Showing papers in "Physics of Fluids in 2004"

An eddy-viscosity subgrid-scale model for turbulent shear flow: Algebraic theory and applications

Abstract: An eddy-viscosity model is proposed and applied in large-eddy simulation of turbulent shear flows with quite satisfactory results. The model is essentially not more complicated than the Smagorinsky model, but is constructed in such a way that its dissipation is relatively small in transitional and near-wall regions. The model is expressed in first-order derivatives, does not involve explicit filtering, averaging, or clipping procedures, and is rotationally invariant for isotropic filter widths. Because of these highly desirable properties the model seems to be well suited for engineering applications. In order to provide a foundation of the model, an algebraic framework for general three-dimensional flows is introduced. Within this framework several types of flows are proven to have zero energy transfer to subgrid scales. The eddy viscosity is zero in the same cases; the theoretical subgrid dissipation and the eddy viscosity have the same algebraic structure. In addition, the model is based on a fundament...

Laminar drag reduction in microchannels using ultrahydrophobic surfaces

Abstract: A series of experiments is presented which demonstrate significant drag reduction for the laminar flow of water through microchannels using hydrophobic surfaces with well-defined micron-sized surface roughness. These ultrahydrophobic surfaces are fabricated from silicon wafers using photolithography and are designed to incorporate precise patterns of microposts and microridges which are made hydrophobic through a chemical reaction with an organosilane. An experimental flow cell is used to measure the pressure drop as a function of the flow rate for a series of microchannel geometries and ultrahydrophobic surface designs. Pressure drop reductions up to 40% and apparent slip lengths larger than 20 μm are obtained using ultrahydrophobic surfaces. No drag reduction is observed for smooth hydrophobic surfaces. A confocal surface metrology system was used to measure the deflection of an air–water interface that is formed between microposts and supported by surface tension. This shear-free interface reduces the ...

Leading-edge tubercles delay stall on humpback whale (Megaptera novaeangliae) flippers

Abstract: The humpback whale (Megaptera novaeangliae) is exceptional among the baleen whales in its ability to undertake acrobatic underwater maneuvers to catch prey. In order to execute these banking and turning maneuvers, humpback whales utilize extremely mobile flippers. The humpback whale flipper is unique because of the presence of large protuberances or tubercles located on the leading edge which gives this surface a scalloped appearance. We show, through wind tunnel measurements, that the addition of leading-edge tubercles to a scale model of an idealized humpback whale flipper delays the stall angle by approximately 40%, while increasing lift and decreasing drag.

A comparative study of the turbulent Rayleigh-Taylor instability using high-resolution three-dimensional numerical simulations: The Alpha-Group collaboration

Abstract: The turbulent Rayleigh–Taylor instability is investigated in the limit of strong mode-coupling using a variety of high-resolution, multimode, three dimensional numerical simulations (NS). The perturbations are initialized with only short wavelength modes so that the self-similar evolution (i.e., bubble diameter Db∝amplitude hb) occurs solely by the nonlinear coupling (merger) of saturated modes. After an initial transient, it is found that hb∼αbAgt2, where A=Atwood number, g=acceleration, and t=time. The NS yield Db∼hb/3 in agreement with experiment but the simulation value αb∼0.025±0.003 is smaller than the experimental value αb∼0.057±0.008. By analyzing the dominant bubbles, it is found that the small value of αb can be attributed to a density dilution due to fine-scale mixing in our NS without interface reconstruction (IR) or an equivalent entrainment in our NS with IR. This may be characteristic of the mode coupling limit studied here and the associated αb may represent a lower bound that is insensiti...

Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at M=2.25

Abstract: A spatially developing supersonic adiabatic flat plate boundary layer flow (at M∞=2.25 and Reθ≈4000) is analyzed by means of direct numerical simulation. The numerical algorithm is based on a mixed weighted essentially nonoscillatory compact-difference method for the three-dimensional Navier–Stokes equations. The main objectives are to assess the validity of Morkovin’s hypothesis and Reynolds analogies, and to analyze the controlling mechanisms for turbulence production, dissipation, and transport. The results show that the essential dynamics of the investigated turbulent supersonic boundary layer flow closely resembles the incompressible pattern. The Van Driest transformed mean velocity obeys the incompressible law-of-the-wall, and the mean static temperature field exhibits a quadratic dependency upon the mean velocity, as predicted by the Crocco–Busemann relation. The total temperature has been found not to be precisely uniform, and total temperature fluctuations are found to be non-negligible. Consiste...

