# Latest papers in fluid mechanics

### Topological mixing of yield stress materials

Author(s): D. R. Lester and A. Chryss

Chaotic mixing of yield stress fluids is considered in a novel static mixer that imparts uniformly efficient mixing due to the underlying topology of the device. Experimental and computational studies indicate that mixing is largely insensitive to flow dynamics, boundary conditions, and fluid rheology.

[Phys. Rev. Fluids 4, 064502] Published Fri Jun 14, 2019

### Shape optimization to suppress the lift oscillation of flow past a stationary circular cylinder

The suppression of lift oscillation of flow past a stationary circular cylinder is studied to delay structural fatigue at low Reynolds numbers in incompressible Newtonian fluid. Grad-based shape optimization is employed to achieve the goal. The optimization objective is the integral of the absolute value of the lift coefficient over a vortex shedding period T. The class-shape function transformation technique is chosen as a shape parameterization method. Moreover, the unsteady adjoint method is employed to calculate the gradients of the objective with respect to shape parameters. Results show that through shape optimization, the strength of vortex shedding is sufficiently suppressed in two-dimensional flow, and the lift oscillation amplitude is reduced by nearly 50%. In addition, the flow stability is significantly improved, and the lift oscillations are completely eliminated at Re = 47–60.

### Controlling the bias error of Fokker-Planck methods for rarefied gas dynamics simulations

Direct simulation Monte-Carlo (DSMC) is the most established method for rarefied gas flow simulations. It is valid from continuum to near vacuum, but in cases involving small Knudsen numbers (Kn), it suffers from high computational cost. The Fokker-Planck (FP) method, on the other hand, is almost as accurate as DSMC for small to moderate Kn, but it does not have the computational drawback of DSMC, if Kn is small [P. Jenny, M. Torrilhon, and S. Heinz, “A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion,” J. Comput. Phys. 229, 1077–1098 (2010) and H. Gorji, M. Torrilhon, and P. Jenny, “Fokker–Planck model for computational studies of monatomic rarefied gas flows,” J. Fluid Mech. 680, 574–601 (2011)]. Especially attractive is the combination of the two approaches leading to the FP-DSMC method. Opposed to other hybrid methods, e.g., coupled DSMC/Navier-Stokes solvers, it is relatively straightforward to couple DSMC with the FP method since both are based on particle solution algorithms sharing the same data structure and having similar components. Regarding the numerical accuracy of such particle methods, one has to distinguish between spatial truncation errors, time stepping errors, statistical errors and bias errors. In this paper, the bias error of the FP method is analyzed in detail, and it is shown how it can be reduced without increasing the particle number to an exorbitant level. The effectiveness of the discussed bias error reduction scheme is demonstrated for uniform shear flow, for which an analytical reference solution was derived.

### Particle number control for direct simulation Monte-Carlo methodology using kernel estimates

The efficiency of stochastic particle schemes for large scale simulations relies on the ability to preserve a uniform distribution of particles in the whole physical domain. While simple particle split and merge algorithms have been considered previously, this study focuses on particle management based on a kernel density approach. The idea is to estimate the probability density of particles and subsequently draw independent samples from the estimated density. To cope with that, novel methods are devised in this work leading to efficient algorithms for density estimation and sampling. For the density inference, we devise a bandwidth with a bounded bias error. Furthermore, the sampling problem is reduced to drawing realizations from a normal distribution, augmented by stratified sampling. Thus, a convenient and efficient implementation of the proposed scheme is realized. Numerical studies using the devised method for direct simulation Monte-Carlo show encouraging performance.

### A dusty gas model-direct simulation Monte Carlo algorithm to simulate flow in micro-porous media

A new efficient direct simulation Monte Carlo (DSMC) method is proposed for the simulation of microporous media based on the dusty gas model (DGM). Instead of simulating gas flow through a microporous medium with a complex geometry of micropores that mimics the physical pore morphology, the DGM-DSMC method replaces it with the gas flow through a system of randomly distributed motionless virtual particles with simple spherical shapes confined in the considered domain. In addition, the interactions of gas molecules with the porous particles are simulated stochastically. For the aim of our study, the DGM is implemented in Bird’s two-dimensional DSMC code. The obtained results for the average velocity of gas flow through microscale porous media with given porosity are verified for different pressure gradients with those reported in the literature where porous particles are modeled physically in the domain. Thereafter, the effective parameters in porous media such as porosity, particle diameter, and rarefaction on flow behavior including velocity profile, apparent gas permeability, and mass flow rate are investigated. A comparison with the results predicted by the Open source Field Operation and Manipulation (OpenFOAM) software suggests that the employed DGM-DSMC is more accurate in highly porous media and its computational cost is considerably low.

