In the present work, a numerical framework is developed for simulating gas-solid flows associated with interaction of a rocket plume on a planetary surface. For this investigation, a unique, two-way coupled, dusty-gas flow model has been developed in the coupled direct simulation Monte Carlo (DSMC)-discrete element method (DEM) framework, which has been applied for dust dispersion on lunar surface. In this model, the gas-gas collisions are modeled probabilistically, whereas grain-grain interactions are computed deterministically. Most importantly, a multiphase fluid-solid two-way coupling model is proposed where the fluid-particle interaction is modeled macroscopically by considering the momentum and energy exchange between the two phases. The use of the DEM approach allows us to model dense granular phase near a planetary regolith. Additionally, the framework allows us to calculate not only the particle trajectories, but also their temperatures. To make the framework efficient for dynamic calculation of drag and heat transfer from gas to grain phase, the same coefficients are precalculated (and used later as a look-up table) for gas flow over an isolated granular particle over a range of speed ratios for free molecular flow conditions. Using the developed framework, a comprehensive numerical study is performed to model dust dispersion associated with lunar landing. The influence of particle diameter on gas and grain phases and dust transportation has been analyzed in the coupled framework. Additionally, the impact of the two-way coupled gas-grain interaction model is analyzed and compared with one-way coupled model.

The preferential accumulation of particles in turbulent flows occurs in many engineering and environmental applications. Recent research reveals that particle preferential accumulation is attributed to multiscale vortex structures in turbulent flows, which affect particle motion and cause particles to remain trapped in particular regions. In this study, the primary goal is to further investigate the mechanisms of particle trapping with emphasis on the effect of the vortex on particle motion. We specifically investigate particle trapping in a 2D unequal-strength counterrotating vortex pair (CVP) using a one-way coupled Euler–Lagrangian method. The small, rigid, spherical, dilute, and heavy particles are considered with the assumption that the particle Reynolds number is low. Using a geometric singular perturbation method to solve the particle motion, we first identify a particle-attracting ring in the potential CVP flow with a circulation ratio $\gamma \in (-0.65,0)$. The particle-attracting ring provides a simple mechanism to explain the occurrence of particle trapping, which is represented by a particle-clustering ring (PCR) in the CVP. We then conduct numerical simulations of particle motion for viscous CVP flows. In the simulations, the CVP is created through vortex–wall interaction, where a primary vortex induces the separation of the new discrete counterrotating vortex from the wall boundary, ultimately leading to the formation of the CVP. Particle trapping in the CVP flow is shown to be robust in the presence of viscosity. The trapping of particles in these viscous simulations has the same dynamical origin as the trapping phenomenon studied for potential CVP flows. The results of this research may help to further comprehend the mechanisms driving the preferential accumulation of particles in turbulent flows.

Numerical solutions of the Enskog equation obtained employing a finite-difference lattice Boltzmann (FDLB) and a direct simulation Monte Carlo–like particle method (PM) are systematically compared to determine the range of applicability of the simplified Enskog collision operator implemented in the lattice Boltzmann framework using the half-range Gauss-Hermite quadratures. Three types of bounded flows of dense gases, namely the Fourier, the Couette, and the Poiseuille flows, are investigated for a wide range of input parameters. For low to moderate reduced density, the proposed FDLB model exhibits commendable accuracy for all bounded flows tested in this study, with substantially lower computational cost than the PM method.

Deterministic lateral displacement (DLD) is a microfluidic method for accurately separating particles by size or deformability. Recent efforts to operate DLD devices in the inertial, rather than in the Stokes flow regime, have been hindered by a loss of separation efficiency and difficulty predicting the separation behavior. One factor contributing to these problems is the onset of inertia-induced flow anisotropy where the average flow direction does not align with the direction of the pressure gradient in the device. We use the lattice-Boltzmann method to simulate two-dimensional flow through a rotated-square DLD geometry with circular pillars at a Reynolds number up to 100 for different gap sizes and rotation angles. We find that anisotropy in this geometry is a nonmonotonous function of Reynolds number and can be positive or negative. This finding is in contradiction to the naive expectation that inertia would always drive flow along the principal direction of the pillar array. Anisotropy tends to increase in magnitude with gap size and rotation angle. By analyzing the traction distribution along the pillar surface, we explain how the change of the flow field upon increasing inertia leads to the observed trends of anisotropy. Our work contributes to a better understanding of the inertial flow behavior in ordered cylindrical porous media, and it might contribute to improved DLD designs for operation in the inertial regime.

