# 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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### Three-dimensional simulation of a rising bubble in the presence of spherical obstacles by the immersed boundary–lattice Boltzmann method

Physics of Fluids, Volume 31, Issue 9, September 2019.

The dynamics of a bubble bypassing or passing between spherical obstacles, which is associated with many industrial applications, is investigated numerically. A gas–liquid–solid interaction model is established by combining the lattice Boltzmann method and the immersed boundary method. The deformation and the surface velocity of the bubble, as well as the streamlines of the flow field, are studied as the bubble bypasses a single spherical obstacle or passes between a pair of such obstacles. It is found that for the case of a single sphere, the rise velocity reaches a minimum value at the moment at which an annular bubble forms and the whole sphere is enveloped by the bubble. The initial distance between the bubble and the sphere, as well as the ratio of their sizes, has distinct influences on bubble shape and rise velocity. For a pair of spherical obstacles, the rise velocity of the bubble reaches a minimum value twice as the bubble rises between the obstacles. The distance between the two obstacles has a stronger influence on bubble motion than does their size, although when the two obstacles are of different sizes, the bubble will deviate toward the smaller one.

The dynamics of a bubble bypassing or passing between spherical obstacles, which is associated with many industrial applications, is investigated numerically. A gas–liquid–solid interaction model is established by combining the lattice Boltzmann method and the immersed boundary method. The deformation and the surface velocity of the bubble, as well as the streamlines of the flow field, are studied as the bubble bypasses a single spherical obstacle or passes between a pair of such obstacles. It is found that for the case of a single sphere, the rise velocity reaches a minimum value at the moment at which an annular bubble forms and the whole sphere is enveloped by the bubble. The initial distance between the bubble and the sphere, as well as the ratio of their sizes, has distinct influences on bubble shape and rise velocity. For a pair of spherical obstacles, the rise velocity of the bubble reaches a minimum value twice as the bubble rises between the obstacles. The distance between the two obstacles has a stronger influence on bubble motion than does their size, although when the two obstacles are of different sizes, the bubble will deviate toward the smaller one.

Categories: Latest papers in fluid mechanics

### Low swirl premixed methane-air flame dynamics under acoustic excitations

Physics of Fluids, Volume 31, Issue 9, September 2019.

In this study, simultaneous particle image velocimetry and planar laser induced fluorescence of hydroxyl radical, chemiluminescence imaging, and hot-wire measurements are utilized to study reacting low swirl flow dynamics under low to high amplitude acoustic excitations. Results show that a temporal weak recirculation zone exists downstream of the flame, which is enlarged in size under acoustic excitations. Investigations show that temporal behaviors of this recirculation zone play a significant role in flame movements and instabilities. As the acoustic wave amplitude increases, the flame lift-off distance changes drastically, resulting in flame instabilities (flashback and blowout) during the excitations. Prior to the flame blowout, although the flame lift-off distance responds periodically to the acoustic perturbations, heat release fluctuations display an aperiodic response. Flame dynamics are further studied by calculated power spectra of acoustic velocity and heat release fluctuations and reconstructed phase portraits of heat release fluctuations. Investigations show that increasing the forcing amplitude results in more deterministic features in the flame dynamics and amplification of the higher harmonic modes in the heat release fluctuations. However, such regular patterns become scattered prior to the flame blowout due to the existence of nonlinearities induced by high amplitude excitations. It is speculated that flame blowout can be a symptom of such nonlinearities. The Rayleigh index is measured to study thermoacoustic couplings. At low amplitude excitations, various coupling patterns occur at the flame. However, such complex patterns are replaced by simple coherent patterns, when the flame is excited by high amplitude acoustic perturbations.

In this study, simultaneous particle image velocimetry and planar laser induced fluorescence of hydroxyl radical, chemiluminescence imaging, and hot-wire measurements are utilized to study reacting low swirl flow dynamics under low to high amplitude acoustic excitations. Results show that a temporal weak recirculation zone exists downstream of the flame, which is enlarged in size under acoustic excitations. Investigations show that temporal behaviors of this recirculation zone play a significant role in flame movements and instabilities. As the acoustic wave amplitude increases, the flame lift-off distance changes drastically, resulting in flame instabilities (flashback and blowout) during the excitations. Prior to the flame blowout, although the flame lift-off distance responds periodically to the acoustic perturbations, heat release fluctuations display an aperiodic response. Flame dynamics are further studied by calculated power spectra of acoustic velocity and heat release fluctuations and reconstructed phase portraits of heat release fluctuations. Investigations show that increasing the forcing amplitude results in more deterministic features in the flame dynamics and amplification of the higher harmonic modes in the heat release fluctuations. However, such regular patterns become scattered prior to the flame blowout due to the existence of nonlinearities induced by high amplitude excitations. It is speculated that flame blowout can be a symptom of such nonlinearities. The Rayleigh index is measured to study thermoacoustic couplings. At low amplitude excitations, various coupling patterns occur at the flame. However, such complex patterns are replaced by simple coherent patterns, when the flame is excited by high amplitude acoustic perturbations.

Categories: Latest papers in fluid mechanics

### Drag reduction in turbulent flow along a cylinder by circumferential oscillating Lorentz force

Physics of Fluids, Volume 31, Issue 9, September 2019.

Direct numerical simulations are performed to study the drag reduction effect in turbulent flow along a cylinder by the circumferential oscillating Lorentz force at the Reynolds number Reτ = 272 based on the reference friction velocity and the thickness of the boundary layer. The maximum drag reduction rate obtained in the present work is 42.6%. The intensity, penetration thickness, distribution (idealized or realistic), and oscillation period of the Lorentz force are all crucial in determining the drag reduction rate. As the Lorentz force is intensified or its penetration thickness and oscillation period increase, the wall friction drag will prominently decrease as long as the circumferential flow is stable. The Stokes layer, introduced by the circumferential oscillating Lorentz force, effectively manipulated the near-wall coherent structures, leading to the decrease of the wall friction drag. However, the occurrence of the force-induced vortices in the near-wall region can also lead to significant drag increase by enhancing the radial momentum transportation due to centrifugal instability. By estimating the energy consumption rate, it is clear that the extra power to implement the Lorentz force is far more than the power saved due to drag reduction, which is the result of the low conductivity of the fluid media. Taking the coupling between the electromagnetic field and the flow field into consideration, the wall friction drag is nearly zero and the turbulence intensity in the near-wall region is very low when the induced Lorentz force is high. But the induced Lorentz drag is greatly increased and the turbulence fluctuations are enhanced in the outer region.

