# Latest papers in fluid mechanics

### Vertically clamped flexible flags in a Poiseuille flow

Vertically clamped flexible flags in an oncoming Poiseuille flow were numerically modeled to investigate the hydrodynamic interaction and dynamics of the flexible flags using the immersed boundary method. The number of flags modeled was increased step by step: a single flag, double flags, triple flags, and a large array of multiple flags were modeled. The flexible flags displayed a flapping mode or a fully deflected mode, depending on the relationship between the elastic inner force and the hydrodynamic force. The bending angle (α), flapping amplitude (A), and period (T) of the single flag decreased as the bending rigidity (γ) increased. In the double and triple flag systems, the bending angle of the first flag reached a steady state as the gap distance (d) increased. The gap distance affected the position of the flag relative to the vortical structures. The vortical structures merged and formed a large vortex. Small vortical structures penetrated the large gap to drive flag flapping and force flag bending. In a large array of multiple flags, all flags were present in the fully deflected mode for a small gap distance. As the gap distance increased, the interactions between the flags increased. The flags were significantly influenced by the inlet and exit conditions.

### Electrically induced droplet ejection dynamics under shear flow

Droplet nucleation, condensation, and transport is a ubiquitous phenomenon observed in various industrial applications involving power generation and energy conversion to enhance heat transfer. Recent studies have shown that electrowetting (EW) has emerged as a new tool to enhance pool boiling heat transfer. In these applications involving heat transfer through pool boiling, the interplay between the incoming air and an EW-induced jumping droplet is instrumental in determining the overall heat transfer enhancement. This study investigates the transport dynamics of EW-induced droplet ejection in shear flow. A high-density ratio based lattice Boltzmann method is employed to model the ejection dynamics, and a geometry-based contact angle formulation is used to capture the three-phase contact line. We observe a characteristic head vortex at the leading end of the droplet, the strength of which increases with an increase in the shear rate. The droplet angle of flight, aspect ratio, and surface energy are found to increase with an increase in the applied voltage. Variations in pulse width induce a phase shift in the temporal evolution of the angle of flight and aspect ratio. Due to an increase in drag forces, the droplet traverses a larger streamwise distance at higher gas densities.

### Acoustic wave propagation at nonadiabatic conditions: The continuum limit of a thin acoustic layer

Author(s): Y. Ben-Ami and A. Manela

Existing studies on sound propagation in rarefied gases are extended to consider wave transmission at nonadiabatic ambient conditions, where arbitrarily large reference temperature and density gradients prevail. Asymptotic analysis of the acoustic field is carried out in the limit of small Knudsen numbers and high actuation frequencies, for both mechanical and thermal wall excitations.

[Phys. Rev. Fluids 5, 033401] Published Wed Mar 04, 2020

### Simultaneous liquid flow and drying on rotating cylinders

Author(s): Chance Parrish and Satish Kumar

A common model problem for discrete-object coating is the flow of a thin nonvolatile liquid film on the outside of a rotating cylinder. However, the behavior of a volatile particle-laden coating on rotating cylinders has yet to be studied and remains an important open problem. In this work, a lubrication-theory-based model is used to (i) examine the effects of various problem parameters on coating behavior, (ii) understand the underlying physical mechanisms, and (iii) provide guidance for improving coating uniformity.

[Phys. Rev. Fluids 5, 034001] Published Wed Mar 04, 2020

### Inner, meso, and outer scales in a differentially heated vertical channel

Reynolds shear stress and Reynolds normal stress in a differentially heated vertical channel were shown in a previous paper to scale by a mixed scale of the friction velocity uτ and the maximum mean vertical velocity Umax. This scale was empirically determined; this work presents a physical understanding of the new scaling. A new dimensional analysis is developed that involves a simple modification of the traditional inner–outer scaling. The functional dependencies in the new dimensional analysis are determined using direct numerical simulation (DNS) data. The DNS data confirm the new physical reasoning and reveal, as follows: (i) The velocity fluctuation variance at the centerline scales with an outer scale, which is the mixed scale uτUmax. (ii) The location of the maximum mean vertical velocity scales as an Obukhov-style length scale, which, in turn, scales as the geometric mean of the inner length scale and the outer length scale. (iii) The temperature fluctuation variance at the centerline scales with an outer temperature scale. (iv) The temperature fluctuation variance peaks in the inner layer, and its peak value scales with an inner temperature scale. The new outer scales obtained from the dimensional analysis are shown to be consistent with the properties of the mean momentum balance equation.

