# Latest papers in fluid mechanics

### The effect of column-shaped discharge duration on induced high-speed flow dynamics

Energy deposition from pulsed plasma-based devices is of research interest due to their promising flow control applications. Here, we report on a combined experimental and numerical study of a high-speed flow induced by a column-shaped, pulsed discharge at low pressure. The energy release time is analyzed based on the relative dynamics of the shock and contact fronts. Time-resolved shadow imaging is performed to capture the evolution of two cylindrical flow discontinuities—a shock wave and a contact surface—from 4 µs up to 25 µs after discharge pulse. The comparison of the experimental data with the numerical predictions confirms that the heating of gas by the pulsed plasma occurs within one microsecond after nanosecond discharge initiation.

### Detection of standing internal gravity waves in experiments with convection over a wavy heated wall

Convection over a wavy heated bottom wall in the air flow has been studied in experiments with the Rayleigh number of ∼108. It is shown that the mean temperature gradient in the flow core inside a large-scale circulation is directed upward, which corresponds to the stably stratified flow. In the experiments with a wavy heated bottom wall, we detect large-scale standing internal gravity waves (IGWs) excited in the regions with the stably stratified flow. The wavelength and the period of these waves are much larger than the turbulent spatial and time scales, respectively. In particular, the frequencies of the observed large-scale waves vary from 0.006 Hz to 0.07 Hz, while the turbulent time in the integral scale is about 0.5 s. The measured spectra of these waves contain several localized maxima that imply an existence of waveguide resonators for large-scale standing IGWs. For comparisons, experiments with convection over a smooth plane bottom wall at the same mean temperature difference between the bottom and upper walls have also been conducted. In these experiments, various locations with a stably stratified flow are also found, and large-scale standing IGWs are observed in these regions.

### Diameter ratio effects in the wake flow of single step cylinders

Vortex interactions behind step cylinders with diameter ratio 2 ≤ D/d ≤ 3 at Reynolds number (ReD) 150 were investigated by directly solving the three-dimensional Navier–Stokes equations. In accordance with the previous paper [C. Tian et al., “Vortex dislocation mechanisms in the near wake of a step cylinder,” J. Fluid Mech. 891, A24 (2020)], some interesting characteristics of vortex dislocations, e.g., two phase difference accumulation mechanisms, the trigger and threshold values of vortex dislocations, antisymmetric vortex interactions, and long N-cell cycles, were observed. By performing a detailed investigation of diameter ratio effects, more features of vortex dynamics were discovered. In addition to the known antisymmetric vortex interactions, a symmetric vortex interaction between neighboring N-cell cycles was observed. The long-time observations revealed an interruption of these two types of vortex interactions. By using a well-validated phase tracking method, we monitored the time trace of the phase difference accumulation process in different D/d cases from which decreasing (known) and increasing (new) phase difference tendencies were identified. Both caused the interruption of continuous symmetric or antisymmetric phenomena but through two distinct mechanisms. Meanwhile, the diameter ratio effects on the trigger and threshold values were discussed. Additionally, the likelihood of antisymmetric or symmetric vortex interactions and increasing or decreasing phase difference tendencies was analyzed. Moreover, diameter ratio effects on shedding frequencies and the extensions of three main vortex cells, i.e., S-, N-, and L-cell vortices, were described.

### Theoretical analysis for flattening of a rising bubble in a Hele–Shaw cell

We calculate the shape and the velocity of a bubble rising in an infinitely large and closed Hele–Shaw cell using Park and Homsy’s boundary condition, which accounts for the change of the three dimensional structure in the perimeter zone. We first formulate the problem in the form of a variational problem and discuss the shape change assuming that the bubble takes an elliptic shape. We calculate the shape and the velocity of the bubble as a function of the bubble size, the gap distance, and the inclination angle of the cell. We show that the bubble is flattened as it rises. This result is in agreement with experiments for large Hele–Shaw cells.

