# Latest papers in fluid mechanics

### Increasing the efficiency and maneuverability of one-hinge swimmer

Understanding the dynamics of micro-organisms will help in developing artificial swimmers for applications like drug delivery. In the present study, a two-dimensional one-hinge swimmer resembling a scallop in Newtonian fluid is explored. To model the one-hinge swimmer, we use bead-spring model and the fluid is simulated using multi-particle collision dynamics with Anderson thermostat. We consider a non-uniform distribution of the bending rigidity along the arms of the swimmer, where we reduce the bending rigidity progressively from the hinge to the end of the arms. The non-uniform arms show higher swimming speed for the same average bending rigidity, thereby enhancing the efficiency of the swimmer. It was observed that the bending rigidity variation along the arm of the swimmer following a geometric sequence was more efficient than linear or quadratic for the same average bending rigidity. We also study the maneuverability of the one-hinge swimmer having asymmetrical bending rigidity for the arms, thereby the swimmer undergoes curved path. We find that depending upon the stiffness of the arm, the swimmer undergoes clockwise or anticlockwise rotation. We also find that the angular and transnational velocities of the swimmer are maximum at approximately the same sperm number [math]. The angular velocity of the swimmer scaled linearly with the amplitude of actuation as predicted by resistive force theory. Finally, we show that in the case of a two-dimensional one-hinge swimmer angular velocity, curvature and the direction of rotation can be controlled by just changing the relative bending rigidity of the arms.

### Nanoparticle dispersion in porous media: Effects of array geometry and flow orientation

Author(s): Deepak Mangal, Jeremy C. Palmer, and Jacinta C. Conrad

We investigate the effects of array geometry and flow orientation on transport of finite-sized particles in ordered arrays using Stokesian dynamics simulations. We find that quiescent diffusion is independent of array geometry over the range of volume fraction of the nanoposts examined. Longitudinal...

[Phys. Rev. E 104, 015102] Published Tue Jul 06, 2021

### Microscopic understanding of the Johari-Goldstein $β$ relaxation gained from nuclear $γ$-resonance time-domain-interferometry experiments

Author(s): K. L. Ngai

Traditionally the study of dynamics of glass-forming materials has been focused on the structural α relaxation. However, in recent years experimental evidence has revealed that a secondary β relaxation belonging to a special class, called the Johari-Goldstein (JG) β relaxation, has properties strong...

[Phys. Rev. E 104, 015103] Published Tue Jul 06, 2021

### Hydrodynamics of a semipermeable inextensible membrane under flow and confinement

Author(s): Bryan Quaife, Ashley Gannon, and Y.-N. Young

The permeating solvent flux across a lipid bilayer membrane depends on both mechanical and osmotic stresses. In the absence of osmolarity, we use numerical simulations to show that the mechanically induced semipermeability (albeit small) can alter the equilibrium shape of a relaxing vesicle over long timescales, or the hydrodynamics of a vesicle going through the strong confinement of a narrow channel. We further quantify the role of membrane tension and bending on the permeating solvent flux.

[Phys. Rev. Fluids 6, 073601] Published Tue Jul 06, 2021

### Thermocapillary effects on eccentric compound drops in Poiseuille flows

Author(s): Sayali N. Jadhav and Uddipta Ghosh

We analytically study the motion and deformation of an eccentric compound drop subject to an externally imposed temperature gradient and suspended in a Poiseuille flow, using a bispherical coordinate system. The temperature gradient alters surface tensions at the drop interfaces and triggers strong Marangoni flows, altering the drop dynamics. While a positive temperature gradient speeds up both drops, a negative gradient can potentially lead to a stable equilibrium where both drops move with the same velocity. The Marangoni effect also enhances deformation, particularly in the inner drop, which may take either a prolate or an oblate shape.

[Phys. Rev. Fluids 6, 073602] Published Tue Jul 06, 2021

### Effects of confinement on absolute and convective instabilities for momentum-driven countercurrent shear layers

Author(s): Jinwei Yang, Matt J. Anderson, Paul J. Strykowski, and Vinod Srinivasan

We present results from the first experimental realization of a two-dimensional confined countercurrent shear layer driven by momentum flows, without the use of suction. Distinct peaks are observed in the frequency spectrum of velocity fluctuations, suggesting the presence of global instabilities. The variation of these frequencies with injected mass flow rate is predicted reasonably well by a spatiotemporal linear stability analysis of local velocity profiles, which checks for the presence of absolute instability, and suggests that confinement destabilizes the shear layer over a broad range of ratio of shear layer thickness to channel width.

