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A diffusion flame in the fuel-oxidizer mixing layer within a narrow channel can be split into several stationary, discrete flame segments at some particular conditions. This unique flame structure has deeply been analyzed in previous literature. In this paper, by performing numerical simulations using a transient, low-Mach number, reacting flow solver in OpenFOAM, unsteady dynamics of separated reaction zones for low Lewis number, hydrogen–oxygen diffusion flames in a 30 × 5 × 0.75 mm3 microchannel are newly discovered. For a variety of inflow rates (H2/O2 flow rate of 300/150, 200/100, and 100/50 sccm) and wall temperatures (Tw = 900, 800, 700, 600, and 500 K) investigated, stable and continuous flame sheets can only be witnessed at large Reynolds numbers or high wall temperatures. Flames at other conditions are found in a discrete form, presenting an unstable and repetitive feature. Specifically, in the wake of the leading, anchored diffusion flame, edge flames with tribrachial structures are consecutively established and then propagate downstream, while eventually end by moving out of the channel, or being extinguished halfway, or behaving in a mixed mode (the two events occur alternately for two successively generated edge flames). Effects of Lewis numbers on flame behaviors are also studied via helium addition to both the fuel and oxidizer stream. Isolated reaction zones at a steady state can be witnessed for a relatively large Lewis number under a high level of addition. [ABSTRACT FROM AUTHOR]

Pattern formation due to oscillating reactions represents variable natural and engineering systems, but previous studies employed only simple flow conditions such as uniform flow and Poiseuille flow. We studied the oscillating reaction in porous media, where dispersion enhanced the spreading of diffusing components by merging and splitting flow channels. We considered the saddle flow, where the stretching rate is constant everywhere. We generated patterns with the Brusselator system and classified them by instability conditions and Péclet number (Pe), which was defined by the stretching rate. The results showed that each pattern formation was controlled by the stagnation point and stable and unstable manifolds of the flow field due to the heterogeneous flow fields and the resulting heterogeneous dispersion fields. The characteristics of the patterns, such as the position of stationary waves parallel to the unstable manifold and the size of local stationary patterns around the stagnation point, were also controlled by Pe. [ABSTRACT FROM AUTHOR]

This research presents an analytical solution to explore a two-dimensional concentration transport of solute in an oscillatory Couette–Poiseuille flow between two parallel plates in the presence of homogeneous and heterogeneous reactions. Mei's homogenization method up to second order approximation is used to find the multi-dimensional concentration distributions, namely, transverse concentration distribution, longitudinal concentration distribution, mean concentration distribution, Taylor dispersion coefficient, and the transverse uniformity simultaneously for three different flow conditions: steady, periodic, and the joint effect of steady and periodic Couette–Poiseuille flow for the first time. The distribution of transverse concentration of solute is studied due to its importance in oil lubrication and industrial applications. The transverse variation rate shows that the introduction of heterogeneous reactions cause transverse non-uniformity, but it is significant to note that homogeneous reaction has no effect on it. Furthermore, the maximum variation rate of the concentration cloud is obtained along the upstream and downstream directions when the boundary absorption is considered at steady and moving plates, respectively. To validate the present analytical model, a comparison is performed with the numerical solution and has achieved an excellent agreement. The outcomes of the present study may be helpful to develop a better understanding of the process of contamination and to prevent the pollution in the flow. [ABSTRACT FROM AUTHOR]

The time-dependent flow of a neon–argon mixture in a microchannel interrupted by a row of oscillating barriers is numerically studied using the Direct Simulation Monte Carlo method in a range of Knudsen numbers from 0.1 to 10 and in a wide range of oscillation frequencies. The emphasis of the study is on the effect of mixture separation. It is demonstrated that in addition to a mid-frequency ("resonance") regime, as discovered in the author's previous works [Kosyanchuk et al., "Numerical simulation of novel gas separation effect in microchannel with a series of oscillating barriers," Microfluid. Nanofluid. 21, 116 (2017) and Kosyanchuk and Pozhalostin, "Non-stationary rarefied gas flow in a plane channel with a series of oscillating barriers," Eur. J. Mech.-B/Fluids 92, 90–99 (2022)], two other enhanced separation regimes at very low and at very high oscillation frequencies are present. It is also demonstrated that the effect in the mid-frequency regime degrades with decreasing Knudsen number and is almost absent for Kn values around 0.1. The effect in the high-frequency regime is shown to be dictated both by the high frequency of barrier oscillations and by the high speed of barrier motion, and it is shown that with decreasing Knudsen number, the impact of barriers speed becomes dominant. The effect in the low-frequency regime is present for all Knudsen numbers and significantly depends on the phases of barrier motion, which is not observed in other regimes. The separation factor in the low-frequency regime also increases with the number of barriers but only up to the level of molecular diffusion. It was also shown that in the low-frequency regime, there is a trade-off between the separation factor and the gas flow rate. [ABSTRACT FROM AUTHOR]

