# Latest papers in fluid mechanics

### Rheological manifestation of microstructural change of colloidal gel under oscillatory shear flow

The rheological manifestation of intra-cycle microstructural change of a model colloidal gel under oscillatory shearing is studied with Brownian dynamics simulation and a fully quantitative sequence of physical process (SPP) technique. The microstructural change of the model colloidal gels is identified with the rigidity concept and correlated with the rheological behavior quantified via the SPP metrics. The model colloidal gel exhibits complex nonlinear stress response in the large amplitude oscillatory shearing (LAOS), which is divided into four physical processes: viscoplastic flow, recovery network structure, early stage yielding with rupture of a few bonds, and late stage yielding accompanying catastrophic structure failure. For each process, the SPP metrics that represent rheological transitions are successfully paired to microstructural changes that are discussed in terms of rigid to soft chain structure change or vice versa. Based on our findings, we further discuss the intra-cycle rheological transition at various oscillatory shearing conditions. We show that larger deformations do not necessarily lead to a broader range of intra-cycle rheological transitions and also that the rigid chain structure affects elasticity differently in floppy and stiff networks. Our study shows that the SPP analysis is a promising tool for microstructure-rheology consistent interpretations of nonlinear rheological behavior.

### Extreme singular events associated with inertial-viscous cusp formation in fluids

Cusp singularities in fluids have been experimentally demonstrated in the past only at a low Reynolds number, Re ≪ 1, and large capillary number, Ca ≫ 1, in Newtonian or non-Newtonian fluids. Here, we show that the collapse of a free surface wave depression cavity can lead to inertial-viscous cusp formation at local Re > 1 and Ca > 1, which gives rise to extreme events, i.e., very high-velocity surface jets. The cavities are generated in a cylindrical container (2R = 10 cm), partially filled with glycerine–water solution, by parametrically forcing the axi-symmetric wave mode beyond the breaking limit. By varying the forcing amplitude and the fluid viscosity, parabolic or cusp singularities manifest, depending on the last stable wave amplitude b that determines the cavity shape. Cusp formation in collapse without bubble pinch-off, leading to very high-velocity surface jets, is obtained when b is close to the singular wave amplitude bs and Ca > 1. The free surface shape is self-similar, changing from an inertial to a viscous regime when the singularity is approached. At cusp singularity, the cavity shape takes the form of (z − Z0)/R ∼ −(r/R)2/3, where Z0 is the final cavity depth. Cavity collapse with bubble pinch-off, which occurs when b > bs, also exhibits a cusp singularity when bs < b ≤ 1.14 bs and Ca > 1, but surface jet velocities are much less because about half of the wave energy is lost.

### Influence of domain size on direct numerical simulation of turbulent flow in a moderately curved concentric annular pipe

Direct numerical simulation (DNS) of turbulent flow in a concentric annular pipe was performed using a pseudo-spectral method computer code. In order to study the effects of computational domain size on the turbulence statistics, 12 test cases of different domain sizes are compared. The characteristics of the velocity field are examined at two different Reynolds numbers. It is observed that the predictive accuracy of the first- and second-order statistics is sensitive to the axial and azimuthal domain sizes. It is also found that the scales and dynamics of turbulence structures vary with the surface curvature of the concave and convex walls. The characteristic length scales of the turbulence structures are identified through a spectral analysis, and it is observed that a minimum computational domain is required in order to accurately capture the near-wall streaky and hairpin structures of a concentric annular pipe flow using DNS.

### Conditional spatially averaged turbulence and dispersion characteristics in flow over two-dimensional dunes

Conditional turbulence and dispersion characteristics in flow over a series of two-dimensional dunes are analyzed by applying the spatial averaging methodology. To this end, the flow data measured over an array of points on the vertical central plane were used. The manifestation of the wake-interference flow over dunes, including the boundary layer diffusion, flow separation, and flow reattachment, is demonstrated by overlapping the vorticity contours on the velocity vector diagram. The vertical distributions of the spatially averaged (SA) streamwise velocity, Reynolds shear and normal stresses, dispersive shear and normal stresses, turbulent kinetic energy (TKE) fluxes, and dispersive kinetic energy (DKE) fluxes are analyzed. It is recognized that the dominance of the conditional SA streamwise velocity associated with the temporal sweep events causes the flow to accelerate temporally. The conditional SA Reynolds stresses and TKE fluxes associated with the temporal ejection events are dominant above the dune crest, whereas those associated with the temporal sweep events are the governing mechanism below the crest. An examination of the conditional dispersive normal stresses and the DKE fluxes reveals that within the upper portion of the roughness sublayer, the dispersive ejection events are the key flow dispersion mechanism, whereas near the dune trough, the dispersive outward interaction events prevail. Furthermore, the temporal ejection events are found to be more persistent, but less frequent, than the temporal sweep events. Besides, the frequencies of the occurrences of the temporal bursting events are higher below the crest than those above it, suggesting the flow to be more turbulent below the crest.