Transport of bubbles in square microchannels

Abstract: Liquid/gas flows are experimentally investigated in 200 and 525 μm square microchannels made of glass and silicon. Liquid and gas are mixed in a cross-shaped section in a way to produce steady and homogeneous flows of monodisperse bubbles. Two-phase flow map and transition lines between flow regimes are examined. Bubble velocity and slip ratio between liquid and gas are measured. Flow patterns and their characteristics are discussed. Local and global dry out of the channel walls by moving bubbles in square capillaries are investigated as a function of the flow characteristics for partially wetting channels. Two-phase flow pressure drop is measured and compared to single liquid flow pressure drop. Taking into account the homogeneous liquid fraction along the channel, an expression for the two-phase hydraulic resistance is experimentally developed over the range of liquid and gas flow rates investigated.

Effects of hydrophobic surface on skin-friction drag

Abstract: Effects of hydrophobic surface on skin-friction drag are investigated through direct numerical simulations of a turbulent channel flow. Hydrophobic surface is represented by a slip-boundary condition on the surface. When a slip-boundary condition is used in the streamwise direction, the skin-friction drag decreases and turbulence intensities and turbulence structures, near-wall streamwise vortices in particular, are significantly weakened. When a slip-boundary condition is used in the spanwise direction, on the other hand, the drag is increased. It is found that near-wall turbulence structures are modified differently, resulting in drag increase. It is also found that the slip length must be greater than a certain value in order to have a noticeable effect on turbulence. An important implication of the present finding is that drag reduction in turbulent boundary layers is unlikely with hydrophobic surface with its slip length on the order of a submicron scale.

Experimental study of the impact of an ink-jet printed droplet on a solid substrate

Abstract: This paper reports on an experimental study of the impact of water droplets on a solid substrate, with a droplet radius between 18 and 42 μm. We optically measured the interface shape during impact. The measured impact sequences show the impact phenomenology, droplet radius as a function of time, and oscillation behavior in the later stages of impact. The measured radius during impact is compared with existing models, and some of the deficiencies of common models are shown. The measured oscillation frequency in the later stage of impact compares well with an available analytical model. In addition, we measured the volume of the small bubble, which forms in the initial impact stage, as a function of impact velocity. The measured volume compares reasonably well with an approximate model based on air entrapment.

Spreading of a granular mass on a horizontal plane

Abstract: The transient surface flow occurring when a cylindrical pile of dry granular material is suddenly allowed to spread on a horizontal plane is investigated experimentally as a function of the released mass M, the initial aspect ratio a of the granular cylinder pile, the properties of the underlying substrate (smooth or rough, rigid or erodible) and the bead size. Two different flow regimes leading to three different deposit morphologies are observed as a function of the initial aspect ratio a, whatever the substrate properties and the bead size. For a≲3, the granular mass spreads through an avalanche on its flanks producing either truncated cone or conical deposits. For a≳3, the upper part of the column descends conserving its shape while the foot of the pile propagates radially outward. The obtained deposit looks like a “Mexican hat” and the slope angle at the foot of the deposit is observed to saturate at a value of the order of 5°. For a given ground and bead size, the flow dynamics and the deposit morph...

