# Latest papers in fluid mechanics

### Experimental and theoretical studies of the fluid elasticity on the motion of macroscopic models of active helical swimmers

This work presents experimental and theoretical studies on the locomotion of helical artificial swimmers at low Reynolds number in both Newtonian and viscoelastic ambient liquids. We examine the effect of fluid elasticity on the propulsive force and torque on the body and speed velocity of the swimmer in terms of two physical parameters: Deborah number (De) and Strouhal number (Sh). For this end, some experiments with prototype microorganisms in creeping flow motion are conducted. In the experiments, a macroscopic swimmer that propels itself by mimicking helical flagella are developed and tested. Three swimming models propelled by a helical tail with different wavelengths are investigated, and their motions examined for both cases: when the ambient solvent is a pure Newtonian viscous fluid and when the base fluid is an elastic polymeric solution. In addition, we also apply the slender body theory and the method of regularized Stokeslet in order to calculate theoretically the force and torque, as function of the Strouhal number (Sh), produced by the helical swimmer moving in a Newtonian fluid. The theoretical results are compared with experimental data, and a very good agreement is observed especially for higher values of Sh within the error bars of the experimental data. In the case of a non-Newtonian base fluid, the flow problem of an Oldroyd-B elastic fluid is solved numerically using a computational code based on a finite element method. The helical swimmer propulsive velocity is calculated in terms of the elastic parameter Deborah number and also compared with the experimental observation when the base fluid is non-Newtonian. It is shown experimentally that the swimming speed increases as the elastic effect in the base fluid increases until a critical Deborah number O(1), when the velocity saturates for a constant value within the experimental error bars. The velocity anisotropy measured experimentally by the ratio of the swimmer speed in two different directions is insensitive to the elastic effect in the base fluids. We complete our discussion on the helical swimmers motion in creeping flow by presenting a comparison between predictions of the speed velocity given by finite elements simulations using an Oldroyd-B model for the base elastic fluid and experimental data. The agreement between the two sets of results is very good within the experimental error bars for the elastic parameter varying from 0 to 2. It may be remarked, however, that while the experimental data tend to saturate at larger De, the simulations results seem to have a continuous increase according to the constitutive model used to describe the base elastic liquid.

### A comparative study on post-stall flow separation control mechanism of steady and unsteady plasma actuators

In order to improve the aerodynamic performance of the wing at post-stall conditions, the experimental comparative investigations on the flow separation control over an ONERA 212 airfoil using steady and unsteady plasma actuators are carried out at Reynolds number of 3.1 × 105. The duty cycle ratio is fixed at 80%, and the non-dimensional unsteady frequency F+ is varied from 0.04 to 1. The lift coefficients are increased by 39.6% and 66%, respectively, after steady and unsteady operations (F+ = 0.08) at an angle of attack of 18°, which indicates that the unsteady actuation is more efficient than steady operation. Meanwhile, the study provides new insight into understanding the post-stall separation flow controlling mechanism. First, different from the general view that the injection of momentum is the controlling mechanism of steady operation, flow control using the steady actuation experiences four stages, namely, flow separation, promoting the instability of the separated shear layer to produce large-scale spanwise vortices, flow re-attachment, and the continuous generation of small-scale vortices in the separated shear layer. Second, flow control with the unsteady operation consists of several quasi-periodic flow processes. Each quasi-cycle is composed of three stages, namely, flow separation, promoting the separation of shear layer instability to produce large-scale spanwise vortices, and flow re-attachment. The off-time of the plasma actuator plays an important role in realizing the control effect of the unsteady actuation, and an effective strategy to promote the control effect of the unsteady operation is proposed based on the propagation time of the induced spanwise vortex.

