# Latest papers in fluid mechanics

### Very large-scale motions in turbulent flows over streamwise traveling wavy boundaries

Author(s): Wu-Yang Zhang, Wei-Xi Huang, and Chun-Xiao Xu

Numerical simulations of turbulent flows over traveling wavy boundaries reveal that very large-scale motions are enhanced by a wavy boundary, but their intensities are decreased as wave phase speed increases. The wave-induced flow provides an extra energy transfer for the very-large-scale motions.

[Phys. Rev. Fluids 4, 054601] Published Tue May 07, 2019

### Shape oscillation of a sessile drop under the effect of high frequency amplitude-modulated magnetic field

The shape oscillation behavior of a sessile mercury drop under the effect of high frequency amplitude-modulated magnetic field (AMMF) is investigated experimentally. It is an effective method to excite the shape oscillation of a liquid metal sessile drop. The high frequency AMMF is generated by a solenoid inductor fed by a specially designed alternating electric current. The surface contour of the sessile drop is observed by a digital camera. At a given modulation frequency and magnetic flux density of the high frequency AMMF, the edge deformations of the drop with azimuthal wave numbers (modes n = 2, 3, 4, 5, 6) were excited. A stability diagram of the shape oscillation of the drop is obtained by analysis of the experimental data. It turns out that when the modulation frequency and magnetic flux density reach a point in the stability diagram which can trigger shape oscillations of the drop of several modes, the shape oscillation of different modes may be seen alternatively.

### Effects of the Atwood number on the Richtmyer-Meshkov instability in elastic-plastic media

Author(s): Qian Chen, Li Li, Yousheng Zhang, and Baolin Tian

The Richtmyer-Meshkov instability of small perturbed single-mode interfaces between an elastic-plastic solid and an inviscid liquid is investigated by theoretical analysis and numerical simulation in this work. A modified model including the Atwood number effect is proposed to describe the long-term...

[Phys. Rev. E 99, 053102] Published Mon May 06, 2019

### Enhanced mixing at inertial microscales using flow-induced flutter

Author(s): Aaron Rips and Rajat Mittal

Flow-induced flutter of flexible flapping membranes can greatly increase scalar mixing in channel flows in the inertial microfluidics regime. We use flow-structure interaction simulations to investigate their flow physics and mixing ability and find rapid mixing with relatively low pressure loss.

[Phys. Rev. Fluids 4, 054501] Published Mon May 06, 2019

### Numerical investigation of planar shock wave impinging on spherical gas bubble with different densities

The interaction between a planar shock wave and a spherical gas bubble containing sulfur hexafluoride, Refrigerant-22, neon, or helium is studied numerically. Influences of the Atwood number (At) on the evolution of the shock wave and gas bubble are clarified by using high-resolution computational simulations. The results show that the difference in the physical properties between the ambient air and the gas bubble has a significant influence on the evolution of wave pattern and bubble deformation. For the fast/slow configuration (At > 0) in the present study (At = 0.67 and 0.51), the incident shock focuses near the interior right interface to form an outward jet. Besides, the mixedness, average vorticity, and the absolute value of circulation all increase as the Atwood number increases. By contrast, for the slow/fast configuration (At < 0) with At = −0.19 and −0.76, the rotational directions of the vorticities formed at the same position are reversed compared with those in the fast/slow configuration, which induces an inward air jet to impact on the gas bubble from the outside. In addition, the mixedness, average vorticity, and the absolute value of circulation all increase as the Atwood number decreases. Nevertheless, regardless of At > 0 or At < 0, the effective volume of the gas bubble basically decreases when the Atwood number decreases. Hence, on the whole, the Atwood number has a nonmonotonic influence on the evolution of effective volume of gas bubble, mixedness, average vorticity, and circulation simultaneously.

