# Latest papers in fluid mechanics

### Vortex system around a step cylinder in a turbulent flow field

The vortex system around the step surface of a step cylinder with a diameter ratio [math] at Reynolds number (ReD) 3900 was investigated by directly solving the three-dimensional Navier–Stokes equations. Formation mechanisms and vortex dynamics of the complex vortex system were studied by performing a detailed investigation of both the time-averaged and instantaneous flow fields. For the time-averaged flow, including the known junction and edge vortices, in total, four horseshoe vortices were observed to form above the step surface in front of the upper small cylinder. The crossflow width of the four horseshoe vortices varies differently as they convect downstream. Moreover, we captured a pair of base vortices and a backside horizontal vortex in the rear part of the step surface behind the small cylinder. For the instantaneous flow, hairpin vortices were found to form between the legs of two counter-rotating horseshoe vortices located on the same side of the step cylinder. Furthermore, in the small step cylinder wake, Kelvin–Helmholtz vortices were observed to shed at an unexpectedly high shedding frequency.

### Stochastic mesoscale circulation dynamics in the thermal ocean

In analogy with similar effects in adiabatic compressible fluid dynamics, the effects of buoyancy gradients on incompressible stratified flows are said to be “thermal.” The thermal rotating shallow water (TRSW) model equations contain three small nondimensional parameters. These are the Rossby number, the Froude number, and the buoyancy parameter. Asymptotic expansion of the TRSW model equations in these three small parameters leads to the deterministic thermal versions of the Salmon's L1 (TL1) model and the thermal quasi-geostrophic (TQG) model, upon expanding in the neighborhood of thermal quasi-geostrophic balance among the flow velocity and the gradients of free surface elevation and buoyancy. The linear instability of TQG at high wavenumber tends to create circulation at small scales. Such a high-wavenumber instability could be unresolvable in many computational simulations, but its presence at small scales may contribute significantly to fluid transport at resolvable scales. Sometimes, such effects are modeled via “stochastic backscatter of kinetic energy.” Here, we try another approach. Namely, we model “stochastic transport” in the hierarchy of models TRSW/TL1/TQG. The models are derived via the approach of stochastic advection by Lie transport (SALT) as obtained from a recently introduced stochastic version of the Euler–Poincaré variational principle. We also indicate the potential next steps for applying these models in uncertainty quantification and data assimilation of the rapid, high-wavenumber effects of buoyancy fronts at these three levels of description by using the data-driven stochastic parametrization algorithms derived previously using the SALT approach.

### Photoisomeric molecular tagging velocimetry with CCVJ

Author(s): Markus J. Schmidt, Benno Käslin, and Thomas Rösgen

The molecular rotor 9-(2-Carboxy-2-cyanovinyl)julolidine (CCVJ) exists in two isomers. While the E isomer, which is present in the absence of light, yields a fluorescent behavior, the Z isomer is a photoproduct with no detectable luminescence. This regenerative behavior is utilized for Molecular Tagging Velocimetry (MTV).

[Phys. Rev. Fluids 6, 044101] Published Tue Apr 06, 2021

### Numerical study of suspensions of nucleated capsules at finite inertia

Author(s): Arash Alizad Banaei, Armin Shahmardi, and Luca Brandt

We perform simulations of suspension of capsules with nucleus in shear flow. Every capsule is modeled as a neo-Hookean hyperelastic membrane enclosing a rigid particle with radius equal to the half capsule radius. The rheology of the suspensions is related to the capsule deformation and orientation when varying the membrane stiffness and capsule volume fraction and compared to the dynamics of capsules without nucleus.

[Phys. Rev. Fluids 6, 044301] Published Tue Apr 06, 2021

### Direct numerical simulations of a supersonic turbulent boundary layer subject to velocity-temperature coupled control

Author(s): Qiang Liu, Zhenbing Luo, Guohua Tu, Xiong Deng, Pan Cheng, and Panfeng Zhang

A velocity-temperature coupled control method is proposed for turbulence drag reduction of supersonic boundary layers. Direct numerical simulations indicate that heated wall blowing achieves the best drag reduction, whereas cooled wall blowing leads to a drag increase. The reduction of mean viscous shear stress is mainly responsible for the drag reduction mechanism, though there is a substantial increase in Reynolds stresses. Nevertheless, the control efficiency of heated wall blowing is low due to high energy consumption, but further investigation is needed.

