Volume 17, Issue 4, April 2005
 LETTERS


Numerical simulation of headon droplet collision: Effect of viscosity on maximum deformation
View Description Hide DescriptionNumerical simulation of headon collision of two equalsize droplets is conducted to observe the effect of viscosity on the maximum deformation amplitude using a movingmesh finitevolume method. Recent experimental results by Willis and Orme [Exp. Fluids34, 28 (2003)] have shown that the maximum deformation amplitude depends on the viscosity coefficient, and thus the percentage of energy that is dissipated until the instant of maximum deformation increases with the increasing fluid viscosity. This observation contradicts previous results by Jiang, Umemura, and Law [J. Fluid Mech.234, 171 (1992)]. The numerical results in this Letter show that the dissipated energy and the maximum deformation depend on the collision Reynolds number, which is consistent with Willis and Orme (2003). However, this dependence decreases with increasing Reynolds number, which suggests that the effect caused by viscosity on maximum deformation becomes insignificant at sufficiently high Reynolds number.

Laminarization of minimal plane Couette flow: Going beyond the basin of attraction of turbulence
View Description Hide DescriptionLaminarization of minimal plane Couetteturbulence is achieved numerically through shorttime imposition of weak spanwise system rotation. A laminarization strategy presented in this Letter is inspired by investigation of the phasespace structure in the vicinity of a recently found unstable periodic orbit [G. Kawahara and S. Kida, “Periodic motion embedded in plane Couetteturbulence: regeneration cycle and burst,” J. Fluid Mech.449, 291 (2001)]. The periodic orbit, which a turbulent state occasionally approaches, and its local stable manifold are found to form the separatrix between the basin of attraction of turbulent and laminar flows. The introduction of the slight rotation during its approach to the periodic orbit enables the state to go beyond the basin of attraction of the turbulence toward the laminar flow. The global stabilization of the unstable periodic orbit by the method of controlling chaos is also performed to accomplish the laminarization without waiting until the natural approach.
 Top

 ARTICLES

 Interfacial Flows

Numerical simulations of interfacial instabilities on a rotating miscible magnetic droplet with effects of Korteweg stresses
View Description Hide DescriptionInterfacial instability of a miscible magnetic droplet in a rotating HeleShaw cell is simulated numerically. The influence of magnetic strengths, the Korteweg stresses, and their coupled effects are first discussed qualitatively by fingering patterns and streamlines. Quantitative measurements are evaluated by interfacial length , number of fingers , and diameter of gyration . The results confirm with coupling rotational effects more vigorous fingering instability occurs on stronger magnetic strengths and less effective surface tensions (Korteweg stresses). Without the effects of Korteweg stresses, significant nonlinear fingering merges occur which lead to reduction in fingering number, early decay of interfacial length and reversed plane trajectories. Before the occurrence of fingering merges, monotonic growths of interfacial lengths, constant fingering numbers, and nearly linear pattern trajectories are observed. If the significant Korteweg stresses are taken into account, the nonlinear merge is prevented and the features of fingering patterns resemble the immiscible situations remarkably. The fingering behavior can be approximated by a master line of within the linear fingering region.

Transient and steady drift currents in waves damped by surfactants
View Description Hide DescriptionIn this paper we study the Lagrangian mean drift induced by spatially damped capillarygravity waves on a surface covered by an elastic film. The analysis is developed with regard to a typical laboratory setup, and explicit solutions for both transient and steady horizontal drift velocities are given. We consider a situation where the film covers the entire surface and is prevented from drifting away, e.g., by a film barrier. The drift below an inextensible film resembles the drift under an ice cover, with a jetlike current in the wave propagation direction just below the surface. If the film is elastic the solution changes drastically. For certain values of the film elasticity parameter the mean flow is in the direction opposite to that of wave propagation in the upper part of the water column.
 Laminar Flows

Sedimentation of particles of general shape
View Description Hide DescriptionWhen a set of complex shaped particles settles down under gravity, they will generally spread in vertical and horizontal directions even though there is no thermal motion since the velocity of complex shaped particle is not in the direction of gravity and depends on the initial orientation. We study the relationship between the dispersion behavior and the particle characteristics. It is shown by theory and simulation that the dispersion behavior can have various types depending on whether the particle is skewed or not or whether the gravity gives a torque or not. The conditions for these cases to happen is discussed and its validity is demonstrated by computer simulation.

