Showing papers in "Journal of Fluid Mechanics in 2015"

Direct numerical simulation of turbulent channel flow up to

Abstract: A direct numerical simulation of incompressible channel flow at a friction Reynolds number ( ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Karman constant . There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits dependence over a short range in wavenumber . Further, consistent with previous experimental observations, when these spectra are multiplied by (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the range.

Turbulent channel flow of dense suspensions of neutrally buoyant spheres

Abstract: Dense particle suspensions are widely encountered in many applications and in environmental flows. While many previous studies investigate their rheological properties in laminar flows, little is known on the behaviour of these suspensions in the turbulent/inertial regime. The present study aims to fill this gap by investigating the turbulent flow of a Newtonian fluid laden with solid neutrally-buoyant spheres at relatively high volume fractions in a plane channel. Direct numerical simulation (DNS) are performed in the range of volume fractions Phi=0-0.2 with an immersed boundary method (IBM) used to account for the dispersed phase. The results show that the mean velocity profiles are significantly altered by the presence of a solid phase with a decrease of the von Karman constant in the log-law. The overall drag is found to increase with the volume fraction, more than one would expect if just considering the increase of the system viscosity due to the presence of the particles. At the highest volume fraction investigated here, Phi = 0.2, the velocity fluctuation intensities and the Reynolds shear stress are found to decrease. The analysis of the mean momentum balance shows that the particle-induced stresses govern the dynamics at high Phi and are the main responsible of the overall drag increase. In the dense limit, we therefore find a decrease of the turbulence activity and a growth of the particle induced stress, where the latter dominates for the Reynolds numbers considered here.

Optimal control of energy extraction in wind-farm boundary layers

Abstract: In very large wind farms the vertical interaction with the atmospheric boundary layer plays an important role, i.e. the total energy extraction is governed by the vertical transport of kinetic energy from higher regions in the boundary layer towards the turbine level. In the current study, we investigate optimal control of wind-farm boundary layers, considering the individual wind turbines as flow actuators, whose energy extraction can be dynamically regulated in time so as to optimally influence the flow field and the vertical energy transport. To this end, we use Large-Eddy Simulations (LES) of a fullydeveloped pressure-driven wind-farm boundary layer in a receding-horizon optimal control framework. For the optimization of the wind-turbine controls, a conjugate-gradient optimization method is used in combination with adjoint LESs for the determination of the gradients of the cost functional. In a first control study, wind-farm energy extraction is optimized in an aligned wind farm. Results are accumulated over one hour of operation. We find that the energy extraction is increased by 16% compared to the uncontrolled reference. This is directly related to an increase of the vertical fluxes of energy towards the wind turbines, and vertical shear stresses increase considerably. A further analysis, decomposing total stresses in dispersive and Reynolds stresses, shows that the dispersive stresses increase drastically, and that the Reynolds stresses decrease on average, but increase in the wake region, leading to better wake recovery. We further observe that also turbulent dissipation levels in the boundary layer increase, and overall the outer layer of the boundary layer enters into a transient decelerating regime, while the inner layer and the turbine region attain a new statistically steady equilibrium within approximately one wind-farm through-flow time. Two additional optimal-control cases study penalization of turbulent dissipation. For the current wind-farm geometry, it is found that the ratio between wind-farm energy extraction and turbulent boundary-layer dissipation remains roughly around 70%, but can be slightly increased with a few percent by penalizing the dissipation in the optimization objective. For a pressure-driven boundary layer in equilibrium, we estimate that such a shift can lead to an increase in wind-farm energy extraction of 6%.

Statistical structure of self-sustaining attached eddies in turbulent channel flow

Abstract: The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend’s attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies in the original theory, providing direct evidence on the existence of Townsend’s attached eddies. It is shown that a single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length between and , where is half the height of the channel, the former is found to be self-similar along and , while the latter is self-similar along and where is the wall-normal direction. The scaling suggests that the smallest attached eddy would be a near-wall coherent motion in the form of a streak and quasi-streamwise vortices aligned to that, whereas the largest one would be an outer motion with a very-large-scale motion (VLSM) and large-scale motions (LSMs) aligned to that. The attached eddies in between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield behaviour consistent with the emergence of spectra in a number of previous studies. Finally, a further discussion is provided, in particular on Townsend’s inactive motion and several recent theoretical findings.

Closed-loop separation control using machine learning

Abstract: We present the first closed-loop separation control experiment using a novel, model-free strategy based on genetic programming, which we call ‘machine learning control’. The goal is to reduce the recirculation zone of backward-facing step flow at manipulated by a slotted jet and optically sensed by online particle image velocimetry. The feedback control law is optimized with respect to a cost functional based on the recirculation area and a penalization of the actuation. This optimization is performed employing genetic programming. After 12 generations comprised of 500 individuals, the algorithm converges to a feedback law which reduces the recirculation zone by 80 %. This machine learning control is benchmarked against the best periodic forcing which excites Kelvin–Helmholtz vortices. The machine learning control yields a new actuation mechanism resonating with the low-frequency flapping mode instability. This feedback control performs similarly to periodic forcing at the design condition but outperforms periodic forcing when the Reynolds number is varied by a factor two. The current study indicates that machine learning control can effectively explore and optimize new feedback actuation mechanisms in numerous experimental applications.