### Sediment erosion in zero-mean-shear turbulence

Turbulence plays an evident role in particle erosion that in many practical situations superimposes with the action of a mean flow. In this paper, the turbulence effect on particle erosion is studied under zero-mean flow conditions, by using the turbulence generated by an oscillating grid. The stirring grid is located more than two mesh size away from the particle layer. The zero-mean flow below the grid has been qualified by revisiting the k–ε model of Matsunaga et al. [Fluid Dyn. Res. 25, 147–165 (1999)]. The turbulence efficiency on the settling/resuspension of the particles is quantified for various turbulence intensities, varying the size, the nature of the particles, and their buoyancy relative to the fluid. We find that the concentrations C of eroded particles collapse fairly well onto a single trend for C ≤ 5 × 10−2, when plotted as a function of the ratio between the flux of turbulent kinetic energy at the particle bed location and the particle settling flux. Above, the concentrations saturate, thus forming a plateau. Particle erosion mechanisms have been investigated in terms of competing forces within an “impulse approach.” Horizontal drag vs friction first leads to a horizontal motion followed by a vertical motion, resulting from vertical drag and lift vs buoyancy. Particle erosion occurs when both force balances are in favor of motion for a duration of 0.1–0.3 Kolmogorov time scale.

### Linear stability analysis of a liquid film down on an inclined plane under oscillation with normal and lateral components in the presence and absence of surfactant

In this work, we first study the interface instability of a fluid layer flowing down on an inclined plane under periodic oscillation having both normal and lateral components. After that, we examine the effect of an insoluble surfactant covering the free surface under normal oscillation, lateral oscillation, and both normal and lateral oscillations. The time periodic linear system, corresponding to the governing equations, is treated using the Chebyshev spectral collocation method for spatial resolution, and for temporal resolution, we use the Floquet theory. We show that the stabilizing effect of normal oscillation amplitude on the gravitational instability, reported by Woods and Lin [J. Fluid Mech. 294, 391 (1995)], is strengthened by introducing lateral oscillation, and this contributes to the complete suppression of this instability. The harmonic and subharmonic zones, initially stable in the work of Woods and Lin [J. Fluid Mech. 294, 391 (1995)], are destabilized by the lateral oscillation, and the first unstable parametric resonance becomes without threshold. Conversely, the unstable domain of the gravitational instability and the second resonance zone reported by Lin, Chen, and Woods [Phys. Fluids 8, 3247 (1996)] can be reduced by introducing normal oscillation. Finally, we show that the surfactant has a stabilizing effect that contributes to accelerate the suppression of the gravitational instability and opposes the destabilizing effect of the lateral oscillation on the first subharmonic resonance to give rise to a competition between the two effects.

### Characterization of the thermal and solutal Marangoni flows of opposite directions developing in a cylindrical liquid bridge under zero gravity

Numerical simulations of the thermo-solutal Marangoni convection developing in a Si–Ge liquid bridge of a floating-zone system have been performed under zero gravity. Half of the liquid bridge was considered as the three-dimensional (3D) computational domain. In this system, the solutal Marangoni convection develops in the direction opposite to the thermal Marangoni convection along the free surface in the bridge, i.e., the thermal Marangoni number, MaT, is negative and the solutal Marangoni number, MaC, is positive. Since the SiGe melt is a low-Prandtl number (Pr = 6.37 × 10−3) and high-Schmidt number (Sc = 14.0) liquid, the temperature field is almost independent of the convective flow and the concentration field determines the transport structures. When MaC is larger than −MaT, the concentration pattern is steady and two-dimensional (2D) axisymmetric. When MaC is smaller than −MaT, we predict two kinds of flow transitions with the increase in |MaT|. If MaC is sufficiently large (MaC ≳ 530), as |MaT| increases, the flow changes from a 2D-steady pattern to a 3D-chaotic behavior at moderate |MaT| (1050 ≲ |MaT| ≲ 2800). We also predict that a second transition and an oscillatory rotating flow occur as |MaT| increases further. The flow becomes 3D-steady at smaller MaC (MaC ≲ 360) with no transition, and the azimuthal wavenumber (m) decreases with increasing |MaT|. Furthermore, the thermo-solutal Marangoni convection in this system can be suppressed almost completely when MaC is approximately equal to −MaT (MaC ≈ −MaT) and the flow becomes periodically stable with weak fluctuations.

