# Latest papers in fluid mechanics

### Thermodynamics and hydrodynamics of spontaneous and forced imbibition in conical capillaries: A theoretical study of conical liquid diode

Thermodynamics and hydrodynamics of spontaneous and forced imbibition of liquid into conical capillaries are studied to assess the feasibility of a conical liquid diode. The analytical formulas for the Laplace pressure and the critical Young's contact angle of the capillary for the onset of spontaneous imbibition are derived using the classical capillary model of thermodynamics. The critical contact angle below which the spontaneous imbibition can occur belongs to the hydrophilic region for the capillary with a diverging radius while it belongs to the hydrophobic region for the capillary with a converging radius. Thus, by choosing Young's contact angle between these two critical contact angles, only the spontaneous imbibition toward the converging radius occurs. Therefore, the capillary with a converging radius acts as the forward direction and that with a diverging radius as the reverse direction of diode. Even under the external applied pressure, the free-energy landscape implies that the forced imbibition occurs only to the forward direction by tuning the applied pressure. Furthermore, the scaling rule of the time scale of imbibition is derived by assuming Hagen–Poiseuille steady flow. Again, the time scale of the forward direction is advantageous compared to the reverse direction when the imbibition to both directions is possible. Therefore, our theoretical analysis shows that a conical capillary acts as a liquid diode.

### A geometrical criterion for the dynamic snap-off event of a non-wetting droplet in a rectangular pore–throat microchannel

In porous media, non-wetting phase droplets snapping off in a constricted microchannel are one of the most common phenomena in two-phase flow processes. In this paper, the application range of the classic quasi-static criterion in rectangular cross section microchannels is obtained. For three different droplet breakup phenomena—total breakup, partial breakup, and non-breakup—observed in experiments when a non-wetting phase droplet passes through a microchannel constriction, the breakup is caused by the droplet neck snapping off in a channel constriction. A critical criterion for the dynamic snap-off event in a two-phase flow is proposed considering the effect of viscous dissipation by mechanical analysis, energy dissipation analysis, and many microfluidic experiments. When the droplet front flows out of the constriction, snap-off will occur if the surface energy release exceeds the required energy for viscous dissipation and kinetic energy conversion. The unique partial breakup phenomenon is affected by droplet surfactant distribution and the acceleration effect in the constriction center. This partial breakup phenomenon in experiments is an essential evidence for the non-uniform distribution of surfactants in the droplet surface. The results of this study contribute to understanding pore-scale mass transfer and flow pattern changes within porous media.

### Confinement effect on the viscoelastic particle ordering in microfluidic flows: Numerical simulations and experiments

Strings of equally spaced particles, also called particle trains, have been employed in several applications, including flow cytometry and particle or cell encapsulation. Recently, the formation of particle trains in viscoelastic liquids has been demonstrated. However, only a few studies have focused on the topic, with several questions remaining unanswered. We here perform numerical simulations and experiments to elucidate the effect of the confinement ratio on the self-ordering dynamics of particles suspended in a viscoelastic liquid and flowing on the centerline of a microfluidic channel. For a fixed channel size, the particles self-order on shorter distances as the particle size increases due to the enhanced hydrodynamic interactions. At relatively low linear concentrations, the relative particle velocities scale with the fourth power of the confinement ratio when plotted as a function of the distance between the particle surfaces normalized by the channel diameter. As the linear concentration increases, the average interparticle spacing reduces and the scaling is lost, with an increasing probability to form strings of particles in contact. To reduce the number of aggregates, a microfluidic device made of an array of trapezoidal elements is fabricated and tested. The particle aggregates reduce down to 5% of the overall particle number, significantly enhancing the ordering efficiency. A good agreement between numerical simulations and experiments is found.

