Showing papers in "Physics of Fluids in 2002"

Apparent fluid slip at hydrophobic microchannel walls

Abstract: Micron-resolution particle image velocimetry is used to measure the velocity profiles of water flowing through 30×300 μm channels. The velocity profiles are measured to within 450 nm of the microchannel surface. When the surface is hydrophilic (uncoated glass), the measured velocity profiles are consistent with solutions of Stokes’ equation and the well-accepted no-slip boundary condition. However, when the microchannel surface is coated with a 2.3 nm thick monolayer of hydrophobic octadecyltrichlorosilane, an apparent velocity slip is measured just above the solid surface. This velocity is approximately 10% of the free-stream velocity and yields a slip length of approximately 1 μm. For this slip length, slip flow is negligible for length scales greater than 1 mm, but must be considered at the micro- and nano scales.

An extrapolation method for boundary conditions in lattice Boltzmann method

Abstract: A boundary treatment for curved walls in lattice Boltzmann method is proposed. The distribution function at a wall node who has a link across the physical boundary is decomposed into its equilibrium and nonequilibrium parts. The equilibrium part is then approximated with a fictitious one where the boundary condition is enforced, and the nonequilibrium part is approximated using a first-order extrapolation based on the nonequilibrium part of the distribution on the neighboring fluid node. Numerical results show that the present treatment is of second-order accuracy, and has well-behaved stability characteristics.

Lagrangian coherent structures from approximate velocity data

Abstract: This paper examines whether hyperbolic Lagrangian structures—such as stable and unstable manifolds—found in model velocity data represent reliable predictions for mixing in the true fluid velocity field. The error between the model and the true velocity field may result from velocity interpolation, extrapolation, measurement imprecisions, or any other deterministic source. We find that even large velocity errors lead to reliable predictions on Lagrangian coherent structures, as long as the errors remain small in a special time-weighted norm. More specifically, we show how model predictions from the Okubo–Weiss criterion or from finite-time Lyapunov exponents can be validated. We also estimate how close the true Lagrangian coherent structures are to those predicted by models.

Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows

Abstract: A simple expression is derived of the componential contributions that different dynamical effects make to the frictional drag in turbulent channel, pipe and plane boundary layer flows. The local skin friction can be decomposed into four parts, i.e., laminar, turbulent, inhomogeneous and transient components, the second of which is a weighted integral of the Reynolds stress distribution. It is reconfirmed that the near-wall Reynolds stress is primarily important for the prediction and control of wall turbulence. As an example, the derived expression is used for an analysis of the drag modification by the opposition control and by the uniform wall blowing/suction.

The development of chaotic advection

Abstract: The concept of chaotic advection was developed some twenty years ago as an outgrowth of work on advection by interacting point vortices. The term “chaotic advection” was first introduced in the title of an abstract for the 35th annual meeting of the American Physical Society (APS) Division of Fluid Dynamics (DFD) in 1982. The main reference, a Journal of Fluid Mechanics paper published in 1984, may be the true “birthdate” of the term. Earlier work from the 1960s by Arnol’d and Henon on advection by steady three-dimensional flows already contained closely related ideas and results but was not widely appreciated. The present paper, based on the 2000 Otto Laporte Memorial Lecture delivered at the 53rd APS/DFD annual meeting, traces these and other precursors and the development of chaotic advection over the past two decades. Some exciting recent developments, such as application to fluid mixing in micro-electromechanical systems (MEMS) and to materials processing, and the introduction of topological methods ...

Velocity field statistics in homogeneous steady turbulence obtained using a high-resolution direct numerical simulation

Abstract: Velocity field statistics in the inertial to dissipation range of three-dimensional homogeneous steady turbulent flow are studied using a high-resolution DNS with up to N=10243 grid points. The range of the Taylor microscale Reynolds number is between 38 and 460. Isotropy at the small scales of motion is well satisfied from half the integral scale (L) down to the Kolmogorov scale (η). The Kolmogorov constant is 1.64±0.04, which is close to experimentally determined values. The third order moment of the longitudinal velocity difference scales as the separation distance r, and its coefficient is close to 4/5. A clear inertial range is observed for moments of the velocity difference up to the tenth order, between 2λ≈100η and L/2≈300η, where λ is the Taylor microscale. The scaling exponents are measured directly from the structure functions; the transverse scaling exponents are smaller than the longitudinal exponents when the order is greater than four. The crossover length of the longitudinal velocity struct...

