# 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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### Fluid-structure investigation of a squid-inspired swimmer

Physics of Fluids, Volume 31, Issue 10, October 2019.

We propose a novel underwater propulsion system inspired by the jet-propelled locomotion mechanism of squids and other cephalopods. A two-dimensional nonaxisymmetric fluid-structural interaction model is developed to illustrate the physical mechanisms involved in the propulsive performance of this design. The model includes a deformable body with a pressure chamber undergoing periodic inflation and deflation motions enabled by attached springs and a nozzle through which the chamber is refilled and discharged (to form a jet). By using an immersed-boundary algorithm, we numerically investigate the dynamics of this system in the tethered mode. The thrust generation is found to increase with the frequency of body deformation, whereas the efficiency reaches a peak at a certain frequency. Examinations of the surrounding flow field illustrate a combination of vortices shed from the body and the nozzle. The optimal efficiency is reached when the nozzle-generated vortices start to dominate the wake. Our simulations also suggest that steady-state response can only be sustained for a few cycles before the wake is disturbed by a symmetry-breaking instability, which significantly affects the propulsive performance. Special strategies are needed to achieve stable long-distance swimming.

We propose a novel underwater propulsion system inspired by the jet-propelled locomotion mechanism of squids and other cephalopods. A two-dimensional nonaxisymmetric fluid-structural interaction model is developed to illustrate the physical mechanisms involved in the propulsive performance of this design. The model includes a deformable body with a pressure chamber undergoing periodic inflation and deflation motions enabled by attached springs and a nozzle through which the chamber is refilled and discharged (to form a jet). By using an immersed-boundary algorithm, we numerically investigate the dynamics of this system in the tethered mode. The thrust generation is found to increase with the frequency of body deformation, whereas the efficiency reaches a peak at a certain frequency. Examinations of the surrounding flow field illustrate a combination of vortices shed from the body and the nozzle. The optimal efficiency is reached when the nozzle-generated vortices start to dominate the wake. Our simulations also suggest that steady-state response can only be sustained for a few cycles before the wake is disturbed by a symmetry-breaking instability, which significantly affects the propulsive performance. Special strategies are needed to achieve stable long-distance swimming.

Categories: Latest papers in fluid mechanics

### The atmospheric Rayleigh-Bénard problem on the f-plane

Physics of Fluids, Volume 31, Issue 10, October 2019.

When applied to a system of sizeable vertical extent that can undergo adiabatic expansion/compression, the Rayleigh-Bénard treatment of convection between two parallel plates, kept at constant temperature, needs to be amended with the consideration of potential temperature as the conserved thermodynamic variable. The fixed-temperature boundary conditions are therefore expressed as a combination of potential temperature and pressure, and this causes the solutions to be a mixture of the odd and even modes of the classical problem. Here, solutions are presented for a rotating system, which supports both stationary and oscillatory modes. While the stationary modes are all stabilized by this mechanism, as was shown previously for a nonrotating system, the oscillatory modes can have a lower critical Rayleigh number than their traditional counterpart, when the Prandtl number is approximately between 0.2 and 1.0.

When applied to a system of sizeable vertical extent that can undergo adiabatic expansion/compression, the Rayleigh-Bénard treatment of convection between two parallel plates, kept at constant temperature, needs to be amended with the consideration of potential temperature as the conserved thermodynamic variable. The fixed-temperature boundary conditions are therefore expressed as a combination of potential temperature and pressure, and this causes the solutions to be a mixture of the odd and even modes of the classical problem. Here, solutions are presented for a rotating system, which supports both stationary and oscillatory modes. While the stationary modes are all stabilized by this mechanism, as was shown previously for a nonrotating system, the oscillatory modes can have a lower critical Rayleigh number than their traditional counterpart, when the Prandtl number is approximately between 0.2 and 1.0.

Categories: Latest papers in fluid mechanics

### On the selection of perturbations for thermal boundary layer control

Physics of Fluids, Volume 31, Issue 10, October 2019.

The convective instability of the natural convection boundary layers of air (Pr = 0.7) in the laminar-to-turbulent transition regime (Ra = 8.7 × 107–1.1 × 109) is investigated by stability analysis in the framework of direct numerical simulations. To understand the spatial and temporal evolution of the convective instability of the thermal boundary layers, small-amplitude random-mode numerical perturbations are first introduced into the boundary condition of the boundary layer flow. The prescribed full spectral perturbations (i.e., white noise) are mostly damped out immediately by a limited upstream boundary layer. A low-frequency band is initially distinct in the upstream near the leading edge but decays spatially as the instability propagates downstream. In contrast, a high-frequency band emerges to finally become the most dominant frequency band in the thermal boundary layer transition regime. To obtain further insights into the nature of the established high-frequency band, single-mode perturbations of various frequencies are then introduced into the boundary layer near the leading edge. It is found that a single-mode perturbation at the peak frequency within the high-frequency band excites the maximum response of the thermal boundary layer, suggesting that the peak frequency is in fact the characteristic frequency or resonance frequency of the thermal boundary layer. The dimensionless form of the dependence of the characteristic frequency on Ra is then found to be fc = 0.07Ra2/3. The single-mode perturbation numerical experiments also revealed the propagation speed of convective instability waves, which was significantly greater than the convection speed of the thermal boundary layer. The smaller the Ra, the larger the difference between the two propagation speeds. A semi-analytical scaling of the wave propagation speed in the form csc ∼ Ra1/2y1/2Pr was derived (y denoting the streamwise location of the boundary layer), providing a predictive correlation that can be used for thermal boundary layer control.

