# Latest papers in fluid mechanics

### Viscoelastic planar elongational flow past an infinitely long cylinder

Following our previous work [K. D. Housiadas and R. I. Tanner, “Viscoelastic shear flow past an infinitely long and freely rotating cylinder,” Phys. Fluids 30, 073101 (2018)], we study analytically the effect of steady planar elongational flow past an infinitely long circular cylinder using asymptotic methods. The ambient fluid is assumed viscoelastic and modelled with the Upper Convected Maxwell, Oldroyd-B, exponential Phan-Thien and Tanner, Giesekus, and Finite Extensibility Nonlinear Elastic model with the Peterlin approximation constitutive equations under isothermal and creeping flow conditions. The solution for all the dependent variables is expanded as an asymptotic power series with the small parameter being the Weissenberg number, Wi, which is defined as the product of the single relaxation time of the fluid times the constant rate of elongation. The resulting sequence of equations is solved analytically up to fourth order in the Weissenberg number. The solution derived here is the first analytical result in the literature for the planar elongational flow of viscoelastic fluids past a cylinder. It reveals the effect of viscoelasticity and all the relevant rheological parameters on the flow variables and the extensional viscosity of the fluid.

### Pore network model for permeability characterization of three-dimensionally-printed porous materials for passive microfluidics

Author(s): Agnese Piovesan, Clement Achille, Rob Ameloot, Bart Nicolai, and Pieter Verboven

Stand-alone and portable lab-on-chips (LOC) can be obtained by exploiting capillary flow in porous media. Polymethylmethacrylate (PMMA) platforms obtained through powder-based three-dimensional (3D) printing are appropriate for capillarity-driven LOCs. However, fluid flow in such platforms needs to ...

[Phys. Rev. E 99, 033107] Published Thu Mar 07, 2019

### Anomalous transport dependence on Péclet number, porous medium heterogeneity, and a temporally varying velocity field

Author(s): Alon Nissan and Brian Berkowitz

We investigate the effects of the Péclet number (Pe) on transport of an inert chemical tracer in heterogeneous porous media. We simulate fluid flow and transport through two-dimensional pore-scale matrices with varying structural complexity. With increasing Pe, the anomalous nature of the transport ...

[Phys. Rev. E 99, 033108] Published Thu Mar 07, 2019

### Velocity probability distribution scaling in wall-bounded flows at high Reynolds numbers

Author(s): M.-W. Ge, Xiang I. A. Yang, and Ivan Marusic

A study on the scaling implications of the attached eddy hypothesis and the large deviation theory on the velocity probability distribution function (PDF) concludes that, when scaled properly, the remote tails of the streamwise and spanwise velocity PDF collapse for flows in the logarithmic layer.

[Phys. Rev. Fluids 4, 034101] Published Thu Mar 07, 2019

### Trapped vorticity for controlled modification of an airfoil's aerodynamic loads

Author(s): Daniel P. Brzozowski, Bojan Vukasinovic, and Ari Glezer

Static and transient responses of an airfoil to bi-directional flow control actuation at the trailing-edge are investigated in wind tunnel experiments. Flow field measurements elucidate control of aerodynamic loads through regulation of trapped vorticity concentrations upstream of the trailing edge.

[Phys. Rev. Fluids 4, 034601] Published Thu Mar 07, 2019

### Flow force measurements and the wake transition in purely inline vortex-induced vibration of a circular cylinder

Author(s): Tyler D. Gurian, Todd Currier, and Yahya Modarres-Sadeghi

We find a novel shedding mode (Alternating-Symmetric) in the vortex-induced vibration response of a cylinder free to oscillate in the inline direction. In this mode, two vortices of opposite sign are shed simultaneously from two sides of the oscillating cylinder, but their sizes alternate per cycle.

[Phys. Rev. Fluids 4, 034701] Published Thu Mar 07, 2019

### Experimental investigation of three-dimensional flow regimes in a cross-shaped reactor

Flow regimes in a cross-shaped reactor with square cross sections of two inlets and two outlets were investigated at 20 ≤ Re ≤ 500, where Re is the Reynolds number. Visualization images on cross sections were obtained by planar laser induced fluorescence, and several flow regimes were identified. Results show that, with increasing Re, a symmetric segregated flow, a steady engulfment flow, an unsteady engulfment flow, and an unsteady symmetric flow emerge in turns. First, the symmetric segregated flow is formed at Re < 48. At 48 ≤ Re < 300, the flow becomes asymmetric and a spiral vortex is formed in the center of the outlet chamber, which is called steady engulfment flow. At 300 ≤ Re ≤ 400, the unsteady engulfment flow occurs and a periodic oscillation is established. With a further increase in Re, the flow regains symmetry to a large extent and is characterized by axial oscillation of the impingement plane in the outlet chamber. For steady engulfment flow, an interesting three-dimensional vortical structure was observed, which rotates around the center axis of the outlet chamber along both outlet channels. For unsteady engulfment flow, the periodic oscillation is characterized by vortex merging and breakup. The flow mechanisms of both steady and unsteady engulfment flows were discussed.