Direct numerical simulations are performed to study the drag reduction effect in turbulent flow along a cylinder by the circumferential oscillating Lorentz force at the Reynolds number Reτ = 272 based on the reference friction velocity and the thickness of the boundary layer. The maximum drag reduction rate obtained in the present work is 42.6%. The intensity, penetration thickness, distribution (idealized or realistic), and oscillation period of the Lorentz force are all crucial in determining the drag reduction rate. As the Lorentz force is intensified or its penetration thickness and oscillation period increase, the wall friction drag will prominently decrease as long as the circumferential flow is stable. The Stokes layer, introduced by the circumferential oscillating Lorentz force, effectively manipulated the near-wall coherent structures, leading to the decrease of the wall friction drag. However, the occurrence of the force-induced vortices in the near-wall region can also lead to significant drag increase by enhancing the radial momentum transportation due to centrifugal instability. By estimating the energy consumption rate, it is clear that the extra power to implement the Lorentz force is far more than the power saved due to drag reduction, which is the result of the low conductivity of the fluid media. Taking the coupling between the electromagnetic field and the flow field into consideration, the wall friction drag is nearly zero and the turbulence intensity in the near-wall region is very low when the induced Lorentz force is high. But the induced Lorentz drag is greatly increased and the turbulence fluctuations are enhanced in the outer region.

Categories: Latest papers in fluid mechanics

### Surfactant-laden droplet behavior on wetting solid wall with non-Newtonian fluid rheology

Physics of Fluids, Volume 31, Issue 9, September 2019.

We develop a coupled lattice-Boltzmann with finite-difference (LB-FD) method to simulate surfactant-laden droplet behaviors on wetting solid wall with non-Newtonian fluid rheology. The effects of the power-law exponent, wettability, force direction, and viscosity ratio on the droplet movement under the shear flow or body force are investigated. It is found that the surfactant-laden droplet moves faster and breaks up more easily than the clean droplet owing to the decreased local interfacial tension. During the initial period of the droplet movement, with the decrease of the power-law exponent of the matrix fluid, the unbalanced Young’s force plays a significant role in prompting droplet spreading along the hydrophilic wall whereas making the droplet recoil along the hydrophobic wall. Under the influence of the shear force, the droplet deformation is strengthened in the shear thickening matrix fluid due to high viscous stress from the external flow. However, under the influence of the body force, droplet deformation is strengthened in the shear thinning matrix fluid because the reduction of the matrix fluid apparent viscosity generates less viscous drag force. Furthermore, the shear thickening pendent droplet is more elongated and shows more flexible behavior than the shear thinning droplet during its falling in the Newtonian matrix fluid. The decrease of the viscosity ratio causes the shear thickening droplet to form the shape of a spherical cap, compared with the shear thinning droplet behaving like a rigid object. The present work not only demonstrates the capacity of the coupled LB-FD method but also sheds light on the mechanism of surfactant-laden droplet dynamics on wetting solid wall where non-Newtonian rheology is considered.

We develop a coupled lattice-Boltzmann with finite-difference (LB-FD) method to simulate surfactant-laden droplet behaviors on wetting solid wall with non-Newtonian fluid rheology. The effects of the power-law exponent, wettability, force direction, and viscosity ratio on the droplet movement under the shear flow or body force are investigated. It is found that the surfactant-laden droplet moves faster and breaks up more easily than the clean droplet owing to the decreased local interfacial tension. During the initial period of the droplet movement, with the decrease of the power-law exponent of the matrix fluid, the unbalanced Young’s force plays a significant role in prompting droplet spreading along the hydrophilic wall whereas making the droplet recoil along the hydrophobic wall. Under the influence of the shear force, the droplet deformation is strengthened in the shear thickening matrix fluid due to high viscous stress from the external flow. However, under the influence of the body force, droplet deformation is strengthened in the shear thinning matrix fluid because the reduction of the matrix fluid apparent viscosity generates less viscous drag force. Furthermore, the shear thickening pendent droplet is more elongated and shows more flexible behavior than the shear thinning droplet during its falling in the Newtonian matrix fluid. The decrease of the viscosity ratio causes the shear thickening droplet to form the shape of a spherical cap, compared with the shear thinning droplet behaving like a rigid object. The present work not only demonstrates the capacity of the coupled LB-FD method but also sheds light on the mechanism of surfactant-laden droplet dynamics on wetting solid wall where non-Newtonian rheology is considered.

Categories: Latest papers in fluid mechanics

### Vortex dynamics in low- and high-extent polymer drag reduction regimes revealed by vortex tracking and conformation analysis

Physics of Fluids, Volume 31, Issue 9, September 2019.

Turbulent flow profiles are known to change between low- (LDR) and high-extent drag reduction (HDR) regimes. It is however not until recently that the LDR-HDR transition is recognized as a fundamental change between two DR mechanisms. Although the onset of DR, which initiates the LDR stage, is explainable by a general argument of polymers suppressing vortices, the occurrence of HDR where flow statistics are qualitatively different and DR effects are observed across a much broader range of wall regions remains unexplained. Recent development of the vortex axis tracking by iterative propagation algorithm allows the detection and extraction of vortex axis-lines with various orientations and curvatures. This new tool is used in this study to analyze the vortex conformation and dynamics across the LDR-HDR transition. Polymer effects are shown to concentrate on vortices that are partially or completely attached to the wall. At LDR, this effect is an across-the-board weakening of vortices which lowers their intensity without shifting their distribution patterns. At HDR, polymers start to suppress the lift-up of streamwise vortices in the buffer layer and prevent their downstream heads from rising into the log-law layer and forming hairpins and other curved vortices. This interrupts the turbulent momentum transfer between the buffer and log-law layers, which offers a clear pathway for explaining the distinct mean flow profiles at HDR. The study depicts the first clear physical picture regarding the changing vortex dynamics between LDR and HDR, which is based on direct evidence from objective statistical analysis of vortex conformation and distribution.

