Latest papers in fluid mechanics
A study with experimental and numerical components is conducted to establish the effect of a two-dimensional surface cavity on the structure and growth rate of a turbulent spot. The spot is artificially created in a two-dimensional laminar boundary layer developing under zero streamwise pressure gradient. Interactions of the turbulent spot and its wake with the Kelvin–Helmholtz rollers of the cavity shear layer are shown to result in significant increases in its lateral and streamwise growth rates. The underlying physics of these developments are identified.
For over a century, reduced order models (ROMs) have been a fundamental discipline of theoretical fluid mechanics. Early examples include Galerkin models inspired by the Orr–Sommerfeld stability equation and numerous vortex models, of which the von Kármán vortex street is one of the most prominent. Subsequent ROMs typically relied on first principles, like mathematical Galerkin models, weakly nonlinear stability theory, and two- and three-dimensional vortex models. Aubry et al. [J. Fluid Mech. 192, 115–173 (1988)] pioneered the data-driven proper orthogonal decomposition (POD) modeling. In early POD modeling, available data were used to build an optimal basis, which was then utilized in a classical Galerkin procedure to construct the ROM, but data have made a profound impact on ROMs beyond the Galerkin expansion. In this paper, we take a modest step and illustrate the impact of data-driven modeling on one significant ROM area. Specifically, we focus on ROM closures, which are correction terms that are added to the classical ROMs in order to model the effect of the discarded ROM modes in under-resolved simulations. Through simple examples, we illustrate the main modeling principles used to construct the classical ROMs, motivate and introduce modern ROM closures, and show how data-driven modeling, artificial intelligence, and machine learning have changed the standard ROM methodology over the last two decades. Finally, we outline our vision on how the state-of-the-art data-driven modeling can continue to reshape the field of reduced order modeling.
Hot-wire measurements are carried out in a decaying turbulence downstream of a grid made up of two juxtaposed perforated plates with different mesh sizes but same solidity. The two perforated plates generate two interacting (quasi–) homogeneous and isotropic decaying turbulent flows with distinct turbulence intensities and integral length scales. The interaction between these two flows leads to the development of a shearless turbulent mixing layer (STML). The main focus is on the decay of the turbulence centerline of the STML. Along the downstream distance x, the Taylor microscale Reynolds number, [math], remains constant, the streamwise velocity variance behaves like [math], and the Taylor microscale (λ) varies as [math]. This indicates that the turbulence on the centerline of the STML decays in a perfectly self-preserving manner at all scales of motion. This is further supported by the very good collapse of the velocity spectra, second-, and third-order velocity structure functions.
We studied the mechanisms of flame acceleration (FA) and deflagration to detonation transition (DDT) triggered by a combination of solid and jet obstacles. The Navier–Stokes equations with a detailed hydrogen–air kinetics model were utilized. Vast Kelvin–Helmholtz instabilities generate intensive turbulence–flame interactions, leading to an increase in surface area and high propagation velocity. The jet position has a significant effect on the FA and DDT. A choking flame and detonation flame are obtained by the transverse jet with different positions and mixing times even though in a lower blockage ratio.
Author(s): Olga I. Vinogradova, Elena F. Silkina, and Evgeny S. Asmolov
Motivated by recent observations of anomalously large deviations of the conductivity currents in confined systems from the bulk behavior, we revisit the theory of ion transport in parallel-plate channels and also discuss how the wettability of a solid and the mobility of adsorbed surface charges imp...
[Phys. Rev. E 104, 035107] Published Wed Sep 22, 2021
Secondary instability of the spike-bubble structures induced by nonlinear Rayleigh-Taylor instability with a diffuse interface
Author(s): Lin Han, Jianjie Yuan, Ming Dong, and Zhengfeng Fan
Laminar-turbulent transition in Rayleigh-Taylor (RT) flows usually starts with infinitesimal perturbations, which evolve into the spike-bubble structures in the nonlinear saturation phase. It is well accepted that the emergence and rapid amplification of the small-scale perturbations are attributed ...