Chaotic advection in a cavity flow with rigid particles
View Description Hide DescriptionThe effect of freely suspended rigid particles on chaotic material transport in a twodimensional cavity flow is studied. We concentrate on the understanding of the mechanism how the presence of a particle affects the dynamical system of the flow. In contrast to the case studied by Vikhansky [“Chaotic advection of finitesingle bodies in a cavity flow,” Phys. Fluids15, 1830 (2003)], we show that even a regular periodic motion of a single particle can induce chaotic advection around the particle, as a result of the perturbation of the flow introduced by the freely rotating solid particle. This perturbation is of a hyperbolic nature. In fact, stretching and folding of the fluid elements are guaranteed by the occurrence of the hyperbolic flow perturbation centered at the particle and by the rotation of the freely suspended particle, respectively. The fluidsolid flow problem has been solved by a fictitiousdomain/finiteelement method based on a rigidring description of the solid particle. A singleparticle system is studied in detail in view of the dynamical systems theory and then extended to two and threeparticle systems.
 Instability and Transition

Twodimensional instability of flow in a rough channel
View Description Hide DescriptionLinear stability of a twodimensional flow in a channel with distributed surface roughness is considered. The structure of the disturbance field is related to the structure of the roughness when the ratio of the respective wave numbers is rational; they are not related if this ratio is irrational. It is shown that the stability problem is not unique in the former case but unique in the latter. It is found that disturbances in the form of traveling waves are destabilized by the presence of the roughness. A very good approximation of the critical Reynolds numbers can be found using only the dominant Fourier mode to represent roughness geometry.

Axisymmetric convective states of pure and binary liquids enclosed in a vertical cylinder and boundary conditions’ influence thereupon
View Description Hide DescriptionThe high Rayleigh number (Ra) axisymmetric convection regimes of pure and (, ) binary liquids are numerically investigated and compared. The fluids are enclosed in a vertical cylinder of aspect ratio and heated from below, with either noslip or freeslip kinematic lateral boundary conditions. Branches of solutions and transitions between states that occur as Ra is varied up to are given, along with a description of the encountered bifurcations. When a freeslip condition is imposed along the circumference of the cell, pure fluid and binary liquid stationary flows are found to become identical at high Ra, an often reported feature. When the lateral boundary condition is set to noslip, the high Ra steady flows of pure and binary liquid, although very similar, undergo different bifurcations. This is related with a locally quasiquiescent region present in both cases, the stability of which controls the flow regime in the whole fluid layer. A branch of resulting oscillatory states thus does not appear in the bifurcation diagram of the binary liquid.

Nonlinear evolution of a swirling jet instability
View Description Hide DescriptionThe nonlinear evolution of the threedimensional instability of a viscous unsteady swirling jet, namely, the Batchelor vortex, is addressed. Two types of initial perturbations are considered: a single unstable normal mode with given azimuthal symmetry and white noise. Three different scenarios have been put into evidence according to the value of the swirl number selected in the unstable range . When helical symmetry is present, the dynamics can be interpreted in a twodimensional framework. More specifically, the process is viewed as the simultaneous action of a destabilizing “instantaneous” swirling jet instability and a stabilizing accelerated viscous diffusion induced by differential rotation. For swirl numbers close to the critical value , this latter effect dominates and leads the vortex to relaminarize in the nonlinear regime. For intermediate values of swirl , it breaks into an array of equal sign vortices containing most of the initial circulation and surrounding a central part with axial velocity. For lower swirl , the initial vortex gives birth to an array of dipoles, the ejection of which drastically increases the structure size. Similar trends are observed on simulations with an initial white noise condition.

The development of helical vortex filaments in a tube
View Description Hide DescriptionWe study the formation of helical vortex filaments in a tube. The helical flow is assumed to be potential except in a very slender core. The boundary conditions are satisfied by introducing a helical image vortex. By assuming an axisymmetric flow upstream and imposing conservation laws, we obtain a set of conditions that must be satisfied by the helical flow downstream. We obtain that, when a generalized swirl parameter reaches a critical value a bifurcation occurs and for there are two solutions for the helical filamentary vortex. Such a bifurcation can be produced by increasing the swirl level of the inlet flow or the radius of the outlet tube, in agreement with experiments. We have discussed the influence of the core size and the Reynolds number on and with these results we have explained some experimental observations.

