We characterise the stress singularity of the Oldroyd-B, Phan-Thien–Tanner (PTT), and Giesekus viscoelastic models in steady planar stick-slip flows. For both PTT and Giesekus models in the presence of a solvent viscosity, the asymptotics show that the velocity field is Newtonian dominated near to the singularity at the join of the stick and slip surfaces. Polymer stress boundary layers are present at both the stick and slip surfaces. By integrating along streamlines, we verify the polymer stress behavior of r−4/11 for PTT and r−5/16 for Giesekus, where r is the radial distance from the singularity. These asymptotic results for PTT and Giesekus do not hold in the limit of vanishing quadratic stress terms for Oldroyd-B. However, we can consider the Oldroyd-B model in the fixed kinematics of a prescribed Newtonian velocity field. In contrast to PTT and Giesekus, this is not the correct balance for the momentum equation but does allow insight into the behavior of the Oldroyd-B equations near the singularity. A three-region asymptotic structure is again apparent with now a polymer stress singularity of r−4/5. The high Weissenberg boundary layer equations are found to manifest themselves at the stick surface and are of thickness r3/2. At the slip surface, dominant balance between the upper convected stress and rate-of-strain terms gives a slip boundary layer of thickness r2. The solution of the slip boundary layer shows that the polymer stress is now singular along the slip surface. These results are supported through numerical integration along streamlines of the Oldroyd-B equations in a Newtonian velocity field. The Oldroyd-B model thus extends the point singularity at the join of the stick and slip surfaces to the whole of slip surface. As such, it does not have a physically meaningful solution in a Newtonian velocity field. We would expect a similar stress behavior for this model in the true viscoelastic velocity field.

The shear-induced migration of concentrated non-Brownian monodisperse suspensions in combined plane Couette-Poiseuille (C-P) flows is studied using a lattice Boltzmann simulation. The simulations are mainly performed for a particle volume fraction of ϕbulk = 0.4 and H/a = 44.3, 23.3, where H and a denote the channel height and radius of suspended particles, respectively. The simulation method is validated in two simple flows, plane Poiseuille and plane Couette flows. In the Poiseuille flow, particles migrate to the mid-plane of the channel where the local concentration is close to the limit of random-close-packing, and a random structure is also observed at the plane. In the Couette flow, the particle distribution remains in the initial uniform distribution. In the combined C-P flows, the behaviors of migration are categorized into three groups, namely, Poiseuille-dominant, Couette-dominant, and intermediate regimes, based on the value of a characteristic force, G, where G denotes the relative magnitude of the body force (P) against the wall-driving force (C). With respect to the Poiseuille-dominant regime, the location of the maximum concentration is shifted from the mid-plane to the lower wall moving in the same direction as the external body force, when G decreases. With respect to the Couette-dominant regime, the behavior is similar to that of a simple shear flow with the exception that a slightly higher concentration of particles is observed near the lower wall. However, with respect to the intermediate value of G, several layers of highly ordered particles are unexpectedly observed near the lower wall where the plane of maximum concentration is located. The locally ordered structure is mainly due to the lateral migration of particles and wall confinement. The suspended particles migrate toward a vanishingly small shear rate at the wall, and they are consequently layered into highly ordered two-dimensional structures at the high local volume fraction.

The suitability of controlled stress large amplitude oscillatory shear (LAOStress) for the characterisation of the nonlinear viscoelastic properties of fully formed fibrin clots is investigated. Capturing the rich nonlinear viscoelastic behaviour of the fibrin network is important for understanding the structural behaviour of clots formed in blood vessels which are exposed to a wide range of shear stresses. We report, for the first time, that artefacts due to ringing exist in both the sample stress and strain waveforms of a LAOStress measurement which will lead to errors in the calculation of nonlinear viscoelastic properties. The process of smoothing the waveforms eliminates these artefacts whilst retaining essential rheological information. Furthermore, we demonstrate the potential of LAOStress for characterising the nonlinear viscoelastic properties of fibrin clots in response to incremental increases of applied stress up to the point of fracture. Alternating LAOStress and small amplitude oscillatory shear measurements provide detailed information of reversible and irreversible structural changes of the fibrin clot as a consequence of elevated levels of stress. We relate these findings to previous studies involving large scale deformations of fibrin clots. The LAOStress technique may provide useful information to help understand why some blood clots formed in vessels are stable (such as in deep vein thrombosis) and others break off (leading to a life threatening pulmonary embolism).

We study the dynamics of the gas flow discontinuities after pulse ionization of a half space in front of a flat shock wave moving in a channel. Pulse volumetric electric discharge initiated in the vicinity of the shock concentrates in front of the shock and heats the gas there. The heating is shown to be very rapid. We use the shadow imaging technique and a high speed camera to study the flow pattern evolution after the discharge. The pattern consists of two shocks separated by a contact surface. This structure corresponds to the classical Riemann problem formulation. Based on the observed pattern, we estimate the amount of discharge energy converted to heat during the discharge time: the rate of temperature increase is in the order of several degrees K per nanosecond.

A specific instability of vortices is found in rotating shallow water equations with horizontal density/temperature gradients, which is used for modelling atmospheric and oceanic mixed layers. The model is re-interpreted as dynamics of rotating non-isentropic two-dimensional gas. The instability, which was not reported previously, develops in a way suggesting its convective character. It appears when anomaly of buoyancy at the center of the vortex and the vorticity have opposite signs (for positive Coriolis parameters), and coexists with the standard barotropic instability, having higher growth rates in a wide range of parameters and leading to efficient mixing at a nonlinear stage.

We consider small oscillations of micro-particles and gaseous bubbles in a viscous fluid around equilibrium states under the action of a sinusoidal external force. Exact solutions to the governing integro-differential equations containing both Stokes and memory-integral drag forces are obtained. The main aim of this study is to clarify the influence of the memory-integral drag force on the resonance characteristics of oscillating particles or gaseous bubbles in a viscous fluid at small Reynolds numbers. The resonant curves (the amplitude versus the frequency of an external force) and phase-frequency dependences are obtained for both these objects and compared with the corresponding dependences of the traditional oscillator with the Stokes drag force only.

Flow around a step cylinder at the Reynolds number 150 was simulated by directly solving the full Navier-Stokes equations. The configuration was adopted from the work of Morton and Yarusevych [“Vortex shedding in the wake of a step cylinder,” Phys. Fluids 22, 083602 (2010)], in which the wake dynamics were systematically described. A more detailed investigation of the vortex dislocation process has now been performed. Two kinds of new loop vortex structures were identified. Additionally, antisymmetric vortex interactions in two adjacent vortex dislocation processes were observed and explained. The results in this letter serve as a supplement for a more thorough understanding of the vortex dynamics in the step cylinder wake.

Arterio-Venous Fistulae (AVF) are regarded as the “gold standard” method of vascular access for patients with end-stage renal disease who require haemodialysis. However, a large proportion of AVF do not mature, and hence fail, as a result of various pathologies such as Intimal Hyperplasia (IH). Unphysiological flow patterns, including high-frequency flow unsteadiness, associated with the unnatural and often complex geometries of AVF are believed to be implicated in the development of IH. In the present study, we employ a Mesh Adaptive Direct Search optimisation framework, computational fluid dynamics simulations, and a new cost function to design a novel non-planar AVF configuration that can suppress high-frequency unsteady flow. A prototype device for holding an AVF in the optimal configuration is then fabricated, and proof-of-concept is demonstrated in a porcine model. Results constitute the first use of numerical optimisation to design a device for suppressing potentially pathological high-frequency flow unsteadiness in AVF.

Amoeboid cells propel by generating pseudopods that are finger-like protrusions of the cell body that continually grow, bifurcate, and retract. Pseudopod-driven motility of amoeboid cells represents a complex and multiscale process that involves bio-molecular reactions, cell deformation, and cytoplasmic and extracellular fluid motion. Here we present a 3D model of pseudopod-driven swimming of an amoeba suspended in a fluid without any adhesion and in the absence of any chemoattractant. Our model is based on front-tracking/immersed-boundary methods, and it combines large deformation of the cell, a coarse-grain model for molecular reactions, and cytoplasmic and extracellular fluid flow. The predicted shapes of the swimming cell from our model show similarity with experimental observations. We predict that the swimming behavior changes from random-like to persistent unidirectional motion, and that the swimming speed increases, with increasing cell deformability and protein diffusivity. The unidirectionality in cell swimming is observed without any external cues and as a direct result of a change in pseudopod dynamics. We find that pseudopods become preferentially focused near the front of the cell and appear in greater numbers with increasing cell deformability and protein diffusivity, thereby increasing the swimming speed and making the cell shape more elongated. We find that the swimming speed is minimum when the cytoplasm viscosity is close to the extracellular fluid viscosity. We further find that the speed increases significantly as the cytoplasm becomes less viscous compared with the extracellular fluid, resembling the viscous fingering phenomenon observed in interfacial flows. While these results support the notion that softer cells migrate more aggressively, they also suggest a strong coupling between membrane elasticity, membrane protein diffusivity, and fluid viscosity.

