# Latest papers in fluid mechanics

### Control of a sedimenting elliptical particle by electromagnetic forces

In this paper, the effectiveness of electromagnetic forces on controlling the motion of a sedimenting elliptical particle is investigated using the immersed interface-lattice Boltzmann method (II-LBM) in which a signed distance function is adopted to apply the jump conditions for the II-LBM and to add external electromagnetic forces. First, mechanisms of electromagnetic control on suppressing vorticity generation based on the vorticity equation and vortex shedding based on the streamwise momentum equation are discussed. Then, systematic investigations are performed to quantify and qualify the effects of the electromagnetic control by changing the electromagnetic strength, the initial orientation angle of the elliptical particle, and the density ratio of the particle to the fluid. To demonstrate the control effect of different cases, comparisons of vorticity fields, particle trajectories, orientation angles, and energy transfers of the particles are presented. The results show that the rotational motion of the particle can be well controlled by appropriate magnitudes of electromagnetic forces. In a relatively high solid to fluid density ratio case where vortex shedding appears, the sedimentation speed can increase nearly 40% and the motion of the particle turns into a steady descending motion once an appropriate magnitude of the electromagnetic force is applied. When the magnitude of the electromagnetic force is excessive, the particle will deviate from the center of the side walls. In addition, the controlling approach is shown to be robust for various initial orientation angles and solid to fluid density ratios.

### Displacement speed analysis of surface propagation in moderately turbulent premixed reacting waves

The propagation of premixed reacting waves can be characterized by a displacement speed Sd at which the local surface of the reaction progress scalar moves respective to flow. Often, Sd is considered through decomposition into three parts of contribution due to the tangential diffusion of curvature, normal diffusion, and reaction. A set of recently derived transport equations for Sd and three of its decomposed parts provides new diagnostics for better understanding reaction wave propagation in a turbulent environment. In this work, those diagnostics are applied on four similarly setup direct numerical simulation cases studying the propagation of moderately perturbed planar reaction waves into homogeneous turbulence, and the reaction waves differ by the density ratio between fresh and burned gases. The data analysis reveals four self-acceleration behaviors: (i) surfaces propagating at large positive (negative) Sd tend to advance (retreat) faster, (ii) surfaces having large positive (negative) curvature tend to become more curved positively (negatively), (iii) thicken wave zones tend to become thicker, and (iv) surface elements accelerate toward their destruction. The extent of the above accelerations all reduces in the reaction wave having a high density ratio. This can be attributed to the turbulence inhibition due to the flow dilatation and viscosity increase across a thermal-expansion enabled reaction wave. The distribution of curvature for the reaction-zone surface skews toward a negative value, i.e., the curvature center pointing to the burned product.

### Global hydrodynamic instability and blowoff dynamics of a bluff-body stabilized lean-premixed flame

We experimentally study the hydrodynamic instability of a lean-premixed flame stabilized behind a circular cylinder. On reducing the equivalence ratio ([math]) at a fixed Reynolds number (ReD), we find that the flame transitions from a steady mode to a varicose mode and then to a sinuous mode. By examining time-resolved CH* chemiluminescence images and analyzing how the Strouhal number scales with ReD, we determine that the varicose mode is convectively unstable, maintained by the amplification of disturbances in the turbulent base flow, whereas the sinuous mode is globally unstable as a result of the constructive interaction between the two diametrically opposite shear layers (Bénard–von Kármán instability). We attribute the emergence of the sinuous global mode to the flame moving sufficiently far downstream with decreasing [math] that it is out of the wavemaker region. Finally, we investigate the lean blowoff dynamics and find that local flame pinch-off, which occurs at the end of the recirculation zone, is a reliable precursor of global flame blowoff.

