Showing papers in "Journal of Fluid Mechanics in 2004"

Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion

Abstract: A new approach to chemistry modelling for large-eddy simulation of turbulent reacting flows is developed. Instead of solving transport equations for all of the numerous species in a typical chemical mechanism and modelling the unclosed chemical source terms, the present study adopts an indirect mapping approach, whereby all of the detailed chemical processes are mapped to a reduced system of tracking scalars. Here, only two such scalars are considered: a mixture fraction variable, which tracks the mixing of fuel and oxidizer, and a progress variable, which tracks the global extent of reaction of the local mixture. The mapping functions, which describe all of the detailed chemical processes with respect to the tracking variables, are determined by solving quasi-steady diffusion-reaction equations with complex chemical kinetics and multicomponent mass diffusion. The performance of the new model is compared to fast-chemistry and steady-flamelet models for predicting velocity, species concentration, and temperature fields in a methane-fuelled coaxial jet combustor for which experimental data are available. The progress-variable approach is able to capture the unsteady, lifted flame dynamics observed in the experiment, and to obtain good agreement with the experimental data, while the fast-chemistry and steady-flamelet models both predict an attached flame.

A diffuse-interface method for simulating two-phase flows of complex fluids

Abstract: Two-phase systems of microstructured complex fluids are an important class of engineering materials. Their flow behaviour is interesting because of the coupling among three disparate length scales: molecular or supra-molecular conformation inside each component, mesoscopic interfacial morphology and macroscopic hydrodynamics. In this paper, we propose a diffuse-interface approach to simulating the flow of such materials. The diffuse-interface model circumvents certain numerical difficulties in tracking the interface in the classical sharp-interface description. More importantly, our energy-based variational formalism makes it possible to incorporate complex rheology easily, as long as it is due to the evolution of a microstructure describable by a free energy. Thus, complex rheology and interfacial dynamics are treated in a unified framework. An additional advantage of our model is that the energy law of the system guarantees the existence of a solution. We will outline the general approach for any two-phase complex fluids, and then present, as an example, a detailed formulation for an emulsion of nematic drops in a Newtonian matrix. Using spectral discretizations, we compute shear-induced deformation, head-on collision and coalescence of drops where the matrix and drop phases are Newtonian or viscoelastic Oldroyd-B fluids. Numerical results are compared with previous studies as a validation of the theoretical model and numerical code. Finally, we simulate the retraction of an extended nematic drop in a Newtonian matrix as a method for measuring interfacial tension.

Maximal deformation of an impacting drop

Abstract: We first study the impact of a liquid drop of low viscosity on a super-hydrophobic surface. Denoting the drop size and speed as are the liquid density and surface tension). This law is also observed to hold on partially wettable surfaces, provided that liquids of low viscosity (such as water) are used. The law is interpreted as resulting from the effective acceleration experienced by the drop during its impact. Viscous drops are also analysed, allowing us to propose a criterion for predicting if the spreading is limited by capillarity, or by viscosity.

Scaling of the energy spectra of turbulent channels

Abstract: The spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to Re at very large ones.

On spray formation

Abstract: We depict and analyse the successive steps of atomization of a liquid jet when a fast gas stream blows parallel to its surface. Experiments performed with various liquids in a fast air flow show that the liquid destabilization proceeds from a two-stage mechanism: a shear instability first forms waves on the liquid. The transient acceleration experienced by the liquid suggests that a Rayleigh–Taylor type of instability is triggered at the wave crests, producing liquid ligaments which further stretch in the air stream and break into droplets.