### Hydrodynamic manipulation cloak for redirecting fluid flow

Due to fluid viscosity, marine vehicles and structures immersed in fluids are inevitably affected by various fluid resistances. To obtain an effective method to eliminate drag and achieve hydrodynamic invisibility, we propose an innovative theory, called arbitrary space transformation (AST) theory, to design hydrodynamic cloaks. This AST theory provides a strategy that enables spatial transformation between different coordinate systems, compressing arbitrary geometric space into a shell-shaped space, thereby realizing the hydrodynamic concealment and excellent drag reduction effect of arbitrary shaped target objects. The flow manipulation cloak shows outstanding performance for eliminating drag and cloaking aquatic and submerged objects under different inflow conditions. In addition, it can reduce the risk of erosion and blockage that cloaked arbitrary shaped objects or organs may encounter by shifting the angles between the inflow and the frontal surface of structures. This investigation enables a powerful means of fluid design, which will make it possible for complex geometries to be undetectable by an external observer and remain hidden in an environment filled with fluid forces.

### Lattice Boltzmann method for simulation of solid–liquid conjugate boiling heat transfer surface with mixed wettability structures

Based on the one-component multiphase lattice Boltzmann method, a novel solid–liquid conjugate boiling heat transfer pseudo-potential lattice Boltzmann (LB) model is tentatively proposed in this paper. By respectively introducing the physical property parameters of solids and liquids into the relaxation time [math] of the temperature distribution equation, different energy transfer rates in solid, liquid, and vapor regions can be successfully predicted. After verifying the accuracy, stability, and reasonability of this model, the bubble detaching behavior and boiling heat transfer performance on the rectangular cavity structure are analyzed through setting different contact angles of the cavity surface and plane heating surface. The results show that the hydrophobic cavity surface can initialize bubble nucleation earlier and obviously increase the bubble detaching frequency because of its gas-bounding character, while the hydrophilic plane heating surface can restrict the expansion of bubbles and delay the appearance of film boiling. Moreover, for uniform wettability surfaces, the bubble detaching period varies in the quadratic equation with the surface contact angle due to the interaction of surface tension and buoyancy, and there is a minimum detaching period. While for the mixed wettability surfaces, the bubble detaching period also has a minimum value with the decrease in the contact angle the cavity surface, but the average bubble detaching diameter basically does not change with the cavity surface contact angle; moreover, the cavity surface contact angle corresponding to the minimum detaching period also increases with the increase in the plane heating surface contact angle. In addition, for the boiling heat transfer surface with cavity structure, the maximum heat flux and temperature gradient occur on the cavity surface, and the local heat flux of the hydrophobic cavity surface is higher than that of the hydrophilic cavity surface. This work will provide useful help for the further development of the conjugate boiling heat transfer LB model and clarify the mechanism of enhanced boiling heat transfer on a mixed wettability surface.

### Fluid structure interaction of a subaqueous pendulum: Analyzing the effect of wake correction via large eddy simulations

The dynamic behavior of a subaqueous cylindrical pendulum and corresponding flow dynamics are investigated. The objectives were twofold: (i) to examine whether the two-dimensional model equations sufficiently capture the three-dimensional dynamics and (ii) to investigate the emerging three-dimensional vortical flow structures. Large eddy simulations with two-way coupling fluid structure interaction were carried out using the immersed boundary method to simulate the motion of the pendulum and its interactions with the initially stagnant water. The resulting pendulum motion is compared against measured data obtained in a series of experimental tests to validate the simulation results and the model equations with and without wake corrections. An analysis of the flow vorticity revealed the development of a vortex ring during the first swing and the formation of tip vortices. The evolution of the vortex rings emerging from the motion of the subaqueous cylindrical pendulum was visualized using Q-criteria showing a reasonable agreement with vortical structures observed in the experiment using particle imaging velocimetry. The hydrodynamic moments acting on the simulated pendulum and the moments calculated from the model equations are analyzed. Using the insights from these numerical simulations, a modification of the wake correction is proposed to enhance the accuracy of the rate of decay and period. The transient effect of coherent flow on pendulum dynamics, especially the added mass effect, is discussed.

