平行化耦合氣體放電與氣流模擬的發展與其於含雜質常壓氦氣介電質電漿束

Abstract

本論文報告使用平行化耦合氣體放電與氣流模擬的發展與其於含雜質常壓氦氣介電質電漿束模擬應用的研究。其中氣體放電模擬採用流體模型，利用有限體積法離散所有方程式，並使用區域分解法 (domain decomposition) 及訊息傳輸介面 (message passing interface, MPI) 將程式平行化，成功的在分散式記憶體的個人電腦叢集系統中執行程式並且有效地減少運算時間。同時，本文結合前人[Hu et al., 2011]所發展的平行化可壓縮氣流場模擬程式研發出耦合式模擬運算法則進行含雜質常壓氦氣介電質電漿束模擬。電漿流體模型所需要的計算時間通常是模擬常壓介電質電漿束的瓶頸。本文提出多尺度時間法 (temporal multi-scale method, TMSM)，利用電子與重粒子的特徵時間尺度差異特性，進一步有效地縮短包含許多氣體種類的電漿流體模型所需要的計算時間。本論文所完成的工作建立了模擬真實常壓介電質電漿束應用的基礎。 論文的第一章介紹研究背景以及論文回顧，而第二章則是描述使用的數值方法與演算法。第三章使用一維的模擬結果討論雜質對於氦氣常壓介電質電漿束的影響。第四章與第五章則分別介紹二維電漿流體模型程式的發展與使用耦合式演算法模擬常壓介電質電漿束。以下將逐一描述各章的重要內容。 由於常壓氦氣介電質電漿於應用上具有其重要性，本文第三章討論使用一維流體模型模擬得到的結果。文中探討使用氣相色譜法 (gas chromatography) 所量得存在於氦氣(99.99%)內雜質對於電漿的影響，並且發現氦氣內所含的雜質對於電漿化學有顯著的改變。無論是否考慮雜質，都沒有在最大電流的瞬間觀察到電中性 (quasi-neutral) 的區域。模擬結果顯示無論氦氣內的雜質對電子密度的影響不大。然而原本He2+ 為不含雜質的氦氣電漿中最主要的離子的角色，在含雜質的氦氣電漿中被N2+ 所取代。而在不含雜質的氦氣電漿中最主要的中性氣體He2* 則被含雜質的氦氣電漿中的基態氧原子取代為最主要的中性氣體。文中亦探討不同水氣含量對於氦氣電漿的影響。結果顯示不同水氣含量的氦氣電漿電子密度差異不大。隨著水氣含量的增加，H2O+取代N2+成為氦氣電漿中最主要的離子。儘管基態氧原子依舊是最主要的中性氣體，氫原子與氫氧根 (hydroxyl) 的密度隨著水氣含量的增加而急劇增加。雖然氦氣內雜質均為少許ppm 的含量，模擬的結果顯示雜質的存在對氦氣電漿的重要性。 本文第四章使用有限體基法發展平行化二維電漿流體模型程式及其在分散式記憶體的個人電腦叢集系統上的實作。為探討模擬氦氣介電質電漿的平行效率，吾人使用各種矩陣預處理 (preconditioning) 方法 (如ASM; additive Swartz method)與矩陣迭代解法 (如GMRES; generalized minimal residual method) 針對不同型別的統御方程式進行數值實驗，測試使用最多達128顆處理器。對於網格數較多的測試問題，在使用128顆處理器的情況下幾乎可以得到線性加速的效果。最後，藉由模擬二維真實常壓介電質電漿束的問題說明所發展的程式具備處理包含複雜電漿化學反應之低溫電漿的應用。 為正確地模擬常壓介電質電漿束，本論文第五章提出耦合數值演算法結合電漿流體模型與氣體模型，並且使用兩種方法加速其計算所需的時間。背景氣體與電漿間藉由交換氣流場模擬所得到的穩態解與電漿流體模型所得到平均源項(source terms)的結果來達到結合兩模型的目的。節省整體計算時間的方法包含於電漿流體模型與氣體模型運用平行計算，以及應用於電漿流體模型的多尺度時間法。兩個模型均使用區域分解法 (domain decomposition) 及訊息傳輸介面 (MPI) 將程式平行化並執行於分散式記憶體的個人電腦叢集系統。多尺度時間法利用電子與重粒子的特徵時間尺度差異特性，於求解重粒子連續方程式的每個時間步 (time step)時，僅考慮化學反應而忽略傳輸項；而所忽略的傳輸項將在每隔一定大小的時間步數回補。在研究的範例中使用多尺度時間法模擬常壓介電質電漿可節省47%的計算時間。文中所提出的耦合數值演算法藉由模擬平板式常壓氦氣介電質電漿束證明其可行性，並且展現第200個週期所得到的結果。由結果發現各種氣體密度分布的情形與背景氣流場分佈息息相關，因此凸顯出常壓介電質電漿束的模擬考慮背景流體的重要性。 論文最後歸納本論文主要的發現，並對相關研究未來的工作方向提出建議。