Turbulence in wall-bounded flows is characterized by stable statistics for the mean flow and the fluctuations both for the case of the ensemble and the time mean. Although in a substantial set of turbulent systems, this stable statistical state corresponds to a stable fixed point of an associated statistical state dynamics (SSD) closed at second order, referred to as S3T, this is not the case for wall turbulence. In wall turbulence the trajectory of the statistical state evolves on a transient chaotic attractor in the S3T statistical state phase space and the time-mean statistical state is neither a stable fixed point of this SSD nor, if the time-mean statistical state is maintained as an equilibrium state, is it stable. Nevertheless, sufficiently small perturbations from the ensemble or time-mean state of wall turbulence are expected to relax back to the mean statistical state following an effective linear dynamics. In this work the dynamics of spanwise uniform perturbations to the time-mean flow are studied using a linear inverse model to identify the linear operator governing the ensemble stability of the ensemble or time-mean state by obtaining the time mean stability properties over the transient attractor of the turbulence identified by the S3T SSD. The ensemble or time-mean stability of an unstable equilibrium can be understood by noting that, even when every member of an ensemble is unstable, the ensemble mean may be stable with perturbations following an identifiable stable dynamics. While simplifying insight into turbulent flows has commonly been obtained by identifying and studying ensemble mean statistical states, less attention has been accorded to identifying and studying the ensemble mean dynamics. We show that, in the case of wall turbulence, even though stable fixed-point SSD equilibria are not available to allow application of traditional perturbation analysis methods to identify the perturbation stability of the mean state, an effective linear stability analysis can be obtained to identify the perturbation dynamics of the ensemble or time-mean statistical state.

We report an experimental study of Rayleigh-Bénard convection of liquid metal thermal convection with a Prandtl number of $\mathrm{Pr}=0.029$ in the cuboid cell of aspect ratios $\mathrm{\Gamma }=\text{width/height}=1/3$. By arranging 48 thermistors and 6 ultrasonic sensors in the sidewall of the cell, the flow mode and corresponding flow and heat transfer characteristics are obtained with Rayleigh number Ra varying from $1.05\times {10}^6$ to $4.01\times {10}^7$. Three typical flow modes are defined from the results of temperature measurements, showing a double-roll mode (DRM) with two vertically stacked counterrotating rolls, a single-roll mode (SRM) that occupies the entire cell and a distorted single-roll mode existing in the transitions between DRM and SRM. Moreover, by gradually increasing the Ra one can observe the flow transition from DRM to SRM by the statistics of the lifetime for each flow mode. The complete Fourier analysis of temperature data shows that the origin of the flow modes can be attributed to the energy transformation between Fourier modes of different orders. When $\mathrm{Ra}\ge 1.19\times {10}^7$, the first Fourier mode energy has accounted for more than 75% of the total energy which is evidence that the SRM is fully established. Furthermore, the measured temperature profiles along the central axis of the cell follow a linear law in the bulk, and the slopes obey power-law scaling with Ra. Regarding the standard deviation of temperature profiles along the central axis of the cell which bulge in the bulk forming the second peak outside the thermal boundary layers at small Ra due to the complex three-dimensional flow structures. Finally, the similar scaling laws of the global heat and momentum transfer of the liquid metal thermal convection in a slender cuboid cell are observed, showing $\mathrm{Nu}\sim {\mathrm{Ra}}^{0.35}$ and $\mathrm{Re}\sim {\mathrm{Ra}}^{0.36}$ for heat and momentum transfer, respectively.

