniscus is nontrivially flat, despite the existence of surface tension forces. Our analysis opens up a paradigm by which the meniscus shape in a groove can be virtually controlled at will, consistent with the specific requirements such as drag reduction, as demanded by the application on hand.

### The jet characteristics of bubbles near mixed boundaries

The jet characteristics of bubbles near mixed boundaries have been the focus of research in many fields. As the associated parameters are complicated, relatively few reports have been published. In this paper, a numerical model is established by considering the influence of the free surface and a mutual vertical wall using the boundary element method. To determine the jet characteristics of collapsing bubbles in different areas, two nondimensional parameters must be investigated: the distance γv from the bubble to the vertical wall and the distance γh from the bubble to the horizontal wall. At the same time, the buoyancy parameter δ cannot be ignored. First, the jet characteristics under an infinite vertical solid wall are discussed; furthermore, the jet direction in the stage of collapsing bubble under combined boundaries without buoyancy is studied, and we find that the variation amplitude of the jet angle changes with the free surface. Considering the buoyancy, we then divide the total area into six regions with different ranges of jet angle under small buoyancy values, allowing the significant effect of buoyancy to be studied as δ increases. In addition, we study the jet velocity qualitatively under the condition of negligible buoyancy and find that a peak jet velocity may exist at mid water depths.

### An investigation for influence of intense thermal convection events on wall turbulence in the near-neutral atmospheric surface layer

Based on the field observation data in the near-neutral atmospheric surface layer (ASL) at the Qingtu Lake Observation Array, a new experimental data processing of the second-order statistic distribution of the high Reynolds number wall turbulence was presented which considered the influence of the intense thermal convection events (ITCEs). Following the conventional data selection in the literature, i.e., |z/L|, it is known that the variation of the large- and/or the very-large-scale motions (LSMs and VLSMs) cannot be effectively performed only by this method, which motivates us to find other factors influencing these turbulent motions, e.g., the ITCEs. From the data analysis of the probability density distribution of vertical heat flux, it is found that although its mean value tends to zero, its variance is large rather than zero, which suggests to us some ITCEs exist in the natural motions, although it has less frequent occurrences. In order to characterize the effect of such ITCEs, an additional parameter ψ for scaling the ratio of the buoyancy force to the viscous force is proposed in the data selection progress. The results show that the greater the |ψ|, the greater the impact of the ITCEs on ASL wall turbulence. Furthermore, our investigation reveals that the ITCEs may be one of the reasons why the VLSMs exhibit the Top-Down mechanism.

### Quasi-classical trajectory-based non-equilibrium chemical reaction models for hypersonic air flows

Phenomenological models, such as Park’s widely used two temperature model, overpredict the reaction rate coefficients at vibrationally cold conditions and underpredict it at vibrationally hot conditions. To this end, two new chemical reaction models, the nonequilibrium total temperature (NETT) and nonequilibrium piecewise interpolation models for the continuum framework are presented. The focus is on matching the reaction rate coefficients calculated using a quasiclassical trajectory based dissociation cross section database. The NETT model is an intuitive model based on physical understanding of the reaction at a molecular level. A new nonequilibrium parameter and the use of total temperature in the exponential term of the Arrhenius fit ensure the NETT model has a simple and straightforward implementation. The efficacy of the new model was investigated for several equilibrium and nonequilibrium conditions in the form of heat bath simulations. Additionally, two-dimensional hypersonic flows around a flat blunt-body were simulated by employing various chemical reaction models to validate the new models using experimental shock tube data. Park’s two temperature model predicted higher dissociation rates and a higher degree of dissociation leading to lower peak vibrational temperatures compared to those predicted by the new nonequilibrium models. Overall, the present work demonstrates that the new nonequilibrium models perform better than Park’s two temperature model, especially in simulations with a high degree of nonequilibrium, particularly as observed in re-entry flows.

### Effects of upstream pipe length on pipe-cavity jet noise

An experimental study is carried out to quantify the acoustic radiation of underexpanded pipe-cavity jet noise. Pipe-cavity configurations with different upstream pipe lengths are studied over a range of Mach numbers. Detailed acoustic measurements such as frequency analysis, sound pressure levels, directivity, and acoustic power analysis are carried out to show the effect of upstream pipe length. Finite element simulations are carried to predict the resonance frequencies of the pipe-cavity. Results of simulation with zero mean flow condition match well with theoretical results and the present experiments. The far-field acoustic spectrum exhibits strong cavity tones and shock associated noise. The results show that the pipe-cavity resonates close to the combined tangential-longitudinal mode. The increase in shear layer thickness tends to attenuate the cavity tones, with a small increase in screech tonal noise. An increase in upstream pipe length leads to a decrease in overall sound pressure levels and acoustic power.

