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

Physics of Fluids, Volume 31, Issue 8, August 2019.

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

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

Categories: Latest papers in fluid mechanics

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

Physics of Fluids, Volume 31, Issue 8, August 2019.

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

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

Categories: Latest papers in fluid mechanics

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

Physics of Fluids, Volume 31, Issue 8, August 2019.

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

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

Categories: Latest papers in fluid mechanics

### A numerical investigation of dynamics of bubbly flow in a ferrofluid by a self-correcting procedure-based lattice Boltzmann flux solver

Physics of Fluids, Volume 31, Issue 8, August 2019.

In this work, the dynamics of bubbly flow in a dielectric ferrofluid under a uniform magnetic field has been numerically studied by a self-correcting procedure-based lattice Boltzmann flux solver. The investigation cases focus specifically on two bubbles merging and a single bubble rising in ferrofluid with a large density ratio under an applied uniform magnetic field. By accounting for the effects of the magnetic field intensity, susceptibility, Reynolds number, and Eotvos number, the mechanisms of bubble motion and deformation in the ferrofluid under the external magnetic field are analyzed.

In this work, the dynamics of bubbly flow in a dielectric ferrofluid under a uniform magnetic field has been numerically studied by a self-correcting procedure-based lattice Boltzmann flux solver. The investigation cases focus specifically on two bubbles merging and a single bubble rising in ferrofluid with a large density ratio under an applied uniform magnetic field. By accounting for the effects of the magnetic field intensity, susceptibility, Reynolds number, and Eotvos number, the mechanisms of bubble motion and deformation in the ferrofluid under the external magnetic field are analyzed.

Categories: Latest papers in fluid mechanics

### Oscillating grid turbulence in shear-thinning polymer solutions

Physics of Fluids, Volume 31, Issue 8, August 2019.

Oscillating grid apparatuses are well known and convenient tools for the fundamental study of turbulence and its interaction with other phenomena since they allow to generate turbulence supposedly homogeneous, isotropic, and free of mean shear. They could, in particular, be used to study turbulence and mass transfer near the interface between non-Newtonian liquids and a gas, as already done in air-water situations. Although frequently used in water and Newtonian fluids, oscillating grid turbulence (OGT) generation has yet been rarely applied and never characterized in non-Newtonian media. The present work consists of a first experimental characterization of the flow properties of shear-thinning polymer (Xanthan Gum, XG) solutions stirred by an oscillating grid. Various polymer concentrations are tested for a single grid stirring condition. The dilute and semidilute entanglement concentration regimes are considered. Liquid phase velocities are measured by Particle Image Velocimetry. The existing mean flow established in the tank is described and characterized, as well as turbulence properties (intensity, decay rate, length scales, isotropy, etc.). OGT in dilute polymer solutions induces an enhanced mean flow compared to water, a similar decay behavior with yet different decay rates, and enhanced turbulence large scales and anisotropy. In the semidilute regime of XG, turbulence and mean flows are essentially damped by viscosity. The evolution of mean flow and turbulence indicators leads to the definition of several polymer concentration subregimes, within the dilute one. Critical concentrations around 20 ppm and 50 ppm are found, comparable to drag reduction characteristic concentrations.

Oscillating grid apparatuses are well known and convenient tools for the fundamental study of turbulence and its interaction with other phenomena since they allow to generate turbulence supposedly homogeneous, isotropic, and free of mean shear. They could, in particular, be used to study turbulence and mass transfer near the interface between non-Newtonian liquids and a gas, as already done in air-water situations. Although frequently used in water and Newtonian fluids, oscillating grid turbulence (OGT) generation has yet been rarely applied and never characterized in non-Newtonian media. The present work consists of a first experimental characterization of the flow properties of shear-thinning polymer (Xanthan Gum, XG) solutions stirred by an oscillating grid. Various polymer concentrations are tested for a single grid stirring condition. The dilute and semidilute entanglement concentration regimes are considered. Liquid phase velocities are measured by Particle Image Velocimetry. The existing mean flow established in the tank is described and characterized, as well as turbulence properties (intensity, decay rate, length scales, isotropy, etc.). OGT in dilute polymer solutions induces an enhanced mean flow compared to water, a similar decay behavior with yet different decay rates, and enhanced turbulence large scales and anisotropy. In the semidilute regime of XG, turbulence and mean flows are essentially damped by viscosity. The evolution of mean flow and turbulence indicators leads to the definition of several polymer concentration subregimes, within the dilute one. Critical concentrations around 20 ppm and 50 ppm are found, comparable to drag reduction characteristic concentrations.

Categories: Latest papers in fluid mechanics

### Flow structure around and heat transfer from cylinders modified from square to circular

Physics of Fluids, Volume 31, Issue 8, August 2019.