It is well known to all of us that there is a shortage of pure drinking water across the globe. Different types of pollutants (metallic and nonmetallic) mix with the water, and they cause several diseases such as cholera, typhoid, and various kinds of skin diseases, and even it is found that these kinds of particles may cause skin cancer. In the current study, an analytical solution of a two-dimensional convection–diffusion equation is obtained using Mei's multi-scale homogenization technique to investigate the influences of homogeneous and heterogeneous reactions on dispersion phenomena of the solute in an oscillatory magneto-hydrodynamics porous medium flow. In the appearance of the applied transverse magnetic field and oscillatory pressure gradient, a mathematical model of magneto-hydrodynamics dispersion between two parallel plates is presented. The analytical expressions of Taylor dispersivity, longitudinal mean and real concentration distributions, transverse concentration distribution, and transverse uniformity rate of the concentration are obtained. Also, the effect of various flow parameters such as Péclet number, Hartmann number, Schmidt number, Darcy number, oscillatory Reynolds number, porous parameter, dispersion time, downstream and upstream locations, chemical heterogeneous boundary reaction, and bulk reaction is discussed. How the transport phenomena of the solute display different natures with the various ranges of Darcy and Hartmann numbers with the aid of homogeneous and heterogeneous boundary reactions are highlighted. To show the effect of the absorption parameters on the transport coefficient, the third-order approximation of concentration is performed. It is seen that the dispersion coefficient ( D T 1 ) corresponding to the purely time-dependent flow increases with the enhancement of the Darcy number (Da). Moreover, it is found that as the Hartmann number (M) enhances, the total dispersivity (DT) decreases. Also, the transverse concentration distribution becomes flat for larger values of the Hartmann number. It is noticed that when D a ≥ 1 , the transverse variation curve turns into a trimodal distribution from a bimodal. This model may be helpful for separating various metallic and nonmetallic particles from the water to reduce the water pollution. [ABSTRACT FROM AUTHOR]

The unsteady dynamics of shock interactions on the crotch of two typical V-shaped blunt leading edges have been investigated numerically and experimentally with a freestream Mach number 6 for different ratios (R), defined as the rounding radius at the crotch to the blunt radius at the leading edge. The primary flow features observed in the shock tunnel experiments are reproduced by the large-eddy simulations. The time-averaged flow structures in the crotch are clearly shown as counterrotating vortices originating from the collision of jets near the stagnation point. These jets and vortices undergo unsteady motions coupled with the dynamics of shock interactions. Of great interest, two typical global oscillations, i.e., swing oscillation and arch-recover oscillation corresponding to the two values of R , are identified. The coherent structures of the oscillations are analyzed using the proper orthogonal decomposition technique. It is demonstrated that the swing oscillation and arch-recover oscillation are characterized by an antisymmetric pattern and a symmetrical pattern, respectively. These two oscillations are also characterized by the energetic middle-frequency components of the broadband wall pressure spectra. Two feedback models are proposed for the prediction of such middle-frequency components. The results show that the swing oscillation causes much more severe pressure load, and the local impingement of the transmitted shock on the crotch is responsible for the peak value of the pressure fluctuation. This study illustrates that the geometry of R has a key impact on the unsteady shock interactions and, therefore, should be considered critically in practical applications, such as the cowl lip of a hypersonic inward-turning inlet. [ABSTRACT FROM AUTHOR]

The development of the Marangoni instability in a two-layer film in the presence of a transverse temperature gradient and a heat source/sink at the liquid-liquid interface is investigated. The problem is solved by means of a linear stability theory and nonlinear simulations. Novel criteria for the development of monotonic and oscillatory instabilities have been formulated. It has been found that the nonlinear development of a monotonic instability leads to a rupture of the bottom layer or the top layer. Numerous types of nonlinear film evolution have been observed in the case of an oscillatory instability, among them alternating roll patterns of different scales and orientations, temporally non-periodic motions, and the rupture of either layer. [ABSTRACT FROM AUTHOR]

