# Latest papers in fluid mechanics

### Study of effect of magnetic field on the axisymmetric vortices produced by a novel vortex generator in a rectangular channel using dynamic mode decomposition

The introduction of a magnetic field greatly influences the nanofluid flow in a channel. The current study uses a novel vortex generator (VG) to produce a couple of axisymmetric vortices behind the VG at Re = 6000. These vortices are significantly affected by the strength of the magnetic field. The considered cases are identical and vary only with the change in intensity of the magnetic flux. Initially, at Ha = 5, both vortices P1 and P2 are stretched; however, vortex P2 is stretched significantly in comparison to vortex P1. Such stretching enhances the rotational speed of the vortices resulting in the increment of the overall heat transfer rate by 7.1%, when compared to the case with no magnetic flux. With the increase in magnetic flux, the produced vortices are stretched to such an extent that results in the loss of the majority of its span, leading to the decrement in heat transfer rate from the heated base plate to the flowing fluid. For Ha = 50, the heat transfer rate registers a loss of about 45.4%. Finally, the study of the dynamic mode decomposition reveals that the first dominant mode is 10 times higher than the second and third dominant modes.

### An adaptive and energy-maximizing control optimization of wave energy converters using an extremum-seeking approach

In this paper, we systematically investigate the feasibility of different extremum-seeking (ES) control and optimization schemes to improve the conversion efficiency of wave energy converters (WECs). Continuous-time and model-free ES schemes based on the sliding mode, relay, least-squares gradient, self-driving, and perturbation-based methods are used to improve the mean extracted power of a heaving point absorber subject to regular and irregular waves. This objective is achieved by optimizing the resistive and reactive coefficients of the power take-off (PTO) mechanism using the ES approach. The optimization results are verified against analytical solutions and the extremum of reference-to-output maps. The numerical results demonstrate that except for the self-driving ES algorithm, the other four ES schemes reliably converge for the two-parameter optimization problem, whereas the former is more suitable for optimizing a single parameter. The results also show that for an irregular sea state, the sliding mode and perturbation-based ES schemes have better convergence to the optimum in comparison to other ES schemes considered here. The convergence of PTO coefficients toward the performance-optimal values is tested for widely different initial values in order to avoid bias toward the extremum. We also demonstrate the adaptive capability of ES control by considering a case in which the ES controller adapts to the new extremum automatically amid changes in the simulated wave conditions. Moreover, no explicit knowledge of (future) wave excitation forces is required in the algorithm, which implies that the model-free ES can be used as a causal controller for WECs. Our results demonstrate that the continuous-time and model-free ES method achieves the optimum within a single simulation, which is in contrast to evolution-based optimization strategies that typically require a large number of (possibly expensive) function evaluations. This makes ES control optimization schemes suitable for nonlinear computational fluid dynamics simulations, where typically evolutionary strategies are used for performing black-box optimization.

### Numerical investigation of the Lorentz force effect on two-point statistics in a turbulent channel flow

Effects of a uniform and static magnetic field in the streamwise direction with different Hartmann numbers on the average structure of velocity and pressure fluctuations in a magneto-hydrodynamic turbulent channel flow are investigated. Direct numerical simulations (DNSs) are performed at low magnetic Reynolds numbers and under subcritical conditions with the bulk Reynolds number Reb = 5600, based on the channel height, using a very long domain to analyze two-point velocity and pressure fluctuations. Comparisons are made with DNS data of channel flow with a spanwise magnetic field and also without a magnetic field. Results indicate a substantial increase in the large-scale flow anisotropy, more alignment of flow structures with the mean flow and substantial elongation of flow structures in the streamwise direction in case of the streamwise magnetic field. On the contrary, the spanwise magnetic field did not have a comparable influence on the large scale flow anisotropy. Streak spacing increased linearly with increasing Hartmann number with the magnetic field in the streamwise direction. The magnetic field in the spanwise direction was more effective in increasing the streak spacing at a lower Hartmann number. The mean size of the quasi-streamwise vortex rolls was not affected with the introduction of a magnetic field. The effect of the Hartmann number on turbulent scales shows that scales grow largely with increasing magnetic field strength. The influence of the magnetic fields on pressure fluctuations was similar in the two cases and confined to large-scale weak correlations, where their length was substantially increased, especially in the spanwise direction.

