# Latest papers in fluid mechanics

### Acoustic stability of nonadiabatic high-energy-density shocks

Author(s): César Huete, Francisco Cobos-Campos, Ernazar Abdikamalov, and Serge Bouquet

Shock waves are very efficient at compressing fluid. Ideally, the maximum mass compression ratio is f+1, where f accounts for molecular degrees of freedom. Sufficiently strong shocks, those that induce very high temperatures downstream, may alter f by adding vibrational modes or promoting molecular dissociation. In addition, the nonadiabaticity of these effects, and others like ionization and/or radiation, also affect the mass compression ratio and other shock properties. These changes ultimately modify the D’yakov-Kontorovich limits associated with the acoustic stability of planar isolated shocks.

[Phys. Rev. Fluids 5, 113403] Published Wed Nov 18, 2020

### Coupled population balance and large eddy simulation model for polydisperse droplet evolution in a turbulent round jet

Author(s): Aditya Aiyer and Charles Meneveau

A hybrid approach is developed to simulate the transport and breakup of droplets in a turbulent round jet. The inflow size distribution is obtained from a one-dimensional parcel model that is coupled to a coarse large-eddy simulation (LES) of a turbulent jet. The LES results are compared to experimental data and show good agreement. Additionally, LES allows us to quantify the distributions of the mean and variability of key quantities of the polydisperse distribution.

[Phys. Rev. Fluids 5, 114305] Published Wed Nov 18, 2020

### Mobility of bidisperse mixtures during bedload transport

Author(s): Rémi Chassagne, Philippe Frey, Raphaël Maurin, and Julien Chauchat

The mobility of bidisperse segregated beds is studied numerically with a coupled fluid discrete element method model in the bedload regime. The transport is observed to be higher when small particles are buried below large ones. This is interpreted as a granular process and a new simple explanation is given in the framework of the μ(I) rheology. A predictive model for the increase of transport is proposed based on granular rheological arguments.

[Phys. Rev. Fluids 5, 114307] Published Wed Nov 18, 2020

### Roughness effects on scalar transport

Author(s): Zvi Hantsis and Ugo Piomelli

In the flow over a smooth wall, the statistics of velocity and temperature, properly normalized, collapse (Reynolds’ analogy); when the wall is rough, this analogy fails. Its failure has long been known to be due to the pressure gradient, which is absent in the scalar transport equation. A study examines how the geometrical features of the roughness affect the failure of the Reynolds’ analogy, by focusing on the transport equations for temperature variance and turbulent kinetic energy.

[Phys. Rev. Fluids 5, 114607] Published Wed Nov 18, 2020

### Decomposition of the mean friction drag in adverse-pressure-gradient turbulent boundary layers

Author(s): Yitong Fan (范钇彤), Weipeng Li (李伟鹏), Marco Atzori, Ramon Pozuelo, Philipp Schlatter, and Ricardo Vinuesa

From an energy budget perspective, the decomposition of mean friction drag in adverse-pressure-gradient turbulent boundary layers is conducted, obtaining contributions associated with dissipation, production, and convection across the boundary layer. In the wall-normal distributions of the decomposed constituents, positions of inner peaks are well scaled in viscous units, whereas outer peaks scale in outer units, regardless of Reynolds number and pressure-gradient magnitude.

[Phys. Rev. Fluids 5, 114608] Published Wed Nov 18, 2020

### A computational study on osmotic chemotaxis of a reactive Janusbot

We explore the chemotaxis of an elliptical double-faced Janus motor (Janusbot) stimulated by a second-order chemical reaction on the surfaces, aA + bB → cC + dD, inside a microfluidic channel. The self-propulsions are modeled considering the full descriptions of hydrodynamic governing equations coupled with reaction–diffusion equations and fluid–structure interaction. The simulations, employing a finite element framework, uncover that the differential rate kinetics of the reactions on the dissimilar faces of the Janusbot help in building up enough osmotic pressure gradient for the motion as a result of non-uniform spatiotemporal variations in the concentrations of the reactants and products around the particle. The simulations uncover that the mass diffusivities of the reactants and products along with the rates of forward and backward reactions play crucial roles in determining the speed and direction of the propulsions. Importantly, we observe that the motor can move even when there is no difference in the total stoichiometry of the reactants and products, (a + b) = (c + d). In such a scenario, while the reaction triggers the motion, the difference in net-diffusivities of the reactants and products develops adequate osmotic thrust for the propulsion. In contrast, for the situations with a + b ≠ c + d, the particle can exhibit propulsion even without any difference in net-diffusivities of the reactants and products. The direction and speed of the motion are dependent on difference in mass diffusivities and reaction rate constants at different surfaces.

