Analysis of viscous dissipation in disk storage systems and similar flow configurations

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.

Traveling wave instability in helical coil flow

“…The CUTEFLOWS solution procedure has been extensively tested by Treidler, 7 Humphrey et al, 8 Tatsutani et al, 15,16 Humphrey et al, 17 and Iglesias et al 18 for calculations in Cartesian and cylindrical coordinate systems. Further testing was conducted to ensure that modifications related to implementing the toroidal coordinate system were correctly accomplished.…”

Numerical Modeling for the Characterization of Flow Excitation for the HDD Disk Vibration Control

“…Especially tangential turbulent flow fluctuation is rapidly dissipated close to the wall due to the viscosity and the normal component is confined by the geometric constraint. Consequently, there are large velocity gradients near wall so that a special treatment is obviously needed for reliable solutions [6]. No exception is applied to LES in terms of the turbulent modeling difficulties at walls.…”

“…Researchers in fluid dynamics discipline have been able to develop sophisticated large size models of rotating flows mainly for the turbine problems since the scalable digital computation power was significantly improved in the early 90's [13]. Meanwhile authors like Humphrey focused the advanced computation facilities to the precise modeling of small scale corotating flows for information storage devices [2,6,7,16]. Recently, given the high performance computation facilities, even more advanced work have been dedicated to the modeling of rotating fluid motion for the estimation of total disk flutter level.…”

Symmetry breaking bifurcation in finite disk flow

“…In these applications nonuniformities in flow can affect disk rotational stability, with the attendant drastic effects on read-write performance; the current readwrite head to disk separation is on the order of 100 nm. None of the investigations listed here [12][13][14][15][16][17][18] address solution multiplicity in the corotating disk flow problem.…”