探討紊流結構物隨時間空間變化對於紊流相關物理特性之影響

Characterization of Turbulent Flow Statistics under the Spatial-temporal Influence of Ejection and Sweep Events in Wall-bounded Turbulent Flows

吳冠廷(Kuan-Ting Wu)

指導教授 ： 蔡宛珊

國立臺灣大學/工學院/土木工程學研究所/碩士(2020年)

https://doi.org/10.6342/NTU202003771

摘要

由於紊流邊界層存在著相干結構物(coherent structures),而這些結構物會影響在紊流邊界層中顆粒的運動。但大部分的研究都僅知道流場中的粒子運動會受這些結構物影響的概念，卻無法瞭解這些結構物造成的確切影響程度。因此，本研究試圖從流體粒子的觀點觀察流場結構物對其之影響。此外，我們試圖將受流場結構物影響與不受其所影響之紊流統計分開，以探討是否存在差異性，進而連結到流體粒子在紊流中的行為。
而在過去的幾十年中，大量研究人員證明，流體結構物中尤其是sweep和ejection事件在湍流統計中都扮演著舉足輕重的角色。因此，在我們的研究中，我們專注於在這兩種結構的影響下對紊流中流體顆粒的表現。那麼，必須先定義可以從紊流中清楚界定sweep和 ejection事件的標準流程。
此外， Meinhart Adrian (1995) 證實紊流邊界層可以分成幾個區域，其內部的沿流向速度大致是均勻的。此後，de Silva等（2017）首先提供了一種方法，可以用來定位均勻動量區域（UMZ），並進一步揭示了在UMZ邊緣附近傾向於出現sweep和ejection事件的情況。基於此現象，我們進而考慮了均勻動量帶邊緣對sweep和ejection事件的影響。藉由引入UMZ邊緣的影響以及辨別流場結構物的評判標準後，我們可獲得這兩種結構的時空特徵的資訊，使紊流中流體粒子運動特性的模擬結果將更加準確。
在我們初步了解sweep和ejection事件的物理特徵之後，這些知識可運用於我們的隨機模型中，以預測瞬時速度場。受Tsai ＆ Huang（2019）的啟發，他們提出了一種基於布朗運動形式的隨機模型，主要是試圖建立紊流中流場結構物與懸浮泥沙顆粒運動之間的聯繫。然而，與他們的模型相比，本研究雖然著重在流場結構物對於流體粒子的表現，並沒有研究懸浮泥沙之運移，但我們進一步取得了sweep和ejection事件的時間與空間的分佈。我們並非透過分布擬合進行模擬得知sweep和ejection事件的物理特質，而是直接從JHU數據庫（JHTDB）提供的DNS數據中提取我們所需的資訊。
然而，基於速度波動存在不對稱行為，而一般布朗運動無法很好地預測。因此，我們在提出的模型中引入了幾何布朗運動，該幾何布朗運動被廣泛用作股票價格的模型。在本研究中，從DNS數據提取目標資訊以捕獲sweep和ejection事件的物理特質開始，我們開發了一種基於幾何布朗運動的替代方法來預測速度場，捕獲速度波動的不對稱行為並以流體粒子的觀點，預測整體流場的統計趨勢。

