# 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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### Vortex-induced vibration and galloping of a circular cylinder in presence of cross-flow thermal buoyancy

Physics of Fluids, Volume 31, Issue 11, November 2019.

The effect of cross-flow thermal buoyancy on vortex-induced vibration (VIV) of a circular cylinder is numerically investigated. An in-house fluid-structure solver based on the sharp-interface immersed boundary method is employed. The cylinder is kept in the uniform flow stream and is mounted elastically such that it is constrained to move in the transverse direction to the flow. The surface of the cylinder is heated at a prescribed temperature, and the thermal buoyancy is imposed in the transverse direction to the flow. Simulations are performed for the following parameters: Reynolds number Re = (50, 150), Prandtl number Pr = 7.1, mass ratio m = 2, reduced velocity UR = [4–15], and Richardson number Ri = [0–4]. We found that the thermal buoyancy could suppress or agitate the VIV. At lower Re (=50) and Ri = (1, 2), we observe the suppression in the VIV; however, there is no suppression for higher Re (=150) for these values of Ri. Galloping is observed for higher values of Ri = (3, 4) for Re = (50, 150). The galloping has been reported for rotationally asymmetric bluff bodies (e.g., D-section cylinder) in previous studies in isothermal flows. We show that a circular cylinder, a rotationally symmetric body, exhibits galloping due to the transversely acting thermal buoyancy at higher Ri.

The effect of cross-flow thermal buoyancy on vortex-induced vibration (VIV) of a circular cylinder is numerically investigated. An in-house fluid-structure solver based on the sharp-interface immersed boundary method is employed. The cylinder is kept in the uniform flow stream and is mounted elastically such that it is constrained to move in the transverse direction to the flow. The surface of the cylinder is heated at a prescribed temperature, and the thermal buoyancy is imposed in the transverse direction to the flow. Simulations are performed for the following parameters: Reynolds number Re = (50, 150), Prandtl number Pr = 7.1, mass ratio m = 2, reduced velocity UR = [4–15], and Richardson number Ri = [0–4]. We found that the thermal buoyancy could suppress or agitate the VIV. At lower Re (=50) and Ri = (1, 2), we observe the suppression in the VIV; however, there is no suppression for higher Re (=150) for these values of Ri. Galloping is observed for higher values of Ri = (3, 4) for Re = (50, 150). The galloping has been reported for rotationally asymmetric bluff bodies (e.g., D-section cylinder) in previous studies in isothermal flows. We show that a circular cylinder, a rotationally symmetric body, exhibits galloping due to the transversely acting thermal buoyancy at higher Ri.

Categories: Latest papers in fluid mechanics

### Formation, growth, and saturation of dry holes in thick liquid films under vapor-mediated Marangoni effect

Physics of Fluids, Volume 31, Issue 11, November 2019.

Films and drops of liquids can change their shapes and move under the spatial gradient of surface tension. A remote volatile liquid of relatively low surface tension can induce such flows because its vapor locally lowers the surface tension of the films and drops. Here, we show that aqueous liquid films thicker than approximately 100 µm can be punctured to immediately expose a dry hole by an overhanging isopropyl alcohol drop, which is attributed to the vapor-mediated Marangoni effect. We construct and corroborate scaling laws to predict the film dynamics, considering the balance of the driving capillary force and resisting viscous and hydrostatic forces as well as the contact angle of the alcohol-adsorbed solid surface. This remote scheme to induce and sustain changes of liquid morphology can be applied for fluid sculpture and patterning for industrial and artistic practices.

Films and drops of liquids can change their shapes and move under the spatial gradient of surface tension. A remote volatile liquid of relatively low surface tension can induce such flows because its vapor locally lowers the surface tension of the films and drops. Here, we show that aqueous liquid films thicker than approximately 100 µm can be punctured to immediately expose a dry hole by an overhanging isopropyl alcohol drop, which is attributed to the vapor-mediated Marangoni effect. We construct and corroborate scaling laws to predict the film dynamics, considering the balance of the driving capillary force and resisting viscous and hydrostatic forces as well as the contact angle of the alcohol-adsorbed solid surface. This remote scheme to induce and sustain changes of liquid morphology can be applied for fluid sculpture and patterning for industrial and artistic practices.

Categories: Latest papers in fluid mechanics

### Internal flow properties in a capillary bore

Physics of Fluids, Volume 31, Issue 11, November 2019.

In this work, a detailed description of the internal flow field in a collapsing bore generated on a slope in a wave flume is given. It is found that in the case at hand, just prior to breaking, the shape of the free surface and the flow field below are dominated by capillary effects. While numerical approximations are able to predict the development of the free surface as it shoals on the laboratory beach, the internal flow field is poorly predicted by standard numerical models.

In this work, a detailed description of the internal flow field in a collapsing bore generated on a slope in a wave flume is given. It is found that in the case at hand, just prior to breaking, the shape of the free surface and the flow field below are dominated by capillary effects. While numerical approximations are able to predict the development of the free surface as it shoals on the laboratory beach, the internal flow field is poorly predicted by standard numerical models.

Categories: Latest papers in fluid mechanics

### Cross-stream migration and coalescence of droplets in a microchannel co-flow using magnetophoresis

Physics of Fluids, Volume 31, Issue 11, November 2019.

