# 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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### Deformation, speed, and stability of droplet motion in closed electrowetting-based digital microfluidics

Physics of Fluids, Volume 31, Issue 6, June 2019.

Electrowetting-based microdrop manipulation has received considerable attention owing to its wide applications in numerous scientific areas based on the digital microfluidics (DMF) technology. However, the techniques for highly precise droplet handling in such microscopic systems are still unclear. In this work, the deformation, speed, and stability of droplet transporting in closed electrowetting-based DMF systems are comprehensively investigated with both theoretical and numerical analyses. First, a theoretical model is derived which governs the droplet motion and includes the influences of the key electrowetting system parameters. After that, a finite volume formulation with a two-step projection method is used for solving the microfluidic flow on a fixed numerical domain. The liquid-gas interface of the droplet is tracked by a coupled level-set and volume-of-fluid method, and the surface tension at the interface is computed by the continuum surface force scheme. A parametric study has been carried out to examine the effects of the static contact angles (θs,ON and θs,OFF), hysteresis effect (Δθ), channel height (H), and electrode size (LE) on droplet shape, speed, and deformation during transport, which unanimously shows that droplet length, neck width, and transport stability are directly related to a dimensionless parameter [math] that only comprises θs,ON, θs,OFF, H, LE, and the hysteresis angle Δθ. Based on the results, the scaling laws for estimating droplet shape and stability of the transport process have been developed, which can be used for promoting the accuracy and efficiency of droplet manipulation in a large variety of droplet-based DMF applications.

Electrowetting-based microdrop manipulation has received considerable attention owing to its wide applications in numerous scientific areas based on the digital microfluidics (DMF) technology. However, the techniques for highly precise droplet handling in such microscopic systems are still unclear. In this work, the deformation, speed, and stability of droplet transporting in closed electrowetting-based DMF systems are comprehensively investigated with both theoretical and numerical analyses. First, a theoretical model is derived which governs the droplet motion and includes the influences of the key electrowetting system parameters. After that, a finite volume formulation with a two-step projection method is used for solving the microfluidic flow on a fixed numerical domain. The liquid-gas interface of the droplet is tracked by a coupled level-set and volume-of-fluid method, and the surface tension at the interface is computed by the continuum surface force scheme. A parametric study has been carried out to examine the effects of the static contact angles (θs,ON and θs,OFF), hysteresis effect (Δθ), channel height (H), and electrode size (LE) on droplet shape, speed, and deformation during transport, which unanimously shows that droplet length, neck width, and transport stability are directly related to a dimensionless parameter [math] that only comprises θs,ON, θs,OFF, H, LE, and the hysteresis angle Δθ. Based on the results, the scaling laws for estimating droplet shape and stability of the transport process have been developed, which can be used for promoting the accuracy and efficiency of droplet manipulation in a large variety of droplet-based DMF applications.

Categories: Latest papers in fluid mechanics

### Asymptotics of a catenoid liquid bridge between two spherical particles with different radii and contact angles

Physics of Fluids, Volume 31, Issue 6, June 2019.

A liquid bridge between two neighboring particles is commonly observed in nature and various industrial processes. An accurate prediction of the profile of a liquid bridge is significantly important in particulate flows, while it is an analytically challenging task as well. In this paper, we develop an asymptotic solution for a catenoid liquid bridge profile, which is the minimal surface ensuring the minimum total surface energy. Our asymptotic solution is based on a rapid convergent predictor-corrector algorithm that considers different factors including boundary conditions, volume conservation, and geometrical relations while providing the relationship between the liquid bridge profile, bridge radius, half-filling angles, and creeping distances. Therefore, this asymptotic solution of the catenoid of the liquid bridge is applicable to general scenarios of any two neighboring particles of either equal or different sizes having identical or different contact angles. In order to validate the proposed asymptotic solution, we performed comprehensive experiments where the observed and predicted liquid bridge profiles and the resultant capillary forces from both the approaches are found closely matching. Moreover, we also investigate and report the influence of the radii ratio, contact angles, particle distances, and the liquid bridge volumes on its profiles.

A liquid bridge between two neighboring particles is commonly observed in nature and various industrial processes. An accurate prediction of the profile of a liquid bridge is significantly important in particulate flows, while it is an analytically challenging task as well. In this paper, we develop an asymptotic solution for a catenoid liquid bridge profile, which is the minimal surface ensuring the minimum total surface energy. Our asymptotic solution is based on a rapid convergent predictor-corrector algorithm that considers different factors including boundary conditions, volume conservation, and geometrical relations while providing the relationship between the liquid bridge profile, bridge radius, half-filling angles, and creeping distances. Therefore, this asymptotic solution of the catenoid of the liquid bridge is applicable to general scenarios of any two neighboring particles of either equal or different sizes having identical or different contact angles. In order to validate the proposed asymptotic solution, we performed comprehensive experiments where the observed and predicted liquid bridge profiles and the resultant capillary forces from both the approaches are found closely matching. Moreover, we also investigate and report the influence of the radii ratio, contact angles, particle distances, and the liquid bridge volumes on its profiles.

Categories: Latest papers in fluid mechanics

### Bowling water drops on water surface

Physics of Fluids, Volume 31, Issue 6, June 2019.

