# Latest papers in fluid mechanics

### Disclosing recurrence properties in fluidized beds

Author(s): F. Dabbagh, S. Pirker, T. Lichtenegger, and S. Schneiderbauer

The time-efficient method of recurrence CFD (rCFD) uses the pseudo-periodic nature of a flow, extrapolating the passive transport quickly to infinity. In that scope, the recurrence/distance matrix for bubbling and turbulent fluidization regimes are investigated to find the recurrence properties. The results indicate the need for posterior spatial filtering in the turbulent regime which, in turn, reveals recurrent uniform superstructures with a clear fingerprint on the distance/recurrence matrix.

[Phys. Rev. Fluids 6, 044310] Published Fri Apr 23, 2021

### Nonlinear stability analysis of transitional flows using quadratic constraints

Author(s): Aniketh Kalur, Peter Seiler, and Maziar S. Hemati

The dynamics of incompressible flows are governed by an interaction between non-normal linear dynamics and a static nonlinearity. We propose a framework for stability analysis that considers the linear dynamics subject to constraints that reflect the fact that the nonlinearity is quadratic and energy conserving. The approach can be used to conduct global, local, and non-modal stability analyses and to uncover dominant nonlinear flow interactions that drive these instabilities.

[Phys. Rev. Fluids 6, 044401] Published Fri Apr 23, 2021

### Near-field coherent structures in circular and fractal orifice jets

Author(s): D. Lasagna, O. R. H. Buxton, and D. Fiscaletti

Near-field coherent structures in turbulent jets from round and square fractal orifices are examined with a Fourier-POD (FPOD) technique at two nozzle diameters from the exit. In the round jet, energy is mostly contained at wavenumber m=0, associated with Kelvin-Helmholtz vortex rings, while coherent structures in the fractal jet at the fundamental azimuthal m=4 capture the most energy. Nevertheless, the radial FPOD profiles are nearly insensitive to orifice geometry, forming a universal distribution with characteristic radial length scaling. Analysis of near-field fluctuations finds that streamwise vorticity and velocity are highly coupled by a lift-up mechanism in both jets.

[Phys. Rev. Fluids 6, 044612] Published Fri Apr 23, 2021

### Phase-field modeling of wetting and balling dynamics in powder bed fusion process

In a powder bed fusion additive manufacturing process, the balling effect has a significant impact on the surface quality of the printing parts. Surface wetting helps the bonding between powder and substrate and the inter-particle fusion, whereas the balling effect forms large spheroidal beads around the laser beam and causes voids, discontinuities, and poor surface roughness during the printing process. To better understand the transient dynamics, a theoretical model with a simplified 2D configuration is developed to investigate the underlying fluid flow and heat transfer, phase transition, and interfacial instability along with the laser heating. We demonstrate that the degree of wetting and fast solidification counter-balance the balling effect, and the Rayleigh–Plateau flow instability plays an important role for cases with relatively low substrate wettability and high scanning rate.

### Stagnation line due to colliding wall jets of two liquid impinging jets on a horizontal surface

When two free liquid jets impinge on a planar surface with their wall jets colliding, a stagnation line is formed between the two wall jets. The location and shape of the stagnation line depend on the free jet flow conditions, fluid properties, impingement orientation of each free jet, and relative positioning of the two free jets. Experiments are conducted to observe and measure stagnation lines formed by two free jets impinging on the upper surface of a transparent plate, and a camera is placed under the plate to take the images of stagnation lines. It is found that changing the fluid and the position and orientation of the two jets causes the stagnation line to change. A theoretical model consisting of momentum analysis of a singe wall jet and momentum balance of two wall jets is derived to predict the stagnation line. It is hypothesized that, when two unequal liquid wall jets collide, the stagnation takes place where the momentum balance between the two jets within the thinner thickness is satisfied. Based on the hypothesis, the developed theoretical model shows good agreement with the experimental results.

