# Latest papers in fluid mechanics

### Multiscaling analysis of buoyancy-driven turbulence in a differentially heated vertical channel

Author(s): Tie Wei

A three-layer structure is proposed for a differentially heated vertical channel, based on the properties of force balance in the mean momentum equation. A three-layer structure is also proposed for the mean heat equation. A multiscaling analysis is developed for the inner and outer layers.

[Phys. Rev. Fluids 4, 073502] Published Thu Jul 25, 2019

### Analysis of the equilibrium wall model for high-speed turbulent flows

Author(s): Prahladh S. Iyer and Mujeeb R. Malik

Available direct numerical simulation databases are used to study the sensitivity of wall model predictions to different eddy viscosity models, damping function scalings, and associated constants. A new “mixedmin2” damping function scaling is proposed, which works better for high-speed flows over a range of conditions.

[Phys. Rev. Fluids 4, 074604] Published Thu Jul 25, 2019

### Modulation of time-mean and turbulent flow by suspended sediment

Author(s): Hadis Matinpour, Sean Bennett, Joseph Atkinson, and Michele Guala

Experiments are conducted to study the effects of suspended sediment on flow dynamics in a mixing box. Results from particle image velocimetry, providing the velocity of the sediment and fluid phases separately, demonstrate the formation of a stratified layer where turbulent modulation increases.

[Phys. Rev. Fluids 4, 074605] Published Thu Jul 25, 2019

### On the origin and structure of a stationary circular hydraulic jump

To elucidate the role played by surface tension on the formation and on the structure of a circular hydraulic jump, the results from three different approaches are compared: the shallow-water (SW) equations without considering surface tension effects, the depth-averaged model (DAM) of the SW equations for a flow with a parabolic velocity profile, and the numerical solutions of the full Navier-Stokes (NS) equations, both considering the effect of surface tension and neglecting it. From the SW equations, the jump can be interpreted as a transition region between two solutions of the DAM, with the jump’s location virtually coinciding with a singularity of the DAM’s solution, associated with the inner edge of a recirculation region near the bottom. The jump’s radius and the flow structure upstream of the jump obtained from the NS simulations practically coincide with the results from the SW equations for any flow rate, liquid properties, and downstream boundary conditions, being practically independent of surface tension. However, the structure of the flow downstream of the jump predicted by the SW equations is quite different from the stationary flow resulting from the NS simulations, which strongly depends on surface tension and on the downstream boundary conditions (radius of the disk). One of the main findings of the present work is that no stationary and axisymmetric circular hydraulic jump is found from the NS simulations above a critical value of the surface tension, which depends on the flow conditions, fluid properties, and downstream conditions.

### Time-resolved turbulent velocity field reconstruction using a long short-term memory (LSTM)-based artificial intelligence framework

This paper focuses on the time-resolved turbulent flow reconstruction from discrete point measurements and non-time-resolved (non-TR) particle image velocimetry (PIV) measurements using an artificial intelligence framework based on long short-term memory (LSTM). To this end, an LSTM-based proper orthogonal decomposition (POD) model is proposed to establish the relationship between velocity signals and time-varying POD coefficients obtained from non-TR-PIV measurements. An inverted flag flow at Re = 6200 was experimentally measured using TR-PIV at a sampling rate of 2000 Hz for the construction of training and testing datasets and for validation. Two different time-step configurations were employed to investigate the robustness and learning ability of the LSTM-based POD model: a single-time-step structure and a multi-time-step structure. The results demonstrate that the LSTM-based POD model has great potential for time-series reconstruction since it can successfully recover the temporal revolution of POD coefficients with remarkable accuracy, even in high-order POD modes. The time-resolved flow fields can be reconstructed well using coefficients obtained from the proposed model. In addition, a relative error reconstruction analysis was conducted to compare the performance of different time-step configurations further, and the results demonstrated that the POD model with multi-time-step structure provided better reconstruction of the flow fields.

### Combining particle-in-cell and direct simulation Monte Carlo for the simulation of reactive plasma flows

A combined approach for the simulation of reactive, neutral, partially or fully ionized plasma flows is presented. This is realized in a code framework named “PICLas” for the approximate solution of the Boltzmann equation by particle based methods. PICLas combines the particle-in-cell method for the collisionless Vlasov–Maxwell system and the direct simulation Monte Carlo method for neutral reactive flows. Basic physical and mathematical modeling of both methods is addressed, and some application examples are presented in order to demonstrate the capabilities and the broad applicability of the solution strategy.

