# Latest papers in fluid mechanics

### Separated boundary layer transition under pressure gradient in the presence of free-stream turbulence

Large-eddy simulation (LES) has been carried out to investigate the transition process of a separated boundary layer on a flat plate. A streamwise pressure distribution is imposed to mimic the suction surface of a low-pressure turbine blade, and the free-stream turbulence intensity at the plate leading edge is 2.9%. A dynamic subgrid scale model is employed in the study, and the current LES results compare well with available experimental data and previous LES results. The transition process has been thoroughly analyzed, and streamwise streaky structures, known as the Klebanoff streaks, have been observed much further upstream of the separation. However, transition occurs in the separated shear layer and is caused by two mechanisms: streamwise streaks and the inviscid K-H instability. Analysis suggests that streamwise streaks play a dominant role in the transition process as those streaks severely disrupt and break up the K-H rolls once they are formed, leading to significant three-dimensional (3D) motions very rapidly. It is also demonstrated in the present study that the usual secondary instability stage under low free-stream turbulence intensity where coherent two-dimensional (2D) spanwise rolls get distorted gradually and eventually broken up into 3D structures has been bypassed.

### Three-dimensional rotation of paramagnetic and ferromagnetic prolate spheroids in simple shear and uniform magnetic field

We examine a time-dependent, three-dimensional rotation of magnetic ellipsoidal particles in a two-dimensional, simple shear flow and a uniform magnetic field. We consider that the particles have paramagnetic and ferromagnetic properties, and we compare their rotational dynamics due to the strengths and directions of the applied uniform magnetic field. We determine the critical magnetic field strength that can pin the particles’ rotations. Above the critical field strength, the particles’ stable steady angles were determined. In a weak magnetic regime (below the critical field strength), a paramagnetic particle’s polar angle will oscillate toward the magnetic field plane while its azimuthal angle will execute periodic rotations. A ferromagnetic particle’s rotation depends on its initial angles and the magnetic field strength and direction. Even when it is exposed to a critical magnetic field strength, its rotational dynamics will either be pinned in or out of the magnetic field plane. In a weak magnetic regime, a ferromagnetic particle will either execute out-of-plane rotations or will oscillate toward the magnetic field plane and perform periodic rotations. For both particles, we analytically determine the peaks and troughs of their oscillations and study their time-dependent rotations through analytical and numerical analyses.

### A generalized minimal residual method-based immersed boundary-lattice Boltzmann flux solver coupled with finite element method for non-linear fluid-structure interaction problems

A generalized minimal residual method (GMRES) based immersed boundary-lattice Boltzmann flux solver (IB-LBFS) coupled with the finite element method (FEM) is presented in this paper for nonlinear fluid-structure interaction (FSI) problems. This approach effectively combines LBFS for the simulation of the flow field, the total Lagrangian FEM for the evaluation of nonlinear structural deformations, and the immersed boundary method (IBM) for the exchange of information on the fluid-solid interface and implementation of boundary conditions. Both the multidirect forcing and the implicit IBM are considered to examine their effects on numerical accuracy and efficiency. Through numerical simulations on flow past a cylinder, it is shown that the implicit IBM with the GMRES for the linear equation system is more efficient and accurate, which justify the conventional misunderstanding that implicit IBM is always less efficient than explicit methods. Numerical simulations on the lid-driven cavity flow in an inclined cavity, incompressible flows of a uniformly accelerated vertical plate, and the flow induced vibrations of a beam attached behind a cylinder in a channel are also successfully carried out and the obtained results are in good agreement with the published data, which verify the reliability and flexibility of the proposed solver for simulating nonlinear FSI problems. After that, the external flows past two hyperelastic cylinder-beam structures at the Reynolds number of 40–300 are studied and three different modes of static, linear, and nonlinear deformations of the beam are obtained, demonstrating its capability of simulating flows with nonlinear FSI problems with multiple deformable objects.

### Wake adjustment and vortex-induced vibration of a circular cylinder with a C-shaped plate at a low Reynolds number of 100

The vortex-induced vibration (VIV) of a circular cylinder with a C-shaped plate arranged in its wake at a low Reynolds number of 100 is numerically investigated in this work using the direct numerical simulation. Four typical streamwise spacing ratios of 1.5, 3, 4.5, and 6 are examined in the computations that were carried out for the range of reduced velocities (Ur = 2–12). In terms of shear layer reattachment, wake interference, and vortex shedding, five flow regimes are identified, i.e., the extended-body regime, the front-face reattachment regime, the shear-layer combination regime, the one-row co-shedding regime, and the two-row co-shedding regime. The wake regime is sensitive to the spacing ratio and the reduced velocity. The switching of the flow regime occurs at the transition between the initial VIV branch and the lower VIV branch, accompanying a phase jump of 180°. Furthermore, the shift of the wake regime leads to the prominent fluctuation of the response amplitude. Among the five regimes, the two-row co-shedding regime has the maximum wake width, resulting in the maximum amplitude. In contrast, the shear layers are elongated in the extended-body regime and hence the prolongation of the vortex formation length, contributing to the suppression of VIV. The best suppression is achieved by placing the C-shaped plate behind the cylinder with a spacing of 1.5D, and the reductions in the lift force and the cross-flow amplitude reach 85.5% and 94.5%, respectively.