### Enhancing oil recovery using an immiscible slug: Lattice Boltzmann simulation by three-phase pseudopotential model

In the oil development process, an immiscible third-phase slug can be injected to the formation temporarily to assist the water flooding, resulting in a three-phase flow underground. In this work, we study slug-assisted water flooding at the pore scale using the three-phase pseudopotential lattice Boltzmann model. We first briefly describe the three-phase pseudopotential model and propose a concise scheme to set the contact angles of the Janus droplet on the solid wall. Then, we simulate the slug-assisted water flooding process in different porous media structures, i.e., a single pore-throat channel, parallel throats, and a heterogeneous porous medium. The simulation results show that oil recovery can be improved effectively with the addition of the third-phase slug. The addition of the third phase results in much more interfacial interaction between different phases, which helps recover trapped oil in pore corners, narrow throats, and the high permeability zone in the porous medium. Moreover, the injection volume, injection timing, contact angle, and viscosity of the third phase influence the oil recovery in different ways. The injected slug can also be trapped in the porous medium, which may result in formation damage. The study explains the enhanced oil recovery mechanisms of slug-assisted water flooding at the pore scale and provides an effective way to design the injection scheme during industrial production.

### Bragg scattering of long waves by an array of floating flexible plates in the presence of multiple submerged trenches

Bragg scattering of long gravity waves by an array of floating elastic plates in the presence of a series of rectangular trenches is studied under the assumption of linearized water wave theory and small amplitude structural response. Bragg reflection occurs in the case of an array of multiple floating flexible plates and trenches in isolation or combination, and the number of sub-harmonic peaks between two consecutive peaks is two less than the number of plates/trenches. In the case of long-wave scattering by an array of trenches in the absence of floating plates, wave reflection becomes zero minimum for a certain fixed wavenumber at the end of the first cycle (as referred to 0 < k1h1 < 0.32), irrespective of the even/odd number of trenches. Furthermore, the Bragg resonant reflection pattern of the second cycle is a mirror image of the reflection occurring in the first cycle. Conversely, the symmetric pattern of Bragg reflection exhibited in the case of an array of trenches does not occur for an array of plates in isolation or for plates and trenches in combination. Between consecutive harmonic peaks, the minima/maxima in the wave reflection occur in the case of the even/odd number of trenches/plates in isolation. In contrast, it occurs within the first cycle in the case of trenches and plates in combination. Between consecutive harmonic peaks, maxima/minima of wave reflection coincide for a certain wavenumber, irrespective of the even/odd number of trenches/plates in isolation. In addition, these maxima attained for a certain wavenumber for the even number of trenches/plates are 180° out of phase to that of minima for an odd number of trenches/plates. However, similar phenomena occur within the first cycle of Bragg resonance in the case of trenches and plates in combination. Moreover, the amplitude of oscillation in the wave reflection increases with an increase in plate rigidity. Time-dependent motion due to Bragg scattering by trenches and plates is demonstrated in different cases.

### The effect of a solid boundary on the propagation of thermodynamic disturbances in a rarefied gas

We study the effect of a rigid boundary on the propagation of thermodynamic disturbances in a gas under non-continuum conditions. We consider a semi-infinite setup confined by an infinite planar wall and introduce initial gas disturbances in the form of density and temperature inhomogeneities. The problem is formulated for arbitrary small-amplitude perturbations and analyzed in the entire range of gas rarefaction rates, governed by the Knudsen (Kn) number. Our results describe the system relaxation to equilibrium, with specific emphasis on the effect of the solid surface. Analytical solutions are obtained in the free-molecular and near-continuum (based on the Navier–Stokes–Fourier and regularized 13 moment equations) regimes and compared with direct simulation Monte Carlo results. The impact of the solid wall is highlighted by comparing between diffuse (adiabatic or isothermal) and specular boundary reflections. Focusing on a case of an initial temperature disturbance, the results indicate that the system relaxation time shortens with increasing Kn. The isothermal boundary consistently reverberates the weakest acoustic disturbance, as the energy carried by the impinging wave is partially absorbed by the surface. The specular and adiabatic wall systems exhibit identical responses in the continuum limit while departing with increasing Kn due to higher-order moment effects. The unsteady normal force exerted by the gas on the surface is quantified and analyzed.