### Influence of cough airflow characteristics on respiratory mucus clearance

A cough is a respiratory reflex for respiratory mucus clearance. The cough airflow dynamics can be characterized by three parameters, which are cough peak flow rate (CPFR), peak velocity time (PVT), and cough expired volume (CEV). In this study, the three-dimensional human respiratory airways from generation 0 to 5 are reconstructed from computerized tomography images. The non-Newtonian property of respiratory mucus is considered. The airflow–mucus interaction phenomenon has been analyzed in time and space based on the Eulerian wall film model. The maximum air velocity and wall shear stress could reach 38 m/s and 14 Pa, respectively, when the CPFR is 6 L/s. In addition, the influence of CPFR, PVT, and CEV on mucus clearance has been studied. The cough efficiency is used to quantify the mucus clearance. The results showed that increasing the cough peak flow rate has no noticeable effect on mucus clearance under normal and low mucus viscosity. Increasing the cough peak flow rate can effectively improve mucus clearance when the mucus viscosity becomes high. Specifically, the CEV has an apparent positive effect on clearing mucus regardless of the viscosity and thickness. This study provides a new research direction to improve mucus clearance by improving the CEV rather than the CPFR for patients with chronic obstructive pulmonary disease, neuromuscular disease, or other pulmonary diseases.

### Morphological effects of leading-edge serrations on the acoustic signatures of mixed flow fan

Leading-edge (LE) noise is a common source of broadband noise for fans that can be suppressed using appended LE serrations. We conduct an integrated study of the morphological effects of interval, length, and inclination angle of owl-inspired LE serrations on the aeroacoustic characteristics of a mixed flow fan using experiments, computational fluid dynamics (CFD), and the Ffowcs Williams–Hawkings (FWH) analogy. A novel method for surface noise strength (SNS) visualization was developed based on the FWH analogy with large-eddy simulations to accurately quantify the spatial distributions of acoustic sources. A CFD-informed index is proposed to evaluate the severity of flow separation with the pressure gradient and verified to be effective in examining the chord-wise separation. Acoustic measurements show the robust trade-off solving capability of the serrations under various morphologies, and the SNS visualizations indicate that the separation-induced LE noise is suppressed considerably. One-third octave analyses suggest that extending serration length can lower separation noise more effectively than shrinking the interval over 100–3000 Hz. A smaller interval is more desirable while an optimal length exists in association with tonal noise. Moreover, small inclination angles ([math]) enable the deceleration of oncoming flows with stagnation relieved, and consequently, further suppress the LE noise, by a flow-buffering effect. Heavy inclination angles ([math]) induce an additional tip vortex, causing high-coherence turbulence impingement noise and resulting in a drastic increase in broadband noise at frequencies exceeding 4000 Hz. Our study, thus, clarifies the morphological effects of LE serrations on aeroacoustic signatures of rotary devices while providing useful methods for acoustic analyses.

### Drag reduction by a rotationally oscillating cylinder with a flexible filament

The hydrodynamic mechanism of drag reduction by a rotationally oscillating cylinder with a flexible filament was explored using the penalty immersed boundary method. A simulation of a stationary cylinder without a filament was also performed for comparison. The effects of the filament length, bending rigidity, oscillatory frequency, and oscillatory amplitude on drag reduction were systematically examined. The underlying mechanism of drag reduction was characterized in terms of the shape deformation of the filament, wake pattern, pressure distribution, and flapping dynamics. Two dominant flapping modes were observed: an oscillation mode with less than half a wave on the filament and an undulation mode with more than one wave on the filament. In the oscillation mode, drag reduction is mainly achieved by the thrust generated by the filament, accompanied by an increase in lift fluctuations. The pressure difference caused by the flapping motion between the upper and lower sides of the filament is the main cause of the thrust. In the undulation mode, drag reduction is realized by both the thrust generated by the filament and the decreased form drag of the cylinder. A filament flapping in the oscillation mode can generate greater thrust than a filament flapping in the undulation mode. A long undulatory filament with relatively low oscillatory amplitude effectively stabilizes the wake, resulting in a decrease in the lift fluctuations.

