The unsteady streamlined motion of a constant property fluid in the unobstructed space between a pair of disks corotating at angular velocity Ω in a fixed cylindrical enclosure is investigated numerically. Two-dimensional (axisymmetric) and three-dimensional calculations are performed using a second-order accurate time-explicit algorithm. The flow configuration corresponds to that investigated experimentally by Schuler et al. [Phys. Fluids A 2, 1760 (1990)]. The steady flow solutions are characterized by a symmetrical pair of counter-rotating toroidal vortices in the cross-stream (r-z) plane. This secondary motion is driven by the radial imbalance between the outward-directed centrifugal force and the inward-directed pressure gradient force. Axisymmetric calculations predict a flow that is steady for Re<22 200, where Re is the Reynolds number based on the disk radius, the tip speed of the disks, and the kinematic viscosity of the fluid. Above this value the motion is unsteady periodic and, while the features of the cross-stream flow pattern are broadly preserved, the symmetry of the motion about the midplane is broken by alternating periodic crossings of the toroidal vortices. This instability is maintained through an interaction that arises between outward-directed fluid in the disk Ekman layers and inward-directed fluid in the return core flow. Three-dimensional calculations at Re=22 200 and 44 400 show that the toroidal vortices acquire a time-varying sinuous shape in the circumferential direction. These calculations reveal circumferentially periodic reversals of the axial velocity component in the cross-stream plane, including the detached shear layer separating the region of motion in solid-body rotation near the hub from the potential core, in agreement with the flow visualization observations of Humphrey and Gor [Phys. Fluids A 5, 2438 (1993)]. The wavelength of this oscillation is shown to be twice that of the circumferential velocity component which is responsible for the nodal distribution of axial vorticity. When plotted on the interdisk midplane, the axial component of vorticity manifests itself as an even integer number, 2n (n=1,2,...), of circumferentially periodic foci. Experiments show that the number of foci decreases in a stepwise manner with increasing Reynolds number. For the conditions of this study, the calculated dimensionless angular velocity of the foci, ΩF/Ω, ranges from 0.55 at Re=22 200 to 0.44 at Re=44 400. These values are close to the present experimental estimate ΩF/Ω=0.5.

A model of a computer hard disk drive was constructed and measurements of the air flow in the unobstructed space between a pair of disks were obtained. The disks were centrally clamped to a common hub, and rotated within an axisymmetric (cylindrical) enclosure or shroud. Measurements of the circumferential velocity component were made at four radial locations and along the midplane at three rotation rates (0 = 300, 1200, and 3600 rpm) using a laser-Doppler velocimeter. The resulting mean and rms circumferential velocity profiles are presented and discussed. The data show that the circumferential velocity component profiles are fairly uniform in the axial direction in the space between the disks, except near the shroud where the flow is strongly sheared. The circumferential velocity peaks at a critical radius. Between the hub and the critical radius location the flow is in solid body rotation. Between the critical radius and the shroud the circumferential velocity decreases to zero, gradually at first and then very quickly as the shroud is approached. Analysis based on simplified force balance considerations facilitates the interpretation of the experimental observations and leads to improved understanding of the complex flow phenomena. Numerical calculations of the present configuration assuming axisymmetric steady flow were performed by Chang et al.(submitted to Int. J. Heat Mass Transfer). These calculations show reasonable agreement with the averaged velocity data but, for the reasons discussed, fail to reproduce features of the rms distribution associated with non turbulent flow unsteadiness.

The Exubera system (Pfizer, New York, NY/Nektar Therapeutics, San Carlos, CA) is an integration of five major new technologies: protein formulation, powder processing, powder filling, drug packaging, and delivery device. The product provides a simple interface, where the patient interacts only with the delivery device and powder packaging. These components were designed together to assure repeatable dosing when used by a wide range of patients under real-world life-style and handling conditions. The device design is purely mechanical, using patient-generated compressed air as the energy source. Upon actuation, a sonic discharge of air through the novel release unit reproducibly extracts, de-agglomerates, and disperses the inhalation powder into a respirable aerosol. A clear holding chamber allows for patient feedback via dose visualization and separates aerosol cloud generation from the inspiratory effort. The Exubera product was tested under a wide range of typical use conditions and potential misuse scenarios and following long-term usage in clinical trials. These comprehensive characterization programs demonstrated robust aerosol and mechanical performance, confirming the design intent of the inhaler. These studies provide assurance of consistent and reliable dose delivery in a real-world use of the product.

It is shown that the Weierstrass-Mandelbrot function simulates the irregularity in a turbulent velocity record and yields correct forms for the energy and dissipation spectra. In particular, the universal properties of a corresponding multi-fractal function are demonstrated by showing its ability to reproduce and explain turbulent flow spectra measured near the walls of straight and curved channels and in the obstructed space between a pair of disks corotating in an axisymmetric enclosure. The simulation capabilities of the multi-fractal function strongly suggest thai turbulence is fractal in the frequency range of the turbulent energy spectrum where the slope of the logarithm of the spectrum, G, is -3 < G < -1. The scale-independent frequency range of the energy spectrum correctly represented by the multi-fractal function includes the isotropic dissipation subrange (-3 < G < -5/3), the inertial subrange (G = -5/3), and the "inner" portion of the anisotropic large-scale subrange ( -5/3 < G < -1).