The convective instability of the natural convection boundary layers of air (Pr = 0.7) in the laminar-to-turbulent transition regime (Ra = 8.7 × 107–1.1 × 109) is investigated by stability analysis in the framework of direct numerical simulations. To understand the spatial and temporal evolution of the convective instability of the thermal boundary layers, small-amplitude random-mode numerical perturbations are first introduced into the boundary condition of the boundary layer flow. The prescribed full spectral perturbations (i.e., white noise) are mostly damped out immediately by a limited upstream boundary layer. A low-frequency band is initially distinct in the upstream near the leading edge but decays spatially as the instability propagates downstream. In contrast, a high-frequency band emerges to finally become the most dominant frequency band in the thermal boundary layer transition regime. To obtain further insights into the nature of the established high-frequency band, single-mode perturbations of various frequencies are then introduced into the boundary layer near the leading edge. It is found that a single-mode perturbation at the peak frequency within the high-frequency band excites the maximum response of the thermal boundary layer, suggesting that the peak frequency is in fact the characteristic frequency or resonance frequency of the thermal boundary layer. The dimensionless form of the dependence of the characteristic frequency on Ra is then found to be fc = 0.07Ra2/3. The single-mode perturbation numerical experiments also revealed the propagation speed of convective instability waves, which was significantly greater than the convection speed of the thermal boundary layer. The smaller the Ra, the larger the difference between the two propagation speeds. A semi-analytical scaling of the wave propagation speed in the form csc ∼ Ra1/2y1/2Pr was derived (y denoting the streamwise location of the boundary layer), providing a predictive correlation that can be used for thermal boundary layer control.

Categories: Latest papers in fluid mechanics

### Relations between skin friction and other surface quantities in viscous flows

Physics of Fluids, Volume 31, Issue 10, October 2019.

This paper presents the derivations of the exact relations between skin friction and other important dynamical and kinematical quantities on a stationary curved surface in a viscous flow by applying the standard methods of differential geometry to the governing partial differential equations in fluid mechanics. In particular, the mathematical structures of the effects of the surface curvature are explicitly expressed, which extend the previous results on a flat surface. These relations reveal that skin friction is intrinsically coupled with surface pressure, temperature, and scalar concentration through the boundary enstrophy flux, heat flux, and mass flux, respectively. As an example, the relation between skin friction and surface pressure is examined in the Oseen flow over a sphere to elucidate the significant effect of the surface curvature at a very small Reynolds number. Two other validation examples are a gravity-driven creeping liquid film flow over a wavy surface and the Falkner-Skan flow over a wedge. Furthermore, the relation is applied to a simulated turbulent channel flow to explore the local near-wall coherent structure and understand its dynamical roles in turbulence production.

This paper presents the derivations of the exact relations between skin friction and other important dynamical and kinematical quantities on a stationary curved surface in a viscous flow by applying the standard methods of differential geometry to the governing partial differential equations in fluid mechanics. In particular, the mathematical structures of the effects of the surface curvature are explicitly expressed, which extend the previous results on a flat surface. These relations reveal that skin friction is intrinsically coupled with surface pressure, temperature, and scalar concentration through the boundary enstrophy flux, heat flux, and mass flux, respectively. As an example, the relation between skin friction and surface pressure is examined in the Oseen flow over a sphere to elucidate the significant effect of the surface curvature at a very small Reynolds number. Two other validation examples are a gravity-driven creeping liquid film flow over a wavy surface and the Falkner-Skan flow over a wedge. Furthermore, the relation is applied to a simulated turbulent channel flow to explore the local near-wall coherent structure and understand its dynamical roles in turbulence production.

Categories: Latest papers in fluid mechanics

### The theory and application of Navier-Stokeslets (NSlets)

Physics of Fluids, Volume 31, Issue 10, October 2019.

Consider a closed body moving in an unbounded fluid that decays to rest in the far-field and governed by the incompressible Navier-Stokes equations. By considering a translating reference frame, this is equivalent to a uniform flow past the body. A velocity representation is given as an integral distribution of Green’s functions of the Navier-Stokes equations which we shall call NSlets. The strength of the NSlets is the same as the force distribution over the body boundary. An expansion for the NSlet is given with the leading-order term being the Oseenlet. To test the theory, the following three two-dimensional steady flow benchmark applications are considered. First, consider uniform flow past a circular cylinder for three cases: low Reynolds number, high Reynolds number, and also intermediate Reynolds numbers at values 26 and 36. These values are chosen because the flow is still steady and has not yet become unsteady. For the low Reynolds number, approximate the NSlet by the leading order Oseenlet term. For the high Reynolds number, approximate the NSlet by the Eulerlet which is the leading order Oseenlet in the high Reynolds number limit. For the intermediate Reynolds numbers, approximate the NSlet by an Eulerlet close to its origin and an Oseenlet further away. Second, consider uniform flow past a slender body with elliptical cross section with Reynolds number Re ∼ 106 and approximate the NSlet by the Eulerlet. Finally, consider the Blasius problem of uniform flow past a semi-infinite flat plate and consider the first three terms in the NSlet approximation.

Consider a closed body moving in an unbounded fluid that decays to rest in the far-field and governed by the incompressible Navier-Stokes equations. By considering a translating reference frame, this is equivalent to a uniform flow past the body. A velocity representation is given as an integral distribution of Green’s functions of the Navier-Stokes equations which we shall call NSlets. The strength of the NSlets is the same as the force distribution over the body boundary. An expansion for the NSlet is given with the leading-order term being the Oseenlet. To test the theory, the following three two-dimensional steady flow benchmark applications are considered. First, consider uniform flow past a circular cylinder for three cases: low Reynolds number, high Reynolds number, and also intermediate Reynolds numbers at values 26 and 36. These values are chosen because the flow is still steady and has not yet become unsteady. For the low Reynolds number, approximate the NSlet by the leading order Oseenlet term. For the high Reynolds number, approximate the NSlet by the Eulerlet which is the leading order Oseenlet in the high Reynolds number limit. For the intermediate Reynolds numbers, approximate the NSlet by an Eulerlet close to its origin and an Oseenlet further away. Second, consider uniform flow past a slender body with elliptical cross section with Reynolds number Re ∼ 106 and approximate the NSlet by the Eulerlet. Finally, consider the Blasius problem of uniform flow past a semi-infinite flat plate and consider the first three terms in the NSlet approximation.