Bouncing motion of spherical particles in fluids

Abstract: We investigate experimentally the bouncing motion of solid spheres onto a solid plate in an ambient fluid which is either a gas or a liquid. In particular, we measure the coefficient of restitution e as a function of the Stokes number, St, ratio of the particle inertia to the viscous forces. The coefficient e is zero at small St, increases monotonically with St above the critical value Stc and reaches an asymptotic value at high St corresponding to the classical “dry” value emax measured in air or vacuum. This behavior is observed for a large range of materials and a master curve e/emax=f(St) is obtained. If gravity is sufficient to describe the rebound trajectory (after the collision) in a gas, this is not the case in a liquid where drag and added-mass effect are important but not sufficient: History forces are shown to be non-negligible even at large Reynolds number.

Dynamic wall modeling for large-eddy simulation of complex turbulent flows

Abstract: The efficacy of large-eddy simulation (LES) with wall modeling for complex turbulent flows is assessed by considering turbulent boundary-layer flows past an asymmetric trailing-edge. Wall models based on turbulent boundary-layer equations and their simpler variants are employed to compute the instantaneous wall shear stress, which is used as approximate boundary conditions for the LES. It is demonstrated that, as first noted by Cabot and Moin [Flow Turb. Combust. 63, 269 (2000)], when a Reynolds-averaged Navier–Stokes type eddy viscosity is used in the wall-layer equations with nonlinear convective terms, its value must be reduced to account for only the unresolved part of the Reynolds stress. A dynamically adjusted mixing-length eddy viscosity is used in the turbulent boundary-layer equation model, which is shown to be considerably more accurate than the simpler wall models based on the instantaneous log law. This method predicts low-order velocity statistics in good agreement with those from the full LES with resolved wall-layers, at a small fraction of the original computational cost. In particular, the unsteady separation near the trailing-edge is captured correctly, and the prediction of surface pressure fluctuations also shows promise.

Particle imaging velocimetry experiments and lattice-Boltzmann simulations on a single sphere settling under gravity

Abstract: A comparison is made between experiments and simulations on a single sphere settling in silicon oil in a box. Cross-correlation particle imaging velocimetry measurements were carried out at particle Reynolds numbers ranging from 1.5 to 31.9. The particle Stokes number varied from 0.2 to 4 and at bottom impact no rebound was observed. Detailed data of the flow field induced by the settling sphere were obtained, along with time series of the sphere’s trajectory and velocity during acceleration, steady fall and deceleration at bottom approach. Lattice–Boltzmann simulations prove to capture the full transient behavior of both the sphere motion and the fluid motion. The experimental data were used to assess the effect of spatial resolution in the simulations over a range of 2–8 grid nodes per sphere radius. The quality of the flow field predictions depends on the Reynolds number. When the sphere is very close to the bottom of the container, lubrication theory has been applied to compensate for the lack of spatial resolution in the simulations.

The stretching of an electrified non-Newtonian jet: A model for electrospinning

Abstract: Electrospinning uses an external electrostatic field to accelerate and stretch a charged polymer jet, and may produce ultrafine “nanofibers.” Many polymers have been successfully electrospun in the laboratory. Recently Hohman et al. [Phys. Fluids, 13, 2201 (2001)] proposed an electrohydrodynamic model for electrospinning Newtonian jets. A problem arises, however, with the boundary condition at the nozzle. Unless the initial surface charge density is zero or very small, the jet bulges out upon exiting the nozzle in a “ballooning instability,” which never occurs in reality. In this paper, we will first describe a slightly different Newtonian model that avoids the instability. Well-behaved solutions are produced that are insensitive to the initial charge density, except inside a tiny “boundary layer” at the nozzle. Then a non-Newtonian viscosity function is introduced into the model and the effects of extension thinning and thickening are explored. Results show two distinct regimes of stretching. For a “mild...

