湍流管道流動的特徵：實驗和直接數值模擬

管道湍流常見於許多工程應用中，深入研究管道湍流對於預測傳熱，混合，以及界面摩擦阻力至關重要。以前的研究主要集中在較大雷諾數下的純壓力驅動（Poiseuille）的流動，而對於低雷諾數下的流動特性尚不清楚。少量的有關Poiseuille流動DNS數值模擬結果表明，在非圓形管道中，當雷諾數接近於流體轉化為湍流的臨界值時，有一個有趣的現象。例如，在方形橫截面管道中，觀察到流場在以不同的二次流動模式為特徵的兩個狀態之間切換，這種現像很可能對傳熱和傳質具有重大的影響。然而這個發現卻從未被實驗驗證過。管道湍流另一重要但尚未研究清楚的領域是減阻（DR）。例如，已經發現即使較小濃度的長鏈柔性聚合物，也可以改變管道中的湍流，導致界面摩擦大幅度減小。然而，至今仍沒有研究將減阻程度和可測量的流體性質聯繫起來。本研究通過實驗和模擬兩種方法，在許多不同的雷諾數範圍內，對牛頓流體和非牛頓流體在管道中的湍流流動進行了研究。管道的形狀包括方形，矩形和圓形。首先確定了純壓力驅動流動在方形管道內開始向湍流轉化的最小雷諾數，並且確定了Coriolis 效應對低埃克曼數流動的重要性。隨後通過實驗獲得在較低雷諾數情況下的平均流體性質和湍流數據。 Uhlmann 等人 (2007)用DNS方法預測了方形管道中湍流的流體場在兩種狀態間相互交換的過程。在該研究中，通過展示在距離管壁一定距離內的平行於中軸的速度的概率密度函數具有雙峰特點，從而驗證了Uhlmann 等人 (2007)的DNS結果。平行於中軸速度和垂直管壁速度的聯合概率密度函數也具有兩個峰，這兩個峰分別對應流體的兩種狀態。通過將泰勒的冷凍湍流假說應用在數據中，我們發現在沿著管道長度方向上也存在空間轉換。本研究通過對零淨通量的管壁驅動流體（(Couette)在方形管道中進行DNS模擬，結果顯示這個過程也存在兩種狀態。這說明這種現像不只存在於Poiseuille流動當中。研究發現，二次級流動與近管壁處流體的噴射和掃向壁面滑行運動有緊密聯繫。而且垂直管壁對流體流動存在穩定化作用，因此其對應的湍流雷諾數比在平面Couette 流動中的要高很多。為了對方形管道中的Couette-Poiseuille流動進行實驗研究，本研究設計並搭建了一個管壁可以移動的新的測試設備。通過在層流區域使用激光多普勒測速儀（LDV）測量流速分佈發現，採用這個設備可以對已經發展成熟的分析結果進行精準重複。本研究給出了將來採用這個新的測試設備對湍流進行研究的建議。最後，本研究重新探索了聚合物減阻問題。首次得到了一個可以直接從聚合物溶液的單個可測量的材料特性定量預測減阻程度的相關性，該材料特性與幾何形狀，濃度及其他實驗變量無關。

關鍵字

湍流；管流

並列摘要

Turbulent duct flows are encountered in a wide range of engineering applications; a fundamental physical understanding of such flows is thus very important for making predictions about heat transfer, mixing and skin friction drag. Previous studies have focused mainly on the purely-pressure driven (Poiseuille) case at relatively large Reynolds numbers (Re), hence the flow characteristics at low Re are not well understood. Limited Poiseuille flow direct numerical simulation (DNS) data show that in non-circular ducts, there exists an interesting phenomenon at Re close to transition to turbulence. Specifically in ducts of square cross-section, the flow field is observed to switch between two states characterised by different secondary flow patterns, thus potentially having serious implications for heat and mass transport. This finding has never been verified experimentally. Another important area in the study of turbulent duct flows, which is yet to be fully understood, is the drag reduction (DR) obtained by seeding with long-chain flexible polymers having high molecular weights. These are known to modify the turbulence field in duct flows when added even at minute concentrations, causing a massive decrease in skin friction; yet it has never been possible to relate the degree of DR to a measurable fluid property. In this study, turbulent duct flows of Newtonian and non-Newtonian fluids over a wide range of Reynolds numbers are investigated both experimentally and numerically. The geometries considered include a square duct, rectangular channel and circular pipe. In purely pressure-driven flow in a square duct, the onset criteria for transition to turbulence is first examined. In so doing, the potential importance of Coriolis effects on this process for low-Ekman-number flows is highlighted. Experimental data on the mean flow properties and turbulence statistics at relatively low Reynolds numbers are then obtained. The alternation of the flow field between two states in the "marginal turbulence" regime in a square duct, originally predicted by the DNS of Uhlmann et al. (2007), is confirmed by bimodal probability density functions of streamwise velocity at certain distances from the wall as well as joint probability density functions of streamwise and wall-normal velocities which feature two peaks highlighting the two states. By applying Taylor's hypothesis of frozen turbulence to the data, it is shown that there is also a spatial switching along the length of the duct. Similarly, direct numerical simulations of zero-net-flux wall-driven (Couette) flow in a square duct reveal an alternation between two states, thus indicating that the phenomenon is not unique to Poiseuille flows. The secondary motions are observed to be closely related to the near-wall ejection and sweep events. Furthermore, the side walls are found to have a stabilising effect on the flow, the critical Reynolds number for transition being much higher than that in plane Couette flow. For an experimental investigation of square duct Couette-Poiseuille flows, a new test section with one moving wall has been designed and constructed. Preliminary Laser Doppler Velocity (LDV) measurements of the velocity profiles in the laminar regime show that the fully developed analytical solution can be accurately reproduced in the facility. Suggestions for future turbulent flow studies in the new test-section have been given. Finally, the polymer DR problem has been revisited, and for the first time, a correlation which allows for quantitative predictions of DR from the knowledge of a single measurable material property of a polymer solution, independent of the geometry, concentration, and other experimental variables is obtained.