A priori and a posteriori tests of inflow conditions for large-eddy simulation

Abstract: Comparisons of inflow conditions for large-eddy simulations of turbulent, wall-bounded flows are carried out. Consistent with previous investigations, it is found that the spectral content of the inflow velocity is important. Inflow conditions based on random-noise, or small-scale eddies only, dissipate quickly. Temporal and spatial filtering of a time series obtained from a separate calculation indicates that it is important to capture eddies of dimensions equal to or larger than the integral length scale of the flow. Three methods for generating inflow velocity fields are tested in a simulation of spatially developing turbulent channel flow. Synthetic turbulence generation methods that introduce realistic length scales are more suitable than uncorrelated random noise, but still require fairly long development lengths before realistic turbulence is established. A recycling method based on the use of turbulent data obtained from a separate calculation, in different flow conditions, was found to result in more rapid transition. A forcing method that includes a control loop also appears to be effective by generating turbulence with the correct Reynolds stresses and correlations within less than ten channel half heights.

Fluctuations in turbulent Rayleigh-Bénard convection: The role of plumes

Abstract: Our unifying theory of turbulent thermal convection [Grossmann and Lohse, J. Fluid. Mech. 407, 27 (2000); Phys. Rev. Lett. 86, 3316 (2001); Phys. Rev. E 66, 016305 (2002)] is revisited, considering the role of thermal plumes for the thermal dissipation rate and addressing the local distribution of the thermal dissipation rate, which had numerically been calculated by Verzicco and Camussi [J. Fluid Mech. 477, 19 (2003); Eur. Phys. J. B 35, 133 (2003)]. Predictions for the local heat flux and for the temperature and velocity fluctuations as functions of the Rayleigh and Prandtl numbers are offered. We conclude with a list of suggestions for measurements that seem suitable to verify or falsify our present understanding of heat transport and fluctuations in turbulent thermal convection.

A generating mechanism for apparent fluid slip in hydrophobic microchannels

Abstract: Fluid slip has been observed experimentally in micro- and nanoscale flow devices by several investigators [e.g., Tretheway and Meinhart, Phys. Fluids 14, L9 (2002); Zhu and Granik, Phys. Rev. Lett. 87, 096105 (2001); Pit et al., Phys. Rev. Lett. 85, 980 (2000); and Choi et al., Phys. Fluids 15, 2897 (2003)]. This paper examines a possible mechanism for the measured fluid slip, for water flowing over a hydrophobic surface. We extend the work of Lum et al. [J. Phys. Chem. B 103, 4570 (1999)], Zhu and Granick [Phys. Rev. Lett. 87, 096105 (2001)], Granick et al. [Nature Materials 2, 221 (2003)], and de Gennes [Langmuir 18, 3413 (2002)], who suggest slip develops from a depleted water region or vapor layer near a hydrophobic surface. By modeling the presence of either a depleted water layer or nanobubbles as an effective air gap at the wall, we calculate slip lengths for flow between two infinite parallel plates. The calculated slip lengths are consistent with experimental values when the gas layer is modeled as a continuum and significantly higher when rarefied gas conditions are assumed. The results suggest that the apparent fluid slip observed experimentally at hydrophobic surfaces may arise from either the presence of nanobubbles or a layer of low density fluid at the surface.

Analysis of convective instability and heat transfer characteristics of nanofluids

Abstract: The convective instability driven by buoyancy and heat transfer characteristics of nanofluids are investigated analytically. This paper proposes a factor which describes the effect of nanoparticle addition on the convective instability and heat transfer characteristics of a base fluid. The Bruggeman model based on the mean field approach for expressing the thermal conductivity enhancement is chosen as a lower bound of the thermal conductivity relationship. The results show that as the density and heat capacity of nanoparticles increase and the thermal conductivity and the shape factor of nanoparticles decrease, the convective motion in a nanofluid sets in easily. The heat transfer coefficient of a nanofluid is enhanced by all parameters with respect to the volume fraction of nanoparticles.

Scaling law in liquid drop coalescence driven by surface tension

Abstract: This Letter reports experimental results on the coalescence of two liquid drops driven by surface tension. Using a high speed imaging system, we studied the early-time evolution of the liquid bridge that is formed upon the initial contact of two liquid drops in air. Experimental results confirmed the scaling law that was proposed by Eggers et al. based on a simple and yet elegant physical argument. We found that the liquid bridge radius rb follows the scaling law rb∝t1/2 in the inertial regime. Further experiments demonstrate that such scaling law is robust when using fluids of different viscosities and surface tensions. The prefactor of the scaling law, rb/t1/2, is shown to be ∝R1/4, where R is the inverse of the drop curvature at the point of contact. The dimensionless prefactor is measured to be in the range of 1.03–1.29, which is lower than 1.62, a prefactor predicted by the numerical simulation of Duchemin et al. for inviscid drop coalescence.