Theoretical analysis on an oscillatory plane Poiseuille flowis conducted in terms of a non-dimensional ratio (η) of the channel half-width to Stokes' layer thickness. The cyclic velocity profiles, the phase shifts and the magnitudes among the driving pressure gradient, the induced wall shear stress, and the volume flux are investigated. Also, the flow physics at a different ratio η is demonstrated. In this study, the mechanism of the driving pressure gradient and the oscillating volume flux is similar to and can be employed to demonstrate the slit flow in the application of the novel vortex flow meter using a slit cylinder as a shedder. When applied to the novel vortex flow meter, the non-dimensional ratio η can be expressed as the relation of the slit width ratio (S/D), the Strouhal number, and the Reynolds number. Finally, a range of η between 0.97 < η < 20 will be suggested for the vortex flow meter at the design stage. Large values of η are employed at a high Reynolds number, and small η is used for low Reynolds number applications. In the novel vortex flow meters, a cylinder with a normal axial slit of width (S) is employed as the shedder. Due to the primary lock-on, the process of vortex shedding synchronizes with the rhythm of slit flow leading to a stable shedding frequency. The value η is well correlated by the value of ηopt obtained by experiments and shows a one-to-one correspondence to the slit ratio at each Reynolds number. Once the design value of ηopt is determined, the optimal slit ratio can be estimated for a fixed applied Reynolds number at the design stage. [ABSTRACT FROM AUTHOR]

The nonlinear dynamics of thin liquid films deposited on various periodically corrugated substrates, both left-right symmetric and asymmetric, subjected to lateral vibration in the high-frequency limit is investigated. The method used to derive the governing evolution equation is based on the long-wave approximation, multiscale time expansion, and averaging over the fast time scale. The resulting evolution equation contains the effects of gravity, capillarity, vibration, and the substrate topology. The initial-boundary-value problem associated with this evolution equation is numerically solved and the system behavior is investigated for a variety of parameter sets. Typical patterns emerging as a result of the film evolution include hump formation within the troughs of the substrate and homogenized coatings whose configuration resembles that of the substrate, as well as the possibility of film rupture. We show that the choice of the vibration parameters and the topological features of the substrate may be used for controlling the shape of the film interface as well as its properties such as the amplitude, continuity, or rupture. Together with the film profiles stationary in terms of the averaged film interface with respect to the slow time scale, time evolution of the total (comprising of the averaged and pulsating components) interfacial profiles and streamline maps is presented to illustrate the film flow. We carry out Floquet stability analysis of periodically replicated steady states for the time-independent problem, linear stability analysis based on a reduced low-order projection approximation for the time-dependent problem, and stability analysis with respect to disturbances of a larger wavelength. We have found also that in the case of two-dimensional corrugated substrates, the vast majority of two-dimensional steady-state flows in terms of the averaged film interface exhibit stability in three dimensions with respect to small perturbations in the transverse spatial direction. [ABSTRACT FROM AUTHOR]

NASA astronaut Pettit has conducted thermocapillary flow experiments in water films suspended in a solid ring onboard the International Space Station (ISS) in 2003 and 2011. In one of these experiments, an oscillatory thermocapillary flow was observed. The developed flow broke its symmetry along the centerline of the film. To the best of our knowledge, there are no studies on such oscillatory thermocapillary flows in thin films, and the flow-mechanism giving rise to such oscillatory flows is also not well understood. In order to shed light on the subject, we have carried out a numerical simulation study. The simulation results have shown that the water film geometry (film surface shape; being concave) is an important parameter and give rise to three oscillatory flow structures in the film, namely, a hydrothermal wave developing near the heated section, a symmetric oscillatory flow due to temperature variations, and a symmetry breaking flow due to the hydrodynamic instability along the free boundary layer (mixing layer) and the development of the hydrothermal waves. Simulation results show that the symmetry-breaking phenomenon observed in the thin film experiment on the ISS can be explained by the hydrodynamic instability and the development of hydrothermal waves. [ABSTRACT FROM AUTHOR]

We study thin film instabilities in liquid films with deformable surface using the lubrication theory. An externally applied vertical temperature gradient may give cause to an instability (Marangoni instability) of the flat motionless film. Contrary to the earlier work where mostly pure fluids were discussed, the focus of the present paper lays on instabilities in mixtures of two completely miscible liquids. We show that the normally found monotonic long-wave instability may turn into an oscillatory one if the two components have a different surface tension and if the Soret coefficient establishes a stabilizing vertical concentration gradient. A systematic derivation of the basic equations in long-wave approximation is given. The character of instabilities is studied using linear stability analysis. Finally, a real system consisting of a water-isopropanol mixture is discussed in some detail. [ABSTRACT FROM AUTHOR]

