# Latest papers in fluid mechanics

### Effects of Reynolds number on vortex structure behind a surface-mounted finite square cylinder with AR = 7

This paper presents the numerical solutions of flow around a surface-mounted square cylinder of aspect ratio h/d = 7 at Reynolds numbers of 652 and 13 041. The aim is to investigate the effect of the Reynolds number, between its medium-to-high range, on the flow and vortex structure around such a cylinder. The present simulations have successfully reproduced the primary flow, as well as the three-dimensional large-scale vortex structure in the wake of the finite wall-mounted body. The observation of base vortices, tip vortices, and a horseshoe vortex is consistent with previous experimental studies. A dipole wake is captured at the higher Reynolds number, while a quadrupole wake is captured for the lower, indicating that the Reynolds number strongly influences the wake structure. In the near-wake region, by plotting the isosurface of instantaneous second invariant of the velocity gradient, the full-loop structure is observed for the quadrupole wake, while the half-loop structure is observed for the dipole wake. In the far-wake region, a braided vortex structure formed by asymmetric hairpin vortices is observed at both Reynolds numbers and a new wake topology is proposed for flows with a similar geometry.

### On the highly unsteady dynamics of multiple thermal buoyant jets in cross flows

Thermal plumes of small scale generated by spatially separated heat sources can form, like atoms in a chemical compound, complex structures of different kinds and with distinct behaviors. The situation becomes even more complex if plumes can interact with imposed vertical shear (a horizontal wind). In this analysis, a “minimal framework” based on the application of a filtering process to the governing balance equations for mass, momentum, and energy (falling under the general heading of “Large Eddy Simulation” approach) is used together with direct numerical simulation to inquiry about the relative importance of buoyancy and vertical shear effects in determining the patterning scenario when highly unsteady dynamics are established (turbulent flow). Emerging patterns range from the flow dominated by a static rising jet produced by the aggregation of plumes that are pushed by horizontal leftward and rightward winds toward the center of the physical domain to convective systems with disconnected thermal pillars of smaller scale, which travel in the same direction of the prevailing wind. The classical sheltering effect, which for flows that are steady “in mean” simply consists of an increased deflection of the leading buoyant jet with respect to the trailing ones, is taken over by a variety of new phenomena, including (but not limited to) fast plume removal-rebirth mechanisms (with local increase in the velocity frequency and shrinkage in the related amplitude), “bubble” formation-rupture, and local departure of the frequency spectrum from the Kolmogorov similarity law.

### Parallel large eddy simulations of transitional flow in a compressor cascade with endwalls

Laminar-turbulent transition and corner separation play a critical role in the aerodynamics of the compressor and are quite sensitive to the changes of flow conditions and external disturbances. However, a deep understanding of such fine flow phenomena poses a great challenge for turbulent methods and computer resources. In order to clarify the impacts of incoming flow states on the three-dimensional transitional flow in a compressor cascade, we construct a parallel Large-Eddy-Simulation (LES) methodology and apply it to a full-span compressor cascade. Both the turbulent and laminar incoming endwall boundary layers are considered at a free-stream turbulence level of 4%, which is typical in the multistage axial-flow compressor environment. The parallel performance of the MPI (Message Passing Interface) model and hybrid MPI-OpenMP (Open Multi-Processing) model is particularly analyzed at a parallel scale of 10 000 CPU (Central Processing Unit) cores. The parallel performance test shows that the efficiency of the MPI model is evidently higher than that of the hybrid MPI-OpenMP model. The LES results indicate that the incoming laminar endwall boundary layer results in a more remarkable reduction in the blade loading near the endwall and a larger total pressure loss than the turbulent one. The incoming endwall boundary layer state shows a significant impact on the evolution process of the endwall turbulence and a small impact on the corner separation and the suction-surface transition. This study demonstrates the ability of the parallel LES method to capture complex transitional-flow structures in compressor cascades and its potential application to the deeper understandings of compressor aerodynamics.

### Nanocatalytic chemohydrodynamic instability: Deposition effects

Author(s): B. Dastvareh, J. Azaiez, and P. A. Tsai

Due to the high surface area to volume ratio of nanoparticles, nanocatalytic reactive flows are widely utilized in various applications, such as water purification, fuel cell, energy storage, and biodiesel production. The implementation of nanocatalysts in porous media flow, such as oil recovery and...