Induced-charge electro-osmosis

Abstract: We describe the general phenomenon of ‘induced-charge electro-osmosis’ (ICEO) – the nonlinear electro-osmotic slip that occurs when an applied field acts on the ionic charge it induces around a polarizable surface. Motivated by a simple physical picture, we calculate ICEO flows around conducting cylinders in steady (DC), oscillatory (AC), and suddenly applied electric fields. This picture, and these systems, represent perhaps the clearest example of nonlinear electrokinetic phenomena. We complement and verify this physically motivated approach using a matched asymptotic expansion to the electrokinetic equations in the thin-double-layer and low-potential limits. ICEO slip velocities vary as $u_s \,{\propto}\,E_0^2 L$, where $E_0$ is the field strength and $L$ is a geometric length scale, and are set up on a time scale $\tau_c \,{=}\,\lambda_D L/D$, where $\lambda_D$ is the screening length and $D$ is the ionic diffusion constant. We propose and analyse ICEO microfluidic pumps and mixers that operate without moving parts under low applied potentials. Similar flows around metallic colloids with fixed total charge have been described in the Russian literature (largely unnoticed in the West). ICEO flows around conductors with fixed potential, on the other hand, have no colloidal analogue and offer further possibilities for microfluidic applications.

The effect of two degrees of freedom on vortex-induced vibration at low mass and damping

Abstract: Although there are a great many papers dedicated to the problem of a cylinder vibrating transverse to a fluid flow (, that one observes a rather dramatic departure from previous results, which would suggest a possible modification to offshore design codes.

Inertial migration of rigid spherical particles in Poiseuille flow

Abstract: An experimental study of the migration of dilute suspensions of particles in Poiseuille flow at Reynolds numbers from the entrance, changes from one centred at the annulus predicted by the theory to one with the particles primarily on the inner annulus. The case of slightly non-neutrally buoyant particles was also investigated. A particle trajectory simulation based on asymptotic theory was performed to facilitate the comparison of theory and the experimental observations.

Exact coherent structures in pipe flow: travelling wave solutions

Abstract: Three-dimensional travelling wave solutions are found for pressure-driven fluid flow through a circular pipe. They consist of three well-defined flow features – streamwise rolls and streaks which dominate and streamwise-dependent wavy structures. The travelling waves can be classified by the and traceable down to a Reynolds number (based on the mean velocity) of 1251. The new solutions are found using a constructive continuation procedure based upon key physical mechanisms thought generic to wall-bounded shear flows. It is believed that the appearance of these new alternative solutions to the governing equations as the Reynolds number is increased is a necessary precursor to the turbulent transition observed in experiments.

Investigation of flow over an oscillating airfoil

Abstract: The characteristics of the unsteady boundary layer and stall events occurring on an oscillating NACA 0012 airfoil were investigated by using closely spaced multiple hot-film sensor arrays at . Aerodynamic forces and pitching moments, integrated from surface pressure measurements, and smoke-flow visualizations were also obtained to supplement the hot-film measurements. Special attention was focused on the behaviour of the spatial-temporal progression of the locations of the boundary-layer transition and separation, and reattachment and relaminarization points, compared to the static values, for a range of oscillation frequency and amplitude both prior to, during and after the stall. The initiation, growth and rearward convection of a leading-edge vortex, and the role of the laminar separation bubble leading to the dynamic stall, as well as the mechanisms responsible for the stall events observed at different test conditions were also characterized. The hot-film measurements were also correlated with the aerodynamic load and pitching moment results to quantify the values of lift increment and stall angle delay as a result of the observed boundary layer and stall events. The results reported here provide an insight into the detailed nature of the unsteady boundary-layer events as well as the stalling mechanisms at work at different stages in the dynamic-stall process.