Categories: Latest papers in fluid mechanics

### Steady laminar plume generated from a heated line in polymer solutions

Physics of Fluids, Volume 31, Issue 10, October 2019.

From the theoretical viewpoint, governing equations are derived for a steady laminar plume generated from a heated line in polymer solutions, in which similarity variables and the single polymer chain model are introduced. The resolved solutions imply that polymers promote the velocity in the centerline-near region but suppress that in the region far from the centerline. The equivalent effect of polymers is understood as producing two space-dependent source terms, which can explain the interaction between polymers and fluid flow from the viewpoint of energy transport. There exists a critical Weissenberg number (Wi) beyond which the promotion effect in the centerline-near region disappears, which results from the competition of stretching and relaxation of the polymer chain. Meanwhile, the corresponding modification of similarity velocity and heat transport are illustrated and validated numerically by single plume flow in polymer solutions. This work thus may contribute to the understanding of the polymer effect on single plume flow and further the heat transport enhancement mechanism in the bulk flow of turbulent Rayleigh-Bénard convection with polymers.

From the theoretical viewpoint, governing equations are derived for a steady laminar plume generated from a heated line in polymer solutions, in which similarity variables and the single polymer chain model are introduced. The resolved solutions imply that polymers promote the velocity in the centerline-near region but suppress that in the region far from the centerline. The equivalent effect of polymers is understood as producing two space-dependent source terms, which can explain the interaction between polymers and fluid flow from the viewpoint of energy transport. There exists a critical Weissenberg number (Wi) beyond which the promotion effect in the centerline-near region disappears, which results from the competition of stretching and relaxation of the polymer chain. Meanwhile, the corresponding modification of similarity velocity and heat transport are illustrated and validated numerically by single plume flow in polymer solutions. This work thus may contribute to the understanding of the polymer effect on single plume flow and further the heat transport enhancement mechanism in the bulk flow of turbulent Rayleigh-Bénard convection with polymers.

Categories: Latest papers in fluid mechanics

### Experimental study of drop impact on a thin fiber

Physics of Fluids, Volume 31, Issue 10, October 2019.

In this paper, we present an experimental study of drop impact on a thin flexible fiber. Detailed dynamics of the collision was captured with a high-speed video camera. Previous studies have presented three modes: capturing, single drop falling, and splitting. However, in our experiments, we observed that a low-speed drop could bounce off a thin fiber. Moreover, the splitting mode was segmented into two different types: low-speed splitting and high-speed splitting. Based on systematic experiments, we rebuilt a regime map consisting of capturing, low-speed splitting, single drop falling, and high-speed splitting. Both the upper and the lower limits of the low-speed splitting were presented. Fiber wettability was found to play an important role in the impact results. Low-speed splitting vanished when a water drop impacts on a nylon fiber coated with a layer of hydrophilic material. Meanwhile, a theoretical model was proposed to predict the fiber dynamics, which fitted well with the experimental results.

In this paper, we present an experimental study of drop impact on a thin flexible fiber. Detailed dynamics of the collision was captured with a high-speed video camera. Previous studies have presented three modes: capturing, single drop falling, and splitting. However, in our experiments, we observed that a low-speed drop could bounce off a thin fiber. Moreover, the splitting mode was segmented into two different types: low-speed splitting and high-speed splitting. Based on systematic experiments, we rebuilt a regime map consisting of capturing, low-speed splitting, single drop falling, and high-speed splitting. Both the upper and the lower limits of the low-speed splitting were presented. Fiber wettability was found to play an important role in the impact results. Low-speed splitting vanished when a water drop impacts on a nylon fiber coated with a layer of hydrophilic material. Meanwhile, a theoretical model was proposed to predict the fiber dynamics, which fitted well with the experimental results.

Categories: Latest papers in fluid mechanics

### Influence of distributed heavy-gas injection on stability and transition of supersonic boundary-layer flow

Physics of Fluids, Volume 31, Issue 10, October 2019.

This study performed a joint theoretical and experimental investigation of the influence of distributed normal-to-the-surface and inclined heavy-gas injection into the near-wall sublayer of a boundary layer through a permeable wall on the laminar-turbulent transition (LTT). Sulfur hexafluoride (SF6) is used as a foreign gas for injection into the boundary layer. It also assessed stability in relation to both natural and artificial (controlled) disturbances of a supersonic flat-plate boundary layer at a free-stream Mach number (M) of 2. It is established, theoretically, that the action of a large molecular weight gas injection on the boundary layer is similar to the action of wall cooling and leads to an increase in boundary layer stability and LTT delay. The influence of injection on the position of transition is estimated by means of the eN method. Principally, the analysis shows the possibility of increasing the transition Reynolds number by means of SF6 injection. Controlled disturbances are introduced in the model boundary layer by means of a point harmonic glow-discharge disturbance generator and are measured by using a hot-wire anemometer. For the first time, it is shown experimentally that distributed injection of the heavy SF6 gas leads to boundary layer stabilization. This is mostly due to the reduction in growth rates of disturbances at higher frequencies, while the LTT shifted to higher Reynolds number values. Good qualitative agreement is achieved between the experimental data obtained with artificially generated disturbances and computations based on linear stability theory.

