ALBERT

Description: This investigation analyzes the effect of vortex wakes on the Lagrangian displacement of particles induced by the passage of an obstacle in a two-dimensional incompressible and inviscid fluid. In addition to the trajectories of individual particles, we also study their drift and the corresponding total drift areas in the Föppl and Kirchhoff potential flow models. Our findings, which are obtained numerically and in some regimes are also supported by asymptotic analysis, are compared to the wakeless potential flow which serves as a reference. We show that in the presence of the Föppl vortex wake, some of the particles follow more complicated trajectories featuring a second loop. The appearance of an additional stagnation point in the Föppl flow is identified as a source of this effect. It is also demonstrated that, while the total drift area increases with the size of the wake for large vortex strengths, it is actually decreased for small circulation values. On the other hand, the Kirchhoff flow model is shown to have an unbounded total drift area. By providing a systematic account of the wake effects on the drift, the results of this study will allow for more accurate modeling of hydrodynamic stirring.

Description: The slow motion of a circular cylinder in a plane Poiseuille flow in a microchannel is analyzed for a wide range of cylinder radii and positions across the channel. The cylinder translates parallel to the channel walls and rotates about its axis. The Stokes approximation is used and the problem is solved analytically using the Papkovich-Fadle eigenfunction expansion and the least-squares method. The stream function and the pressure distribution of the flow field are obtained as results. The force and moment exerted on the cylinder, and the pressure change far from the cylinder, are calculated and shown as functions of the size and location of the cylinder. The results confirm some reciprocal relations exactly. In particular, the translational and rotational velocities of the drifting cylinder in the existing Poiseuille flow are determined. The induced pressure change, when the cylinder drifts in the Poiseuille flow, is also calculated. Some typical streamline patterns, depending on the size and location of the cylinder, are shown and discussed. When the cylinder translates and/or rotates in the channel blocked at infinity, a series of Moffatt eddies appears far from the cylinder in the channel, as expected.

Description: Interactions between capillary and elastic effects are relevant to a variety of applications from micro- and nano-scale manufacturing to biological systems. In this work, we investigate capillary flows in flexible, millimeter-scale cylindrical elastic tubes. We demonstrate that surface tension can cause sufficiently flexible tubes to collapse and coalesce spontaneously through non-axisymmetric buckling, and develop criteria for the initial deformation and complete collapse of a circular tube. Experimental results for capillary rise and evaporation of a liquid in a flexible tube are presented, and several regimes are seen for the equilibrium state of a flexible tube deforming under capillary pressure. Deformations of the tube walls are measured in different regimes and compared with a shell theory model. Analysis and experimental results show that despite the complex and non-axisymmetric deformed shapes of cylindrical structures, the elastocapillary length used in previous literature for flat plates and sheets can be used to predict the behavior of flexible tubes.

Description: We present laboratory experimental results demonstrating that librational forcing of an ellipsoidal container of water can produce intense motions through the mechanism of a libration driven elliptical instability (LDEI). These libration studies are conducted using an ellipsoidal acrylic container filled with water. A particle image velocimetry method is used to measure the 2D velocity field in the equatorial plane over hundreds libration cycles for a fixed Ekman number, E = 2 × 10 −5 . In doing so, we recover the libration induced base flow and a time averaged zonal flow. Further, we show that LDEI in non-axisymmetric container geometries is capable of driving both intermittent and saturated turbulent motions in the bulk fluid. Additionally, we measure the growth rate and amplitude of the LDEI induced excited flow in a fully ellipsoidal container at more extreme parameters than previously studied [Noir et al. , “Experimental study of libration-driven flows in nonaxisymmetric containers,” Phys. Earth Planet. Inter. 204-205 , 1 (2012); Cébron et al. , Phys. Fluids 24 , 061703, “Libration driven elliptical instability,” (2012)]. Excitation of bulk filling turbulence by librational forcing provides a mechanism for transferring rotational energy into turbulent fluid motion and thus can play an important role in the thermal evolution, interior dynamics, and magneto-hydrodynamics of librating bodies, as appear to be common in solar system settings [e.g., Comstock and Bills, “A solar system survey of forced librations in longitude,” J. Geophys. Res. Planets 108 , 1 (2003)].

Description: We numerically study the displacement flow of two iso-viscous Newtonian fluids in an inclined two-dimensional channel, formed by two parallel plates. The results are complementary to our previous studies on displacement flows in pipes and channels. The heavier displacing fluid moves the lighter displaced fluid in the downward direction. Three dimensionless groups largely describe these flows: the densimetric Froude number ( Fr ), the Reynolds number ( Re ), and the duct inclination (β). As a first order approximation, we are able to classify different flow regimes phenomenologically in a two-dimensional ( Fr ; Re cosβ/ Fr )-plane and provide leading order expressions for the transitions between different regimes. The stabilizing and/or de-stabilizing effects of the imposed mean flow on buoyant exchange flows (zero imposed velocity) are described for a broad range of dimensionless parameters.

Description: Compressible granular materials are involved in many applications, some of them being related to energetic porous media. Gas permeation effects are important during their compaction stage, as well as their eventual chemical decomposition. Also, many situations involve porous media separated from pure fluids through two-phase interfaces. It is thus important to develop theoretical and numerical formulations to deal with granular materials in the presence of both two-phase interfaces and gas permeation effects. Similar topic was addressed for fluid mixtures and interfaces with the Discrete Equations Method (DEM) [R. Abgrall and R. Saurel, “Discrete equations for physical and numerical compressible multiphase mixtures,” J. Comput. Phys. 186 (2), 361-396 (2003)] but it seemed impossible to extend this approach to granular media as intergranular stress [K. K. Kuo, V. Yang, and B. B. Moore, “Intragranular stress, particle-wall friction and speed of sound in granular propellant beds,” J. Ballist. 4 (1), 697-730 (1980)] and associated configuration energy [J. B. Bdzil, R. Menikoff, S. F. Son, A. K. Kapila, and D. S. Stewart, “Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues,” Phys. Fluids 11 , 378 (1999)] were present with significant effects. An approach to deal with fluid-porous media interfaces was derived in Saurel et al. [“Modelling dynamic and irreversible powder compaction,” J. Fluid Mech. 664 , 348-396 (2010)] but its validity was restricted to weak velocity disequilibrium only. Thanks to a deeper analysis, the DEM is successfully extended to granular media modelling in the present paper. It results in an enhanced version of the Baer and Nunziato [“A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials,” Int. J. Multiphase Flow 12 (6), 861-889 (1986)] model as symmetry of the formulation is now preserved. Several computational examples are shown to validate and illustrate method’s capabilities.

Description: We perform a theoretical and numerical study of the Coulomb-driven electroconvection flow of a dielectric liquid between two coaxial cylinders. The specific case, where the inner to outer diameter ratio is 0.5, is analyzed. A strong unipolar injection of ions either from the inner or outer cylinder is considered to introduce free charge carriers into the system. A finite volume method is used to solve all governing equations including Navier-Stokes equations and a simplified set of Maxwell’s equations. The flow is characterized by a subcritical bifurcation in the finite amplitude regime. A linear stability criterion and a nonlinear one that correspond to the onset and stop of the flow motion, respectively, are linked with a hysteresis loop. In addition, we also explore the behavior of the system for higher values of the stability parameter. For inner injection, we observe a transition between the patterns made of 7 and 8 cells, before an oscillatory regime is attained. Such a transition leads to a second finite amplitude stability criterion. A simple modal analysis reveals that the competition of different modes is at the origin of this behavior. The charge density, as well as velocity field distributions is provided to help understand the bifurcation behavior.

Description: Phytoplankton patchiness, namely the heterogeneous distribution of microalgae over multiple spatial scales, dramatically impacts marine ecology. A spectacular example of such heterogeneity occurs in thin phytoplankton layers (TPLs), where large numbers of photosynthetic microorganisms are found within a small depth interval. Some species of motile phytoplankton can form TPLs by gyrotactic trapping due to the interplay of their particular swimming style (directed motion biased against gravity) and the transport by a flow with shear along the direction of gravity. Here we consider gyrotactic swimmers in numerical simulations of the Kolmogorov shear flow, both in laminar and turbulent regimes. In the laminar case, we show that the swimmer motion is integrable and the formation of TPLs can be fully characterized by means of dynamical systems tools. We then study the effects of rotational Brownian motion or turbulent fluctuations (appearing when the Reynolds number is large enough) on TPLs. In both cases, we show that TPLs become transient, and we characterize their persistence.

Description: The model of gas bubble growth in high-viscous gas-saturated magmatic melt, subjected to rapid decompression, is presented in the current study. It is shown that consideration of unsteady character of the process is extremely important in a wide range of supersaturation. The analytical solution is found for the profile of dissolved gas concentration and the rate of bubble growth. The model of kinetics of overall degassing is developed. This model is based on distinguishing the so-called “forbidden” zone in the melt volume with suppressed formation of the new nucleation sites. The simple analytical dependences of the number of nucleating bubbles and typical nucleation time on the value of initial decompression were derived together with time dependence of volumetric concentration of the gas phase. Our results match the available experimental data.

Description: We investigate the effect of viscosity contrast on the stability of gravitationally unstable, diffusive layers in porous media. Our analysis helps evaluate experimental observations of various diffusive (boundary) layer models that are commonly used to study the sequestration of CO 2 in brine aquifers. We evaluate the effect of viscosity contrast for two basic models that are characterized with respect to whether or not the interface between CO 2 and brine is allowed to move. We find that diffusive layers are in general more unstable when viscosity decreases with depth within the layer compared to when viscosity increases with depth. This behavior is in contrast to the one associated with the classical displacement problem of gravitationally unstable diffusive layers that are subject to mean flow. For the classical problem, a greater instability is associated with the displacement of a more viscous, lighter fluid along the direction of gravity by a less viscous, heavier fluid. We show that the contrasting behavior highlighted in this study is a special case of the classical displacement problem that depends on the relative strength of the displacement and buoyancy velocities. We demonstrate the existence of a critical viscosity ratio that determines whether the flow is buoyancy dominated or displacement dominated. We explain the new behaviors in terms of the interaction of vorticity components related to gravitational and viscous effects.

Description: The development of a round liquid jet under the influence of a confined coaxial flow of an immiscible liquid of comparable density (central to annular flow density ratio of 8:10) was investigated in the vicinity of the nozzle exit. Two flow regimes were considered; one where the annular flow is faster than the central jet, so the central liquid jet is accelerated and one where the annular flow is slower, so the central liquid jet is decelerated. The central jet was visualised by high speed photography. Three modes of jet development were identified and classified in terms of the Reynolds number, Re, of the central jet which was in the range of 525 〈 Re 〈 2725, a modified definition of the Weber number, We, which allows the distinction between accelerating and deceleration flows and was in the range of −22 〈 We 〈 67 and the annular to central Momentum Ratio, MR, of the two streams which was in the range of 3.6 〈 MR 〈 91. By processing the time resolved jet images using Proper Orthogonal Decomposition (POD), it was possible to reduce the description of jet morphology to a small number of spatial modes, which isolated the most significant morphologies of the jet development. In this way, the temporal and spatial characteristics of the instabilities on the interface were clearly identified which highlights the advantages of POD over direct observation of the images. Relationships between the flow parameters and the interfacial waves were established. The wavelength of the interfacial instability was found to depend on the velocity of the fastest moving stream, which is contrary to findings for fluids with large density differences.

Description: Interaction of a vortex ring impinging on multiple permeable screens orthogonal to the ring axis was studied to experimentally investigate the persistence and decay of vortical structures inside the screen array using digital particle image velocimetry in a refractive index matched environment. The permeable screens had porosities (open area ratios) of 83.8%, 69.0%, and 55.7% and were held by a transparent frame that allowed the screen spacing to be changed. Vortex rings were generated using a piston-cylinder mechanism at nominal jet Reynolds numbers of 1000, 2000, and 3000 with piston stroke length-to-diameter ratios of 2 and 3. The interaction of vortex rings with the porous medium showed a strong dependence of the overall flow evolution on the screen porosity, with a central flow being preserved and vortex ring-like structures (with smaller diameter than the primary vortex ring) being generated near the centerline. Due to the large rod size used in the screens, immediate reformation of the transmitted vortex ring with size comparable to the primary ring (as has been observed with thin screens) was not observed in most cases. Since the screens have lower complexity and high open area ratios, centerline vortex ring-like flow structures formed with comparable size to the screen pore size and penetrated through the screens. In the case of low porosity screens (55.7%) with large screen spacing, re-emergence of large scale (large separation), weak vortical structures/pairs (analogous to a transmitted vortex ring) was observed downstream of the first screen. Additional smaller scale vortical structures were generated by the interaction of the vortex ring with subsequent screens. The size distribution of the generated vortical structures were shown to be strongly affected by porosity, with smaller vortical structures playing a stronger role as porosity decreased. Finally, porosity significantly affected the decay of total energy, but the effect of screen spacing decreased as porosity decreased.

Description: Vortex cavitation forming in the leading-edge vortices of a delta wing was examined to determine how the individual cavitation bubbles incepted, grew, interacted with the underlying vortical flow and produced acoustic tones. The non-cavitating vortical flow over the delta wing was chosen to be similar to those previously reported in the literature. It was found that vortex breakdown was unaffected by the presence of incipient and developed vortex cavitation bubbles in the vortex core. While some cavitation bubbles incepted, grew, and collapsed relatively quickly, others reached an equilibrium position wherein the bubble tip was stationary in the laboratory frame at a particular location along the vortex axis. For a given attack angle, the equilibrium location moved upstream with a reduction in free stream cavitation number. It is shown that the existence of these stationary vortex bubbles is possible when there is a balance between the axial growth of the bubble along the vortex axis and the opposite motion of the axial jetting flow in the vortex core, and only a single equilibrium position is possible along the axially evolving vortex for a given free stream cavitation number. These transient and stationary vortex bubbles emit significant cavitation noise upon inception, growth, and collapse. The spectral content of the noise produced was expected to be related to the interaction of the bubble with the surrounding vortical flow in a manner similar to that reported in previous studies, where sustained tones were similar to the underlying vortex frequency. However, in the present study, the dominant frequency and higher harmonics of the tones occur at a higher frequency than that of the underlying vortex. Hence, it is likely that the highly elongated stationary bubbles have higher-order volume oscillations compared to the two-dimensional radial mode of the vortex cores of vortex cavitation bubbles with much smaller diameter-to-length ratios.

