# Latest papers in fluid mechanics

### Particle motion nearby rough surfaces

Author(s): Christina Kurzthaler, Lailai Zhu, Amir A. Pahlavan, and Howard A. Stone

Natural and microfluidic environments display a variety of confining surfaces with structured topographies, which modify the surrounding flow fields and impact nearby particle motion. We study a non-Brownian spherical particle sedimenting nearby a random, rough surface by using an analytical theory and numerical simulations. Roughness of the wall induces fluctuations in the velocity of the fall, leading to a quadratic increase of the variance of the displacements at long times.

[Phys. Rev. Fluids 5, 082101(R)] Published Mon Aug 17, 2020

### Interaction and breakup of droplet pairs in a microchannel Y-junction

Author(s): Simon S. Schütz, Jian Wei Khor, Sindy K. Y. Tang, and Tobias M. Schneider

Droplets pushed through small channels can undergo breakup, which limits the throughput in microfluidic applications. We combine theory, numerical simulation, and experiments to explain and quantify the underlying physical breakup process for interacting droplet pairs in a Y-junction. Breakup is driven by spatially varying Young-Laplace pressures, which drive the formation of a neck and a subsequent Rayleigh-Plateau-like pinch-off in the leading droplet. Quantitative analysis suggests that fast interface deformations can dynamically generate Marangoni stresses that significantly impact the dynamics.

[Phys. Rev. Fluids 5, 083605] Published Mon Aug 17, 2020

### Start-up and cessation of steady shear and extensional flows: Exact analytical solutions for the affine linear Phan-Thien–Tanner fluid model

Exact analytical solutions for start-up and cessation flows are obtained for the affine linear Phan-Thien–Tanner fluid model. They include the results for start-up and cessation of steady shear flows, of steady uniaxial and biaxial extensional flows, and of steady planar extensional flows. The solutions obtained show that at start-up of steady shear flows, the stresses go through quasi-periodic exponentially damped oscillations while approaching their steady-flow values (so that stress overshoots are present); at start-up of steady extensional flows, the stresses grow monotonically, while at cessation of steady shear and extensional flows, the stresses decay quickly and non-exponentially. The steady-flow rheology of the fluid is also reviewed, the exact analytical solutions obtained in this work for steady shear and extensional flows being simpler than the alternative formulas found in the literature. The properties of steady and transient solutions, including their asymptotic behavior at low and high Weissenberg numbers, are investigated in detail. Generalization to the multimode version of the Phan-Thien–Tanner model is also discussed. Thus, this work provides a complete analytical description of the rheology of the affine linear Phan-Thien–Tanner fluid in start-up, cessation, and steady regimes of shear and extensional flows.

### On the genesis and evolution of barchan dunes: Hydrodynamics

Barchans are an important signature of turbulent atmospheric and aquatic flows on parts of the Earth’s surface where the supply of sediments is scarce. Khosronejad and Sotiropoulos [“On the genesis and evolution of barchan dunes: Morphodynamics,” J. Fluid Mech. 815, 117–148 (2017)] demonstrated that high-fidelity hydro-morphodynamic large-eddy simulation (LES) can replicate sub-aqueous barchan fields exhibiting the geometric features and morphodynamic interactions observed in nature. Herein, we first validate the ability of our LES method to simulate mean flow and turbulence statistics over a frozen barchan dune created in a control laboratory experiment. We then analyze our high-fidelity LES datasets to elucidate the hydrodynamic phenomena that drive the previously identified morphodynamic interactions at various stages of subaqueous barchan dune evolution, from flatbed to quasi-equilibrium. We uncover and quantify the hydrodynamic mechanisms that cause (i) the initiation of crescent microfeatures on the initial flatbed; (ii) the development of three-dimensional barchan dunes; and (iii) several other phenomena that occur during the barchan field maturation, such as the birth of new small barchans and the exposure of the underlying bedrock in the wake of the barchans. Defining a dimensionless timescale, i.e., the saturation timescale, as a function of the saturation length scale, we attempt to categorize for the first time various temporal stages of barchan field development. We show that the barchan field has specific characteristics corresponding to each of the barchan stage developments in terms of both the flow field and the bed topology. Comparing the simulation results of transverse and barchan dunes, we illustrate that the two dune types have similar topographic and hydrodynamics characteristics until bedrock exposure occurs.