This study performed a joint theoretical and experimental investigation of the influence of distributed normal-to-the-surface and inclined heavy-gas injection into the near-wall sublayer of a boundary layer through a permeable wall on the laminar-turbulent transition (LTT). Sulfur hexafluoride (SF6) is used as a foreign gas for injection into the boundary layer. It also assessed stability in relation to both natural and artificial (controlled) disturbances of a supersonic flat-plate boundary layer at a free-stream Mach number (M) of 2. It is established, theoretically, that the action of a large molecular weight gas injection on the boundary layer is similar to the action of wall cooling and leads to an increase in boundary layer stability and LTT delay. The influence of injection on the position of transition is estimated by means of the eN method. Principally, the analysis shows the possibility of increasing the transition Reynolds number by means of SF6 injection. Controlled disturbances are introduced in the model boundary layer by means of a point harmonic glow-discharge disturbance generator and are measured by using a hot-wire anemometer. For the first time, it is shown experimentally that distributed injection of the heavy SF6 gas leads to boundary layer stabilization. This is mostly due to the reduction in growth rates of disturbances at higher frequencies, while the LTT shifted to higher Reynolds number values. Good qualitative agreement is achieved between the experimental data obtained with artificially generated disturbances and computations based on linear stability theory.

Categories: Latest papers in fluid mechanics

### Translational and rotational motion of disk-shaped Marangoni surfers

Physics of Fluids, Volume 31, Issue 10, October 2019.

In this paper, we study the Marangoni propulsion of a neutrally buoyant disk-shaped object at the air-water interface. Self-propulsion was achieved by coating the back of the disk with either soap or isopropyl alcohol in order to generate and then maintain a surface tension gradient across the surfer. As the propulsion strength and the resulting disk velocity were increased, a transition from a straight-line translational motion to a rotational motion was observed. Although spinning had been observed before for asymmetric objects, these are the first observations of spinning of a geometrically axisymmetric Marangoni surfer. Particle tracking and particle image velocimetry measurements were used to interrogate the resulting flow field and understand the origin of the rotational motion of the disk. These measurements showed that as the Reynolds number was increased, interfacial vortices attached to sides of the disk were formed and intensified. Beyond a critical Reynolds number of Re > 120, a vortex was observed to shed resulting in an unbalanced torque on the disk that caused it to rotate. The interaction between the disk and the confining wall of the Petri dish was also studied. Upon approaching the bounding wall, a transition from straight-line motion to rotational motion was observed at significantly lower Reynolds numbers than on an unconfined interface. Interfacial curvature was found to either enhance or eliminate rotational motion depending on whether the curvature was repulsive (concave) or attractive (convex).

In this paper, we study the Marangoni propulsion of a neutrally buoyant disk-shaped object at the air-water interface. Self-propulsion was achieved by coating the back of the disk with either soap or isopropyl alcohol in order to generate and then maintain a surface tension gradient across the surfer. As the propulsion strength and the resulting disk velocity were increased, a transition from a straight-line translational motion to a rotational motion was observed. Although spinning had been observed before for asymmetric objects, these are the first observations of spinning of a geometrically axisymmetric Marangoni surfer. Particle tracking and particle image velocimetry measurements were used to interrogate the resulting flow field and understand the origin of the rotational motion of the disk. These measurements showed that as the Reynolds number was increased, interfacial vortices attached to sides of the disk were formed and intensified. Beyond a critical Reynolds number of Re > 120, a vortex was observed to shed resulting in an unbalanced torque on the disk that caused it to rotate. The interaction between the disk and the confining wall of the Petri dish was also studied. Upon approaching the bounding wall, a transition from straight-line motion to rotational motion was observed at significantly lower Reynolds numbers than on an unconfined interface. Interfacial curvature was found to either enhance or eliminate rotational motion depending on whether the curvature was repulsive (concave) or attractive (convex).

Categories: Latest papers in fluid mechanics

### Statistical analysis of temperature distribution on vortex surfaces in hypersonic turbulent boundary layer

Physics of Fluids, Volume 31, Issue 10, October 2019.

The nonuniform temperature distribution (NUTD) on the coherent vortex surfaces of hypersonic turbulent boundary layer (TBL) is studied using the conditional sampling technique. The direct numerical simulation data of Mach 8 flat-plate TBL flows with different wall temperatures, Tw/T∞ = 10.03 and 1.9, are used for this research, and the coherent vortex surface is identified by the Ω-criterion. Two characteristic sides of the vortex are defined, which are represented by the positive and negative streamwise velocity fluctuations (±u′) of the vortex surfaces. The conditional sampling results between the mean temperature of the two sides show that there is a significant difference of up to 20% at the same wall-normal location. Furthermore, the velocity-temperature fluctuation correlations (Ru′T′ and Rv′T′) at the characteristic sides of vortex surfaces are studied. It is found that the temperature fluctuations are redistributed by the vortex rotational motion that has taken effect through Ru′T′ and Rv′T′ and then lead to the NUTD. The NUTD features are changed quantitatively by wall cooling but share the similar mechanism as that of the higher-temperature case.

The nonuniform temperature distribution (NUTD) on the coherent vortex surfaces of hypersonic turbulent boundary layer (TBL) is studied using the conditional sampling technique. The direct numerical simulation data of Mach 8 flat-plate TBL flows with different wall temperatures, Tw/T∞ = 10.03 and 1.9, are used for this research, and the coherent vortex surface is identified by the Ω-criterion. Two characteristic sides of the vortex are defined, which are represented by the positive and negative streamwise velocity fluctuations (±u′) of the vortex surfaces. The conditional sampling results between the mean temperature of the two sides show that there is a significant difference of up to 20% at the same wall-normal location. Furthermore, the velocity-temperature fluctuation correlations (Ru′T′ and Rv′T′) at the characteristic sides of vortex surfaces are studied. It is found that the temperature fluctuations are redistributed by the vortex rotational motion that has taken effect through Ru′T′ and Rv′T′ and then lead to the NUTD. The NUTD features are changed quantitatively by wall cooling but share the similar mechanism as that of the higher-temperature case.