[Phys. Rev. E 100, 053102] Published Fri Nov 08, 2019

### Shear viscosity of bimodal capsule suspensions in simple shear flow

Author(s): Hiroki Ito, Daiki Matsunaga, and Yohsuke Imai

A well-known rheological property of a suspension of two sizes of rigid particles is a reduction in the shear viscosity. A numerical analysis shows that for bimodal capsule suspensions, the extent of the viscosity reduction is amplified by the deformability of the capsules.

[Phys. Rev. Fluids 4, 113601] Published Thu Nov 07, 2019

### Effect of soluble surfactant on the motion of a confined droplet in a square microchannel

Surfactants are widely used in the manipulation of drop motion in microchannels, which is commonly involved in many applications, e.g., surfactant assisted oil recovery and droplet microfluidics. This study is dedicated to a crucial fundamental problem, i.e., the effects of a soluble surfactant on drop motion and their underlying mechanisms, which is an extension of our previous work of an insoluble-surfactant-covered droplet in a square microchannel [Z. Y. Luo, X. L. Shang, and B. F. Bai, “Marangoni effect on the motion of a droplet covered with insoluble surfactant in a square microchannel,” Phys. Fluids 30, 077101 (2018)]. We make essential improvements to our own three-dimensional front-tracking finite-difference model, i.e., by further integrating the equation governing surfactant transport in the bulk fluid and surfactant mass exchange between the drop surface and bulk fluid. We find that the soluble surfactant generally enlarges the droplet-induced extra pressure loss compared to the clean droplet, and enhancing surfactant adsorption tends to intensify such an effect. We focus specifically on the influences of four soluble-surfactant-relevant dimensionless parameters, including the Biot number, the dimensionless adsorption depth, the Damkohler number, and the bulk Peclet number. Most importantly, we discuss the mechanisms underlying the soluble surfactant effect, which consists of two aspects similar to the insoluble case, i.e., the reduced surface tension to decrease droplet-induced extra pressure loss and the enlarged Marangoni stress playing the opposite role. Surprisingly, we find that the enlarged Marangoni stress always makes the predominant contribution over the reduced surface tension in the effects of above-mentioned four soluble-surfactant-relevant dimensionless parameters on drop motion. This finding explains why the droplet-induced extra pressure loss increases with the film thickness, which is opposite to that observed for clean droplets.

### On the time-evolution of resonant triads in rotational capillary-gravity water waves

We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes, and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero, we recover the well known integrable three-wave system.

### A composite dynamic mode decomposition analysis of turbulent channel flows

In this contribution, we consider the Dynamic Mode Decomposition (DMD) framework as a purely data-driven tool to investigate both standard and actuated turbulent channel databases via Direct Numerical Simulation (DNS). Both databases have comparable Reynolds number Re ≈ 3600. The actuation consists in the imposition of a streamwise-varying sinusoidal spanwise velocity at the wall, known to lead to drag reduction. Specifically, a composite-based DMD analysis is conducted, with hybrid snapshots composed by skin friction and Reynolds stresses. A small number of dynamic modes (∼3–9) are found to recover accurately the DNS Reynolds stresses near walls. Moreover, the DMD modes retrieved propagate at a range of phase speeds consistent with those reported in the literature. We conclude that composite DMD is an attractive, purely data-driven tool to study turbulent flows. On the one hand, DMD is helpful to identify features associated with the drag, and on the other hand, it reveals the changes in flow structure when actuation is imposed.

### An extended Kozeny-Carman-Klinkenberg model for gas permeability in micro/nano-porous media

Gas transport in micropores/nanopores deviates from classical continuum calculations due to nonequilibrium in gas dynamics. In such a case, transport can be classified by the Knudsen number (Kn) as the ratio of gas mean free path and characteristic flow diameter. The well-known Klinkenberg correction and its successors estimate deviation from existing permeability values as a function of Kn through a vast number of modeling attempts. However, the nonequilibrium in a porous system cannot be simply modeled using the classical definition of the Kn number calculated from Darcy’s definition of the pore size or hydraulic diameter. Instead, a proper flow dimension should consider pore connectivity in order to characterize the rarefaction level. This study performs a wide range of pore-level analysis of gas dynamics with different porosities, pore sizes, and pore throat sizes at different Kn values in the slip flow regime. First, intrinsic permeability values were calculated without any rarefaction effect and an extended Kozeny-Carman model was developed by formulating the Kozeny-Carman constant by porosity and pore to throat size ratio. Permeability increased by increasing the porosity and decreasing the pore to throat size ratio. Next, velocity slip was applied on pore surfaces to calculate apparent permeability values. Permeability increased by increasing Kn at different rates depending on the pore parameters. While the characterization by the Kn value calculated with pore height or hydraulic diameter did not display unified behavior, relating permeability values with the Kn number calculated from the equivalent height definition created a general characterization based on the porosity independent from the pore to throat size ratio. Next, we extended the Klinkenberg equation by calculating unknown Klinkenberg coefficients which were found as a simple first order function of porosity regardless of the corresponding pore connectivity. The extended model as a combination of Kozeny-Carman for intrinsic permeability and Klinkenberg for apparent permeability correction yielded successful results.