A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime

Abstract: Direct numerical simulations (DNS) are conducted for turbulent flow through pipes with three-dimensional sinusoidal roughnesses explicitly represented by body-conforming grids. The same viscous-scaled roughness geometry is first simulated at a range of different Reynolds numbers to investigate the effects of low Reynolds numbers and low , where is the pipe radius and is the roughness height. Results for the present class of surfaces show that the Hama roughness function is only marginally affected by low Reynolds numbers (or low ), and observations of outer-layer similarity (or lack thereof) show no signs of sensitivity to Reynolds number. Then, building on this, a systematic approach is taken to isolate the effects of roughness height and wavelength in a turbulent wall-bounded flow in both transitionally rough and fully rough regimes. Current findings show that while the effective slope (which for the present sinusoidal surfaces is proportional to ) is an important roughness parameter, the roughness function must also depend on some measure of the viscous roughness height. A simplistic linear–log fit clearly illustrates the strong correlation between and both the roughness average height (which is related to ) and for the surfaces simulated here, consistent with published literature. Various definitions of the virtual origin for rough-wall turbulent pipe flow are investigated and, for the surfaces simulated here, the hydraulic radius of the pipe appears to be the most suitable parameter, and indeed is the only virtual origin that can ever lead to collapse in the total stress. First- and second-order statistics are also analysed and collapses in the outer layer are observed for all cases, including those where the largest roughness height is a substantial proportion of the reference radius (low ). These results provide evidence that turbulent pipe flow over the present sinusoidal surfaces adheres to Townsend’s notion of outer-layer similarity, which pertains to statistics of relative motion.

Well-posed and ill-posed behaviour of the -rheology for granular flow

Abstract: In light of the successes of the Navier–Stokes equations in the study of fluid flows, similar continuum treatment of granular materials is a long-standing ambition. This is due to their wide-ranging applications in the pharmaceutical and engineering industries as well as to geophysical phenomena such as avalanches and landslides. Historically this has been attempted through modification of the dissipation terms in the momentum balance equations, effectively introducing pressure and strain-rate dependence into the viscosity. Originally, a popular model for this granular viscosity, the Coulomb rheology, proposed rate-independent plastic behaviour scaled by a constant friction coefficient . Unfortunately, the resultant equations are always ill-posed. Mathematically ill-posed problems suffer from unbounded growth of short-wavelength perturbations, which necessarily leads to grid-dependent numerical results that do not converge as the spatial resolution is enhanced. This is unrealistic as all physical systems are subject to noise and do not blow up catastrophically. It is therefore vital to seek well-posed equations to make realistic predictions. The recent -rheology is a major step forward, which allows granular flows in chutes and shear cells to be predicted. This is achieved by introducing a dependence on the non-dimensional inertial number in the friction coefficient . In this paper it is shown that the -rheology is well-posed for intermediate values of , but that it is ill-posed for both high and low inertial numbers. This result is not obvious from casual inspection of the equations, and suggests that additional physics, such as enduring force chains and binary collisions, becomes important in these limits. The theoretical results are validated numerically using two implicit schemes for non-Newtonian flows. In particular, it is shown explicitly that at a given resolution a standard numerical scheme used to compute steady-uniform Bagnold flow is stable in the well-posed region of parameter space, but is unstable to small perturbations, which grow exponentially quickly, in the ill-posed domain.

Numerical and experimental study of mechanisms responsible for turbulent secondary flows in boundary layer flows over spanwise heterogeneous roughness

Abstract: We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned ‘strips’). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl’s secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses – from above – and subsequent lateral ejection in order to preserve conservation of mass.

