Volume 19, Issue 6, June 2007

We study the effect of slip and noslip wall boundaries on the decay rate of a passive scalar in a spatially smooth and random in time velocity field. Numerical simulations are carried out to verify the effect of the peripheral (nearwall) regions on the decay of the scalar variance. Using two kinematic flow models with simple velocity fields, we show that, in the case of slip boundaries, the passive scalar is characterized by an initial rapid stirring followed by an exponential decay of the scalar variance. In stark contrast, results for the case with noslip boundaries show that, following an initial rapid stirring of the scalar within the bulk, there is an intermediatetime regime where the variance follows a powerlaw decay. This intermediate regime is established as a result of the trapping of the scalar in the peripheral regions near the noslip walls. Finally, the behavior of the scalar variance switches to a final regime that is characterized by an exponential decay rate. The results presented here indicate that the recent ensemblebased theories regarding the evolution of a passive scalar in the peripheral regions correctly predict the main stages of the scalar evolution that arise in a single flow realization.
 LETTERS


Pair velocity correlations among swimming Escherichia coli bacteria are determined by forcequadrupole hydrodynamic interactions
View Description Hide DescriptionThis Letter examines the pair velocity correlations among Escherichia coli (E. coli) bacteria swimming freely in a microfluidic channel. A large number of bacterial tracks are obtained using a particle tracking algorithm, and the longitudinal and transverse pair velocity correlation functions are evaluated. A theoretical analysis traces the origin of correlated motion between bacterial pairs to the translation of a bacterium driven by the forcequadrupole velocity disturbance caused by the swimming of neighboring bacteria. Both theory and experiments indicate that the longitudinal and transverse correlation functions are positive and negative, respectively.

The wimple: A rippled deformation of a wetting film during its drainage
View Description Hide DescriptionIt has long been accepted that hydrodynamicpressure in a draining fluid film can cause inversion of curvature of a fluidfluid interface, creating the socalled dimple. However, it was recently discovered that a different shape, dubbed a wimple, can be formed if a bubble/drop is initially in the field of repulsive surface forces, so that a wettingfilm is formed. The film profile then includes a central region in which the film remains thin, surrounded by a ring of greater film thickness and bounded at the outer edge by a barrier rim. This shape later evolves to a conventional dimple, which then drains in the usual way. Here we carry out numerical simulations of the draining film evolution that allow us to uncover the physical mechanism responsible for wimple formation. Simple analytical estimates are then obtained for characteristic times of different stages of drainage, and are shown to be in good agreement with experimental data. We demonstrate that wimpling is a general phenomenon that can be encountered in many different systems.

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

Spatially periodic reversing core in a twistedfin generated swirling pipe flow
View Description Hide DescriptionExperimental results for swirling turbulent flow in a pipe, generated by a 180° twisted fin inside the pipe, are presented. The results show that the core region undergoes a spatially periodic change in direction of rotation from counterrotating to corotating and back to counterrotating flow relative to the main swirling flow. Up to four transitions in direction of rotation have been recorded with a twocomponent laserDoppler velocimeter downstream of the swirl generating fin. The Reynolds number is varied from to and the average swirl number varies from to downstream of the fin. The underlying cause of the periodicity in the direction of rotation of flow in the core region is conjectured to be based on the secondary flows generated by a pair of corotating helical vortices forming upstream at the spiralshaped swirl generating fin.

Turbulence generator using a precessing sphere
View Description Hide DescriptionWe propose a precessing sphere as a tabletop turbulence generator, which has less uncertainty in the setting of control parameters and the resulting high flowreproducibility. The precession is realized by rotating the spin axis of a sphere around another axis (the precession axis). In our experiments, the two axes are fixed at right angles. The flow inside the sphere is governed only by two nondimensional parameters, one being (the Reynolds number defined by the maximum peripheral velocity around the spin axis) and the other being (the rate of precession). The range of parameters for sustaining turbulence is revealed by the timeseries analysis of velocity fields measured by particle image velocimetry. Welldeveloped turbulence can be sustained even for of the order of a few percent when is beyond a few thousands.