### Controlled symmetry breaking and vortex dynamics in intersecting flows

Vortices are a ubiquitous feature in complex flows and turbulence, but their dynamics are challenging to study due to their typically transient nature. Here, we perform a detailed study of the vortex dynamics and interactions associated with a symmetry-breaking flow instability at a 4-way intersection. By precisely controlling the flow rate (hence the Reynolds number, Re) of the flow about a critical value, we are able to induce the merging of two co-rotating vortices into a single structure and similarly to induce a single vortex to split into two. Using quantitative flow velocimetry, both processes are recorded with high spatial and temporal resolution. We find that both the merging and the splitting of vortices are exponential processes, with a rate that depends on the imposed Re. The vortex dynamics in our system are intimately connected with the symmetry-breaking transition and are affected by the degree of vortex confinement, which we control by varying the aspect ratio (α) of the flow geometry. We show how the confinement affects the fundamental nature of the flow transition, which varies from super through subcritical as α is increased. Our results are of direct relevance to understanding and predicting flow transitions and vortex dynamics in flow intersections, particularly in confined environments such as in microfluidic (lab-on-a-chip) devices and in the circulatory system, and may be relevant to the prediction of vortex interactions in general.

### Linear analysis of non-local physics in homogeneous turbulent flows

Characterization of non-local physical mechanisms is one of the important challenges toward deeper understanding of turbulent flows. In this investigation, we study the role of pressure in the evolution of three-dimensional incompressible homogeneous turbulent flows. We find that the evolution of turbulence, the nature of inertial physics, and pressure action are dependent on the mean flow invariants. We identify and explain the intercomponent energy transfer induced by the rapid pressure strain correlation for different regimes of flow. Additionally, the structuring effect of pressure on turbulent fluctuations of different alignments is determined and explicated. We exhibit that in regimes of flow where the action of the pressure strain correlation is significant, there is a switching of the flow evolution between diametric stages of evolution. This phenomenon is explained, and its lack of amenability to single-point turbulence modeling is detailed.

### Electric field induced droplet deformation and breakup in confined shear flows

Author(s): Rattandeep Singh, Supreet Singh Bahga, and Amit Gupta

Deformation or breakup of a droplet suspended in confined shear flows and subjected to an electric field is investigated numerically. A contrasting behavior of the droplet depending upon the electrical properties of the fluids is reported.

[Phys. Rev. Fluids 4, 033701] Published Wed Mar 06, 2019

### Instability of precession driven Kelvin modes: Evidence of a detuning effect

Author(s): Johann Herault, André Giesecke, Thomas Gundrum, and Frank Stefani

Experiments in a precessing cylinder filled with water show signatures of azimuthally drifting inertial waves. These modes originate from a triadic resonance and their characteristic frequency dependence is explained by a detuning mechanism due to the slowdown of the background flow.

[Phys. Rev. Fluids 4, 033901] Published Wed Mar 06, 2019

### Microscale wave breaking in stratified air-water pipe flow

We perform an experimental analysis of two-phase stratified wavy pipe flow, with the aim to detect and quantify the effect of small scale wave breaking. Particle image velocimetry is employed to analyze the velocity fields below individual waves, and a threshold for the vorticity on the leeward side of the crest is used to assess active wave breaking. Keeping the liquid flow rate constant, we analyze five experimental cases with increasing gas flow rates. The cases span the flow map from when first interfacial waves are observed, to the “amplitude saturation” regime, where the rms interface elevation is independent of the gas flow rate. While some wave breaking events are observed also in the wave-growth regime, wave breaking is found to be much more frequent when the gas flow rate is increased into the amplitude saturation regime, and 35%-40% of the waves passing the measurement section are assessed to be in a state of active breaking in this regime. A conditional averaging of the flow field is performed, and the turbulent dissipation rate below breaking and non-breaking waves is estimated. The effect of microscale breaking is observed down to a depth of 10 mm below the water surface. Below the crest of microscale breaking waves, the turbulent dissipation rate is increased by a factor 2.5 to 4 compared with non-breaking waves. This fraction increases with Usg, implying that the breaking events become more energetic as the gas flow rate is increased.