Experimental study on bubble dynamics subject to buoyancy

Abstract: This paper is concerned with the dynamics of large bubbles subject to various strengths of buoyancy effects, which are associated with applications for underwater explosion. The bubble is produced by electric discharge in a low-pressure tank to enhance the buoyancy effects. Experiments are carried out for a bubble in an infinite field, below a free surface and above a rigid boundary. The effects of buoyancy are reflected by the dimensionless parameter , where , , , and are the maximum bubble radius, ambient pressure, saturated vapour pressure, density of water and the acceleration of gravity respectively. A systematic study of buoyancy effects is carried out for a wide range of from 0.034 to 0.95. A series of new phenomena and new features is observed. The bubbles recorded are transparent, and thus we are able to display and study the jet formation, development and impact on the opposite bubble surface as well as the subsequent collapsing and rebounding of the ring bubble. Qualitative analyses are carried out for the bubble migration, jet velocity and jet initiation time, etc. for different values of . When a bubble oscillates below a free surface or above a rigid boundary, the Bjerknes force due to the free surface (or rigid boundary) and the buoyancy are in opposite directions. Three situations are studied for each of the two configurations: (i) the Bjerknes force being dominant, (ii) the buoyancy force being dominant and (iii) the two forces being approximately balanced. For case (iii), we further consider two subcases, where both the balanced Bjerknes and buoyancy forces are weak or strong. When the Bjerknes and buoyancy forces are approximately balanced over the pulsation, some representative bubble behaviours are observed: the bubble near free surface is found to split into two parts jetting away from each other for small , or involutes from both top and bottom for large . A bubble above a rigid wall is found to be subject to contraction from the lateral part leading to bubble splitting. New criteria are established based on experimental results for neutral collapses where there is no dominant jetting along one direction, which correlate well with the criteria of Blake et al. (J. Fluid Mech., vol. 170, 1986, pp. 479–497; J. Fluid Mech., vol. 181, 1987, pp. 197–212) but agree better with the experimental and computational results.

On fluid–particle dynamics in fully developed cluster-induced turbulence

Abstract: At sufficient mass loading and in the presence of a mean body force (e.g. gravity), an initially random distribution of particles may organize into dense clusters as a result of momentum coupling with the carrier phase. In statistically stationary flows, fluctuations in particle concentration can generate and sustain fluid-phase turbulence, which we refer to as cluster-induced turbulence (CIT). This work aims to explore such flows in order to better understand the fundamental modelling aspects related to multiphase turbulence, including the mechanisms responsible for generating volume-fraction fluctuations, how energy is transferred between the phases, and how the cluster size distribution scales with various flow parameters. To this end, a complete description of the two-phase flow is presented in terms of the exact Reynolds-average (RA) equations, and the relevant unclosed terms that are retained in the context of homogeneous gravity-driven flows are investigated numerically. An Eulerian–Lagrangian computational strategy is used to simulate fully developed CIT for a range of Reynolds numbers, where the production of fluid-phase kinetic energy results entirely from momentum coupling with finite-size inertial particles. The adaptive filtering technique recently introduced in our previous work (Capecelatro et al., J. Fluid Mech., vol. 747, 2014, R2) is used to evaluate the Lagrangian data as Eulerian fields that are consistent with the terms appearing in the RA equations. Results from gravity-driven CIT show that momentum coupling between the two phases leads to significant differences from the behaviour observed in very dilute systems with one-way coupling. In particular, entrainment of the fluid phase by clusters results in an increased mean particle velocity that generates a drag production term for fluid-phase turbulent kinetic energy that is highly anisotropic. Moreover, owing to the compressibility of the particle phase, the uncorrelated components of the particle-phase velocity statistics are highly non-Gaussian, as opposed to systems with one-way coupling, where, in the homogeneous limit, all of the velocity statistics are nearly Gaussian. We also observe that the particle pressure tensor is highly anisotropic, and thus additional transport equations for the separate contributions to the pressure tensor (as opposed to a single transport equation for the granular temperature) are necessary in formulating a predictive multiphase turbulence model.

Mechanism of frequency lock-in in vortex-induced vibrations at low Reynolds numbers

Abstract: In this study, a CFD-based linear dynamics model combined with the direct Computational Fluid Dynamics/Computational Structural Dynamics (CFD/CSD) simulation method is utilized to study the physical mechanisms underlying frequency lock-in in vortex-induced vibrations (VIVs). An identification method is employed to construct the reduced-order models (ROMs) of unsteady aerodynamics for the incompressible flow past a vibrating cylinder at low Reynolds numbers ( ). Reduced-order-model-based fluid–structure interaction models for VIV are also constructed by coupling ROMs and structural motion equations. The effects of the natural frequency of the cylinder, mass ratio and structural damping coefficient on the dynamics of the coupled system at are investigated. The results show that the frequency lock-in phenomenon at low Reynolds numbers can be divided into two patterns according to different induced mechanisms. The two patterns are ‘resonance-induced lock-in’ and ‘flutter-induced lock-in’. When the natural frequency of the cylinder is in the vicinity of the eigenfrequency of the uncoupled wake mode (WM), only the WM is unstable. The dynamics of the coupled system is dominated by resonance. Meanwhile, for relatively high natural frequencies (i.e. greater than the eigenfrequency of the uncoupled WM), the structure mode becomes unstable, and the coupling between the two unstable modes eventually leads to flutter. Flutter is the root cause of frequency lock-in and the higher vibration amplitude of the cylinder than that of the resonance region. This result provides evidence for the finding of De Langre (J. Fluids Struct., vol. 22, 2006, pp. 783–791) that frequency lock-in is caused by coupled-mode flutter. The linear model exactly predicts the onset reduced velocity of frequency lock-in compared with that of direct numerical simulations. In addition, the transition frequency predicted by the linear model is in close coincidence with the amplitude of the lift coefficient of a fixed cylinder for high mass ratios. Therefore, it confirms that linear models can capture a significant part of the inherent physics of the frequency lock-in phenomenon.

