# Physics of Fluids

Table of Contents for Physics of Fluids. List of articles from both the latest and ahead of print issues.

*Updated:*2 days 18 hours ago

### On coughing and airborne droplet transmission to humans

Physics of Fluids, Volume 32, Issue 5, May 2020.

Our understanding of the mechanisms of airborne transmission of viruses is incomplete. This paper employs computational multiphase fluid dynamics and heat transfer to investigate transport, dispersion, and evaporation of saliva particles arising from a human cough. An ejection process of saliva droplets in air was applied to mimic the real event of a human cough. We employ an advanced three-dimensional model based on fully coupled Eulerian–Lagrangian techniques that take into account the relative humidity, turbulent dispersion forces, droplet phase-change, evaporation, and breakup in addition to the droplet–droplet and droplet–air interactions. We computationally investigate the effect of wind speed on social distancing. For a mild human cough in air at 20 °C and 50% relative humidity, we found that human saliva-disease-carrier droplets may travel up to unexpected considerable distances depending on the wind speed. When the wind speed was approximately zero, the saliva droplets did not travel 2 m, which is within the social distancing recommendations. However, at wind speeds varying from 4 km/h to 15 km/h, we found that the saliva droplets can travel up to 6 m with a decrease in the concentration and liquid droplet size in the wind direction. Our findings imply that considering the environmental conditions, the 2 m social distance may not be sufficient. Further research is required to quantify the influence of parameters such as the environment’s relative humidity and temperature among others.

Our understanding of the mechanisms of airborne transmission of viruses is incomplete. This paper employs computational multiphase fluid dynamics and heat transfer to investigate transport, dispersion, and evaporation of saliva particles arising from a human cough. An ejection process of saliva droplets in air was applied to mimic the real event of a human cough. We employ an advanced three-dimensional model based on fully coupled Eulerian–Lagrangian techniques that take into account the relative humidity, turbulent dispersion forces, droplet phase-change, evaporation, and breakup in addition to the droplet–droplet and droplet–air interactions. We computationally investigate the effect of wind speed on social distancing. For a mild human cough in air at 20 °C and 50% relative humidity, we found that human saliva-disease-carrier droplets may travel up to unexpected considerable distances depending on the wind speed. When the wind speed was approximately zero, the saliva droplets did not travel 2 m, which is within the social distancing recommendations. However, at wind speeds varying from 4 km/h to 15 km/h, we found that the saliva droplets can travel up to 6 m with a decrease in the concentration and liquid droplet size in the wind direction. Our findings imply that considering the environmental conditions, the 2 m social distance may not be sufficient. Further research is required to quantify the influence of parameters such as the environment’s relative humidity and temperature among others.

Categories: Latest papers in fluid mechanics

### On the shock change equations

Physics of Fluids, Volume 32, Issue 5, May 2020.

We revisit and derive the shock change equations relating the dynamics of a shock wave with the partial derivatives describing the motion of a reactive fluid with the general equation of state in a stream-tube with arbitrary area variation. We specialize these to a perfect gas in which we obtain all shock change equations in closed form. These are further simplified for strong shocks. We discuss the general usefulness of these equations in problems of reactive compressible flow and in the development of intrinsic evolution equations for the shock, such as the approximations made by Whitham and Sharma.

We revisit and derive the shock change equations relating the dynamics of a shock wave with the partial derivatives describing the motion of a reactive fluid with the general equation of state in a stream-tube with arbitrary area variation. We specialize these to a perfect gas in which we obtain all shock change equations in closed form. These are further simplified for strong shocks. We discuss the general usefulness of these equations in problems of reactive compressible flow and in the development of intrinsic evolution equations for the shock, such as the approximations made by Whitham and Sharma.

Categories: Latest papers in fluid mechanics

### Investigation of liquid metal drop impingement on a liquid metal surface under the influence of a horizontal magnetic field

Physics of Fluids, Volume 32, Issue 5, May 2020.

Considering the existence of a horizontal magnetic field, we experimentally investigate the process of a liquid metal drop with high surface tension impacting a film of the same liquid. High-speed photography is adopted here to capture the dynamics of the interaction between the drop and the liquid film. We observe three typical outcomes after drop impact on the film, namely, symmetric crown, asymmetric crown, and prompt splashing, among which the asymmetric crown is first discovered by the present experiments. Moreover, the experimental variables, such as the drop size, impact velocity, initial film thickness, and intensity of the magnetic field, are included to study the three outcomes in detail. For crown formation, the external horizontal magnetic field changes the shape of the crown from symmetric to asymmetric during the crown expansion process, while for prompt splashing, the external horizontal magnetic field promotes splashing from the liquid layer where the drop and the liquid film meet and reduces the critical Weber number where prompt splashing occurs. Therefore, the present experimental results conclusively prove that the external horizontal magnetic field affects the process of liquid metal drop impact on a liquid metal film. Finally, by selecting a typical case, we carried out the direct numerical simulation to calculate the distribution of the magnetic-field-induced Lorentz force inside the droplet after impact, which helps us fully understand the phenomena observed.

