Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number
Flow past a sphere with an oscillation in the free-stream velocity and unsteady drag at finite Reynolds number
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DOI：
10.1017/s0022112092003434
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发表时间：
1992-04
影响因子：
3.7
通讯作者：
R. Mei;R. Adrian
中科院分区：
文献类型：
--
作者：
R. Mei;R. Adrian
考虑在小雷诺数Re下自由流速度波动较小的静止球体上的非定常流。在St [Lt] Re [Lt] 1的限制下，得到了非常小频率ω下非定常流的频率相关（或加速度相关）部分的匹配渐近解，其中St为Strouhal数。发现非定常阻力的加速度相关部分与St ~ ω成正比，而不是由Stokes解预测的ω 1 / 2相关。因此，即使雷诺数很小，巴塞特历史力的表达式在大时间内也是不正确的。本文的结果与Mei， Lawrence & Adrian（1991）对相同小雷诺数的非定常流用有限差分法的数值结果比较好。利用因果关系原理，结合小Re时的解析结果、低频时有限Re时的数值结果和高频时Stokes的结果，提出了历史力在时域上的修正表达式。通过傅里叶变换与任意频率下的有限差分结果的比较证实了这一点。修正的历史力有一个积分核，衰减为t−2，而不是t 1 / 2，在小和有限雷诺数的大时间。
Unsteady flow over a stationary sphere with a small fluctuation in the free-stream velocity is considered at small Reynolds number, Re. A matched asymptotic solution is obtained for the frequency-dependent (or the acceleration-dependent) part of the unsteady flow at very small frequency, ω, under the restriction St [Lt ] Re [Lt ] 1, where St is the Strouhal number. The acceleration-dependent part of the unsteady drag is found to be proportional to St ∼ ω instead of the ω½ dependence predicted by Stokes’ solution. Consequently, the expression for the Basset history force is incorrect for large time even for very small Reynolds numbers. Present results compare well with the previous numerical results of Mei, Lawrence & Adrian (1991) using a finite-difference method for the same unsteady flow at small Reynolds number. Using the principle of causality, the present analytical results at small Re, the numerical results at finite Re for low frequency, and Stokes’ results for high frequency, a modified expression for the history force is proposed in the time domain. It is confirmed by comparing with the finite-difference results at arbitrary frequency through Fourier transformation. The modified history force has an integration kernel that decays as t−2, instead of t½, at large time for both small and finite Reynolds numbers.