Turbulent flow profiles are known to change between low- (LDR) and high-extent drag reduction (HDR) regimes. It is however not until recently that the LDR-HDR transition is recognized as a fundamental change between two DR mechanisms. Although the onset of DR, which initiates the LDR stage, is explainable by a general argument of polymers suppressing vortices, the occurrence of HDR where flow statistics are qualitatively different and DR effects are observed across a much broader range of wall regions remains unexplained. Recent development of the vortex axis tracking by iterative propagation algorithm allows the detection and extraction of vortex axis-lines with various orientations and curvatures. This new tool is used in this study to analyze the vortex conformation and dynamics across the LDR-HDR transition. Polymer effects are shown to concentrate on vortices that are partially or completely attached to the wall. At LDR, this effect is an across-the-board weakening of vortices which lowers their intensity without shifting their distribution patterns. At HDR, polymers start to suppress the lift-up of streamwise vortices in the buffer layer and prevent their downstream heads from rising into the log-law layer and forming hairpins and other curved vortices. This interrupts the turbulent momentum transfer between the buffer and log-law layers, which offers a clear pathway for explaining the distinct mean flow profiles at HDR. The study depicts the first clear physical picture regarding the changing vortex dynamics between LDR and HDR, which is based on direct evidence from objective statistical analysis of vortex conformation and distribution.

Categories: Latest papers in fluid mechanics

### Coupling effect on shocked double-gas cylinder evolution

Physics of Fluids, Volume 31, Issue 9, September 2019.

Interaction of a weak planar shock wave with double heavy gas cylinders has been investigated, focusing on coupling effect on the post-shock flow. In experiments, the ideal two-dimensional discontinuous double heavy gas cylinders with controllable initial conditions are generated by soap film technique, and the shocked flow is captured by a high-speed schlieren photography. Two different initial center spacings of cylinders are considered to highlight the coupling effect. As the center spacing reduces, the coupling effect occurs earlier and becomes more prominent. The coupling effect greatly promotes the inner vortex motions near the symmetry axis relative to the outer ones, resulting in the formation of the mushroom and twisted jets. The fusion of the inner vortices completely differs from the observation in previous experimental work in which the inner vortices separate from each other. Quantitatively, the motion of the upstream interface in streamwise direction is obtained, and can be predicted by a nonlinear model considering the coupling effect. Besides, a vortex model is proposed based on the induction equation of point vortex, and the effect of the mutual interferences among vortices on the vortex motions can be well evaluated.

Interaction of a weak planar shock wave with double heavy gas cylinders has been investigated, focusing on coupling effect on the post-shock flow. In experiments, the ideal two-dimensional discontinuous double heavy gas cylinders with controllable initial conditions are generated by soap film technique, and the shocked flow is captured by a high-speed schlieren photography. Two different initial center spacings of cylinders are considered to highlight the coupling effect. As the center spacing reduces, the coupling effect occurs earlier and becomes more prominent. The coupling effect greatly promotes the inner vortex motions near the symmetry axis relative to the outer ones, resulting in the formation of the mushroom and twisted jets. The fusion of the inner vortices completely differs from the observation in previous experimental work in which the inner vortices separate from each other. Quantitatively, the motion of the upstream interface in streamwise direction is obtained, and can be predicted by a nonlinear model considering the coupling effect. Besides, a vortex model is proposed based on the induction equation of point vortex, and the effect of the mutual interferences among vortices on the vortex motions can be well evaluated.

Categories: Latest papers in fluid mechanics

### Modulation of sound waves for flow past a rotary oscillating cylinder in a non-synchronous region

Physics of Fluids, Volume 31, Issue 9, September 2019.

Modulation of sound waves for the laminar flow past a rotary oscillating circular cylinder has been studied for a free-stream Reynolds number Re = 150 and Mach number M = 0.2. Modulation of sound waves has been observed if the combination of applied rotary oscillation frequency and amplitude belongs to the nonsynchronous region where the hydrodynamic and acoustic quantities vary with the vortex shedding frequency as well as the applied forcing frequency. Two-dimensional direct numerical simulations (DNS) are carried out on a highly refined grid using high resolution physical dispersion relation preserving schemes for a nondimensional forcing frequency-ratio range 0.1 ≤ fr ≤ 2.0 at a nondimensional surface speed A1 = 0.1. Both the synchronous and the nonsynchronous zones are identified based on the time-varying fluctuations in the lift and the drag coefficients. In the nonsynchronous zone, modulation phenomena of the lift and the drag coefficients are explained by plotting the stream-function contours over multiple vortex shedding cycles. The modulation periods associated with the fluctuating lift and the drag coefficients are different for some cases. This particular observation is in contrast with the observation expressed in the previous studies investigating similar problems. Disturbance pressure fields obtained from the present DNS data are used to analyze the characteristics of radiated sound fields, especially in the nonsynchronous zone. Information related to aerodynamic sound sources has been obtained using approximated Lighthill’s stress tensor, and it is shown that the aerodynamic sound sources also display the modulation phenomenon similar to that observed in the vortex shedding process. Sound fields related to the nonsynchronous zone also exhibit the modulation phenomenon and are governed by the shedding frequency, the forcing frequency, and their linear combinations. Radiated sound field characteristics are further related to the time-varying fluctuations of the lift and the drag coefficients using Curle’s acoustic analogy. Modulated sound waves observed along the upstream and the transverse directions have similar time variation as that of the drag and the lift coefficients, respectively. The phenomenon of beat formation has been observed for the ranges 0.9 ≤ fr ≤ 0.99 and 1.2 ≤ fr ≤ 1.4. Although the observed modulation of sound waves varies significantly with the forcing frequency-ratio, the net radiated sound power has almost remained constant in the nonbeating, nonsynchronous zone. Furthermore, it is confirmed that the dominant sound modes obtained during the proper orthogonal decomposition of disturbance pressure fields in the nonsynchronous zone are related to the shedding frequency-ratio, the forcing frequency-ratio, and their linear combinations.