### Variational approach to droplet transport via bendotaxis: Thin film dynamics and model reduction

Author(s): Zhen Zhang and Tiezheng Qian

Bendotaxis has recently been proposed as a mechanism for self-transport of droplets at small scales. When an active droplet undergoes self-transport via bendotaxis, interfacial, elastic, and active forces jointly determine the droplet motion in a deformable channel. Through simulations of thin-film dynamics and a model reduction based on Onsager’s variational principle, we show that wettability and activity can jointly operate to enhance or weaken the self-transport effect of bendotaxis, depending on the sign of wettability (hydrophobic or hydrophilic) on the channel wall and the sign of activity (contractile or extensile) in the droplet.

[Phys. Rev. Fluids 7, 044002] Published Wed Apr 20, 2022

### Elliptical particle suspensions in Couette flow

Author(s): Xuechao Liu, Haibo Huang, and Xi-yun Lu

The roles of inertia (Re) and particle aspect ratio (Ar) on the rheology of elliptical particle suspensions are investigated. Scaling trends are found between the viscosity and the particle alignment for any Re considered here. Different mechanisms of stress are calculated. Besides the major contribution of stresslet, Reynolds stress contributes more as Ar and Re increase.

[Phys. Rev. Fluids 7, 044303] Published Wed Apr 20, 2022

### Analysis and modeling of bubble-induced agitation from direct numerical simulation of homogeneous bubbly flows

Author(s): A. du Cluzeau, G. Bois, N. Leoni, and A. Toutant

Using direct numerical simulations of homogeneous bubbly flows, an analysis of velocity fluctuations is performed and a methodology for development of a bubble-induced agitation (pseudoturbulence) model described. This process is based on separating two causes of velocity fluctuations in the liquid: Agitation resulting from wakes and their collective interactions; and nonturbulent fluctuations due to averaged wakes and potential flows around bubbles. An energy conversion signature is observed, revealing the importance of nonlinear interactions. A model is proposed which gives satisfactory results on our database for a wide range of bubble Reynolds numbers and is consistent with experiments.

[Phys. Rev. Fluids 7, 044604] Published Wed Apr 20, 2022

### Instability of a heavy gas layer induced by a cylindrical convergent shock

The instability of a heavy gas layer (SF6 sandwiched by air) induced by a cylindrical convergent shock is studied experimentally and numerically. The heavy gas layer is perturbed sinusoidally on its both interfaces, such that the shocked outer interface belongs to the standard Richtmyer–Meshkov instability (RMI) initiated by the interaction of a uniform shock with a perturbed interface, and the inner one belongs to the nonstandard RMI induced by a rippled shock impacting a perturbed interface. Results show that the development of the outer interface is evidently affected by the outgoing rarefaction wave generated at the inner interface, and such an influence relies on the layer thickness and the phase difference of the two interfaces. The development of the inner interface is insensitive (sensitive) to the layer thickness for in-phase (anti-phase) layers. Particularly, the inner interface of the anti-phase layers presents distinctly different morphologies from the in-phase counterparts at late stages. A theoretical model for the convergent nonstandard RMI is constructed by considering all the significant effects, including baroclinic vorticity, geometric convergence, nonuniform impact of a rippled shock, and the startup process, which reasonably predicts the present experimental and numerical results. The new model is demonstrated to be applicable to RMI induced by a uniform or rippled cylindrical shock.

