Showing papers in "Physics of Fluids in 2013"

One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to δ+ ≈ 2000

Abstract: One-point statistics are presented for new direct simulations of the zero-pressure-gradient turbulent boundary layer in the range Reθ = 2780–6680, matching channels and pipes at δ+ ≈ 1000–2000. For tripped boundary layers, it is found that the eddy-turnover length is a better criterion than the Reynolds number for the recovery of the largest flow scales after an artificial inflow. Beyond that limit, the integral parameters, mean velocities, Reynolds stresses, and pressure fluctuations of the new simulations agree very well with the available numerical and experimental data, but show clear differences with internal flows when expressed in wall units at the same wall distance and Reynolds number. Those differences are largest in the outer layer, independent of the Reynolds number, and apply to the three velocity components. The logarithmic increase with the Reynolds number of the maximum of the streamwise velocity and pressure fluctuations is confirmed to apply to experimental and numerical internal and ext...

Near-wall turbulence

Abstract: The current state of knowledge about the structure of wall-bounded turbulent flows is reviewed, with emphasis on the layers near the wall in which shear is dominant, and particularly on the logarithmic layer. It is shown that the shear interacts with scales whose size is larger than about one third of their distance to the wall, but that smaller ones, and in particular the vorticity, decouple from the shear and become roughly isotropic away from the wall. In the buffer and viscous layers, the dominant structures carrying turbulent energy are the streamwise velocity streaks, and the vortices organize both the dissipation and the momentum transfer. Farther from the wall, the velocity remains organized in streaks, although much larger ones than in the buffer layer, but the vortices lose their role regarding the Reynolds stresses. That function is taken over by wall-attached turbulent eddies with sizes and lifetimes proportional to their heights. Two kinds of eddies have been studied in some detail: vortex clusters, and ejections and sweeps. Both can be classified into a detached background, and a geometrically self-similar wall-attached family. The latter is responsible for most of the momentum transfer, and is organized into composite structures that can be used as models for the attached-eddy hierarchy hypothesized by Townsend [“Equilibrium layers and wall turbulence,” J. Fluid Mech.11, 97–120 (1961)]. The detached component seems to be common to many turbulent flows, and is roughly isotropic. Using a variety of techniques, including direct tracking of the structures, it is shown that an important characteristic of wall-bounded turbulence is temporally intermittent bursting, which is present at all distances from the wall, and in other shear flows. Its properties and time scales are reviewed, and it is shown that bursting is an important part of the production of turbulent energy from the mean shear. It is also shown that a linearized model captures many of its characteristics.

Experimental study of skin friction drag reduction on superhydrophobic flat plates in high Reynolds number boundary layer flow

Abstract: In this paper, we report the measurement of skin friction drag on superhydrophobic-coated flat plates in high Reynolds (Re) number boundary layer flows, using a high-speed towing tank system. Aluminum flat plates with a large area (4 feet × 2 feet, 3/8 in. thick) and sharpened leading/trailing edges (1 in. long) were prepared as a boundary layer flow model. Spray coating of hydrophobic nanoparticles was applied to make two different types of superhydrophobic coatings: one with low contact angle and high contact angle hysteresis, and the other with high contact angle and low contact angle hysteresis. Skin friction drag of the superhydrophobic plates was measured in the flow speed up to 30 ft/s to cover transition and turbulent flow regimes (105 < ReL < 107), and was compared to that of an uncoated bare aluminum plate. A significant drag reduction was observed on the superhydrophobic plate with high contact angle and low contact angle hysteresis up to ∼30% in transition regime (105 < ReL < 106), which is attributed to the shear-reducing air layer entrapped on the superhydrophobic surface. However, in fully turbulence regime (106 < ReL < 107), an increase of drag was observed, which is ascribed to the morphology of the surface air layer and its depletion by high shear flow. The texture of superhydrophobic coatings led to form a rugged morphology of the entrapped air layer, which would behave like microscale roughness to the liquid flow and offset the drag-reducing effects in the turbulent flow. Moreover, when the superhydrophobic coating became wet due to the removal of air by high shear at the boundary, it would amplify the surface roughness of solid wall and increase the drag in the turbulent flow. The results illustrate that drag reduction is not solely dependent on the superhydrophobicity of a surface (e.g., contact angle and air fraction), but the morphology and stability of the surface air layer are also critical for the effective drag reduction using superhydrophobic surfaces, especially in high Re number turbulent flow regimes.