On the generation of a spiraltype vortex breakdown in an enclosed cylindrical container
View Description Hide DescriptionEarlier experimental studies [see H. U. Vogel, “Experimentelle Ergebnisse über die Laminare Strömung in einem zylindrischen Gehäuse mit darin rotierender Scheibe,” MaxPlanckInst. Bericht 6 (1968) and M. P. Escudier, “Observations of the flow produced in cylindrical container by a rotating endwall,” Exp. Fluids2, 189 (1984)] showed that vortex breakdown in an enclosed cylindrical container with one rotating endwall could exhibit either one, two, or three recirculating bubbles depending on the combination of Reynolds number Re and aspect ratio , at least for . However, a recent numerical study by Serre and Bontoux [“Vortex breakdown in a threedimensional swirling flow,” J. Fluid Mech.459, 347 (2002)] at showed that under some conditions, an Sshape vortex structure follows by a spiraltype vortex breakdown could also be produced. This finding is most interesting because, to the best of our knowledge, a spiraltype vortex breakdown in an enclosed cylindrical container has not been produced previously in experiments. The aim of the present investigation is to verify if these vortex structures can be produced under laboratory conditions. Experiments conducted using dye visualization techniques confirm their existence, even for as low as 3.65. However, attempts to produce similar vortex structures in low aspect ratio cases by “artificially” introducing three dimensionality into the flow was less successful. Here, the confined environment makes a bubbletypevortex breakdown extremely robust, and the imposed asymmetry merely distorts the bubble geometry. The present study also reveals that the formation of a bubbletypevortex breakdown is associated with helical instability of decreasing wavelength, and the Sshape structure is linked with a similar instability of increasing wavelength.
 Turbulent Flows

Topological model of flow regimes in the plane of symmetry of a surfacemounted obstacle
View Description Hide DescriptionFlow visualization between Reynolds numbers of 2000 and 6500 in the endwall region of an obstacle mounted on a flat plate revealed presence of a multiple vortex system. Three Reynoldsnumber dependent regimes were identified. With increasing Reynolds number the vortex system transitioned from a static system to a toandfro oscillating system and finally to a sheddingsplitting system. These observations have been used to infer flowtopologies in the plane of symmetry of the juncture from startup through all three regimes.

Sensitivity to tab disturbance of the mean flow structure of nonswirling jet and swirling jet in crossflow
View Description Hide DescriptionSensitivity to tab disturbance of the mean flow structure of nonswirling jet in crossflow (JICF) and swirling jet in crossflow (SJICF) is investigated. For the swirling jet, the nonzero tangential velocity, nonzero circulation jet configuration is employed. The configuration allows for the development of the skewed mixing layer at each lateral edge of the jet not to be obscured and modulated by the jet crossstream boundary layer and the associated vorticity of the opposite sign to that of the imposed swirl. In the investigation, a heated jet is used and the temperature distributions in the cross planes downstream of the jets are surveyed upto , where is the effective velocity ratio and is the diameter of the jet exit. A single stationary tab is alternately placed at eight different azimuthal positions along the periphery of the jet exit. For both JICF and SJICF, the results show that the mean flow structure is most sensitive to tab disturbance in the region centered on the pressurewindward to the windward position and is less sensitive in the leeward region. Specifically, for JICF the sensitive region covers approximately from lateral to windward; for SJICF, from pressure to suctionwindward when moving in the same rotational sense as the swirl. The tab disturbance in these sensitive regions has pronounced and effectively lasting effect on the flow structure; the transformed structure persists downstream to the last measurement station. These results indicate that the generation mechanism of the flow structure in both jets is sensitive to tab disturbance in these regions. They also suggest it to be closely related to the development of the skewed mixing layer along the surrounding crossflow direction and around the jet exit column.