Determination of the critical Shields number for particle erosion in laminar flow
View Description Hide DescriptionWe present reproducible experimental measurements for the onset of grain motion in laminar flow and find a constant critical Shields number for particle erosion, i.e., , over a large range of small particle Reynolds number:. Comparison with previous studies found in the literature is provided.

 ARTICLES

 Viscous and NonNewtonian Flows

A magnetically actuated ball valve applicable for smallscale fluid flows
View Description Hide DescriptionWe present three possible designs for magnetically actuated ball valves that can be scaled down to nanometer length scales. Analytical expressions are presented for the hydraulic resistance of the ball valve as a function of geometric parameters and the state of the valve, and we also present analytical expressions for the hydrodynamic force on the magnetic bead that functions as the ball in the valve. We verify these expressions numerically and calculate the magnetic forces that can be exerted on the magnetic bead using the proposed structures. Finally, for typical parameters we show that these structures will be able to withstand a back pressure between 3 and regardless of the size of the bead/ball.
 Particulate, Multiphase, and Granular Flows

Characteristics of transitional multicomponent gaseous and dropladen mixing layers from direct numerical simulation: Composition effects
View Description Hide DescriptionTransitional states are obtained by exercising a model of multicomponentliquid (MCliquid) dropevaporation in a threedimensional mixing layer at larger Reynolds numbers, Re, than in a previous study. The gas phase is followed in an Eulerian frame and the multitude of drops is described in a Lagrangian frame. Complete dynamic and thermodynamic coupling between phases is included. The liquid composition, initially specified as a singleGamma (SG) probability distribution function (PDF) depending on the molar mass, is allowed to evolve into a linear combination of two SGPDFs, called the doubleGamma PDF (DGPDF). The compositions of liquid and vapor emanating from the drops are calculated through four moments of their PDFs, which are dropspecific and locationspecific, respectively. The mixing layer is initially excited to promote the double pairing of its four initial spanwise vortices, resulting into an ultimate vortex in which small scales proliferate. Simulations are performed for four liquids of different compositions, and the effects of the initial mass loading and initial freestream gas temperature are explored. For reference, simulations are also performed for gaseous multicomponent mixing layers for which the effect of is investigated in the directnumericalsimulation–accessible regime. The results encompass examination of the global layer characteristics, flow visualizations, and homogeneousplane statistics at transition. Comparisons are performed with previous pretransitional MCliquid simulations and with transitional singlecomponent (SC) liquiddropladen mixing layer studies. Contrasting to pretransitional MCflows, the vorticity and drop organization depend on the initial gas temperature, this being due to drop/turbulence coupling. The vaporcomposition mean molar mass and standard deviation distributions strongly correlate with the initial liquidcomposition PDF. Unlike in pretransitional situations, regions of large composition standard deviation no longer necessarily coincide with those of large mean molar mass. The rotational and composition characteristics are all liquidspecific and the variation among liquids is amplified with increasing freestream gas temperature. The classical energy cascade is found to be of similar strength, but the smallest scales contain orders of magnitude less energy than SC flows, which is confirmed by the larger viscous dissipation for MCflows. The kinetic energy and dissipation are liquidspecific and the variation among liquids is amplified with increasing freestream gas temperature. The gas composition, of which the first four moments are calculated, is shown to be close to, but distinct from, a SGPDF. Eulerian and Lagrangian statistics of gasphase quantities show that the different observation framework may affect the perception of the flow.
 Laminar Flows