### Edge flame propagation statistics in igniting monodisperse droplet-laden mixtures

The effects of droplet diameter, overall (i.e., liquid+gaseous phases) equivalence ratio, and turbulence intensity on the edge flame propagation statistics for localized forced ignition of uniformly dispersed n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on direct numerical simulations data. It has been found that the edge flame structure becomes increasingly prominent for large overall equivalence ratios and droplet diameters. Although the mean edge flame speed has been found to be positive and its most probable value remains comparable to the theoretical value for laminar edge flames in purely gaseous mixtures, the mean values have been found to decrease and the probabilities of finding locally negative edge flame speeds have been found to increase with increasing turbulence intensity. The marginal probability density function and curvature and strain rate dependences of the edge flame speed have been found to be principally governed by the displacement speed of the fuel mass fraction isosurface intersecting the stoichiometric mixture fraction isosurface. The displacement speed of the stoichiometric mixture fraction isosurface has also been found to influence the local scalar gradient dependences of the edge flame speed in this configuration, especially for large droplets. The displacement speed of the fuel mass fraction isosurface Sd has been found to be principally governed by leading order contributions of the reaction and molecular diffusion components and the evaporation contribution remains weak in comparison to these leading order contributors. The local edge flame speed exhibits nonlinear curvature and strain rate dependences and its variation with the magnitudes of both fuel mass fraction and mixture fraction gradients has been found to be nonmonotonic for all cases considered here. The correlations of the edge flame speed with curvature, strain rate, and scalar gradient have been found to be qualitatively similar to the corresponding statistics reported in the existing literature for edge flames in purely gaseous mixtures. Additionally, the curvature and tangential strain rate dependences of the edge flame speed have been found to be dependent on the droplet size and overall equivalence ratio, and these dependences become weak for cases with large droplets.

### Response to “Comment on ‘A periodic grain consolidation model of porous media’” [Phys. Fluids 31, 109101 (2019)]

### Comment on “A periodic grain consolidation model of porous media” [Phys. Fluids A 1, 38 (1989)]

In this document, we correct the friction coefficient values presented in Table III in a study by Larson and Higdon [“A periodic grain consolidation model of porous media,” Phys. Fluids A 1, 38 (1989)]. The authors addressed the problem of Stokes flow through periodic arrays of (non)overlapping spheres and determined the friction coefficients. It appears that the volume of the overlapping region of spheres was not taken into account, which affected the total solid concentration and systematically biased the corresponding friction coefficient values. We correct the sphere concentration and friction coefficients, and validate our approach with lattice-Boltzmann simulations. The suggested correction is valid in the case of overlapping spheres only, when the volume of the overlapping region is positive.

### Hydrodynamics and rheology of a vesicle doublet suspension

Author(s): Bryan Quaife, Shravan Veerapaneni, and Y.-N. Young

Effects of membrane-membrane adhesion on vesicle hydrodynamics are studied theoretically (using lubrication theory) and numerically (using time-adaptive boundary integral simulations). Novel vesicle dynamics are quantified to help design future microfluidic experiments to probe membrane adhesion.

[Phys. Rev. Fluids 4, 103601] Published Thu Oct 10, 2019

### Influence of Langmuir adsorption and viscous fingering on transport of finite size samples in porous media

Author(s): Chinar Rana, Satyajit Pramanik, Michel Martin, A. De Wit, and Manoranjan Mishra

We combine two known independent phenomena, viscous fingering dynamics in miscible fluids and nonlinear wave fronts, to investigate how these two nonlinear dynamics interact. The difference between cases with/without nonlinear adsorption of solute arise in creation/annihilation of nonlinear waves.

[Phys. Rev. Fluids 4, 104001] Published Thu Oct 10, 2019

### Inertial migration of a deformable particle in pipe flow

Author(s): Dhiya Alghalibi, Marco E. Rosti, and Luca Brandt

A study of the migration of a hyperelastic particle suspended in a Newtonian pipe flow for different Reynolds numbers and elasticity is presented. The particle deforms and undergoes a lateral displacement while traveling downstream through the pipe, finally focusing at the pipe centerline.