The final stage of the collapse of a cavitation bubble close to a rigid boundary

Abstract: The final stage of the collapse of a laser-produced cavitation bubble close to a rigid boundary is studied both experimentally and theoretically. The temporal evolution of the liquid jet developed during bubble collapse, shock wave emission and the behavior of the “splash” effect are investigated by using high-speed photography with up to 5 million frames/second. For a full understanding of the bubble–boundary interaction, numerical simulations are conducted by using a boundary integral method with an incompressible liquid impact model. The results of the numerical calculations provided the pressure contours and the velocity vectors in the liquid surrounding the bubble as well as the bubble profiles. The comparisons between experimental and numerical data are favorable with regard to both bubble shape history and translational motion of the bubble. The results are discussed with respect to the mechanism of cavitation erosion.

Application of lattice Boltzmann method to simulate microchannel flows

Abstract: Microflow has become a popular field of interest due to the advent of microelectromechanical systems. In this work, the lattice Boltzmann method, a particle-based approach, is applied to simulate the two-dimensional isothermal pressure driven microchannel flow. Two boundary treatment schemes are incorporated to investigate their impacts to the entire flow field. We pay particular attention to the pressure and the slip velocity distributions along the channel in our simulation. We also look at the mass flow rate which is constant throughout the channel and the overall average velocity for the pressure-driven flow. In addition, we include a simulation of shear-driven flow in our results for verification. Our numerical results compare well with those obtained analytically and experimentally. From this study, we may conclude that the lattice Boltzmann method is an efficient approach for simulation of microflows.

Elliptic blending model: A new near-wall Reynolds-stress turbulence closure

Abstract: A new approach to modeling the effects of a solid wall in one-point second-moment (Reynolds-stress) turbulence closures is presented. The model is based on the relaxation of an inhomogeneous (near-wall) formulation of the pressure–strain tensor towards the chosen conventional homogeneous (far-from-a-wall) form using the blending function ?, for which an elliptic equation is solved. The approach preserves the main features of Durbin’s Reynolds-stress model, but instead of six elliptic equations (for each stress component), it involves only one, scalar elliptic equation. The model, called “the elliptic blending model,” offers significant simplification, while still complying with the basic physical rationale for the elliptic relaxation concept. In addition to model validation against direct numerical simulation in a plane channel for Re? = 590, the model was applied in the computation of the channel flow at a “real-life” Reynolds number of 106, showing a good prediction of the logarithmic profile of the mean velocity.

Experimental studies on the shape and path of small air bubbles rising in clean water

Abstract: This Letter reports experiments on the shape and path of air bubbles (diameter range 0.1–0.2 cm) rising in clean water. We find that bubbles in this diameter range have two steady shapes, a sphere and an ellipsoid, depending on the size of the capillary tube from which they detach. The spherical bubbles move significantly slower than the ellipsoidal ones of equivalent volume. Bubbles with diameter less than about 0.15 cm rise rectilinearly. The larger spherical bubbles follow zigzag paths while the larger ellipsoidal bubbles follow spiral paths.

A new method for significantly reducing drop radius without reducing nozzle radius in drop-on-demand drop production

Abstract: The lack of a simple method for generating drops whose radii (Rd) are much smaller than those (R) of nozzles which produce them has heretofore been a major limitation of the drop-on-demand technique. Therefore, the only reliable way to reduce Rd to date has been to reduce R. A new method is reported which allows an order of magnitude reduction in drop volume while using the same nozzle. It is shown that the key to forming drops with Rd

A framework for predicting accuracy limitations in large-eddy simulation

Abstract: The accuracy of large-eddy simulations is limited, among other things, by the quality of the subgrid parametrization and the numerical contamination of the smaller retained flow structures. We characterize the total simulation error in terms of the “subgrid-activity” s, which measures the relative turbulent dissipation rate (0⩽s⩽1) and the “subgrid resolution” r. This analysis is applied to turbulent mixing of a “Smagorinsky fluid” using a finite volume discretization of fourth order accuracy. On fixed coarse grids, i.e., at constant computational cost, the total simulation error decreases monotonically with filter width Δ for large s while for smaller s the total error may even increase with decreasing Δ. The corresponding modeling- and spatial discretization-error contributions are quantified at various resolutions.