Direct numerical simulation of transition in a sharp cone boundary layer at Mach 6: fundamental breakdown

Abstract: Direct numerical simulations (DNS) were performed to investigate the laminar–turbulent transition in a boundary layer on a sharp cone with an isothermal wall at Mach 6 and at zero angle of attack. The motivation for this research is to make a contribution towards understanding the nonlinear stages of transition and the final breakdown to turbulence in hypersonic boundary layers. In particular, the role of second-mode fundamental resonance, or (K-type) breakdown, is investigated using high-resolution ‘controlled’ transition simulations. The simulations were carried out for the laboratory conditions of the hypersonic transition experiments conducted at Purdue University. First, several low-resolution simulations were carried out to explore the parameter space for fundamental resonance in order to identify the cases that result in strong nonlinear interactions. Subsequently, based on the results from this study, a set of highly resolved simulations that proceed deep into the turbulent breakdown region have been performed. The nonlinear interactions observed during the breakdown process are discussed in detail in this paper. A detailed description of the flow structures that arise due to these nonlinear interactions is provided and an analysis of the skin friction and heat transfer development during the breakdown is presented. The controlled transition simulations clearly demonstrate that fundamental breakdown may indeed be a viable path to complete breakdown to turbulence in hypersonic cone boundary layers at Mach 6.

Evolution of zero-pressure-gradient boundary layers from different tripping conditions

Abstract: In this paper we study the spatial evolution of zero-pressure-gradient (ZPG) turbulent boundary layers from their origin to a canonical high-Reynolds-number state. A prime motivation is to better understand under what conditions reliable scaling behaviour comparisons can be made between different experimental studies at matched local Reynolds numbers. This is achieved here through detailed streamwise velocity measurements using hot wires in the large University of Melbourne wind tunnel. By keeping the unit Reynolds number constant, the flow conditioning, contraction and trip can be considered unaltered for a given boundary layer’s development and hence its evolution can be studied in isolation from the influence of inflow conditions by moving to different streamwise locations. Careful attention was given to the experimental design in order to make comparisons between flows with three different trips while keeping all other parameters nominally constant, including keeping the measurement sensor size nominally fixed in viscous wall units. The three trips consist of a standard trip and two deliberately ‘over-tripped’ cases, where the initial boundary layers are over-stimulated with additional large-scale energy. Comparisons of the mean flow, normal Reynolds stress, spectra and higher-order turbulence statistics reveal that the effects of the trip are seen to be significant, with the remnants of the ‘over-tripped’ conditions persisting at least until streamwise stations corresponding to and trip heights are reached (which is specific to the trips used here), at which position the non-canonical boundary layers exhibit a weak memory of their initial conditions at the largest scales , where is the boundary layer thickness. At closer streamwise stations, no one-to-one correspondence is observed between the local Reynolds numbers ( , or etc.), and these differences are likely to be the cause of disparities between previous studies where a given Reynolds number is matched but without account of the trip conditions and the actual evolution of the boundary layer. In previous literature such variations have commonly been referred to as low-Reynolds-number effects, while here we show that it is more likely that these differences are due to an evolution effect resulting from the initial conditions set up by the trip and/or the initial inflow conditions. Generally, the mean velocity profiles were found to approach a constant wake parameter as the three boundary layers developed along the test section, and agreement of the mean flow parameters was found to coincide with the location where other statistics also converged, including higher-order moments up to tenth order. This result therefore implies that it may be sufficient to document the mean flow parameters alone in order to ascertain whether the ZPG flow, as described by the streamwise velocity statistics, has reached a canonical state, and a computational approach is outlined to do this. The computational scheme is shown to agree well with available experimental data.

Effects of spanwise spacing on large-scale secondary flows in rough-wall turbulent boundary layers

Abstract: Large-scale secondary flows can sometimes appear in turbulent boundary layers formed over rough surfaces, creating low- and high-momentum pathways along the surface (Barros & Christensen, J. Fluid Mech., vol. 748, 2014, R1). We investigate experimentally the dependence of these secondary flows on surface/flow conditions by measuring the flows over streamwise strips of roughness with systematically varied spanwise spacing. We find that the large-scale secondary flows are accentuated when the spacing of the roughness elements is roughly proportional to the boundary layer thickness ${\it\delta}$?, and do not appear for cases with finer spacing. Cases with coarser spacing also generate ${\it\delta}$?-scale secondary flows with tertiary flows in the spaces in between. These results show that the ratio of the spanwise length scale of roughness heterogeneity to the boundary layer thickness is a critical parameter for the occurrence of these secondary motions in turbulent boundary layers over rough walls.