[Phys. Rev. E 104, 035108] Published Wed Sep 22, 2021
We present experimental results of rotating downslope gravity currents performed at the Coriolis Platform in Grenoble, France. A novel experimental design to produce the downslope gravity flow has been employed using an axisymmetric configuration and a uniform flow injection that enabled the study of the long-term evolution of surface baroclinic vortices and of the gravity current, monitoring at the same time the evolution of the global circulation and the vorticity produced in the central deep area. The structure of the current, its relevant scales, and the characteristics of the generated surface vortices fairly agree with previous results in the literature in smaller scale installations. Discrepancies are attributable to the influence of both topographic Rossby waves and viscous effects that are much reduced in the Coriolis platform. Rotating intrusive gravity currents in a two-layer stratified ambient behave very differently from dense currents following the bottom slope. Substantial differences appear for the induced global circulation, which depend on the nature of the intrusion, with a strong influence of the rotation rate. In particular, intruding gravity currents give rise to a strong turbulent environment at intermediate and bottom depths in the central area, with submesoscale vortices (i.e., with a typical size smaller than the Rossby deformation radius) and a large variety of scales. In contrast, when the dense current follows the bottom slope, no significant vorticity production in the bottom and intermediate layers is reported. This clearly suggests that bottom boundary layers detaching from the boundary and propagating toward the ambient interior as in intrusive currents give an important contribution to the turbulence dynamics.
As a mode-1 internal tide (IT) propagates across a geostrophic current V(x, z), we have investigated the amount of IT energy reflected from the current and the impact of the current on the transmitted wave field. These are quantified by considering the reflection coefficient R and the linear modal energy conversion Pn, where n is the modal number. Here, a linear theory built upon idealized barotropic currents is presented. Fully nonlinear numerical simulations are used for the baroclinic currents. We conclude that the reflection is determined by the horizontal shear of the current Vx through varying the effective frequency feff. The modal energy conversion Pn is determined by the vertical shear of the current Vz, i.e., the horizontal variation of the density ρx as a result of the thermal wind relation. The current can increase R up to around 50%. However, Pn is less than 6% among all our simulations. This indicates that IT can propagate through the current without losing much of its structure and the interaction is mostly linear.
The stability of basic buoyant flow in a vertical fluid layer induced by temperature and solute concentration differences between the vertical boundaries is investigated. The linear dynamics of the perturbed flow is formulated as an eigenvalue problem and solved numerically by employing the Chebyshev collocation method. The validity of Squire's theorem is proved, and therefore, two-dimensional motions are considered. The neutral stability curves defining the threshold of linear instability and the critical values of the thermal Grashof number and wave number at the onset of instability are determined for various values of the Prandtl number [math], the solute Grashof number [math], and the Lewis number [math]. The magnitude of the Prandtl number at which the transition from stationary to travelling-wave mode occurs can be either increased or decreased by tuning the values of [math] and [math]. For certain combinations of the parameters, there exist one or two closed disconnected travelling-wave neutral curves emphasizing the necessity of multiple thermal Grashof numbers to embark upon the stability of fluid flow, a result of contrast to that of the single-diffusive fluid layer. The mechanism of modal instability is deciphered by using the method of energy budget and four different modes of instability are identified, one of which is new and due entirely to the presence of solutal buoyancy.