### Aspect ratio dependence of Rayleigh-Bénard convection of cold water near its maximum density in box-shaped containers

The aim of this research is to understand the effect of the aspect ratio on the heat transfer ability and hydrodynamics characteristics of Rayleigh-Bénard convection of cold water near its maximum density in box-shaped containers. The Rayleigh number is fixed at 109, density inversion parameters are 0.3, 0.5 and 0.7, and the aspect ratio ranges from 1/60 to 1. Results indicate that the average Nusselt number presents a weak dependence on the aspect ratio at the large aspect ratio (A > 0.3). However, it reaches the maximum and then drops when the aspect ratio decreases from A = 0.3. Large scale circulations are observed for containers at the large aspect ratio, and the confinement of sidewalls weakens the large-scale circulation and eventually destructs it. At the large aspect ratio, the velocity fluctuation near the sidewalls is stronger than that in the center zone, because plumes primarily move along the sidewalls of the container. At a small aspect ratio, more plumes appear in the center of the container, where the fluctuation is stronger than that near sidewalls. The effect of cold plumes on the flow is reduced as the density inversion parameter increases. Therefore, the flow is mainly driven by hot plumes, and the velocity magnitude and fluctuation decrease significantly.

### Aerodynamic interaction of collective plates in side-by-side arrangement

In the tip-reversal upstroke of avian flight, individual feathers twist so as to create gaps between them. Although this behavior allows the feathers to function as individual lift-generating bodies, the lift generation mechanism of these multiple bodies remains unclear. This paper reports a numerical investigation of multiple stationary plates arranged side by side in a uniform flow. The aim is to elucidate the collective mechanism of the flow generated by the plates and the lift contribution of each plate. The angle of attack of each plate and the gap between the plates are varied to determine their influence on the flow and lift of the collection of plates. The time-averaged lift increases from the lowermost to the uppermost plate, and, at a high angle of attack, the total lift coefficient of the plates becomes greater than that of a single plate solely placed in a uniform flow. At a high angle of attack, vortex shedding from the upper plates is synchronized with some phase difference, resulting in synchronized lift fluctuations for individual plates and a reduction in the overall fluctuation amplitude. With an optimal gap ratio and angle of attack, the collective behavior of plates in side-by-side arrangement can be advantageous to enhance lift-generation performance.

### On the onset of convection in a highly permeable vertical porous layer with open boundaries

The unstable nature of buoyant flow in a vertical porous slab with a pure conduction temperature distribution is investigated. The permeable and isothermal boundaries are subject to a temperature difference, which is responsible for the basic stationary and parallel vertical flow in the slab. The momentum transfer is modeled by adopting the Darcy–Forchheimer law, thus including the quadratic form-drag contribution. The instability to small-amplitude perturbations is tested by parameterizing the basic stationary flow through the Darcy–Rayleigh number and the form-drag number. The modal analysis is carried out numerically with a pressure–temperature formulation of the governing equations for the perturbations. The neutral stability curves and the critical values of the wave number and of the Darcy–Rayleigh number are obtained for different prescribed values of the form-drag number.

### The unification of disparate rheological measures in oscillatory shearing

Oscillatory shearing is a popular method to understand transient nonlinear rheology. Various viscoelastic metrics have been used to analyze oscillatory rheology with different perspectives. We present a translation between various viscoelastic metrics for oscillatory rheology, using the framework of sequence of physical processes (SPPs) as a basis. The relation between the SPP metrics and Fourier-based metrics, such as Fourier sine and cosine coefficients, and large and minimum strain and rate metrics is provided. The meaning of the curvature in elastic and viscous Lissajous figures is explained with the sign of the SPP viscoelastic metrics. A low dimensional interpretation of the SPP framework is presented, featuring the center, size, and orientation of a deltoid in a transient Cole-Cole plot. Finally, we show how statistical information regarding the amount of change exhibited by the SPP metrics over a period of oscillation can be used to enhance the presentation and understanding of traditionally performed amplitude sweep experiments.