Considering the existence of a horizontal magnetic field, we experimentally investigate the process of a liquid metal drop with high surface tension impacting a film of the same liquid. High-speed photography is adopted here to capture the dynamics of the interaction between the drop and the liquid film. We observe three typical outcomes after drop impact on the film, namely, symmetric crown, asymmetric crown, and prompt splashing, among which the asymmetric crown is first discovered by the present experiments. Moreover, the experimental variables, such as the drop size, impact velocity, initial film thickness, and intensity of the magnetic field, are included to study the three outcomes in detail. For crown formation, the external horizontal magnetic field changes the shape of the crown from symmetric to asymmetric during the crown expansion process, while for prompt splashing, the external horizontal magnetic field promotes splashing from the liquid layer where the drop and the liquid film meet and reduces the critical Weber number where prompt splashing occurs. Therefore, the present experimental results conclusively prove that the external horizontal magnetic field affects the process of liquid metal drop impact on a liquid metal film. Finally, by selecting a typical case, we carried out the direct numerical simulation to calculate the distribution of the magnetic-field-induced Lorentz force inside the droplet after impact, which helps us fully understand the phenomena observed.

Categories: Latest papers in fluid mechanics

### On the onset of negative lift in a symmetric airfoil at very small angles of attack

Physics of Fluids, Volume 32, Issue 5, May 2020.

The variation of the lift coefficient in a symmetric airfoil (NACA 0012 profile) at very small angles of attack is studied experimentally and numerically for a range of low chord-based Reynolds numbers, Re. Experimentally, the non-linearity around the zero angle of attack leading to a switch in sign on the lift was observed for a big enough aspect ratio at Re = 40 × 103. The existence of the negative lift for wing models with the biggest aspect ratio suggests that the three-dimensional effects are negligible. Therefore, two-dimensional simulations were performed to understand the cause of the negative lift. For the cases with the negative lift, the flow displays an interesting feature of pre-alignment with the chord upstream of the profile. Furthermore, it was found that the negative lift is directly related to the positive net circulation (anti-clockwise) around the airfoil.

The variation of the lift coefficient in a symmetric airfoil (NACA 0012 profile) at very small angles of attack is studied experimentally and numerically for a range of low chord-based Reynolds numbers, Re. Experimentally, the non-linearity around the zero angle of attack leading to a switch in sign on the lift was observed for a big enough aspect ratio at Re = 40 × 103. The existence of the negative lift for wing models with the biggest aspect ratio suggests that the three-dimensional effects are negligible. Therefore, two-dimensional simulations were performed to understand the cause of the negative lift. For the cases with the negative lift, the flow displays an interesting feature of pre-alignment with the chord upstream of the profile. Furthermore, it was found that the negative lift is directly related to the positive net circulation (anti-clockwise) around the airfoil.

Categories: Latest papers in fluid mechanics

### Peak instability in an elastic interface ferrofluid

Physics of Fluids, Volume 32, Issue 5, May 2020.

The instability of an elastic interface separating a ferrofluid and a nonmagnetic fluid subjected to an applied magnetic field perpendicular to the initially undisturbed interface is investigated in the effectively two-dimensional environment of a vertical, rectangular Hele-Shaw cell. By using a third-order mode-coupling perturbative scheme, and considering that the elastic interface has a curvature-dependent bending rigidity, the emergence of elastic ferrofluid peaks is detected at the onset of nonlinearities. In this context, the approximate profile of the interface is obtained. It is also shown that the morphology of the resulting peaks is sensitive to changes in a dimensionless magnetoelastic number (relative measure of magnetic and elastic forces), as well as in a bending rigidity fraction parameter, which expresses variations in the bending rigidity with the local interface curvature.

The instability of an elastic interface separating a ferrofluid and a nonmagnetic fluid subjected to an applied magnetic field perpendicular to the initially undisturbed interface is investigated in the effectively two-dimensional environment of a vertical, rectangular Hele-Shaw cell. By using a third-order mode-coupling perturbative scheme, and considering that the elastic interface has a curvature-dependent bending rigidity, the emergence of elastic ferrofluid peaks is detected at the onset of nonlinearities. In this context, the approximate profile of the interface is obtained. It is also shown that the morphology of the resulting peaks is sensitive to changes in a dimensionless magnetoelastic number (relative measure of magnetic and elastic forces), as well as in a bending rigidity fraction parameter, which expresses variations in the bending rigidity with the local interface curvature.

Categories: Latest papers in fluid mechanics

### Low-frequency unsteadiness of shock-wave/boundary-layer interaction in an isolator with background waves

Physics of Fluids, Volume 32, Issue 5, May 2020.