### Low-dimensional model of the large-scale circulation of turbulent Rayleigh-Bénard convection in a cubic container

Author(s): Dandan Ji and Eric Brown

Low-dimensional models are desirable for turbulent flow problems that are otherwise impractical to solve. A model describing the dynamics of the orientation of convection rolls as diffusion in a potential determined by the shape of the cell is tested. In a cubic Rayleigh-Bénard convection cell, measurements confirm the model prediction of a four-well potential, along with advected oscillation modes centered around potential minima at corners, driven by turbulent fluctuations with a restoring force due to the noncircular shape of the cell cross section.

[Phys. Rev. Fluids 5, 064606] Published Fri Jun 12, 2020

### Reduced order modeling-based discrete unified gas kinetic scheme for rarefied gas flows

Boltzmann solvers face significant difficulty in simulating rarefied flows at high Knudsen numbers. In this flow regime, the gas distribution function is widely scattered and highly concentrated with a very steep slope in the particle velocity space. In order to capture the feature of such a flow, the Boltzmann solvers such as the Discrete Unified Gas Kinetic Scheme (DUGKS) discretize the particle velocity space with a very fine mesh (many discrete particle velocities) using the Discrete Velocity Method (DVM) due to which the load for computation becomes unendurable. In this paper, a Reduced Order Modeling (ROM) method is used to generate a reduced discrete velocity space for the DUGKS. More specifically, the discrete empirical interpolation method [S. Chaturantabut and D. C. Sorensen, SIAM J. Sci. Comput. 32, 2737–2764 (2010)] is used to select the dominant nodes in the original discrete velocity space to form a reduced discrete velocity space, which represents important dynamical characteristics. In this way, most grid points in the discrete velocity space, which are of negligible importance on the integration, are removed in practical computation, which yields a significant improvement in computational efficiency. The proposed ROM approach is not limited to a specific DVM-based solver. For illustration, in this paper, we developed the Reduced Order Modeling-based Discrete Unified Gas Kinetic Scheme (ROM-DUGKS) by applying the reduced velocity space to the conventional DUGKS. Validations are performed in both low-speed and hypersonic rarefied flows at various Knudsen numbers. The results show that the ROM-DUGKS is much more efficient than the original DUGKS while still maintaining high accuracy. This significant improvement in computational efficiency will unleash the potential of the DVM-based solvers such as the DUGKS for practical applications to rarefied flow problems.

### Bacterial chemotaxis in thin fluid layers with free surface

Thin fluid layers are common natural habitats for various species of aerobic bacteria. Collective behaviors in bacterial colonies caused by chemotaxis can form complex bioconvection patterns, which often work in favor of the colony’s survival and growth. The connection between the biology of bacterial aerotaxis and the physics of buoyancy effects caused by non-uniform suspension density is numerically investigated for a suspension of oxytactic bacteria placed in the Petri dish. The upper surface is free and open to the atmosphere, and through it oxygen diffuses into the suspension. Surface tension and dynamic contact line are incorporated into the mathematical and numerical models. A comparison has been made between dynamic free surface and fixed free surface models, and differences have been revealed. The parametric study in the case of dynamic free surface has been performed, and the non-linear dynamics of the phenomenon has been investigated. Resulting from upward aerotaxis and downward gravitational force, Rayleigh–Taylor-like instabilities develop between layers of different densities in the suspension. Bacterial plume patterns and their dynamics, such as sinking, merging, and birth of new plumes, characterize the phenomenon for particular intervals of dimensionless parameters. Accordingly, categorization of the phenomenon based on bacterial plume evolution has been made, and significant intervals of dimensionless parameters have been extracted.