A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow

Abstract: Superhydrophobic surfaces have attracted much attention lately as they present the possibility of achieving a substantial skin-friction drag reduction in turbulent flows. In this paper, the effects of a superhydrophobic surface, consisting of microgrates aligned in the flow direction, on skin-friction drag in turbulent flows were investigated through direct numerical simulation of turbulent channel flows. The superhydrophobic surface was modeled through a shear-free boundary condition on the air-water interface. Dependence of the effective slip length and resulting skin-friction drag on Reynolds number and surface geometry was examined. In laminar flows, the effective slip length depended on surface geometry only, independent of Reynolds number, consistent with an existing analysis. In turbulent flows, the effective slip length was a function of Reynolds number, indicating its dependence on flow conditions near the surface. The resulting drag reduction was much larger in turbulent flows than in laminar flows, and near-wall turbulence structures were significantly modified, suggesting that indirect effects resulting from modified turbulence structures played a more significant role in reducing drag in turbulent flows than the direct effect of the slip, which led to a modest drag reduction in laminar flows. It was found that the drag reduction in turbulent flows was well correlated with the effective slip length normalized by viscous wall units.

Direct numerical simulation of electroconvective instability and hydrodynamic chaos near an ion-selective surface

Abstract: We present a comprehensive analysis of transport processes associated with electrohydrodynamic chaos in electrokinetic systems containing an ion-selective surface. The system considered is an aqueous symmetric binary electrolyte between an ion-selective surface and a stationary reservoir. Transport is driven by an external electric field. Using direct numerical simulations (DNS) of the coupled Poisson–Nernst–Planck and Navier–Stokes equations in 2D we show significant transitions in flow behavior from coherent vortex pairs to fully chaotic multi-layer vortex structures with a broadband energy spectrum. Additionally, we demonstrate that these vortices can eject both positive and negative free charge density into the bulk of the domain and completely disrupt the structure of the traditionally described extended space charge region. The resulting dynamical behavior poses a challenge for traditional asymptotic modeling that relies on the quasi-electroneutral bulk assumption. Furthermore, we quantify for the first time the relative importance of energy dissipation due to viscous effects in various transport regimes. Finally, we present a framework for the development of ensemble-averaged models (similar to Reynolds Averaged Navier–Stokes equations) and assess the importance of the unclosed terms based on our DNS data.

Spontaneous autophoretic motion of isotropic particles

Abstract: Suspended colloidal particles interacting chemically with a solute can self-propel by autophoretic motion when they are asymmetrically patterned (Janus colloids). Here we demonstrate theoretically that such anisotropy is not necessary for locomotion and that the nonlinear interplay between surface osmotic flows and solute advection can produce spontaneous and self-sustained motion of isotropic particles. Solving the classical autophoretic framework for isotropic particles, we show that, for given material properties, there exists a critical particle size (or Peclet number) above which spontaneous symmetry-breaking and autophoretic motion occur. A hierarchy of instabilities is further identified for quantized critical Peclet numbers.

On the transition between two-phase and single-phase interface dynamics in multicomponent fluids at supercritical pressures