Low-frequency unsteadiness is investigated through wind tunnel experiments and numerical simulations of the internal flow in a supersonic isolator with background waves generated by a 14° wedge in a freestream with a Mach number of 2.94. The power spectra, coherence, and phase analyses of high-frequency pressure signals and schlieren images provide a local and global description of the unsteadiness. The upstream mechanism exhibits a significant influence on the unthrottled flow field. In the weak interactions of small separation flow, the pressure fluctuation between two adjacent incident points has a strong correlation in a large frequency range, while only large-amplitude shock oscillations are exhibited in the pressure fluctuations at the boundary layer. The downstream mechanism dominates the asymmetric shock motion in the throttled flow field. The profiles of the power spectrum and standard deviation both exhibit two peaks at the upstream and downstream peripheries of the wall separation patterns. Two types of oscillations can be identified through the pressure data, and type III is established from the analysis of schlieren images. The oscillation behavior of the three types is obtained through the power spectral analysis of a series of schlieren snapshots. The frequency of the occurrence and the one-cycle amplitude of different oscillation types are significantly different. By combining the coherence and phase analyses with the corresponding schlieren images and pressure data, the feedback mechanism of the three oscillation types is determined. This study combines the low-frequency unsteadiness in supersonic internal flows with the multiple separation regions caused by complex background waves.

Low-frequency unsteadiness is investigated through wind tunnel experiments and numerical simulations of the internal flow in a supersonic isolator with background waves generated by a 14° wedge in a freestream with a Mach number of 2.94. The power spectra, coherence, and phase analyses of high-frequency pressure signals and schlieren images provide a local and global description of the unsteadiness. The upstream mechanism exhibits a significant influence on the unthrottled flow field. In the weak interactions of small separation flow, the pressure fluctuation between two adjacent incident points has a strong correlation in a large frequency range, while only large-amplitude shock oscillations are exhibited in the pressure fluctuations at the boundary layer. The downstream mechanism dominates the asymmetric shock motion in the throttled flow field. The profiles of the power spectrum and standard deviation both exhibit two peaks at the upstream and downstream peripheries of the wall separation patterns. Two types of oscillations can be identified through the pressure data, and type III is established from the analysis of schlieren images. The oscillation behavior of the three types is obtained through the power spectral analysis of a series of schlieren snapshots. The frequency of the occurrence and the one-cycle amplitude of different oscillation types are significantly different. By combining the coherence and phase analyses with the corresponding schlieren images and pressure data, the feedback mechanism of the three oscillation types is determined. This study combines the low-frequency unsteadiness in supersonic internal flows with the multiple separation regions caused by complex background waves.

Categories: Latest papers in fluid mechanics

### Ultimate fate of a dynamical bubble/droplet system following acoustic vaporization

Physics of Fluids, Volume 32, Issue 5, May 2020.

The phase-change of a liquid droplet induced by a supply of acoustic energy is known as “Acoustic Droplet Vaporization,” and it represents a versatile tool for medical applications. In an attempt to understand the complex mechanisms that drive the vaporization threshold, a theoretical concentric three phase model (bubble of vapor dodecafluoropentane + layer of liquid dodecafluoropentane + water) is used to compute numerical simulations of the vapor bubble time evolution. The dynamics are sorted into different regimes depending on their shared characteristic and the system ultimate fate. Those regimes are then organized within a phase diagram that collects all the possible dynamics and that predicts whether the complete vaporization occurs or not.

The phase-change of a liquid droplet induced by a supply of acoustic energy is known as “Acoustic Droplet Vaporization,” and it represents a versatile tool for medical applications. In an attempt to understand the complex mechanisms that drive the vaporization threshold, a theoretical concentric three phase model (bubble of vapor dodecafluoropentane + layer of liquid dodecafluoropentane + water) is used to compute numerical simulations of the vapor bubble time evolution. The dynamics are sorted into different regimes depending on their shared characteristic and the system ultimate fate. Those regimes are then organized within a phase diagram that collects all the possible dynamics and that predicts whether the complete vaporization occurs or not.

Categories: Latest papers in fluid mechanics

### Dispersion of solute in straining flows and boundary layers

Physics of Fluids, Volume 32, Issue 5, May 2020.

Solute dispersion due to an instantaneously released source in steady, laminar, axisymmetric flows with an axial inflow and radial outflow is investigated analytically. Attention is given to large-time characteristics of dispersion, where the concentration reduces in proportion to e−2λτ, where λ is an eigenvalue that depends on the axial inflow and τ is the time measured in units of axial-diffusion times. Prospects of some other flows are also considered.

Solute dispersion due to an instantaneously released source in steady, laminar, axisymmetric flows with an axial inflow and radial outflow is investigated analytically. Attention is given to large-time characteristics of dispersion, where the concentration reduces in proportion to e−2λτ, where λ is an eigenvalue that depends on the axial inflow and τ is the time measured in units of axial-diffusion times. Prospects of some other flows are also considered.

Categories: Latest papers in fluid mechanics

### The aerodynamic performance of passive wing pitch in hovering flight

Physics of Fluids, Volume 32, Issue 5, May 2020.