Modulation of sound waves for the laminar flow past a rotary oscillating circular cylinder has been studied for a free-stream Reynolds number Re = 150 and Mach number M = 0.2. Modulation of sound waves has been observed if the combination of applied rotary oscillation frequency and amplitude belongs to the nonsynchronous region where the hydrodynamic and acoustic quantities vary with the vortex shedding frequency as well as the applied forcing frequency. Two-dimensional direct numerical simulations (DNS) are carried out on a highly refined grid using high resolution physical dispersion relation preserving schemes for a nondimensional forcing frequency-ratio range 0.1 ≤ fr ≤ 2.0 at a nondimensional surface speed A1 = 0.1. Both the synchronous and the nonsynchronous zones are identified based on the time-varying fluctuations in the lift and the drag coefficients. In the nonsynchronous zone, modulation phenomena of the lift and the drag coefficients are explained by plotting the stream-function contours over multiple vortex shedding cycles. The modulation periods associated with the fluctuating lift and the drag coefficients are different for some cases. This particular observation is in contrast with the observation expressed in the previous studies investigating similar problems. Disturbance pressure fields obtained from the present DNS data are used to analyze the characteristics of radiated sound fields, especially in the nonsynchronous zone. Information related to aerodynamic sound sources has been obtained using approximated Lighthill’s stress tensor, and it is shown that the aerodynamic sound sources also display the modulation phenomenon similar to that observed in the vortex shedding process. Sound fields related to the nonsynchronous zone also exhibit the modulation phenomenon and are governed by the shedding frequency, the forcing frequency, and their linear combinations. Radiated sound field characteristics are further related to the time-varying fluctuations of the lift and the drag coefficients using Curle’s acoustic analogy. Modulated sound waves observed along the upstream and the transverse directions have similar time variation as that of the drag and the lift coefficients, respectively. The phenomenon of beat formation has been observed for the ranges 0.9 ≤ fr ≤ 0.99 and 1.2 ≤ fr ≤ 1.4. Although the observed modulation of sound waves varies significantly with the forcing frequency-ratio, the net radiated sound power has almost remained constant in the nonbeating, nonsynchronous zone. Furthermore, it is confirmed that the dominant sound modes obtained during the proper orthogonal decomposition of disturbance pressure fields in the nonsynchronous zone are related to the shedding frequency-ratio, the forcing frequency-ratio, and their linear combinations.

Categories: Latest papers in fluid mechanics

### An embedded boundary approach for efficient simulations of viscoplastic fluids in three dimensions

Physics of Fluids, Volume 31, Issue 9, September 2019.

We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modeled by generalized Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelizable computations on block-structured grids. In this context, geometric features are handled by the embedded boundary approach, which requires specialized treatment only in cells intersecting or adjacent to the boundary. This constitutes the first published implementation of an embedded boundary algorithm for simulating flow of viscoplastic fluids on structured grids. The underlying algorithm employs a two-stage Runge-Kutta method for temporal discretization, in which viscous terms are treated semi-implicitly and projection methods are utilized to enforce the incompressibility constraint. We augment the embedded boundary algorithm to deal with the variable apparent viscosity of the fluids. Since the viscosity depends strongly on the strain rate tensor, special care has been taken to approximate the components of the velocity gradients robustly near boundary cells, both for viscous wall fluxes in cut cells and for updates of apparent viscosity in cells adjacent to them. After performing convergence analysis and validating the code against standard test cases, we present the first ever fully three-dimensional simulations of creeping flow of Bingham plastics around translating objects. Our results shed new light on the flow fields around these objects.

We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modeled by generalized Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelizable computations on block-structured grids. In this context, geometric features are handled by the embedded boundary approach, which requires specialized treatment only in cells intersecting or adjacent to the boundary. This constitutes the first published implementation of an embedded boundary algorithm for simulating flow of viscoplastic fluids on structured grids. The underlying algorithm employs a two-stage Runge-Kutta method for temporal discretization, in which viscous terms are treated semi-implicitly and projection methods are utilized to enforce the incompressibility constraint. We augment the embedded boundary algorithm to deal with the variable apparent viscosity of the fluids. Since the viscosity depends strongly on the strain rate tensor, special care has been taken to approximate the components of the velocity gradients robustly near boundary cells, both for viscous wall fluxes in cut cells and for updates of apparent viscosity in cells adjacent to them. After performing convergence analysis and validating the code against standard test cases, we present the first ever fully three-dimensional simulations of creeping flow of Bingham plastics around translating objects. Our results shed new light on the flow fields around these objects.

Categories: Latest papers in fluid mechanics

### A phase-field-based lattice Boltzmann modeling of two-phase electro-hydrodynamic flows

Physics of Fluids, Volume 31, Issue 9, September 2019.

In this paper, a simple and accurate lattice Boltzmann (LB) model based on phase-field theory is developed to study the two-phase electro-hydrodynamics flows. In this model, three LB equations are utilized to solve the Allen-Cahn equation for the phase field, the Poisson equation for the electric potential, and the Navier-Stokes equation for the flow field. To test the proposed model, the deformation of a single droplet under a uniform electric field is considered. It is found that under a small deformation, the results are in good agreement with the previous work. For a large deformation, however, the theoretical results would give a large deviation, while the present results are close to the available numerical work.

In this paper, a simple and accurate lattice Boltzmann (LB) model based on phase-field theory is developed to study the two-phase electro-hydrodynamics flows. In this model, three LB equations are utilized to solve the Allen-Cahn equation for the phase field, the Poisson equation for the electric potential, and the Navier-Stokes equation for the flow field. To test the proposed model, the deformation of a single droplet under a uniform electric field is considered. It is found that under a small deformation, the results are in good agreement with the previous work. For a large deformation, however, the theoretical results would give a large deviation, while the present results are close to the available numerical work.