Abstract: A theory that explains the operating pressures where liquid injection processes transition from exhibiting classical two-phase spray atomization phenomena to single-phase diffusion-dominated mixing is presented. Imaging from a variety of experiments have long shown that under certain conditions, typically when the pressure of the working fluid exceeds the thermodynamic critical pressure of the liquid phase, the presence of discrete two-phase flow processes become diminished. Instead, the classical gas-liquid interface is replaced by diffusion-dominated mixing. When and how this transition occurs, however, is not well understood. Modern theory still lacks a physically based model to quantify this transition and the precise mechanisms that lead to it. In this paper, we derive a new model that explains how the transition occurs in multicomponent fluids and present a detailed analysis to quantify it. The model applies a detailed property evaluation scheme based on a modified 32-term Benedict-Webb-Rubin equation of state that accounts for the relevant real-fluid thermodynamic and transport properties of the multicomponent system. This framework is combined with Linear Gradient Theory, which describes the detailed molecular structure of the vapor-liquid interface region. Our analysis reveals that the two-phase interface breaks down not necessarily due to vanishing surface tension forces, but due to thickened interfaces at high subcritical temperatures coupled with an inherent reduction of the mean free molecular path. At a certain point, the combination of reduced surface tension, the thicker interface, and reduced mean free molecular path enter the continuum length scale regime. When this occurs, inter-molecular forces approach that of the multicomponent continuum where transport processes dominate across the interfacial region. This leads to a continuous phase transition from compressed liquid to supercritical mixture states. Based on this theory, a regime diagram for liquid injection is developed that quantifies the conditions under which classical sprays transition to dense-fluid jets. It is shown that the chamber pressure required to support diffusion-dominated mixing dynamics depends on the composition and temperature of the injected liquid and ambient gas. To illustrate the method and analysis, we use conditions typical of diesel engine injection. We also present a companion set of high-speed images to provide experimental validation of the presented theory. The basic theory is quite general and applies to a wide range of modern propulsion and power systems such as liquid rockets, gas turbines, and reciprocating engines. Interestingly, the regime diagram associated with diesel engine injection suggests that classical spray phenomena at typical injection conditions do not occur.

Reynolds-number scaling of turbulent channel flow

Abstract: Results of an experimental study of smooth-wall, fully developed, turbulent channel flow are presented. The Reynolds number (Rem) based on the channel height and the bulk mean velocity ranged from 10 000 to 300 000. The present results indicate that the skin-friction coefficient (Cf) closely follows a power law for Rem < 62 000. At higher Reynolds numbers, Cf is best described by a log law. Detailed two-component velocity measurements taken at friction Reynolds numbers of Reτ = 1000–6000 indicate that the mean flow and Reynolds shear stress display little or no Reynolds-number dependence. The streamwise Reynolds normal stress (u′2¯+), on the other hand, varies significantly with Reynolds number. The inner peak in u′2¯+ is observed to grow with Reynolds number. Growth in u′2¯+ farther from the wall is documented over the entire range of Reynolds number giving rise to a plateau in the streamwise Reynolds normal stress in the overlap region of the profile for Reτ = 6000. The wall-normal Reynolds normal stres...

Large-eddy simulation of highly underexpanded transient gas jets

Abstract: Large-eddy simulations (LES) based on scale-selective implicit filtering are carried out in order to study the effect of nozzle pressure ratios on the characteristics of highly underexpanded jets. Pressure ratios ranging from 4.5 to 8.5 with Reynolds numbers of the order 75 000–140 000 are considered. The studied configuration agrees well with the classical picture of the structure of highly underexpanded jets. Similarities and differences between simulation and experiments are discussed by comparing the concentration field structures from LES and planar laser induced fluorescence data. The transient stages, leading eventually to the highly underexpanded state, are visualized and investigated in terms of a phase diagram revealing the shock speeds and duration of the transient stages. For the studied nozzle pressure ratio range, the Mach disk dimensions are found to be in good agreement with literature data and experimental observations. It is observed how the nozzle pressure ratio influences the Mach disk width, and thereby the slip line separation, which leads to co-annular jets with inner and outer shear layers at higher pressure ratios. The improved mixing with increasing pressure ratio is demonstrated by the probability density functions of the concentration. The coherent structures downstream of the Mach disk are identified using proper orthogonal decomposition (POD). The structures indicate a helical mode originating from the shear layers of the jet. Despite the relatively low energy content of the dominant POD modes, the frequencies of the POD time coefficients explain the dominant frequencies in the pressure fluctuation spectra.

Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface

Abstract: Dry, frictional, steady-state granular flows down an inclined, rough surface are studied with discrete particle simulations. From this exemplary flow situation, macroscopic fields, consistent with the conservation laws of continuum theory, are obtained from microscopic data by time-averaging and spatial smoothing (coarse-graining). Two distinct coarse-graining length scale ranges are identified, where the fields are almost independent of the smoothing length w. The smaller, sub-particle length scale, w ≪ d, resolves layers in the flow near the base boundary that cause oscillations in the macroscopic fields. The larger, particle length scale, w ≈ d, leads to smooth stress and density fields, but the kinetic stress becomes scale-dependent; however, this scale-dependence can be quantified and removed. The macroscopic fields involve density, velocity, granular temperature, as well as strain-rate, stress, and fabric (structure) tensors. Due to the plane strain flow, each tensor can be expressed in an inherently anisotropic form with only four objective, coordinate frame invariant variables. For example, the stress is decomposed as: (i) the isotropic pressure, (ii) the “anisotropy” of the deviatoric stress, i.e., the ratio of deviatoric stress (norm) and pressure, (iii) the anisotropic stress distribution between the principal directions, and (iv) the orientation of its eigensystem. The strain rate tensor sets the reference system, and each objective stress (and fabric) variable can then be related, via discrete particle simulations, to the inertial number, I. This represents the plane strain special case of a general, local, and objective constitutive model. The resulting model is compared to existing theories and clearly displays small, but significant deviations from more simplified theories in all variables – on both the different length scales.

Compressive Sensing Based Machine Learning Strategy For Characterizing The Flow Around A Cylinder With Limited Pressure Measurements

Abstract: Compressive sensing is used to determine the flow characteristics around a cylinder (Reynolds number and pressure/flow field) from a sparse number of pressure measurements on the cylinder. Using a supervised machine learning strategy, library elements encoding the dimensionally reduced dynamics are computed for various Reynolds numbers. Convex L1 optimization is then used with a limited number of pressure measurements on the cylinder to reconstruct, or decode, the full pressure field and the resulting flow field around the cylinder. Aside from the highly turbulent regime (large Reynolds number) where only the Reynolds number can be identified, accurate reconstruction of the pressure field and Reynolds number is achieved. The proposed data-driven strategy thus achieves encoding of the fluid dynamics using the L2 norm, and robust decoding (flow field reconstruction) using the sparsity promoting L1 norm.

Dissolution-driven convection in a Hele-Shaw cell

Abstract: Motivated by convection in the context of geological carbon-dioxide (CO2) storage, we present an experimental study of dissolution-driven convection in a Hele–Shaw cell for Rayleigh numbers R in the range 100 < R < 1700. We use potassium permanganate (KMnO4) in water as an analog for CO2 in brine and infer concentration profiles at high spatial and temporal resolution and accuracy from transmitted light intensity. We describe behavior from first contact up to 65% average saturation and measure several global quantities including dissolution flux, average concentration, amplitude of perturbations away from pure one-dimensional diffusion, and horizontally averaged concentration profiles. We show that the flow evolves successively through distinct regimes starting with a simple one-dimensional diffusional profile. This is followed by linear growth in which fingers are initiated and grow quasiexponentially, independently of one-another. Once the fingers are well-established, a flux-growth regime begins as fresh fluid is brought to the interface and contaminated fluid removed, with the flux growing to a local maximum. During this regime, fingers still propagate independently. However, beyond the flux maximum, fingers begin to interact and zip together from the root down in a merging regime. Several generations of merging occur before only persistent primary fingers remain. Beyond this, the reinitiation regime begins with new fingers created between primary existing ones before merging into them. Through appropriate scaling, we show that the regimes are universal and independent of layer thickness (equivalently R) until the fingers hit the bottom. At this time, progression through these regimes is interrupted and the flow transitions to a saturating regime. In this final regime, the flux gradually decays in a manner well described by a Howard-style phenomenological model.

Modeling of structural uncertainties in Reynolds-averaged Navier-Stokes closures

Abstract: Estimation of the uncertainty in numerical predictions by Reynolds-averaged Navier-Stokes closures is a vital step in building confidence in such predictions. An approach to model-form uncertainty quantification that does not assume the eddy-viscosity hypothesis to be exact is proposed. The methodology for estimation of uncertainty is demonstrated for plane channel flow, for a duct with secondary flows, and for the shock/boundary-layer interaction over a transonic bump.

