# Latest papers in fluid mechanics

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

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.

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

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.

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

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.

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

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.

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

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).

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

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.

### Bubble merger in initial Richtmyer-Meshkov instability on inverse-chevron interface

Author(s): Xu Guo, Zhigang Zhai, Ting Si, and Xisheng Luo

Inverse-chevron interfaces with various initial amplitudes and wavelengths are used in shock tube experiments to study bubble competition in the Richtmyer-Meshkov instability. We find that width growth of the large interface is enhanced and that of the small interface is more affected and inhibited.

[Phys. Rev. Fluids 4, 092001(R)] Published Mon Sep 30, 2019

### Stability of viscous fingering in lifted Hele-Shaw cells with a hole

Author(s): Sachin D. Kanhurkar, Vardhan Patankar, Tanveer ul Islam, Prasanna S. Gandhi, and Amitabh Bhattacharya

Theory, simulations, and experiments are used to study liquid-air interfacial instability of lifted Hele Shaw cells (LHSCs) with a hole in the center. The stability map provides a design framework for using multihole LHSCs to generate stable meshlike patterns in the liquid film.

[Phys. Rev. Fluids 4, 094003] Published Mon Sep 30, 2019

### Diffused-interface Rayleigh-Taylor instability with a nonlinear equation of state

Author(s): Jason Olsthoorn, Edmund W. Tedford, and Gregory A. Lawrence

An investigation of the impact of a nonlinear equation of state on the evolution of the Rayleigh-Taylor instability is presented. The nonlinear density relation introduces asymmetry in the growing plumes about the density interface, preferentially generating kinetic energy in the lower layer.

[Phys. Rev. Fluids 4, 094501] Published Mon Sep 30, 2019

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

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.

### Direct numerical simulation of vortex-induced instability for a zero-pressure-gradient boundary layer

Author(s): Aditi Sengupta, V. K. Suman, and Tapan K. Sengupta

Vortex-induced instability caused by a free-stream vortical excitation is explored here quantitatively with the help of controlled computational results. First, the computed results are compared with experimental results in Lim *et al.* [Exp. Fluids **37**, 47 (2004)] for the purpose of validation of the ...

[Phys. Rev. E 100, 033118] Published Thu Sep 26, 2019

### Effects of isothermal stratification strength on vorticity dynamics for single-mode compressible Rayleigh-Taylor instability

Author(s): Scott A. Wieland, Peter E. Hamlington, Scott J. Reckinger, and Daniel Livescu

The effects of initial stratification on single-mode Rayleigh-Taylor instability are examined using fully compressible wavelet-based direct numerical simulations. Such instabilities are widespread and are found in inertial confinement fusion, supernova ignition fronts, x-ray bursts, and geophysics.

[Phys. Rev. Fluids 4, 093905] Published Thu Sep 26, 2019

### Fully resolved simulations of a stationary finite-sized particle in wall turbulence over a rough bed

Author(s): Xing Li, S. Balachandar, Hyungoo Lee, and Bofeng Bai

Direct numerical simulations are used to investigate forces on a stationary finite-sized particle in wall turbulence over a rough bed of hemispherical particles. Results show that lift is the main contributor of wall-normal force and can be well predicted with proper application of existing models.

[Phys. Rev. Fluids 4, 094302] Published Thu Sep 26, 2019

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

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.

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

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.

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

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.

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

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.

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

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.

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

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.

### Stratified flow past a prolate spheroid

Author(s): Jose L. Ortiz-Tarin, K. C. Chongsiripinyo, and S. Sarkar

Simulation of density-stratified flow past an elongated body reveals substantial differences with respect to a sphere in flow separation, the near wake and internal waves. As stratification increases (Fr decreases), the fluid experiences vertical/sideways deflection and the separated region changes.

[Phys. Rev. Fluids 4, 094803] Published Wed Sep 25, 2019