# Latest papers in fluid mechanics

### Comparison of the properties of segregated layers in a bidispersed fluidized bed to those of a monodispersed fluidized bed

Author(s): Yinuo Yao, Craig S. Criddle, and Oliver B. Fringer

Since industrial fluidized-bed reactors typically operate with polydispersed particles, approximating such reactors as the superposition of corresponding monodispersed fluidized beds would greatly simplify their design and operation. To examine the validity of this superposition, we evaluate the effects of bidispersity by comparing three-dimensional liquid-solid monodispersed and segregated bidipsersed fluidized beds. This work demonstrates that, despite the clear segregation into layers that behave like monodispersed beds, the transition region is governed by complex bidispersed mechanisms that cannot be explained in terms of the particle behavior in the segregated layers.

[Phys. Rev. Fluids 6, 084306] Published Fri Aug 27, 2021

### Transient aggregation of particles at interfaces

Author(s): Antoine Lagarde, Christophe Josserand, and Suzie Protière

The formation of an axisymmetric monolayer of dense particles at a liquid interface is explored in order to study the interaction between numerous objects of different sizes randomly distributed on a liquid surface. The individual motion of each bead cannot be solved but the overall clustering can be described statistically. The clustering dynamics of this system with a long-range interaction varies during the aggregation process. The cluster-size distribution evolves with a self-similar mechanism and we observe a well-defined transition between two aggregating regimes that we can characterize.

[Phys. Rev. Fluids 6, 084307] Published Fri Aug 27, 2021

### Linear analysis of Rayleigh-Taylor instability in viscoelastic materials

Author(s): J. N. Gou, W. T. Zan, Y. B. Sun, and C. Wang

Rayleigh-Taylor instability (RTI) has become a powerful tool for determining the mechanical properties of materials under extreme conditions. In this paper, we first present the exact and approximate linear dispersion relations for RTI in viscoelastic materials based on the Maxwell and Kelvin-Voigt ...

[Phys. Rev. E 104, 025110] Published Fri Aug 27, 2021

### Macroscopic and microscopic hydrodynamic mixing of stratified suspensions

Author(s): Yasufumi Yamamoto, Koki Yamada, Yohsuke Tanaka, and Shusaku Harada

We conducted numerical experiments to investigate the mixing of stratified suspensions containing different types of particles. We used a point-force two-way coupling method. We studied the mixing behavior of stratified suspensions and we discovered two types of mixing: microscopic (individual-parti...

[Phys. Rev. E 104, 025111] Published Fri Aug 27, 2021

### Conformal invariance of the 1-point statistics of the zero-isolines of $2d$ scalar fields in inverse turbulent cascades

Author(s): M. Wacławczyk, V. N. Grebenev, and M. Oberlack

For three decades there have been speculations about the existence of conformal invariance in two-dimensional turbulence and possible implications thereof. These speculations have been confirmed by numerical experiments. However, there is a scarcity of relevant analytical studies on this topic. In our work we analyze the underlying equation for the one-point probability density function of a scalar in two-dimensional turbulence. We derive conditions under which the probability measure is conformally invariant and show that with this transformation certain statistics of non-homogeneous fields can be derived based on solutions of the homogeneous one.

[Phys. Rev. Fluids 6, 084610] Published Thu Aug 26, 2021

### Large-scale structures of scalar and velocity in a turbulent jet flow

Author(s): Jesse Reijtenbagh, Jerry Westerweel, and Willem van de Water

In a turbulent jet flow, finite-time Lyapunov exponents gauge the exponentially fast spreading of fluid parcels. To observe their fine structure, we moved our Particle Image Velocimetry and Laser-Induced Fluorescence cameras with the mean flow. The resulting remarkable shapes in the figure are linked to the organization of a dispersed fluorescent tracer.

[Phys. Rev. Fluids 6, 084611] Published Thu Aug 26, 2021

### Reciprocal theorem for calculating the flow rate–pressure drop relation for complex fluids in narrow geometries

Author(s): Evgeniy Boyko and Howard A. Stone

A key aspect in understanding pressure-driven flows of non-Newtonian fluids in narrow and confined geometries is the relationship between the flow rate and pressure drop. Using the Lorentz reciprocal theorem, we derive a closed-form expression for the flow rate-pressure drop relation of complex fluids in narrow channels of arbitrary shape, which holds for a wide class of viscoelastic and shear-thinning constitutive models. For the weakly non-Newtonian limit, our theory provides the first-order non-Newtonian correction for the flow rate-pressure drop relation solely using the corresponding Newtonian solution, eliminating the need to solve the non-Newtonian flow problem.

[Phys. Rev. Fluids 6, L081301] Published Thu Aug 26, 2021

### Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows

Author(s): Jie Shen, Zhiming Lu, Lian-Ping Wang, and Cheng Peng

In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme. Four different particle-fluid density ratios are considered to explore how particles with different particle-flui...