An electric field has been extensively used to manipulate fluids and particles via electrokinetic flow in microchannels and nanochannels for various lab-on-a-chip applications. Recent studies have demonstrated the action of a dielectrophoretic-like lift force on near-wall particles in an electrokinetic flow due to the particles’ modifications of the field-line structure adjacent to a planar wall. This work presents a fundamental investigation of the lateral migration of dielectric particles in the electrokinetic flow of buffer solutions of varying molar concentrations through a straight rectangular microchannel. We find that the particle migration-induced electrokinetic centerline focusing is significantly enhanced with the decrease of the buffer concentration. This observed phenomenon may be attributed to the increased surface conduction effect in a lower-concentration buffer that yields a larger Dukhin number, Du. It seems qualitatively consistent with a recent theoretical study that predicts a greater wall-induced electrical lift with the increasing value of the Dukhin number for Du ≥ 1.

The purpose of this work is to evaluate the recently derived Onsager-Burnett (OBurnett) equations [N. Singh, R. S. Jadhav, and A. Agrawal, “Derivation of stable Burnett equations for rarefied gas flows,” Phys. Rev. E 96, 013106 (2017)] for force-driven compressible plane Poiseuille flow. This classical internal flow problem depicts several non-equilibrium phenomena, for instance, non-constant pressure profile in the transverse direction and tangential heat flux, which are not captured by the classical Navier-Stokes-Fourier equations. The results of OBurnett equations for conserved and non-conserved variables are validated against the existing direct simulation Monte Carlo (DSMC) and molecular dynamics (MD) simulation results. These results suggest that the OBurnett equations are able to predict most of the variables well with respect to DSMC and MD simulation results. We find that the OBurnett equations predict a strictly monotonic pressure profile, in contrast to the bimodal profile predicted by the DSMC results and the conventional Burnett equations, but in agreement with the molecular dynamics simulation results. The equations also recover the non-zero tangential heat flux but fail to capture the peculiar temperature dip at the center, owing to its second order accuracy. These results suggest that the evaluated equations are accurate in predicting the non-equilibrium phenomena observed in the rarefied gas flows for the case considered.

For ultra-thin gas lubrication, the surface-to-volume ratio increases dramatically when the flow geometry is scaled down to the micro/nano-meter scale, where surface roughness, albeit small, may play an important role in gas slider bearings. However, the effect of surface roughness on the pressure and load capacity (force) in gas slider bearings has been overlooked. In this paper, on the basis of the generalized Reynolds equation, we investigate the behavior of a gas slider bearing, where the roughness of the slider surface is characterized by the Weierstrass-Mandelbrot fractal function, and the mass flow rates of Couette and Poiseuille flows are obtained by deterministic solutions to the linearized Bhatnager-Gross-Krook equation. Our results show that the surface roughness reduces the local mass flow rate as compared to the smooth channel, but the amount of reduction varies for Couette and Poiseuille flows of different Knudsen numbers. As a consequence, the pressure rise and load capacity in the rough bearing become larger than the ones in the smooth bearing in the slip and early transition flow regimes, e.g., a 6% roughness could lead to an increase of 20% more bearing load capacity. However, this situation is reversed in the free-molecular flow regime, as the ratio of the mass flow rates between Couette and Poiseuille flows is smaller than that in the smooth channel. Interestingly, between the two extremes, we have found a novel “rarefaction cloaking” effect, where the load capacity of a rough bearing equals to that of a smooth bearing at a certain range of Knudsen numbers, as if the roughness does not exist.

This paper presents investigations on the partial coalescence of an aqueous drop with an organic-aqueous interface with and without surfactants. The organic phase was different silicone oils and the aqueous phase was a glycerol-water solution at different concentrations. It is found that when the surfactant Span 80 is introduced into the organic phase, the partial coalescence region is reduced in the Oh–Bo coalescence map. The range of the inertio-capillary regime reduces when surfactants are present, while the drop size ratio decreases with increasing surfactant concentration. The velocity fields inside the aqueous drop were studied with high speed particle image velocimetry for the first time. In the surfactant-free system, it was found that the inward motion of the fluids at the upper part of the drop favours the generation of a liquid cylinder at the early stages of coalescence. The pressure gradient created by the downward stream at the bottom of the liquid cylinder drives the pinch-off of the secondary drop. When surfactants are present, the rupture of the film between the drop and the interface occurs at an off-axis location. The liquid cylinder formed in this case is not symmetric and does not lead to pinch-off. It is also found that the vortices inside the droplet have little impact on the partial coalescence.

In this paper, we investigate the pore structure and the impacts of Haines jumps on the change in preferential pathways (called the dynamic breakthrough) during fluid percolation through thin porous media. Two capillaries connected in parallel are used to represent a thin porous medium, and Haines jumps are observed through the formation of droplets. Using a droplet growth model and experimental visualisations, the change in preferential pathways is shown to be strongly influenced by the pore lengths, pore radii ratios, and droplet detachment volumes. This work provides a better understanding of the redevelopment of continuous fluid paths observed through thin porous media in electrochemical systems.

A rectangular grid formed by liquid filaments on a partially wetting substrate evolves in a series of breakups leading to arrays of drops with different shapes distributed in a rather regular bidimensional pattern. Our study is focused on the configuration produced when two long parallel filaments of silicone oil, which are placed upon a glass substrate previously coated with a fluorinated solution, are crossed perpendicularly by another pair of long parallel filaments. A remarkable feature of this kind of grids is that there are two qualitatively different types of drops. While one set is formed at the crossing points, the rest are consequence of the breakup of shorter filaments formed between the crossings. Here, we analyze the main geometric features of all types of drops, such as shape of the footprint and contact angle distribution along the drop periphery. The formation of a series of short filaments with similar geometric and physical properties allows us to have simultaneously quasi identical experiments to study the subsequent breakups. We develop a simple hydrodynamic model to predict the number of drops that results from a filament of given initial length and width. This model is able to yield the length intervals corresponding to a small number of drops, and its predictions are successfully compared with the experimental data as well as with numerical simulations of the full Navier–Stokes equation that provide a detailed time evolution of the dewetting motion of the filament till the breakup into drops. Finally, the prediction for finite filaments is contrasted with the existing theories for infinite ones.

A thorough physical understanding of gas entrainment within a liquid pool is established using a pair of fully submerged cylinders with an opposite but symmetric rotational field. An asymmetric version of such entrainment of gaseous filaments inside a liquid has been demonstrated in our earlier work [P. Kumar, A. K. Das and S. K. Mitra, Phys. Fluids 29, 022101 (2017)]. Here, our efforts focus on revealing the governing factors and understanding the stages of alteration from a stratified to an undulating interface for a wide range of symmetric cylinder rotations. Interfacial configurations such as an upper rounded crest, a bubble-ejecting jet, and a non-collapsible jet with an air pocket in the stagnant zone are obtained as the cylinder rotation increases. Near the critical capillary number, air pinch-off into a filament and subsequent stable collapse of this filament into bubbles were observed. As the rotation-driven capillary number increased, we noted the formation of an entrained jet of gaseous-phase forming air pockets in the region, which resulted in a diverging rotational field. Our analysis of the fluid stream explains the interfacial configurations and corresponding entrainment patterns based on fundamental physics. The power-law fit (Y = KXm) of the cusp profiles revealed close agreement with numerically obtained interfaces. We propose correlation coefficients as a function of the capillary number. We also assess the dependence of the entrainment pattern on cylinder submergence and spacing.