A numerical study has been conducted for the flow of a dilute particleladen gas moving past one or more tubes undergoing erosion. A nonorthogonal body-fitted coordinate system was used to calculate three tube configurations for laminar and turbulent flow regimes. The sssumption of one-way coupling allows the calculation of individual particle velocities from the fluid flow field. The significant effects of turbulent velocity fluctuations are taken into account by means of the stochastic separated flow model. The particle flow field information is then used to predict circumferential distributions of particle flux and erosion. Predictions of trajectories for the case of two in-line tubes show that particles with inertia numbers X > 1 will strike many tubes in a tube bank due to particle rebounding from tube surfaces. By contrast, particles with X -= 1 are entrained in the bulk flow between tubes. In general, the effect of increasing the particle-gas suspension temperature is to couple the particle-fluid motion more closely through viscous drag and, thus, to decrease erosion. Introduction The problem of interestThe erosion of tubes in tube banks by particles suspended in gas flows is a major problem in the power industry. Such erosion is especially important in the reheaters and economizers of coalfired boilers utilizing fluidized bed combustors. A survey of the literature on the subject, available in Schuh (1987), has uncovered a considerable amount of work on single-phase flow and heat transfer for single tubes, but less for the case of tube banks. In addition, much of what is available for tube banks tends to be semiempirical or qualitative in nature and often in the vein of correlations for predicting overall values of pressure drop and heat transfer. The level of corresponding information relating to particle-laden gas flows, especially the effects of fluid motion on particle motion and hence on tube erosion, is virtually nil.The study reported here is part of a research effort aimed at measuring and rendering predictable the flow of dilute concentrations of solid spherical particles suspended in isothermal gas streams moving past one or two in-line tubes, or past a tube in a tube bank. The turbulent flow regime is of special interest for

A numerical investigation was undertaken to characterize the laminar flow and heat transfer in axisymmetric coaxial corotating shrouded disk configurations. Attention was focused on calculation conditions favoring steady, stable, symmetric solutions of the conservation equations. The justification for this is based on velocity measurements obtained in a test section that matches the numerical configuration. Calculations were performed to investigate the dependence of the flow characteristics on disk angular velocity, disk spacing, and the disk–shroud gap width. Conditions involving a radial throughflow (blowing) and/or an axially directed disk–shroud gap flow were also predicted. In the region of the shroud the results show a strong sensitivity of the flow and heat transfer to variations in the flow Reynolds number (rotation) and Rossby number (blowing). By contrast, the flow was found to be less dependent on the disk spacing and the disk–shroud gap width for the conditions investigated. The introduction of an axially directed disk–shroud gap flow significantly alters the flow and heat transfer characteristics in the region between two disks. This finding is important for the improved design and control of corotating disk systems.

No abstract

Flows in rotating magnetic disk storage systems and similar devices are prone to instabilities and the viscous generation of heat. Serious degradation in the performance of disk storage systems occurs when differential thermal expansion, due to the maldistribution of heat, and flow-induced vibrations result in track misregistration by the magnetic read/write heads. Submicron flying heights and micron track widths exacerbate such alignment difficulties. High rotation speeds, also characterizing the emerging disk storage technology, impose significant torque requirements. Experimental measurements of torque obtained by Daily and Nece [J. Basic Eng. Trans ASME 82, 217 (1960)] for a single disk, and by Hudson and Eibeck [J. Fluids Eng. 113, 648 (1991)] for a disk stack with and without obstructions, both in cylindrical enclosures, are found in this study to be correctly correlated by the analytically derived equation, TNo≡Ttotρ/Nμ2R2 = (2C1 + C2H/R2) × [Re/(1 − tL/HR2)]3/2+m, where TNo is a newly defined dimensionsless torque number, Re is the Reynolds number of the interdisk flow; H, R2, t, and L are geometrical length scales; and, C1, C2, and m are experimentally determined constants of order unity. Regressions to the experimental data of these authors yield values for C1, C2, and m in this equation which offer a combination of accuracy and universality not previously available. Moderate amounts of imposed radially directed flows in the spaces between unobstructed pairs of corotating disks are shown, via numerical calculation, to affect the interdisk flow fields quite notably. Analysis of results obtained solving the Navier–Stokes equations, assuming unsteady, axisymmetric, streamlined flow at low speeds of rotation shows that sucking air radially inward in the interdisk space, rather than blowing it radially outwards, substantially reduces the torque required to rotate the disks relative to the unventilated condition. Notwithstanding, depending on how the sucking condition is implemented, in obstructed geometries the reduction in torque may come at the expense of flow instabilities that could affect magnetic head read/write performance, a problem requiring close attention in the application of present findings to the improved design of disk storage systems.