# Latest papers in fluid mechanics

### Rotational separation after temporary coalescence in binary droplet collisions

Author(s): Kuo-Long Pan, Kuan-Ling Huang, Wan-Ting Hsieh, and Chi-Ru Lu

In binary drop impact, in addition to reflexive separation and stretching separation, which occur at low and high impact angles (B), respectively, rotational separation is found at intermediate B. A generic model is developed to examine the scenarios and the interplay of various factors.

[Phys. Rev. Fluids 4, 123602] Published Mon Dec 02, 2019

### Deep learning of turbulent scalar mixing

Author(s): Maziar Raissi, Hessam Babaee, and Peyman Givi

Based on recent developments in physics-informed deep learning and deep hidden physics models, we put forth a framework for discovering turbulence models from scattered and potentially noisy spatio-temporal measurements of the probability density function.

[Phys. Rev. Fluids 4, 124501] Published Mon Dec 02, 2019

### Rapid mixing in microchannel using standing bulk acoustic waves

We present a technique for mixing the fluids in a microchannel using ultrasonic waves. Acoustic mixing is driven by the acoustic body force, which depends on the density gradient and speed of the sound gradient of the inhomogeneous fluid domain. In this work, mixing of fluids in a microchannel is achieved via an alternating multinode mixing method, which employs acoustic multinode standing waves of time-varying wavelengths at regular time intervals. The proposed technique is rapid, efficient, and found to enhance the mixing of fluids significantly. It is shown that the mixing time due to acoustic mixing (2–3 s) is reduced by two orders of magnitude compared to the mixing time only due to diffusion (400 s). Furthermore, we investigate the effects of the acoustic mixing on different fluid flow configurations and sound wave propagation directions as they have a direct influence on mixing time and have rarely been addressed previously. Remarkably, it is found that mixing performance is strongly dependent on the direction of the acoustic wave propagation. The acoustic field propagated parallel to the fluid-fluid interface mixes fluids rapidly (2–3 s) as compared to the acoustic field propagated perpendicular to the fluid-fluid interface (40 s).

### The use of flow type dependent strain reduction factor to improve fiber orientation predictions for an injection molded center-gated disk

To predict fiber orientation for injection molded parts, it is important to use a slow-kinetics orientation model and pay careful attention to the role of flow kinematics on orientation evolution speed. A model incorporating the impact of flow type on the fiber reorientation rate was tested by comparing with experimental data measured in an injection molded center-gated disk for both short and long glass fiber thermoplastics. Unlike the existing orientation models using a constant factor, a variable strain reduction factor (SRF) is expressed as a function of an objective flow-type parameter reflecting local flow kinematics. The use of this model improved the fiber orientation predictions at locations where the constant SRF, obtained from simple shear flow, deviated significantly from that based on the local flow kinematics.

### Effects of salinity on the onset of elastic turbulence in swirling flow and curvilinear microchannels

Elastic turbulence, which is sensitive to geometry and polymer rheology, has shown great potential for improving the performance of mixing, heat transfer, and even oil recovery. Recent studies showed the importance of the rheological properties of polymer solutions on the onset of elastic turbulence. However, variations of rheological properties based on polymer sensitivities such as salinity and its corresponding effects on the elastic turbulence have not been revealed. This work investigated systematically the effects of salinity on the onset of elastic turbulence in both swirling flow and curvilinear microchannels. The variations of statistical properties, such as probability distribution functions (PDFs) and power spectral density of injected power (PSD), were analyzed for characterization. The onset conditions of elastic turbulence are postponed by high salinity, which is consistent with the mixing performance in a curvilinear microchannel. A salinity independent power-law exponent at a value of −4.3 is observed in a fully developed elastic regime for all polymer solutions. Particularly, the diffusion of fluorescein at a low flow rate in the microchannel is possible due to the existence of a steady secondary flow before the onset of elastic instability.

