# 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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### Droplet impact induced large deflection of a cantilever

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

The phenomenon of a droplet impacting on an elastic solid surface exists in wide and versatile natural and industrial areas, which is involved with the interplay between elasticity and droplet dynamics. In the present work, we have made a comprehensive study on the process of a droplet impacting on a cantilever resulting in large deformation. The morphology of the droplet is observed, and the maximum deflection of the cantilever with respect to the initial velocity, apparent contact angle, and surface tension of the droplet is calculated by the developed theoretical model, which matches the experimental results very well. These findings may aid to engineer new energy harvesting devices and microsensors, and are also promising for many agricultural and industrial applications.

The phenomenon of a droplet impacting on an elastic solid surface exists in wide and versatile natural and industrial areas, which is involved with the interplay between elasticity and droplet dynamics. In the present work, we have made a comprehensive study on the process of a droplet impacting on a cantilever resulting in large deformation. The morphology of the droplet is observed, and the maximum deflection of the cantilever with respect to the initial velocity, apparent contact angle, and surface tension of the droplet is calculated by the developed theoretical model, which matches the experimental results very well. These findings may aid to engineer new energy harvesting devices and microsensors, and are also promising for many agricultural and industrial applications.

Categories: Latest papers in fluid mechanics

### On the basic concepts of the direct simulation Monte Carlo method

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

In this paper, the basic ideas underlying the Direct Simulation Monte Carlo (DSMC) method are examined and a novel nonhomogeneous N-particle kinetic equation describing the randomized mathematical model of DSMC is derived. It is shown that different collision-partner selection schemes, including No-Time-Counter (NTC) and Bernoulli-trials schemes, are approximations of the general transition operator of the randomized model. The popular collision-partner selection schemes, represented by the standard NTC and Bernoulli-trials approximations of the general transition operator, represented by Simplified Bernoulli-trials and Generalized Bernoulli-trials schemes, are tested on the one-dimensional rarefied gas heat transfer problem against conditions of two approximation limits: first, leading to the Boltzmann equation and, second, leading to the novel N-particle kinetic one.

In this paper, the basic ideas underlying the Direct Simulation Monte Carlo (DSMC) method are examined and a novel nonhomogeneous N-particle kinetic equation describing the randomized mathematical model of DSMC is derived. It is shown that different collision-partner selection schemes, including No-Time-Counter (NTC) and Bernoulli-trials schemes, are approximations of the general transition operator of the randomized model. The popular collision-partner selection schemes, represented by the standard NTC and Bernoulli-trials approximations of the general transition operator, represented by Simplified Bernoulli-trials and Generalized Bernoulli-trials schemes, are tested on the one-dimensional rarefied gas heat transfer problem against conditions of two approximation limits: first, leading to the Boltzmann equation and, second, leading to the novel N-particle kinetic one.

Categories: Latest papers in fluid mechanics

### Effect of particle size ratio on shear-induced onset of particle motion at low particle Reynolds numbers: From high shielding to roughness

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

We study incipient motion of single beads on regular substrates made of spherical particles of a different size in steady shear flow at small particle Reynolds numbers. We cover a large range of sizes: from small beads that are highly shielded from the shear flow by the substrate spheres, and hence, are susceptible to the flow through the interstices of the substrate, to beads fully exposed to the flow, where the substrate rather acts like roughness of an otherwise flat surface. Numerical and experimental studies agree within measurement uncertainty. To describe the findings, we extend a recently derived model for particles of equal size which was validated over a wide range of substrates [Agudo et al., “Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers,” J. Fluid Mech. 825, 284–314 (2017)]. The extended model covers the entire spectrum of size ratios, where the critical Shields number varies from about zero to infinity. The model properly describes the numerical and experimental data. For well exposed beads, we find a scaling law between the critical Shields number and the size ratio between mobile bead and substrate spheres with an exponent of −1.

We study incipient motion of single beads on regular substrates made of spherical particles of a different size in steady shear flow at small particle Reynolds numbers. We cover a large range of sizes: from small beads that are highly shielded from the shear flow by the substrate spheres, and hence, are susceptible to the flow through the interstices of the substrate, to beads fully exposed to the flow, where the substrate rather acts like roughness of an otherwise flat surface. Numerical and experimental studies agree within measurement uncertainty. To describe the findings, we extend a recently derived model for particles of equal size which was validated over a wide range of substrates [Agudo et al., “Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers,” J. Fluid Mech. 825, 284–314 (2017)]. The extended model covers the entire spectrum of size ratios, where the critical Shields number varies from about zero to infinity. The model properly describes the numerical and experimental data. For well exposed beads, we find a scaling law between the critical Shields number and the size ratio between mobile bead and substrate spheres with an exponent of −1.