This work aims at numerically investigating the influence of corner modification on the flow structure around and heat transfer from a square cylinder at a Reynolds number Re = 150 based on the cylinder width d and freestream velocity. The sharp corners of the square cylinder are rounded with r/d = 0 (square), 0.125, 0.25, 0.375, and 0.5 (circular), where r is the radius of the corner. The rounded corners have a profound effect on the flow structure from the perspective of flow separation, vortex strength, separation bubble, and wake bubble each playing a role in heat transfer from different surfaces of the cylinder. The boundary layer having a higher friction coefficient on the front and side surfaces leads to a higher local heat transfer. A shorter wake bubble renders a higher heat transfer from the rear surface. The increase in r/d from 0 to 0.5 leads to a 33% enhancement in the heat transfer from the cylinder. The enhancement largely results from a shrink in the wake bubble and an increase in vortex strength. The minimum time-mean drag and fluctuating forces are achieved at r/d = 0.25 and 0.125, respectively. The effect of r/d in various Reynolds averaged quantities is discussed.

This work aims at numerically investigating the influence of corner modification on the flow structure around and heat transfer from a square cylinder at a Reynolds number Re = 150 based on the cylinder width d and freestream velocity. The sharp corners of the square cylinder are rounded with r/d = 0 (square), 0.125, 0.25, 0.375, and 0.5 (circular), where r is the radius of the corner. The rounded corners have a profound effect on the flow structure from the perspective of flow separation, vortex strength, separation bubble, and wake bubble each playing a role in heat transfer from different surfaces of the cylinder. The boundary layer having a higher friction coefficient on the front and side surfaces leads to a higher local heat transfer. A shorter wake bubble renders a higher heat transfer from the rear surface. The increase in r/d from 0 to 0.5 leads to a 33% enhancement in the heat transfer from the cylinder. The enhancement largely results from a shrink in the wake bubble and an increase in vortex strength. The minimum time-mean drag and fluctuating forces are achieved at r/d = 0.25 and 0.125, respectively. The effect of r/d in various Reynolds averaged quantities is discussed.

Categories: Latest papers in fluid mechanics

### Numerical simulations of a stick-slip spherical particle in Poiseuille flow

Physics of Fluids, Volume 31, Issue 8, August 2019.

The dynamics of a stick-slip “Janus” spherical particle suspended in a Newtonian fluid flowing in a cylindrical microchannel is studied by direct numerical simulations. Partial slip is imposed on half of the particle surface, whereas the no-slip boundary condition is present on the other half. The finite element method is used to solve the balance equations under creeping flow conditions. The translational and rotational velocities of the particle are evaluated at several orientations and distances from the tube centerline. The trajectories are then reconstructed by solving the kinematic equations where the velocities are taken by interpolating the simulation data. The particle dynamics is investigated by varying the initial position and orientation, the slip parameter, and the confinement ratio. The results, presented in terms of particle trajectories and phase portraits, highlight the existence of two relevant regimes: a periodic oscillation or a migration toward the tube axis for particle positions sufficiently far from or near the centerline, respectively. The basin of attraction of the tube axis grows with particle confinement and slip coefficient although the dynamics is qualitatively unaffected.

The dynamics of a stick-slip “Janus” spherical particle suspended in a Newtonian fluid flowing in a cylindrical microchannel is studied by direct numerical simulations. Partial slip is imposed on half of the particle surface, whereas the no-slip boundary condition is present on the other half. The finite element method is used to solve the balance equations under creeping flow conditions. The translational and rotational velocities of the particle are evaluated at several orientations and distances from the tube centerline. The trajectories are then reconstructed by solving the kinematic equations where the velocities are taken by interpolating the simulation data. The particle dynamics is investigated by varying the initial position and orientation, the slip parameter, and the confinement ratio. The results, presented in terms of particle trajectories and phase portraits, highlight the existence of two relevant regimes: a periodic oscillation or a migration toward the tube axis for particle positions sufficiently far from or near the centerline, respectively. The basin of attraction of the tube axis grows with particle confinement and slip coefficient although the dynamics is qualitatively unaffected.

Categories: Latest papers in fluid mechanics

### Particles dispersion and deposition in inhomogeneous turbulent flows using continuous random walk models

Physics of Fluids, Volume 31, Issue 8, August 2019.