### Generalized regimes for the formation of stratified regions during freezing of multi-component mixtures

Stratified double-diffusive layers (DDLs) in fluidic mixtures such as oceans, magma, and latte typically contain alternating low gradient mixing regions separated by high gradient interfaces. The prior knowledge is restricted to the formation of layers, but the existence of DDLs, under prolonged freezing conditions, as well as in multicomponent mixtures, is not yet understood well. In this work, a new observation depicting the existence of a life-cycle for a double-diffusive layer is revealed with the help of real-time observations of unidirectional freezing of multicomponent mixtures. The observations showed a systematic occurrence of the onset, formation, disappearance, and recurrence of the DDLs when freezing conditions prevailed for longer durations of time. The results also include first-ever observations of compositional stratification in a ternary mixture, which depends on the regimes and nature of buoyant convection. The ternary experiments also demonstrated the formation of DDLs much closer to the solidifying mush, which shed light on retaining the stratified layers in the frozen state. Furthermore, the hypothesized life-cycle of the DDL was mapped to the regimes of occurrence and the nonexistence of DDLs in the mixture phase diagrams of binary and ternary systems, with a threshold composition difference and the corresponding critical Rayleigh number. This distinction of the regimes on the phase diagram shows a striking correlation with a reduced ternary phase diagram of igneous rocks, thus providing a suitable basis for explaining the formation of layered rocks.

### On the analytical solution of the two-phase Couette flow with wall transpiration

The two-phase Couette flow with transpiration through both walls is considered, where there is a constant blowing v0 at the lower wall and a corresponding suction at the upper wall. The interface between both fluids is initially flat and, hence, stays flat as it moves upward at the constant speed of the transpiration velocity [math]. The corresponding initial value problem is subject to three dimensionless numbers consisting of the Reynolds number Re and the viscosity and density ratios, ϵ and γ. The solution is obtained by the unified transform method (Fokas method) in the form of an integral representation depending on initial and all boundary values including the Dirichlet and Neumann values at the interface. The unknown values at the moving interface are determined by a system of linear Volterra integral equations (VIEs). The VIEs are of the second kind with continuous and bounded kernels. Hence, the entire two-phase spatiotemporal 1 + 1 system has dimensionally reduced. The system of VIEs is solved via a standard marching method. For the numerical computation of the complex integral contours, a parameterized hyperbola is used. The influence of the dimensionless numbers Re, γ, and ϵ is studied exemplarily. The most notable effect results from ϵ that gives rise to a kink in the velocity at the moving interface. Both ratios, ϵ and γ, allow for very different flow regimes in each fluid phase such as nearly pure Couette flows and transpiration dominated flows with strongly curved velocity profiles. Those regimes are mainly determined by the effective Reynolds number in the respective phases.

### Control of flow and heat transfer over two inline square cylinders

Laminar flow around and heat transfer from two inline square cylinders under an active flow control (uniform blowing and suction) are numerically investigated at Reynolds numbers of 70–150, a Prandtl number of 0.71, and a cylinder-gap spacing (G) ratio of G/d = 1–5, where d is the cylinder side. A finite-volume code based on a collocated grid arrangement is employed in the two-dimensional numerical simulations. Uniform blowing and suction are applied to the upstream cylinder only (referred to as UFC) or applied to both cylinders (referred to as OFC). The purpose of using these two flow controls is to reduce time-mean and fluctuating forces and to suppress vortex shedding. The noncontrol case is referred to as the reference case where vortex shedding occurs from both cylinders for G/d ≥ 3 and from the downstream cylinder only for G/d < 3. For UFC, vortex shedding from the upstream cylinder is suppressed for G/d = 1–5 examined. A drag reduction of more than 50% occurs for the upstream cylinder with G/d = 1–5, while the downstream cylinder has such a high drag reduction for G/d ≥ 3 only. In the case of OFC, vortex shedding from either cylinder is suppressed while the time-mean and fluctuating forces reduce for the entire G/d range. The maximum reduction in the total drag force (sum of both cylinders) is about 70%. The blowing hinders heat transfer from the cylinders while the suction enhances it.

