# Latest papers in fluid mechanics

### Angular momentum transport and flow organization in Taylor-Couette flow at radius ratio of $η=0.357$

Author(s): Andreas Froitzheim, Sebastian Merbold, Rodolfo Ostilla-Mónico, and Christoph Egbers

Experimental and numerical investigations find that in a wide-gap turbulent Taylor-Couette flow, Nuω features nonconstant effective scaling with ReS due to the curvature-dependent limited capacity of the outer cylinder to emit plumes. For counterrotation, strengthened turbulent Taylor vortices cause a torque maximum at μmax=-0.123.

[Phys. Rev. Fluids 4, 084605] Published Wed Aug 14, 2019

### Impact of the Lewis number on finger flame acceleration at the early stage of burning in channels and tubes

For premixed combustion in channels and tubes with one end open, when a flame is ignited at the centerline at the closed end of the pipe and it propagates toward the open one, significant flame acceleration occurs at an early stage of the combustion process due to formation of a finger-shaped flame front. This scenario is tagged “finger flame acceleration” (FFA), involving an initially hemispherical flame kernel, which subsequently acquires a finger shape with increasing surface area of the flame front. Previous analytical and computational studies of FFA employed a conventional assumption of equidiffusivity when the thermal-to-mass-diffusivity ratio (the Lewis number) is unity (Le = 1). However, combustion is oftentimes nonequidiffusive (Le ≠ 1) in practice such that there has been a need to identify the role of Le in FFA. This demand is addressed in the present work. Specifically, the dynamics and morphology of the Le ≠ 1 flames in two-dimensional (2D) channels and cylindrical tubes are scrutinized by means of the computational simulations of the fully compressible reacting flow equations, and the role of Le is identified. Specifically, the Le > 1 flames accelerate slower as compared with the equidiffusive ones. In contrast, the Le < 1 flames acquire stronger distortion of the front, experience the diffusional-thermal combustion instability, and thereby accelerate much faster than the Le = 1 flames. In addition, combustion in a cylindrical configuration shows stronger FFA than that under the same burning conditions in a 2D planar geometry.

### Surface parametric instability of star-shaped oscillating liquid drops

The star-shaped oscillation of water drops has been observed in various physical situations under vertical excitation with different sources. In the past, the motion of such drops was simplified to two dimensions and only the azimuthal oscillation modes were considered. The parametric instability mechanism explained with the 2D (two-dimensional) model and the corresponding dispersion relation are not satisfactory. In this paper, we show that the external excitation induces a Faraday-wave-like parametric instability on the upper surface of the drop, and the surface patterns and azimuthal oscillations are coupled to produce star-shaped oscillations, which induces a significant softening to oscillation frequencies. We build a 3D (three-dimensional) theoretical model, in which the surface patterns and azimuthal oscillations are connected via kinematical boundary conditions and vary at the same frequency. Given the surface and azimuthal mode numbers, we propose a quasi-3D dispersion relation, which shows better consistency with the experimental data compared with the previous quasi-2D dispersion relation. Our theoretical model provides a more accurate description of the dynamics of liquid drops and will motivate a wide range of applications.