This article investigates both theoretically and numerically a novel mechanism of bubble detachment by an electrowetting-driven interfacial wave, inspired by droplet control and manipulation via electrowetting. Electrowetting-on-dielectric can be used to modulate the contact point movement at the water-air interface in a thin liquid film. Rapid oscillation of the contact line is achieved by a swift change of voltage under an AC signal. When disturbed with such contact angle changes, the interfacial wave between two immiscible fluids disrupts bubble dynamics. Numerical modeling reveals that an air bubble on a hydrophobic surface can be detached by the trough of such a wave. The frequency of the interfacial wave is twice the voltage frequency. A higher voltage frequency leads to a smaller amplitude and higher celerity of the wave, while a lower voltage frequency leads to a larger wave amplitude and lower celerity. The bubble can easily detach when the voltage frequency is 10 Hz. However, the bubble fails to detach when the voltage frequency is 100 Hz. This approach can be useful to improve two-phase cooling performance.

The turbulent structure of a channel flow of Xanthan Gum (XG) polymer solution is experimentally investigated and compared with water flow at a Reynolds number of Re = 7200 (based on channel height and properties of water) and Reτ = 220 (based on channel height and friction velocity, uτ0). The polymer concentration is varied from 75, 100, and 125 ppm to reach the point of maximum drag reduction (MDR). Measurements are carried out using high-resolution, two-component Particle Image Velocimetry (PIV) to capture the inner and outer layer turbulence. The measurements showed that the logarithmic layer shifts away from the wall with increasing polymer concentration. The slopes of the mean velocity profile for flows containing 100 and 125 ppm XG are greater than that measured for XG at 75 ppm, which is parallel with the slope obtained for deionized water. The increase in slope results in thickening buffer layer. At MDR, the streamwise Reynolds stresses are as large as those of the Newtonian flow while the wall-normal Reynolds stresses and Reynolds shear stresses are significantly attenuated. The sweep-dominated region in the immediate vicinity of the wall extends further from the wall with increasing polymer concentration. The near-wall skewness intensifies towards positive streamwise fluctuations and covers a larger wall-normal length at larger drag reduction values. The quadrant analysis at y+ 0 = 25 shows that the addition of polymers inclines the principal axis of v versus u plot to almost zero (horizontal) as the joint probability density function of fluctuations becomes symmetric with respect to the u axis at MDR. The reduction of turbulence production is mainly associated with the attenuation of the ejection motions. The spatial-correlation of the fluctuating velocity field shows that increasing the polymer concentration increases the spatial coherence of u fluctuations in the streamwise direction while they appear to have the opposite effect in the wall-normal direction. The proper orthogonal decomposition of velocity fluctuations shows that the inclined shear layer structure of Newtonian wall flows becomes horizontal at the MDR and does not contribute to turbulence production.

We discuss the entropy generation minimization for electro-osmotic flow of a viscoelastic fluid through a parallel plate microchannel under the combined influences of interfacial slip and conjugate transport of heat. We use in this study the simplified Phan-Thien–Tanner model to describe the rheological behavior of the viscoelastic fluid. Using Navier’s slip law and thermal boundary conditions of the third kind, we solve the transport equations analytically and evaluate the global entropy generation rate of the system. We examine the influential role of the following parameters on the entropy generation rate of the system, viz., the viscoelastic parameter (εDe2), Debye–Hückel parameter κ¯, channel wall thickness (δ), thermal conductivity of the wall (γ), Biot number (Bi), Peclet number (Pe), and axial temperature gradient (B). This investigation finally establishes the optimum values of the abovementioned parameters, leading to the minimum entropy generation of the system. We believe that results of this analysis could be helpful in optimizing the second-law performance of microscale thermal management devices, including the micro-heat exchangers, micro-reactors, and micro-heat pipes.

This paper considers the linear stability of confined planar impinging jet flow of a non-Newtonian inelastic fluid. The rheology is shear rate dependent with asymptotic Newtonian behavior in the zero shear limit, and the analysis examines both shear thinning and shear thickening behavior. The planar configuration is such that the width of the inlet nozzle is smaller than the distance from the jet exit to the impinging surface, giving an aspect ratio e = 8 for which two-dimensional time dependent flow is readily manifest. For values of the power-law index n in the range 0.4≤n≤1.1, the bi-global linear stability of the laminar flow is analyzed for Newtonian Reynolds numbers Re ≲200. The calculations show that for certain values of n, including the Newtonian value n = 1, the steady flow exhibits multiplicity leading to hysteresis in the primary separation vortex reattachment point and a consequent jump in stability behavior. Even in the absence of hysteresis, relatively small changes in viscosity significantly affect stability characteristics. For Newtonian and mildly shear thinning or shear thickening fluids, an unstable flow shows a decaying perturbation growth rate as Re is increased, and for certain values of n, the flow may be restabilized at a larger Re before eventually becoming unstable again. This decay in the growth rate of the critical antisymmetric mode may be correlated as a function of the reattachment point RP of the primary separation vortex in the underlying steady flow. Representative results are analyzed in detail and discussed in the context of some experimental observations of time-dependent Newtonian impinging flow. The stability results are used to construct the neutral stability curve (n, Re) that displays multiplicity and contains several cusp points associated with flow restabilization and hysteresis. Integration of the full nonlinear equation reveals the structure of the time periodic flow field for both Newtonian and non-Newtonian fluids at Reynolds numbers well beyond the instability threshold.

In this work, an analytical solution for the pressure-driven flow of a discontinuous shear-thickening (DST) fluid in a planar channel is presented. In order to model the fluid rheology, a regularized inverse-biviscous model is adopted. This involves a region of finite thickness to model the sharp jump in viscosity, and it is consistent with momentum conservation. In the limit of vanishing thickness, the truly DST behavior is obtained. Analytical results are validated by numerical simulations under steady and start-up flow using the smoothed particle hydrodynamics method. Flow results are investigated and discussed for different values of the model parameters.

In this paper, we numerically investigate the hydrodynamic interaction between a self-rotation rotator and passive particles in a two-dimensional confined cavity at two typical Reynolds numbers according to the different flow features. Both the fluid-particle interaction and particle-particle interaction through fluid media are taken into consideration. The results show that from the case of a rotator and one passive particle to the case of a rotator and two passive particles, the system becomes much more complex because the relative displacement between the rotator and the passive particles and the velocity of passive particles are strongly dependent on the Reynolds number and the initial position of passive particles. For the system of two particles, the passive particle gradually departs from the rotator although its relative displacement to the rotator exhibits a periodic oscillation at the lower Reynolds number. Furthermore, the relative distance between the two particles and the rotator’s rotational frequency are responsible for the oscillation amplitude and frequency of the passive particle’s velocity. For the system of three particles, the passive particle’s velocities exhibit a superposition of a large amplitude oscillation and a small amplitude oscillation at the lower Reynolds number, and the large amplitude oscillation will disappear at the higher Reynolds number. The change of the included angle of the two passive particles is dependent on the initial positions of the passive particles at the lower Reynolds number, whereas the included angle of the two passive particles finally approaches a fixed value at the higher Reynolds number. It is interesting that the two passive particles periodically approach and depart from each other when the included angle is not equal to π, while all the three particles (including the rotator) keep the positions in a straight line when the included angle is equal to π because the interference between two passive particles disappears. In addition, the passive particle rotates not only around the rotator but also around its own axis, and the rotation speed of the former is far greater than that of the latter.

Granular materials are ubiquitous in our daily life and inherent in multitudinous industrial processes. Differences in the granular properties such as size and density inevitably induce segregation. By means of the discrete element method, a binary-size mixture in a three-dimensional rotating drum is numerically simulated to explore the segregation dynamics of the granular material along the axial direction. Snapshots of the distribution of the two particle types in the rotating drum are presented with respect to time to illustrate the spatial evolution of the size-induced segregation structure. The space-time plots of various axial characteristics indicate that (i) radial segregation does not affect the axial distribution of total mass and mass fraction, but axial segregation leads to the formation of axial bands; (ii) greater non-dimensionalized collision forces for both the large and small particles develop where the large particles dominate; and (iii) axial segregation gives rise to the variation of the gyration radii of both particle types along the drum length. In addition, axial flow of both particle types in both directions indicates the dynamic axial exchanges, and the effect of the end walls on the axial flow direction is limited to less than 25% of the drum length from the end walls.