### Numerical investigation of instability and transition to chaos in electro-convection of dielectric liquids between concentric cylinders

The two-dimensional (2D) electro-convection (EC) flow of dielectric liquids between two concentric cylindrical electrodes driven by unipolar injection of ions is investigated numerically. The finite volume method is used to resolve the spatiotemporal distributions of the flow field, electric field, and charge density. The flow transition routes from steady laminar to chaotic flow states are studied in various scenarios where the mobility parameter M of the dielectric liquids varies from 5 to 200. The dynamic characteristics and bifurcation routes of the EC flow depend on the electric Rayleigh number T, a ratio of the electric force to viscous force, and the mobility parameter M. For increasing T, three different transition routes from a convective steady-state to chaos via different intermediate states are observed. The flow states have been quantified by the power spectral density distribution and phase space trajectory of the velocity. The fractal dimensions and Lyapunov exponents are calculated to identify the chaotic flow. The increase in the mobility parameter M leads to a shorter and more direct route with fewer intermediate states when bifurcating to chaos. In addition, the power scale of charge transport that is defined by the electric Nusselt number Ne and T is discussed when the EC flow develops into electro-turbulence.

### Observations of a sweeping jet actuator for flow separation control of a backward-facing ramp

Author(s): H. D. Lim and Zhen Lyu

The three-dimensional flow features produced by a single sweeping jet actuator in a flow separation control application is investigated using stereoscopic PIV. By varying the freestream Reynolds number and actuator’s position, noticeable differences in the near-field vortex dynamics, local flow entrainment levels, and geometry of the separation bubble can be observed. Insights into these three-dimensional flow features and its effects on flow separation control are offered which may be useful in further improving the efficiency of these actuators and optimizing their operating conditions.

[Phys. Rev. Fluids 6, 043902] Published Thu Apr 22, 2021

### Flow structure and loads over inclined cylindrical rodlike particles and fibers

Author(s): Mohammed Kharrouba, Jean-Lou Pierson, and Jacques Magnaudet

We use fully-resolved simulations to predict the force and torque acting on a long cylinder or a fiber inclined with respect to the incoming flow. Results obtained in the viscous regime are compared with predictions of the slender-body theory, possibly incorporating finite-inertia corrections. Numerical results are used to build approximate models for the force and torque valid from creeping-flow conditions up to the upper limit of the stationary inertial regime.

[Phys. Rev. Fluids 6, 044308] Published Thu Apr 22, 2021

### Discrete ion stochastic continuum overdamped solvent algorithm for modeling electrolytes

Author(s): D. R. Ladiges, A. Nonaka, K. Klymko, G. C. Moore, J. B. Bell, S. P. Carney, A. L. Garcia, S. R. Natesh, and A. Donev

When modeling electrolytes, molecular scale features, for example the electric double layer, often play a role in determining meso- and macro-scale dynamics. These features cannot be captured by continuum fluid dynamics based approaches, and direct simulation methods such as molecular dynamics can be computationally expensive. Here we present a mesoscale approach for the simulation of electrolytes which alleviates these issues: the discrete ion stochastic continuum overdamped solvent (DISCOS) method.

[Phys. Rev. Fluids 6, 044309] Published Thu Apr 22, 2021

### Hierarchical parcel-swapping representation of turbulent mixing. III. Origins of correlation patterns observed in turbulent boundary layers

Author(s): Alan R. Kerstein

The influence of a local fluctuation in a turbulent boundary layer can propagate in many directions, potentially resulting in correlation patterns that reflect the common origin of the propagating disturbances. This process-based origin of correlation patterns is complementary to the well-known statistical signatures of organized structures. The present study introduces a novel conceptual framework termed ‘cascade analogy’ that systematizes the analysis of process-based correlations. Predicted behaviors are supported by previously reported measurements and by computational modeling involving a newly formulated reduced version of hierarchical parcel swapping (HiPS).