### Bridging inertial and dissipation range statistics in rotating turbulence

We investigate the connection between the inertial range and the dissipation range statistics of rotating turbulence through detailed simulations of a helical shell model and a multifractal analysis. In particular, by using the latter, we find an explicit relation between the (anomalous) scaling exponents of equal-time structure functions in the inertial range in terms of the generalized dimensions associated with the energy dissipation rate. This theoretical prediction is validated by detailed simulations of a helical shell model for various strengths of rotation from where the statistics of the dissipation rate and, thus, the generalized dimensions, as well as the inertial range, in particular, the anomalous scaling exponents, are extracted. Our work also underlines a surprisingly good agreement—such as that in the spatial structure of the energy dissipation rates and the decrease in inertial range intermittency with increasing strengths of rotation—between solutions of the Navier–Stokes equation in a rotating frame with those obtained from low-dimensional, dynamical systems such as the shell model, which are not explicitly anisotropic. Finally, we perform direct numerical simulations of the Navier–Stokes equation, with the Coriolis force incorporated, to confirm the robustness of the conclusions drawn from our multifractal and shell model studies.

### Flow and stability of a gravity-driven thin film over a locally heated porous wall

Stability analysis is performed for a gravity-driven thin liquid film flowing down a locally heated porous substrate. Using the lubrication approximation, the governing equations are simplified to derive the evolution equation for the free surface of the liquid film. The Beaver-Joseph condition is employed at the interface of the porous layer and the liquid film. The base profiles are mainly influenced by parameters that appear due to non-uniform heating. Linear stability analysis is performed and reported that both thermocapillary and rivulet instabilities are enhanced with increasing values of the Marangoni number, Biot number, and Beavers–Joseph coefficient and decreasing values of the Darcy number. Dependence of critical Darcy number on the porous layer thickness and the Beavers–Joseph coefficient is presented. It is also shown that the full Darcy model can be replaced with an approximated slip model. The growth rate from nonlinear computations is consistent with the linear stability analysis.

### Turbulence-obstacle interactions in the Lagrangian framework: Applications for stochastic modeling in canopy flows

Author(s): Ron Shnapp, Yardena Bohbot-Raviv, Alex Liberzon, and Eyal Fattal

High turbulent dissipation in inhomogeneous flows can lead to a quasihomogeneous regime of Lagrangian statistics at small scales. This is shown in a canopy flow by an analysis of experimental Lagrangian trajectories. Furthermore, the analysis shows that Lagrangian statistics are affected by turbulence-obstacle interaction, leading to a short velocity decorrelation timescale and attenuation of the Kolmogorov constant for the Lagrangian structure function.

[Phys. Rev. Fluids 5, 094601] Published Tue Sep 01, 2020

### Scaling of turbulent kinetic energy and dissipation in turbulent wall-bounded flows

Author(s): Tie Wei

The dissipation of turbulent kinetic energy (TKE) in wall-bounded turbulent flows is found to scale with the Kolmogorov wall velocity, not the friction velocity as previously suggested. A new scaling is also developed for the peak value of the TKE. The new scaling is verified against direct numerical simulation data and is justified by dimensional analysis.

[Phys. Rev. Fluids 5, 094602] Published Tue Sep 01, 2020

### Breakup morphology of expelled respiratory liquid: From the perspective of hydrodynamic instabilities

Understanding the breakup morphology of an expelled respiratory liquid is an emerging interest in diverse fields to enhance the efficacious strategies to attenuate disease transmission. In this paper, we present the possible hydrodynamic instabilities associated with expelling the respiratory liquid by a human. For this purpose, we have performed experiments with a cylindrical soap film and air. The sequence of the chain of events was captured with high-speed imaging. We have identified three mechanisms, namely, Kelvin–Helmholtz (K–H) instability, Rayleigh–Taylor (R–T) instability, and Plateau–Rayleigh (P–R) instability, which are likely to occur in sequence. Furthermore, we discuss the multiple processes responsible for drop fragmentation. The processes such as breakup length, rupture, ligament, and drop formation are documented with a scaling factor. The breakup length scales with We−0.17, and the number of ligaments scales as [math]. In addition, the thickness of the ligaments scales as We−0.5. Here, We and Bo represent the Weber and Bond numbers, respectively. It was also demonstrated that the flapping of the liquid sheet is the result of the K–H mechanism, and the ligaments formed on the edge of the rim appear due to the R–T mechanism, and finally, the hanging drop fragmentation is the result of the P–R instability. Our study highlights that the multiple instabilities play a significant role in determining the size of the droplets while expelling a respiratory liquid. This understanding is crucial to combat disease transmission through droplets.