### Interfacial dynamics of immiscible binary fluids through ordered porous media: The interplay of thermal and electric fields

We report the interplay of electrical and thermal fields on the interfacial dynamics of two immiscible fluids inside a periodic porous domain. The alternating current electrothermal mechanism is employed to generate the two phase flow. The surfaces of the porous blocks are wetted with wettability conditions which are manifested by a predefined static contact angle. Depending on the surface affinity and the electrical parameters, two distinctive spatio-temporal regimes can be identified, namely, trapping of the displaced fluid between the two consecutive porous blocks (formation of liquid bridge) and merging of contact lines after traveling the obstacle (complete interface recovery). Results show that liquid bridge formation and complete interface recovery are strongly influenced by the viscosity and thermal conductivity contrasts, in addition to the relevant electro-thermal parameters.

### Effect of the Prandtl number on the instabilities of the thermocapillary flow in an annular pool

This paper is devoted to the instability mechanisms of the thermocapillary flow in an annular pool. The stability limit of the axisymmetric basic state was studied over a wide range of Prandtl numbers (0.001 ≤ Pr ≤ 6.7) using linear stability analysis based on the spectral element method. The results demonstrate five types of instabilities, and the corresponding instability mechanisms were revealed by disturbance energy analysis. In particular, in the narrow range 1.4 ≤ Pr ≤ 1.53, with the increase in the Marangoni number, three transitions between the axisymmetric steady flow and the three-dimensional oscillatory flow were found, owing to the coupling and interaction of the hydrodynamic and hydrothermal instability mechanisms.

### Dynamic mode tracking and control with a relaxation method

Computational Fluid Dynamics (CFD) usually requires advanced and accurate diagnostics to help improve our understanding especially in the context of fully unsteady 3D simulations. To do so, two kinds of tools exist today: operator-based and data-based analyses. The most well known data-based analysis used in fluid mechanics is probably the dynamic mode decomposition. This method has indeed shown to be powerful to study CFD results without assumption. It is, however, memory consuming and very sensitive to noise while being used a posteriori. The objective of the following contribution is to relax such issues thanks to an operator-based analysis called Dynamic Mode Tracking (DMT). Based on the well-known selective frequency damping method, DMT relies on a specific implementation allowing the identification of flow activity of specific interest as the data are generated. The method shows to be well adapted for flows exhibiting a clear limit cycle with multiple specific frequencies. Focusing on one of these frequencies, DMT parameters can be adapted to study its temporal evolution giving insight into the mode spatial and temporal features. Thanks to DMT, a variant called Dynamic Mode Tracking and Control (DMTC) allows then to control the identified feature in the CFD simulation. To do so, DMT is coupled with the flow equations thanks to a feedback relaxation method resulting in an artificial control of the flow physics for a specific feature. The development and application of DMT as well as DMTC are illustrated on three problems. First, a simple flow problem based on the propagation of three acoustics waves to evidence the tracking capability of DMT is presented. The second example deals with the vortex shedding of a cylinder wake. For these two cases, DMTC is then applied to demonstrate the capacity of the approach. Finally, the method is applied to a complex configuration: a 3D swirled burner exhibiting a thermo-acoustic instability.

### Numerical investigation of solitary wave slamming on an oscillating wave surge converter

A solitary wave slamming on an Oscillating Wave Surge Converter (OWSC) is numerically investigated using a time-domain higher-order boundary element method with fully non-linear boundary conditions. A stretched coordinate is implemented to improve the numerical efficiency as long as the slamming peak pressure occurs. The potential of the thin long jet is assumed to vary linearly, while the process of jet detaching is simulated through the domain decomposition method so that the local highly oscillatory pressure can be avoided. Two auxiliary functions are applied simultaneously to decouple the mutual dependence between the flap motion and the fluid flow. A unique mesh scheme is employed to simulate the free surface with strong deformation, through which the smallest meshes are distributed near the largest pressure gradient on the body and the mesh size increases gradually at a ratio. The validity of the present model to simulate the solitary wave and the slamming event is verified, respectively, based on which relatively comprehensive parameter studies are then performed. Through analyzing the flap’s motion states, the free surface profiles, and the pressure distributions, it is found that several unique phenomena and mechanisms exist in the solitary waves slamming on an OWSC.