The suitability of the normalized Langevin stochastic equation with appropriate drift correction for simulation of instantaneous fluctuation velocities in inhomogeneous turbulent flows was studied. The Reynolds Stress Transport turbulence model of the ANSYS-Fluent code was used to evaluate the inhomogeneous turbulent flow properties in a two-dimensional duct flow. The simulation results were then used in an in-house Matlab particle tracking code and the trajectories of about 2 × 105 randomly distributed particles in the channel were evaluated by solving the particle equation of motion including the drag and Brownian forces under the one-way coupling assumption. The performance of the Continuous Random Walk (CRW) stochastic model using the conventional nonnormalized, as well as the normalized Langevin equations without and with the drift term for predicting a uniform distribution for the fluid-tracer particles in an inhomogeneous turbulent flow was examined. The accuracy of these models in predicting the deposition velocities and distribution of solid particles with diameters ranging from 10 nm to 30 μm was also carefully examined. In addition, the effects of including the finite-inertia coefficient in the drift term and using the corrected root mean square normal velocity in the near-wall region on the accuracy of the results were emphasized. By exploring the concentration profiles and deposition velocities of particles resulting from different CRW models, it was concluded that the Normalized-CRW model including the appropriate drift term leads to the most accurate results.

The suitability of the normalized Langevin stochastic equation with appropriate drift correction for simulation of instantaneous fluctuation velocities in inhomogeneous turbulent flows was studied. The Reynolds Stress Transport turbulence model of the ANSYS-Fluent code was used to evaluate the inhomogeneous turbulent flow properties in a two-dimensional duct flow. The simulation results were then used in an in-house Matlab particle tracking code and the trajectories of about 2 × 105 randomly distributed particles in the channel were evaluated by solving the particle equation of motion including the drag and Brownian forces under the one-way coupling assumption. The performance of the Continuous Random Walk (CRW) stochastic model using the conventional nonnormalized, as well as the normalized Langevin equations without and with the drift term for predicting a uniform distribution for the fluid-tracer particles in an inhomogeneous turbulent flow was examined. The accuracy of these models in predicting the deposition velocities and distribution of solid particles with diameters ranging from 10 nm to 30 μm was also carefully examined. In addition, the effects of including the finite-inertia coefficient in the drift term and using the corrected root mean square normal velocity in the near-wall region on the accuracy of the results were emphasized. By exploring the concentration profiles and deposition velocities of particles resulting from different CRW models, it was concluded that the Normalized-CRW model including the appropriate drift term leads to the most accurate results.

Categories: Latest papers in fluid mechanics

### Experimental analysis of one-dimensional Faraday waves on a liquid layer subjected to horizontal vibrations

Physics of Fluids, Volume 31, Issue 8, August 2019.

In this paper, we experimentally show the synchronous (harmonic) nature of the primary surface waves formed on a layer of water (∼1 mm) pinned to a glass substrate and subjected to horizontal (lateral) vibrations. With well-controlled experiments, we attenuated cross-waves and studied the primary standing waves in a one-dimensional wave configuration, with a high precision mechanical vibrator, capable of generating a range of forcing frequencies (100–500 Hz) and amplitudes (1–5 µm). We demonstrate that the emergence of instability (in the form of standing waves) depends upon the forcing amplitude and frequency and the average thickness of the liquid layer. Experiments reveal that the surface remains stable for sufficiently thin and thick layers of the liquid, while instability appears for thicknesses in between the two mentioned lower and upper limits. We show and analyze that, for the average liquid thickness of h = 1.5 mm, asymmetric modes of oscillations appear on the liquid surface; however, with a change in the film thickness and length of the surface profile, symmetric modes may occur as well (h = 2 mm). The problem studied here, i.e., a liquid film with pinned contact lines subjected to horizontal vibrations, shows some of the characteristics of an infinitely extended lateral liquid film, a liquid layer in a container with walls, and a sessile droplet.

In this paper, we experimentally show the synchronous (harmonic) nature of the primary surface waves formed on a layer of water (∼1 mm) pinned to a glass substrate and subjected to horizontal (lateral) vibrations. With well-controlled experiments, we attenuated cross-waves and studied the primary standing waves in a one-dimensional wave configuration, with a high precision mechanical vibrator, capable of generating a range of forcing frequencies (100–500 Hz) and amplitudes (1–5 µm). We demonstrate that the emergence of instability (in the form of standing waves) depends upon the forcing amplitude and frequency and the average thickness of the liquid layer. Experiments reveal that the surface remains stable for sufficiently thin and thick layers of the liquid, while instability appears for thicknesses in between the two mentioned lower and upper limits. We show and analyze that, for the average liquid thickness of h = 1.5 mm, asymmetric modes of oscillations appear on the liquid surface; however, with a change in the film thickness and length of the surface profile, symmetric modes may occur as well (h = 2 mm). The problem studied here, i.e., a liquid film with pinned contact lines subjected to horizontal vibrations, shows some of the characteristics of an infinitely extended lateral liquid film, a liquid layer in a container with walls, and a sessile droplet.

Categories: Latest papers in fluid mechanics

### Geostrophic adjustment on the equatorial beta-plane revisited

Physics of Fluids, Volume 31, Issue 8, August 2019.