Categories: Latest papers in fluid mechanics

### Meltblown technology for production of polymeric microfibers/nanofibers: A review

Physics of Fluids, Volume 31, Issue 9, September 2019.

This work summarizes the current state of knowledge in the area of meltblown technology for production of polymeric nonwovens with specific attention to utilized polymers, die design, production of nanofibers, the effect of process variables (such as the throughput rate, melt rheology, melt temperature, die temperature, air temperature/velocity/pressure, die-to-collector distance, and speed) with relation to nonwoven characteristics as well as to typical flow instabilities such as whipping, die drool, fiber breakup, melt spraying, flies, generation of small isolated spherical particles, shots, jam, and generation of nonuniform fiber diameters.

This work summarizes the current state of knowledge in the area of meltblown technology for production of polymeric nonwovens with specific attention to utilized polymers, die design, production of nanofibers, the effect of process variables (such as the throughput rate, melt rheology, melt temperature, die temperature, air temperature/velocity/pressure, die-to-collector distance, and speed) with relation to nonwoven characteristics as well as to typical flow instabilities such as whipping, die drool, fiber breakup, melt spraying, flies, generation of small isolated spherical particles, shots, jam, and generation of nonuniform fiber diameters.

Categories: Latest papers in fluid mechanics

### Turbulent drag reduction in Taylor-Couette flows using different super-hydrophobic surface configurations

Physics of Fluids, Volume 31, Issue 9, September 2019.

Turbulent drag reduction (DR) in an incompressible Taylor-Couette flow configuration using different patterns of “idealized” superhydrophobic surfaces (SHS) on rotating inner-wall is investigated using direct numerical simulations (DNS). Three dimensional DNS studies based on the finite difference method in cylindrical annuli of aspect ratio (Γ) = 6.0 and radius ratios (η) = 0.5 and 0.67 have been performed at Reynolds numbers (Re) 4000 and 5000. The SHS comprised of streamwise or azimuthal microgrooves (MG), spanwise or longitudinal MG, grooves inclined to the streamwise direction (spiral), and microposts. The SHS have been modeled as shearfree areas. We were able to achieve a maximum DR up to 34% for the streamwise aligned SHS, while we got drag enhancement of 4% for the spiral SHS at η = 0.67. The SHS cause slip at the wall as well as near-wall turbulence modification, both governing the DR. We have tried to understand the role of the effective slip and modified turbulence dynamics responsible for DR by analyzing the statistics of mean flow, velocity fluctuations, Reynolds stresses, turbulence kinetic energy (TKE), and near-wall streaks. Most of the results show enhanced production of near-wall streamwise velocity fluctuations and TKE resulting in near-wall turbulence enhancement, yet we observed DR for most of the cases, thereby implying slip to be the dominant contributor to DR in comparison to modified near-wall turbulence.

Turbulent drag reduction (DR) in an incompressible Taylor-Couette flow configuration using different patterns of “idealized” superhydrophobic surfaces (SHS) on rotating inner-wall is investigated using direct numerical simulations (DNS). Three dimensional DNS studies based on the finite difference method in cylindrical annuli of aspect ratio (Γ) = 6.0 and radius ratios (η) = 0.5 and 0.67 have been performed at Reynolds numbers (Re) 4000 and 5000. The SHS comprised of streamwise or azimuthal microgrooves (MG), spanwise or longitudinal MG, grooves inclined to the streamwise direction (spiral), and microposts. The SHS have been modeled as shearfree areas. We were able to achieve a maximum DR up to 34% for the streamwise aligned SHS, while we got drag enhancement of 4% for the spiral SHS at η = 0.67. The SHS cause slip at the wall as well as near-wall turbulence modification, both governing the DR. We have tried to understand the role of the effective slip and modified turbulence dynamics responsible for DR by analyzing the statistics of mean flow, velocity fluctuations, Reynolds stresses, turbulence kinetic energy (TKE), and near-wall streaks. Most of the results show enhanced production of near-wall streamwise velocity fluctuations and TKE resulting in near-wall turbulence enhancement, yet we observed DR for most of the cases, thereby implying slip to be the dominant contributor to DR in comparison to modified near-wall turbulence.

Categories: Latest papers in fluid mechanics

### Nonlinear interaction and coalescence features of oscillating bubble pairs: Experimental and numerical study

Physics of Fluids, Volume 31, Issue 9, September 2019.

Nonlinear interaction and coalescence features of oscillating bubble pairs are investigated experimentally and numerically. The spark technique is used to generate in-phase bubble pairs with similar size and the simulation is performed with the compressible volume of fluid (VOF) solver in OpenFOAM. The initial conditions for the simulation are determined from the reference case, where the interbubble distance is sufficiently large and the spherical shape is maintained at the moment of maximum volume. Although the microscopic details of the coalescing behaviors are not focused, the compressible VOF solver reproduces the important features of the experiment and shows good grid convergence. We systematically investigate the effects of the dimensionless interbubble distance γ (scaled by the maximum bubble radius) and define three different coalescing patterns, namely, coalescence due to the expansion in the first cycle for γ < 1.1 (Pattern I), bubble breaking up and collapsing together with coalescence at the initial rebounding stage for 1.1 < γ < 2.0 (Pattern II), and coalescence of the rebounding toroidal bubbles for 2.0 < γ < 3.65 (Pattern III). For Pattern I, prominent gas flow and velocity fluctuation can be observed in the coalescing region, which may induce the annular protrusion in the middle of the coalesced bubble. For Patterns II and III, migration of the bubbles toward each other during the collapsing and rebounding stages greatly facilitates the bubble coalescence.