### Inertial migration of circular particles in Poiseuille flow of a power-law fluid

The immersed boundary-lattice Boltzmann method is used to study the inertial migration of particles in Poiseuille flow of a power-law fluid. The effects of Reynolds number, power-law index, and blockage ratio on the formation of particle trains are explored. The results show that single particle with different initial positions reach the same equilibrium position for the same power-law index. The stable equilibrium position moves closer to the centerline under the higher power-law index and blockage ratio. One-line of eight particles distributed initially at a vertical position will migrate laterally to the vicinity of the wall and form single-line particle trains. The particle spacing is unstable and increases when particles migrate to the equilibrium position. The inertial focusing length is an important factor for analyzing the formation of particle trains, which will be longer with increasing the power-law index. The mean particle spacing will be reduced with increasing Re and blockage ratio. Two-lines of 12 particles distributed initially and abreast along both sides of the centerline will migrate to the vicinity of the wall and form staggered particle trains. Due to the multiparticles interaction, the final particle equilibrium position will deviate from the single particle equilibrium position. The axial spacing between two neighboring particles is stable or fluctuates within a certain range. The particle spacing decreases with increasing the power-law index and blockage ratio, and with decreasing Re. The shear-thinning fluid is beneficial to the formation of single-line particle trains and staggered particle trains.

### Particle-laden thin-film flow in helical channels with arbitrary shallow cross-sectional shape

Particle-laden flows in helical channels are of interest for their applications in spiral particle separators used in the mining and mineral processing industries. In this paper, we extend the previous work of Lee, Stokes, and Bertozzi [“Behaviour of a particle-laden flow in a spiral channel,” Phys. Fluids 26, 043302 (2014)] by studying thin-film flows of monodisperse particle-laden fluid in helically wound channels of arbitrary centerline curvature and torsion and arbitrary cross-sectional shape. In the case where the particles are uniformly distributed through the depth of the film, significant analytic progress can be made yielding insight into the influence of channel geometry on particle distribution across the channel cross section: the governing equations reduce to a single nonlinear ordinary differential equation, which is readily integrated numerically to obtain the solution subject to appropriate boundary conditions. Motivated by possible application to the design of spiral separators, we consider the effects of changing the channel centerline geometry, the cross-sectional shape and the particle density on the resulting flows, and the radial distribution of particles. Our results support the findings in the work of Arnold, Stokes, and Green [“Thin-film flow in helically wound rectangular channels of arbitrary torsion and curvature,” J. Fluid Mech. 764, 76–94 (2015)] regarding the effect of channel centerline geometry and cross-sectional shape on flows in particle-free regions. In particle-rich regions, similar effects are seen although the primary velocity is lower due to increased effective mixture viscosity. Of key interest is the effect of channel geometry on the focusing of the particles for given fluxes of fluid and particles. We find that introducing a trench into the channel cross section, a feature often used in commercial spiral particle separators, leads to a smaller radial width of the particle-rich region, i.e., sharper focusing of the particles, which is consistent with experiments showing that channel geometry influences particle separation in a spiral separator.

### Mechanism of end-gas autoignition induced by flame-pressure interactions in confined space

The main objective of this work is to comprehensively provide a fundamental understanding of the entire process of the flame-pressure wave interactions with end-gas autoignition and detonation development in a confined chamber by two-dimensional numerical simulations with a stoichiometric hydrogen/air mixture. The flame dynamics, pressure wave propagation, and its structure evolution, together with the mechanism of autoignition and detonation development in the end gas, are analyzed in detail. Six stages, including spherical flame, finger flame, flame with its skirt touching the sidewalls, flame-pressure wave interactions, end-gas autoignition induced by the flame-pressure wave interactions, and detonation development, are observed for the flame development in the confined space. The results demonstrate that the flame-pressure wave multi-interactions result in violent oscillations of the flame shape and speed. Three stages of flame shape evolution during each interaction, backward propagation of the flame front, stretch of the flame front at the boundary layer, and formation of the tulip flame, are captured. A new mechanism in terms of combined effects of the viscous boundary layer and pressure waves is provided for the formation of the tulip flame. It is also found that the velocity distributions in the boundary layer show the trend of increase first and then decrease after the pressure waves pass the fields twice in the opposite directions. The autoignition occurrence and detonation initiation at different positions and different moments in the end-gas region are analyzed. It is indicated that the nonuniform temperature distribution induced by the reflections of pressure waves and the specific pressure wave structures can be responsible for this phenomenon.