In our daily experience, the drops falling on a water pool usually immediately merge into water. The liquid drops floating at different environments are fascinating but attract less attention. Here, we report that the water drops are capable of floating on a water surface without heating, shearing, or oscillating the water pool. Water drops are generated from a beveled needle and fall on the clean water in an acrylic container. Water drops released from a beveled needle are found to travel on the water surface in a speed of tens of millimeter/second for several centimeters, which can be adjusted by the injection rate. A particle image velocimetry (PIV) technique is employed on the air, water drop, and water pool to confirm the rotation-induced shear effect for the delay coalescence. TiO2 particles and water aerosols served as visualized particles for PIV measurements in air, drop, and water pool. We show that the water drop can float on the water surface if it rotates or slides fast enough. The relative motion of the drop and the underneath surface plays an important role in the delay coalescence. The flow in the air layer between the drop and water pool not only shears the drop but also replenishes the loss of squeeze-out air in the thin layer.

In our daily experience, the drops falling on a water pool usually immediately merge into water. The liquid drops floating at different environments are fascinating but attract less attention. Here, we report that the water drops are capable of floating on a water surface without heating, shearing, or oscillating the water pool. Water drops are generated from a beveled needle and fall on the clean water in an acrylic container. Water drops released from a beveled needle are found to travel on the water surface in a speed of tens of millimeter/second for several centimeters, which can be adjusted by the injection rate. A particle image velocimetry (PIV) technique is employed on the air, water drop, and water pool to confirm the rotation-induced shear effect for the delay coalescence. TiO2 particles and water aerosols served as visualized particles for PIV measurements in air, drop, and water pool. We show that the water drop can float on the water surface if it rotates or slides fast enough. The relative motion of the drop and the underneath surface plays an important role in the delay coalescence. The flow in the air layer between the drop and water pool not only shears the drop but also replenishes the loss of squeeze-out air in the thin layer.

Categories: Latest papers in fluid mechanics

### Passive vortical flows enhance mass transport in the interior of a coral colony

Physics of Fluids, Volume 31, Issue 6, June 2019.

Corals exchange nutrients and dissolved gases with the surrounding environment for metabolic purposes. A recent study demonstrated that corals can actively stir quiescent water columns and produce vortical flows that enhance mass transfer rates by up to 400%. Here, three-dimensional immersed-boundary simulations of the flow through a Pocillopora meandrina colony demonstrate that the passive geometric features of the branching colony produce highly vortical internal flows that enhance mass transfer at the interior of the colony, compensating almost exactly for flows speed reductions there of up to 64% so that the advection time scale remains roughly constant throughout the colony.

Corals exchange nutrients and dissolved gases with the surrounding environment for metabolic purposes. A recent study demonstrated that corals can actively stir quiescent water columns and produce vortical flows that enhance mass transfer rates by up to 400%. Here, three-dimensional immersed-boundary simulations of the flow through a Pocillopora meandrina colony demonstrate that the passive geometric features of the branching colony produce highly vortical internal flows that enhance mass transfer at the interior of the colony, compensating almost exactly for flows speed reductions there of up to 64% so that the advection time scale remains roughly constant throughout the colony.

Categories: Latest papers in fluid mechanics

### Numerical study of thermocapillary migration of a bubble in a channel with an obstruction

Physics of Fluids, Volume 31, Issue 6, June 2019.

Fully resolved numerical simulations are used to examine the thermocapillary motion of a two- and three-dimensional fully deformable bubble in a channel with an obstruction. A front-tracking/finite volume method is used to solve the Navier-Stokes equations coupled with the energy conservation equation. The results show that, for a fixed obstruction and channel size, the influence coefficient α, defined as the ratio of arrival time in channels with and without an obstruction, increases with increasing Marangoni (Ma) number for both two- and three-dimensional flows, whereas an increase in the Reynolds (Re) number leads to an increase in the influence coefficient in two-dimensional flows but a decrease in three-dimensional flows. Moreover, a change in the Capillary (Ca) number does not have a visible effect on the thermocapillary motion if the width of the narrow part of the channel is larger than the bubble diameter. Results for both two- and three-dimensional flows show that the influence coefficient increases dramatically with an increase in the obstruction size W, and a larger obstruction makes the dependence of α on the fluid parameters more obvious.

Fully resolved numerical simulations are used to examine the thermocapillary motion of a two- and three-dimensional fully deformable bubble in a channel with an obstruction. A front-tracking/finite volume method is used to solve the Navier-Stokes equations coupled with the energy conservation equation. The results show that, for a fixed obstruction and channel size, the influence coefficient α, defined as the ratio of arrival time in channels with and without an obstruction, increases with increasing Marangoni (Ma) number for both two- and three-dimensional flows, whereas an increase in the Reynolds (Re) number leads to an increase in the influence coefficient in two-dimensional flows but a decrease in three-dimensional flows. Moreover, a change in the Capillary (Ca) number does not have a visible effect on the thermocapillary motion if the width of the narrow part of the channel is larger than the bubble diameter. Results for both two- and three-dimensional flows show that the influence coefficient increases dramatically with an increase in the obstruction size W, and a larger obstruction makes the dependence of α on the fluid parameters more obvious.

Categories: Latest papers in fluid mechanics

### Fluid dynamics of oscillatory flow in three-dimensional branching networks

Physics of Fluids, Volume 31, Issue 6, June 2019.