### Interfacial behavior of surfactant-covered double emulsion in extensional flow

Author(s): Hee Min Lee, Se Bin Choi, Jong Hyun Kim, and Joon Sang Lee

We analyze the interface-interface interactions of a surfactant-covered double emulsion using the lattice Boltzmann method and study the interaction of the inner and outer interfaces and the local surfactant distribution under a uniaxial extensional flow. First, the capillary effects are analyzed. U...

[Phys. Rev. E 102, 053104] Published Fri Nov 06, 2020

### Microfluidic filament thinning of aqueous, fibrillar methylcellulose solutions

Author(s): Athena E. Metaxas, McKenzie L. Coughlin, Clayton K. Hansen, Frank S. Bates, Timothy P. Lodge, and Cari S. Dutcher

Filament stretching using a flow-focusing microfluidic device coupled with image analysis has emerged as a promising method to resolve extensional properties of low viscosity, low molecular weight solutions. This method was used to calculate extensional properties of aqueous methylcellulose (MC) solutions at varying NaCl concentrations, where transient changes in filament diameter were used to calculate the flow-driven, apparent extensional viscosity of each solution. The increase in apparent extensional viscosity at room temperature as the NaCl concentration increases is attributed to the presence of a fibrillar MC network formed in solution.

[Phys. Rev. Fluids 5, 113302] Published Fri Nov 06, 2020

### Thermal boundary layer structure in convection with and without rotation

Author(s): Robert S. Long, Jon E. Mound, Christopher J. Davies, and Steven M. Tobias

The thermal boundary layer is identified and studied using numerical simulations of Rayleigh-Bénard convection. Different methods of defining the thermal boundary layer are investigated when applied to fixed temperature or fixed heat-flux boundary conditions. The crossover in advective and conductive heat flux is a robust way to define the thermal boundary layer.

[Phys. Rev. Fluids 5, 113502] Published Fri Nov 06, 2020

### Cooperative drag reduction in turbulent flows using polymer additives and superhydrophobic walls

Author(s): Anoop Rajappan and Gareth H. McKinley

The injection of long-chain polymer additives and the water-repellent (or superhydrophobic) texturing of submerged solid walls, have both evolved independently over the years into effective, stand-alone methods for frictional drag reduction in wall-bounded turbulent flows. Experiments performed in turbulent Taylor-Couette flow demonstrate that the two techniques, when combined carefully, result in an additive effect, producing significant enhancements in the overall level of drag reduction achieved.

[Phys. Rev. Fluids 5, 114601] Published Fri Nov 06, 2020

### Specialization of tuna: A numerical study on the function of caudal keels

Tunas are known for their extraordinary swimming performance, which is accomplished through various specializations. The caudal keels, a pair of lateral keel-like structures along the caudal peduncle, are a remarkable specialization in tunas and have convergently arisen in other fast-swimming marine animals. In the present study, the hydrodynamic function of caudal keels in tuna was numerically investigated. A three-dimensional model of yellowfin tuna with caudal keels was constructed based on previous morphological and anatomical studies. Vortical structures and pressure distributions are analyzed to determine the mechanisms of thunniform propulsion. A leading-edge vortex and a trailing-edge vortex are attached to the caudal fin and enhance the thrust. By comparing models of tuna with and without caudal keels, it is demonstrated that caudal keels generate streamwise vortices that result in negative pressure and reduce the transverse force amplitude. Moreover, the orientations of the streamwise vortices induced by caudal keels are opposite to those on the pressure side of the caudal fin. Therefore, caudal keels reduce the negative effects of the streamwise vortices adjacent to the caudal fin and thereby enhance the thrust on the caudal fin. A systematic study of the effects of variations in the Strouhal number (St), the Reynolds number (Re), and the cross-sectional shape of the body on the swimming of tuna is also presented. The effects of caudal keels are magnified as Re and St increase, whereas the cross-sectional shape has no major influence on the caudal keel mechanism.