### Spatiotemporal linear stability of viscoelastic free shear flows: Dilute regime

We report the temporal and spatiotemporal stability analyses of antisymmetric, free shear, viscoelastic flows obeying the Oldroyd-B constitutive equation in the limit of low to moderate Reynolds number (Re) and Weissenberg number (We). The resulting fourth-order Orr-Sommerfeld equation is reduced to a set of six auxiliary equations that are numerically integrated starting from the rescaled far-field conditions, i.e., via Compound Matrix Method. The temporal stability analysis indicates that with increasing We, (a) the entire range of the most unstable mode is shifted toward longer waves (i.e., the entire region of temporal instability is gradually concentrated near zero wavenumber), (b) the vorticity structure contours are dilated, and (c) the residual Reynolds stresses are diminished. All these analogous observations previously reported in the inertial limit [J. Azaiez and G. M. Homsy, “Linear stability of free shear flow of viscoelastic liquids,” J. Fluid Mech. 268, 37–69 (1994).] suggest a viscoelastic destabilization mechanism operating at low and moderate Re. The Briggs idea of analytic continuation is deployed to classify regions of temporal stability, absolute and convective instabilities, as well as evanescent modes. The main result is that the free shear flow of dilute polymeric liquids is either (absolutely/convectively) unstable for all Re or the transition to instability occurs at comparatively low Re, a finding attributed to the fact that viscoelasticity aggravates instabilities via shear-induced anisotropy and the slow relaxation effects.

### Rheological signatures of aging in hard sphere colloidal glasses

Colloidal glasses are out-of-equilibrium in nature. When such materials are quenched from a shear-melted state into a quiescent one, their structure freezes due to entropic caging of the constituents. However, thermal fluctuations allow slow structural evolution, a process known as aging, in favor of minimizing free energy. Here, we examine the rheological signatures of aging, in a model system of nearly hard sphere colloidal glass. Subtle changes in the linear viscoelastic properties are detected with the age of the colloidal glass where viscous modulus shows a decrease with aging whereas the elastic modulus remains unaffected. This is associated with the slowing-down of long-time out-of-cage dynamics as the glass ages. On the contrary, nonlinear rheological measurements such as start-up shear flow, stress relaxation, and creep experiments show a strong dependence on sample age. Moreover, creep and stress relaxation experiments show ample evidence of avalanche type processes that occur during aging of colloidal glasses. Finally, comparison of creep and start-up shear flow measurements indicate that the latter is more energy efficient in inducing flow in colloidal glasses irrespective of aging dynamics.

### Superfluidity inside carbon nanotubes

Author(s): Leonid. V. Mirantsev

Molecular dynamics simulations of equilibrium structures and flows of nonpolar argon atoms confined by single-walled carbon nanotubes (SWCNTs) with circular cross section and rectangular cross section having the same area and the ratio between its sides 1:4 have been performed. It has been shown tha...

[Phys. Rev. E 100, 023106] Published Tue Aug 13, 2019

### Self-propulsion of a helical swimmer in granular matter

Author(s): Rogelio Valdés, Verónica Angeles, Elsa de la Calleja, and Roberto Zenit

An experimental study of the motion of a self-propelled helix in granular matter shows that there is an optimal pitch angle at which the swimming speed reaches a maximum value. The measurements are compared with predictions with granular resistive force theory, leading to good agreement.

[Phys. Rev. Fluids 4, 084302] Published Tue Aug 13, 2019

### Reynolds number effect on drag control via spanwise wall oscillation in turbulent channel flows

The effect of Reynolds number (Reτ) on drag reduction using spanwise wall oscillation is studied through direct numerical simulation of incompressible turbulent channel flows with Reτ ranging from 200 to 2000. For the nondimensional oscillation period T+ = 100 with maximum velocity amplitude A+ = 12, the drag reduction ([math]) decreases from 35.3% ± 0.5% at Reτ = 200 to 22.3% ± 0.7% at Reτ = 2000. The oscillation frequency ω+ for maximum [math] slightly increases with Reτ, i.e., from ω+ ≈ 0.06 at Reτ = 200 to 0.08 at Reτ = 2000, with [math]. These results show that [math] progressively decreases with increasing Reτ. Turbulent statistics and coherent structures are examined to explain the degradation of drag control effectiveness at high Reτ. Fukagata, Iwamoto, and Kasagi analysis in combination with the spanwise wavenumber spectrum of Reynolds stresses reveals that the decreased drag reduction at higher Reτ is due to the weakened effectiveness in suppressing the near-wall large-scale turbulence, whose contribution continuously increases due to the enhanced modulation and penetration effect of the large-scale and very large-scale motions in the log and outer regions. Both the power-law model ([math]) and the log-law model [DR = f(Reτ, ΔB), where ΔB is the vertical shift of the log-law intercept under control] are examined here by comparing them with our simulation data, from these two models we predict more than 10% drag reduction at very high Reynolds numbers, say, Reτ = 105.