### Active flow control using deep reinforcement learning with time delays in Markov decision process and autoregressive policy

Classical active flow control (AFC) methods based on solving the Navier–Stokes equations are laborious and computationally intensive even with the use of reduced-order models. Data-driven methods offer a promising alternative for AFC, and they have been applied successfully to reduce the drag of two-dimensional bluff bodies, such as a circular cylinder, using deep reinforcement-learning (DRL) paradigms. However, due to the onset of weak turbulence in the wake, the standard DRL method tends to result in large fluctuations in the unsteady forces acting on the cylinder as the Reynolds number increases. In this study, a Markov decision process (MDP) with time delays is introduced to model and quantify the action delays in the environment in a DRL process due to the time difference between control actuation and flow response along with the use of a first-order autoregressive policy (ARP). This hybrid DRL method is applied to control the vortex-shedding process from a two-dimensional circular cylinder using four synthetic jet actuators at a freestream Reynolds number of 400. This method has yielded a stable and coherent control, which results in a steadier and more elongated vortex formation zone behind the cylinder, hence, a much weaker vortex-shedding process and less fluctuating lift and drag forces. Compared to the standard DRL method, this method utilizes the historical samples without additional sampling in training, and it is capable of reducing the magnitude of drag and lift fluctuations by approximately 90% while achieving a similar level of drag reduction in the deterministic control at the same actuation frequency. This study demonstrates the necessity of including a physics-informed delay and regressive nature in the MDP and the benefits of introducing ARPs to achieve a robust and temporal-coherent control of unsteady forces in active flow control.

### Publisher's Note: “Waves on the equatorial β-plane in the presence of a uniform zonal flow: Beyond the Doppler shift” [Phys. Fluids 34, 046603 (2022)]

### On the generation and destruction mechanisms of arch vortices in urban fluid flows

This study uses higher-order dynamic mode decomposition to analyze a high-fidelity database of the turbulent flow in an urban environment consisting of two buildings separated by a certain distance. We recognize the characteristics of the well-known arch vortex forming on the leeward side of the first building and document this vortex's generation and destruction mechanisms based on the resulting temporal modes. We show that the arch vortex plays a prominent role in the dispersion of pollutants in urban environments, where its generation leads to an increase in their concentration; therefore, the reported mechanisms are of extreme importance for urban sustainability.

### Effect of free-stream turbulence properties on different transition routes for a zero-pressure gradient boundary layer

The natural and bypass routes to boundary-layer transition to turbulence are traditionally investigated independently in fluid mechanics applications. Nevertheless, in certain flow regimes both mechanisms could coexist and interact. In this work, large-eddy simulations (LES) were performed for a zero-pressure gradient boundary layer developing over a flat plate to investigate the transition mechanism for variable free-stream turbulent properties. Four different combinations of turbulence intensity and integral length scale were analyzed, and two main transition mechanisms were observed. High free-stream turbulence intensity instigates pure bypass transition through the amplification of a continuous Orr–Sommerfeld (O–S) mode that breaks down after secondary instability. Instead, at low free-stream turbulence intensity, discrete and continuous O–S modes interact and are both involved in the transition process. Visual inspection of the LES snapshots provides a detailed insight in Tollmien–Schlichting (TS) waves–streaks mutual interaction and clearly identifies two main mechanisms involved in turbulence breakdown. On one hand, TS waves trigger varicose instability of streaky structures. On the other hand, streaks cause secondary instability of TS waves with emerging Λ-structure formation. Then, dynamic mode decomposition (DMD) is applied to extract the main stability properties for both types of transition route and to highlight coherent structure dynamics, which is hardly observable in the literature. Specifically, for low-medium free-stream turbulence levels, DMD extracts unstable modes clearly related to streaks–TS waves interaction and leading to the formation of Λ structures. Therefore, the streaks–TS waves interaction is proved to be destabilizing and to trigger secondary instability leading to turbulence breakdown.