[Phys. Rev. Fluids 6, 073901] Published Tue Jul 06, 2021

### Effect of aspect ratio on flow through and around a porous disk

Author(s): Tingting Tang, Jin Xie, Shimin Yu, Jianhui Li, and Peng Yu

This study provides distinct and complementary information regarding laminar flow through and around porous bluff bodies. For low permeable cases, the recirculating wake behind a thinner disk is longer than that behind a thicker disk; while the opposite trend is observed for high permeable cases. The bifurcation diagrams for wake-existence can be collapsed on roughly the same curve when varying with Darcy number (Da) modified by the aspect ratio, which are also observed for the drag coefficient and the flow rate at the rear surface of the disk. The aspect ratio does not have large effects on the vorticity accumulation and the vorticity decay rate for fixed Reynolds number and Da.

[Phys. Rev. Fluids 6, 074101] Published Tue Jul 06, 2021

### Third-order structure function in the logarithmic layer of boundary-layer turbulence

Author(s): Jin-Han Xie, Charitha de Silva, Rio Baidya, Xiang IA Yang, and Ruifeng Hu

We derive a logarithmic law for the third-order streamwise structure function in the logarithmic layer of a boundary layer. The derivation is based on Townsend’s hypothesis and the Navier-Stokes equation. In addition to the logarithmic law, we get the Townsend-Perry constant via asymptotic matching. Both the scaling and the constant agree well with high Reynolds number data.

[Phys. Rev. Fluids 6, 074602] Published Tue Jul 06, 2021

### Turbulence in a wedge: The case of the mixing layer

Author(s): Yves Pomeau and Martine Le Berre

Modeling of turbulent flows remains a very challenging unsolved problem. Based on symmetries of the fluid equations we propose closure equations expressing the Reynolds stress as a quadratic nonlocal functional of the time averaged velocity field only, contrary to RANS models based upon algebraic handling of the fluid equations which lead to complex nonlinear partial differential equations. We test our model on a mixing layer behind a splitter plate in the limit of infinite Reynolds number. We predict the angular spreading of the turbulent domain as a function of the velocity difference, which has not, to our knowledge, been done with other turbulence models in three-dimensional geometry.

[Phys. Rev. Fluids 6, 074603] Published Tue Jul 06, 2021

### Effect of free-stream inclination and buoyancy on flow past a square cylinder in large-scale heating regime

The combined effects of free-stream inclination (α) and heating [[math]] on aerodynamic and heat transfer parameters are studied at fixed Reynolds number (Re = 100), Prandtl number (Pr = 0.71), cylinder inclination ([math]), Froude number (Fr = 1.0), and Mach number (M = 0.1) in the large-scale heating regime. For this purpose, a non-Oberbeck–Boussinesq compressible model for thermally perfect gases incorporating volumetric straining as well as transport property variations under large-scale heating is employed. The free-stream inclination (α) is varied in the range [[math]] while the over-heat ratio (ϵ) is varied in the range of [0, 1]. It is found that at small free-stream inclinations ([math]), increase in heating causes a significant increase in mean drag coefficient, while at large α ([math]), heating has little effect on mean drag coefficient. The mean lift coefficient (CL) increases by increasing ϵ for any value of α except α = 0. At a fixed heating level, the variation of mean CL is very non-monotonic with lower values at [math] and [math]. It is found that the increase in flow inclination from [math] to [math] reduces the sensitivity of Strouhal number (St) to heating. For [math], mean Nusselt number exhibits a non-monotonic trend with increase in α and attains a maximum value at [math]. However, for [math], heat transfer decreases with increase in α and is maximum for aligned flow ([math]).