Categories: Latest papers in fluid mechanics

### Experimental and theoretical study of swept-wing boundary-layer instabilities. Unsteady crossflow instability

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

Extensive combined experimental and theoretical investigations of the linear evolution of unsteady (in general) Cross-Flow (CF) and three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. CF-instability characteristics are investigated in detail at an angle of attack of −5° when this kind of instability dominates in the laminar-turbulent transition process, while the 3D TS-instability characteristics are studied at an angle of attack of +1.5° when this kind of instability is predominant in the transition process. All experimental results are deeply processed and compared with results of calculations based on several theoretical approaches. For the first time, very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved both for unsteady CF- and 3D TS-instability modes for the case of a boundary layer developing on a real swept airfoil. The first part of the present study (this paper) is devoted to the description of the case of CF-dominated transition, while the TS-dominated case will be described in detail in a subsequent second part of this investigation.

Extensive combined experimental and theoretical investigations of the linear evolution of unsteady (in general) Cross-Flow (CF) and three-dimensional (3D) Tollmien-Schlichting (TS) instability modes of 3D boundary layers developing on a swept airfoil section have been carried out. CF-instability characteristics are investigated in detail at an angle of attack of −5° when this kind of instability dominates in the laminar-turbulent transition process, while the 3D TS-instability characteristics are studied at an angle of attack of +1.5° when this kind of instability is predominant in the transition process. All experimental results are deeply processed and compared with results of calculations based on several theoretical approaches. For the first time, very good quantitative agreement of all measured and calculated stability characteristics of swept-wing boundary layers is achieved both for unsteady CF- and 3D TS-instability modes for the case of a boundary layer developing on a real swept airfoil. The first part of the present study (this paper) is devoted to the description of the case of CF-dominated transition, while the TS-dominated case will be described in detail in a subsequent second part of this investigation.

Categories: Latest papers in fluid mechanics

### Control effect of micro vortex generators on attached cavitation instability

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

The control effect of micro-vortex generators (VGs) on the instability of attached cavitation was investigated in a series of experiments. The micro-VGs, located at the leading edge of a NACA0015 hydrofoil, were used to alter the near-wall flow and control the attached cavitation dynamics. The effect of the nondimensional height of micro-VGs on the nondimensional cavity length was quantitatively evaluated by regression equations through response surface methodology. The micro-VGs increased the nondimensional cavity length. The counter-rotating streamwise vortices induced by micro-VGs had a rectifying effect on the near-wall flow and withstood the flow disturbance in the spanwise direction. Additionally, the micro-VGs partially suppressed Rayleigh–Taylor instability and Kelvin–Helmholtz instability arising from reverse flow underneath the cavity. Under a partial cavity oscillation (PCO) condition, the growth of sheet cavitation was highly two-dimensional in the spanwise direction, and the cloud cavity shedding had a strict periodicity with a smaller Strouhal number (St) than for the smooth hydrofoil. The shedding cloud cavity was captured in a single spanwise vortex core, which was advected toward the trailing edge of the hydrofoil. The transition from PCO to transitional cavity oscillation (TCO) occurred when the cavity length was larger than 0.8 of chord length. Under the TCO condition, the concave cavity closure line of sheet cavitation on the hydrofoil showed perfect symmetry and the St was nearly constant. As a result of our investigation, the micro-VGs have high potential to manipulate and control the attached cavitation dynamics.

The control effect of micro-vortex generators (VGs) on the instability of attached cavitation was investigated in a series of experiments. The micro-VGs, located at the leading edge of a NACA0015 hydrofoil, were used to alter the near-wall flow and control the attached cavitation dynamics. The effect of the nondimensional height of micro-VGs on the nondimensional cavity length was quantitatively evaluated by regression equations through response surface methodology. The micro-VGs increased the nondimensional cavity length. The counter-rotating streamwise vortices induced by micro-VGs had a rectifying effect on the near-wall flow and withstood the flow disturbance in the spanwise direction. Additionally, the micro-VGs partially suppressed Rayleigh–Taylor instability and Kelvin–Helmholtz instability arising from reverse flow underneath the cavity. Under a partial cavity oscillation (PCO) condition, the growth of sheet cavitation was highly two-dimensional in the spanwise direction, and the cloud cavity shedding had a strict periodicity with a smaller Strouhal number (St) than for the smooth hydrofoil. The shedding cloud cavity was captured in a single spanwise vortex core, which was advected toward the trailing edge of the hydrofoil. The transition from PCO to transitional cavity oscillation (TCO) occurred when the cavity length was larger than 0.8 of chord length. Under the TCO condition, the concave cavity closure line of sheet cavitation on the hydrofoil showed perfect symmetry and the St was nearly constant. As a result of our investigation, the micro-VGs have high potential to manipulate and control the attached cavitation dynamics.

