D/h = 5 (Re = ) (fast Fourier transformation, FFT). ν.. x r 1(b). ( ). 1 N--S Gaussian (large eddy simulation, LES) U i

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1 ) 2) ( ) Re = D/h = 5. x/d = 1, 2 8 (fast Fourier transformation, FFT) 3 : St 2 = St 1 = St 3 = r/d = O35 A doi / CORRELATION SPECTRUM ANALYSIS IN THE NEAR WAKE BEHIND A DISK 1) ZHONG Wei 2) YANG Jianzhi ZHANG Xintai LIU Quan LIU Minghou (Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei , China) Abstract A large eddy simulation (LES) is conducted in the near wake behind a circular disk at Re = with the diameter-thickness ratio D/h = 5. Through fast Fourier transformation (FFT) of the fluctuating velocities at x/d = 1, 2 and 8, three characteristic frequencies are identified, with corresponding Strouhal numbers being 0.035, and It is shown that St 2 = 0.123, is the natural vortex shedding frequency, as in agreement with previous research results; St 1 = 0.035, the smaller one, may be related to the combined action of the recirculation zone s pump motion and the azimuthal rotation of the shedding location near the shear layer; St 3 = , might result from the instability of the turbulent shear layer. The correlation coefficients, the coherent spectrum and the phase spectrum are calculated between two points with different separation angles in the same axial section of r/d = 2.8. Due to the vortex shedding, the correlation coefficients fluctuate between positive and negative values in the intervals of 30 or 45 degrees. This indicates that the position of the vortex shedding is random in the azimuthal direction. Key words circular disk, near wake, large eddy simulation, correlation analysis.. [1].. Re. [2-4] ) ( , ). 2), somoby@126.com

162 2014 36... D/h = 5 (Re = 22 000) (fast Fourier transformation, FFT). ν.. x r 1(b). ( 168 80 72).

2 D/h = 5 (Re = ) (fast Fourier transformation, FFT). ν.. x r 1(b). ( ). 1 N--S Gaussian (large eddy simulation, LES) U i x i = 0 (1) U j t + U iu j x i = 1 p + ν 2 U j ρ x j x 2 i τ ij x i (2), U i p ν τ ij = U i U j U i U j. LES Smagorinsky τ ij = 2 (C SD ) 2 S S ij (3) C SD Smagorinsky S ij [6]. LES. SIMPLE. [5] Zhang [6] LES (Re = ) (Re ). (Re = ) [6]. D = 4 cm h = 8 mm 20D 10D [7], 5D 1(a). U Re = U D/ν = (a) (b) 1 2 FFT (Re = ) x/d = 1, 2 8 FFT [8] 2 x/d r/d = 0, (power spectral density, PSD). 2 log10. 3 r/d = 2.8 (r/d = 0) (r/d = 0.8). Johansson [4] m = 0. ( Re = [1] : Re = , 500,

3 Shenoy [1] (St = 0.113). ( 2) [2]. [1,7] Shenoy [1] Re = 280. Re = 280 [1]. Tomboulides [7] St = Rodriguez [9] Re = (direct numerical simulation, DNS) x/d = 3 r/d = Re = [7] ).. Re = St 2 = [3-4]. x/d = 8 r/d = Berger [2]. [9]. [1-2] 2 x/d = 2 r/d = 0.8 St 3 = [1.3, 1.7] Berger [2]. x/d = 8 r/d = 0.8, 2.8 ( 2). x/d = 1 r/d = St 3 ( 2).

4 x/d = 1, 2 8 R xy 3 5. r/d = 0 r/d = 0 r/d = 0.1 ( 3).. 3 (u, v, w, p) R θ u 3 p 180 x/d = x/d = 8 0. v, w. 180 v w x/d = , 0.05 x/d = , r/d = 0.8 ( 4) r/d = 2.8 ( 5) 3. 3 (r/d = 0.1) 4 r/d = v, w 3 W St 1 = ( ). u p θ [2-3] r/d = (r/D = 0.1) 4(r/D = 0.8) θ. 2 r/d = 2.8 St 2. r/d = u, v, w 3 St 2.