Characteristics of twodimensional flow around a rotating circular cylinder near a plane wall
View Description Hide DescriptionWe simulate a twodimensional incompressible flow around a rotating circular cylinder near a plane wall at the Reynolds number by using the lattice Boltzmannequation with multiple relaxation times. We investigate the flow pattern in the parameter space of the rotational rate and the normalized gap , where is the angular velocity of the cylinder, and are the cylinder radius and diameter, respectively, is the inflow velocity, and is the gap between the cylinder and the wall. We quantify the effects of and on the hydrodynamic forces and the frequency of vortex shedding from the cylinder. Our results indicate that two critical values of , and , exist, which depend on . The flow is steady when , while it has a wake of a regular vortex street when . When , the flow is aperiodic. We observe that the mean drag coefficient is a monotonically increasing function of when . When , is no longer a monotonic function of . The mean drag coefficient varies significantly in the range , and so do the rootmeansquare values of the lift and drag coefficients, and . When , the wall effect diminishes.

Slip and accommodation coefficients from rarefaction and roughness in rotating microscale disk flows
View Description Hide DescriptionAccommodation coefficients are determined from experimental results and analysis based on the NavierStokes equations for rotationinduced flows in Cshaped fluid chamber passages formed between a rotating disk and a stationary surface. A firstorder boundary condition is used to model the slip flow. The fluid chamber passage height ranges from to give Knudsen numbers from 0.0025 to 0.031 for air and helium. In all cases, roughness size is large compared to molecular mean free path. The unique method presented for deducing tangential momentum accommodation coefficients gives values with less uncertainty compared to procedures that rely on flows in stationary tubes and channels. When channel height is defined at the tops of the roughness elements, slip velocity magnitudes and associated accommodation coefficients are a result of rarefaction at solidgas interfaces and shear at the gasgas interfaces. With this arrangement, tangential accommodation coefficients obtained with this approach decrease, and slip velocity magnitudes increase, at a particular value of Knudsen number, as the level of surface roughness increases. At values of the mean roughness height greater than , accommodation coefficients then appear to be lower in air flows than in helium flows, when compared for a particular roughness configuration. When channel height is defined midway between the crests and troughs of the roughness elements, nondimensional pressure rise data show little or no dependence on the level of disk surface roughness and working fluid. With this arrangement, slip is largely independent of surface roughness magnitude and mostly due to rarefaction, provided the appropriate channel height is chosen to define the roughness height.
 Instability and Transition

Spatial resolution enhancement/smoothing of stereo–particleimagevelocimetry data using properorthogonaldecomposition–based and Kriging interpolation methods
View Description Hide DescriptionMethods for data reconstruction and spatial enhancement of experimental data for a transitional boundary layer with laminar separation bubble are investigated. Particularly, proper orthogonal decomposition (POD) is applied to direct numerical simulation (DNS) data to extract the DNSbased POD modes, which are projected onto the experimental data (via a leastsquares procedure) in order to obtain model coefficients. These model coefficients are then used to reconstruct, “interpolate,” and smooth the experimental data based on the DNS modes. In addition, in order to compare and assess the effectiveness of the present DNSbased procedure, Kriging interpolation is performed on the experimental (as well as numerical) data. These procedures are applied to time periodic (experimental) instantaneous spanwise vorticity at a constant spanwise location. We have demonstrated that particleimagevelocimetry (PIV)based POD modes can be smoothed by Kriging interpolation, thus a noisefree reconstruction of PIV data can be achieved. It is also found that for very low resolution experimental data, DNSbased interpolation is superior over Kriging interpolation. On the other hand, Kriging interpolation based on the Gaussian correlation model works very well for sufficiently high resolution experimental data. The correlation parameter can be used to control the degree of smoothness in the data reconstruction. Both procedures effectively eliminate the unwanted noise in the experimental data. One important difference between the two procedures is that, with quite some confidence, the DNSbased procedure can also be used for “extrapolation” since the model coefficients do not depend on spatial variation. In fact, we show that nearwall spanwise vorticity, which is not available from experimental data, can be recovered faithfully. Moreover, the enhancement (interpolation and smoothing) of full threedimensional PIV data has been performed by Kriging interpolation employing a Gaussian correlation model.