Categories: Latest papers in fluid mechanics

### Modeling of mass transfer enhancement in a magnetofluidic micromixer

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

The use of magnetism for various microfluidic functions such as separation, mixing, and pumping has been attracting great interest from the research community as this concept is simple, effective, and of low cost. Magnetic control avoids common problems of active microfluidic manipulation such as heat, surface charge, and high ionic concentration. The majority of past works on micromagnetofluidic devices were experimental, and a comprehensive numerical model to simulate the fundamental transport phenomena in these devices is still lacking. The present study aims to develop a numerical model to simulate transport phenomena in microfluidic devices with ferrofluid and fluorescent dye induced by a nonuniform magnetic field. The numerical results were validated by experimental data from our previous work, indicating a significant increase in mass transfer. The model shows a reasonable agreement with experimental data for the concentration distribution of both magnetic and nonmagnetic species. Magnetoconvective secondary flow enhances the transport of nonmagnetic fluorescent dye. A subsequent parametric analysis investigated the effect of the magnetic field strength and nanoparticle size on the mass transfer process. Mass transport of the fluorescent dye is enhanced with increasing field strength and size of magnetic particles.

The use of magnetism for various microfluidic functions such as separation, mixing, and pumping has been attracting great interest from the research community as this concept is simple, effective, and of low cost. Magnetic control avoids common problems of active microfluidic manipulation such as heat, surface charge, and high ionic concentration. The majority of past works on micromagnetofluidic devices were experimental, and a comprehensive numerical model to simulate the fundamental transport phenomena in these devices is still lacking. The present study aims to develop a numerical model to simulate transport phenomena in microfluidic devices with ferrofluid and fluorescent dye induced by a nonuniform magnetic field. The numerical results were validated by experimental data from our previous work, indicating a significant increase in mass transfer. The model shows a reasonable agreement with experimental data for the concentration distribution of both magnetic and nonmagnetic species. Magnetoconvective secondary flow enhances the transport of nonmagnetic fluorescent dye. A subsequent parametric analysis investigated the effect of the magnetic field strength and nanoparticle size on the mass transfer process. Mass transport of the fluorescent dye is enhanced with increasing field strength and size of magnetic particles.

Categories: Latest papers in fluid mechanics

### Improved theoretical model of two-dimensional flow field in a severely narrow circular pipe

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

Based on the two-dimensional theory of a Newtonian incompressible fluid, an improved model is proposed by combining Reynolds stresses of new disturbance factors and velocity polynomials. It is used to solve the Reynolds averaged Navier-Stokes equation for flow through a severely narrow pipe at the continuous change of the Reynolds number from laminar flow to turbulence. Both axial and radial velocity polynomials are considered in the momentum integral method. Under boundary and symmetry conditions, a first-order differential equation for a coefficient of the axial velocity with the disturbance factors is derived. Using a numerical shooting method to solve the equation, the axial distributions of pressure are obtained in the range of Reynolds numbers from 20 to 105 when the degree of stenosis equals 0.4 or 0.9. Also, under a lower Reynolds number, the velocity profiles in axial and radial directions, the streamlines at downstream and the wall shear stresses (WSS) in narrow regions are illustrated. The disturbance factors introduced can sensitively regulate the variation of inertia, pressure gradient, and viscosity term in the Reynolds averaged Navier-Stokes equation. With an increase in the Reynolds number and the parameters from 0.02 to 20 in the disturbance factors, the axial and radial velocities reverse at some narrow regions gradually, the WSS falls to below zero downstream, and the pressure drop increases in the narrow section of the pipe. It is implied that the pressure drop plays an important role in artery collapse when it is less than 40% stenosis. When the percentage of stenosis is increased to more than 40% and the Reynolds number is only 200, WSS gradually exceeds the tolerance of endothelial cells in blood vessels. The increase in pressure drop at downstream and WSS at upstream leads to the aggravation of vascular stenosis and exfoliation of the atherosclerotic plaque.

Based on the two-dimensional theory of a Newtonian incompressible fluid, an improved model is proposed by combining Reynolds stresses of new disturbance factors and velocity polynomials. It is used to solve the Reynolds averaged Navier-Stokes equation for flow through a severely narrow pipe at the continuous change of the Reynolds number from laminar flow to turbulence. Both axial and radial velocity polynomials are considered in the momentum integral method. Under boundary and symmetry conditions, a first-order differential equation for a coefficient of the axial velocity with the disturbance factors is derived. Using a numerical shooting method to solve the equation, the axial distributions of pressure are obtained in the range of Reynolds numbers from 20 to 105 when the degree of stenosis equals 0.4 or 0.9. Also, under a lower Reynolds number, the velocity profiles in axial and radial directions, the streamlines at downstream and the wall shear stresses (WSS) in narrow regions are illustrated. The disturbance factors introduced can sensitively regulate the variation of inertia, pressure gradient, and viscosity term in the Reynolds averaged Navier-Stokes equation. With an increase in the Reynolds number and the parameters from 0.02 to 20 in the disturbance factors, the axial and radial velocities reverse at some narrow regions gradually, the WSS falls to below zero downstream, and the pressure drop increases in the narrow section of the pipe. It is implied that the pressure drop plays an important role in artery collapse when it is less than 40% stenosis. When the percentage of stenosis is increased to more than 40% and the Reynolds number is only 200, WSS gradually exceeds the tolerance of endothelial cells in blood vessels. The increase in pressure drop at downstream and WSS at upstream leads to the aggravation of vascular stenosis and exfoliation of the atherosclerotic plaque.