Description: Laminar flow over a periodic array of cylindrical surface roughness elements is simulated with an immersed boundary spectral method both to validate the method for subsequent studies and to examine how persistent streamwise vortices are introduced by a low Reynolds number roughness element. Direct comparisons are made with prior studies at a roughness-based Reynolds number Re k (= U ( k ) k / ν ) of 205 and a diameter to spanwise spacing ratio d / λ of 1/3. Downstream velocity contours match present and past experiments very well. The shear layer developed over the top of the roughness element produces the downstream velocity deficit. Upstream of the roughness element, the vortex topology is found to be consistent with juncture flow experiments, creating three cores along the recirculation line. Streamtraces stemming from these upstream cores, however, have unexpectedly little effect on the downstream flowfield as lateral divergence of the boundary layer quickly dissipates their vorticity. Long physical relaxation time of the recirculating wake behind the roughness remains a prominent issue for simulating this type of flowfield.

Description: Solutal Marangoni instability (SMI) is investigated both in 2D and 3D using a combined Cahn-Hilliard and Navier-Stokes model in a finite system. Fe-Sn is chosen as a representative alloy system since the phase diagram reveals a region with a miscibility gap, where two liquid phases, namely, the Fe-rich phase L 1 and the Sn-rich phase L 2 , are in chemical equilibrium. In 3D, considering a perturbed liquid cylinder ( L 2 phase) with a length of λ and a radius of R 0 embedded in the middle of a simulation box of λ × H × H (length × width × height) surrounded by the phase L 1 , we find that the perturbation induced Marangoni flow is either clockwise or anti-clockwise depending on the mean curvature difference between the convex and concave regions which is affected by the ratio of λ/ R 0 . The critical ratio of λ/ R 0 for SMI is shown to be invariant for different Marangoni numbers as well as independent of the geometrical properties of the L 1 phase. In 2D, a perturbed liquid pipe with a length of λ and a radius of R 0 embedded in the middle of a simulation box of λ × H (length × height) is taken into account. Due to different curvature constitution, the critical ratio of λ/ R 0 for SMI depends on the height of the L 1 phase.

Description: For several years, a promising Plasma Synthetic Jet actuator for high-speed flow control has been under development at ONERA. So far, its confined geometry and small space-time scales at play have prevented its full experimental characterization. Complementary accurate numerical simulations are then considered in this study in order to provide a complete aerothermodynamic description of the actuator. Two major obstacles have to be overcome with this approach: the modeling of the energy deposited by the electric arc and the accurate computation of the transient response of the cavity generating the pulsed jet. To solve the first problem, an Euler solver coupled with an electric circuit model was used to evaluate the energy deposition in the cavity. Such a coupling is performed by considering the electric field between the two electrodes. The second issue was then addressed by injecting these source terms in large Eddy simulations of the entire actuator. Aerodynamic results were finally compared with Schlieren visualizations. Using the proposed methodology, the temporal evolution of the jet front is remarkably well predicted.

Description: Snapshot and classical proper orthogonal decomposition (POD) are used to examine the large-scale, energetic motions in fully developed turbulent pipe flow at Re D = 47,000 and 93,000. The snapshot POD modes come in pairs, representing the same azimuthal mode number but with a simple phase shift. The first 10 snapshot POD modes, associated with the very large scale motions (VLSMs), contribute 43% of the average Reynolds shear stress, and for first 80 modes u ′ and v ′ are anti-correlated so that they all contribute to positive shear stress events. The attached motions are contained in the lower order modes, and detached motions do not appear until snapshot POD mode numbers ≥15. We find that snapshot POD can introduce mode mixing, which is avoided in classical POD. Classical POD also gives frequency information, confirming that the low order modes capture well the behavior of the very large scale motions.

Description: We explore the instabilities developed in a fluid in which viscosity depends on temperature. In particular, we consider a dependency that models a very viscous (and thus rather rigid) lithosphere over a convecting mantle. To this end, we study a 2D convection problem in which viscosity depends on temperature by abruptly changing its value by a factor of 400 within a narrow temperature gap. We conduct a study which combines bifurcation analysis and time-dependent simulations. Solutions such as limit cycles are found that are fundamentally related to the presence of symmetry. Spontaneous plate-like behaviors that rapidly evolve towards a stagnant lid regime emerge sporadically through abrupt bursts during these cycles. The plate-like evolution alternates motions towards either the right or the left, thereby introducing temporary asymmetries on the convecting styles. Further time-dependent regimes with stagnant and plate-like lids are found and described.

Description: We study the shock wave structure in a rarefied polyatomic gas based on a simplified model of extended thermodynamics in which the dissipation is due only to the dynamic pressure. In this case the differential system is very simple because it is a variant of Euler system with a new scalar equation for the dynamic pressure [T. Arima, S. Taniguchi, T. Ruggeri, and M. Sugiyama, Phys. Lett. A376, 2799–2803 (2012)]. It is shown that this theory is able to describe the three types of the shock wave structure observed in experiments: the nearly symmetric shock wave structure (Type A, small Mach number), the asymmetric structure (Type B, moderate Mach number), and the structure composed of thin and thick layers (Type C, large Mach number).

Description: In this paper, the scaling property of the inverse energy cascade and forward enstrophy cascade of the vorticity filed ω( x , y ) in two-dimensional (2D) turbulence is analyzed. This is accomplished by applying a Hilbert-based technique, namely Hilbert-Huang transform, to a vorticity field obtained from a 8192 2 grid-points direct numerical simulation of the 2D turbulence with a forcing scale k f = 100 and an Ekman friction. The measured joint probability density function p ( C , k ) of mode C i ( x ) of the vorticity ω and instantaneous wavenumber k ( x ) is separated by the forcing scale k f into two parts, which correspond to the inverse energy cascade and the forward enstrophy cascade. It is found that all conditional probability density function p ( C | k ) at given wavenumber k has an exponential tail. In the inverse energy cascade, the shape of p ( C | k ) does collapse with each other, indicating a nonintermittent cascade. The measured scaling exponent ζ ω I ( q ) is linear with the statistical order q , i.e., ζ ω I ( q ) = − q / 3 , confirming the nonintermittent cascade process. In the forward enstrophy cascade, the core part of p ( C | k ) is changing with wavenumber k , indicating an intermittent forward cascade. The measured scaling exponent ζ ω F ( q ) is nonlinear with q and can be described very well by a log-Poisson fitting: ζ ω F ( q ) = 1 3 q + 0.45 1 − 0 . 43 q . However, the extracted vorticity scaling exponents ζ ω ( q ) for both inverse energy cascade and forward enstrophy cascade are not consistent with Kraichnan's theory prediction. New theory for the vorticity field in 2D turbulence is required to interpret the observed scaling behavior.

Description: We report experimental observations of the controlled deformation of a dielectric liquid jet subjected to a local high-voltage electrostatic field in the direction normal to the jet. The jet deforms to the shape of an elliptic cylinder upon application of a normal electrostatic field. As the applied electric field strength is increased, the elliptic cylindrical jet deforms permanently into a flat sheet, and eventually breaks-up into droplets. We interpret this observation—the stretch of the jet is in the normal direction to the applied electric field—qualitatively using the Taylor-Melcher leaky dielectric theory, and develop a simple scaling model that predicts the critical electric field strength for the jet-to-sheet transition. Our model shows a good agreement with experimental results, and has a form that is consistent with the classical drop deformation criterion in the Taylor-Melcher theory. Finally, we statistically analyze the resultant droplets from sheet breakup, and find that increasing the applied electric field strength improves droplet uniformity and reduces droplet size.

Description: Normal impingement of a single droplet on a thin liquid film is investigated numerically solving the axisymmetric Navier-Stokes equations. Gravity and viscosity are taken into account whereas compressibility effects are neglected. Two phases are tracked by means of volume of fluid method and adaptive mesh refinement is used to increase accuracy of the interface. Numerical results are validated both qualitatively and quantitatively using experimental measurements. Effects of gas density, gas viscosity, and film thickness on the crown behavior are studied. Influence of droplet deviation from spherical shape on the crown behavior is investigated. It is shown that increasing the gas density leads to reduction of crown radius evolution rate, while gas viscosity does not affect the rate of crown radius evolution. Development rate of crown height decreases by increasing the gas density. Reynolds number and splashing regime can change the effect of gas viscosity on the crown height evolution. Deviation of droplet from sphere can change behavior of crown completely as result of change in droplet mass center position. Difference between numerical results and experimental ones is justified using different droplet shapes.

Description: We present an analytical study of peak mode isotachophoresis (ITP), and provide closed form solutions for sample distribution and electric field, as well as for leading-, trailing-, and counter-ion concentration profiles. Importantly, the solution we present is valid not only for the case of fully ionized species, but also for systems of weak electrolytes which better represent real buffer systems and for multivalent analytes such as proteins and DNA. The model reveals two major scales which govern the electric field and buffer distributions, and an additional length scale governing analyte distribution. Using well-controlled experiments, and numerical simulations, we verify and validate the model and highlight its key merits as well as its limitations. We demonstrate the use of the model for determining the peak concentration of focused sample based on known buffer and analyte properties, and show it differs significantly from commonly used approximations based on the interface width alone. We further apply our model for studying reactions between multiple species having different effective mobilities yet co-focused at a single ITP interface. We find a closed form expression for an effective-on rate which depends on reactants distributions, and derive the conditions for optimizing such reactions. Interestingly, the model reveals that maximum reaction rate is not necessarily obtained when the concentration profiles of the reacting species perfectly overlap. In addition to the exact solutions, we derive throughout several closed form engineering approximations which are based on elementary functions and are simple to implement, yet maintain the interplay between the important scales. Both the exact and approximate solutions provide insight into sample focusing and can be used to design and optimize ITP-based assays.

Description: A novel waveform modified from the standard-sinusoidal function is adopted to enhance the virtual aeroshaping effect of the synthetic jets positioned at the front stagnation point of a circular cylinder. The waveform is characterized by a control parameter, namely, the suction duty cycle factor k , which is the ratio of the time duration of the suction cycle to that of the blowing cycle. The strength of the synthetic jet vortex pair is enhanced by increasing the suction duty cycle factor. The periodic closed envelope forms upstream of the circular cylinder for k ≤ 1.00, while the quasi-steady open envelope forms for k ≥ 2.00, acting the virtual aeroshaping effect. As a result, both the statistical characteristics and the vortex dynamics of the near-wake flow field change with the suction duty cycle factor. The recirculation region downstream of the circular cylinder becomes smaller or even disappears, and thus, the drag coefficient over the circular cylinder is reduced by increasing the suction duty cycle factor to k ≥ 1.00. The statistical mean and fluctuating velocities show corresponding changes in the near wake with the different wake patterns. For k ≤ 0.50, the wake vortex shows the antisymmetric shedding mode which is similar with the natural case. For 1.00 ≤ k ≤ 2.00, the wake vortex shows the bistable state mode, where vortex sheds with symmetric or antisymmetric mode; the antisymmetric shedding mode dominates the global flow field for k = 1.00, while it is the symmetric shedding mode that dominates the flow field for k = 2.00. For k = 4.00, it shows the antisymmetric shedding mode with a shorter vortex formation length than the natural case. The above findings indicate that the virtual aeroshaping effect of the synthetic jets can be enhanced by increasing the suction duty cycle factor so as to increase the momentum coefficient while keeping other control parameters unchanged, providing us another way for effective flow control.

Description: The dynamics of vapor-liquid interface are important because interfacial instability determines bubble growth, detachment frequency, waiting time, shape of bubbles, and the interrelationship between bubble formation sites. In this study, a detailed numerical simulation has been performed to understand the transition in bubble release pattern and multimode bubble formation in saturated pool boiling. The interfaces drop down alternatively at the nodes and antinodes of the wavelengths dictated by Rayleigh-Taylor instability and Taylor-Helmholtz instability. Due to higher degrees of superheat, vapor jets emanate from nodes and antinodes. An attempt has been made to predict the maximum and minimum heat fluxes during saturated pool boiling.

Description: We present a combination of experiment, theory, and modelling on laminar mixing at large Péclet number. The flow is produced by oscillating electromagnetic forces in a thin electrolytic fluid layer, leading to oscillating dipoles, quadrupoles, octopoles, and disordered flows. The numerical simulations are based on the Diffusive Strip Method (DSM) which was recently introduced (P. Meunier and E. Villermaux, “The diffusive strip method for scalar mixing in two-dimensions,” J. Fluid Mech.662, 134–172 (2010)) to solve the advection-diffusion problem by combining Lagrangian techniques and theoretical modelling of the diffusion. Numerical simulations obtained with the DSM are in reasonable agreement with quantitative dye visualization experiments of the scalar fields. A theoretical model based on log-normal Probability Density Functions (PDFs) of stretching factors, characteristic of homogeneous turbulence in the Batchelor regime, allows to predict the PDFs of scalar in agreement with numerical and experimental results. This model also indicates that the PDFs of scalar are asymptotically close to log-normal at late stages, except for the large concentration levels which correspond to low stretching factors.