Material flow in a rectangular quasi-two-dimensional silo discharging simultaneously through two orifices has been investigated. A number of variations of the proximity of the sidewall of the silo with an individual orifice and the distance between the two orifices have been tried. It has been observed that beyond a certain distance between the two orifices, a neutral axis parallel to the axes of the orifices can be identified. The neutral axis divides the flow field in the silo between two non-interfering zones each of which is created due to the flow through a single orifice. Flow field created by a single orifice on the other hand depends on its proximity to the sidewall. Based on the above observation, an extension of the kinematic model for material discharge through a single orifice has been extended for predicting the velocity field during simultaneous discharge through two orifices. Based on the distance between two orifices, the limitation of this model has also been predicted.

Interface-resolved direct numerical simulations of the particle-laden turbulent flows in a square duct are performed with a direct-forcing fictitious domain method. The effects of the finite-size particles on the mean and root-mean-square (RMS) velocities are investigated at the friction Reynolds number of 150 (based on the friction velocity and half duct width) and the particle volume fractions ranging from 0.78% to 7.07%. Our results show that the mean secondary flow is enhanced and its circulation center shifts closer to the center of the duct cross section when the particles are added. The reason for the particle effect on the mean secondary flow is analyzed by examining the terms in the mean streamwise vorticity equation. It is observed that the particles enhance the gradients of the secondary Reynolds normal stress difference and shear stress in the near-wall region near the corners, which we think is mainly responsible for the enhancement in the mean secondary flow. Under a prescribed driving pressure gradient, the presence of particles attenuates the bulk velocity and the turbulent intensity. All particle-induced effects are intensified with increasing particle volume fraction and decreasing particle size, if other parameters are fixed. In addition, the particles accumulate preferentially in the near-corner region. The effects of the type of the collision model (i.e., if friction and damping are included or not) on the results are found significant, but not so significant to bring about qualitatively different results.

Head-on collisions between droplets and spherical particles are examined for water droplets in the diameter range between 170 μm and 280 μm and spherical particles in the diameter range between 500 μm and 2000 μm. The droplet velocities range between 6 m/s and 11 m/s, while the spherical particles are fixed in space. The Weber and Ohnesorge numbers and ratio of droplet to particle diameter were between 92 < We < 1015, 0.0070 < Oh < 0.0089, and 0.09 < Ω < 0.55, respectively. The droplet-particle collisions are first quantified in terms of the outcome. In addition to the conventional deposition and splashing regimes, a regime is observed in the intermediate region, where the droplet forms a stable crown, which does not breakup but propagates along the particle surface and passes around the particle. This regime is prevalent when the droplets collide on small particles. The characteristics of the collision at the onset of rim instability are also described in terms of the location of the film on the particle surface and the orientation and length of the ejected crown. Proper orthogonal decomposition identified that the first 2 modes are enough to capture the overall morphology of the crown at the splashing threshold.

Binary collision of unequal-size droplets was investigated numerically by using the front tracking method, with particular emphasis in studying the kinetic energy recovery and the interface hysteresis of bouncing droplets. The numerical results were sufficiently validated against the high-quality experimental data in the literature to verify the quantitative predictivity of the numerical methodology in simulating droplet bouncing. Distinct stages of droplet deformation and viscous dissipation during droplet collision were revealed and explained for their dependence on the Weber number and the size ratio. A linear fitting formula that well correlates the kinetic energy recovery factor of bouncing droplets with various collision parameters was proposed and would be practically useful in modeling inelastic droplet bouncing in Lagrangian spray simulation. As an interesting post-collision characteristic of bouncing droplets, the interface hysteresis was found to favor smaller droplet deformation by decreasing the size ratio or decreasing the Weber number or increasing the Ohnesorge number.

The effects of dilatancy on the collapse dynamics of granular materials in air or in a liquid are studied experimentally and numerically. Experiments show that dilatancy has a critical effect on the collapse of granular columns in the presence of an ambient fluid. Two regimes of the collapse, one being quick and the other being slow, are observed from the experiments and the underlying reasons are analyzed. A two-fluid smoothed particle hydrodynamics model, based on the granular-fluid mixture theory and the critical state theory, is employed to investigate the complex interactions between the solid particles and the ambient water. It is found that dilatancy, resulting in large effective stress and large frictional coefficient between solid particles, helps form the slow regime. Small permeability, representing large inter-phase drag force, also retards the collapse significantly. The proposed numerical model is capable of reproducing these effects qualitatively.

Euler-Lagrange simulations of gas-solid flows in unbounded domains have been performed to study sub-grid modeling of the filtered drag force for non-cohesive and cohesive particles. The filtered drag forces under various microstructures and flow conditions were analyzed in terms of various sub-grid quantities: the sub-grid drift velocity, which stems from the sub-grid correlation between the local fluid velocity and the local particle volume fraction, and the scalar variance of solid volume fraction, which is a measure to identify the degree of local inhomogeneity of volume fraction within a filter volume. The results show that the drift velocity and the scalar variance exert systematic effects on the filtered drag force. Effects of particle and domain sizes, gravitational accelerations, and mass loadings on the filtered drag are also studied, and it is shown that these effects can be captured by both sub-grid quantities. Additionally, the effect of cohesion force through the van der Waals interaction on the filtered drag force is investigated, and it is found that there is no significant difference on the dependence of the filtered drag coefficient of cohesive and non-cohesive particles on the sub-grid drift velocity or the scalar variance of solid volume fraction. The assessment of predictabilities of sub-grid quantities was performed by correlation coefficient analyses in a priori manner, and it is found that the drift velocity is superior. However, the drift velocity is not available in “coarse-grid” simulations and a specific closure is needed. A dynamic scale-similarity approach was used to model drift velocity but the predictability of that model is not entirely satisfactory. It is concluded that one must develop a more elaborate model for estimating the drift velocity in “coarse-grid” simulations.

A direct numerical simulation is applied to investigate three-dimensional unsteady flow characteristics around a finite wall-mounted square cylinder with an aspect ratio of 7 at a Reynolds number (Re) of 40-250. Determination of Re for the onset of vortex shedding and Re influence on the wake structure and integral parameters are the major objectives of the current research. The results show that the vortex shedding inception occurs within the range of 75 < Re < 85. Re has a considerable effect on the mean wake topology and integral parameters. As such, the wake flow changes from a dipole to a quadrupole type, when the flow changes from steady to unsteady. A transition flow commences at Re = 150-200, where the wake instabilities are intensified with increasing Re, and the force signal oscillation alters from a sinusoidal to a chaotic type. Finally, the wake flow becomes turbulent at Re > 200.

In this research article, we investigated the phenomena of a buoyancy-driven cross-flow impinging on a bulk flow from the inlet for a flow past a pair of side-by-side square cylinders in a confined channel wall (which are kept in an adiabatic condition), a special case of an “internal flow” type problem. The density difference in the flow was achieved through a subtle temperature difference between the ambient fluid and the solid walls present in the domain. The study has been carried out at the Reynolds number Re = 1–40 for a transverse gap ratio s/d = 0.7–10 and the Richardson number Ri = 0–1 at a constant value of the Prandtl number Pr = 50. During a rigorous parametric study, we found that the mixed convection not only brings an early unsteadiness in the flow but also fetches an early formation of different flow regimes at Re = 40. An effort has been made to identify the precise near-wake formations leading to the vortex shedding processes in a mixed convection flow for a various range of s/d values. Different flow regimes can be identified efficiently through a unique combination of occurrences for dominant frequencies in terms of the Strouhal number St of primary, secondary, and harmonic frequencies in the flow. The time variant lift plots indicate that the unsteady periodicity in the flow varies from sinusoidal nature at s/d = 0.7 (single body type flow) to square wave (non-sinusoidal periodic waveform) for s/d = 1.5 (chaotic flow) and finally getting back to sinusoidal at s/d = 6 (non-interacting flow). We have also encountered the drastic pattern changes in the flow which occurred due to the onset of recirculation followed by the transition of steady to unsteady periodic nature with Re = 1–40 for all the values of s/d. This case is analyzed in detail through the study of various flow parameters.

