# Latest papers in fluid mechanics

### Resolvent-based modeling of coherent wave packets in a turbulent jet

Author(s): Lutz Lesshafft, Onofrio Semeraro, Vincent Jaunet, André V. G. Cavalieri, and Peter Jordan

Linear instability analysis, performed on the mean flow of a fully turbulent jet, provides quantitatively correct predictions of the energetic coherent turbulent structures found in experiments. It is concluded that the most energetic structures in jet turbulence are governed by linear dynamics.

[Phys. Rev. Fluids 4, 063901] Published Thu Jun 06, 2019

### Self-similar and disordered front propagation in a radial Hele-Shaw channel with time-varying cell depth

Author(s): C. Vaquero-Stainer, M. Heil, A. Juel, and D. Pihler-Puzović

An air bubble expanding into a viscous liquid in the small gap between parallel plates deforms into highly branched, continuously evolving interfacial fingering patterns. By separating the plates following a power law in time, it is found that the interface can also form self-similar fingering patterns.

[Phys. Rev. Fluids 4, 064002] Published Thu Jun 06, 2019

### Self-organization in purely viscous non-Newtonian turbulence

Author(s): H. J. Seybold, H. A. Carmona, H. J. Herrmann, and J. S. Andrade, Jr.

Snapshot of vortex structure in a shear-thickening fluid in fully developed turbulence. Colors from blue to red go from low to high vorticities. Relative to Newtonian fluids, shear-thinning fluids adjust to have an augmented dissipation inside vortices, the opposite of shear-thickening fluids.

[Phys. Rev. Fluids 4, 064604] Published Thu Jun 06, 2019

### Lagrangian description of the unsteady flow induced by a single pulse of a jellyfish

Author(s): Jin-Tae Kim and Leonardo P. Chamorro

Lagrangian statistics and pair dispersion induced by an isolated pulse of a small jellyfish are quantified with 3D particle tracking velocimetry. Lagrangian velocity shows more intense mixing in the radial direction and reveals three stages dominated by flow acceleration, mixing, and dissipation.

[Phys. Rev. Fluids 4, 064605] Published Thu Jun 06, 2019

### Flow pattern of double-cavity flow at high Reynolds number

The flow structure in a turbulent double-cavity flow has been studied experimentally and numerically. The dynamics of the two-component instantaneous velocity vector fields measured by an optical smoke image velocimetry method and calculated using the ANSYS Fluent 19.2 software has been derived. For a wide range of dynamic similarity numbers of shape factor and ReL, the flow resistance coefficients for the cavity and relative flow mass transfer with the cavities have been estimated; three characteristic flow regimes of double-cavity flow have been distinguished and described; the flow pattern map via the ReL number and shape factor has been obtained.

### Large eddy simulation of hydrodynamic turbulence using renormalized viscosity

We employ renormalized viscosity to perform large eddy simulations (LESs) of decaying homogeneous and isotropic turbulence in a cubical domain. We perform a direct numerical simulation (DNS) on 5123 and 2563 grids and LES on 323, 643, and 1283 grids with the same initial conditions in the resolved scales for a flow with Taylor Reynolds number Reλ = 210. We observe good agreement between LES and DNS results for the temporal evolution of turbulence kinetic energy Eu(t), kinetic energy spectrum Eu(k), and kinetic energy flux Πu(k). Also, the large-scale structures of the flow in LES are similar to those in DNS. These results establish the suitability of our renormalized viscosity scheme for LES.

### Laminar dispersion at low and high Peclet numbers in a sinusoidal microtube: Point-size versus finite-size particles

This paper adopts Brenner’s homogenization theory to investigate dispersion properties, over a wide range of Peclet values, of point-size and finite-size particles in sinusoidal cylindrical microchannels in the presence of a pressure-driven Stokes flow field. The periodic alternation of entropic barriers/traps can unexpectedly increase the effective finite-size particle velocity as well as decrease the effective dispersion coefficient for both point-size and finite-size particles, for large values of the radial Peclet number. While this phenomenon has a simple explanation for tracer particles, its understanding for finite-size particles is not trivial and goes through the analysis of the localization feature of the equilibrium unit-cell particle density [math]0(x) and how this spatial nonuniformity impacts upon the effective particle velocity and on the solution of the so-called b field, controlling the large scale axial dispersion coefficient. Unfortunately, dispersion reduction cannot be exploited for the sake of the separation of particles having different radii because the separation performance of a hydrodynamic sinusoidal column turns out to be worse than that of a standard straight column for experimentally feasible Peclet values. Interesting analytical results for long-wavelength sinusoidal channels are obtained by a long-wave asymptotic expansion. Both zero-order and first-order terms for the asymptotic expansion of the [math]0(x) measure and of the b field are obtained, thus exploring a wide range of Peclet values and deriving an analytical expression for the Taylor dispersion coefficient.