Displacement amplitude scaling of a twodimensional synthetic jet
View Description Hide DescriptionA twodimensional synthetic jet is studied numerically by solving the incompressible, unsteady, Reynoldsaveraged, Navier–Stokes equations and using a turbulencemodel. Rather than a resonant cavity, the synthetic jet is supplied by a fully developed channel flow. Results for two exit geometries, a sharp exit and a rounded exit, and several dimensionless stroke lengths are compared. This study focuses on the effect of the displacement amplitude (stroke length) on the power required to form the jet, the net momentum flux downstream of the exit, the formation threshold, and the spatial development of the synthetic jet. It is shown that the channel flow development length, the selfsimilar region, and the region from which the jet draws fluid all scale on the stroke length. It is also demonstrated that the power required to form the jet increases with stroke length as does the resultant momentum flux. Finally, the power required to form a synthetic jet is significantly smaller for a rounded exit compared to a sharpedged exit.

The subgridscale models based on coherent structures for rotating homogeneous turbulence and turbulent channel flow
View Description Hide DescriptionThe subgridscale (SGS) models based on the coherent structure in gridscale flow fields are proposed and are applied to (non)rotating homogeneous turbulences and turbulent channel flows. The eddy viscosity is modeled by a coherent structure function (CSF) with a fixed modelparameter. The CSF is defined as the second invariant normalized by the magnitude of a velocity gradient tensor and plays a role of wall damping. The probability density function of the CSF is nonGaussian showing an intermittency effect. The model parameter is locally determined, and it is always positive and has a small variance. These models satisfy a correct asymptotic behavior to a wall for incompressible flows. It is shown that the SGS models with an energydecay suppression function which indicates also a pseudobackscatter are consistent with the asymptotic material frame indifference in a rotating frame. Since the CSF characterizing turbulent flows has relation to the SGS energy dissipation, the present SGS models are applicable not only to (non)rotating homogeneous and shear turbulences but also to laminar flows. The proposed models have almost the same performance as the dynamic Smagorinsky model for (non)rotating homogeneous turbulences and turbulent channel flows, but these models do not need to average or clip the model parameter, use an explicit walldamping function, or change the fixedparameter, so that they are suitable for engineering applications of largeeddy simulation.

Comparisons of flow structure above dimpled surfaces with different dimple depths in a channel
View Description Hide DescriptionFlowstructural characteristics over dimple surfaces located on one wall of a rectangular channel with three different dimple depths (, 0.2, and 0.3) are studied experimentally. Reynolds number based on channel height ranges from 2100 to 20 000, and the ratio of channel height to dimple print diameter is 1.0. Presented are instantaneous flow visualizationimages, spectra of longitudinal velocity fluctuations,vortex pair frequency information, and timeaveraged surveys and profiles of different quantities. Regardless of dimple depth, primary vortex pairs are periodically ejected from the central parts of each dimple and exist in conjunction with edge vortex pairs present near the spanwise edges of staggered dimples. As dimple depth increases, larger deficits of total pressure and streamwise velocity are present, along with higher magnitudes of timeaveraged streamwise vorticity,vortex circulation, and longitudinal Reynolds normal stress. Bigger and stronger vortices with increased turbulencetransport capabilities are thus produced by deeper dimples. Ensembleaveraged power spectral density profiles show that primary vortex pair ejection frequencies range from , and edge vortex pair oscillation frequencies range from , with similar distributions as the Reynolds number varies, regardless of dimple depth.

Unsteady flow evolution in swirl injector with radial entry. I. Stationary conditions
View Description Hide DescriptionThe vortical flowdynamics in a gasturbine swirl injector were investigated by means of large eddy simulations. The flow enters the injector through three sets of radialentry, counterrotating swirl vanes. The formulation treats the Favrefiltered conservation equations in three dimensions along with a subgridscale model, and is solved numerically using a densitybased, finitevolume approach with explicit time marching. Several methods, including proper orthogonal decomposition, spectral analysis, and flow visualization, are implemented to explore the flowdynamics in the complex threedimensional flowfields. Various underlying mechanisms dictating the flow evolution, such as vortex breakdown, the Kelvin–Helmholtz instability, and helical instability, as well as their interactions, are studied for different swirl numbers. The flowfield exhibits wellorganized motion in a low swirlnumber case, in which the vortex shedding arising from shear instabilities downstream of the guide vanes drives acoustic oscillations of the mixed first tangential and first radial mode. The flowfield, however, becomes much more complicated at high swirl numbers, with each subregime dominated by different structures and frequency contents.