Categories: Latest papers in fluid mechanics

### Boundary slip phenomena in multicomponent gas mixtures

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

The slip phenomena in multicomponent gas mixtures are studied. The moment equations, derived from the linearized Boltzmann equation by using the 13-moment approximation of the Grad’s method, are used to obtain the full (containing the contribution from the Knudsen layer) and asymptotic (valid far from the plane physical boundary of the domain) expressions for the nonequilibrium macroscopic parameters of the mixture species. The latter relations are employed to deduce the expressions for the mixture slip velocity and the viscous, thermal, and diffusion slip coefficients by using the modified Maxwell method and the diffuse-specular model of molecule scattering on the wall. The derived relations for the slip coefficients are given in the convenient form expressed in terms of basic transport coefficients, such as partial viscosity and thermal conductivity coefficients, diffusion and thermal diffusion coefficients, and coefficients of molecule momentum accommodation at the wall. The expressions found are used to calculate the slip coefficients for binary (He-Ar) and ternary (He-Ar-Xe) gas mixtures. The numerical results are in good agreement with the data calculated by using other methods.

The slip phenomena in multicomponent gas mixtures are studied. The moment equations, derived from the linearized Boltzmann equation by using the 13-moment approximation of the Grad’s method, are used to obtain the full (containing the contribution from the Knudsen layer) and asymptotic (valid far from the plane physical boundary of the domain) expressions for the nonequilibrium macroscopic parameters of the mixture species. The latter relations are employed to deduce the expressions for the mixture slip velocity and the viscous, thermal, and diffusion slip coefficients by using the modified Maxwell method and the diffuse-specular model of molecule scattering on the wall. The derived relations for the slip coefficients are given in the convenient form expressed in terms of basic transport coefficients, such as partial viscosity and thermal conductivity coefficients, diffusion and thermal diffusion coefficients, and coefficients of molecule momentum accommodation at the wall. The expressions found are used to calculate the slip coefficients for binary (He-Ar) and ternary (He-Ar-Xe) gas mixtures. The numerical results are in good agreement with the data calculated by using other methods.

Categories: Latest papers in fluid mechanics

### Startup steady shear flow from the Oldroyd 8-constant framework

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

One good way to explore fluid microstructure, experimentally, is to suddenly subject the fluid to a large steady shearing deformation and to then observe the evolving stress response. If the steady shear rate is high enough, the shear stress and also the normal stress differences can overshoot, and then they can even undershoot. We call such responses nonlinear and this experiment shear stress growth. This paper is devoted to providing exact analytical solutions for interpreting measured nonlinear shear stress growth responses. Specifically, we arrive at the exact solutions for the Oldroyd 8-constant constitutive framework. We test our exact solution against the measured behaviors of two wormlike micellar solutions. At high shear rates, these solutions overshoot in stress growth without subsequent undershoot. The micellar solutions present linear behavior at low shear rates; otherwise, their behavior is nonlinear. Our framework provides slightly early underpredictions of the overshoots at high shear rates. The effect of salt concentration on the nonlinear parameters is explored.

One good way to explore fluid microstructure, experimentally, is to suddenly subject the fluid to a large steady shearing deformation and to then observe the evolving stress response. If the steady shear rate is high enough, the shear stress and also the normal stress differences can overshoot, and then they can even undershoot. We call such responses nonlinear and this experiment shear stress growth. This paper is devoted to providing exact analytical solutions for interpreting measured nonlinear shear stress growth responses. Specifically, we arrive at the exact solutions for the Oldroyd 8-constant constitutive framework. We test our exact solution against the measured behaviors of two wormlike micellar solutions. At high shear rates, these solutions overshoot in stress growth without subsequent undershoot. The micellar solutions present linear behavior at low shear rates; otherwise, their behavior is nonlinear. Our framework provides slightly early underpredictions of the overshoots at high shear rates. The effect of salt concentration on the nonlinear parameters is explored.

