High-order thermal effects in oscillatory couette flow of a rarefied gas

Yaron Ben-Ami, Avshalom Manela

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We study the response of a rarefied gas in a slab to the motion of its boundaries in the tangential direction. In difference from previous investigations, we consider boundaries displacements at nonsmall Mach (Ma) numbers, coupling the dynamic and thermodynamic gas states, and deviating the system from its low-velocity isothermal condition. The problem is studied in the entire range of gas rarefaction rates, combining limit case ballistic- and continuum-flow analyses with direct simulation Monte Carlo computations. A nonlinear solution is derived in the ballistic regime for arbitrary velocity profiles and amplitudes. At near-continuum conditions, a slip-flow time-periodic solution is obtained for the case of oscillatory boundary motion, by expanding the flow field in an asymptotic Mach power series. The effect of replacing between isothermal and adiabatic surfaces is examined. The results indicate that, at all Knudsen (Kn) numbers, the thermodynamic fields and normal velocity component are dominated by double-frequency (and descending higher-order even-frequency harmonic) time dependence, in difference from the fundamental-frequency time dependence dominating the tangential gas velocity. At continuum-limit conditions, this stems from the quadratic viscous dissipation term (negligible at low-Mach conditions), coupling the square of the tangential velocity gradient as a forcing term. System nonlinearity also results in an unsteady normal force acting on the boundaries, overcoming the tangential force with increasing Ma. In marked difference from the latter, the normal force either decreases with Kn, or, at sufficiently small actuation frequencies, varies nonmonotonically with Kn, reaching a maximum at some intermediate rarefaction conditions.

Original languageEnglish
Title of host publication59th Israel Annual Conference on Aerospace Sciences, IACAS 2019
Pages236-254
Number of pages19
ISBN (Electronic)9781510882782
StatePublished - 2019
Event59th Israel Annual Conference on Aerospace Sciences, IACAS 2019 - Tel-Aviv and Haifa, Israel
Duration: 6 Mar 20197 Mar 2019

Publication series

Name59th Israel Annual Conference on Aerospace Sciences, IACAS 2019

Conference

Conference59th Israel Annual Conference on Aerospace Sciences, IACAS 2019
Country/TerritoryIsrael
CityTel-Aviv and Haifa
Period6/03/197/03/19

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering

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