Volume 10, Issue 9, September 1998
 ARTICLES


Dynamic light scattering in shear flow
View Description Hide DescriptionWe describe a new dynamic light scattering technique for measuringdiffusion in sheared suspensions. It involves a scattering geometry with two crossing laser beams. A detailed analysis of the correlation function of scattered light is given. The viability of our method is demonstrated in an experiment where the effect of Taylor diffusion on the scattered light correlation function is measured.

The general motion of a circular disk in a Brinkman medium
View Description Hide DescriptionSolutions of the Brinkman equation for the arbitrary motion of a circular disk are obtained which examine for the first time the effect of particle orientation on the particle drag and torque. Four elementary motions are studied analytically: broadside translation, edgewise translation, rotation about the axis of symmetry, and rotation about the diameter. These motions are closely related to the analogous unsteady oscillation of a disk in Stokes flow [Zhang and Stone, J. Fluid Mech. (1998)]. However, our solution procedure differs in that the problems are formulated using a general solution of the Brinkman equation and are solved by reducing the dual integral equations arising from the mixed boundary conditions in the plane of the disk to a Fredholm integral equation of the second type. Asymptotic results for the drag and torque are derived for both small and large values of the permeability parameter α defined by where a is the radius of the disk and the Darcy permeability. In contrast to the Stokesian motion of a disk, where the drag differs by only a factor of 1.5 for broadside and edgewise translational motion, and is isotropic for rotation about any axis through its center, there is a large difference in the drag and torque with increasing α. In a Brinkman medium, the drag on the disk is proportional to α for edgewise motion and to for broadside motion and the torque is proportional to for outofplane rotation and to α for inplane rotation. For intermediate values of α, the integral equations are solved numerically for the drag and torque exerted by the porous medium on the disk. These results are of importance in probing the microstructure of the porous medium and thus provide a way to test the validity of the effective medium approach.

Motions of anisotropic particles: Application to visualization of threedimensional flows
View Description Hide DescriptionThe aim of the paper is to get insight into flow patterns visualized by suspended anisotropic reflective particles. The motion of triaxial ellipsoids embedded in a threedimensional flow, i.e., which cannot be reduced to a local plane Couette flow, is calculated. Both the asymptotic trajectory and the transient time to reach it are discussed. These results are used to simulate laser sheetvisualizations of two classical threedimensional flows (Taylor–Couette vortices and flow between rotating disks) where the particle history is shown to be negligible. The simulated visualizations are well compared to experimental ones but the paper addresses the fact that the legitimate question of what shows the visualization does not have a simple answer. Nevertheless, these results open the way for quantitative comparisons between computational fluid dynamics and experimental visualizations.

Soret coefficient of nanoparticles in ferrofluids in the presence of a magnetic field
View Description Hide DescriptionExperiments on a nonstationary separation of nanometersized particles of hydrocarbonbased ferrocolloids in a flat vertical thermal diffusion column are performed. By using a modified separation theory which accounts for a onedimensional mixed (thermal and concentration) convection in the column, the Soret coefficient of lyophilized nanoparticles from the separation curves are calculated. It is shown that in a zero magnetic field particles are transferring toward decreasing temperatures. The thermal diffusion ratio reaches a value A significant influence of a uniform magnetic fieldB on particle separation is observed. If B is oriented along the temperature gradient a strong decrease in thermal diffusion coefficient takes place whereas the transversal field causes an intensification of particle thermophoretic transfer. Both effects qualitatively well agree with theoretical predictions based on a hydrodynamic theory of particle thermomagnetophoretic motion.

The effect of bulk viscosity on temperature relaxation near the critical point
View Description Hide DescriptionThe heat transfer near the critical point is governed not only by diffusion,convection, and radiation, but also by a thermomechanical coupling called the Piston Effect. This fourth mode of heat transfer is responsible for the socalled critical speeding up, which contradicts the first expectation of a critical slowing down of the heat diffusion. So far, the viscosity has been neglected in all the existing theoretical models of the Piston Effect. The aim of this paper is to present a comprehensive model of the Piston Effect, written for a realfluid equation of state and including the critical divergence of the bulk viscosity. It is shown in particular that when the critical point is neared, the heat transfer goes faster and faster, until a point is reached where viscous stresses are no longer negligible. When going closer to the critical point, the heat transfer then slows down again; a regime of critical slowing down is entered. This phenomenon should happen sufficiently far from the critical temperature to allow experimental checks. Moreover, it could be used as an indirect way of measuring the critical divergence of the bulk viscosity.