A semi-analytical model is presented for pressure-driven flow through a channel, where local pressure loss is incurred at a sudden change in the boundary condition: from no-slip to partial-slip. Assuming low-Reynolds-number incompressible flow and periodic stick–slip wall patterning, the problems for parallel-plate and circular channels are solved using the methods of eigenfunction expansion and point match. The present study aims to examine in detail how the flow will evolve, on passing through the cross section at which the change in the slip condition occurs, from a no-slip parabolic profile to a less sheared profile with a boundary slip. The present problem is germane to, among other applications, flow through a channel bounded by superhydrophobic surfaces, which intrinsically comprise an array of no-slip and partial-slip segments. Results are presented to show that the sudden change in the boundary condition will result in additional resistance to the flow. Near the point on the wall where a slip change occurs is a region of steep pressure gradient and intensive vorticity. The acceleration of near-wall fluid particles in combination with the no-slip boundary condition leads to a very steep velocity gradient at the wall, thereby a sharp increase in the wall shear stress, shortly before the fluid enters the channel with a slippery wall. Results are also presented to show the development of flow in the entrance region in the slippery channel. The additional pressure loss can be represented by a dimensionless loss parameter, which is a pure function of the slip length for channels much longer than the entrance length.

In this work, we investigate the motion, interaction, and simultaneous collision between many initially stable vortex rings arranged symmetrically in two initial configurations, three and six rings making an angle of 60 and 120° between their straight path lines, respectively. We report results for laminar vortex rings in air obtained through numerical simulations of the ring velocity, pressure, and vorticity fields, both in free flight and during the entire collision. Each collision was studied for small Reynolds numbers Re<103 based on both the self-induced velocity and diameter of the ring. The case of three rings produces secondary vortical structures formed by laterally expanding dipolar arms with top and bottom secondary vortex rings. The case of six colliding rings produces, as secondary structures, two big rings moving in opposite directions, a process that reminds us of the head-on collision of two rings [T. T. Lim and T. B. Nickels, “Instability and reconnection in the head-on collision of two vortex rings,” Nature 357, 225–227 (1992)] under a hypothetical time reversal transformation. Both collisions display a characteristic kinetic energy evolution where mean collision stages can be identified within the range of Reynolds numbers investigated here.

An analysis of heat transfer in non-uniformly heated corrugated slots has been carried out. A sinusoidal corrugation is placed at the lower plate that is exposed to heating consisting of uniform and sinusoidal components, while the upper smooth plate is kept isothermal. The phase difference ΩTL describes the shift between the heating and geometric non-uniformities. The analysis is limited to heating conditions that do not give rise to secondary motions. Depending on ΩTL, the conductive heat flow is directed either upwards, or downwards, or is eliminated. Its magnitude is smallest for the long-wavelength systems and largest for the short-wavelength systems, and it increases proportionally to the corrugation amplitude and heating intensity. The same heating creates horizontal temperature gradients that give rise to convection whose form depends on ΩTL. Convection consists of counter-rotating rolls with the size dictated by the system wavelength when the hot spots (points of maximum temperature) overlap either with the corrugation tips or with the corrugation bottoms. Thermal drift forms for all other values of ΩTL. The convective heat flow is always directed upwards, and it is the largest in systems with wavelengths comparable to the slot height. The magnitude of the overall heat flow increases proportionally to the heating intensity when conductive effects dominate and proportionally to the second power of the heating intensity when convection dominates. It also increases proportionally to the corrugation amplitude. The system characteristics are dictated by convection when the relative position of the heating and corrugation patterns eliminates conduction. Addition of the uniform heating component amplifies the above processes, while uniform cooling reduces them. The processes described above are qualitatively similar for all Prandtl numbers of practical interest with the magnitude of the convective heat flow increasing with Pr.

In this paper, we report two novel theoretical approaches to examine a fast-developing flow in a thin fluid gap, which is widely observed in industrial applications and biological systems. The problem is featured by a very small Reynolds number and Strouhal number, making the fluid convective acceleration negligible, while its local acceleration is not. We have developed an exact solution for this problem which shows that the flow starts with an inviscid limit when the viscous effect has no time to appear and is followed by a subsequent developing flow, in which the viscous effect continues to penetrate into the entire fluid gap. An approximate solution is also developed using a boundary layer integral method. This solution precisely captures the general behavior of the transient fluid flow process and agrees very well with the exact solution. We also performed numerical simulation using Ansys-CFX. Excellent agreement between the analytical and the numerical solutions is obtained, indicating the validity of the analytical approaches. The study presented herein fills the gap in the literature and will have a broad impact on industrial and biomedical applications.

A compulsory element of all textbooks on natural convection has been a detailed similarity analysis for laminar natural convection on a heated semi-infinite vertical plate and a routinely used boundary condition for such analysis is u = 0 at x = 0. The same boundary condition continues to be assumed in related theoretical analyses, even in recent publications. The present work examines the consequence of this long-held assumption, which appears to have never been questioned in the literature, on the fluid dynamics and heat transfer characteristics. The assessment has been made here by solving the Navier-Stokes equations numerically with two boundary conditions—one with constrained velocity at x = 0 to mimic the similarity analysis and the other with no such constraints simulating the case of a heated vertical plate in an infinite expanse of the quiescent fluid medium. It is found that the fluid flow field given by the similarity theory is drastically different from that given by the computational fluid dynamics (CFD) simulations with unconstrained velocity. This also reflects on the Nusselt number, the prediction of the CFD simulations with unconstrained velocity being quite close to the experimentally measured values at all Grashof and Prandtl numbers (this is the first time theoretically computed values of the average Nusselt number Nu¯ are found to be so close to the experimental values). The difference of the Nusselt number (ΔNu¯) predicted by the similarity theory and that by the CFD simulations (as well as the measured values), both computed with a high degree of precision, can be very significant, particularly at low Grashof numbers and at Prandtl numbers far removed from unity. Computations show that within the range of investigations (104 ≤ GrL ≤ 108, 0.01 ≤ Pr ≤ 100), the maximum value of ΔNu¯ may be of the order 50%. Thus, for quantitative predictions, the available theory (i.e., similarity analysis) can be rather inadequate. With the help of the CFD simulations, the details of the fluid dynamics, particularly the physics of fluid entrainment, are thoroughly studied. It is shown that the relative proportions of the fluid entrainment from the bottom, top, and side of the vertical plate depend on the size of the region of interest (ROI). As the size of the ROI is made large, most of the entrained fluid comes from the bottom, a little bit from the top and almost no fluid enters from the side; the nature of entrainment is opposite in the similarity analysis for which all the fluid enters from the side and no fluid enters either from the bottom or the top. The two sets of CFD simulations establish, in particular, the conclusion that it is the inappropriateness of the age-old boundary condition u = 0 at x = 0, and not the boundary layer approximation, that is the principal cause for the vulnerability of the standard similarity analyses (and integral theories) for natural convection. The CFD solutions further demonstrate the effects of finite length and finite thickness of the plate on the flow field and the shape of the buoyant jet. The different boundary conditions on the two sides of the vertical plate and the presence of its finite thickness make the buoyant jet bend over the top edge of the plate and make the evolution of entrainment from the two sides of the free buoyant jet different. The entrainment velocity from the two sides, however, equilibrates at a certain distance above the plate. The asymmetry in the velocity and temperature fields above the plate decreases more rapidly when Pr is smaller and GrL is greater. It is shown that sufficiently above the plate, the distributions of axial velocity and temperature in the buoyant jet tend to be symmetric with respect to an axis that seems to pass through the vertical mid-plane of the plate, i.e., the jet tends to lose its history of origination.

The heuristic Fermi-Neumann box model is used to study the non-Boussinesq lock exchange flows in an infinite horizontal channel. This allowed us to find the asymptotic growth laws for intrusion tongues at a late stage of their development. It is shown that these laws are essentially different. The classical scenario of the linear growth x1∝t is supported only by the lower (heavy) intrusion tongue. The same is not true for the upper (light) intrusion tongue that obeys the law x2∝t/lnt.

