# New Papers in Fluid Mechanics

### Unexpected secondary flows in reverse nonequilibrium shear flow simulations

Author(s): Antonia Statt, Michael P. Howard, and Athanassios Z. Panagiotopoulos

Surprising secondary flows develop in reverse nonequilibrium simulations when the simulation box is elongated in the direction of flow.

[Phys. Rev. Fluids 4, 043905] Published Thu Apr 25, 2019

### Solute transport in two-zone packed tube flow: Long-time asymptotic expansion

Previous studies of solute transport in two-zone packed tube flows focused only on the cross-sectional mean concentration, a Gaussian distribution with advection velocity and Taylor dispersivity. This work analytically investigates the complete spatial concentration distribution. The two-dimensional (longitudinal and transverse) concentration distribution is obtained, by Chatwin’s long-time asymptotic technique: Edgeworth expansion. Non-Gaussian distribution effects like skewness and kurtosis are included in the asymptotic solution. Three cases with different porosity distributions between zones are studied to illustrate the impact of heterogeneity of media distributions on solute dispersion. The variation of porosity distributions can lead to great changes in velocity profiles, positions of local maxima of the concentration distribution, and basic characteristics of the cross-sectional mean concentration distribution, such as dispersivity, skewness, and kurtosis. Additionally, zones have largely different in zone-cross-sectional mean concentration distributions in the initial stage of solute transport.

### Near-bed turbulence structures in water-worked and screeded gravel-bed flows

Coherent structures and their impact on the near-bed time-averaged flow structure in a water-worked gravel-bed (WGB) and a screeded gravel-bed (SGB) are analyzed. Instantaneous velocities were measured using a particle image velocimetry system in the WGB and SGB flows in a flume with rectangular cross section. To ascertain the response of the WGB with respect to the SGB to the coherent structures, the time- and double-averaged flow, and the spatially averaged (SA) turbulence parameters, the experimental flow conditions for both the beds were kept identical. The surface gravels in the WGB were spatially organized owing to the water action. By contrast, the surface gravels in the SGB were randomly poised. These result in a higher roughness height in the WGB than in the SGB. Time series analysis for the instantaneous velocity and vorticity on a central vertical plane along the streamwise direction proves that the coherent structures in the near-bed flow zone are constituted by rapidly and slowly moving fluid streaks. Besides, the time-averaged streamwise velocity, vorticity, turbulence level, third-order correlations, and turbulent kinetic energy (TKE) budget are analyzed in the WGB and SGB. Their contours are plotted on the central vertical plane to study their spatial distributions. In addition, the SA higher-order correlations and TKE budget in the WGB and SGB are examined. A comparative study infers that the higher roughness in the WGB than in the SGB causes both the time-averaged and SA turbulence parameters in the former to be greater than those in the latter.

### Numerical investigation on the collapse of a bubble cluster near a solid wall

Author(s): Lingxin Zhang, Jing Zhang, and Jian Deng

This paper studies numerically the collapse of a cluster of cavitation bubbles (as a primitive model for a bubble cloud) near a solid wall. The homogeneous two-phase mixture model is used, with the liquid-vapor interface resolved by volume of fluid method. The liquid is treated as compressible, allo...

[Phys. Rev. E 99, 043108] Published Wed Apr 24, 2019

### Density-stable displacement flow of immiscible fluids in inclined pipes

Author(s): Olamide Oladosu, Aqib Hasnain, Paris Brown, Ian Frigaard, and Kamran Alba

Displacement of a water-based solution by an oil-based one is studied experimentally. Applications are found in cleaning-in-place processes present in the petroleum and food processing industries. An interesting wall pinning effect due to wetting/nonwetting properties of solutions is observed.

[Phys. Rev. Fluids 4, 044007] Published Wed Apr 24, 2019

### Drop impacting on a single layer of particles: Evolution of ring without particles

In this study, we examined the impacts of a millimeter sized water drop hitting a layer of uniformly distributed particles on a hydrophilic/hydrophobic glass slide. A ring/disc structure without particles was formed and modified by two mechanisms: pushout and pullback. The pushout factor dominated the process when the drop hit on the hydrophilic glass slide, while the pullback factor played a decisive role during impact on the hydrophobic surface. The rebound of a drop on the hydrophobic surface formed a disc-shaped ring. We showed that the ratio of the effects of these two factors on the ring/disc width were independent from the impact speed, in both experimental and scaling analyses. Our results also suggested that higher hydrophobicity of a water drop on the hydrophobic glass slide, instead of a polymethyl methacrylate (PMMA) particle surface, resulted in a lower maximum spreading distance when the drop hit the PMMA particle layer on a hydrophobic surface.