The effect of shape on the hydrodynamics of a hemispheroid projecting from a plate in irrotational fluid
View Description Hide DescriptionIn this paper, we examine the problem of hemispheroid that is compliantly hinged to a plate oscillating with infinitesimal motions in fluid that can be modeled as irrotational. We use this model to understand the effect of the size and shape of hair bundles of sensory cells in the inner ear on hair bundle hydrodynamics at high frequencies. In response to the oscillating plate, the hemispheroid translates and rotates in the plane of the oscillation. Since the equations of motion are linear, the solution can be described as the superposition of the response due to translation of the hemispheroid and the plate, and the response due to rotation of the hemispheroid. The solution can be found by solving Laplace’s equation in prolate and oblate spheroidal coordinates. The response due to translational motion is the same as that derived in Hydrodynamics, 6th ed. (Dover, New York, 1945) for a full spheroid undergoing translational motion. The response due to rotational motion of the hemispheroid about its hinge has not been previously derived. The hydrodynamic pressure, torque, and drag on the hemispheroid as a function of hemispheroidal shape are presented. A good match was obtained for results of the model and measurements of a neural tuning curve of the alligator lizard.

The instability growth leading to a liquid sheet breakup
View Description Hide DescriptionThe instability growth leading to a liquid sheet breakup has been studied with the objective of improving the understanding of the fundamental mechanisms of atomization. A threedimensional Lagrangian code based on vortex dynamics methods has been implemented to track the air/liquid interfaces treated as inviscid vortex sheets. The results of these numerical simulations indicate a possible explanation for the presence of transverse and longitudinal filaments observed in liquid sheet airassisted atomization experiments.

Numerical study of instability in a horizontal porous channel with bottom heating and forced horizontal flow
View Description Hide DescriptionWe study the twodimensional convective patterns in a long horizontal porous layer heated from below, where a nonzero crossflow is imposed. Indeed experiments show that timeperiodic planar flows are found at moderate values of the flow rate. Within the framework of the Darcy law, above the absolute threshold, varied endconditions lead to oscillatory patterns, which are more or less similar to each other in the bulk of the device but present differences near the extremities. Depending on the boundaryconditions, the numerical simulation may produce patterns which are spaceperiodic traveling rolls or waves of amplitude modulated within a stationary region, with envelopes in the form of fronts. Spaceperiodic boundaryconditions yield wavelengths linked to the total length of the device, which sets the frequency. Input boundaryconditions breaking translational invariance along the direction of the main flow yield different structures and select the temporal period. Most attention is paid to inletconditions imposing a linear profile of temperature (at the entrance of the device). We study the variations of the frequency vs the seeping flow rate and the filtration Rayleigh number. The length of the resulting front is also considered.

Paramagnetic liquid bridge in a gravitycompensating magnetic field
View Description Hide DescriptionMagnetic levitation was used to stabilize cylindrical columns of a paramagneticliquid in air between two solid supports. The maximum achievable length to diameter ratio was ∼(3.10±0.07), very close to the Rayleigh–Plateau limit of π. For smaller R, the stability of the column was measured as a function of the Bond number, which could be continuously varied by adjusting the strength of the magnetic field.

Highorder azimuthal instabilities on a cylindrical liquid jet driven by temporal and spatial perturbations
View Description Hide DescriptionA method has been developed to drive a cylindrical liquid jet unstable for deformations with axial wavelengths shorter than the circumference of the jet and azimuthal mode numbers greater than The benefit of this method is that a cylindrical liquid jet can be broken into a spray with an average diameter smaller than the diameter of the initial jet. The higherorder instabilities were created by establishing initial conditions for the jet in space and time at the nozzle. An electromechanical transducer creates the applied temporal initial condition which is a sinusoidally varying velocity perturbation added to the steady velocity of the jet. The amplitude of the velocity perturbation can be as large as the jet’s steady velocity and the energy in the applied velocity perturbation drives the instability. The spatial perturbation is created by placing perturbations in the circumference of the nozzle. As the velocity perturbation travels on the jet, its leading edge steepens and the trailing edge broadens in a manner analogous to the steepening of a pressure pulse in a compressible gas. If the driven velocity perturbation is sufficiently large, a shock or jump forms on the leading edge of the velocity pulse and the jet may break up into higherorder modes. A theoretical analysis of the breakup process, based on an adaptation of compressible fluid shock theory, is used to derive a fundamental lower bound on the spray’s Sauter mean diameter as a function of the velocity perturbation amplitude. Techniques for approaching the theoretical minimum spray diameter by using the higherorder modes to atomize liquid jets are discussed.