[Phys. Rev. Fluids 4, 104201] Published Thu Oct 10, 2019

### Dynamic Leidenfrost behaviors of different fluid drops on superheated surface: Scaling for vapor film thickness

For an impact drop on a superheated surface, the dynamic Leidenfrost temperature, TLF, depends on several parameters such as impact velocity, vapor layer thickness, and thermophysical properties of the fluids. In this letter, we derived a scaling formula for TLF using the well-known balance relation between the pressures exerted by drop impact and evaporated vapor flow. As the TLF scale intrinsically requires estimating the vapor film thickness δv, it should be scaled based on the consideration of relevant physics postulated on the impact drop and evaporated vapor. Thus, for proper scaling of δv, we considered the drop–vapor interface deformation by drop inertial and surface tension forces during initial impact of drop. Results showed that δv could be scaled with drop diameter D0 and Weber number We. For drops with low We (<10), δv scaled to ∼D0We−1/4 and ∼D0We−2/5 for drops with higher We. The explicit scale for TLF agreed well with present experimental data.

### Bi-global stability analysis in curvilinear coordinates

A method is developed to solve biglobal stability functions in curvilinear systems which avoids reshaping of the airfoil or remapping the disturbance flow fields. As well, the biglobal stability functions for calculation in a curvilinear system are derived. The instability features of the flow over a NACA (National Advisory Committee for Aeronautics) 0025 airfoil at two different angles of attack, corresponding to a flow with a separation bubble and a fully separated flow, are investigated at a chord-based Reynolds number of 100 000. The most unstable mode was found to be related to the wake instability, with a dimensionless frequency close to one. For the flow with a separation bubble, there is an instability plateau in the dimensionless frequency ranging from 2 to 5.5. After the plateau and for an increasing dimensionless frequency, the growth rate of the most unstable mode decreases. For a fully separated flow, the plateau is narrower than that for the flow with a separation bubble. After the plateau, with an increased dimensionless frequency, the growth rate of the most unstable mode decreases and then increases once again. The growth rate of the upstream shear layer instability was found to be larger than that of the downstream shear layer instability.

### Asymmetric vortexes induced traveling drop on an oscillatory liquid bath

The traveling and dancing behaviors of the bouncing drops on the oscillating liquid bath have been reported in several investigations. It was shown that the normal force during the impact of the drop on an inclined liquid surface is responsible for the traveling of a 0.8 mm-sized drop. Here, we report that a pair of vortexes can be induced by the repeated impact of a 2 mm-sized drop on an oscillatory liquid bath. The traveling of a large drop on the oscillatory liquid bath with an inclined bottom is found to be associated with the induced asymmetric vortex flow underneath the liquid surface. The effect of the vortex flow becomes significant for the size of a drop larger than 1.8 mm. Two-coupled drops with different sizes are found to be self-propelled on the oscillatory liquid bath with a flat bottom. The coupled drops propagate toward the direction of the small-sized drop. The distribution of the vortex flow is investigated by the particle image velocimetry (PIV) technique and the numerical simulation of the acoustic streaming model. PIV measurement and numerical simulation of the speed distribution of the vortex flows induced by the single bouncing drop and two-coupled drops show consistent results. It is suspected that the traveling of two-coupled drops is associated with the motion of the small drop and the liquid flow near the liquid surface.

### Air-water meniscus shape in superhydrophobic triangular microgroove is dictated by a critical pressure under dynamic conditions

We bring out a critical force for shape transition of air-water meniscus in superhydrophobic triangular microgrooves under dynamic conditions, considering an intricate interplay of the viscous and capillary forces. A closed form theoretical expression for the critical force depicts its explicit dependence on the groove geometry and relevant physical properties. A negative value of this critical force denotes a convex meniscus shape, whereas a positive value signifies a concave meniscus shape. Considering the shape transition, the critical pressure is further interpreted to denote a physical condition under which the meniscus is nontrivially flat, despite the existence of surface tension forces. Our analysis opens up a paradigm by which the meniscus shape in a groove can be virtually controlled at will, consistent with the specific requirements such as drag reduction, as demanded by the application on hand.

### The jet characteristics of bubbles near mixed boundaries

The jet characteristics of bubbles near mixed boundaries have been the focus of research in many fields. As the associated parameters are complicated, relatively few reports have been published. In this paper, a numerical model is established by considering the influence of the free surface and a mutual vertical wall using the boundary element method. To determine the jet characteristics of collapsing bubbles in different areas, two nondimensional parameters must be investigated: the distance γv from the bubble to the vertical wall and the distance γh from the bubble to the horizontal wall. At the same time, the buoyancy parameter δ cannot be ignored. First, the jet characteristics under an infinite vertical solid wall are discussed; furthermore, the jet direction in the stage of collapsing bubble under combined boundaries without buoyancy is studied, and we find that the variation amplitude of the jet angle changes with the free surface. Considering the buoyancy, we then divide the total area into six regions with different ranges of jet angle under small buoyancy values, allowing the significant effect of buoyancy to be studied as δ increases. In addition, we study the jet velocity qualitatively under the condition of negligible buoyancy and find that a peak jet velocity may exist at mid water depths.