### Modeling of sub-grid conditional mixing statistics in turbulent sprays using machine learning methods

Deep artificial neural networks (ANNs) are used for modeling sub-grid scale mixing quantities such as the filtered density function (FDF) of the mixture fraction and the conditional scalar dissipation rate. A deep ANN with four hidden layers is trained with carrier-phase direct numerical simulations (CP-DNS) of turbulent spray combustion. A priori validation corroborates that ANN predictions of the mixture fraction FDF and the conditional scalar dissipation rate are in very good agreement with CP-DNS data. ANN modeled solutions show much better performance with a mean error of around 1%, which is one order of magnitude smaller than that of standard modeling approaches such as the β-FDF and its modified version. The predicted conditional scalar dissipation rate agrees very well with CP-DNS data over the entire mixture fraction space, whereas conventional models derived for pure gas phase combustion fail to describe ⟨N|ξ = η⟩ in regions with higher mixture fraction and low probability. In the second part of this paper, uncertainties associated with ANN predictions are analyzed. It is shown that a suitable selection of training sets can reduce the size of the necessary test database by ∼50% without compromising the accuracy. Feature importance analysis is used to analyze the importance of different combustion model parameters. While the droplet evaporating rate, the droplet number density, and the mixture fraction remain the dominant features, the influence of turbulence related parameters only becomes important if turbulence levels are sufficiently high.

### Turbulence anisotropy and intermittency in open-channel flows on rough beds

An experimental campaign, based on Particle Image Velocimetry measurements in a laboratory flume with different median sediment sizes in the no-motion condition, has been carried out aiming at investigating the effects of bed roughness on turbulence anisotropy in two different vertical zones of the turbulent open-channel flow. An analysis of turbulence anisotropy, which relies on second-order structure functions and anisotropy angle, has been performed. The scale-dependent anisotropy level has been quantified, verifying the tendency of the system to span from large-scale anisotropy, due to the main shear of the boundary layer, to small-scale isotropy. Isotropy is well-established for the largest sediment sizes. High-order structure function analysis reveals that intermittency is more pronounced in the near-bed layers, where the flow is more populated by coherent vortices. Spectral anisotropy and intermittency strongly characterize the transport properties of turbulence and are, therefore, important phenomena for natural bed rivers.

### A reactive molecular dynamics study of hyperthermal atomic oxygen erosion mechanisms for graphene sheets

Carbon-based composite materials are widely used in the aerospace field due to their light weight and excellent physical/chemical properties. The mechanisms of the erosion process, e.g., surface catalysis and ablation, during the impact of oxygen atoms, however, remain unclear. In this study, the surface catalysis and ablation behavior during the erosion process of hyperthermal atomic oxygens were achieved through the molecular dynamics method with the reactive force field potential. The concomitant impacts of energy flux density of energetic oxygen atoms, the presence of multiple layers beneath the graphene sheet, and the morphology of graphite surfaces, i.e., graphite basal plane, armchair (AC) edge surface, and zigzag edge surface, respectively, were discussed. The results show that the adsorption of oxygen atoms dominates at the beginning by generating O2 molecules, suggesting the importance of surface catalytic for any ablation study. A unique “layer-by-layer” ablation phenomenon by hyperthermal atomic oxygen is observed for multi-layered graphite slab, and the ablation rate reduces as the number of graphene layers increases. The morphology/structure of the surface shows significant effects on the ablation rate, with AC surfaces showing the largest etching rate and the basal one showing the lowest. The low binding energies of the AC edge are responsible for the difficulty in the formation of stable functional group structures to resist the etching of high-enthalpy oxygen atoms. Such revelation of the detailed surface catalysis and ablation mechanism at the atomistic scale provides insight into design of future materials for the augmentation of the thermal protection effect.

### A vapor–liquid equilibrium induced Lewis number effect in real-gas shear layers: A theoretical study

In this work, the relevance of the multi-phase thermodynamic model based on the vapor–liquid equilibrium (VLE) assumption over the single-phase model is discussed. An emphasis on the importance of the non-linear coupling between thermodynamic, transport, and governing equations is given from a macroscopic point of view by analyzing the mixing effects on a spatial mixing layer in real-gas (non-ideal) conditions. The goal is to prove the existence of an important difference between the two thermodynamic models and, therefore, establish the foundations on the effects that VLE induces in a fluid flow. The results indicate that differences in micro-mixing, ultimately changing the vortex dynamics, are directly related to the imbalance between the heat and mass transfer that occurs within the VLE mixing region of a shear layer.