### Magnetic field induced ferrofluid droplet breakup in a simple shear flow at a low Reynolds number

The breakup phenomenon of a ferrofluid droplet in a simple shear flow under a uniform magnetic field is numerically investigated in this paper. The numerical simulation, based on the finite element method, uses a level set method to capture the dynamic evolution of the droplet interface between the two phases. Focusing on small Reynolds numbers (i.e., Re ≤ 0.03), systematic numerical simulations are carried out to analyze the effects of magnetic field strength, direction, and viscosity ratio on the breakup phenomenon of the ferrofluid droplet. The results suggest that applying a magnetic field along α = 45° and 90° relative to the flow direction initiates breakup in a ferrofluid droplet at a low capillary number in the Stokes flow regime, where the droplet usually does not break up in a shear flow alone. At α = 0° and 135°, the magnetic field suppresses breakup. Also, there exists a critical magnetic bond number, Bocr, below which the droplet does not rupture, which is also dependent on the direction of the magnetic field. Additionally, the effect of the viscosity ratio on droplet breakup is examined at variable magnetic bond numbers. The results indicate a decrease in the critical magnetic bond number Bocr values for more viscous droplets. Furthermore, more satellite droplets are observed at α = 45° compared to α = 90°, not only at higher magnetic field strengths but also at larger viscosity ratios.

### Comparison between the Q criterion and Rortex in the application of an in-stream structure

A newly proposed vortex identification method, namely, Rortex, is used to visualize the vortex structures around an in-stream deflector with a large eddy simulation. A comparison with the well-known vortex identification method, the Q criterion, indicates that the Q criterion and Rortex can both capture the main vortex structures in the flow field. However, both the modified Q criterion and the wavelet analysis reveal that Rortex excludes the shear information on the deposited sand surface, while the Q criterion cannot. As a result, Rortex is more suitable for vortex identification.

### Aerosol transport in a breathing alveolus

The present study aims to develop a fundamental understanding of the complex nature of fluid flow and particle transport dynamics in the alveolar region of the lungs. The acinus has a fine-scaled structure which allows for gas exchange in the blood. We model the transport characteristics of a single alveolar duct, which represents a single unit of the fine-scale acinar structure. A straight duct, with an expanding/contracting hemispherical bulb at one end, is used as a simplified approximation of a breathing alveolus. The diffusion of respiratory gases is considered across the boundary of the hemispherical bulb in order to account for the gas exchange. The transport equations are solved numerically using an Eulerian-Eulerian approach. The transport of aerosol particles could be demarcated into transient and time-periodic regimes, each with significantly different characteristics. While diffusion is observed to be the main cause of particle transport in the transient regime, the periodic nature of advective particle motion dominates in the time-periodic regime. Surprisingly, particle transport toward the acinus is observed even in a time-periodic breathing flow due to the nonlinear advective acceleration. A reduction in the particle size is observed to substantially aid the transport of aerosols. While gas exchange and increase in breathing frequency aid aerosol transport, the increase in the rate of aerosol transfer is observed to merely lower the aerosol concentration within the duct.

### Experimental investigation of gravity-driven film flow inside an inclined corrugated pipe

Gravity-driven film flow through an inclined corrugated pipe is experimentally investigated following field observations of unsteady, periodic flow patterns. Initial experiments confirmed surging flow at the pipe outlet as originally observed in the field. Fluorescence imaging of the film flow inside the pipe was then applied to examine the traveling wave behavior that leads to surging flow at the outlet. To our knowledge, this is the first investigation of traveling wave behavior in film flow in a corrugated pipe. The effect of flow rate and angle of inclination was studied in both experiments, with the characteristics of the traveling waves becoming the focus of the investigation. Similar to film flows over two-dimensional periodic topography, a statically deformed free surface with a wavelength approximately equivalent to the corrugations developed at all flow rates and angles examined with an amplitude that increased with angle of inclination. In contrast to film flows over two-dimensional periodic topography, the statically deformed free-surface amplitude was independent of the flow rate. Comparative to some two-dimensional studies, traveling waves developed from ambient noise through a strongly selective process. Traveling waves were observed to be approximately nondispersive and having nearly constant frequency and wavelength regardless of the flow rate or angle of inclination. The consistency in traveling wave character with changes in the angle and flow rate seems stronger than that seen for two-dimensional flows. Comparisons with large-scale flow applications, such as stepped spillways, indicate similarities in flow behavior that should be studied further.