The mechanism of pattern formation in the flow between two corotating disks in a stationary enclosure and its transition are investigated experimentally, and the experimental results are confirmed by numerical simulation. Particle image velocimetry and laser-Doppler-velocimetry measurements are achieved in the experiment, and the data acquired are examined by using Fourier decomposition analyses and applying the bifurcation theory. Two distinct modes of oscillatory instability are identified as origins that break the axisymmetry of the flow; one originates from the detached shear layer and the other from the outer boundary layer along the enclosure. The former instability is found to lead to the polygonal patterns, which have been reported in previous papers, while the latter instability induces a flow with a shift-and-reflect symmetry, having small spiral vortices along the outer boundary. A mixed-mode polygonal flow, which is surrounded by small vortices is observed at large Reynolds numbers. We identify two transition routes to the mixed-mode flow by adopting two different driving processes of the disk rotation. [ABSTRACT FROM AUTHOR]

Motivated by recent experiments on the hovering of passive bodies, we demonstrate how a simple shape-changing body can hover or ascend in an oscillating background flow. We study this ratcheting effect through numerical simulations of the two-dimensional Navier–Stokes equations at intermediate Reynolds number. This effect could describe a viable means of locomotion or transport in such environments as a tidal pool with wave-driven sloshing. We also consider the velocity burst achieved by a body through a rapid increase in its aspect ratio, which may contribute to the escape dynamics of such organisms as jellyfish. [ABSTRACT FROM AUTHOR]

The long-wave instability of a vertical multicomponent fluid layer is investigated. The basic state is a plane parallel flow with linear profiles of temperature and composition in the cross section. The compositional stratification is induced by the Soret effect. The problem is reduced to that without cross-diffusion effect by a linear change of composition and separation ratios that characterize the Soret separation. This is the first report where such transformation is derived for the equations of multicomponent convection with thermal diffusion. It simplifies the system reducing the number of control parameters and can be applied to a variety of multidiffusive convection problems (e.g., Rayleigh–Bénard configuration). It is shown that the long-wave instability is caused by the interplay between the basic flow and concentration waves with long scale in the vertical direction. In the general case of n-component mixture, several stable regions in the parameter space are identified. A complete parametric study for ternary fluid revealed complex instability scenarios in the long-wave limit: monotonic instability in a certain range of Grashof numbers, the transition from monotonic to oscillatory instability with increasing Grashof, etc. The physical mechanisms underlying this complex behavior are discussed and explained. In addition to the long-wave stability analysis, we performed numerical calculations for finite wave numbers. These calculations showed that the monotonic long-wave perturbations represent the most unstable modes. [ABSTRACT FROM AUTHOR]

The fluid dynamics of oscillating elastic beams underpin the operation of many modern technological devices ranging from micromechanical sensors to the atomic force microscope. While viscous effects are widely acknowledged to have a strong influence on these dynamics, fluid compressibility is commonly neglected. Here, we theoretically study the three-dimensional flow fields that are generated by the motion of flexible cylinders immersed in viscous compressible fluids and discuss the implications of compressibility in practice. We consider cylinders of circular cross section and flat blades of zero thickness that are executing flexural and torsional oscillations of arbitrary wave number. Exact analytical solutions are derived for these flow fields and their resulting hydrodynamic loads. [ABSTRACT FROM AUTHOR]

The free sinking motion of small spheres is experimentally investigated in a laboratory tank filled up with continuously stratified salt solutions. Special attention is paid to the late stage oscillations around the gravitational equilibrium level. Such motion is generated by slowly decaying weak internal waves originating from the interaction of the solid sphere with the surrounding fluid. The temporal decay of oscillation amplitudes and velocities can be best described by a power law of exponent value close to -3/2. Up to our best knowledge, none of the existing theories can predict a similar algebraic decay. [ABSTRACT FROM AUTHOR]

The temporal evolution of the near-wake behind a circular cylinder undergoing rotational oscillatory motion with a relatively high forcing frequency has been investigated experimentally using a dynamic particle image velocimetry velocity field measurement technique. Experiments were carried out varying the frequency ratio FR (=ff/fn), the ratio of the forcing frequency ff to the natural vortex shedding frequency fn, in the range of 0.0 (stationary) to 1.0 at an oscillation amplitude of θA=30° and Reynolds number of Re=4.14×103. Depending on the forcing condition (FR), the near-wake flow showed markedly different flow regimes: stationary (FR=0.0), non-lock-on (FR=0.4) and lock-on (FR=1.0) regimes. However, at all the frequency ratios tested, the power spectral density distributions showed a single dominant peak at the same vortex shedding frequency. As the forcing frequency was increased, the rotational oscillatory motion of the cylinder decreased the length of the vortex formation region and enhanced the mutual interaction between large-scale vortices across the wake centerline. In particular, the entrainment of ambient fluid seemed to play an important role in controlling the near-wake flow and shear-layer instability. The shear-layer instability showed different mechanisms compared with the case of small oscillation amplitude. A strong vortex motion appeared in the near-wake region. In addition, the rotational oscillatory motion of the cylinder changed the local mean flow structure significantly; thereby mean velocity profiles for each frequency ratio varied markedly in the vortex formation region. The configuration of vorticity contours shrunk toward the cylinder as the frequency ratio was increased. The temporally resolved flow information extracted in the present work is useful for understanding the evolution of vortex structure and analyzing the effects of open-loop active flow control technique on the near-wake flow structure. [ABSTRACT FROM AUTHOR]