### Vortex induced vibrations of wind turbine blades: Influence of the tip geometry

The present investigation used numerical simulations to study the vortex induced vibrations (VIVs) of a 96 m long wind turbine blade. The results of this baseline shape were compared with four additional geometry variants featuring different tip extensions. The geometry of the tip extensions was generated through the variation of two design parameters: the dihedral angle bending the blade out of the rotor plane and the sweep angle bending the blade in the rotor plane. The applied numerical methods relied on a fluid structure interaction (FSI) approach, coupling a computational fluid dynamics solver with a multi-body structural solver. The methodology followed for locating VIV regions was based on the variation of the inclination angle. This variable was defined as the angle between the freestream velocity and the blade axis, being 0° when these vectors were normal and positive when a velocity component from tip to root was introduced. For the baseline geometry, the FSI simulations predicted significant blade vibrations for inclination angles between 47.5° and 60° with a maximum peak-to-peak amplitude of 2.3 m. The installation of the different tip extensions on the blade geometry was found to significantly modify the inclination angles where VIV was observed. In particular, the simulations of three of the tip designs showed a shifting of several degrees for the point where the maximum vibrations were recorded. For the specific tip geometry where only the sweep angle was taken into account, a total mitigation of the VIV was observed.

### Effect of Couette component on the stability of Poiseuille flow of a Bingham fluid–porous system: Modal and non-modal approaches

In this study, both modal and non-modal stability analyses are attempted in case of Couette–Poiseuille flow of a Bingham fluid overlying a porous layer. Such a flow configuration is widely encountered in the geophysical context in case of oil drilling. The solution of the modal problem yields no unstable eigenvalue, similar to the flow of a viscoplastic fluid in a non-porous channel configuration. Thus, non-modal analysis is performed to throw light on the short-time characteristics. The primary goal is to unveil the complex interplay between the upper plate velocity (Couette component) and the parameters characterizing the porous layer in dictating the flow transition characteristics. The current study is possibly the first attempt at investigating the effect of the Couette flow on the stability of a fluid–porous system for any kind of non-Newtonian fluid and reveals marked departure from the results reported in the literature for a similar flow configuration involving Newtonian rheology. The reason for the deviation is attributed to the role of yield stress, quantified by the Bingham number, and its complex interaction with the Couette number and porous layer parameters (depth, permeability, anisotropy, inhomogeneity, etc.). The relative interaction between fluid and porous modes in an environment of non-linear viscosity variation (owing to the rheology of the viscoplastic fluid), coupled with enhanced shearing (imparted by the Couette component), is found to demonstrate unique, non-monotonic flow transition characteristics. The possible physical mechanism governing short-time (non-modal) amplifications via interaction between the mean shear flow and the perturbation waves is also explored in detail.

### Binary gas mixture outflow into vacuum through an orifice

The results of a numerical study of a binary gas mixture outflow from a source with specified stagnation parameters into vacuum through a round orifice are presented. Silver and helium atoms (with a mass ratio of 26.95) are selected as a mixture species. The near free-molecular, transitional, and near-continuum regimes of the flow are considered with the direct simulation Monte Carlo method used for the computations. The results of simulations show that the rarefaction degree and the mole composition of the mixture have a significant impact on the spatial variation of flow parameters and the flow rates through the orifice. At all degrees of rarefaction, the variation in the dimensionless flow rate (related to the free-molecular flow rate) of the mixture is a non-monotonic function of the mole fraction of the species with a maximum/minimum (for the mass/particle flux). The presence of a light carrier gas (helium) leads to the acceleration, axial focusing, and increase in the flow rate of the heavy species (silver). The velocity slip of light and heavy species is observed at all degrees of rarefaction under consideration. The effect of the increasing density of heavy species near the orifice plane is revealed. The spatial variation of mole fractions of species on the degree of rarefaction is studied. The results of the study are compared to available analytical and experimental data, and the simulation results of pure gas outflow obtained by other authors.

### Ultrasound-enhanced mass transfer during single-bubble diffusive growth

Author(s): Álvaro Moreno Soto, Pablo Peñas, Guillaume Lajoinie, Detlef Lohse, and Devaraj van der Meer

The effect of ultrasound on the diffusive growth of a single spherical bubble growing on a substrate in supersaturated carbonated water is quantified. It is found that the diffusive growth of surface bubbles can be easily enhanced by 2 orders of magnitude during volumetric resonance. This convective growth is shown to be caused by vigorous acoustic microstreaming arising from the nonspherical bubble oscillations.

