# Latest papers in fluid mechanics

### Bubble dynamics and pressure field characteristics of underwater detonation gas jet generated by a detonation tube

An underwater detonation tube (DT) experiment is carried out in a water tank to investigate the bubble dynamics and pressure field characteristics of an underwater detonation gas jet. In the experiment, a 0.78 liter DT filled with a 0.29 MPa methane–oxygen mixture (equivalent to 0.85 mg of TNT, trinitrotoluene) is detonated. By means of high-speed photography and pressure field measurements, the jet process is divided into four different stages. The evolution patterns and features of the four stages are characterized according to the morphology of the detonation gas bubble, and the dimensionless parameters of the bubble dynamics are defined and calculated using image post-processing. The transmitted shock wave and pressure pulsations of the bubble oscillations are extracted using a low-pass filter with a cutoff frequency of 1000 Hz. The time intervals between consecutive pressure peaks are compared with the oscillation periods obtained from parameter studies of bubble dynamics. The bubble dynamics generated by the sudden release of detonation products in the first oscillation are found to be similar to those of underwater explosions. An expansion-necking structure is observed, formed by the impulsive release of the remaining detonation gas from the DT. A numerical simulation is conducted under the same filling conditions as the experiment to supplement the experimental results. The experiment demonstrates the feasibility of underwater detonation gas jets, which could provide an alternative means of generating pulsation bubbles.

### Energetic motions in turbulent partially filled pipe flow

Turbulent partially filled pipe flow was investigated using stereoscopic particle imaging velocimetry in the cross-stream plane for a range of flow depths at a nominally constant Reynolds number of 30 000 (based on the bulk velocity and hydraulic diameter). Unlike full pipe flow, which is axisymmetric, the turbulent kinetic energy exhibits significant azimuthal (and radial) variation. Proper orthogonal decomposition (POD) of the fluctuating velocity field indicates that the leading-order POD modes occupy the “corners” where the free surface meets the pipe wall and that these modes, which are closely linked to the instantaneous cellular structure, contribute nearly a quarter of the overall turbulent kinetic energy. Spatial distributions of the large- and very-large-scale motions (LSMs/VLSMs) estimated from pseudo-instantaneous three-dimensional velocity fields reveal a preference for the sides (in close proximity to the free surface) and bottom quadrant of the pipe. That the LSMs and VLSMs are shown to populate a region spanning the width of the free surface, as well as the corners, strongly suggests that there is a dynamical connection between LSMs/VLSMs and the instantaneous cellular structures in turbulent partially filled pipe flow, which can explain the spatial redistribution of the turbulent kinetic energy.

### Energetic motions in turbulent partially filled pipe flow

Turbulent partially filled pipe flow was investigated using stereoscopic particle imaging velocimetry in the cross-stream plane for a range of flow depths at a nominally constant Reynolds number of 30 000 (based on the bulk velocity and hydraulic diameter). Unlike full pipe flow, which is axisymmetric, the turbulent kinetic energy exhibits significant azimuthal (and radial) variation. Proper orthogonal decomposition (POD) of the fluctuating velocity field indicates that the leading-order POD modes occupy the “corners” where the free surface meets the pipe wall and that these modes, which are closely linked to the instantaneous cellular structure, contribute nearly a quarter of the overall turbulent kinetic energy. Spatial distributions of the large- and very-large-scale motions (LSMs/VLSMs) estimated from pseudo-instantaneous three-dimensional velocity fields reveal a preference for the sides (in close proximity to the free surface) and bottom quadrant of the pipe. That the LSMs and VLSMs are shown to populate a region spanning the width of the free surface, as well as the corners, strongly suggests that there is a dynamical connection between LSMs/VLSMs and the instantaneous cellular structures in turbulent partially filled pipe flow, which can explain the spatial redistribution of the turbulent kinetic energy.