[Phys. Rev. Fluids 6, 044603] Published Tue Apr 06, 2021

### Interaction and vectoring of parallel rectangular twin jets in a turbulent boundary layer

Author(s): Girish K. Jankee and Bharathram Ganapathisubramani

Large scale application of synthetic jet actuators requires the implementation of an array of such devices. We investigate the interaction between parallel rectangular twin synthetic jets and an incoming turbulent boundary layer, using stereoscopic PIV measurements. By varying critical parameters, such as the orifice separation distance and the phase difference between the jets, we observed noticeable differences in the vectoring behavior and related shear stresses. These results may be useful in establishing optimum configurations and operating conditions for synthetic jet arrays, in the context of flow control and drag reduction.

[Phys. Rev. Fluids 6, 044701] Published Tue Apr 06, 2021

### Effect of self-assembly on fluorescence in magnetic multiphase flows and its application on the novel detection for COVID-19

In the present study, the magnetic field induced self-assembly processes of magnetic microparticles in an aqueous liquid (the pure magnetic fluid) and nonmagnetic microparticles in ferrofluid (the inverse magnetic fluid) are experimentally investigated. The microparticles are formed into chain-like microstructures in both the pure magnetic fluid and the inverse magnetic fluid by applying the external magnetic field. The fluorescence parameters of these self-assembled chain-like microstructures are measured and compared to those without the effect of magnetic field. It is found that the fluorescence in the pure magnetic fluid is weakened, because the scattering and illuminating areas are reduced in the microstructures. On the contrary, the fluorescence in the inverse magnetic fluid is enhanced, because more fluorescent nonmagnetic microparticles are enriched and become detectable under the effect of the magnetic dipole force and the magnetic levitational force, and their unnecessary scattering can be absorbed by the surrounding ferrofluid. The average enhancement of the fluorescence area ratio in the inverse magnetic fluid with 3 μm nonmagnetic microparticles reaches 112.92%. The present work shows that the inverse magnetic fluid has advantages such as low cost, no scattering effect, stable fluorescence intensity, and relatively low magnetic resistance. In the end, a prototype design for the novel detection of coronavirus disease 2019 based on the magnetic field induced self-assembly in the inverse magnetic fluid is proposed, which could support the epidemic prevention and control.

### Single- and dual-mode Rayleigh–Taylor instability at microscopic scale

The microscopic Rayleigh–Taylor instability (RTI) is studied via molecular dynamics (MD) simulation for single- and dual-mode interfaces under a strong acceleration. The growth behavior of microscopic RTI as well as the underlying regime exhibits considerable differences from the macroscopic counterpart. At a microscopic scale, the flow Reynolds number is very low and thus viscosity effect plays an important role, namely, it suppresses the growth of overall perturbation amplitude and also damps the growth of harmonics. As a result, the microscopic RTI presents a much weaker nonlinearity. Also, the motion of atoms produces random fluctuations to the evolving interface, which cause the detachment of droplets from the spike under the action of surface tension at late stages. In addition, the mode coupling behavior in dual-mode RTI at a microscopic scale is evidently different from the macroscopic counterpart, and a new prescription dominating the growth of each mode is proposed. Based on these findings, a semi-empirical model applicable to the microscopic RTI from early to late stages is developed, which gives a satisfactory prediction of the MD results.