Manipulation of aqueous droplets in microchannels has great significance in various emerging applications such as biological and chemical assays. Magnetic-field based droplet manipulation that offers unique advantages is consequently gaining attention. However, the physics of magnetic field-driven cross-stream migration and the coalescence of aqueous droplets with an aqueous stream are not well understood. Here, we unravel the mechanism of cross-stream migration and the coalescence of aqueous droplets flowing in an oil based ferrofluid with a coflowing aqueous stream in the presence of a magnetic field. Our study reveals that the migration phenomenon is governed by the advection (τa) and magnetophoretic (τm) time scales. Experimental data show that the dimensionless equilibrium cross-stream migration distance δ* and the length [math] required to attain equilibrium cross-stream migration depend on the Strouhal number, St = (τa/τm), as δ* = 1.1 St0.33 and [math], respectively. We find that the droplet-stream coalescence phenomenon is underpinned by the ratio of the sum of magnetophoretic (τm) and film-drainage time scales (τfd) and the advection time scale (τa), expressed in terms of the Strouhal number (St) and the film-drainage Reynolds number (Refd) as ξ = (τm + τfd)/τa = (St−1 + Refd). Irrespective of the flow rates of the coflowing streams, droplet size, and magnetic field, our study shows that droplet-stream coalescence is achieved for ξ ≤ 50 and ferrofluid stream width ratio w* < 0.7. We utilize the phenomenon and demonstrated the extraction of microparticles and HeLa cells from aqueous droplets to an aqueous stream.

Manipulation of aqueous droplets in microchannels has great significance in various emerging applications such as biological and chemical assays. Magnetic-field based droplet manipulation that offers unique advantages is consequently gaining attention. However, the physics of magnetic field-driven cross-stream migration and the coalescence of aqueous droplets with an aqueous stream are not well understood. Here, we unravel the mechanism of cross-stream migration and the coalescence of aqueous droplets flowing in an oil based ferrofluid with a coflowing aqueous stream in the presence of a magnetic field. Our study reveals that the migration phenomenon is governed by the advection (τa) and magnetophoretic (τm) time scales. Experimental data show that the dimensionless equilibrium cross-stream migration distance δ* and the length [math] required to attain equilibrium cross-stream migration depend on the Strouhal number, St = (τa/τm), as δ* = 1.1 St0.33 and [math], respectively. We find that the droplet-stream coalescence phenomenon is underpinned by the ratio of the sum of magnetophoretic (τm) and film-drainage time scales (τfd) and the advection time scale (τa), expressed in terms of the Strouhal number (St) and the film-drainage Reynolds number (Refd) as ξ = (τm + τfd)/τa = (St−1 + Refd). Irrespective of the flow rates of the coflowing streams, droplet size, and magnetic field, our study shows that droplet-stream coalescence is achieved for ξ ≤ 50 and ferrofluid stream width ratio w* < 0.7. We utilize the phenomenon and demonstrated the extraction of microparticles and HeLa cells from aqueous droplets to an aqueous stream.

Categories: Latest papers in fluid mechanics

### Similarities between the structure functions of thermal convection and hydrodynamic turbulence

Physics of Fluids, Volume 31, Issue 11, November 2019.

In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

In this paper, we analyze the scaling of velocity structure functions of turbulent thermal convection. Using high-resolution numerical simulations, we show that the structure functions scale similar to those of hydrodynamic turbulence, with the scaling exponents in agreement with the predictions of She and Leveque [“Universal scaling laws in fully developed turbulence,” Phys. Rev. Lett. 72, 336–339 (1994)]. The probability distribution functions of velocity increments are non-Gaussian with wide tails in the dissipative scales and become close to Gaussian in the inertial range. The tails of the probability distribution follow a stretched exponential. We also show that in thermal convection, the energy flux in the inertial range is less than the viscous dissipation rate. This is unlike in hydrodynamic turbulence where the energy flux and the dissipation rate are equal.

Categories: Latest papers in fluid mechanics

### Unidirectional large-amplitude oscillatory shear flow of human blood

Physics of Fluids, Volume 31, Issue 11, November 2019.

Blood is a non-Newtonian suspension of red and white cells, platelets, fibrinogen, and cholesterols in Newtonian plasma. To assess its non-Newtonian behaviors, this work considers a newly proposed blood test, unidirectional large-amplitude oscillatory shear flow (udLAOS). In the laboratory, we generate this experiment by superposing LAOS onto steady shear flow in such a way that the shear rate never changes sign. It is thus intended to best represent the unidirectional pulsatile flow in veins and arteries. To model human blood, we consider the simplest model that can predict infinite-shear viscosity, the corotational Jeffreys fluid. We arrive at an exact analytical expression for the shear stress response of this model fluid. We discover fractional harmonics comprising the transient part of the shear stress response and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. We generalize the corotational Jeffreys fluid to multimode to best represent three blood samples from three healthy but different donors. To further improve our model predictions, we consider the multimode Oldroyd 8-constant framework, which contains the corotational Jeffreys fluid as a special case. In other words, by advancing from the multimode corotational Jeffreys fluid to the multimode Oldroyd 8-constant framework, five more model parameters are added, yielding better predictions. We find that the multimode corotational Jeffreys fluid adequately describes the steady shear viscosity functions measured for three different healthy donors. We further find that adding two more specific nonlinear constants to the multimode corotational Jeffreys fluid also adequately describes the behaviors of these same bloods in udLAOS. This new Oldroyd 5-constant model may find usefulness in monitoring health through udLAOS.