The process of geostrophic adjustment of localized large-scale pressure anomalies in the standard adiabatic shallow-water model on the equatorial beta-plane is revisited, and it is shown that the standard scenario of generation of westward-moving Rossby and eastward-moving Kelvin waves, which underlies the classical Gill theory of tropical circulation due to a localized heating, is not unique. Depending on the strength and aspect ratio of the initial perturbation, the response to the initial perturbation in the western sector can be dominated by inertia-gravity waves. The adjustment in the diabatic moist-convective shallow water model can be totally different and produces, depending on parameters, either Gill-like response or eastward-moving coherent dipolar structures of the type of equatorial modons, which do not appear in the “dry” adjustment, or vortices traveling, respectively, northwest in the Northern and southwest in the Southern hemispheres.

The process of geostrophic adjustment of localized large-scale pressure anomalies in the standard adiabatic shallow-water model on the equatorial beta-plane is revisited, and it is shown that the standard scenario of generation of westward-moving Rossby and eastward-moving Kelvin waves, which underlies the classical Gill theory of tropical circulation due to a localized heating, is not unique. Depending on the strength and aspect ratio of the initial perturbation, the response to the initial perturbation in the western sector can be dominated by inertia-gravity waves. The adjustment in the diabatic moist-convective shallow water model can be totally different and produces, depending on parameters, either Gill-like response or eastward-moving coherent dipolar structures of the type of equatorial modons, which do not appear in the “dry” adjustment, or vortices traveling, respectively, northwest in the Northern and southwest in the Southern hemispheres.

Categories: Latest papers in fluid mechanics

### Instability of a smooth shear layer through wave interactions

Physics of Fluids, Volume 31, Issue 8, August 2019.

Wave interaction theory can be used as a tool to understand and predict instability in a variety of homogeneous and stratified shear flows. It is, however, most often limited to piecewise-linear profiles of the shear layer background velocity, in which stable vorticity wave modes can be easily identified and their interaction quantified. This approach to understanding shear flow instability is extended herein to smooth shear layer profiles. We describe a method, by which the stable vorticity wave modes can be identified, and show that their interaction results in an excellent description of the stability properties of the smooth shear layer, thus demonstrating the presence of the wave interaction mechanism in smooth shear flows.

Wave interaction theory can be used as a tool to understand and predict instability in a variety of homogeneous and stratified shear flows. It is, however, most often limited to piecewise-linear profiles of the shear layer background velocity, in which stable vorticity wave modes can be easily identified and their interaction quantified. This approach to understanding shear flow instability is extended herein to smooth shear layer profiles. We describe a method, by which the stable vorticity wave modes can be identified, and show that their interaction results in an excellent description of the stability properties of the smooth shear layer, thus demonstrating the presence of the wave interaction mechanism in smooth shear flows.

Categories: Latest papers in fluid mechanics

### Analytical prediction of electrowetting-induced jumping motion for droplets on hydrophobic substrates

Physics of Fluids, Volume 31, Issue 8, August 2019.

Electric voltage applied in electrowetting can induce spreading of a liquid droplet on solid substrates and yield significant contact angle reduction, which has been widely used for manipulating individual droplets in microfluidics and lab-on-a-chip devices, and even for creating jumping motion of droplets. Here, we present a theoretical closed-form expression of lift-off velocity to predict electrowetting-induced jumping motion of a droplet on hydrophobic substrates. In particular, we consider a liquid droplet wetting on a hydrophobic surface with a voltage applied between the droplet and the substrate. By turning off the applied voltage, the energy stored in the droplet deformation by electrowetting releases and may be sufficient to overcome the energy barrier for detachment. Based on the energy conservation of the droplet-substrate system, we derive a closed-form formula to predict the droplet jumping velocity in terms of the Young contact angle, the Lippmann-Young contact angle, and the Ohnesorge number. The validity of the theoretical prediction is confirmed by comparing the predicted jumping velocities with both experimental observations and numerical simulations. The predictive formula indicates that the jumping motion can be enhanced by increasing the Young contact angle and decreasing the Lippmann-Young contact angle or the Ohnesorge number. Also, a phase diagram of droplet jumping motion is constructed based on this model, which provides insights on accurate control of the electrowetting-induced jumping motion of droplets on hydrophobic surfaces.

Electric voltage applied in electrowetting can induce spreading of a liquid droplet on solid substrates and yield significant contact angle reduction, which has been widely used for manipulating individual droplets in microfluidics and lab-on-a-chip devices, and even for creating jumping motion of droplets. Here, we present a theoretical closed-form expression of lift-off velocity to predict electrowetting-induced jumping motion of a droplet on hydrophobic substrates. In particular, we consider a liquid droplet wetting on a hydrophobic surface with a voltage applied between the droplet and the substrate. By turning off the applied voltage, the energy stored in the droplet deformation by electrowetting releases and may be sufficient to overcome the energy barrier for detachment. Based on the energy conservation of the droplet-substrate system, we derive a closed-form formula to predict the droplet jumping velocity in terms of the Young contact angle, the Lippmann-Young contact angle, and the Ohnesorge number. The validity of the theoretical prediction is confirmed by comparing the predicted jumping velocities with both experimental observations and numerical simulations. The predictive formula indicates that the jumping motion can be enhanced by increasing the Young contact angle and decreasing the Lippmann-Young contact angle or the Ohnesorge number. Also, a phase diagram of droplet jumping motion is constructed based on this model, which provides insights on accurate control of the electrowetting-induced jumping motion of droplets on hydrophobic surfaces.