The present study is aimed at understanding and thoroughly documenting the complex unsteady fluid dynamics in six generations of a model human bronchial tree, comprising 63 straight sections and 31 bifurcation modules, during a complete breathing cycle. The computational task is challenging since the complexity of an elaborate network is augmented with adopted stringent criteria for spatial and temporal accuracy and convergence at each time step (10−8 for each scaled residual). The physical understanding of the fluid dynamics of steady expiratory flow is taken to a similar level of fine details that have been previously established for steady inspiratory flow in earlier publications of the authors. The effects of three-dimensional arrangement of the same branches on the oscillatory flow structure are determined. It is found that the quasisteady assumption is approximately valid in the neighborhood of the peak flow rate, both during inspiration and expiration. Unsteady effects are at their maximum during the changeover from expiration to inspiration and inspiration to expiration. At these time instants, regions of bidirectional flow are observed in all branches with significant secondary motion at various cross sections (none of these features can be predicted by steady state simulations). It is described how the symmetry of the solution with respect to both space and time—found in the oscillating, fully developed flow in a pipe—are destroyed in the unsteady effects that occur in the oscillating flow in a branching network. As the Womersley number is increased, the unsteady effects at all branches increase, and bidirectional flow exists over a greater portion of a cycle. The flow division at a bifurcation module during inspiratory flow generates large asymmetry in the flow field with nonuniform mass flow distribution among the branches of a generation (even in a geometrically symmetric network), whereas flow combination at the same bifurcation module during expiratory flow tends to produce more symmetry in the flow field, displaying essential irreversibility of fluid dynamics.

The present study is aimed at understanding and thoroughly documenting the complex unsteady fluid dynamics in six generations of a model human bronchial tree, comprising 63 straight sections and 31 bifurcation modules, during a complete breathing cycle. The computational task is challenging since the complexity of an elaborate network is augmented with adopted stringent criteria for spatial and temporal accuracy and convergence at each time step (10−8 for each scaled residual). The physical understanding of the fluid dynamics of steady expiratory flow is taken to a similar level of fine details that have been previously established for steady inspiratory flow in earlier publications of the authors. The effects of three-dimensional arrangement of the same branches on the oscillatory flow structure are determined. It is found that the quasisteady assumption is approximately valid in the neighborhood of the peak flow rate, both during inspiration and expiration. Unsteady effects are at their maximum during the changeover from expiration to inspiration and inspiration to expiration. At these time instants, regions of bidirectional flow are observed in all branches with significant secondary motion at various cross sections (none of these features can be predicted by steady state simulations). It is described how the symmetry of the solution with respect to both space and time—found in the oscillating, fully developed flow in a pipe—are destroyed in the unsteady effects that occur in the oscillating flow in a branching network. As the Womersley number is increased, the unsteady effects at all branches increase, and bidirectional flow exists over a greater portion of a cycle. The flow division at a bifurcation module during inspiratory flow generates large asymmetry in the flow field with nonuniform mass flow distribution among the branches of a generation (even in a geometrically symmetric network), whereas flow combination at the same bifurcation module during expiratory flow tends to produce more symmetry in the flow field, displaying essential irreversibility of fluid dynamics.

Categories: Latest papers in fluid mechanics

### Pressure-driven flow focusing of two miscible liquids

Physics of Fluids, Volume 31, Issue 6, June 2019.

Flow focusing consists in injecting a core liquid into another surrounding flowing sheath liquid. Here we investigate experimentally the influence of imposing pressure to generate coflow of two miscible liquids. We inject water in the central inlet of a cross-junction microfluidic device and different mixtures of glycerol-water in the two lateral inlets. A pressure generator is used to control the flows, and the established flow rates are monitored in both inlets. We draw a state diagram that delimits the regions of the coflow, the inner and outer back flows. We measure the width of the jet as a function of different control parameters: the inlet pressures, the flow rates, the viscosity contrast, and the channel aspect ratio. We show that the jet width can be controlled by tuning the internal to external pressure ratio solely, provided that the viscosity contrast is low. We discuss the possibility to use such a system to center particles in a channel.

Flow focusing consists in injecting a core liquid into another surrounding flowing sheath liquid. Here we investigate experimentally the influence of imposing pressure to generate coflow of two miscible liquids. We inject water in the central inlet of a cross-junction microfluidic device and different mixtures of glycerol-water in the two lateral inlets. A pressure generator is used to control the flows, and the established flow rates are monitored in both inlets. We draw a state diagram that delimits the regions of the coflow, the inner and outer back flows. We measure the width of the jet as a function of different control parameters: the inlet pressures, the flow rates, the viscosity contrast, and the channel aspect ratio. We show that the jet width can be controlled by tuning the internal to external pressure ratio solely, provided that the viscosity contrast is low. We discuss the possibility to use such a system to center particles in a channel.

Categories: Latest papers in fluid mechanics

### Counterflow and wall stagnation flow with three-dimensional strain

Physics of Fluids, Volume 31, Issue 5, May 2019.

Three-dimensional (3D) viscous counterflows and wall stagnation flows are analyzed with differing normal strain rates in each of the three directions. Reduction of the equations to a similar form is obtained allowing for variations in density due to temperature and composition, heat conduction, and, for the counterflow, mass diffusion and the presence of a flame. Solutions to the Navier-Stokes equations are obtained without the boundary-layer approximation. For the steady and unsteady incompressible counterflows, analytical solutions are obtained for the flow field and the scalar fields subject to heat and mass transfer. In steady, variable-density configurations, a set of ordinary differential equations (ODEs) governs the two transverse velocity and the axial velocity profiles as well as the scalar-field variables. Diffusion rates for mass, momentum, and energy depend on the two normal strain rates parallel to the counterflow interface or the wall and thereby not merely on the sum of those two strain rates. For thin diffusion flames, the location, burning rate, and peak temperature are readily obtained. Solutions for planar flows and axisymmetric flows are obtained as limits here. Results for the velocity and scalar fields are found for a full range of the distribution of normal strain rates between the two transverse directions, various Prandtl number values, and various ambient (or wall) temperatures. For counterflows with flames and stagnation layers with hot walls, velocity overshoots are seen in the viscous layer, yielding an important correction of theories based on a constant-density assumption.