In this paper, we propose to explore experimentally the origin of the onset of motion in a well-known Carbopol gel, a concentrated suspension of microgels, when submitted to a vertical temperature gradient, namely, the Rayleigh-Bénard Convection (RBC). We consider three possible scenarios: (i) the gel behaves as an elasto-viscoplastic material, (ii) the gel presents a low-stress viscosity μ+ below the yield stress τy, and (iii) the gel can be considered as a two phase system, say the microgels and the solvent, i.e., a porous medium. We propose a complete rheological characterization of Carbopol 940. Creep measurements lead to obtain an instantaneous viscosity plateau μ+∼tm with m≈1. For the first time, we measure and provide permeability values k in the Carbopol gels. We show that k = O(10−14) m2 and k∝τy0.2. Our study focuses on the reference case of the RBC with no-slip conditions at walls, and new results are provided. The results lead to the conclusion that the control parameter is the (inverse) of the yield number Y, ratio between the yield stress and the buoyancy stress, and they show that the critical value is 1/Yc≈80 for no-slip conditions. One shows that both scenarios (i) and (ii) lead to recover 1/Y as the control parameter. By considering the Carbopol gels as porous media [scenario (iii)], one finds that the critical porous Rayleigh-Darcy number is Rap = O(10−4).

This paper validates the theory of linear stability as applied to a fluid flowing down a vertically inclined plane using experimental comparison. The theoretically predicted mode 1 instability, corresponding to a surface wave oscillating at half the forcing frequency, is found to exist alongside the mode 2 instability, corresponding to a surface wave oscillating at the forcing frequency. Instability onset amplitude and frequency were compared, and an investigation of wavenumber with forcing amplitude at several distinct frequencies further confirmed the validity of the theory. A study of the wavenumber trend revealed distinct differences in the stability and development of the surface wave with increasing forcing amplitude. An analysis of the Womersley number, which expresses the ratio of the oscillatory inertia force to the viscous shear force, provides a physical indication of the differences in the wavenumber trend observed.

The flow in the off-design operation of a Francis turbine may lead to the formation of spiral vortex breakdowns in the draft tube, a diffuser installed after the runner. The spiral vortex breakdown, also named a vortex rope, may induce several low-frequency fluctuations leading to structural vibrations and a reduction in the overall efficiency of the turbine. In the present study, synchronized particle image velocimetry, pressure, and turbine flow parameter (Q, H, α, and T) measurements have been carried out in the draft tube cone of a high head model Francis turbine. The transient operating condition from the part load to the best efficiency point was selected to investigate the mitigation of the vortex rope in the draft tube cone. The experiments were performed 20 times to assess the significance of the results. A precession frequency of 1.61 Hz [i.e., 0.29 times the runner rotational frequency (Rheingans frequency)] is observed in the draft tube cone. The frequency is captured in both pressure and velocity data with its harmonics. The accelerating flow condition at the center of the cone with a guide vane opening is observed to diminish the spiral form of the vortex breakdown in the quasi-stagnant region. This further mitigates the stagnant part of the cone with a highly dominated axial flow condition of the turbine at the best efficiency point. The disappearance of the stagnant region is the most important state in the present case, which mitigates the spiral vortex breakdown of the cone at high Reynolds numbers. In contrast to a typical transition, a new type of transition from wake to jet is observed during the mitigation of the breakdown. The obtained 2D instantaneous velocity fields demonstrate the disappearance region of shear layers and stagnation in the cone. The results also demonstrate the existence of high axial velocity gradients in an elbow draft tube cone.

Spin-up of turbulent channel flow forced with a constant mean pressure gradient is prolonged because the flow accelerates due to an imbalance between the driving pressure gradient and total bottom stress. To this end, a method ensuring a time invariant volume-averaged streamwise velocity during spin-up is presented and compared to simulations forced with a mean pressure gradient for both linear and logarithmic initial velocity profiles. The comparisons are made for open-channel flow with a friction Reynolds number Reτ of 500. Additional simulations with Reτ ranging from 1 to 400 are also run to confirm validity of the method for a range of Reynolds numbers. While the method eliminates spin-up time related to approaching the target volume-averaged velocity, spin-up time is still required for the flow to transition to turbulence and reach statistical equilibrium. Therefore, the time evolution of turbulence in response to different initial velocity profiles and random perturbations is investigated. Simulations initialized with linear velocity profiles trigger turbulence and reach statistical equilibrium sooner than those initialized with logarithmic profiles given the same initial perturbations, a manifestation of the increased shear created by linear profiles. The results suggest that, combined with appropriate initial conditions, ensuring a time invariant volume-averaged streamwise velocity can reduce the computational time associated with spin-up of turbulent open-channel flows by at least a factor of five.

Direct numerical simulations of fully developed turbulent channel flows with wavy walls are undertaken. The wavy walls, skewed with respect to the mean flow direction, are introduced as a means of emulating a Spatial Stokes Layer (SSL) induced by in-plane wall motion. The transverse shear strain above the wavy wall is shown to be similar to that of a SSL, thereby affecting the turbulent flow and leading to a reduction in the turbulent skin-friction drag. However, some important differences with respect to the SSL case are brought to light too. In particular, the phase variations of the turbulent properties are accentuated and, unlike in the SSL case, there is a region of increased turbulence production over a portion of the wall, above the leeward side of the wave, thus giving rise to a local increase in dissipation. The pressure- and friction-drag levels are carefully quantified for various flow configurations, exhibiting a combined maximum overall-drag reduction of about 0.6%. The friction-drag reduction is shown to behave approximately quadratically for small wave slopes and then linearly for higher slopes, whilst the pressure-drag penalty increases quadratically. The transverse shear-strain layer is shown to be approximately Reynolds-number independent when the wave geometry is scaled in wall units.

At the crossroad between flow topology analysis and turbulence modeling, a priori studies are a reliable tool to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent flows. In this paper, properties of the SGS features in the framework of a large-eddy simulation are studied for a turbulent Rayleigh-Bénard convection (RBC). To do so, data from direct numerical simulation (DNS) of a turbulent air-filled RBC in a rectangular cavity of aspect ratio unity and π spanwise open-ended distance are used at two Rayleigh numbers Ra∈{108,1010} [Dabbagh et al., “On the evolution of flow topology in turbulent Rayleigh-Bénard convection,” Phys. Fluids 28, 115105 (2016)]. First, DNS at Ra = 108 is used to assess the performance of eddy-viscosity models such as QR, Wall-Adapting Local Eddy-viscosity (WALE), and the recent S3PQR-models proposed by Trias et al. [“Building proper invariants for eddy-viscosity subgrid-scale models,” Phys. Fluids 27, 065103 (2015)]. The outcomes imply that the eddy-viscosity modeling smoothes the coarse-grained viscous straining and retrieves fairly well the effect of the kinetic unfiltered scales in order to reproduce the coherent large scales. However, these models fail to approach the exact evolution of the SGS heat flux and are incapable to reproduce well the further dominant rotational enstrophy pertaining to the buoyant production. Afterwards, the key ingredients of eddy-viscosity, νt, and eddy-diffusivity, κt, are calculated a priori and revealed positive prevalent values to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. The topological analysis suggests that the effective turbulent diffusion paradigm and the hypothesis of a constant turbulent Prandtl number are only applicable in the large-scale strain-dominated areas in the bulk. It is shown that the bulk-dominated rotational structures of vortex-stretching (and its synchronous viscous dissipative structures) hold the highest positive values of νt; however, the zones of backscatter energy and counter-gradient heat transport are related to the areas of compressed focal vorticity. More arguments have been attained through a priori investigation of the alignment trends imposed by existing parameterizations for the SGS heat flux, tested here inside RBC. It is shown that the parameterizations based linearly on the resolved thermal gradient are invalid in RBC. Alternatively, the tensor-diffusivity approach becomes a crucial choice of modeling the SGS heat flux, in particular, the tensorial diffusivity that includes the SGS stress tensor. This and other crucial scrutinies on a future modeling to the SGS heat flux in RBC are sought.

The concept of dynamic large eddy simulation (LES) is highly attractive: such methods can dynamically adjust to changing flow conditions, which is known to be highly beneficial. For example, this avoids the use of empirical, case dependent approximations (like damping functions). Ideally, dynamic LES should be local in physical space (without involving artificial clipping parameters), and it should be stable for a wide range of simulation time steps, Reynolds numbers, and numerical schemes. These properties are not trivial, but dynamic LES suffers from such problems over decades. We address these questions by performing dynamic LES of periodic hill flow including separation at a high Reynolds number Re = 37 000. For the case considered, the main result of our studies is that it is possible to design LES that has the desired properties. It requires physical consistency: a PDF-realizable and stress-realizable LES model, which requires the inclusion of the turbulent kinetic energy in the LES calculation. LES models that do not honor such physical consistency can become unstable. We do not find support for the previous assumption that long-term correlations of negative dynamic model parameters are responsible for instability. Instead, we concluded that instability is caused by the stable spatial organization of significant unphysical states, which are represented by wall-type gradient streaks of the standard deviation of the dynamic model parameter. The applicability of our realizability stabilization to other dynamic models (including the dynamic Smagorinsky model) is discussed.