### Evaluation of oil production potential in fractured porous media

Based on rock samples of tight oil reservoirs in the buried hills of North China, conventional gas flooding and high-speed centrifugal experiments at different pressures were carried out. Combined with nuclear magnetic resonance experiments, an evaluation method of oil production potential in fractured porous media was established to quantitatively study the gas flooding potential of target reservoirs. Results indicated that the “gas fingering phenomenon” is serious in conventional gas flooding experiments of fractured cores even under low pressures because of fractures. With an increase in flooding pressure, the changes of T2 (T2 relaxation time) spectrum and displacement percentage are relatively small, which means that the displacement efficiency has not been improved significantly (the flooding pressure for these three cores increased from 0.014 MPa to 2.6 MPa, with an average increase in displacement percentage of 6.3%). High-speed centrifugation can realize “homogeneous displacement” of the cores and overcome the influence of gas channeling. With an increase in the displacement pressure, the T2 spectrum and percentage of displaced oil varied obviously, and the displacement efficiency improved greatly (the flooding pressure for these three cores increases from 0.014 MPa to 2.6 MPa, with an average percentage of displaced oil being increased to 16.16%). Using the method of this study, 13 cores of the target reservoir were evaluated for gas flooding potential. The percentage of available pores in the target reservoir ranges from 17.64% to 58.54%, with an average of 33.84%. Movable fluid controlled by microthroats in the reservoirs larger than 0.1 mD is about 20%, while that in the reservoirs smaller than 0.1 mD is about 5%. This study indicates that the development of fractures and microfractures controls the physical properties and fluid productivity of reservoirs.

### A numerical study on bubble dynamics in sinusoidal channels

In the present work, we investigate the dynamics of a bubble, rising inside a vertical sinusoidal wavy channel. We carry out a detailed numerical investigation using a dual grid level set method coupled with a finite volume based discretization of the Navier–Stokes equation. A detailed parametric investigation is carried out to identify the fate of the bubble as a function of Reynolds number, Bond number, and the amplitude of the channel wall and represented as a regime map. At a lower Reynolds number (high viscous force), we find negligible wobbling (path instability) in the dynamics of the bubble rise accompanied only with a change in shape of the bubble. However, at a higher Reynolds number, we observe an increase in the wobbling of the bubble due to the lowered viscous effects. Conversely, at a lower Bond number, we predict a stable rise of the bubble due to higher surface tension force. However, with a gradual increase in the Bond number, we predict a periodic oscillation which further tends to instigate the instability in the dynamics. With a further increase in the Bond number, a significant reduction in instability is found unlike a higher Reynolds number with only change in the shape of the bubble. At lower values of Reynolds numbers, Bond numbers, and channel wall amplitudes, the instability is discernible; however, with an increase in the channel wall amplitude, the bubble retains integrity due to higher surface tension force. At a higher Bond number and channel wall amplitude, a multiple breakup in the form of secondary bubbles is observed. We propose a correlation which manifests the average bubble rise velocity and the fluctuating velocity (due to channel waviness) as a function of Reynolds number, Bond number, and channel wall amplitude. Finally, we conclude that the bubble dynamics pertinent to the offset channels with varying amplitudes does not remain the same as that of the symmetric channel.

### On the role of rarefaction/compression waves in Richtmyer-Meshkov instability with reshock

Richtmyer-Meshkov instability (RMI) with reshock is characterized with the interaction between the mixing zone (MZ) and multiple waves, of which the process has not been fully understood so far. A direct numerical simulation of RMI with reshock, in which the shock initially propagates from a light fluid to a heavy one, is carried out. After the reshock, the MZ is accelerated by rarefaction and compression waves alternatively with decaying strength, during which the mixing zone is accelerated as a whole system and a mean-velocity gradient is evident in the MZ. Although the velocity field is quite complex during rarefaction/compression waves, the scaled profiles of mean volume fraction are not essentially different from those before the first rarefaction wave. A budget analysis reveals that the production of turbulent kinetic energy by the pressure and velocity gradient dominates during the first rarefaction and compression waves. The sign of the pressure-gradient production is opposite to that of the velocity-gradient production, with the amplitude of the former one being larger than that of the latter one. Rarefaction waves contribute to the turbulent motions while compression waves consume turbulence energy. The increment of MZ width is accompanied with formation of large-scale structures. These structures are stretched after the reshock, during the rarefaction waves, and compressed during the compression waves.