Electro-osmotic flow through nanochannel with different surface charge configurations: A molecular dynamics simulation study
Electro-osmotic flow behavior through rectangular graphene nanochannels with different charge (negative in nature) configurations is discussed in detail using non-equilibrium molecular dynamics (MD) simulations. Alternate patterning of charged and neutral stripes on the surface of the nanochannel lowers the water permeance and electro-osmotic flow velocity through the nanochannel. For all of the charge configurations, water permeance and electro-osmotic velocity through the nanochannel increase as surface charge density (σ) increases from 0.005 to 0.025 C m−2. This can be attributed to the increase in the number of counterions (Na+ ions) near the surface of the nanochannel. However, with further increase in σ, water permeance and electro-osmotic velocity through the nanochannel gradually decrease despite the increase in the number of counterions near the surface of the nanochannel. This is because of the significant increase in electrostatic interaction between the water molecules and the surface of the nanochannel. At a lower value of σ ([math] C m−2), the overall interaction between the water molecules and the surface of the nanochannel is significantly dominated by van der Waals (vdW) interactions (electrostatic/vdW [math]). The slip velocity of water molecules in the charged stripe portion of the wall (SlipCharge) is higher as compared to the slip velocity of water molecules in the neutral stripe portion (SlipNeutral) except at [math] cm−2. This difference between SlipCharge and SlipNeutral is highest at [math] C m−2 with SlipCharge > SlipNeutral, for all of the charge configurations.
Integrating multiple physical properties of microchannel gas flow to extend the Navier–Stokes equations over a wide Knudsen number range
Gas flow in microchannels can be predicted by the Navier–Stokes equations with slip boundary conditions, but only limited to a slightly rarefied flow regime. To improve that, the considerations of the effective mean free path and the volume diffusion phenomena were introduced to the non-kinetic model by previous studies separately. In this study, these two effects, along with the newly proposed wall-to-wall-collision effect, are integrated to extend the Navier–Stokes equations for the planar Poiseuille flows over a wide Knudsen number ([math]) range. The dimensionless mass flow rates calculated by the proposed model can be consistent among different working fluids or flow conditions and mostly agree with the experimental data with [math]. This analysis facilitates an understanding of the mutual effects on the physical properties of microchannel gas flows and shows a promising prospect for developing a non-kinetic model for highly rarefied flows.
Simulating the collision of a moving droplet against a moving particle: Impact of Bond number, wettability, size ratio, and eccentricity
This paper presents a direct numerical simulation for the collision of a moving droplet against a moving particle under gravity, based on the pseudopotential lattice Boltzmann model. The effects of Bond number (Bo), particle surface wettability, particle–droplet size ratio (α), and eccentricity ratio (B) on the collision processes are investigated comprehensively. Six findings are reported and analyzed for the first time: (1) an agglomeration process is observed for the collision with a very small Bond number. During the agglomeration process, the vertical velocity of the particle will experience a deceleration, and the deceleration will become weak against the increase in the Bond number. (2) The wettability will influence the variation of the vertical velocity of the moving particle remarkably. The vertical velocity of the neutral particle is nearly linearly accelerated, but the lyophilic particle experiences an obvious deceleration. In addition, the velocity history of the lyophobic particle shows a nonlinear acceleration. (3) The increase in the particle–droplet size ratio will postpone the emergence of the deceleration process. Therefore, the appearance of the peak vertical velocity is delayed against the increase in the particle–droplet size ratio. (4) For different eccentricity ratios, the differences of the velocities (e.g., the horizontal, vertical, and angular velocity) are very small in the beginning of collision, while a big difference appears with time elapses. Besides, the variation of velocities becomes very obvious. (5) There is a critical value for B, where the horizontal velocity, vertical velocity, and angular velocity of the particle investigated in the work all will reach their maximum values. (6) A rebound regime is observed when a moving droplet collides vertically against a moving particle. In the available literature, a rebound regime was observed only when a droplet colliding against a fixed particle, but never for a vertically moving particle. The present research reveals when a rebound process will appear. The finding here may shed some light on the mechanism of the collision of a moving droplet against a moving particle.