### Inspiratory leakage flow fraction for surgical masks with varying gaps and filter materials

Leakage flows due to a poor fit can greatly reduce the mask protection efficiency. However, accurate quantification of leakages is lacking due to the absence of standardized tests and difficulties in quantifying mask gaps. The objective of this study is to quantify the leakage flows around surgical masks with gaps of varying areas and locations. An integrated ambient–mask–face–airway model was developed with a pleated surgical mask covering an adult's face, nose, and chin. To study the gap effects, the mask edge along the facile interface was divided into different domains, which could be prescribed either as the mask media or air. A low Reynolds number k-ω turbulence model with porous media was used to simulate inspiratory flows. Experimentally measured resistances of two surgical masks were implemented in porous media zones. Results show that even a small gap of 1-cm2 area could cause a 17% leakage. A gap area of 4.3 cm2 at the nose bridge, the most frequent misfit when wearing a surgical mask, led to a leakage of 60%. For a given mask, the increase rate of leakage slowed down with the increasing gap area. For a given gap, the leakage fraction is 30–40% lower for a mask with a resistance of 48.5 Pa than a mask of 146.0 Pa. Even though the flow dynamics were very different among gaps at different locations, the leakage intensity appeared relatively insensitive to the gap location. Therefore, correlations for the leakage as a function of the gap area were developed for the two masks.

### Numerical analysis of interaction between turbulent structures and transient sheet/cloud cavitation

This paper through the in-house code numerically examines the cavitation–vortex–turbulence interaction mechanism. The high grid resolution can obtain a more detailed flow field structure, which is helpful to reveal the relationship between cavitation occurrence and development and local turbulent flow field. Results are presented for a three-dimensional NACA66 hydrofoil fixed at an 8° angle of attack under a moderate Reynolds number of 1 × 106 and sheet/cloud cavitating conditions. Numerical simulations are performed via the boundary data immersion method coupled with the artificial compressibility method through a Fortran-based code. The results show that the numerical predictions are capable of capturing the unsteady cavitation characteristics, in accordance with the quantitative features observed in high-speed cavitation tunnel experiments. The evolution of the transient cavitating flow can be divided into three stages: growth of the attached sheet cavity, development of a re-entrant jet, and cloud shedding downstream. The Liutex method is applied to capture the vortex structure. Further analysis of the process of enstrophy transport reveals that cavitation promotes vortex production and increases the enstrophy as the cavity becomes more unstable. Moreover, the structure of the vortex gradually evolves from a vortex tube to a U-type vortex, Ω-type vortex, and streamwise vortex. Finally, the interaction between cavitation and turbulence is expounded using the turbulent energy transport equation, which demonstrates that cavitation promotes the production, diffusion, and dissipation of turbulent kinetic energy, while the viscous transport term only acts during the process of cloud cavity shedding.

### Erratum: “Electron heating and cooling in hypersonic flows” [Phys. Fluids 33, 046105 (2021)]

### Planform evolution of a sinuous channel triggered by curvature and autogenic width oscillations due to generic grain transport

We study the dynamics of an erodible sinuous channel subject to combined curvature and autogenic width oscillations. We find that generic grain transport (both bedload and suspended load transport) amplifies lateral stretching of the channel centerline and enhances the maximum width-variation amplitude and curvature ratio in their temporal dynamics by displaying a phase lag. However, in the initial and mature stages, the planform dynamics asymptotically approaches the conventional limits. The planform evolution is found to be influenced by four key parameters: Shields number, relative roughness, channel aspect ratio, and shear Reynolds number. The findings of this study, to the best of our knowledge, represent the first analytical investigation of the planform evolution of a sinuous channel driven by generic grain transport.

### Reynolds number dependence of turbulent heat transfer over irregular rough surfaces

To study the scaling of turbulent heat transfer over a rough surface, we performed a series of direct numerical simulations on turbulent heat transfer over a three-dimensional irregular rough surface with varying the friction Reynolds numbers and relative roughness values. We considered rough surfaces with three different relative roughness values of 1/1.9, 1/4.3, and 1/9.0, and the simulations were performed at three friction Reynolds numbers of 115, 250, and 550. The temperature was treated as a passive scalar with a Prandtl number of unity. Regarding the scaling of the Reynolds analogy factor, which is defined as the ratio of the doubled Stanton number to the skin friction coefficient, a correlation function with the skin friction coefficient, equivalent roughness, and Prandtl number provides an accurate account of the effects of relative roughness, roughness Reynolds number, and friction Reynolds number. For scaling the turbulent momentum and energy fluxes, we introduced the decomposition of the turbulent fluxes into the smooth wall profiles at matched friction Reynolds numbers and their deviatoric components. The baseline smooth wall profile was found to account for the effect of the friction Reynolds number, while the deviatoric component incorporated the effect of the roughness Reynolds number. The dispersion fluxes, namely, the dispersive covariance and dispersion heat flux, were dominantly affected by the roughness Reynolds number rather than the friction Reynolds number. To obtain a better understanding of the effect of wall roughness on the momentum and heat transfer mechanisms, we analyzed the spatial and time-averaged momentum and energy equations and discussed the physical mechanisms that caused a decrease in the mean velocity and temperature from smooth wall profiles.