Description: Janus droplets are compound droplets that consist of two adhering drops of different fluids that are suspended in a third fluid. We use the Shan-Chen lattice Boltzmann method for multicomponent mixtures to simulate Janus droplets at rest and in shear. In this simulation model, interfacial tensions are not known a priori from the model parameters and must be determined using numerical experiments. We show that interfacial tensions obtained with the Young-Laplace law are consistent with those measured from the equilibrium geometry. The regimes of adhering, separated, and engulfing droplets were explored. Two different adhesion geometries were considered for two-dimensional simulations of Janus droplets in shear. The first geometry resembles two adhering circles with small overlap. In the second geometry, the two halves are semicircular. For both geometries, the rotation rate of the droplet depends on its orientation. The width of the periodic simulation domain also affects the rotation rate of both droplet types up to an aspect ratio of 6:1 (width:height). While the droplets with the first geometry oscillated about the middle of the domain, the droplets of the second geometry did not translate while rotating. A four-pole vortex structure inside droplets of the second geometry was found. These simulations of single Janus droplets reveal complex behaviour that implies a rich range of possibilities for the rheology of Janus emulsions.

Description: Understanding the physics of water evaporation from saline porous media is important in many natural and engineering applications such as durability of building materials and preservation of monuments, water quality, and mineral-fluid interactions. We applied synchrotron x-ray micro-tomography to investigate the pore-scale dynamics of dissolved salt distribution in a three dimensional drying saline porous media using a cylindrical plastic column (15 mm in height and 8 mm in diameter) packed with sand particles saturated with CaI 2 solution (5% concentration by mass) with a spatial and temporal resolution of 12 μ m and 30 min, respectively. Every time the drying sand column was set to be imaged, two different images were recorded using distinct synchrotron x-rays energies immediately above and below the K-edge value of Iodine. Taking the difference between pixel gray values enabled us to delineate the spatial and temporal distribution of CaI 2 concentration at pore scale. Results indicate that during early stages of evaporation, air preferentially invades large pores at the surface while finer pores remain saturated and connected to the wet zone at bottom via capillary-induced liquid flow acting as evaporating spots. Consequently, the salt concentration increases preferentially in finer pores where evaporation occurs. Higher salt concentration was observed close to the evaporating surface indicating a convection-driven process. The obtained salt profiles were used to evaluate the numerical solution of the convection-diffusion equation (CDE). Results show that the macro-scale CDE could capture the overall trend of the measured salt profiles but fail to produce the exact slope of the profiles. Our results shed new insight on the physics of salt transport and its complex dynamics in drying porous media and establish synchrotron x-ray tomography as an effective tool to investigate the dynamics of salt transport in porous media at high spatial and temporal resolution.

Description: The behaviour of low Reynolds number, non-Boussinesq fountains from four different nozzle geometries (one circular and three rectangular nozzles) are studied. High speed laser schlieren imaging is used to study the fountain behaviour (frequency and penetration height). Bi-orthogonal decomposition and dynamic mode decomposition (DMD) are used to understand the unsteady characteristics of fountains. The flow regimes of fountains are classified as steady, flapping, and flapping-bobbing type. The DMD technique successfully separates the bobbing oscillation from the combined flapping-bobbing oscillation of the fountain. The frequency of the flapping oscillation, and the frequency of the bobbing oscillation in the flapping-bobbing regime scales as St h Fr h = C 1 and S t h F r h 2 = C 2 , respectively, where the characteristic length scale is the smallest dimension ( h ) of the nozzle. The mean steady state penetration heights ( Z s / h ) of “forced” low Reynolds number non-Boussinesq fountains are independent of nozzle shape (circular and rectangular), and scales linearly with the Froude number.

Description: The large-scale properties of self-similar unstably stratified homogeneous (USH) turbulence are investigated using an eddy-damped quasi-normal markovianized approximation of the nonlinear term. This analysis shows that a special role is played by the wave vectors contained in the equatorial plane, i.e., the plane perpendicular to gravity. It is indeed in this plane that turbulent spectra reach their maxima and evolve linearly from their initial condition when their initial infrared exponent is smaller than 4. At other angles, this property is not satisfied and turbulent spectra eventually undergo an evolution dominated by nonlinear backscattering processes. The self-similar evolution of USH turbulence is also shown to be related to the properties of large scales. In particular, the asymptotic growth rate of the mixing length depends on the initial infrared exponent in the equatorial plane. Besides, the self-similar asymptotic values of the concentration and velocity correlations also depend on the properties of large scales. This allows to derive relations between the correlations and the growth rate parameter.

Description: Secondary flow cells are commonly observed in straight laboratory channels, where they are often associated with duct corners. Here, we present velocity measurements acquired with an acoustic Doppler current profiler in a straight reach of the Seine river (France). We show that a remarkably regular series of stationary flow cells spans across the entire channel. They are arranged in pairs of counter-rotating vortices aligned with the primary flow. Their existence away from the river banks contradicts the usual interpretation of these secondary flow structures, which invokes the influence of boundaries. Based on these measurements, we use a depth-averaged model to evaluate the momentum transfer by these structures, and find that it is comparable with the classical turbulent transfer.

Description: Analysis of fluxes across the turbulent/non-turbulent interface (TNTI) of turbulent boundary layers is performed using data from two-dimensional particle image velocimetry (PIV) obtained at high Reynolds numbers. The interface is identified with an iso-surface of kinetic energy, and the rate of change of total kinetic energy ( K ) inside a control volume with the TNTI as a bounding surface is investigated. Features of the growth of the turbulent region into the non-turbulent region by molecular diffusion of K , viscous nibbling, are examined in detail, focussing on correlations between interface orientation, viscous stress tensor elements, and local fluid velocity. At the level of the ensemble (Reynolds) averaged Navier-Stokes equations (RANS), the total kinetic energy K is shown to evolve predominantly due to the turbulent advective fluxes occurring through an average surface which differs considerably from the local, corrugated, sharp interface. The analysis is generalized to a hierarchy of length-scales by spatial filtering of the data as used commonly in Large-Eddy-Simulation (LES) analysis. For the same overall entrainment rate of total kinetic energy, the theoretical analysis shows that the sum of resolved viscous and subgrid-scale advective flux must be independent of scale. Within the experimental limitations of the PIV data, the results agree with these trends, namely that as the filter scale increases, the viscous resolved fluxes decrease while the subgrid-scale advective fluxes increase and tend towards the RANS values at large filter sizes. However, a definitive conclusion can only be made with fully resolved three-dimensional data, over and beyond the large dynamic spatial range presented here. The qualitative trends from the measurement results provide evidence that large-scale transport due to the energy-containing eddies determines the overall rate of entrainment, while viscous effects at the smallest scales provide the physical mechanism ultimately responsible for entrainment. Data spanning over a decade in Reynolds number suggest that the fluxes (or the entrainment velocity) scale with the friction velocity (or equivalently the local turbulent fluctuating velocity), whereas Taylor microscale and boundary-layer thickness are the appropriate length scales at small and large filter sizes, respectively.

Description: In a recent direct numerical simulation (DNS) study [P. K. Yeung and K. R. Sreenivasan, “ Spectrum of passive scalars of high molecular diffusivity in turbulent mixing,” J. Fluid Mech.716, R14 (2013)] with Schmidt number as low as 1/2048, we verified the essential physical content of the theory of Batchelor, Howells, and Townsend [“Small-scale variation of convected quantities like temperature in turbulent fluid. 2. The case of large conductivity,” J. Fluid Mech.5, 134 (1959)] for turbulent passive scalar fields with very strong diffusivity, decaying in the absence of any production mechanism. In particular, we confirmed the existence of the −17/3 power of the scalar spectral density in the so-called inertial-diffusive range. In the present paper, we consider the DNS of the same problem, but in the presence of a uniform mean gradient, which leads to the production of scalar fluctuations at (primarily) the large scales. For the parameters of the simulations, the presence of the mean gradient alters the physics of mixing fundamentally at low Peclet numbers. While the spectrum still follows a −17/3 power law in the inertial-diffusive range, the pre-factor is non-universal and depends on the magnitude of the mean scalar gradient. Spectral transfer is greatly reduced in comparison with those for moderately and weakly diffusive scalars, leading to several distinctive features such as the absence of dissipative anomaly and a new balance of terms in the spectral transfer equation for the scalar variance, differing from the case of zero gradient. We use the DNS results to present an alternative explanation for the observed scaling behavior, and discuss a few spectral characteristics in detail.

Description: A non-equilibrium wall-model based on unsteady 3D Reynolds-averaged Navier-Stokes (RANS) equations has been implemented in an unstructured mesh environment. The method is similar to that of the wall-model for structured mesh described by Wang and Moin [Phys. Fluids14, 2043–2051 (2002)], but is supplemented by a new dynamic eddy viscosity/conductivity model that corrects the effect of the resolved Reynolds stress (resolved turbulent heat flux) on the skin friction (wall heat flux). This correction is crucial in predicting the correct level of the skin friction. Unlike earlier models, this eddy viscosity/conductivity model does not have a stress-matching procedure or a tunable free parameter, and it shows consistent performance over a wide range of Reynolds numbers. The wall-model is validated against canonical (attached) transitional and fully turbulent flows at moderate to very high Reynolds numbers: a turbulent channel flow at Re τ = 2000, an H-type transitional boundary layer up to Re θ = 3300, and a high Reynolds number boundary layer at Re θ = 31 000. Application to a separated flow over a NACA4412 airfoil operating close to maximum lift is also considered to test the performance of the wall-model in complex non-equilibrium flows.

Description: Conventional shallow water theory successfully reproduces many key features of the Jovian atmosphere: a mixture of coherent vortices and stable, large-scale, zonal jets whose amplitude decreases with distance from the equator. However, both freely decaying and forced-dissipative simulations of the shallow water equations in Jovian parameter regimes invariably yield retrograde equatorial jets, while Jupiter itself has a strong prograde equatorial jet. Simulations by Scott and Polvani [“Equatorial superrotation in shallow atmospheres,” Geophys. Res. Lett.35, L24202 (2008)] have produced prograde equatorial jets through the addition of a model for radiative relaxation in the shallow water height equation. However, their model does not conserve mass or momentum in the active layer, and produces mid-latitude jets much weaker than the equatorial jet. We present the thermal shallow water equations as an alternative model for Jovian atmospheres. These equations permit horizontal variations in the thermodynamic properties of the fluid within the active layer. We incorporate a radiative relaxation term in the separate temperature equation, leaving the mass and momentum conservation equations untouched. Simulations of this model in the Jovian regime yield a strong prograde equatorial jet, and larger amplitude mid-latitude jets than the Scott and Polvani model. For both models, the slope of the non-zonal energy spectra is consistent with the classic Kolmogorov scaling, and the slope of the zonal energy spectra is consistent with the much steeper spectrum observed for Jupiter. We also perform simulations of the thermal shallow water equations for Neptunian parameter values, with a radiative relaxation time scale calculated for the same 25 mbar pressure level we used for Jupiter. These Neptunian simulations reproduce the broad, retrograde equatorial jet and prograde mid-latitude jets seen in observations. The much longer radiative time scale for the colder planet Neptune explains the transition from a prograde to a retrograde equatorial jet, while the broader jets are due to the deformation radius being a larger fraction of the planetary radius.

Description: The hydrodynamic interaction of two deformable vesicles in shear flow induces a net displacement, in most cases an increase of their distance in the transverse direction. The statistical average of these interactions leads to shear-induced diffusion in the suspension, both at the level of individual particles which experience a random walk made of successive interactions, and at the level of suspension where a nonlinear down-gradient diffusion takes place, an important ingredient in the structuring of suspension flows. We make an experimental and computational study of the interaction of a pair of lipid vesicles in shear flow by varying physical parameters, and investigate the decay of the net lateral displacement with the distance between the streamlines on which the vesicles are initially located. This decay and its dependency upon vesicle properties can be accounted for by a simple model based on the well established law for the lateral drift of a vesicle in the vicinity of a wall. In the semi-dilute regime, a determination of self-diffusion coefficients is presented.

Description: The magnetohydrodynamic Richtmyer-Meshkov instability is investigated for the case where the initial magnetic field is unperturbed and aligned with the mean interface location. For this initial condition, the magnetic field lines penetrate the perturbed density interface, forbidding a tangential velocity jump and therefore the presence of a vortex sheet. Through simulation, we find that the vorticity distribution present on the interface immediately after the shock acceleration breaks up into waves traveling parallel and anti-parallel to the magnetic field, which transport the vorticity. The interference of these waves as they propagate causes the perturbation amplitude of the interface to oscillate in time. This interface behavior is accurately predicted over a broad range of parameters by an incompressible linearized model derived presently by solving the corresponding impulse driven, linearized initial value problem. Our use of an equilibrium initial condition results in interface motion produced solely by the impulsive acceleration. Nonlinear compressible simulations are used to investigate the behavior of the transverse field magnetohydrodynamic Richtmyer-Meshkov instability, and the performance of the incompressible model, over a range of shock strengths, magnetic field strengths, perturbation amplitudes and Atwood numbers.

Description: We investigate experimentally the statistical properties of bedload transport induced by a steady, uniform, and laminar flow. We focus chiefly on lateral transport. The analysis is restricted to experiments where the flow-induced shear stress is just above the threshold for sediment transport. We find that, in this regime, the concentration of moving particles is low enough to neglect interactions between themselves. We can therefore represent bedload as a thin layer of independent walkers travelling over the bed surface. In addition to their downstream motion, the particles show significant fluctuations of their cross-stream velocity, likely due to the roughness of the underlying sediment bed. This causes particles to disperse laterally. Based on thousands of individual trajectories, we show that this lateral spreading is the manifestation of a random walk. The experiments are entirely consistent with Fickian diffusion.

