Unsteady motion of a slightly rarefied gas caused by a plate oscillating in its normal direction
Unsteady motion of a slightly rarefied gas caused by a plate oscillating in its normal direction
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DOI：
10.1103/physrevfluids.2.013402
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发表时间：
2017-01
期刊：
影响因子：
--
通讯作者：
K. Aoki;S. Kosuge;T. Fujiwara;T. Goudon
中科院分区：
文献类型：
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作者：
K. Aoki;S. Kosuge;T. Fujiwara;T. Goudon
本文研究了稀薄气体在两平行平板间的非定常运动，当其中一个平板沿其法向作简谐振动时，小Knudsen数采用可压缩Navier-Stokes方程，系统地推导了相应的温度跃变条件。在正确的边界条件下，对方程组进行数值求解，得到非定常流场。特别是，时间周期的解决方案建立在以后的时间进行了详细研究，它表明，一个周期的平均振荡部分的动量和能量从振荡板转移到休息一个采取非零值的线性理论相反。这证实了基于Bhatnagar-Gross-Krook模型的Boltzmann方程在中等Knudsen数下的数值结果[T. Tsuji和K.青木，微流体。纳米流体16，1033（2014）]。它还表明，气体的时间周期运动指数快速的时间。
Unsteady motion of a rarefied gas between two parallel plates caused when one of the plates starts a harmonic oscillation in its normal direction is investigated under a slightly rarefied condition, i.e., for small Knudsen numbers. The compressible Navier-Stokes equations are employed and their appropriate temperature jump condition is derived systematically. The equations with the correct boundary conditions are solved numerically to give the unsteady flow field. In particular, the time-periodic solution established at later times is investigated in detail and it is shown that the one-period average of the oscillating part of the momentum and that of the energy transferred from the oscillating plate to the resting one take nonzero values in contrast to the linear theory. This confirms the numerical result based on the Bhatnagar-Gross-Krook model of the Boltzmann equation for intermediate Knudsen numbers [T. Tsuji and K. Aoki, Microfluid. Nanofluid. 16, 1033 (2014)]. It is also shown that the gas approaches the time-periodic motion exponentially fast in time.