Inertial migration of a rigid sphere in three-dimensional Poiseuille flow

Abstract: Inertial lift forces are exploited within inertial microfluidic devices to position, segregate and sort particles or droplets. However, the forces and their focusing positions can currently only be predicted by numerical simulations, making rational device design very difficult. Here we develop theory for the forces on particles in microchannel geometries. We use numerical experiments to dissect the dominant balances within the Navier–Stokes equations and derive an asymptotic model to predict the lateral force on the particle as a function of particle size. Our asymptotic model is valid for a wide array of particle sizes and Reynolds numbers, and allows us to predict how focusing position depends on particle size.

Maximizing the efficiency of a flexible propulsor using experimental optimization

Abstract: Experimental gradient-based optimization is used to maximize the propulsive efficiency of a heaving and pitching flexible panel. Optimum and near-optimum conditions are studied via direct force measurements and particle image velocimetry (PIV). The net thrust and power scale predictably with the frequency and amplitude of the leading edge, but the efficiency shows a complex multimodal response. Optimum pitch and heave motions are found to produce nearly twice the efficiencies of optimum heave-only motions. Efficiency is globally optimized when (i) the Strouhal number is within an optimal range that varies weakly with amplitude and boundary conditions; (ii) the panel is actuated at a resonant frequency of the fluid–panel system; (iii) heave amplitude is tuned such that trailing-edge amplitude is maximized while the flow along the body remains attached; and (iv) the maximum pitch angle and phase lag are chosen so that the effective angle of attack is minimized. The multi-dimensionality and multi-modality of the efficiency response demonstrate that experimental optimization is well-suited for the design of flexible underwater propulsors.

Regimes during liquid drop impact on a liquid pool

Abstract: Water drops falling on a deep pool can either coalesce to form a vortex ring or splash, depending on the impact conditions. The transition between coalescence and splashing proceeds via a number of intermediate steps, such as thick and thin jet formation and gas-bubble entrapment. We perform simulations to determine the conditions under which bubble entrapment and jet formation occur. A regime map is established for Weber numbers ranging from 50 to 300 and Froude numbers from 25 to 600. Vortex ring formation is seen for all of the regimes; it is greater for the coalescence regime and less in the case of the thin jet regime.

Turbulent boundary layer statistics at very high Reynolds number

Abstract: Measurements are presented in zero-pressure-gradient, flat-plate, turbulent boundary layers for Reynolds numbers ranging from to ( ). The wind tunnel facility uses pressurized air as the working fluid, and in combination with MEMS-based sensors to resolve the small scales of motion allows for a unique investigation of boundary layer flow at very high Reynolds numbers. The data include mean velocities, streamwise turbulence variances, and moments up to 10th order. The results are compared to previously reported high Reynolds number pipe flow data. For , both flows display a logarithmic region in the profiles of the mean velocity and all even moments, suggesting the emergence of a universal behaviour in the statistics at these high Reynolds numbers.

On the mechanism of turbulent drag reduction with super-hydrophobic surfaces

Abstract: The mechanism of turbulent drag reduction (DR) with super-hydrophobic (SH) surfaces is investigated by direct numerical simulation (DNS) and analysis of the governing equations in channel flow. The DNS studies were performed using lattice Boltzmann methods in channels with ‘idealized’ SH surfaces on both walls, comprised of longitudinal micro-grooves (MG), transverse MG, or micro-posts. DRs of to , to , and to were realized in DNS with longitudinal MG, transverse MG, and micro-posts, respectively. By mathematical analysis of the governing equations, it is shown that, in SH channel flows with any periodic SH micro-pattern on the walls, the magnitude of DR can be expressed as , where the first term represents the DR resulting from the effective slip on the walls, and the second term represents the DR or drag increase (DI) resulting from modifications to the turbulence dynamics and any secondary mean flows established in the SH channel compared to a channel flow with no-slip walls at the same bulk Reynolds number as the SH channel. Comparison of this expression to DNS results shows that, with all SH surface micro-patterns studied, between 80 % and 100 % of the DR in turbulent flow arises from the effective slip on the walls. Modifications to the turbulence dynamics contribute no more than 20 % of the total DR with longitudinal MG or micro-posts of high shear-free fraction (SFF), and a DI with transverse MG or micro-posts of moderate SFF. The effect of the SH surface on the normalized dynamics of turbulence is found to be small in all cases, and confined to additional production of turbulence kinetic energy (TKE) within a thin ‘surface layer’ of thickness of the order of the width of surface micro-indentations. Outside of this ‘surface layer’, the normalized dynamics of turbulence proceeds as in a turbulent channel flow with no-slip walls at the friction Reynolds number of the SH channel flow.

Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence

Abstract: In order that it be correctly characterized, irreversible turbulent mixing in stratified fluids must distinguish between adiabatic ‘stirring’ and diabatic ‘mixing’. Such a distinction has been formalized through the definition of a diapycnal diffusivity, (Winters & D’Asaro, J. Fluid Mech., vol. 317, 1996, pp. 179–193) and an appropriate mixing efficiency, (Caulfield & Peltier, J. Fluid Mech., vol. 413, 2000, pp. 1–47). Equivalent attention has not been paid to the definitions of a corresponding momentum diffusivity and hence an appropriately defined turbulent Prandtl number . In this paper, the diascalar framework of Winters & D’Asaro (1996) is first reformulated to obtain an ‘Osborn-like’ formula in which the correct definition of irreversible mixing efficiency is shown to replace the flux Richardson number which Osborn (J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89) assumed to characterize this efficiency. We advocate the use of this revised representation for diapycnal diffusivity since the proposed reformulation effectively removes the simplifying assumptions on which the original Osborn formula was based. We similarly propose correspondingly reasonable definitions for and by eliminating the reversible component of the momentum production term. To explore implications of the reformulations for both diapycnal and momentum diffusivity we employ an extensive series of direct numerical simulations (DNS) to investigate the properties of the shear-induced density-stratified turbulence that is engendered through the breaking of a freely evolving Kelvin–Helmholtz wave. The DNS results based on the proposed reformulation of are compared with available estimations due to the mixing length model, as well as both the Osborn–Cox and the Osborn models. Estimates based upon the Osborn–Cox formulation are shown to provide the closest approximation to the diapycnal diffusivity delivered by the exact representation. Through compilation of the complete set of DNS results we explore the characteristic dependence of on the buoyancy Reynolds number as originally investigated by Shih et al. (J. Fluid Mech., vol. 525, 2005, pp. 193–214) in their idealized study of homogeneous stratified and sheared turbulence, and show that the validity of their results is only further reinforced through analysis of the turbulence produced in the more geophysically relevant Kelvin–Helmholtz wave life-cycle ansatz. In contrast to the results described by Shih et al. (2005) however, we show that, besides , a vertically averaged measure of the gradient Richardson number may equivalently characterize the turbulent mixing at high . Based on the dominant driving processes involved in irreversible mixing, we categorize the intermediate (i.e. ) and high (i.e. ) range of as ‘buoyancy-dominated’ and ‘shear-dominated’ mixing regimes, which together define a transition value of . Mixing efficiency varies non-monotonically with both and , with its maximum (on the order of 0.2–0.3) occurring in the ‘buoyancy-dominated’ regime. Unlike which is very sensitive to the correct choice of (i.e. ), we show that is almost insensitive to the choice of (i.e. ) so long as is not close to unity, which implies for the entire range of . The turbulent Prandtl number is consequently shown to decrease monotonically with and may be (to first order) simply approximated by itself. Assuming , or (as is common in large-scale numerical models of the ocean general circulation), is also suggested to be a questionable assumption.

Dynamics of laser-induced bubble pairs

Abstract: The interaction of two laser-induced bubbles in bulk water is investigated. The strength and direction of the emerging liquid jets can be controlled by adjusting the relative bubble positions, the time difference between bubble generation, and the laser pulse energies determining the bubble sizes. Experimental and numerical studies are performed for millimetre-sized bubble pairs. Taking bubbles of equal energy, a maximum jet velocity is found for close anti-phase bubbles, i.e. when the second bubble is produced at the maximum volume of the first one and the bubble walls are almost touching and not merging. Under these conditions, one bubble produces a fast jet with a peak velocity of about that reaches a distance into the surrounding liquid of at least three times the maximum bubble radius. Collapse of the other bubble results in a slow jet of large mass that rapidly converts into a ring vortex. Correspondingly, the interaction with adjacent structures is dominated either by localized jet impact or by shear stresses extending over a larger area. Furthermore, interactions between micrometre-sized bubble pairs are investigated numerically to understand and predict how the effects of the physical parameters on bubble dynamics would change when the bubbles become smaller. The results are discussed with respect to micropumping and opto-injection.

Combustion noise is scale-free: transition from scale-free to order at the onset of thermoacoustic instability

Abstract: We investigate the scale invariance of combustion noise generated from turbulent reacting flows in a confined environment using complex networks. The time series data of unsteady pressure, which is the indicative of spatiotemporal changes happening in the combustor, is converted into complex networks using the visibility algorithm. We show that the complex networks obtained from the low-amplitude, aperiodic pressure fluctuations during combustion noise have scale-free structure. The power-law distributions of connections in the scale-free network are related to the scale invariance of combustion noise. We also show that the scale-free feature of combustion noise disappears and order emerges in the complex network topology during the transition from combustion noise to combustion instability. The use of complex networks enables us to formalize the identification of the pattern (i.e. scale-free to order) during the transition from combustion noise to thermoacoustic instability as a structural change in topology of the network.