### Vortex dynamics during acoustic-mode transition in channel branches

The vortex dynamics during acoustic mode transition in channel branches were experimentally investigated with phase-locking particle image velocimetry (PIV) measurements. Particularly, a real-time waveform recognition approach, based on an offline pressure analysis by dynamic mode decomposition (DMD) and a real-time computation by field programmable gate array, was established. In the offline DMD analysis, energetic pressure DMD modes during acoustic mode transition were extracted from pressure data measured by a pressure transducer array and found to agree well with the natural acoustic standing-wave modes numerically determined from an acoustic modal analysis. The acoustic mode transition process was classified into three successive phases: Phase-I: hybrid acoustic modulations, Phase-II: no acoustic modulation, and Phase-III: third-order acoustic modulation. Subsequently, the vortex dynamics corresponding to Phase-I and Phase-III were determined by phase-locking PIV measurements with the real-time waveform recognition approach. The results are summarized as follows. (1) The vortex dynamics coupled with the first acoustic standing-wave mode in Phase-I were related to the first shear layer hydrodynamic mode in channel branches. (2) The vortex dynamics coupled with the second acoustic standing-wave mode in Phase-I were recognized as the signatures of the second shear layer hydrodynamic mode. (3) However, in Phase-III of the acoustic mode transition, modulated by the third acoustic standing-wave mode, the corresponding vortex dynamics fully developed into a second shear layer hydrodynamic mode. This work provides a better understanding of the complex vortex dynamics of channel flows with broad implications for industrial piping systems.

### On the generation of vorticity and hydrodynamics of vortex ring during liquid drop impingement

In this work, we investigate the phenomenon of vortex generation and formation of a vortex ring when a liquid drop impinges on a miscible liquid surface. Although the formation of a vortex ring for this system has been studied for more than a century, little is known about its exact mechanism of generation and how its hydrodynamics is related to the shape of the drop. This is due to the complexity involved in the conversion of the initially generated vorticity into a vortex ring. To cast light on this intriguing phenomenon, time-resolved high-speed imaging with high magnification is used. This allows us to probe deeper into the vortex generation process and study the formation of the ring. We make a comprehensive study of the effect of drop impingement height and drop shape at the time of impact on the vortex generation and the hydrodynamics of the ring. The effect of crater evolution on the hydrodynamics of the vortex ring is studied in terms of its diameter and translational velocity. By examining the role of the shape of the crater on vortex ring penetration, we answer the question why the most penetrating vortex rings are generated by a prolate shaped drop.

### Flow and heat transfer characteristics of a nanofluid between a square enclosure and a wavy wall obstacle

A mathematical model for the natural convection flow and heat transfer of a nanofluid in an annulus enclosed by a square cylinder and a wavy wall cylinder is developed. Using vorticity-stream function formulation, we first derive governing equations in the Cartesian coordinates. Then, these equations are transformed utilizing coordinate transformations into a system of equations valid for the present physical domain. The problem is solved using the finite difference method. It is found that for higher values of the volume fraction of nanoparticles, the number of undulations of the wavy wall of the inner cylinder and Rayleigh number, the strength of streamlines significantly increases. However, the amplitude of undulations diminishes the intensity of streamlines. The isotherms are also strongly influenced by these parameters. Contrary to this, the Nusselt number at the inner and outer cylinders is remarkably increased due to the increase of the volume fraction of nanoparticles, amplitude of undulations, and Rayleigh number. For the higher volume fraction of nanoparticles and Rayleigh number, the average Nusselt number at the inner and outer cylinders is higher. The maximum and minimum values of the velocity profile increase with the higher Rayleigh number. Nevertheless, the converse scenario is observed for the larger amplitude of undulation and volume fraction of nanoparticles. The temperature near the inner cylinder noticeably decreases with the increase of the Rayleigh number, whereas it slowly reduces for higher amplitude of undulations. Above all, this investigation might be helpful for the researchers in regard to the approach of making a more complex geometry by using coordinate transformations. Furthermore, the results could provide vital information about the problems in current technological applications.