Three-dimensional (3D) viscous counterflows and wall stagnation flows are analyzed with differing normal strain rates in each of the three directions. Reduction of the equations to a similar form is obtained allowing for variations in density due to temperature and composition, heat conduction, and, for the counterflow, mass diffusion and the presence of a flame. Solutions to the Navier-Stokes equations are obtained without the boundary-layer approximation. For the steady and unsteady incompressible counterflows, analytical solutions are obtained for the flow field and the scalar fields subject to heat and mass transfer. In steady, variable-density configurations, a set of ordinary differential equations (ODEs) governs the two transverse velocity and the axial velocity profiles as well as the scalar-field variables. Diffusion rates for mass, momentum, and energy depend on the two normal strain rates parallel to the counterflow interface or the wall and thereby not merely on the sum of those two strain rates. For thin diffusion flames, the location, burning rate, and peak temperature are readily obtained. Solutions for planar flows and axisymmetric flows are obtained as limits here. Results for the velocity and scalar fields are found for a full range of the distribution of normal strain rates between the two transverse directions, various Prandtl number values, and various ambient (or wall) temperatures. For counterflows with flames and stagnation layers with hot walls, velocity overshoots are seen in the viscous layer, yielding an important correction of theories based on a constant-density assumption.

Categories: Latest papers in fluid mechanics

### Dispersion due to combined pressure-driven and electro-osmotic flows in a channel surrounded by a permeable porous medium

Physics of Fluids, Volume 31, Issue 5, May 2019.

The combined electro-osmotic and pressure-driven flows (PDFs) have pronounced impacts on the solute transport in permeable porous media, particularly mixing and separation processes. However, the relationship between the physical properties of the permeable porous media and the combined electro-osmotic and PDFs still needs further investigation. This study focuses on the transport of a neutral nonreacting solute in a channel with permeable porous walls under the combined effects of electro-osmotic and PDFs. With the aid of perturbation theory and asymptotic analysis, the equivalent one-dimensional equations governing the solute concentrations in the channel and permeable porous medium under the combined velocity are derived. Based on this, an exact analytical expression relating the dispersion coefficient with the physical properties of the permeable porous medium and the combined flow is obtained. The model parameters exerting the most influence on the results are identified through sensitivity analysis. The proposed model is compared and validated with several previously developed models in the literature. The findings of this study can pave the way for the quantitatively design of solute transport through microporous coatings and porous microfluidic membranes.

The combined electro-osmotic and pressure-driven flows (PDFs) have pronounced impacts on the solute transport in permeable porous media, particularly mixing and separation processes. However, the relationship between the physical properties of the permeable porous media and the combined electro-osmotic and PDFs still needs further investigation. This study focuses on the transport of a neutral nonreacting solute in a channel with permeable porous walls under the combined effects of electro-osmotic and PDFs. With the aid of perturbation theory and asymptotic analysis, the equivalent one-dimensional equations governing the solute concentrations in the channel and permeable porous medium under the combined velocity are derived. Based on this, an exact analytical expression relating the dispersion coefficient with the physical properties of the permeable porous medium and the combined flow is obtained. The model parameters exerting the most influence on the results are identified through sensitivity analysis. The proposed model is compared and validated with several previously developed models in the literature. The findings of this study can pave the way for the quantitatively design of solute transport through microporous coatings and porous microfluidic membranes.

Categories: Latest papers in fluid mechanics

### Kinetic modeling of unsteady hypersonic flows over a tick geometry

Physics of Fluids, Volume 31, Issue 5, May 2019.

Hypersonic separated flows over the so-called “tick” geometry have been studied using the time-accurate direct simulation Monte Carlo (DSMC) method and global linear theory. The free stream condition for two experimental cases studied in the free-piston shock tunnel (named T-ADFA) was modeled. These two cases span a Knudsen number from transitional to continuum, a Mach number of about 10, a free stream enthalpy from 10 to 3 MJ/kg, a Reynolds number varying by a factor of four, and a leading edge geometry varied from sharp to one with a bevel of 0.2 mm. For the first time, the time dependence of flow macroparameters on the leading edge nose radius and the Reynolds number are studied using global linear theory. High-fidelity DSMC simulations showed that the temporal behavior of the separation region, which has significant effects on the surface parameters, depends closely on the leading edge bluntness and wall temperature. The formation of a secondary vortex was seen in about 2 ms for the sharp leading edge, whereas in the rounded leading edge geometry, it formed at earlier 0.7 ms. At a steady state, the size and structure of the separation zone, vortex structures, and surface parameters predicted by DSMC were found to be in good agreement with computational fluid dynamics for the higher density case. Finally, linear stability theory showed that for some leading edge shapes and flow densities, the time to reach the steady state was longer than the facility measurement time.