The development of a hybrid algorithm of plasma fluid model (PFM) and gas flow model (GFM) for simulating the atmospheric-pressure dielectric barrier discharge jet (APDBDJ) is reported in this thesis. The gas discharge is modeled by plasma fluid model, discretized through finite-volume method, and parallelized with domain decomposition using message passing interface (MPI) and employed on distributed-memory PC cluster that reduces runtime significantly. The hybrid numerical algorithm is proposed by combining a previously developed parallelized compressible flow equation solver [Hu et al., 2011] to simulate the helium APDBDJ considering impurities in this thesis. A temporal multi-scale method (TMSM), taking advantage of the difference of characteristic timescale between electron and heavy particles, is proposed to further reduce the runtime of PFM dramatically in simulations involving with a large amount of species. The effort of this thesis establishes the foundation in simulating realistic APDBDJs. Chapter 1 of the thesis introduces the research background and motivation, and review of previous studies, and Chapter 2 describes the numerical methods and developed algorithm in detail. The results of one-dimensional simulation considering the impurities on the helium APDBDJ are presented in Chapter. 3. Chapter 4 and 5 depict the development of 2D parallel PFM code and the hybrid numerical algorithm of PFM and GFM for simulating APDBDJ respectively. The major findings of the thesis and some recommendations for future work are summarized in Chapter 6. More details of each chapter from Chapter 3 are described as follows in turn. In Chapter 3, the effect of helium impurities (trace amounts of O2, N2 and H2O), measured by the gas chromatography, have been explored and found that the discharge chemistry changes dramatically by considering the impurities. Results have found that the discharges with and without impurities have no quasi-neutral region at the instant of maximum current density. Both discharges with and without impurities have similar levels of electron densities; however, N2+ is found to be the most dominant ion with considering impurities, instead of He2+ in helium discharge without impurities in the breakdown region. In addition, ground-state atomic oxygen is the most dominant neutral species (except the background species) when considering impurities, instead of He2* without considering impurities. The influence of different levels of water vapor is also investigated. The electron densities of helium discharges with various levels of water vapor (1, 5 and 10 ppm) remain at essentially the same level as the amount of water vapor changes. However, the H2O+ replaces the N2+ as the dominant ion as the water vapor increases. Although the ground-state atomic oxygen is still the dominant neutral species, the densities of atomic hydrogen and hydroxyl increase significantly as the water vapor increases. The results show the importance of considering impurities in the helium discharges though the levels of impurities are typical several to tens ppm. In Chapter 4, the thesis reports the development of a two-dimensional plasma fluid modeling code using the cell-centered finite-volume method and its parallel implementation on a distributed-memory PC cluster. Parallel performance of simulating helium APDBDJ resulting from using different degrees of overlapping in the additive Schwarz method (ASM) with preconditioned generalized minimal residual method (GMRES) for different modeling equations is investigated for a small and a large test problem, respectively, employing up to 128 processors. For the large test problem, almost linear speedup can be obtained using 128 processors. Finally, a large-scale realistic two-dimensional APDBDJ problem is employed to demonstrate the capability of the developed fluid modeling code for simulating the low temperature plasma with complex chemical reactions. In Chapter 5, this thesis proposes a hybrid numerical algorithm which couples weakly the PFM and GFM, and two acceleration approaches for simulating the APDBDJ. The weak coupling between gas flow and discharge is introduced by transferring between the results obtained from the steady-state solution of the GFM and cycle-averaged source terms of the PFM respectively. Approaches of reducing the overall runtime include parallel computing of the GFM and the PFM solvers, and employing a TMSM for PFM. Parallel computing of both solvers is realized using the domain decomposition method with message passing interface (MPI) on distributed-memory PC cluster. The TMSM considers only the source and sink terms of chemical reactions by ignoring the transport terms when integrating temporally the continuity equations of heavy species at each time step, and the ignored transport terms are restored only at an interval of several time marching steps. The total reduction of runtime is 47% by applying the TMSM to the example of APDBDJ as presented in this study. Application of the proposed hybrid algorithm is demonstrated by simulating a parallel-plate helium APDBDJ impinging onto a substrate, in which the cycle-averaged properties of the 200th cycle are presented. The distribution patterns of species densities are strongly correlated by the background gas flow pattern, which shows that consideration of gas flow in APDBDJ simulations is critical. In Chapter 6, major findings of this thesis are summarized and recommendations for the future work are outlined.