Nonlinear interaction and coalescence features of oscillating bubble pairs are investigated experimentally and numerically. The spark technique is used to generate in-phase bubble pairs with similar size and the simulation is performed with the compressible volume of fluid (VOF) solver in OpenFOAM. The initial conditions for the simulation are determined from the reference case, where the interbubble distance is sufficiently large and the spherical shape is maintained at the moment of maximum volume. Although the microscopic details of the coalescing behaviors are not focused, the compressible VOF solver reproduces the important features of the experiment and shows good grid convergence. We systematically investigate the effects of the dimensionless interbubble distance γ (scaled by the maximum bubble radius) and define three different coalescing patterns, namely, coalescence due to the expansion in the first cycle for γ < 1.1 (Pattern I), bubble breaking up and collapsing together with coalescence at the initial rebounding stage for 1.1 < γ < 2.0 (Pattern II), and coalescence of the rebounding toroidal bubbles for 2.0 < γ < 3.65 (Pattern III). For Pattern I, prominent gas flow and velocity fluctuation can be observed in the coalescing region, which may induce the annular protrusion in the middle of the coalesced bubble. For Patterns II and III, migration of the bubbles toward each other during the collapsing and rebounding stages greatly facilitates the bubble coalescence.

Categories: Latest papers in fluid mechanics

### High-speed film-thickness measurements between a collapsing cavitation bubble and a solid surface with total internal reflection shadowmetry

Physics of Fluids, Volume 31, Issue 9, September 2019.

The time evolution of the liquid-film thickness of a single cavitation bubble in water collapsing onto a solid surface is measured. To this end, total internal reflection (TIR) shadowmetry is developed, a technique based on TIR and the imaging of shadows of an optical structure on a polished glass surface. The measurements are performed at frame rates up to 480 kHz. Simultaneous high-speed imaging of the bubble shape at up to 89 kHz allows relating the evolution of the film thickness to the bubble dynamics. With a typical maximum bubble radius of 410 µm, we varied the nondimensional stand-off distance γ from 0.47 to 1.07. We find that during the first collapse phase, the bubble does not come in direct contact with the solid surface. Instead, when the bubble collapses, the jet impacts on a liquid film that always resides between the bubble and solid. At jet impact, it is 5–40 µm thick, depending on γ. Also, during rebound, at any given point in time, most or all of the then overall toroidal bubble is not in contact with the solid surface.

The time evolution of the liquid-film thickness of a single cavitation bubble in water collapsing onto a solid surface is measured. To this end, total internal reflection (TIR) shadowmetry is developed, a technique based on TIR and the imaging of shadows of an optical structure on a polished glass surface. The measurements are performed at frame rates up to 480 kHz. Simultaneous high-speed imaging of the bubble shape at up to 89 kHz allows relating the evolution of the film thickness to the bubble dynamics. With a typical maximum bubble radius of 410 µm, we varied the nondimensional stand-off distance γ from 0.47 to 1.07. We find that during the first collapse phase, the bubble does not come in direct contact with the solid surface. Instead, when the bubble collapses, the jet impacts on a liquid film that always resides between the bubble and solid. At jet impact, it is 5–40 µm thick, depending on γ. Also, during rebound, at any given point in time, most or all of the then overall toroidal bubble is not in contact with the solid surface.

Categories: Latest papers in fluid mechanics

### Mechanisms for turbulent separation control using plasma actuator at Reynolds number of 1.6 × 106

Physics of Fluids, Volume 31, Issue 9, September 2019.

We have conducted large-eddy simulations of turbulent separated flows over a NACA0015 airfoil with control by a plasma actuator. The Reynolds number based on the chord length is 1 600 000, and the angle of attack is 20.1°. At this angle of attack, the flow around the airfoil is fully separated. The effects of the location and operating conditions of the plasma actuator on the separation control are investigated. The plasma actuator is set at the leading edge, the turbulent reattachment point, or near the turbulent separation point. The nondimensional burst frequency (F+) is set to 1, 4, or 100. These frequencies are determined based on the dominant frequencies of the turbulent separated flow field of the no control case. A continuous actuation case has also been conducted. The location of the actuator where it most effectively suppresses the separation is the one closest to the turbulent separation point. In the burst mode case, the nondimensional burst frequency of unity is most effective in terms of the increase in the lift. To clarify the effective control mechanism, five objectives for turbulent separation control are compared. The results show that it is difficult to suppress the turbulent separation using the same strategies as in laminar separation control. The effective mechanism for turbulent separation control by burst actuation is found to be inducing the pairing of large-scale vortices near the airfoil surface. This large-scale vortex pairing induces freestream momentum into the boundary layer, leading to separation suppression. In addition, three other control effects can be achieved by varying the operating settings of the plasma actuator. The drag is slightly improved by reducing the length of the laminar separation bubble through high-frequency actuation from the leading edge.

We have conducted large-eddy simulations of turbulent separated flows over a NACA0015 airfoil with control by a plasma actuator. The Reynolds number based on the chord length is 1 600 000, and the angle of attack is 20.1°. At this angle of attack, the flow around the airfoil is fully separated. The effects of the location and operating conditions of the plasma actuator on the separation control are investigated. The plasma actuator is set at the leading edge, the turbulent reattachment point, or near the turbulent separation point. The nondimensional burst frequency (F+) is set to 1, 4, or 100. These frequencies are determined based on the dominant frequencies of the turbulent separated flow field of the no control case. A continuous actuation case has also been conducted. The location of the actuator where it most effectively suppresses the separation is the one closest to the turbulent separation point. In the burst mode case, the nondimensional burst frequency of unity is most effective in terms of the increase in the lift. To clarify the effective control mechanism, five objectives for turbulent separation control are compared. The results show that it is difficult to suppress the turbulent separation using the same strategies as in laminar separation control. The effective mechanism for turbulent separation control by burst actuation is found to be inducing the pairing of large-scale vortices near the airfoil surface. This large-scale vortex pairing induces freestream momentum into the boundary layer, leading to separation suppression. In addition, three other control effects can be achieved by varying the operating settings of the plasma actuator. The drag is slightly improved by reducing the length of the laminar separation bubble through high-frequency actuation from the leading edge.

