實驗方式產生之均勻等向性紊流場及其於兩相流之應用

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楊自森(Tzu-Sen Yang) 查詢紙本館藏

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論文名稱

實驗方式產生之均勻等向性紊流場及其於兩相流之應用
(Laboratory Isotropic Turbulence and Its Applications to Two-Phase Flows)

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摘要(中)

摘要
本論文的重點是利用實驗方式產生近似均勻等向性紊流場，並利用此流場進行兩相流之關連性探討。本研究旨於提出全面性與系統化的分析方法，藉以瞭解紊流及兩相流間之時、空關連性。實驗是透過一液態垂直振動網柵紊流場以及十字型氣態紊流場，藉以產生低至中等雷諾數之零平均速度近似均勻等向性紊流場，其中泰勒尺度的雷諾數變化範圍控制在20至200之間。此外，為了鑑別具多層次尺度結構的紊流場之時、空特性，結合高解析度、高速之數位質點影像測速技術，以及小波轉換的訊號診測分析方法，便可在不做任何假設條件下，同時獲得隨時間演變及空間變化的流場資訊，進而進行完整且詳細地紊流小尺度運動學參數之計算。
本研究的第一個目標是界定紊流場於消散區以及慣性區範圍內的時、空間歇性。在消散區範圍內，研究發現高強度的渦度場，就空間分佈的幾何特性而言其所構成集中的小尺度結構尺寸約為紊流場Kolmogorov長度尺度的十倍：然而就時間演變來說，小尺度結構的變化約為Kolmogorov的時間尺度。此結果將有助於探討重質點下沈速度以及預混火焰等兩相紊流研究時，提供重要的參數條件。在慣性區範圍內，利用延伸自相似的標度律方法，研究發現各個方向的時、空標度律指數均相同，亦證明現行的紊流場其於標度範圍內的確存在均勻等向的特性。本研究的另一目標是重質點於近似均勻等向性紊流場中自重下沈現象的行為模式探討。研究結果顯示紊流場的確可以增加質點的下沈速度，使之大於未受紊流作用時的終端速度；此外，下沈現象最顯著的條件是當質點的反應時間與紊流場Kolmogorov時間尺度一致，且質點的終端速度與紊流擾動速度於相同的量級時發生。本研究並首次進行重質點對近似均勻等向性紊流場能量頻譜的耦合及調製效應的研究與比較，結果顯示不論質點的反應時間大於、等於或小於Kolmogorov的時間尺度，各方向的紊流場能量頻譜均會發生增益的現象，亦即高於未受重質點作用下的能量頻譜分佈：另一方面，此頻譜的變化也將導致荷載重質點之紊流場間歇性程度的提升，而最大的增幅均在質點的反應時間與紊流場Kolmogorov時間尺度一致的狀況下發生，主要因素是在此條件下質點濃度場會出現最強的偏好性聚集現象，並且受到質點下沈速度的增加將致使重力方向的間歇性程度高於其他方向的變化。

摘要(英)

This thesis focuses on the topic of laboratory isotropic turbulence and its applications to two-phase flows. The aim of this study is to provide a comprehensive and systematic analysis of what and how the spatio-temporal relationships between turbulence and two-phase flows. Experiments were conducted in an aqueous vibrating-grids-turbulence (VGT) and a gas phase near-isotropic turbulence to generate low to moderate Reynolds number turbulence with zero-mean velocity, where the Reynolds number, Rel, based on the Taylor microscale λ can be varied from 20 to 200 for the present study. In an effort to ascertain both the spatial and temporal properties of turbulence that are related to the large hierarchy of scales involved, a high-resolution, high-speed digital particle image velocimetry (DPIV) technique, together with the wavelet analyses, is developed so that the detailed three-dimensional spatio-temporal (x-y-t) measurements of the kinematic aspects of small-scale turbulent structures can be obtained simultaneously without any assumption and hypothesis.
The first objective of the present work is to identify the turbulent spatiotemporal intermittency in the dissipation and inertial ranges. We found that the characteristic spatial and temporal intermittent scales of intense vorticity structures in the dissipation range occur around 10 h and tk, where h and tk are the Kolmogorov length and time scales, respectively. These results are useful for further study of particle settling and/or premixed flames interacting with stationary near-isotropic turbulence. On the other hand, using the extended self-similarity (ESS) scaling, we found that in the inertial range the spatiotemporal scaling exponents for both high-order longitudinal and transverse velocity structure functions are identical. The second objective is to investigate the solid particle settling behaviours in a stationary homogeneous isotropic turbulence. The mean settling velocity, Vs, of solid particles was measured using both particle tracking velocimetry (PTV) in the VGT system and DPIV in the gaseous system. For the VGT system, we found that Vs > Vt and (Vs - Vt)/Vt reaches its maximum of about 7 % around St » 1, even when the particle Reynolds number Rep is as large as 25 at which Vt/vk » 10, where the Stokes number St = tp/tk, tp is the particle’s relaxation time, vk is the Kolmogorov velocity scale, and Vt is the particle’s terminal velocity. On the other hand, for the gaseous system the mean settling velocity reaches its maximum of 0.13 u¢ when St 1.0 and Vt/u¢ 0.5 for Rep ≤ 1 and Reλ = 120. In addition, non-uniform particle concentration fields (preferential accumulation) are observed and most significant when St 1.0. It is also found that the particle preferential accumulation is highly related to the scaling of the small intense vorticity structures; the particle cluster thickness is nearly the spacing between the small intense vorticity structures, and the time passage of the clustered particle is tk. By comparing the average wavelet spectra between unladen (neutral particle) and laden (heavy particle) turbulent flows at a fixed Rel, turbulence augmentation of energy spectra in the gravitational direction is found over the entire frequency domain, whereas in the transverse direction augmentation occurs only at higher frequencies beyond the Taylor microscale. Finally, a simple physical model based on the phenomenology of the energy balance concept for turbulence generation and dissipation by the descending heavy particles is proposed to predict the value of ul’/u’, where ul’ and u’ are the r.m.s. fluctuating velocity of laden and unladen turbulent flows, respectively. The predicted values agree reasonably well with the experimental results. This suggests that the assumptions based on the scaling of the small intense vorticity structures and the slip velocity at which the maximum probability distribution occurs are adequate, especially when St 1.0 for the present study.