Categories: Latest papers in fluid mechanics

### On the concept and theory of induced drag for viscous and incompressible steady flow

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

For steady flow, one usually decomposes the total drag into different components by wake-plane integrals and seeks their reduction strategies separately. Unlike the body-surface stress integral, the induced drag as well as the profile drag has been found to depend on the streamwise location of the wake plane used for drag estimate. It gradually diminishes as the wake plane moves downstream, which was often attributed to numerical dissipation. In this paper, we present an exact general force-breakdown theory and its numerical demonstrations for viscous incompressible flow over an arbitrary aircraft to address this puzzling issue. Based on the theory, the induced and profile drags do depend inherently on the wake-plane location rather than being merely caused by numerical dissipation. The underlying mechanisms are identified in terms of the components, moments, and physical dissipation of the Lamb-vector field produced by the aircraft motion. This theoretical prediction is fully consistent with the linear far-field force theory that the induced drag finally vanishes and the profile drag increases to the total drag at an infinitely far field for viscous flow. Moreover, as a product of this exact theory, a new compact midwake approximation for the induced drag is proposed for the convenience of routine wake survey in industry. Its prediction is similar to conventional formulas for attached flow but behaves much better for separated flow.

For steady flow, one usually decomposes the total drag into different components by wake-plane integrals and seeks their reduction strategies separately. Unlike the body-surface stress integral, the induced drag as well as the profile drag has been found to depend on the streamwise location of the wake plane used for drag estimate. It gradually diminishes as the wake plane moves downstream, which was often attributed to numerical dissipation. In this paper, we present an exact general force-breakdown theory and its numerical demonstrations for viscous incompressible flow over an arbitrary aircraft to address this puzzling issue. Based on the theory, the induced and profile drags do depend inherently on the wake-plane location rather than being merely caused by numerical dissipation. The underlying mechanisms are identified in terms of the components, moments, and physical dissipation of the Lamb-vector field produced by the aircraft motion. This theoretical prediction is fully consistent with the linear far-field force theory that the induced drag finally vanishes and the profile drag increases to the total drag at an infinitely far field for viscous flow. Moreover, as a product of this exact theory, a new compact midwake approximation for the induced drag is proposed for the convenience of routine wake survey in industry. Its prediction is similar to conventional formulas for attached flow but behaves much better for separated flow.

Categories: Latest papers in fluid mechanics

### On heat transport and energy partition in thermal convection with mixed boundary conditions

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

A two-dimensional square enclosure thermally insulated on the vertical walls and heated nonuniformly on the horizontal walls is numerically studied in comparison with the classical Rayleigh-Bénard (RB) convection in the range of Rayleigh number 105 ≤ Ra ≤ 109. Two possible configurations, namely, (1) HCCH and (2) HCHC, are studied in which a unit step function describes the conduction wall temperature as a combination of hot (H) and cold (C) temperatures. The first two letters (of HCCH or HCHC) represent the applied thermal conditions on the bottom wall and the last two letters represent those on the top wall. In the mentioned configurations, the average temperature difference between the bottom and top walls is zero, yet the complex convection state is observed. The diagonally aligned large-scale elliptic roll observed in the RB convection for the Rayleigh number Ra = 108 is found to be replaced by a circular roll in HCCH and a square roll in HCHC. The mean and fluctuating temperature fields in cases of HCCH and HCHC are significantly high as compared to the RB case. We found that heat transport is higher for HCCH and HCHC as compared to the RB convection in a range of 105 ≤ Ra < 108. The increase in heat transport is due to (1) an increase in the background potential energy in the case of HCCH and (2) an increase in the available potential energy in the case of HCHC, which is confirmed by using the global energy budget.

A two-dimensional square enclosure thermally insulated on the vertical walls and heated nonuniformly on the horizontal walls is numerically studied in comparison with the classical Rayleigh-Bénard (RB) convection in the range of Rayleigh number 105 ≤ Ra ≤ 109. Two possible configurations, namely, (1) HCCH and (2) HCHC, are studied in which a unit step function describes the conduction wall temperature as a combination of hot (H) and cold (C) temperatures. The first two letters (of HCCH or HCHC) represent the applied thermal conditions on the bottom wall and the last two letters represent those on the top wall. In the mentioned configurations, the average temperature difference between the bottom and top walls is zero, yet the complex convection state is observed. The diagonally aligned large-scale elliptic roll observed in the RB convection for the Rayleigh number Ra = 108 is found to be replaced by a circular roll in HCCH and a square roll in HCHC. The mean and fluctuating temperature fields in cases of HCCH and HCHC are significantly high as compared to the RB case. We found that heat transport is higher for HCCH and HCHC as compared to the RB convection in a range of 105 ≤ Ra < 108. The increase in heat transport is due to (1) an increase in the background potential energy in the case of HCCH and (2) an increase in the available potential energy in the case of HCHC, which is confirmed by using the global energy budget.