### Characteristics of swirling and precessing flows generated by multiple confined jets

An experimental study is reported of the interaction between multiple isothermal jets within a cylindrical chamber under conditions relevant to a wide range of engineering applications, including the confined swirl combustors, industrial mixers, and concentrated solar thermal devices. The particle image velocimetry technique was used to investigate the swirling and precessing flows generated with four rotationally symmetric inlet pipes at a fixed nozzle Reynolds number of ReD = 10 500 for two configurations of swirl angle (5° and 15°) and two alternative tilt angles (25° and 45°). The measurements reveal three distinctive rotational flow patterns within the external recirculation zone (ERZ) and the central recirculation zone (CRZ) for these configurations. It was found that the mean and root-mean-square flow characteristics of the swirl within the chamber depend strongly on the relative significance of the ERZ and CRZ, with the swirling velocity being higher in the CRZ than that in the ERZ. A precessing vortex core was identified for all experimental conditions considered here, although its significance was less for the cases with a dominant CRZ.

### Deformation and rupture of compound cells under shear: A discrete multiphysics study

This paper develops a three-dimensional numerical model for the simulation of cells in simple shear flow. The model is based on Discrete Multi-Physics (DMP), a meshless particle-based method that couples the smoothed particle hydrodynamics and the mass-spring model. In this study, the effect of the nucleus in cells is investigated for a broad range of capillary numbers. It is shown that the nucleus size affects the deformation of the cell. Moreover, oscillations are observed in the tank-treading motion of the membrane when capillary number and nucleus size are both sufficiently large. Additionally, DMP shows that the cell and nuclei may experience rupture under extreme flow conditions.

### On the relevance of kinematics for cavitation implosion loads

This study presents a novel physical model to convert the potential energy contained in vaporous cavitation into local surface impact power and an acoustic pressure signature caused by the violent collapse of these cavities in a liquid. The model builds on an analytical representation of the solid angle projection approach by Leclercq et al. [“Numerical cavitation intensity on a hydrofoil for 3D homogeneous unsteady viscous flows,” Int. J. Fluid Mach. Syst. 10, 254–263 (2017)]. It is applied as a runtime post-processing tool in numerical simulations of cavitating flows. In the present study, the model is inspected in light of the time accurate energy balance during the cavity collapse. Analytical considerations show that the potential cavity energy is first converted into kinetic energy in the surrounding liquid [D. Obreschkow et al., “Cavitation bubble dynamics inside liquid drops in microgravity,” Phys. Rev. Lett. 97, 094502 (2006)] and focused in space before the conversion into shock wave energy takes place. To this end, the physical model is complemented by an energy conservative transport function that can focus the potential cavity energy into the collapse center before it is converted into acoustic power. The formulation of the energy focusing equation is based on a Eulerian representation of the flow. The improved model is shown to provide physical results for the acoustic wall pressure obtained from the numerical simulation of a close-wall vapor bubble cloud collapse.

### Rotational instabilities in microchannel flows

Mixing in numerous medical and chemical applications, involving overly long microchannels, can be enhanced by inducing flow instabilities. The channel length is thus shortened in the inertial microfluidics regime due to the enhanced mixing, thereby making the device compact and portable. Motivated by the emerging applications of a lab on a compact disk based microfluidic devices, we analyze the linear stability of rotationally actuated microchannel flows commonly deployed for biochemical and biomedical applications. The solution of the coupled system of Orr-Sommerfeld and Squire equations yields the growth rate and the neutral curves for the Coriolis force-driven instability. We report on the existence of four different types of unstable modes (Type-I to Type-IV) at low rotation numbers. Furthermore, Types-I and II exhibit competing characteristics, signifying that Type-II can play an important role in the transition to turbulence. Type-III and Type-IV modes have relatively lower growth rates, but the associated normal velocity has an oscillatory nature near the center of the channel. Thus, we infer that Types-III and IV might cause strong mixing locally by virtue of strong velocity perturbation in proximity to the various point depths. Moreover, the situation is reliable if the channel is too short to allow for the amplification of Types-I and II. We quantify the potential of all the unstable modes to induce such localized mixing near an imaginary interface (near a hyphothetical interface) inside the flow using the notion of penetration depth. This study also presents an instability regime diagram obtained from the parametric study over a range of Reynolds numbers, rotation numbers, and streamwise and spanwise wavenumbers to assist the design of efficient microchannels. Further insight into the mechanism of energy transfer, drawn from the evaluation of the kinetic-energy budget, reveals how the Reynolds stress first transfers energy from the mean flow to the streamwise velocity fluctuations. The Coriolis force, thereafter, redistributes the axial momentum into spanwise and wall-normal directions, generating the frequently observed roll-cell structures. A qualitative comparison of our predictions with the reported experiments on roll-cells indicates a good agreement.