### Numerical simulation of electrovortex flows in cylindrical fluid layers and liquid metal batteries

Author(s): W. Herreman, C. Nore, P. Ziebell Ramos, L. Cappanera, J.-L. Guermond, and N. Weber

Electrovortex flows occur whenever thin electrodes are put in contact with wider liquid metal regions. An investigation shows that in liquid metal batteries, electrovortex flows can become so intense they can compromise the layered structure of the battery and cause a short circuit.

[Phys. Rev. Fluids 4, 113702] Published Wed Nov 06, 2019

### Lagrangian investigation of pseudo-turbulence in multiphase flow using superposable wakes

Author(s): W. C. Moore and S. Balachandar

A method is introduced for approximating the fully resolved flow through a monodisperse array of spheres using only the locations of the spheres and the volume-averaged Reynolds number. A pseudoturbulence stress model is proposed for use in a Lagrangian framework.

[Phys. Rev. Fluids 4, 114301] Published Wed Nov 06, 2019

### Intermittency of an incompressible passive vector convected by isotropic turbulence

Author(s): Jingyuan Yang, Toshiyuki Gotoh, Hideaki Miura, and Takeshi Watanabe

Direct numerical simulations of an incompressible passive vector in turbulence find that high pseudo-enstrophy domains are sheet-like, unlike the tube structure of the high enstrophy domain. The scaling exponents of the structure functions are intermediate between the velocity and passive scalar.

[Phys. Rev. Fluids 4, 114602] Published Wed Nov 06, 2019

### Formation and decay of eddy currents generated by crossed surface waves

Author(s): V. M. Parfenyev, S. V. Filatov, M. Yu. Brazhnikov, S. S. Vergeles, and A. A. Levchenko

We observe experimentally how two crossed standing surface waves excite a regular lattice of near-surface vortices. The dynamics of formation and decay of the lattice coincides with that predicted by our theoretical model. The mass transport in the vortices is primarily determined by Eulerian flow.

[Phys. Rev. Fluids 4, 114701] Published Wed Nov 06, 2019

### Universal formulation of central-moments-based lattice Boltzmann method with external forcing for the simulation of multiphysics phenomena

The cascaded or central-moments-based lattice Boltzmann method (CM-LBM) is a robust alternative to the more conventional Bhatnagar-Gross-Krook-LBM for the simulation of high-Reynolds number flows. Unfortunately, its original formulation makes its extension to a broader range of physics quite difficult. In addition, it relies on CMs that are derived in an ad hoc manner, i.e., by mimicking those of the Maxwell-Boltzmann distribution to ensure their Galilean invariance a posteriori. This work aims at tackling both issues by deriving Galilean invariant CMs in a systematic and a priori manner, thanks to the Hermite polynomial expansion framework. More specifically, the proposed formalism fully takes advantage of the D3Q27 discretization by relying on the corresponding set of 27 Hermite polynomials (up to the sixth-order) for the derivation of both the discrete equilibrium state and the forcing term in an a priori manner. Furthermore, while keeping the numerical properties of the original CM-LBM, this work leads to a compact and simple algorithm, representing a universal methodology based on CMs and external forcing within the lattice Boltzmann framework. To support these statements, mathematical derivations and a comparative study with four other forcing schemes are provided. The universal nature of the proposed methodology is eventually proved through the simulation of single phase, multiphase (using both pseudopotential and color-gradient formulations), and magnetohydrodynamic flows.

### Deionization shock driven by electroconvection in a circular channel

Author(s): Zhibo Gu, Bingrui Xu, Peng Huo, Shmuel M. Rubinstein, Martin Z. Bazant, and Daosheng Deng

The deionization shock in microstructures has been essentially attributed to surface charge. It is demonstrated that deionization shock can also be driven by bulk electroconvection up to millimeter scale, shedding light on a new design for shock electrodialysis for desalination and water purification.

[Phys. Rev. Fluids 4, 113701] Published Tue Nov 05, 2019

### Higher-order realizable algebraic Reynolds stress modeling based on the square root tensor

Author(s): Kazuhiro Inagaki, Taketo Ariki, and Fujihiro Hamba

A higher-order realizable algebraic Reynolds stress modeling is proposed based on the square root tensor of the Reynolds stress. This model is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity, such as an axially rotating pipe flow.