Categories: Latest papers in fluid mechanics

### Solitary wave slamming induced by an asymmetric wedge through three degrees of freedom free motions

Physics of Fluids, Volume 31, Issue 9, September 2019.

A time-domain higher-order boundary element method with fully nonlinear boundary conditions is developed to simulate the slamming of an asymmetric wedge entering freely and obliquely into a solitary wave in three degrees of freedom (3DOF). A third order analytical solution based on the Korteweg-de Vries equation is used to simulate the solitary wave incident boundary conditions. In the numerical model of slamming, a stretched coordinate system is applied to maintain numerical accuracy and stability at the initial stage. The thin long jet layer is generated along the wedge surface by assuming linear variation of the jet layer potential. A rotation scheme of the stretched coordinate system is adopted to avoid fluid particle leaving or entering the wedge surface. Some auxiliary functions are employed to decouple the intercoupling motions in 3DOF. The present model is verified by comparing with the published numerical results. Various parametric studies are carried out. Detailed results through the free surface, pressure distribution, accelerations, and velocities are provided to show the slamming effects, and their physical implications are discussed.

A time-domain higher-order boundary element method with fully nonlinear boundary conditions is developed to simulate the slamming of an asymmetric wedge entering freely and obliquely into a solitary wave in three degrees of freedom (3DOF). A third order analytical solution based on the Korteweg-de Vries equation is used to simulate the solitary wave incident boundary conditions. In the numerical model of slamming, a stretched coordinate system is applied to maintain numerical accuracy and stability at the initial stage. The thin long jet layer is generated along the wedge surface by assuming linear variation of the jet layer potential. A rotation scheme of the stretched coordinate system is adopted to avoid fluid particle leaving or entering the wedge surface. Some auxiliary functions are employed to decouple the intercoupling motions in 3DOF. The present model is verified by comparing with the published numerical results. Various parametric studies are carried out. Detailed results through the free surface, pressure distribution, accelerations, and velocities are provided to show the slamming effects, and their physical implications are discussed.

Categories: Latest papers in fluid mechanics

### An explicit expression for the calculation of the Rortex vector

Physics of Fluids, Volume 31, Issue 9, September 2019.

Recently, a vector called Rortex was proposed and successfully applied to identify the local fluid rotation with both the rotation axis and strength. The first implementation relies on the real Schur decomposition of the velocity gradient tensor, resulting in a relatively long computational time. Subsequently, a mathematically equivalent eigenvector-based definition of Rortex was introduced with an improved implementation. Unfortunately, this definition still tends to be an algorithmic description rather than an explicit one and involves two successive cumbersome coordinate rotations. In this paper, a simple and explicit expression for the calculation of the Rortex vector, which is based on a special (transposed) Schur form of the velocity gradient tensor, is presented. The explicit expression is consistent with the previous definition but avoids the explicit calculation of the coordinate rotation, and thus can significantly simplify the implementation. According to the explicit expression, a new implementation is proposed and validated by a large eddy simulation of the flow transition around a NACA0012 airfoil and a direct numerical simulation of the boundary layer transition on a flat plate.

Recently, a vector called Rortex was proposed and successfully applied to identify the local fluid rotation with both the rotation axis and strength. The first implementation relies on the real Schur decomposition of the velocity gradient tensor, resulting in a relatively long computational time. Subsequently, a mathematically equivalent eigenvector-based definition of Rortex was introduced with an improved implementation. Unfortunately, this definition still tends to be an algorithmic description rather than an explicit one and involves two successive cumbersome coordinate rotations. In this paper, a simple and explicit expression for the calculation of the Rortex vector, which is based on a special (transposed) Schur form of the velocity gradient tensor, is presented. The explicit expression is consistent with the previous definition but avoids the explicit calculation of the coordinate rotation, and thus can significantly simplify the implementation. According to the explicit expression, a new implementation is proposed and validated by a large eddy simulation of the flow transition around a NACA0012 airfoil and a direct numerical simulation of the boundary layer transition on a flat plate.

Categories: Latest papers in fluid mechanics

### Numerical simulation of the production of three-dimensional sediment dunes

Physics of Fluids, Volume 31, Issue 9, September 2019.

Knowledge of the relationship between sediment motion and flow conditions is fundamental to our understanding of three-dimensional sediment dune development in river and coastal environments. In this study, numerical simulations were performed on a mobile flat sand bed. The simulation results provide important insights into the coupling between migrating bedforms and turbulent stratified flow in the open channel. The formation of micro sand waves can be divided into three stages. First, the initial defects appear on the bed at the beginning of the process and are closely correlated with the instantaneous flow velocity just before the bed is destabilized. Second, the defects in areas of high instantaneous flow velocity are washed away, while the defects in areas of low instantaneous flow velocity grow in length and height due to sediment deposition. Finally, a constant wake zone where sediment continues to accumulate forms downstream of the micro sand wave. Despite the formation of micro waves, the near-bed flow velocity and turbulent structures play important roles as sand passes from upstream dune crests to downstream ones. The high flow velocity breaks O-shaped dune crests and drives excess sand to the downstream dune crests. The near-bed vortices usually occur at the stoss sides of the dunes, and most are elongated in the spanwise direction.

Knowledge of the relationship between sediment motion and flow conditions is fundamental to our understanding of three-dimensional sediment dune development in river and coastal environments. In this study, numerical simulations were performed on a mobile flat sand bed. The simulation results provide important insights into the coupling between migrating bedforms and turbulent stratified flow in the open channel. The formation of micro sand waves can be divided into three stages. First, the initial defects appear on the bed at the beginning of the process and are closely correlated with the instantaneous flow velocity just before the bed is destabilized. Second, the defects in areas of high instantaneous flow velocity are washed away, while the defects in areas of low instantaneous flow velocity grow in length and height due to sediment deposition. Finally, a constant wake zone where sediment continues to accumulate forms downstream of the micro sand wave. Despite the formation of micro waves, the near-bed flow velocity and turbulent structures play important roles as sand passes from upstream dune crests to downstream ones. The high flow velocity breaks O-shaped dune crests and drives excess sand to the downstream dune crests. The near-bed vortices usually occur at the stoss sides of the dunes, and most are elongated in the spanwise direction.