Finite amplitude stability of attachment line boundary layers
View Description Hide DescriptionTwodimensional nonlinear equilibrium solutions for the swept Hiemenz flow attachment line boundary layer are directly computed by solving the full NavierStokes equations as a nonlinear eigenvalue problem. The equations are discretized using the twopoint fourth order compact scheme and the resulting nonlinear homogeneous equations are solved using the NewtonRaphson iteration technique. It is found that for Reynolds numbers larger than the linear critical Reynolds number of 583, the nonlinear neutral surfaces form open curves. The results showed that the subcritical instability exists near the upper branch neutral curve and supercritical equilibrium solutions exist near the lower branch. These conclusions are in agreement with the weakly nonlinear theory. However, at higher amplitudes away from the linear neutral points the nonlinear neutral surfaces show subcritical instability at lower and higher wave number regions. At Reynolds numbers lower than the critical value, the nonlinear neutral surfaces form closed loops. By reducing the Reynolds number, we found that the nonlinear critical point occurs at a Reynolds number of 511.3, below which all the twodimensional disturbances will decay. The secondary instability of these equilibrium solutions is investigated using the Floquet theory. The results showed that these twodimensional finite amplitude neutral solutions are unstable to threedimensional disturbances.

Görtler vortices in wall jet flow on a rotating cylinder
View Description Hide DescriptionHotwire anemometry, smoke visualization and nonlinear calculations were used to study the wall jet on a cylinder with rotation. It was found that streamwise vortices are amplified in convex wall jet flow without rotation and that the maximum amplitude was higher than for the concave case. Furthermore, the transition region was located downstream compared with the concave wall jet. Rotation was found to destabilize the convex wall jet, i.e., the transition region appeared upstream compared with nonrotation.

Advection of mass fraction in forced, homogeneous, compressible turbulence
View Description Hide DescriptionIn nearly isothermal, compressible turbulence of a nondense gas the mass fraction of an embedded passive scalar satisfies the same formal conservation equation as a passive scalar in incompressible turbulence. Direct numerical simulation of this system shows that the compressible turbulence modes are less efficient than the incompressible in transporting scalar spectral content from large to small scales. It is argued that the cause of this outcome is the reduced size of the integral length scale of the compressible velocity components vis á vis that of the incompressible velocity components, and this also explains the experimentally observed ineffectiveness of the dilatational velocity modes in determining scalar flux in homogeneous, compressible turbulence with a uniform mean scalar gradient.

On the alignment of strain, vorticity and scalar gradient in turbulent, buoyant, nonpremixed flames
View Description Hide DescriptionThe alignment of vorticity and scalar gradient with the eigendirections of the rate of strain tensor is investigated in turbulent buoyant nonpremixed horizontal and vertical flames. The uniqueness of a buoyant nonpremixed flame is that it contains regions with distinct alignment characteristics. The strainenstrophy angle Ψ is used to identify these regions. Examination of the vorticity field and the vorticity production in these different regions indicates that Ψ and consequently the alignment properties near the flame surface identified by the mixture fraction band differ from those in the fuel region, and the oxidizer region, The band shows straindominance resulting in vorticity/α alignment while (and for the vertical flame) band(s) show(s) vorticity/β alignment. The implication of this result is that the scalar dissipation, attains its maximum value always near These results are also discussed within the framework of recent dynamical results [Galanti et al., Nonlinearity 10, 1675 (1997)] suggesting that the NavierStokes equations evolve towards an attracting solution. It is shown that the properties of such an attracting solution are also consistent with our results of buoyant turbulent nonpremixed flames.

Lagrangian acceleration measurements at large Reynolds numbers
View Description Hide DescriptionWe report experimental measurements of Lagrangianaccelerations in a turbulent water flow between counterrotating disks for Taylor–Reynolds numbers Particle tracks were recorded by imaging tracer particles onto a position sensitive photodiode, and Lagrangian information was obtained from fits to the position versus time data. Several challenges associated with extracting Lagrangian statistical quantities from particle tracks are addressed. The acceleration variance is obtained as a function of Reynolds number and shows good agreement with Kolmogorov (1941) scaling. The Kolmogorov constant for the acceleration variance is found to be

The formation and evolution of synthetic jets
View Description Hide DescriptionA nominally plane turbulent jet is synthesized by the interactions of a train of counterrotating vortex pairs that are formed at the edge of an orifice by the timeperiodic motion of a flexible diaphragm in a sealed cavity. Even though the jet is formed without net mass injection, the hydrodynamic impulse of the ejected fluid and thus the momentum of the ensuing jet are nonzero. Successive vortex pairs are not subjected to pairing or other subharmonic interactions. Each vortex of the pair develops a spanwise instability and ultimately undergoes transition to turbulence, slows down, loses its coherence and becomes indistinguishable from the mean jet flow. The trajectories of vortex pairs at a given formation frequency scale with the length of the ejected fluid slug regardless of the magnitude of the formation impulse and, near the jet exit plane, their celerity decreases monotonically with streamwise distance while the local mean velocity of the ensuing jet increases. In the far field, the synthetic jet is similar to conventional 2D jets in that crossstream distributions of the timeaveraged velocity and the corresponding rms fluctuations appear to collapse when plotted in the usual similarity coordinates. However, compared to conventional 2D jets, the streamwise decrease of the mean centerline velocity of the synthetic jet is somewhat higher and the streamwise increase of its width and volume flow rate is lower This departure from conventional selfsimilarity is consistent with the streamwise decrease in the jet’s momentum flux as a result of an adverse streamwise pressure gradient near its orifice.

