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.