Blood is a non-Newtonian suspension of red and white cells, platelets, fibrinogen, and cholesterols in Newtonian plasma. To assess its non-Newtonian behaviors, this work considers a newly proposed blood test, unidirectional large-amplitude oscillatory shear flow (udLAOS). In the laboratory, we generate this experiment by superposing LAOS onto steady shear flow in such a way that the shear rate never changes sign. It is thus intended to best represent the unidirectional pulsatile flow in veins and arteries. To model human blood, we consider the simplest model that can predict infinite-shear viscosity, the corotational Jeffreys fluid. We arrive at an exact analytical expression for the shear stress response of this model fluid. We discover fractional harmonics comprising the transient part of the shear stress response and both integer and fractional harmonics, the alternant part. By fractional, we mean that these occur at frequencies other than integer multiples of the superposed oscillation frequency. We generalize the corotational Jeffreys fluid to multimode to best represent three blood samples from three healthy but different donors. To further improve our model predictions, we consider the multimode Oldroyd 8-constant framework, which contains the corotational Jeffreys fluid as a special case. In other words, by advancing from the multimode corotational Jeffreys fluid to the multimode Oldroyd 8-constant framework, five more model parameters are added, yielding better predictions. We find that the multimode corotational Jeffreys fluid adequately describes the steady shear viscosity functions measured for three different healthy donors. We further find that adding two more specific nonlinear constants to the multimode corotational Jeffreys fluid also adequately describes the behaviors of these same bloods in udLAOS. This new Oldroyd 5-constant model may find usefulness in monitoring health through udLAOS.

Categories: Latest papers in fluid mechanics

### Graeme A. Bird

Physics of Fluids, Volume DSMC2019, Issue 1, November 2019.

Categories: Latest papers in fluid mechanics

### Graeme A. Bird

Physics of Fluids, Volume 31, Issue 11, November 2019.

Categories: Latest papers in fluid mechanics

### Flow analysis of a shock wave at pulse ionization: Riemann problem implementation

Physics of Fluids, Volume 31, Issue 11, November 2019.

An experimental study of the plasma-gas dynamic fluid formed after pulse ionization of the gas flow with a plane shock wave with Mach number 2.2–4.8 is carried out. Nanosecond volume discharge with UV preionization was switched on when the shock moved in a tube channel test section. Energy input occurs in the low-pressure gas volume separated by the shock surface within a time less than 200–300 ns; a single shock wave breaks into three discontinuities in accordance with the 1D Riemann problem solution. The initial (plasma-dynamic) stage of the flow in the nanosecond time range is visualized by glow recording; the supersonic gas processes in the microsecond time range are recorded using high-speed shadow imaging. Quantitative information about the dynamics of the shocks and contact surface (plots of horizontal distance) was obtained within time up to 25 µs. A region with an increased gas-discharge plasma glow intensity, after the discharge electric current termination, was recorded in the time interval from 0.3 to 1.5 µs; it was explained by a jump in gas temperature and density between the new shock wave and the contact discontinuity.

An experimental study of the plasma-gas dynamic fluid formed after pulse ionization of the gas flow with a plane shock wave with Mach number 2.2–4.8 is carried out. Nanosecond volume discharge with UV preionization was switched on when the shock moved in a tube channel test section. Energy input occurs in the low-pressure gas volume separated by the shock surface within a time less than 200–300 ns; a single shock wave breaks into three discontinuities in accordance with the 1D Riemann problem solution. The initial (plasma-dynamic) stage of the flow in the nanosecond time range is visualized by glow recording; the supersonic gas processes in the microsecond time range are recorded using high-speed shadow imaging. Quantitative information about the dynamics of the shocks and contact surface (plots of horizontal distance) was obtained within time up to 25 µs. A region with an increased gas-discharge plasma glow intensity, after the discharge electric current termination, was recorded in the time interval from 0.3 to 1.5 µs; it was explained by a jump in gas temperature and density between the new shock wave and the contact discontinuity.

Categories: Latest papers in fluid mechanics

### In-depth description of electrohydrodynamic conduction pumping of dielectric liquids: Physical model and regime analysis

Physics of Fluids, Volume 31, Issue 11, November 2019.

In this work, we discuss the fundamental aspects of Electrohydrodynamic (EHD) conduction pumping of dielectric liquids. We build a mathematical model of conduction pumping that can be applied to all sizes, down to microsized pumps. In order to do this, we discuss the relevance of the Electrical Double Layer (EDL) that appears naturally on nonmetallic substrates. In the process, we identify a new dimensionless parameter related to the value of the zeta potential of the substrate-liquid pair, which quantifies the influence of these EDLs on the performance of the pump. This parameter also describes the transition from EHD conduction pumping to electro-osmosis. We also discuss in detail the two limiting working regimes in EHD conduction pumping: ohmic and saturation. We introduce a new dimensionless parameter, accounting for the electric field enhanced dissociation that, along with the conduction number, allows us to identify in which regime the pump operates.

