# Latest papers in fluid mechanics

### Turbulent boundary layer perturbation by two wall-mounted cylindrical roughness elements arranged in tandem: Effects of spacing and height ratio

The perturbation of a turbulent boundary layer by two cylindrical roughness elements in close proximity was experimentally investigated in a water channel using planar particle image velocimetry. The two cylinders were arranged in tandem with center-to-center streamwise spacings of 2d, 4d, and 6d, where d is the diameter of the cylinders. The downstream cylinder had a fixed height 0.2δ, where δ is the incoming boundary layer thickness; the height of the upstream cylinder was varied to achieve upstream to downstream cylinder height ratios of 1, 0.75, and 0.5. The flow measurements were made at Reδ = 56 800 and included measurements over an isolated cylinder as a baseline case. The results highlight the effects of sheltering by an upstream cylinder on the wake of the downstream cylinder. Flow features in the wake, including the downwash, upwash, recirculation zone, velocity deficit, Reynolds shear stress, and turbulent kinetic energy (TKE), are dependent on the degree of sheltering, which is reliant on both the streamwise spacing and height ratio. Overall, sheltering results in a reduction in the downwash and size of the recirculation zone past the downstream cylinder. The magnitude and spatial distribution of the Reynolds shear stress and TKE varied significantly from those past the isolated cylinder. Depending on the streamwise spacing and height ratio, the presence of an upstream cylinder has the potential to enhance or reduce the Reynolds shear stress past the downstream cylinder. For example, the maximum Reynolds shear stress in the near wake was approximately doubled for a spacing of 2d and a height ratio of 0.5 and nearly halved for a spacing of 2d and a height ratio of 1 (relative to that past the isolated cylinder). The variations in these flow features across the 9 considered arrangements suggest changes to the wake and its vortical structures due to the presence of an upstream cylinder. The results highlight the potential of flow control through a pair of roughness elements in close proximity to achieve desired outcomes such as reduced or redistributed Reynolds shear stress and TKE, relative to the isolated cylinder.

### Deformation characteristics and energy conversion during droplet impact on a water surface

The present work studies experimentally and numerically the impact of water droplets with different Weber numbers (We) on a water surface. Correlations between Weber number and geometric sizes of central jet, secondary droplet, and secondary central jet are analyzed using linear regression. The experimental and numerical results are compared qualitatively and quantitatively and show good agreement. In addition, the energy conversion during the impact process is calculated using a numerical integration method. It is concluded that the ratio of the secondary droplet to the initial droplet diameters is approximately within 1.2–2, and this diameter ratio correlates linearly with the Weber number within the experimental ranges tested. When 360 < We < 713, the secondary central jet is generated. Moreover, the target liquid adsorbs around 70% of the initial total energy. The total energy remains around 64% when the cavity reaches its maximum depth, whereas it remains around 39% when the kinetic energy of the central jet reaches its minimum.

### Shear-rate dependence of thermodynamic properties of the Lennard-Jones truncated and shifted fluid by molecular dynamics simulations

It was shown recently that using the two-gradient method, thermal, caloric, and transport properties of fluids under quasi-equilibrium conditions can be determined simultaneously from nonequilibrium molecular dynamics simulations. It is shown here that the influence of shear stresses on these properties can also be studied using the same method. The studied fluid is described by the Lennard-Jones truncated and shifted potential with the cut-off radius [math]. For a given temperature T and density ρ, the influence of the shear rate on the following fluid properties is determined: pressure p, internal energy u, enthalpy h, isobaric heat capacity cp, thermal expansion coefficient αp, shear viscosity η, and self-diffusion coefficient D. Data for 27 state points in the range of T ∈ [0.7, 8.0] and ρ ∈ [0.3, 1.0] are reported for five different shear rates ([math]). Correlations for all properties are provided and compared with literature data. An influence of the shear stress on the fluid properties was found only for states with low temperature and high density. The shear-rate dependence is caused by changes in the local structure of the fluid which were also investigated in the present work. A criterion for identifying the regions in which a given shear stress has an influence on the fluid properties was developed. It is based on information on the local structure of the fluid. For the self-diffusivity, shear-induced anisotropic effects were observed and are discussed.