### Numerical investigation on the forming and ordering of staggered particle train in a square microchannel

An in-depth understanding of inertial-focusing mechanism is significant to developing high-throughput microfluidic devices. This paper numerically studies the forming and ordering of a staggered particle train in a square microchannel using the immersed boundary-lattice Boltzmann method. Effects of the particle Reynolds number (Rep) and average length fraction (⟨Lf⟩) are mainly concerned, where ⟨Lf⟩ describes the initial particle concentration. Results reveal that the staggered particle train has two distribution patterns depending on ⟨Lf⟩, namely, Continuous Pattern that particles uniformly distributed in the channel and Discontinuous Pattern that an interruption occurs in the train. A detailed train-forming process is provided. Particles within the train are approximately uniformly distributed in both patterns; thus, influencing factors of this uniform interparticle spacing [(L/D)uni] are investigated. A critical ⟨Lf⟩ (⟨Lf⟩*) is defined, dividing determinants of (L/D)uni into Rep-dependent and ⟨Lf⟩-dependent areas. The flow fields and forces acting on the particles were analyzed for further investigation. Four forces are considered: shear gradient lift force, wall-induced lift force, attractive forces, and repulsive forces. Analysis shows that the latter two forces play an essential role in forming a train and the vortex or counterflow is crucial in determining interparticle spacing. Finally, the lagging, translational, and angular velocities were employed to describe particle dynamic characteristics. These parameters are decisively affected by Rep and slightly by ⟨Lf⟩. Inertial-focusing behaviors of a single particle are also compared. The present study is expected to help understand the inertial-focusing behaviors of staggered particle trains and provide a reference for practical applications of microfluidics devices.

### Vortex wakes of tip loaded rotors at low Reynolds numbers

The effect of tip tabs on the flow field of a three bladed rotor/propeller is investigated experimentally. The experiments are run at chord Reynolds numbers of [math]. The tab angles of attack of [math] with respect to the rotation of the rotor are used to vary the tab loading. The rotor wakes and thrust characteristics at positive angles of attack, when the tip loading is outward, are qualitatively similar to those with no-tabs. In contrast, when the tip loading is inward at zero and negative angles of attack, the vortex wake is radically altered; the thrust nearly vanishes, even reverses with increasing inward loading. The key factors influencing the behavior of the wake are the vortex systems of the tabs and their associated downwash. The downwash is inward for the outward tab loading and causes increased volume and momentum flux in the rotor wake, and it is outward for the inward tab loading and causes expansion of the wake and nearly complete loss of thrust. When the tab loading is inward, a quasi-steady bound ring vortex system forms around at the rim of the rotor disk. At tab angle of [math], the flow direction on the pressure side of the rotor disk reverses.

### Energy and flux budget closure theory for passive scalar in stably stratified turbulence

The energy and flux budget (EFB) closure theory for a passive scalar (non-buoyant and non-inertial particles or gaseous admixtures) is developed for stably stratified turbulence. The physical background of the EFB turbulence closures is based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy as well as the turbulent flux of particles. The EFB turbulence closure is designed for stratified geophysical flows from neutral to very stable stratification, and it implies that turbulence is maintained by the velocity shear at any stratification. In a steady-state, expressions for the turbulent flux of the passive scalar and the anisotropic non-symmetric turbulent diffusion tensor are derived, and universal flux Richardson number dependencies of the components of this tensor are obtained. The diagonal component in the vertical direction of the turbulent diffusion tensor is suppressed by strong stratification, while the diagonal components in the horizontal directions are not suppressed, but they are dominant in comparison with the other components of the turbulent diffusion tensor. This implies that any initially created strongly inhomogeneous particle cloud is evolved into a thin pancake in a horizontal plane with very slow increase in its thickness in the vertical direction. The turbulent Schmidt number (the ratio of the eddy viscosity and the vertical turbulent diffusivity of the passive scalar) linearly increases with the gradient Richardson number. The physics of such a behavior is related to the buoyancy force that causes a correlation between fluctuations of the potential temperature and the particle number density. This correlation that is proportional to the product of the vertical turbulent particle flux and the vertical gradient of the mean potential temperature reduces the vertical turbulent particle flux. Considering the applications of these results to the atmospheric boundary-layer turbulence, the theoretical relationships are derived, which allows us to determine the turbulent diffusion tensor as a function of the vertical coordinate measured in the units of the local Obukhov length scale. The obtained relations are potentially useful in modeling applications of particle dispersion in the atmospheric boundary-layer turbulence and free atmosphere turbulence.

### Unveiling the thermal-induced molecular dynamics in fluids: A graph-based heat flow analysis

This paper is the first report of delineating the potential of the graph features in unveiling the complex molecular dynamics in fluids by analyzing the thermal lens signal during the transient heat flow. For this, the thermal lens signals of the three fluids (acetone, ethylene glycol, and coconut oil) of different viscosities are subjected to the complex network analysis after curve fitting the signal. The dynamics is further investigated by segmenting the signal into two. When the rapid change of enthalpy appears as clusters in the graph, the quasi-steady state appears as uncorrelated nodes. The increased enthalpy in the second region accounts for the low refractive index, random molecular dynamics, and uncorrelated nodes. The transition time demarcating the two regions is found to increase with the viscosity of the fluid. The role of viscosity on the features of the graph is also clearly brought out. This study unveils the potential of graph-based features in the heat flow analysis and their suitability for applications in thermal engineering.