### Simulations of stably stratified flow past two spheres at Re = 300

Flows past two spheres immersed in a horizontally moving, linearly stratified fluid are investigated at a moderate Reynolds number of 300. Characterization of flow patterns considers representative geometrical configurations defined by varying both the distance between the spheres and their relative orientation to the free stream direction. Simulations are performed on unstructured meshes chosen to accurately resolve the dynamics of fluids in regions close to the spheres for Froude numbers [math]. Results illustrate the evolution of boundary layers, separation, and the wakes interaction under the influence of a gravity induced buoyancy force. Computations utilize a limited area, nonhydrostatic model employing non-oscillatory forward-in-time integration based on the multidimensional positive definite advection transport algorithm. The model solves the Navier–Stokes equations in the incompressible Boussinnesq limit, suitable for describing a range of mesoscale atmospheric flows. Results demonstrate that stratification progressively dominates the flow patterns as the Froude number decreases and that the interactions between the two spheres' wakes bear a resemblance to atmospheric flows past hills.

### Eigenmode analysis of membrane stability in inviscid flow

Author(s): Christiana Mavroyiakoumou and Silas Alben

We study the stability of a thin membrane (of zero bending rigidity) with a vortex sheet as a nonlinear eigenvalue problem in the parameter space of membrane mass (R1) and pretension (T0). With both ends fixed light membranes become unstable by a divergence instability and heavy membranes lose stability by flutter and divergence for a T0 that increases with R1. With the leading edge fixed and trailing edge free, or both edges free, membrane eigenmodes transition in shape across the stability boundary. We find good quantitative agreement with unsteady time-stepping simulations at small amplitude, but only qualitative similarities with the eventual steady-state large-amplitude motions.

[Phys. Rev. Fluids 6, 043901] Published Mon Apr 05, 2021

### Constrained large-eddy simulation of turbulent flow over rough walls

Author(s): Wen Zhang, Minping Wan, Zhenhua Xia, Jianchun Wang, Xiyun Lu, and Shiyi Chen

Structures of wall turbulence due to the mean shear created by the wall are generated. Numerical tests are performed with the rough-wall-like mean shear imposed in the near-wall region without resolving the surface roughness in the constrained large-eddy simulation. The results indicate that the major effects of roughness on wall turbulence can be well reproduced.

[Phys. Rev. Fluids 6, 044602] Published Mon Apr 05, 2021

### Local force calculations by an improved stress tensor discontinuity-based immersed boundary–lattice Boltzmann method

In the immersed boundary method, the volume force that is applied to enforce the no-slip boundary condition is equivalent to a discontinuity in the stress tensor across the boundary. In the stress tensor discontinuity-based immersed boundary–lattice Boltzmann method, which was proposed in our previous study [Suzuki and Yoshino, “A stress tensor discontinuity-based immersed boundary–lattice Boltzmann method,” Comput. Fluids 172, 593–608 (2018)], the boundary is represented by Lagrangian points that are independent of the background grid, and the discontinuity in the stress tensor is calculated on these points from desired particle distribution functions that satisfy the no-slip boundary condition based on the bounce-back condition. Although this method allows computation of the force locally acting on the boundary, the local force has a spurious oscillation along the boundary. In the present study, we remedy this problem by relaxing the bounce-back condition. To confirm the improvement achieved by using the new method, we apply it to simulate typical benchmark problems involving two- and three-dimensional flows with stationary or moving boundaries. We find that the proposed approach can effectively eliminate the spurious oscillation of the local force, and the results obtained with the improved method show good agreement with other numerical and experimental results. In addition, as an application of the proposed method to local force calculation, we investigate the effect of lift enhancement due to wing–wake interaction on a two-dimensional butterfly-like flapping wing.

### Full-scale simulation of self-propulsion for a free-running submarine

It is important to predict the self-propulsion performance of full-scale marine vessels during the design stage. With the development of high-performance computational techniques, full-scale ship-free running simulations focused on self-propulsion performance are receiving increased attention. This study presents the results of computational fluid dynamics (CFD) simulations for a full-scale submarine propelled by a high-skew propeller. An in-house CFD code with the dynamic overset grid approach is used to simulate the rotational motion of the propeller. First, model- and full-scale simulations focused on submarine resistance and propeller open-water performance are conducted, enabling a systematic convergence study of the model. The self-propulsion performance is then predicted at the model scale, and comparisons with other available results show only small discrepancies. Finally, full-scale submarine self-propulsion simulations are conducted and the results are compared with those from the model-scale simulations with the addition of skin friction correction. Discussions on the differences between model- and full-scale self-propulsion results are presented including propeller performance, pressure distribution, boundary layer, and wake flow.