In this work, we discuss the fundamental aspects of Electrohydrodynamic (EHD) conduction pumping of dielectric liquids. We build a mathematical model of conduction pumping that can be applied to all sizes, down to microsized pumps. In order to do this, we discuss the relevance of the Electrical Double Layer (EDL) that appears naturally on nonmetallic substrates. In the process, we identify a new dimensionless parameter related to the value of the zeta potential of the substrate-liquid pair, which quantifies the influence of these EDLs on the performance of the pump. This parameter also describes the transition from EHD conduction pumping to electro-osmosis. We also discuss in detail the two limiting working regimes in EHD conduction pumping: ohmic and saturation. We introduce a new dimensionless parameter, accounting for the electric field enhanced dissociation that, along with the conduction number, allows us to identify in which regime the pump operates.

Categories: Latest papers in fluid mechanics

### Eulerian conditional statistics of turbulent flow in a macroscale multi-inlet vortex chemical reactor

Physics of Fluids, Volume 31, Issue 11, November 2019.

The conditional velocity time averages (⟨Ui|ξ⟩) and conditional mixture fraction time averages (⟨Φ|ωi⟩) were computed based on the Eulerian approach from the experimental data measured in a macroscale multi-inlet vortex chemical reactor. The conditioning events were determined by equally sized intervals of the sample space variable for the mixture fraction (ξ) and the velocity vector (ωi). The experimental data, which consisted of instantaneous velocities and concentration fields for two Reynolds numbers (Re = 3250 and 8125), were acquired using the simultaneous stereoscopic particle image velocimetry (stereo-PIV) and planar laser induced fluorescence techniques. Two mathematical models, the linear approximation and probability density function (PDF) gradient diffusion, were validated by experimental results. The results of the velocity conditioned on the mixture fraction demonstrated that the linear model works well in a low turbulence region away from the reactor center. Near the reactor center, high velocity gradients coupled with low concentration gradients reduce the accuracy of the linear model predictions. Nevertheless, an excellent agreement was found for the conditional events within ±2Φrms (mixture fraction root mean square). Due to lower concentration gradient in the tangential direction, the linear model better predicted the tangential velocity component for all locations investigated. The PDF model with an isotropic turbulent diffusivity performed inadequately for the tangential and axial velocity components. A modified version of the PDF model that considers the three components of the turbulent diffusivity produced a better agreement with the experimental data especially in the spiral arms regions of significant concentration gradients. Furthermore, the mixture fraction conditioned on the velocity vector components showed a more linear behavior near the reactor center, where the PDF of the mixture fraction is a Gaussian distribution. As the concentration gradients became prominent away from the reactor, ⟨Φ|ωi⟩ also deviated from the linear pattern. This was especially remarkable for the mixture fraction conditioned on the tangential velocity. The overall prediction of ⟨Φ|ωi⟩ improves at higher Reynolds number as the fluid mixing is enhanced.

The conditional velocity time averages (⟨Ui|ξ⟩) and conditional mixture fraction time averages (⟨Φ|ωi⟩) were computed based on the Eulerian approach from the experimental data measured in a macroscale multi-inlet vortex chemical reactor. The conditioning events were determined by equally sized intervals of the sample space variable for the mixture fraction (ξ) and the velocity vector (ωi). The experimental data, which consisted of instantaneous velocities and concentration fields for two Reynolds numbers (Re = 3250 and 8125), were acquired using the simultaneous stereoscopic particle image velocimetry (stereo-PIV) and planar laser induced fluorescence techniques. Two mathematical models, the linear approximation and probability density function (PDF) gradient diffusion, were validated by experimental results. The results of the velocity conditioned on the mixture fraction demonstrated that the linear model works well in a low turbulence region away from the reactor center. Near the reactor center, high velocity gradients coupled with low concentration gradients reduce the accuracy of the linear model predictions. Nevertheless, an excellent agreement was found for the conditional events within ±2Φrms (mixture fraction root mean square). Due to lower concentration gradient in the tangential direction, the linear model better predicted the tangential velocity component for all locations investigated. The PDF model with an isotropic turbulent diffusivity performed inadequately for the tangential and axial velocity components. A modified version of the PDF model that considers the three components of the turbulent diffusivity produced a better agreement with the experimental data especially in the spiral arms regions of significant concentration gradients. Furthermore, the mixture fraction conditioned on the velocity vector components showed a more linear behavior near the reactor center, where the PDF of the mixture fraction is a Gaussian distribution. As the concentration gradients became prominent away from the reactor, ⟨Φ|ωi⟩ also deviated from the linear pattern. This was especially remarkable for the mixture fraction conditioned on the tangential velocity. The overall prediction of ⟨Φ|ωi⟩ improves at higher Reynolds number as the fluid mixing is enhanced.

Categories: Latest papers in fluid mechanics

### Intermittent locomotion of a self-propelled plate

Physics of Fluids, Volume 31, Issue 11, November 2019.

Many fish and marine animals swim in a combination of active burst and passive coast phases, which is known as burst-and-coast swimming. The immersed boundary method was used to explore the intermittent locomotion of a three-dimensional self-propelled plate. The degree of intermittent locomotion can be defined in terms of the duty cycle (DC = Tb/Tf), which is the ratio of the interval of the burst phase (Tb) to the total flapping period (Tf = Tb + Tc), where Tc is the interval of the coast phase. The average cruising speed ([math]), the input power ([math]), and the swimming efficiency (η) were determined as a function of the duty cycle (DC). The maximum [math] arises for DC = 0.9, whereas the maximum η arises for DC = 0.3. The hydrodynamics of the intermittent locomotion was analyzed by examining the superimposed configurations of the plate and the phase map. The characteristics of the flapping motions in the burst and coast phases are discussed. A modal analysis was performed to examine the role of the flapping motion in the propulsion mechanism. The velocity map and the vortical structures are visualized to characterize qualitatively and quantitatively the influence of intermittent locomotion on propulsion.