Modeling the spatial characteristics of extrusion flow instabilities for styrene-butadiene rubbers: Investigating the influence of molecular weight distribution, molecular architecture, and temperature
The extrusion flow instabilities of three commercial styrene-butadiene rubbers (SBR) are investigated as a function of molecular weight distribution (MWD); molecular architecture (linear, branched); and temperature. The samples have multimodal MWD, with the main component being SBR and a low amount, less than 10 wt. %, of low-molecular weight hydrocarbons. Deviation from the Cox–Merz rule at high angular frequencies/shear rates becomes intense as the amount of medium-molecular weight component increases. Optical analysis is used to identify and quantify spatial surface distortions, specifically wavelength (λ) and height (h), of the different types of extrusion flow instabilities. Qualitative constitutive models are reviewed and used to fit the experimental data for the spatial characteristics of extrusion flow instability. The fitting parameters as obtained by the models are correlated with molecular properties of the materials. It is found that the characteristic spatial wavelength (λ) increases as the extrusion temperature decreases. Hence, the influence of temperature on the spatial characteristic wavelength is investigated and an Arrhenius behavior is observed.
Aneurysms of saccular shape are usually associated with a slow, almost stagnant blood flow, as well as a consequent emergence of blood clots. Despite the practical importance, there is a lack of computational models that could combine platelet aggregation, precise biorheology, and blood plasma coagulation into one efficient framework. In the present study, we address both the physical and biochemical effects during thrombosis in aneurysms and blood recirculation zones. We use continuum description of the system and partial differential equation-based model that account for fluid dynamics, platelet transport, adhesion and aggregation, and biochemical cascades of plasma coagulation. The study is focused on the role of transport and accumulation of blood cells, including contact interactions between platelets and red blood cells (RBCs), coagulation cascade triggered by activated platelets, and the hematocrit-dependent blood rheology. We validated the model against known experimental benchmarks for in vitro thrombosis. The numerical simulations indicate an important role of RBCs in spatial propagation and temporal dynamics of the aneurysmal thrombus growth. The local hematocrit determines the viscosity of the RBC-rich regions. As a result, a high hematocrit slows down flow circulation and increases the presence of RBCs in the aneurysm. The intensity of the flow in the blood vessel associated with the aneurysm also affects platelet distribution in the system, as well as the steady shape of the thrombus.
Atomically thin flat sheets of carbon, called graphene, afford interesting opportunities to study the role of orientation in suspensions. In this work, we use general rigid bead-rod theory to arrive at general expressions from first principles for the complex viscosity of graphene suspensions. General rigid bead-rod theory relies entirely on suspension orientation to explain the elasticity of the liquid. We obtain analytical expressions for the complex viscosity of triangular and hexagonal graphene sheets of arbitrary size. We find good agreement with new complex viscosity measurements.
Multi-bifurcation behaviors of staged swirl flames fueled with methane at atmospheric pressure are experimentally investigated by varying the global equivalence ratio ([math]). Based on the characteristics of measured pressure oscillations and the associated results of phase space reconstruction, recurrence plots, and synchrosqueezing-transform-based time-frequency analysis, the multi-bifurcation behaviors of this thermoacoustic system with four different stability regimes have been identified. With incremental increase in [math] from 0.55 to 0.79, these four stability regimes follow the sequence of a quiet mode (Regime I), the first limit cycle with moderate oscillations (Regime II), an intermediate state with intermittent bursts of multi-modes (Regime III), and the second limit cycle with much stronger oscillations (Regime IV). The flame dynamics in Regimes II and IV undergoing limit cycle oscillations are compared. The flame structure in Regime II displays an attached twin-flame structure, the same as that observed in Regime I. However, a large-scale periodic convective motion is found in Regime IV, which is identified to be the main thermoacoustic driving factor in the local Rayleigh index maps. Further experiments are carried out by continuously increasing [math] to examine the synchrosqueezing-transform spectra of transient processes during the two bifurcations. The present investigation is instrumental in obtaining a fundamental understanding of nonlinearity and multi-bifurcation of thermoacoustic instabilities in centrally staged swirl combustors, which is vital in guiding the early stage design and developing detection/control strategies in practical low-emission combustion systems.
