# Physics of Fluids

Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.

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### Evaporating droplets in shear turbulence

Physics of Fluids, Volume 32, Issue 7, July 2020.

This paper investigates droplets that evaporate and cluster in shear turbulence with direct numerical simulations. The flows are statistically stationary and homogeneous, which reduces the physical complexity and simplifies the statistical analysis. The mass loadings are about 0.1, the Stokes numbers are about 1, and the Taylor-scale Reynolds numbers are about 60. The simulations show that the clusters are anisotropic and inclined toward the flow direction on large scales, but isotropic on small scales. When the mass loading increases, the clusters contain more droplets, but their size remains unchanged, and the droplets in clusters experience higher vapor mass fractions. When the Stokes number increases, the clusters contain fewer droplets and become larger, and the droplets in clusters experience lower vapor mass fractions. When the Reynolds number increases, the clusters contain more, smaller droplets and become smaller, and the inclination angles of the clusters change.

This paper investigates droplets that evaporate and cluster in shear turbulence with direct numerical simulations. The flows are statistically stationary and homogeneous, which reduces the physical complexity and simplifies the statistical analysis. The mass loadings are about 0.1, the Stokes numbers are about 1, and the Taylor-scale Reynolds numbers are about 60. The simulations show that the clusters are anisotropic and inclined toward the flow direction on large scales, but isotropic on small scales. When the mass loading increases, the clusters contain more droplets, but their size remains unchanged, and the droplets in clusters experience higher vapor mass fractions. When the Stokes number increases, the clusters contain fewer droplets and become larger, and the droplets in clusters experience lower vapor mass fractions. When the Reynolds number increases, the clusters contain more, smaller droplets and become smaller, and the inclination angles of the clusters change.

Categories: Latest papers in fluid mechanics

### Accumulated densities of sedimenting particles in turbulent flows

Physics of Fluids, Volume 32, Issue 7, July 2020.

We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated together with an isotropic homogeneous turbulent flow. We study the spatial distribution of particles when they are collected on a plane at non-asymptotic times. We relate the resulting coarse-grained particle density to the history of the stretching rate along the particle trajectory and the projection of the density onto the accumulation plane and analyze the deviation from homogeneity in terms of the Reynolds number and the settling velocity. We identify two regimes that arise during the early and well-mixed stages of advection. In the former regime, more inhomogeneity in the particle distribution is introduced for decreasing settling velocity or increasing Reynolds number, while the tendencies are opposite in the latter regime. A resonant-like crossover is found between these two regimes where inhomogeneity is maximal.

We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated together with an isotropic homogeneous turbulent flow. We study the spatial distribution of particles when they are collected on a plane at non-asymptotic times. We relate the resulting coarse-grained particle density to the history of the stretching rate along the particle trajectory and the projection of the density onto the accumulation plane and analyze the deviation from homogeneity in terms of the Reynolds number and the settling velocity. We identify two regimes that arise during the early and well-mixed stages of advection. In the former regime, more inhomogeneity in the particle distribution is introduced for decreasing settling velocity or increasing Reynolds number, while the tendencies are opposite in the latter regime. A resonant-like crossover is found between these two regimes where inhomogeneity is maximal.

Categories: Latest papers in fluid mechanics

### A mathematical model for the numerical simulations of traveling ionospheric disturbances/atmospheric gravity waves generated by the Joule heating

Physics of Fluids, Volume 32, Issue 7, July 2020.

Traveling ionospheric disturbances (TIDs) and atmospheric gravity waves (AGWs) generated by the Joule heating produced from intensified auroral electrojet and/or intense particle precipitation in the auroral and subauroral regions during geomagnetic storms and which propagate downward toward the lower (neutral) atmosphere are numerically simulated using a simple two-dimensional mathematical model for internal gravity waves propagating in the lower atmosphere. An explicit expression for the Joule heating is obtained, and the characteristics of the simulated TIDs/AGWs (e.g., buoyancy frequency, wavenumbers, cutoff wavelength, speed, structures) are also examined and compared with the results obtained from observations. As may be seen in the observations, small-scale TIDs/AGWs with wavelengths shorter than 100 km, medium-scale TIDs/AGWs with wavelengths of several hundred kilometers, and large-scale TIDs/AGWs with wavelengths longer than 1000 km generated by the Joule heating were modeled and numerically simulated. For example, observations have revealed that the Joule heating can generate TID/AGW pairs. The developed numerical model was used to simulate medium-scale TID/AGW wave packet pairs, and the results (wavelength, speed, structure) are in agreement with SuperDARN observations reported by Sofko and Huang, 2000. TIDs/AGWs with shorter horizontal wavelengths are more trapped than those with longer wavelengths (medium- and large-scale TIDs/AGWs). Their cutoff horizontal wavelength was approximated using the linear stability theory of AGWs. The approximated cutoff horizontal wavelength suggests that not all simulated small-scale disturbances with horizontal wavelengths shorter than 100 km are traveling as may be seen in the observations.

Traveling ionospheric disturbances (TIDs) and atmospheric gravity waves (AGWs) generated by the Joule heating produced from intensified auroral electrojet and/or intense particle precipitation in the auroral and subauroral regions during geomagnetic storms and which propagate downward toward the lower (neutral) atmosphere are numerically simulated using a simple two-dimensional mathematical model for internal gravity waves propagating in the lower atmosphere. An explicit expression for the Joule heating is obtained, and the characteristics of the simulated TIDs/AGWs (e.g., buoyancy frequency, wavenumbers, cutoff wavelength, speed, structures) are also examined and compared with the results obtained from observations. As may be seen in the observations, small-scale TIDs/AGWs with wavelengths shorter than 100 km, medium-scale TIDs/AGWs with wavelengths of several hundred kilometers, and large-scale TIDs/AGWs with wavelengths longer than 1000 km generated by the Joule heating were modeled and numerically simulated. For example, observations have revealed that the Joule heating can generate TID/AGW pairs. The developed numerical model was used to simulate medium-scale TID/AGW wave packet pairs, and the results (wavelength, speed, structure) are in agreement with SuperDARN observations reported by Sofko and Huang, 2000. TIDs/AGWs with shorter horizontal wavelengths are more trapped than those with longer wavelengths (medium- and large-scale TIDs/AGWs). Their cutoff horizontal wavelength was approximated using the linear stability theory of AGWs. The approximated cutoff horizontal wavelength suggests that not all simulated small-scale disturbances with horizontal wavelengths shorter than 100 km are traveling as may be seen in the observations.

