| 摘要: | 本研究利用數位質點影像測速儀(digital particle image velocimetry，DPIV)與小波轉換(wavelet transform)，針對著名的Taylor-Couette (TC)流場中尚未被詳細探討的無特徵紊流(featureless turbulence)，首度定量量測分析其重要的時間與空間尺度及頻譜特性。無特徵紊流乃由兩同軸內外長圓柱於特定轉速下反向旋轉而得，經Andereck et al. (1986)液態流場觀測發現沒有比內外圓柱間隙尺度更大的特徵結構存在，故稱之為無特徵紊流。Ronney團隊(1995)由雷射都普勒測速量儀(laser Doppler velocimetry，LDV)得知，液態無特徵紊流之平均速度近似零並且具有相當均勻的空間特性。本實驗首度進行氣態無特徵紊流之DPIV量測，擷取氣態流場之軸向、徑向和切線方向之時序與空間速度資訊，接著利用小波轉換分解速度尺度，進一步獲得流場之尺度、能量頻譜與間歇性特性。本研究回答下列三個問題：(1)如何辨識無特徵紊流？(2)無特徵紊流之能量生成與消散之關鍵的時空特徵尺度為何？(3)固態重粒子(密度遠大於流體)在無特徵紊流中的下沉機制為何？我們發現無特徵紊流三個維度之速度分量，其平均速度相對於其紊流強度皆可被忽略，且其瞬時速度之機率密度函數皆呈高斯分布，此氣態流場結果與Ronney團隊液態流場結果相符。任一維度之能量頻譜在慣性區(inertial range)內的遞減斜率皆呈-5/3，顯示無特徵紊流具有全展紊流(fully-developed turbulence)的基本特性。間歇性會隨著渦漩尺度變小而增強，證實無特徵紊流具有活躍的小尺度活動，且由小波分析所得之間歇性最強的尺度大小與傳統紊流理論公式所估算之最小尺度值其量級(order of magnitude)相符。在二相紊流研究中，我們採用同一條件之無特徵紊流場，搭配平均粒徑為40與60 ?m的玻璃重粒子，其Rep = VtDp/?皆小於1，故在自由落下之過程仍受線性阻力，待其達終端速度後才進入無特徵紊流場，其中Vt、Dp和?分別是重粒子之終端速度、粒徑以及流體之運動黏滯係數。相對應之Stokes數(St = ?p/?K，其中?p和?K分別是重粒子達終端速度所需的時間與流場之Kolmogorov時間尺度)為6或13的玻璃重粒子，其下沉軌跡深受流場內反向對轉之非定常渦漩對的影響，會沿著渦漩周圍呈現加速、減速或形成水平運動。重粒子之下沉速度，最高甚至可達終端速度的兩倍以上，其增幅約為流場均方根紊流強度的一半。 This study aims to measure and analyze important spatiotemporal characteristics of featureless turbulence of the well-known Taylor-Couette (TC) flow using high-speed, high-resolution digital particle image velocimetry (DPIV) and wavelet analyses. Featureless turbulence is generated by two concentric counter-rotating, at some specific rotating speeds, inner and outer long cylinders. Andereck et al. (1986) via liquid flow visualization had first noticed that no dominant large structures being larger than the annulus gap width can be observed, so they named it featureless turbulence. Ronney et al. (1995) showed that this liquid flow is nearly homogeneous across the annulus with the negligible mean velocity by laser Doppler velocimetry (LDV). DPIV measurement of gaseous featureless turbulence was first conducted here, and the radial, axial and azimuthal velocity data of this flow were acquired. By decomposing the obtained spatiotemporal velocity data by wavelet transform, the subsequent scale, energy spectrum and intermittency analyses were obtained for the analyses. Focuses are placed on the following three goals. (1) By what means can featureless turbulence be recognized? (2) What are the characteristic spatiotemporal scales relevant to energy production and dissipation of featureless turbulence? (3) Does the preferential sweeping exist for the particle settling? We found that every velocity component is of a near-Gaussian distribution with the negligible mean velocity comparative to its turbulence intensity everywhere in the flow, so that this flow is near homogeneous, consistent with the previous result (Ronney et al. 1995). Energy spectra showed a -5/3 decaying slope in the inertial subrange, proving the essential factor of fully-developed turbulence. Intermittency level was found to increase as the eddy scale decreases, validating existence of the violent small scale motion. The highest intermittency showed up at the same order of magnitude of the estimated smallest scale. In two-phase study, the settling phenomenon of heavy glass particles was observed. The glass particles that were subject to a linear drag force (Rep = VtDp/? < 1, where Vt, Dp and ? are the terminal velocity and the diameter of the heavy particle, and the kinematic viscosity of the fluid), St ≈ 6 or 13 (St = ?p/?K, where ?p and ?K are respectively the particle relaxation time and the Kolmogorov time scale), were found to response well to vortex structures in featureless turbulence, and showed a preferential sweeping along down flow side of the periphery of the strong vortex structure. An apparent change in motion of the particle due to the strong vortex pairing was observed, and in some cases the particle appeared in horizontal movement, but others the particle settling rate could be twice as the original value, about half of the turbulence intensity in raise. |