In this paper, the Vogel–Escudier flow is studied at an aspect ratio of 2.5 and a Reynolds number range of 330–3000. An attempt is made to control the vortex breakdown bubbles using a thin rod in co- and counter-rotation cases. The flow is studied qualitatively using planar laser-induced fluorescence and quantitatively using particle image velocimetry measurements. In terms of swirl strength, defined as the ratio of Reynolds numbers of the disk and control rod, a complete suppression and subsequent reemergence of vortex breakdown bubbles is observed at 56 and 37, respectively. Counter-rotation shows a slight decrease until −150 and a periodic and aperiodic shedding of the vortices at −112 and −75. An attempt is made to explain the flow behavior by experimental and analytical means taking into consideration the azimuthal plane flow using the swirl decay mechanism. Further, experiments are performed for time varying co- and counter-rotations for various combinations of amplitude and frequency. The anomalous behavior at high frequencies of destabilization of vortices in co-rotation and a milder change in counter-rotation is observed.
When two sessile droplets of miscible fluids come into contact, the coalescence process can be significantly delayed owing to the competition between the capillary and Marangoni effects. It is important to reveal the mechanism of the deformation and displacement of the sessile droplets at the early stage of the delayed coalescence, which determines the self-stabilized shape and joint motion of the two droplets later on. In this work, we numerically investigate the early-stage dynamics of the delayed coalescence between two sessile droplets of equal size and laden with aqueous mixtures of different solvent mass fractions. A three-dimensional numerical model is adopted based on lubrication theory and is validated by comparison against previous experimental results. Through simulation, we first showed how the concentration transport is coupled with droplet deformation. Then, we explained the underlying mechanism of delayed coalescence by analyzing the liquid bridge numerically and theoretically. A scaling law for the duration of liquid bridge growth is given and agrees well with the numerical results. Finally, the effects of the solubility on the dynamics are investigated. Our study reveals how the capillary and Marangoni effects dominate the flow during the early stage of the delayed coalesce and thus determine its following behavior.
The locomotion of a flapping flexible plate with different shapes and non-uniform chordwise stiffness distribution in a stationary fluid is studied numerically. The normalized effective bending stiffness [math] for three-dimensional plates with arbitrary stiffness distribution and shape parameters is proposed, and the overall bending stiffness of non-uniform plates with different shapes is reasonably characterized. It is found that the propulsion performance in terms of cruising speed and efficiency of the self-propelled flapping plate mainly depends on the effective bending stiffness. Plates with moderate flexibility [math] show better propulsion performance. Meanwhile, both a large area moment of the plate and a flexible anterior are favorable to significantly improve their propulsive performance. The evolution of vortical structures and the pressure distribution on the upper and lower surfaces of the plate are analyzed, and the inherent mechanism is revealed. These findings are of great significance to the optimal design of propulsion systems with different fins or wings.
We numerically study impact processes on dense suspensions using the lattice Boltzmann method to elucidate the connection between the elastic rebound of an impactor and relations among the impact speed u0, maximum force acting on the impactor [math], and elapsed time [math] to reach [math]. We find that [math] emerges in the early stage of the impact, while the rebound process takes place in the late stage. We find a crossover of [math] from the u0 independent regime for low u0 to a power law regime satisfying [math] with [math] for high u0. Similarly, [math] satisfies [math] with [math] for high u0. Both power-law relations for [math] and [math] vs u0 for high u0 are independent of the system size, but the rebound phenomenon strongly depends on the depth of the container for suspensions. Thus, we indicate that the rebound phenomenon is not directly related to the relations among u0, [math] and [math]. We propose a floating + force chain model, where the rebound process is caused by an elastic term that is proportional to the number of the connected force chains from the impactor to the bottom plate. On the other hand, there are no elastic contributions in the relations for [math] and [math] against u0 because of the absence of percolated force chains in the early stage. This phenomenology predicts [math] and [math] for high u0 and also recovers the behavior of the impactor quantitatively even if there is the rebound process.