Categories: Latest papers in fluid mechanics

### Characterization of three-dimensional vortical structures in the wake past a circular cylinder in the transitional regime

Physics of Fluids, Volume 32, Issue 7, July 2020.

The flow past a circular cylinder in the transitional regime at Re = 2000 has been thoroughly investigated via well resolved direct numerical simulation with a spectral element code. Spanwise periodic boundary conditions of at least Lz ≥ 2.5D are required to properly reproduce first and second order turbulent statistics in the cylinder wake. A Kelvin–Helmholtz instability can already be detected at this relatively low Reynolds number at the flapping shear layers issued from either side of the cylinder. The instability, with a frequency fKH ≃ 0.84 that is in excellent agreement with published experimental results, arises only occasionally and the associated spanwise vortices are subject to spanwise localization. We show that while Kármán vortices remain predominantly two-dimensional, streamwise vortical structures appearing along the braids connecting consecutive vortices are mainly responsible for rendering the flow three-dimensional. These structures may appear in isolation or in vortex pairs and have a typical spanwise wavelength of around λz ≃ 0.20–0.28 at a location at (x, y) = (3, 0.5), as measured via Hilbert transform along probe arrays with spanwise orientation. In line with experimental and numerical results at higher Re = 3900, the size of the structures drops in the very near-wake to a minimum at x ≃ 2.5 and then steadily grows to asymptotically attain a finite maximum for x ≳ 20. A time-evolution-based stability analysis of the underlying two-dimensional vortex shedding flow, which happens to be chaotic, shows that the fastest growing perturbations in the linear regime have a spanwise periodicity λz ≃ 0.3 and are located in the very near-wake, right within the braid that connects the last forming Kármán vortex with the previous one, thus hinting at a close relation with the fully developed vortical structures observed in full-fledged three-dimensional computations.

The flow past a circular cylinder in the transitional regime at Re = 2000 has been thoroughly investigated via well resolved direct numerical simulation with a spectral element code. Spanwise periodic boundary conditions of at least Lz ≥ 2.5D are required to properly reproduce first and second order turbulent statistics in the cylinder wake. A Kelvin–Helmholtz instability can already be detected at this relatively low Reynolds number at the flapping shear layers issued from either side of the cylinder. The instability, with a frequency fKH ≃ 0.84 that is in excellent agreement with published experimental results, arises only occasionally and the associated spanwise vortices are subject to spanwise localization. We show that while Kármán vortices remain predominantly two-dimensional, streamwise vortical structures appearing along the braids connecting consecutive vortices are mainly responsible for rendering the flow three-dimensional. These structures may appear in isolation or in vortex pairs and have a typical spanwise wavelength of around λz ≃ 0.20–0.28 at a location at (x, y) = (3, 0.5), as measured via Hilbert transform along probe arrays with spanwise orientation. In line with experimental and numerical results at higher Re = 3900, the size of the structures drops in the very near-wake to a minimum at x ≃ 2.5 and then steadily grows to asymptotically attain a finite maximum for x ≳ 20. A time-evolution-based stability analysis of the underlying two-dimensional vortex shedding flow, which happens to be chaotic, shows that the fastest growing perturbations in the linear regime have a spanwise periodicity λz ≃ 0.3 and are located in the very near-wake, right within the braid that connects the last forming Kármán vortex with the previous one, thus hinting at a close relation with the fully developed vortical structures observed in full-fledged three-dimensional computations.

Categories: Latest papers in fluid mechanics

### Influence of diametral acoustic mode on cavity flow dynamics: Zonal large eddy simulation and proper orthogonal decomposition

Physics of Fluids, Volume 32, Issue 7, July 2020.

The influence of a diametral acoustic mode on the flow dynamics was numerically investigated for an axisymmetric cavity system with vortex-excited acoustic resonances occurring at high Reynolds numbers and low Mach numbers. The zonal large eddy simulation (ZLES) was conducted to simulate the flow-acoustic coupling fields by the first three diametral acoustic modes at their maximum resonance intensities, respectively. First, the ZLES-simulated acoustic pressure pulsations were well validated by a preliminary acoustic modal analysis and acoustic pressure measurements in the literature. Subsequently, the acoustic-driven cavity flow dynamics were comprehensively demonstrated in terms of the time-averaged flow quantities, shear layer quantities, and high-order turbulence quantities. The results demonstrated that the shear layer momentum thickness, velocity fluctuations, and Reynolds shear stresses were remarkably intensified by the strong resonances with the first and second diametral acoustic modes. Simultaneously, large-scale helical vortex tubes were formed within the cavity, yielding an intensified flow three-dimensionality. Thereafter, the dominant flow modes behind the acoustic-driven cavity flow dynamics were extracted using the data-driven proper orthogonal decomposition from the highly noisy ZLES database. It was found that the first diametral acoustic mode significantly enhanced the dominant positions of the vertical flow-oscillation mode, yielding a large-scale flapping behavior of the mainstream flow, while the second diametral acoustic mode would modulate the cavities to synchronously absorb/release the flow streaks, resulting in the alternating expansion and compression behaviors of the mainstream flow.