### Effect of dual vortex shedding on airfoil tonal noise generation

To improve understanding of dual vortex shedding over a trailing edge with regard to airfoil tonal noise generation, synchronized velocity and noise measurements are conducted on a NACA (National Advisory Committee for Aeronautics) 0012 airfoil at angle of attack near zero and a Reynolds number of 220 000. Instantaneous flow fields obtained by particle image velocimetry show the development of separated shear layer, vortex roll-up, and vortex breakup near the airfoil trailing edge. The time-averaged flow fields feature separation bubbles on both sides, and the root mean square values of streamwise velocity fluctuations show triple peak structures. The velocity spectra agree well with the noise spectra in terms of broadband humps and discrete tones. Through proper orthogonal decomposition (POD) analysis, the most energetic modes are identified, which represent global structures in the flow field. The trailing edge noise being an integral effect of the velocity fluctuation near the trailing edge, the POD analysis provides an alternative view for understanding the noise generation mechanism. The first and second modes are dominated by out-of-phase vortex shedding along the airfoil surface and in the near wake, which dominates the high amplitude noise emission process. The third and fourth modes represent in-phase vortex shedding, which dominates the low amplitude noise emission process. The noise source region is determined by the correlation between the velocity and sound pressure, which shows approximately the same periodic pattern as the first and second POD modes.

### Numerical and experimental study on high-speed hydrogen–oxygen combustion gas flow and aerodynamic heating characteristics

The need to increase the payload capacity of the rockets motivates the development of high-power rocket engines. For a chemical propulsion system, this results in an increasing thermal load on the structure, especially the combustion chamber and nozzle must be able to withstand the extreme thermal load caused by high-temperature and high-pressure combustion gas. In order to protect the structure from the effect of increasing heat flux, it is necessary to counteract such effect with more advanced thermal management technology. This requires us to accurately predict the aerodynamic heating of the structure by high-temperature and high-speed combustion gas. In this study, a high-temperature combustion gas tunnel developed in the laboratory is used to produce high-speed combustion gas. Combined with the results of numerical calculation, the flow and aerodynamic heating characteristics of air and hydrogen–oxygen combustion gas under the same total temperature and pressure are analyzed and compared. The comparison revealed that the combustion gas flow in the nozzle has higher static temperature, velocity, and smaller Mach number. When the combustion gas flows around the sphere, the shock standoff distance and stagnation pressure are smaller than those of air, and the wall heat flux is much larger than that of air. The active chemical reaction in the combustion gas makes the aerodynamic heating of the structure more severe. Finally, through the analysis of a large amount of data, a semi-empirical formula for the heat flux of the stagnation point heated by a high-speed hydrogen and oxygen equivalent ratio combustion gas is obtained.

### Electrowetting of a leaky dielectric droplet under a time-periodic electric field

Author(s): Dipin S. Pillai, Kirti Chandra Sahu, and Ranga Narayanan

We develop a simplified nonlinear model for the dynamics of a highly wetting sessile droplet under an alternating (AC) electrostatic field. The model is suitable for weakly conducting fluids with charges confined on the interface, and reproduces the perfect conductor and dielectric droplet limits. The effect of Maxwell stress on droplet shape deformation (DSD) and contact line motion (CLM) are of particular interest. We show the emergence of a favorable forcing frequency which leads to maximum amplitude in DSD and CLM, a consequence of competition between forcing and wetting timescales. Further, the effect of different fluid electromechanical properties on DSD and CLM are investigated.

[Phys. Rev. Fluids 6, 073701] Published Fri Jul 02, 2021

### Publisher's Note: “A scaling improved inner–outer decomposition of near-wall turbulent motions” [Phys. Fluids 33, 045120 (2021)]

### Low-frequency, spanwise oscillation in a finite-width cavity at Mach 1.5

A joint experimental–computational program examined low-frequency, spanwise oscillations in supersonic flow over a finite-width cavity. Lowpass-filtered rear wall surface pressure revealed that shear layer impingement was most often biased to one side of the wall, switching sides at a frequency two orders of magnitude below resonance. Therefore, a bifurcation into two spanwise-asymmetric, mirrored, quasi-steady states could be defined. The states were described by biased impingement/ejection near the rear wall, asymmetry of the shear layer, and centrifugal inner-cavity flow. Resonance amplitudes were also found to be spatially modulated by the low-frequency flow switching. A yawed inflow was found to force one of the asymmetric states.