### Constitutive theory of inhomogeneous turbulent flow based on two-scale Lagrangian formalism

A self-consistent closure theory is developed for inhomogeneous turbulent flow, which enables systematic derivations of the turbulence constitutive relations without relying on any empirical parameters. The double Lagrangian approach based on the mean and fluctuation velocities allows us to describe a wide variety of correlations in a consistent manner with both Kolmogorov’s inertial-range scaling and general-covariance principle.

### Dynamics of quantized vortex filaments under a local induction approximation with second-order correction

We study a second-order local induction approximation (LIA) for the dynamics of a single open quantized vortex filament (such as those filaments arising in superfluid helium). While for a classical vortex filament, this second-order correction can be interpreted as a correction due to the inclusion of axial flow within a filament core, in the quantized filament case, this second order correction can be viewed as a correction due to variable condensate healing length. We compare the evolution of the decay rate, transverse velocity, and rotational velocity of Kelvin waves along vortex filaments under this model to that of the first order LIA of Schwarz for quantized vortex filaments, as well as to a corresponding nonlocal model involving Biot-Savart integrals for the self-induced motion of the vortex filament. For intermediate wavenumbers, the second-order model solutions show improved agreement with the nonlocal Biot-Savart model, due to an additional control parameter. We also consider the stability of Kelvin waves under the second-order corrections; these results allow us to understand the Donnelly-Glaberson instability in the context of the second-order model. The second-order corrections tend to stabilize the resulting solutions, in agreement with what was previously found from the nonlocal Biot-Savart formulation, yet still permit a local description of the vortex filament in terms of a partial differential equation (akin to the first-order LIA) rather than an integro-differential equation.

### Drag enhancement and turbulence attenuation by small solid particles in an unstably stratified turbulent boundary layer

Point-particle direct numerical simulations of particle-laden flows have been conducted to investigate the complex coupling between inertial particles, buoyancy force, and strong shear flows in an unstably stratified turbulent boundary layer over a flat plate. Two-way coupling and particle-particle collisions, i.e., four-way coupling, are considered in the dilute gas-solid flows. The simulation results indicate that the presence of inertial particles with diameter smaller than the Kolmogorov length scale tends to reduce the thermal displacement thickness and enthalpy thickness, while increasing the mean skin-friction coefficient and Nusselt number. The feedback force exerted by the particles on the fluid is found to contribute largely to the drag enhancement. The turbulence intensities and temperature fluctuations are significantly attenuated in the particle-laden flows with respect to the unladen flow. The budgets of the turbulent kinetic energy show that the particles have direct and indirect effects on the modulation of turbulence. On the one hand, the production and the viscous dissipation rate are suppressed by the particles in most regions of the boundary layer. On the other hand, the particle-turbulence interactions produce an extra energy source in the inner layer, while causing an additional energy sink in the outer layer of the boundary layer. These combined effects lead to the pronounced turbulence attenuation observed in this study.