Hypersonic separated flows over the so-called “tick” geometry have been studied using the time-accurate direct simulation Monte Carlo (DSMC) method and global linear theory. The free stream condition for two experimental cases studied in the free-piston shock tunnel (named T-ADFA) was modeled. These two cases span a Knudsen number from transitional to continuum, a Mach number of about 10, a free stream enthalpy from 10 to 3 MJ/kg, a Reynolds number varying by a factor of four, and a leading edge geometry varied from sharp to one with a bevel of 0.2 mm. For the first time, the time dependence of flow macroparameters on the leading edge nose radius and the Reynolds number are studied using global linear theory. High-fidelity DSMC simulations showed that the temporal behavior of the separation region, which has significant effects on the surface parameters, depends closely on the leading edge bluntness and wall temperature. The formation of a secondary vortex was seen in about 2 ms for the sharp leading edge, whereas in the rounded leading edge geometry, it formed at earlier 0.7 ms. At a steady state, the size and structure of the separation zone, vortex structures, and surface parameters predicted by DSMC were found to be in good agreement with computational fluid dynamics for the higher density case. Finally, linear stability theory showed that for some leading edge shapes and flow densities, the time to reach the steady state was longer than the facility measurement time.

Categories: Latest papers in fluid mechanics

### Publisher’s Note: “An experimental study on the effect of swirl number on pollutant formation in propane bluff-body stabilized swirl diffusion flames” [Phys. Fluids 31, 055105 (2019)]

Physics of Fluids, Volume 31, Issue 5, May 2019.

Categories: Latest papers in fluid mechanics

### Hydrodynamic interaction for rigid dumbbell suspensions in steady shear flow

Physics of Fluids, Volume 31, Issue 5, May 2019.

From kinetic molecular theory, we can attribute the rheological behaviors of polymeric liquids to macromolecular orientation. The simplest model to capture the orientation of macromolecules is the rigid dumbbell. For a suspension of rigid dumbbells, subject to any shear flow, for instance, we must first solve the diffusion equation for the orientation distribution function. From this distribution, we then calculate the first and second normal stress differences. To get reasonable results for the normal stress differences in steady shear flow, one must account for hydrodynamic interaction between the dumbbell beads. However, for the power series expansions for these normal stress differences, three series arise. The coefficients for two of these series, (ck, dk), are not known, not even approximately, beyond the second power of the shear rate. Analytical work on many viscoelastic material functions in shear flow must be checked for consistency, in their steady shear flow limits, against these normal stress difference power series expansions. For instance, for large-amplitude oscillatory shear flow, we must recover the power series expansions in the limits of low frequency. In this work, for (ck, dk), we arrive at the exact expressions for the first 18 of these coefficients.

From kinetic molecular theory, we can attribute the rheological behaviors of polymeric liquids to macromolecular orientation. The simplest model to capture the orientation of macromolecules is the rigid dumbbell. For a suspension of rigid dumbbells, subject to any shear flow, for instance, we must first solve the diffusion equation for the orientation distribution function. From this distribution, we then calculate the first and second normal stress differences. To get reasonable results for the normal stress differences in steady shear flow, one must account for hydrodynamic interaction between the dumbbell beads. However, for the power series expansions for these normal stress differences, three series arise. The coefficients for two of these series, (ck, dk), are not known, not even approximately, beyond the second power of the shear rate. Analytical work on many viscoelastic material functions in shear flow must be checked for consistency, in their steady shear flow limits, against these normal stress difference power series expansions. For instance, for large-amplitude oscillatory shear flow, we must recover the power series expansions in the limits of low frequency. In this work, for (ck, dk), we arrive at the exact expressions for the first 18 of these coefficients.

Categories: Latest papers in fluid mechanics

### Effect of pressure-dilatation on energy spectrum evolution in compressible turbulence

Physics of Fluids, Volume 31, Issue 5, May 2019.

The effect of internal-kinetic energy exchange on transient spectral energy transfer in compressible turbulence is investigated. We derive the spectral evolution equations for kinetic energy and pressure fields to highlight the key mechanisms that affect the turbulence spectral evolution. Direct numerical simulations of decaying isotropic turbulence are performed from solenoidal, dilatational, and mixed velocity initial conditions. It is shown that internal-kinetic energy exchange arising due to pressure-dilatation renders the dilatational kinetic energy amplitudes at large scales of motion to be oscillatory. The oscillatory behavior of amplitude diminishes with increasing wavenumber. The dilatational energy spectrum also exhibits a wider range of scales due to its inherent tendency to form shocks. The findings are expected to lead to an improved understanding of energy dynamics in high-speed compressible flows.

The effect of internal-kinetic energy exchange on transient spectral energy transfer in compressible turbulence is investigated. We derive the spectral evolution equations for kinetic energy and pressure fields to highlight the key mechanisms that affect the turbulence spectral evolution. Direct numerical simulations of decaying isotropic turbulence are performed from solenoidal, dilatational, and mixed velocity initial conditions. It is shown that internal-kinetic energy exchange arising due to pressure-dilatation renders the dilatational kinetic energy amplitudes at large scales of motion to be oscillatory. The oscillatory behavior of amplitude diminishes with increasing wavenumber. The dilatational energy spectrum also exhibits a wider range of scales due to its inherent tendency to form shocks. The findings are expected to lead to an improved understanding of energy dynamics in high-speed compressible flows.

Categories: Latest papers in fluid mechanics

### Empirical scaling analysis of supersonic jet control using steady fluidic injection

Physics of Fluids, Volume 31, Issue 5, May 2019.