Categories: Latest papers in fluid mechanics

### Three-dimensional shock interactions and vortices on a V-shaped blunt leading edge

Physics of Fluids, Volume 31, Issue 8, August 2019.

The three-dimensional flow on a plate with a V-shaped blunt leading edge (VsBLEP) is investigated numerically and experimentally at a freestream Mach number 6. A complex saddle-shaped shock front is observed on this VsBLEP under the interactions between the detached shock (DS) induced by the swept blunt leading edge and the bow shock (BS) induced by the crotch. It is demonstrated that a new type of spatial transition exists on this saddle-shaped shock front, which involves the transition of shock interactions (i.e., DS and BS) from the same family upstream of the crotch to opposite families downstream of the crotch. Moreover, this transition is quantitatively identified according to the shock-induced spanwise velocity along the inflection line between DS and BS, which is of great importance because it affects the crossflow significantly. The inward crossflow induced by the swept blunt leading edge is enhanced in the region where the DS and BS are from the same family, and the shear layers generated in this region converge gradually to the spanwise symmetry plane, which results in the formation of a streamwise counter-rotating vortex pair (CVP). In the region where the DS and BS turn to opposite families, the inward crossflow is eliminated, and a five-shock structure is identified downstream of the crotch. The CVP remains close to the spanwise symmetry plane as it trails downstream, showing a far-reaching influence on the flowfield. This study indicates that the V-shaped blunt leading edge affects the downstream flow significantly and therefore should be examined carefully in practical applications, such as in the design of an inlet cowl lip.

The three-dimensional flow on a plate with a V-shaped blunt leading edge (VsBLEP) is investigated numerically and experimentally at a freestream Mach number 6. A complex saddle-shaped shock front is observed on this VsBLEP under the interactions between the detached shock (DS) induced by the swept blunt leading edge and the bow shock (BS) induced by the crotch. It is demonstrated that a new type of spatial transition exists on this saddle-shaped shock front, which involves the transition of shock interactions (i.e., DS and BS) from the same family upstream of the crotch to opposite families downstream of the crotch. Moreover, this transition is quantitatively identified according to the shock-induced spanwise velocity along the inflection line between DS and BS, which is of great importance because it affects the crossflow significantly. The inward crossflow induced by the swept blunt leading edge is enhanced in the region where the DS and BS are from the same family, and the shear layers generated in this region converge gradually to the spanwise symmetry plane, which results in the formation of a streamwise counter-rotating vortex pair (CVP). In the region where the DS and BS turn to opposite families, the inward crossflow is eliminated, and a five-shock structure is identified downstream of the crotch. The CVP remains close to the spanwise symmetry plane as it trails downstream, showing a far-reaching influence on the flowfield. This study indicates that the V-shaped blunt leading edge affects the downstream flow significantly and therefore should be examined carefully in practical applications, such as in the design of an inlet cowl lip.

Categories: Latest papers in fluid mechanics

### Cell trapping in Y-junction microchannels: A numerical study of the bifurcation angle effect in inertial microfluidics

Physics of Fluids, Volume 31, Issue 8, August 2019.

The majority of microfluidic technologies for cell sorting and isolation involve bifurcating (e.g., Y- or T-shaped junction) microchannels to trap the cells of a specific type. However, the microfluidic trapping efficiency remains low, independently of whether the cells are separated by a passive or an active sorting method. Using a custom computational algorithm, we studied the migration of separated deformable cells in a Y-junction microchannel, with a bifurcation angle ranging from 30° to 180°. Single or two cells of initially spherical shape were considered under flow conditions corresponding to inertial microfluidics. Through the numerical simulation, we identified the effects of cell size, cytoplasmic viscoelasticity, cortical tension, flow rate, and bifurcation angle on the critical separation distance for cell trapping. The results of this study show that the trapping and isolation of blood cells, and circulating tumor cells in a Y-junction microchannel was most efficient and least dependent on the flow rate at the bifurcation angle of 120°. At this angle, the trapping efficiency for white blood cells and circulating tumor cells increased, respectively, by 46% and 43%, in comparison with the trapping efficiency at 60°. The efficiency to isolate invasive tumor cells from noninvasive ones increased by 32%. This numerical study provides important design criteria to optimize microfluidic technology for deformability-based cell sorting and isolation.