On the mechanism of elasto-inertial turbulence

Abstract: Elasto-inertial turbulence (EIT) is a new state of turbulence found in inertial flows with polymer additives. The dynamics of turbulence generated and controlled by such additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 (based on the bulk and the channel height) are used to study the formation and dynamics of elastic instabilities and their effects on the flow. The flow topology of EIT is found to differ significantly from Newtonian wall-turbulence. Structures identified by positive (rotational flow topology) and negative (extensional/compressional flow topology) second invariant Qa isosurfaces of the velocity gradient are cylindrical and aligned in the spanwise direction. Polymers are significantly stretched in sheet-like regions that extend in the streamwise direction with a small upward tilt. The Qa cylindrical structures emerge from the sheets of high polymer extension, in a mechanism of energy transfer from the fluctuations of the polymer stress work to the turbulent kinetic energy. At subcritical Reynolds numbers, EIT is observed at modest Weissenberg number (Wi, ratio polymer relaxation time to viscous time scale). For supercritical Reynolds numbers, flows approach EIT at large Wi. EIT provides new insights on the nature of the asymptotic state of polymer drag reduction (maximum drag reduction), and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian flows observed in some polymeric flows.

Dynamic non-equilibrium wall-modeling for large eddy simulation at high Reynolds numbers

Abstract: A dynamic non-equilibrium wall-model for large-eddy simulation at arbitrarily high Reynolds numbers is proposed and validated on equilibrium boundary layers and a non-equilibrium shock/boundary-layer interaction problem. The proposed method builds on the prior non-equilibrium wall-models of Balaras et al. [AIAA J. 34, 1111–1119 (1996)]10.2514/3.13200 and Wang and Moin [Phys. Fluids 14, 2043–2051 (2002)]10.1063/1.1476668: the failure of these wall-models to accurately predict the skin friction in equilibrium boundary layers is shown and analyzed, and an improved wall-model that solves this issue is proposed. The improvement stems directly from reasoning about how the turbulence length scale changes with wall distance in the inertial sublayer, the grid resolution, and the resolution-characteristics of numerical methods. The proposed model yields accurate resolved turbulence, both in terms of structure and statistics for both the equilibrium and non-equilibrium flows without the use of ad hoc corrections. Cr...

Bi-stability in the turbulent wake past parallelepiped bodies with various aspect ratios and wall effects

Abstract: The turbulent wake past parallelepiped bodies with a rectangular blunt trailing edge of height H and width W is investigated in wall proximity: various aspect ratios H* = H/W ∈ [0.51, 1.63] and ground clearances C* = C/W ∈ [0, 1.00] are explored at a Reynolds number of 4.5 × 104 based on the body width W. Base pressure measurements and particle image velocimetry show that the close wake often undergoes antisymmetric instabilities that can be either in the lateral direction (parallel to the wall) or in the vertical direction (normal to the wall). The instantaneous wake presents preferred states with high degrees of asymmetry; in some configurations, topology shifts are observed after long time scales Tl ∼ 103W/U0 leading to bistable behaviors. The effect of ground proximity is thoroughly studied for H* = 0.74 corresponding to the reference Ahmed geometry and for a case with a height dimension larger than its width H* = 1/0.74 = 1.34. When C* > 0.08, it is found that the Ahmed body is bistable in the latera...

Short time dynamics of viscous drop spreading

Abstract: Liquid drops start spreading directly after coming into contact with a solid substrate. Although this phenomenon involves a three-phase contact line, the spreading motion can be very fast. We experimentally study the initial spreading dynamics, characterized by the radius of the wetted area, for viscous drops. Using high-speed imaging with synchronized bottom and side views gives access to 6 decades of time resolution. We show that short time spreading does not exhibit a pure power-law growth. Instead, we find a spreading velocity that decreases logarithmically in time, with a dynamics identical to that of coalescing viscous drops. Remarkably, the contact line dissipation and wetting effects turn out to be unimportant during the initial stages of drop spreading.