關鍵字(中)

★ 均勻等向性紊流場
★ 兩相流

關鍵字(英)

★ isotropic turbulence
★ two-phase flows

論文目次

Page
Abstract ii
Acknowledgement iv
Table of Contents v
List of Tables viii
List of Figures ix
Nomenclature xvii
I Introduction and Background ……………………………………………… 1
Chapter 1 Introduction………………….……………………………………… 2
1.1 Why Study Homogeneous Isotropic Turbulence? ……...…………………… 2
1.2 Why Study Two-Phase Flows? …………………………...………………… 4
1.3 Thesis Outline……………………………………………………………..… 5
Chapter 2 Review of Relevant Literature………………………………..… 8
2.1 Selected Topics in Homogeneous Isotropic Turbulence………………….…..8
2.1.1 The Theory of Kolmogorov in 1941…………………………………....8
2.1.2 Cascade Models of Intermittency 11
2.1.3 The Small-Scale Structure of Turbulence 16
2.1.4 Evaluations of the Taylor Hypothesis 17
2.1.5 Summary of the Previous Work on Homogeneous Isotropic
Turbulence 20
2.2 Selected Topics in Particle Settling Problems 22
2.2.1 Particle Behavior in Dilute System 22
2.2.2 Settling Velocity of Heavy Particles in Turbulence 24
2.2.3 Particle-Fluid Two-Way Coupling Interaction 27
2.2.4 Particle-Laden Two-Phase Turbulence Modeling 28
2.3 Selected Topics in Premixed Turbulent Combustion 29
2.3.1 Flamelet Models 29
2.3.2 Flame Surface Density Modeling 30
2.4 Selected Topics in Laser Diagnostics 32
2.4.1 Planer Laser-Induce Fluorescence Technique 32
2.4.2 Optical Velocimetry for Turbulent Flow Measurements 33
II Experimental Studies 36
Chapter 3 Experimental Apparatus and Conditions 37
3.1 Vibrating-Grids Turbulence 37
3.1.1 Flow Facility 37
3.1.2 Experimental Conditions 37
(a) Flow Operating Conditions and Turbulence Properties 38
(b) PLIF Imaging System 40
(c) Particle Seeding System 40
(d) Choice of Heavy Particles and Operating Conditions 41
3.2 Cruciform Gaseous Chamber Turbulence 43
3.2.1 Flow Facility 44
3.2.2 Experimental Conditions 44
(a) Flow Operating Conditions and Turbulence Properties 44
(b) Particle Seeding System 46
(c) Choice of Heavy Particles and Operating Conditions 47
Chapter 4 Experimental Diagnostics 49
4.1 Laser Diagnostics 49
4.1.1 PLIF System 49
4.1.2 PTV System 51
4.1.3 DPIV and DPIA System 53
(a) Hardware overview 53
(b) DPIV Analysis Algorithm 53
(c) DPIV Accuracy 57
(d) DPIA Analysis Algorithm 58
4.2 Wavelet Transforms and Mutiresolution Signal Analysis 61
4.2.1 The Continuous Morlet Wavelet Transform 62
(a) Detection and Characterization of Singularities 62
(b) The Wavelet Energy Spectra 64
(c) The Level of Intermittency 65
4.2.2 The Discrete Haar Wavelet Transform 66
(a) Wavelet-based Velocity Structure Function 66
(b) Wavelet-based Extended Self Similarity 66
Chapter 5 Results: Homogeneous Isotropic Turbulence 68
5.1 Wavelet Energy Spectrum 68
5.2 The Intense Vorticity Structures in Turbulence 69
5.3 The Quantitative Analysis of Spatiotemporal Intermittency 72
5.4 The Distribution of Velocity Increments 76
5.5 The Spatiotemporal Scaling Properties 77
5.6 Assessment of the Taylor’s Hypothesis 83
5.7 Discussion 86
Chapter 6 Results: Applications to Two-Phase Flows 89
6.1 Vibrating Grids Turbulence 89
6.1.1 Flame Surface Density Modeling 89
(a) Flame surface densities 89
(b) Curvature term 91
6.1.2 Particle Settling Behavior 92
(a) Settling rates for heavy particles 93
(b) Temporal response of heavy particles 96
6.2 Cruciform Gaseous Turbulence 99
6.2.1 Concentration Distribution of Heavy Particles 99
6.2.2 Settling Rates for Heavy Particles 104
6.2.3 Particle-Fluid Two-Way Coupling 109
III Concluding Remarks 114
Chapter 7 Conclusions 115
7.1 Conclusions 115
7.2 Recommendations for Future Work 122
Bibliography 125
Appendix 202
Scaling Exponents of Energy Dissipation Rate 202

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指導教授

施聖洋(Shenqyang Shy)

審核日期

2003-7-8

推文