# Latest papers in fluid mechanics

### Lift coefficient of bubble sliding inside turbulent boundary layers in an inclinable channel flow

The behavior of bubbles traveling in the proximity of a tilted wall is studied experimentally to understand the fundamental sliding motion of bubbles inside turbulent boundary layers along an inclined wall. The qualitative visualization of sliding bubbles confirms the contribution of bubble buoyancy on the sliding motion for negative and positive inclinations of the channel. An opto-acoustic combined measurement technique is adopted to explore the sliding motion. Liquid velocity profiles in the bubbly flow and the distance between the wall and bottom of the bubble are obtained using the ultrasound pulsed Doppler method, while the bubble diameters and velocities are obtained from particle-tracking type image processing. The combined measurements reveal that the velocity of bubbles decreases under the negative slope condition and increases under the positive slope condition due to opposite buoyancy effects. In addition, the distance between the wall and bottom of the bubble increases with an increase in negative inclination. The lift coefficient is derived from the measured variables using a force–balance equation among the buoyancy, lift, and surface tension. Finally, we propose modeling equations for the lift coefficient expressed in terms of the Reynolds, Weber, and Bond numbers, which apply to the bubbles inside boundary layers.

### On the nonlinear thermal stress, thermal creep, and thermal edge flows in triangular cavities

Here, rarefied thermally driven flow is investigated in two-dimensional equilateral triangular cavities with different uniform wall temperatures. We used three different solvers, i.e., the direct simulation Monte Carlo solver, discrete unified gas kinetic scheme solver, and continuum set of equations of a slow non-isothermal flow solver. Two main cases were considered; in the first case, the cavity's base is considered hot, and the other sides were set cold. In the second case, the right half of the bottom wall was regarded as a diffuse reflector with high temperature, while the left half of the bottom border was set as a specular reflector. The adjacent side walls were set cold with diffuse reflector boundary conditions. The imposed temperature difference/wall boundary condition induces various vortices in the geometry. In case 1, we observe that principal vortices appearing in the triangle are due to nonlinear thermal stress effects, and the thermal creep effects cause other smaller, confined ones. In case 2, a thermal edge flow is set up from the specular wall on the way to the diffusive hot wall, creating a large vortex in the geometry. As the Knudsen number decreases, another small vortex appears near the left cold border.

### Swimming of an inertial squirmer array in a Newtonian fluid

An immersed boundary-lattice Boltzmann method is employed to simulate a squirmer (a classical self-propelled model) array swimming in a Newtonian fluid. The swimming Reynolds number Res is set in the range 0.05 ≤ Res ≤ 5 to study three typical arrays (i.e., the two-squirmer, triangular-squirmer, and quadrilateral-squirmer arrays) in their swimming speed, their power expenditure (P), and their hydrodynamic efficiency (η). Our results show that the two-pusher array with a smaller ds (the distance between the squirmers) yields a slower speed in contrast to the two-puller array, where a smaller ds yields a faster speed at Res ≥ 1 (“pusher” is propelled from the rear and “puller” from the front). The regular triangular-pusher (triangular-puller) array with θ = −60° (the included angle between the squirmers) swims faster (slower) than that with θ = 60°; the quadrilateral-pusher (quadrilateral-puller) array with model 2 swims faster (slower) than model 1 (the models are to be defined later). It is also found that a two-puller array with a larger ds is more likely to become unstable than that with a smaller ds. The triangular-puller array with θ = 60° is more likely to become unstable than that with θ = 60°; the quadrilateral-puller array with model 1 becomes unstable easier than that with model 2. In addition, a larger ds generally results in a less energy expenditure. A faster squirmer array yields a higher η, except for two extraordinarily puller arrays. A quantitative relation for η with ReU > 1 is obtained approximately, in that the increasing ratio of η is proportional to an exponent of the motion Reynolds number ReU.