### Flow structure and heat transfer of electro-thermo-convection in a dielectric liquid layer

Electrothermohydrodynamic flow of dielectric liquid in a square cavity driven by the simultaneous action of Coulomb and buoyancy forces is studied numerically. A high resolution upwind scheme is applied to study the flow bifurcations and heat transfer. We focus on the strong injection case with the nondimensional injection parameter C fixed at C = 10. Two Prandtl numbers Pr = 1 and Pr = 10, two Rayleigh numbers Ra = 105 and Ra = 106, as well as two mobility numbers M = 10 and M = 20 are considered to evaluate the dependence of flow structure and heat transfer on these parameters. Multistates are found to coexist in a wide range of parameter regimes. Various flow patterns such as one-cell, two-cell, four-cell, and multicell flow are observed. The electric field is found to enhance heat transfer more efficiently for large Prandtl number fluid at low mobility parameter and relatively low Rayleigh number.

### A three-dimensional modeling for coalescence of multiple cavitation bubbles near a rigid wall

The Boundary Integral Method (BIM) has been widely and successfully applied to cavitation bubble dynamics; however, the physical complexities involved in the coalescence of multiple bubbles are still challenging for numerical modeling. In this study, an improved three-dimensional (3D) BIM model is developed to simulate the coalescence of multiple cavitation bubbles near a rigid wall, including an extreme situation when cavitation bubbles are in contact with the rigid wall. As the first highlight of the present model, a universal topological treatment for arbitrary coalescence is proposed for 3D cases, combined with a density potential method and an adaptive remesh scheme to maintain a stable and high-accuracy calculation. Modeling for the multiple bubbles attached to the rigid boundary is the second challenging task of the present study. The effects of the rigid wall are modeled using the method of image; thus, the boundary value problem is transformed to the coalescence of real bubbles and their images across the boundary. Additionally, the numerical difficulties associated with the splitting of a toroidal bubble and self-coalescence due to the self-film-thinning process of a coalesced bubble are successfully overcome. The present 3D model is verified through convergence studies and further validated by the purposely conducted experiments. Finally, representative simulations are carried out to elucidate the main features of a coalesced bubble near a rigid boundary and the flow fields are provided to reveal the underlying physical mechanisms.

### Particle size selection in capillary instability of locally heated coaxial fiber

Author(s): Saviz Mowlavi, Isha Shukla, P.-T. Brun, and François Gallaire

An analysis of the drop-size selection mechanism in a locally heated silicon-in-silica coaxial fiber is presented. Surprisingly, it is found that the size of the silicon drops is independent of the linear stability properties of the system and is instead set by nonlinear effects.

[Phys. Rev. Fluids 4, 064003] Published Tue Jun 18, 2019

### Three-dimensional flow dynamics and mixing in a gas-centered liquid-swirl coaxial injector at supercritical pressure

Three-dimensional flow dynamics and mixing in a gas-centered liquid-swirl coaxial injector at supercritical pressure is numerically studied using the large-eddy-simulation technique. In this class of injectors, typical of liquid-fueled propulsion engines, high-temperature gaseous oxygen (GOX) is axially delivered into the center tube and kerosene is tangentially injected through discrete orifices into the coaxial annulus. The operating conditions and geometry mimic those of the main injector elements used in staged-combustion propulsion engines. The present work details the full three-dimensional flow evolution over the entire injector configuration, including axial and circumferential dynamics that are essential for small-scale mixing between GOX and kerosene. Various key flow structures and instability mechanisms in the injector, including axial and azimuthal shear-layer instabilities, secondary instabilities (baroclinic torque and volume dilatation), centrifugal instability, flow recirculation, and acoustic motion, are identified. The significance of these instability mechanisms is explored in the context of streamwise and azimuthal vorticity transport. The GOX core is found to exhibit a hexagonal shape, mainly due to the interactions of vortex rings detached from the center post and coaxial annulus. For comparison, a cylindrical sector of the configuration is also simulated. The results of the present study will support the design and development of high-performance injectors for future propulsion applications.

### Role of the near-tip region of a fin in fish propulsion

Author(s): F. J. Huera-Huarte and Morteza Gharib

We examine the effects of locally altering the tip region of a periodic flapping fin system with a low order robotic model and load, motion, and wake measurements. This actuation modifies propulsive performance and unveils the importance of the phase difference between the fin and the tip.

