Flow-Control Mechanisms Associated with a Circular Cylinder with a Normal Slit

本論文係以Ansys/Fluent分析當雷諾數(Re)為200時，圓柱開縫處、邊界層、周圍流場，以及尾流之結構變化；並針對具往復振盪運動之間隙流進行理論分析。間距比率(S/D)範圍從0.03到0.3，許多關鍵結果簡述如下。在圓柱下游的卡門渦列在圓柱開縫通道上下端開口處誘發具有異相位的週期性壓力差，藉以驅使開縫間隙中流體以零淨通量形式進行週期性噴出/吸入。間隙流的噴出/吸入可視為對邊界層的週期性擾動，其效果明顯減緩了開縫出口近壁區域的黏滯阻尼，並延緩了開縫圓柱後表面的邊界層流分離，進而減少了尾流的渦漩成形長度。隨著間距比率的變化，間隙流與尾流渦列之頻率與振幅響應，僅有輕度相位偏移，清楚證明主要鎖定的特性，但是此鎖定現象僅發生於高於自然溢散頻率的範圍。本研究結果指出:當雷諾數為200時，最佳間距比率為S/D = 0.21。另外，針對具往復振盪之間隙流進行理論分析發現:間距比率、司特勞克數(St)以及雷諾數等參數與無因次參數η具有特定關係。當應用在渦流流量計之設計時，雷諾數介於2×〖10〗^2與8.5×〖10〗^4之間，建議η值在0.97至20範圍之內。每個雷諾數值對應唯一的η值，其最佳值ηopt可經由實驗量測或與數值模擬獲得。一旦決定了設計階段ηopt值，特定雷諾數之最佳間距比率就可準確地估算出來。Flow simulation around circular cylinder with a normal slit at Reynolds number (Re) 200 is conducted using Ansys/Fluent, and the theoretical analysis on an oscillatory slit flow is also presented. The slit ratio (S/D) ranges from 0.03 to 0.3. Some critical outcomes are outlined. The oscillatory slit flow is driven by alternate variations of the pressure difference between two slit openings (or exits), in form of periodic blowing/suction with zero net mass flux (ZNMF). Blowing/suction is regarded as the periodic perturbation to the boundary layer-flow to delay the flow separation along the rear surface and reduce the formation length of the Kármán vortex street. For all slit ratios studied, the frequency and amplitude responses, as well as the slight phase shift clearly demonstrate the primary lock-on of the wake. Nevertheless the one-sided lock-on frequency range lies only within f_a⁄(f_so>1). The results indicate that the optimal S/D is limited to S⁄D=0.21 at Re = 200. When applied to the novel vortex flowmeter, the non-dimensional parameter η can be related to S/D, Strouhal number (St) and Re. In the design stage, the range 0.97<η<20 is suggested for Re=2×〖10〗^2~8.5×〖10〗^4. The optimal value η_opt can be obtained by experiments and simulation, and the optimal S/D can be estimated for a fixed applied Re at the design stage.聲明(Declaration) i 摘要 ii Abstract iii 要點(Highlights) iv 致謝(Acknowledgements) v 目錄(Contents) vi 圖目錄(List of Figures) ix 表目錄(List of Tables) xvii 符號表(Notation) xviii Chapter 1. Introduction 1 1-1 Motivation 1 1-2 Literature Review 1 1-3 Unresolved Issues and Proposal 5 Chapter 2. Analysis and Simulation of the Slit Cylinder Flow 9 2-1 Dimensional Analysis 9 2-2 Simulation Methodology 10 2-2-1 Governing Equations and Parameters 10 2-2-2 Flow Domain and Boundary Conditions 11 2-2-3 Validation of CFD Results 12 Chapter 3. Slit Flow Characteristics 19 3-1 Flow Characteristics at Slit Exit 20 3-2 Flow Flux through Slit 22 3-3 Driving Source and Volume Flux at Slit Opening 24 3-4 Control Volume Analysis 25 Chapter 4. Evolution of the Boundary-Layer Flow 45 4-1 Phase-Locked Boundary-Layer Flow Characteristics 45 4-2 Incipience of Separation and Reattachment of the Boundary-Layer Flow 47 4-3 Mean Location of Boundary-Layer Separation and Vortex Formation Length 49 Chapter 5. Primary Lock-On of the Wake 63 5-1 Frequency and Amplitude Responses within fa/fso>1 63 5-2 Phase Shift between Flow Structures of Various S/D 65 5-3 Scenarios Leading to Primary Lock-On 66 Chapter 6. A Link to the Design of Vortex Flowmeter with Slit Cylinder 75 6-1 Analytical Solution for Oscillatory Plane Poiseuille Flow 75 6-2 Cyclical Velocity Profiles 79 6-3 Relationship between Pressure Gradient, Wall Shear Stress and Volume Flux 81 6-3-1 Driving Pressure Gradient and Wall Shear Stress 81 6-3-2 Driving Pressure Gradient and Volume Flux 83 6-4 Optimal Slit Width of the Vortex Flowmeter 84 Chapter 7. Conclusions and Future Work 100 7-1 Concluding Remarks 100 7-2 Further Work 101 7-2-1 Change of Wake Flow due to Periodic Forcing 101 7-2-2 Oscillatory Plane Poiseuille Viscometer 104 Reference 115 Appendices 121 A. Dimensional analysis of flow around the circular cylinder with a normal slit 121 B. Phase Shift between Pressure Gradient and Volume Flux 124 C. Phase Shift between Pressure Gradient and Wall Shear Stress 129 D. Forces Acting upon the Control Surfaces 13