Categories: Latest papers in fluid mechanics

### Evaporation-induced flow around a droplet in different gases

Physics of Fluids, Volume 31, Issue 9, September 2019.

It is known from recent studies that evaporation induces flow around a droplet at atmospheric conditions. This flow is visible even for slowly evaporating liquids like water. In the present study, we investigate the influence of the ambient gas on the evaporating droplet. We observe from the experiments that the rate of evaporation at atmospheric temperature and pressure decreases in a heavier ambient gas. The evaporation-induced flow in these gases for different liquids is measured using particle image velocimetry and found to be very different from each other. However, the width of the disturbed zone around the droplet is seen to be independent of the evaporating liquid and the size of the needle (for the range of needle diameters studied), and only depends on the ambient gas used.

It is known from recent studies that evaporation induces flow around a droplet at atmospheric conditions. This flow is visible even for slowly evaporating liquids like water. In the present study, we investigate the influence of the ambient gas on the evaporating droplet. We observe from the experiments that the rate of evaporation at atmospheric temperature and pressure decreases in a heavier ambient gas. The evaporation-induced flow in these gases for different liquids is measured using particle image velocimetry and found to be very different from each other. However, the width of the disturbed zone around the droplet is seen to be independent of the evaporating liquid and the size of the needle (for the range of needle diameters studied), and only depends on the ambient gas used.

Categories: Latest papers in fluid mechanics

### Accelerating deep reinforcement learning strategies of flow control through a multi-environment approach

Physics of Fluids, Volume 31, Issue 9, September 2019.

Deep Reinforcement Learning (DRL) has recently been proposed as a methodology to discover complex active flow control strategies [Rabault et al., “Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control,” J. Fluid Mech. 865, 281–302 (2019)]. However, while promising results were obtained on a simple 2-dimensional benchmark flow at a moderate Reynolds number, considerable speedups will be required to investigate more challenging flow configurations. In the case of DRL trained with Computational Fluid Dynamics (CFD) data, it was found that the CFD part, rather than training the artificial neural network, was the limiting factor for speed of execution. Therefore, speedups should be obtained through a combination of two approaches. The first one, which is well documented in the literature, is to parallelize the numerical simulation itself. The second one is to adapt the DRL algorithm for parallelization. Here, a simple strategy is to use several independent simulations running in parallel to collect experiences faster. In the present work, we discuss this solution for parallelization. We illustrate that perfect speedups can be obtained up to the batch size of the DRL agent, and slightly suboptimal scaling still takes place for an even larger number of simulations. This is, therefore, an important step toward enabling the study of more sophisticated fluid mechanics problems through DRL.

Deep Reinforcement Learning (DRL) has recently been proposed as a methodology to discover complex active flow control strategies [Rabault et al., “Artificial neural networks trained through deep reinforcement learning discover control strategies for active flow control,” J. Fluid Mech. 865, 281–302 (2019)]. However, while promising results were obtained on a simple 2-dimensional benchmark flow at a moderate Reynolds number, considerable speedups will be required to investigate more challenging flow configurations. In the case of DRL trained with Computational Fluid Dynamics (CFD) data, it was found that the CFD part, rather than training the artificial neural network, was the limiting factor for speed of execution. Therefore, speedups should be obtained through a combination of two approaches. The first one, which is well documented in the literature, is to parallelize the numerical simulation itself. The second one is to adapt the DRL algorithm for parallelization. Here, a simple strategy is to use several independent simulations running in parallel to collect experiences faster. In the present work, we discuss this solution for parallelization. We illustrate that perfect speedups can be obtained up to the batch size of the DRL agent, and slightly suboptimal scaling still takes place for an even larger number of simulations. This is, therefore, an important step toward enabling the study of more sophisticated fluid mechanics problems through DRL.

Categories: Latest papers in fluid mechanics

### Thermodynamic effects on Venturi cavitation characteristics

Physics of Fluids, Volume 31, Issue 9, September 2019.

In this paper, the thermodynamic effect is systematically studied by Venturi cavitation in a blow-down type tunnel for the first time, using water at temperatures up to relatively high levels and at controlled dissolved gas contents in the supply reservoir (measured by dissolved oxygen, DO). The mean attached cavity length [math] is chosen to reveal the thermodynamic effect, and the cavitation characteristics are analyzed from the experiments. With an increase in the thermodynamic parameter Σ*, a decrease in [math] vs the pressure recovery number κ is observed, which is consistent with suppression of cavitation by the thermodynamic effect, but the decrease is related not only to this effect. Based on the experimental results, a model is presented of the attached cavity cloud that develops from the Venturi throat. It is found that either the length of this cloud oscillates stably around a mean value or the cloud breaks regularly at some upstream position, allowing that a detached cavity cloud is shed, flows downstream, and collapses while the remaining attached cloud regenerates. Applying this model to experimental results obtained first with cold water, then with hot water, we find that when the mean length of the attached cavity cloud oscillates stably, temperature increase causes reduction of the mean cavitation length. This is interpreted to be a consequence of the thermodynamic effect. When detachment of large cavity clouds occurs, the mean length is increased at temperature increase. This is a consequence of cloud configuration changes being superposed on changes due to the thermodynamic effect. These observations explain conflicting results reported for attached cavity clouds in relation to the thermodynamic effect. The gas content in the water is found to be without significance within the range of DO tested.