### A smoothed particle hydrodynamics simulation of fiber-filled composites in a non-isothermal three-dimensional printing process

The mechanical and thermal behavior of nonisothermal fiber-filled composites in a three-dimensional printing process is studied numerically with a smoothed particle hydrodynamics method. A classical microstructure-based fiber suspension model with a temperature-dependent power-law viscosity model and a microstructure constitutive model is implemented to model a fiber-filled system. The fiber microstructure is described by a second-order tensor A2 which describes the spatially averaged orientation of the fibers. Two benchmark cases are presented to validate the reliability of the present implementation. Three typical printing modes are tested to assess the characteristics of printed layers. The results show that the printed layer becomes thicker, and the fiber alignment in the printing direction is enhanced in the bottom half of the layer and reduced in the top half due to the existence of nonisothermal effects in the process. The variation in fiber orientation becomes larger with increasing fiber concentration. By increasing the Peclet number, the deposited layer thickness reduces and the fiber alignment in the printing direction is enhanced in the top half and reduced in the bottom half. The evolution of the orientation and the velocity gradient tensors projected along several streamlines are discussed to illustrate the effects of the temperature and different printing modes on the deposited layer.

### Contraction of a shear-thinning axisymmetric cavity

We investigate the capillary driven collapse of a small contracting cavity or hole in a shear-thinning fluid. We find that shear-thinning effects accelerate the collapse of the cavity by decreasing the apparent liquid viscosity near the cavity’s moving front. Scaling arguments are used to derive a power-law relationship between the size of the cavity and the rate of collapse. The scaling predictions are then corroborated and fully characterized using high-fidelity simulations. The new findings have implications for natural and technological systems including neck collapse during microbubble pinch-off, the integrity of perforated films and biological membranes, the stability of bubbles and foams in the food industry, and the fabrication of nanopore based biosensors.

### Numerical study of two balls settling in viscoelastic fluids from an initial vertical configuration

In this article, we have investigated, via numerical simulation, the interaction of two identical balls settling in a vertical square tube filled with a viscoelastic fluid. For two balls released in Oldroyd-B fluids, one on top of the other initially, we have observed two possible scenarios, among others: either the trailing ball catches up the leading one to form a doublet (dipole) or the balls separate with a stable final distance. If the ball density is slightly larger than the fluid density, the two balls form a doublet, either vertical or tilted. If one further increases the ball density, the two balls still form a doublet if the initial distance is small enough, but for larger initial distances at higher elasticity numbers, the balls move away from each other and their distance reaches a stable constant. Factors influencing doublet formation are (possibly among others) the ball density, the ball initial distance, and the fluid elasticity number. When settling in finite extendable nonlinear elastic–Chilcott and Rallison fluids, low values of the coil maximal extension limit enhance ball separation.

### Topological equivalence between two classes of three-dimensional steady cavity flows: A numerical-experimental analysis

The present study concerns Lagrangian transport and (chaotic) advection in three-dimensional (3D) flows in cavities under steady and laminar conditions. The main goal is to investigate topological equivalences between flow classes driven by different forcing; streamline patterns and their response to nonlinear effects are examined. To this end, we consider two prototypical systems that are important in both natural and industrial applications: a buoyancy-driven flow (differentially heated configuration with two vertical isothermal walls) and a lid-driven flow governed by the Grashof (Gr) and the Reynolds (Re) numbers, respectively. Symmetries imply fundamental similarities between the streamline topologies of these flows. Moreover, nonlinearities induced by fluid inertia and buoyancy (increasing Gr) in the buoyancy-driven flow vs fluid inertia (increasing Re) and single- or double-wall motion in the lid-driven flow cause similar bifurcations of the Lagrangian flow topology. These analogies imply that Lagrangian transport is governed by universal mechanisms, and differences are restricted to the manner in which these phenomena are triggered. Experimental validation of key aspects of the Lagrangian dynamics is carried out by particle image velocimetry and 3D particle-tracking velocimetry.

### Numerical simulation of rolling pad instability in cuboid liquid metal batteries

The rolling pad instability is caused by electromagnetic interactions in systems of horizontal layers with strongly different electric conductivities. We analyze the instability for a simplified model of a liquid metal battery, a promising device for large-scale stationary energy storage. Numerical simulations of the flow and the dynamics of electromagnetically coupled interfacial waves are performed using OpenFOAM. This work confirms the earlier conclusions that the instability is a significant factor affecting the battery’s operation. The critical role played by the ratio between the density differences across the two interfaces is elucidated. It is found that the ratio determines the stability characteristics and the type (symmetrically or antisymmetrically coupled) of dominant interfacial waves.