### Stokes’s flow of a bumpy shaft inside a cylinder and a model for predicting the roughness of the shaft

A microshaft may become rough due to corrosion, abrasion, and deposition when it has been operating in a viscous fluid. It is of importance to investigate the effects and to estimate the level of the shaft’s surface roughness. In this study, we consider a bumpy shaft with its shape modeled by the product of two cosinoidal functions; the roughness ε is defined to be the ratio of the amplitude of the product to the mean radius b of the shaft. First, we consider the Couette flow of the shaft in a viscous fluid enclosed by a rotating smooth cylinder. A perturbation analysis is carried out for the Stokes equation with respect to ε up to the second-order with the key parameters including the azimuthal wave number n and the axial wave number α of the roughness, as well as the mean radius b. In addition, a perturbation analysis is performed for the Poiseuille flow in the gap between the shaft and the shrouded cylinder so that we have complete information for estimating the mean roughness of the shaft. Moreover, numerical simulations are carried out for the torque acting on the shaft at selected b, ε, and wave numbers n, α for verifying the accuracy of the perturbation results. It is shown that the mean torque M acting on the unit area of the bumpy shaft and the total flow rate Q of the Poiseuille flow are both modified by a second-order term of roughness in ε, namely, M = M0 + ε2η and Q = Q0 − ε22πχ, where M0 and Q0 denote the torque and the flow rate, respectively, for the smooth shaft. The net effects are conveniently written as η = η1 + η2 and χ = χ1 + χ2, both comprising two components: η1 = η1 (b) < 0 (pure deficit) increases with increasing b and χ1 = χ1 (b) first increases and then decreases again with increasing b, while η2 and χ2 are complex functions of b, n, and α. For a given density of roughness Ac = nα, there exists an intermediate n at which the mean torque M is minimized, while the total flow rate Q is maximized. The main results are thoroughly derived with all the steps of derivation explained physically, and their relationships to the various geometrical parameters are used to establish a simplified model for predicting the shaft roughness within the range of reasonable accuracy.

### Modulated wall motion approach for augmenting slug flow heat transfer between two micro-parallel plates

Liquid–liquid slug flow heat transfer in microchannels has been an interesting topic of research to many researchers. However, the heat transfer studies available in the existing literature deal with stationary walls of the microchannels. In the present work, a modulated motion is prescribed to the walls of the channel in the transverse direction during oil–water slug flow between micro-parallel plates. The influence of frequency and amplification factor of the modulated wall motion as well as capillary number on the droplet shape, film thickness, pressure drop, and heat transfer rate under uniform wall heat flux conditions is investigated computationally. The heat transfer results for the modulated wall motion case show a significant improvement over liquid-only flow and slug flow without any wall motion. Besides, the effect of slug length on the heat transfer has also been discussed for both modulated and unmodulated wall motions of the channel. A mean absolute deviation of 2%–75% in the pressure drop obtained from the numerical studies and existing semi-empirical models for stationary walls for the studied Capillary numbers is observed. This suggests that a better formulation is required for the pressure drop model. In addition, although Nusselt numbers are found to be in reasonable agreement with the existing model for stationary walls, requirement for the formulation of a generalized model considering the effect of wall oscillations is also suggested. This study proposes a new perspective for heat dissipation in micro-scale channels and promotes flow and heat transfer studies, which could bring benefits to relevant applications.

### Tracking the flapping motion of flow separation using pointwise measurement

In recent investigations of the unsteadiness of flow separation, time-resolved whole-field information, such as the temporal variation of reverse flow area and proper orthogonal decomposition modes, is commonly used to quantify the flapping motion of separation bubbles. In the present study, we explore the possibility of tracking the flapping motion of flow separation using only pointwise measurements. A generalized framework for designing the optimal number and positions of measurement points is presented and assessed using time-resolved particle image velocimetry measurement data for turbulent flow separations induced by a broad range of two- and three-dimensional surface-mounted bluff bodies. Two models are proposed to approximate the temporal variation of reverse flow area over the bluff bodies. These two models require only the mean reattachment length, mean velocity at the body height in the oncoming flow, and time-resolved single- or two-point measurements of streamwise velocity. The optimal location for the single-point model is in the rear part of the mean separation bubble around the highest elevation of the mean separating streamline. While the single-point model predicts the temporal variation of reverse flow area reasonably well, it consistently misidentifies the subdominant frequency of reverse flow area as the dominant one. For the two-point model, one measurement point is in the rear part of the mean separation bubble and the other measurement point is slightly downstream of the mean reattachment point. The two-point model reproduces the temporal variation as well as the dominant frequency of reverse flow area remarkably well. Overall, the present study proposes a simple and reliable method to track the temporal variation of reverse flow area and holds promise for the future development of active closed-loop flow control based on real-time flapping motion of separation bubbles.