### Numerical modeling of the dynamics of bubble oscillations subjected to fast variations in the ambient pressure with a coupled level set and volume of fluid method

Author(s): Indrajit Chakraborty

A numerical method for modeling and understanding the dynamics of bubble oscillations subjected to fast variations in the ambient pressure is proposed under low Mach number conditions. In the present work, the method uses a single-fluid continuum formalism of weakly compressible axisymmetric Navier-...

[Phys. Rev. E 99, 043107] Published Tue Apr 23, 2019

### The theory and application of eulerlets

Consider a fixed body in a uniform flow field in the limit as the Reynolds number approaches infinity and the flow field remains steady. Instead of using standard techniques and theory for describing the problem, a new method is employed based upon the concept of matching two different Green’s integral representations over a common boundary, one given by approximations valid in the near-field and the other by approximations in the far-field. Further novelty arises from the choice of a near-field, that is, the Euler flow matched to an Oseen flow far-field. This entails introducing and defining eulerlets that are Green’s functions of the Euler equation. One important consequence of the model is the presence of a new Euler wake velocity not captured in standard models. This has a constant unchanging downstream profile and arises from the matching to the far-field Oseen wake velocity. It is then shown how this representation reduces to classical inviscid ideal flow aerodynamics when applied to flow past aerofoils and wings. It is also shown how it reduces to slender body flow theory. Finally, the formulation is tested on uniform flow past a circular cylinder for mean-steady subcritical laminar flow and turbulent flow. The inviscid impermeability boundary condition is used, the drag coefficient is specified, and a constant distribution of drag eulerlets is modeled. The forward flow separation and pressure drop in the wake are captured and compare favorably with experiment. The future expectation is the modeling of multiple general shaped bodies.

### The physics of twin-fluid jet-in-crossflow at atmospheric and jet-engine operating conditions

Efforts to mitigate jet engine emissions produced a class of swirl-stabilized combustors in which a rich pilot-flame in the center of the swirl-cup anchors an outer-annulus of lean-premixed main-flame. Fuel distribution within the annulus must be carefully controlled to allow stable combustion while avoiding excessive swirl-cup heating and flashbacks. This was traditionally achieved by placing plain jet-in-crossflow (JICF) fuel injectors around the swirl-cup; however, a recent increase in engine operating pressure and temperature along with demand for leaner fuel-air mixtures made the traditional approach untenable. Hence, modern swirl-cup designs begin to adopt a new fuel-injection technique called the “twin-fluid JICF (TF-JICF)” where a sleeve of air is co-injected with the liquid jet to modify its spray-pattern. TF-JICF is a nascent variation of the JICF that is not well understood, especially at elevated pressures. Hence, an experimental investigation of TF-JICF spray behaviors was performed by our group, covering the operating conditions of 1.5–9.5 atm in crossflow pressure, 175–1050 in crossflow Weber number, 5–40 in momentum flux-ratio, and 0%–150% in air-nozzle pressure-drop, at the crossflow temperature of 150 °C and velocity of 75 m/s. Part 1 of the investigation’s results, which identified four distinct flow regimes and nonmonotonic penetration trends in TF-JICF, was published in the work of Tan et al., “The regimes of twin-fluid jet-in-crossflow at atmospheric and jet-engine operating conditions,” Phy. Fluids 30, 025101 (2018). The current paper expands upon the previous report by elucidating key spray features and potential mechanisms (e.g., transitions between crossflow-driven atomization, air-driven shear-atomization, and air-driven prompt-atomization) within each TF-JICF regime, thereby providing a conceptual framework of TF-JICF for future studies.

### Characteristics of hydrogen jet combustion in a high-enthalpy supersonic crossflow

The facilitation of a stable combustion process is of utmost importance for the realizability and performance of hypersonic propulsion systems. To elucidate the turbulent combustion characteristics, wall-modeled large eddy simulations of a transverse jet injection into a heated supersonic flow are conducted employing a detailed reaction mechanism. The computation framework utilizes an adaptive central-upwind weighted essentially nonoscillatory (WENO-CU) scheme to achieve the sixth-order accuracy in smooth flowfields, while keeping a good shock-capturing ability. The reacting zones agree well with experimental measurements in terms of the instantaneous distribution of OH radicals. And the flame penetration height has been predicted with an error of less than 17%. It is found that the turbulent reacting flow is dominated by nonpremixed combustion mainly taking place in the near-wall region and jet windward shear-layer. Moreover, the autoignition process, which plays a critical role in stabilizing supersonic combustion, shows to favor a fuel-lean or not very fuel-rich environment of a high enthalpy. Local scalar dissipation induced by turbulence gives rise to a rapid fuel mixing with the surrounding air. However, this effect may also lead to the decrease in local temperature.

