# Latest papers in fluid mechanics

### Shape evolutions of moving fluid threads under asymmetrical confinements

This paper presents a combined experimental and numerical investigation designed to improve our understanding of how the shape of moving fluid threads evolves under asymmetrical confinements in both circular and square microchannels. Microfluidic devices with two junctions are designed to control the length of the fluid thread at the first junction and the deformation of the fluid thread at the second junction. Three different flow modes: nonbreakup, loosely confined breakup, and tightly confined breakup, are identified for varying lengths of fluid threads and capillary number, and two boundaries are identified between the three modes. The deformation dynamics of the fluid threads evolving as difference modes are addressed to consider the effects of thread length and capillary number. Numerical simulations are carried out to determine how the curvature evolves for different flow modes in the square microchannel. The evolution of interface profiles is obtained numerically over a wide range of capillary number. Stop-flow simulations are then carried out to identify both the critical shape for the onset of the capillary instability during tightly confined breakup and the corresponding curvature distribution. This critical shape is found to be corresponding to the fluid thread with the critical length at the transitive boundary between the loosely confined and tightly confined situations.

### Ionic diffusioosmotic transport in nanochannels grafted with pH-responsive polyelectrolyte brushes modeled using augmented strong stretching theory

In this paper, we study the diffusioosmotic (DOS) transport in a nanochannel grafted with pH-responsive polyelectrolyte (PE) brushes and establish brush-functionalization-driven enhancement in induced nanofluidic electric field and electrokinetic transport. The PE brushes are modeled using our recently developed augmented strong stretching theory. We consider the generation of the DOS transport due to the imposition of a salt concentration gradient along the length of the nanochannel. The presence of the salt concentration gradient induces an electric field that has an osmotic (associated with the flow-driven migration of the ions in the induced electric double layer) and an ionic (associated with the conduction current) component. These two components evolve in a manner such that the electric field in the brush-grafted nanochannel is larger (smaller) in magnitude than that in the brush-less nanochannels for the case where the electric field is positive (negative). Furthermore, we quantify the DOS flow velocity and establish that for most of the parameter choices, the DOS velocity, which is a combination of the induced pressure-gradient-driven chemiosmotic component and the induced electric field driven electroosmotic transport, is significantly larger for the nanochannels grafted with backbone-charged PE brushes (i.e., brushes where the charge is distributed along the entire length of the brushes) as compared to brush-free nanochannels or nanochannels grafted with PE brushes containing charges on their non-grafted ends.

### The levitation of a sphere by two parallel turbulent jets

Two vertical turbulent round jets are used to levitate a spherical particle. First, a symmetric configuration is investigated with the two jets of equal flow rates. A structure reminiscent of a pitchfork bifurcation is reported and characterized between a double trap configuration for low flow rates and a single trap regime at higher flow rates. A second configuration is then studied with the flow rates that differ between the left and right jets. In this case, a preferential transition toward the jet of a higher flow rate is reported and quantified. A model is presented predicting the force field for the symmetric and asymmetric configurations. The model is compared to the force field measurements realized with a particle on a flexible cantilever. Finally, a particle dynamics simulation is proposed to analyze in more detail the transition for the levitation in the symmetric and asymmetric configurations.

### Numerical study of roundness effect on flow around a circular cylinder

Imperfectly round bridge stay cable cross section is speculated to be a key factor for wind-induced large-amplitude cable vibrations observed on site. A delayed detached eddy simulation implemented in Open source Field Operation and Manipulation is used to investigate the flow structure around and in the near-wake of an imperfectly round circular cylinder and the corresponding aerodynamic forces at a Reynolds number of 104 and an attack angle of 0° or 45°. With the increase in roundness imperfection, both monotonic and non-monotonic changes of the mean surface pressure and the wake velocity are found when the cylinder is normal to the flow. At an attack angle of 45° and when the roundness ratio is e/D = 4%, it is found that the geometric imperfection in the cross-sectional shape of the cylinder allows it to the retention of more axial flow in the proximity of the cylinder leeward surface due to a shorter recirculation length. The vortex formed by the intensified axial flow would interact with the conventional von Kármán vortex formation at a frequency a few times lower than that of the latter and lead to intermittently amplified transverse lift. This reveals that imperfect roundness in the cross section of a circular cylinder could be an excitation source of low frequency vibration. Thus, it provides evidence that this kind of geometric imperfection, which commonly exists in real stay cables, could contribute to the mechanisms that trigger large-amplitude or even divergent cable motion, such as dry inclined cable galloping on site.