### The role of surface wettability on the heat transfer in liquid-liquid two-phase flow in a microtube

Liquid-liquid two-phase flow is capable of boosting heat transfer in microdevices compared to the single-phase and gas-liquid flows. A thorough investigation is performed here to characterize the heat transfer in water-oil flow in a microtube. Finite element method along with the level-set model is employed for numerical simulation. A main part of this paper is devoted to studying the effect of wettability on the heat transfer performance. Four contact angles of 0°, 30°, 150°, and 180° are investigated, which revealed that the contact angle of 150° produces the highest Nusselt number (Nu). Triple points form at this contact angle, and the slugs slide on the wall, which results in more significant wall shear and slip velocity on the wall. Based on the observed flow configuration, a novel idea is developed to use the nonuniform distribution of contact angle to augment the local Nu. It is observed that changing the wall from hydrophobic to hydrophilic will locally increase Nu around the transition point. In addition to the contact angle, the slug length, frequency of slug generation, and the film thickness around the slugs affect Nu. Three Weber numbers (We) at four contact angles are examined by varying the flow rate of the oil phase in the next part of the paper. We affects Nu by changing the frequency of slug generation and consequently its length. Finally, the effect of film thickness is scrutinized at various capillary numbers (Ca). The film thickness increases with Ca which reduces the heat removal rate.

### Scaling of the production of turbulent kinetic energy and temperature variance in a differentially heated vertical channel

Author(s): Tie Wei

Identity equations are derived for the global turbulent kinetic energy (TKE) and temperature variance production. Shear-produced TKE is found to scale as uτUmax2 and buoyancy-produced TKE scales as uτ2Umax. Scalings for temperature variance production and dissipation are also revealed.

[Phys. Rev. Fluids 4, 081501(R)] Published Mon Aug 12, 2019

### Steady flow of one uniformly rotating fluid layer above another immiscible uniformly rotating fluid layer

Author(s): P. D. Weidman and M. R. Turner

We find exact similarity solutions of the Navier-Stokes equations for the steady laminar flow of two immiscible, uniformly rotating fluid layers. For layers which counter-rotate too strongly a self-similar solution does not exist, as given by a condition we find on the angular velocity ratio.

[Phys. Rev. Fluids 4, 084002] Published Mon Aug 12, 2019

### Thermal effect on drainage flow of a viscous gas from a semisealed narrow channel

Author(s): Wei Huang and Kang Ping Chen

A thermal analysis shows that even without an imposed temperature drop, a gas-expansion-induced transient temperature decrease can slow viscous gas drainage from a semisealed channel with adiabatic walls. At given density drop, gas drains out faster as initial-to-final temperature ratio increases.

[Phys. Rev. Fluids 4, 084202] Published Mon Aug 12, 2019

### Multifluid flows in a vertical channel undergoing topology changes: Effect of void fraction

Author(s): Jiacai Lu and Gretar Tryggvason

Numerical simulations of turbulent multifluid flows, undergoing changes of the interface topology, are carried out using a front-tracking–finite-volume method. The results for varying void fractions show that the flow starts to depart from the bubbly regime at a void fraction of about 15%.