Visual characteristics and initial growth rates of round cryogenic jets at subcritical and supercritical pressures

Abstract: Cryogenic liquids initially at a subcritical temperature were injected through a round tube into an environment at a supercritical temperature and at various pressures ranging from subcritical to supercritical values. Pure N2 and O2 were injected into environments composed of N2, He, Ar, and various mixtures of CO+N2. The results were photographically observed and documented near the exit region using a CCD camera illuminated by a short duration backlit strobe light. At low subcritical chamber pressures, the jets showed surface irregularities that amplified downstream, exhibiting intact, shiny, but wavy (sinuous) surface features that eventually broke up into irregularly shaped small entities. A further increase of chamber pressure at constant jet initial and ambient temperatures caused the formation of many small droplets to be ejected from the surface of the jet similar to what is observed in the second wind-induced jet breakup regime. As the chamber pressure was further increased, the transition to a f...

Convective flows in rapidly rotating spheres and their dynamo action

Abstract: The present understanding of convection in rotating spherical fluid shells is reviewed and some recent results on coherent structures and magnetic field generation are considered in detail. The constraints exerted by the Coriolis force leads to unusual properties not found in nonrotating systems, such as vacillations, localized convection, and chaotic relaxation oscillations. The central role played by the differential rotation generated by the Reynolds stress of convection in the case of Prandtl numbers of the order unity or less is emphasized. Magnetic fields generated through the dynamo process offer new degrees of freedom. Through the braking of the differential rotation the Lorentz force contributes to an enhanced heat transport.

Displacement of a two-dimensional immiscible droplet in a channel

Abstract: We used the lattice Boltzmann method to study the displacement of a two-dimensional immiscible droplet subject to gravitational forces in a channel. The dynamic behavior of the droplet is shown, and the effects of the contact angle, Bond number (the ratio of gravitational to surface forces), droplet size, and density and viscosity ratios of the droplet to the displacing fluid are investigated. For the case of a contact angle less than or equal to 90°, at a very small Bond number, the wet length between the droplet and the wall decreases with time until a steady shape is reached. When the Bond number is large enough, the droplet first spreads and then shrinks along the wall before it reaches steady state. Whether the steady-state value of the wet length is greater or less than the static value depends on the Bond number. When the Bond number exceeds a critical value, a small portion of the droplet pinches off from the rest of the droplet for a contact angle less than 90°; a larger portion of the droplet is entrained into the bulk for a contact angle equal to 90°. For the nonwetting case, however, for any Bond number less than a critical value, the droplet shrinks along the wall from its static state until reaching the steady state. For any Bond number above the critical value, the droplet completely detaches from the wall. Either increasing the contact angle or viscosity ratio or decreasing the density ratio decreases the critical Bond number. Increasing the droplet size increases the critical Bond number while it decreases the critical capillary number.

Velocity filtered density function for large eddy simulation of turbulent flows

Abstract: A methodology termed the “velocity filtered density function” (VFDF) is developed and implemented for large eddy simulation (LES) of turbulent flows. In this methodology, the effects of the unresolved subgrid scales (SGS) are taken into account by considering the joint probability density function of all of the components of the velocity vector. An exact transport equation is derived for the VFDF in which the effects of the SGS convection appear in closed form. The unclosed terms in this transport equation are modeled. A system of stochastic differential equations (SDEs) which yields statistically equivalent results to the modeled VFDF transport equation is constructed. These SDEs are solved numerically by a Lagrangian Monte Carlo procedure in which the Ito–Gikhman character of the SDEs is preserved. The consistency of the proposed SDEs and the convergence of the Monte Carlo solution are assessed by comparison with results obtained by an Eulerian LES procedure in which the corresponding transport equation...

Kinetic theory for identical, frictional, nearly elastic spheres

Abstract: We derive a simple kinetic theory for collisional flows of identical, slightly frictional, nearly elastic spheres that is based on a physically realistic model for a frictional collision between two spheres. When the coefficient of friction is small, the equations of balance for rotational momentum and energy can be solved in approximation. This permits the rotational temperature to be related to the translation temperature and the introduction of an effective coefficient of restitution in the rate of dissipation of translation fluctuation energy. With this incorporation of the additional loss of translational energy to friction and the rotational degrees of freedom, the structure of the resulting theory is the same as for frictionless spheres.