Many chemical and environmental processes involve the formation of a polydispersed particulate phase in a turbulent carrier flow. Frequently, the immersed particles are characterized by an intrinsic property such as the particle size, and the distribution of this property across a sample population is taken as an indicator for the quality of the particulate product or its environmental impact. In the present article, we propose a comprehensive model and an efficient numerical solution scheme for predicting the evolution of the property distribution associated with a polydispersed particulate phase forming in a turbulent reacting flow. Here, the particulate phase is described in terms of the particle number density whose evolution in both physical and particle property space is governed by the population balance equation (PBE). Based on the concept of large eddy simulation (LES), we augment the existing LES-transported probability density function (PDF) approach for fluid phase scalars by the particle number density and obtain a modeled evolution equation for the filtered PDF associated with the instantaneous fluid composition and particle property distribution. This LES-PBE-PDF approach allows us to predict the LES-filtered fluid composition and particle property distribution at each spatial location and point in time without any restriction on the chemical or particle formation kinetics. In view of a numerical solution, we apply the method of Eulerian stochastic fields, invoking an explicit adaptive grid technique in order to discretize the stochastic field equation for the number density in particle property space. In this way, sharp moving features of the particle property distribution can be accurately resolved at a significantly reduced computational cost. As a test case, we consider the condensation of an aerosol in a developed turbulent mixing layer. Our investigation not only demonstrates the predictive capabilities of the LES-PBE-PDF model but also indicates the computational efficiency of the numerical solution scheme.

Kolmogorov’s similarity turbulence theory in a Lagrangian frame is assessed with new direct numerical simulations of isotropic turbulence with and without hyperviscosity, which attain higher Reynolds numbers than previously available. It is demonstrated that hyperviscous simulations can be used to accurately predict the second order Lagrangian velocity structure function (LVSF-2) in the inertial range, by using an original new procedure. The results strongly support Kolmogorov’s Lagrangian similarity assumption and allow the universal constant of LVSF-2 to be computed with a new level of confidence with C0=7.4±0.2.

Turbulent Richtmyer–Meshkov instability (RMI) is investigated through a series of high resolution three-dimensional simulations of two initial conditions with eight independent codes. The simulations are initialised with a narrowband perturbation such that instability growth is due to non-linear coupling/backscatter from the energetic modes, thus generating the lowest expected growth rate from a pure RMI. By independently assessing the results from each algorithm and computing ensemble averages of multiple algorithms, the results allow a quantification of key flow properties as well as the uncertainty due to differing numerical approaches. A new analytical model predicting the initial layer growth for a multimode narrowband perturbation is presented, along with two models for the linear and non-linear regimes combined. Overall, the growth rate exponent is determined as θ=0.292±0.009, in good agreement with prior studies; however, the exponent is decaying slowly in time. Also, θ is shown to be relatively insensitive to the choice of mixing layer width measurements. The asymptotic integral molecular mixing measures Θ=0.792±0.014, Ξ=0.800±0.014, and Ψ=0.782±0.013 are lower than some experimental measurements but within the range of prior numerical studies. The flow field is shown to be persistently anisotropic for all algorithms, at the latest time having between 49% and 66% higher kinetic energy in the shock parallel direction compared to perpendicular and does not show any return to isotropy. The plane averaged volume fraction profiles at different time instants collapse reasonably well when scaled by the integral width, implying that the layer can be described by a single length scale and thus a single θ. Quantitative data given for both ensemble averages and individual algorithms provide useful benchmark results for future research.

The intermittency of turbulent superfluid helium is explored systematically in a steady wake flow from 1.28 K up to T>2.18K using a local anemometer. This temperature range spans relative densities of superfluids from 96% down to 0%, allowing us to test numerical predictions of enhancement or depletion of intermittency at intermediate superfluid fractions. Using the so-called extended self-similarity method, scaling exponents of structure functions have been calculated. No evidence of temperature dependence is found on these scaling exponents in the upper part of the inertial cascade, where turbulence is well developed and fully resolved by the probe. This result supports the picture of a profound analogy between classical and quantum turbulence in their inertial range, including the violation of self-similarities associated with inertial-range intermittency.

In this paper, a gradient-based refinement of the rotation rate-based Smagorinsky (RoSM) subgrid scale (SGS) model is presented. The refined model satisfies the Galilean invariance condition generally, without any assumptions. The suggested model retains the advantages offered by the original RoSM, thus being simple and efficient. It provides a Smagorinsky model constant that is always positive, with low fluctuations in space and time, without the need for any numerical stability control algorithms. The validity of the proposed SGS model is shown through three test cases, namely, a turbulent channel flow, subcritical flow past a stationary cylinder, and a spatially developing free round jet. The refined RoSM provides comparable results with the dynamic Smagorinsky, while matching well to reference data. The refined RoSM is shown to be computationally efficient, being 20% faster than the dynamic Smagorinsky model.

In this work, we investigate the influence of compressibility on vorticity-strain rate dynamics. Well-resolved direct numerical simulations of compressible homogeneous isotropic turbulence performed over a cubical domain of 10243 are employed for this study. To clearly identify the influence of compressibility on the time-dependent dynamics (rather than on the one-time flow field), we employ a well-validated Lagrangian particle tracker. The tracker is used to obtain time correlations between the instantaneous vorticity vector and the strain-rate eigenvector system of an appropriately chosen reference time. In this work, compressibility is parameterized in terms of both global (turbulent Mach number) and local parameters (normalized dilatation-rate and flow field topology). Our investigations reveal that the local dilatation rate significantly influences these statistics. In turn, this observed influence of the dilatation rate is predominantly associated with rotation dominated topologies (unstable-focus-compressing, stable-focus-stretching). We find that an enhanced dilatation rate (in both contracting and expanding fluid elements) significantly enhances the tendency of the vorticity vector to align with the largest eigenvector of the strain-rate. Further, in fluid particles where the vorticity vector is maximally misaligned (perpendicular) at the reference time, vorticity does show a substantial tendency to align with the intermediate eigenvector as well. The authors make an attempt to provide physical explanations of these observations (in terms of moment of inertia and angular momentum) by performing detailed calculations following tetrads {approach of Chertkov et al. [“Lagrangian tetrad dynamics and the phenomenology of turbulence,” Phys. Fluids 11(8), 2394–2410 (1999)] and Xu et al. [“The pirouette effect in turbulent flows,” Nat. Phys. 7(9), 709–712 (2011)]} in a compressible flow field.

We present a joint experimental and numerical study of the flow structure within a cylindrical chamber generated by planar-symmetric isothermal jets, under conditions of relevance to a wide range of practical applications, including the Hybrid Solar Receiver Combustor (HSRC) technology. The HSRC features a cavity with a coverable aperture to allow it to be operated as either a combustion chamber or a solar receiver, with multiple burners to direct a flame into the chamber and a heat exchanger that absorbs the heat from both energy sources. In this study, we assess the cases of two or four inlet jets (simulating the burners), configured in a planar-symmetric arrangement and aligned at an angle to the axis (αj) over the range of 0°–90°, at a constant inlet Reynolds number of ReD = 10 500. The jets were positioned in the same axial plane near the throat and interact with each other and the cavity walls. Measurements obtained with particle image velocimetry were used together with numerical modeling employing Reynolds-averaged Navier-Stokes methods to characterize the large-scale flow field within selected configurations of the device. The results reveal a significant dependence of the mean flow-field on αj and the number of inlet jets (Nj). Four different flow regimes with key distinctive features were identified within the range of αj and Nj considered here. It was also found that αj has a controlling influence on the extent of back-flow through the throat, the turbulence intensity, the flow stability, and the dominant recirculation zone, while Nj has a secondary influence on the turbulence intensity, the flow stability, and the transition between each flow regime.