### Real-fluid phase transition in cavitation modeling considering dissolved non-condensable gas

In this article, a fully compressible two-phase flow model combined with a multi-component real-fluid phase equilibrium solver is proposed for cavitation modeling. The model is able to simulate the dissolving process of non-condensable gas through resolving the real-fluid phase change equations. A three-dimensional cavitating nozzle test is considered to validate the suggested model. The achieved numerical results have been compared to the available x-ray experiments. The results have confirmed that the model can tackle the phase transition phenomena including gas dissolving and homogeneous nucleation processes. Thus, the cavitation inception has been modeled dynamically when the fluid crosses the phase boundary from the single-phase state to the two-phase state and vice versa. The effects of non-condensable gas on the cavitation inception, development, and unsteadiness have been particularly analyzed, based on the large eddy simulations and x-ray experiments. Finally, the encountered challenges are mentioned, aiming at providing recommendations for similar research studies.

### On the grid dependence of hydrodynamic stability analysis in solid rocket motors

In this numerical study, we investigate the grid dependence of the Chebyshev collocation algorithm for flow stability analysis of solid rocket motors. Conventional analyses tend to focus on how the errors of the individual eigenvalues depend on the level of grid refinement. Here, we perform a structural error analysis to estimate the overall error of the computed spectrum. First, we validate the structural error analysis on a structural oscillation problem with analytical spectra, yielding a simple linear relation between the number of converged eigenvalues and the number of grid points. We then apply the analysis to Taylor–Culick flow, yielding a similar relation for the converged eigenvalue points. We find that the structural error analysis provides reliable criteria for the grid computation in flow stability analysis of a real solid rocket motor. In studies involving numerical spectra, the proposed structural error provides an alternative tool for error analysis of problems such as Taylor–Culick flow, where the computed individual eigenvalues do not necessarily converge to fixed values with increasing grid refinement.

### Three-dimensional electroconvective vortices in cross flow

Author(s): Yifei Guan, James Riley, and Igor Novosselov

This study focuses on the three-dimensional (3D) electrohydrodynamic flow instability between two parallel electrodes driven by unipolar charge injection with and without cross flow. Lattice Boltzmann method with a two-relaxation time model is used to compute flow patterns. In the absence of cross f...

[Phys. Rev. E 101, 033103] Published Tue Mar 03, 2020

### Generation of nonlinear internal waves by flow over topography: Rotational effects

Author(s): C. Yuan, R. Grimshaw, E. Johnson, and A. Whitfield

We use the forced Ostrovsky equation to investigate the generation of internal waves excited by a constant background current flowing over localized topography in the presence of background rotation. As is now well known in the absence of background rotation, the evolution scenarios fall into three ...

[Phys. Rev. E 101, 033104] Published Tue Mar 03, 2020

### Experimental study on impulse waves generated by gravitational collapse of rectangular granular piles

Towering in many gorges of reservoirs and coastal zones, pillar rock masses may collapse and fall due to foundation crushing, and the impact on water by debris leads to impulse waves. In this study, the process of impulse wave induction by the gravitational collapse of granular piles was investigated using particle image velocimetry. The experimental results showed that the collapse process of partially submerged particles was significantly different from that of dry particles. Near the water surface, particles moved outward in a reversed “S” shape. In the presence of water at the slope foot, the time and the distance traveled by the particles were reduced. The hydraulic effects such as water entrainment, vortex, rolling, and viscous drag exacerbated the energy dissipation of the granular piles, thus reducing particle mobility. Thirty five experiments suggested that the impulse waves induced by granular piles could be categorized as bores, solitary waves and nonlinear transition waves according to the functional inequality, which consisted of the aspect ratio and the relative thickness. The fitted formula for the run-out of partially submerged granular piles and the corresponding maximum wave amplitudes was derived by nonlinear regression of the experimental data. In comparison with previous formulas, these formulas are power functions consisting of aspect ratio and relative thickness and are highly suitable for predicting the collapse of granular piles and the impulse waves induced as the correlation coefficients of calculated results by these formulas and the measured values exceeded 0.93.

### Dispersion of particles in two-dimensional circular vortices

The spreading of n particles simultaneously released is modeled numerically and analytically using a Langevin’s equation. In the numerical experiments, particles are dispersed utilizing the random walk technique plus advection caused by a vortex with rigid-body rotation (RV) or irrotational (IV). In each vortex, the dispersion is described analyzing the statistical behavior of the particles’ position as a function of time t. In the RV case, analytical expressions for the statistics indicate (like the numerical experiments) that the dispersion or variance is linear in t and the diffusion coefficient D depends on the angular speed Ω of the vortex. If the time scale of the random walk is much smaller than the rotation period (i.e., Δt ≪ 2π/Ω), then D decreases lightly if Ω increases relative to a pure two-dimensional (2D) random walk. In the experiments of the IV in which all particles start at the same point, we observe an asymmetric dispersion (the cloud becomes a comet and then a spiral), which leads to a rapid growth in the variance proportional to t3 in the first time steps. This anomalous dispersion occurs while the particles distribute around the origin and the spiral reaches to form a belt. Afterward, the variance grows linearly in t as in standard dispersion, but D is in general larger than the case without the vortex, even if initially the particles formed a ring around the origin. D tends to increase with the circulation for more intense vortices.