### An experimental study of the water entry trajectories of truncated cone projectiles: The influence of nose parameters

We report on an experimental study of the trajectories of truncated cone projectiles on water entry. The water entry trajectory stability is of great significance to the motion control of projectile. In this paper, the truncated cone nose shape can be described by the area of the leading plane and the cone angle α. Two high-speed cameras are used to capture the trajectories of the projectiles and the initial stage of cavity dynamics. We reveal that the trajectory stability of a projectile is highly dependent on the wetted surface of the nose, which is determined by the location of the separation line between the surfaces of the cavity and body. The increase in the leading plane area is beneficial to the formation of a stable trajectory, in which only the leading plane is wetted. In an unstable trajectory case, the large hydrodynamic moment from the wetted surface on the side of the nose causes a significant rotation of the projectile. However, for the projectile with the cone angle [math], though the side of the nose is fully wetted, the trajectory of the projectile turns into stable again. Results show that the attitude deflection of the projectile is determined by the cone angle of the nose. It is also found that the attitude deflection results in an irregular cavity, which further aggravates the rotation of the projectile. We quantify the relationship between the trajectory stability and two nose parameters systematically, and a phase diagram is obtained for a large parameter space. The findings in this work can be used as a reference for future designs to ensure stable trajectories on water entry.

### A numerical approach on the selection of the purge flow rate in an atomic layer deposition (ALD) process

The variation of the purge flow rate is investigated in a reactor scale simulation of a typical atomic layer deposition (ALD) process. The investigation in its context addresses the possible issues of inadequate deposition rates with regard to the purge flow rate. A three-dimensional reactor is numerically implemented to simulate the physical and chemical processes to fabricate aluminum oxide (Al2O3) thin films. The purge flow rate disparity is focused to examine the effects within the fluid flow, mass transport, along with the chemical kinetics of the ALD process. The fabrication process employs trimethyl-aluminum and ozone (O3) as the metal and oxidant precursors, respectively, and inert argon as the purge gas. The reactor operation is set up to operate at a pressure of 10 torrs, with a substrate temperature of 200 °C. Three purge flow rates of 20, 10, and 5 sccm, respectively, have been examined. It was discovered that the slower flow rate showed, superior mass fraction distribution, reached unity surface coverage, and a time extensive surface deposition rate. A prolonged ozone exposure was crucial in providing an adequately oxidized substrate. The 20, 10, and 5 sccm purge flow rate growth obtained a 0.58, 0.85, and 1.6 Å/cycle, respectively. These findings revealing close similarities to experimental behaviors and recorded growths.

### Wake modes of a freely vibrating square cylinder

The cross-stream flow-induced vibrations of a square cylinder of mass ratio, [math], are studied numerically at a fixed Reynolds number, Re, of 250. The reduced speed, [math], is varied from 1 to 10 independent of Re. The flow-induced vibrations of a square cylinder have been previously investigated either by decoupling [math] from Re or by coupling [math] with Re. While most of the studies available in the literature follow the former approach, those dealing with [math] do not provide a detailed account of the branches of dynamic response, hysteresis, and wake patterns. The current effort aims at contributing to these research gaps. The vibrations are purely vortex-induced, and the dynamic response within synchronization is found to be composed of an initial branch, its extension or extended initial branch, and lower branch. For a square-section oscillator, the extended initial branch is resolved for the first time. The most noteworthy outcome of this work is perhaps the resolution of asymmetric as well as one-sided wake modes at certain reduced speeds. The one-sided shedding occurs either from the top or bottom surface of the oscillator. At [math], the non-zero mean lift changes sign in successive oscillation cycles, indicating that the solutions are bistable. The resolved asymmetric and one-sided modes are associated with positive and negatives values of mean lift, respectively. A very interesting result of this study is the mismatch of wake modes obtained at non-hysteretic [math] using forward and backward computations.