Following our previous work [Kumar et al., “Fluidic injectors for supersonic jet control,” Phys. Fluids 30(12), 126101 (2018)], we experimentally investigate the effect of fluidic injection on the mixing enhancement of a Mach 2.0 jet. The mass flow rate ratio Cm of the injectors to that of the main jet and the expansion ratio pe/pa (where pe and pa are the nozzle exit and atmospheric pressures, respectively) to understand the mixing capability at design and off-design conditions are examined in detail. Extensive Pitot pressure measurements are performed along the jet centerline, and the jet stream has been visualized using the shadowgraph technique in the orthogonal planes of the manipulated jet. The mixing capability of the manipulated jet quantified based on the reduction in supersonic core length [math] exhibits a strong dependence on Cm and pe/pa. Empirical scaling analysis of the jet control reveals that the relationship [math] = f1(Cm, pe, pa, D, d) may be reduced to [math] = f2(ξ), where f1 and f2 are different functions and the scaling factor ξ = [math], where MR is the momentum ratio of the injector to the main jet, D and d are the nozzle exit diameter and the injector exit diameter, respectively. The scaling parameter [math] = f2(ξ) provides important insights into the jet control physics.

Following our previous work [Kumar et al., “Fluidic injectors for supersonic jet control,” Phys. Fluids 30(12), 126101 (2018)], we experimentally investigate the effect of fluidic injection on the mixing enhancement of a Mach 2.0 jet. The mass flow rate ratio Cm of the injectors to that of the main jet and the expansion ratio pe/pa (where pe and pa are the nozzle exit and atmospheric pressures, respectively) to understand the mixing capability at design and off-design conditions are examined in detail. Extensive Pitot pressure measurements are performed along the jet centerline, and the jet stream has been visualized using the shadowgraph technique in the orthogonal planes of the manipulated jet. The mixing capability of the manipulated jet quantified based on the reduction in supersonic core length [math] exhibits a strong dependence on Cm and pe/pa. Empirical scaling analysis of the jet control reveals that the relationship [math] = f1(Cm, pe, pa, D, d) may be reduced to [math] = f2(ξ), where f1 and f2 are different functions and the scaling factor ξ = [math], where MR is the momentum ratio of the injector to the main jet, D and d are the nozzle exit diameter and the injector exit diameter, respectively. The scaling parameter [math] = f2(ξ) provides important insights into the jet control physics.

Categories: Latest papers in fluid mechanics

### Retarded hydrodynamic interaction between two spheres immersed in a viscous incompressible fluid

Physics of Fluids, Volume 31, Issue 5, May 2019.

Retarded or frequency-dependent hydrodynamic interactions are relevant for velocity relaxation of colloidal particles immersed in a fluid, sufficiently close that their flow patterns interfere. The interactions are also important for periodic motions, such as occur in swimming. Analytic expressions are derived for the set of scalar mobility functions of a pair of spheres. Mutual hydrodynamic interactions are evaluated in one-propagator approximation, characterized by a single Green function acting between the two spheres. Self-mobility functions are evaluated in a two-propagator approximation, characterized by a single reflection between the two spheres. The approximations should yield accurate results for intermediate and long distances between the spheres. Both translations and rotations are considered. For motions perpendicular to the line of centers, there is a translation-rotation coupling. Extensive use is made of Faxén theorems, which yield the hydrodynamic force and torque acting on a sphere in an incident oscillating flow. The derived results are important for the study of velocity relaxation of two interacting spheres immersed in a fluid and for the study of swimming of assemblies of spheres.

Retarded or frequency-dependent hydrodynamic interactions are relevant for velocity relaxation of colloidal particles immersed in a fluid, sufficiently close that their flow patterns interfere. The interactions are also important for periodic motions, such as occur in swimming. Analytic expressions are derived for the set of scalar mobility functions of a pair of spheres. Mutual hydrodynamic interactions are evaluated in one-propagator approximation, characterized by a single Green function acting between the two spheres. Self-mobility functions are evaluated in a two-propagator approximation, characterized by a single reflection between the two spheres. The approximations should yield accurate results for intermediate and long distances between the spheres. Both translations and rotations are considered. For motions perpendicular to the line of centers, there is a translation-rotation coupling. Extensive use is made of Faxén theorems, which yield the hydrodynamic force and torque acting on a sphere in an incident oscillating flow. The derived results are important for the study of velocity relaxation of two interacting spheres immersed in a fluid and for the study of swimming of assemblies of spheres.

Categories: Latest papers in fluid mechanics

### The influence of dipolar particle interactions on the magnetization and the rotational viscosity of ferrofluids

Physics of Fluids, Volume 31, Issue 5, May 2019.

The effect of the dipolar particle interactions on the behavior of ferrofluids under a shear flow is not yet well understood. The equilibrium magnetization in the absence of flow is studied in Paper I [A. P. Rosa, G. C. Abade, and F. R. Cunha, “Computer simulation of equilibrium magnetization and microstructure in magnetic fluids,” Phys. Fluids 29(9), 092006 (2017)]. In this paper, we present the results of magnetization and rheology in terms of a rotational viscosity obtained by applying Brownian dynamics simulations for a periodic magnetic suspension, where the many body long-range dipole-dipole interactions are calculated by the Ewald summation technique. The dependence of these macroscopic properties on the dipolar interactions is explored in ferrofluids undergoing both weak and strong shear flows in the presence of a uniform magnetic field. Through the simulations, the suspension microstructure is also analyzed in order to characterize the interplay between the structure and the investigated macroscopic properties. We show that for weak shear flows the dipole-dipole interactions produces a magnetization increasing. In contrast, a decrease in the ferrofluid magnetization with the shear rate is substantially intensified as the dipolar interactions are accounted for. Therefore, for strong shear flows, the dipolar interactions always have an effect of decreasing magnetization. In addition, while the dipolar particle interactions produce an increase in the rotational viscosity for weak flows, variations in the same property are not perceptible under the condition of strong flows. The numerical simulations show chain-structure formation oriented in the direction of the magnetic field (i.e., perpendicular to the direction of the shear) for weak flows, which explains the remarkable increasing of the suspension rotational viscosity as a function of the applied magnetic field and of the dipolar interactions parameters. A detailed comparison shows that our simulation results of magnetization and the rotational viscosity are in excellent agreement with approximate theoretical predictions reported in the literature for the case of noninteracting particles.