Instability of electrokinetic microchannel flows with conductivity gradients

Abstract: Electrokinetic flow is leveraged in a variety of applications, and is a key enabler of on-chip electrophoresis systems. An important sub-class of electrokinetic devices aim to pump and control electrolyte working liquids with spatial gradients in conductivity. These high-gradient flows can become unstable under the application of a sufficiently strong electric field. In this work the instability physics is explored using theoretical and numerical analyses, as well as experimental observations. The flow in a long, rectangular-cross-section channel is considered. A conductivity gradient is assumed to be orthogonal to the main flow direction, and an electric field is applied in the streamwise direction. It is found that such a system exhibits a critical electric field above which the flow is highly unstable, resulting in fluctuating velocities and rapid stirring. Modeling results compare well with experimental observations. The model indicates that the fluid forces associated with the thin dimension of the c...

A numerical investigation of wall effects up to high blockage ratios on two-dimensional flow past a confined circular cylinder

Abstract: A finite volume method based on a velocity-only formulation is used to solve the flow field around a confined circular cylinder in a channel in order to investigate lateral wall proximity effects on stability, Strouhal number, hydrodynamic forces and wake structure behind the cylinder for a wide range of blockage ratios (0.1<β⩽0.9) and Reynolds numbers (0

A numerical study of cryogenic fluid injection and mixing under supercritical conditions

Abstract: The evolution of a cryogenic fluid jet initially at a subcritical temperature and injected into a supercritical environment, in which both the pressure and temperature exceed the thermodynamic critical state, has been investigated numerically. The model accommodates full conservation laws and real-fluid thermodynamics and transport phenomena. All of the thermophysical properties are determined directly from fundamental thermodynamics theories, along with the use of the corresponding state principles. Turbulence closure is achieved using a large-eddy-simulation technique. As a specific example, the dynamics of a nitrogen fluid jet is studied systematically over a broad range of ambient pressure. Owing to the differences of fluid states and flow conditions between the jet and surroundings, a string of strong density-gradient regimes is generated around the jet surface and exerts a stabilizing effect on the flow development. The surface layer acts like a solid wall that transfers the turbulent kinetic energy...

Experimental and theoretical investigation of the nonmodal growth of steady streaks in a flat plate boundary layer

Abstract: An experimental and theoretical investigation aimed at describing the nonmodal growth of steady and spanwise periodic streamwise streaks in a flat plate boundary layer is presented. Stable laminar streaks are experimentally generated by means of a spanwise periodic array of small cylindrical roughness elements fixed on the plate. The streamwise evolution of the streaks is measured and it is proved that, except in a small region near the roughness elements, they obey the boundary layer scalings. The maximum achievable amplitude is mainly determined by the relative height of the roughness elements. Results are compared with numerical simulations of optimal and suboptimal boundary layer streaks. The theory is able to elucidate some of the discrepancies recently noticed between experimentally realizable nonmodal growth and optimal perturbation theory. The key factor is found to be the wall normal location and the extension of the laminar standing streamwise vortices inducing the streaks. The differences among previous experimental works can be explained by different dominating streak generation mechanisms which can be linked to the geometry and to the ratio between the roughness height and the boundary layer scale.