### Phase transition in time-reversible Navier-Stokes equations

Author(s): Vishwanath Shukla, Bérengère Dubrulle, Sergey Nazarenko, Giorgio Krstulovic, and Simon Thalabard

We present a comprehensive study of the statistical features of a three-dimensional (3D) time-reversible truncated Navier-Stokes (RNS) system, wherein the standard viscosity ν is replaced by a fluctuating thermostat that dynamically compensates for fluctuations in the total energy. We analyze the st...

[Phys. Rev. E 100, 043104] Published Wed Oct 09, 2019

### Normal form of synchronization and resonance between vorticity waves in shear flow instability

Author(s): Eyal Heifetz and Anirban Guha

A minimal model of linearized two-dimensional shear instabilities can be formulated in terms of an action-at-a-distance, phase-locking resonance between two vorticity waves, which propagate counter to their local mean flow as well as counter to each other. Here we analyze the prototype of this inter...

[Phys. Rev. E 100, 043105] Published Wed Oct 09, 2019

### How evaporation and condensation lead to self-oscillations in the single-branch pulsating heat pipe

Author(s): Albert Tessier-Poirier, Thomas Monin, Étienne Léveillé, Stéphane Monfray, Fabien Formosa, and Luc G. Fréchette

The physics behind the instability at the source of oscillations in a single-branch pulsating heat pipe is investigated. Oscillations produced by the resonator increase in amplitude when pressure induced by evaporation-condensation (positive feedback mechanism) overcomes the viscous losses (dissipation).

[Phys. Rev. Fluids 4, 103901] Published Wed Oct 09, 2019

### Flow field evolution and entrainment in a free surface plunging jet

Author(s): Syed Harris Hassan, Tianqi Guo, and Pavlos P. Vlachos

An investigation finds that in free-surface plunging jets, shear layer vortices form right below the free surface, then develop and disintegrate faster than vortices in canonical free jets. This leads to shorter potential cores, faster decay of the mean centerline velocity, and enhanced liquid entrainment from the ambient.

[Phys. Rev. Fluids 4, 104603] Published Wed Oct 09, 2019

### Effect of electrostatic forces on the distribution of drops in turbulent channel flows

The effect of electrostatic forces on the distribution of drops in turbulent channel flows is examined by direct numerical simulations. The droplets and suspending fluid are assumed to be leaky dielectric fluids. We set the electrical conductivity ratio (R = σi/σo) smaller than the dielectric permittivity ratio (S−1 = εi/εo) to drive the flow from the drop poles to their equators. The results show that an applied external electric field has a significant effect on the microstructure and the flow properties. For flows without an electric field, where the Mason (Mn) number is infinity, the drops aggregated in the core of the channel and the liquid streamwise velocity are similar to those in single-phase flow. For Mn = 0.1, a low electric intensity, most of the drops are driven to the walls due to the unbalanced electric force on the drop interface. For Mn = 0.05, drops are more likely to stick together because of the stronger combination of electrohydrodynamic effect and dielectrophoretic force between drops. Therefore, the number of drops in the middle of the channel increases while still many drops are in the wall layer. For Mn = 0.007, the electric intensity is very strong and all the drops in the channel tend to line up and form columns spanning the channel width. These columns become unstable when the flow drives them close to each other. It is also found that an increase of the electric intensity can lead to an increase in the average wall shear stress. In addition, the liquid streamwise velocity will become more uniform, which means the effective viscosity of the system is increased, when Mn = 0.007.

### Intermittent fluid connectivity during two-phase flow in a heterogeneous carbonate rock

Author(s): Catherine Spurin, Tom Bultreys, Branko Bijeljic, Martin J. Blunt, and Samuel Krevor

Subsurface fluid flow is ubiquitous in nature, and understanding the interaction of multiple fluids as they flow within a porous medium is central to many geological, environmental, and industrial processes. It is assumed that the flow pathways of each phase are invariant when modeling subsurface fl...

[Phys. Rev. E 100, 043103] Published Tue Oct 08, 2019

### Thermoconvective instabilities in a horizontal porous annulus with an external wavy wall

Author(s): Jabrane Belabid

A numerical analysis reveals that the heat transfer inside a horizontal porous annulus filled with a saturated porous medium depends strongly on the waviness of the cold wall. Particular attention is paid to the influence of the waviness parameters on the thermoconvective instabilities.

[Phys. Rev. Fluids 4, 103501] Published Tue Oct 08, 2019

### Experimental investigation of vertical turbulent transport of a passive scalar in a boundary layer: Statistics and visibility graph analysis

Author(s): G. Iacobello, M. Marro, L. Ridolfi, P. Salizzoni, and S. Scarsoglio

The dynamics of a passive scalar plume is experimentally studied in a rough-wall turbulent boundary layer. Besides classical statistics, complex networks are exploited to highlight the temporal structure of vertical turbulent transport series in terms of occurrence and intensity of extreme events.