We analyze the effect of large-scale coherent structures on the deposition of low-inertia particles in a turbulent pipe flow using extended proper orthogonal decomposition (EPOD) and spectral analysis. We perform direct numerical simulations (DNSs) at two the Reynolds numbers 5300 and 10 300 (based on bulk parameters) with the particles released at the pipe inlet. The equilibrium Eulerian model is employed for calculating particle velocity, and the analysis is limited to particles with Stokes number (based on wall units) less than 1. Increasing the Stokes number increases the energy at small streamwise wavelengths (due to inertial clustering), and the spectral energy peak moves from ${\lambda }_z^{+}\approx 1000$ to ${\lambda }_z^{+}\approx 150$. The spectral peak in the $({\lambda }_z^{+},y^{+})$ plane, where $y^{+}$ is the wall-normal distance, moves from the buffer layer to the logarithmic region. Gravity has a substantial effect on the POD mode shapes. For the downward flow, a second peak appears closer to the center. A new Fukagata-Iwamoto-Kasagi (FIK) identity is derived for the wall deposition rate coefficient (Sherwood number, Sh) and employed to quantify the contributions of the mean and fluctuating velocity and particle concentration fields for different Stokes, Froude, and Reynolds numbers. Modes with azimuthal wave numbers $k_{\theta }$ equal to three or four are found to contribute most to deposition. Application of the developed methodology to higher Reynolds number can elucidate the role of large- and very-large-scale flow structures on particle deposition to the wall. It is well known these structures leave their footprint at the wall but their contribution to deposition is not well understood.

Granular bed motion induced by a liquid shear flow is considered as a model of bedload. This flow is characterized by a localization of the granular flow close to the upper surface of the bed. In such a framework, the paper aims at discussing and proposing continuum effective models describing the physical properties, as the rheology, of the two-phase granular suspension at a so-called mesoscale larger than the grain size. The main questions addressed here concern the relevance and the extension of effective rheological models for granular suspensions often extracted from simple-shear flow configurations in a viscous limit, to situations of both granular shear localization as in bedload and weakly inertial flow regime. For this purpose, we consider the steady transport of a granular bed by a laminar Couette fluid flow above it and close to the onset of motion, for a grain-to-fluid density ratio of 2.5, as silica in water, and a range of particle Reynolds numbers ${\text{Re}}_p\in [0.1,10]$ and Shields numbers $\theta \in [0.1,0.7]$. To provide accurate continuum models, the dynamics into the granular shear layer has to be first known down to a scale smaller than each grain, a so-called microscale. Numerical simulations are thus performed at the microscale at which individual grain dynamics is resolved, using an immersed boundary method (IBM) coupled to a discrete element method (DEM) granular solver. Upscaling is then performed to obtain the equivalent momentum balance at the mesoscale, characterized by continuum phases, using a spatial averaging method on volume element larger than the grain diameter. This approach allows us obtaining stresses, strains, and their relationships for the fluid phase, the granular phase, and the equivalent mixture, independently. The main contribution of this work is threefold: (i) we highlight the relevance of mesoscopic rheological continuum law for localized granular shear flow; (ii) we extract rheological models from direct numerical simulations (IBM/DEM) in a weakly inertial regime, going beyond purely viscous situations; and (iii) we extend Coulomb-like model $\mu \left(I\right)$ of a granular suspension to incorporate fluid/particle inertial effects showing a different dependence of fluid phase and granular phase contributions with dimensionless numbers.

We present an approach to study the shear-induced diffusion of particles in suspensions with continuous particle-size distribution by addressing the migration of local moments of the size distribution. This approach replaces studying fluxes of particles of particular sizes. The physical problem is redefined in terms of fluxes of moments and their conservation. Particle-size distribution at each point is consequently obtained from the resulting moments, by solving inverse problems locally. The approach is applicable to any composite suspension, depending only on the initial size distribution in it. A particular example of migration in a circular tube is described. Results include concentration inhomogeneity, moments’ distribution, and the consequent local continuous particle-size distributions. We present stationary physical flow parameters and the similarity and difference from cases of monodispersed suspensions. For example, while in most cases of particle concentration, the general phenomena resemble the migration directions observed in monodisperse suspensions, there are cases, associated with extreme input high or low concentrations, where further accumulation of specific sizes at locations close to domain boundaries are encountered. This basic study will enhance better understanding of the complex behavior and properties of multiphase systems.