Numerical investigations of flow over a sphere in the subcritical and supercritical regimes

Abstract: The flow field around a sphere in an uniform flow has been analyzed numerically for conditions corresponding to the subcritical (laminar separation) and supercritical (turbulent separation) regimes spanning a wide range of Reynolds numbers (104–106). Particular attention has been devoted to assessing predictions of the pressure distribution, skin friction, and drag as well as to understanding the changes in the wake organization and vortex dynamics with the Reynolds number. The unsteady turbulent flow is computed using detached-eddy simulation, a hybrid approach that has Reynolds-averaged Navier–Stokes behavior near the wall and becomes a large eddy simulation in the regions away from solid surfaces. For both the subcritical and supercritical solutions, the agreement with experimental measurements for the mean drag and pressure distribution over the sphere is adequate; differences in skin friction exist due to the simplistic treatment of the attached boundary layers in the computations. Improved agreement in the skin-friction distribution is obtained for the supercritical flows in which boundary layer transition is fixed at the position observed in experiments conducted at the same Reynolds numbers. For the subcritical flows the Strouhal number, St, associated with the large-scale shedding is predicted at St∼0.195 along with a higher frequency component associated with the development of the Kelvin–Helmholtz instabilities in the detached shear layers. If in the subcritical regime the wake assumes a helical-like form due to the shedding of hairpin-like vortices at different azimuthal angles, in the supercritical regime the wake structure is characterized by “regular” shedding of hairpin-like vortices at approximately the same azimuthal angle and at a much higher frequency (St∼1.3) that is practically independent of the Reynolds number and not sensitive to the position of laminar-to-turbulent transition.

Assessment of inflow boundary conditions for compressible turbulent boundary layers

Abstract: A description of different inflow methodologies for turbulent boundary layers, including validity and limitations, is presented. We show that the use of genuine periodic boundary conditions, in which no alteration of the governing equations is made, results in growing mean flow and decaying turbulence. Premises under which the usage is valid are presented and explained, and comparisons with the extended temporal approach [T. Maeder, N. A. Adams, and L. Kleiser, “Direct simulation of turbulent supersonic boundary layers by an extended temporal approach,” J. Fluid Mech. 429, 187 (2001)] are used to assess the validity. Extending the work by Lund et al. [J. Comput. Phys. 140, 233 (1998)], we propose an inflow generation method for spatial simulations of compressible turbulent boundary layers. The method generates inflow by reintroducing a rescaled downstream flow field to the inlet of a computational domain. The rescaling is based on Morkovin’s hypothesis [P. Bradshaw, “Compressible turbulent shear layers,” Annu. Rev. Fluid Mech. 9, 33 (1977)] and generalized temperature–velocity relationships. This method is different from other existing rescaling techniques [S. Stolz and N. A. Adams, “Large-eddy simulation of high-Reynolds-number supersonic boundary layers using the approximate deconvolution model and a rescaling and recycling technique,” Phys. Fluids 15, 2398 (2003); G. Urbin and D. Knight, “Large-eddy simulation of a supersonic boundary layer using an unstructured grid,” AIAA J. 39, 1288 (2001)], in that a more consistent rescaling is employed for the mean and fluctuating thermodynamic variables. The results are compared against the well established van Driest II theory and indicate that the method is efficient and accurate.

Flow induced coalescence of drops in a viscous fluid

Abstract: This paper summarizes recent experimental studies of flow-induced coalescence of viscous drops in a viscous fluid in the absence of inertial effects. These studies are based on visual observations of small drops (20–100 μm diameter) that collide in the linear flows generated by a four-roll mill. We consider a pair of polymeric fluids that are Newtonian under the flow conditions relevant to coalescence phenomena, and in addition consider the effect of adding a “copolymer” of the two polymers to the interface, which acts as a surfactant. By direct observation, we can generate quantitative data on the collision trajectories and the conditions for coalescence. These observations have also uncovered several “new” phenomena. Among these are the fact that coalescence frequently occurs during the part of the collision after the drops have already rotated to a configuration where they are being pulled apart by the external flow. This occurs for at least some of the collision trajectories for all fluids where the v...

Enhanced diffusion due to motile bacteria

Abstract: The effect of bacterial motion on the diffusion of a molecule of high molecular weight is studied by observing the mixing of two streams of fluid in a microfluidic flow cell. We show that the presence of motile E. coli bacteria in one of the streams results in a marked increase in the effective diffusion coefficient of Dextran, which rises linearly with the concentration of bacteria from a baseline value of 0.2×10−7 to 0.8×10−7 (cm2/s) at a concentration of 2.1×109/ml (approximately 0.5% by volume). Furthermore, we observe that the diffusion process is also observed to undergo a change from standard Fickian diffusion to a superdiffusive behavior in which the diffusion exponent rises from 0.5 to 0.55 as the concentration of bacteria rises from 0 to 2.1×109/ml.