Holmboe modes revisited
View Description Hide DescriptionA scaling analysis is presented better identifying the conditions in which the Boussinesq approximation may be used to study shear disturbances like that of Holmboe modes. The classic Holmboe normal modeinstability is then reanalyzed by including baroclinic effects whose introduction alters the onset of Holmboe’s travelingwave instability depending on the direction of the propagating modes. Since the introduction of baroclinicity is tantamount to relaxing the Boussinesq assumption, it means that in the presence of shear there is now a vertical variation of the horizontal momentum flux that alters the phase speed and structure of the classic Holmboe modes; the physical source of their broken rightleft propagatory symmetry is associated with this physical effect. Furthermore, the regions of parameter space in which Holmboe’s classic analysis predicts there to be nonpropagating double instabilities now supports propagating Holmboe modes when baroclinic effects are included. We also find that a globally constant shear profile behaves as a stabilizing agent, in contradiction to the destabilizing role that shear normally plays in the classic KelvinHelmholtz problem of a sheardensity interface. The general relationship between the normal modes of this type of system to that of the continuous spectrum is also noted. We also find that the baroclinic effects explored here probably do not manifest in terrestrial oceanographic and laboratory conditions, although they may do so in atmospheres.

Evolution of mushroomtype structures behind a heated cylinder
View Description Hide DescriptionThe threedimensional transition in the wake flow behind a heated cylinder occurs at a much lower Reynolds number than for the unheated case. The threedimensional transition is initialized in the nearwake by the formation of shaped structures and manifests itself in the farwake as escaping mushroomtype structures from the upper vortices. In this study, both experimental and numerical techniques are used to investigate the origin and development of these mushroomtype structures. The formation of the mushroomtype structures is associated with the occurrence of shaped vortices in the nearwake. Hot fluid between the legs and the head of the shaped structure is lifted up. This liftup process together with the action of buoyancy pulls out hot fluid from the upper vortex cores, resulting in a mushroomtype structure, which is comprised of a socalled stem and cap. Hot fluid is continuously transported through the stem to the advancing front of the mushroomtype structure. Finally, a pinchoff phenomenon is observed of the cap, ending up as a buoyant vortex ring. An analytical model is presented for the pinchoff process.
 Turbulent Flows

Inner and outer scalings in rough surface zero pressure gradient turbulent boundary layers
View Description Hide DescriptionA new set of experiments have been performed in order to study the effects of surface roughness and Reynolds number on a zero pressure gradient turbulent boundary layer. In order to properly capture the dependence of the single point statistics, consecutive measurements of 11 streamwise locations were performed which enabled the use of the full boundary layer equations to calculate the skin friction. This quantity was obtained within 3% and 5% accuracy for smooth and rough surfaces, respectively. For the sand grain type roughnesses used, only the Zagarola and Smits scaling, , was able to remove the effects of roughness and Reynolds number from the velocity profiles in outer variables. However, each scaling used for the velocity deficit profiles resulted in selfsimilar solutions for fixed experimental conditions. When examining the Reynolds stresses in the inner region [i.e., ], the component showed the largest influence of roughness, where the high peak near the wall was decreased and became nearly flat for the fully rough regime profiles. In addition, the Reynolds stresses in outer variables showed selfsimilarity for fixed experimental conditions. However, as the roughness parameter, increases, all Reynolds stress profiles became similar in shape indicating increased isotropy near the wall. Furthermore, the boundary layer parameters also showed a considerable increase due to roughness.