### Parametric sensitivities of the generalized binomial Langevin–multiple mapping conditioning model

The binomial Langevin model (BLM) predicts mixture fraction statistics including higher moments excellently, but imposing boundedness for the large scalar spaces typically associated with chemically reacting flows becomes intractable. This central difficulty can be removed by using the mixture fraction as the reference variable in a generalized multiple mapping conditioning (MMC) approach. The resulting probabilistic BLM–MMC formulation has several free parameters that impact the turbulence–chemistry interactions in complex flows: the dissipation timescale ratio, the locality in selecting pairs of particles for mixing, and the fraction of particles mixed per time step. The impact of parametric variations on the behavior of the BLM–MMC model is investigated for a complex flow featuring auto-ignition to determine model sensitivities and identify optimal values. It is shown that only the mixture fraction rms is sensitive to the dissipation timescale ratio with the expected behavior of an increased ratio leading to a reduction in rms. Controlling locality by increasing the maximum possible distance between paired particles in reference space has a similar impact. Increasing the fraction of particles mixed only affects reacting scalars by advancing ignition. The modified Curl's model is used for the mixing process and the specified amount of mixing principally controls the local extinction and reignition behavior. It is further shown that the standard value of the dissipation timescale ratio is satisfactory; the amount of mixing should be half that specified by Curl's model; and the distance between particle pairs in reference space should be proportional to the diffusion length scale.

### An implicit kinetic inviscid flux for predicting continuum flows in all speed regimes

In this study, the kinetic inviscid flux (KIF) is improved and coupled with an implicit strategy. The KIF is a recently proposed numerical method, which is a dynamic combination of the kinetic flux vector splitting (KFVS) method and the totally thermalized transport (TTT) method. The inherent microscopic mechanism of the KFVS makes the KIF good at solving shock waves and avoiding the numerical shock instability phenomenon. When developing the implicit KIF, it is noticed that, in boundary layers, the KFVS part of the KIF not only reduces the accuracy but also seriously reduces the Courant–Friedrichs–Lewy (CFL) number. As a result, a new weight is proposed in this paper to combine the KFVS method with the TTT method properly. Besides admitting the use of larger CFL numbers, this new weight also contributes to more accurate numerical results like pressure, friction coefficient, and heat flux when solving shock waves, boundary layers, and complex supersonic/hypersonic flows. To examine the validity, accuracy, and efficiency of the proposed method, six numerical test cases covering the whole speed regime are conducted, including the hypersonic viscous flow past a cylinder, the hypersonic double-cone flow, the hypersonic double-ellipsoid flow, the laminar shock-boundary layer interaction, the supersonic flow around a ramp segment and the subsonic lid-driven cavity flow.

### A fluid–structure interaction simulation on the wake-induced vibration of tandem cylinders with pivoted rotational motion

This paper predicts the wake-induced vibration of tandem cylinders with pivoted rotational or translational motion using the fluid–structure interaction technique. Large eddy simulation using a dynamic Smagorinsky subgrid-scale model is applied for the turbulent flow. Structural computation is applied to obtain the displacement of the downstream cylinder in the cross-flow direction. Conditions such as damping ratio, natural frequency, and mass ratio of pivoted rotational motion are the same as those of translational motion. The computational conditions are [math], corresponding to [math], respectively. The unsteady characteristics of lift, drag, and cross-flow motion of tandem cylinders are investigated. Distributions of pressure, [math] criterion, vorticity, and streakline are also investigated. Finally, the energy harvesting capability of the pendulum system is compared with the translation system.