Categories: Latest papers in fluid mechanics

### Experimental study on cavity dynamics of projectile water entry with different physical parameters

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

In this paper, we investigate the influences of nose shape, impact velocity (8–14 m/s), and impact angle (60°–90°) on cavity dynamics when a projectile enters water. The Froude number, which characters the kinetic energy against gravitational potential, ranges from 280 to 850. It is found that the cavity diameter changes for different nose shapes, and an elongated cavity is achieved as the impact speed increases. The cavity pinch-off phenomenon is characterized. Experimental data reveal that the nose shape, impact velocity, and impact angle change the pinch-off depth and pinch-off time slightly by changing the occurrence time of the surface seal. For blunt nose shapes, greater impact velocity speeds up the surface seal and then quickens the pinch-off, thus reducing both the pinch-off depth and pinch-off time. Generally, the pinch-off depth follows the Fr1/3 law in our experiments. Cavity ripples were observed after pinch-off, and the wavelength, amplitude, and rippling frequency were measured. The wavelength of a ripple remains constant throughout, and all ripples are fixed with the experimental frame. The rippling frequencies are approximately identical to the Minnaert frequency. The impact velocity significantly changes the rippling frequency by affecting the radius of the air cavity.

In this paper, we investigate the influences of nose shape, impact velocity (8–14 m/s), and impact angle (60°–90°) on cavity dynamics when a projectile enters water. The Froude number, which characters the kinetic energy against gravitational potential, ranges from 280 to 850. It is found that the cavity diameter changes for different nose shapes, and an elongated cavity is achieved as the impact speed increases. The cavity pinch-off phenomenon is characterized. Experimental data reveal that the nose shape, impact velocity, and impact angle change the pinch-off depth and pinch-off time slightly by changing the occurrence time of the surface seal. For blunt nose shapes, greater impact velocity speeds up the surface seal and then quickens the pinch-off, thus reducing both the pinch-off depth and pinch-off time. Generally, the pinch-off depth follows the Fr1/3 law in our experiments. Cavity ripples were observed after pinch-off, and the wavelength, amplitude, and rippling frequency were measured. The wavelength of a ripple remains constant throughout, and all ripples are fixed with the experimental frame. The rippling frequencies are approximately identical to the Minnaert frequency. The impact velocity significantly changes the rippling frequency by affecting the radius of the air cavity.

Categories: Latest papers in fluid mechanics

### Electric field-induced pinch-off of a compound droplet in Poiseuille flow

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

We address the pinch-off dynamics of a compound droplet that is suspended in a carrier fluid in a parallel plate microchannel. The droplet is subjected to a transverse electric field in the presence of an imposed pressure-driven flow. When a concentric compound droplet migrates in a pressure driven flow, the inner droplet deviates from the concentric position and forms an eccentric configuration that finally leads to the pinch-off of the outer shell. Our results reveal that the temporal evolution of droplet eccentricity as well as the kinetics of the thinning of the outer droplet is markedly influenced by the strength of the electric field as well as the electric properties of the fluids. We also bring out the conversion of different modes of droplet pinch-off, such as the equatorial cap breakup or the equatorial hole-puncture mode, by altering the electric field strength and electrical properties of the fluids. We also identify the relevant pointers that dictate the pinch-off time as well as the location of the pinch-off. This, in turn, opens up novel means of modulating the morphology of double emulsion in a confined channel by applying an electric field.

We address the pinch-off dynamics of a compound droplet that is suspended in a carrier fluid in a parallel plate microchannel. The droplet is subjected to a transverse electric field in the presence of an imposed pressure-driven flow. When a concentric compound droplet migrates in a pressure driven flow, the inner droplet deviates from the concentric position and forms an eccentric configuration that finally leads to the pinch-off of the outer shell. Our results reveal that the temporal evolution of droplet eccentricity as well as the kinetics of the thinning of the outer droplet is markedly influenced by the strength of the electric field as well as the electric properties of the fluids. We also bring out the conversion of different modes of droplet pinch-off, such as the equatorial cap breakup or the equatorial hole-puncture mode, by altering the electric field strength and electrical properties of the fluids. We also identify the relevant pointers that dictate the pinch-off time as well as the location of the pinch-off. This, in turn, opens up novel means of modulating the morphology of double emulsion in a confined channel by applying an electric field.

Categories: Latest papers in fluid mechanics

### Exact results on the large-scale stochastic transport of inertial particles including the Basset history term

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

The Maxey-Riley equation and its simplified versions represent the most widespread tool to investigate dynamics and dispersion of inertial small particles in turbulent flows. The numerical solution of such models is often very challenging, and some of their terms, such as the molecular diffusivity or the Basset history force, are often neglected to reduce the complexity upon suitable approximations. Here, we propose exact results with regard to the rate of transport on large time scales in random shear flows. These can be expediently used as a benchmark to develop and assess algorithms when solving this class of stochastic integrodifferential problems on large time scales.

The Maxey-Riley equation and its simplified versions represent the most widespread tool to investigate dynamics and dispersion of inertial small particles in turbulent flows. The numerical solution of such models is often very challenging, and some of their terms, such as the molecular diffusivity or the Basset history force, are often neglected to reduce the complexity upon suitable approximations. Here, we propose exact results with regard to the rate of transport on large time scales in random shear flows. These can be expediently used as a benchmark to develop and assess algorithms when solving this class of stochastic integrodifferential problems on large time scales.