### Distortion of pipe-flow development by boundary layer growth and unconstrained inlet conditions

This study extends the analysis of the canonical developing pipe-flow problem to realistic inlet conditions affecting emerging jets. A comparison of simulations to existing theory reveals adverse phenomena caused by the inlet: the velocity profile inversion and flow separation (vena contracta) at a sharp inlet. Beginning with the simple uniform inflow, the inversion is shown to persists at significantly higher Re (Re = 2000) than previously reported. It is found to be caused by the theory’s neglected radial velocity, resulting from the boundary layer’s displacement effect. Rescaling of the inlet axial coordinate is shown to collapse all centerline velocity curves above Re = 100, thus elucidating the known weak dependence of entrance-length on Re. The sharp-inlet separation bubble is found not to occur below Re ≅ 320 although this inlet profile overrides the boundary layer’s effect. Furthermore, the bubble’s downstream length increases rapidly with Re, whereas its upstream length grows gradually and proportionally to its thickness—here identified as its characteristic-scale. Beyond the bubble, the profile relaxes to a monotonic form—captured beyond x/(Re·R) = 0.005, if theory is modified using the bubble’s characteristic-scale. This scale also sets the threshold which differentiates between a sharp-inlet regime, accompanied by a separation bubble, and a rounded-inlet one without it. The latter regime relaxes more rapidly to the monotonic profile—captured already beyond x = 2R. Finally, the modified idealized theory is demonstrated as a useful design tool—explicitly relating nozzle length to characteristics of emerging free-surface and submerged jets.

### Direct numerical simulation and Reynolds-averaged Navier-Stokes modeling of the sudden viscous dissipation for multicomponent turbulence

Author(s): Alejandro Campos and Brandon E. Morgan

Simulations of a turbulent multicomponent fluid mixture undergoing isotropic deformations are carried out to investigate the sudden viscous dissipation. This dissipative mechanism was originally demonstrated using simulations of an incompressible single-component fluid [S. Davidovits and N. J. Fisch...

[Phys. Rev. E 99, 063103] Published Wed Jun 05, 2019

### Investigation of shear rates of rolling adhesion on leukocytes with bending of microvilli

Author(s): Tai-Hsien Wu and Dewei Qi

A leukocyte model is used to show how different flow shear rates affect bending deformation of the microvilli and adhesive bond forces.

[Phys. Rev. Fluids 4, 063101] Published Wed Jun 05, 2019

### Experimental and numerical determination of Darcy's law for yield stress fluids in porous media

Author(s): D. Bauer, L. Talon, Y. Peysson, H. B. Ly, G. Batôt, T. Chevalier, and M. Fleury

Experiments and three-dimensional numerical simulations of yield stress fluids in heterogeneous porous media show that, as a result of this disorder, the fluid flows through a single channel near a critical pressure. Beyond that, the number of open channels increases with the pressure applied.

[Phys. Rev. Fluids 4, 063301] Published Wed Jun 05, 2019

### Slightly deformable Darcy drop in linear flows

Author(s): Y.-N. Young, Yoichiro Mori, and Michael J. Miksis

When a poroelastic spherical drop is under a uniaxial extension flow or a shear flow, the elastic network deforms in response to the external fluid viscous stress. A small-deformation analysis is conducted to investigate effects of interfacial slip and permeability on flow around the drop.

[Phys. Rev. Fluids 4, 063601] Published Wed Jun 05, 2019

### An experimental study of the dynamic aerodynamic characteristics of a yaw-oscillating wind turbine airfoil

The design of large wind turbines requires a comprehensive and accurate analysis of the dynamic loads of airfoils, so it is of great importance to study the dynamic aerodynamic characteristics of a yaw-oscillating airfoil. In this paper, using “electronic cam” technology and synchronous acquisition of dynamic data, a wind tunnel test of yaw oscillation for the airfoil dynamic “sweep effect” is carried out for the first time, providing previously missing lateral dynamic test data. The results show that the aerodynamic curves of the yaw-oscillating airfoil have an obvious hysteresis effect, induced mainly by a periodic pressure fluctuation on the airfoil suction surface, and the aerodynamic hysteresis characteristics are enhanced with increasing oscillation frequency, initial angle of attack, and amplitude. The hysteresis loops of the lift and pressure drag, as a function of yaw angle, follows a “W” shape, the hysteresis loop of the pitching moment follows an “M” shape, and the hysteresis loop of the unsteady lift increment follows an “∞” shape. The aerodynamic force of the airfoil under negative stroke is higher than that under positive stroke, and the aerodynamic coefficients decrease clearly with increasing oscillation frequency under positive stroke. The pressure fluctuation on the airfoil surface is due to a periodic generation, development, movement, breakdown, dissipation, and reconstruction of shear layer vortices, leading edge vortices, trailing edge vortices, and dynamic separation vortices. The dynamic aerodynamic hysteresis of the yaw-oscillating airfoil occurs essentially because of the dynamic interaction between vortex and vortex, or vortex and airfoil surface boundary layer.