Insect wings can passively maintain a high angle of attack during each flapping stroke without the aid of the active pitching motion due to the torsional flexibility of the wing basal region. However, there is no clear understanding of how torsional wing flexibility should be designed for achieving optimal aerodynamic performance. In this work, a computational study was conducted to investigate the passive pitching mechanism of a fruit fly wing in hovering flight using a torsional spring model. The torsional wing stiffness was characterized by the Cauchy number, a ratio between the aerodynamic force and the structural elastic force. Different flapping patterns including zero-deviation, figure-8, and oval-shaped flapping trajectories were evaluated along a horizontal stroke plane. The aerodynamic forces and associated unsteady flow structures were simulated using an in-house immersed-boundary-method based computational fluid dynamics solver. A parametric study on the Cauchy number was performed with a Reynolds number of 300. According to the analysis of the aerodynamic performance, we found that a balance of high lift and high lift-to-power ratio can be achieved in a particular range of Cauchy numbers (0.15–0.30) for all different flapping trajectories. This range is consistent with the Cauchy number calculated based on the experimental measurements of a fruit fly in the literature. In addition, 3D wake structures generated by the passive flapping wings were analyzed in detail. The findings of this work could provide important implications for designing more efficient flapping-wing micro-air vehicles.

Insect wings can passively maintain a high angle of attack during each flapping stroke without the aid of the active pitching motion due to the torsional flexibility of the wing basal region. However, there is no clear understanding of how torsional wing flexibility should be designed for achieving optimal aerodynamic performance. In this work, a computational study was conducted to investigate the passive pitching mechanism of a fruit fly wing in hovering flight using a torsional spring model. The torsional wing stiffness was characterized by the Cauchy number, a ratio between the aerodynamic force and the structural elastic force. Different flapping patterns including zero-deviation, figure-8, and oval-shaped flapping trajectories were evaluated along a horizontal stroke plane. The aerodynamic forces and associated unsteady flow structures were simulated using an in-house immersed-boundary-method based computational fluid dynamics solver. A parametric study on the Cauchy number was performed with a Reynolds number of 300. According to the analysis of the aerodynamic performance, we found that a balance of high lift and high lift-to-power ratio can be achieved in a particular range of Cauchy numbers (0.15–0.30) for all different flapping trajectories. This range is consistent with the Cauchy number calculated based on the experimental measurements of a fruit fly in the literature. In addition, 3D wake structures generated by the passive flapping wings were analyzed in detail. The findings of this work could provide important implications for designing more efficient flapping-wing micro-air vehicles.

Categories: Latest papers in fluid mechanics

### The impact of heterogeneous pin based micro-structures on flow dynamics and heat transfer in micro-scale heat exchangers

Physics of Fluids, Volume 32, Issue 5, May 2020.

Overheating is the most important limiting factor for efficient performance of miniature electronic devices. Porous microfluidic systems are recently introduced as a promising remedy to this problem. Increasing the heat removal using porous microfluidic systems comes at the cost of increased hydrodynamic friction in the device. In this study, we focus on the flow dynamics in microchannels with embedded heterogeneous porous structures to identify effective parameters to make porous patterns with less friction while maintaining a high heat transfer rate. The heterogeneous porous structures are defined using columns of pins with different pin sizes. We analyze the flow dynamics and heat transfer using quantitative and qualitative flow patterns, energy distribution, and particle tracking analyses. We find that the structure of the porous medium plays an important role in the hydrodynamic flow distribution and as a result on the overall heat transfer characteristics. While higher heat transfer rates in homogeneous porous media are proportional to higher friction, heterogeneous porous media revealed more complex flow dynamics. It was shown that an optimized distribution of the pins in the microchannel can lead to the systems where the heat transfer increases and, at the same time, the frictions decrease. We show that the columns at either end of the porous medium are the ones that affect flow dynamics and heat transfer the most.

Overheating is the most important limiting factor for efficient performance of miniature electronic devices. Porous microfluidic systems are recently introduced as a promising remedy to this problem. Increasing the heat removal using porous microfluidic systems comes at the cost of increased hydrodynamic friction in the device. In this study, we focus on the flow dynamics in microchannels with embedded heterogeneous porous structures to identify effective parameters to make porous patterns with less friction while maintaining a high heat transfer rate. The heterogeneous porous structures are defined using columns of pins with different pin sizes. We analyze the flow dynamics and heat transfer using quantitative and qualitative flow patterns, energy distribution, and particle tracking analyses. We find that the structure of the porous medium plays an important role in the hydrodynamic flow distribution and as a result on the overall heat transfer characteristics. While higher heat transfer rates in homogeneous porous media are proportional to higher friction, heterogeneous porous media revealed more complex flow dynamics. It was shown that an optimized distribution of the pins in the microchannel can lead to the systems where the heat transfer increases and, at the same time, the frictions decrease. We show that the columns at either end of the porous medium are the ones that affect flow dynamics and heat transfer the most.