An alternative approach to simulate dynamic, recurrent flows with very large time steps is presented. Data-driven forecasts based on the method of analogs are made employing a set of precomputed time series segments of flow fields. These predictions are then corrected with the evolved deviation between initial flow state and its nearest neighbor in the database. The evolution of these deviations is obtained from the convolution with the propagator of the linearized Navier-Stokes equations, where linearization takes place around the most similar state in the database. The error $E_{\text{lin}}$ due to this approximation implies the appropriate distance function to determine nearest-neighbor fields. We tested the method on the simple case of 2D vortex shedding behind a cylinder at Reynolds numbers in the range of 200 with step sizes of up to 200 times larger than those used to generate the underlying data with the PISO algorithm. Short-term forecasts showed a high degree of accuracy with errors correlating well with $E_{\text{lin}}$ for a number of case variations. But also after many steps, the predicted flow fields remained in close agreement with high-fidelity CFD calculations with relative errors on the order of $1\%$ for the temporal averages. Furthermore, excellent conservation behavior of global properties like total momentum and kinetic energy was observed.

In this study, an efficient deep-learning model is developed to predict unavailable parameters, e.g., streamwise velocity, temperature, and pressure from available velocity components. This model, termed mapping generative adversarial network (M-GAN), consists of a label information generator (LIG) and an enhanced super-resolution generative adversarial network. LIG can generate label information helping the model to predict different parameters. The GAN-based model receives the label information from LIG and existing velocity data to generate the unavailable parameters. Two-dimensional (2D) Rayleigh-Bénard flow and turbulent channel flow are used to evaluate the performance of M-GAN. First, M-GAN is trained and evaluated by two-dimensional direct numerical simulation (DNS) data of a Rayleigh-Bénard flow. From the results, it can be shown that M-GAN can predict temperature distribution from the two-dimensional velocities. Furthermore, DNS data of turbulent channel flow at two different friction Reynolds numbers ${\text{Re}}_{\tau }=180$ and 550 are applied simultaneously to train the M-GAN and examine its predicting ability for the pressure fields and the streamwise velocity from the other two velocity components. The instantaneous and statistical results of the predicted data agree well with the DNS data, even for the flow at ${\text{Re}}_{\tau }=395$, indicating that M-GAN can be trained to learn the mapping function of the unknown fields with good interpolation capability.

The comprehension of stratified flows is important for geophysical and astrophysical applications. The weak wave turbulence theory aims to provide a statistical description of internal gravity waves propagating in the bulk of such flows. However, internal gravity waves are usually perturbed by other structures present in stratified flow, namely the shear modes and the vortical modes. In order to check whether a weak internal gravity wave turbulence regime can occur, we perform direct numerical simulations of stratified turbulence without shear modes and with or without vortical modes at various Froude and buoyancy Reynolds numbers. We observe that removing vortical modes naturally helps to have a better overall balance between poloidal kinetic energy, involved in internal gravity waves, and potential energy. However, conversion between kinetic energy and potential energy does not necessarily show fluctuations around zero in our simulations, as we would expect for a system of weak waves. A spatiotemporal analysis reveals that removing vortical modes helps to concentrate the energy around the wave frequency, but it is not enough to observe a weak wave turbulence regime. Yet we observe that internal gravity waves whose frequency are large compared to the eddy turnover time are present, and we also find evidences for slow internal gravity waves interacting by triadic resonance instabilities in our strongly stratified flows simulations. Finally, we propose conditions that should be fulfilled in order to observe a weak internal gravity wave turbulence regime in real flows.

Understanding the behavior of the kinetic energy spectrum and flux in two-dimensional (2D) turbulent thermal convection remains a challenge. In this paper, using high-resolution direct numerical simulation of Rayleigh-Bénard convection for Rayleigh numbers ${10}^{11}$–${10}^{14}$ and unit Prandtl number, we show that 2D turbulent convection exhibits Bolgiano-Obukhov scaling. At small wave numbers, where buoyancy feeds energy to the velocity field, kinetic energy exhibits inverse cascade. Consequently, the kinetic energy spectrum scales as $k^{-11/5}$ and the kinetic energy flux shows $k^{-4/5}$ scaling at small wave numbers. Buoyancy is weakened at large wave numbers, and this leads to a constant enstrophy cascade and $k^{-3}$ kinetic energy spectrum, similar to 2D hydrodynamic turbulence. However, the entropy spectrum exhibits a bispectrum with the upper branch varying as $k^{-2}$. We also observe constant entropy flux in the inertial range. Finally, we also draw a connection between the entropy flux in the dissipation range and the entropy dissipation rate in the bulk.