### Numerical analysis of the interaction of two underwater explosion bubbles using the compressible Eulerian finite-element method

This paper presents numerical investigations of the nonlinear interactions between two underwater explosion (UNDEX) bubbles using the compressible Eulerian finite-element method (EFEM). The volume of fluid method is applied to capture the multi-fluid interface. In this model, the high-temperature and high-pressure gaseous products inside the UNDEX bubble are described by the equation of state for Jones–Wilkins–Lee, which allows us to consecutively simulate the propagation of the primary explosion shock wave and multi-period bubble pulsations. To verify the efficiency and accuracy of the present model, comparisons with experimental data are performed, showing that both the dynamic behaviors of oscillating bubbles and the pressure profiles of primary shock waves, bubble pulsations, and jetting loads are highly consistent. In addition, it is found that the EFEM model can satisfactorily reproduce the complex characteristics of interacting bubbles, such as the coalescence and splitting that occur during later pulsating cycles in bubbles. On this basis, the effects of the initial bubble–bubble distance γbb and buoyancy parameter δ on the features of bubble interactions and the corresponding pressure loads in the flow field are analyzed and discussed. In particular, the pressure induced by two identical UNDEX bubbles (each generated by detonation of an explosive with weight W) is compared to that induced by a single bubble generated by an explosive with weight W or 2W to provide the basic technical support and reference for the design of multiple-weapon attacks in military engineering applications.

### Heat transfer in magnetohydrodynamic nanofluid flow past a circular cylinder

Multi-phase modeling considering the nanofluid heterogeneity and slip velocity is not explored in simulating nanofluid flow and heat transfer at higher Reynolds numbers (Re). A comprehensive study of turbulent flow around hot circular cylinders is lacking. The flow patterns are not tackled, and the relationship between flow behaviors and force variations due to the influencing parameters is not established. The heat transfer enhancement and hydrodynamics with forced convection in a rectangular duct are investigated using Ansys FLUENT 15.0, applying a nodal spectral-element method based on the Eulerian-mixture model. The current investigation focuses on demonstrating the correlation between high Re values, size of the bluff body in relation to duct height, nanoparticle volume fraction, magnetic field strength, and heat transfer for magnetohydrodynamic flow. In general, the Nusselt number (Nu) increases with Re, cylinder diameter in relation to duct height, and nanoparticle volume fraction (ϕ) and decreases with the Hartmann number (Ha), except at Ha 0 ≤ 20. Nu increases with Ha from 0 to 20 with a drastic increase up to Ha = 10 and moderate from 10 to 20 with augment of Ha. The best heat transfer enhancement case is reported with the identification of ideal influencing parameters. The significant finding is that the control of flow over a circular cylinder for heat transfer enhancement using different parameters significantly changes vortical structures in the wake and reduces mean drag and lift fluctuations, destabilizes the shear layer and reattaches the flow on the surface before main separation, which delays main separation and decreases drag, and finally reduces the lift fluctuations.

### Shear electroconvective instability in electrodialysis channel under extreme depletion and its scaling laws

Author(s): Wei Liu, Yueting Zhou, and Pengpeng Shi

The electroconvective instability (ECI) in an electrodialysis channel under a strong electric field is studied here. The phenomenon of ECI with extreme depletion (ECI-HD) is reported; that is, the overlapping vortices cause the extreme depletion zone to propagate in the horizontal direction. Using s...

[Phys. Rev. E 101, 043105] Published Fri Apr 17, 2020

### Secondary instability of Mack mode disturbances in hypersonic boundary layers over micro-porous surface

In laminar hypersonic boundary layers, it is known that secondary instability plays a crucial role in transition to turbulence. The secondary instability usually includes the fundamental mode, the subharmonic mode, and the detuned mode. Considerable research exists on the secondary instability mechanism in hypersonic boundary layers with the smooth wall condition. The topic of using micro-porous surfaces for disturbance stabilization has recently drawn interest. The stabilization and, thus, a possible delay in the transition arise due to a reduction in the growth rate of the primary Mack mode by the porous surface. This paper focuses on investigating whether the secondary instability mechanism of Mack modes can also be affected by a surface porosity condition. It is known that the primary Mack mode linear disturbances are changed significantly on the porous surface, and how it subsequently influences the secondary instability of the modified time varying basic flow is our concern. The analysis demonstrates that on the porous surface, as the amplitude of the primary Mack mode increases, the fundamental mode is not stable. Instead, the fundamental mode amplifies rapidly with increasing primary amplitudes. At larger secondary instability spanwise wavenumbers, when the primary amplitude exceeds a certain threshold value, the fundamental modes surpass the subharmonic modes and dominate the secondary instability. However, when the spanwise wavenumber is relatively small, especially at the spanwise wavenumber corresponding to the maximum growth rate of the subharmonic mode, the fundamental modes are weakened and lose their dominant position. We find that corresponding to different amplitudes of primary Mack mode disturbances affected by the porosity parameters, there are no strongly preferred interaction modes that dominate the secondary instability; this contrasts with smooth wall findings. We further find that the larger the pore size or porosity, the more severe the suppression of the fundamental mode.