### A posteriori tests of subgrid-scale models in an isothermal turbulent channel flow

This paper studies the large-eddy simulation (LES) of isothermal turbulent channel flows. We investigate zero-equation algebraic models without wall function or wall model: functional models, structural models, and mixed models. In addition to models from the literature, new models are proposed and their relevance is examined. Dynamic versions of each type of model are also analyzed. The performance of the subgrid-scale models is assessed using the same finite difference numerical method and physical configuration. The friction Reynolds number of the simulations is 180. Three different mesh resolutions are used. The predictions of large-eddy simulations are compared to those of a direct numerical simulation filtered at the resolution of the LES meshes. The results are more accurate than those of a simulation without model. The predictions of functional eddy-viscosity models can be improved using constant-parameter or dynamic tensorial methods.

### Three-dimensional flow structures in X-shaped junctions: Effect of the Reynolds number and crossing angle

We study numerically the three-dimensional (3D) dynamics of two facing flows in an X-shaped junction of two circular channels crossing at an angle α. The distribution of the fluids in the junction and in the outlet channels is determined as a function of α and the Reynolds number Re. Our goal is to describe the different flow regimes in the junction and their dependence on α and Re. We also explore to which extent two-dimensional (2D) simulations are able to describe the flow within a 3D geometry. In the 3D case, at large Re’s (≳50) and α’s (≳60°), axial vorticity (i.e., parallel to the outlet axis) of magnitude increasing both with α and Re develops in the outlet channels and cannot be reproduced by 2D numerical simulations. At lower angles (α ≲ 60°), instead, a mean vorticity component perpendicular to the junction plane is present: both its magnitude and the number of the corresponding vortices (i.e., recirculation zones) increase as α decreases. These vortices appear in both 2D and 3D simulations but at different threshold values of α and Re. At very low Re’s (≲5) and α’s (∼15°), the flow structure in 3D simulations is nearly 2D but its quantitative characteristics differ from 2D simulations. As Re increases, this two-dimensionality disappears, while vortices due to flow separation appear in the outlet channels.

### Analysis of rolling friction effects on oblique rebound by redefining tangential restitution and friction

The planar oblique impact of a homogeneous sphere on an infinitely massive rough plane is described assuming that normal and tangential restitution mechanisms operate independently of friction, and that frictional effects include not only the usual Coulomb model but also rolling friction effects. This formulation extends early models including rolling friction effects in the description of impact events to include the independent friction restitution closure. The model yields velocity-independent equations for postimpact linear and angular velocities in four impact regimes, namely, sliding plus rolling, sliding nonrolling, stick plus rolling, and stick nonrolling whose predictions are compared with experimental data from the literature.

### Theoretical and numerical study on high frequency vibrational convection: Influence of the vibration direction on the flow structure

Thermal convection induced simultaneously by horizontal temperature gradient and vibration in a rectangular cavity filled with molten silicon is investigated numerically and theoretically. The time averaged equations of convection are solved in the high-frequency vibration approximation. The Chebyshev spectral collocation method and a Newton-type method based on the Frechet derivative are used in the numerical solution of the streamfunction formulation of the incompressible Navier-Stokes equations. Validation by comparison with previous studies has been performed. Different values of the Grashof number Gr and vibrational Grashof number Grv and all the possible orientations of the vibrations are considered. Numerical results show that depending on the vibration direction, the flow can be amplified or damped, with even the possibility of flow inversion which can occur between critical vibration angles α1 and α2. A general theoretical expression is derived relating these critical angles and the ratio of vibrational to buoyant convection parameters, Grv/Gr. A very good agreement between the theoretical and numerical results is obtained.

### The effect of fluid shear on oscillating bubbly flows

The impact of fluid shear on the bubble distribution in channel flows with periodically oscillating pressure gradient is examined by direct numerical simulations. Equal-sized and nearly circular bubbles are placed randomly in the channel at the initial time. In the absence of shear, the bubbles form columns spanning the width of the channel, but a strong enough shear breaks up the columns, leading to a more random bubble distribution. The effect of the nondimensional shear rate on the flow can be divided into low shear rate, moderate shear rate, and high shear rate regimes. The flow dynamics is also influenced by the Reynolds and the Euler number, and when these numbers decrease, the low shear rate regime, with stable tilted columns of bubbles, becomes smaller. Comparison of results for two- and three-dimensional flows shows that the dynamics observed in two-dimensional flows is also found in three dimensions.