In this paper, the thermodynamic effect is systematically studied by Venturi cavitation in a blow-down type tunnel for the first time, using water at temperatures up to relatively high levels and at controlled dissolved gas contents in the supply reservoir (measured by dissolved oxygen, DO). The mean attached cavity length [math] is chosen to reveal the thermodynamic effect, and the cavitation characteristics are analyzed from the experiments. With an increase in the thermodynamic parameter Σ*, a decrease in [math] vs the pressure recovery number κ is observed, which is consistent with suppression of cavitation by the thermodynamic effect, but the decrease is related not only to this effect. Based on the experimental results, a model is presented of the attached cavity cloud that develops from the Venturi throat. It is found that either the length of this cloud oscillates stably around a mean value or the cloud breaks regularly at some upstream position, allowing that a detached cavity cloud is shed, flows downstream, and collapses while the remaining attached cloud regenerates. Applying this model to experimental results obtained first with cold water, then with hot water, we find that when the mean length of the attached cavity cloud oscillates stably, temperature increase causes reduction of the mean cavitation length. This is interpreted to be a consequence of the thermodynamic effect. When detachment of large cavity clouds occurs, the mean length is increased at temperature increase. This is a consequence of cloud configuration changes being superposed on changes due to the thermodynamic effect. These observations explain conflicting results reported for attached cavity clouds in relation to the thermodynamic effect. The gas content in the water is found to be without significance within the range of DO tested.

Categories: Latest papers in fluid mechanics

### Turbulent transport and mixing in the multimode narrowband Richtmyer-Meshkov instability

Physics of Fluids, Volume 31, Issue 9, September 2019.

The mean momentum and heavy mass fraction, turbulent kinetic energy, and heavy mass fraction variance fields, as well as the budgets of their transport equations are examined several times during the evolution of a narrowband Richtmyer-Meshkov instability initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3. The results are computed using the “quarter scale” data from four algorithms presented in the θ-group study of Thornber et al. [“Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer-Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)]. The present study is inspired by a previous similar study of Rayleigh-Taylor instability and mixing using direct numerical simulation data by Schilling and Mueschke [“Analysis of turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow using direct numerical simulation data,” Phys. Fluids 22, 105102 (2010)]. In addition to comparing the predictions of the data from four implicit large-eddy simulation codes, the budgets are used to quantify the relative importance of the terms in the transport equations, and the balance of the terms is employed to infer the numerical dissipation. Terms arising from the compressibility of the flow are examined, in particular the pressure-dilatation. The results are useful for validation of large-eddy simulation and Reynolds-averaged modeling of Richtmyer-Meshkov instability.

The mean momentum and heavy mass fraction, turbulent kinetic energy, and heavy mass fraction variance fields, as well as the budgets of their transport equations are examined several times during the evolution of a narrowband Richtmyer-Meshkov instability initiated by a Mach 1.84 shock traversing a perturbed interface separating gases with a density ratio of 3. The results are computed using the “quarter scale” data from four algorithms presented in the θ-group study of Thornber et al. [“Late-time growth rate, mixing, and anisotropy in the multimode narrowband Richtmyer-Meshkov instability: The θ-group collaboration,” Phys. Fluids 29, 105107 (2017)]. The present study is inspired by a previous similar study of Rayleigh-Taylor instability and mixing using direct numerical simulation data by Schilling and Mueschke [“Analysis of turbulent transport and mixing in transitional Rayleigh-Taylor unstable flow using direct numerical simulation data,” Phys. Fluids 22, 105102 (2010)]. In addition to comparing the predictions of the data from four implicit large-eddy simulation codes, the budgets are used to quantify the relative importance of the terms in the transport equations, and the balance of the terms is employed to infer the numerical dissipation. Terms arising from the compressibility of the flow are examined, in particular the pressure-dilatation. The results are useful for validation of large-eddy simulation and Reynolds-averaged modeling of Richtmyer-Meshkov instability.

Categories: Latest papers in fluid mechanics

### Determination of the volume fraction in (water-gasoil-air) multiphase flows using a simple and low-cost technique: Artificial neural networks

Physics of Fluids, Volume 31, Issue 9, September 2019.

The precise prediction of the volume fraction in three-phase flows plays an important role in the petroleum and process industries. In this study, attenuation gamma rays (single pencil beam) and multilayer perceptron neural networks were used to precisely predict the volume fraction percentage in water-gasoil-air three-phase flows. The detection system uses just one 137Cs source (single energy of 662 keV) and one NaI(Tl) detector in order to calculate the transmitted beams. The experimental setup was simulated using the MCNPX code to provide the required data for the neural network. The volume fraction percentage was measured with a root mean square error of 2.48 and a mean relative error percentage of less than 7.08%. The proposed setup is the best and simplest design for reducing radiation hazards and cost.

The precise prediction of the volume fraction in three-phase flows plays an important role in the petroleum and process industries. In this study, attenuation gamma rays (single pencil beam) and multilayer perceptron neural networks were used to precisely predict the volume fraction percentage in water-gasoil-air three-phase flows. The detection system uses just one 137Cs source (single energy of 662 keV) and one NaI(Tl) detector in order to calculate the transmitted beams. The experimental setup was simulated using the MCNPX code to provide the required data for the neural network. The volume fraction percentage was measured with a root mean square error of 2.48 and a mean relative error percentage of less than 7.08%. The proposed setup is the best and simplest design for reducing radiation hazards and cost.

Categories: Latest papers in fluid mechanics