Mode-switching and nonlinear effects in compressible flow over a cavity

Abstract: 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-fr...

On some common features of drop impact on liquid surfaces

Abstract: The impact of a drop on liquid surfaces is studied experimentally and theoretically in the region of the fully developed splashing. In order to reveal the influence of viscosity and target liquid depth on the resulting flow patterns, the experiments were carried out with water and 70% glycerol–water solution, and for different target liquid depths. Based on the experimental observations, a dynamic model of the central jet formation at the cavity collapse is developed. This model predicts an emergence of a liquid flow up into the central jet and simultaneously a small flow velocity downward and allows us to evaluate the velocities of these two flows. A theoretical model for the cavity submergence is presented. This model gives the constant velocity of the cavity submergence which is half the initial drop impact velocity. Analytical solution for the gravity–capillary cavity collapse has been derived and provides a good fit to the experimental results. Theoretical analysis and experiments have shown that the maximum cavity radius and the cavity collapse time depend on both the Froude number and the dimensionless capillary length.

Large eddy simulation and experimental studies of a confined turbulent swirling flow

Abstract: Laser Doppler velocimetry (LDV) measurement and large eddy simulation (LES) were used to study confined isothermal turbulent swirling flows in a model dump combustor. The aim was to gain deeper understanding of the flow and turbulence structures in dump combustors and to examine the capability of LES for prediction of turbulent swirling flows. A refractive index matching technique is used in the LDV measurement to improve the near-wall data. A high-order finite difference scheme on Cartesian grids with a scale-similarity subfilter scale model is used in the LES. Turbulent inflow boundary conditions with different energy spectra, different outflow boundary conditions, and grid resolutions are tested in the LES. Three test cases with different swirl numbers and Reynolds numbers are studied in the measurements and the simulations. The Reynolds numbers range from 10 000 to 20 000, and the swirl number is varied from 0 to 0.43. With appropriate inflow, outflow boundary conditions, and fine grid resolution, the LES results are in fairly good agreement with the LDV data. The experimental and numerical results show that turbulence in the dump combustor is highly anisotropic behind the sudden expansion and in the internal recirculation zone near the axis of the combustor. Turbulence decays rapidly along the streamwise direction downstream, and the structure of turbulence depends highly on the level of inlet swirl. At low swirl numbers, turbulence is primarily generated in the shear layer behind the sudden expansion; at high swirl numbers the near axis flow becomes very unstable and vortex breakdown occurs. The shear layer near the axis of the combustor caused by vortex breakdown generates most of the turbulent kinetic energy. Large-scale motions (coherent structures) are found in the near axis vortex breakdown region. A helical flow in the guiding pipe breaks down near the sudden expansion to form a large bubble-like recirculation zone whose center moves slowly around the axis. Downstream of the bubble the core of the rotational large scale azimuthal flow motion is off the combustor axis and rotates around the axis at a frequency about 18-25 Hz (Strouhal number about 0.17-0.4). As the swirl number increases the coherent structure becomes more evident, and the internal recirculation zone moves upstream. LES successfully simulated the vortex breakdown, the internal recirculation zones and the anisotropic turbulence structures for all the swirl numbers considered. (C) 2004 American Institute of Physics.