Categories: Latest papers in fluid mechanics

### Flapping dynamics of a flexible plate with Navier slip

Physics of Fluids, Volume 31, Issue 9, September 2019.

Seaweed and fish have slippery outer surfaces because of the secretion of a layer of mucus. Navier slip arises when the component of the tangential velocity at a wall is proportional to the strain. The hydrodynamics of a three-dimensional flexible plate with Navier slip was explored by using the immersed boundary method in an effort to scrutinize the effects on plate hydrodynamics of a slip boundary mimicking the mucus layers of seaweed and fish. For comparison, simulations with the no-slip condition were also performed. Two cases were chosen for simulation: a flexible plate with a fixed leading edge and a flexible plate with a heaving leading edge in a uniform flow. For the fixed plate, the velocity gradient and the total drag were determined to examine the influence of the slip surface. Drag was significantly reduced by the slip. The slip surface lessens the velocity gradient near the wall and suppresses the flapping motion. The drag reduction process was characterized by using the distributions of vorticity and pressure. The hydrodynamics of the heaving flexible plate with Navier slip was explored in terms of thrust generation. The flapping motion was mainly governed by the input heaving condition and a large form drag was exerted on the flexible plate. The net thrust, input power, and Froude efficiency were determined as a function of the bending rigidity. A large net thrust for the heaving plate was generated by the slip. The velocity ratio was employed to interpret the correlation between the slip velocity and the flapping motion.

Seaweed and fish have slippery outer surfaces because of the secretion of a layer of mucus. Navier slip arises when the component of the tangential velocity at a wall is proportional to the strain. The hydrodynamics of a three-dimensional flexible plate with Navier slip was explored by using the immersed boundary method in an effort to scrutinize the effects on plate hydrodynamics of a slip boundary mimicking the mucus layers of seaweed and fish. For comparison, simulations with the no-slip condition were also performed. Two cases were chosen for simulation: a flexible plate with a fixed leading edge and a flexible plate with a heaving leading edge in a uniform flow. For the fixed plate, the velocity gradient and the total drag were determined to examine the influence of the slip surface. Drag was significantly reduced by the slip. The slip surface lessens the velocity gradient near the wall and suppresses the flapping motion. The drag reduction process was characterized by using the distributions of vorticity and pressure. The hydrodynamics of the heaving flexible plate with Navier slip was explored in terms of thrust generation. The flapping motion was mainly governed by the input heaving condition and a large form drag was exerted on the flexible plate. The net thrust, input power, and Froude efficiency were determined as a function of the bending rigidity. A large net thrust for the heaving plate was generated by the slip. The velocity ratio was employed to interpret the correlation between the slip velocity and the flapping motion.

Categories: Latest papers in fluid mechanics

### Numerical study of the stress singularity in stick-slip flow of the Phan-Thien Tanner and Giesekus fluids

Physics of Fluids, Volume 31, Issue 9, September 2019.

Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer stress behavior around the stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and natural stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The natural stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian.

Stick-slip flow is a challenging viscoelastic benchmark problem due to the presence of a separation or transition point at the die exit where a sudden change in flow boundary conditions occurs. We present numerical simulations of transient planar stick-slip flow of the Phan-Thien–Tanner (PTT) and Giesekus fluids, investigating the polymer stress behavior around the stress singularity at the stick-slip point, confirming the asymptotic results presented by Evans et al. [“Stresses of the Oldroyd-B, PTT and Giesekus fluids in a Newtonian velocity field near the stick-slip singularity,” Phys. Fluids 29, 1–33 (2017)]. In order to improve the numerical knowledge about this viscoelastic benchmark problem, two distinct mathematical methodologies are used for comparison in the computational simulations: the Cartesian and natural stress formulations. The former is widely applied in computational rheology, while the latter is used for the first time in the context of this problem. The natural stress formulation gives improved convergence results both temporally and spatially near to the singularity while maintaining the same global flow characteristics as the Cartesian.

Categories: Latest papers in fluid mechanics

### Performance and mechanism analysis of nanosecond pulsed surface dielectric barrier discharge based plasma deicer

Physics of Fluids, Volume 31, Issue 9, September 2019.

Ice accretion on aircraft surfaces, especially on wings, may do harm to the aerodynamic performance and safety of an aircraft. In this work, de-icing experiments on an NACA0012 airfoil model were conducted in an icing wind tunnel using nanosecond pulsed surface dielectric barrier discharge (nSDBD) actuator under typical glaze icing conditions. The spatial-temporal distribution of the temperature and the dynamic process of de-icing on the surface of the airfoil were obtained and analyzed. Accreted ice with an average thickness of 3 mm can be removed within 4 s by nSDBD, and then the ice never appeared again on the plasma-protected zone. In the whole de-icing process, the ice on the plasma-protected zone was “cut” and the adhesion force between the ice layer and airfoil surface was reduced by the heat generated by the plasma actuator. The “cut” ice layer was blown downstream by aerodynamic force of the incoming flow. It can be concluded that both the thermal effects of the nSDBD actuator and the aerodynamic force of the incoming flow contribute to the de-icing performance.

Ice accretion on aircraft surfaces, especially on wings, may do harm to the aerodynamic performance and safety of an aircraft. In this work, de-icing experiments on an NACA0012 airfoil model were conducted in an icing wind tunnel using nanosecond pulsed surface dielectric barrier discharge (nSDBD) actuator under typical glaze icing conditions. The spatial-temporal distribution of the temperature and the dynamic process of de-icing on the surface of the airfoil were obtained and analyzed. Accreted ice with an average thickness of 3 mm can be removed within 4 s by nSDBD, and then the ice never appeared again on the plasma-protected zone. In the whole de-icing process, the ice on the plasma-protected zone was “cut” and the adhesion force between the ice layer and airfoil surface was reduced by the heat generated by the plasma actuator. The “cut” ice layer was blown downstream by aerodynamic force of the incoming flow. It can be concluded that both the thermal effects of the nSDBD actuator and the aerodynamic force of the incoming flow contribute to the de-icing performance.