Categories: Latest papers in fluid mechanics

### Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning

Physics of Fluids, Volume 32, Issue 5, May 2020.

This paper focuses on the active flow control of a computational fluid dynamics simulation over a range of Reynolds numbers using deep reinforcement learning (DRL). More precisely, the proximal policy optimization (PPO) method is used to control the mass flow rate of four synthetic jets symmetrically located on the upper and lower sides of a cylinder immersed in a two-dimensional flow domain. The learning environment supports four flow configurations with Reynolds numbers 100, 200, 300, and 400, respectively. A new smoothing interpolation function is proposed to help the PPO algorithm learn to set continuous actions, which is of great importance to effectively suppress problematic jumps in lift and allow a better convergence for the training process. It is shown that the DRL controller is able to significantly reduce the lift and drag fluctuations and actively reduce the drag by ∼5.7%, 21.6%, 32.7%, and 38.7%, at Re = 100, 200, 300, and 400, respectively. More importantly, it can also effectively reduce drag for any previously unseen value of the Reynolds number between 60 and 400. This highlights the generalization ability of deep neural networks and is an important milestone toward the development of practical applications of DRL to active flow control.

This paper focuses on the active flow control of a computational fluid dynamics simulation over a range of Reynolds numbers using deep reinforcement learning (DRL). More precisely, the proximal policy optimization (PPO) method is used to control the mass flow rate of four synthetic jets symmetrically located on the upper and lower sides of a cylinder immersed in a two-dimensional flow domain. The learning environment supports four flow configurations with Reynolds numbers 100, 200, 300, and 400, respectively. A new smoothing interpolation function is proposed to help the PPO algorithm learn to set continuous actions, which is of great importance to effectively suppress problematic jumps in lift and allow a better convergence for the training process. It is shown that the DRL controller is able to significantly reduce the lift and drag fluctuations and actively reduce the drag by ∼5.7%, 21.6%, 32.7%, and 38.7%, at Re = 100, 200, 300, and 400, respectively. More importantly, it can also effectively reduce drag for any previously unseen value of the Reynolds number between 60 and 400. This highlights the generalization ability of deep neural networks and is an important milestone toward the development of practical applications of DRL to active flow control.

Categories: Latest papers in fluid mechanics

### Sedimentation of large particles in a suspension of colloidal rods

Physics of Fluids, Volume 32, Issue 5, May 2020.

The sedimentation at low Reynolds numbers of large, non-interacting spherical inclusions in networks of model monodisperse, slender colloidal rods is investigated. The influence of rod concentration, rod length, and inclusion stress on the inclusion’s creeping motion is investigated. The decrease in sedimentation speeds as a function of rod concentration is compared to the Stokes law, using the zero-shear viscosity from the Doi–Edwards theory for semi-dilute colloidal rod solutions. The experimental speeds display the same concentration dependence as the zero-shear viscosity and are, thus, strongly dependent on the rod length. The speed is, however, a fraction of 2 and 4 lower than expected for rods of 0.88 μm and 2.1 μm, respectively. The results for both rod lengths superimpose when plotted against the overlap concentration, hinting at an extra dependence on the entanglement.

The sedimentation at low Reynolds numbers of large, non-interacting spherical inclusions in networks of model monodisperse, slender colloidal rods is investigated. The influence of rod concentration, rod length, and inclusion stress on the inclusion’s creeping motion is investigated. The decrease in sedimentation speeds as a function of rod concentration is compared to the Stokes law, using the zero-shear viscosity from the Doi–Edwards theory for semi-dilute colloidal rod solutions. The experimental speeds display the same concentration dependence as the zero-shear viscosity and are, thus, strongly dependent on the rod length. The speed is, however, a fraction of 2 and 4 lower than expected for rods of 0.88 μm and 2.1 μm, respectively. The results for both rod lengths superimpose when plotted against the overlap concentration, hinting at an extra dependence on the entanglement.

Categories: Latest papers in fluid mechanics

### Experimental investigations of crater formation on granular bed subjected to an air-jet impingement

Physics of Fluids, Volume 32, Issue 5, May 2020.

The crater formation on granular particle beds is important for engineering applications, chemical and process industries as well as for an explanation of related natural phenomena. In this article, experimental studies on the formation of a crater and the subsequent movement of granular particles are carried out. Granular beds consisting of mono-dispersed or poly-dispersed spherical glass-beads are subjected to an air-jet impingement. The impinging air-jet causes creation of craters of various sizes and shapes (such as saucer shape, parabolic shape, parabolic shape with an intermediate region, U shape, and craters with conical slants with a curved bottom surface). The experimental observations reveal two predominant regimes, categorized based on the crater stability, namely, a stable regime or an unstable regime. The mechanisms for the crater formation such as viscous erosion, diffused gas eruption, bearing capacity failure, and diffusion driven flow or combination of them are identified. It is observed that the steady-state depth of a crater increases linearly with an increase in the air-jet flow-rate. The temporal growth of crater depth shows logarithmic variation for a given flow rate. A regime map of the observed crater shapes is presented.