Numerical simulation of vortex-induced vibration of a square cylinder at a low Reynolds number

Abstract: Vortex-induced vibrations (VIV) of a square cylinder at a Reynolds number of 100 and a low mass ratio of 3 are studied numerically by solving the Navier-Stokes equations using the finite element method. The equation of motion of the square cylinder is solved to simulate the vibration and the Arbitrary Lagrangian Eulerian scheme is employed to model the interaction between the vibrating cylinder and the fluid flow. The numerical model is validated against the published results of flow past a stationary square cylinder and the results of VIV of a circular cylinder at low Reynolds numbers. The effect of flow approaching angle (α) on the response of the square cylinder is investigated. It is found that α affects not only the vibration amplitude but also the lock-in regime. Among the three values of α (α = 0°, 45°, and 22.5°) that are studied, the smallest vibration amplitude and the narrowest lock-in regime occur at α = 0°. It is discovered that the vibration locks in with the natural frequency in two regimes of reduced velocity for α = 22.5°. Single loop vibration trajectories are observed in the lock-in regime at α = 22.5° and 45°, which is distinctively different from VIV of a circular cylinder. As a result, the vibration frequency in the in-line direction is the same as that in the cross-flow direction.

Low-frequency unsteadiness in the vortex formation region of a circular cylinder

Abstract: The presence of low-frequency fluctuations in the wake of bluff bodies have been observed in several investigations. Even though the flow past a circular cylinder at Re = 3900 (Re = UrefD/ν) has been the object of several experimental and numerical investigations, there is a large scattering in the average statistics in the near wake. In the present work, the flow dynamics of the near wake region behind a circular cylinder has been investigated by means of direct numerical simulations and statistics have been computed for more than 858 shedding cycles. The analysis of instantaneous velocity signals of several probes located in the vortex formation region, point out the existence of a low-frequency fluctuation at the non-dimensional frequency of fm = 0.0064. This large-scale almost periodic motion seems to be related with the modulation of the recirculation bubble which causes its shrinking and enlargement over the time. Two different configurations have been identified: (i) a high-energy mode with larger ...

Three-dimensional flow structure and aerodynamic loading on a revolving wing

Abstract: A numerical study is conducted to examine the vortex structure and aerodynamic loading on a revolving wing in quiescent flow. A high-fidelity, implicit large eddy simulation technique is employed to simulate a revolving wing configuration consisting of a single, aspect-ratio-one rectangular plate extended out a distance of half a chord from the rotational axis at a fixed angle relative to the axis. Shortly after the onset of the motion, the rotating wing generates a coherent vortex system along the leading-edge. This vortex system remains attached throughout the motion for the range of Reynolds numbers explored, despite the unsteadiness and vortex breakdown observed at higher Reynolds numbers. The average and instantaneous wing loading also increases with Reynolds number. At a fixed Reynolds number, the attachment of the leading-edge vortex is also shown to be insensitive to the geometric angle of the wing. Additionally, the flow structure and forcing generated by a purely translating wing is investigated and compared with that of the revolving wing. Similar features are present at the inception of the motion, however, the two flows evolve very differently for the remainder of the maneuver. Comparisons of the revolving wing simulations with recent experimental particle image velocimetry (PIV) measurements using a new PIV-like data reduction technique applied to the computational solution show very favorable agreement. The success of the data reduction technique demonstrates the need to compare computations and experiments of differing resolutions using similar data-analysis techniques.

How linear is wall-bounded turbulence?

Abstract: The relevance of Orr's inviscid mechanism to the transient amplification of disturbances in shear flows is explored in the context of bursting in the logarithmic layer of wall-bounded turbulence. The linearized problem for the wall normal velocity is first solved in the limit of small viscosity for a uniform shear and for a channel with turbulent-like profile, and compared with the quasiperiodic bursting of fully turbulent simulations in boxes designed to be minimal for the logarithmic layer. Many properties, such as time and length scales, energy fluxes between components, and inclination angles, agree well between the two systems. However, once advection by the mean flow is subtracted, the directly computed linear component of the turbulent acceleration is found to be a small part of the total. The temporal correlations of the different quantities in turbulent bursts imply that the classical model, in which the wall-normal velocities are generated by the breakdown of the streamwise-velocity streaks, is a better explanation than the purely autonomous growth of linearized bursts. It is argued that the best way to reconcile both lines of evidence is that the disturbances produced by the streak breakdown are amplified by an Orr-like transient process drawing energy directly from the mean shear, rather than from the velocity gradients of the nonlinear streak. This, for example, obviates the problem of why the cross-stream velocities do not decay once the streak has broken down.