Effect of high rotation rates on the laminar flow around a circular cylinder

Abstract: A two-dimensional numerical study on the laminar flow past a circular cylinder rotating with a constant angular velocity was carried out. The objectives were to obtain a consistent set of data for the drag and lift coefficients for a wide range of rotation rates not available in the literature and a deeper insight into the flow field and vortex development behind the cylinder. First, a wide range of Reynolds numbers (0.01⩽Re⩽45) and rotation rates (0⩽α⩽6) were considered for the steady flow regime, where α is the circumferential velocity at the cylinder surface normalized by the free-stream velocity. Furthermore, unsteady flow calculations were carried out for one characteristic Reynolds number (Re=100) in the typical two-dimensional (2D) vortex shedding regime with α varying in the range 0⩽α⩽2. Additionally, the investigations were extended to very high rotation rates (α⩽12) for which no data exist in the literature. The numerical investigations were based on a finite-volume flow solver enhanced by multi...

Effect of free rotation on the motion of a solid sphere in linear shear flow at moderate Re

Abstract: The effect of free rotation on the drag and lift forces on a solid sphere in unbounded linear shear flow is investigated. The sphere Reynolds number, Re=|ur|d/ν, is in the range 0.5–200, where ur is the slip velocity. Direct numerical simulations of three-dimensional flow past an isolated sphere are performed using spectral methods. The sphere is allowed to rotate and translate freely in the shear flow in response to the hydrodynamic forces and torque acting on it. The effect of free rotation is studied in a systematic way by considering three sets of simulations. In the first set of simulations, we study how fast a pure rotational or translational motion of the sphere approaches steady state. The “history” effect of rotational and translational motions are compared. Results at high Re are found to be significantly different from the analytical prediction based on low Re theory. In steady simulations, the sphere is allowed to rotate in a torque-free condition. The torque-free rotation rate and the drag an...

Stabilization of Tollmien–Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer

Abstract: In this Letter we show by numerical simulation that streamwise streaks of sufficiently large amplitude are able to stabilize Tollmien–Schlichting waves in zero pressure gradient boundary layers at least up to Re=1000. This stabilization is due to the spanwise averaged part of the nonlinear basic flow distortion induced by the streaks and occurs for streak amplitudes lower than the critical threshold beyond which secondary inflectional instability is observed. A new control strategy is implemented using optimal perturbations in order to generate the streaks.

Jet formation in bubbles bursting at a free surface

Abstract: We study numerically bubbles bursting at a free surface and the subsequent jet formation The Navier–Stokes equations with a free surface and surface tension are solved using a marker-chain approach Differentiation and boundary conditions near the free surface are satisfied using least-squares methods Initial conditions involve a bubble connected to the outside atmosphere by a preexisting opening in a thin liquid layer The evolution of the bubble is studied as a function of bubble radius A jet forms with or without the formation of a tiny air bubble at the base of the jet The radius of the droplet formed at the tip of the jet is found to be about one tenth of the initial bubble radius A series of critical radii exist, for which a transition from a dynamics with or without bubbles exist For some parameter values, the jet formation is close to a singular flow, with a conical cavity shape and a large curvature or cusp at the bottom This is compared to similar singularities investigated in other contexts such as Faraday waves

Transient airflow structures and particle transport in a sequentially branching lung airway model

Abstract: Considering oscillatory laminar incompressible three-dimensional flow in triple planar and nonplanar bifurcations representing generations three to six of the human respiratory system, air flow fields and micron-particle transport have been simulated under normal breathing and high-frequency ventilation (HFV) conditions. A finite-volume code (CFX4.3 from AEA Technology, Pittsburgh, PA) and its user-enhanced FORTRAN programs were validated with experimental velocity data points for a single bifurcation. The airflow structures and micron-particle motion in the triple bifurcations were analyzed for a representative normal breathing cycle as well as HFV condition. While both the peak inspiratory and expiratory velocity profiles for the low Womersley case (α=0.93) agree well with those of instantaneously equivalent steady-state cases, some differences can be observed between flow acceleration and deceleration at off-peak periods or near flow reversal, especially during inspiratory flow. Similarly, the basic features of instantaneous particle motion closely resemble the steady-state case at equivalent inlet Reynolds numbers. The preferential concentration of particles caused by the coherent vortical structures was found in both inhalation and exhalation; however, it is more complicated during expiration. The effects of Womersley number and non-planar geometries as well as the variations in secondary flow intensity plus pressure drops across various bifurcations under normal breathing and HFV conditions were analyzed as well. This work may elucidate basic physical insight of aerosol transport relevant in dosimetry-and-health-effect studies as well as for drug aerosol delivery analyses.