Thermal convection phenomena of viscoelastic fluids in a closed-top porous square box heated from below are studied numerically based on a modified Darcy’s law, where two characteristic time constants λ and [variant_greek_epsilon] are used to describe the viscoelastic properties of the fluid. Results for three set values of λ and [variant_greek_epsilon] are obtained for a Darcy-Rayleigh number up to 400, and show very different heat transport characteristics from those of Newtonian fluids. Two types of thermal convection are shown to be possible. Oscillatory convection due to the viscoelastic properties of the fluid precedes the onset of steady convection due to thermal boundary instability. After steady convection sets in, it tends to suppress oscillatory convection. The interaction between the two types of thermal convection causes the flow patterns in the porous layer to be more complicated than those of Newtonian fluids. Furthermore, thermal convection of viscoelastic fluids in porous layers undergoes earlier bifurcations with increase of Ra than those of Newtonian fluids and the occurrence of bifurcation is earlier for larger values of λ/[variant_greek_epsilon] in our study. Finally, our numerical results show that scaling laws exist for thermal convection of viscoelastic fluids in porous layers, and specific scaling laws were obtained by the least-squares fitting technique to describe the Nu versus Ra relationship in different regimes of Ra and for the three cases studied in this work. [ABSTRACT FROM AUTHOR]

The existence of multiple modes of instability in Rayleigh-Bénard or Marangoni-Bénard situations has been known for many years. This existence is shown for the first time for low-Prandtl-number flows in three-dimensional cavities heated from the side. For such a situation, the study of the flow transitions has long remained a challenge, as these transitions occur in already very intense flows. The study is possible here thanks to performing numerical methods, and the ten first instability modes are determined for a wide range of aspect ratios and Prandtl number values. The most striking feature of our results is the very frequent change of leading mode when aspect ratios or Prandtl number are changed, which indicates different flow structures triggered at the transitions, either steady or oscillatory and breaking some of the symmetries of the problem. [ABSTRACT FROM AUTHOR]

Purcell’s scallop theorem defines the type of motions of a solid body—reciprocal motions—which cannot propel the body in a viscous fluid with zero Reynolds number. For example, the flapping of a wing is reciprocal and, as was recently shown, can lead to directed motion only if its frequency Reynolds number, Ref, is above a critical value of order one. Using elementary examples, we show the existence of oscillatory reciprocal motions which are effective for all arbitrarily small values of the frequency Reynolds number and induce net velocities scaling as Refα (α>0). This demonstrates a continuous breakdown of the scallop theorem with inertia. [ABSTRACT FROM AUTHOR]

The deformation and breakup of droplets in a steady and uniform electric field were experimentally investigated. Droplets of silicone oil suspended in more electric-conducting caster oil undergoes the three following modes of deformation when subjected to an electric field: oblate deformation with a symmetric axis oriented close to parallel with the electric field, oblate deformation with a symmetric axis oriented obliquely to the electric field, and an oscillatory oblate–prolate deformation synchronized with a sit-up motion. Each droplet during the oscillatory motion is simultaneously observed from two directions, and the flow in the droplet is visualized by a tracer particle method. The oscillatory motion is revealed to involve electrorotation of the droplet. The conditions under which each of the three deformation modes or droplet breakup occurs are identified. [ABSTRACT FROM AUTHOR]