### Non-isothermal mixing characteristics in the extreme near-field of a turbulent jet in hot crossflow

The nonreacting and reacting jet in crossflow (JICF) is an important flow configuration for effective mixing and combustion in practical applications. Many studies in the literature exist that examine the overall mixing characteristics of an isothermal, unconfined, nonreacting JICF. This experimental study examines the mixing characteristics in the very near field (s/d ≤ 3) of a nonreacting jet in a hot crossflow of combustion products (1500 K), a configuration relevant to gas turbine combustion. A range of jet-to-crossflow momentum flux ratios (5.2 ≤ J ≤ 24.2) and jet-to-crossflow density ratios (3.2 ≤ ρj/ρcf ≤ 7.8) was studied for a round jet with fully developed turbulent pipe flow and 4% mean turbulence intensity at the jet exit. Temperature measurements were made using planar laser Rayleigh scattering. Jet trajectory, jet centerline concentration decay based on adiabatic mixing assumption, Favre-averaged scalar dissipation, and scalar mixing time scales were determined as a function of the above-mentioned jet parameters. The observed center-plane mixing metrics indicated that better near field mixing was exhibited for lower values of the momentum flux ratio and larger values of density ratio in the extreme near field of the jet. As the momentum flux ratio was increased, windward and leeward mixing around the elongated potential core decreased, as indicated by the relative temperatures in these regions. The magnitude of scalar dissipation in the windward region decreased as the jet momentum flux increased, while the leeward dissipation region increased in size and magnitude as the momentum flux ratio increased. When the density ratio was decreased toward unity, both the windward and leeward dissipation regions reduced in size and magnitude.

### Wall-modeled large-eddy simulations of spanwise rotating turbulent channels—Comparing a physics-based approach and a data-based approach

We develop wall modeling capabilities for large-eddy simulations (LESs) of channel flow subjected to spanwise rotation. The developed models are used for flows at various Reynolds numbers and rotation numbers, with different grid resolutions and in differently sized computational domains. We compare a physics-based approach and a data-based machine learning approach. When pursuing a data-based approach, we use the available direct numerical simulation data as our training data. We highlight the difference between LES wall modeling, where one writes all flow quantities in a coordinate defined by the wall-normal direction and the near-wall flow direction, and Reynolds-averaged Navier-Stokes modeling, where one writes flow quantities in tensor forms. Pursuing a physics-based approach, we account for system rotation by reformulating the eddy viscosity in the wall model. Employing the reformulated eddy viscosity, the wall model is able to predict the mean flow correctly. Pursuing a data-based approach, we train a fully connected feed-forward neural network (FNN). The FNN is informed about our knowledge (although limited) on the mean flow. We then use the trained FNNs as wall models in wall modeled LES (WMLES) and show that it predicts the mean flow correctly. While it is not the focus of this study, special attention is paid to the problem of log-layer mismatch, which is common in WMLES. Our study shows that log-layer mismatch, or rather, linear-layer mismatch in WMLES of spanwise rotating channels, is not present at high rotation numbers, even when the wall-model/LES matching location is at the first grid point.

### Mitigating tip vortex cavitation by a flexible trailing thread

Tip Vortex Cavitation (TVC) is a major issue in design and operation of axial hydraulic machines. We investigate the capacity of a flexible trailing thread in alleviating TVC by analyzing the flow-induced motion. For this purpose, a nylon thread with three diameters is cut in various lengths and attached to the tip of an elliptical hydrofoil. The selected threads are flexible enough to become unstable and start to flutter under almost all the tested flow conditions. Due to the vortical flow, an oscillating thread is forced to spiral around the vortex axis. The resulting rotational motion is shown to decelerate the axial velocity in and around the vortex core via two possible mechanisms: first by exerting a local drag and taking energy from the flow and second by increasing the flow fluctuations and turbulent mixing. Our results reveal that a thread becomes more effective in TVC suppression when it is comparable in size with the viscous core of the tip vortex. In fact, a sufficiently thick thread may be sucked into the vortex core under the effect of the pressure field. This results in the hereby-called “whipping” motion that consists of the quasiperiodic coincidence of a part of the thread and the tip vortex axis close to the root. Compared with the rotational motion, the whipping motion is found superior in mitigating TVC. We propose a model that predicts that whipping motion, in contrast to rotational motion, could lead to viscous core thickening, which is validated by the velocity measurements.