關鍵字

紊流模擬 ； 紊流 ； 條件速度分解 ； 隨機模型 ； 幾何布朗運動

並列摘要

The motion of suspended sediment particles very close to flow particle because of its diameter is sufficiently small. Therefore, if the information of turbulent statistics can be obtained, the information of suspended sediment particles can be extended. For example, the velocity of suspended sediment particles can be treated as the superposition of flow velocity and sediment particle settling velocity. Therefore, before to investigate the statistics of suspended sediment particle, the physics in turbulent fluids should be clarified. This study provides the connection between simulated sediment particle statistics and the flow velocity whose fluctuation will be affected by the presence of coherent structures in wall-bounded turbulent flow.
Over the last decades, many investigators have demonstrated that turbulent boundary layers are populated by a hierarchy of recurrent structures, normally referred to as the coherent structures. Based on our analysis, there is a difference between the statistics with the influence of coherent structures and without the influence of them. Thus, it is desirable to gain a better understanding of the spatial-temporal characteristics of coherent structures and their impact on fluid particles. Furthermore, the ejection and sweep events play an important role in turbulent statistics and suspended sediment particles movements confirmed by Noguchi Nezu (2009). Therefore, this study focuses on the characterizations of flow particles under the influence of these two structures so that the research for suspended sediment particle movements can be executed in the future.
Meinhart Adrian (1995) first highlighted the existence of UMZ, which affects the spatial distribution of LSMs. After that, de Silva et al. (2017) began with a description of a detection criterion that was utilized previously to locate uniform momentum zones (UMZ). They further revealed a scenario of ejection and sweep events tend to present near the UMZ edges. Based on this observation, we also consider the effect of edges of the uniform momentum zone on the presence of ejection and sweep events. Comprehensively, we believe that if more information on spatial and temporal features of these two structures can be incorporate into the particle tracking model, the simulation of fluid particle movement can be more accurate.
In this study, detection of the existence of UMZ is the preprocess of identifying the coherent structures. After the edges of UMZ are determined, the identification procedure of ejection and sweep events from turbulent flow data should be defined. As such, an integrated criterion of distinguishing ejection and sweep events is proposed. Based on the integrated criterion, the physical characterizations of coherent structures from experimental data can be obtained.
Accounting for the interaction between the spatial distribution of coherent structures and the existence of UMZ in wall-bounded turbulence for the prediction of fluid and sediment particle movement is critical. Therefore, based on the knowledge of coherent structures, this study can further focuses on the influence of coherent structures on fluid particles and separates the statistics of turbulence affected by the coherent structures from those unaffected.
After initially understanding the physical features of ejection and sweep events, this knowledge should be applied to proposed stochastic model to predict the instantaneous fluid velocity field in this field. Inspired by Tsai Huang (2019) who proposed a stochastic model whose form is based on Brownian motion, this study further improves the spatial distribution of ejection and sweep events, especially in the wall-normal direction. Different from their work, this study places more attention on utilizing a stochastic model to construct the whole fluid velocity field. Instead of sampling the suggested distribution, this study directly extracts the information from the DNS data provided by JHU Databases (JHTDB) using multiple criteria. Additionally, since the streamwise velocity fluctuation exhibits an asymmetric behavior in which Brownian motion cannot reproduce very well, this study introduces the Geometric Brownian motion, which is widely utilized as modeling the stock price, in our proposed model to solve this dilemma and make the simulation closer to reality.
In this study, starting from extracting the targeted information from DNS data to capturing the properties of ejection and sweep events, this study has developed an alternative approach based on Geometric Brownian motion to predict the fluid velocity field and capture the asymmetric behavior of velocity fluctuation. Besides, this study provides the preliminary idea of the linkage between spatial-temporal distribution of coherent structures and the flow velocity fluctuation.

並列關鍵字

turbulence simulation ； turbulent flows ； Conditional velocity decomposition ； stochastic model ； Geometric Brownian motion

參考文獻

Adrian, R., Christensen, K. Liu, Z.-C., 2000, "Analysis and interpretation of instantaneous turbulent velocity fields," Experiments in fluids, 29(3), pp. 275-290.

Adrian, R. J. Marusic, I., 2012, "Coherent structures in flow over hydraulic engineering surfaces," Journal of Hydraulic Research, 50(5), pp. 451-464.

Adrian, R. J., Meinhart, C. D. Tomkins, C. D., 2000, "Vortex organization in the outer region of the turbulent boundary layer," Journal of fluid Mechanics, 422, pp. 1-54.

Agostini, L. Leschziner, M. A., 2014, "On the influence of outer large-scale structures on near-wall turbulence in channel flow," Physics of Fluids, 26(7).

Ancey, C., Davison, A., Böhm, T., Jodeau, M. Frey, P., 2008, "Entrainment and motion of coarse particles in a shallow water stream down a steep slope," Journal of Fluid Mechanics, 595, pp. 83-114.