### Stream broadening due to fluid shear across the wider transverse dimension of a free-flow zone electrophoresis channel

While the pressure-gradient applied along the length of a free-flow zone electrophoresis (FFZE) chamber is known to produce a parabolic flow profile for the carrier electrolyte across the narrower channel dimension (typically the channel depth), additional fluid shear can arise across the channel width due to a variety of reasons. Most commonly, any variation in the pressure-drop or channel depth across this wider dimension can lead to a gradient in the liquid flow velocity along it, significantly altering the stream broadening and, thereby, the separation performance of the assay. This article assesses the effect of such fluid shear on stream broadening during the FFZE process by describing a mathematical framework for solving the relevant advection-diffusion equation based on the method-of-moments approach. A closed-form expression for the leading order term describing the additional contribution to the spatial stream variance has been derived considering a small linear gradient in the liquid velocity across the wider transverse dimension of the FFZE chamber. The noted analysis predicts this contribution to be governed by two Péclet numbers that are evaluated based on the axial pressure-driven flow and transverse electrophoretic solute velocities. More importantly, this contribution is shown to vary quadratically with the axial distance traversed by the analyte stream as opposed to the classical linear variation known for all other stream broadening contributions in FFZE systems. The results from the analytic theory have been validated with Monte Carlo simulations, which also establish a time and length scale over which the noted analytical results are applicable.

### Flame evolution in shock-accelerated flow under different reactive gas mixture gradients

Author(s): Yuejin Zhu, Longkun Gao, Kai Hong Luo, Jianfeng Pan, Zhenhua Pan, and Penggang Zhang

The interaction between a planar shock wave and a spherical flame is studied numerically for an ethylene-oxygen-nitrogen gas mixture. Influences of different initial reactive gas mixture gradients on the shock-flame interaction are investigated by using high-resolution computational simulations. The...

[Phys. Rev. E 100, 013111] Published Tue Jul 23, 2019

### Bubble formation in freezing droplets

Author(s): Fuqiang Chu, Xuan Zhang, Shaokang Li, Haichuan Jin, Jun Zhang, Xiaomin Wu, and Dongsheng Wen

Near the freezing ice front in sessile droplets, air dissolved in the liquid water is observed to separate out to form many isolated bubbles, making the ice droplets porous media instead of tight ice beads.

[Phys. Rev. Fluids 4, 071601(R)] Published Tue Jul 23, 2019

### Effect of streamwise cross-sectional variation on liquid retention in liquid-infused substrates under an external flow

Author(s): L. Mazor, H. A. Stone, and I. Jacobi

Streamwise variations in the cross section of liquid-infused substrates are shown to affect their ability to retain liquid when exposed to an external, immiscible shear flow, with potential implications for the design and manufacturing of omniphobic and drag-reducing surfaces.

[Phys. Rev. Fluids 4, 074003] Published Tue Jul 23, 2019

### Trapping of metallic nanoparticles under the free surface of superfluid helium in a static electric field

Electrically charged metallic microparticles and nanoparticles have been trapped under a free surface of superfluid 4He in a vertical static electric field. We report the details of the trapping technique and the observed dynamics of the trapped particles moving along the surface and driven by surface waves, by a static horizontal electric field, and by a thermal counterflow within the surface layer of liquid He.

### Porosity effects in laminar fluid flow near permeable surfaces

Author(s): Changwoo Kang and Parisa Mirbod

This work analyzes the porosity effects on laminar flow and drag reduction of Newtonian fluids flowing over and through permeable surfaces. A fully developed laminar flow in a channel partially replaced with a porous material is considered. The analytical solutions for the velocity and shear stress ...

[Phys. Rev. E 100, 013109] Published Mon Jul 22, 2019

### Nonaxisymmetric magnetorotational instability in spherical Couette flow

Author(s): Domenico G. Meduri, François Lignières, and Laurène Jouve

We investigate numerically the flow of an electrically conducting fluid in a rapidly rotating spherical shell where the inner boundary spins slightly faster than the outer one. The magnetic field evolves self-consistently from an initial dipolar configuration of weak amplitude, and a toroidal field ...

[Phys. Rev. E 100, 013110] Published Mon Jul 22, 2019