The influence of a diametral acoustic mode on the flow dynamics was numerically investigated for an axisymmetric cavity system with vortex-excited acoustic resonances occurring at high Reynolds numbers and low Mach numbers. The zonal large eddy simulation (ZLES) was conducted to simulate the flow-acoustic coupling fields by the first three diametral acoustic modes at their maximum resonance intensities, respectively. First, the ZLES-simulated acoustic pressure pulsations were well validated by a preliminary acoustic modal analysis and acoustic pressure measurements in the literature. Subsequently, the acoustic-driven cavity flow dynamics were comprehensively demonstrated in terms of the time-averaged flow quantities, shear layer quantities, and high-order turbulence quantities. The results demonstrated that the shear layer momentum thickness, velocity fluctuations, and Reynolds shear stresses were remarkably intensified by the strong resonances with the first and second diametral acoustic modes. Simultaneously, large-scale helical vortex tubes were formed within the cavity, yielding an intensified flow three-dimensionality. Thereafter, the dominant flow modes behind the acoustic-driven cavity flow dynamics were extracted using the data-driven proper orthogonal decomposition from the highly noisy ZLES database. It was found that the first diametral acoustic mode significantly enhanced the dominant positions of the vertical flow-oscillation mode, yielding a large-scale flapping behavior of the mainstream flow, while the second diametral acoustic mode would modulate the cavities to synchronously absorb/release the flow streaks, resulting in the alternating expansion and compression behaviors of the mainstream flow.

Categories: Latest papers in fluid mechanics

### Effects of external magnetic fields on the rheology and magnetization of dilute emulsions of ferrofluid droplets in shear flows

Physics of Fluids, Volume 32, Issue 7, July 2020.

We present a study of the effects of external magnetic fields on the dynamics of ferrofluid droplets in suspension and its impacts on the rheology of dilute magnetic emulsions. Our analysis considers a single two-dimensional droplet of a superparamagnetic ferrofluid in an immiscible, non-magnetizable liquid. The two-phase system is confined in a channel between parallel plates and undergoes a simple shear flow under the influence of a uniform external magnetic field. We present a theoretical formulation for the stress tensor of dilute suspensions of ferrofluid droplets in which the stresslet accounts for a magnetic field-induced traction across the droplet surface. Remarkably, the stresslet is no longer symmetric in the presence of external magnetic fields. The complex configuration of the droplet leads to a misalignment between the bulk magnetization and the external magnetic field. As a result, internal torques appear in the magnetic emulsion even when both liquid phases are symmetric fluids. We also present a comprehensive investigation of the configuration and magnetization of the suspended ferrofluid droplet as a function of the intensity and direction of the external field. Then, the stresslet is used to explore how external magnetic fields affect the rheology of dilute magnetic emulsions in terms of the shear viscosity, rotational viscosity, and first normal stress difference. Our predictions show that external magnetic fields can be effectively adjusted to control the dynamics at the droplet level and the rheology of magnetic emulsions.

We present a study of the effects of external magnetic fields on the dynamics of ferrofluid droplets in suspension and its impacts on the rheology of dilute magnetic emulsions. Our analysis considers a single two-dimensional droplet of a superparamagnetic ferrofluid in an immiscible, non-magnetizable liquid. The two-phase system is confined in a channel between parallel plates and undergoes a simple shear flow under the influence of a uniform external magnetic field. We present a theoretical formulation for the stress tensor of dilute suspensions of ferrofluid droplets in which the stresslet accounts for a magnetic field-induced traction across the droplet surface. Remarkably, the stresslet is no longer symmetric in the presence of external magnetic fields. The complex configuration of the droplet leads to a misalignment between the bulk magnetization and the external magnetic field. As a result, internal torques appear in the magnetic emulsion even when both liquid phases are symmetric fluids. We also present a comprehensive investigation of the configuration and magnetization of the suspended ferrofluid droplet as a function of the intensity and direction of the external field. Then, the stresslet is used to explore how external magnetic fields affect the rheology of dilute magnetic emulsions in terms of the shear viscosity, rotational viscosity, and first normal stress difference. Our predictions show that external magnetic fields can be effectively adjusted to control the dynamics at the droplet level and the rheology of magnetic emulsions.

Categories: Latest papers in fluid mechanics

### Effects of partial slip on the local-global linear stability of the infinite rotating disk boundary layer

Physics of Fluids, Volume 32, Issue 7, July 2020.

A numerical investigation is undertaken on the effect of small-scale surface roughness on the local absolute and global stability of the flow due to a rotating disk. Surface roughness is modeled via the imposition of the partial-slip wall boundary condition, with radial and concentric anisotropic roughnesses and isotropic roughness considered. The effect of the partial-slip parameters on the neutral characteristics for absolute instability is presented, while the azimuthal mode numbers required for global linear instability to occur are determined for the genuine inhomogeneous base flow. Predictions for the threshold values for the azimuthal mode numbers needed for globally unstable behavior are also computed by coupling solutions of the Ginzburg–Landau equation with the local linear stability properties obtained using the homogeneous flow approximation. These are found to be in excellent agreement with the exact values realized from the numerical simulations. In general, surface roughness is demonstrated to stabilize the absolute instability and the global linear instabilities.

A numerical investigation is undertaken on the effect of small-scale surface roughness on the local absolute and global stability of the flow due to a rotating disk. Surface roughness is modeled via the imposition of the partial-slip wall boundary condition, with radial and concentric anisotropic roughnesses and isotropic roughness considered. The effect of the partial-slip parameters on the neutral characteristics for absolute instability is presented, while the azimuthal mode numbers required for global linear instability to occur are determined for the genuine inhomogeneous base flow. Predictions for the threshold values for the azimuthal mode numbers needed for globally unstable behavior are also computed by coupling solutions of the Ginzburg–Landau equation with the local linear stability properties obtained using the homogeneous flow approximation. These are found to be in excellent agreement with the exact values realized from the numerical simulations. In general, surface roughness is demonstrated to stabilize the absolute instability and the global linear instabilities.

Categories: Latest papers in fluid mechanics

### Deep water gravity wave triad resonances on uniform flow

Physics of Fluids, Volume 32, Issue 7, July 2020.