### Jetting behavior as a bubble bursts in free space

The phenomenon of bubble bursting is very common in nature and is of prime importance in various technologies and industrial processes. Similar to interfacial bubbles, the process of a bubble bursting in free space, that is, the rupture of bubbles surrounded by air, often results in jet flows. However, the location and mechanism of the jet flows are different from those produced by interfacial bubbles. This paper describes the results of several experiments conducted to investigate the behavior of a bubble bursting in free space, especially the jet flows that occur at the end of the process. The results show that viscosity has a strong inhibitory effect on both the droplets (film drops and jet drops) and the jet resulting from bubble bursting. Based on experimental results, we establish a phase diagram for the jetting behavior in terms of the Reynolds number (Re) and the Ohnesorge number (Oh) and discover the existence of threshold conditions. Jetting occurs in the zone where Oh is less than some threshold value Ohc and Re is greater than some threshold value Rec, whereas a liquid clump appears in the zone where Oh > Ohc and Re < Rec. For 0.002 < Oh < 0.272 and 65 < Re < 52 633, we find that Rec = 503 ± 136 and Ohc = 0.079 ± 0.001. A schematic of the events that occur during bubble bursting depicting the forces at play is subsequently analyzed, and the role of viscosity at the moment of jetting is highlighted. The results of this study can be used to inhibit or increase the formation of droplets in numerous applications.

### On spontaneous appearance of internal waves in an open-pool-type research reactor

Variation of temperature in time and space was recorded at multiple vertical locations in the course of initiation of a heated water layer in an open-pool research reactor of the Soreq Nuclear Research Center. The pool was initially filled with warm water, and heavier cooler water was then injected at the bottom of the facility. Different modes of coolant injection were employed in two different experiments. In both cases, a finite width thermocline that separated cool water at the lower part of the pool from the warm water in its upper part was observed. The thermocline gradually moved up eventually attaining a constant raise velocity. In both experiments, the thermocline characteristics were different, but wave-trains with notable temperature fluctuations were observed within the thermocline. The characteristic frequencies of oscillations were below the Brunt–Väisälä frequencies that characterize the density gradient within the thermoclines. The finite dimensions of the tank impose conditions in which standing internal waves with the length commensurate with tank size can be expected. The oscillations were thus associated with resonant internal waves excited by disturbances introduced by the coolant flow at the lower part of the pool. In both experiments, the measured wave spectra agree with the results of linear analysis of two-layer and three-layer stratification models.

### Flows between orthogonally stretching parallel plates

Navier–Stokes equilibrium solutions of a viscous fluid confined between two infinite parallel plates that can independently stretch or shrink in orthogonal directions are studied. It is assumed that the admissible solutions satisfy spatial self-similarity in the stretching or shrinking perpendicular coordinates. The nonlinear steady boundary-value problem is discretized using a spectral Legendre method, and equilibrium solutions are found and tracked in the two-dimensional parameter space by means of pseudo-arclength continuation Newton–Krylov schemes. Different families of solutions have been identified, some of which are two-dimensional and correspond to the classical Wang and Wu self-similar flows arising in a plane channel with one stretching–shrinking wall [Wang, C.-A. and Wu, T.-C., “Similarity solutions of steady flows in a channel with accelerating walls,” Comput. Math. Appl. 30, 1–16 (1995)]. However, a large variety of three-dimensional solutions have also been found, even for low stretching or shrinking rates. When slightly increasing those rates, some of these solutions disappear at saddle-node bifurcations. By contrast, when both plates are simultaneously stretching or shrinking at higher rates, a wide variety of new families of equilibria are created and annihilated in the neighborhood of cuspidal codimension-2 bifurcation points. This behavior has similarities with the one observed in other planar and cylindrical self-similar flows.

### Stability of a reverse Karman vortex street

The reverse vortex street differs from the ordinary Karman vortex street in the direction of the rotation of the vortices. Such a street is formed behind the oscillating airfoils in the flow. It is of interest in connection with studies of the aerodynamics of flapping wings. It is known that the vortex wake behind a symmetric airfoil performing symmetric oscillations in a certain range of parameters becomes asymmetric, which leads to the appearance of a nonzero average lift. Reasons of the symmetry violation are associated with the instability of the reverse vortex street, but the mechanism of this instability is currently not well understood. In this work, the analysis of the stability of the reverse vortex street is carried out on the basis of the theory developed by Karman for infinite rows of point vortices. In contrast to the Karman model, in this work, semi-infinite rows with periodically arising new vortices at their ends are considered. This is the first time this model has been used. It is shown that the periodic appearance of new vortices radically affects the characteristics of the street stability. It is found that the violation of the symmetry of the reverse vortex street is associated with its instability to bending perturbations, while the ordinary Karman vortex street behind the body is unstable to varicose perturbations. Regions of instability are determined.

