Measurement of Continuum Breakdown During Disk Spindown in Low-Pressure Air Tathagata Acharya, * Jordan Falgoust, † and Michael James Martin ‡ Louisiana State University, Baton Rouge, Louisiana 70803 and Richard Eric Rasmussen § Guidance Dynamics Corporation, Simi Valley, California 93063 DOI: 10.2514/1.T4305 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 I. Introduction V ISCOUS flows begin to experience continuum breakdown as the length scales of the flow approach the mean free path of the gas. This is quantified by the Knudsen number: Kn  λ∕L (1) where λ is the mean free path, and L is the length scale of the flow [1]. Boyd et al. defined a gradient length scale given by L  Q dQ∕dl (2) where Q is the fastest varying macroscopic quantity, and dQ∕dl is the maximum gradient within the local flowfield [2]. Q may be quantities such as velocity, density, or flow rate. Continuum breaks down as the molecular distribution function gradually diverges from the equilibrium limit. As the mean free path between two successive collisions of gas molecules approaches the length scale of the flow, the molecules do not collide often enough to maintain an equilibrium velocity distribution. This effect is quantified by an increase in the Knudsen number. In the continuum flow regime, the length scale far exceeds the mean free path and is of the order of 0.00001. At the slip flow limit, the Knudsen number is of the order of 0.01 or less. The transition flow regime is assumed to exist between Knudsen numbers 0.01 and 1. As the Knudsen number exceeds 1, the flow regime is assumed to be free molecular [1]. It may be shown that the Knudsen number is related to the Mach number M and the Reynolds number Re by combining the definitions of Mach number, Reynolds number, and the kinetic theory of gases [3]: Kn   πγ 2 r M Re (3) Because for boundary-layer flows in the laminar flow regime, the boundary-layer thickness is proportional to the square root of Presented as Paper 2012-3192 at the 43rd AIAA Thermophysics Conference, New Orleans, LA, 25–28 June 2012; received 14 October 2013; revision received 13 November 2014; accepted for publication 7 December 2014; published online 27 February 2015. Copyright © 2014 by Tathagata Acharya. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-6808/15 and $10.00 in correspondence with the CCC. *Doctoral Researcher, Mechanical Engineering. † Undergraduate Researcher, Mechanical Engineering. ‡ Assistant Professor, Mechanical Engineering. § President. 281 JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER Vol. 29, No. 2, April–June 2015 Downloaded by VIRGINIA TECH on February 20, 2016 | http://arc.aiaa.org | DOI: 10.2514/1.T4305