### Effective Navier-slip in non-Newtonian fluid flows over corrugated surfaces

In this study, we show that complex local flow fields, particularly those near corrugated surfaces, can be accurately reproduced with effective Navier-slip boundary conditions over an imaginary smooth surface, in which the normalized slip length can be considered as a surface property even for non-Newtonian fluid flows. The expression for the normalized slip length was derived analytically using the effective viscosity and effective shear rate in a pressure-driven channel flow with a corrugated surface, based on the two-parameter model by separating geometrical and rheological factors with the effective viscosity concept. Our framework was established on the combination of the force balance approach for slip length characterization and the flow quantification method based on the energy dissipation rate. Effects of corrugated patterns with various aspect ratios were investigated. For verification, an example stick–slip–stick flow problem was tested and the results were compared with those of direct simulations. We report that the dimensionless normalized slip length appears to be almost constant and independent of the flow rate (or pressure drop). This implies that the normalized slip length is nearly independent of rheological properties. In addition, the dimensionless slip length of non-Newtonian fluids was found to be close to that of a Newtonian fluid, and it depends on the flow geometry itself.

### Exploring the signature of distributed pressure measurements on non-slender delta wings during axial and vertical gusts

For a broad range of aerodynamic bodies, vortex structures arising from perturbations such as gusts cause characteristic surface pressure signatures that are coupled to the observed aerodynamic loads. The present study evaluates the extent to which sparsely measured pressure signatures can be used to identify the spatio-temporal evolution of vortex structures and, specifically, their relationship to the bulk aerodynamic loads. A non-slender delta wing experiencing axial and vertical gusts under various initial stall conditions is selected as a test case. Time-resolved loads, distributed surface pressures, and time-resolved flow fields (particle image velocimetry) are collected for a wide range of parameters in a towing-tank facility. By linearly mapping the sparse pressure data to the aerodynamic loads, the spatio-temporal relation of loads and pressure can be extracted. The static mapping coefficients are determined through linear regression at each incidence angle as well as for an angle-independent (aggregate) case. Despite slightly larger errors when compared to the angle-specific fits, the aggregate method maintains a good fit quality over all angles of attack and thereby provides a robust pressure-load mapping. Thus, the existence of a common mechanism across gusts and angles of attack is identified despite the stark differences in flow conditions, i.e., light vs deep dynamic stall. In addition, the lasso regularization used in the study provides valuable insight into sensor reduction. The distribution of fewer regression predictors indicates specific pressure ports that capture the footprint of dominant flow features and thereby suggest sensitive locations for future clusters of sensors.

### Shear-induced lift force on spheres in a viscous linear shear flow at finite volume fractions

Several studies have shown a significant increase in drag on a distribution of solid spherical particles within a fluid with increasing particle volume fraction. As a result, many empirical drag laws accounting for the dependence on the Reynolds number and volume fraction can be found in the literature. This study investigates the possibility of a similar effect of the particle volume fraction on the mean hydrodynamic lift force on randomly distributed spherical particles in a linear shear flow. Particle-resolved direct numerical simulations are performed to evaluate the mean lift force, and the results are compared with the case of an isolated particle in a linear shear flow for the same Reynolds number and shear rate. The mean lift force acting on the particles appears to remain nearly the same as that on an isolated particle. However, due to the influence of neighboring particles, there is a substantial force variation in transverse directions on each individual particle, whose magnitude is comparable to the mean drag force. The distribution of drag force in a linear shear flow is shown to be nearly the same as in a uniform flow at the same volume fraction and Reynolds number. A simple stochastic model based on a Gaussian distribution is presented for the lift force variation, and its performance is compared to the prediction of the deterministic pairwise interaction extended point-particle model.

### The dynamics of liquid films, as described by the diffuse-interface model

The dynamics of a thin layer of liquid between a flat solid substrate and an infinitely thick layer of saturated vapor is examined. The liquid and vapor are two phases of the same fluid governed by the diffuse-interface model. The substrate is maintained at a fixed temperature, but in the bulk of the fluid, the temperature is allowed to vary. The slope ε of the liquid/vapor interface is assumed to be small, as is the ratio of its thickness to that of the film. Three asymptotic regimes are identified, depending on the vapor-to-liquid density ratio [math]/ρl. If [math]/ρl ∼ 1 (which implies that the temperature is comparable, but not necessarily close, to the critical value), the evolution of the interface is driven by the vertical flow due to liquid/vapor phase transition, with the horizontal flow being negligible. In the limit [math]/ρl → 0, it is the other way around, and there exists an intermediate regime, [math]/ρl ∼ ε4/3, where the two effects are of the same order. Only the [math]/ρl → 0 limit is mathematically similar to the case of incompressible (Navier–Stokes) liquids, whereas the asymptotic equations governing the other two regimes are of different types.