### Cavitation and ventilation modalities during ditching

The flow taking place in the rear part of the fuselage during the emergency landing on water is investigated experimentally in realistic conditions. To this aim, tests on a double curvature specimen have been performed at horizontal velocities ranging from 21 m/s to 45 m/s. Test data highlight different cavitation and/or ventilation modalities which are strongly dependent on the horizontal velocity, with substantial changes in the flow features occurring with velocity variations of few meters per second. For the specimen considered here, the inception of the cavitation is found at about 30 m/s, confirming that scaled model tests performed at small horizontal velocities are unable to capture the hydrodynamics correctly. By analyzing pressure data, underwater movies, and force measurements, it is shown that the transition from the cavitation to ventilation condition has a significant effect on the longitudinal distribution of the loading which, together with inertia, aerodynamic loads, and engine thrust, governs the aircraft dynamics.

### Flow-induced vibration of a flexible triangular cable at low Reynolds numbers

Flow-induced vibrations of an infinite long flexible cable with a triangular cross section allowed to oscillate in the cross-flow direction are numerically studied based on a high-order spectral element method at Re = 100 and 200. A tensioned beam model governs the dynamics of the triangular cable and the selected tension leads to single wave vibrations. The main focus of the present study is to explore the response of the flexible triangular cable, with the aim of providing new insights into the essential features of flow-induced vibrations of the long flexible body with an asymmetric cross section. The numerical results show that for the angle of attack α = 60° in which one of the sides of the triangular cable is facing the incoming flow, the oscillation of the cable is dominated by vortex-induced vibrations (VIVs) at Re = 100, while a combination of strong VIV and weak galloping is excited at Re = 200. As compared to the flow past a flexible cable with a circular cross section at the same conditions, the dynamics responses of the triangular cable are significantly vigorous, which is evidenced further in energy transfers and wake dynamics as well. It is also revealed that the secondary vortex generated at the trailing edge of the triangle plays an important role in the wake evolution process. Finally, additional simulations at α = 0° are conducted and the results show that the responses are suppressed strikingly with very weak amplitudes, implying that the wake dynamics is desynchronized against the vibration of the flexible cable.

### Geometric optimization of riblet-textured surfaces for drag reduction in laminar boundary layer flows

Micro-scale riblets are shown to systematically modify viscous skin friction in laminar flows at high Reynolds numbers. The textured denticles of native sharkskin are widely cited as a natural example of this passive drag reduction mechanism. Since the structure of a viscous boundary layer evolves along the plate, the local frictional drag changes are known empirically to be a function of the length of the plate in the flow direction, as well as the riblet spacing, and the ratio of the height to spacing of the riblets. Here, we aim to establish a canonical theory for high Reynolds number laminar flow over V-groove riblets to explore the self-similarity of the velocity profiles and the evolution of the total frictional drag exerted on plates of different lengths. Scaling analysis, conformal mapping, and numerical calculations are combined to show that the potential drag reduction achieved using riblet surfaces depends on an appropriately rescaled form of the Reynolds number and on the aspect ratio of the riblets (defined in terms of the ratio of the height to spacing of the texture). We show that riblet surfaces require a scaled Reynolds number lower than a maximum threshold to be drag-reducing and that the change in drag is a nonmonotonic function of the aspect ratio of the riblet texture. This physical scaling and the computational results presented here can be used to explain the underlying physical mechanism of this mode of passive drag reduction to rationalize the geometric dimensions of shark denticles, as well as the results of experiments with shark denticle replicas of various sizes, and guide designs for optimizing the textural parameters that result in friction-reducing surfaces.