[Phys. Rev. Fluids 5, 063605] Published Thu Jun 11, 2020

### Velocity and acceleration statistics in particle-laden turbulent swirling flows

Author(s): Sofía Angriman, Pablo D. Mininni, and Pablo J. Cobelli

Particle-laden turbulent flows in von Karman laboratory experiments and in Taylor-Green direct numerical simulations display remarkable similarities, both for tracers as well as for inertial particles. A method to test models for particle dynamics in turbulent flows, exploiting these similarities, is presented. The effect of the mean flow is also considered, showing how it impacts scaling properties of particles’ statistics, and how it affects inertial range behavior.

[Phys. Rev. Fluids 5, 064605] Published Thu Jun 11, 2020

### Self-induced flows enhance the levitation of Leidenfrost drops on liquid baths

Author(s): Benjamin Sobac, Laurent Maquet, Alexis Duchesne, Hatim Machrafi, Alexey Rednikov, Pierre Dauby, Pierre Colinet, and Stéphane Dorbolo

In a study of the Leidenfrost levitation of a droplet on a hot liquid bath, rather than, classically, on an extremely hot plate, an existential feedback is revealed. The droplet induces a bath flow, whose fickle structure is explored both experimentally and theoretically. In turn, the flow drastically enhances the heat transfer to the droplet by convective means, thus ensuring such an evaporative levitation despite the poorly conducting liquid medium of the bath.

[Phys. Rev. Fluids 5, 062701(R)] Published Tue Jun 09, 2020

### Deformation of a conducting drop in a randomly fluctuating electric field

Author(s): Rajarshi Sengupta, Lynn M. Walker, and Aditya S. Khair

The interaction of surrounding drops is modeled as a temporally fluctuating electric field around a test drop. Because of the field-squared dependence, the drop deformation is larger under a fluctuating electric field than under a steady field. Consequently, drop breakup is observed at mean capillary numbers smaller than the critical capillary number for breakup under a steady field. Moreover, fluctuations drive drop breakup faster than a steady field.

[Phys. Rev. Fluids 5, 063701] Published Tue Jun 09, 2020

### Energy cascade at the turbulent/nonturbulent interface

Author(s): Y. Zhou and J. C. Vassilicos

Interscale energy transfers at the turbulent/non-turbulent interface are from small to large scales near the interface’s tangent plane where motions are predominantly stretching, but from large to small scales in other directions where motions are predominantly compressive. This predominance is partly due to extreme compressive motions which can be significantly more likely than extreme stretching motions even where motions are on average stretching.

[Phys. Rev. Fluids 5, 064604] Published Tue Jun 09, 2020

### Injection of a heavy fluid into a light fluid in a closed-end pipe

We report experimental results on the injection of a heavy fluid into a light one in a closed-end pipe, inclined at intermediate angles. The injection of the heavy fluid is made using an inner duct with a smaller diameter than that of the pipe in which the light fluid is placed. The fluids used are miscible and Newtonian, and they have the same viscosity. Our observation shows that, during the removal/replacement of the light fluid by the heavy fluid, at least four distinct flow stages can be identified: (i) initial buoyant jet of the heavy fluid, (ii) development of a mixing region, (iii) slumping flow of the heavy fluid, and (iv) heavy fluid front reaching the pipe end and returning toward the mixing region. Using high-speed camera images along with the ultrasound Doppler velocimetry and laser induced fluorescence data, the flow characteristics in these flow stages are quantified, and they are described in detail vs the dimensionless groups that govern the flow dynamics, namely, the Froude number ([math]), the Reynolds number ([math]), the Archimedes number ([math]), and the pipe inclination angle ([math]). While our findings are of fundamental importance, they can also be used to provide a fluid mechanics understanding of the dump bailing method in the plug and abandonment (P&A) of oil and gas wells.