Conditions for three-wave resonance between surface gravity waves on uniform current in deep water are found. The resonances occur because waves propagating downstream are elongated (relative to their still water form), whereas waves propagating upstream are contracted. Under certain conditions, the elongation and contraction is to such an extent that the difference between the wavenumbers closes resonance with a third wave. In contrast, the existing literature assumes there is no deep water gravity wave triad resonance on uniform current. Rather, the lowest order nonlinear resonance is assumed to be a four-wave interaction. In this sense, the results represent a new class of resonances. Moreover, since triads are of a lower order than four-wave interactions, the effects of the new triad resonances will be, by definition, an order of magnitude greater (in wave slope ka) than the strongest known resonances for the assumed conditions. Thus, the results represent a new and important mechanism of wave growth and energy exchange between surface gravity waves.

Conditions for three-wave resonance between surface gravity waves on uniform current in deep water are found. The resonances occur because waves propagating downstream are elongated (relative to their still water form), whereas waves propagating upstream are contracted. Under certain conditions, the elongation and contraction is to such an extent that the difference between the wavenumbers closes resonance with a third wave. In contrast, the existing literature assumes there is no deep water gravity wave triad resonance on uniform current. Rather, the lowest order nonlinear resonance is assumed to be a four-wave interaction. In this sense, the results represent a new class of resonances. Moreover, since triads are of a lower order than four-wave interactions, the effects of the new triad resonances will be, by definition, an order of magnitude greater (in wave slope ka) than the strongest known resonances for the assumed conditions. Thus, the results represent a new and important mechanism of wave growth and energy exchange between surface gravity waves.

Categories: Latest papers in fluid mechanics

### Thermokinetic transport of dilatant/pseudoplastic fluids in a hydrophobic patterned micro-slit

Physics of Fluids, Volume 32, Issue 7, July 2020.

The flow enhancement and convective heat transfer along with entropy generation analysis are studied numerically in a micro-slit with alternating hydrodynamic slip patches. The advances in molecular simulations and micro-scale experiments confirmed that the slip of fluid on the solid surfaces occurred at small scale flows and the traditional no-slip boundary conditions cannot be applicable for the flow simulation at the micro- and nano-scale. The coupled Poisson–Boltzmann–Navier–Stokes equations dealing with an external electric potential are involved for the flow enhancement and entropy generation analysis of non-Newtonian fluids in a micro-slit with periodic slips. From the finite volume simulation, it is observed that the drag force effect is very strong along the wall for the transportation and mixing of fluids. This effect is found to be minimized by imposing periodic hydrophobic slippage along the boundary. An additional pressure gradient is generated by imposing electrokinetic pumping, resulting in a higher velocity gradient in the flow direction in the presence of viscous dissipation and Joule heating effects. The results are predicted in terms of the flow enhancement factor (Ef) (which provides maximum species transport), the average heat transfer rate (Nu), and the average entropy generation due to fluid friction, heat transfer, and Joule heating effects. The advantages and disadvantages of utilizing slip conditions are discussed, which has large scale applications on drug delivery and DNA analysis and sequencing, since cell damage due to pumping will be minimized.

The flow enhancement and convective heat transfer along with entropy generation analysis are studied numerically in a micro-slit with alternating hydrodynamic slip patches. The advances in molecular simulations and micro-scale experiments confirmed that the slip of fluid on the solid surfaces occurred at small scale flows and the traditional no-slip boundary conditions cannot be applicable for the flow simulation at the micro- and nano-scale. The coupled Poisson–Boltzmann–Navier–Stokes equations dealing with an external electric potential are involved for the flow enhancement and entropy generation analysis of non-Newtonian fluids in a micro-slit with periodic slips. From the finite volume simulation, it is observed that the drag force effect is very strong along the wall for the transportation and mixing of fluids. This effect is found to be minimized by imposing periodic hydrophobic slippage along the boundary. An additional pressure gradient is generated by imposing electrokinetic pumping, resulting in a higher velocity gradient in the flow direction in the presence of viscous dissipation and Joule heating effects. The results are predicted in terms of the flow enhancement factor (Ef) (which provides maximum species transport), the average heat transfer rate (Nu), and the average entropy generation due to fluid friction, heat transfer, and Joule heating effects. The advantages and disadvantages of utilizing slip conditions are discussed, which has large scale applications on drug delivery and DNA analysis and sequencing, since cell damage due to pumping will be minimized.

Categories: Latest papers in fluid mechanics

### Hydrodynamics and instabilities of falling liquid film over a non-uniformly heated inclined wavy bottom

Physics of Fluids, Volume 32, Issue 7, July 2020.

Hydrodynamics and instabilities of a thin viscous liquid film flowing down an undulated inclined plate with linear temperature variation have been investigated. Using the long-wave expansion method, a non-linear evolution equation for the development of the free surface is derived under the assumption that the bottom undulations are of moderate steepness. A normal mode approach has been considered to take into account the linear stability of the film to investigate both the spatial and temporal instabilities, while the method of multiple scales is used to obtain the Ginzburg–Landau-type worldly equation for studying the weakly non-linear stability solutions. The numerical study has been carried out in python with a newly developed library Scikit–FDif. The entire investigation is done for a general bottom profile followed by a case study with a sinusoidal topography. The case study reveals that the Marangoni effect destabilizes the film flow throughout the domain, whereas the bottom steepness ζ gives a dual effect for the linear stability. In the “uphill” portion, an increase in ζ stabilizes the flow, and in the “downhill” portion, an increase in ζ gives a destabilizing effect. Furthermore, a weakly non-linear study shows that both supercritical and subcritical solutions are possible for the system. It is noted that the unconditional stable region decreases and all the other region increases in the “downhill” portion in comparison with the “uphill” portion for a fixed set of parameters. The stability analysis of a truncated bimodal system is investigated. The spatial uniform solution of the complex Ginzburg–Landau equation for sideband disturbances has also been discussed. Numerical simulation indicates that a different kind of finite-amplitude permanent wave exists. The amplitudes and the phase speeds of the wave are dependent on thermocapillary as well as the bottom steepness.