### On the use of the Lambert function in solving non-Newtonian flow problems

We consider unidirectional flows of ideal or regularized Bingham fluids as well as viscoelastic fluids for which analytical solutions can be derived in terms of the Lambert W function. Explicit expressions are derived for the radius of the yielded region in partially yielded circular and axial Couette flows. Analytical solutions are also derived for the velocity and the volumetric flow rate in the plane and axisymmetric Poiseuille flows of a Windhab fluid, which is a combination of the Bingham and Papanastasiou models, and for the shear stress in the plane Couette flow of an exponential Phan–Thien–Tanner fluid. Finally, the Lambert function is used to solve the Poiseuille flow of a power-law fluid and the Newtonian circular Couette flow with wall slip and non-zero slip yield stress by means of a regularized slip equation, which is valid for any value of the wall shear stress.

### Wingtip vortex structure in the near-field of swept-tapered wings

Wingtip vortices are an important phenomenon in fluid dynamics due to their complex and negative impacts. Despite numerous studies, the current understanding of the inner vortex is very limited; thus, a basis for the design of effective wingtip geometry and vortex manipulation is narrow. This work examines the structure of the trailing vortex shed from a swept-tapered wing, analogous to a commercial aircraft topology. Stereoscopic particle imaging velocimetry has been utilized to compare the vortex structure and development through several angles of attack at various downstream stations for a fixed Reynolds number (Re = 1.5 × 106). After correcting for vortex meander through helicity-based spatial localization of the vortex core, relationships between the vortex core velocity/vorticity fields, core shape, and turbulent properties have been examined. Subsequently, the vortex is found to exhibit a layered structure with slow linear rates of dissipation indicative of laminar diffusion mechanisms, despite being a turbulent vortex. The turbulent kinetic energy distribution in the vortex signals that relaminarization of the inner core occurs. Consideration of the streamline curvature around the core, via examination of the local Richardson number, indicated that a laminar core structure had formed within which large-scale turbulent eddies could not contribute to the turbulent diffusion of vorticity away from the core. The normalized circulation within the vortex core has been shown to exhibit self-similar behavior typical of the fully developed axisymmetric vortices.

### A structural subgrid-scale model for the collision-related statistics of inertial particles in large-eddy simulations of isotropic turbulent flows

In large-eddy simulations of particle-laden isotropic turbulent flows, the collision of inertial particles is strongly influenced by missing small-scale turbulence. In this paper, we apply the Kinematic Simulation with Approximate Deconvolution (KSAD) model to determine the contribution of small-scale turbulence to the motion of inertial particles and improve the prediction accuracy of the radial distribution function (RDF) and radial relative velocity (RRV), which are closely related to particle collisions. Different values of Stokes numbers (St), which are defined as the ratio of the particle response time to the Kolmogorov time scale, are considered. The KSAD model significantly improves the prediction accuracy of the RRV for all considered St. For the prediction of RDF, good agreement between the KSAD model and direct numerical simulations is only observed for large St, i.e., St ≥ 2.0. To explore the reason for the poor prediction of the KSAD model for small St, we compare the Eulerian statistics of the flow fields and the Lagrangian properties of the particles from different simulations and find the key reason is that the Gaussian turbulence generated in the kinematic simulation model is inadequate in recovering the vortex centrifugal effect of small-scale turbulence on the inertial particle clustering at small St.

### Publisher’s Note: “Accumulated densities of sedimenting particles in turbulent flows” [Phys. Fluids 32, 075104 (2020)]

### Dense gas flow simulations in ultra-tight confinement

Modeling dense gas flows inside channels with sections comparable to the diameter of gas molecules is essential in porous medium applications, such as in non-conventional shale reservoir management and nanofluidic separation membranes. In this paper, we perform the first verification study of the Enskog equation by using particle simulation methods based on the same hard-sphere collisions dynamics. Our in-house Event-Driven Molecular Dynamics (EDMD) code and a pseudo-hard-sphere Molecular Dynamics (PHS-MD) solver are used to study force-driven Poiseuille flows in the limit of high gas densities and high confinements. Our results showed (a) very good agreement between EDMD, PHS-MD, and Enskog solutions across density, velocity, and temperature profiles for all the simulation conditions and (b) numerical evidence that deviations exist in the normalized mass flow rate vs Knudsen number curve compared to the standard curve without confinement. While we observe slight deviations in the Enskog density and velocity profiles from the MD when the reduced density is greater than 0.2, this limit is well above practical engineering applications, such as in shale gas. The key advantages of promoting the Enskog equation for upscaling flows in porous media lie in its ability to capture the non-equilibrium physics of tightly confined fluids while being computationally more efficient than fundamental simulation approaches, such as molecular dynamics and derivative solvers.