Categories: Latest papers in fluid mechanics

### Active control of vortex-induced vibration of a circular cylinder using machine learning

Physics of Fluids, Volume 31, Issue 9, September 2019.

We demonstrate the use of high-fidelity computational fluid dynamics simulations in machine-learning based active flow control. More specifically, for the first time, we adopt the genetic programming (GP) to select explicit control laws, in a data-driven and unsupervised manner, for the suppression of vortex-induced vibration (VIV) of a circular cylinder in a low-Reynolds-number flow (Re = 100), using blowing/suction at fixed locations. A cost function that balances both VIV suppression and energy consumption for the control is carefully chosen according to the knowledge obtained from pure blowing/suction open-loop controls. By implementing reasonable constraints to VIV amplitude and actuation strength during the GP evolution, the GP-selected best ten control laws all point to suction-type actuation. The best control law suggests that the suction strength should be nonzero when the cylinder is at its equilibrium position and should increase nonlinearly with the cylinder’s transverse displacement. Applying this control law suppresses 94.2% of the VIV amplitude and achieves 21.4% better overall performance than the best open-loop controls. Furthermore, it is found that the GP-selected control law is robust, being effective in flows ranging from Re = 100 to 400. On the contrary, although the P-control can achieve similar performance as the GP-selected control at Re = 100, it deteriorates in higher Reynolds number flows. Although for demonstration purpose the chosen control problem is relatively simple, the training experience and insights obtained from this study can shed some light on future GP-based control of more complicated problems.

We demonstrate the use of high-fidelity computational fluid dynamics simulations in machine-learning based active flow control. More specifically, for the first time, we adopt the genetic programming (GP) to select explicit control laws, in a data-driven and unsupervised manner, for the suppression of vortex-induced vibration (VIV) of a circular cylinder in a low-Reynolds-number flow (Re = 100), using blowing/suction at fixed locations. A cost function that balances both VIV suppression and energy consumption for the control is carefully chosen according to the knowledge obtained from pure blowing/suction open-loop controls. By implementing reasonable constraints to VIV amplitude and actuation strength during the GP evolution, the GP-selected best ten control laws all point to suction-type actuation. The best control law suggests that the suction strength should be nonzero when the cylinder is at its equilibrium position and should increase nonlinearly with the cylinder’s transverse displacement. Applying this control law suppresses 94.2% of the VIV amplitude and achieves 21.4% better overall performance than the best open-loop controls. Furthermore, it is found that the GP-selected control law is robust, being effective in flows ranging from Re = 100 to 400. On the contrary, although the P-control can achieve similar performance as the GP-selected control at Re = 100, it deteriorates in higher Reynolds number flows. Although for demonstration purpose the chosen control problem is relatively simple, the training experience and insights obtained from this study can shed some light on future GP-based control of more complicated problems.

Categories: Latest papers in fluid mechanics

### Building a Maxey–Riley framework for surface ocean inertial particle dynamics

Physics of Fluids, Volume 31, Issue 9, September 2019.

A framework for the study of surface ocean inertial particle motion is built from the Maxey–Riley set. A new set is obtained by vertically averaging each term of the original set, adapted to account for Earth’s rotation effects, across the extent of a sufficiently small spherical particle that floats at an assumed unperturbed air–sea interface with unsteady nonuniform winds and ocean currents above and below, respectively. The inertial particle velocity is shown to exponentially decay in time to a velocity that lies close to an average of seawater and air velocities, weighted by a function of the seawater-to-particle density ratio. Such a weighted average velocity turns out to fortuitously be of the type commonly discussed in the search-and-rescue literature, which alone cannot explain the observed role of anticyclonic mesoscale eddies as traps for marine debris or the formation of great garbage patches in the subtropical gyres, phenomena dominated by finite-size effects. A heuristic extension of the theory is proposed to describe the motion of nonspherical particles by means of a simple shape factor correction, and recommendations are made for incorporating wave-induced Stokes drift and allowing for inhomogeneities of the carrying fluid density. The new Maxey–Riley set outperforms an ocean adaptation that ignored wind drag effects and the first reported adaption that attempted to incorporate them.

A framework for the study of surface ocean inertial particle motion is built from the Maxey–Riley set. A new set is obtained by vertically averaging each term of the original set, adapted to account for Earth’s rotation effects, across the extent of a sufficiently small spherical particle that floats at an assumed unperturbed air–sea interface with unsteady nonuniform winds and ocean currents above and below, respectively. The inertial particle velocity is shown to exponentially decay in time to a velocity that lies close to an average of seawater and air velocities, weighted by a function of the seawater-to-particle density ratio. Such a weighted average velocity turns out to fortuitously be of the type commonly discussed in the search-and-rescue literature, which alone cannot explain the observed role of anticyclonic mesoscale eddies as traps for marine debris or the formation of great garbage patches in the subtropical gyres, phenomena dominated by finite-size effects. A heuristic extension of the theory is proposed to describe the motion of nonspherical particles by means of a simple shape factor correction, and recommendations are made for incorporating wave-induced Stokes drift and allowing for inhomogeneities of the carrying fluid density. The new Maxey–Riley set outperforms an ocean adaptation that ignored wind drag effects and the first reported adaption that attempted to incorporate them.

Categories: Latest papers in fluid mechanics

### Maximum spreading of droplets impacting spherical surfaces

Physics of Fluids, Volume 31, Issue 9, September 2019.