Transient growth of stationary disturbances in a flat plate boundary layer

Abstract: Theoretical and direct numerical simulation models of transient algebraic growth in boundary layers have advanced significantly without an adequate, parallel experimental effort. Experiments that feature disturbances excited by high levels of freestream turbulence or distributed surface roughness show behavior consistent with optimal-disturbance theories but cannot address the theories’ key predictions concerning the growth and decay of disturbances at specific spanwise wavenumbers. The present experiment seeks to provide such data for a flat plate boundary layer using a spanwise roughness array to excite controlled stationary disturbances. The results show that although general trends and qualitative behaviors are correctly captured by optimal-disturbance theories, significant quantitative differences exist between the theories’ predictions and the current experimental measurements. Discrepancies include the location of the wall-normal disturbance profiles’ maxima and the streamwise location of the maximum energy growth. While these discrepancies do not argue against the validity of transient-growth theory in general, they do indicate that correct modeling of receptivity to realistic disturbances is critical and that realistic stationary disturbances can exhibit strongly nonoptimal behavior.

On the virtual aeroshaping effect of synthetic jets

Abstract: The ability of synthetic jets to form large mean recirculation zones in a crossflow is investigated using numerical simulations. It has been suggested that this so-called virtual aeroshaping effect is one mechanism through which synthetic jets affect separation reduction. Here the interaction of a two-dimensional synthetic jet with a flat-plate Blasius boundary layer is simulated and we examine the effect that key flow parameters have on the formation of these mean recirculation zones. The current simulations also suggest a simple scaling for this effect which could prove useful in the design and deployment of these devices.

Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops

Abstract: The axisymmetric formation of drops of Newtonian liquids from a vertical capillary into air is governed by the three-dimensional but axisymmetric Navier–Stokes system and appropriate boundary and initial conditions. Algorithms for obtaining accurate solutions of the resulting two-dimensional (2D) system of equations have recently been developed by Wilkes et al. [Phys. Fluids 11, 3577 (1999)], but are computationally intensive. A one-dimensional (1D) model based on simplification of the governing 2D system through the use of the slender-jet approximation has gained popularity in recent years [Eggers, Rev. Mod. Phys. 69, 865 (1997)]. Such 1D algorithms not only result in great computational savings but appear to capture well the physics of drop formation as has been learned through a somewhat limited number of studies [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Brenner et al., Phys. Fluids 9, 1573 (1997)]. Indeed, existing 1D analyses [Eggers and Dupont, J. Fluid Mech. 262, 205 (1994); Brenner et al...

Further accuracy and convergence results on the modeling of flows down inclined planes by weighted-residual approximations

Abstract: We study the reliability of two-dimensional models of film flows down inclined planes obtained by us [Ruyer-Quil and Manneville, Eur. Phys. J. B 15, 357 (2000)] using weighted-residual methods combined with a standard long-wavelength expansion. Such models typically involve the local thickness h of the film, the local flow rate q, and possibly other local quantities averaged over the thickness, thus eliminating the cross-stream degrees of freedom. At the linear stage, the predicted properties of the wave packets are in excellent agreement with exact results obtained by Brevdo et al. [J. Fluid Mech. 396, 37 (1999)]. The nonlinear development of waves is also satisfactorily recovered as evidenced by comparisons with laboratory experiments by Liu et al. [Phys. Fluids 7, 55 (1995)] and with numerical simulations by Ramaswamy et al. [J. Fluid Mech. 325, 163 (1996)]. Within the modeling strategy based on a polynomial expansion of the velocity field, optimal models have been shown to exist at a given order in the long-wavelength expansion. Convergence towards the optimum is studied as the order of the weighted-residual approximation is increased. Our models accurately and economically predict linear and nonlinear properties of film flows up to relatively high Reynolds numbers, thus offering valuable theoretical and applied study perspectives.