全速域平行化氣體流動程式之發展及其在低溫電漿之應用

Abstract

本論文研究目的主為發展與驗證一個平行化二維/二維軸對稱氣體流動模型程式，應用於全速域可壓縮、黏滯性流體，及具有處理流體與固體間之共軛熱傳遞與適用於稀薄氣體問題之研究。數值方法主要是使用有限體積法(FVM, Finite Volume Method)之結構性同位網格(collocated grid)來離散統御方程式求解。Extended SIMPLE演算法運用1972年Patankar與Spalding所發展之SIMPLE (Semi-Implicit Method for Pressure-Linked Equation)演算法為基礎，透過猜測-修正的方法得到壓力場，求解流體之壓力、速度、溫度與氣體組成成份之分布等流體性質。此程式可以廣泛的應用於模擬各種不同的氣壓、不同的氣體流速與不同氣體組成成份之全速域流場。模擬結果並與研究文獻相互驗證比對。 研究主體主要分為三個部份。在論文第一部份，主要為建立並且驗證一個平行化二維/二維軸對稱氣體流動模型程式。程式中所使用的統御方程式包含流體的質量，動量，能量與組成成份之守恆方程式，運用有限體積法之結構性同位網格加以離散求解。模擬結果已與研究文獻結果互相驗證比較。程式平行化方面使用ASM (Additive Schwarz Method)作為矩陣預處理法(preconditioner) ，搭配GMRES或BiCGS方法解析線性方程式矩陣。程式平行化效率的測試則是使用國立中央大學的V’ger cluster system (Xeon 3GHz dual-core dual-CPU)作為測試平台。針對微尺度超音速流體問題使用800,000個結構性網格操作在64個處理器的狀況下， 測試結果顯示平行化效率仍能維持在70%。 論文的第二部份：主要利用所發展之全速域平行化二維/二維軸對稱氣體流動模型程式結合實驗室成員洪捷粲博士[2010]與林昆模博士[2012]所發展之平行化二維/二維軸對稱低溫非熱平衡電漿流體模型程式研究（1）混合氫氣與矽烷的電漿輔助化學氣相沈積電漿源在600 mTorr操作氣壓下的流體特性。 (2) 常壓微尺度氫氣電漿之流場與熱傳分析，(3)氫氣介電質放電電漿（DBD, Dielectric Barrier Discharge）在頻率25 kHz，760 Torr操作氣壓下之研究。 論文的第三部分，由於電漿相關參數不易量測，故透過氣體流動模型針對氫氣介電質放電電漿在不同電極長度( 5 mm及25 mm)，不同氣體流量(10 ~ 30 slm)，以及改變基材至電漿噴流出口的距離加以模擬，以探討電漿對流場與熱傳特性之影響。 論文最後除了總結研究的成果，並針對未來的研究方向提出建議。

A parallelized 2D/2D-axisymmetric pressure-based, finite-volume gas flow model has been developed for simulating compressible, viscous, heat conductive and rarefied gas flows at all speeds with conjugate heat transfer. The governing equations are solved on the structured, collocated grid using a finite volume method. An extended SIMPLE algorithm for compressible flow simulation is proposed which is based on the SIMPLE scheme developed by Patankar and Spalidinf [1972]. The flow properties are solved by a prediction/correction algorithm. Applications with wide range of pressures, flow speeds, and various species concentrations are demonstrated by comparing with previous simulations wherever possible. Research in this thesis is divided into three major phases, which are briefly described in the following in turn. In the first phase, a parallelized 2D/2D-axisymmetric gas flow model was developed and verified. The discretized equations, including continuity equation, momentum equation, energy equation and species equation are solved by the parallel ASM (Additive Schwarz Method) and GMRES or BCGS schemes, which are used as the preconditioner and linear matrix equation solver, respectively. The developed code was validated by comparing with previous published simulations wherever available for both low- and high-speed gas flows. Parallel performance for a micro-scale supersonic flow problem (800,000 computational cells) is tested on the V’ger cluster system (Xeon 3GHz dual-core dual-CPU) at National Central University up to 64 processors. Parallel efficiency of the developed gas flow model using 64 processors is about 70%. In the second phase, (1) A chamber-scale gas discharge of plasma enhanced chemical vapor deposition (PECVD) with silane/hydrogen as the precursors, which was used for depositing hydrogenated amorphous silicon thin film, (2) A helium micro-cell plasma and (3) A two-dimensional helium DBD (Dielectric-barrier discharge) driven by 25 kHz distorted sinusoidal voltages were simulated using the developed gas flow model coupling with parallelized 2D fluid modeling codes developed by Hung [2010] and Lin [2012]. The simulation results show that there are significant differences between the cases with and without considering neutral flow and thermal field. In the third part, a parametric study was performed to determine the influences of the system configurations, and the flow conditions on the flow and heat transfer characteristics of a helium dielectric-barrier discharge atmospheric-pressure plasma jet. Recommendations of future research are also outlined at the end of this thesis.