The stability of channel flow modulated by oscillatory wall suction/blowing is investigated using linear stability analysis together with Floquet theory based on numerical calculation and asymptotic expansion. Two typical flows with either the driven pressure gradient or the flow rate constant are considered. The basic flows subject to the oscillatory wall suction/blowing are time periodic with multiple frequency components. The stability problem is formulated into a time-dependent eigenvalue problem, and the Floquet exponents are obtained using a spectral collocation method. It is revealed that the periodic wall suction/blowing induces the Stokes layer, which interacts with the disturbance shear wave and eventually affects the disturbance growth. Results show that the modulations of the oscillatory wall suction/blowing to the channel flows have a destabilizing effect and the similar stability characteristics of both the typical flows occur. Critical Reynolds numbers and wave numbers are predicted for a wide range of parameters. Asymptotic expansions of the growth rate at small amplitude Δ of the oscillatory wall suction/blowing are developed. The correction terms for the growth rate occur in O(Δ2) and are positive, indicating that the flow is destabilized. It is found that the destabilizing effect is mainly connected to the steady corrections of the mean flow profile in the O(Δ2) terms. [ABSTRACT FROM AUTHOR]

We describe a chemical oscillatory phenomenon which occurs as follows: a pendant drop of water is immersed in a viscous oil, both phases containing reagents which react to produce a surfactant at the interface. As the drop falls away from the tip of a small needle, the remaining interface spontaneously elongates into a sharp cone and ejects small droplets from the pointed tip. The tip then either contracts and re-elongates periodically, or remains steadily elongated. Small droplets continue to be ejected in either case, and the phenomenon persists over a period of tens of minutes. Quantitative measurements connect these chemically driven phenomena with studies in four-roll mills. A mechanism is proposed by which these phenomena are sustained by Marangoni stresses. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A quasi-geostrophic, or β, model of nonlinear thermal convection in rapidly rotating spherical fluid shells is investigated. We study time dependent instabilities for a range of Rayleigh number and Ekman number with a Prandtl number set to the unity. Above the onset of convection, increasing the Rayleigh number for a given Ekman number, we reproduce the sequence of bifurcations described by Busse [Phys. Fluids 14, 1301 (2002)] for the three-dimensional case: A first transition results in vacillating flow; a second transition gives rise to chaotic oscillations in time and localized convection in space; then a third leads to quasi-periodic relaxation oscillations. This study shows that the quasigeostrophic model encompasses the desired bifurcation sequence. It allows the investigation of a range of Ekman numbers unavailable to three-dimensional models with present computing resources. Decreasing the Ekman number, we unexpectedly found that all three transitions occur for marginally supercritical Rayleigh number. The range of Rayleigh number for which the amplitude of convection is steady vanishes in the asymptotic limit of small Ekman numbers. This effect could significantly alter the nature of the instability characterizing the onset of convection in particular whether it is a supercritical or subcritical bifurcation. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Density inhomogeneities in granular flows can dramatically influence microscopic and macroscopic properties. Here, we numerically examine dilute rapid granular flows in the Couette geometry via large-scale particle-dynamic simulations, and characterize development of nonuniform particle distributions. For monodisperse grains we observe density waves in two- and three-dimensional computational domains of varying aspect ratios. Both fully developed and transient states are quantified using Fourier methods. For inelastic, planar (two-dimensional) flows exceeding a minimum solids fraction, one-dimensional, high-density clusters—well-known features of inelastic materials—align parallel to the walls. Above a critical streamwise length, these are destabilized by two-dimensional antisymmetric modes with wavelength ∼100 particle diameters. We relate oscillatory behavior to an underlying physical mechanism of the slow drift of clusters towards walls and their subsequent bursting. Further streamwise or spanwise expansions permit additional wave numbers to be expressed in these directions. In “shallow” three-dimensional flows, the planar wave types initially survive. As depth is increased above a critical value, cross-stream invariance experiences symmetry preserving instabilities to form coherent structures resembling steady and wavy Taylor–Couette fluid vortices. Their presence strongly impacts macroscopic behavior, as regions of sustained vorticity develop, and stresses and granular temperatures deviate by up to an order of magnitude from mean values. The influence of solids fraction, particle size, material elasticity, surface friction, polydispersity, and gravity are considered, and instabilities are found to intensify as collisional dissipation rises. For planar flows, transient and fully developed density distributions share many parametric responses with previous continuum results using kinetic theory. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Multiple distinct peaks of comparable strength in unsteady pressure autospectra often characterize compressible flow-induced cavity oscillations. It is unclear whether these different large-amplitude tones (i.e., Rossiter modes) coexist or are the result of a mode-switching phenomenon. The cause of additional peaks in the spectrum, particularly at low frequency, is also unknown. This article describes the analyses of unsteady pressure data in a cavity using time-frequency methods, namely the short-time Fourier transform (STFT) and the continuous Morlet wavelet transform, and higher-order spectral techniques. The STFT and wavelet analyses clearly show that the dominant mode switches between the primary Rossiter modes. This is verified by instantaneous schlieren images acquired simultaneously with the unsteady pressures. Furthermore, the Rossiter modes experience some degree of low-frequency amplitude modulation. An estimate of the modulation frequency, obtained from the wavelet analysis, matches the low-frequency peak seen in the autospectrum. Higher-order spectral methods were employed to investigate potential quadratic nonlinear interactions between the Rossiter modes and to determine if they are responsible for the low-frequency mode present in the autospectrum. In turn, this low-frequency mode could interact with the Rossiter modes to modulate their amplitude. Significant nonlinearities, in the form of sum and difference frequencies of the Rossiter modes, are present in the l/d=2 cavity at M[sub ∞]=0.4, while nonlinear effects are much smaller in the l/d=4 at M[sub ∞]=0.6. The bispectral analysis indicates that quadratic interactions between Rossiter modes in the near-field pressure are not responsible for the observed low-frequency peak in the pressure autospectrum. Furthermore, the low-frequency mode does not exhibit a strong nonlinear coupling with the Rossiter modes. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