Direct numerical simulation of a plane turbulent walljet including scalar mixing
View Description Hide DescriptionDirect numerical simulation is used to study a turbulent plane walljet including the mixing of a passive scalar. The Reynolds and Mach numbers at the inlet are and , respectively, and a constant coflow of 10% of the inlet jet velocity is used. The passive scalar is added at the inlet enabling an investigation of the walljet mixing. The selfsimilarity of the inner and outer shear layers is studied by applying inner and outer scaling. The characteristics of the walljet are compared to what is reported for other canonical shear flows. In the inner part, the walljet is found to closely resemble a zero pressure gradient boundary layer, and the outer layer is found to resemble a free plane jet. The downstream growth rate of the scalar is approximately equal to that of the streamwise velocity in terms of the growth rate of the halfwidths. The scalar fluxes in the streamwise and wallnormal direction are found to be of comparable magnitude. The scalar mixing situation is further studied by evaluating the scalar dissipation rate and the mechanical to mixing time scale ratio.

Unsteadiness of an axisymmetric separatingreattaching flow: Numerical investigation
View Description Hide DescriptionThe separated flow over a cylinder elongated by another cylinder of a smaller diameter is investigated numerically at the high subsonic regime using zonal detached eddy simulation (ZDES) and compared with the experimental data of Deprés, Reijasse, and Dussauge [AIAA J.42, 2541 (2004)]. First, it is shown that this axisymmetric step flow has much in common with the twodimensional facing step flows as regards the shear layer instability process. Second, the statistical and spectral properties of the pressure fluctuations are scrutinized. Close to the step, the surface pressure signature is characterized by low frequencies (where and denote, respectively, the mean reattachment length and freestream velocity) and an upstream velocity of while in the second halfpart of the recirculation higher frequencies fluctuations at and a downstream convection velocity are the dominant features. The current calculation shows that the separated bubble dynamics depends on very complex interactions of large eddies formed in the upstream free shear layer with the wall in the reattachment region. These structures are shed with a nondimensional frequency of about 0.2. Besides, it has been observed that the secondary corner vortex experiences a cycle of growth and decay. The correspondence between the frequencies of this secondary corner vortex dynamics and the flapping motion suggests that there should be different aspects of the same motion. These results show that there is an ordered structure in this axisymmetric separating/reattaching flow which is dominated by large scale coherent motion. This is confirmed by a twopoint correlation analysis of the pressure signals showing that the flow is dominated by highly coherent antisymmetric modes at the flapping and vortex shedding frequencies whose signatures are evidenced in the spectrum of the computed buffet loads. Possible onsets of a largescale selfsustained motion of the separated area are finally discussed and the existence of an absolute instability of the axisymmetric recirculation bubble originating from a region located near the middle of the recirculating zone is conjectured.

Effects of openloop and closedloop control on subsonic cavity flows
View Description Hide DescriptionThis work presents an experimental investigation of the effects of open and closedloop control techniques on the flow structure and surface pressure signature in subsonic cavityflows. The cases include the uncontrolled (baseline) Mach 0.30 flow over a shallow cavity of aspect ratio 4 with Reynolds number based on the cavity depth of , and four actively controlledflows. The controlled cases include openloop at two discrete frequencies and two closedloop cases: parallel proportional with time delay and reducedorder modelbased linear quadratic. Measurements and analyses include particle image velocimetry, spectra and spectrograms of surface pressure and velocity fluctuations, flow visualization, and proper orthogonal decomposition. Data are presented and analyzed in an effort to better understand the behavior of the cavityflow in response to a variety of actuation cases. Results show that both open and closedloop control have significant effects on the flow dynamics and surface pressure behavior. In addition, the results reveal substantial differences between the effects of each type of openloop and closedloop control.

