Richard M. Lueptow

Spatio-temporal character of non-wavy and wavy Taylor-Couette flow

The stability of supercritical Couette flow has been studied extensively, but few measurements of the velocity field of flow have been made. Particle image velocimetry (PIV) was used to measure the axial and radial velocities in a meridional plane for non-wavy and wavy Taylor–Couette flow in the annulus between a rotating inner cylinder and a fixed outer cylinder with fixed end conditions. The experimental results for the Taylor vortex flow indicate that as the inner cylinder Reynolds number increases, the vortices become stronger and the outflow between pairs of vortices becomes increasingly jet-like. Wavy vortex flow is characterized by azimuthally wavy deformation of the vortices both axially and radially. The axial motion of the vortex centres decreases monotonically with increasing Reynolds number, but the radial motion of the vortex centres has a maximum at a moderate Reynolds number above that required for transition. Significant transfer of fluid between neighbouring vortices occurs in a cyclic fashion at certain points along an azimuthal wave, so that while one vortex grows in size, the two adjacent vortices become smaller, and vice versa. At other points in the azimuthal wave, there is an azimuthally local net axial flow in which fluid winds around the vortices with a sense corresponding to the axial deformation of the wavy vortex tube. These measurements also confirm that the shift-and-reflect symmetry used in computational studies of wavy vortex flow is a valid approach.

An experimental study of the flowing granular layer in a rotating tumbler

Granular flow in a rotating tumbler is of theoretical and industrial significance. However, in spite of its relative simplicity, little is known about the dynamics of the top flowing layer. Here we present an experimental study of the velocity field within the fluidized layer of monodisperse particles in a quasi-2D (two-dimensional) rotating tumbler in the rolling flow regime using particle tracking velocimetry. The granular flow is illuminated by a laser flash and recorded using a charge coupled device camera. Image processing is used to remove the experimental noise and to achieve sub-pixel accuracy in calculating the particle displacements. The ensemble-averaged streamwise and transverse velocity profiles are calculated based on the particle displacements for three angular velocities and three bead sizes. The normalized streamwise velocity profile is linear throughout the fluidized layer, but becomes logarithmic as it enters the “fixed” bed where slow particle rearrangements dominate. The rms velocitie...

Stability of axial flow in an annulus with a rotating inner cylinder

Flow between concentric cylinders with the inner cylinder rotating and an axial pressure gradient imposed in the annulus reveals a rich variety of flow regimes depending on the flow conditions. The occurrence of these flow regimes was studied experimentally by both visually and optically detecting the transition from one flow regime to another over a wide range of Taylor numbers for moderate axial Reynolds numbers. Seven flow regimes of toroidal vortices were identified, including Taylor vortices, wavy vortices, random wavy vortices, modulated wavy vortices, turbulent modulated wavy vortices, turbulent wavy vortices, and turbulent vortices. The toroidal vortices in these flow regimes look similar to the corresponding vortices when there is no axial flow, except that they translate with the axial flow at a speed slightly greater than the bulk axial velocity. Three flow regimes of helical vortices were observed at low Taylor numbers, including laminar helical vortices, stationary helical vortices, and wavy ...

A dynamical systems approach to mixing and segregation of granular materials in tumblers

The physics of granular matter is one of the big questions in science. Granular matter serves as a prototype of collective systems far from equilibrium and fundamental questions remain. At the same time, an understanding of granular matter has tremendous practical importance. Among practical problems, granular mixing and its interplay with segregation is arguably at the top of the list in terms of impact. Granular mixing in three-dimensional systems is complicated, as flow induces segregation by particle size or density. Several approaches and points of view for analysis are possible in principle, ranging from continuum to discrete. Flow and segregation in three-dimensional systems is seemingly complicated; however, to a reasonable approximation, all of the dynamics takes place in a thin flowing surface layer. This observation, coupled with key experimental results, leads to a simple, compact and extensible continuum-based dynamical systems framework applicable to time-periodic flow in quasi-two-dimensional tumblers and three-dimensional systems (such as spheres and cubes) rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points can be investigated using symmetry concepts; the character of the periodic points and associated manifolds provides a skeleton for the flow and a template for segregation processes occurring in the flow.

Computer-aided calibration of X-probes using a look-up table

A simple method for the computer-aided calibration of an X-probe is described. This method requires the X-probe to be pitched in the free-stream at several velocities. From the corresponding output voltages, a calibration look-up table can be generated. The technique requires fewer assumptions than traditional methods based on Kings law.

