| 摘要: | 本論文實驗量測表面具蜂巢結構之向外傳播球狀火焰的自我加速特性，以及分析其是否具自我相似性(self-similar)或局部自我相似性(locally similar)。在層流球狀火焰向外傳播的過程中，可能會受到三種不穩定性的影響，分別為：(1)熱擴散不穩定性(當Lewis數Le = DT/DM < 1，即熱質擴散係數比小於1，其會在很小火焰半徑R即產生)，(2)流力不穩定性(天生的火焰不穩定性)和(3)浮力不穩定性(當R約達5cm以上時)。這些不穩定性的影響，會使火焰表面持續產生蜂巢或皺褶結構，進而使火焰表面積增加並使傳播速率增快，導致球狀火焰的自我加速。在過去的研究中，計算球狀火焰自我加速的耦合公式，均以火焰平均半徑(Rav)隨時間(t)變化之冪次法則指數(α)來決定，即Rav = R0 + A(t-t0)α，其中R0和t0為球狀火焰開始產生蜂巢結構時之火焰半徑和時間，A為實驗常數。因R0和t0會因實驗之條件不同而有所變化，這會影響α值之正確性。有鑑於此，最近普林斯頓大學Law和其研究團隊(Wu et al. 2013)想出一可規避R0和t0之方法，即對Rav = Atα作時間微分以獲取火焰傳播速率(SF)，其中SF = dRav/dt = αA1/αRav(α - 1)/α，如此可由對數座標SF vs. Rav之斜率d = (α - 1)/α，來正確地決定α值。Law 團隊找到球狀火焰自我加速指數α值，在任一固定壓力(p)和當量比(φ)條件下，α值為一定值，即球狀火焰具自我相似性傳播(self-similar propagation)，且其值較α = 1.5小很多，故他們不認為球狀火焰具有自我紊流化之特性。
本研究採用Law團隊所提出決定α值之方法，針對高壓貧油氫/空氣和甲烷/空氣燃氣進行一系列實驗，藉由高速高解析度球狀火焰紋影影像，量測Rav和t之關係，以獲取SF與Rav之關係圖，進而求得α值。實驗結果顯示，氫/空氣混合燃氣在p = 0.5atm和φ = 0.6時(Le ? 0.44)，由於受到熱擴散不穩定性(Le < 1)與流力不穩定性(高壓環境火焰厚度變小，越易發生)的影響，可清楚看見火焰在其發展初始階段，即會在火焰表面產生蜂巢狀結構。隨著蜂巢結構持續地增加發展，導致球狀火焰之自我加速。我們首度發現此自我加速具局部相似之特性，即α值會有一轉折非為一定值。在較小氫球狀火焰半徑(12mm ? Rav < 2.7mm)時，α = 1.30，此值與Law團隊在相同條件所得之α = 1.26相當接近；而隨著t增加， Rav會持續擴展，當27mm ? Rav < 50mm，α值會增加至1.42，顯示氫球狀火焰傳播具局部相似(locally similar)而非一般所認為之自我相似(self-similar)。有關接近化學計量比之甲烷/空氣燃氣(φ = 0.9
Le ? 1)和在p = 5atm條件下，球狀火焰起初以近乎等速(α = 1.02)發展一段時間後，在Rav大約為30mm處，球狀火焰之自我加速開始產生，此時α值增加至1.15 (30 mm ? Rav < 4.3mm)；令人驚訝的是，當球狀火焰隨時間持續成長(43mm ? Rav < 70mm)，其α值可增加至1.47，相當接近理論上認為可產生自我紊流化α = 1.5之預測值。本研究結果，對了解預混火焰不穩定性和其動態行為有重要之貢獻。
This thesis measures self-acceleration characteristics of expanding cellular spherical flames and analyzes whether such self-acceleration propagation is either self-similar in time (t), if it holds for all t, or locally similar, if it holds only for a specific period of t. Propagation of laminar spherical flames is subjected to three possible flame front instabilities, namely: (1) thermal-diffusional instability (when the Lewis number, Le = DT/DM which is the heat and mass diffusion coefficient ratio, is less than 1, occurring at relatively small flame radius (R)
(2) hydrodynamic instability (an inherent flame instability)
(3) buoyancy instability (when R is approximately larger than 50mm). These flame front instabilities can result in cellular structures and/or wrinkles over the flame front surface upon flame propagation that continuously develop, so that the flame surface area is increased and thus the global flame propagation rate is also increased, leading to self-acceleration of expanding spherical flame. In previous studies, the power-law acceleration exponent (α) was commonly determined by a fitting formula of Rav = R0 + A(t-t0)α, where Rav is the flame average radius, R0 and t0 are the corresponding radius and time on the onset of flame wrinkling, and A is an experimental constant. However, values of R0 and t0 depend on the experimental conditions that can influence the correctness of α. Very recently, Law and his coworkers (Wu et al. 2013) found a better way to determine α without using R0 and t0 , that is to take the time derivation of Rav = Atα to obtain the flame propagation speed [SF = dRav/dt = αA1/αRav(α-1)/α] and thus α can be more accurately determined from the slope [d = (α - 1)/α] of the log-log plot of SF vs. Rav data. They found that α is a constant value at any given pressure (p) and equivalence ratio (φ) for H2/air mixtures, suggesting that self-accelerating cellular spherical flames are self-similar propagation, same as other previous studies. However, their α values ranging from 1.17~1.37 are generally smaller than 1.5, a value for self-turbulization.
The present study applies the same method as Law’s group to determine α. Focus is placed on high-pressure combustion experiments, including both lean hydrogen/air mixtures at φ = 0.6 and p = 0.5atm where Le ? 0.44 and near-stoichiometric methane/air mixtures at φ = 0.9 and p = 0.5atm where Le ? 1. Using high-speed high resolution Schlieren imaging technique to record and measure the time evolution of Rav, SF can be then determine from dRav/dt and α can be thus obtained. Results show that for lean H2/air case (Le << 1), cellular structures are observed at the very early stage of flame propagation due to thermal-diffusional and hydrodynamic instabilities. The cells continuously develop leading to flame self-acceleration. Most importantly, it is found that such acceleration is locally similar (not self-similar) where a transition on values of α is found. When 12mm ? Rav < 27mm, α = 1.30, while α increases to 1.42 when Rav ? 27mm. For the CH4/air case with Le ? 1, the spherical flame first expands at an almost constant propagation rate for a considerable long period of time where α = 1.02, then self-acceleration of cellular spherical flame starts to initiate around Rav ? 30mm where α increases to 1.15 for 30mm ? Rav < 43mm, and finally and surprisingly the value of α jumps to 1.47 for 43mm ? Rav < 70mm, a value closely matching with the theoretical vale (α = 1.5) for self-turbulization. These results are important to our further understanding of flames front instabilities and dynamics. |