Gravity currents produced by lock exchange

Abstract: The dynamics of gravity currents are believed to be strongly influenced by dissipation due to turbulence and mixing between the current and the surrounding ambient fluid. This paper describes new theory and experiments on gravity currents produced by lock exchange which suggest that dissipation is unimportant when the Reynolds number is sufficiently high. Although there is mixing, the amount of energy dissipated is small, reducing the current speed by a few percent from the energy-conserving value. Benjamin (J. Fluid Mech. vol. 31, 1968, p. 209) suggests that dissipation is an essential ingredient in gravity current dynamics. We show that dissipation is not important at high Reynolds number, and provide an alternative theory that predicts the current speed and depth based on energy-conserving flow that is in good agreement with experiments. We predict that in a deep ambient the front Froude number is 1, rather than the previously accepted value of √ 2. New experiments are reported for this case that support the new theoretical value. This paper provides an analysis of the motion of a gravity current produced by lock exchange. In a lock exchange experiment, fluids of different densities initially at rest are separated by a vertical barrier – the lock gate – in a tank. When the gate is removed, differences in the hydrostatic pressure cause the denser fluid to flow in one direction along the bottom boundary of the tank, while the lighter fluid flows in the opposite direction along the top boundary of the tank. Figure 1 shows the initial configurations for lock exchange flows: a full-depth release when the depths of heavy and light fluid on both sides of the gate are equal is shown in (a )a nd apartial-depth release when the dense fluid occupies only a fraction of the full depth is shown in (b). Figure 2 shows the flow resulting from a full-depth lock release experiment. In this case the densities on the two sides of the lock gate are very similar (the density ratio γ = ρ1/ρ2 < 1 is close to unity). A dense gravity current travels to the right along the lower boundary and a buoyant current travels to the left along the upper boundary. Visually the flows are very nearly symmetric, and the dense and light fronts travel at almost the same speeds (figure 2b). The currents occupy about half the channel depth in each case, although they may be shallower immediately behind the head where there is mixing. The speeds of the two currents are constant within experimental resolution. Previous similar observations led Benjamin (1968) to develop a theory for the propagation of a steadily advancing current. He considered one half of the flow shown in figure 2(a), say the dense current only. In a frame of reference moving with the current, the front

Drops on a conical wire

Abstract: We study experimentally the behaviour of a drop deposited on a conical fibre. It is shown that for wetting liquids, such a drop spontaneously moves towards the region of lower curvature. The driving force is measured and shown to be a gradient of Laplace pressure, which allows us to characterize the dynamics of these self-propelling drops. We conclude by discussing the efficiency of this device for drying a solid initially coated with a liquid film.

Transition in boundary layers subject to free-stream turbulence

Abstract: The effect of high levels of free-stream turbulence on the transition in a Blasius boundary layer is studied by means of direct numerical simulations, where a synthetic turbulent inflow is obtained as superposition of modes of the continuous spectrum of the Orr–Sommerfeld and Squire operators. In the present bypass scenario the flow in the boundary layer develops streamwise elongated regions of high and low streamwise velocity and it is suggested that the breakdown into turbulent spots is related to local instabilities of the strong shear layers associated with these streaks. Flow structures typical of the spot precursors are presented and these show important similarities with the flow structures observed in previous studies on the secondary instability and breakdown of steady symmetric streaks.Numerical experiments are performed by varying the energy spectrum of the incoming perturbation. It is shown that the transition location moves to lower Reynolds numbers by increasing the integral length scale of the free-stream turbulence. The receptivity to free-stream turbulence is also analysed and it is found that two distinct physical mechanisms are active depending on the energy content of the external disturbance. If low-frequency modes diffuse into the boundary layer, presumably at the leading edge, the streaks are induced by streamwise vorticity through the linear lift-up effect. If, conversely, the free-stream perturbations are mainly located above the boundary layer a nonlinear process is needed to create streamwise vortices inside the shear layer. The relevance of the two mechanisms is discussed.

Aeroacoustics of hot jets

Abstract: A systematic study has been undertaken to quantify the effect of jet temperature on the noise radiated by subsonic jets. Nozzles of different diameters were tested to uncover the effects of Reynolds number. All the tests were carried out at Boeing's Low Speed Aeroacoustic Facility, with simultaneous measurement of thrust and noise. It is concluded that the change in spectral shape at high jet temperatures, normally attributed to the contribution from dipoles, is due to Reynolds number effects and not dipoles. This effect has not been identified before. A critical value of the Reynolds number that would need to be maintained to avoid the effects associated with low Reynolds number has been estimated to be 400 000. It is well-known that large-scale structures are the dominant generators of noise in the peak radiation direction for high-speed jets. Experimental evidence is presented that shows the spectral shape at angles close to the jet axis from unheated low subsonic jets to be the same as from heated supersonic jets. A possible mechanism for the observed trend is proposed. When a subsonic jet is heated with the Mach number held constant, there is a broadening of the angular sector in which peak radiation occurs. Furthermore, there is a broadening of the spectral peak. Similar trends have been observed at supersonic Mach numbers. The spectral shapes in the forward quadrant and in the near-normal angles from unheated and heated subsonic jets also conform to the universal shape obtained from supersonic jet data. Just as for unheated jets, the peak frequency at angles close to the jet axis is independent of jet velocity as long as the acoustic Mach number is less than unity. The extensive database generated in the current test programme is intended to provide test cases with high-quality data that could be used for the evaluation of theoretical/semi-theoretical jet noise prediction methodologies.