Erosion and deposition are represented as the evolution of solid bodies due to the forces exerted by the fluid or air on the contact surfaces, which both often lead to reconfiguration and change of the topology and structure of the porous media. These processes are notably very complicated and challenging to study. In this work, we formulate simplified and idealized mathematical models to examine the internal evolution of flow networks in the setting of cylindrical channels, undergoing a unidirectional flow, by using asymptotic and numerical techniques. Starting from the Stokes equations combined with the advection-diffusion equation for solid transport, we propose a model to construct a complete analysis of both the erosion and deposition. The considered approach is of the form of threshold laws: the fluid-solid interface erosion and deposition occur when the total shear stress is, respectively, greater or lower than some specified critical values, depending on the solid material. As a consequence of the erosion and deposition, the radii of the channels in the structure expand and shrink, respectively, due to several key parameters, which we find and investigate in this paper. We also perform a parametric study to quantify the correlation between these threshold values and the particle concentration in the flow. A comprehensive parametric study of the constructed model reveals that the final configuration of the structure can be predicted from the system parameters.

Caustics in the dynamics of heavy particles in turbulence accelerate particle collisions. The rate $\mathcal{J}$ at which these singularities form depends sensitively on the Stokes number $\mathrm{St}$, the nondimensional inertia parameter. Exact results for this sensitive dependence have been obtained using Gaussian statistical models for turbulent aerosols. However, direct numerical simulations of heavy particles in turbulence yield much larger caustic-formation rates than predicted by the Gaussian theory. To understand the possible mechanisms explaining this difference, we analyze a non-Gaussian statistical model for caustic formation in the limit of small $\mathrm{St}$. We show that at small $\mathrm{St}$, $\mathcal{J}$ depends sensitively on the tails of the distribution of Lagrangian fluid-velocity gradients. This explains why different authors obtained different $\mathrm{St}$-dependencies of $\mathcal{J}$ in numerical-simulation studies. The most likely gradient fluctuation that induces caustics at small $\mathrm{St}$, by contrast, is the same in the non-Gaussian and Gaussian models. Direct numerical simulation results for particles in turbulence show that the optimal fluctuation is similar, but not identical, to that obtained by the model calculations.

An adequate comprehension of the flow regimes and mixing process inside microreactors is a crucial factor to obtain high reaction yields. In the present paper, we carry out jointly simulations and experiments to characterize the flow regimes and reaction occurring in a X-microreactor up to Reynolds number, Re, based on the inlet bulk velocity and mixing channel hydraulic diameter, equal to 600. For $\text{Re}>375$, an unsteady periodic regime is found, characterized by the presence of a central vortical flow structure that periodically collapses leading to symmetric vorticity shedding in both outlet channels. In the meanwhile, two counterrotating vortices form in the confluence region of the inlet streams, come closer, and merge creating again the central vortex. Compared to the steady engulfment regime, previously described in the literature and characterized by a single steady central vortex, a higher mixing degree is found in the unsteady regime. However, despite the increased mixing, the reaction yield remains similar, as the enhanced mixing is counterbalanced by the reduced residence time of the reactants. Based on the obtained results we developed a model to predict the reaction yield, given the mixing degree and the nominal kinetic constant as input data. The proposed law successfully predicts the reaction yield in all the flow regimes, including the unsteady engulfment one regime, and for the Damköhler numbers in the range ${10}^{-1}<\text{Da}<{10}^3$ (chemistry slower and faster than flow convection).