The majority of microfluidic technologies for cell sorting and isolation involve bifurcating (e.g., Y- or T-shaped junction) microchannels to trap the cells of a specific type. However, the microfluidic trapping efficiency remains low, independently of whether the cells are separated by a passive or an active sorting method. Using a custom computational algorithm, we studied the migration of separated deformable cells in a Y-junction microchannel, with a bifurcation angle ranging from 30° to 180°. Single or two cells of initially spherical shape were considered under flow conditions corresponding to inertial microfluidics. Through the numerical simulation, we identified the effects of cell size, cytoplasmic viscoelasticity, cortical tension, flow rate, and bifurcation angle on the critical separation distance for cell trapping. The results of this study show that the trapping and isolation of blood cells, and circulating tumor cells in a Y-junction microchannel was most efficient and least dependent on the flow rate at the bifurcation angle of 120°. At this angle, the trapping efficiency for white blood cells and circulating tumor cells increased, respectively, by 46% and 43%, in comparison with the trapping efficiency at 60°. The efficiency to isolate invasive tumor cells from noninvasive ones increased by 32%. This numerical study provides important design criteria to optimize microfluidic technology for deformability-based cell sorting and isolation.

Categories: Latest papers in fluid mechanics

### Conditional dynamic subfilter modeling

Physics of Fluids, Volume 31, Issue 8, August 2019.

A novel “conditional” variation of the dynamic approach for modeling of large eddy simulation subfilter terms is derived and tested. In contrast to the traditional dynamic closure, which stabilizes “raw” dynamic coefficients by averaging across ensembles of expected statistical homogeneity, the novel variation averages conditionally on some set of scalars whose local values are expected to correlate with the local degree of turbulence. Simulations of a nonpremixed jet flame show that the conditional dynamic model is both tractable and stable and produces predictions which are essentially indistinguishable from the traditional dynamic closure, although both models give suboptimal predictions. Future work could potentially improve the predictions of both models—facilitating a fairer comparison—by considering a more uniform or “pancake-like” grid.

A novel “conditional” variation of the dynamic approach for modeling of large eddy simulation subfilter terms is derived and tested. In contrast to the traditional dynamic closure, which stabilizes “raw” dynamic coefficients by averaging across ensembles of expected statistical homogeneity, the novel variation averages conditionally on some set of scalars whose local values are expected to correlate with the local degree of turbulence. Simulations of a nonpremixed jet flame show that the conditional dynamic model is both tractable and stable and produces predictions which are essentially indistinguishable from the traditional dynamic closure, although both models give suboptimal predictions. Future work could potentially improve the predictions of both models—facilitating a fairer comparison—by considering a more uniform or “pancake-like” grid.

Categories: Latest papers in fluid mechanics

### Pore-scale study of counter-current imbibition in strongly water-wet fractured porous media using lattice Boltzmann method

Physics of Fluids, Volume 31, Issue 8, August 2019.

Oil recovery from naturally fractured reservoirs with low permeability rock remains a challenge. To provide a better understanding of spontaneous imbibition, a key oil recovery mechanism in the fractured reservoir rocks, a pore-scale computational study of the water imbibition into an artificially generated dual-permeability porous matrix with a fracture attached on top is conducted using a recently improved lattice Boltzmann color-gradient model. Several factors affecting the dynamic countercurrent imbibition processes and the resulting oil recovery have been analyzed, including the water injection velocity, the geometry configuration of the dual permeability zones, interfacial tension, the viscosity ratio of water to oil phases, and fracture spacing if there are multiple fractures. Depending on the water injection velocity and interfacial tension, three different imbibition regimes have been identified: the squeezing regime, the jetting regime, and the dripping regime, each with a distinctively different expelled oil morphology in the fracture. The geometry configuration of the high and low permeability zones affects the amount of oil that can be recovered by the countercurrent imbibition in a fracture-matrix system through transition of the different regimes. In the squeezing regime, which occurs at low water injection velocity, the build-up squeezing pressure upstream in the fracture enables more water to imbibe into the permeability zone closer to the fracture inlet thus increasing the oil recovery factor. A larger interfacial tension or a lower water-to-oil viscosity ratio is favorable for enhancing oil recovery, and new insights into the effect of the viscosity ratio are provided. Introducing an extra parallel fracture can effectively increase the oil recovery factor, and there is an optimal fracture spacing between the two adjacent horizontal fractures to maximize the oil recovery. These findings can aid the optimal design of water-injecting oil extraction in fractured rocks in reservoirs such as oil shale.