Description: We study the behavior of heavy inertial particles in the flow field of two like-signed vortices. In a frame co-rotating with the two vortices, we find that stable fixed points exist for these heavy inertial particles; these stable frame-fixed points exist only for particle Stokes number St 〈 St cr . We estimate St cr and compare this with direct numerical simulations, and find that the addition of viscosity increases the St cr slightly. We find that the rate at which particles fall into the fixed points increases until the fixed points disappear at St = St cr . These frame-fixed points are between fixed points and limit cycles in character.

Description: The paper reports a new phenomenon—vortex flows in isothermal magnetic fluids in the vicinity of the localized source of magnetic field (magnetized iron sphere) induced by the drift of drop-like aggregates. Although the observed magnetic precipitation of drop-like aggregates resembles an ordinary rainfall in the Earth atmosphere, its origin and nature are quite different. In magnetic fluids this “rain” is induced by the non-uniform magnetic field and occurs at the scale of 1 mm, not at the scale of several kilometers as in the Earth atmosphere. The reason of this phenomenon is that the applied magnetic field initiates phase transition of “gas-liquid” type which is accompanied by formation of condensed phase represented by drop-like aggregates with the characteristic dimension of about tens of micrometers elongated along the field lines. Inhomogeneous spatial distribution of drop-like aggregates leads to deviation of the ponderomotive force, which is responsible for the formation of vortex flows in the fluid. The “rain” is the primary reason for the vortex flows and it lasts until all magnetic particles capable of condensing into drop-like aggregates precipitate at the surface of the condensation core (iron sphere). Thus, vortex flows induced by drop-like aggregate magnetophoresis represent one variant of “gas-liquid” phase transition. Hydrodynamic flows intensify mass transfer in vicinity of magnetic condensation core and considerably speed it up.

Description: Compressive sampling is well-known to be a useful tool used to resolve the energetic content of signals that admit a sparse representation. The broadband temporal spectrum acquired from point measurements in wall-bounded turbulence has precluded the prior use of compressive sampling in this kind of flow, however it is shown here that the frequency content of flow fields that have been Fourier transformed in the homogeneous spatial (wall-parallel) directions is approximately sparse, giving rise to a compact representation of the velocity field. As such, compressive sampling is an ideal tool for reducing the amount of information required to approximate the velocity field. Further, success of the compressive sampling approach provides strong evidence that this representation is both physically meaningful and indicative of special properties of wall turbulence. Another advantage of compressive sampling over periodic sampling becomes evident at high Reynolds numbers, since the number of samples required to resolve a given bandwidth with compressive sampling scales as the logarithm of the dynamically significant bandwidth instead of linearly for periodic sampling. The combination of the Fourier decomposition in the wall-parallel directions, the approximate sparsity in frequency, and empirical bounds on the convection velocity leads to a compact representation of an otherwise broadband distribution of energy in the space defined by streamwise and spanwise wavenumber, frequency, and wall-normal location. The data storage requirements for reconstruction of the full field using compressive sampling are shown to be significantly less than for periodic sampling, in which the Nyquist criterion limits the maximum frequency that can be resolved. Conversely, compressive sampling maximizes the frequency range that can be recovered if the number of samples is limited, resolving frequencies up to several times higher than the mean sampling rate. It is proposed that the approximate sparsity in frequency and the corresponding structure in the spatial domain can be exploited to design simulation schemes for canonical wall turbulence with significantly reduced computational expense compared with current techniques.

Description: This paper presents extensive acoustic measurements on jets impinging on surfaces of various surface roughness values. Besides surface roughness, the effects of nozzle-to-plate spacing distance and nozzle pressure ratio are also investigated. Turbulent mixing noise and tonal noise are explained using far-field wall-jet velocity and impingement region temperature fields. The results demonstrate that roughness of the impingement plate widens the staging region of impingement noise. In general, high speed jet impinging on a rough plate generates less noise compared to a smooth plate. When tones are removed from the spectra, it is found that acoustic power monotonically decreases with increasing surface roughness. Thermal imaging in the stagnation region indicates that whenever tones are present, the temperature at the stagnation region is high. Further, sound pressure directivity pattern of impingement noise is constructed by superimposing a wall-jet and a free jet in the appropriate orientations.

Description: We investigate the elasticity of an isolated, threefold junction of soap films (Plateau border), which displays static undulations when liquid rapidly flows into it. By analyzing the shape of the Plateau border (thickness R and transverse displacement) as a function of the liquid flow rate Q , we show experimentally and theoretically that the elasticity of the Plateau border is dominated by the bending of the soap films pulling on the Plateau border. In this asymptotic regime, the undulation wavelength obeys the scaling law ∼ Q 2   R −2 and the decay length ∼ Q 2   R −4 .

Description: The case of a turbulent round jet impinging perpendicularly onto a rotating, heated disc is investigated, in order to understand the mechanisms at the origin of the influence of rotation on the radial wall jet and associated heat transfer. The present study is based on the complementary use of an analysis of the orders of magnitude of the terms of the mean momentum and Reynolds stress transport equations, available experiments, and dedicated Reynolds-averaged Navier–Stokes computations with refined turbulence models. The Reynolds number Re j = 14 500, the orifice-to-plate distance H = 5 D , where D is the jet-orifice diameter, and the four rotation rates were chosen to match the experiments of Minagawa and Obi [“Development of turbulent impinging jet on a rotating disk,” Int. J. Heat Fluid Flow25, 759–766 (2004)] and comparisons are made with the Nusselt number distribution measured by Popiel and Boguslawski [“Local heat transfer from a rotating disk in an impinging round jet,” J. Heat Transfer108, 357–364 (1986)], at a higher Reynolds number. The overestimation of turbulent mixing in the free-jet before the impact on the disk is detrimental to the prediction of the impingement region, in particular of the Nusselt number close to the symmetry axis, but the self-similar wall jet developing along the disk is correctly reproduced by the models. The analysis, experiments, and computations show that the rotational effect do not directly affect the outer layer, but only the inner layer of the wall jet. A noteworthy consequence is that entrainment at the outer edge of the wall jet is insensitive to rotation, which explains the dependence of the wall-jet thickness on the inverse of the non-dimensional rotation rate, observed in the experiments and the Reynolds stress model computations, but not reproduced by the eddy-viscosity models, due to the algebraic dependence to the mean flow. The analysis makes moreover possible the identification of a scenario for the appearance of rotational effects when the rotation rate is gradually increased. For weak rotation rates, the rotation-induced boundary layer appears but does not break the self-similar solution observed for the case without rotation. For intermediate rotation rates, the production of the azimuthal Reynolds stress becomes much stronger than other components, leading to a complete modification of the turbulence anisotropy which is reproduced only by Reynolds stress models. For strong rotation rates, centrifugal effects dominate, leading to an acceleration and thinning of the jet, and consequently an increase of turbulent production and heat transfer, reproduced by all the turbulence models.

Description: Microfluidic channels are powerful means of control of minute volumes such as droplets. These droplets are usually conveyed at will in an externally imposed flow which follows the geometry of the micro-channel. It has recently been pointed out by Dangla et al. [“Trapping microfluidic drops in wells of surface energy,” Phys. Rev. Lett.107(12), 124501 (2011)] that the motion of transported droplets may also be stopped in the flow, when they are anchored to grooves which are etched in the channels top wall. This feature of the channel geometry explores a direction that is usually uniform in microfluidics. Herein, this anchoring effect exploiting the three spatial directions is studied combining a depth averaged fluid description and a geometrical model that accounts for the shape of the droplet in the anchor. First, the presented method is shown to enable the capture and release droplets in numerical simulations. Second, this tool is used in a numerical investigation of the physical mechanisms at play in the capture of the droplet: a localized reduced Laplace pressure jump is found on its interface when the droplet penetrates the groove. This modified boundary condition helps the droplet cope with the linear pressure drop in the surrounding fluid. Held on the anchor the droplet deforms and stretches in the flow. The combination of these ingredients leads to recover the scaling law for the critical capillary number at which the droplets exit the anchors C a ★ ∝ h 2 / R 2 where h is the channel height and R the droplet undeformed radius.

Description: We present a numerical study of nanosecond pulsed dielectric barrier discharge (DBD) actuator operating in quiescent air at atmospheric condition. Our study concentrates on plasma discharge induced fluid dynamics and on exploration of parametric space of interest for voltage pulse in an attempt to shed some light into elucidation of the mechanisms whereby the generated shock wave propagates through and affects the external flow. Specifically, a one-dimensional, self-similar, local ionization kinetic model recently developed to predict key parameters of nanosecond pulsed plasma discharge is coupled with the compressible Navier-Stokes equations possibly for the first time. Within the considered range of parameters of the plasma model which is justified for the modeling of surface nanosecond pulsed discharge at atmospheric pressure, our coupled method is able to provide satisfactory prediction of the shock structure generated by the actuator for comparison with experiment, not only in the qualitative shock wave shape but also in quantitative shock front displacement. We provide a comprehensive analysis of the gas heating, shock wave initiation and evolution processes. For example, the characteristic time of the rapid localized heating responsible for shock wave generation, which is yet to be quantified experimentally, is found to be ∼350 ns. We conduct a parametric investigation by varying the peak voltage from 10 kV to 50 kV and rise time from 5 ns to 150 ns. The pressure wave whose behavior is found to be dominated by input voltage amplitude, introduces highly transient, localized disturbance to the quiescent air. In addition, the vortex induced by the shock passage is relatively weak. The interplay of the induced flows by a few successive plasma discharges operating at continuous mode does not appear to be significant, especially at low voltage amplitude.

Description: In this paper, we investigate the decay of incompressible homogeneous isotropic turbulence in a variable viscosity fluid. The viscosity coefficient is assumed to depend linearly on a scalar, representing either a temperature or a concentration, and obeying a simple advection-diffusion equation. At high Reynolds numbers, Direct Numerical Simulations (DNS) allow us to confirm the validity of Taylor's postulate that the dissipation is independent from the viscosity and its fluctuations. At low Reynolds numbers, we report the presence of extra energy at small scales due to these variable viscosity effects. This implies that the turbulent kinetic energy decreases less rapidly as a function of time in variable viscosity fluids. In order to explain this phenomenon and quantify its importance on the turbulent flow, we propose a statistical approach based on an eddy-damped quasi-normal Markovian (EDQNM) spectral closure which takes into account the nonlinearity introduced by variable viscosity. It is shown that this latter additional term is of constant sign in the energy spectrum equation and reduces the dissipation of the flow as observed. Also, by assuming the dominance of distant interactions between wave numbers, we can propose a simple formula expressing that variable viscosity effects lead to an effective reduction of the mean viscosity proportional to the variance of viscosity fluctuations.

Description: Liquid droplets flowing through a rectangular microfluidic channel develop a vortical flow field due to the presence of shear forces from the surrounding fluid. In this paper, we present an experimental and computational study of droplet velocities and internal flow patterns in a rectangular pressure-driven flow for droplet diameters ranging from 0.1 to 2 times the channel height. Our study shows excellent agreement with asymptotic predictions of droplet and interfacial velocities for infinitesimally small droplets. As the droplet diameter nears the size of the channel height, the droplet velocity slows significantly, and the changing external flow field causes a qualitative change in the location of internal vortices. This behavior is relevant for future studies of mass transfer in microfluidic devices.

Description: Laboratory experiments are performed to examine the formation of a crater in sediment by an impinging vertical turbulent jet. Light attenuation and a “depositometer,” which records conductivity through the bed from an array of electrodes, are used to measure the crater depth as a function of space and time. The onset of crater formation and deepening is best characterized in terms of the Rouse number, Rs (proportional to the particle settling speed divided by the centerline jet speed), rather than Shields number, Sh (proportional to the stress divided by the particle weight per unit area). The critical Rouse number, Rs c , is found to increase with the particle Reynolds number, Re p , as a power law with exponent 0.45 ± 0.03 for Re p ranging between 0.6 and 160. For smaller Rs, the crater is observed to deepen at a near-constant speed, while the crater radius remains constant. Bedload transport, measured in terms of the crater deepening speed, is determined to increase as Re p times the difference between Rs c and Rs.

Description: We report the experimental studies of the statistical and scaling properties of the fully developed turbulent regime in von Karman swirling flow between counter-rotating disks with and without blades using the only global measurements of the spatially averaged torque Γ and pressure p fluctuations in water and water-sugar solutions of different viscosities in the same cell geometry. We show that for all fluids under investigation probability distribution functions (PDFs) of the torque fluctuations δΓ/Γ rms are Gaussian in both the laminar and turbulent regimes and for the both types of the stirrers. On the contrary, PDFs of the pressure fluctuations change from Gaussian in the laminar regime into the skewed shape with the exponential tails toward low-pressure events for both the entrainment methods. Both the friction coefficient C f and normalized rms of the pressure fluctuations C p are independent of Re in the fully developed turbulent regime for all fluids under study and found in a good quantitative agreement with the previous results. We also observe that the internal flow variables such as the normalized torque Γ ¯ / V p r m s versus the “internal” Reynolds number Re rms = ( p rms /ρ) 1/2 R ρ/η instead of the global variables C f , C p versus Re show sharp transition into the well developed turbulent regime. We find that the scaling exponents of the fundamental characteristics based only on Γ and p measurements in the range of fully developed turbulent flow, namely, the integral, Taylor, and Kolmogorov dissipation lengths, as well as the Taylor-based Reynolds number R λ , are in rather fair agreement with the predictions. We would like to emphasize that scaling of the main turbulent parameters R λ , λ, η d obtained via the global variables is a very non-trivial result. It is not obvious that measurements based on the global quantities will provide the predicted scaling relations. The result on such scaling obtained previously strongly disagrees with the scaling predictions. Indeed, both Γ ¯ and p rms are averaged over the cell volume as well as all spatial scales, whereas the swirling flow is neither isotropic nor homogeneous. So the global variables being averaged over all spatial scales get contributions from the scales larger and smaller than those from the inertial range of scales. And finally, the normalized characteristic frequencies f p / f rot found in both the torque and pressure frequency power spectra in the fully developed turbulent regime have close values, are independent of Re , and associated with either the rotation or oscillation frequency of the main vortex.