### Comparative study on numerical performances of log-conformation representation and standard conformation representation in the simulation of viscoelastic fluid turbulent drag-reducing channel flow

In this paper, a new derivation process of the log-conformation governing equation for viscoelastic fluid flows is presented by using the Taylor series definition of the matrix logarithm. Based on the log-conformation representation (LCR) and standard conformation representation (CR) methods, the turbulent drag-reducing channel flow of viscoelastic fluid described by the Oldroyd-B constitutive model is simulated by the finite difference method. The comparison illustrates that the turbulent drag reduction (DR) effect under the condition of a low Weissenberg number (Wi = 1) or moderate Weissenberg number (Wi = 5) can be successfully reproduced by the CR method but is very difficult to be obtained by the LCR method at the same grid resolution if the commonly used interpolation approaches in the computing domain (i.e., log domain) are employed. Further research reveals that the interpolation method of log-conformation tensor involved is one of the dominant reasons responsible for the disability to obtain a turbulent DR effect by using the LCR method. If the interpolation is performed in a physical domain, the turbulent DR effect can be reproduced by using the LCR method. If the interpolation involved in the CR method is carried out in a log domain, the turbulent DR phenomenon can still be simulated but with a weakened DR effect. In sum, this study demonstrates that the commonly used interpolation approaches in the log domain should be responsible for the poor performance of the LCR method.

### Quantifying the role of Darrieus–Landau instability in turbulent premixed flame speed determination at various burner sizes

To probe the impact of Darrieus–Landau (DL) instability on turbulent premixed flame propagation at various burner sizes, methane–air premixed flames from five Bunsen-type burners with different nozzle diameters (4 mm, 6 mm, 8 mm, 10 mm, and 12 mm) were investigated at Reynolds numbers ranging from 1000 to 8500. The flame curvatures used to identify DL instability were determined using Mie scatter images captured by a particle image velocimetry system. The flame speed was further derived by applying an asymmetric hypothesis to the images. The energy-frequency spectrum of the inflow disturbance was determined using a hot-wire anemometry system, and specific wavelet transform analysis was performed to investigate the dependence of DL instability on the proportion of effective disturbances (P ed ) and quantify the role of DL instability in determining the turbulent flame speed. The results showed that the burner diameter had an obvious effect on the presence of DL instability and its role in flame propagation. The ability of DL instability to enhance the flame curvature skewness and the turbulent flame speed was closely related to P ed . P ed increased when the burner diameter increased from 6 mm to 12 mm, thus enhancing the DL instability. Changing the burner diameter also affected the interplay between DL instability and turbulence. The above interactions and their effects on the flame speed during the change of inflow disturbances could be formulated by P ed . Finally, a P ed -based correlation was proposed to describe the dependence of the turbulent flame speed on the burner size.

### Motion and clustering of bonded particles in narrow solid–liquid fluidized beds

This paper presents an experimental and numerical investigation of solid–liquid fluidized beds consisting of bonded spheres in very narrow tubes, i.e., when the ratio between the tube and grain diameters is small. In narrow beds, high confinement effects have proved to induce crystallization, jamming, and different patterns, which can be intensified or modified if some grains are bonded together. In order to investigate that, we produced duos and trios of bonded aluminum spheres with a diameter of 4.8 mm and formed beds consisting either of 150–300 duos or 100–200 trios in a 25.4 mm-ID pipe, which were submitted to water velocities above those necessary for fluidization. For the experiments, we filmed the bed with high-speed and conventional cameras and processed the images, obtaining measurements at both the bed and grain scales. For the numerical part, we computed the bed evolution for the same conditions with a computational fluid dynamics–discrete element method code. Our results show distinct motions for individual duos and trios and different structures within the bed. We also found that jamming may occur suddenly for trios, where even the microscopic motion (fluctuation at the grain scale) stops, calling into question the fluidization conditions for those cases.

### Non-normal effect of the velocity gradient tensor and the relevant subgrid-scale model in compressible turbulent boundary layer

The non-normal effects of the velocity gradient tensor (VGT) in a compressible turbulent boundary layer are studied by means of the Schur decomposition of the VGT into its normal and non-normal parts. Based on the analysis of the relative importance of them, it is found that the non-normal part significantly affects the dynamics of the VGT in the wall-bounded turbulent flow and the relevant non-normal effect has a dominant influence on the enstrophy and dissipation. It is revealed that the deviatoric part of the pressure Hessian is associated with the non-normal effect and the isotropic part is associated with the normal effect. The pressure Hessian significantly influences the vortex stretching. The non-normal effect reinforces the preferences for the vorticity vector to align with the intermediate strain-rate eigenvector and to be perpendicular to the extensive and compressive strain-rate eigenvector in the near-wall region. The non-normal effect also reduces the intermediate eigenvalue of the strain-rate tensor. Furthermore, a subgrid scale (SGS) model that separately considers the normal and non-normal effects is proposed based on the above characters and is verified to give a better prediction of the SGS dissipations in the wall-bounded turbulent flow.