Axisymmetric collapses of granular columns

Abstract: Experimental observations of the collapse of initially vertical columns of small grains are presented. The experiments were performed mainly with dry grains of salt or sand, with some additional experiments using couscous, sugar or rice. Some of the experimental flows were analysed using high-speed video. There are three different flow regimes, dependent on the value of the aspect ratio a = hi/ri ,w herehi and ri are the initial height and radius of the granular column respectively. The differing forms of flow behaviour are described for each regime. In all cases a central, conically sided region of angle approximately 59 ◦ , corresponding to an aspect ratio of 1.7, remains undisturbed throughout the motion. The main experimental results for the final extent of the deposit and the time for emplacement are systematically collapsed in a quantitative way independent of any friction coefficients. Along with the kinematic data for the rate of spread of the front of the collapsing column, this is interpreted as indicating that frictional effects between individual grains in the bulk of the moving flow only play a role in the last instant of the flow, as it comes to an abrupt halt. For a< 1.7, the measured final runout radius, r∞, is related to the initial radius by r∞ = ri(1 + 1.24a); while for 1.7

A continuum and molecular dynamics hybrid method for micro- and nano-fluid flow

Abstract: A hybrid multiscale method is developed for simulating micro- and nano-scale fluid flows. The continuum Navier–Stokes equation is used in one flow region and atomistic molecular dynamics in another. The spatial coupling between continuum equations and molecular dynamics is achieved through constrained dynamics in an overlap region. The proposed multiscale method is used to simulate sudden-start Couette flow and channel flow with nano-scale rough walls, showing quantitative agreement with results from analytical solutions and full molecular dynamics simulations for different parameter regimes. Potential applications of the proposed multiscale method are discussed.

Further observations on the mean velocity distribution in fully developed pipe flow

Abstract: The measurements by Zagarola & Smits (1998) of mean velocity profiles in fully developed turbulent pipe flow are repeated using a smaller Pitot probe to reduce the uncertainties due to velocity gradient corrections. A new static pressure correction (McKeon & Smits 2002) is used in analysing all data and leads to significant differences from the Zagarola & Smits conclusions. The results confirm the presence of a power-law region near the wall and, for Reynolds numbers greater than 230×10^3 (R+ >5×10^3), a logarithmic region further out, but the limits of these regions and some of the constants differ from those reported by Zagarola & Smits. In particular, the log law is found for 600

An asymptotic theory for the interaction of waves and currents in coastal waters

Abstract: A multi-scale asymptotic theory is derived for the evolution and interaction of currents and surface gravity waves in water of finite depth, under conditions typical of coastal shelf waters outside the surf zone. The theory provides a practical and useful model with which wave–current coupling may be explored without the necessity of resolving features of the flow on space and time scales of the primary gravity-wave oscillations. The essential nature of the dynamical interaction is currents modulating the slowly evolving phase of the wave field and waves providing both phase-averaged forcing of long infra-gravity waves and wave-averaged vortex and Bernoulli-head forces and hydrostatic static set-up for the low-frequency current and sea-level evolution equations. Analogous relations are derived for wave-averaged material tracers and density stratification that include advection by horizontal Stokes drift and by a vertical Stokes pseudo-velocity that is the incompressible companion to the horizontal Stokes velocity. Illustrative solutions are analysed for the special case of depth-independent currents and tracers associated with an incident surface wave field and a vortex with O(1) Rossby number above continental shelf topography.