Hydrodynamics and instabilities of a thin viscous liquid film flowing down an undulated inclined plate with linear temperature variation have been investigated. Using the long-wave expansion method, a non-linear evolution equation for the development of the free surface is derived under the assumption that the bottom undulations are of moderate steepness. A normal mode approach has been considered to take into account the linear stability of the film to investigate both the spatial and temporal instabilities, while the method of multiple scales is used to obtain the Ginzburg–Landau-type worldly equation for studying the weakly non-linear stability solutions. The numerical study has been carried out in python with a newly developed library Scikit–FDif. The entire investigation is done for a general bottom profile followed by a case study with a sinusoidal topography. The case study reveals that the Marangoni effect destabilizes the film flow throughout the domain, whereas the bottom steepness ζ gives a dual effect for the linear stability. In the “uphill” portion, an increase in ζ stabilizes the flow, and in the “downhill” portion, an increase in ζ gives a destabilizing effect. Furthermore, a weakly non-linear study shows that both supercritical and subcritical solutions are possible for the system. It is noted that the unconditional stable region decreases and all the other region increases in the “downhill” portion in comparison with the “uphill” portion for a fixed set of parameters. The stability analysis of a truncated bimodal system is investigated. The spatial uniform solution of the complex Ginzburg–Landau equation for sideband disturbances has also been discussed. Numerical simulation indicates that a different kind of finite-amplitude permanent wave exists. The amplitudes and the phase speeds of the wave are dependent on thermocapillary as well as the bottom steepness.

Categories: Latest papers in fluid mechanics

### Hydrodynamics of a compound drop in plane Poiseuille flow

Physics of Fluids, Volume 32, Issue 7, July 2020.

We numerically investigate the hydrodynamics of a two-dimensional compound drop in a plane Poiseuille flow under Stokes regime. A neutrally buoyant, initially concentric compound drop is released into a fully developed flow, where it migrates to its equilibrium position. Based on the results, we find that the core–shell interaction affects the dynamics of both the core and the compound drop. During the initial transient period, the core revolves about the center of the compound drop due to the internal circulation inside the shell. At equilibrium, depending upon the nature of the flow field inside the shell, we identify two distinct core behaviors: stable state and limit-cycle state. In the stable state, the core stops revolving and moves outward very slowly. The core in the limit-cycle state continues to revolve in a nearly fixed orbit with no further inward motion. The presence of the core affects both deformation and migration dynamics of the compound drop. A comparison with the simple drop reveals that the core enhances the deformation of the compound drop. The outward moving core in the stable state pushes the compound drop toward the walls, while the revolving core in the limit-cycle state causes the compound drop to oscillate at its equilibrium position. The migration of the compound drop also affects the eccentricity of the core significantly. From the parametric study, we find that the core affects the compound drop dynamics only at intermediate sizes, and an increase in any parameter sufficiently causes a transition from the limit-cycle state to the stable state.

We numerically investigate the hydrodynamics of a two-dimensional compound drop in a plane Poiseuille flow under Stokes regime. A neutrally buoyant, initially concentric compound drop is released into a fully developed flow, where it migrates to its equilibrium position. Based on the results, we find that the core–shell interaction affects the dynamics of both the core and the compound drop. During the initial transient period, the core revolves about the center of the compound drop due to the internal circulation inside the shell. At equilibrium, depending upon the nature of the flow field inside the shell, we identify two distinct core behaviors: stable state and limit-cycle state. In the stable state, the core stops revolving and moves outward very slowly. The core in the limit-cycle state continues to revolve in a nearly fixed orbit with no further inward motion. The presence of the core affects both deformation and migration dynamics of the compound drop. A comparison with the simple drop reveals that the core enhances the deformation of the compound drop. The outward moving core in the stable state pushes the compound drop toward the walls, while the revolving core in the limit-cycle state causes the compound drop to oscillate at its equilibrium position. The migration of the compound drop also affects the eccentricity of the core significantly. From the parametric study, we find that the core affects the compound drop dynamics only at intermediate sizes, and an increase in any parameter sufficiently causes a transition from the limit-cycle state to the stable state.

Categories: Latest papers in fluid mechanics

### On the breakup of a permeating oil droplet in crossflow filtration: Effects of viscosity contrast

Physics of Fluids, Volume 32, Issue 7, July 2020.

The critical velocity of dislodgment of a permeating oil droplet in crossflow filtration is an important parameter in the analysis of the filtration of produced water systems using membrane technology. In this work, the effects of the viscosity contrast between the droplet and the surrounding fluid on the critical velocity of dislodgment are investigated. In the limit when the viscosity of the droplet approaches infinity, the gripping of the crossflow field on the droplet is maximum. When the viscosity contrast is finite, the smaller the viscosity contrast is, the smaller the gripping becomes. In order to highlight this effect, a comprehensive computational fluid dynamics study is conducted. A permeating droplet in the crossflow field is considered with the viscosity contrast ranging within two orders of magnitude. For each scenario, the critical velocity of dislodgment is determined by increasing the velocity incrementally until breakup occurs for every viscosity contrast. It is found that an increase in the viscosity contrast results in a decrease in the critical velocity of dislodgment. This represents a direct manifestation of the effect of the gripping of the droplet by the crossflow field, which increases as the viscosity contrast increases. Modification of the critical velocity of dislodgment, therefore, needs to be considered to account for this effect of viscosity contrast. The formula that was developed to estimate the critical velocity of dislodgment has been modified, and comparison with simulation gives a very good match.

The critical velocity of dislodgment of a permeating oil droplet in crossflow filtration is an important parameter in the analysis of the filtration of produced water systems using membrane technology. In this work, the effects of the viscosity contrast between the droplet and the surrounding fluid on the critical velocity of dislodgment are investigated. In the limit when the viscosity of the droplet approaches infinity, the gripping of the crossflow field on the droplet is maximum. When the viscosity contrast is finite, the smaller the viscosity contrast is, the smaller the gripping becomes. In order to highlight this effect, a comprehensive computational fluid dynamics study is conducted. A permeating droplet in the crossflow field is considered with the viscosity contrast ranging within two orders of magnitude. For each scenario, the critical velocity of dislodgment is determined by increasing the velocity incrementally until breakup occurs for every viscosity contrast. It is found that an increase in the viscosity contrast results in a decrease in the critical velocity of dislodgment. This represents a direct manifestation of the effect of the gripping of the droplet by the crossflow field, which increases as the viscosity contrast increases. Modification of the critical velocity of dislodgment, therefore, needs to be considered to account for this effect of viscosity contrast. The formula that was developed to estimate the critical velocity of dislodgment has been modified, and comparison with simulation gives a very good match.