### Motion of a neutrally buoyant circular particle in a clockwise double-lid-driven square cavity

The motion of a neutrally buoyant circular particle in a clockwise double-lid-driven square cavity is studied with the lattice Boltzmann method. To understand, predict, and control the motion of the circular particle, the effect of the initial position, particle size, and Reynolds number is studied. The center of the square cavity is a fixed point, where the circular particle remains stationary all the time; otherwise, the circular particle is stabilized at the limit cycle, which is created by the inertia of the circular particle, confinement of the boundaries of the square cavity, and vortex behavior. The effect of the particle size on the motion of the circular particle is obvious, with the increase in the particle size, the confinement of the boundaries becomes stronger, and the limit cycle shrinks toward the center of the square cavity. With the increase in the Reynolds number, the fluid flow becomes stronger, two symmetric secondary vortices at the top left and bottom right corners develop, and the limit cycle is squashed along the leading diagonal of the square cavity.

### Flow dynamics and azimuthal behavior of the self-excited acoustic modes in axisymmetric shallow cavities

Self-excitation of acoustic resonance in axisymmetric cavities can lead to a complex flow–acoustic coupling, which may result in severe noise generation. In this work, a large eddy simulation is performed to model the different flow–sound coupling mechanisms during the self-excitation of various excitable acoustic modes in an axisymmetric shallow cavity configuration with an aspect ratio of L/d = 1 over the lock-in region. The compressible Navier–Stokes equations are solved at a resolution sufficient to capture the flow and the acoustic dynamics. The excitation of three acoustic modes of different aerodynamic characteristics over the range of the tested flow velocities was observed. These modes are a stationary diametral mode, a spinning diametral mode, and a longitudinal mode. The initiation and separation of vortices over the cavity mouth accompanying the self-excitation of each mode involve different dynamics. If two antisymmetric series of vortical crescents separate successively at the leading edge, a stationary acoustic mode is excited. The formation of a continuously rotating helical vortex, connecting the leading edge and the trailing edge, leads to the excitation of the diametral spinning mode. The excitation of the longitudinal mode is associated with symmetric rings of vortices. Complex patterns of flow velocities and Reynolds stresses in the circumferential direction are observed for the diametral modes but not for the longitudinal mode. In all cases, the excitation of acoustic resonance requires a synchronization of the vortex separation and impingement processes, which is necessary for efficient feedback to sustain the flow–sound coupling mechanism.

### Surface declination governed asymmetric sessile droplet evaporation

This article reports droplet evaporation kinetics on inclined substrates. Comprehensive experimental and theoretical analyses of the droplet evaporation behavior for different substrate declinations, wettability, and temperatures have been presented. Sessile droplets with substrate declination exhibit a distorted shape and evaporate at different rates compared to droplets on the same horizontal substrate, and exhibit more frequent changes in regimes of evaporation. The slip-stick and jump-stick modes are prominent during evaporation. For droplets on inclined substrates, the evaporative flux is also asymmetric and governed by the initial contact angle dissimilarity. Due to a smaller contact angle at the rear contact line, it is the zone of a higher evaporative flux. Particle image velocimetry shows increased internal circulation velocity within the inclined droplets. Asymmetry in the evaporative flux leads to higher temperature gradients, which ultimately enhances the thermal Marangoni circulation near the rear of the droplet where the evaporative flux is highest. A model is adopted to predict the thermal Marangoni advection velocity, and good match is obtained. The declination angle and imposed thermal conditions compete and lead to morphed evaporation kinetics than those of droplets on horizontal heated surfaces. Even weak movements of the contact line alter the evaporation dynamics significantly, by changing the shape of the droplet from an ideally elliptical to an almost spherical cap, which ultimately reduces the evaporative flux. The lifetime of the droplet is modeled by modifying available models for a non-heated substrate, to account for the shape asymmetry. The present observations may find strong implications toward microscale thermo-hydrodynamics.