Description: Numerical computations are presented to study the effect of soluble surfactant on the deformation and breakup of an axisymmetric drop or bubble stretched by an imposed linear strain flow in a viscous fluid. At the high values of bulk Peclet number Pe in typical fluid-surfactant systems, there is a thin transition layer near the interface in which the surfactant concentration varies rapidly. The large surfactant gradients are resolved using a fast and accurate “hybrid” numerical method that incorporates a separate, singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the free boundary problem. The method is used to investigate the dependence of drop deformation on parameters that characterize surfactant solubility. We also compute resolved examples of tipstreaming, and investigate its dependence on parameters such as flow rate and bulk surfactant concentration.

Description: Multi-scale analysis is widely adopted in turbulence research for studying flow structures corresponding to specific length scales in the Kolmogorov spectrum. In the present work, a new methodology based on novel optimization techniques for scale decomposition is introduced, which leads to a bandpass filter with prescribed properties. With this filter, we can efficiently perform scale decomposition using Fourier transform directly while adequately suppressing Gibbs ringing artifacts. Both 2D and 3D scale decomposition results are presented, together with qualitative and quantitative analysis. The comparison with existing multi-scale analysis technique is conducted to verify the effectiveness of our method. Validation of this decomposition technique is demonstrated both qualitatively and quantitatively. The advantage of the proposed methodology enables a precise specification of continuous length scales while preserving the original structures. These unique features of the proposed methodology may provide future insights into the evolution of turbulent flow structures.

Description: Direct numerical simulations (DNS) are conducted for a Mach 2.75 turbulent boundary layer interacting with an impinging shock at three different shock incidence angles. The accuracies of DNS calculations are established by checking the convergence of flow statistics for various grids, by comparing the generated results with those in the literature and also by the balance of contributing terms in the turbulent kinetic energy equation. Instantaneous flow visualizations show the significant effect of shock on turbulence structure in the shock-boundary layer interaction zone and also in the flow downstream of the interaction region. The separation bubbles exhibit highly unsteady and three-dimensional behavior and are larger for stronger shocks but the maximum probability of flow separation is found to be independent of the shock strength. The differences between Reynolds- and Favre-averaged quantities are also observed to be small and largely independent of the shock intensity. The turbulent kinetic energy is amplified across the shock, mainly by the production term in the turbulent kinetic energy equation. The amplification of enstrophy across the shock zone is found to be due to the vortex stretching term in the enstrophy transport equation. A detailed examination of the terms in the turbulent kinetic equation shows a strong coupling between the mean and turbulent fields in the interaction region with energy being continuously exchanged from one field to another. However, the compressibility-related terms in the transport equations for turbulent kinetic energy and enstrophy are found to be small for the simulated flows.

Description: Lotus-type porous metals are a promising alternative for compact heat transfer applications. In lotus-type porous fins, jet impingement and transverse mixing play important roles for heat transfer: jets emerging from the pores impinge on the following fin and enhance heat transfer performance, while the transverse fluid motion advects heat away from the fin surface. By means of magnetic resonance imaging we have performed mean flow and scalar transport measurements through scaled-up replicas of two kinds of lotus-type porous fins: one with a deterministic hole pattern and staggered alignment, and one with a random hole pattern, but the same porosity and mean pore diameter. The choice of geometric parameters (fin spacing, thickness, porosity, and hole diameter) is based on previous thermal studies. The Reynolds number based on the mean pore diameter and inner velocity ranges from 80 to 3800. The measurements show that in the random hole pattern the jet characteristic length scale is substantially larger with respect to the staggered hole pattern. The random geometry also produces long coherent vortices aligned with the streamwise direction, which improves the transverse mixing. The random hole distribution causes the time mean streamlines to meander in a random-walk manner, and the diffusivity coefficient associated to the mechanical dispersion (which is nominally zero in the staggered hole configuration) is several times larger than the fluid molecular diffusivity at the higher Reynolds numbers. From the trends in maximum streamwise velocity, streamwise vorticity, and mechanical diffusivity, it is inferred that the flow undergoes a transition to an unsteady/turbulent regime around Reynolds number 300. This is supported by the measurements of concentration of an isokinetic non-buoyant plume of scalar injected upstream of the stack of fins. The total scalar diffusivity for the fully turbulent regime is found to be 22 times larger than the molecular diffusivity, but only 6 times higher than the mechanical diffusivity, indicating that the latter plays a significant role for heat transfer and mixing.

Description: In this article, we discuss flows in shallow, stratified horizontal layers of two immiscible fluids. The top layer is an electrolyte which is electromagnetically driven and the bottom layer is a dielectric fluid. Using a quasi-two-dimensional approximation, which assumes a horizontal flow whose direction is independent of the vertical coordinate, we derive a generalized two-dimensional vorticity equation describing the evolution of the horizontal flow. Also, we derive an expression for the vertical profile of the horizontal velocity field. Measuring the horizontal velocity fields at the electrolyte-air and electrolyte-dielectric interfaces using particle image velocimetry, we validate the theoretical predictions of the horizontal velocity and its vertical profile for steady as well as for freely decaying Kolmogorov-like flows. Our analysis shows that by increasing the viscosity of the electrolyte relative to that of the dielectric, one may significantly improve the uniformity of the flow in the electrolyte, yielding excellent agreement between the analytical predictions and the experimental measurements.

Description: We investigate the direct enstrophy cascade of two-dimensional decaying turbulence in a flowing soap film channel. We use a coarse-graining approach that allows us to resolve the nonlinear dynamics and scale-coupling simultaneously in space and in scale. From our data, we verify an exact relation due to Eyink [“Local energy flux and the refined similarity hypothesis,” J. Stat. Phys.78, 335–351 (1995); Eyink “Exact results on scaling exponents in the 2D enstrophy cascade,” Phys. Rev. Lett.74, 3800–3803 (1995)] between traditional 3rd-order structure function and the enstrophy flux obtained by coarse-graining. We also present experimental evidence that enstrophy cascades to smaller (larger) scales with a 60% (40%) probability, in support of theoretical predictions by Merilees and Warn [“On energy and enstrophy exchanges in two-dimensional non-divergent flow ,” J. Fluid Mech.69, 625–630 (1975)] which appear to be valid in our flow owing to the ergodic nature of turbulence. We conjecture that their kinematic arguments break down in quasi-laminar 2D flows. We find some support for these ideas by using an Eulerian coherent structure identification technique, which allows us to determine the effect of flow topology on the enstrophy cascade. A key finding is that “centers” are inefficient at transferring enstrophy between scales, in contrast to “saddle” regions which transfer enstrophy to small scales with high efficiency.

Description: We studied the terminal velocity of a packed array of bubbles, a bubble cluster, rising in different fluids: a Newtonian fluid, an elastic fluid with nearly constant viscosity (Boger fluid), and a viscoelastic fluid with a shear dependent viscosity, for small but finite Reynolds numbers (1 × 10 −4 〈 Re 〈 4). In all three cases, the cluster velocity increased with the total volume, following the same trend as single bubbles. For the case of clusters in elastic fluids, interestingly, the so-called velocity discontinuity was not observed, unlike the single bubble case. In addition to the absence of jump velocity, the clusters did not show the typical teardrop shape of large bubbles in viscoelastic fluids and the strength of the negative wake is much weaker than the one observed behind single bubbles. Dimensional analysis of the volume-velocity plots allowed us to show that, while the equivalent diameter (obtained from the total cluster volume) is the appropriate length to determine buoyancy forces and characteristic shear rates, the individual bubble size is the appropriate scale to account for surface forces.

Description: The dynamics and multiple-cycle evolution of the incompressible flow induced by a moving piston through the open valve of a motored piston-cylinder assembly was investigated using direct numerical simulation. A spectral element solver, adapted for moving geometries using an Arbitrary Lagrange/Eulerian formulation, was employed. Eight cycles were simulated and the ensemble- and azimuthally-averaged data were found to be in good agreement with experimentally determined means and fluctuations at all measured points and times. During the first half of the intake stroke the flow field is dominated by the dynamics of the incoming jet and the vortex rings it creates. With decreasing piston speed a large central ring becomes the dominant flow feature until the top dead center. The flow field at the end of the previous cycle is found to have a dominant effect on the jet breakup and the vortex ring dynamics below the valve and on the observed significant cyclic variations. Based on statistical averaging, the evolution of the turbulent flow field during the first half of the intake stroke is dominated by the jet breakup process leading to a strongly anisotropic behavior. In the second part of the intake stroke, the decrease of the incoming jet velocity results in a more isotropic behavior.

Description: This paper presents the linear stability analysis of an interface between air and an insulating liquid subjected to a perpendicular electric field, in the presence of unipolar injection of charge. Depending on the characteristics of the liquid and the depth of the liquid layer two different instability thresholds may be found. One of them is characterized by a wavelength of the order of the liquid layer thickness and corresponds to the well-known volume instability of a liquid layer subjected to charge injection. The other one is characterized by a wavelength some ten times the liquid layer thickness and corresponds to the so-called rose-window instability, an instability associated to the balance of surface stresses.

Description: An alternative framework for parameterizing stably stratified shear-flow turbulence is presented. Using dimensional analysis, four non-dimensional parameters of interest are identified that consider the independent effects of stratification, shear, viscosity, and scalar diffusivity. In the interest of geophysical applications, the problem is further simplified by considering only high Reynolds number flow. This leads to a two-dimensional parameter space based on a buoyancy strength parameter (i.e., an inverse Froude number) and a shear strength parameter. Consideration for the gradient Richardson number allows the space to be divided into an unforced regime, a shear-dominated regime, and a buoyancy-dominated regime. On this basis, a large database of direct numerical simulation and laboratory data from various sources is evaluated. Of particular interest is the observed length scale of overturning. Overturns are found to scale with k 1/2 / N in the buoyancy-dominated regime, k 1/2 / S in the shear-dominated regime, and k 3/2 /ε in the unforced regime, where k , N , S , and ε are the turbulent kinetic energy, buoyancy frequency, mean shear rate, and turbulent kinetic energy dissipation rate, respectively. Implications for estimates of diapycnal mixing in the ocean are discussed and a new parameterization for eddy diffusivity is presented.

Description: We quantify the strength of the waves and their impact on the energy cascade in rotating turbulence by studying the wave number and frequency energy spectrum, and the time correlation functions of individual Fourier modes in numerical simulations in three dimensions in periodic boxes. From the spectrum, we find that a significant fraction of the energy is concentrated in modes with wave frequency ω ≈ 0, even when the external forcing injects no energy directly into these modes. However, for modes for which the period of the inertial waves τ ω is faster than the turnover time τ NL , a significant fraction of the remaining energy is concentrated in the modes that satisfy the dispersion relation of the waves. No evidence of accumulation of energy in the modes with τ ω = τ NL is observed, unlike what critical balance arguments predict. From the time correlation functions, we find that for modes with τ ω 〈 τ sw (with τ sw the sweeping time) the dominant decorrelation time is the wave period, and that these modes also show a slower modulation on the timescale τ NL as assumed in wave turbulence theories. The rest of the modes are decorrelated with the sweeping time, including the very energetic modes with ω ≈ 0.

Description: We propose a new mechanism for bubble nucleation triggered by the rubbing of solid surfaces immersed in a liquid, in which the fluid molecules squeezed between the solids are released with high kinetic energy into the bulk of the liquid, resulting in the nucleation of a vapor bubble. Molecular dynamics simulations with a superheated Lennard-Jones fluid are used to evidence this mechanism. Nucleation is observed at the release of the squeezed molecules, for squeezing pressures above a threshold value and for all the relative velocities between the solids that we investigate. We show that the total kinetic energy of the released molecules for a single release event is proportional to the number of molecules released, which depends on the squeezing pressure, but is independent of the velocity.

Description: The Reynolds number scaling of flow topology in the eigenframe of the strain-rate tensor is investigated for wall-bounded flows, which is motivated by earlier works showing that such topologies appear to be qualitatively universal across turbulent flows. The databases used in the current study are from direct numerical simulations (DNS) of fully developed turbulent channel flow (TCF) up to friction Reynolds number Re τ ≈ 1500, and a spatially developing, zero-pressure-gradient turbulent boundary layer (TBL) up to Re θ ≈ 4300 ( Re τ ≈ 1400). It is found that for TCF and TBL at different Reynolds numbers, the averaged flow patterns in the local strain-rate eigenframe appear the same consisting of a pair of co-rotating vortices embedded in a finite-size shear layer. It is found that the core of the shear layer associated with the intense vorticity region scales on the Kolmogorov length scale, while the overall height of the shear layer and the distance between the vortices scale well with the Taylor micro scale. Moreover, the Taylor micro scale collapses the height of the shear layer in the direction of the vorticity stretching. The outer region of the averaged flow patterns approximately scales with the macro scale, which indicates that the flow patterns outside of the shear layer mainly are determined by large scales. The strength of the shear layer in terms of the peak tangential velocity appears to scale with a mixture of the Kolmogorov velocity and root-mean-square of the streamwise velocity scaling. A quantitative universality in the reported shear layers is observed across both wall-bounded flows for locations above the buffer region.