Categories: Latest papers in fluid mechanics

### Three-dimensional printing of diamagnetic microparticles in paramagnetic and diamagnetic media

Physics of Fluids, Volume 32, Issue 7, July 2020.

We present an analytical model that explains the motion of finite-size diamagnetic particles in paramagnetic or diamagnetic fluid media. Our model problem is the magnetic field-assisted three-dimensional assembly of carboxylate microspheres in a gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) solution that is placed in a cuboid. The trajectory of each microparticle is determined through a time marching solution of its equation of motion. The effects of the (1) magnetic field distribution and (2) magnetic susceptibility of the paramagnetic solution, which depends on the Gd-DTPA concentration, on the dynamics of particle assembly are identified. Validation of the analytical model is provided through experimental measurements. For the first time, we demonstrate that it is possible to form structures of diamagnetic particles in diamagnetic fluid media, for which we select the assembly of graphene in water.

We present an analytical model that explains the motion of finite-size diamagnetic particles in paramagnetic or diamagnetic fluid media. Our model problem is the magnetic field-assisted three-dimensional assembly of carboxylate microspheres in a gadolinium-diethylenetriaminepentaacetic acid (Gd-DTPA) solution that is placed in a cuboid. The trajectory of each microparticle is determined through a time marching solution of its equation of motion. The effects of the (1) magnetic field distribution and (2) magnetic susceptibility of the paramagnetic solution, which depends on the Gd-DTPA concentration, on the dynamics of particle assembly are identified. Validation of the analytical model is provided through experimental measurements. For the first time, we demonstrate that it is possible to form structures of diamagnetic particles in diamagnetic fluid media, for which we select the assembly of graphene in water.

Categories: Latest papers in fluid mechanics

### Flow-induced vibration of inherently nonlinear structures with applications in energy harvesting

Physics of Fluids, Volume 32, Issue 7, July 2020.

This paper proposes a novel design for a flow-induced vibration-based energy harvester, consisting of an elastic L-shaped beam, with an inherent nonlinearity in its structural stiffness as an alternative to the classical cantilever beam used in conventional fluidic energy harvester designs. The L-shaped beam supports a prism at its tip and undergoes large-amplitude galloping oscillations. The results from wind tunnel experiments show that by replacing a conventional linear structure that supports the prism with a nonlinear one, the high frequency flow components, shed from the tip prism, were capable of exciting the oscillations of the structure at higher harmonics of the main resonance, thus enhancing the power density of the energy harvester. As a result of improved power density values, the proposed harvester design holds great potential to be used as advanced space-efficient energy harvesters.

This paper proposes a novel design for a flow-induced vibration-based energy harvester, consisting of an elastic L-shaped beam, with an inherent nonlinearity in its structural stiffness as an alternative to the classical cantilever beam used in conventional fluidic energy harvester designs. The L-shaped beam supports a prism at its tip and undergoes large-amplitude galloping oscillations. The results from wind tunnel experiments show that by replacing a conventional linear structure that supports the prism with a nonlinear one, the high frequency flow components, shed from the tip prism, were capable of exciting the oscillations of the structure at higher harmonics of the main resonance, thus enhancing the power density of the energy harvester. As a result of improved power density values, the proposed harvester design holds great potential to be used as advanced space-efficient energy harvesters.

Categories: Latest papers in fluid mechanics

### Influence of glow discharge on evolution of disturbance in a hypersonic boundary layer: The effect of second mode

Physics of Fluids, Volume 32, Issue 7, July 2020.

This is the companion volume on the effects of artificial disturbance on the transition process of a boundary layer over a flat plate. The artificial disturbance with the frequency in the range of second-mode instability is introduced into the boundary layer by glowing discharge on the surface of the plate. Experiments are performed using Rayleigh-scattering visualization, wall pressure pulsations measurement, and high-frequency schlieren visualization in the Φ300 mm hypersonic quiet wind tunnel at Peking University. It is found that the second-mode instability waves are stimulated remarkably by the artificial disturbance, and the boundary layer transition is triggered effectively. The second-mode instability interacts with the first mode via a phase-lock mechanism, which leads to the rapid amplification of the first mode and the moving forward of transition location.

This is the companion volume on the effects of artificial disturbance on the transition process of a boundary layer over a flat plate. The artificial disturbance with the frequency in the range of second-mode instability is introduced into the boundary layer by glowing discharge on the surface of the plate. Experiments are performed using Rayleigh-scattering visualization, wall pressure pulsations measurement, and high-frequency schlieren visualization in the Φ300 mm hypersonic quiet wind tunnel at Peking University. It is found that the second-mode instability waves are stimulated remarkably by the artificial disturbance, and the boundary layer transition is triggered effectively. The second-mode instability interacts with the first mode via a phase-lock mechanism, which leads to the rapid amplification of the first mode and the moving forward of transition location.

Categories: Latest papers in fluid mechanics

### Behavior of particle swarms at low and moderate Reynolds numbers using computational fluid dynamics—Discrete element model

Physics of Fluids, Volume 32, Issue 7, July 2020.

In the present study, the sedimentation of a swarm of mono-sized particles is investigated using the Computational Fluid Dynamics–Discrete Element Model (CFD-DEM) approach. The computational approach employed was able to accurately predict the breakup pattern of the swarm of particles into secondary clusters. The rate of leakage of the particles from the cluster (in the creeping flow regime) was found to linearly increase with an increase in the initial number of particles present in the sedimenting cluster. The breakup pattern of the cluster of particles was found to be highly sensitive to the shape of the outer domain. At Rec = 5, the sedimentation of the cluster in a cylindrical outer domain was observed to break up into six secondary blobs (k = 6), whereas for a square and a rectangular outer domain, the breakup resulted in four (k = 4) and two (k = 2) secondary blobs, respectively. Besides, the CFD-DEM approach was found to be in excellent agreement with the experimental data as opposed to the Oseenlet point particle approach, which could not accurately predict the settling velocities for a sedimenting cluster at a finite Rec and high solid fraction (Rec = 14, ϕs ≈ 0.5).