### Numerical study of a bubble driven micromixer based on thermal inkjet technology

An efficient microfluidic mixing approach utilizing the periodic explosive boiling mechanism from the thermal inkjet technology is proposed in this work. The main purpose of the work is to examine the effect of the configuration of thin-film microheaters on the mixing performance of the simple Y-microchannel via numerical simulations. The proposed micromixer can drive the mixing flow without an external pump because the repeated growth-collapse cycles of the vapor bubble result in a pumping effect in the microchannel. The adaptive Cartesian grid based finite-volume method is employed to solve the Navier-Stokes equations with the volume-of-fluid method for tracking the vapor-liquid interface. The complex dynamics of the vapor bubble induced by pulse heating is simplified as a gas polytropic expansion/compression process. Four microheater configurations are examined with the proposed numerical method. Our results have shown that mixing is limited for the microheater placed symmetrically along the center plane of the downstream branch of the Y-micromixer. However, for the asymmetrically placed microheater, mixing is greatly improved due to the secondary crossflow and asymmetric vortex created by the bubble collapse. When two off-centered microheaters are used and fired alternately, the mixing performance is further enhanced by disturbing the flow in a wiggling manner. Finally, when the microheaters are placed in the inlet channels instead of the downstream channel, periodic alternate switching of inlet flows due to the bubble actuation can effectively segment the mixing species, which results in the highest mixing index of 0.956 among all four configurations. The proposed micromixer shows great promise in the microfluidic mixing applications due to its simplicity and high efficiency.

### Small-scale flow topologies in decaying isotropic turbulence laden with finite-size droplets

Author(s): Michael S. Dodd and Lluís Jofre

The small-scale flow topologies in droplet-resolved direct numerical simulations of isotropic turbulence are classified using tensor invariants. The results show that when approaching the droplet surface, the flow topologies fundamentally change from those found in isotropic turbulence to boundary-layer-like structures.

[Phys. Rev. Fluids 4, 064303] Published Thu Jun 13, 2019

### Frozen waves in turbulent mixing layers

Author(s): Benoît-Joseph Gréa and Antoine Briard

The horizontal vibrations of an interface between miscible fluids trigger a parametric instability, leading to frozen wave patterns. Theory and numerical simulations reveal that the mixing layer size varies as the square of the forcing amplitude in the turbulent regime.

[Phys. Rev. Fluids 4, 064608] Published Thu Jun 13, 2019

### Strong turbulence for vibrating plates: Emergence of a Kolmogorov spectrum

Author(s): Gustavo Düring, Christophe Josserand, Giorgio Krstulovic, and Sergio Rica

In the low viscosity liquid and zero thickness vibrating elastic sheet, turbulent behavior is observed. We find the same Kolmogorov spectrum cascade for energy redistribution per scale Ek∼P2/3k−5/3 in both, apparently, completely disparate physical situations.

[Phys. Rev. Fluids 4, 064804] Published Thu Jun 13, 2019

### Droplet impact induced large deflection of a cantilever

The phenomenon of a droplet impacting on an elastic solid surface exists in wide and versatile natural and industrial areas, which is involved with the interplay between elasticity and droplet dynamics. In the present work, we have made a comprehensive study on the process of a droplet impacting on a cantilever resulting in large deformation. The morphology of the droplet is observed, and the maximum deflection of the cantilever with respect to the initial velocity, apparent contact angle, and surface tension of the droplet is calculated by the developed theoretical model, which matches the experimental results very well. These findings may aid to engineer new energy harvesting devices and microsensors, and are also promising for many agricultural and industrial applications.

### Vectorial structure of the near-wall premixed flame

Author(s): Peipei Zhao, Lipo Wang, and Nilanjan Chakraborty

A turbulent premixed flame anchored by a solid wall can reach a statistically stationary state. Overall the configuration is counterflowlike. Flame-wall interactions under such conditions are key to understanding combustion in a confined space and in developing wall flame models. A numerical study is presented.

[Phys. Rev. Fluids 4, 063203] Published Wed Jun 12, 2019

### Turning strategies for plunging elastic plate propulsor

Author(s): Peter D. Yeh, Ersan Demirer, and Alexander Alexeev

Complex actuation of a caudal fin can generate turning moments enabling underwater swimmer navigation. A numerical study explores the hydrodynamics resulting from two actuation strategies leading to pitching and yaw moments.