[Phys. Rev. Fluids 6, 044611] Published Thu Apr 22, 2021

### Shock motion inside a varying cross-section channel and consequences on the downstream flow

Author(s): Florian Hermet, Jérémie Gressier, and Nicolas Binder

Using numerical simulations shock wave physics in a constant area channel behind a convergent or divergent channel is investigated. It is found that shock wave propagation in the downstream uniform area region is influenced by the post-shock flow unsteadinesses. A detailed flow description is provided and a quasi-steady model for determining the waves intensity at large times is proposed. Moreover, this study points out the limits of the use of Whitham’s theory in a variable area channel.

[Phys. Rev. Fluids 6, 044802] Published Thu Apr 22, 2021

### A new criterion of coalescence-induced microbubble detachment in three-dimensional microfluidic channel

This work is motivated by an experiment of microbubble transport in a polymer microfluidic gas generation device where coalescence-induced detachment exhibits. We numerically study three-dimensional microbubble coalescence using the graphics processing unit accelerating free energy lattice Boltzmann method with cubic polynomial boundary conditions. The focus is on the coalescence-induced microbubble detachment (CIMD) in microfluidics. From the experimental observation, we identified that size inequality between two-parent bubbles and the size of the father (large) bubble are key factors to determine if a CIMD will occur. First, the analytical relationship between equilibrium contact angle and dimensionless wetting potential and experimental results of coalescence with and without CIMD are employed for the verification and validation, respectively. From eighteen experimental and computational cases, we derive a new criterion for CIMD: CIMD occurs when the two-parent bubbles are (nearly) equal with a relatively large radius. The underlying mechanism behind this criterion is explored by the time evolution of the velocity vector field, vorticity field, and kinetic energy in the entire coalescence. It is found that the symmetric capillary force drives the formation of vertical flow stream to the horizontal alignment of parent bubbles and the blockage of the downward stream due to the solid interface promotes the intensity of the upward stream. Meanwhile, large-sized parent bubbles transfer a large amount of kinetic energy from the initial free surface energy, which is essential to lead a CIMD in the post-coalescence stage. Such a new criterion is expected to impact the design and optimization of microfluidics in various applications.

### An active body in a Phan-Thien and Tanner fluid: The effect of the third polar squirming mode

An active, self-propelled, spherical microbody in a weakly viscoelastic matrix fluid is investigated theoretically using analytical techniques. The Upper-Convected Maxwell (UCM), Oldroyd-B, and exponential Phan-Thien and Tanner (ePTT) constitutive equations, along with the spherical squirmer model, are utilized. The contribution of the elastic stress in the governing equations give rise to three dimensionless numbers: the viscosity ratio, β, the Weissenberg number, Wi, and the ePTT rheological parameter, ε. Moreover, the squirmer model is characterized by three dimensionless parameters related to the fluid velocity on the surface of the body: the primary and secondary slip parameters [math] and μ, respectively, and the swirl parameter [math]. It is shown that the viscoelastic stress for the UCM and Oldroyd-B models becomes singular at a critical Weissenberg number, which depends only on the slip parameters, generalizing the findings previously reported for μ = 0 by Housiadas et al. [“Squirmers with swirl at low Weissenberg number,” J. Fluid Mech. 911, A16 (2021)]. When the ePTT model is utilized, the singularity is removed. The mechanism behind the speed and rotation rate enhancement associated with the secondary slip and swirl parameters is also investigated. It is demonstrated that, regardless of the values of the slip parameters, the swimming velocity of the body is enhanced by swirl, and for a sufficiently large ζ, its speed becomes larger than its speed in a Newtonian fluid with the same viscosity. Emphasis on the role of the secondary slip parameter is also given. It is shown that it affects substantially the force contributions on the body leading to a great variety of swimming behaviors. Its effect is quite complicated and sometimes similar to, or even more important than, the effect caused by the choice of the constitutive model.