Many fish and marine animals swim in a combination of active burst and passive coast phases, which is known as burst-and-coast swimming. The immersed boundary method was used to explore the intermittent locomotion of a three-dimensional self-propelled plate. The degree of intermittent locomotion can be defined in terms of the duty cycle (DC = Tb/Tf), which is the ratio of the interval of the burst phase (Tb) to the total flapping period (Tf = Tb + Tc), where Tc is the interval of the coast phase. The average cruising speed ([math]), the input power ([math]), and the swimming efficiency (η) were determined as a function of the duty cycle (DC). The maximum [math] arises for DC = 0.9, whereas the maximum η arises for DC = 0.3. The hydrodynamics of the intermittent locomotion was analyzed by examining the superimposed configurations of the plate and the phase map. The characteristics of the flapping motions in the burst and coast phases are discussed. A modal analysis was performed to examine the role of the flapping motion in the propulsion mechanism. The velocity map and the vortical structures are visualized to characterize qualitatively and quantitatively the influence of intermittent locomotion on propulsion.

Categories: Latest papers in fluid mechanics

### Exact moment analysis of transient dispersion properties in periodic media

Physics of Fluids, Volume 31, Issue 11, November 2019.

This paper develops a homogenization approach, based on the introduction of exact local and integral moments, to investigate the temporal evolution of effective dispersion properties of point-sized and finite-sized particles in periodic media. The proposed method represents a robust and computationally efficient continuous approach, alternative to stochastic dynamic simulations. As a case study, the exact moment method is applied to analyze transient dispersion properties of point-sized and finite-sized particles in sinusoidal tubes under the action of a pressure-driven Stokes flow. The sinusoidal structure of the tube wall induces a significant variation of the axial velocity component along the axial coordinate. This strongly influences the transient behavior of the effective axial velocity [math] and of the dispersivity [math], both exhibiting wide and persistent temporal oscillations, even for a steady (not-pulsating) Stokes flow. For a pointwise injection of solute particles on the symmetry axis, many interesting features appear: negative values of the dispersion coefficient [math], values of [math] larger than the asymptotic value [math], and anomalous temporal scaling of the axial variance of the particle distribution. All these peculiar features found a physical and theoretical explanation by adopting simple transport models accounting for the axial and radial variation of the axial velocity field and its interaction with molecular diffusion.

This paper develops a homogenization approach, based on the introduction of exact local and integral moments, to investigate the temporal evolution of effective dispersion properties of point-sized and finite-sized particles in periodic media. The proposed method represents a robust and computationally efficient continuous approach, alternative to stochastic dynamic simulations. As a case study, the exact moment method is applied to analyze transient dispersion properties of point-sized and finite-sized particles in sinusoidal tubes under the action of a pressure-driven Stokes flow. The sinusoidal structure of the tube wall induces a significant variation of the axial velocity component along the axial coordinate. This strongly influences the transient behavior of the effective axial velocity [math] and of the dispersivity [math], both exhibiting wide and persistent temporal oscillations, even for a steady (not-pulsating) Stokes flow. For a pointwise injection of solute particles on the symmetry axis, many interesting features appear: negative values of the dispersion coefficient [math], values of [math] larger than the asymptotic value [math], and anomalous temporal scaling of the axial variance of the particle distribution. All these peculiar features found a physical and theoretical explanation by adopting simple transport models accounting for the axial and radial variation of the axial velocity field and its interaction with molecular diffusion.

Categories: Latest papers in fluid mechanics

### Effects of Reynolds number on vortex structure behind a surface-mounted finite square cylinder with AR = 7

Physics of Fluids, Volume 31, Issue 11, November 2019.

This paper presents the numerical solutions of flow around a surface-mounted square cylinder of aspect ratio h/d = 7 at Reynolds numbers of 652 and 13 041. The aim is to investigate the effect of the Reynolds number, between its medium-to-high range, on the flow and vortex structure around such a cylinder. The present simulations have successfully reproduced the primary flow, as well as the three-dimensional large-scale vortex structure in the wake of the finite wall-mounted body. The observation of base vortices, tip vortices, and a horseshoe vortex is consistent with previous experimental studies. A dipole wake is captured at the higher Reynolds number, while a quadrupole wake is captured for the lower, indicating that the Reynolds number strongly influences the wake structure. In the near-wake region, by plotting the isosurface of instantaneous second invariant of the velocity gradient, the full-loop structure is observed for the quadrupole wake, while the half-loop structure is observed for the dipole wake. In the far-wake region, a braided vortex structure formed by asymmetric hairpin vortices is observed at both Reynolds numbers and a new wake topology is proposed for flows with a similar geometry.