Description: The stability of a thread of fluid deposited on a flat solid substrate is studied numerically by means of the Finite Element Method in combination with an Arbitrary Lagrangian-Eulerian technique. A good agreement is observed when our results are compared with predictions of linear stability analysis obtained by other authors. Moreover, we also analysed the influence of inertia for different contact angles and found that inertia strongly affects the growth rate of the instability when contact angles are large. By contrast, the wave number of the fastest growing mode does not show important variations with inertia. The numerical technique allows us to follow the evolution of the free surface instability until comparatively late stages, where the filament begins to break into droplets. The rupture pattern observed for several cases shows that the number of principal droplets agrees reasonably well with an estimation based on the fastest growing modes.

Description: We investigate the dynamics of an insoluble surfactant on the surface of a thin viscous fluid spreading inward to fill a surfactant-free region. During the initial stages of surfactant self-healing, Marangoni forces drive an axisymmetric ridge inward to coalesce into a growing central distension; this is unlike outward spreading, in which the ridge only decays. In later dynamics, the distension slowly decays and the surfactant concentration equilibrates. We present results from experiments in which we simultaneously measure the surfactant concentration (using fluorescently tagged lipids) and the fluid height profile (via laser profilometry). We compare the results to simulations of a mathematical model using parameters from our experiments. For surfactant concentrations close to but below the critical monolayer concentration, we observe agreement between the height profiles in the numerical simulations and the experiment, but disagreement in the surfactant distribution. In experiments at lower concentrations, the surfactant spreading and formation of a Marangoni ridge are no longer present, and a persistent lipid-free region remains. This observation, which is not captured by the simulations, has undesirable implications for applications where uniform coverage is advantageous. Finally, we probe the generality of the effect, and find that distensions of similar size are produced independent of initial fluid thickness, size of initial clean region, and surfactant type.

Description: Numerical simulations are used to investigate the effect of variation of the aspect ratio and the structure of pitching motions on the energy extraction efficiency and wake topology of flapping foils. The central aim is to predict the energy extraction performance and efficiency of a flapping-foil-based energy harvesting system (EHS) in realistic working conditions with finite aspect ratios. A sinusoidal heaving motion is imposed upon the foil, as well as both a sinusoidal pitching motion and a variety of trapezoidal-like periodic pitching motions. The simulations employ a finite-volume method with body-fitted moving grids, allowing the capture of flow structure near the foil surface. A detailed analysis of the hydrodynamic performance shows two peaks per periodic cycle in the lift force time histories or equivalently, the energy extraction time histories. The first primary peak corresponds to an effective angle of attack around 15.4°, indicating good attachment of the flow on the foil surface without significant flow separation. The secondary peak corresponds to a leading edge vortex (LEV) travelling on the foil surface. The shape of the LEV is altered markedly as the aspect ratio varies, and consequently the secondary peak in the lift force time history is strongly affected by the effects of three-dimensionality for foils with smaller aspect ratios. By examining the relationship between energy extraction efficiency and aspect ratio, a critical aspect ratio of AR = 4 is identified for sinusoidal pitching motions, below which the three-dimensional low-aspect-ratio characteristics dominate the flow evolution. Therefore, the compromise between higher energy extraction efficiency and lower costs of manufacturing and installation suggests that an aspect ratio around AR = 4 is the most appropriate choice for a real EHS. Furthermore, although trapezoidal-like pitching motions are known to improve the efficiency in flows restricted to two dimensions, particularly for non-optimal angle of attack, the efficiency of such flows is even more strongly affected by three-dimensional motions, with substantial efficiency loss even for AR = 8. This suggests that the implementation of efficiency improvement strategies obtained by two-dimensional studies should be treated with caution when extended to real three-dimensional flows.

Description: We study the liquid flow inside a recessed gas-centered swirl coaxial injector, where a swirled liquid flowing against an outer wall is destabilized by a central fast gas stream. We present measurements of the liquid intact length inside the injector, as a function of swirl number and dynamic pressure ratio. We propose a simple model to account for the effect of these parameters. We next study the surface instability inside the injector: its frequency is measured for several swirl angles, and as a function of gas velocity. Results are first confronted to the predictions of an inviscid linear stability analysis including swirl, and second to the predictions of a viscous linear stability analysis where swirl is not included. The viscous analysis captures the experimental frequency.

Description: This article presents a quasi-laminar stability approach to identify in high-Reynolds number flows the dominant low-frequencies and to design passive control means to shift these frequencies. The approach is based on a global linear stability analysis of mean-flows, which correspond to the time-average of the unsteady flows. Contrary to the previous work by Meliga et al. [“Sensitivity of 2-D turbulent flow past a D-shaped cylinder using global stability,” Phys. Fluids24, 061701 (2012)], we use the linearized Navier-Stokes equations based solely on the molecular viscosity (leaving aside any turbulence model and any eddy viscosity) to extract the least stable direct and adjoint global modes of the flow. Then, we compute the frequency sensitivity maps of these modes, so as to predict before hand where a small control cylinder optimally shifts the frequency of the flow. In the case of the D-shaped cylinder studied by Parezanović and Cadot [J. Fluid Mech.693, 115 (2012)], we show that the present approach well captures the frequency of the flow and recovers accurately the frequency control maps obtained experimentally. The results are close to those already obtained by Meliga et al. , who used a more complex approach in which turbulence models played a central role. The present approach is simpler and may be applied to a broader range of flows since it is tractable as soon as mean-flows — which can be obtained either numerically from simulations (Direct Numerical Simulation (DNS), Large Eddy Simulation (LES), unsteady Reynolds-Averaged-Navier-Stokes (RANS), steady RANS) or from experimental measurements (Particle Image Velocimetry - PIV) — are available. We also discuss how the influence of the control cylinder on the mean-flow may be more accurately predicted by determining an eddy-viscosity from numerical simulations or experimental measurements. From a technical point of view, we finally show how an existing compressible numerical simulation code may be used in a black-box manner to extract the global modes and sensitivity maps.

Description: Spiral gravity separators are devices used in mineral processing to separate particles based on their specific gravity or size. The spiral geometry allows for the simultaneous application of gravitational and centripetal forces on the particles, which leads to segregation of particles. However, this segregation mechanism is not fundamentally understood, and the spiral separator literature does not tell a cohesive story either experimentally or theoretically. While experimental results vary depending on the specific spiral separator used, present theoretical works neglect the significant coupling between the particle dynamics and the flow field. Using work on gravity-driven monodisperse slurries on an incline that empirically accounts for this coupling, we consider a monodisperse particle slurry of small depth flowing down a rectangular channel that is helically wound around a vertical axis. We use a thin-film approximation to derive an equilibrium profile for the particle concentration and fluid depth and find that, in the steady state limit, the particles concentrate towards the vertical axis of the helix, leaving a region of clear fluid.

Description: The turbulent flow inside a rotating channel provided with transverse ribs along one wall is studied by means of two-dimensional time-resolved particle image velocimetry. The measurement set-up is mounted on the same rotating disk with the test section, allowing to obtain the same accuracy and resolution as in a non-rotating rig. The Reynolds number is 15 000, and the rotation number is 0.38. As the ribbed wall is heated, both the Coriolis force and the centrifugal force play a role in the fluid dynamics. The mean velocity fields highlight the major impact of the rotational buoyancy (characterized by a buoyancy number of 0.31) on the flow along the leading side of the duct. In particular, since the flow is directed radially outward, the near-wall layers experience significant centripetal buoyancy. The recirculation area behind the obstacles is enlarged to the point of spanning the whole inter-rib space. Also the turbulent fluctuations are significantly altered, and overall augmented, with respect to the non-buoyant case, resulting in higher turbulence levels far from the rib. On the other hand the centrifugal force has little or no impact on the flow along the trailing wall. Vortex identification, proper orthogonal decomposition, and two-point correlations are used to highlight rotational effects, and in particular to determine the dominant scales of the turbulent unsteady flow, the time-dependent behavior of the shear layer and of the recirculation bubble behind the wall-mounted obstacles, the lifetime and advection velocity of the coherent structures.

Description: This study established the connection in turbulent boundary layers between the first two dominant proper orthogonal decomposition (POD) modes and the instantaneous large-scale turbulence structures. The velocity fields consistent with the signature velocity fields of the hairpin vortex packets in two-dimensional PIV (particle image velocimetry) measurement planes are observed as the major contributors to the first two POD modes. Another kind of equally important turbulence structure is the large region of Q4 vectors, which may possibly be obtained by slicing the outskirts of the three-dimensional structure of the hairpin vortex packet by PIV planes. The streamwise Reynolds normal stress, Reynolds shear stress, and the length scales of the two-point velocity correlation coefficients ρ uu and ρ uv are noticeably decreased without those large-scale turbulence structures contributing significantly to the first POD mode. Similarity of these results is observed at a higher Reynolds number.

Description: Experimental and analytical results are presented on two identical bio-inspired hydrofoils oscillating in a side-by-side configuration. The time-averaged thrust production and power input to the fluid are found to depend on both the oscillation phase differential and the transverse spacing between the foils. For in-phase oscillations, the foils exhibit an enhanced propulsive efficiency at the cost of a reduction in thrust. For out-of-phase oscillations, the foils exhibit enhanced thrust with no observable change in the propulsive efficiency. For oscillations at intermediate phase differentials, one of the foils experiences a thrust and efficiency enhancement while the other experiences a reduction in thrust and efficiency. Flow visualizations reveal how the wake interactions lead to the variations in propulsive performance. Vortices shed into the wake from the tandem foils form vortex pairs rather than vortex streets. For in-phase oscillation, the vortex pairs induce a momentum jet that angles towards the centerplane between the foils, while out-of-phase oscillations produce vortex pairs that angle away from the centerplane between the foils.

Description: A three-dimensional, nonperturbative, semiclassical analytic model of vibrational energy transfer in collisions between a rotating diatomic molecule and an atom, and between two rotating diatomic molecules (Forced Harmonic Oscillator–Free Rotation model) has been extended to incorporate rotational relaxation and coupling between vibrational, translational, and rotational energy transfer. The model is based on analysis of semiclassical trajectories of rotating molecules interacting by a repulsive exponential atom-to-atom potential. The model predictions are compared with the results of three-dimensional close-coupled semiclassical trajectory calculations using the same potential energy surface. The comparison demonstrates good agreement between analytic and numerical probabilities of rotational and vibrational energy transfer processes, over a wide range of total collision energies, rotational energies, and impact parameter. The model predicts probabilities of single-quantum and multi-quantum vibrational-rotational transitions and is applicable up to very high collision energies and quantum numbers. Closed-form analytic expressions for these transition probabilities lend themselves to straightforward incorporation into DSMC nonequilibrium flow codes.

Description: Turbulent jets and plumes are commonly encountered in natural and industrial environments, and have been the objects of seminal works on turbulent free shear flows. The dynamics of turbulent jets is most often described as a function of the so-called entrainment coefficient, α, which quantifies the entrainment of ambient fluid into the jets. This key parameter has been determined in numerous and extensive experimental, numerical, and theoretical studies of axisymmetric jets. However, data remain scarce on turbulent planar jets. Available studies have shown that at low distance from the source, α increases with the source Reynolds number, and that α increases with distance from the source for large source Reynolds number. But no link has been made between these two kinds of observation so far. To study the relative influence of source Reynolds number, Re 0 , and distance from source on entrainment in planar turbulent jets, we perform new experiments at low Re 0 (between 59 and 424) with three different aspect ratio (185, 370, and 925) and at small and large distances from the source. Our experimental results show no systematic variations of α as a function of Re 0 or as a function of the distance from the source. To interpret these observations, we develop a formalism based on the flow velocity profiles, which yields an expression of α as a function of the evolution of the Reynolds shear stress and of the turbulent fluctuations of the radial and vertical velocities. We obtain that the main contribution to entrainment is related to the turbulent shear stress, and that second-order fluctuations of the velocity account for the observed variations of α. The evolution to a fully self-similar regime in which these fluctuations are fully negligible is too slow at small Re 0 for this regime to be observed in our experiments, even at the largest distances from the source.

Description: We present a method to determine, using only velocity field data, the time-averaged energy flux J and total radiated power P for two-dimensional internal gravity waves. Both J and P are determined from expressions involving only a scalar function, the stream function ψ. We test the method using data from a direct numerical simulation for tidal flow of a stratified fluid past a knife edge. The results for the radiated internal wave power given by the stream function method agree to within 0.5% with results obtained using pressure and velocity data from the numerical simulation. The results for the radiated power computed from the stream function agree well with power computed from the velocity and pressure if the starting point for the stream function computation is on a solid boundary, but if a boundary point is not available, care must be taken to choose an appropriate starting point. We also test the stream function method by applying it to laboratory data for tidal flow past a knife edge, and the results are found to agree with the direct numerical simulation. The supplementary material includes a Matlab code with a graphical user interface that can be used to compute the energy flux and power from two-dimensional velocity field data.

Description: A novel closed-loop control methodology is introduced to stabilize a cylinder wake flow based on images of streaklines. Passive scalar tracers are injected upstream the cylinder and their concentration is monitored downstream at certain image sectors of the wake. An AutoRegressive with eXogenous inputs mathematical model is built from these images and a Generalized Predictive Controller algorithm is used to compute the actuation required to stabilize the wake by adding momentum tangentially to the cylinder wall through plasma actuators. The methodology is new and has real-world applications. It is demonstrated on a numerical simulation and the provided results show that good performances are achieved.