### Coupled fine-scale modeling of the wettability effects: Deformation and fracturing

Multiphase flow in porous media has been thoroughly studied over the years and its importance is encountered in several areas related to geo-materials. One of the most important parameters that control multiphase flow in any complex geometry is wettability, which is an affinity of a given fluid toward a surface. In this paper, we have quantified the effects of wettability on deformation in porous media, along with other parameters that are involved in this phenomenon. To this end, we conducted numerical simulations on a porous medium by coupling the exchanged forces between the fluid and solid. To include the effect of wettability in the medium, we used the Fictitious Domain methodology and coupled it with volume of fluid through which one can model more than one fluid in the system. To observe the effect of wettability on dynamic processes in the designated porous medium, such as deformation, particle–particle contact stresses, particle velocity, and injection pressure, a series of systematic computations were conducted where wettability is varied through five different contact angles. We found that wettability not only controls the fluid propagation patterns but also affects drag forces exerted on the particles during injection such that larger deformations are induced for particles with lower wettability. Our results are also verified against experimental tests.

### Design exploration and optimization under uncertainty

Computational strategies that explicitly quantify uncertainties are becoming increasingly used in aerospace applications to improve the consistency in reliability, robustness, and performance of designs. A major source of uncertainty in simulations is due to the structural assumptions invoked in the formulation of turbulence models. Accounting for the turbulence model-form uncertainty has been described as “the greatest challenge” in simulation-based engineering design. Despite its importance, design exploration and optimization under turbulence model-form uncertainty is an avenue that has not been investigated in depth in prior literature. In this investigation, we outline methodologies for the design analysis, exploration, and robust optimization under model-form uncertainty due to Reynolds averaged Navier–Stokes models. We exhibit how interval uncertainty estimates enable the use of alternative criteria for decision making under uncertainty in engineering design. It is shown that such criteria can lead to different design choices in design exploration. Finally, we carry out design optimization under mixed uncertainties by using the perturbation framework in conjunction with polynomial chaos expansions. We introduce an approach for engineering design optimization under uncertainty that utilizes physics-based uncertainty estimation along with decision theory criteria under uncertainty to produce designs that are more robust to turbulence model uncertainties. These methodologies are illustrated via their application to complex turbulent flow cases, pertinent to aerospace design applications.

### Homogeneous isotropic turbulence in four spatial dimensions

Direct numerical simulation is performed for the forced Navier–Stokes equation in four spatial dimensions. Well equilibrated, long time runs at sufficient resolution were obtained to reliably measure spectral quantities, the velocity derivative skewness, and the dimensionless dissipation rate. Comparisons to corresponding two- and three-dimensional results are made. Energy fluctuations are measured, and the results show a clear reduction moving from three to four dimensions. The dynamics show simplifications in four dimensions with a picture of increased forward energy transfer resulting in an extended inertial range with a smaller Kolmogorov scale. This enhanced forward transfer is linked to our finding of increased dissipative anomaly and velocity derivative skewness.

### Numerical investigation of magnetic multiphase flows by the fractional-step-based multiphase lattice Boltzmann method

In the present study, a fractional-step-based multiphase lattice Boltzmann (LB) method coupled with a solution of a magnetic field evolution is developed to predict the interface behavior in magnetic multiphase flows. The incompressible Navier–Stokes equations are utilized for the flow field, while the Cahn–Hilliard equation is adopted to track the interface, and these governing equations are solved by reconstructing solutions within the LB framework with the prediction–correction step based on a fractional-step method. The proposed numerical model inherits the excellent performance of kinetic theory from the LB method and integrates the good numerical stability from the fractional-step method. Meanwhile, the macroscopic variables can be simply and directly calculated by the equilibrium distribution functions, which saves the virtual memories and simplifies the computational process. The proposed numerical model is validated by simulating two problems, i.e., a bubble rising with a density ratio of 1000 and a viscosity ratio of 100 and a stationary circular cylinder under an external uniform magnetic field. The interfacial deformations of a ferrofluid droplet in organic oil and an aqueous droplet in ferrofluid under the external magnetic field are, then, simulated, and the underlying mechanisms are discussed. Moreover, the rising process of a gas bubble in the ferrofluid is investigated, which shows that the rising velocity is accelerated under the effect of the external magnetic field. All the numerical examples demonstrate the capability of the present numerical method to handle the problem with the interfacial deformation in magnetic multiphase flows.