### Visualization of methane hydrate decomposition interface and analyses of decomposition rate and interfacial configuration

Composed of methane gas and cage-like water molecules, methane hydrate is expected to have innovative engineering applications, such as gas transportation. In this study, a methane hydrate decomposition interface is visualized qualitatively, and the decomposition rate is discussed. To clarify the decomposition mechanism, consideration is given to the dynamic decomposition interface and the variation of the decomposition rate. In the present experiment, methane hydrate is formed around a water droplet and decomposed by depressurization in the gas phase, the dynamic variation of the decomposition interface is observed precisely using a high-resolution camera, and three different depressurization conditions are used to confirm the interfacial change. It is found that the decomposition rate and dynamic shape change of the decomposition interface depend on the difference between the equilibrium pressure and that of the gas phase. In addition, the decomposition time is discussed using the decomposition model, and it is estimated that the present experimental decomposition rate corresponds to a lower activation energy for decomposition compared with that of the model by other authors. It is assumed that the decomposition proceeds under nearly reaction-limited conditions. Additionally, the interfacial deformation and collapse are observed in the case of pressure reduction near the equilibrium pressure, and validation is provided by a numerical simulation considering the heat and mass transfer near the interface. The numerical results suggest that the decomposition is affected by the interfacial configuration and the nearby temperature and concentration distributions.

### Water-wave interaction with submerged porous elastic disks

Hydroelastic interaction between water waves and submerged porous elastic disks of negligible thickness in water of finite depth is investigated under the assumption of small amplitude water-wave motion and structural response. The disks are either simply supported or clamped at their edges. Wave power can be absorbed/dissipated by the disks due to their porosity. A theoretical model based on the linear potential flow theory and eigenfunction matching method is developed to solve the wave scattering problem of the submerged disks. An indirect method, employing Kochin functions, is derived based on Green’s theorem to evaluate the wave power absorption/dissipation, and it produces accurate results at a lower computational cost than the conventional method. This theoretical model is applied to perform a multi-parameter study on the performance of a single submerged porous elastic disk, and an array of disks as well, particularly, in terms of near-field wave motion, disk deflection, far-field scattering coefficient, and wave power absorption/dissipation. Deploying multiple disks in an array is found to be a more promising approach for wave power absorption/dissipation compared to enlarging the area of a single disk.

### Stability of electrically conducting liquid flow driven by a rotating magnetic dipole in a ring channel

The stability of electrically conducting liquid flow in a cylindrical ring channel is studied numerically. The flow is driven by a rotating magnetic dipole placed at the ring’s center. Depending on ring’s width, two distinct flow regimes are observed. In a narrow ring, the flow itself and its instability resemble the related rotating magnetic field driven flow in a cylinder. This changes in a wide ring when an intense radial jet develops on the midplane. Within this jet, the driving magnetic force is overwhelmed by inertial and viscous forces similar to how it occurs in the boundary layer flow. The instability develops as an azimuthally periodic wave-like deformation of this jet. Non-uniform driving force and the viscous boundary layer at the inner side wall are supposed as the main ingredients of the jet formation.

### Particle Residence Time in pulsatile post-stenotic flow

Particle Residence Time (PRT), a measure of a fluid element’s transit time through a region of interest, is a clear indicator of recirculation. The PRT of fluid recirculating downstream of an idealized stenosis geometry is found to vary dramatically under pulsatile flow conditions. Two-dimensional particle tracking velocimetry is used to track particles directly as they exit the stenosis geometry and are entrained into the region of recirculation immediately downstream. A Lagrangian approach permits long pathlines to be drawn, describing each particle’s motion from the instant they enter the domain. PRT along each pathline is compared here for three mean Reynolds numbers; specifically, Rem = 4800, 9600, and 14 400. The pulsatile waveforms are characterized by Strouhal numbers of 0.04, 0.08, and 0.15 and amplitude ratios of 0.50 and 0.95. As the mean Reynolds number is increased, higher fluid velocities are shown to lower PRT. However, the strength of PRT is truly revealed when highlighting the influence pulsatility has on the degree of mixing beyond the stenosis throat. Higher Strouhal numbers correlate with roll-up across the shear layer and increased PRT distribution at all Reynolds numbers in consideration. Similarly, strong temporal velocity gradients generated by a high amplitude ratio carry large volumes of fluid from the jet deep into the recirculation region, contributing to greater PRT.