Unsteady flow evolution in swirl injectors with radial entry. II. External excitations
View Description Hide DescriptionOur previous study on turbulent flows in a gasturbine swirl injector was extended to explore the effects of externally impressed excitations on the unsteady flow evolution. Threedimensional largeeddy simulations were conducted to investigate the responses of the injector flowfield by imposing periodical oscillations of the mass flow rate at the entrance over a wide range of frequencies. Results show that the impressed disturbances are decomposed and propagate in two different modes because of their distinct propagating mechanisms in swirl injectors. The flow oscillation in the streamwise direction travels in the form of acoustic wave, whereas the oscillation in the circumferential direction is convected downstream with the local flow velocity. The vortex breakdown is mainly controlled by the dynamics in the core region near the axis, not so much by the excitation in the main flow passage surrounding the central recirculation zone. External excitations only exert minor influences on the mean flow properties due to the broadband characteristics of the injector flow. One exception is in the outer shearlayer region when the forcing frequency matches the intrinsic frequency of vortex shedding, and the mixing process of two counterrotating swirl flows is considerably enhanced. The dynamic response of the injector flow, however, depends significantly on the forcing frequency in terms of the acoustic admittance and the mass transfer functions. Energy can be transferred among the various structures in the flowfield under external excitations, causing highly nonuniform spatial and temporal distributions of the oscillatory flow properties at the injector exit. The mass transfer function between the injector exit and entrance at the forcing frequency could be substantially greater than unity when the disturbance resonates with the injector flow. The injector essentially acts as an amplifier under this condition.

Optimality of the dynamic procedure for largeeddy simulations
View Description Hide DescriptionWe present a database analysis to obtain a precise evaluation of the accuracy limitations associated with the popular dynamic eddyviscosity model in largeeddy simulation. We consider decaying homogeneous isotropic turbulence at two different Reynolds numbers, i.e., and 100. The largeeddy simulation errors associated with the dynamic model are compared with those arising in the “static” Smagorinsky model. A large number of systematically varied simulations using the Smagorinsky model provides a detailed impression of the dependence of the total simulation error on (i) the spatial resolution and (ii) the resolution of the subgrid dissipation length. This error behavior also induces an “optimal refinement trajectory” which specifies the particular Smagorinsky parameter, in terms of the spatial resolution, for which the total error is minimal. In contrast, the dynamic model gives rise to a selfconsistently determined “dynamic trajectory” that represents the dependence of the dynamic coefficient on the spatial resolution. This dynamic trajectory is compared with the optimal refinement trajectory as obtained from the full database analysis of the Smagorinsky fluid. It is shown that the dynamic procedure in which the tophat test filter is adopted, predicts values for the eddy viscosity as function of resolution and Reynolds number, which quite closely follow the main trends established in the optimal refinement trajectory. Furthermore, a sensitivity analysis, including dependency on testfilter width and filter shape, is discussed. Total simulation errors, due to interacting discretization, and modeling errors associated with the dynamic procedure may be a factor 2 higher compared to the optimum; still the dynamic procedure represents one of the very few selfcontained and efficient errorreduction strategies when increasing the spatial resolution.
 Compressible Flows

Use of the degenerated Reynolds equation in solving the microchannel flow problem
View Description Hide DescriptionIn this paper, the author proposes that the generalized Reynolds equation employed in the gas film lubrication problems, where the flow rates of the Poiseuille flow are calculated from the Boltzmann equation, can be degenerated for solving the microchannel flow problem in the transitional regime. Using this approach, the calculated results of pressure distribution in long microchannels show excellent agreement with the experimental data and the result of the information preservation (IP) method. The results in short microchannels show excellent agreement with the direct simulation Monte Carlo method and the IP method. The lattice Boltzmann method solution of the microchannel flow is examined by comparison with the degenerated Reynolds equation calculations and the disagreement in the pressure distribution confirms that the lattice Boltzmann method is unsuitable for the solution of the microelectromechanical systems(MEMS)flows in transitional regime. For microchannel flows, the degenerated Reynolds equation can serve as a criterion having the merits of kinetic theory for testing various methods intending to solve rarefied gas flow problems in MEMSdevices in the transitional flow regime.