### Numerical study of unsteady viscoelastic flow past two side-by-side circular cylinders

In this study, numerical simulation is conducted to understand the two-dimensional viscoelastic flows past two side-by-side circular cylinders at a Reynolds number of 100. The Peterlin approximation of the finitely extensible nonlinear elastic model is adopted to describe the non-linear modulus of elasticity and the finite extendibility of polymer macromolecules. The flow behavior and time-averaged forces that act on the two cylinders are investigated over a wide range of parameter space, i.e., the Weissenberg number (We), from 0 to 8, and the spacing between the two cylinders (LD), from 0.1D to 3.0D (D denotes the diameter of each cylinder). Similar to the corresponding Newtonian flow, the viscoelastic flow gradually undergoes six transitions as LD increases. However, these transitions are delayed in the viscoelastic flow, particularly at a high We. As a result, three distinct flow modes remain within the above-mentioned LD range at a high We. With increasing We, the total drag acting on the two cylinders increases for all LD values, and the repulsive force between the two cylinders gradually decreases for a lower LD value but increases for a higher LD value. Both the intensity and frequency of force fluctuation decrease as We increases. The findings of the present study may provide new insight into the multi-body wake dynamics in the viscoelastic flow.

### Connection between pore-scale and macroscopic flow characteristics of recirculating wake behind a porous cylinder

The wake structure behind a porous square cylinder is numerically investigated by using both pore-scale and macroscopic approaches. The pore-scale simulations (PSSs) concern about the steady flow through and around square arrays of multiple circular cylinders with a wide range of solid fraction. The macroscopic porous media model (PMM) employed is the generalized equation, where the dimensionless permeability Dam is assigned based on the macroscopic permeability Das estimated from PSS via Darcy’s law. The connection between pore-scale and macroscopic flow properties is studied in terms of the flow pattern, the geometric parameters, and the occurrence of the recirculating wake behind the array. It is found that the consistency between PSS and PMM is highly dependent on the ratio of Das and Dam. Discussions in terms of the scale analysis of PMM, the discrepancy between Dam and Das, and the effects of stress-jump parameters are also provided.

### Modeling of salt finger convection through a fluid-saturated porous interface: Representative elementary volume scale simulation and effect of initial buoyancy ratio

Simultaneous existence of solute gradients along with temperature gradients in a double diffusive system is favorable to the onset of salt finger convection and this phenomenon has been investigated for several decades due to its efficient mixing mechanism. However, relatively few works were focused on the double diffusive process through a fluid-saturated porous interface (FPI), which could be applied in a variety of scenarios such as the directional solidification of concentrated alloys or mixing zones in coastal freshwater aquifers. In this paper, we consider the evolution of double-diffusive salt finger through FPI with a single-domain approach adopted for the solution of flow in a composite region made up of a fluid layer overlying a porous layer. Comparisons with existing numerical results show great agreement and demonstrate that flows through a fluid–porous system can be predicted with good accuracy by the proposed method. Several cases spanning a range of initial buoyancy ratio [math] from 2 to 7 are conducted to study the structure and behavior of salt finger together with key issues being focused on the effect of initial buoyancy ratio on flux variations. Differing from in stratified fluid layers, salt finger through FPI shows an asymmetric structure in which the growth rate in the fluid layer is much greater and the finger column in the porous layer presents a squarer shape. It is found that under the condition of low initial buoyancy ratios, the potential energy stored in the unstable stratification of salinity converted more into kinetic energy, which enhances the mixture of heat and masses in the vertical direction.