A modified kinetic theory for frictional granular flows in dense and dilute regimes

Abstract: Continuum modeling of granular and gas-solid flows generally involves the use of a kinetic-theory (KT) model for the particulate phase, and the most widely used KT models have been derived for dilute flows of smooth, frictionless spheres. In reality, however, granular particles are frictional and can achieve dense packing, and these features must be taken into account to improve rheological predictions in these flow scenarios. Existing approaches in the literature for producing closed-form KT-based models employ empirical modifications to adapt the original models for use in dense and frictional systems. In this article, we investigate the capacity for such modifications to improve the rheological predictions of the Garzo–Dufty (GD) KT model [V. Garzo and J. W. Dufty, “Dense fluid transport for inelastic hard spheres,” Phys. Rev. E 59, 5895–5911 (1999)]10.1103/PhysRevE.59.5895. On the basis of molecular dynamics simulations of homogeneous, simple shear flows of soft, frictional spheres, we propose a new expression for the radial distribution function at contact as well as modifications to the GD expressions for shear stress and energy dissipation rate. These changes account for dense-regime scalings observed in inertial-number models as well as the effects of interparticle friction while preserving the dynamic nature of the KT model.

Experimental manipulation of wall turbulence: a systems approach

Abstract: We review recent progress, based on the approach introduced by McKeon and Sharma [J. Fluid Mech. 658, 336–382 (2010)10.1017/S002211201000176X], in understanding and controlling wall turbulence. The origins of this analysis partly lie in nonlinear robust control theory, but a differentiating feature is the connection with, and prediction of, state-of-the-art understanding of velocity statistics and coherent structures observed in real, high Reynolds number flows. A key component of this line of work is an experimental demonstration of the excitation of velocity response modes predicted by the theory using non-ideal, but practical, actuation at the wall. Limitations of the approach and promising directions for future development are outlined.

Stability of viscous long liquid filaments

Abstract: We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity and the aspect ratio, and the initial perturbations of its surface. We find that the instability of long viscous filaments can be completely explained by the Rayleigh-Plateau instability, whereas a low viscous filament can also break up due to end pinching. We analytically derive the transition between stable collapse and breakup in the Ohnesorge number versus aspect ratio phase space. Our result is confirmed by numerical simulations based on the slender jet approximation and explains recent experimental findings by Castrejon-Pita et al.

A proposed modification to Lundgren's physical space velocity forcing method for isotropic turbulence

Abstract: As an alternative to spectral space velocity field forcing techniques commonly used in simulation studies of isotropic turbulence,Lundgren [Linearly forced isotropic turbulence,” in Annual Research Briefs (Center for Turbulence Research, Stanford, 2003), pp. 461–473] proposed and Rosales and Meneveau [“Linear forcing in numerical simulations of isotropic turbulence: Physical space implementations and convergence properties,” Phys. Fluids17, 095106 (2005)] validated a physical space forcing method termed “linear forcing.” Linear forcing has the advantages of being less memory intensive, less computationally expensive, and more easily extended to variable density simulations. However, this forcing method generates turbulent statistics that are highly oscillatory, requiring extended simulation run times to attain time-invariant properties. A slight modification of the forcing term is proposed, and it is shown to reduce this oscillatory nature without altering the turbulent physics.

Flow induced vibration of two rigidly coupled circular cylinders in tandem and side-by-side arrangements at a low Reynolds number of 150

Abstract: Flow induced vibration of two rigidly coupled identical circular cylinders in tandem and side-by-side arrangements at a low Reynolds number of 150 is studied numerically. The two cylinders vibrate in the cross-flow direction and have the same displacement. The Navier-Stokes equations are solved by the finite element method and the equation of motion of the cylinders is solved by the fourth-order Runge-Kutta algorithm. Simulations are conducted for a constant mass ratio of 2 and the gap ratios (defined as the ratio of the centre-to-centre distance between the two cylinders L to the cylinder diameter D) of 1.5, 2, 4, and 6. The reduced velocities range from 0.5 to 15 with an increment of 0.5 for the tandem arrangement and from 0.5 to 30 with an increment of 0.5 for the side-by-side arrangement. It is found that the gap between the two cylinders has significant effect on the response. For a tandem arrangement, the lock-in regime of the reduced velocity is narrower than that of a single cylinder for L/D = 1.5...