### Splashing behavior of impacting droplets on grooved superhydrophobic surfaces

During water droplet impingement onto a rice-leaf-inspired grooved superhydrophobic surface, the unidirectional textures can reduce the solid–liquid contact time through modifying the droplet impact dynamics. The influence of the groove geometry on the splashing of impacting droplets is still unrevealed. In this study, we experimentally identify the droplet bouncing and splashing regimes on grooved superhydrophobic surfaces of varying parameters. Asymmetric spreading and retracting of droplets are observed on the surfaces, accompanied by obvious liquid jets generated within the grooves. As the impact velocity increases, secondary droplets are ejected from the rim of the liquid jets, which is the onset of droplet splashing on the grooved superhydrophobic surfaces. We find that the critical Weber number for the splash of liquid jets decreases with the groove width but increases with the droplet diameter. Scaling analysis is performed to model the splashing criteria and explain its dependence on groove parameters and droplet properties. This research advances the understanding of droplet splashing dynamics on textured superhydrophobic surfaces, which is promising for some agricultural and industrial applications.

### Multiple instabilities of thermocapillary flow in a cylindrical pool with a rotating disk on the free surface

Author(s): Jinchao He, Hao Liu, Qiulin Li, Na Zhang, Mi Nie, and Weina Mao

The thermocapillary flow instabilities of silicon melt in a cylindrical pool with a rotating disk on the free surface (a simplified model of the Czochralski crystal growth) are numerically investigated by using the linear stability analysis. The complete neutral or critical stability curves are dete…

[Phys. Rev. E 105, 055101] Published Tue May 03, 2022

### Prediction and manipulation of hydrodynamic rogue waves via nonlinear spectral engineering

Author(s): Alexey Tikan, Felicien Bonnefoy, Giacomo Roberti, Gennady El, Alexander Tovbis, Guillaume Ducrozet, Annette Cazaubiel, Gaurav Prabhudesai, Guillaume Michel, Francois Copie, Eric Falcon, Stephane Randoux, and Pierre Suret

In this work, we realize the mathematically predicted universal mechanism of the local emergence of Peregrine solitons in water tank experiments, with a particular aim to control the point of the soliton occurrence in space-time by employing the inverse scattering transform for the synthesis of the initial data. Using this approach, we are able to engineer a localized wave packet with a prescribed solitonic and radiative content, evolving in a rogue wave at a predicted position from the wave maker.

[Phys. Rev. Fluids 7, 054401] Published Tue May 03, 2022

### Horizontal dam-break flow past a blocking-drag region

A one-dimensional model framework of unsteady free-surface flow through a blocking-drag region is developed, tested, and applied to understand the dam-break flow past a rectangular building. This is achieved by studying the steady-state, adjustment to steady-state, and the unsteady response of a blocking-drag region. Three steady flow regimes are identified based on the Froude number upstream and downstream of a blocking-drag region: a subcritical state, a choked state with a subcritical-supercritical transition, and a supercritical state. The interaction between a dam-break flow and a blocking-drag region can be mostly understood from the quasi-steady analysis using the variation of the Froude number with time, and comparing the upstream and downstream Froude number scatter plots against the steady curve. The force time-series depends on the height of the precursor layer and the position of the blocking-drag region relative to the lock-length. This model provides considerable insight into the types of flow characteristics observed at low/high Froude numbers and goes some way to clarifying the relationship between the drag force and the dam-break flow properties.

### Multi-fidelity modeling to predict the rheological properties of a suspension of fibers using neural networks and Gaussian processes

Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications. There are multiple factors, such as fiber aspect ratio and volume fraction, that play a significant role in altering the rheological behavior of suspensions. Three-dimensional (3D) numerical simulations of coupled differential equations of the suspension of fibers are computationally expensive and time-consuming. Machine learning algorithms can be trained on the available data and make predictions for the cases where no numerical data are available. However, some widely used machine learning surrogates, such as neural networks, require a relatively large training dataset to produce accurate predictions. Multi-fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified constitutive equations, can pave the way for more accurate predictions. Here, we focus on neural networks and the Gaussian processes with two levels of fidelity, i.e., high and low fidelity networks, to predict the steady-state rheological properties, and compare them to the single-fidelity network. High-fidelity data are obtained from direct numerical simulations based on an immersed boundary method to couple the fluid and solid motion. The low-fidelity data are produced by using constitutive equations. Multiple neural networks and the Gaussian process structures are used for the hyperparameter tuning purpose. Results indicate that with the best choice of hyperparameters, both the multi-fidelity Gaussian processes and neural networks are capable of making predictions with a high level of accuracy with neural networks demonstrating marginally better performance.