### Hydrostatic pressure and interfacial tension induce mode instability in wave propagation along a liquid-filled microtubule

Wave propagation in microtubules plays an important role in cell function and engineering applications. Interfacial tension and hydrostatic pressure significantly affect such wave propagation in liquid-filled microtubules, but it remains elusive how they influence the dispersion relation. To address this, we develop a theoretical model based on Flügge’s theory, with interfacial tension and hydrostatic pressure duly accounted for. We then employ the model to analyze the dispersion relation of axisymmetric and non-axisymmetric waves. The difference between interfacial tension and hydrostatic pressure is found to affect the dispersion relation. With the increase in interfacial tension, wave velocity increases for all modes of axisymmetric waves under different hydrostatic pressures. With the increase in interfacial tension or decrease in hydrostatic pressure, wave velocity increases for the first mode of the non-axisymmetric wave but non-monotonously changes for the second and third modes of the non-axisymmetric wave. Notably, increasing the difference between dimensionless hydrostatic pressure (μ) and dimensionless interfacial tension (λ) can lead to mode instability. For the axisymmetric wave, the second mode becomes unstable when |μ-λ| is sufficiently large. For the non-axisymmetric wave, the first mode becomes unstable when |μ-λ| is large enough and the second mode becomes unstable only when μ-λ is positive and large enough. The developed theory enables a better understanding of the effect of the environment on signal transmission in cells and provides guidelines in nondestructive testing with microtubules.

### Targeted turbulent structure control in wall-bounded flows via localized heating

A targeted turbulent flow control strategy, based on selective heating of streamwise-aligned heat strips, is assessed for drag reduction using direct numerical simulations of variable viscosity and compressible turbulent channel flows. As increasing the temperature of a gas increases its viscosity, heating is generally an unfavorable drag mitigation approach. However, through a selective spatial arrangement of the heating array, the slight increase in viscosity and decrease in density can serve to modify the organization of the streamwise-aligned structures and the likelihood of the ejection and sweep events near the wall. This can, under specific conditions, lead to a very modest drag reduction. The optimal spatial arrangement is identified using a bidimensional empirical mode decomposition and targets the near-wall, large-scale turbulent motion. The drag coefficient, at constant mass flow rate, remains unchanged with heating despite up to an 11% increase in the local viscosity above the heating strips. When accounting for the viscosity variation in the drag reduction calculation, an effective drag reduction of 6% is observed.

### Numerical investigation of control of dynamic stall over a NACA0015 airfoil using dielectric barrier discharge plasma actuators

The control of dynamic stall over a periodically pitching NACA 0015 airfoil using alternating current (AC) and nanosecond (NS) dielectric barrier discharge (DBD) plasma actuators is investigated by means of numerical simulation. This study employs a two-dimensional unsteady Reynolds averaged Navier–Stokes (URANS) approach to resolve the flow control process. The pulsed AC and NS plasma discharges are modeled by an empirical body force model and a sophisticated self-similar plasma formulation, respectively. Our study concentrates on the resolution of detailed control process of dynamic stall under DBD plasma forcing at two Reynolds numbers (Re) as well as on comparison of AC and NS plasma actuations in terms of control mechanism and authority. It appears that the dynamic stall without control at both moderate Reynolds number of Re = 2.5 × 105 and high Reynolds number of Re = 7.5 × 105 can be categorized into the so-called trailing edge stall. The trailing edge stall initiates with flow reversal near the trailing edge. Regarding the dynamic stall control, it is found that the jet flow produced by AC DBD or residual heat of NS DBD is responsible for inducing large-scale spanwise vortices, which, in turn, dominate the flow control. For the moderate Re flow, AC and NS plasma actuators have comparable performance and both achieve good control authority. However, for the dynamic stall control at high Re, the NS DBD achieves surprising success in enhancing lift of the airfoil and reducing aerodynamic hysteresis, whereas AC DBD nearly has no effect on the flow. It is found that the superiority of the NS plasma actuator over other control means is due to the thermal convection characteristic peculiar to NS plasma discharge. This characteristic makes the NS DBD plasma actuator more flexible in extending its influence region and acquiring a better control effect.