### An investigation for influence of intense thermal convection events on wall turbulence in the near-neutral atmospheric surface layer

Based on the field observation data in the near-neutral atmospheric surface layer (ASL) at the Qingtu Lake Observation Array, a new experimental data processing of the second-order statistic distribution of the high Reynolds number wall turbulence was presented which considered the influence of the intense thermal convection events (ITCEs). Following the conventional data selection in the literature, i.e., |z/L|, it is known that the variation of the large- and/or the very-large-scale motions (LSMs and VLSMs) cannot be effectively performed only by this method, which motivates us to find other factors influencing these turbulent motions, e.g., the ITCEs. From the data analysis of the probability density distribution of vertical heat flux, it is found that although its mean value tends to zero, its variance is large rather than zero, which suggests to us some ITCEs exist in the natural motions, although it has less frequent occurrences. In order to characterize the effect of such ITCEs, an additional parameter ψ for scaling the ratio of the buoyancy force to the viscous force is proposed in the data selection progress. The results show that the greater the |ψ|, the greater the impact of the ITCEs on ASL wall turbulence. Furthermore, our investigation reveals that the ITCEs may be one of the reasons why the VLSMs exhibit the Top-Down mechanism.

### Quasi-classical trajectory-based non-equilibrium chemical reaction models for hypersonic air flows

Phenomenological models, such as Park’s widely used two temperature model, overpredict the reaction rate coefficients at vibrationally cold conditions and underpredict it at vibrationally hot conditions. To this end, two new chemical reaction models, the nonequilibrium total temperature (NETT) and nonequilibrium piecewise interpolation models for the continuum framework are presented. The focus is on matching the reaction rate coefficients calculated using a quasiclassical trajectory based dissociation cross section database. The NETT model is an intuitive model based on physical understanding of the reaction at a molecular level. A new nonequilibrium parameter and the use of total temperature in the exponential term of the Arrhenius fit ensure the NETT model has a simple and straightforward implementation. The efficacy of the new model was investigated for several equilibrium and nonequilibrium conditions in the form of heat bath simulations. Additionally, two-dimensional hypersonic flows around a flat blunt-body were simulated by employing various chemical reaction models to validate the new models using experimental shock tube data. Park’s two temperature model predicted higher dissociation rates and a higher degree of dissociation leading to lower peak vibrational temperatures compared to those predicted by the new nonequilibrium models. Overall, the present work demonstrates that the new nonequilibrium models perform better than Park’s two temperature model, especially in simulations with a high degree of nonequilibrium, particularly as observed in re-entry flows.

### Effects of upstream pipe length on pipe-cavity jet noise

An experimental study is carried out to quantify the acoustic radiation of underexpanded pipe-cavity jet noise. Pipe-cavity configurations with different upstream pipe lengths are studied over a range of Mach numbers. Detailed acoustic measurements such as frequency analysis, sound pressure levels, directivity, and acoustic power analysis are carried out to show the effect of upstream pipe length. Finite element simulations are carried to predict the resonance frequencies of the pipe-cavity. Results of simulation with zero mean flow condition match well with theoretical results and the present experiments. The far-field acoustic spectrum exhibits strong cavity tones and shock associated noise. The results show that the pipe-cavity resonates close to the combined tangential-longitudinal mode. The increase in shear layer thickness tends to attenuate the cavity tones, with a small increase in screech tonal noise. An increase in upstream pipe length leads to a decrease in overall sound pressure levels and acoustic power.

### Phase transition in time-reversible Navier-Stokes equations

Author(s): Vishwanath Shukla, Bérengère Dubrulle, Sergey Nazarenko, Giorgio Krstulovic, and Simon Thalabard

We present a comprehensive study of the statistical features of a three-dimensional (3D) time-reversible truncated Navier-Stokes (RNS) system, wherein the standard viscosity ν is replaced by a fluctuating thermostat that dynamically compensates for fluctuations in the total energy. We analyze the st...

[Phys. Rev. E 100, 043104] Published Wed Oct 09, 2019

### Normal form of synchronization and resonance between vorticity waves in shear flow instability

Author(s): Eyal Heifetz and Anirban Guha

A minimal model of linearized two-dimensional shear instabilities can be formulated in terms of an action-at-a-distance, phase-locking resonance between two vorticity waves, which propagate counter to their local mean flow as well as counter to each other. Here we analyze the prototype of this inter...

[Phys. Rev. E 100, 043105] Published Wed Oct 09, 2019