### Effects of velocity skewness on the linear stability of the oscillatory Stokes layer

The effects of velocity skewness on the oscillating Stokes layer are investigated. Linear stability characteristics for the family of velocity-skewed time-periodic flows are determined using Floquet theory. Neutral stability curves and critical parameter settings for instability and the structure of the eigenfunctions are presented. Velocity skewness establishes a stabilizing effect and increases the critical Reynolds number for the onset of linear instability to larger values than that found in the non-skewed Stokes layer. Solutions indicate that disturbances develop in the direction that the wall velocity achieves a maximum absolute value.

### Perturbatively conserved higher nonlocal integral invariants of free-surface deep-water gravity waves

We exhibit a set of six explicit higher nonlocal integral invariants of free-surface deep-water gravity waves conserved in lowest nontrivial orders of perturbation in the amplitude of the surface displacement.

### Study of formation mechanism of double metal plasma jets in a low-current pulsed vacuum arc discharge

Plasma jet formation was studied in a vacuum arc configured with a conical cathode located inside a hollow cylindrical anode. The outside of this anode was insulated, except at a 0.4 mm diameter micropore. The grounded vacuum chamber also served as an anode. The hollow cylindrical anode was connected to the grounded chamber anode through a resistor R. 170 A 14 μs arcs were excited by a pulse generator comprised of a series connection of a 0.1 F capacitor bank charged to 12 kV, a 200 μH inductor, and a 30 Ω resistor. Two plasma jets formed during the arc discharge, one originating from the cathode tip and the other through the micropore. It was found that when R was increased from 0 Ω to 1 MΩ, (1) the plasma jet originating at the micropore weakened, (2) the peak current to the hollow cylindrical anode decreased from 73 A to 0, and (3) the peak arc current decreased from 176 A to 150 A. Plasma jet velocities for R = 0 were inferred from the difference between electron current peak times at two probes, to be 9 km/s for the plasma jet from the cathode and 27 km/s for the plasma jet at the micropore.

### The joint probability density function of mixture fraction, reaction progress variable, and total enthalpy in a stratified, swirl-stabilized turbulent flame

The three-condition version of the uniform conditional state combustion model makes use of the mixture fraction, progress variable, and normalized total enthalpy as conditioning variables to build a three-dimensional conditional manifold for chemistry. In order to map the solution in conditional space into the flow domain, the joint Probability Density Function (PDF) of the conditioning variables needs to be modeled. In simulations, presumed functions (i.e., β-PDF for the mixture fraction and progress variable and δ-PDF for total enthalpy) are often used for modeling the marginal PDFs. In this work, the measurements from the Cambridge/Sandia burner are employed to obtain the marginal PDFs for the conditioning variables at various points in the reacting domain. The measurements are then combined from all positions in space to form conditional PDFs of the normalized total enthalpy for various values of the other two variables. In the vicinity of the flame brush, the marginal PDF of the normalized total enthalpy resembles a bimodal Gaussian distribution; nonetheless, the conditional PDFs for this variable are nearly Gaussian distributions. The correlation coefficients between the conditioning variables are also investigated, and the assumption of their statistical independence is examined. To consider the association between the conditioning variables for modeling, the copula concept is introduced, and the performances of three different copulas are tested. Furthermore, the statistical moments of the conditioning variables are computed from the experimental data at different points and are utilized for modeling the joint PDF of the conditioning variables from two different approaches that are compared.