The effect of the dipolar particle interactions on the behavior of ferrofluids under a shear flow is not yet well understood. The equilibrium magnetization in the absence of flow is studied in Paper I [A. P. Rosa, G. C. Abade, and F. R. Cunha, “Computer simulation of equilibrium magnetization and microstructure in magnetic fluids,” Phys. Fluids 29(9), 092006 (2017)]. In this paper, we present the results of magnetization and rheology in terms of a rotational viscosity obtained by applying Brownian dynamics simulations for a periodic magnetic suspension, where the many body long-range dipole-dipole interactions are calculated by the Ewald summation technique. The dependence of these macroscopic properties on the dipolar interactions is explored in ferrofluids undergoing both weak and strong shear flows in the presence of a uniform magnetic field. Through the simulations, the suspension microstructure is also analyzed in order to characterize the interplay between the structure and the investigated macroscopic properties. We show that for weak shear flows the dipole-dipole interactions produces a magnetization increasing. In contrast, a decrease in the ferrofluid magnetization with the shear rate is substantially intensified as the dipolar interactions are accounted for. Therefore, for strong shear flows, the dipolar interactions always have an effect of decreasing magnetization. In addition, while the dipolar particle interactions produce an increase in the rotational viscosity for weak flows, variations in the same property are not perceptible under the condition of strong flows. The numerical simulations show chain-structure formation oriented in the direction of the magnetic field (i.e., perpendicular to the direction of the shear) for weak flows, which explains the remarkable increasing of the suspension rotational viscosity as a function of the applied magnetic field and of the dipolar interactions parameters. A detailed comparison shows that our simulation results of magnetization and the rotational viscosity are in excellent agreement with approximate theoretical predictions reported in the literature for the case of noninteracting particles.

Categories: Latest papers in fluid mechanics

### Taylor-Couette flow of shear-thinning fluids

Physics of Fluids, Volume 31, Issue 5, May 2019.

The flow between two concentric cylinders, one of which is rotating (Taylor-Couette flow), has been the focus of extensive research, due to the number of flow instabilities that may occur and its use in various industrial applications. We examine Taylor-Couette flow of Newtonian and shear-thinning fluids (solutions of xanthan gum in water/glycerol) using a combination of particle-image velocimetry and flow visualization for a wide range of Reynolds number, spanning the circular Couette flow, Taylor vortex flow, and wavy vortex flow regimes. Shear thinning is associated with an increase in the axial wavelength and has a nonmonotonic effect on the critical Reynolds number for transition to Taylor vortex flow and wavy vortex flow. The magnitude of vorticity and the strength of the radial jets transporting fluid away from the inner cylinder (“outward jets”) are both reduced in shear-thinning fluids relative to the Newtonian case; the vorticity in the shear-thinning fluids also tends to concentrate at the edges of vortices, rather than in the cores. In the wavy vortex flow regime for Newtonian fluids, the amplitudes of the waves at the “inward jets” (moving toward the inner cylinder) are low compared to those at the outward jets. However, for the shear-thinning fluids, the amplitudes of the waves at both the inward and outward jets tend to be significantly larger. Finally, shear thinning is associated with greater variations in time and space: we observe slow drifts in the axial positions of vortices and spatial variations in the amplitudes of the wavy instability, which are absent in Newtonian fluids.

The flow between two concentric cylinders, one of which is rotating (Taylor-Couette flow), has been the focus of extensive research, due to the number of flow instabilities that may occur and its use in various industrial applications. We examine Taylor-Couette flow of Newtonian and shear-thinning fluids (solutions of xanthan gum in water/glycerol) using a combination of particle-image velocimetry and flow visualization for a wide range of Reynolds number, spanning the circular Couette flow, Taylor vortex flow, and wavy vortex flow regimes. Shear thinning is associated with an increase in the axial wavelength and has a nonmonotonic effect on the critical Reynolds number for transition to Taylor vortex flow and wavy vortex flow. The magnitude of vorticity and the strength of the radial jets transporting fluid away from the inner cylinder (“outward jets”) are both reduced in shear-thinning fluids relative to the Newtonian case; the vorticity in the shear-thinning fluids also tends to concentrate at the edges of vortices, rather than in the cores. In the wavy vortex flow regime for Newtonian fluids, the amplitudes of the waves at the “inward jets” (moving toward the inner cylinder) are low compared to those at the outward jets. However, for the shear-thinning fluids, the amplitudes of the waves at both the inward and outward jets tend to be significantly larger. Finally, shear thinning is associated with greater variations in time and space: we observe slow drifts in the axial positions of vortices and spatial variations in the amplitudes of the wavy instability, which are absent in Newtonian fluids.

Categories: Latest papers in fluid mechanics

### Ceiling effects on the aerodynamics of a flapping wing at hovering condition

Physics of Fluids, Volume 31, Issue 5, May 2019.