Oil recovery from naturally fractured reservoirs with low permeability rock remains a challenge. To provide a better understanding of spontaneous imbibition, a key oil recovery mechanism in the fractured reservoir rocks, a pore-scale computational study of the water imbibition into an artificially generated dual-permeability porous matrix with a fracture attached on top is conducted using a recently improved lattice Boltzmann color-gradient model. Several factors affecting the dynamic countercurrent imbibition processes and the resulting oil recovery have been analyzed, including the water injection velocity, the geometry configuration of the dual permeability zones, interfacial tension, the viscosity ratio of water to oil phases, and fracture spacing if there are multiple fractures. Depending on the water injection velocity and interfacial tension, three different imbibition regimes have been identified: the squeezing regime, the jetting regime, and the dripping regime, each with a distinctively different expelled oil morphology in the fracture. The geometry configuration of the high and low permeability zones affects the amount of oil that can be recovered by the countercurrent imbibition in a fracture-matrix system through transition of the different regimes. In the squeezing regime, which occurs at low water injection velocity, the build-up squeezing pressure upstream in the fracture enables more water to imbibe into the permeability zone closer to the fracture inlet thus increasing the oil recovery factor. A larger interfacial tension or a lower water-to-oil viscosity ratio is favorable for enhancing oil recovery, and new insights into the effect of the viscosity ratio are provided. Introducing an extra parallel fracture can effectively increase the oil recovery factor, and there is an optimal fracture spacing between the two adjacent horizontal fractures to maximize the oil recovery. These findings can aid the optimal design of water-injecting oil extraction in fractured rocks in reservoirs such as oil shale.

Categories: Latest papers in fluid mechanics

### Stability of downslope flows to two-dimensional perturbations

Physics of Fluids, Volume 31, Issue 8, August 2019.

We consider the stability problem for wide, uniform stationary open flows down a slope with constant inclination under gravity. Depth-averaged equations are used with arbitrary bottom friction as a function of the flow depth and depth-averaged velocity. The stability conditions for perturbations propagating along the flow are widely known. In this paper, we focus on the effect of oblique perturbations that propagate at an arbitrary angle to the velocity of the undisturbed flow. We show that under certain conditions, oblique perturbations can grow even when the perturbations propagating along the flow are damped. This means that if oblique perturbations exist, the stability conditions found in the investigation of the one-dimensional problem are insufficient for the stability of the flow. New stability criteria are formulated as explicit relations between the slope and the flow parameters. The ranges of the growing disturbances propagation angles are indicated for unstable flows.

We consider the stability problem for wide, uniform stationary open flows down a slope with constant inclination under gravity. Depth-averaged equations are used with arbitrary bottom friction as a function of the flow depth and depth-averaged velocity. The stability conditions for perturbations propagating along the flow are widely known. In this paper, we focus on the effect of oblique perturbations that propagate at an arbitrary angle to the velocity of the undisturbed flow. We show that under certain conditions, oblique perturbations can grow even when the perturbations propagating along the flow are damped. This means that if oblique perturbations exist, the stability conditions found in the investigation of the one-dimensional problem are insufficient for the stability of the flow. New stability criteria are formulated as explicit relations between the slope and the flow parameters. The ranges of the growing disturbances propagation angles are indicated for unstable flows.

Categories: Latest papers in fluid mechanics

### Nonlinear dispersive Alfvén waves interaction in magnetized plasma

Physics of Fluids, Volume 31, Issue 8, August 2019.

This study is concerned with the nonlinear interactions between pairs of intersecting Alfvén waves in a magnetized plasma and used the modified Korteweg–de Vries equation to study nonlinear interactions. The modulation instability analysis shows the existence of periodic traveling wave solution in the system. Two different types of waves interaction solutions, namely, the periodic wave interaction solutions and the solitary wave interaction ones, are captured analytically. It is found that the wave resonance for the periodic waves interaction could happen as various wave numbers are nearly the same. In this case, the subsidiary waves could not be neglected. It is also found that the interaction for solitary waves, different solitons eventually regain their original states. The solitons with higher energy possess more speed as compared to the low energy solitons. The phenomenon of Alfvén wave interaction can be of importance for understanding the transport mechanism of magnetic waves in various processes of heating and transport of energy in space, solar wind, and astrophysical plasma.

This study is concerned with the nonlinear interactions between pairs of intersecting Alfvén waves in a magnetized plasma and used the modified Korteweg–de Vries equation to study nonlinear interactions. The modulation instability analysis shows the existence of periodic traveling wave solution in the system. Two different types of waves interaction solutions, namely, the periodic wave interaction solutions and the solitary wave interaction ones, are captured analytically. It is found that the wave resonance for the periodic waves interaction could happen as various wave numbers are nearly the same. In this case, the subsidiary waves could not be neglected. It is also found that the interaction for solitary waves, different solitons eventually regain their original states. The solitons with higher energy possess more speed as compared to the low energy solitons. The phenomenon of Alfvén wave interaction can be of importance for understanding the transport mechanism of magnetic waves in various processes of heating and transport of energy in space, solar wind, and astrophysical plasma.