### Effects of size ratio and inter-cylinder spacing on wake transition in flow past finite inline circular cylinders mounted on plane surface

Three-dimensional numerical computations have been carried out in flow past two inline finite-height circular cylinders using Open Source Field Operation and Manipulation. Investigations have been carried out for the varying Reynolds number (Re) ranging from 150 to 300. The diameter of the upstream cylinder is varied in such a way that the size ratio (SR, ratio of the diameter of the upstream cylinder to that of the downstream cylinder) takes values of 0.25, 0.5, and 1.0. For each size of the upstream cylinder, the downstream cylinder is placed at different locations in the streamwise direction. Effects of Re, SR, and inter-cylinder spacing (S) on three-dimensional unsteady wake characteristics behind upstream and downstream cylinders have been examined using iso-Q surfaces. Unsteady wake oscillations in both the wakes are analyzed qualitatively and quantitatively in terms of Hilbert spectra and the degree of stationarity using the transverse velocity component in the wake. Different flow regimes for upstream and downstream wakes have been identified and discussed with the change in Re, SR, and S. Transitions in the wake flow are illustrated using vorticity contours, frequency spectra, and bifurcation diagram. The level of wake synchronization in the upstream wake, downstream wake, and between both the wakes has been identified with the help of the cross correlation function.

### Thin-film evolution and fingering instability of self-rewetting films flowing down an inclined plane

This paper examines the evolution patterns and essential mechanisms of flow instability of a self-rewetting fluid (SRF) coating on an inclined plane. Considering that the self-rewetting liquid has an anomalous surface tension with temperature change, some interesting phenomena will be found and should be explained. Using the thin-film model, the evolution equation of the air–liquid interface is derived, and the thickness of the liquid film is determined by a fourth-order partial differential equation. Taking T 0 (temperature corresponding to the minimum of surface tension) as a cutoff point, two representative cases of the nonlinear flow are comprehensively discussed. One is the case of T i > T 0, and the other is T i < T 0 (interfacial temperature T i ). Based on traveling wave solutions, linear stability analysis (LSA) of the small perturbation applied to the initial condition is given, and the results of LSA are confirmed and explained by the numerical simulations. Results show that the inclined angle and the Weber number always stabilize the free surface, while the Marangoni effect and the Biot number play different roles for the two cases. As T i − T 0 varies from a negative value to a positive value, the Marangoni effect switches to the reverse Marangoni effect. With T i − T 0 < 0, the Marangoni effect enhances the fingering instability, while the Marangoni effect makes the flow more stable if T i − T 0 > 0. The Biot number Bi = 1 corresponds to the most unstable state for T i < T 0 and to the most stable state for T i > T 0.

### Magnified heat transfer from curved surfaces: A scaling prediction

We report the first definitive Nusselt number scale of thermal boundary layers from curved surfaces characterized by the proposed non-dimensional curvature parameter ξ = R 0/(H Ra −1/4), where R 0 denotes the radius of a curved surface, H denotes the corresponding finite height, and Ra denotes the global Rayleigh number of a virtual reference thermal boundary layer on a vertical flat surface. The Nusselt number scale is given by Nu ∼ ξ −1/5 Ra 1/4 in which Nu ∼ Ra 1/4 is the scale for the flat surface case, revealing that curved thermal boundary layers could present times-of-magnitude larger heat flux with the curvature parameter being ξ ≪ 1. The velocity and thickness scales are also given by [math] and [math].

### Slippage effect on interfacial destabilization driven by standing surface acoustic waves under hydrophilic conditions

Author(s): J. Muñoz, J. Arcos, I. Campos-Silva, O. Bautista, and F. Méndez

The influence of the slippage phenomenon over the interfacial dynamics of a millimeter-order fluid drop exposed to surface acoustic wave atomization is numerically studied under hydrophilic conditions. Implementation of the Navier-slip model into the governing hydrodynamic equations yields an interfacial evolution equation. The solution suggests that slippage at the wall constitutes a valuable phenomenon to manipulate the parent drop geometric aspect ratio and consequently the characteristic aerosol size during the atomization process.