### Mathematical constraints on the scaling exponents in the inertial range of fluid turbulence

The dominant view in the theory of fluid turbulence assumes that, once the effect of the Reynolds number is negligible, moments of order n of the longitudinal velocity increment, ([math]), can be described by a simple power-law [math], where the scaling exponent ζn depends on n and, except for [math], needs to be determined. In this Letter, we show that applying Hölder's inequality to the power-law form [math] (with [math]; L is an integral length scale) leads to the following mathematical constraint: [math]. When we further apply the Cauchy–Schwarz inequality, a particular case of Hölder's inequality, to [math] with [math], we obtain the following constraint: [math]. Finally, when Hölder's inequality is also applied to the power-law form [math] (this form is often used in the extended self-similarity analysis) while assuming [math], it leads to [math]. The present results show that the scaling exponents predicted by the 1941 theory of Kolmogorov in the limit of infinitely large Reynolds number comply with Hölder's inequality. On the other hand, scaling exponents, except for ζ3, predicted by current small-scale intermittency models do not comply with Hölder's inequality, most probably because they were estimated in finite Reynolds number turbulence. The results reported in this Letter should guide the development of new theoretical and modeling approaches so that they are consistent with the constraints imposed by Hölder's inequality.

### Mechanisms of entrainment in a turbulent boundary layer

Data from direct numerical simulation of a zero-pressure-gradient incompressible turbulent boundary layer (TBL) [You and Zaki, “Conditional statistics and flow structures in turbulent boundary layers buffeted by free-stream disturbances,” J. Fluid Mech. 866, 526 (2019)] are analyzed to examine the entrainment process. The two mechanisms by which the outer irrotational flow can be entrained into the turbulent region and their relative contribution to the growth of the spatially developing boundary layer are evaluated: (i) nibbling is the enstrophy transport across the turbulent/non-turbulent interface (TNTI), and (ii) engulfment is the entrapment of pockets of irrotational flow inside the TBL prior to finally breaking apart. The relative importance of the two mechanisms depends on the normalized vorticity threshold adopted to identify the TNTI. Our choice of this threshold highlights the structure of the TNTI and entrainment within this layer by engulfment of irrotational pockets. The sizes of the engulfed pockets are of the same order as the heads of the hairpin vortices underneath the TNTI. The vortices straddle larger streaky structures of internal layers and cause handle shaped deformations on the TNTI, which leads to engulfment as they fold onto themselves and entrap the external potential flow. Three dynamical regions are distinguished: a TNTI region (interface layer), an adjustment region, and the turbulent core. The first of these is further sub-divided into a viscous superlayer and a turbulent sublayer. It is shown as the irrotational fluid elements cross the interface layer toward the turbulent core, a smooth transition from the non-focal topology to the well-known primarily focal topology of fully developed turbulence occur. The viscous superlayer is similar to previously studied flow configurations, such as jets and mixing layers. In contrast, vorticity stretching in the turbulent sublayer is significantly weaker in the boundary layer relative to free-shear flows, which results in a smaller rate of entrainment by nibbling.

### Time-averaging and temporal-filtering in wall-modeled large eddy simulation

A turbulent channel flow at a Reynolds number of [math] is solved based on the spatially filtered Navier–Stokes equations using large eddy simulation and an in-house code. A nonequilibrium wall model is implemented to predict the flow in the wall layer based on the Reynolds-averaged approach. To mitigate the log-layer mismatch, which is often encountered in wall modeling, two temporal schemes are introduced to average the wall layer solution and to filter the flow information input to the wall layer. It is found that the time periods used for the time-averaging and temporal-filtering schemes affect the performance of the wall model. The results show that shorter time periods enable the wall model to respond to the flow structures in the outer layer and correctly predict the friction velocity. However, the prediction of the friction velocity also depends on the location of the matching point. Locating the matching point further from the wall results in better performance due to the compatibility of the subgrid scale model with the grid resolution further from the wall. The temporal-filtering scheme is used to remove nonessential high-frequency wavelengths that can disturb the functionality of wall modeling. Various combinations of the time-averaging and temporal-filtering time periods are investigated for different locations of the matching point. Overall, it is concluded that using a shorter period for time-averaging and a temporal-filtering period comparable to the turbulent diffusion timescale leads to improved results.