Large eddy simulation of a nonpremixed reacting jet: Application and assessment of subgridscale combustion models
View Description Hide DescriptionResults from large eddy simulations(LES) and direct numerical simulations (DNS) of a twodimensional, spatially developing, compressible planar free jet undergoing an idealized, exothermic, chemical reaction of the type are presented in order to assess several subgridscale (SGS) combustionmodels. Both a priori and a posteriori assessments are conducted. The SGS turbulencemodel used is the dynamic Smagorinsky model (DSM). Two classes of SGS combustionmodels are employed in this study. These include the conserved scalar approach and the direct closure approach. Specifically, the SGS combustionmodels involve several forms of direct filtered reaction rate closures, including a scale similarity filtered reaction rate model (SSFRRM), and a mixing controlled strained laminar flamelet model (SLFM) in the form of thermochemical state relationships, obtained from the DNS, and two assumed forms for the subgrid mixture fraction filtered density function (FDF). In general, LES results are in reasonable agreement with DNS results and highlight the performance of the various SGS combustionmodels. In particular, in the context of the present study, it is found that: (1) the SLFM cases overpredict product formation due to their inability to capture finiterate chemistry effects; (2) due to the relatively low values of the SGS mixture fraction variance in the flow under study, the SLFM results are not sensitive to the form of the assumed FDF; and (3) in comparison to the other models investigated, the SSFRRM combustionmodel provides the best agreement with the DNS for product formation.

On the modification of the nearwall coherent structure in a threedimensional turbulent boundary layer on a free rotating disk
View Description Hide DescriptionAn experimental study has been performed on a sheardriven threedimensional turbulent boundary layer in equilibrium over a rotating disk. The objective of the present study is to investigate the modification of the nearwall coherent structure in the threedimensional turbulent boundary layer developed in this flow. Twopoint velocity measurements are carried out with two Xwire probes which are aligned in the local wallparallel mean velocity direction, which show that strong asymmetries exist in the velocity crosscorrelation coefficient in the spanwise direction, and also in the conditionally averaged velocity signals in the vicinity of a strong ejection or sweep, as was shown by Littell and Eaton [J. Fluid Mech. 266, 175 (1994)]. However, a quadrant analysis reveals that the Reynoldsshearstressproducing eddies are nearly symmetric in the spanwise direction and those asymmetries are attributed to the changes in the negativeReynoldsshearstressproducing motions which have less relation to the streamwise coherent structures.

Trajectory and entrainment of a round jet in crossflow
View Description Hide DescriptionThis paper examines the trajectory and entrainment characteristics of a round jet in crossflow. A series of large eddy simulations was performed at Reynolds numbers of 1050 and 2100 and at jet to crossflow velocity ratios of 2.0 and 3.3. Trajectories, which are defined based on the mean streamlines on the centerplane, all collapse to a single curve far from the jet exit, and this curve can be represented with a power law fit. Within this power law region, entrainment of crossflow fluid is shown to be the primary mechanism by which the jet trajectory is determined. Upstream of the power law region, near the jet exit, jet trajectory varies from changes in pressure drag and from differences in the turbulence intensities in the incoming pipe flow.

Dynamics of the velocity gradient tensor invariants in isotropic turbulence
View Description Hide DescriptionThe evolution of the invariants ( and ) of the velocity gradient tensor in homogeneous isotropic turbulence is investigated using data from direct numerical simulation (DNS). The concepts of conditional average time rate of change of the invariants and conditional mean trajectories (CMT) in invariant phase space are introduced to study the dynamics of this flow. The resulting dynamical system in the phase space is a clockwise spiral with a stable focus at the origin, illustrating that in the mean, the cyclic sequence of topological evolution following a fluid particle is unstablenode/saddle/saddle (UN/S/S)→stablenode/saddle/saddle (SN/S/S)→stablefocus/stretching (SF/S)→unstablefocus/contracting (UF/C). The mean rates of change of and , i.e., are found to be negligible near the right branch of the null discriminant curve, indicating that this curve is an attractor in the space. The effects of both the diffusion term and the anisotropic part of the pressure Hessian term on the dynamics of the invariants have also been analyzed using the conditional averages. Both contributions are found to be important in the dynamics of the velocity gradient invariants. Based on these results the extent of the validity of the modelequations governing the evolution of and proposed by Cantwell [Phys. Fluids A 4, 782 (1992)] and Dopazo et al. [“Velocity gradients in turbulent flows. Stochastic models,” Ninth Symposium on “Turbulent Shear Flows,” Kyoto, Japan, 1993, pp. 2621–2625] are discussed.