### On the cavity-actuated supersonic mixing layer downstream a thick splitter plate

We propose a cavity as an actuator to actuate the supersonic mixing layer downstream a thick splitter plate. The cavity-actuated case at Re = 1.73 × 105 is simulated using large eddy simulation. The forced dynamics is resolved by the cluster-based network model (CNM) from a probabilistic point of view. Introducing a cavity obtains a 50% increase in the growth rate of vorticity thickness. The recirculation region immediately downstream the trailing edge of the splitter plate is largely reduced, which contributes to the advanced and fast growth of the redeveloping mixing layer. The cavity oscillation induces three-dimensional features that are beneficial to the small-scale mixing. Spectral analysis reveals that the cavity-actuated flow field exhibits the phenomena of the strict frequency-lock and temporal mode-switching. The CNM successfully resolves the intermittent dynamics of the supersonic mixing layer using only ten centroids. The CNM’s outcomes reveal two flow regimes of the unforced case: the Kelvin–Helmholtz vortex and vortex pairing. The cavity oscillation significantly affects the flow patterns of the centroids, which exhibit flow structures closely associated with the wake mode and shear-layer mode of the cavity oscillations. The dynamics of the cavity-actuated case is tamed into a strictly periodic transition loop among ten clusters undergoing the cyclic motion of the cluster energy fluctuation from the maximum to the minimum. Each centroid of the cavity-actuated case transports much more turbulent kinetic energy than that of the unforced case. Overall, the cavity-actuated attractor gets a 3.27 times increase in the energy fluctuation.

### Analytical model for predicting maximum spread of droplet impinging on solid surfaces

In the present study, we develop a theoretical approach to predict the maximum spread of a liquid droplet on a dry solid surface. By using the dynamics of the gas layer entrapped underneath the droplet during initial stages of spreading, we determine the initial spread velocity of the droplet. The predicted spread velocity is used to model viscous dissipation and spread time of the droplet, post-impact. We also reformulate the surface energy of the droplet at the maximum spread to account for the presence of a rim formed at the periphery of the droplet. Incorporating the renewed terms into an energy conservation equation, the maximum spread of the droplet is predicted. The constructed model is validated with both the in-house experiments and the literature performed for various liquids and surfaces. The study also examines the existing scaling laws available to predict the maximum spread in inertial and viscous regimes and compares them with the model. Results reveal that the proposed model effectively predicts maximum spread values even at a low Weber number, despite variations in wettability values. The scaling laws were found to be inefficient in predicting the maximum spread for water at a low Weber number as they do not account for the effect of the surface wettability.

### Design and optimization of a water jet-based biomimetic antifouling model for marine structures

Marine structures, such as ship hulls and offshore platforms, are basic elements in marine engineering. Due to the harsh ocean environment, marine structures are prone to adhesion and corrosion by marine biofouling. The biomimetic antifouling technology has been recognized as the most promising solution to marine biofouling, while there is still a long way to go to take this technology outside of research laboratories. In order to develop practical biomimetic antifouling techniques, this work presents a new water jet-based biomimetic antifouling model for marine structures to prevent the enrichment of biofouling. First, a semi-empirical formula is proposed based on the Schlichting self-similar solution to determine the effective width of the water jet. Then, a numerical simulation model is established to investigate the effects of the jet parameters (such as the jet aperture, jet velocity, and jet hole spacing) on the water jet distribution. Subsequently, visualization experiments are carried out to compare and validate the numerical simulation results. Finally, the simulation data are used to train a genetic neural network to predict the effective jet coverage ratio. The optimal parameters of the antifouling model are obtained corresponding to the largest effective jet coverage ratio. The findings of this study deliver a practical biomimetic antifouling technique for marine structures.