[Phys. Rev. Fluids 4, 063103] Published Mon Jun 17, 2019

### Bypass transition delay using oscillations of spanwise wall velocity

Author(s): Prabal S. Negi, Maneesh Mishra, Philipp Schlatter, and Martin Skote

Bypass transition in boundary layers is governed by streak instability. An investigation of the effect of oscillatory wall-control on bypass transition shows that transition delay is due to streak attenuation via the modification of the eigenfunction of the Orr-Sommerfeld operator.

[Phys. Rev. Fluids 4, 063904] Published Mon Jun 17, 2019

### Intruders in disguise: Mimicry effect in granular gases

In general, the total kinetic energy in a multicomponent granular gas of inelastic and rough hard spheres is unequally partitioned among the different degrees of freedom. On the other hand, partial energy equipartition can be reached, in principle, under appropriate combinations of the mechanical parameters of the system. Assuming common values of the coefficients of restitution, we use kinetic-theory tools to determine the conditions under which the components of a granular mixture in the homogeneous cooling state have the same translational and rotational temperatures as those of a one-component granular gas (“mimicry” effect). Given the values of the concentrations and the size ratios, the mimicry effect requires the mass ratios to take specific values, the smaller spheres having a larger particle mass density than the bigger spheres. The theoretical predictions for the case of an impurity immersed in a host granular gas are compared against both direct simulation Monte Carlo and molecular dynamics simulations with a good agreement.

### Large-eddy simulation of an open-channel flow bounded by a semi-dense rigid filamentous canopy: Scaling and flow structure

We have carried out a large-eddy simulation of a turbulent open-channel flow over a marginally dense, fully submerged, rigid canopy. The canopy is made of a set of rigid, slender cylinders normally mounted on a solid wall. The flow in the canopy is resolved stem-by-stem by means of an immersed boundary method. It is found that the flow behavior can be categorized according to the velocity distribution into two separate spatial regions: the canopy itself and the outer region above it. Within the region occupied by the canopy elements, the velocity magnitude is found to be related to the local shear stress. Outside the canopy, a logarithmic velocity profile matching the canonical turbulent open-channel flow over rough walls is recovered albeit the strong manipulation exerted by the canopy on the buffer layer. In the innermost layer, the presence of the stems is responsible for redistributing the local momentum fluctuations from a streamwise to a spanwise leading component, inhibiting the survival of the wall streamwise velocity streaks. On the other hand, the outer region presents a structure very similar to the well-known logarithmic boundary layer with the presence of large and energetic streamwise velocity streaks generated by a system of quasistreamwise vortices. These vortices strongly contribute to the intracanopy fluctuations through vigorous sweep and ejection events that affect all the region occupied by the stems. Consistent with the results of previous investigations [H. Nepf, “Flow and transport in regions with aquatic vegetation,” Annu. Rev. Fluid Mech. 44, 123–142 (2012)], it is found that the inflection point in the mean velocity profile, produced by the drag discontinuity at the canopy tip, promotes the appearance of another system of spanwise oriented vorticity structures. However, different from previous results reported in the literature [J. Finnigan, “Turbulence in plant canopies,” Annu. Rev. Fluid Mech. 32, 519–571 (2000)], in our simulations, the presence of alternating head up–head down hairpin vortices generated by a mutual induction of the counter-rotating spanwise vortices is not observed. Instead, we advocate that the modulation of the spanwise coherent vorticity is due to the action of the external logarithmic layer structures (i.e., the outer streamwise vortices that penetrate the canopy) rather than by upwash and downwash motions induced by the mutual interaction of the spanwise rollers.

### Analytical study of oscillatory flow of Maxwell fluid through a rectangular tube

In the present study, the oscillatory flow of Maxwell fluid in a long tube with a rectangular cross section is considered. The analytical expressions for velocity profile and phase difference are obtained, and particularly, the singularities of the exact solution are discussed. Furthermore, the convenient expressions of velocity and phase difference are given explicitly for calculations. The effects of the relaxation time and Deborah number on the velocity profile and phase difference are discussed numerically and graphically.

### 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