### Diameter and charge of the first droplet emitted in electrospray

The first droplet produced by a low-conductivity pendant/sessile droplet subject to a strong electric field is particularly important at the fundamental level because, in contrast to steady electrospray phenomena, its ejection entails complex charge relaxation and electrokinetic processes. Besides, it is technologically relevant because of its very small diameter and large electric charge per unit volume. In this work, we present an experimental technique to measure with unprecedented accuracy the diameter of the droplet and to determine for the first time its electric charge. We discuss both the advantages of our technique over possible alternatives and the limitations of the method. The proposed method is applied to two alcohols with electrical conductivities of the order of a few μS/m. The high sensitivity of our experimental technique allows us to determine the influence of both the magnitude and the polarity of the applied voltage on the size and charge of the ejected droplet. The electric charge of the first-emitted droplet lies in the interval [math] (qR is the Rayleigh limit of charge) for the two liquids analyzed. These experimental values are slightly larger than those obtained from theoretical predictions. The value of [math] for the first droplet is very relevant because it can be regarded as an upper bound of those of the droplets subsequently emitted in the cone-jet mode of electrospray.

### Experimental study of uni- and bi-directional exchange flows in a large-scale rotating trapezoidal channel

A large-scale experimental study has been conducted at the Coriolis Rotating Platform to investigate the dynamics of uni- and bi-directional exchange flows along a channel with a trapezoidal cross section under the influence of background rotation. High-resolution two-dimensional particle image velocimetry and micro-conductivity probes were used to obtain detailed velocity fields and density profiles of the exchange flow generated across the channel under different parametric conditions. Experimental measurements give new insight into the stratified-flow dynamics dependence on the magnitude of Burger number, defined as the ratio of the Rossby radius to the channel width, such that values lower than 0.5 characterize unsteady exchange flows. The measurements highlight the role that both ambient rotation and net-barotropic forcing have on the geostrophic adjustment of the dense outflowing layer and on the corresponding counter-flowing water layer fluxes. The coupled effect of these two parametric conditions largely affects the transverse velocity distribution and, for the largest net-barotropic flow in the upper fresh water layer, leads to the partial blockage of the lower saline outflow. Moreover, an increase in the mixing layer thickness, associated with larger rotation rates, and due the interface dynamics, is observed, with shear-driven interfacial instabilities analyzed to highlight the influence of both ambient rotation and net-barotropic forcing.

### Effect of visco-plastic and shear-thickening/thinning characteristics on non-Newtonian flow through a pipe bend

This study investigates the influence of the rheological parameters on the unyielded zone, pressure drop, and secondary flow pattern of non-Newtonian fluid like fresh cement mortar through a pipe bend with different curvatures. The regularized Herschel–Bulkley model is employed in the framework of lattice Boltzmann method to model the effects of the visco-plastic and shear-thickening/thinning characteristics with variations on the yielding stress σ0 and the power-law index n. The sharper curvature, higher power-law index contributes to a smaller and more asymmetric unyielded zone and even vanishes for curvature radius [math] and n = 1.4, as the width and distribution of plug region are governed by the comparison between yielding stress and shear stress. The increased yielding stress and power-law index lead to an increase in the total pressure drop and additional pressure loss; however, their variations with respect to the curvature radius display an opposite trend. The intensity of the helical secondary flow in the elbow, primarily governed by the competition between the centrifugal and viscous force, is reduced to about one quarter when σ0 and n increase from 0 Pa and 0.6 to 50 Pa and 1.4.

### Numerical investigations of head-on collisions of binary unequal-sized droplets on superhydrophobic walls

Droplet head-on impact is widely encountered in nature, industry, and agricultural applications. In our study, a two-dimensional axisymmetric model, using the volume-of-fluid method, is built to simulate unequally sized droplet head-on impact on a superhydrophobic surface. The collision regime, after droplet coalescence, is obtained with dimensionless parameters, as well as the contact time, maximum spreading diameter, restitution coefficient, and viscous dissipation. When the impact droplet is larger than the stationary droplet on the substrate, the merged droplet can easily jump up. At high Bond numbers (Bo) or high Ohnesorge numbers (Oh), the merged droplet cannot jump up due to significant gravitational effects or viscous effects, respectively. The energy for droplet jumping mainly comes from the released surface energy after the coalescence of father and mother droplets. The contact time of a droplet with the superhydrophobic substrate is proportional to the Weber number to the 0.5th power (We0.5), and the maximum spreading diameter of a merged droplet is proportional to We0.2. With an increasing size ratio of the father droplet to the mother droplet, both the contact time and maximum spreading diameter increase. These findings will help gain insights into the dynamics of droplet head-on impact.