Categories: Latest papers in fluid mechanics

### Evolution of rivulets during spreading of an impinging water jet on a rotating, precoated substrate

Physics of Fluids, Volume 31, Issue 8, August 2019.

The spreading of a liquid film across a rotating surface is inherently unstable due to the centrifugal force, which causes the formation of rivulets along the spreading front. This instability produces a rich diversity of spreading patterns and is important to control for the optimization of spin-coating and spin-rinsing of silicon wafers during the fabrication of microelectronics. The present work is an experimental investigation of the evolution of rivulets arising from this instability during the spreading of an impinging water jet across a rotating substrate that is precoated with a thin, aqueous film. To characterize these rivulets, we developed a high-speed imaging apparatus and image-processing software that traces the spreading front over time. We show how the morphology of the spreading front is qualitatively affected by varying the Reynolds number of the impinging jet, the ratio of centrifugal to Coriolis forces, and the type of liquid used to precoat the substrate. For quantitative analysis of rivulets, we measured the “compactness ratio” of the spreading front, which quantifies deviation from a circular spreading front. We used the compactness ratio to demonstrate that rivulets are suppressed most strongly at low rotation rates, at high flow rates, and on substrates precoated with water, although with notable exceptions.

The spreading of a liquid film across a rotating surface is inherently unstable due to the centrifugal force, which causes the formation of rivulets along the spreading front. This instability produces a rich diversity of spreading patterns and is important to control for the optimization of spin-coating and spin-rinsing of silicon wafers during the fabrication of microelectronics. The present work is an experimental investigation of the evolution of rivulets arising from this instability during the spreading of an impinging water jet across a rotating substrate that is precoated with a thin, aqueous film. To characterize these rivulets, we developed a high-speed imaging apparatus and image-processing software that traces the spreading front over time. We show how the morphology of the spreading front is qualitatively affected by varying the Reynolds number of the impinging jet, the ratio of centrifugal to Coriolis forces, and the type of liquid used to precoat the substrate. For quantitative analysis of rivulets, we measured the “compactness ratio” of the spreading front, which quantifies deviation from a circular spreading front. We used the compactness ratio to demonstrate that rivulets are suppressed most strongly at low rotation rates, at high flow rates, and on substrates precoated with water, although with notable exceptions.

Categories: Latest papers in fluid mechanics

### Multirotor wind turbine wakes

Physics of Fluids, Volume 31, Issue 8, August 2019.

To fulfill the increasing need for large power generation by wind turbines, the concept of multirotor wind turbines has recently received attention as a promising alternative to conventional massive single-rotor wind turbines. To shed light on the viability of this concept, large-eddy simulation is employed in this study to compare wake flow properties of a multirotor wind turbine with those of a single-rotor turbine. The wake of a multirotor turbine is found to recover faster at short downwind distances, where the whole wake is characterized as an array of localized high velocity-deficit regions associated with each rotor. However, as the wake moves downstream, rotor wakes start interacting with each other until they eventually form a single wake. This transition from a wake array to a single wake adversely affects the initial fast recovery of multirotor turbine wakes. A budget analysis of mean kinetic energy is performed to analyze the energy transport into the wake before and after this transition. In addition, the effect of different geometrical configurations on wake characteristics of a multirotor turbine was examined. We found that the recovery rate of multirotor turbine wakes is enhanced by the increase in rotor spacing, whereas the number and rotation direction of rotors do not play a significant role in the wake recovery. A simple analytical relationship is also developed to predict the streamwise distance at which the transition from a wake array to a single wake occurs for multirotor wind turbines.

To fulfill the increasing need for large power generation by wind turbines, the concept of multirotor wind turbines has recently received attention as a promising alternative to conventional massive single-rotor wind turbines. To shed light on the viability of this concept, large-eddy simulation is employed in this study to compare wake flow properties of a multirotor wind turbine with those of a single-rotor turbine. The wake of a multirotor turbine is found to recover faster at short downwind distances, where the whole wake is characterized as an array of localized high velocity-deficit regions associated with each rotor. However, as the wake moves downstream, rotor wakes start interacting with each other until they eventually form a single wake. This transition from a wake array to a single wake adversely affects the initial fast recovery of multirotor turbine wakes. A budget analysis of mean kinetic energy is performed to analyze the energy transport into the wake before and after this transition. In addition, the effect of different geometrical configurations on wake characteristics of a multirotor turbine was examined. We found that the recovery rate of multirotor turbine wakes is enhanced by the increase in rotor spacing, whereas the number and rotation direction of rotors do not play a significant role in the wake recovery. A simple analytical relationship is also developed to predict the streamwise distance at which the transition from a wake array to a single wake occurs for multirotor wind turbines.

Categories: Latest papers in fluid mechanics