Exact regularized point particle method for multiphase flows in the two-way coupling regime

Abstract: Particulate flows have mainly been studied under the simplifying assumption of a one-way coupling regime where the disperse phase does not modify the carrier fluid. A more complete view of multiphase flows can be gained calling into play two-way coupling effects, i.e. by accounting for the inter-phase momentum exchange, which is certainly relevant at increasing mass loading. In this paper we present a new methodology rigorously designed to capture the inter-phase momentum exchange for particles smaller than the smallest hydrodynamical scale, e.g. the Kolmogorov scale in a turbulent flow. The momentum coupling mechanism exploits the unsteady Stokes flow around a small rigid sphere, where the transient disturbance produced by each particle is evaluated in a closed form. The particles are described as lumped point masses, which would lead to the appearance of singularities. A rigorous regularization procedure is conceived to extract the physically relevant interactions between the particles and the fluid which avoids any 'ad hoc' assumption. The approach is suited for high-efficiency implementation on massively parallel machines since the transient disturbance produced by the particles is strongly localized in space. We will show that hundreds of thousands of particles can be handled at an affordable computational cost, as demonstrated by a preliminary application to a particle-laden turbulent shear flow.

The lamellar description of mixing in porous media

Abstract: We develop a general framework for modelling mixing in porous media flows, in which the scalar mixture is represented as an ensemble of lamellae evolving through stretching, diffusion and coalescence. Detailed numerical simulations in Darcy scale heterogeneous permeability fields are used to analyse the lamella deformation process, which controls the local concentration gradients and thus the evolution of the concentration mixture through stretching enhanced diffusion. The corresponding Lagrangian deformation process is shown to be well modelled by a Langevin equation with multiplicative noise, which can be coupled with diffusion to predict the temporal evolution of the concentration probability density function (PDF). At late times, lamella interaction is enforced by confinement of the mixture within the dispersion area. This process is shown to be well represented by a random aggregation model, which quantifies the frequency of lamella coalescence and allows us to predict the temporal evolution of the concentration PDF in this regime. The proposed theoretical framework provides an accurate prediction of the concentration PDFs at all investigated times, heterogeneity levels and Peclet numbers. In particular, it relates the temporal behaviour of mixing, as quantified by concentration moments, scalar dissipation rate or spatial increments of concentration, to the degree of structural heterogeneity.

Dynamics of particle migration in channel flow of viscoelastic fluids

Abstract: The migration of a sphere in the pressure-driven channel flow of a viscoelastic fluid is studied numerically. The effects of inertia, elasticity, shear-thinning viscosity, secondary flows and the blockage ratio are considered by conducting fully resolved direct numerical simulations over a wide range of parameters. In a Newtonian fluid in the presence of inertial effects, the particle moves away from the channel centreline. The elastic effects, however, drive the particle towards the channel centreline. The equilibrium position depends on the interplay between the elastic and inertial effects. Particle focusing at the centreline occurs in flows with strong elasticity and weak inertia. Both shear-thinning effects and secondary flows tend to move the particle away from the channel centreline. The effect is more pronounced as inertia and elasticity effects increase. A scaling analysis is used to explain these different effects. Besides the particle migration, particle-induced fluid transport and particle migration during flow start-up are also considered. Inertial effects, shear-thinning behaviour, and secondary flows are all found to enhance the effective fluid transport normal to the flow direction. Due to the oscillation in fluid velocity and strong normal stress differences that develop during flow start-up, the particle has a larger transient migration velocity, which may be potentially used to accelerate the particle focusing.

Phase diagram for droplet impact on superheated surfaces

Abstract: We experimentally determine the phase diagram for impacting ethanol droplets on a smooth, sapphire surface in the parameter space of Weber number We versus surface temperature T. We observe two transitions, namely the one towards splashing (disintegration of the droplet) with increasing We, and the one towards the Leidenfrost state (no contact between the droplet and the plate due to a lasting vapour film) with increasing T. Consequently, there are four regimes: contact and no splashing (deposition regime), contact and splashing (contact–splash regime), neither contact nor splashing (bounce regime), and finally no contact, but splashing (film–splash regime). While the transition temperature TL to the Leidenfrost state depends weakly, at most, on We in the parameter regime of the present study, the transition Weber number WeC towards splashing shows a strong dependence on T and a discontinuity at TL. We quantitatively explain the splashing transition for T

Evaporation of sessile drops: a three-dimensional approach

Abstract: The evaporation of non-axisymmetric sessile drops is studied by means of experiments and three-dimensional direct numerical simulations (DNS). The emergence of azimuthal currents and pairs of counter-rotating vortices in the liquid bulk flow is reported in drops with non-circular contact area. These phenomena, especially the latter, which is also observed experimentally, are found to play a critical role in the transient flow dynamics and associated heat transfer. Non-circular drops exhibit variable wettability along the pinned contact line sensitive to the choice of system parameters, and inversely dependent on the local contact-line curvature, providing a simple criterion for estimating the approximate contact-angle distribution. The evaporation rate is found to vary in the same order of magnitude as the liquid–gas interfacial area. Furthermore, the more complex case of drops evaporating with a moving contact line (MCL) in the constant contact-angle mode is addressed. Interestingly, the numerical results demonstrate that the average interface temperature remains essentially constant as the drop evaporates in the constant-angle (CA) mode, while this increases in the constant-radius (CR) mode as the drops become thinner. It is therefore concluded that, for increasing substrate heating, the evaporation rate increases more rapidly in the CR mode than in the CA mode. In other words, the higher the temperature the larger the difference between the lifetimes of an evaporating drop in the CA mode with respect to that evaporating in the CR mode.