Experimental observations, numerical simulations, and theoretical analysis are conducted to investigate the impacting dynamics of water droplets on spherical surfaces. A volume of fluid numerical model coupled with a dynamic contact angle model with consideration of the gravity effect is established and validated by comparing the evolutions of droplet profiles and spreading factors obtained from the simulations and the experiments in both the present work and literature. The effects of the Weber number, contact angle, and sphere-to-droplet diameter ratio (D*) on the droplet impacting on a spherical surface are further studied by numerically calculating the spreading factor and the spreading arc angle corresponding to the two-dimensional wetting arc at the maximum spreading state. The results indicate that both the maximum spreading factor and arc angle increase with increasing Weber number and reducing contact angle. When the sphere-to-droplet diameter ratio is reduced, the maximum spreading factor remains almost unchanged for [math] but it shows a significant increase for [math]. The maximum spreading arc angle keeps going up with reducing diameter ratio under all conditions even for [math]. As the Weber number increases and the contact angle decreases, the effect of the diameter ratio on the maximum spreading becomes more conspicuous. Based on the energy conservation, a theoretical model considering the gravity effect is developed to describe the maximum spreading factor of an impacting droplet on a spherical surface. The maximum spreading factors obtained from the theoretical model yield a deviation of ±15% as compared with those from the experiments and simulations.

Experimental observations, numerical simulations, and theoretical analysis are conducted to investigate the impacting dynamics of water droplets on spherical surfaces. A volume of fluid numerical model coupled with a dynamic contact angle model with consideration of the gravity effect is established and validated by comparing the evolutions of droplet profiles and spreading factors obtained from the simulations and the experiments in both the present work and literature. The effects of the Weber number, contact angle, and sphere-to-droplet diameter ratio (D*) on the droplet impacting on a spherical surface are further studied by numerically calculating the spreading factor and the spreading arc angle corresponding to the two-dimensional wetting arc at the maximum spreading state. The results indicate that both the maximum spreading factor and arc angle increase with increasing Weber number and reducing contact angle. When the sphere-to-droplet diameter ratio is reduced, the maximum spreading factor remains almost unchanged for [math] but it shows a significant increase for [math]. The maximum spreading arc angle keeps going up with reducing diameter ratio under all conditions even for [math]. As the Weber number increases and the contact angle decreases, the effect of the diameter ratio on the maximum spreading becomes more conspicuous. Based on the energy conservation, a theoretical model considering the gravity effect is developed to describe the maximum spreading factor of an impacting droplet on a spherical surface. The maximum spreading factors obtained from the theoretical model yield a deviation of ±15% as compared with those from the experiments and simulations.

Categories: Latest papers in fluid mechanics

### Growth dynamics of bubbles on a pore-patterned surface under reduced pressure

Physics of Fluids, Volume 31, Issue 9, September 2019.

The growth dynamics of bubbles has been extensively studied for several decades. However, a thorough understanding of the morphological evolution of bubbles on pore-patterned surfaces through the coalescence of adjacent bubbles induced by expansion is still lacking. This study aims to quantitatively investigate the coalescence of adjacent bubbles in drops on customized microscale pore-patterned surfaces from the bottom view under different atmospheric pressures. The results demonstrate that the coalescence status and the size of bubbles can be controlled by adjusting the atmospheric pressure and are also in good agreement with the theoretical analysis results. This work provides insight into the underlying physics of growing bubbles on a pore-patterned surface; this is important for research on gas–fluid–solid interfacial slips and surface drag reduction.

The growth dynamics of bubbles has been extensively studied for several decades. However, a thorough understanding of the morphological evolution of bubbles on pore-patterned surfaces through the coalescence of adjacent bubbles induced by expansion is still lacking. This study aims to quantitatively investigate the coalescence of adjacent bubbles in drops on customized microscale pore-patterned surfaces from the bottom view under different atmospheric pressures. The results demonstrate that the coalescence status and the size of bubbles can be controlled by adjusting the atmospheric pressure and are also in good agreement with the theoretical analysis results. This work provides insight into the underlying physics of growing bubbles on a pore-patterned surface; this is important for research on gas–fluid–solid interfacial slips and surface drag reduction.

Categories: Latest papers in fluid mechanics

### Linear stability of confined coaxial jets in the presence of gas velocity oscillations with heat and mass transfer

Physics of Fluids, Volume 31, Issue 9, September 2019.

In this work, the linear temporal stability of a confined coaxial jet has been examined in the presence of gas velocity oscillations with heat and mass transfer. The viscous potential flow theory was applied to account for the liquid and gas viscosities. Results suggest that gas velocity oscillations have a destabilizing effect. The forcing frequency restrained the instability in the parametric unstable region but enhanced the instability in the Kelvin-Helmholtz (K-H) unstable region. Heat and mass transfer decreased the curvature of the surface wave directly and enhanced the hydrodynamic force via the phase change. Heat and mass transfer had a stabilizing effect on the capillary instability, and a dual effect on K-H instability without oscillations. Results similar to the K-H instability were discovered when the oscillations were considered. Gas viscosity played a destabilizing role with the effect of heat and mass transfer, especially reducing the critical velocity for the appearance of the instability; moreover, the liquid viscosity had a stabilizing effect for all the cases discussed.

In this work, the linear temporal stability of a confined coaxial jet has been examined in the presence of gas velocity oscillations with heat and mass transfer. The viscous potential flow theory was applied to account for the liquid and gas viscosities. Results suggest that gas velocity oscillations have a destabilizing effect. The forcing frequency restrained the instability in the parametric unstable region but enhanced the instability in the Kelvin-Helmholtz (K-H) unstable region. Heat and mass transfer decreased the curvature of the surface wave directly and enhanced the hydrodynamic force via the phase change. Heat and mass transfer had a stabilizing effect on the capillary instability, and a dual effect on K-H instability without oscillations. Results similar to the K-H instability were discovered when the oscillations were considered. Gas viscosity played a destabilizing role with the effect of heat and mass transfer, especially reducing the critical velocity for the appearance of the instability; moreover, the liquid viscosity had a stabilizing effect for all the cases discussed.

Categories: Latest papers in fluid mechanics