Nearwall passive scalar transport at high Prandtl numbers
View Description Hide DescriptionVery accurate numerical simulations of a passive scalar field in the turbulent channel and flume flow were performed at frictionReynolds numbers and and Prandtl numbers , . Direct numerical simulation is used for description of the velocity field. The temperature field is described with the LESlike approach with the smallest resolved temperature scales equal to the smallest scales of the velocity field. The consistency of the applied physical modelling and pseudospectral scheme is first tested with comparison of the results with the existing DNS simulations of F. Schwertfirm and M. Manhart [Proceedings of Turbulence, Heat, and Mass Transfer (2006)] at and . The sensitivity of the method to the grid refinement and time step variations is performed with simulations at and . Both tests show that the proposed approach produces very accurate mean temperature profiles, heat transfer coefficients, and other loworder moments of the turbulent thermal field. It is shown that the mean temperature profiles near the wall can be accurately predicted even when the temperature scales between the Batchelor and Kolmogorov scale are not resolved. The key to the success of the proposed approach lies in the fact that the largescale structures govern the turbulentheat transfer at high Prandtl numbers. Resolved spectra of the temperature fluctuations and the rms temperature fluctuations in the diffusive sublayer and the thermal buffer layer are practically unaffected by the unresolved temperature scales. The contribution of the subKolmogorov thermal scales becomes relevant above the thermal buffer layer, where the unresolved temperature scales affect spectra and rms temperature fluctuations, but not the loglaw shape of the mean temperature profile and the mean heat transfer coefficient. Further results are obtained at , , , and , , . These results are compared with Kader empirical temperature profiles and other available experimental and numerical results. Significant difference in the mean temperature profiles is demonstrated between the profiles calculated at frictionReynolds numbers 150 and 395. Kader correlation is shown to be very accurate at higher Reynolds number but underpredicts temperatures at low Reynolds number.

Particle image velocimetry study of turbulent flow over transverse square ribs in an asymmetric diffuser
View Description Hide DescriptionThe objective of this paper is to study the combined effects of rib roughness and adverse pressure gradient produced in an asymmetric diffuser on turbulent flows. The twodimensional asymmetric diffuser was comprised of a straight flat floor and a curved roof. The diffuser section was preceded and followed by straight parallel walls. The complete test conditions were comprised of a reference smooth floor and repeated arrays of transverse square ribs glued onto the floor to produce three pitchtoheight ratios, , 6, and 8. The curved roof was kept smooth in all the experiments. For each of the four test conditions, a particle image velocimetry was used to conduct detailed velocity measurements within the diverging section and also at locations upstream and downstream of the diverging section. From these measurements, the mean streamlines, mean velocities,turbulent intensities, Reynolds shear stress, and production terms in the transport equations for the turbulent kinetic energy and Reynolds stresses were obtained. The results obtained in the diverging section showed that the boundary layers that developed on the ribs thickened considerably at the expense of those adjacent to the roof opposite to the ribs. The streamlines and mean velocity profiles over the ribs showed that adverse pressure gradient increased the roughness sublayer substantially. Adverse pressure gradient and rib roughness also increased the drag and levels of the turbulent intensities, Reynolds shear stress and production terms compared to smoothwall zero pressure gradient turbulent boundary layer. It appears, however, that adverse pressure gradient enhanced turbulence more effectively than it increased drag.

Evolution of a forced stratified mixing layer
View Description Hide DescriptionLaboratory measurements were carried out in a spatially developing stably stratified shear layer generated downstream of a splitter plate. The instabilities were controlled using a flapper spanning the entire shear layer, with the flapper forced at the fastest growing frequency of the primary [KelvinHelmholtz (KH)]instability. The measurements were taken as the KH instabilities roll up, break down, and degenerate into stratified turbulence. Both stratified and homogeneous shear layers were considered, the latter acting as the “baseline” case. The measurements included the streamwise and vertical velocities (made using Xwire hot film probes), which allowed calculation of the mean and velocities,turbulent kinetic energy (TKE) dissipation, and TKE production. The density and its gradients were measured using miniature conductivity probes. The measurements and flow visualization elicited interesting features of KH evolution, namely that KH billows may be turbulent from the onset, the TKE dissipation is largest at early stages of evolution, the production of TKE is a maximum at the breakdown of billows, the decay of turbulence to fossilized motions and concomitant formation of fine (layered) structure occur rapidly after the breakdown of billows, and episodic rebirth of (zombie) turbulence develops before a final permanently fossilized state is achieved.