This paper applies the singularity method to obtain analytic solutions for oblate spheroids in Stokes flow, and to obtain numerical results for prolate and oblate spheroids undergoing oscillatory translation, and oscillatory rotation. To apply the method to oblate spheroids, singularities are placed along an imaginary focal length. A novel method is used to determine the hydrodynamic torque by deriving Green’s functions for torque for the unsteady rotlet, stresslet, and potential quadrupole. The results agree with analytic solutions for high and low frequencies, the results of previous studies, and results calculated using the boundary element method. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Planar-laser-induced fluorescence (PLIF) measurements have been used to investigate the mean passive scalar field in round zero-net-mass-flux jets in cross-flow (ZNMF-JICF). The ZNMF-JICF are formed in a working fluid without net transfer of mass across the system boundary during one period of oscillation. Ensemble-averaged PLIF images of sixteen different ZNMF-JICF are studied and compared. Two distinct flow regimes are observed; single trajectory ZNMF-JICF and multiple trajectory ZNMF-JICF. Single trajectory ZNMF-JICF demonstrate mixing of the bulk of the fluid outside the upstream boundary layer, while multiple trajectory ZNMF-JICF can penetrate more deeply into the ambient cross-flow. A critical Strouhal number of St[sub crit]=0.02 was found for the generation apparatus that can be used to distinguish between these two regimes. The penetration of the single trajectory ZNMF-JICF does not exhibit the same dependence on velocity ratio observed in the measurements of continuous JICF. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We study the stability of a planar solid-melt boundary during directional solidification of a binary alloy when the solid is being periodically vibrated in the direction parallel to the boundary (or equivalently, under a far field uniform and oscillatory flow parallel to the planar boundary). The analysis is motivated by directional solidification experiments under the low level residual acceleration field characteristic of a microgravity environment, and possible effects on crystal growth in space. It is known that periodic modulation of the solid-melt interface under the conditions stated induces second order stationary streaming flows within a boundary layer adjacent to the interface, the thickness of which is the same as the wavelength of the modulation. We derive an effective solute transport equation by averaging over the fast time scale of the oscillatory flow, and obtain the resulting dispersion relation for a small disturbance of a planar interface. We find both regions of stationary and oscillatory instability. For small ratios of the viscous to solutal layer thicknesses, s, the flow generally destabilizes the planar interface. For s=1, the flow stabilizes the stationary branch, but it can also excite an oscillatory instability. For large s, the effect of the flow is small. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Investigates the nonlinear oscillatory dynamics of free droplets with diameter between 0.1 and 0.4 centimeters, using ultrasonic and electrostatic levitation techniques. Static shape of ultrasonically levitated drops in an electric field; Shape oscillations driven by modulated ultrasonic radiation force; Nonlinear characteristics of driven large amplitude drop shape oscillations.

Examines the coupling between vibrational relaxation and dissociation in nitrogen. Vibrational energy equation; Oscillator models; Vibration-dissociation coupling models; Governing equations; Vibrational relaxation time.