Aspect-ratio dependency of Rayleigh-Bénard convection in box-shaped containers

Abstract: We report on a numerical study of the aspect-ratio dependency of Rayleigh-Benard convection, using direct numerical simulations. The investigated domains have equal height and width while the aspect ratio Γ of depth per height is varied between 1/10 and 1. The Rayleigh numbers Ra for this study variate between 105 and 109, while the Prandtl number is Pr=0.786. The main focus of the study concerns the dependency of the Nusselt number Nu and the Reynolds number Re on Ra and Γ. It turns out that due to Γ, differences to the cubic case (i.e., Γ = 1) in Nu of up to 55% and in Re of up to 97% occur, which decrease for increasing Ra. In particular for small Γ sudden drops in the Ra-scaling of Nu and Re appear for Ra≈106. Further analysis reveals that these correspond to the onset of unsteady motion accompanied by changes in the global flow structure. The latter is investigated by statistical analysis of the heat flux distribution on the bottom and top plates and a decomposition of the instantaneous flow fields i...

Locomotion of a flapping flexible plate

Abstract: The locomotion of a flapping flexible plate in a viscous incompressible stationary fluid is numerically studied by an immersed boundary-lattice Boltzmann method for the fluid and a finite element method for the plate. When the leading-edge of the flexible plate is forced to heave sinusoidally, the entire plate starts to move freely as a result of the fluid-structure interaction. Mechanisms underlying the dynamics of the plate are elucidated. Three distinct states of the plate motion are identified and can be described as forward, backward, and irregular. Which state to occur depends mainly on the heaving amplitude and the bending rigidity of the plate. In the forward motion regime, analysis of the dynamic behaviors of the flapping flexible plate indicates that a suitable degree of flexibility can improve the propulsive performance. Moreover, there exist two kinds of vortex streets in the downstream of the plate which are normal and deflected wake. Further the forward motion is compared with the flapping-based locomotion of swimming and flying animals. The results obtained in the present study are found to be consistent with the relevant observations and measurements and can provide some physical insights into the understanding of the propulsive mechanisms of swimming and flying animals.

Probing high-Reynolds-number effects in numerical boundary layers

Abstract: We study the high-Reynolds-number behavior of a turbulent boundary layer in the low supersonic regime through very-large-scale direct numerical simulation (DNS). For the first time a Reynolds number is attained in DNS (Reτ=δ/δv≈4000, where δ is the boundary layer thickness and δv is the viscous length scale) at which theoretical predictions and experiments suggest the occurrence of phenomena pertaining to the asymptotic Reynolds number regime. From comparison with previous DNS data at lower Reynolds number we find evidence of a continuing trend toward a stronger imprint of the outer-layer structures onto the near-wall region. This effect is clearly manifested both in flow visualizations, and in energy spectra. More than a decade of nearly-logarithmic variation is observed in the mean velocity profiles, with log-law constants k ≈ 0.394, C ≈ 4.84, and a trend similar to experiments. We find some supporting evidence for the debated existence of a k−1 region in the power spectrum of streamwise velocity fluctu...

Minimal transition thresholds in plane Couette flow

Abstract: Subcritical transition to turbulence requires finite-amplitude perturbations. Using a nonlinear optimisation technique in a periodic computational domain, we identify the perturbations of plane Couette flow transitioning with least initial kinetic energy for Re ⩽ 3000. We suggest a new scaling law Ec = O(Re−2.7) for the energy threshold vs. the Reynolds number, in quantitative agreement with experimental estimates for pipe flow. The route to turbulence associated with such spatially localised perturbations is analysed in detail for Re = 1500. Several known mechanisms are found to occur one after the other: Orr mechanism, oblique wave interaction, lift-up, streak bending, streak breakdown, and spanwise spreading. The phenomenon of streak breakdown is analysed in terms of leading finite-time Lyapunov exponents of the associated edge trajectory.