In the present study, the sedimentation of a swarm of mono-sized particles is investigated using the Computational Fluid Dynamics–Discrete Element Model (CFD-DEM) approach. The computational approach employed was able to accurately predict the breakup pattern of the swarm of particles into secondary clusters. The rate of leakage of the particles from the cluster (in the creeping flow regime) was found to linearly increase with an increase in the initial number of particles present in the sedimenting cluster. The breakup pattern of the cluster of particles was found to be highly sensitive to the shape of the outer domain. At Rec = 5, the sedimentation of the cluster in a cylindrical outer domain was observed to break up into six secondary blobs (k = 6), whereas for a square and a rectangular outer domain, the breakup resulted in four (k = 4) and two (k = 2) secondary blobs, respectively. Besides, the CFD-DEM approach was found to be in excellent agreement with the experimental data as opposed to the Oseenlet point particle approach, which could not accurately predict the settling velocities for a sedimenting cluster at a finite Rec and high solid fraction (Rec = 14, ϕs ≈ 0.5).

Categories: Latest papers in fluid mechanics

### Two-equation and multi-fluid turbulence models for Richtmyer–Meshkov mixing

Physics of Fluids, Volume 32, Issue 7, July 2020.

This paper concerns an investigation of two different approaches in modeling the turbulent mixing induced by the Richtmyer–Meshkov instability (RMI): A two-equation K-L multi-component Reynolds-averaged Navier–Stokes model and a two-fluid model. We have improved the accuracy of the K-L model by implementing new modifications, including a realizability condition for the Reynolds stress tensor and a threshold in the production of the turbulence kinetic energy. We examine the models in the one-dimensional (1D) form in the (re)-shocked mixing of a double-planar air and sulfur-hexafluoride (SF6) interface of the Atwood number |At| ≃ 0.6853. Furthermore, we investigated the models’ accuracy to RMI-induced mixing of a (re)-shocked planar-inverse chevron air–SF6 interface. Relevant integral quantities in time, as well as instantaneous profiles and contour plots, are used to assess the models’ accuracy against high-resolution implicit large eddy simulations. The proposed modifications improve the efficiency of the K-L model. The model is designed as a simple model capable of capturing the self-similar growth of Rayleigh–Taylor and Richtmyer–Meshkov flows. The two-fluid model remains more accurate but is also computationally more expensive.

This paper concerns an investigation of two different approaches in modeling the turbulent mixing induced by the Richtmyer–Meshkov instability (RMI): A two-equation K-L multi-component Reynolds-averaged Navier–Stokes model and a two-fluid model. We have improved the accuracy of the K-L model by implementing new modifications, including a realizability condition for the Reynolds stress tensor and a threshold in the production of the turbulence kinetic energy. We examine the models in the one-dimensional (1D) form in the (re)-shocked mixing of a double-planar air and sulfur-hexafluoride (SF6) interface of the Atwood number |At| ≃ 0.6853. Furthermore, we investigated the models’ accuracy to RMI-induced mixing of a (re)-shocked planar-inverse chevron air–SF6 interface. Relevant integral quantities in time, as well as instantaneous profiles and contour plots, are used to assess the models’ accuracy against high-resolution implicit large eddy simulations. The proposed modifications improve the efficiency of the K-L model. The model is designed as a simple model capable of capturing the self-similar growth of Rayleigh–Taylor and Richtmyer–Meshkov flows. The two-fluid model remains more accurate but is also computationally more expensive.

Categories: Latest papers in fluid mechanics

### On sustaining turbulence production in interacting supersonic streamwise vortices

Physics of Fluids, Volume 32, Issue 7, July 2020.

Interacting supersonic streamwise vortices have been investigated as a means to enhance mixing at supersonic velocities. However, the turbulence dynamics associated with this class of flow has been left largely unexplored despite turbulence playing a major role in the achievement of molecular mixing. For this reason, the process of turbulent kinetic energy production in interacting supersonic streamwise vortices is investigated in this work. Specifically, the link between the mean flow motion and turbulence, represented by the production term of the turbulent transport equation, is analyzed. An approach is proposed in which the mean flow strain rates can be cast such that their intensity and morphology properly couple with the requirements imposed by the Reynolds stresses that, in the framework of this work, are shown to be intimately linked with the resulting plume morphology. The analysis is leveraged for the design of a mode of vortex interaction targeted to maintain a positive production of turbulent kinetic energy in the downstream evolution. The resulting configuration was experimentally investigated in a Mach 2.5 flow by stereoscopic particle image velocimetry. The results from these experiments show that the turbulence production remained positive and sustained turbulence levels, a unique result in the available literature. The role of turbulence anisotropy and the principal direction of negative planar strain rates are highlighted in detail in this work.

Interacting supersonic streamwise vortices have been investigated as a means to enhance mixing at supersonic velocities. However, the turbulence dynamics associated with this class of flow has been left largely unexplored despite turbulence playing a major role in the achievement of molecular mixing. For this reason, the process of turbulent kinetic energy production in interacting supersonic streamwise vortices is investigated in this work. Specifically, the link between the mean flow motion and turbulence, represented by the production term of the turbulent transport equation, is analyzed. An approach is proposed in which the mean flow strain rates can be cast such that their intensity and morphology properly couple with the requirements imposed by the Reynolds stresses that, in the framework of this work, are shown to be intimately linked with the resulting plume morphology. The analysis is leveraged for the design of a mode of vortex interaction targeted to maintain a positive production of turbulent kinetic energy in the downstream evolution. The resulting configuration was experimentally investigated in a Mach 2.5 flow by stereoscopic particle image velocimetry. The results from these experiments show that the turbulence production remained positive and sustained turbulence levels, a unique result in the available literature. The role of turbulence anisotropy and the principal direction of negative planar strain rates are highlighted in detail in this work.