Description: Evolving vortex sheets generally form singularities in finite time. The vortex blob model is an approach to regularize the vortex sheet motion and evolve past singularity formation. In this paper, we thoroughly compare two such regularizations: the Krasny-type model and the Beale-Majda model. It is found from a linear stability analysis that both models have exponentially decaying growth rates for high wavenumbers, but the Beale-Majda model has a faster decaying rate than the Krasny model. The Beale-Majda model thus gives a stronger regularization to the solution. We apply the blob models to the two example problems: a periodic vortex sheet and an elliptically loaded wing. The numerical results show that the solutions of the two models are similar in large and small scales, but are fairly different in intermediate scales. The sheet of the Beale-Majda model has more spiral turns than the Krasny-type model for the same value of the regularization parameter δ. We give numerical evidences that the solutions of the two models agree for an increasing amount of spiral turns and tend to converge to the same limit as δ is decreased. The inner spiral turns of the blob models behave differently with the outer turns and satisfy a self-similar form. We also examine irregular motions of the sheet at late times and find that the irregular motions shrink as δ is decreased. This fact suggests a convergence of the blob solution to the weak solution of infinite regular spiral turns.

Description: The present work develops the theoretical framework to describe oscillations of fluid clusters. The basic physical phenomena are presented and justified assumptions lead to the final set of equations for different types of oscillations (pinned/sliding). The special combination of a liquid cluster surrounded by a rigid solid matrix and a gas is investigated in more detail. Furthermore, a classification of oscillating fluid clusters is presented using a one-dimensional oscillator model. This classification includes three dynamic properties: mass, eigenfrequency, and damping whereas conceptual implementation and limitations for use in multiphase theories are clearly indicated. The frequency dependent flow profile leads to frequency dependence of the dynamic parameters. This is discussed and represented by dimensionless numbers.

Description: Two motions of oscillation and vacillating breathing (swing) of red blood cell with a stiffened membrane have been observed in bounded Poiseuille flows [L. Shi, T.-W. Pan, and R. Glowinski, “Deformation of a single blood cell in bounded Poiseuille flows,” Phys. Rev. E85, 16307 (2012)]. To understand such motions, we have compared them with the oscillating motion of a neutrally buoyant particle of the same shape in Poiseuille flow in a narrow channel since a suspended cell is actually a neutrally buoyant entity. In a narrow channel, the particle can be held in the central region for a while with its mass center moving up and down if it is placed at the centerline initially. Its inclination angle oscillates at the beginning; but its range of oscillation keeps increasing and at the end the particle tumbles when the particle migrates away from the centerline due to the inertia effect. When the particle mass center is restricted to move only on the channel centerline, the inclination angle has been locked to a fixed angle without oscillation. Since the mass center of a deformable cell always migrates toward the channel central region in Poiseuille flow, its inclination angle behaves similar to the aforementioned oscillating motion of the particle as long as the cell keeps the long body shape and moves up and down. But when the up-and-down oscillation of the cell mass center damps out, the oscillating motion of the inclination angle also damps out and the cell inclination angle also approaches to a fixed angle.

Description: A numerical study of pinned, oscillating water clusters is presented. Two main models represent a liquid bridge between the walls of two particles and a water column enclosed in a slender pore channel, respectively. Variations include material properties (density, viscosity, surface tension, contact angle) and geometric properties (volume, slenderness, winding, interfacial areas). They are initially based on water clusters in 1 mm pore-space, which are weakly damped at eigenfrequencies around a few hundred Hz. Stiffness and damping are characterized by eigenfrequency and damping coefficient of an equivalent 1-dim. harmonic-oscillator model. Finally, frequency dependence of the dynamical properties is demonstrated. The comprehensive quantitative analysis extends and explains relationships between geometric and material properties and the response to harmonic stimulation. Furthermore, interpolation functions of characteristic dynamic properties are provided for use in multiphase theories. The frequency dependence of cluster stiffness and damping was proven and of limited influence on the stimulation of two typical, weakly damped liquid clusters.

Description: We have constructed a simple one-dimensional model of capillary break-up to demonstrate the thinning behaviour of particulate suspensions previously observed in experiments. The presence of particles increases the bulk viscosity of a fluid and so is expected to retard thinning and consequently delay the time to break-up. However, experimental measurements suggest that once the filament thins to approximately five particle diameters, the thinning no longer follows the behaviour predicted by the bulk viscosity; instead thinning is “accelerated” due to the effects of finite particle size. Our model shows that accelerated thinning arises from variations in local particle density. As the filament thins, fluctuations in the local volume fraction are amplified, leading ultimately to particle-free sections in the filament. The local viscosity of the fluid is determined from the local particle density, which is found by tracking individual particles within the suspension. In regions of low particle density, the fluid is less viscous and can therefore thin more easily. Thus, we are able to model the accelerated thinning regime found in experiments. Furthermore, we observe a final thinning regime in which the thinning is no longer affected by particle dynamics but follows the behaviour of the solvent.

Description: The complex multiscale physics of nano-particle laden functional droplets in a reacting environment is of fundamental and applied significance for a wide variety of applications ranging from thermal sprays to pharmaceutics to modern day combustors using new brands of bio-fuels. Formation of homogenous nucleated bubbles at the superheat limit inside vaporizing droplets (with or without nanoparticles) represents an unstable system. Here we show that self-induced boiling in burning functional pendant droplets can produce severe volumetric shape oscillations. Internal pressure build-up due to ebullition activity ejects bubbles from the droplet domain causing undulations on the droplet surface and oscillations in bulk. Through experiments, we establish that the degree of droplet deformation depends on the frequency and intensity of these bubble expulsion events. In a distinct regime of single isolated bubble residing in the droplet, however, pre-ejection transient time is identified by Darrieus-Landau evaporative instability, where bubble-droplet system behaves as a synchronized driver-driven system with bulk bubble-shape oscillations being imposed on the droplet. The agglomeration of nanophase additives modulates the flow structures within the droplet and also influences the bubble inception and growth leading to different levels of instabilities.

Description: In this article, the fluid dynamics of work transfer within the narrow spacing (usually of the order of 100 μm) of multiple concentric discs of a Tesla disc turbomachine (turbine or compressor) has been analysed theoretically and computationally. Both the overall work transfer and its spatial development have been considered. It has been established that the work transfer mechanism in a Tesla disc turbomachine is very different from that in a conventional turbomachine, and the formulation of the Euler's work equation for the disc turbomachine contains several conceptual subtleties because of the existence of complex, three dimensional, non-uniform, viscous flow features. A work equivalence principle has been enunciated, which establishes the equality between the magnitudes of work transfer determined rigorously from two different approaches—one based on the shear stress acting on the disc surfaces and the other based on the change in angular momentum of the fluid. Care is needed in identifying the shear stress components that are responsible for the generation or absorption of useful power. It is shown from the Reynolds transport theorem that mass-flow-averaged tangential velocities (as opposed to the normally used area-averaged values) must be used in determining the change in angular momentum; the calculation has to be carefully formulated since both radial velocity (that determines throughput) and tangential velocity (that generates torque) depend strongly on the coordinate perpendicular to the disc surfaces. The principle of work transfer has been examined both in the absolute and relative frames of reference, revealing the subtle role played by Coriolis force. The concept of a new non-dimensional quantity called the torque potential fraction ( Δ H ̃ ) is introduced. The value of Δ H ̃ at any radial position increases with a decrease in inter-disc spacing. The computational fluid dynamic analysis shows that, for small value of inter-disc spacing and high value of tangential speed ratio, most of the angular momentum of the fluid is transferred to the surfaces of the discs in the inlet region and correspondingly, the value of the torque potential fraction is very high even in the inlet region. On the other hand, for larger inter-disc spacing, the change in angular momentum in the radial direction is more uniformly distributed between the inlet and the outlet, and the value of the torque potential fraction increases gradually with decreasing radius. The complex (sometimes continuous, sometimes disjointed) three-dimensional shapes of the iso-surfaces of U θ r  (product of absolute tangential velocity and radius) have been shown, for the first time, which provide insight into the fluid dynamics of work transfer within corotating discs.

Description: Vortex-induced vibration (VIV) of a rigid circular cylinder of finite length subject to uniform steady flow is investigated numerically. The study is focused on the effect of the free end on the response of the cylinder. The vibration of the cylinder is confined only in the cross-flow direction. Three-dimensional Navier-Stokes equations are solved by the Petrov-Galerkin finite element method and the equation of the motion is solved for the cylinder displacement. Simulations are conducted for a constant mass ratio of 2, a constant Reynolds number of 300 and cylinder length to diameter ratios of L / D = 1, 2, 5 10, and 20. It is found that the vortex shedding in the wake of a fixed cylinder is suppressed if the cylinder length is less than 2 cylinder diameters. However, if the cylinder is allowed to vibrate, VIV happens at L / D = 1 and 2 and the response amplitudes at these two cylinder lengths are comparable with that of a 2D-cylinder. The vortices that are shed from a short cylinder of L / D = 1 and 2 are found to be generated from the free-end of the cylinder and convected toward the top end of the cylinder by the upwash velocity. They are found to be nearly perpendicular to the cylinder span. The wake flow in a vibrating cylinder with L / D greater than 5 includes the vortex shedding flow at the top part of the cylinder and the end-induced vortex shedding near the free-end of the cylinder. The phase difference between the sectional lift coefficient and the vibration displacement near the free-end of the cylinder changes from 0° to 180° at higher reduced velocity than that near the top end. Strong variation of the flow along the cylinder span occurs at reduced velocities where the lift coefficient near the free-end and that near the top end are in anti-phase with each other.

Description: We investigate the cyclical stick-slip motion of water nanodroplets on a hydrophilic substrate viewed with and stimulated by a transmission electron microscope. Using a continuum long wave theory, we show how the electrostatic stress imposed by non-uniform charge distribution causes a pinned convex drop to deform into a toroidal shape, with the shape characterized by the competition between the electrostatic stress and the surface tension of the drop, as well as the charge density distribution which follows a Poisson equation. A horizontal gradient in the charge density creates a lateral driving force, which when sufficiently large, overcomes the pinning induced by surface heterogeneities in the substrate disjoining pressure, causing the drop to slide on the substrate via a cyclical stick-slip motion. Our model predicts step-like dynamics in drop displacement and surface area jumps, qualitatively consistent with experimental observations.

Description: Turbulent sink flows over smooth or rough walls with sand-grain roughness are studied using large-eddy and direct numerical simulations. Mild and strong levels of acceleration are applied, yielding a wide range of Reynolds number ( Re θ = 372 − 2748) and cases close to the reverse-transitional state. Flow acceleration and roughness are shown to exert opposite effects on boundary-layer integral parameters, on the Reynolds stresses, budgets of turbulent kinetic energy, and properties of turbulent structures in the vicinity of the rough surface; statistics exhibit similarity when plotted using inner scaling for cases with the same roughness Reynolds number, k + . Acceleration leads to a decrease of k + , while roughness increases it. For cases with higher k + , the low-speed streaks become destabilized, and turbulent structures near the wall are distributed more uniformly in the wall-parallel plane; they are less extended in the streamwise direction, but more densely packed. Higher k + also causes decorrelation of the outer-layer hairpin packets with the near-wall structures, probably due to the direct impact of random roughness elements on the hairpin legs. Wall-similarity applies for the fully turbulent cases, in which the outer-layer turbulent statistics are affected by acceleration only. It is shown that being in the hydraulically smooth regime is a necessary condition for reverse-transition, supporting the idea that relaminarization starts from the inner region, where roughness effects dominate.

Description: We present global heat-transfer and local temperature measurements, in an asymmetric parallelepiped Rayleigh-Bénard cell, in which controlled square-studs roughnesses have been added. A global heat transfer enhancement arises when the thickness of the boundary layer matches the height of the roughnesses. The enhanced regime exhibits an increase of the heat transfer scaling. Local temperature measurements have been carried out in the range of parameters where the enhancement of the global heat transfer is observed. They show that the boundary layer at the top of the square-stub roughness is thinner than the boundary layer of a smooth plate, which accounts for most of the heat-transfer enhancement. We also report multistability at long time scales between two enhanced heat-transfer regimes. The flow structure of both regimes is imaged with background-oriented synthetic Schlieren and reveals intermittent bursts of coherent plumes.

Description: The linear stability characteristics of pressure-driven miscible two-fluid flow with same density and varying viscosities in a channel with velocity slip at the wall are examined. A prominent feature of the instability is that only a band of wave numbers is unstable whatever the Reynolds number is, whereas shorter wavelengths and smaller wave numbers are observed to be stable. The stability characteristics are different from both the limiting cases of interface dominated flows and continuously stratified flows in a channel with velocity slip at the wall. The flow system is destabilizing when a more viscous fluid occupies the region closer to the wall with slip. For this configuration a new mode of instability, namely the overlap mode, appears for high mass diffusivity of the two fluids. This mode arises due to the overlap of critical layer of dominant instability with the mixed layer of varying viscosity. The critical layer contains a location in the flow domain at which the base flow velocity equals the phase speed of the most unstable disturbance. Such a mode also occurs in the corresponding flow in a rigid channel, but absent in either of the above limiting cases of flow in a channel with slip. The flow is unstable at low Reynolds numbers for a wide range of wave numbers for low mass diffusivity, mimicking the interfacial instability of the immiscible flows. A configuration with less viscous fluid adjacent to the wall is more stable at moderate miscibility and this is also in contrast with the result for the limiting case of interface dominated flows in a channel with slip, where the above configuration is more unstable. It is possible to achieve stabilization or destabilization of miscible two-fluid flow in a channel with wall slip by appropriately choosing the viscosity of the fluid layer adjacent to the wall. In addition, the velocity slip at the wall has a dual role in the stability of flow system and the trend is influenced by the location of the mixed layer, the location of more viscous fluid and the mass diffusivity of the two fluids. It is well known that creating a viscosity contrast in a particular way in a rigid channel delays the occurrence of turbulence in a rigid channel. The results of the present study show that the flow system can be either stabilized or destabilized by designing the walls of the channel as hydrophobic surfaces, modeled by velocity slip at the walls. The study provides another effective strategy to control the flow system.