### Numerical study on the flow over two circular disks in tandem arrangement

The flows over the two circular disks in tandem arrangement at low Reynolds numbers are numerically studied using large-eddy simulations. Both disks have the same aspect ratio (χ = d/w = 5, where d and w are, respectively, the diameter and the thickness of the disk), while the upstream disk has a coaxial hole in D diameter. First, the effect of the Reynolds number on the near-wake evolution of the tandem disks with spacing of l/d = 0.1 is investigated. Compared with a single circular disk, it is found that the upstream apertured disk (D/d = 0.2) delays the wake transition. Four bifurcations, i.e., “Steady state,” “Zig-zig,” “Zig-Zag,” and “Weakly chaotic” modes, are captured at critical Reynolds numbers of 178, 207, 212, and 275, respectively. Second, the effect of disk spacing on near-wake evolution is studied for Re = 200 and D/d = 0.2. The wake is steady and planar-symmetric at l/d = 1, in which a totally new wake mode characterized by a three-thread wake is observed. The wake becomes unsteady but planar-symmetric at l/d = 1.5. At l/d = 2, however, the planar-symmetric wake structures are all broken. The upstream disk wake retains planar-symmetry, while the downstream disk wake is similar to the “Reflectional-symmetry-broken” mode in a single disk wake. The planar symmetry is recovered for both disks at l/d = 6. It is found that for l/d > 3, the interaction between the two disks becomes weaker as the spacing increases. Finally, the effect of disk spacing on the drag and lift coefficients for each disk is examined. When disk spacing is constant, the lift coefficient of the upstream disk is always lower than that of the downstream disk. The drag coefficient of each disk in tandem is smaller than that of a single disk. With the increase in disk spacing, the drag coefficient of the upstream disk changes little while the drag coefficient of the downstream disk increases rapidly.

### Advection of droplet collision in centrifugal microfluidics

Centrifugal microfluidics has been developed into a powerful technology in chemistry and biology. Its carrier devices allow us to control flows without external pumps, integrate multiple functions onto a disk, and reduce the consumption of reagents or samples. In centrifugal microfluidics, an artificial gravitational field, which determines the volume forces imposed on the microfluid, can be created by the rotating operation of a disc-like microfluidic chip. Centrifugal microfluidics can be a preponderant approach for droplet manipulation because the dimensionless numbers (e.g., the Reynolds number and the Bond number) of the microflows can be controlled by the reasonable design of such a disc-like chip. To study the advection of droplets in a centrifugal microfluidic chip, this paper presents a numerical investigation for the droplet collisions under different Bond numbers and Reynolds numbers. The progress of the collision advection is simulated by solving laminar flow equations and phase-field equations. The distribution of the mixed droplets is described using particle tracking methods. By evaluating the extending ratio of the interface and the barycenter deviation, it is demonstrated that the Bond number and Reynolds number affect different aspects of the advection. For instance, higher Bond numbers produce larger barycenter deviation and higher Reynolds numbers generate a more chaotic distribution. These simulations reveal the advection of droplet collisions under different Bond numbers and Reynolds numbers. Revealing the effects of these dimensionless numbers and advection mechanism can promote more reasonable design and operation of the centrifugal microfluidic platforms.

### Effect of interaction between a particle cluster and a single particle on particle motion and distribution during sedimentation: A numerical study

The interaction between a particle cluster and a single particle during sedimentation is studied with the lattice Boltzmann method, where the effects of the initial distance and particle number on the motion and distribution of the particle cluster are investigated. Compared to the case without the single particle, the motion and distribution of the particle cluster are affected significantly due to the effect of the single particle. Due to the interaction between the particle cluster and the single particle, the particle-particle interaction becomes stronger; compared to the case without the single particle, the velocity fluctuation of the particle cluster is much more intensive. Besides, the particle cluster is scattered by the single particle, and the distribution of the particle cluster becomes more inhomogeneous.

### High jump of impinged droplets before Leidenfrost state

Author(s): Lu Qiu, Swapnil Dubey, Fook Hoong Choo, and Fei Duan

Unlike the traditionally reported Leidenfrost droplet which only floats on a thin film of vapor, we observe a prominent jump of the impinged droplets in the transition from the contact boiling to the Leidenfrost state. The vapor generation between the droplet and the substrate is vigorous enough to ...

[Phys. Rev. E 99, 033106] Published Tue Mar 05, 2019