This paper presents the numerical solutions of flow around a surface-mounted square cylinder of aspect ratio h/d = 7 at Reynolds numbers of 652 and 13 041. The aim is to investigate the effect of the Reynolds number, between its medium-to-high range, on the flow and vortex structure around such a cylinder. The present simulations have successfully reproduced the primary flow, as well as the three-dimensional large-scale vortex structure in the wake of the finite wall-mounted body. The observation of base vortices, tip vortices, and a horseshoe vortex is consistent with previous experimental studies. A dipole wake is captured at the higher Reynolds number, while a quadrupole wake is captured for the lower, indicating that the Reynolds number strongly influences the wake structure. In the near-wake region, by plotting the isosurface of instantaneous second invariant of the velocity gradient, the full-loop structure is observed for the quadrupole wake, while the half-loop structure is observed for the dipole wake. In the far-wake region, a braided vortex structure formed by asymmetric hairpin vortices is observed at both Reynolds numbers and a new wake topology is proposed for flows with a similar geometry.

Categories: Latest papers in fluid mechanics

### On the highly unsteady dynamics of multiple thermal buoyant jets in cross flows

Physics of Fluids, Volume 31, Issue 11, November 2019.

Thermal plumes of small scale generated by spatially separated heat sources can form, like atoms in a chemical compound, complex structures of different kinds and with distinct behaviors. The situation becomes even more complex if plumes can interact with imposed vertical shear (a horizontal wind). In this analysis, a “minimal framework” based on the application of a filtering process to the governing balance equations for mass, momentum, and energy (falling under the general heading of “Large Eddy Simulation” approach) is used together with direct numerical simulation to inquiry about the relative importance of buoyancy and vertical shear effects in determining the patterning scenario when highly unsteady dynamics are established (turbulent flow). Emerging patterns range from the flow dominated by a static rising jet produced by the aggregation of plumes that are pushed by horizontal leftward and rightward winds toward the center of the physical domain to convective systems with disconnected thermal pillars of smaller scale, which travel in the same direction of the prevailing wind. The classical sheltering effect, which for flows that are steady “in mean” simply consists of an increased deflection of the leading buoyant jet with respect to the trailing ones, is taken over by a variety of new phenomena, including (but not limited to) fast plume removal-rebirth mechanisms (with local increase in the velocity frequency and shrinkage in the related amplitude), “bubble” formation-rupture, and local departure of the frequency spectrum from the Kolmogorov similarity law.

Thermal plumes of small scale generated by spatially separated heat sources can form, like atoms in a chemical compound, complex structures of different kinds and with distinct behaviors. The situation becomes even more complex if plumes can interact with imposed vertical shear (a horizontal wind). In this analysis, a “minimal framework” based on the application of a filtering process to the governing balance equations for mass, momentum, and energy (falling under the general heading of “Large Eddy Simulation” approach) is used together with direct numerical simulation to inquiry about the relative importance of buoyancy and vertical shear effects in determining the patterning scenario when highly unsteady dynamics are established (turbulent flow). Emerging patterns range from the flow dominated by a static rising jet produced by the aggregation of plumes that are pushed by horizontal leftward and rightward winds toward the center of the physical domain to convective systems with disconnected thermal pillars of smaller scale, which travel in the same direction of the prevailing wind. The classical sheltering effect, which for flows that are steady “in mean” simply consists of an increased deflection of the leading buoyant jet with respect to the trailing ones, is taken over by a variety of new phenomena, including (but not limited to) fast plume removal-rebirth mechanisms (with local increase in the velocity frequency and shrinkage in the related amplitude), “bubble” formation-rupture, and local departure of the frequency spectrum from the Kolmogorov similarity law.

Categories: Latest papers in fluid mechanics

### Parallel large eddy simulations of transitional flow in a compressor cascade with endwalls

Physics of Fluids, Volume 31, Issue 11, November 2019.

Laminar-turbulent transition and corner separation play a critical role in the aerodynamics of the compressor and are quite sensitive to the changes of flow conditions and external disturbances. However, a deep understanding of such fine flow phenomena poses a great challenge for turbulent methods and computer resources. In order to clarify the impacts of incoming flow states on the three-dimensional transitional flow in a compressor cascade, we construct a parallel Large-Eddy-Simulation (LES) methodology and apply it to a full-span compressor cascade. Both the turbulent and laminar incoming endwall boundary layers are considered at a free-stream turbulence level of 4%, which is typical in the multistage axial-flow compressor environment. The parallel performance of the MPI (Message Passing Interface) model and hybrid MPI-OpenMP (Open Multi-Processing) model is particularly analyzed at a parallel scale of 10 000 CPU (Central Processing Unit) cores. The parallel performance test shows that the efficiency of the MPI model is evidently higher than that of the hybrid MPI-OpenMP model. The LES results indicate that the incoming laminar endwall boundary layer results in a more remarkable reduction in the blade loading near the endwall and a larger total pressure loss than the turbulent one. The incoming endwall boundary layer state shows a significant impact on the evolution process of the endwall turbulence and a small impact on the corner separation and the suction-surface transition. This study demonstrates the ability of the parallel LES method to capture complex transitional-flow structures in compressor cascades and its potential application to the deeper understandings of compressor aerodynamics.