### On the total enthalpy behavior inside a shock wave

The total enthalpy behavior inside a shock wave in a dilute monatomic gas has been numerically studied for various values of Mach and Prandtl numbers with the continuum (the Navier–Stokes–Fourier equations) and kinetic (the Shakhov model and the direct simulation Monte Carlo method) approaches. A significant difference between the results by the continuum and kinetic approaches has been observed for the internal shock wave structure. In a wide range of the free-stream Mach numbers, the continuum approach predicts qualitatively similar behavior of total enthalpy distributions that can be of a concave, constant, or convex shape depending on the Prandtl number. The more sophisticated kinetic approach predicts a more complicated form of total enthalpy profiles: e.g., an inflection point for Mach numbers around two and Prandtl numbers close to unity. The evolution of the total enthalpy in the shock is determined by the balance of heat conduction and mechanical work of normal viscous stress—processes that are predicted inaccurately by using the Navier–Stokes–Fourier equations at high Mach numbers.

### Measurement of fluid viscosity based on droplet microfluidics

We demonstrate an efficient method that can precisely measure the viscosity of fluids based on droplet microfluidics. For our design of the droplet microfluidic viscometer, the volume of the fluid sample required for testing the fluid viscosity is on the order of nanoliters. In particular, a T-junction microdroplet generator is designed for the production of monodisperse droplets, and the flow rates of the continuous and dispersed phases are controlled by the pressure-driven microfluidic device. By giving a specified viscosity of the dispersed phase, the viscosity of the continuous phase can be measured, while considering the linear relation between the droplet length and the flow-rate ratio of the two phases, the linear relation between the droplet length and the viscosity ratio of the two phases can be obtained. For our design of the T-junction microdroplet generator, the viscosity ratio of the two phases can be predicted by testing the length of droplets formed in the microchannel, and therefore, the fluid viscosity of the continuous phase can be calculated. More importantly, the comparison between the measured and the given viscosity of the continuous phase is provided for three different geometries of the T-junctions, and consequently, the testing precision of the fluid viscosity can be validated experimentally.

### Asymptotic scaling of drag in flat-plate turbulent boundary layers

A new asymptotic −1/2 power-law scaling is derived from the momentum integral equation for the drag in flat-plate turbulent boundary layers. In the limit of infinite Reynolds number, the appropriate velocity scale for drag is found to be M/ν, where M is the boundary layer kinematic momentum rate and ν is the fluid kinematic viscosity. Data covering a wide range of Reynolds numbers remarkably collapse to a universal drag curve in the new variables. Two models, discrete and continuous, are proposed for this universal drag curve, and a robust drag estimation method, based on these models, is also presented.

### Aerodynamic performance of a free-flying dragonfly—A span-resolved investigation

We present a quantitative characterization of the unsteady aerodynamic features of a live, free-flying dragonfly under a well-established flight condition. In particular, our investigations cover the span-wise features of vortex interactions between the fore- and hind-pairs of wings that could be a distinctive feature of a high aspect ratio tandem flapping wing pair. Flapping kinematics and dynamic wing-shape deformation of a dragonfly were measured by tracking painted landmarks on the wings. Using it as the input, computational fluid dynamics analyses were conducted, complemented with time-resolved particle image velocimetry flow measurements to better understand the aerodynamics associated with a dragonfly. The results show that the flow structures around hindwing’s inner region are influenced by forewing’s leading edge vortex, while those around hindwing’s outer region are more influenced by forewing’s shed trailing edge vortex. Using a span-resolved approach, we found that the forewing–hindwing interactions affect the horizontal force (thrust) generation of the hindwing most prominently and the modulation of the force generation is distributed evenly around the midspan. Compared to operating in isolation, the thrust of the hindwing is largely increased during upstroke, albeit the drag is also slightly increased during the downstroke. The vertical force generation is moderately affected by the forewing–hindwing interactions and the modulation takes place in the outer 40% of the hindwing span during the downstroke and in the inner 60% of the span during the upstroke.