### Publisher's Note: “Contribution of flow topology to the kinetic energy flux in hypersonic turbulent boundary layer” [Phys. Fluids 34, 046103 (2022)]

### Linear and weakly nonlinear dominant dynamics in a boundary layer flow

The aim of this paper is to investigate the linear and weakly nonlinear dynamics in flow over a flat-plate with leading edge. Linear optimal and suboptimal inflow perturbations are obtained using a Lagrangian multiplier technique. In particular, the suboptimal inflow conditions and the corresponding downstream responses are investigated in detail for the first time. Unlike the suboptimal dynamics reported in other canonical cases such as the backward-facing step flow, the growth rate of the suboptimal perturbation is in the same order as the optimal one, and both of them depend on the lift-up mechanism even though they are orthogonal. The suboptimal mode has an additional layer of vorticity that penetrates into the boundary layer farther downstream, generating a second patch of high- and low-speed streaks. The farther suboptimal ones spread to the free-stream without entering the boundary layer. The weakly nonlinear dynamics are examined by decomposing the flow field into multiple orders of perturbations using the Volterra series. Small structures in the higher order perturbations mainly concentrate in the region farther away from wall, suggesting a mechanism of outward perturbation developments, which is opposite with the well reported inward development of perturbations, i.e., from free-stream to boundary layer. The significance of these modes is then demonstrated through a prediction of flow field from the inflow condition by exploiting the orthogonality of the modes.

### Particle–liquid transport in curved microchannels: Effect of particle volume fraction and size in Dean flow

Microfluidic transport in spiral channels is a promising flow-driven mechanism for applications such as cell sorting and particle focusing. Spiral channels have unique curvature-driven flow characteristics that trigger Dean flow, forcing the liquid to be displaced toward the outer wall of the microchannel due to centrifugal force. Despite the growing popularity of these applications, there is a lack of physical understanding of such particle–fluid two-phase transport in a spiral microchannel. To address this gap, in this paper we employ a coupled particle-transport-microfluidic-flow (two-phase) computational fluid dynamics model for probing such two-phase transport in a curved microchannel that gives rise to Dean flow. Our simulations reveal that the presence of the particles has two effects: (1) they reduce the Dean flow effect of skewing the flow field toward the outer wall, that is, the flow becomes more symmetric (or the velocity maximum moves toward the center of the channel) and (2) there is a significant alteration in the vortex patterns associated with the Dean flow. We quantify the drag and lift forces experienced by the particles and propose that the corresponding particle-imparted drag and the lift forces on the continuous phase counter the effect of the curvature-driven centrifugal force on the continuous phase, thereby altering the Dean flow characteristics. Furthermore, we anticipate that such precise quantification of the forces experienced by these particles, present in finitely large concentration in microfluidic Dean flow, will be critical in designing Dean flow effect driven size-based microfluidic particle separation.

### Contact line dynamics of pulsatile fluid interfaces modulated by patterned substrates

We study the dynamics of microfluidic fronts driven by pulsatile pressures in the presence of patches of hydrophilic wetting on the walls of the confining media. To do so, we use a recently developed phase-field model that takes inertia into account. We track the interface position in channels with different spacing between the patches and observe that the smaller the spacing, the faster the advancement of the front. We find that the wetting patterning induces a modulating dynamics of the contact line that causes an effective wetting, which in turn determines the modulation of the interface velocity. We characterize the modulation frequency in terms of wetting pattern, inertia, and surface tension, via the capillary pressure, viscosity, and confinement.

### Effect of vorticity transport on flow structure in the tip region of axial compressors

Numerical simulations are carried out to investigate the flow structure in the blade tip region of axial compressors. Various tip clearance heights and end wall motion conditions in a linear compressor cascade are studied to assess the effect of vorticity transport on the tip leakage flow (TLF). Moreover, the effect of vorticity transport on the TLF in a compressor rotor at different operating conditions is studied using delayed detached eddy simulation. The results show that the vorticity transport at both the blade tip and the end wall plays an important role in the roll-up and evolution of the tip leakage vortex (TLV), resulting in great impacts on the loss and stability of the TLV. It is found that the TLV is composed of a two-layer structure. The inner vortex core region formed by the vorticity transport from the blade tip shear layer to the TLV has a great effect on the strength and loss of the vortex, and the structure of the outer shear layer is altered by the secondary vortex formed by the vorticity transport from the end wall shear layer and thus affects the stability of the TLV. By the mechanism of the vorticity transport, the effects of the clearance height, the end wall motion, and the non-uniform clearance as a control method can be explained uniformly. The new understanding of the TLF structure and the vorticity transport mechanism helps to improve the performance of axial compressors by controlling the vorticity transport of the TLF.