### A numerical investigation of methane ignition in supercritical CO2

The supercritical CO2 power cycle (sCO2) is a relatively new technology, which promises to reduce CO2 emissions with potentially higher efficiencies. However, due to challenging conditions posed by supercritical pressures, the ignition phenomena in sCO2 combustion are relatively less understood and studied. The primary objective of the current study is to elucidate ignition processes using homogeneous ignition calculations (HMI) and two-dimensional direct numerical simulations (DNS). To accurately model the supercritical conditions, the employed formulation includes the cubic Peng–Robinson equation of state, mass, and heat flux vectors derived from nonequilibrium thermodynamics and compressible form of governing equations. For selection of a suitable chemical mechanism, HMI calculations are employed to investigate the performance of existing skeletal mechanisms against shock-tube experimental data. The chemical characteristics of ignition are further studied using path flux and sensitivity analysis, with CH3O2 chemistry exhibiting the largest effect on accelerating the ignition process. Different chemical pathways of fuel breakdown are also discussed to aid in interpretation of subsequent DNS case. In the DNS case, autoignition of a two-dimensional mixing layer perturbed with pseudoturbulence is simulated. The ignition is found to be delayed compared to the HMI case, with the ignition kernels forming in a spotty manner. The two phenomena are primarily attributed to variation of scalar dissipation within the mixing layer. The ignition kernels expand and evolve into a tribrachial edge flame propagating along the stoichiometric isosurface. Further investigation on the structure of edge flame revealed an asymmetrical structure, with CH4 molecules being entirely consumed in the triple point region of the flame along the stoichiometric isosurface, and more stable fuels like CO burning in the non-premixed branch of the edge flame. The edge flame propagation speeds are also calculated, with variations found to be correlated with scalar dissipation and upstream progress variable of the reacting mixture.

### Chemical reaction of Ni/Al interface associated with perturbation growth under shock compression

The exothermic reaction of Ni/Al laminates always starts from the interface, and the role of interfacial instability in the shock-induced chemical reaction has not been clarified. This work reports the Richtmyer–Meshkov (RM) instability growth, atomic diffusion, and chemical reaction of Ni/Al interface under shock compression based on atomistic simulations. For shocking from Al to Ni, the interface experiences finite collapse and exhibits weak localized reaction. The diffusion of solid Ni to molten Al will be inhibited due to the formation of NiAl phase, and continuous inter-diffusion occurs with the melting of Ni. For shocking from Ni to Al, a small amount of NiAl structure is formed due to the atomic residue during defect collapse. RM instability growth is observed at higher shock intensity, which significantly promotes the atomic mixing and results in a power-law increase in the number of diffusing atoms. Meanwhile, the chemical reaction propagates rapidly from the vortex to the head of the spike accompanied by the decomposition of many clusters, with the nonlinear development of RM instability. The number and the size of Ni clusters no more satisfy the simple power-law relationship for which we propose an improved power-law distribution. Interestingly, the growth of nanoscale perturbation approximately satisfies the logarithmic law with time, but the linear growth stage is inhibited due to significant inter-diffusion, especially for the small wavelength. Thus, the mixing width and the reaction degree are positively correlated with the initial wavelength in our simulation scale, which is contrary to the RM growth law of the free surface.