### Direct numerical simulation of multiscale flow physics of binary droplet collision

Direct numerical simulations are performed to investigate the multiscale flow physics of binary droplet collision over a wide range of Weber numbers and impact factors. All possible collision outcomes, including bouncing (both head-on and off-center), coalescence, reflexive separation, and stretching separation, are considered. The theoretical formulation is based on a complete set of conservation equations for both the liquid and gas phases. An improved volume-of-fluid technique, which is augmented by an adaptive mesh refinement algorithm, is used to track the liquid/gas interface. Several local refinement criteria are validated and employed to improve the computational accuracy and efficiency substantially. In particular, a thickness-based refinement technique is implemented for treating cases involving extremely thin gas films between droplets. The smallest numerical grid is ∼10 nm, which is on the order of 10−5 times the initial droplet diameter. A photorealistic visualization technique is employed to gain direct insights into the detailed collision dynamics, including both the shape evolution and mass relocation. The numerical framework allows us to systematically investigate the underlying mechanisms and processes, such as gas-film drainage and energy and mass transfer, at scales sufficient to resolve the near-field dynamics during droplet collision. The nonmonotonic transition of bouncing and merging outcomes for head-on collision is identified by varying the Weber number over two orders of magnitude. A geometric relation defining the droplet interactions is developed. Analytical models are also established to predict the mass transfer between colliding droplets.

### Elastohydrodynamics of a deformable porous packing in a channel competing under shear and pressure gradient

Elastohydrodynamics of a deformable porous medium sandwiched between two parallel plates is investigated under the influence of an externally applied pressure gradient as well as an induced shear due to the movement of the upper plate. Biphasic mixture theory is used to describe the macroscopic governing equations for the fluid velocity and the solid displacement, assuming the deformable porous medium as a continuum space. The corresponding reduced mathematical model is a coupled system of elliptic partial differential equations. It is assumed that the fluid at the lower plate experiences slip due to the surface roughness of the plate. The exact solution for unidirectional fluid velocity and solid deformation resembling plain Poiseuille–Couette flow are presented for steady and unsteady states. Asymptotic analysis of the biphasic mixture in the case of low and high Darcy numbers is performed to validate the obtained solution using Prandtl’s matching technique. It is observed that the Womersley number dictates whether the fluid is trapped inside the channel or escapes the channel. The competition between the shear and the pressure gradient is analyzed, and a critical criterion is established that dictates the dominant factor. A mathematical analysis of the current problem is invaluable in understanding the mechanical behavior of biomass under pressure-driven flow in applications such as tissue engineering or shear driven flow inside endothelial glycocalyx layers, which are discussed in brief. In this context, our analysis on the extent of tissue deformation in response to frequency variations is expected to give useful insights to identify the right diagnosis.

### Determination of the transition mass ratio for onset of galloping of a square cylinder at the least permissible Reynolds number of 150

The Den Hartog stability criterion tests for galloping of an oscillator. A square cylinder satisfies this and is susceptible to galloping. This criterion being necessary for occurrence of galloping appears insufficient as certain parameters, i.e., angle of incidence, α; mass ratio, m*; damping ratio, ζ; reduced speed, U*; and Reynolds number, Re; also assume key roles in determining if the oscillator motion is vortex-induced vibrations (VIV) or galloping. At Re ≈ 150 and U* ≈ 10 or smaller, a square cylinder does not gallop despite satisfying the Den Hartog criterion. By coupling U* and Re, K. Sourav and S. Sen [“Transition of VIV-only motion of a square cylinder to combined VIV and galloping at low Reynolds numbers,” Ocean Eng. 187, 106208-1–106208-19 (2019)] two-degrees-of-freedom motion over Re ≤ 250, the minimum m* or [math] as 3.4 below which galloping cannot develop. For transverse-only motion, X. Li et al. [“Mode competition in galloping of a square cylinder at low Reynolds number,” J. Fluid Mech. 867, 516–555 (2019)] considered U* = 40 only and determined [math] at the least permissible Re of 150. For α = 0° and ζ = 0, we determine the [math] numerically at Re = 150. By analyzing the transverse response and oscillation frequency over an extended U* range of 10–60, a novel “VIV-galloping transition map” is generated in the m*–U* plane. From this map, the value of [math] converges to 3.4. The [math] decays as [math]. The conditions leading to “VIV forever” of a square cylinder are also identified.

### Large deviations, singularity, and lognormality of energy dissipation in turbulence

Author(s): Itzhak Fouxon and Changhoon Lee

We study implications of the assumption of power-law dependence of moments of energy dissipation in turbulence on the Reynolds number Re, holding due to intermittency. We demonstrate that at Re→∞ the dissipation's logarithm divided by lnRe converges with probability one to a negative constant. This ...

[Phys. Rev. E 101, 061101(R)] Published Mon Jun 08, 2020