Measurement of Continuum Breakdown During Disk Spindown in Low-Pressure Air

Abstract

The deceleration torque during spindown of a disk is measured across a range of air pressures on three aluminum disks. The diameters of the disk are 0.15, 0.17, and 0.21 m; the range of pressures is 0.71 Pa to atmospheric pressure; and the angular velocities range approximately from 400 to 3300 rpm. The results are compared to computational fluid dynamics for the continuum flow regime and analytical results for the free molecular flow regime. The torque is nondimensionalized using dynamic viscosity of air, instantaneous angular velocity, and the disk diameter and is plotted against Reynolds number. Results show that the nondimensional curves from atmospheric pressure through 100 Pa collapse on each other for all disk diameters and agree with computational-fluid-dynamics results. At low pressures, the nondimensional torque does not change with Reynolds number. The analytically obtained free molecular flow torque is compared with the experimental results at the lowest ambient pressures, and the value of momentum accommodation coefficient is computed to be 0.74 0.02. The value is consistent for all disk sizes. The scale used for nondimensionalization suggests self-similarity, and therefore continuity, in the spindown experiments between pressures of 100 Pa and atmospheric pressure. The deviation of the nondimensional curves below this pressure suggests continuum breakdown. Nomenclature c = thermal velocity D = disk diameter d m = molecular collision diameter G 0 o = nondimensional wall shear stress I = moment of inertia k = Boltzmann constant Kn = Knudsen number L = length M = Mach number M D = disk mass m= mass of the gas molecule n i = particle number density P i = incident pressure Re D = Reynolds number based on diameter r o = disk outer radius r i = shaft diameter T i = incident temperature T = torque T = nondimensional torque V = velocity α = angular deceleration γ = specific heat ratio ε = experimental uncertainty λ = mean free path ρ g = gas density σ n = normal momentum accommodation coefficient σ t = tangential momentum accommodation coefficient ω = frequency