Laminar separation bubble development on an airfoil emitting tonal noise

Abstract: The subject of this experimental study is the feedback effects due to tonal noise emission in a laminar separation bubble (LSB) formed on the suction side of an airfoil in low Reynolds number flows. Experiments were performed on a NACA 0012 airfoil for a range of chord-based Reynolds numbers at angle of attack , where laminar boundary layer separation is encountered on both sides of the airfoil. Simultaneous time-resolved, two-component particle image velocimetry (PIV) measurements, unsteady surface pressure and far-field acoustic pressure measurements were employed to characterize flow development and acoustic emissions. Amplification of disturbances in separated shear layers on both the suction and pressure sides of the airfoil leads to shear layer roll-up and shedding of vortices from separation bubbles. When the vortices do not break up upstream of the trailing edge, the passage of these structures over the trailing edge generates tonal noise. Acoustic feedback between the trailing edge noise source and the upstream separation bubble narrows the frequency band of amplified disturbances, effectively locking onto a particular frequency. Acoustic excitation further results in notable changes to the overall separation bubble characteristics. Roll-up vortices forming on the pressure side, where the bubble is located closer to the trailing edge, are shown to define the characteristic frequency of pressure fluctuations, thereby affecting the disturbance spectrum on the suction side. However, when the bubble on the pressure side is suppressed via boundary layer tripping, a weaker feedback effect is also observed on the suction side. The results give a detailed quantitative description of the observed phenomenon and provide a new outlook on the role of coherent structures in separation bubble dynamics and trailing edge noise generation.

Bubble dynamics in a viscoelastic medium with nonlinear elasticity

Abstract: In a variety of recently developed medical procedures, bubbles are formed directly in soft tissue and may cause damage. While cavitation in Newtonian liquids has received significant attention, bubble dynamics in tissue, a viscoelastic medium, remains poorly understood. To model tissue, most previous studies have focused on Maxwell-based viscoelastic fluids. However, soft tissue generally possesses an original configuration to which it relaxes after deformation. Thus, a Kelvin–Voigt-based viscoelastic model is expected to be a more appropriate representation. Furthermore, large oscillations may occur, thus violating the infinitesimal strain assumption and requiring a nonlinear/finite-strain elasticity description. In this article, we develop a theoretical framework to simulate spherical bubble dynamics in a viscoelastic medium with nonlinear elasticity. Following modern continuum mechanics formalism, we derive the form of the elastic forces acting on a bubble for common strain-energy functions (e.g. neo-Hookean, Mooney–Rivlin) and incorporate them into Rayleigh–Plesset-like equations. The main effects of nonlinear elasticity are to reduce the violence of the collapse and rebound for large departures from the equilibrium radius, and increase the oscillation frequency. The present approach can readily be extended to other strain-energy functions and used to compute the stress/deformation fields in the surrounding medium.

Transport of a dilute active suspension in pressure-driven channel flow

Abstract: Confined suspensions of active particles show peculiar dynamics characterized by wall accumulation, as well as upstream swimming, centreline depletion and shear trapping when a pressure-driven flow is imposed. We use theory and numerical simulations to investigate the effects of confinement and non-uniform shear on the dynamics of a dilute suspension of Brownian active swimmers by incorporating a detailed treatment of boundary conditions within a simple kinetic model where the configuration of the suspension is described using a conservation equation for the probability distribution function of particle positions and orientations, and where particle–particle and particle–wall hydrodynamic interactions are neglected. Based on this model, we first investigate the effects of confinement in the absence of flow, in which case the dynamics is governed by a swimming Peclet number, or ratio of the persistence length of particle trajectories over the channel width, and a second swimmer-specific parameter whose inverse measures the strength of propulsion. In the limit of weak and strong propulsion, asymptotic expressions for the full distribution function are derived. For finite propulsion, analytical expressions for the concentration and polarization profiles are also obtained using a truncated moment expansion of the distribution function. In agreement with experimental observations, the existence of a concentration/polarization boundary layer in wide channels is reported and characterized, suggesting that wall accumulation in active suspensions is primarily a kinematic effect that does not require hydrodynamic interactions. Next, we show that application of a pressure-driven Poiseuille flow leads to net upstream swimming of the particles relative to the flow, and an analytical expression for the mean upstream velocity is derived in the weak-flow limit. In stronger imposed flows, we also predict the formation of a depletion layer near the channel centreline, due to cross-streamline migration of the swimming particles towards high-shear regions where they become trapped, and an asymptotic analysis in the strong-flow limit is used to obtain a scale for the depletion layer thickness and to rationalize the non-monotonic dependence of the intensity of depletion upon flow rate. Our theoretical predictions are all shown to be in excellent agreement with finite-volume numerical simulations of the kinetic model, and are also supported by recent experiments on bacterial suspensions in microfluidic devices.