Categories: Latest papers in fluid mechanics

### Passive control of coaxial jet with supersonic primary jet and sonic secondary jet

Physics of Fluids, Volume 32, Issue 7, July 2020.

The mixing enhancement of a coaxial jet with a Mach 1.4 primary jet and sonic secondary jet, at different convective Mach numbers, is presented in this study. Rectangular tabs of aspect ratios (AR = h/[math], where h and [math] are the tab height and width, respectively) 2.0 and 0.75 were employed to manipulate the primary and secondary jets, respectively. The primary jet (C0) and coaxial jet without control or manipulation (C1) are studied in order to decouple the effects of rectangular tabs on jet mixing. Four different tab configurations were studied, viz., tabs placed in the primary jet (C2), tabs placed in the secondary jet (C3), and tabs placed in both primary and secondary jets with the relative orientation between them of 0° (C4) and 90° (C5), to document the effect of tabs on mixing. The supersonic core length [math] of the manipulated jet was used as a measure to quantify the mixing performance of the manipulated jet. The secondary flow reduces the growth rate of the primary shear layer and elongates the supersonic core length. This study reveals that the manipulated jet emulates the characteristic of a non-circular jet. Primary tabs are highly effective in reducing the supersonic core length of the coaxial jet than secondary tabs, and hence, the jet mixing increases. Two different flow categories of the manipulated jet have been identified. The physical reason behind the observed jet mixing and flow categories have been presented based on arguments related to changes in the flow field and shock structure.

The mixing enhancement of a coaxial jet with a Mach 1.4 primary jet and sonic secondary jet, at different convective Mach numbers, is presented in this study. Rectangular tabs of aspect ratios (AR = h/[math], where h and [math] are the tab height and width, respectively) 2.0 and 0.75 were employed to manipulate the primary and secondary jets, respectively. The primary jet (C0) and coaxial jet without control or manipulation (C1) are studied in order to decouple the effects of rectangular tabs on jet mixing. Four different tab configurations were studied, viz., tabs placed in the primary jet (C2), tabs placed in the secondary jet (C3), and tabs placed in both primary and secondary jets with the relative orientation between them of 0° (C4) and 90° (C5), to document the effect of tabs on mixing. The supersonic core length [math] of the manipulated jet was used as a measure to quantify the mixing performance of the manipulated jet. The secondary flow reduces the growth rate of the primary shear layer and elongates the supersonic core length. This study reveals that the manipulated jet emulates the characteristic of a non-circular jet. Primary tabs are highly effective in reducing the supersonic core length of the coaxial jet than secondary tabs, and hence, the jet mixing increases. Two different flow categories of the manipulated jet have been identified. The physical reason behind the observed jet mixing and flow categories have been presented based on arguments related to changes in the flow field and shock structure.

Categories: Latest papers in fluid mechanics

### On the use of leading-edge serrations for noise control in a tandem airfoil configuration

Physics of Fluids, Volume 32, Issue 7, July 2020.

Passive noise control for a tandem NACA 65-710 airfoil configuration is experimentally investigated by applying leading-edge serrations on the rear airfoil. With a sliding side-plate mechanism that allows the rear airfoil to move in the vertical direction relative to the front airfoil, the position of maximum turbulence interaction noise is first identified from the far-field noise measurements. Subsequently, detailed static surface pressure distribution and unsteady surface pressure fluctuations are acquired to shed more light on the physical phenomenon and underlying noise-reduction mechanism of the leading-edge serrations. The far-field noise measurements confirm that a notable turbulence interaction noise reduction can be achieved from 600 Hz < f < 3000 Hz, agreeing well with the previous literature on the effectiveness of the leading-edge serrations. The near-field hydrodynamic analyses obtained using remote-sensing techniques of the fluctuating pressure fields over the airfoil show that a significant reduction in the surface pressure fluctuation levels up to 20 dB/Hz can be observed at the serrated-tip plane of the rear serrated airfoil close to the leading-edge regions, over the range of frequencies investigated. Although reduction can also be observed on the serrated-root plane, the magnitude is much less significant. The present results suggest that the modification of the unsteady loading on the rear airfoil by the leading-edge serrations plays a crucial role in the reduction of turbulence interaction noise in the tandem airfoil configuration, which may find practical application for noise reduction in aerodynamic systems involving rows of airfoils, such as contra-rotating open rotors and outlet guide vanes.

Passive noise control for a tandem NACA 65-710 airfoil configuration is experimentally investigated by applying leading-edge serrations on the rear airfoil. With a sliding side-plate mechanism that allows the rear airfoil to move in the vertical direction relative to the front airfoil, the position of maximum turbulence interaction noise is first identified from the far-field noise measurements. Subsequently, detailed static surface pressure distribution and unsteady surface pressure fluctuations are acquired to shed more light on the physical phenomenon and underlying noise-reduction mechanism of the leading-edge serrations. The far-field noise measurements confirm that a notable turbulence interaction noise reduction can be achieved from 600 Hz < f < 3000 Hz, agreeing well with the previous literature on the effectiveness of the leading-edge serrations. The near-field hydrodynamic analyses obtained using remote-sensing techniques of the fluctuating pressure fields over the airfoil show that a significant reduction in the surface pressure fluctuation levels up to 20 dB/Hz can be observed at the serrated-tip plane of the rear serrated airfoil close to the leading-edge regions, over the range of frequencies investigated. Although reduction can also be observed on the serrated-root plane, the magnitude is much less significant. The present results suggest that the modification of the unsteady loading on the rear airfoil by the leading-edge serrations plays a crucial role in the reduction of turbulence interaction noise in the tandem airfoil configuration, which may find practical application for noise reduction in aerodynamic systems involving rows of airfoils, such as contra-rotating open rotors and outlet guide vanes.

Categories: Latest papers in fluid mechanics