Laminar-turbulent transition and corner separation play a critical role in the aerodynamics of the compressor and are quite sensitive to the changes of flow conditions and external disturbances. However, a deep understanding of such fine flow phenomena poses a great challenge for turbulent methods and computer resources. In order to clarify the impacts of incoming flow states on the three-dimensional transitional flow in a compressor cascade, we construct a parallel Large-Eddy-Simulation (LES) methodology and apply it to a full-span compressor cascade. Both the turbulent and laminar incoming endwall boundary layers are considered at a free-stream turbulence level of 4%, which is typical in the multistage axial-flow compressor environment. The parallel performance of the MPI (Message Passing Interface) model and hybrid MPI-OpenMP (Open Multi-Processing) model is particularly analyzed at a parallel scale of 10 000 CPU (Central Processing Unit) cores. The parallel performance test shows that the efficiency of the MPI model is evidently higher than that of the hybrid MPI-OpenMP model. The LES results indicate that the incoming laminar endwall boundary layer results in a more remarkable reduction in the blade loading near the endwall and a larger total pressure loss than the turbulent one. The incoming endwall boundary layer state shows a significant impact on the evolution process of the endwall turbulence and a small impact on the corner separation and the suction-surface transition. This study demonstrates the ability of the parallel LES method to capture complex transitional-flow structures in compressor cascades and its potential application to the deeper understandings of compressor aerodynamics.

Categories: Latest papers in fluid mechanics

### Effect of soluble surfactant on the motion of a confined droplet in a square microchannel

Physics of Fluids, Volume 31, Issue 11, November 2019.

Surfactants are widely used in the manipulation of drop motion in microchannels, which is commonly involved in many applications, e.g., surfactant assisted oil recovery and droplet microfluidics. This study is dedicated to a crucial fundamental problem, i.e., the effects of a soluble surfactant on drop motion and their underlying mechanisms, which is an extension of our previous work of an insoluble-surfactant-covered droplet in a square microchannel [Z. Y. Luo, X. L. Shang, and B. F. Bai, “Marangoni effect on the motion of a droplet covered with insoluble surfactant in a square microchannel,” Phys. Fluids 30, 077101 (2018)]. We make essential improvements to our own three-dimensional front-tracking finite-difference model, i.e., by further integrating the equation governing surfactant transport in the bulk fluid and surfactant mass exchange between the drop surface and bulk fluid. We find that the soluble surfactant generally enlarges the droplet-induced extra pressure loss compared to the clean droplet, and enhancing surfactant adsorption tends to intensify such an effect. We focus specifically on the influences of four soluble-surfactant-relevant dimensionless parameters, including the Biot number, the dimensionless adsorption depth, the Damkohler number, and the bulk Peclet number. Most importantly, we discuss the mechanisms underlying the soluble surfactant effect, which consists of two aspects similar to the insoluble case, i.e., the reduced surface tension to decrease droplet-induced extra pressure loss and the enlarged Marangoni stress playing the opposite role. Surprisingly, we find that the enlarged Marangoni stress always makes the predominant contribution over the reduced surface tension in the effects of above-mentioned four soluble-surfactant-relevant dimensionless parameters on drop motion. This finding explains why the droplet-induced extra pressure loss increases with the film thickness, which is opposite to that observed for clean droplets.

Surfactants are widely used in the manipulation of drop motion in microchannels, which is commonly involved in many applications, e.g., surfactant assisted oil recovery and droplet microfluidics. This study is dedicated to a crucial fundamental problem, i.e., the effects of a soluble surfactant on drop motion and their underlying mechanisms, which is an extension of our previous work of an insoluble-surfactant-covered droplet in a square microchannel [Z. Y. Luo, X. L. Shang, and B. F. Bai, “Marangoni effect on the motion of a droplet covered with insoluble surfactant in a square microchannel,” Phys. Fluids 30, 077101 (2018)]. We make essential improvements to our own three-dimensional front-tracking finite-difference model, i.e., by further integrating the equation governing surfactant transport in the bulk fluid and surfactant mass exchange between the drop surface and bulk fluid. We find that the soluble surfactant generally enlarges the droplet-induced extra pressure loss compared to the clean droplet, and enhancing surfactant adsorption tends to intensify such an effect. We focus specifically on the influences of four soluble-surfactant-relevant dimensionless parameters, including the Biot number, the dimensionless adsorption depth, the Damkohler number, and the bulk Peclet number. Most importantly, we discuss the mechanisms underlying the soluble surfactant effect, which consists of two aspects similar to the insoluble case, i.e., the reduced surface tension to decrease droplet-induced extra pressure loss and the enlarged Marangoni stress playing the opposite role. Surprisingly, we find that the enlarged Marangoni stress always makes the predominant contribution over the reduced surface tension in the effects of above-mentioned four soluble-surfactant-relevant dimensionless parameters on drop motion. This finding explains why the droplet-induced extra pressure loss increases with the film thickness, which is opposite to that observed for clean droplets.

Categories: Latest papers in fluid mechanics

### On the time-evolution of resonant triads in rotational capillary-gravity water waves

Physics of Fluids, Volume 31, Issue 11, November 2019.

We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes, and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero, we recover the well known integrable three-wave system.

We investigate an effect of the resonant interaction in the case of one-directional propagation of capillary-gravity surface waves arising as the free surface of a rotational water flow. Specifically, we assume constant vorticity in the body of the fluid which physically corresponds to an underlying current with a linear horizontal velocity profile. We consider the interaction of three distinct modes, and we obtain the dynamic equations for a resonant triad. Setting the constant vorticity equal to zero, we recover the well known integrable three-wave system.

Categories: Latest papers in fluid mechanics

### A composite dynamic mode decomposition analysis of turbulent channel flows

Physics of Fluids, Volume 31, Issue 11, November 2019.