### Analysis of inertial migration of neutrally buoyant particle suspensions in a planar Poiseuille flow with a coupled lattice Boltzmann method-discrete element method

In this study, a hybrid numerical framework for modelling solid-liquid multiphase flow is established with a single-relaxation-time lattice Boltzmann method and the discrete element method implemented with the Hertz contact theory. The numerical framework is then employed to systematically explore the effect of particle concentration on the inertial migration of neutrally buoyant particle suspensions in planar Poiseuille flow. The results show that the influence of particle concentration on the migration is primarily determined by the characteristic channel Reynolds number Re0. For relatively low Re0 (Re0 < 20), the migration behaviour can only be observed at a very low particle concentration (≤5%). However, when Re0 > 20 the migration behaviour can be observed at a high concentration (≥20%). Furthermore, a focusing number Fc is proposed to characterise the degree of inertial migration. It was found that the inertial migration can be classified into three regimes depending on two critical values of the focusing number, Fc+ and Fc−: (i) when Fc > Fc+, a full inertial migration occurs; (ii) when Fc < Fc−, particles are laterally unfocused; and (iii) when Fc− < Fc < Fc+, a partially inertial migration takes place.

### Near-wall dynamics of inertial particles in dilute turbulent channel flows

This investigation considers the effect of the Stokes number on the near-wall particle dynamics of two-phase (solid-fluid) turbulent channel flows. The spectral element method-based direct numerical simulation code Nek5000 is used to model the fluid phase at a shear Reynolds number, Reτ = 180. Dispersed particles are tracked using a Lagrangian approach with one-way coupling. Eulerian fluid and particle statistics are gathered and analyzed to determine the effect of the Stokes number, first on macroscopic statistics. Previous work of this nature indicates that mean streamwise particle velocities and root-mean-square velocity fluctuations are reduced in the bulk and increased very close to the wall, an effect which is stronger with increased particle Stokes number or inertial particles. This phenomenon has important consequences for mechanisms such as particle deposition and preferential concentration, and so for the first time, this work aims to elucidate the dynamics of this effect through rigorous analysis on various scales. An in-depth force analysis indicates the importance of the lift force, even at increased Stokes numbers, in predicting particle motion in the buffer layer and log-law regions. It is also observed that pressure gradient and virtual mass forces are significant close to the wall. Alongside bulk velocity and acceleration statistics, microscopic behavior is analyzed by considering region-based particle dynamics. Probability density functions are used to determine the effect of the Stokes number on particle motion in three near-wall regions, as well as within the bulk flow. It is observed that at higher Stokes numbers, the viscous sublayer contains particles with dynamic properties similar to those present in the buffer layer. This suggests rapid interlayer migration in the wall direction, causing increased particle turbulence intensities in near-wall regions. A local flow topology classification method is also used to correlate particle behavior with near-wall coherent turbulent structures, and a mechanism for particle sweep toward the wall is suggested. Finally, low-speed streak accumulation and interlayer particle fluxes are considered and the extent of mixing for low and high Stokes numbers is discussed.

### Publisher’s Note: “Effect of near-wake jet on the lock-in of a freely vibrating square cylinder” [Phys. Fluids 31, 053603 (2019)]

### Droplet impact and flow into a gap between parallel plates

Droplet impact on irregular, rough, or porous substrates can lead to inertia driven liquid penetration during droplet spread, air entrapment in voids, and triple-phase contact line pinning. This work focuses on inertia driven flow inside of a model long, narrow pore. We impacted 2 mm diameter water drops on long narrow gaps, photographing the impact and penetration with a high-speed camera, to understand how the flow develops and behaves inside these gaps. The experimental conditions varied were the velocity of impact (0.06–1.5 m/s) and the gap spacing between the plates (50–150 µm). The influence of inertia on the flow between the plates is negligible for impact velocities less than 0.5 m/s and can be predicted using a simple analytical model. Drops flow into larger gaps faster than smaller gaps at all impact velocities. Drops flow faster into gaps as impact velocity increases, but this has diminishing returns: at sufficiently high impact velocity the drop will cleave, which prevents a significant portion of the drop from flowing into the gap. Analytical models are presented to predict conditions under which the droplet will cleave and the rate of liquid penetration into the gap due to capillary forces.