### Large eddy simulations and modal decomposition analysis of flow past a cylinder subject to flow-induced vibration

Large eddy simulations (LES) are carried out to investigate the flow around a vibrating cylinder in the subcritical Reynolds number regime at Re = 3900. Three reduced velocities, Ur = 3, 5, and 7, are chosen to investigate the wake structures in different branches of a vortex-induced vibration (VIV) lock-in. The instantaneous vortical structures are identified to show different coherent flow structures in the wake behind the vibrating cylinder for various branches of VIV lock-in. The combined effects of the frequency and amplitude of the oscillation on the flow pattern in the wake region, the hydrodynamic quantities of the cylinder, and the spanwise length scale of the energetic wake flow structures are discussed in detail. It is found that the typical spanwise lengths of the flow structures are [math] at Ur = 5 and [math] at [math] in the near-wake region and level out at [math] further downstream. Furthermore, multiscale proper orthogonal decomposition (mPOD) is used to analyze the dominant flow features in the wake region. With the increasing Ur, the total kinetic energy contribution of superharmonic modes increases and the contribution of subharmonic modes decreases. The dominant flow characteristics associated with the vortex shedding and their super harmonics, and the low-frequency modulation of the wake flow can be captured by the mPOD modes.

### Characteristics of enhanced mixing induced by plate jet actuation in supersonic flow

The fast and efficient mixing of fuel and oxidizers under supersonic conditions is of great importance for improving the performance of scramjet engines. The mixing process in the inner flow of a scramjet combustor is heavily inhibited by compressibility effects. In this paper, the novel strategy of plate jet actuation is proposed, and its effects on mixing augmentation are analyzed by employing numerical programs developed in-house. The fine vortex structures induced by the plate jet actuation are well captured, and the dynamic behaviors of newly observed T-shaped structures are analyzed in detail. It is found that in plate jet actuation flow, Kelvin–Helmholtz (K–H) vortices induced by K–H instability coexist with T-shaped structures induced by jet actuation instability. The interaction of adjacent T-shaped structures leads to the distortion and breakup of large-scale structures, which can obviously improve the interfaces of upper and lower streams. The distribution of the turbulence intensity along the streamwise direction suggests that with the introduction of plate jet actuation, more intense fluctuations occur in the flow. The growth process of mixing layer thickness indicates that with plate jet actuation, a sharp increase in mixing thickness can be achieved in the near flow field. The results of structural topology analysis show that upper plate jet actuation can produce structures with larger sizes, and the distortion and penetration process of these structures can entrain more upper and lower streams into the mixing region. It is suggested that the present proposed strategy is a good candidate for mixing enhancement with the application of scramjet combustors.

### Comparative study of transonic shock–boundary layer interactions due to surface heating and cooling on an airfoil

Implicit large eddy simulation results are compared to investigate the effects of wall-heating and wall-cooling on shock–boundary layer interaction over an airfoil. Heat flux is provided on the suction surface of the airfoil from [math] to [math] for a Mach number of 0.72 and a Reynolds number based on chord of [math]. Flow quantities are compared for the effects of heating and cooling. Numerical Schlieren snapshots reveal an oscillation of the shock wave and its interaction with upstream propagating Kutta waves generated from the trailing edge of the airfoil. Quantitative data obtained from these Schlieren snapshots and the mean aerodynamic load values indicate a reduction in frequency of oscillation of shock wave and a decrease in shock strength for the case of heating. Flow control by heating shows higher fluctuations in flow features evident from instantaneous quantities. Both imposed excitations lead to a marginal increase in aerodynamic efficiency (lift/drag). We also compare the integral aerodynamic parameters, such as lift and drag coefficients, and their ratio, [math]. The simulations reported here follow the techniques used in Sengupta et al. [“Thermal control of transonic shock–boundary layer interaction over a natural laminar flow airfoil,” Phys. Fluids 33(12), 126110 (2021)].