The crater formation on granular particle beds is important for engineering applications, chemical and process industries as well as for an explanation of related natural phenomena. In this article, experimental studies on the formation of a crater and the subsequent movement of granular particles are carried out. Granular beds consisting of mono-dispersed or poly-dispersed spherical glass-beads are subjected to an air-jet impingement. The impinging air-jet causes creation of craters of various sizes and shapes (such as saucer shape, parabolic shape, parabolic shape with an intermediate region, U shape, and craters with conical slants with a curved bottom surface). The experimental observations reveal two predominant regimes, categorized based on the crater stability, namely, a stable regime or an unstable regime. The mechanisms for the crater formation such as viscous erosion, diffused gas eruption, bearing capacity failure, and diffusion driven flow or combination of them are identified. It is observed that the steady-state depth of a crater increases linearly with an increase in the air-jet flow-rate. The temporal growth of crater depth shows logarithmic variation for a given flow rate. A regime map of the observed crater shapes is presented.

Categories: Latest papers in fluid mechanics

### Structure functions and invariants of the anisotropic Reynolds stress tensor in turbulent flows on water-worked gravel beds

Physics of Fluids, Volume 32, Issue 5, May 2020.

In this paper, a statistical description of turbulence in flow on a water-worked gravel-bed is presented by applying the laws of turbulence in conjunction with the double-averaging methodology. To this end, a laboratory experiment was performed, in which the gravel-bed was worked by flowing water. From the Taylor frozen-in approximation, the energy spectra of streamwise velocity fluctuation reveal the existence of the inertial subrange (lying between the energy containing and the dissipation ranges), where the turbulent kinetic energy (TKE) dissipation rate is constant. It is revealed that, in this range, Kolmogorov’s 4/5-law for the spatial increments of streamwise velocity is valid, thus allowing an accurate estimation of the TKE dissipation rate. Although Monin–Yaglom’s 4/3-law for the third-order mixed structure function provides a behavior similar to that of Kolmogorov’s 4/5-law, the estimation of the TKE dissipation rate by Monin–Yaglom’s 4/3-law is not quite accurate, owing to the departure from the isotropic turbulence at large scales. Therefore, the present study demonstrates the validity of this statistical approach (Kolmogorov’s 4/5-law) to investigate the turbulence at small scales. Besides, the data plots for an anisotropy invariant map suggest that near-bed anisotropic turbulence tends to reduce to the three-dimensional isotropic turbulence with an increase in the vertical distance, indicating a relaxation of the effects of bed roughness on anisotropic turbulence toward the free surface.

In this paper, a statistical description of turbulence in flow on a water-worked gravel-bed is presented by applying the laws of turbulence in conjunction with the double-averaging methodology. To this end, a laboratory experiment was performed, in which the gravel-bed was worked by flowing water. From the Taylor frozen-in approximation, the energy spectra of streamwise velocity fluctuation reveal the existence of the inertial subrange (lying between the energy containing and the dissipation ranges), where the turbulent kinetic energy (TKE) dissipation rate is constant. It is revealed that, in this range, Kolmogorov’s 4/5-law for the spatial increments of streamwise velocity is valid, thus allowing an accurate estimation of the TKE dissipation rate. Although Monin–Yaglom’s 4/3-law for the third-order mixed structure function provides a behavior similar to that of Kolmogorov’s 4/5-law, the estimation of the TKE dissipation rate by Monin–Yaglom’s 4/3-law is not quite accurate, owing to the departure from the isotropic turbulence at large scales. Therefore, the present study demonstrates the validity of this statistical approach (Kolmogorov’s 4/5-law) to investigate the turbulence at small scales. Besides, the data plots for an anisotropy invariant map suggest that near-bed anisotropic turbulence tends to reduce to the three-dimensional isotropic turbulence with an increase in the vertical distance, indicating a relaxation of the effects of bed roughness on anisotropic turbulence toward the free surface.

Categories: Latest papers in fluid mechanics

### Analytic similarity solutions of the Navier–Stokes equations for a jet in a half space with the no-slip boundary condition

Physics of Fluids, Volume 32, Issue 5, May 2020.

We consider steady axisymmetric no-swirl viscous flows in a half space driven by a concentrated force. A method of finding physically meaningful similarity solutions of the Navier–Stokes equations with finite values of mass and momentum fluxes satisfying the no-slip boundary condition is developed. A new one-parameter set of analytic similarity solutions that describes impinging or emerging jets depending on the value of the parameter is found. A unique emerging-jet solution can be found for an arbitrary value of the Reynolds number. The accomplished analysis of momentum balance has resulted in an algorithm to estimate the best parameter of the similarity solution corresponding to the given physical characteristics of the jet source.