[Phys. Rev. E 104, 025109] Published Thu Aug 26, 2021

### Developing horizontal convection against stable temperature stratification in a rectangular container

Author(s): Daisuke Noto, Tomomi Terada, Takatoshi Yanagisawa, Takehiro Miyagoshi, and Yuji Tasaka

Developing stages of horizontal convection observed during transitions from conduction to thermally equilibrated convection states are studied with visualization experiments imposing horizontally differential heating at the top of low-temperature water. Due to the absence of destabilizing thermal sources, convective rolls, which are localized on the horizontal plane on which differential heating is imposed, are formed only by the baroclinic torque driving force against a braking force due to stable temperature stratification. We find a nondimensional parameter for the balance of the braking force relaxing with time and the baroclinic torque driving force.

[Phys. Rev. Fluids 6, 083501] Published Wed Aug 25, 2021

### Emptying-filling boxes with non-Boussinesq plumes and fountains

Author(s): R. Mehaddi, P. Boulet, M. Koutaiba, O. Vauquelin, and F. Candelier

When a light fluid is continuously released from the top (as a fountain) or from the bottom (as a plume) into a box with a top opening, a buoyant layer of constant thickness and density forms under the ceiling at steady state. Both configurations have been investigated using theoretical approaches and small scale air-helium experiments. As a practical application, for a fixed buoyant flux, the fountain and the plume configurations have been compared with respect to their mixing efficiency.

[Phys. Rev. Fluids 6, 083801] Published Wed Aug 25, 2021

### Bifurcation structure of unstable periodic orbits in plane Couette flow with the Smagorinsky model

Author(s): Eiichi Sasaki, Genta Kawahara, and Javier Jiménez

To study the dynamical properties of plane Couette turbulence, this paper describes unstable periodic orbits (UPOs) in a large eddy simulation (LES) system with a Smagorinsky-type eddy viscosity model. At a moderately high Reynolds number, the UPO of the present study possesses spanwise vortices in the central region of the channel, which seem to be caused by a streak instability. These stretched vortices are shown to enhance transfer of the streamwise turbulent momentum, as in developed near-wall turbulence.

[Phys. Rev. Fluids 6, 084608] Published Wed Aug 25, 2021

### Direct numerical simulation of turbulent elliptical pipe flow under system rotation about the major axis

Author(s): Rafael Hurtado Rosas, Zhao-Ping Zhang, and Bing-Chen Wang

The effect of Coriolis forces on the turbulent flow in an elliptical pipe subjected to spanwise rotation has been studied using direct numerical simulations (DNS). In response to the system rotation, large-scale secondary flows appear in the cross-stream plane as a pair of counter-rotating vortices, which significantly impact the turbulence statistics and structures of the flow. The characteristics of the turbulence field is investigated in both physical and spectral spaces through analyses of the first- and second-order statistical moments, as well as the budget balance of the Reynolds stress transport equation and coherent flow structures.

[Phys. Rev. Fluids 6, 084609] Published Wed Aug 25, 2021

### Spanwise structuring and rivulet formation in suspended falling liquid films

Author(s): Manuel Rietz, Reinhold Kneer, Benoit Scheid, and Wilko Rohlfs

In thin films flowing down the underside of an inclined planar substrate, surface topology is known to evolve towards a spanwise structuring of rivulets. While experiments imply a connection between long-term spanwise structuring and primary instabilities (PI) of the film surface at low Reynolds number (Re), this connection is not conclusive if a larger parameter space of Re and Kapitza number (Ka) is considered. Using an integral boundary layer model for falling liquid films and varying imposed initial conditions, Re, Ka, and wall inclination, we numerically investigate long-term rivulet evolution and its connection to PI, obtaining excellent concordance with previous experimental data.

[Phys. Rev. Fluids 6, 084805] Published Wed Aug 25, 2021

### Unexpected scaling of interstitial velocities with permeability due to polymer retention in porous media

Author(s): Shima Parsa, Ahmad Zareei, Enric Santanach-Carreras, Eliza J. Morris, Ariel Amir, Lizhi Xiao, and David A. Weitz

Flow and retention of polymer in porous media result in an unexpected reduction in medium permeability. Our experiment and simulation of polymer retention show that these changes are a direct consequence of pore blockage and diversion of flow through the medium. Despite the complex changes in flow after polymer retention, we introduce a simple scaling for the distribution of pore-level velocities based on the bulk permeability of the medium.

[Phys. Rev. Fluids 6, L082302] Published Wed Aug 25, 2021

### Turbulence and capillary waves on bubbles

Author(s): Peleg Emanuel and Alexander Feigel

We present a link between the theory of deep water waves and that of bubble surface perturbations. Theory correspondence is shown analytically for small wavelengths in the linear regime and investigated numerically in the nonlinear regime. To do so, we develop the second-order spatial perturbation e...