### Influence of the wettability on the liquid breakup in planar prefilming airblast atomization using a coupled lattice Boltzmann–large eddy simulation model

In this paper, an efficient coupled lattice Boltzmann–large eddy simulation model [X. An et al., “Coupled lattice Boltzmann-large eddy simulation model for three-dimensional multiphase flows at large density ratio and high Reynolds number,” Phys. Rev. E 104, 045305 (2021)] based on the Allen–Cahn phase-field theory is introduced for simulating the liquid breakup in planar prefilming airblast atomization. This is the first time that the lattice Boltzmann method is used in the three-dimensional numerical investigation of prefilming airblast atomization to the best of our knowledge. The present model utilizes two evolution equations: one is used to capture the fluid interface, and another is adopted to solve hydrodynamic properties. An advanced multiple-relaxation-time scheme is also applied for the collision operator to enhance the numerical stability. To investigate the influence of the wettability on the liquid breakup accurately, a simple and efficient wetting boundary scheme is delicately designed and strictly validated. Additionally, to evaluate the atomization quality intuitively, an atomization efficiency coefficient is proposed for characterizing the liquid breakup process. The numerical results reveal that the influence of the wettability lies in the liquid accumulation phenomenon at the edge of the prefilmer and the droplet movement in the vertical direction. The atomization quality adopting a non-wetting prefilmer is better than other cases, according to the atomization efficiency coefficients, the mean droplet equivalent diameters with their size distribution proportions, and the atomization angles in the vertical direction. In addition, it is also found that the droplet proportion above the prefilmer increases as the contact angle increases, and the proportions on both sides of the prefilmer account for 50% at the contact angle of 90°.

### A simple hydrodynamic-particle method for supersonic rarefied flows

In the practical aerospace industry, the supersonic rarefied effect presents multiscale characteristics from the near-continuum regime to the free molecular regime. In this paper, a simple hydrodynamic-particle method (SHPM) is proposed to efficiently capture the multiscale properties for the supersonic rarefied flow. To combine the conventional computational fluid dynamics solver with the particle-based method, the weights are theoretically derived from the integral solution of the Boltzmann Bhatnagar–Gross–Krook equation. The present numerical method is validated by test cases of supersonic shock wave structure, Sod shock-tube, and supersonic flow around the circular cylinder. Numerical results demonstrate that the SHPM could capture the multiscale properties from the continuum regime to the rarefied regime.

### Development of a smart active respirator for comfortable and hygienic breathing

The current COVID-19 pandemic has increased the use of facial masks globally, which of late have registered their presence as a part of our civilization. The N95 mask is one of the most popular choices under the current situation. However, the available masks cannot provide breathing comfort for an extended period, which results in rebreathing of exhaled air that is CO2 rich, and which remains in the breathing space of the respirator. Furthermore, problems like moisture settlement on the covered area of the face due to the multiple layers of fabric-like material causes significant discomfort. Hence, the need for a mask with an air-purification activity is the need of the hour. The present innovation relates to the invention of a mask that is battery-powered or solar-operated and addresses the aforementioned problems. This mask not only regulates the airflow, which is beneficial to our body in every way, but also lowers the discomfort of sweating and heating. The effect of the addition of the self-developed active respirator to the commercially available masks on the inspired CO2 level, thermal comfort, and speech clarity has been demonstrated in this study. We have exhibited through in vitro experiments that the filtration capability of the active-respirator improvised mask, we call the Bose shield, does not deter from that of the standard N95 mask. To our understanding, the use of this novel mask can reduce the occurrence of CO2 rebreathing in respiratory protective devices and its impact on workers who inevitably wear them for a prolonged period of time.