We consider steady axisymmetric no-swirl viscous flows in a half space driven by a concentrated force. A method of finding physically meaningful similarity solutions of the Navier–Stokes equations with finite values of mass and momentum fluxes satisfying the no-slip boundary condition is developed. A new one-parameter set of analytic similarity solutions that describes impinging or emerging jets depending on the value of the parameter is found. A unique emerging-jet solution can be found for an arbitrary value of the Reynolds number. The accomplished analysis of momentum balance has resulted in an algorithm to estimate the best parameter of the similarity solution corresponding to the given physical characteristics of the jet source.

Categories: Latest papers in fluid mechanics

### Three-dimensional simulation of wind tunnel diffuser to study the effects of different divergence angles on speed uniform distribution, pressure in outlet, and eddy flows formation in the corners

Physics of Fluids, Volume 32, Issue 5, May 2020.

Despite the widespread use of diffusers in various industries, there is no comprehensive research so far. This is expressive on how the flow diffuses throughout the diffuser geometry, the amount of non-uniformity of speed distribution at the outlet, and the rate of eddy flows at the corners. The present study simulated a three-dimensional diffuser with a square geometry at different divergence angles in order to obtain a better understanding of the flow diffusion across the geometry, velocity distribution at the outlet, and reverse flow. Moreover, the aspect ratio and the Reynolds number were considered constant in all cases. The turbulence model was used along with a high-resolution discretization and a root-mean-square convergence criterion to solve this problem. The speed was substantially reduced to nearly zero at corners of the diffuser with a square cross section. Reverse flow and eddy currents were also observed in the same regions. By increasing the divergence angle, this effect was further intensified, and in addition to the corners, flow separation and eddy currents were formed in the regions close to the wall due to the adverse pressure gradient. The maximum velocity and flow distribution at the outlet cross section was located in the central region, which was intensified by increasing the divergence angle. The deviation of the average velocity at the diffuser outlet with a divergence angle of 5°, with a completely uniform velocity distribution at the outlet, was observed to be 15.3%. This deviation grew with an increase in divergence angle and reached 128.9% at a divergence angle of 30°.

Despite the widespread use of diffusers in various industries, there is no comprehensive research so far. This is expressive on how the flow diffuses throughout the diffuser geometry, the amount of non-uniformity of speed distribution at the outlet, and the rate of eddy flows at the corners. The present study simulated a three-dimensional diffuser with a square geometry at different divergence angles in order to obtain a better understanding of the flow diffusion across the geometry, velocity distribution at the outlet, and reverse flow. Moreover, the aspect ratio and the Reynolds number were considered constant in all cases. The turbulence model was used along with a high-resolution discretization and a root-mean-square convergence criterion to solve this problem. The speed was substantially reduced to nearly zero at corners of the diffuser with a square cross section. Reverse flow and eddy currents were also observed in the same regions. By increasing the divergence angle, this effect was further intensified, and in addition to the corners, flow separation and eddy currents were formed in the regions close to the wall due to the adverse pressure gradient. The maximum velocity and flow distribution at the outlet cross section was located in the central region, which was intensified by increasing the divergence angle. The deviation of the average velocity at the diffuser outlet with a divergence angle of 5°, with a completely uniform velocity distribution at the outlet, was observed to be 15.3%. This deviation grew with an increase in divergence angle and reached 128.9% at a divergence angle of 30°.

Categories: Latest papers in fluid mechanics

### Gravel packing: How does it work?

Physics of Fluids, Volume 32, Issue 5, May 2020.

Oil and gas wells undergo completion operations before being able to produce. In the case where the surrounding reservoir is poorly consolidated, a popular method is open hole gravel packing. This proceeds by pumping a sand suspension along the annular region between the borehole wall and a cylindrical screen, sized to allow hydraulic conductivity but to prevent the passage of sand. Kilometers of sand can be successfully placed in horizontal wells, in what is called α–β packing. Although widely used, there is no clear and concise explanation of how these operations work, i.e., How does a steady (and apparently stable) traveling α-wave emerge? We develop such a model and explanation here. We explain how bed height is selected via coupling between the inner and outer annuli and from the combined hydraulic relations of inner and outer annuli. We investigate the effects of important parameters such as the slurry flow rate, mean solid concentration, washpipe diameter, and leak-off rate on gravel packing flows, to give a fluid mechanics framework within which this process can be easily understood.

Oil and gas wells undergo completion operations before being able to produce. In the case where the surrounding reservoir is poorly consolidated, a popular method is open hole gravel packing. This proceeds by pumping a sand suspension along the annular region between the borehole wall and a cylindrical screen, sized to allow hydraulic conductivity but to prevent the passage of sand. Kilometers of sand can be successfully placed in horizontal wells, in what is called α–β packing. Although widely used, there is no clear and concise explanation of how these operations work, i.e., How does a steady (and apparently stable) traveling α-wave emerge? We develop such a model and explanation here. We explain how bed height is selected via coupling between the inner and outer annuli and from the combined hydraulic relations of inner and outer annuli. We investigate the effects of important parameters such as the slurry flow rate, mean solid concentration, washpipe diameter, and leak-off rate on gravel packing flows, to give a fluid mechanics framework within which this process can be easily understood.