The ceiling effect on the aerodynamics of a hovering flapping wing is investigated by solving the three-dimensional incompressible Navier-Stokes equations. Computations have been carried out for some parameters including the distance between the wing and the ceiling, the Reynolds number, the stroke amplitude, and the mid-stroke angle of incidence. The ceiling effect on the force production and vortical structures around the wing is analyzed. It is shown that the ceiling effect increases the aerodynamic forces. This improvement in force production in the ceiling effect is caused by the increments both in the relative velocity of oncoming flow and the effective angle of attack of the wing. The underlying mechanism is that the presence of the ceiling acts as a mirror as if there exists a mirroring leading-edge vortex (LEV). This mirroring LEV not only increases the relative velocity of the oncoming flow ahead of the wing but also produces an upwash to the oncoming flow, hence increasing the effective angle of attack of the wing.

The ceiling effect on the aerodynamics of a hovering flapping wing is investigated by solving the three-dimensional incompressible Navier-Stokes equations. Computations have been carried out for some parameters including the distance between the wing and the ceiling, the Reynolds number, the stroke amplitude, and the mid-stroke angle of incidence. The ceiling effect on the force production and vortical structures around the wing is analyzed. It is shown that the ceiling effect increases the aerodynamic forces. This improvement in force production in the ceiling effect is caused by the increments both in the relative velocity of oncoming flow and the effective angle of attack of the wing. The underlying mechanism is that the presence of the ceiling acts as a mirror as if there exists a mirroring leading-edge vortex (LEV). This mirroring LEV not only increases the relative velocity of the oncoming flow ahead of the wing but also produces an upwash to the oncoming flow, hence increasing the effective angle of attack of the wing.

Categories: Latest papers in fluid mechanics

### On the role of vortical structures in aerodynamic performance of a hovering mosquito

Physics of Fluids, Volume 31, Issue 5, May 2019.

Mosquitoes have slimmer wings, higher flapping frequencies, and much lower amplitudes than most other insects. These unique features signify special aerodynamic mechanisms. Besides the leading-edge vortex, which is one of the most common mechanisms of flapping-wing flight, mosquitoes have two distinctive mechanisms: trailing-edge vortex and rotational drag. In this study, the three-dimensional flow field around a hovering mosquito is simulated by using the immersed boundary method. The numerical results agree well with previous experimental data. Mechanisms unique to mosquitoes are identified from the instantaneous pressure and vorticity fields. The flow domains, containing several vortical structures produced by the flapping wings, are divided into different regions for quantitatively analyzing the contribution of vortical structures to the lift. Advection of the trailing-edge vortex and production of the leading-edge vortex each contribute peaks in lift. Passive deformation of the wings is also important, as it stabilizes delayed stall and decreases by 26% the maximum aerodynamic power required for hovering flight. In addition, the lift coefficient and power economy are improved as the Reynolds number increases, which explains the better ability of larger mosquitoes to seek and feed on hosts from the aerodynamic point of view.

Mosquitoes have slimmer wings, higher flapping frequencies, and much lower amplitudes than most other insects. These unique features signify special aerodynamic mechanisms. Besides the leading-edge vortex, which is one of the most common mechanisms of flapping-wing flight, mosquitoes have two distinctive mechanisms: trailing-edge vortex and rotational drag. In this study, the three-dimensional flow field around a hovering mosquito is simulated by using the immersed boundary method. The numerical results agree well with previous experimental data. Mechanisms unique to mosquitoes are identified from the instantaneous pressure and vorticity fields. The flow domains, containing several vortical structures produced by the flapping wings, are divided into different regions for quantitatively analyzing the contribution of vortical structures to the lift. Advection of the trailing-edge vortex and production of the leading-edge vortex each contribute peaks in lift. Passive deformation of the wings is also important, as it stabilizes delayed stall and decreases by 26% the maximum aerodynamic power required for hovering flight. In addition, the lift coefficient and power economy are improved as the Reynolds number increases, which explains the better ability of larger mosquitoes to seek and feed on hosts from the aerodynamic point of view.

Categories: Latest papers in fluid mechanics

### Numerical simulation of the interaction of two shear layers in double backward-facing steps

Physics of Fluids, Volume 31, Issue 5, May 2019.

In this paper, Navier-Stokes equations were solved with high-order accurate schemes to investigate the basic structure and regularity of the flow field during the interaction of a supersonic jet and a codirectional supersonic incoming flow. A double backward-facing step model was proposed to investigate the interaction between the jet/supersonic incoming flow shear layers. The two shear layers interact to produce a secondary jet. The secondary jet produced by the action has a unique periodicity that is related to the overall oscillation of the shear layer. The secondary jet is generated when the horizontal angle of the jet shear layer reaches a certain value. This paper focused on the analysis and discussion of the periodicity of the secondary jet. When the aspect ratio is different, the period of the secondary jet changes significantly. However, when the static pressure ratio is different, the period of the secondary jet does not change much.

In this paper, Navier-Stokes equations were solved with high-order accurate schemes to investigate the basic structure and regularity of the flow field during the interaction of a supersonic jet and a codirectional supersonic incoming flow. A double backward-facing step model was proposed to investigate the interaction between the jet/supersonic incoming flow shear layers. The two shear layers interact to produce a secondary jet. The secondary jet produced by the action has a unique periodicity that is related to the overall oscillation of the shear layer. The secondary jet is generated when the horizontal angle of the jet shear layer reaches a certain value. This paper focused on the analysis and discussion of the periodicity of the secondary jet. When the aspect ratio is different, the period of the secondary jet changes significantly. However, when the static pressure ratio is different, the period of the secondary jet does not change much.

Categories: Latest papers in fluid mechanics