### Investigation of cavitation and vapor shedding mechanisms in a Venturi nozzle

Cavitating flow dynamics are investigated in an axisymmetric converging–diverging Venturi nozzle. Computational Fluid Dynamics (CFD) results are compared with those from previous experiments. New analysis performed on the quantitative results from both datasets reveals a coherent trend and shows that the simulations and experiments agree well. The CFD results have confirmed the interpretation of the high-speed images of the Venturi flow, which indicated that there are two vapor shedding mechanisms that exist under different running conditions: re-entrant jet and condensation shock. Moreover, they provide further details of the flow mechanisms that cannot be extracted from the experiments. For the first time with this cavitating Venturi nozzle, the re-entrant jet shedding mechanism is reliably achieved in CFD simulations. The condensation shock shedding mechanism is also confirmed, and details of the process are presented. These CFD results compare well with the experimental shadowgraphs, space–time plots, and time-averaged reconstructed computed tomography slices of vapor fraction.

### Dynamics of water injection in an oil-wet reservoir rock at subsurface conditions: Invasion patterns and pore-filling events

Author(s): Abdulla Alhosani, Alessio Scanziani, Qingyang Lin, Sajjad Foroughi, Amer M. Alhammadi, Martin J. Blunt, and Branko Bijeljic

We use fast synchrotron x-ray microtomography to investigate the pore-scale dynamics of water injection in an oil-wet carbonate reservoir rock at subsurface conditions. We measure, *in situ*, the geometric contact angles to confirm the oil-wet nature of the rock and define the displacement contact ang...

[Phys. Rev. E 102, 023110] Published Fri Aug 14, 2020

### Equilibrium and nonequilibrium molecular dynamics methods to compute the first normal stress coefficient of a model polymer solution

Author(s): A. G. Menzel, P. J. Daivis, and B. D. Todd

The first normal pressure (or stress) difference is directly computed from the local values of the pressure tensor components in molecular dynamics simulations of planar Poiseuille flow for a low molecular weight polymeric fluid. The resulting zero shear rate normal pressure difference agrees very well with the value computed using homogeneous shear simulations and the SLLOD algorithm, and less well with the result of the Coleman-Markowitz equation evaluated at equilibrium. This resolves doubts about the effects of homogeneous thermostats in homogeneous nonequilibrium molecular dynamics simulations.

[Phys. Rev. Fluids 5, 084201] Published Fri Aug 14, 2020

### Particle accumulation structures in noncylindrical liquid bridges under microgravity conditions

Author(s): Paolo Capobianchi and Marcello Lappa

We numerically investigate Particle Accumulation Structures (PAS) in noncylindrical liquid bridges (LB) for a high Prandtl number liquid. The work examines the morphological evolution of these structures in weightless conditions for various Marangoni and Stokes numbers, tracer densities, aspect ratios and LB volumes. Additionally, a model is used to interpret the increased ability of concave LBs to support these phenomena over a wider range of the particle Stokes number. The model relies mainly on geometrical factors, i.e., the relationship among the interface curvature, fluid streamline topology, and particle mass effects.

[Phys. Rev. Fluids 5, 084304] Published Fri Aug 14, 2020

### Energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations

This study investigates the energy budget of a viscoelastic planar liquid sheet in the presence of gas velocity oscillations. The energy budget is studied in different unstable regions, and the results are very different from those obtained for steady basic flow. The work done by surface tension and aerodynamic forces is periodic, leading to the growth of standing waves on liquid sheets. The positive work done by aerodynamic forces is the main cause of the instability, as for steady basic flow. However, treating the negative work of the surface tension as an increment in the surface energy is an effective means of determining the instability mechanisms. The unsteady basic flow causes the rate of change in the work done by viscosity and elasticity to vary periodically. An increase in elasticity and a decrease in deformation retardation promote the instability by increasing the work done by the gas medium, with reduced dissipation only as a secondary factor. This effect is more significant in parametric unstable regions than in the Kelvin–Helmholtz unstable region.

### Inertial migration of spherical particles in channel flow of power law fluids

The cross-stream inertial migration of neutrally buoyant particles in a power law fluid in a pressure-driven flow between two parallel walls is studied using three-dimensional numerical simulations. The particles are modeled as rigid and compliant spherical shells filled with a Newtonian fluid. Our simulations show that the particles in the flow equilibrate at stable off-center positions that depend on the particle size and fluid power exponent. In a shear thickening fluid, the equilibrium position is insensitive to the particle size. In a shear thinning fluid, an additional unstable off-center equilibrium position emerges for smaller particles, which leads to the accumulation of such particles at the channel centerline. We find that these equilibrium positions are insensitive to the magnitude of the channel Reynolds number and particle elasticity. The results of our study have applications to sorting, focusing, and separation of synthetic particles and biological cells.