### Numerical investigation of the impacting and freezing process of a single supercooled water droplet

In order to study the mechanism of ice formation after water droplets produced by splashing waves attach to ship superstructure in cold ocean regions, a numerical framework that considers the effect of supercooling degree on the meso-scale water droplet freezing is developed to explore the freezing mechanism of water droplets after impacting. This model can track the solid–liquid and air–liquid interface together using a coupled volume-of-fluid and level set multiphase method and Enthalpy-Porosity phase change method. The model introduces a mixed fraction to describe the problem of three-phase unification. The simulation results of the center freezing height and droplet spreading factor in this paper are consistent with the experimental results in related literature, which verifies the accuracy of the framework. The study includes a detailed description of the dynamic and thermodynamics mechanism of the water droplet. The influence factors of droplet impacting and freezing process are analyzed. The analysis results show that the surface wettability, supercooling degree, and impact velocity have a great influence on the freezing behavior of droplets. This model can deepen the understanding of icing mechanism on ship superstructure surface, provide an indication for engineers to develop an accurate prediction method of ice accretion on ship superstructure surface.

### Effect of wall slip on vertical film drainage in presence of soluble surfactants

A mathematical model is established to investigate a vertical gravity-driven drainage flow containing a soluble surfactant when considering the effect of wall slip. The lubrication theory is employed to obtain the evolution equations describing film thickness, surface velocity, surfactant concentrations at the air–liquid, solid–liquid interface, and in the bulk. The influence of constant slip length bc and variable slip length bs varying with surfactant concentration on the drainage dynamics is investigated compared with the case of no-slip bo, and the mechanism of the film thinning and the backflow caused by wall slip is examined. Simulated results show that the wall slip has a significant impact on the dynamics of the film drainage compared with the no-slip case. For the case of constant slip length, the wall slip accelerates the film thinning in the early stage. At the middle stage, the wall slip enhances the Marangoni effect and surface velocity rapidly decreases, causing a surface backflow phenomenon at the film bottom; the higher the slip length, the more obvious surface backflow. In the late stage, surface backflow weakens, and the film thickness is less than that of bo. For the case of variable slip length, in the early stage, the film thickness and surface velocity are between those of bo and bc; at the middle stage, a weak surface backflow is evolved at the film bottom; in the late stage, the film thickness is close to that of bc, and the surfactant concentration is lower than those of bo and bc.

### Identification of traveling crossflow waves under real hypersonic flight conditions

Understanding crossflow instabilities in three-dimensional boundary layers triggered by either traveling crossflow waves or stationary crossflow vortices is of great importance for modeling, predicting, and controlling hypersonic laminar-turbulent transition. However, due to very limited available flight experiment data, the crossflow instability under real flight conditions is still far from fully understood. To gain further insight, the raw data of a recent model flight experiment conducted by China Aerodynamics Research and Development Center have been thoroughly analyzed in the present study. The instrumented model is an inclined blunt cone mounted with several pressure sensors. Distinct low-frequency signals detected by these pressure sensors are peaked at about 10 kHz, which are in good agreement with the traveling-crossflow-wave frequencies with the largest N factors predicted by the eN method. Moreover, propagation velocities and wave angles of these signals obtained from correlation analysis also agree with the results from linear stability theory. The present study confirms that the detected low-frequency signals are traveling crossflow waves and provides the first evidence of traveling crossflow waves under real flight conditions.

### Knudsen diffusion differs from Fickian diffusion

We investigate the gas transport enhancement through nanotubes, relative to the prediction by the prevailing century-old Knudsen diffusion model. This enhancement is usually attributed to the partly specular molecular reflections at the smooth nanotube surface, which break the model assumption of completely diffusive reflections. However, an oversighted cause of the discrepancy between the measurement and theory that we found is that even for the gas transport with completely diffusive reflections, the Knudsen diffusion model based on Fick's first law is accurate only for long nanotubes. Additionally, for smooth nanotubes with partly specular reflections, the Knudsen diffusion model is also invalid even if the diffusion coefficient is corrected to account for the atomic-scale surface smoothness. On the other hand, the Knudsen diffusion model might be used for interpretations instead of predictions, and then the diffusion coefficient inferred from the measured mass flow rate could be completely different from the actual value. All those discrepancies and confusions stem from the implementation of Fick's first law can be avoided by using the molecular transmission probability obtained by the kinetic theory to quantify the flow rate of the Knudsen diffusion process. This work provides the correction to the Knudsen diffusion model for accurate predictions of gas diffusion through nanotubes and better interpretations of experimental measurements.