Description: We analyze the dynamical response of an isothermal liquid bridge to a step change in the mass force magnitude by numerically solving the three-dimensional Navier-Stokes equations. We study the free surface oscillations caused by both axial and lateral pulses of the mass force. The oscillation amplitude and the dynamical stability limit are calculated for different values of the parameters characterizing the fluid configuration. We examine the stability of one of the liquid bridges to be analyzed in the Japanese and European Research Experiment on Marangoni Instabilities experiment on board of the International Space Station (ISS). We study the response of that liquid bridge to real g -jitter on board of the ISS.

Description: State-resolved analyses of N + N 2 are performed using the direct simulation Monte Carlo (DSMC) method. In describing the elastic collisions by a state-resolved method, a state-specific total cross section is proposed. The state-resolved method is constructed from the state-specific total cross section and the rovibrational state-to-state transition cross sections for bound-bound and bound-free transitions taken from a NASA database. This approach makes it possible to analyze the rotational-to-translational, vibrational-to-translational, and rotational-to-vibrational energy transfers and the chemical reactions without relying on macroscopic properties and phenomenological models. In nonequilibrium heat bath calculations, the results of present state-resolved DSMC calculations are validated with those of the master equation calculations and the existing shock-tube experimental data for bound-bound and bound-free transitions. In various equilibrium and nonequilibrium heat bath conditions and 2D cylindrical flows, the DSMC calculations by the state-resolved method are compared with those obtained with previous phenomenological DSMC models. In these previous DSMC models, the variable soft sphere, phenomenological Larsen-Borgnakke, quantum kinetic, and total collision energy models are considered. From these studies, it is concluded that the state-resolved method can accurately describe the rotational-to-translational, vibrational-to-translational, and rotational-to-vibrational transfers and quasi-steady state of rotational and vibrational energies in nonequilibrium chemical reactions by state-to-state kinetics.

Description: Nanopores, either biological, solid-state, or ultrathin pierced graphene, are powerful tools which are central to many applications, from sensing of biological molecules to desalination and fabrication of ion selective membranes. However, the interpretation of transport through low aspect-ratio nanopores becomes particularly complex as 3D access effects outside the pores are expected to play a dominant role. Here, we report both experiments and theory showing that, in contrast to naïve expectations, long-range mutual interaction across an array of nanopores leads to a non-extensive, sub-linear scaling of the global conductance on the number of pores N . A scaling analysis demonstrates that the N-dependence of the conductance depends on the topology of the network. It scales like G ∼ N /log  N for a 1D line of pores, and like G ∼ N for a 2D array, in agreement with experimental measurements. Our results can be extended to alternative transport phenomena obeying Laplace equations, such as diffusive, thermal, or hydrodynamic transport. Consequences of this counter-intuitive behavior are discussed in the context of transport across thin membranes, with applications in energy harvesting.

Description: We compute the spatial optimal energy amplification of steady inflow perturbations in a non-parallel wake and analyse their stabilizing action on the global mode instability. The optimal inflow perturbations, which are assumed spanwise periodic and varicose, consist in streamwise vortices that induce the downstream spatial transient growth of streamwise streaks. The maximum energy amplification of the streaks increases with the spanwise wavelength of the perturbations, in accordance with previous results obtained for the temporal energy growth supported by parallel wakes. A family of increasingly streaky wakes is obtained by forcing optimal inflow perturbations of increasing amplitude and then solving the nonlinear Navier-Stokes equations. We show that the linear global instability of the wake can be completely suppressed by forcing optimal perturbations of sufficiently large amplitude. The attenuation and suppression of self-sustained oscillations in the wake by optimal 3D perturbations is confirmed by fully nonlinear numerical simulations. We also show that the amplitude of optimal spanwise periodic (3D) perturbations of the basic flow required to stabilize the global instability is much smaller than the one required by spanwise uniform (2D) perturbations despite the fact that the first order sensitivity of the global eigenvalue to basic flow modifications is zero for 3D spanwise periodic modifications and non-zero for 2D modifications. We therefore conclude that first-order sensitivity analyses can be misleading if used far from the instability threshold, where higher order terms are the most relevant.

Description: The ability to compute rarefied, ionized hypersonic flows is becoming more important as missions such as Earth reentry, landing high-mass payloads on Mars, and the exploration of the outer planets and their satellites are being considered. A recently introduced molecular-level chemistry model, the quantum-kinetic, or Q-K, model that predicts reaction rates for gases in thermal equilibrium and non-equilibrium using only kinetic theory and fundamental molecular properties, is extended in the current work to include electronic energy level transitions and reactions involving charged particles. Like the Q-K procedures for neutral species chemical reactions, these new models are phenomenological procedures that aim to reproduce the reaction/transition rates but do not necessarily capture the exact physics. These engineering models are necessarily efficient due to the requirement to compute billions of simulated collisions in direct simulation Monte Carlo (DSMC) simulations. The new models are shown to generally agree within the spread of reported transition and reaction rates from the literature for near equilibrium conditions.

Description: This article describes a generalization of the method of moments, called extended method of moments (EMM), for dispersion in periodic structures composed of impermeable or permeable porous inclusions. Prescribing pre-computed steady state velocity field in a single periodic cell, the EMM sequentially solves specific linear stationary advection-diffusion equations and restores any-order moments of the resident time distribution or the averaged concentration distribution. Like the pioneering Brenner's method, the EMM recovers mean seepage velocity and Taylor dispersion coefficient as the first two terms of the perturbative expansion. We consider two types of dispersion: spatial dispersion, i.e., spread of initially narrow pulse of concentration, and temporal dispersion, where different portions of the solute have different residence times inside the system. While the first (mean velocity) and the second (Taylor dispersion coefficient) moments coincide for both problems, the higher moments are different. Our perturbative approach allows to link them through simple analytical expressions. Although the relative importance of the higher moments decays downstream, they manifest the non-Gaussian behaviour of the breakthrough curves, especially if the solute can diffuse into less porous phase. The EMM quantifies two principal effects of bi-modality, as the appearance of sharp peaks and elongated tails of the distributions. In addition, the moments can be used for the numerical reconstruction of the corresponding distribution, avoiding time-consuming computations of solute transition through heterogeneous media. As illustration, solutions for Taylor dispersion, skewness, and kurtosis in Poiseuille flow and open/impermeable stratified systems, both in rectangular and cylindrical channels, power-law duct flows, shallow channels, and Darcy flow in parallel porous layers are obtained in closed analytical form for the entire range of Péclet numbers. The high-order moments and reconstructed profiles are compared to their predictions from the advection-diffusion equation for averaged concentration, based on the same averaged seepage velocity and Taylor dispersion coefficient. In parallel, we construct Lattice-Boltzmann equation (LBE) two-relaxation-times scheme to simulate transport of a passive scalar directly in heterogeneous media specified by discontinuous porosity distribution. We focus our numerical analysis and assessment on (i) truncation corrections, because of their impact on the moments, (ii) stability, since we show that stable Darcy velocity amplitude reduces with the porosity, and (iii) interface accuracy which is found to play the crucial role. The task is twofold: the LBE supports the EMM predictions, while the EMM provides non-trivial benchmarks for the numerical schemes.

Description: The effect of adverse pressure gradients (APG) on boundary layer stability, breakdown, and heat-transfer overshoot is investigated. Flat plate isothermal boundary layers initially at Mach 6 with APG imposed through the freestream boundary condition are simulated using suction and blowing to produce boundary layer instabilities. The three different transition mechanisms compared are first mode oblique breakdown, second mode oblique breakdown, and second mode fundamental resonance. For all of the transition mechanisms, an adverse pressure gradient increases the linear growth rates and quickens the transition to turbulence. However, the nonlinear breakdown for all three transition mechanisms is qualitatively the same as for a zero pressure gradient boundary layer. First mode oblique breakdown leads to the earliest transition location and an overshoot in heat transfer in the transitional region. Both types of Mack second mode forcing lead to a transitional boundary layer but even with the increased growth rates and N factors produced by the adverse pressure gradient, the breakdown process is still more gradual than first mode oblique breakdown because the primary Mack second mode instabilities saturate and produce streaks that breakdown further downstream.

Description: It is shown theoretically that an electric field can be used to control and suppress the classical Rayleigh-Taylor instability found in stratified flows when a heavy fluid lies above lighter fluid. Dielectric fluids of arbitrary viscosities and densities are considered and a theory is presented to show that a horizontal electric field (acting in the plane of the undisturbed liquid-liquid surface), causes growth rates and critical stability wavenumbers to be reduced thus shifting the instability to longer wavelengths. This facilitates complete stabilization in a given finite domain above a critical value of the electric field strength. Direct numerical simulations based on the Navier-Stokes equations coupled to the electrostatic fields are carried out and the linear theory is used to critically evaluate the codes before computing into the fully nonlinear stage. Excellent agreement is found between theory and simulations, both in unstable cases that compare growth rates and in stable cases that compare frequencies of oscillation and damping rates. Computations in the fully nonlinear regime supporting finger formation and roll-up show that a weak electric field slows down finger growth and that there exists a critical value of the field strength, for a given system, above which complete stabilization can take place. The effectiveness of the stabilization is lost if the initial amplitude is large enough or if the field is switched on too late. We also present a numerical experiment that utilizes a simple on-off protocol for the electric field to produce sustained time periodic interfacial oscillations. It is suggested that such phenomena can be useful in inducing mixing. A physical centimeter-sized model consisting of stratified water and olive oil layers is shown to be within the realm of the stabilization mechanism for field strengths that are approximately 2 × 10 4   V/m.

Description: We simulate forced quasi-static magnetohydrodynamic turbulence and investigate the anisotropy, energy spectrum, and energy flux of the flow, specially for large interaction parameters ( N ). We show that the angular dependence of the energy spectrum is well quantified using Legendre polynomials. For large N , the energy spectrum is exponential. Our direct computation of energy flux reveals an inverse cascade of energy at low wavenumbers, similar to that in two-dimensional turbulence. We observe the flow be two-dimensional (2D) for moderate N ( N ∼ 20), and two-dimensional three-component (2D-3C) type for N ⩾ 27. In our forced simulation, the transition from 2D to 2D-3C occurs at higher value of N than that in Favier et al. [“On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence ,” Phys. Fluids22, 075104 (2010)] who employ decaying simulations.

Description: In studies of turbulent boundary layers at high Reynolds number, the term “roughness transition” is generally an implicit reference to the case of a streamwise step-change in roughness length (whether the roughness length is associated with surface fluxes of momentum, temperature, humidity, or some other quantity). This roughness configuration and flow response has received broad attention. Here, in contrast, we consider turbulent wall-bounded flows over transverse roughness transitions using large-eddy simulation. This is accomplished simply by aligning the boundary layer freestream direction parallel to momentum roughness length transitions, instead of perpendicular. In the present cases, the bounding surface is composed of two “high roughness” strips placed between three “low roughness” strips. The influences of two parameters are evaluated: (1) λ, the ratio of the high roughness length to the low roughness length; and (2) L s , the width of the high roughness strips. In the immediate vicinity of the roughness change, the abrupt wallstress variation induces transverse turbulent mixing which is the source of a δ-scale secondary flow, recently described as a low momentum pathway (LMP) by Mejia-Alvarez et al. [“Structural attributes of turbulent flow over a complex topography ,” Coherent Flow Structures at the Earth's Surface (Wiley-Blackwell, 2013), Chap. 3, pp. 25–42] and Mejia-Alvarez and Christensen [“Wall-parallel stereo PIV measurements in the roughness sublayer of turbulent flow overlying highly-irregular roughness,” Phys. Fluids , 25 , 115109]. LMPs are spatially stationary and flanked by δ-scale counter-rotating vortices which serve to pump fluid vertically from the wall, ultimately leading to a spanwise variation in the boundary layer depth (for flows over surface roughness with a converging-diverging riblet pattern, spanwise variation of δ was also found in recent experiments by Nugroho et al. [“Large-scale spanwise periodicity in a turbulent boundary layer induced by highly ordered and direction surface roughness ,” Int. J. Heat Fluid Flow 41, 90–102 (2013)]. Mean velocity and transverse Reynolds stresses are used to determine the mixing length associated with transverse mixing. In general, we find that variations in L s and λ have a strong and mild impact on the secondary flow pattern, respectively.

Description: A numerical study on the settling behaviour of particles in shear‑thinning thixotropic fluids has been conducted. The numerical scheme was based on the volume of fluid model, with the solid particle being likened to a fluid with very high viscosity. The validity of this model was confirmed through comparisons of the flow field surrounding a sphere settling in a Newtonian fluid with the analytical results of Stokes. The rheology model for the fluid was time‑dependent, utilising a scalar parameter that represents the integrity of a “structural network,” which determines its shear thinning and thixotropic characteristics. The results of this study show that the flow field surrounding the settling sphere is highly localised, with distinct regions of disturbed/undisturbed fluids. The extension of these regions depends on the relaxation time of the fluid, as well as its shear thinning characteristics, and reflects the drag force experienced by the sphere. As the sphere settles, a region of sheared fluid that has significantly lower values of viscosity is formed above the sphere. This region slowly recovers in structure in time. As a result, a sphere that falls in a partially recovered domain (e.g., due to the shearing motion of an earlier sphere) tends to attain a greater velocity than the terminal velocity value. This was found to be true even in cases where the “resting time” of the fluid was nearly twice the relaxation time of the fluid. The results of this study could provide a framework for future analysis on the time‑dependent settling behaviour of particles in thixotropic shear‑thinning fluids.