[Phys. Rev. Fluids 4, 064101] Published Wed Jun 12, 2019

### Inertial effects on the dynamics of rigid heavy fibers in isotropic turbulence

Author(s): Sofia Kuperman, Lilach Sabban, and René van Hout

Holographic cinematography is used to measure rotational and translational dynamics of inertial fibers in isotropic turbulence. Results show that for the present parameter range, translational motion is similar to that for spheres. In contrast, tumbling rates peaked at an intermediate Stokes number.

[Phys. Rev. Fluids 4, 064301] Published Wed Jun 12, 2019

### Quantitative study of the rheology of frictional suspensions: Influence of friction coefficient in a large range of viscous numbers

Author(s): William Chèvremont, Bruno Chareyre, and Hugues Bodiguel

A numerical study of sheared suspensions of frictional and frictionless rigid spheres finds that macroscopic friction in granular suspensions is nearly independent of interparticle contact friction, and besides contact lubrication, the viscous contribution of the pore fluid is negligibly small.

[Phys. Rev. Fluids 4, 064302] Published Wed Jun 12, 2019

### Evolution of a line vortex in stratified flow

Author(s): Surupa Shaw and John P. McHugh

A pair of distributed vortices in stratified flow disintegrate sooner than a traditional vortex pair and form multiple coherent vortex structures.

[Phys. Rev. Fluids 4, 064803] Published Wed Jun 12, 2019

### On the basic concepts of the direct simulation Monte Carlo method

In this paper, the basic ideas underlying the Direct Simulation Monte Carlo (DSMC) method are examined and a novel nonhomogeneous N-particle kinetic equation describing the randomized mathematical model of DSMC is derived. It is shown that different collision-partner selection schemes, including No-Time-Counter (NTC) and Bernoulli-trials schemes, are approximations of the general transition operator of the randomized model. The popular collision-partner selection schemes, represented by the standard NTC and Bernoulli-trials approximations of the general transition operator, represented by Simplified Bernoulli-trials and Generalized Bernoulli-trials schemes, are tested on the one-dimensional rarefied gas heat transfer problem against conditions of two approximation limits: first, leading to the Boltzmann equation and, second, leading to the novel N-particle kinetic one.

### Analysis of nonequidiffusive premixed flames in obstructed channels

Author(s): Abdulafeez Adebiyi, Olatunde Abidakun, Gbolahan Idowu, Damir Valiev, and V’yacheslav Akkerman

The impact of the Lewis number on ultrafast premixed flame acceleration in channels equipped with comb-shaped arrays of tightly spaced obstacles attached to the walls is studied by the computational simulations of the reacting flow equations, including fully compressible hydrodynamics.

[Phys. Rev. Fluids 4, 063201] Published Tue Jun 11, 2019

### Unresolved stress tensor modeling in turbulent premixed V-flames using iterative deconvolution: An <i>a priori</i> assessment

Author(s): Z. M. Nikolaou, Y. Minamoto, and L. Vervisch

The application of an iterative deconvolution modeling framework for the unresolved stresses in turbulent and reacting flows is demonstrated using high-fidelity direct numerical simulation data of premixed rod-stabilized V-flames.

[Phys. Rev. Fluids 4, 063202] Published Tue Jun 11, 2019

### Influence of a small amount of noncondensable gas on shock wave generation inside a collapsing vapor bubble

Author(s): Kyohei Yamamoto, Kazumichi Kobayashi, Masao Watanabe, Hiroyuki Fujii, Misaki Kon, and Hiroyuki Takahira

A numerical study of the collapse of a vapor bubble finds that a small amount of noncondensable molecules affects the temperature profile inside the collapsing vapor bubble, preventing shock wave generation inside the collapsing bubble.

[Phys. Rev. Fluids 4, 063603] Published Tue Jun 11, 2019

### Vortex merging in a laminar separation bubble under natural and forced conditions

Author(s): J. W. Kurelek, S. Yarusevych, and M. Kotsonis

Experiments find that vortex merging occurs naturally in a laminar separation bubble. Acoustic forcing at the subharmonic and fundamental vortex shedding frequency promotes and inhibits merging, respectively. In all cases, merging occurs in the aft portion of the bubble in a spanwise nonuniform manner.

[Phys. Rev. Fluids 4, 063903] Published Tue Jun 11, 2019