### Characterizing deviation from equilibrium in direct simulation Monte Carlo simulations

A fundamental and yet computationally feasible parameter based on the characteristic function of the velocity distribution function (VDF) is proposed for determining the deviation from near-equilibrium conditions in rarefied flow simulations using the direct simulation Monte Carlo (DSMC) method. The proposed parameter utilizes the one-to-one correspondence between the VDF and its characteristic function (or Fourier transform), thereby correlating the deviation of the VDF (from a Chapman-Enskog VDF) with the deviation of the characteristic function (also from that of a Chapman-Enskog VDF). The results are first presented for an unsteady Bobylev solution for approach to equilibrium in 0-D, free-molecular Fourier-Couette flow problem and the Mott-Smith solution for the shock wave all of which have analytical solutions for the VDF, thereby confirming that the proposed parameter indeed captures the deviation from near-equilibrium conditions accurately. The utility of the proposed parameter is then demonstrated using two benchmark problems—Couette flow (over a range of Knudsen numbers) and structure of a normal shock (for upstream Mach numbers of 1.5, 3, and 5)—solved using the DSMC method. While the current work only presents results for benchmark one-dimensional DSMC simulations, the approach can be extended easily to rarefied flows in higher dimensions. Therefore, the proposed parameter has the potential to be used for understanding the nature of VDF and its deviation from near-equilibrium conditions at all locations in a flow field without the need for explicitly sampling the VDF.

### Role of Jakob number in Leidenfrost phenomena unveiled by theoretical modeling

The Leidenfrost phenomenon in its most common form is encountered when a droplet is levitated and driven by its own vapor. The recently discovered “cold Leidenfrost phenomenon” expands this phenomenon into low-temperature regimes. Although various theoretical models have been proposed, analytical exploration on generalized dimensionless laws is still absent. In this work, we elucidated the role of the dimensionless Jakob number in the Leidenfrost phenomenon through theoretical modeling. The model was verified by examining the cold Leidenfrost phenomenon of both a dry ice nub on the surface of water and a liquid nitrogen droplet on a smooth silicon surface. Regardless of the specific configuration, the dimensionless temperature distribution in the vapor film only depends on the Jakob number of the vapor and presents linear dependence when the Jakob number is below 0.25. This theoretical model would facilitate the exploration of physics for Leidenfrost events and, therefore, guide prediction as well as the design of applications in the future.

### Radial planetary vorticity tilting in the leading-edge vortex of revolving wings

Previous studies suggested that Coriolis acceleration and spanwise flow both played key roles in stabilizing the leading-edge vortex (LEV) in revolving wings. The current study examined a mechanism that relates the effects of Coriolis acceleration, spanwise flow, and the tilting of the planetary vorticity on removing the radial component of LEV vorticity. Specifically, the fluid particles moving with the spanwise flow toward the wing tip are expected to experience tangential Coriolis acceleration in the wing-fixed rotating frame; therefore, a vertical gradient in spanwise flow can create a vertical gradient in the Coriolis acceleration, which will in turn produce oppositely signed radial vorticity within the LEV. This gradient of Coriolis acceleration corresponds to the radial component of planetary vorticity tilting (PVTr) that reorients the planetary vorticity into the spanwise (radial) direction, therefore producing oppositely signed radial vorticity. Using an in-house, immersed-boundary-method flow solver, this mechanism was investigated alongside the other vorticity dynamics for revolving wings of varying aspect ratio (AR = 3, 5, and 7) and Reynolds number (Re = 110 and 1400). Analyses of vorticity dynamics showed that the PVTr consistently produced oppositely signed vorticity for all values of AR and Re investigated, although other three-dimensional phenomena play a similar but more dominant role when Re = 1400. In addition, the relative strength of the PVTr increased with increasing AR due to a decrease in the magnitude of advection. Finally, a dimensional analysis was performed on the advection and PVTr for the different AR and Re.

### In-phase synchronization between two auto-oscillating bubbles

Author(s): Dang Minh Nguyen, Muttikulangara Swaminathan Sanathanan, Jianmin Miao, David Fernandez Rivas, and Claus-Dieter Ohl

Two bubbles communicate with each other acoustically without being affected by any external sound field. We have performed an experiment showing that at the right distance, their connection becomes strong enough that they synchronize perfectly and eventually merge as one.

[Phys. Rev. Fluids 4, 043601] Published Mon Apr 22, 2019

### Comparing free surface and interface motion in electromagnetically driven thin-layer flows

Author(s): Benjamin C. Martell, Jeffrey Tithof, and Douglas H. Kelley

Particles at the top and bottom of a thin fluid layer are simultaneously tracked to measure how well such experiments model two-dimensional flow. Top and bottom flow directions align well. The bottom-to-top speed ratio nearly matches laminar predictions, even for chaotic flow, except in misaligned regions.

[Phys. Rev. Fluids 4, 043904] Published Mon Apr 22, 2019