Categories: Latest papers in fluid mechanics

### Direct numerical simulation of transitional and turbulent round jets: Evolution of vortical structures and turbulence budget

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

Direct numerical simulation of transitional and turbulent round jets is reported in a comparative framework. Such a comparison is central toward revealing the roles that molecular viscosity and vorticity intensification play in the evolution of jets. The initial and intermediate evolution is differentiated based on the assessment of the starting jet, roll-up frequency, dynamics of vortex rings, and emergence of the secondary instability. Long-term behavior is differentiated based on the assessment of preferred mode frequency, time averaged vortical structures, half jet-width, and volume flow rate obtained from the time-averaged velocity field. The present study demonstrates that viscous damping of cross-stream vorticity plays a key role in establishing helical instability as the dominant mode in long-term evolution of the transitional jet. On the contrary, varicose mode is dominant in the turbulent jet, despite preferred mode frequency being the same in both cases. Finally, a novel attempt is made toward comparing individual terms constituting turbulence budget between both regimes. Through such a comparison, relative dominance of various transport mechanisms governing the evolution of turbulence kinetic energy [math] is revealed. It is observed that terms accounting for a forward cascade of [math] from inertial to smallest scales are comparatively larger for the turbulent jet, while those accounting for the backscatter of [math] are comparatively larger for the transitional jet. It is also established that turbulence dissipation is evidently the same for both jets. Thus, the property of turbulence dissipation being independent of Reynolds number for turbulent jets can also be extrapolated to transitional jets.

Direct numerical simulation of transitional and turbulent round jets is reported in a comparative framework. Such a comparison is central toward revealing the roles that molecular viscosity and vorticity intensification play in the evolution of jets. The initial and intermediate evolution is differentiated based on the assessment of the starting jet, roll-up frequency, dynamics of vortex rings, and emergence of the secondary instability. Long-term behavior is differentiated based on the assessment of preferred mode frequency, time averaged vortical structures, half jet-width, and volume flow rate obtained from the time-averaged velocity field. The present study demonstrates that viscous damping of cross-stream vorticity plays a key role in establishing helical instability as the dominant mode in long-term evolution of the transitional jet. On the contrary, varicose mode is dominant in the turbulent jet, despite preferred mode frequency being the same in both cases. Finally, a novel attempt is made toward comparing individual terms constituting turbulence budget between both regimes. Through such a comparison, relative dominance of various transport mechanisms governing the evolution of turbulence kinetic energy [math] is revealed. It is observed that terms accounting for a forward cascade of [math] from inertial to smallest scales are comparatively larger for the turbulent jet, while those accounting for the backscatter of [math] are comparatively larger for the transitional jet. It is also established that turbulence dissipation is evidently the same for both jets. Thus, the property of turbulence dissipation being independent of Reynolds number for turbulent jets can also be extrapolated to transitional jets.

Categories: Latest papers in fluid mechanics

### A new additive decomposition of velocity gradient

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

To avoid the infinitesimal rotation nature of the Cauchy-Stokes decomposition of velocity gradient, the letter proposes an new additive decomposition in which one part is a SO(3) rotation tensor Q = exp W.

To avoid the infinitesimal rotation nature of the Cauchy-Stokes decomposition of velocity gradient, the letter proposes an new additive decomposition in which one part is a SO(3) rotation tensor Q = exp W.

Categories: Latest papers in fluid mechanics

### Flow pattern of double-cavity flow at high Reynolds number

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

The flow structure in a turbulent double-cavity flow has been studied experimentally and numerically. The dynamics of the two-component instantaneous velocity vector fields measured by an optical smoke image velocimetry method and calculated using the ANSYS Fluent 19.2 software has been derived. For a wide range of dynamic similarity numbers of shape factor and ReL, the flow resistance coefficients for the cavity and relative flow mass transfer with the cavities have been estimated; three characteristic flow regimes of double-cavity flow have been distinguished and described; the flow pattern map via the ReL number and shape factor has been obtained.

The flow structure in a turbulent double-cavity flow has been studied experimentally and numerically. The dynamics of the two-component instantaneous velocity vector fields measured by an optical smoke image velocimetry method and calculated using the ANSYS Fluent 19.2 software has been derived. For a wide range of dynamic similarity numbers of shape factor and ReL, the flow resistance coefficients for the cavity and relative flow mass transfer with the cavities have been estimated; three characteristic flow regimes of double-cavity flow have been distinguished and described; the flow pattern map via the ReL number and shape factor has been obtained.