### Phase decomposition analysis on oscillatory Rayleigh–Bénard turbulence

We carry out numerical simulations of oscillatory Rayleigh–Bénard convection under lateral periodic conditions over the Rayleigh number range of [math] and the vibration frequency range of [math]. It is demonstrated that high-frequency vibration achieves a significant enhancement of the intensity of convective flows and the heat-transport efficiency. The phase decomposition method is adopted to distinguish between the vibration-generated oscillatory flows and the fluctuating fields. It is shown that although the contribution of oscillatory flows on heat transport vanishes, the oscillating properties in near-wall regions introduce a strong shear effect to increase the intensity of fluctuating velocities both in the bulk regime and within boundary layers, destabilize thermal boundary layers, and trigger massive eruptions of thermal plumes, which achieves an enhancement of heat transfer. Our results further reveal a universal scaling law between the vibrational Reynolds and Rayleigh numbers, i.e., [math], which can be well described by our proposed analytical model. Moreover, it is shown that vibrational influences are different for the fluctuating velocity and temperature fields.

### Dynamics of a pair of paramagnetic particles in shear flows under a uniform magnetic field

We numerically investigated the particle–particle interaction and relative motion of a pair of equal-sized magnetic particles in simple shear and plane Poiseuille flows. Two-dimensional numerical models were created by using direct numerical simulations, which are based on the finite element method and arbitrary Lagrangian–Eulerian approach with full consideration of particle–particle, particle–magnetic field, particle–flow field interactions. The effects of direction and strength of magnetic field on the dynamics of the particles in simple shear and plane Poiseuille flows were investigated, respectively. In the simple shear flow, the presence of magnetic field can show stabilizing or destabilizing effect on the particle trajectories, depending on the direction of the magnetic field. Specifically, the particles initially located at closed trajectories moved closer and closer when the magnetic field is applied at 0°and 135°, while they moved further apart and separated when the field is applied at 90°. In the plane Poiseuille flow, the magnetic field changed the relative motion of two particles: it induced two particles to form a chain when a strong magnetic field is applied at 0°and 135°; it separated the two particles when a strong magnetic field is applied at 45°and 90°. This work offers insights toward understanding the mechanisms of particle–particle interaction in magnetorheological fluids in simple shear or plane Poiseuille flows under a uniform magnetic field.

### Dynamics of a droplet on a polymer brush in channel flow

Using dissipative particle dynamics, we simulate an immiscible oil droplet on a polymer brush under a channel flow. Above a critical flow velocity, the droplet slides on the brush surface with contact angle hysteresis. Interestingly, we found the critical sliding velocity to be constant across droplet sizes and interphase interactions. Further increase in flow velocity results in droplet detachment and liftoff from the brush surface. Under poor solvent conditions, large droplets may deform into an airfoil shape, increasing the critical liftoff velocity. On an oleophilic brush, the droplet desorbs and spreads, instead of liftoff. Together, our results show surprisingly rich dynamics coupling three-way interactions between either soft or liquid phases. The present study has implications on the design of polymer brushes, as well as the removal of droplets from soft surfaces using hydrodynamics.

### A one-dimensional model of liquid laminar flows with large Reynolds numbers in tapered microchannels

In this article, we construct a novel one-dimensional model of microfluidic laminar flows in tapered circular and rectangular channels assuming the flow in channels fully developed. In the model, we take into account the inertance and dynamic pressure terms. The model can be used for a wide range of flows: from the pure capillary flow regime, where the capillary forces are the main driver of the liquid in the channel, to the external pressure flow regime where the external pressure applied to the liquid at the entrance to the channel is much larger than the capillary pressure in the channel, so that the capillary force can be ignored. We apply the model to rectangular Y-shape junctions, where the base channel is connected to a reservoir and the end channels are exposed to atmospheric air. We show that, in asymmetric Y-shape junctions, there can be a time of “meniscus arrest,” where only one of the two channels with a smaller radius fills, and, the other one, with a larger radius, is arrested. The time of meniscus arrest decreases with an increase in the applied external pressure; when this pressure becomes large enough, the meniscus arrest disappears. In this article, we also investigate the applicability of the fully developed flow approximation assumed in the model.