5 第 2 期钟伟等圆盘近尾迹流场相关谱分析 165 图 4 不同下游位置在剪切层附近 (r/d = 0.8) 各脉动量相关系数的周向分布图 5 不同下游位置在外尾迹 (r/d = 2.8) 各脉动量相关系数的周向分布速度脉动相关系数以 30 或 45 为周期间隔呈现有规律的正负波动表明 St1 的结构不像圆柱绕流尾迹中卡门涡街那样上下两排涡交替脱落而是随机脱落圆盘周向各个位置都可能是脱落点. 由于脱落时间不同而出现相关系数的正负波动与 Berger 等 [2] 实验观测结果一致. 3.2 相干函数考虑图 2 中只有 r/d = 2.8 处功率谱才有明显的自然脱落频率峰值因此参考信号探针固定在尾迹外 y/d = 2.8, z = 0 处而另一探针则沿 r/d = 2.8

6 ( ) 6, 7. 6 x/d = 1,2 8 θ 45, 90, γxy(f) 2 St 2 = x/d = 2 8 St 2 x/d = 1 FFT FFT St St 1. 6(a) x/d = 1 4 St , 0.31, St > , 0.00, Lee [10] θ = 90. x/d = 1 x/d = 2 8 6(b) 6(c) x/d = 8 St 2 x/d = 1 ( 6(a)) St = [0.2, 0.7]. ϕ xy (f) 7. 3 St 2 x/d = 1. 7(b) x/d = 2 2St 2 θ = St θ = θ = θ = θ 7 θ

7 x/d = 8. x/d = 2 8 ( x/d = 2 2St 1 ) θ = θ = θ = Re = FFT 3 St 2 = St 1 = [2-3] St 3 = x/d = x/d = 1 2 x/d = 8 St x/d = Shenoy AR, Kleinstreuer C. Flow over a thin circular disk at low to moderate Reynolds numbers. J Fluid Mech, 2008, 605: Berger E, Scholz D, Schumm M. Coherent vortex structures in the wake of a sphere and a circular disk at rest and under forced vibrations. Journal of Fluids and Structures, 1990, 4: Miau JJ, Leu TS, Liu TW, et al. On vortex shedding behind a circular disk. Exp. in Fluids, 1997, 23(3): Johansson PBV, George WK, Woodward SH. Proper orthogonal decomposition of an axisymmetric turbulent wake behind a disk. Phys Fluids, 2002, 14(7): (3): (Zhao Pinghui, Ye Taohong, Zhu Minming, et al. Study of the large eddy simulation of a circular jet. Journal of Engineering Thermophysics, 2012, 33(3): (in Chinese)) 6 Zhang P, Han C, Chen Y. Large eddy simulation of flows after a bluff-body: coherent structures and mixing properties. Journal of Fluids and Structures, 2013, 42: Tomboulides AG, Orszag SA. Numerical investigation of transitional and weak turbulent flow past a sphere. J Fluid Mech, 2000, 416: ,,.., 2004, 26(1): (Wang Minghao, Fu Song, Zhang Guanghua. Spectrum characteristics of turbulent natural convection between two vertical walls. Mechanics in Engineering, 2004, 26(1): (in Chinese)) 9 Rodriguez I, Borell K, Lehmkuhl D, et al. Direct numerical simulation of the flow over a sphere at Re = J Fluid Mech, 2011, 679: Lee SJ, Bearman PW. An experimental investigation of the wake structure behind a disk. Journal of Fluids and Structures, 1992, 6(4): ( : ) ( 200 ) 7,,.., 2005, 27(6): , 2002, 24(6): , 2000, 30(2): Harris TA, Kotzalas MN Wan Changsen. Analysis of Rolling Element Bearings. London: Mechanical Engineering Publication Ltd, FAG Kugelfischer AG ( : )

[1] Nielsen [2]. Richardson [3] Baldock [4] 0.22 mm 0.32 mm Richardson Zaki. [5-6] mm [7] 1 mm. [8] [9] 5 mm 50 mm [10] [11] [12] -- 40% 50%

[1] Nielsen [2]. Richardson [3] Baldock [4] 0.22 mm 0.32 mm Richardson Zaki. [5-6] mm [7] 1 mm. [8] [9] 5 mm 50 mm [10] [11] [12] -- 40% 50% 38 2 2016 4 -- 1,2, 100190, 100083 065007 -- 0.25 mm 2.0 mm d 10 = 0.044 mm 640 3 300. Richardson--Zaki,,, O359 A doi 10.6052/1000-0879-15-230 EXPERIMENTAL STUDY OF FLUID-SOLID TWO-PHASE FLOW IN A VERTICAL