[Phys. Rev. Fluids 4, 084301] Published Mon Aug 12, 2019

### Turbulent structures of shock-wave diffraction over 90° convex corner

The turbulent structures and long-time flow dynamics of shock diffraction over 90° convex corner associated with an incident shock Mach number Ms = 1.5 are investigated by large eddy simulation (LES). The average evolution of the core of the primary vortex is in agreement with the previous two dimensional studies. The Type-N wall shock structure is found to be in excellent agreement with the previous experimental data. The turbulent structures are well resolved and resemble those observed in the experimental findings. Subgrid scale dissipation and subgrid scale activity parameter are quantified to demonstrate the effectiveness of the LES. An analysis based on turbulent-nonturbulent interface reveals that locally incompressible regions exhibit the universal teardrop shape of the joint probability density function of the second and third invariants of the velocity gradient tensor. Stable focus stretching (SFS) structures dominate throughout the evolution in these regions. Stable node/saddle/saddle structures are found to be predominant at the early stage in locally compressed regions, and the flow structures evolve to more SFS structures at later stages. On the other hand, the locally expanded regions show a mostly unstable nature. From the turbulent kinetic energy, we found that the pressure dilatation remains important at the early stage, while turbulent diffusion becomes important at the later stage. Furthermore, the analysis of the resolved vorticity transport equation reveals that the stretching of vorticity due to compressibility and stretching of vorticity due to velocity gradients plays an important role compared to diffusion of vorticity due to viscosity as well as the baroclinic term.

### Evolution of high frequency waves in shoaling and breaking wave spectra

Mathematical derivation and numerical verification of a wave transformation model in the frequency domain are discussed. The model is a fully dispersive nonlinear wave model and is derived based on the boundary value problem. Transforming the problem in the frequency domain and using multiple scale analysis in space and perturbation theory, the model is expanded up to second order in wave steepness. This fully dispersive nonlinear wave model is a set of evolution equations which explicitly contains quadratic near-resonant interactions. The comparison between the presented model, the existing fully dispersive model, and a nearshore model with different sets of laboratory and field data shows that the presented model provides significant improvements particularly at higher frequency.

### Interaction of cylindrical converging shocks with an equilateral triangular SF6 cylinder

Based on the compressible large eddy simulation method, combined with the hybrid scheme of the weighted essentially nonoscillatory scheme and the tuned central difference scheme, the interaction of the cylindrical converging shock wave with an equilateral triangle SF6 cylinder is numerically simulated in this work. The numerical results clearly show the evolution of the interface induced by the Richtmyer-Meshkov instability due to the interaction of the converging shock and the interface, which are in good agreement with previous experimental results. However, the numerical results reveal clearly the evolution and characteristics of the shock wave structures, and find that there are five times of shock focusing during the interaction process of shock waves with the interfaces. The characteristics of the mean flow, the width and growth rate of the mixing-layer, the circulation evolution, and history of the mixing ratio have also been quantitatively analyzed and it was found that the secondary reflected shock can lead to rapid mixing. Meanwhile, a dynamic mode decomposition method is applied to extract the coherent structures for discovering the mechanism of turbulent mixing.

### Analytical solutions of incompressible laminar channel and pipe flows driven by in-plane wall oscillations

Emerging flow control strategies have been proposed to tackle long-lasting problems, for instance, precise mixing of chemicals and turbulent drag reduction. Employing actuators imposing in-plane wall oscillations are particularly popular. This paper investigates incompressible laminar rectangular channel and circular pipe flows driven by uniform and traveling wave in-plane wall oscillations. A comprehensive set of exact analytical solutions are presented describing parallel and concentric flows. Dimensionless groups are identified, and it is described how they characterize the one- and two-dimensional time-dependent velocity and pressure fields. The solutions enable to compute the oscillating boundary layer thickness. It is demonstrated that the dimensionless groups and the boundary layer thickness narrows the region of interest within the parameter space. In particular, the oscillating boundary layer thickness obtained from these laminar flows estimates a “radius of action” within which flow features can be altered to boost mixing or reduce turbulent friction drag. The results are suitable for software validation and verification, may open the way to promising complex wall oscillations, and ease the optimization task that delays the industrial application of flow controls.