### Instability of the realizable k–ε turbulence model beneath surface waves

Recent research has proved that most widely used two-equation turbulence closure models are unconditionally unstable in regions of nearly potential flow having finite strain, as commonly found beneath non-breaking surface waves. In this work, we extend such analysis to consider the popular realizable k–ε turbulence model. It is proved that this model, unlike all others thus far analyzed, is only conditionally unstable in such regions due to the addition of viscosity in the ε dissipation term. A method for formally stabilizing the model in the problematic regions is likewise developed. The results of the analysis, using both standard and stabilized turbulence closures, are confirmed via numerical simulations of progressive surface wave trains using a computational fluid dynamics model. Important qualitative differences are likewise demonstrated in simulations involving spilling breaking waves. (In the above, k is the turbulent kinetic energy density, and ε is the turbulence dissipation rate.)

### Numerical investigation of two hollow cylindrical droplets vertically impacting on dry flat surface simultaneously

In this paper, the effect of two hollow droplets’ impact on a solid substrate is numerically studied. A coupled level set and volume of fraction method is used to investigate the fluid dynamics and heat transfer characteristics of two hollow cylindrical droplets vertically impacting on a dry flat surface simultaneously. Numerical results show that, different from two continuous dense droplets, counter-jet at impact point (CJIP) is observed as a distinguished feature during the two hollow droplets’ impact process. However, counter-jet at symmetric point (CJSP) is formed in the vicinity of the symmetric point for both two hollow and dense cylindrical droplets. The analysis of pressure and velocity distribution is performed. It is shown that the formation of CJSP and CJIP is mainly caused by the pressure gradient. Upon further analysis of average heat flux, the formation of CJIP and the liquid shell rupture are the two main factors determining that the hollow droplet has a lower heat transfer capacity with the flat solid wall than that of the dense droplet. Through the investigation about the effect of impact velocity on fluid flow and heat transfer characteristics, the spread factor, the height of CJSP and CJIP, and the average heat flux will all increase with higher impact velocity. These results will provide a better understanding of hollow droplet impingement and heat transfer on flat surfaces.

### A particle-based ellipsoidal statistical Bhatnagar–Gross–Krook solver with variable weights for the simulation of large density gradients in micro- and nano-nozzles

This paper demonstrates the efficiency of a modified particle based Ellipsoidal Statistical Bhatnagar–Gross–Krook (ESBGK) solver to simulate micro-nozzles. For this, the common particle ESBGK algorithm is adapted to handle variable particle weights including the creation of additional particles in regions with low statistical samples and merging of particles in dense regions. After the description of the methods and their implementation, the simulation results of a micro-nozzle geometry using the Direct Simulation Monte Carlo, the common particle ESBGK, and the proposed modified ESBGK method are compared concerning accuracy and efficiency. All three methods show good agreement; however, the modified ESBGK method has the highest efficiency, saving a factor of around 500 of computational time to produce a comparable statistical sample size in the rarefied expansion region.

### Machine learning open-loop control of a mixing layer

We develop an open-loop control system using machine learning to destabilize and stabilize the mixing layer. The open-loop control law comprising harmonic functions is explored using the linear genetic programming in a purely data-driven and model-free manner. The best destabilization control law exhibits a square wave with two alternating duty cycles. The forced flow presents a 2.5 times increase in the fluctuation energy undergoing early multiple vortex-pairing. The best stabilization control law tames the mixing layer into pure Kelvin–Helmholtz vortices without following vortex-pairing. The 23% reduction of fluctuation energy is achieved under the dual high-frequency actuations.

### Persistence behavior of heat and momentum fluxes in convective surface layer turbulence

The characterization of heat and momentum fluxes in wall-bounded turbulence is of paramount importance for a plethora of applications ranging from engineering to Earth sciences. Nevertheless, how the turbulent structures associated with velocity and temperature fluctuations interact to produce the emergent flux signatures has not been evident until now. In this work, we investigate this fundamental issue by studying the switching patterns of intermittently occurring turbulent fluctuations from one state to another, a phenomenon called persistence. We discover that the persistence patterns for heat and momentum fluxes are widely different. Moreover, we uncover power-law scaling and length scales of turbulent motions that cause this behavior. Furthermore, by separating the phases and amplitudes of flux events, we explain the origin and differences between heat and momentum transfer efficiencies in convective turbulence. Our findings provide a new understanding of the connection between flow organization and flux generation mechanisms, two cornerstones of turbulence research.