Categories: Latest papers in fluid mechanics

### Large eddy simulation of hydrodynamic turbulence using renormalized viscosity

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

We employ renormalized viscosity to perform large eddy simulations (LESs) of decaying homogeneous and isotropic turbulence in a cubical domain. We perform a direct numerical simulation (DNS) on 5123 and 2563 grids and LES on 323, 643, and 1283 grids with the same initial conditions in the resolved scales for a flow with Taylor Reynolds number Reλ = 210. We observe good agreement between LES and DNS results for the temporal evolution of turbulence kinetic energy Eu(t), kinetic energy spectrum Eu(k), and kinetic energy flux Πu(k). Also, the large-scale structures of the flow in LES are similar to those in DNS. These results establish the suitability of our renormalized viscosity scheme for LES.

We employ renormalized viscosity to perform large eddy simulations (LESs) of decaying homogeneous and isotropic turbulence in a cubical domain. We perform a direct numerical simulation (DNS) on 5123 and 2563 grids and LES on 323, 643, and 1283 grids with the same initial conditions in the resolved scales for a flow with Taylor Reynolds number Reλ = 210. We observe good agreement between LES and DNS results for the temporal evolution of turbulence kinetic energy Eu(t), kinetic energy spectrum Eu(k), and kinetic energy flux Πu(k). Also, the large-scale structures of the flow in LES are similar to those in DNS. These results establish the suitability of our renormalized viscosity scheme for LES.

Categories: Latest papers in fluid mechanics

### Laminar dispersion at low and high Peclet numbers in a sinusoidal microtube: Point-size versus finite-size particles

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

This paper adopts Brenner’s homogenization theory to investigate dispersion properties, over a wide range of Peclet values, of point-size and finite-size particles in sinusoidal cylindrical microchannels in the presence of a pressure-driven Stokes flow field. The periodic alternation of entropic barriers/traps can unexpectedly increase the effective finite-size particle velocity as well as decrease the effective dispersion coefficient for both point-size and finite-size particles, for large values of the radial Peclet number. While this phenomenon has a simple explanation for tracer particles, its understanding for finite-size particles is not trivial and goes through the analysis of the localization feature of the equilibrium unit-cell particle density [math]0(x) and how this spatial nonuniformity impacts upon the effective particle velocity and on the solution of the so-called b field, controlling the large scale axial dispersion coefficient. Unfortunately, dispersion reduction cannot be exploited for the sake of the separation of particles having different radii because the separation performance of a hydrodynamic sinusoidal column turns out to be worse than that of a standard straight column for experimentally feasible Peclet values. Interesting analytical results for long-wavelength sinusoidal channels are obtained by a long-wave asymptotic expansion. Both zero-order and first-order terms for the asymptotic expansion of the [math]0(x) measure and of the b field are obtained, thus exploring a wide range of Peclet values and deriving an analytical expression for the Taylor dispersion coefficient.

This paper adopts Brenner’s homogenization theory to investigate dispersion properties, over a wide range of Peclet values, of point-size and finite-size particles in sinusoidal cylindrical microchannels in the presence of a pressure-driven Stokes flow field. The periodic alternation of entropic barriers/traps can unexpectedly increase the effective finite-size particle velocity as well as decrease the effective dispersion coefficient for both point-size and finite-size particles, for large values of the radial Peclet number. While this phenomenon has a simple explanation for tracer particles, its understanding for finite-size particles is not trivial and goes through the analysis of the localization feature of the equilibrium unit-cell particle density [math]0(x) and how this spatial nonuniformity impacts upon the effective particle velocity and on the solution of the so-called b field, controlling the large scale axial dispersion coefficient. Unfortunately, dispersion reduction cannot be exploited for the sake of the separation of particles having different radii because the separation performance of a hydrodynamic sinusoidal column turns out to be worse than that of a standard straight column for experimentally feasible Peclet values. Interesting analytical results for long-wavelength sinusoidal channels are obtained by a long-wave asymptotic expansion. Both zero-order and first-order terms for the asymptotic expansion of the [math]0(x) measure and of the b field are obtained, thus exploring a wide range of Peclet values and deriving an analytical expression for the Taylor dispersion coefficient.

Categories: Latest papers in fluid mechanics

### Constitutive theory of inhomogeneous turbulent flow based on two-scale Lagrangian formalism

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

A self-consistent closure theory is developed for inhomogeneous turbulent flow, which enables systematic derivations of the turbulence constitutive relations without relying on any empirical parameters. The double Lagrangian approach based on the mean and fluctuation velocities allows us to describe a wide variety of correlations in a consistent manner with both Kolmogorov’s inertial-range scaling and general-covariance principle.

A self-consistent closure theory is developed for inhomogeneous turbulent flow, which enables systematic derivations of the turbulence constitutive relations without relying on any empirical parameters. The double Lagrangian approach based on the mean and fluctuation velocities allows us to describe a wide variety of correlations in a consistent manner with both Kolmogorov’s inertial-range scaling and general-covariance principle.

Categories: Latest papers in fluid mechanics