A pseudohomogeneous model is developed and used to analyze the onset of reaction-driven convection in an open rectangular box containing a porous medium. For exothermic reactions, the one-dimensional conduction state exhibits multiplicity as well as oscillatory behavior. Singularity theory is used to classify the different possible bifurcation diagrams of conduction states, along with their stabilities. Linear instability theory is used to determine the stability of the conduction states to convective perturbations. The dependence of both simple zero and Hopf bifurcation neutral stability curves on various problem parameters is presented. It is shown that the Lewis number, Le (ratio of thermal to mass diffusivity), has a pronounced effect on the stability boundaries. Increasing the value of Le, shifts the stationary stability boundary toward higher Rayleigh numbers (Ra). It is also shown that in the region of multiple conduction solutions, there exists a critical value of Lewis number, Le[SUB1] (resp., Le[SUB2] below which the entire ignited (resp., extinguished) conduction branch is stable to convective perturbations for O

This work explores the wake dynamics of systems with three bluff bodies with variable spacing. Studies of single-wake systems have shown that coherent wake vortices have a regular and predictable periodicity. A growing literature of dual-wake studies has shown that multi-wake systems are more stochastic than single-wake systems, and their dynamics are highly dependent on the spacing between the wakes. Here, we expand on this literature by investigating three-wake systems and find that the coherent dynamics of the wakes are highly intermittent. We use proper orthogonal decomposition to extract the most energetic modes of the three-wake system at six bluff-body spacings that span a range of dynamical “regimes.” After describing the time-dependent behavior of the interacting wakes in these regimes, we use a statistical approach to describe the relative phase between oscillations in each of the wakes, identifying regimes where oscillations are more or less random. Interestingly, the wake oscillations are less random when the bluff bodies are positioned very close and relatively far from each other. In between these two extremes, an intermediary regime is identified where the wake oscillations are almost completely random; this finding parallels data from the dual-wake literature. Finally, we discuss the implications of the observed behaviors and possible future directions for this work. [ABSTRACT FROM AUTHOR]

The transition in the primary oscillatory mode in an open cavity has been experimentally investigated and the associated characteristics in a Mach 1.71 flow has been analyzed. The length-to-depth (L/D) ratios of the rectangular cavities are varied from 1.67 to 3.33. Unsteady pressure measurement and flow visualization are employed to understand the transitional flow physics. Flow visualization revealed the change in oscillation pattern from longitudinal mode to transverse mode and is also characterized by the presence of two bow shocks at the trailing edge instead of one. The transition is found to occur between L/D 1.67 and 2, marked by a change in the feedback mechanism, resulting in a shift from the vortex circulation driven transverse feedback mode to the oscillating shear layer driven longitudinal feedback mode. Cavities oscillating in the transition mode exhibit multiple tones of comparable strength. Correlation analysis indicated the shift in the feedback mechanism. Wavelet analysis revealed the temporal behaviour of tones during transition. Tone switching is observed in deeper cavities and is attributed to the occurrence of two bow shocks as evident from the temporo-spectral characteristics of transition that affects the shear layer modal shape. [ABSTRACT FROM AUTHOR]

An approach based on the generalized reciprocal theorem is presented to derive the well-known result for the drag force exerted on a rigid sphere translating in a viscous fluid in an arbitrary manner. The use of generalized reciprocal theorem allows one to bypass the calculation of stress distribution over the particle surface in order to compute the force. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The dynamic response of a gas bubble entrapped in a cavity on the surface of a submerged solid subject to an acoustic field is investigated in the linear approximation. We derive semi-analytical expressions for the resonance frequency, damping, and interface shape of the bubble. For the liquid phase, we consider two limit cases: potential flow and unsteady Stokes flow. The oscillation frequency and interface shape are found to depend on two dimensionless parameters: the ratio of the gas stiffness to the surface tension stiffness, and the Ohnesorge number, representing the relative importance of viscous forces. We perform a parametric study and show, among others, that an increase in the gas pressure or a decrease in the surface tension leads to an increase in the resonance frequency until an asymptotic value is reached. [ABSTRACT FROM AUTHOR]

Rigid fibers suspended in a viscous, Newtonian fluid at high concentrations can be aligned in the direction perpendicular to the flow-gradient plane (vorticity direction) by applying an oscillatory shear flow. A simple model, which considers only excluded volume and self-mobilities, can accurately predict the orientation distributions measured in experiments by Franceschini et al. ['Transverse alignment of fibers in a periodically sheared suspension: An absorbing phase transition with a slowly varying control parameter,' Phys. Rev. Lett. 107, 250603 (2011)]. Furthermore, simulations reveal that the alignment of the fibers in the vorticity direction depends strongly on the presence of the bounding walls. [ABSTRACT FROM AUTHOR]

The influence of the horizontal component of the temperature gradient on nonlinear oscillatory convective regimes, developed under the joint action of buoyant and thermocapillary effects in the 47 v2 silicone oil-water system, is investigated. Cavities with different lengths have been considered. Transitions between oscillatory flow regimes with different symmetry properties and steady flows have been studied. It is shown that under the action of the horizontal component of the temperature gradient, specific asymmetric oscillatory flow develops in the system. [ABSTRACT FROM AUTHOR]