### On the lattice Boltzmann method and its application to turbulent, multiphase flows of various fluids including cryogens: A review

Cryogenic fluids are used in a myriad of different applications not limited to green fuels, medical devices, spacecraft, and cryoelectronics. In this review, we elaborate on these applications and synthesize recent lattice Boltzmann methods (LBMs) including collision operators, boundary conditions, grid-refinement techniques, and multiphase models that have enabled the simulation of turbulence, thermodynamic phase change, and non-isothermal effects in a wide array of fluids, including cryogens. The LBM has reached a mature state over the last three decades and become a strong alternative to the conventional Navier–Stokes equations for simulating complex, rarefied, thermal, multiphase fluid systems. Moreover, the method's scalability boosts the efficiency of large-scale fluid flow computations on parallel clusters, including heterogeneous clusters with graphics card-based accelerators. Despite this maturity, the LBM has only recently experienced limited use in the study of cryogenic fluid systems. Therefore, it is fitting to emphasize the usefulness of the LBM for simulating computationally prohibitive, complex cryogenic flows. We expect that the method will be employed more extensively in the future owing to its simple representation of molecular interaction and consequently thermodynamic changes of state, surface tension effects, non-ideal effects, and boundary treatments, among others.

### Implementation of a hybrid Lagrangian filtered density function–large eddy simulation methodology in a dynamic adaptive mesh refinement environment

Multispecies mixing processes play an important role in many engineering, biological, and environmental applications. Since simulating mixing flows can be useful to understand its physics and to study industrial issues, this work aims to develop the basis of a methodology able to simulate the physics of multiple-species mixing flows, using a hybrid large eddy simulation/Lagrangian filtered density function (FDF) method on an adaptive, block-structured mesh. A computational model of notional particles transport on a distributed processing environment is built using a parallel Lagrangian map. This map connects the Lagrangian information with the Eulerian framework of the in-house code MFSim, in which transport equations are solved. The Lagrangian composition FDF method, through the Monte Carlo technique, performs algebraic calculations over an ensemble of notional particles and provides composition fields statistically equivalent to those obtained by finite volume numerical solution of partial differential equations. Finally, to maintain high accuracy in the system of stochastic differential equations solver when an adaptive mesh refinement environment is used, a methodology for ensuring mass conservation is developed to preserve at least the statistical moments up to order two, even in the case of annihilation or cloning of a large number of notional particles in one time step, ensuring the applicability of Lagrangian FDF methods in dynamically adaptive grid refinement.

### Evaluating flow-field and expelled droplets in the mockup dental clinic during the COVID-19 pandemic

In the setting of widespread severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) community transmission, reducing the exposure risk on dental professionals and the next patients is the key to reopening dental services in this pandemic environment. The study is motivated by the lack of understanding of the flow-field characteristics and droplet distribution during aerosol-generating procedures. The particle image velocimetry measurements with high temporal and spatial resolutions were performed under ultrasonic scaling in the mockup experimental dental clinic. Compared with other methods focusing on the settled droplet particles, the study focused on the visualization of suspended droplets. From the results of the velocity vector and trajectory map, the high-level contaminated area will be within 1 m from the oral cavity. The vortex structures were identified by the vorticity index. In the surface near the patient's head, a counterclockwise vortex would carry some droplets and contaminate this region. The small droplets circulated in the turbulence cloud and the droplet nuclei generated by dehydration are the two primary sources of suspended particles, which may cause airborne transmission in the dental clinic. About 65%–74% of the droplets in ultrasonic scaling were in the range of 50–180 [math]. The research will provide references to the development of the precaution measures to reduce the SARS-CoV-2 exposure risk of dental professionals.