An experimental study of particle effects on drop formation

Abstract: The formation of drops of particulate suspensions composed of spherical, neutrally buoyant, noncolloidal particles in a viscous liquid is examined experimentally. The suspensions are investigated over a range of particle volume fractions, φ=nπdp3/6 where n is the particle number density and dp is the particle diameter (dp=212–250 μm in most of the experiments), and for flow through three tubes of outer diameters d=0.16, 0.32 and 0.64 cm; the corresponding inner diameters are 0.10, 0.22, and 0.53 cm. Drop formation in the dripping mode and the transition from dripping to jetting are investigated. In the dripping mode, the behavior of low-φ suspensions (φ⩽0.10) is markedly different from that of higher-φ suspensions (0.15⩽φ⩽0.40), with a transition in the qualitative behavior over a relatively narrow range of concentrations. Pinch-off structures for low-φ suspensions are similar to that of the pure liquid, consisting of a long slender liquid thread connecting a hemispherical cap of liquid at the orifice to ...

Intermittent distribution of heavy particles in a turbulent flow

Abstract: The retardation of weakly inertial particles depends on the acceleration of the ambient fluid, so the particle concentration n is determined by the divergence of Lagrangian acceleration which we study by direct numerical simulations. We demonstrate that the second moment of the concentration coarse-grained over the scale r behaves as an approximate power law: 〈nr2〉∼rα. We study the dependencies of the exponent α on the Reynolds number, of the Stokes number, and on the settling velocity. We find numerically that the theoretical lower bound previously suggested [Falkovich et al., Nature 419, 151 (2002)] correctly estimates the order of magnitude (within a factor 2 to 4) as well as the dependencies on the Reynolds, Stokes, and Froude numbers. The discrepancy grows with the Reynolds number and the Froude number. We analyze the possible physical mechanism responsible for that behavior.

Direct numerical simulations of isotropic compressible turbulence: Influence of compressibility on dynamics and structures

Abstract: In the present paper the statistical properties of compressible isotropic turbulence are analyzed by means of direct numerical simulations. The scope of the work is to evaluate the influence of compressibility on the time evolution of mean turbulence properties and to quantify the statistical properties of turbulent structures, their dynamics and similarities with the incompressible case. Simulations have been carried out at various turbulent Mach numbers and compressibility ratios by using a conservative hybrid scheme that relies on an optimized weighted essentially nonoscillatory approach for the convective terms and compact differencing for the viscous contributions. In order to identify similarities with incompressible turbulence we have also carried out an analysis in the plane of the second (Q*) and third (R*) invariants of the anisotropic part of the deformation rate tensor. The simulations show that the joint probability density function (Q*,R*) has a universal structure, as found in incompressibl...

Vortex ring formation at the open end of a shock tube: A particle image velocimetry study

Abstract: The vortex ring generated subsequent to the diffraction of a shock wave from the open end of a shock tube is studied using particle image velocimetry. We examine the early evolution of the compressible vortex ring for three-exit shock Mach numbers, 1.1, 1.2, and 1.3. For the three cases studied, the ring formation is complete at about tUb/D=2, where t is time, Ub is fluid velocity behind shock as it exits the tube and D is tube diameter. Unlike in the case of piston generated incompressible vortex rings where the piston velocity variation with time is usually trapezoidal, in the shock-generated vortex ring case the exit fluid velocity doubles from its initial value Ub before it slowly decays to zero. At the end of the ring formation, its translation speed is observed to be about 0.7 Ub. During initial formation and propagation, a jet-like flow exists behind the vortex ring. The vortex ring detachment from the tailing jet, commonly referred to as pinch-off, is briefly discussed.

Drop coalescence through a liquid/liquid interface

Abstract: Particle image velocimetry (PIV) experiments were conducted to study the coalescence of single drops through planar liquid/liquid interfaces. Sequences of velocity vector fields were obtained with a high-speed video camera and subsequent PIV analysis. Two ambient liquids with different viscosity but similar density were examined resulting in Reynolds numbers based on a surface tension velocity of 10 and 26. Prior to rupture, the drops rested on a thin film of ambient liquid above an underlying interface. After rupture, which was typically off-axis, the free edge of the thin film receded rapidly allowing the drop fluid to sink into the bulk liquid below. Vorticity generated in the collapsing fluid developed into a vortex ring straddling the upper drop surface. The ring core traveled radially inward with a ring-shaped capillary wave effectively pinching the upper drop surface and increasing the drop collapse speed. The inertia of the collapse deflected the interface downward before it rebounded upward. Duri...