Categories: Latest papers in fluid mechanics

### Transition to chaos for buoyant flows in a groove heated from below

Physics of Fluids, Volume 32, Issue 5, May 2020.

In this paper, the transition to chaos for buoyant flows in a groove heated from below is analyzed using a three-dimensional numerical model. With a Prandtl number of 0.71 and an aspect ratio of 0.5, numerical simulations are performed for Rayleigh number Ra from 100 to 105. This wide range covers the transition process to chaos, the first change being the instability of the primary steady symmetric flow in the form of a symmetry-breaking pitchfork bifurcation between Ra = 1.5 × 103 and 1.6 × 103 that tilts the buoyant flow toward one or the other sidewall of the groove. A second pitchfork bifurcation to the three-dimensional flow occurs between Ra = 5.3 × 103 and 5.4 × 103. A Hopf bifurcation is observed between Ra = 5.6 × 103 and 5.7 × 103 at which the buoyant flow in the groove becomes temporally periodic; this is followed by a sequence of further bifurcations including period-doubling and quasi-periodic bifurcations. Finally, the buoyant flow becomes chaotic when bulge motion appears along the groove between Ra = 6.5 × 103 and 6.6 × 103. Limit points, limit cycles, attractors, maximum Lyapunov exponents, and power spectral density are presented to analyze typical buoyant flows in the transition to chaos. Additionally, the heat and mass transfer is quantified for the different regimes.

In this paper, the transition to chaos for buoyant flows in a groove heated from below is analyzed using a three-dimensional numerical model. With a Prandtl number of 0.71 and an aspect ratio of 0.5, numerical simulations are performed for Rayleigh number Ra from 100 to 105. This wide range covers the transition process to chaos, the first change being the instability of the primary steady symmetric flow in the form of a symmetry-breaking pitchfork bifurcation between Ra = 1.5 × 103 and 1.6 × 103 that tilts the buoyant flow toward one or the other sidewall of the groove. A second pitchfork bifurcation to the three-dimensional flow occurs between Ra = 5.3 × 103 and 5.4 × 103. A Hopf bifurcation is observed between Ra = 5.6 × 103 and 5.7 × 103 at which the buoyant flow in the groove becomes temporally periodic; this is followed by a sequence of further bifurcations including period-doubling and quasi-periodic bifurcations. Finally, the buoyant flow becomes chaotic when bulge motion appears along the groove between Ra = 6.5 × 103 and 6.6 × 103. Limit points, limit cycles, attractors, maximum Lyapunov exponents, and power spectral density are presented to analyze typical buoyant flows in the transition to chaos. Additionally, the heat and mass transfer is quantified for the different regimes.

Categories: Latest papers in fluid mechanics

### New similarity reductions and exact solutions for helically symmetric viscous flows

Physics of Fluids, Volume 32, Issue 5, May 2020.

In the present paper, we derive exact solutions for the helically invariant Navier–Stokes equations. The approach is based on an invariant solution ansatz emerging from the Galilean group in helical coordinates, which leads to linear functions in the helical coordinate ξ = az + bφ for the two helical velocity components uξ and uη. The variables z and φ are the usual cylinder coordinates. Starting from this approach, we derive a new equation for the radial velocity component ur in the helical frame, for which we found two special solutions. Moreover, we present an exact linearization of the Navier–Stokes equations by seeking exact solutions in the form of Beltrami flows. Using separation of variables, we found exponentially decaying time-dependent solutions, which consist of trigonometric functions in the helical coordinate ξ and of confluent Heun-type functions in the radial direction.

In the present paper, we derive exact solutions for the helically invariant Navier–Stokes equations. The approach is based on an invariant solution ansatz emerging from the Galilean group in helical coordinates, which leads to linear functions in the helical coordinate ξ = az + bφ for the two helical velocity components uξ and uη. The variables z and φ are the usual cylinder coordinates. Starting from this approach, we derive a new equation for the radial velocity component ur in the helical frame, for which we found two special solutions. Moreover, we present an exact linearization of the Navier–Stokes equations by seeking exact solutions in the form of Beltrami flows. Using separation of variables, we found exponentially decaying time-dependent solutions, which consist of trigonometric functions in the helical coordinate ξ and of confluent Heun-type functions in the radial direction.

Categories: Latest papers in fluid mechanics

### Publisher’s Note: “Turbulent drag induced by low surface roughness at transonic speeds: Experimental/numerical comparisons” [Phys. Fluids 32, 045108 (2020)]

Physics of Fluids, Volume 32, Issue 5, May 2020.

Categories: Latest papers in fluid mechanics