Critical assessment of turbulent drag reduction through spanwise wall oscillations

Abstract: Direct numerical simulations of the incompressible Navier–Stokes equations are employed to study the turbulent wall-shear stress in a turbulent channel flow forced by lateral sinusoidal oscillations of the walls. The objective is to produce a documented database of numerically computed friction reductions. To this aim, the particular numerical requirements for such simulations, owing for example to the time-varying direction of the skin-friction vector, are considered and appropriately accounted for. A detailed analysis of the dependence of drag reduction on the oscillatory parameters allows us to address conflicting results hitherto reported in the literature. At the Reynolds number of the present simulations, we compute a maximum drag reduction of 44.7%, and we assess the possibility for the power saved to be higher than the power spent for the movement of the walls (when mechanical losses are neglected). A maximum net energy saving of 7.3% is computed. Furthermore, the scaling of the amount of drag reduction is addressed. A parameter, which depends on both the maximum wall velocity and the period of the oscillation, is found to be linearly related to drag reduction, as long as the half-period of the oscillation is shorter than a typical lifetime of the turbulent near-wall structures. For longer periods of oscillation, the scaling parameter predicts that drag reduction will decrease to zero more slowly than the numerical data. The same parameter also describes well the optimum period of oscillation for fixed maximum wall displacement, which is smaller than the optimum period for fixed maximum wall velocity, and depends on the maximum displacement itself.

Secondary Flow in Sharp Open-channel Bends

Abstract: Secondary currents are a characteristic feature of flow in open-channel bends. Besides the classical helical motion (centre-region cell), a weaker and smaller counter-rotating circulation cell (outer-bank cell) is often observed near the outer bank, which is believed to play an important role in bank erosion processes. The mechanisms underlying the circulation cells, especially the outer-bank cell, are still poorly understood, and their numerical simulation still poses problems, not least due to lack of detailed experimental data. The research reported herein provides detailed experimental data on both circulation cells in an open-channel bend such as found in nature. Furthermore, the underlying dynamics are investigated by simultaneously analysing the vorticity equation and the kinetic energy transfer between the mean flow and the turbulence. This shows that turbulence plays a minor role in the generation of the centre-region cell, which is mainly due to the centrifugal force. By accounting for the feedback between the downstream velocity profile and the centre-region cell, a strongly simplified vorticity balance is shown to yield accurate predictions of the velocities in the centre region. For strong curvatures, however, a fully threedimensional flow description is required. Due to the non-monotonic velocity profiles, the centrifugal force favours the outer-bank cell. Moreover, terms related to the anisotropy of the cross-stream turbulence, induced by boundary proximity, are of the same order of magnitude and mainly enhance the outer-bank cell. Both mechanisms strengthen each other. The occurrence of the outer-bank cell is shown to be not just due to flow instability, like in the case of curved laminar flow, but also to kinetic energy input from turbulence.

Expanded analogy between Boltzmann kinetic theory of fluids and turbulence

Abstract: We demonstrate that the effects of turbulent fluctuations have a striking resemblance to those of microscale (thermal) fluctuations in laminar flows, even to higher order in the Knudsen number. This suggests that there may be a good basis for understanding turbulence in terms of Boltzmann kinetic theory. If so, turbulence may be better described in terms of ‘mixing times’ rather than the more classical ‘mixing lengths’. Comparisons are made to Reynolds-stress turbulence models.

On the coherent drag-reducing and turbulence-enhancing behaviour of polymers in wall flows

Abstract: Numerical simulations of turbulent polymer solutions using the FENE-P model are used to characterize the action of polymers on turbulence in drag-reduced flows. The energetics of turbulence is investigated by correlating the work done by polymers on the flow with turbulent structures. Polymers are found to store and to release energy to the flow in a well-organized manner. The storage of energy occurs around near-wall vortices as has been anticipated for a long time. Quite unexpectedly, coherent release of energy is observed in the very near-wall region. Large fluctuations of polymer work are shown to re-energize decaying streamwise velocity fluctuations in high-speed streaks just above the viscous sublayer. These distinct behaviours are used to propose an autonomous regeneration cycle of polymer wall turbulence, in the spirit of Jimenez & Pinelli (1999).