### Intelligent ship anti-rolling control system based on a deep deterministic policy gradient algorithm and the Magnus effect

Anti-rolling devices are widely used in modern shipboard components. In particular, ship anti-rolling control systems are developed to achieve a wide range of ship speeds and efficient anti-rolling capabilities. However, factors that are challenging to solve accurately, such as strong nonlinearities, a complex working environment, and hydrodynamic system parameters, limit the investigation of the rolling motion of ships at sea. Moreover, current anti-rolling control systems still face several challenges, such as poor nonlinear adaptability and manual parameter adjustment. In this regard, this study developed a dynamic model for a ship anti-rolling system. In addition, based on deep reinforcement learning (DRL), an efficient anti-rolling controller was developed using a deep deterministic policy gradient (DDPG) algorithm. Finally, the developed system was applied to a ship anti-rolling device based on the Magnus effect. The advantages of reinforcement learning adaptive control enable controlling an anti-rolling system under various wave angles, ship speeds, and wavelengths. The results revealed that the anti-rolling efficiency of the intelligent ship anti-rolling control method using the DDPG algorithm surpassed 95% and had fast convergence. This study lays the foundation for developing a DRL anti-rolling controller for full-scale ships.

### Hydrodynamics of slender swimmers near deformable interfaces

Author(s): Sankalp Nambiar and J. S. Wettlaufer

We study the coupled hydrodynamics between a force- and torque-free slender microswimmer and an interface with a deformation that is influenced by both surface tension and bending elasticity. For an interface separating two fluids with arbitrary viscosities, the role of the swimmer orientation, the fluid and interface properties on the swimmer migration is examined. The nature of the short-time swimmer migration depends crucially on its orientation and the fluid viscosity ratio. When a swimmer is in the more viscous fluid and parallel or perpendicular to the interface, the short-time swimmer migration is opposite to that of the long-time migration.

[Phys. Rev. Fluids 7, 054001] Published Mon May 02, 2022

### Unified scale laws for transient convective boundary layers: From flat to curved boundary layers

Author(s): Yang Liu and Changhui Liu

Transient natural convection boundary layer flow is studied at Pr>1 and the curvature effect is specifically and fundamentally explored. Important scale laws, i.e. boundary layer thickness δt and characteristic velocity uz of the transient and steady states and the cut-off time ts of the initial growth, are proposed and validated. We find that for cylinder radius much larger than the boundary layer thickness, the present scaling relations reduce to those of the classic flat boundary layer. The most curved boundary layer we examine is 26 times thicker than the cylinder radius. We show that the present scaling set is accurate for all flow conditions bounded by the two limiting scenarios.

[Phys. Rev. Fluids 7, 054101] Published Mon May 02, 2022

### Cavitation strength of oxygen–nitrogen solutions under pulse stretching

The tensile strength of oxygen–nitrogen solutions has been investigated in tension waves of length 3 μs with amplitudes to –10 MPa. The temperature dependences of the limiting stretches of solutions with nitrogen contents of 0.25, 0.50, and 0.75 mole fractions have been determined at temperatures from 90 to 130 K. Experimental data have been compared with calculations by the classical nucleation theory.

### Closure modeling in near-wall region of steep resolution variation for partially averaged Navier-Stokes simulations

Author(s): Chetna Kamble, Sharath Girimaji, Pooyan Razi, Pedram Tazraei, and Stefan Wallin

Accurate representation of the near-wall flow physics at high Reynolds numbers is computationally prohibitive for many uniform resolution turbulence models. Therefore, a closure with spatially varying resolution is sought which seamlessly transitions from low resolution RANS near-wall to high-resolution PANS in the outer region. This new modeling strategy systematically accounts for the energy exchange terms between the resolved and unresolved scales in the region of resolution change. By ensuring energy conservation and equilibrium boundary layer (EBL) scaling, the model accurately captures the flow behavior near-wall for turbulent channel flow at high Reynolds numbers.

[Phys. Rev. Fluids 7, 044608] Published Fri Apr 29, 2022

### Central mean temperature scaling in compressible turbulent channel flows with symmetric isothermal boundaries

Author(s): Yubin Song, Peng Zhang, Yilang Liu, and Zhenhua Xia

Originating from the generalized Reynolds analogy theory, an empirical scaling for the central mean temperature in compressible turbulent channel flow with symmetric isothermal boundaries is proposed. The empirical scaling is quite accurate and most of the relative errors are below 1.5% as assessed by available direct numerical simulation data at various Reynolds and Mach numbers. The mean temperature profile can be quantitatively obtained through the mean velocity with empirical scaling.

[Phys. Rev. Fluids 7, 044606] Published Thu Apr 28, 2022