### Correction and improvement of a widely used droplet–droplet collision outcome model

The widely used droplet–droplet collision outcome model distinguishing stretching separation (SS) and fast coalescence (FC) (named SS/FC model) proposed by Jiang et al. [J. Fluid Mech. 234, 171 (1992)] is corrected and improved in this study. By re-deriving the momentum conservation, the correct mathematical expression of the tangential velocity along the sliding direction is obtained. Moreover, to reduce the uncertainties of model applications, the model is improved by expressing the constants as a function of the Ohnesorge number and droplet size ratio. The validation results demonstrate the effectiveness of the improved SS/FC model.

### A note on a swirling squirmer in a shear-thinning fluid

Micro-organisms and artificial microswimmers often move in biological fluids displaying complex rheological behaviors, including viscoelasticity and shear-thinning viscosity. A comprehensive understanding of the effectiveness of different swimming gaits in various types of complex fluids remains elusive. The squirmer model has been commonly used to represent different types of swimmers and probe the effects of different types of complex rheology on locomotion. While many studies focused only on squirmers with surface velocities in the polar direction, a recent study has revealed that a squirmer with swirling motion can swim faster in a viscoelastic fluid than in Newtonian fluids [Binagia et al., J. Fluid Mech. 900, A4, (2020)]. Here, we consider a similar setup but focus on the sole effect due to shear-thinning viscosity. We use asymptotic analysis and numerical simulations to examine how the swirling flow affects the swimming performance of a squirmer in a shear-thinning but inelastic fluid described by the Carreau constitutive equation. Our results show that the swirling flow can either increase or decrease the speed of the squirmer depending on the Carreau number. In contrast to swimming in a viscoelastic fluid, the speed of a swirling squirmer in a shear-thinning fluid does not go beyond the Newtonian value in a wide range of parameters considered. We also elucidate how the coupling of the azimuthal flow with shear-thinning viscosity can produce the rotational motion of a swirling pusher or puller.

### Inertial migration of oblate spheroids in a plane channel

We discuss an inertial migration of oblate spheroids in a plane channel, where the steady laminar flow is generated by a pressure gradient. Our lattice Boltzmann simulations show that spheroids orient in the flow, so that their minor axis coincides with the vorticity direction (a log-rolling motion). Interestingly, for spheroids of moderate aspect ratios, the equilibrium positions relative to the channel walls depend only on their equatorial radius a. By analyzing the inertial lift force, we argue that this force is proportional to a3b, where b is the polar radius, and conclude that the dimensionless lift coefficient of the oblate spheroid does not depend on b and is equal to that of the sphere of radius a.

### Natural circulation pump with asymmetrical heat transfer wall as the element of Büttiker–Landauer thermal ratchet

Technology that makes use of waste heat or low-grade energy is important for addressing worldwide energy security concerns. This study proposes the application of a natural circulation pump employing an asymmetrical heat transfer wall as the element of a Büttiker–Landauer (BL) thermal ratchet powered by waste heat. Furthermore, experiments for evaluating the proposed arrangement’s performance were conducted. We demonstrated experimentally that we can realize water circulation in a channel owing to the localized non-equilibrium nature of the pump’s asymmetrical heat transfer wall. In addition, we propose a framework for evaluating the pump’s performance. Our proposal is expected to result in the uptake of practical applications for BL ratchets.

### Unsteady magnetohydrodynamic flow of generalized second grade fluid through porous medium with Hall effects on heat and mass transfer

This work investigates the unsteady magnetohydrodynamic flow of generalized second grade fluid through a porous medium with Hall effects on heat and mass transfer. The second grade fluid with a fractional derivative is used for the constitutive equation. A second-order fractional backward difference formula in the temporal direction and a spectral collocation method in the spatial direction are proposed to solve the model numerically. In the numerical implementation, a fast method is applied to decrease the memory requirement and computational cost. The velocity, temperature, and concentration profiles are discussed through graphs. The effects of various parameters on the velocity profiles, temperature field, and concentration field are shown. Results indicate that as the fractional derivative γ increases and the Hall parameter m decreases, the amplitudes of the velocity components decrease.