The mixing transition in Rayleigh-Taylor instability

Abstract: A large-eddy simulation technique is described for computing Rayleigh-Taylor instability. The method is based on high-wavenumber-preserving subgrid-scale models, combined with high-resolution numerical methods. The technique is verified to match linear stability theory and validated against direct numerical simulation data. The method is used to simulate Rayleigh-Taylor instability at a grid resolution of 1152 3 . The growth rate is found to depend on the mixing rate. A mixing transition is observed in the flow, during which an inertial range begins to form in the velocity spectrum and the rate of growth of the mixing zone is temporarily reduced. By measuring growth of the layer in units of dominant initial wavelength, criteria are established for reaching the hypothetical self-similar state of the mixing layer. A relation is obtained between the rate of growth of the mixing layer and the net mass flux through the plane associated with the initial location of the interface. A mix-dependent Atwood number is defined, which correlates well with the entrainment rate, suggesting that internal mixing reduces the layer's growth rate

Size, shape and dynamics of large-scale turbulent flow structures in a gravel-bed river

Abstract: In this paper, we present a detailed investigation of the size, scale and dynamics of macro-turbulent flow structures in gravel-bed rivers. We used an array of seven electromagnetic current meters with high resolution in both space and time to measure the streamwise velocity fluctuations in a gravel-bed river. The array was deployed successively in various configurations in order to quantify the vertical, lateral and longitudinal extent of the flow structures and to estimate their advecting velocities. To depict the spatial and temporal properties of the flow structures, we used space–time velocity matrices, space–time correlation analysis and coherent-structure detection schemes. The results show that the large-scale turbulent flow structures in a gravel-bed river occupy the entire depth of the flow and that they are elongated and narrow. The length of the structures is 3 to 5 times the flow depth while the width is between 0.5 and 1 times flow depth. In spite of the high roughness of the bed, these values are similar to those reported in the literature for laboratory experiments on large-scale turbulent flow structures. The dynamics of the large-scale turbulent flow structures investigated using flow visualization highlight the interactions between the outer flow region and the near-bed region. Our evidence suggests that large-scale flow incursions trigger ejections in the near-bed region that can develop into megabursts that can reach the water surface.

Numerical study of flow past an impulsively started cylinder by the lattice-Boltzmann method

Abstract: In this paper a systematic numerical study of flow past an impulsively started circular cylinder at low and moderate Reynolds numbers using a lattice-Boltzmann algorithmic approach is presented together with an extended volumetric boundary scheme. Results agree well with some well-known previous works. It is demonstrated that in the nearly incompressible limit, this approach is able to provide accurate direct numerical simulations of unsteady flows with curved geometry.

Spherical capsules in three-dimensional unbounded Stokes flows: effect of the membrane constitutive law and onset of buckling

Abstract: The dynamic response of an initially spherical capsule subject to different externally imposed flows is examined. The neo-Hookean and Skalak et al. (Biophys. J., vol. 13 (1973), pp. 245–264) constitutive laws are used for the description of the membrane mechanics, assuming negligible bending resistance. The viscosity ratio between the interior and exterior fluids of the capsule is taken to be unity and creeping-flow conditions are assumed to prevail. The capillary number , beyond the interval of stability, the membrane has two tips along the direction of elongation where the deformation is most severe, and no equilibrium shapes could be identified. For both regions outside the interval of stability, the membrane model is not appropriate and bending resistance is essential to obtain realistic capsule shapes. This pattern persists for the two constitutive laws that were used, with the Skalak et al. law producing a wider stability interval than the neo-Hookean law owing to its strain hardening nature.