### Turbulence in a hypersonic compression ramp flow

Author(s): Stephan Priebe and M. Pino Martín

Using direct numerical simulation, the shock wave–turbulent boundary layer interaction (STBLI) generated by a compression ramp in Mach 7 flow is investigated. The behavior of turbulence in hypersonic STBLI has not been investigated as extensively in the literature as in supersonic interactions. This work describes the evolution of mean and fluctuating quantities, including velocity and temperature fluctuations, providing insight into the behavior of turbulence in a hypersonic STBLI.

[Phys. Rev. Fluids 6, 034601] Published Tue Mar 02, 2021

### Simulation and characterization of the laminar separation bubble over a NACA-0012 airfoil as a function of angle of attack

Author(s): Eltayeb Eljack, Julio Soria, Yasir Elawad, and Tomohisa Ohtake

Airfoils operating at low Reynolds number have a proclivity to induce a laminar separation bubble (LSB) on their upper surface. We investigate the effects of angle of attack on the characteristics of the LSB and the flow field around a NACA0012 airfoil. Large-eddy simulations show that there are three distinct angle-of-attack regimes: a pre-stall attached flow, a near stall separating-attaching flow, and a full stall separated flow without reattachment.

[Phys. Rev. Fluids 6, 034701] Published Tue Mar 02, 2021

### X-ray phase contrast and absorption imaging for the quantification of transient cavitation in high-speed nozzle flows

High-flux synchrotron radiation has been employed in a time-resolved manner to characterize the distinct topology features and dynamics of different cavitation regimes arising in a throttle orifice with an abrupt flow-entry contraction. Radiographs obtained though both x-ray phase-contrast and absorption imaging have been captured at 67 890 frames per second. The flow lies in the turbulent regime (Re = 35 500), while moderate (CN = 2.0) to well-established (CN = 6.0) cavitation conditions were examined encompassing the cloud and vortical cavitation regimes with pertinent transient features, such as cloud-cavity shedding. X-ray phase-contrast imaging, exploiting the shift in the x-ray wave phase during interactions with matter, offers sharp-refractive index gradients in the interface region. Hence, it is suitable for capturing fine morphological fluctuations of transient cavitation structures. Nevertheless, the technique cannot provide information on the quantity of vapor within the orifice. Such data have been obtained utilizing absorption imaging, where beam attenuation is not associated with scattering and refraction events, and hence can be explicitly correlated with the projected vapor thickness in line-of-sight measurements. A combination of the two methods is proposed as it has been found that it is capable of quantifying the vapor content arising in the complex nozzle flow while also faithfully illustrating the dynamics of the highly transient cavitation features.