### Revisiting a class of modified pseudopotential lattice Boltzmann models for single-component multiphase flows

Since its emergence, the pseudopotential lattice Boltzmann (LB) method has been regarded as a straightforward and practical approach for simulating single-component multiphase flows. However, its original form always results in a thermodynamic inconsistency, which, thus, impedes its further application. Several strategies for modifying the force term have been proposed to eliminate this limitation. In this study, four typical and widely used improved schemes—Li's single-relaxation-time (SRT) scheme [Li et al., “Forcing scheme in pseudopotential lattice Boltzmann model for multiphase flows,” Phys. Rev. E 86, 016709 (2012)] and multiple-relaxation-times (MRT) scheme [Li et al., “Lattice Boltzmann modeling of multiphase flows at large density ratio with an improved pseudopotential model,” Phys. Rev. E 87, 053301 (2013)], Kupershtokh's SRT scheme [Kupershtokh et al., “On equations of state in a lattice Boltzmann method,” Comput. Math. Appl. 58, 965 (2009)], and Huang's MRT scheme [Huang and Wu, “Third-order analysis of pseudopotential lattice Boltzmann model for multiphase flow,” J. Comput. Phys. 327, 121 (2016)]—are systematically analyzed and intuitively compared after an extension of the MRT framework. The theoretical and numerical results both indicate that the former three schemes are specific forms of the last one, which thus help further understand the improvements of these pseudopotential LB models for achieving thermodynamic consistency. In addition, we modified the calculation of the additional source term in the LB evolution equation. Numerical results for stationary and moving droplets confirm the higher accuracy.

### Perimeter leakage of face masks and its effect on the mask's efficacy

Recent studies have shown that the effectiveness of the face masks depends not only on the mask material but also on their fit on faces. The mask porosity and fit dictate the amount of filtered flow and perimeter leakage. Lower porosity is usually associated with better filtration; however, lower porosity results in higher perimeter leakage. The resulting leakage jets generated from different types of faces and different mask porosities are of particular interest. Direct numerical simulations of the flow dynamics of respiratory events while wearing a face mask can be used to quantify the distribution of the perimeter leaks. Here, we present a novel model for porous membranes (i.e., masks) and use it to study the leakage pattern of a fabric face mask on a realistic face obtained from a population study. The reduction in perimeter leakage with higher porosities indicates that there would be an optimal porosity such that the total leakage and maximum leakage velocities are reduced. The current model can be used to inform the quantification of face mask effectiveness and guide future mask designs that reduce or redirect the leakage jets to limit the dispersion of respiratory aerosols.

### Molecular insight of the interface evolution of silicon carbide under hyperthermal atomic oxygen impact

One of the key challenges faced by hypersonic flying is the complex thermal–mechanical–chemical coupling effect between thermal protection materials and non-equilibrium flow environment. Silicon carbide (SiC) has drawn much attention due to its superior physical and chemical characteristics, and its performance under hyperthermal atomic oxygen (AO) impact, however, is still little known. This work investigates the effects of various SiC crystalline polytypes, surface temperature, and crystal orientations on the SiC interface evolution by hyperthermal AO collisions via the reactive molecular dynamics method. The results showed that SiC surface erosion is highly dependent on the temperature and the presence of different interfacial structures. In the range of 500–2000 K, the proceeding of the passive oxidation advances the amorphous SiO2/SiC interface and the formation of SixOy phase weakens the surface catalytic characteristics and mechanical properties. The presence of defects, such as dangling bonds at the gas–solid interface, caused by different surface orientations affects the anti-erosion capabilities of SiC significantly, which may limit its further wide applications.