Scaling of the streamwise velocity component in turbulent pipe flow

Abstract: Statistics of the streamwise velocity component in fully developed pipe flow are examined for Reynolds numbers in the range 5.5 x 10^4 ≤ ReD ≤ 5.7 x 10^6. Probability density functions and their moments (up to sixth order) are presented and their scaling with Reynolds number is assessed. The second moment exhibits two maxima: the one in the viscous sublayer is Reynolds-number dependent while the other, near the lower edge of the log region, follows approximately the peak in Reynolds shear stress. Its locus has an approximate (R^+)^{0.5} dependence. This peak shows no sign of ‘saturation’, increasing indefinitely with Reynolds number. Scalings of the moments with wall friction velocity and $(U_{cl}-\overline{U})$ are examined and the latter is shown to be a better velocity scale for the outer region, y/R > 0.35, but in two distinct Reynolds-number ranges, one when ReD 7 x 10^4. Probability density functions do not show any universal behaviour, their higher moments showing small variations with distance from the wall outside the viscous sublayer. They are most nearly Gaussian in the overlap region. Their departures from Gaussian are assessed by examining the behaviour of the higher moments as functions of the lower ones. Spectra and the second moment are compared with empirical and theoretical scaling laws and some anomalies are apparent. In particular, even at the highest Reynolds number, the spectrum does not show a self-similar range of wavenumbers in which the spectral density is proportional to the inverse streamwise wavenumber. Thus such a range does not attract any special significance and does not involve a universal constant.

Erosion and deposition of particles on a bed sheared by a viscous flow

Abstract: Experiments are reported on the dynamics of a bed of particles sheared by a viscous Couette flow in an annular channel, with emphasis on the distributions of particle velocities, durations and lengths of the small saltation flights, and surface density of the moving particles. The velocity distributions are shown to decay approximately exponentially, with mean value, U p , equal to 0.1 γd, where y is the shear rate and d is the particle diameter. The duration of the flights does not depend on the shear rate, and is equal to 15 times the settling time d/V S , where V S is the Stokes settling velocity. Starting from an initially loosely packed bed, the surface density of the moving particles, N p , was observed to decrease slowly over several days, unlike their velocity which remains constant with time. This decay is related to the increase of the threshold shear rate for particle motion, and corresponds to rearrangement of the particles near the bed surface (armouring). When the stationary state is reached, N p depends linearly on the shear rate, so that the particle flow rate, Q p = N p U p , is a quadratic function of the shear rate. Two theoretical models are proposed to account for these observations. In the first one, the erosion and deposition rates are modelled using the two hydrodynamic time scales: the inverse shear rate γ -1 for the erosion rate, and the settling time d/V S for the deposition rate. This model accounts for the linear dependence of Np on the shear rate. The second model was developed to capture the slow decrease of Np, by considering the trapping of moving particles into troughs of the bed. This trapping model does recover the main features observed experimentally, although the characteristic time for the decrease of Np still remains too short. Our observations are, finally, compared to existing numerical and experimental studies on turbulent flows.

A two-species model of aeolian sand transport

Abstract: The transport of sand by wind results from the equilibrium between the erosion of grains dragged by the flow and the resulting slow down of the wind velocity. The dynamical mechanisms governing the saturation of the sand flux are investigated theoretically. We first demonstrate that previous models, based on the assumption that all the grains have the same trajectory, are either not self-consistent or lead to unstable solutions. A model based on a discrete number of states is derived, which solves these problems. Two well-defined species of grain appear, which correspond to saltons (high-energy grains) and reptons (grains ejected from the sand bed by the impact of saltons). They play specific roles: the negative feedback of the transport on the wind is limited to the reptation layer while most of the transport is due to saltation. The model is further simplified, benefiting from the existence of these two species and the dependencies of the threshold velocity, the saturated flux, the aerodynamic roughness and the saturation length are derived and compared to experimental measurements.

Simultaneous measurements of scalar and velocity field evolution in turbulent crossflowing jets

Abstract: Simultaneous planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) yield measurements of two-dimensional jet fluid concentration and velocity fields in turbulent crossflowing jets. The jet-to-crossflow velocity ratio is r = 5.7 and the jet exit Reynolds number is approximately 5000. The measurements are focused on the developing region of the flow. Two flow configurations are studied, one in which the jet nozzle is flush with the tunnel wall and the other where the nozzle protrudes into the uniform region of the tunnel flow. The jet nozzle in both cases is a simple pipe. The averaged scalar and velocity fields show a strong similarity in growth rates and centreline decay rates between the two nozzle configurations when using the centreline downstream coordinate s