[Phys. Rev. Fluids 4, 104501] Published Tue Oct 08, 2019

### Energy-based analysis and anisotropic spectral distribution of internal gravity waves in strongly stratified turbulence

Author(s): Naoto Yokoyama and Masanori Takaoka

The weak turbulence of internal gravity waves and the strong turbulence of eddies coexist in stratified turbulence. The wave-number range of the anisotropic weak-wave turbulence is identified based on energy decomposition and characteristic time scales.

[Phys. Rev. Fluids 4, 104602] Published Tue Oct 08, 2019

### Inertial effects in triple-layer core-annular pipeline flow

Triple-layer core-annular flow is a novel methodology for efficient heavy oil transportation. As usual, high shear rates concentrating in a lubricating fluid layer reduce the pressure drop significantly. Novel is the use of a viscoplastic fluid bounding the lubricant and protecting the transported core. For sufficiently large yield stress, the skin remains unyielded, preventing any interfacial instabilities. By shaping the skin, we generate lubrication forces to counterbalance buoyancy of the core fluid, i.e., an eccentric position of the core is the result of buoyancy and lubrication forces balancing. Here, we extend the feasibility of this method to large pipes and higher flow rates by considering the effects of inertia and turbulence in the lubrication layer. We show that the method can generate enough lubrication force to balance the buoyancy force for a wide range of density differences and pipe sizes if the proper shape is imposed on the unyielded skin.

### Notable effect of the subgrid-scale stress anisotropy on mean-velocity prediction through budget of the grid-scale Reynolds-shear stress

In large eddy simulation (LES), the mean-velocity distribution in wall turbulence depends strongly on the distribution of the ensemble-averaged Reynolds (Re) shear stress, which consists of two parts: the resolved grid-scale (GS) and unresolved subgrid-scale (SGS) components. As the grid resolution becomes coarser, the GS component decreases and thus the SGS component must increase to compensate for this. The GS decrease is originally caused by filtering, through which the power spectrum is cut off mainly in the high-wavenumber region. Therefore, the SGS model has been discussed mostly in terms of the energy transfer between the GS and SGS components. Recently, however, some studies have found that the SGS-stress anisotropy directly influences instantaneous GS vortex motions. This also means that the SGS stress may have a large effect on the ensemble-averaged GS Re stress because the instantaneous fluctuation of the SGS stress correlates with that of the velocity gradient in the GS budget. In this study, we investigate in detail the effect of the SGS stress on predicting the resolved GS Re shear stress through its budget. For this purpose, we perform a priori tests with highly resolved LES data of a plane channel flow. The knowledge obtained is then confirmed by a posteriori tests for various grid resolutions and Reynolds numbers. It is found that the SGS-stress anisotropy is very important for providing a reasonable trend of the GS Re shear stress, leading to more accurate prediction of the mean velocity for coarse-grid resolutions.

### Application of two-branch deep neural network to predict bubble migration near elastic boundaries

Compared to the drawbacks of traditional experimental and numerical methods for predicting bubble migration, such as high experimental costs and complex simulation operations, the data-driven approach of using deep neural network algorithms can provide an alternative method. The objective of this paper is to construct a two-branch deep neural network (TBDNN) model in order to improve the high-fidelity bubble migration results and further reduce dependence on the quantity of experimental data. A TBDNN model is obtained by embedding the features of the Kelvin impulse into a basic deep neural network (BDNN) system. The results show that compared to the original BDNN model, TBDNN performs much better in accurately predicting bubble migration based on the same amount of training data. Using the TBDNN model, the critical condition of bubble oscillation at a fixed location can be detected under the influence of boundary properties (normalized stiffness and mass) and bubble standoff. Furthermore, the initial position of the bubble and normalized stiffness of boundaries have a positive correlation with bubble migration, whereas normalized mass has a negative impact. It was found that the normalized mass of boundaries plays the most important role in affecting bubble migration compared to the standoff and stiffness when using the method of variable sensitivity analysis.

### Solutal convection induced by dissolution

Author(s): Julien Philippi, Michael Berhanu, Julien Derr, and Sylvain Courrech du Pont

The buoyancy instability occurring at the interface of a soluble body suddenly immersed in a quiescent solvent is explored. Numerical simulations are used to derive and confirm scaling laws based on a constant solutal Rayleigh number. Dissolution erosion rates are predicted in some geological situations.

[Phys. Rev. Fluids 4, 103801] Published Mon Oct 07, 2019

### Sedimentation of a small sphere in stratified fluid

Author(s): Hojun Lee, Itzhak Fouxon, and Changhoon Lee

An extensive theoretical and numerical study of gravitational settling of small particles in a stratified fluid was performed. Adopting the integral equation on surface traction, we derived the drag enhancement due to stratification at low Reynolds and Peclet numbers, and confirmed with simulations.

[Phys. Rev. Fluids 4, 104101] Published Mon Oct 07, 2019