### A direct numerical simulation study of the influence of flame-generated vorticity on reaction-zone-surface area in weakly turbulent premixed combustion

Direct numerical simulation data obtained from two statistically stationary, one-dimensional, planar, weakly turbulent, premixed flames are analyzed in order to examine the influence of flame-generated vorticity on the surface area of the reaction zone. The two flames are associated with the flamelet combustion regime and are characterized by two significantly different density ratios σ = 7.53 and 2.5, with all other things being roughly equal. The obtained results indicate that generation of vorticity due to baroclinic torque within flamelets can impede wrinkling of the reaction surface, reduce its area, and, hence, decrease the burning rate. Thus, these results call for revisiting the widely accepted concept of combustion acceleration due to flame-generated turbulence. In particular, in the case of σ = 7.53, the local stretch rate, which quantifies the local rate of increase or decrease in the surface area, is predominantly negative in regions characterized by a large magnitude of enstrophy or a large magnitude of the baroclinic torque term in the enstrophy transport equation, with the effect being more pronounced at larger values of the mean combustion progress variable. If the density ratio is low, e.g., σ = 2.5, the baroclinic torque weakly affects the vorticity field within the mean flame brush and the aforementioned effect is not pronounced.

### Pumping flow model in a microchannel with propagative rhythmic membrane contraction

A pumping flow model in a microchannel with a single attached membrane subjected to propagative contraction is presented in this article. The lubrication theory is used to approximate the induced flow field at a low Reynolds number flow regime. A well-posed expression for the wall profile is derived to describe the membrane propagative mode of rhythmic contractions. Unlike our previously derived pumping model “nonpropagative” where at least two membranes that operate with time-lag are required to produce unidirectional flow, the present results demonstrate that an inelastic channel with a single membrane contraction that operates in a “propagative” mode can produce unidirectional flow and work as a micropump. The model can be used to understand flow transport in many biological systems including but not limited to insect respiration, urine flow, and fluid dynamics of duodenum and intestine. The present pumping paradigm is relatively easy to fabricate and is expected to be useful in many biomedical applications.

### Response modes of erythrocytes in high-frequency oscillatory shear flows

Due to its capability of duplicating the deformation scenario of erythrocytes (red blood cells), in in vivo time scales, passing through interendothelial slits in the spleen, the understanding of the dynamic response of erythrocytes in oscillatory shear flows is of critical importance to the development of an effective in vitro methodology to study the mechanics, metabolism, and aging procedure in vivo [R. Asaro et al., “Erythrocyte aging, protection via vesiculation: An analysis methodology via oscillatory flow,” Front. Physiol. 9, 1607 (2018)]. Accordingly, we conducted a systematic computational investigation of the dynamics of erythrocytes in high-frequency oscillatory shear flows by using a fluid-cell interaction model based on the Stokes-flow framework and a multiscale structural depiction of the cell. Within the range of parameters we consider, we identify five different response modes (wheeling, tilted wheeling, tank treading mode 1, tank treading mode 2, and irregular). The occurrence and stability of these response modes depend on the frequency of the flow, the peak capillary number, the viscosity ratio, the initial orientation of the cell, and the stress-free state of the protein skeleton. Through long-term simulations [[math] periods], mode switching events have been discovered, during which the cell transfers from one mode to another, often via an intermediate transient mode. The deformation of the skeleton and the contact stress between the skeleton and the lipid bilayer are computed since these are of direct importance to describing vital cell phenomena such as vesiculation by which the cell protects itself from premature elimination.

### Clusterlike instabilities in bubble-plume-driven flows

Author(s): Sai Ankit Etha, Anupam Jena, and Rajaram Lakkaraju

Continuous release of gas bubbles in large numbers from a localized source in a liquid column, popularly known as “bubble plumes”, is very relevant in nature and industries. The bubble plumes morphologically consist of a long continuous stem supporting a dispersed head. Through our direct numerical ...

[Phys. Rev. E 99, 053101] Published Wed May 01, 2019

### Role of parasitic modes in nonlinear closure via the resolvent feedback loop

Author(s): Kevin Rosenberg, Sean Symon, and Beverley J. McKeon

The representation of self-sustaining processes via resolvent analysis for turbulent flows is improved where the resolvent operator is not low rank by approximating the nonlinear forcing using parasitic modes, with analogy to weakly nonlinear analysis near critical Reynolds numbers.

[Phys. Rev. Fluids 4, 052601(R)] Published Wed May 01, 2019