### Turbulent flow characteristics in an 84-pin rod bundle for typical and damaged spacer grids

Hexagonal rod bundles arranged in a tightly packed triangular lattice are extensively used for heat transfer and energy generation applications. Staggered spacer grids are used to maintain the structural integrity of gas-cooled fast reactor (GFR) fuel assemblies, while inducing localized turbulence in flow. Damage to these spacer grids results in a disruption of flow fields within these hexagonal fuel bundles. Experimental flow visualizations are critical to identify the differences in local flow properties that the structural damage may cause. This experimental research investigates the flow-field characteristics at a near-wall and center plane in a prototypical 84-pin GFR fuel assembly. Newly installed typical spacers and spacers subject to naturally occurring damage due to material degradation over prolonged experimentation were investigated. Velocity fields were acquired by utilizing the matched-index-of-refraction method to obtain time-resolved particle image velocimetry measurements for a Reynolds number of 12 000. Reynolds decomposition statistical results divulged differences in the time-averaged velocity, velocity fluctuations, flow anisotropy, and Reynolds stress distributions. Galilean decomposition demarcated the influence of spacer grid damage on the velocity fields. To extract turbulent structures and elucidate mechanisms of flow instabilities, proper orthogonal decomposition analysis was employed. Reduced order flow reconstructions enabled the application of vortex identification algorithms to determine the spatial and statistical characteristics of vortices generated. This research work provides unique experimental data on the spacer grid condition-dependent flow. The results offer a deeper understanding of fluid dynamics behavior to support GFR rod bundle design efforts and computational fluid dynamics model validation.

### On the maximal spreading of drops impacting onto a no-slip substrate

We numerically study the impact of a liquid drop onto no-slip rigid substrates with different wettabilities using a diffuse interface method, aiming to obtain a universal model for the maximal spreading of the impacting drop at moderate Weber numbers. We find that the wettability plays an important role in the maximal spreading and that the ratio of the surface energy to the initial kinetic energy of the drop at the maximal spreading, η, follows [math] at high fixed Reynolds numbers, where We is the Weber number. Taking account of the wettability effect, we obtain a scaling law at high Reynolds numbers from an analysis of energy transformation. This scaling law is compatible with the one derived from the momentum balance at the high impact velocity by Clanet et al. [“Maximal deformation of an impacting drop,” J. Fluid Mech. 517, 199–208 (2004)]. Moreover, we attribute it to the presence of a viscous–capillary regime, in which the viscous dissipation of the kinetic energy from the substrate is as significant as the kinetic energy transformed into the surface energy. Accordingly, we identify a new impact parameter, which makes all the numerical results of maximum drop deformation (from the viscous regime to the viscous–capillary regime with Reynolds number up to 104) collapse onto a single curve. Finally, we propose a universal model, the predictions of which are shown to agree well with numerical results for a wide range of Weber and Reynolds numbers.

### Experimental and numerical investigation of compressibility effects on velocity derivative flatness in turbulence

Compressibility effects on the velocity derivative flatness [math] are investigated by experiments with opposing arrays of piston-driven synthetic jet actuators (PSJAs) and direct numerical simulations (DNS) of statistically steady compressible isotropic turbulence and temporally evolving turbulent planar jets with subsonic or supersonic jet velocities. Experiments using particle image velocimetry show that nearly homogeneous isotropic turbulence is generated at the center of a closed box from interactions between supersonic synthetic jets. The dependencies of [math] on the turbulent Reynolds number [math] and the turbulent Mach number MT are examined both experimentally and using DNS. Previous studies of incompressible turbulence indicate a universal relationship between [math] and [math]. However, both experiments and DNS confirm that [math] increases relative to the incompressible turbulence via compressibility effects. Although [math] tends to be larger with MT in each flow, the [math] in the turbulent jets and the turbulence generated from PSJAs deviate from those in incompressible turbulence at lower MT compared with isotropic turbulence sustained by a solenoidal forcing. The PSJAs and supersonic planar jets generate strong pressure waves, and the wave propagation can cause an increased [math], even at low MT. These results suggest that the compressibility effects on [math] are not solely determined from a local value of MT and depend on the turbulence generation process.