### Enhanced stability of free viscous films due to surface viscosity

The stability of a thin liquid film bounded by two free surfaces is examined in the presence of insoluble surface-active agents. This study is broadly aimed at understanding enhanced stability of emulsions with the increasing surface concentration of surface-active agents. Surface-active agents not only cause gradients in surface tension but could also render surface viscosity to be significant, which could vary with surface concentration. We employ two phenomenological models for surface viscosity, a linear viscosity model and a nonlinear viscosity model. In the latter, surface viscosity diverges at a critical concentration, which is termed the “jamming” limit. We show that rupture can be significantly delayed with high surface viscosity. An analysis of the “jamming” limit reveals that [math] provides a simple criterion for enhanced stability, where [math], [math], and M are the normalized initial surfactant concentration, disjoining pressure number, and Marangoni number, respectively. Nonlinear simulations suggest that high surface viscosity renders free films remarkably stable in the jamming limit, and their free surfaces behave like immobile interfaces consistent with experimental observations. Furthermore, it is shown that rupture times can be arbitrarily increased by tuning the initial surfactant concentration, offering a fluid dynamical route to stabilization of thin films.

### Stability and transition on a Coandă cylinder

An experimental stability and transition investigation of a centrifugally unstable wall jet blown from a slot over a circular Coandă cylinder was conducted using flow visualization and particle image velocimetry. Clear and unambiguous observations of spontaneously generated stationary streamwise structures, never observed previously, were analyzed using standard image processing techniques. These structures ultimately exhibited a secondary time-dependent wavy instability that was followed by transition to turbulence. A modified Görtler number, based on the slot height, was used as a basis for comparison to linear stability theory and was directly related to the Reynolds number via geometric scaling. Direct observation of the vortices allowed the identification of an upper limit to the critical Görtler number of 6.3 that bracketed the value of 3.5 from the linear stability theory. The vortical shear layer grew exponentially along the azimuth and was characterized by a Reynolds number dependent growth rate parameter. Extrapolation of the growth rate parameter to zero furnished a critical Görtler number of 3.1 ± 1.25 (95% CI) that compared remarkably well with the linear stability theory. The shear layer separation angle did not vary monotonically with the Reynolds number: as the Reynolds number increased, the thicker boundary layer was more susceptible to separation, and thus, the separation angle, relative to the slot, decreased. However, following transition to turbulence at higher Reynolds numbers (≈400), the high-momentum fluid near the wall, resulting from turbulent mixing, produced a subsequent increase in the separation angle.

### Wakes of rotorcraft in advancing flight: A large-eddy simulation study

We perform the large-eddy simulation of the flow past a helicopter rotor to support the investigation of rotorcraft wake characteristics and decay mechanisms. A hybrid Lagrangian–Eulerian vortex particle–mesh method is employed to simulate the wake development with the blades modeled using immersed lifting lines. The validity of the numerical approach is first evaluated through a comparison of the rotor trim parameters with experimental results. Then, the rotor wake at low, medium, and high advance ratios is simulated up to 30 rotor diameters. The wake generation and roll-up are described (i) qualitatively using rotor polar plots and three-dimensional (3D) vortex dynamics visualizations and (ii) quantitatively using classical integral diagnostics in cross sections. The highly 3D unsteady near wake transitions to a system dominated by two parallel vortices over a distance that depends on the advance ratio. This process is accelerated by the multiple interactions between successive tip vortices, supporting the generation of self-induced turbulence and uncovering a mechanism of vorticity alignment along the streamwise axis. The vortices in the far wake are compared to typical aircraft ones and exhibit less compact cores and faster decaying energy. Finally, we illustrate the loss of time periodicity in the far wake using the power spectral density of the kinetic energy, and the backscattering of energy from high rotor harmonics to lower frequencies, as complementary evidence of the intense vortex interaction activity.