Velocity field for Taylor – Couette flow with an axial flow

The flow in the gap between an inner rotating cylinder concentric with an outer stationary cylinder with an imposed pressure-driven axial flow was studied experimentally using particle image velocimetry (PIV) in a meridional plane of the annulus. The radius ratio was η=0.83 and the aspect ratio was Γ=47. Velocity vector fields for nonwavy toroidal and helical vortices show the axial flow winding around vortices. When the axially averaged axial velocity profile is removed from the velocity field in a meridional plane, the velocity field looks much like it would with no imposed axial flow except that the vortices translate axially and the distortion of the azimuthal velocity contours in meridional plane related to the vortices is shifted axially by the axial flow. The velocity vector fields for wavy vortices also show axial flow winding around the vortices. Again, removing the axial velocity profile results in a flow that appears similar to that with no axial flow. The path of the vortices is generally axia...

Reverse osmosis filtration for space mission wastewater: membrane properties and operating conditions

Reverse osmosis (RO) is a compact process that has potential for the removal of ionic and organic pollutants for recycling space mission wastewater. Seven candidate RO membranes were compared using a batch stirred cell to determine the membrane flux and the solute rejection for synthetic space mission wastewaters. Even though the urea molecule is larger than ions such as Na+, Cl-, and NH4+, the rejection of urea is lower. This indicates that the chemical interaction between solutes and the membrane is more important than the size exclusion effect. Low pressure reverse osmosis (LPRO) membranes appear to be most desirable because of their high permeate flux and rejection. Solute rejection is dependent on the shear rate, indicating the importance of concentration polarization. A simple transport model based on the solution-diffusion model incorporating concentration polarization is used to interpret the experimental results and predict rejection over a range of operating conditions. Grant numbers: NAG 9-1053.

Inertial particle motion in a Taylor Couette rotating filter

In rotating filtration, which is based on supercritical cylindrical Couette flow with a rotating porous inner cylinder, the motion of particles in the suspension depends on both centrifugal sedimentation and transport due to the vortical motion of Taylor vortices. We have simulated the motion of dilute, rigid, spherical particles in Taylor Couette flow using computational particle tracking in an analytic velocity field for flow just above the transition to supercritical Taylor vortex flow. Neutrally buoyant particles follow fluid streamlines closely, but not exactly due to the curvature of the velocity field very near the particle. The motion of particles with a density greater than the fluid is primarily determined by the competition between the centrifugal sedimentation related to the primary cylindrical Couette flow and the secondary radial and axial transport of the Taylor vortex flow. As a result, particles that start near the outer edge of a vortex spiral inward toward a limit cycle orbit. Likewise,...

Effect of interstitial fluid on a granular flowing layer

A dominant aspect of granular flows is flow in thin surface layers. While an understanding of the dynamics of dry granular surface flow has begun to emerge, the case of flow when air is completely replaced by a liquid is largely unexplored. Experiments were performed using particle tracking velocimetry (PTV) in a quasi-two-dimensional rotating tumbler to measure the velocity field within the flowing layer of monodisperse spherical particles fully submerged in liquids, a granular slurry, for a range of Froude numbers, bead sizes, fluid densities and fluid viscosities. The thickness of the flowing layer and the angle of repose with a liquid interstitial fluid are generally larger than for the dry system under similar conditions, although the shear rate is generally smaller

Hydrodynamic stability of viscous flow between rotating porous cylinders with radial flow

A linear stability analysis has been carried out for flow between porous concentric cylinders when radial flow is present. Several radius ratios with corotating and counter‐rotating cylinders were considered. The radial Reynolds number, based on the radial velocity at the inner cylinder and the inner radius, was varied from −30 to 30. The stability equations form an eigenvalue problem that was solved using a numerical technique based on the Runge–Kutta method combined with a shooting procedure. The results reveal that the critical Taylor number at which Taylor vortices first appear decreases and then increases as the radial Reynolds number becomes more positive. The critical Taylor number increases as the radial Reynolds number becomes more negative. Thus, radially inward flow and strong outward flow have a stabilizing effect, while weak outward flow has a destabilizing effect on the Taylor vortex instability. Profiles of the relative amplitude of the perturbed velocities show that radially inward flow sh...