### Analysis of the water flow inside tire grooves of a rolling car using refraction particle image velocimetry

In order to better understand the hydroplaning phenomenon, local velocity measurements of water flow are performed inside the tire grooves of a real car rolling through a water puddle. Velocity fields are obtained by combining refraction Particle Image Velocimetry (r-PIV) illumination, seeding fluorescent particles, and either the classical two dimensional two components or the two dimensional three components stereoscopic recording arrangements. The presence of some bubble columns inside the grooves is highlighted by separate visualization using the fluorescent contrast technique evidencing two phase flow characteristics. A simple predictive model is proposed supporting the r-PIV analysis. It provides useful information to adjust the focusing distance and to understand the effect of the bubble column presence on the recorded r-PIV images, especially for the seeding particles located in the upper part of the grooves, as fluorescent light is attenuated by the bubbles. Also, the predictions provided by the model are compatible with the measurements. The velocity fields inside the grooves are analyzed using ensemble averaging performed over a set of independent snapshots, recorded with the same operating parameters. The variability of the longitudinal velocity distribution measured in a groove for several independent runs is explained by different mechanisms, like the random position of fluorescent seeding particles at various heights of the groove, the hydrodynamic interactions between longitudinal and transverse grooves, and the random location of the transverse grooves from one run to another. Three velocity components in cross sections of the longitudinal grooves are obtained using the stereoscopic arrangement. They are compatible with the presence of some longitudinal vortices assumed in the literature. The number of vortices is shown to be dependent on the aspect ratio characterizing a groove's rectangular cross section. We demonstrate, from measurements performed for several car velocities, that the velocity distribution inside longitudinal grooves shows self-similarity when using specific dimensionless length and velocity scales. Hydrodynamic interactions between longitudinal and transverse grooves are discussed on the basis of a mass budget; a fluid/structure interaction mechanism is proposed in order to correlate the overall direction of the flow in a transverse groove with its location inside the contact zone. Finally, some physical mechanisms are suggested for the birth of longitudinal vortices.

### Experimental characterization of air-saturated porous material via low-frequencies ultrasonic transmitted waves

An improved acoustic method is proposed for measuring the tortuosity and the viscous and thermal characteristic lengths of air-saturated porous materials via low-frequency ultrasonic transmitted waves (70 kHz–110 kHz). The equivalent fluid model is considered. The interaction between the saturated fluid and the structure is taken into account in two frequency response factors: the dynamic tortuosity of the medium and the dynamic compressibility of the air which are described by their high-frequency expansion in powers of the viscous and thermal skin depth, either limiting the expansion to the first two leading terms or the first three leading terms with the introduction of two new viscous and thermal shape factors. These two new factors play an important role in stabilizing and improving the inverted parameters of the tortuosity and the viscous and thermal characteristic lengths in the frequency band considered. The inverse problem is solved numerically in the frequency domain by minimizing the spectrum of simulated and experimental transmitted signals. Optimized parameters of tortuosity, viscous and thermal characteristic lengths, and viscous and thermal shape factors are obtained simultaneously. The tests are carried out with three samples of plastic foam. The results obtained by the two procedures are discussed and compared to those given in the literature.

### Aerodynamic interaction of bristled wing pairs in fling

Tiny flying insects of body lengths under 2 mm use the “clap-and-fling” mechanism with bristled wings for lift augmentation and drag reduction at a chord-based Reynolds number (Re) on [math]. We examine the wing–wing interaction of bristled wings in fling at Re = 10 as a function of initial inter-wing spacing (δ) and degree of overlap between rotation and linear translation. A dynamically scaled robotic platform was used to drive physical models of bristled wing pairs with the following kinematics (all angles relative to vertical): (1) rotation about the trailing edge to angle θr, (2) linear translation at a fixed angle (θt), and (3) combined rotation and linear translation. The results show that (1) the cycle-averaged drag coefficient decreased with increasing θr and θt and (2) decreasing δ increased the lift coefficient owing to increased asymmetry in the circulation of leading and trailing edge vortices. A new dimensionless index, reverse flow capacity (RFC), was used to quantify the maximum possible ability of a bristled wing to leak the fluid through the bristles. The drag coefficients were larger for smaller δ and θr despite larger RFC, likely due to the blockage of inter-bristle flow by shear layers around the bristles. Smaller δ during early rotation resulted in the formation of strong positive pressure distribution between the wings, resulting in an increased drag force. The positive pressure region weakened with increasing θr, which in turn reduced the drag force. Tiny insects have been previously reported to use large rotational angles in fling, and our findings suggest that a plausible reason is to reduce drag forces.