[Phys. Rev. Fluids 4, 114601] Published Tue Nov 05, 2019

### The extrudate swell singularity of Phan-Thien–Tanner and Giesekus fluids

The stress singularity for Phan-Thien–Tanner (PTT) and Giesekus viscoelastic fluids is determined for extrudate swell (commonly termed die swell). In the presence of a Newtonian solvent viscosity, the solvent stress dominates the polymer stresses local to the contact point between the solid (no-slip) surface inside the die and the free (slip) surface outside the die. The velocity field thus vanishes like [math], where r is the radial distance from the contact point and λ0 is the smallest Newtonian eigenvalue (dependent upon the angle of separation between the solid and free surfaces). The solvent stress thus behaves like [math] and dominates the polymer stresses, which are like [math] for PTT and [math] for Giesekus. The polymer stresses require boundary layers at both the solid and free surfaces, the thicknesses of which are derived. These results do not hold for the Oldroyd-B fluid.

### Direct numerical simulations of multi-mode immiscible Rayleigh-Taylor instability with high Reynolds numbers

In this paper, we conduct the high-resolution direct numerical simulations of multimode immiscible Rayleigh-Taylor instability (RTI) with a low Atwood number (At = 0.1) using an improved phase field lattice Boltzmann method. The effect of the Reynolds number on the evolutional interfacial dynamics and bubble/spike amplitudes is first investigated by considering its wide range, from 100 up to a high value of 30 000. The numerical results show that, for sufficiently large Reynolds numbers, a sequence of distinguishing stages in the immiscible RTI can be observed, which includes the linear growth, saturated velocity growth, and chaotic development stages. At the late stage, the RTI induces a complex topology structure of the interface and a mass of dissociative drops can be significantly observed in the system. The accelerations of the bubble and spike front are also measured, and it is reported that their normalized values at the late time are, respectively, approximate to the constant values of around 0.025 and 0.027, exhibiting a terminally quadratic growth. As the Reynolds number is reduced to small ones, the multiple disturbances of the RTI are found to merge into a larger one at the initial stage. Then, the evolutional interfaces display the patterns familiar from the single-mode RTI. The phase interfaces in the whole process become very smooth without the appearance of the breakup phenomenon, and the spike and bubble velocities at the late time approach constant values. Furthermore, we also analyze the effects of the initial conditions in terms of the perturbation wavelength and amplitude, and it is found that the instability undergoes a faster growth at the intermediate stage for a larger wavelength, while the late-time bubble and spike growth rates are insensitive to the changes of the initially perturbed wavelength and amplitude.

### Wake transitions and laminar separation bubble in the flow past an Eppler 61 airfoil

The flow past an Eppler 61 airfoil at 10° angle to the free-stream is investigated numerically for 100 ≤ Re ≤ 87 000. Vortex shedding is observed beyond Re ∼ 600 and three-dimensionality sets in at Re ∼ 1280.9 via the mode C instability and hairpin vortex structures that grow with an increase in Re. At larger Re, the shear layer vortices, arising from the instability of the separated shear layer, interact with the flow close to the airfoil and cause it to reattach. A Laminar Separation Bubble (LSB) forms at Re ∼ 20 000 and beyond. The airfoil experiences a very significant increase in the lift and a decrease in the drag at the formation of LSB. Although the flow is three-dimensional, the primary mechanism of the formation of LSB appears to be two-dimensional. The length of the LSB decreases with an increase in Re. The variation of the shear layer and primary wake frequency, with Re, is studied. Both follow the power law. However, the variation before and after the formation of LSB is quite different. Unlike the primary wake frequency, the shear layer frequency suffers a jump at the formation of LSB. Wake formation length (Lf), estimated via the spatial distribution of Reynolds stress, exhibits spanwise periodicity at the onset of three-dimensionality.

### Numerical investigation of nanoporous evaporation using direct simulation Monte Carlo

Author(s): Benzi John, Ryan Enright, James E. Sprittles, Livio Gibelli, David R. Emerson, and Duncan A. Lockerby

We numerically study the thin film evaporation process enabled by nanoporous membranes for electronic device cooling. Results show that the net evaporative mass flux is determined by an interplay between physical effects, quantified by the Knudsen number, porosity, evaporation coefficient, and meniscus shape.

[Phys. Rev. Fluids 4, 113401] Published Mon Nov 04, 2019