The statistical relationships among the turbulence structures of the streamwise velocity fluctuations along the streamwise and azimuthal directions in a turbulent pipe flow were examined using direct numerical simulation data at Reτ = 3008. Two-point correlations of the streamwise velocity fluctuations showed a linear relationship between the streamwise and azimuthal length scales (lx and lθ), where lθ/lx = 0.07 along the wall-normal distance, indicating the long coherent structures called very-large-scale motions (VLSMs). The one-dimensional pre-multiplied energy spectra of the streamwise velocity fluctuations showed that the streamwise and the azimuthal wavelengths (λx and λθ) grew linearly along the wall-normal distance, λx/y = 20 and λθ/y = 7, respectively. The ratio between the two linear relationships was determined to be λθ/λx = 0.35, indicative of large-scale motions (LSMs). The energetic modes obtained from a proper orthogonal decomposition (POD) analysis using the translational invariance method showed that the averaged helical angles of the wall mode (ix < iθ; β < 0.1 rad, where ix and iθ are the streamwise and azimuthal mode numbers and β is the helical angle) and lift mode (ix ≥ iθ; β ≥ 0.1 rad) were related to lθ/lx = 0.07 (VLSMs) and λθ/λx ≈ 0.35 (LSMs), respectively. The superposition of the energetic POD modes showed the superimposed X-shaped patterns. The helical angle of the wall mode in the near-wall region was similar to that in the outer region, implying the existence of the VLSMs in the entire wall-normal distance. The LSMs showed more inclined X-shaped patterns. The LSMs were concatenated with the azimuthal offsets to form meandering VLSMs. Most of the VLSMs and LSMs in the near-wall region inclined smaller and larger than 10° (0.17 rad), respectively. In the core region, VLSMs were distributed more helically along the azimuthal direction due to the space limitations of the pipe geometry.

The interaction between internal waves and submarine seamounts is three-dimensional (3D). In this work, we conduct laboratory experiments to investigate the role of the three-dimensional seamount on the reflection of internal waves. Experimental results show that the energy of internal waves is focused after the reflection and the phase of the internal wave front become curved. The energy of the focusing region was nearly 2 times as that of the scattering region. There is a strong internal wave induced mean flow whose strength is nearly as high as 50% of that of the reflected internal wave. The mean flow was generated by the variation of the velocity amplitude in both the x axis and y axis. These results indicate that the reflection from the 3D seamount could lead to a complex spatial distribution of the internal wave and a different energy conversion process.

The film blowing process is one of the most important polymer processing operations, widely used for producing bi-axially oriented film products in a single-step process. Among the instabilities observed in this film blowing process, i.e., draw resonance and helical motion occurring on the inflated film bubble, the helical instability is a unique phenomenon portraying the snake-like undulation motion of the bubble, having the period on the order of few seconds. This helical instability in the film blowing process is commonly found at the process conditions of a high blow-up ratio with too low a freezeline position and/or too high extrusion temperature. In this study, employing an analogy to the buckling instability for falling viscous threads, the compressive force caused by the pressure difference between inside and outside of the film bubble is introduced into the simulation model along with the scaling law derived from the force balance between viscous force and centripetal force of the film bubble. The simulation using this model reveals a close agreement with the experimental results of the film blowing process of polyethylene polymers such as low density polyethylene and linear low density polyethylene.

The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at unique exact analytical solutions for the normal stress difference responses to large-amplitude oscillatory shear (LAOS) flow. The nonlinearity of the polymeric liquids, triggered by LAOS, causes these responses at even multiples of the test frequency. We call responses at a frequency higher than twice the test frequency higher harmonics. We find the new exact analytical solutions to be compact and intrinsically beautiful. These solutions reduce to those of our previous work on the special case of the corotational Maxwell fluid. Our solutions also agree with our new truncated Goddard integral expansion for the special case of the corotational Jeffreys fluid. The limiting behaviors of these exact solutions also yield new explicit expressions. Finally, we use our exact solutions to see how η∞ affects the normal stress differences in LAOS.

The rheological characterisation of viscoelastic materials undergoing a sol-gel transition at the Gel Point (GP) has important applications in a wide range of industrial, biological, and clinical environments and can provide information regarding both kinetic and microstructural aspects of gelation. The most rigorous basis for identifying the GP involves exploiting the frequency dependence of the real and imaginary parts of the complex shear modulus of the critical gel (the system at the GP) measured under small amplitude oscillatory shear conditions. This approach to GP identification requires that rheological data be obtained over a range of oscillatory shear frequencies. Such measurements are limited by sample mutation considerations (at low frequencies) and, when experiments are conducted using combined motor-transducer (CMT) rheometers, by instrument inertia considerations (at high frequencies). Together, sample mutation and inertia induced artefacts can lead to significant errors in the determination of the GP. Overcoming such artefacts is important, however, as the extension of the range of frequencies available to the experimentalist promises both more accurate GP determination and the ability to study rapidly gelling samples. Herein, we exploit the frequency independent viscoelastic properties of the critical gel to develop and evaluate an enhanced rheometer inertia correction procedure. The procedure allows acquisition of valid GP data at previously inaccessible frequencies (using CMT rheometers) and is applied in a study of the concentration dependence of bovine gelatin gelation GP parameters. A previously unreported concentration dependence of the stress relaxation exponent (α) for critical gelatin gels has been identified, which approaches a limiting value (α = 0.7) at low gelatin concentrations, this being in agreement with previous studies and theoretical predictions for percolating systems at the GP.

Extensional viscosity is a key property of complex fluids that greatly influences the non-equilibrium behavior and processing of polymer solutions, melts, and colloidal suspensions. In this work, we use microfluidics to determine steady extensional viscosity for polymer solutions by directly observing particle migration in planar extensional flow. Tracer particles are suspended in semi-dilute solutions of DNA and polyethylene oxide, and a Stokes trap is used to confine single particles in extensional flows of polymer solutions in a cross-slot device. Particles are observed to migrate in the direction transverse to flow due to normal stresses, and particle migration is tracked and quantified using a piezo-nanopositioning stage during the microfluidic flow experiment. Particle migration trajectories are then analyzed using a second-order fluid model that accurately predicts that migration arises due to normal stress differences. Using this analytical framework, extensional viscosities can be determined from particle migration experiments, and the results are in reasonable agreement with bulk rheological measurements of extensional viscosity based on a dripping-onto-substrate method. Overall, this work demonstrates that non-equilibrium properties of complex fluids can be determined by passive yet non-linear microrheology.

The dynamics of a single laminar buoyant plume in a FENE-P (finitely extensible nonlinear elastic-Peterlin) fluid has been investigated by performing a series of direct simulations over a range of Weissenberg numbers. Examination of this flow has given insight into the heat transfer reduction phenomenon observed recently in more complex Rayleigh-Benard turbulence. The simulations, which were performed with a Rayleigh number of 2.53×106 and a maximal polymeric extension of L = 100, show that the wall heat flux is reduced by about 28% at a Weissenberg number of 20, which is in reasonable agreement with the results obtained in Rayleigh-Benard turbulence. In addition, the global flow kinetic energy was reduced by about one order of magnitude.

By exploiting the reciprocal theorem of Stokes flow, we find an explicit expression for the first order slip length correction, for small protrusion angles, and for transverse shear over a periodic array of curved menisci. The result is the transverse flow analogue of the longitudinal flow result of Sbragaglia and Prosperetti [“A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces,” Phys. Fluids 19, 043603 (2007)]. For small protrusion angles, it also generalizes the dilute-limit result of Davis and Lauga [“Geometric transition in friction for flow over a bubble mattress,” Phys. Fluids 21, 011701 (2009)] to arbitrary no-shear fractions. While the leading order slip lengths for transverse and longitudinal flow over flat no-shear slots are well-known to differ by a factor of 2, the first order slip length corrections for weakly protruding menisci in each flow are found to be identical.

Translational and rotational swimming at small Reynolds numbers of a planar assembly of identical spheres immersed in an incompressible viscous fluid is studied on the basis of a set of equations of motion for the individual spheres. The motion of the spheres is caused by actuating forces and forces derived from a direct interaction potential, as well as hydrodynamic forces exerted by the fluid as frictional and added mass hydrodynamic interactions. The translational and rotational swimming velocities of the assembly are deduced from momentum and angular momentum balance equations. The mean power required during a period is calculated from an instantaneous power equation. Expressions are derived for the mean swimming velocities and the mean power, valid to second order in the amplitude of displacements from the relative equilibrium positions. Hence these quantities can be evaluated for prescribed periodic displacements. Explicit calculations are performed for three spheres interacting such that they form an equilateral triangle in the rest frame of the configuration.