### Leading-edge bluntness effects in hypervelocity flat plate flow

The combined effects of leading-edge bluntness and high enthalpy are examined for hypersonic flat plate flow. Experimental pressure and heat transfer data are presented for both sharp and blunt leading-edge flat plates. For the sharp leading-edge flows, the data are in agreement with perfect gas theory. For the blunt leading-edge flows, the low and high enthalpy pressure data approach the perfect gas blast wave theory as the flow proceeds downstream, consistent with earlier studies at low enthalpy. Toward the front of the plate, the heat transfer data lie above the corresponding values obtained with the sharp leading-edge configuration. The difference between sharp and blunt leading-edge heat transfer levels appears to be smaller at high enthalpy. This seems to be due to dissociation which occurs in the nose region, thus reducing the shock stand-off distance and increasing the chemical potential enthalpy of the flow. When the presence of dissociated species in the flow is accounted for, the data close to the leading-edge are seen to compare well with perfect gas bluntness–viscous similitudes. Farther downstream, the measured heat transfer values are greater than the perfect gas theoretical predictions for blunt leading-edge flow, and closer to both the corresponding predictions at chemical equilibrium, and sharp leading-edge theory for perfect gas flow.

### Large axisymmetric surface deformation and dewetting in the flow above a rotating disk in a cylindrical tank: Spin-up and permanent regimes

Author(s): Wen Yang, Ivan Delbende, Yann Fraigneau, and Laurent Martin Witkowski

Accurate measurements and axisymmetric numerical simulations of the spin-up of a fluid driven by a rotating disk are carried out. In particular, disk dewetting is taken into account. This constitutes a solid benchmark and paves the way for future numerical investigations on the three-dimensional regime of rotating polygons, for example.

[Phys. Rev. Fluids 5, 044801] Published Tue Apr 14, 2020

### Flow separation around a square cylinder at low to moderate Reynolds numbers

Flow (of a Newtonian and incompressible fluid) separation around a square cylinder for Reynolds numbers (Re) in the range of 10–400 is investigated through direct numerical simulations. In contrast to the general belief that for a square cylinder, the flow would always separate at the leading and/or trailing edges of the cylinder, this study shows that the flow (both time-averaged and instantaneous) may not separate at the sharp corners for a certain range of moderate Re values. Instead, separation emerges at approximately a quarter of the cylinder length downstream of the leading edge at critical Re values of 100.36 and 96 for the time-averaged and instantaneous flows, respectively. With the increase in Re, the time-averaged separation location gradually moves toward the leading edge, while its instantaneous variation range reduces. The evolution of the separation pattern with Re is categorized with a fine Re resolution of 1. A critical point is identified at Re = 156 (for the time-averaged flow), where a saddle point emerges away from the upper/lower surface of the cylinder to give rise to wake flow entrainment to the upper/lower side of the cylinder. The rate of the entrained flow is governed by the location of the saddle point. The flow three-dimensionality occurring at Re > 165.7 affects the location of the saddle point but has almost no influence on the location of the separation point. The corresponding physical mechanism is explained.

### Shrinkage induced flow during directional solidification of pure substance in a bottom cooled cavity: A study on flow reversal phenomena

Development and proposition of a numerical model to capture the shrinkage induced flow during directional solidification of a pure substance in a bottom cooled cavity are carried out. A novel numerical scheme involving fixed grid-based volume fraction updating is proposed to track the solid–liquid interface, considering the inclusion of the shrinkage effect. Directional solidification in bottom cooled orientation is of particular interest since shrinkage and buoyancy effects oppose each other. The results from the proposed numerical model indicated the existence of an unprecedented flow reversal phenomenon during the progression of the solidification process, caused by the opposing nature of shrinkage and buoyancy effects. The flow reversal phenomena predicted by the numerical model are validated by conducting experiments involving directional solidification of coconut oil in a bottom cooled cavity. Qualitative and quantitative measurements of the velocity field and interface growth are obtained using the particle image velocimetry technique and compared with three dimensional numerical results. Once the flow reversal phenomena are established through numerical and experimental evidences, case studies are performed, considering varying material properties, cold boundary temperatures, initial temperatures of the melt, and cavity heights to find the effect of each of these parameters on flow reversal phenomena. The parametric study also allowed us to check the robustness and consistency of the proposed model. The proposed model will serve as an important milestone toward the development of numerical models for capturing macro-scale shrinkage defects and prediction of composition heterogeneity during directional alloy solidification.