[Phys. Rev. E 104, 025108] Published Tue Aug 24, 2021

### Dynamics of a helical swimmer crossing viscosity gradients

Author(s): Christian Esparza López, Jorge Gonzalez-Gutierrez, Francisco Solorio-Ordaz, Eric Lauga, and Roberto Zenit

We study how helical swimmers move across a viscosity gradient, motivated by the need to understand how such heterogenous environments affect the motion of microorganisms. We find that the swimmer’s speed can be either decreased or increased while crossing the viscosity gradient, depending on the orientation of the tail and the gradient of viscosity. Our experimental findings are sustained by good agreement with a resistive-force based model.

[Phys. Rev. Fluids 6, 083102] Published Mon Aug 23, 2021

### Beyond actuator line arrays in active flow control studies: Lessons from a genetic algorithm approach

Author(s): Fernando Zigunov, Prabu Sellappan, and Farrukh Alvi

Active flow control with microjets in crossflow is a promising technology to improve the performance of many engineering flows. Predicting effective placement for the microjets at the surface of the aerodynamic model remains an unsolved challenge due to the complex interactions between the jets and the main flow. We propose and demonstrate a fully experimental, model-free approach using a solenoid array and a genetic algorithm to find a highly effective actuator pattern for drag reduction in the flow over a simplified fuselage afterbody, deploying thousands of actuator configurations in a single experiment and reaching a configuration that achieves a 10% reduction in drag.

[Phys. Rev. Fluids 6, 083903] Published Mon Aug 23, 2021

### Effects of porous walls on near-wall supersonic turbulence

Author(s): Yongkai Chen and Carlo Scalo

Modification to the structure of wall-bounded turbulence due to the presence of porous walls has been investigated in the low and high supersonic regime. For sufficiently high degrees of wall permeability, streamwise-traveling surface waves are triggered and stay confined in the buffer layer region. These waves yield a sinusoidal modulation of the near-wall turbulent ejection and burst events.

[Phys. Rev. Fluids 6, 084607] Published Mon Aug 23, 2021

### Distribution of liquid flow in a pore network during evaporation

Author(s): Rui Wu and C. Y. Zhao

The variation of the distribution of the liquid flow in porous media during evaporation is still a puzzle. We resolve it with the pore network modeling approach. The distribution of the evaporation-induced liquid flow in a pore network composed of about 2.5 million pores is determined. The probabili...

[Phys. Rev. E 104, 025107] Published Mon Aug 23, 2021

### Influence of the pivot location on the thrust and propulsive efficiency performance of a two-dimensional flapping elliptic airfoil in a forward flight

In this article, the effect of the pivot point location on the thrust performance of a two-dimensional sinusoidal flapping elliptic airfoil in a forward flight condition is investigated using numerical simulations and in-house water tunnel experiments. On the chord line, three different pivot locations at a distance of 0.25c, 0.5c, and 0.75c from the leading edge of the airfoil are considered, where c is the chord length of the airfoil. The flapping frequency and effective angle of attack are varied to investigate the propulsive performance of the airfoil at a Reynolds number of 5000. It is noticed that a modification in the pivot location significantly influences the linear velocity distribution, the evolution of the leading-edge vortex, and the near wake region on the airfoil. Consequently, both the transient and time-averaged thrust coefficient of the flapping airfoil is considerably affected. In addition, we have observed when the flapping frequency is increased, the time-averaged thrust coefficient of the airfoil tends to increase up to a critical Strouhal number and deteriorates thereafter. The same trend of time-averaged thrust coefficient is seen at all considered pivot locations and effective angle of attacks. Our finding suggests, at the high flapping frequency, the formation of rotation induced adverse suction region around the airfoil and delay in the shedding of the leading edge vortex developed in the previous flapping stroke are the primary sources, attributing to the thrust deterioration of the flapping airfoil with symmetric pivot location 0.5c. On the other hand, the thrust degrading effects at the two asymmetric pivot locations, 0.25c and 0.75c, are triggered by the adverse suction regions induced by asymmetric airfoil-surface velocity distribution as well as airfoil-wake vortices interaction. Moreover, the thrust degradation can be postponed to a higher critical Strouhal number if the airfoil pivot location is set near the leading edge and higher amplitude of effective angle of attack is followed. Besides, we found that the airfoil propulsive efficiency is affected due to a change in the aerodynamic power co-efficient with the modification of the pivot location. Furthermore, our observation concludes that the pivot location at 0.25c from the leading edge has maximum time-averaged thrust and propulsive efficiency performances at least for the range of pivot locations, flapping frequencies, and effective angle of attacks examined here.