[Phys. Rev. Fluids 6, 024002] Published Wed Feb 03, 2021

### Nanoflows induced by MEMS and NEMS: Limits of two-dimensional models

Author(s): Alyssa T. Liem, Atakan B. Ari, Chaoyang Ti, Mark J. Cops, James G. McDaniel, and Kamil L. Ekinci

The mechanical oscillations of a miniaturized resonator generate viscous oscillatory nanoflows in the surrounding fluid. As a result, the fluid presents an effective added mass and damping to the resonator, which is commonly predicted by a two-dimensional flow model. Here, the limitations to the two-dimensional model are examined when a substrate and axial flow are present. Results from experiments and three-dimensional finite element models are presented to illustrate where and why the two-dimensional flow models break down.

[Phys. Rev. Fluids 6, 024201] Published Tue Feb 02, 2021

### Flow structure and turbulence in the near field of an immiscible buoyant oil jet

Author(s): Xinzhi Xue, Lakshmana Dora Chandrala, and Joseph Katz

Simultaneous applications of particle image velocimetry and planar laser-induced fluorescence in a refractive index matched facility are used to visualize the phase distribution and measure velocity in an immiscible low Reynolds number buoyant oil jet injected into water. Initially, mixing involves entrainment of water ligaments inward and oil ligaments outward, followed by phase fragmentation into blobs and then droplets. Phase-based conditioning reveals spatially varying discrepancies between the velocity and all Reynolds stress components in the oil and water phases. Trends are attributed to intermittency and differences in turbulence production rate.

[Phys. Rev. Fluids 6, 024301] Published Tue Feb 02, 2021

### Inertial torque on a small spheroid in a stationary uniform flow

Author(s): F. Jiang, L. Zhao, H. I. Andersson, K. Gustavsson, A. Pumir, and B. Mehlig

How anisotropic particles rotate and orient in a flow depends on the hydrodynamic torque they experience. The torque acting on a small spheroid in a uniform flow is computed by numerically solving the Navier-Stokes equations. Overall, the numerical results provide a justification of recent theories for the orientation statistics of ice crystals settling in cold clouds.

[Phys. Rev. Fluids 6, 024302] Published Tue Feb 02, 2021

### Laboratory model for plastic fragmentation in the turbulent ocean

Author(s): Christophe Brouzet, Raphaël Guiné, Marie-Julie Dalbe, Benjamin Favier, Nicolas Vandenberghe, Emmanuel Villermaux, and Gautier Verhille

We study the fragmentation of deformable and brittle fibers in the inertial range of turbulence using laboratory experiments and numerical simulations. The fragmentation process is shown to be limited at small scales by a physical cut-off length due to fluid-structure interactions of the object with turbulence, and thus independent of the fiber brittleness. This scenario, comprehensively modeled by an evolution equation, leads to the accumulation of fragments slightly longer than the cut-off scale, as smaller fragments are too short to be deformed and broken by the turbulence. This result may improve our understanding of microplastic formation in the ocean.

[Phys. Rev. Fluids 6, 024601] Published Tue Feb 02, 2021

### Fluid dynamics and epidemiology: Seasonality and transmission dynamics

Epidemic models do not account for the effects of climate conditions on the transmission dynamics of viruses. This study presents the vital relationship between weather seasonality, airborne virus transmission, and pandemic outbreaks over a whole year. Using the data obtained from high-fidelity multi-phase, fluid dynamics simulations, we calculate the concentration rate of Coronavirus particles in contaminated saliva droplets and use it to derive a new Airborne Infection Rate (AIR) index. Combining the simplest form of an epidemiological model, the susceptible–infected–recovered, and the AIR index, we show through data evidence how weather seasonality induces two outbreaks per year, as it is observed with the COVID-19 pandemic worldwide. We present the results for the number of cases and transmission rates for three cities, New York, Paris, and Rio de Janeiro. The results suggest that two pandemic outbreaks per year are inevitable because they are directly linked to what we call weather seasonality. The pandemic outbreaks are associated with changes in temperature, relative humidity, and wind speed independently of the particular season. We propose that epidemiological models must incorporate climate effects through the AIR index.