In this contribution, we consider the Dynamic Mode Decomposition (DMD) framework as a purely data-driven tool to investigate both standard and actuated turbulent channel databases via Direct Numerical Simulation (DNS). Both databases have comparable Reynolds number Re ≈ 3600. The actuation consists in the imposition of a streamwise-varying sinusoidal spanwise velocity at the wall, known to lead to drag reduction. Specifically, a composite-based DMD analysis is conducted, with hybrid snapshots composed by skin friction and Reynolds stresses. A small number of dynamic modes (∼3–9) are found to recover accurately the DNS Reynolds stresses near walls. Moreover, the DMD modes retrieved propagate at a range of phase speeds consistent with those reported in the literature. We conclude that composite DMD is an attractive, purely data-driven tool to study turbulent flows. On the one hand, DMD is helpful to identify features associated with the drag, and on the other hand, it reveals the changes in flow structure when actuation is imposed.

In this contribution, we consider the Dynamic Mode Decomposition (DMD) framework as a purely data-driven tool to investigate both standard and actuated turbulent channel databases via Direct Numerical Simulation (DNS). Both databases have comparable Reynolds number Re ≈ 3600. The actuation consists in the imposition of a streamwise-varying sinusoidal spanwise velocity at the wall, known to lead to drag reduction. Specifically, a composite-based DMD analysis is conducted, with hybrid snapshots composed by skin friction and Reynolds stresses. A small number of dynamic modes (∼3–9) are found to recover accurately the DNS Reynolds stresses near walls. Moreover, the DMD modes retrieved propagate at a range of phase speeds consistent with those reported in the literature. We conclude that composite DMD is an attractive, purely data-driven tool to study turbulent flows. On the one hand, DMD is helpful to identify features associated with the drag, and on the other hand, it reveals the changes in flow structure when actuation is imposed.

Categories: Latest papers in fluid mechanics

### An extended Kozeny-Carman-Klinkenberg model for gas permeability in micro/nano-porous media

Physics of Fluids, Volume 31, Issue 11, November 2019.

Gas transport in micropores/nanopores deviates from classical continuum calculations due to nonequilibrium in gas dynamics. In such a case, transport can be classified by the Knudsen number (Kn) as the ratio of gas mean free path and characteristic flow diameter. The well-known Klinkenberg correction and its successors estimate deviation from existing permeability values as a function of Kn through a vast number of modeling attempts. However, the nonequilibrium in a porous system cannot be simply modeled using the classical definition of the Kn number calculated from Darcy’s definition of the pore size or hydraulic diameter. Instead, a proper flow dimension should consider pore connectivity in order to characterize the rarefaction level. This study performs a wide range of pore-level analysis of gas dynamics with different porosities, pore sizes, and pore throat sizes at different Kn values in the slip flow regime. First, intrinsic permeability values were calculated without any rarefaction effect and an extended Kozeny-Carman model was developed by formulating the Kozeny-Carman constant by porosity and pore to throat size ratio. Permeability increased by increasing the porosity and decreasing the pore to throat size ratio. Next, velocity slip was applied on pore surfaces to calculate apparent permeability values. Permeability increased by increasing Kn at different rates depending on the pore parameters. While the characterization by the Kn value calculated with pore height or hydraulic diameter did not display unified behavior, relating permeability values with the Kn number calculated from the equivalent height definition created a general characterization based on the porosity independent from the pore to throat size ratio. Next, we extended the Klinkenberg equation by calculating unknown Klinkenberg coefficients which were found as a simple first order function of porosity regardless of the corresponding pore connectivity. The extended model as a combination of Kozeny-Carman for intrinsic permeability and Klinkenberg for apparent permeability correction yielded successful results.

Gas transport in micropores/nanopores deviates from classical continuum calculations due to nonequilibrium in gas dynamics. In such a case, transport can be classified by the Knudsen number (Kn) as the ratio of gas mean free path and characteristic flow diameter. The well-known Klinkenberg correction and its successors estimate deviation from existing permeability values as a function of Kn through a vast number of modeling attempts. However, the nonequilibrium in a porous system cannot be simply modeled using the classical definition of the Kn number calculated from Darcy’s definition of the pore size or hydraulic diameter. Instead, a proper flow dimension should consider pore connectivity in order to characterize the rarefaction level. This study performs a wide range of pore-level analysis of gas dynamics with different porosities, pore sizes, and pore throat sizes at different Kn values in the slip flow regime. First, intrinsic permeability values were calculated without any rarefaction effect and an extended Kozeny-Carman model was developed by formulating the Kozeny-Carman constant by porosity and pore to throat size ratio. Permeability increased by increasing the porosity and decreasing the pore to throat size ratio. Next, velocity slip was applied on pore surfaces to calculate apparent permeability values. Permeability increased by increasing Kn at different rates depending on the pore parameters. While the characterization by the Kn value calculated with pore height or hydraulic diameter did not display unified behavior, relating permeability values with the Kn number calculated from the equivalent height definition created a general characterization based on the porosity independent from the pore to throat size ratio. Next, we extended the Klinkenberg equation by calculating unknown Klinkenberg coefficients which were found as a simple first order function of porosity regardless of the corresponding pore connectivity. The extended model as a combination of Kozeny-Carman for intrinsic permeability and Klinkenberg for apparent permeability correction yielded successful results.

Categories: Latest papers in fluid mechanics