### Thermocapillary instabilities in a liquid layer subjected to an oblique temperature gradient: Effect of a prescribed normal temperature gradient at the substrate

We consider thermocapillary instability in a three-dimensional liquid layer with a deformable interface with an ambient gas phase and subjected to an oblique temperature gradient when the temperature gradient at the substrate is prescribed. We demonstrate that this configuration leads to a drastic change in the instability features with respect to those emerging when either a purely vertical temperature gradient (VTG) or a purely horizontal temperature gradient (HTG) is present. In the case of the return flow as the base state, the spanwise long-wave instability mode dominates except for the range of small Bond numbers Bo. Slippage at the substrate has a stabilizing (destabilizing) effect on streamwise (spanwise) long-wave modes in the presence of a HTG. In the case of linear flow as the base state, both streamwise and spanwise long-wave modes play a major role in the instability onset depending on the ratio between the HTG and the VTG η for higher values of the capillary number Ca, e.g., Ca > 0.001. However, for lower values of Ca, e.g., Ca < 0.001, streamwise and spanwise instability modes become finite-waves at large η. In contrast to the return flow, for the linear flow, slippage at the substrate destabilizes both long-wave modes.

### Asymptotic properties of mixing length closures for turbulent pipe flow

Turbulence is investigated as the Reynolds number approaches infinity for the flow of an incompressible fluid through straight pipes with a circular cross section under the assumptions that the continuum hypothesis holds, the pipe wall is smooth, and the mixing length closure constructed by Cantwell [“A universal velocity profile for smooth wall pipe flow,” J. Fluid Mech. 878, 834–874 (2019)] is sufficiently accurate to allow the extrapolation to Reynolds numbers beyond the range of the Princeton superpipe data used as a foundation for the closure model. Two sets of scales are introduced to set up two sets of dimensionless equations and two Reynolds numbers for the near wall region (Re, inner scaling) and the center part of the pipe flow (Rτ, outer scaling). It is shown analytically that the turbulent flow asymptotically approaches a two-layer structure: The core of the pipe flow becomes uniform with constant mean velocity and zero shear stress in the outer scaling and the near wall region (inner scaling) with the mean velocity satisfying the law of the wall and non-zero shear stress. The core part of the flow pushes, as Rτ → ∞, the near wall layer to the boundary restricting it to a cylindrical subdomain with zero volume.

### COVID-19 transmission in the first presidential debate in 2020

The infection risks of Biden, Wallace, and the audience by Trump and the first lady were assessed during the first presidential debate. The debate scene was established numerically, and two cases, i.e., only Trump being infected and both Trump and the first lady being infected, were set up for risk analysis. The infection probabilities at different positions were assessed by using the Wells–Riley equation with consideration of the effects of air distribution and face mask. It was concluded that (1) the infection risks of Biden and Wallace were lower due to the reasonable distance from Trump, with the maximum probability of 0.34% at 40 quanta/h for both Trump and the first lady being infected; (2) the infection probabilities in the audience area were lower for the long distance from the debate stage, with the maximum probability of 0.35%. Wearing masks resulted in a notable decrease in the infection probability to 0.09%; and (3) there was a certain local area surrounding Trump and the first lady with a relatively greater infection probability. The preliminary analysis provides some reference for protection of the next presidential debate and other public events.

### Evaluation of an accurate and consistent mathematical model of an elbow flowmeter derived from the Navier–Stokes equation

Models derived from the free swirl theory, forced swirl mathematical models, and regression models provide inaccurate predictions of the behavior of elbow flowmeters. To generate an accurate model, we employ the Navier–Stokes equation considering an orthogonal coordinate system according to a curved surface. Thereby, we derive a mathematical model to measure the parameters associated with elbow flowmeters. The effects of physical parameters such as geometric parameters, ratio of bend to diameter, and Reynolds number are investigated. We obtained a relative error below 0.5% upon comparison of the theoretical model calculations and experimental results. This indicates that the proposed model is accurate and useful for future research and industrial production design of elbow flowmeters.

### Analysis of flame-flame interactions in premixed hydrocarbon and hydrogen flames

Author(s): S. Trivedi, H. Kolla, J. H. Chen, and R. S. Cant

Flame-flame interactions play an important role in altering flame surface area and fuel consumption rate but have received comparatively little attention so far. An investigation into the statistics of flame-flame interaction events in the progress variable space aims to quantify the relative frequency of occurrence of these events and looks at the topology of each type of interaction. Understanding the statistics and the topology can help to identify the overall influence of flame-flame interactions on flame properties and, in future, help to model these effects.

[Phys. Rev. Fluids 5, 113201] Published Tue Nov 17, 2020