We study the hydrodynamic interaction between a microswimmer and a deformable interface when the swimmer can stochastically reorient itself. We consider a force- and torque-free swimmer, modeled as a slender body, that can execute random orientation tumbles or active Brownian rotations in the plane of the deformable interface. When the swimmer is in the more viscous fluid, our analysis shows that both tumbles and Brownian rotations acting on timescales comparable to that of interface deformations can lead to a pusher-type swimmer rotating away from the interface, while enhancing its attraction towards the interface. In turn, the intrinsic orientational stochasticity of the microswimmer favors a stronger migration of pushers towards the interface at short times, but migration away from the interface in the long-time limit. However, irrespective of the viscosity ratio of the two fluid medium, the tendency of a pusher to align parallel to the interface is suppressed; the results for puller-type swimmers are the opposite. Our study has potential consequences for the residence time of swimming microorganisms near deformable boundaries.

Using fluid displacement in a Hele-Shaw cell, we experimentally demonstrate the arresting effect of an imposed flow on a phase separation occurring in a growing liquid-liquid interfacial region, unlike in an initially homogeneous single-phase mixture quenched within the miscibility gap. Increasing the imposed flow rate reduces the exponent α in the form $\mathrm{\Delta }A\propto t^{\alpha }$, where $\mathrm{\Delta }A$ is the increase in the area occupied by the displacing fluid owing to phase separation. We show that α can be expressed as a function of the ratio of the phase separation rate to the flow rate on a single curve, indicating that the competition between the imposed flow and phase separation rates determines the degree of the interfacial phase separation. The arresting effect and the mechanism are verified by a numerical simulation.

The flow field around bioinspired magnetic-responsive soft materials that mimic the symmetry-breaking mechanisms in swimming animals, such as pteropods and manta rays, is studied using the tomographic particle image velocimetry (tomo-PIV) technique. Magnetic-responsive material appendages are actuated by an oscillating external magnetic field. The fluid flow induced by two types of actuation is quantified. First, a single actuation mode involves alternating upward and downward bending motions. Second, an asymmetric multimodal actuation encompasses upward folding and downward bending motions by locating an asymmetric joint at the midpoint of the appendage. The formed vorticity field, vortex structure, and viscous energy dissipation rate in the surrounding fluid are observed to be weaker for the multimodal actuation case. The multimodal appendage moves with reduced flow resistance, leading to faster appendage velocity during the downward power stroke. Furthermore, the study examines the effect of an asymmetric magnetic field cycle on the flow field by extending the time interval of the applied positive voltage (upstroke motion) compared to the duration of the negative applied voltage (downstroke motion). The asymmetric cycle and extended stopping period provide time for greater dissipation of the formed vorticity field. Thus, the peak values of vorticity and viscous dissipation rate decrease to smaller magnitudes compared to the symmetric cycle case. These findings demonstrate that the utilization of symmetry-breaking morphology and an asymmetric cycle enhances stroke performance, offering promising avenues for achieving greater effectiveness in underwater propulsion.

Electrophoresis in complex (non-Newtonian) fluidic media is becoming increasingly prominent owing to its applications in a wide variety of separation processes. Although most particles that undergo electrophoresis carry nonuniform surface charge, their motion in complex fluidic media has been addressed only recently, while many other separation processes also use externally imposed flows. Despite this, the impact of external flows on the electrophoretic motion of such particles in non-Newtonian fluids still remains largely unexplored. To address this, here we develop a semianalytical framework using a combination of matched asymptotic expansion and regular perturbation to examine the trajectories of nonuniformly charged particles suspended in a viscoelastic medium, subject to imposed shear flow and electric field. We assume the particle's surface charge to be weak but otherwise arbitrary, the electrical double layer to be thin, the suspending medium to obey the Oldroyd-B constitutive relation, and the overall flow to be weakly viscoelastic. Our results reveal that in the presence of imposed flows, any particle carrying a nonuniform surface charge will likely undergo cross-stream migration when the suspending medium is viscoelastic. It is shown that the very nature of a particle's trajectory and the extent of its migration will strongly depend on whether the imposed flow or the electrophoretic propulsion dominates particle motion. This is further supported by a reduced order model derived for Newtonian fluids, using which particles' velocities and their trajectories may be deduced without a detailed knowledge of the flow field. We demonstrate that in the limit of weak viscoelasticity, the general conclusions from this reduced order model may indeed be extended beyond the realm of Newtonian fluids. Our framework may be useful towards improving particle separation relevant to many biochemical applications.